




<!DOCTYPE html>






    










<html lang="en"
      
        
      
      
        

        

        
        
            
        
        
        
        
        

      class="pb-page"
         data-request-id="a1c0ea82fd43f351-ARN"  

>

    
        <head data-pb-dropzone="head">
            

<meta charset="UTF-8">






    
        
            
        
    
        
            
        
    
        
            
        
    
        
    
        
    
        
            
                
                
<title>PNAS – Explore High-Impact Scientific Research Across Disciplines from One of the World’s Most-Cited Journals</title>





                
            
        
    







    
        
            
        
    
        
            
                
                



    
        
    

                
            
        
    
        
            
        
    
        
    
        
    
        
            
        
    










    









    

    
    

    
    
    
    

    
    
        
            <link rel="icon" href="/products/pnas/releasedAssets/images/favicon/favicon-f7229df5ea4aa1e206bbb00228dc8de4.ico" type="image/x-icon"/>
        
        
        
        
        
        
    

    
    
            <link rel="stylesheet" href="/products/pnas/releasedAssets/css/build-312dc58cdd1cbe033575.css" media="all" id="build-style-sheet">
        <link rel="stylesheet" href="/products/pnas/releasedAssets/css/print-312dc58cdd1cbe033575.css"media="print">
    
        <script nonce="a1c0ea82fd43f351-ARN">
        try {
            document.documentElement.classList.add('js');
        } catch (e) {
        }
    </script>
     
    





















    
        
            
                
                
                
                    
                    


    

<script nonce="a1c0ea82fd43f351-ARN">
    window.addEventListener('load', () => {
        PNASdataLayer ={"ecommerce":{},"page":{"pageInfo":{"pageTitle":"PNAS – Explore High-Impact Scientific Research Across Disciplines from One of the World’s Most-Cited Journals","pageURL":"https://www.pnas.org/"},"attributes":{}},"user":{"geo":"Finland","registeredUser":"no","authenticated":"no","access":"yes","groups":["All users group","Unknown Users","All users no webcrawlers","Anonymous Users","No Report Group","All group users group"]}};
        if (PNASdataLayer) {
            var ua = navigator.userAgent;
            var deviceType = "desktop";
            var width = window.innerHeight || document.documentElement.clientHeight || document.body.clientHeight;
            var hight = window.innerWidth || document.documentElement.clientWidth || document.body.clientWidth;
            if (/(tablet|ipad|playbook|silk)|(android(?!.*mobi))/i.test(ua)) deviceType = "etc";
            if (/Mobile|iP(hone|od)|Android|BlackBerry|IEMobile|Kindle|Silk-Accelerated|(hpw|web)OS|Opera M(obi|ini)/.test(ua)) deviceType = "mobile";
            PNASdataLayer.site = {};
            PNASdataLayer.site.userAgent = ua;
            PNASdataLayer.site.device = deviceType;
            PNASdataLayer.site.viewport = width + "x" + hight;
        }

        window.dataLayer = window.dataLayer || []
        window.dataLayer.push({
            'event': 'get-meta-data',
            'pnasDataLayer': PNASdataLayer
        })
    });
</script>



                    
                
            
        
    
        
            
                
                
                
                
                
            
        
    
        
            
                
                
                
                    
                    <meta name="robots" content="noarchive"/><meta name="description" content="Explore cutting-edge research across biological, physical, and social sciences from PNAS—the flagship journal of the National Academy of Sciences." />





































    <meta property="og:title" content="PNAS – Explore High-Impact Scientific Research Across Disciplines from One of the World’s Most-Cited Journals"/>
    <meta property="og:type" content="Website">
    <meta property="og:url" content="https://www.pnas.org/">
    <meta property="og:image" content="http://www.pnas.org/pb-assets/images/Logos/header-logo/logo.svg"/>
    <meta property="og:site_name" content="PNAS"/>
    <meta property="og:description" content="Explore cutting-edge research across biological, physical, and social sciences from PNAS—the flagship journal of the National Academy of Sciences."/>



<meta name="viewport" content="width=device-width,initial-scale=1"><meta name="event_group_key" content="288461b4-a81b-4ec6-8e04-50fc33f89681"/>
<meta name="citation_pdf_url" content="">

<meta name="citation_doi" content="">



    












                    
                
            
        
    
        
    
        
    
        
            
                
                
                
                
                
            
        
    




<meta http-equiv="X-UA-Compatible" content="IE=edge">
<script type="text/javascript" nonce="a1c0ea82fd43f351-ARN">var addthis_config={data_track_clickback:false}</script>
<link rel="stylesheet"
	    type="text/css"
	    href="/pb-assets/styles/pnas-styles-1766506067190.css">
	<script defer
			src="https://static.cloudflareinsights.com/beacon.min.js/v652eace1692a40cfa3763df669d7439c1639079717194"
			integrity="sha512-Gi7xpJR8tSkrpF7aordPZQlW2DLtzUlZcumS8dMQjwDHEnw9I7ZLyiOj/6tZStRBGtGgN6ceN6cMH8z7etPGlw=="
			data-cf-beacon='{"rayId":"6e65fb942de2942c","token":"4fddf4ff2db74c469c27e6f3ddde2174","version":"2021.12.0","si":100}'
			crossorigin="anonymous"/ nonce="a1c0ea82fd43f351-ARN">
	<script defer
			src="https://static.cloudflareinsights.com/beacon.min.js/v652eace1692a40cfa3763df669d7439c1639079717194"
			integrity="sha512-Gi7xpJR8tSkrpF7aordPZQlW2DLtzUlZcumS8dMQjwDHEnw9I7ZLyiOj/6tZStRBGtGgN6ceN6cMH8z7etPGlw=="
			data-cf-beacon='{"rayId":"6e9db4c0dd526450","token":"4fddf4ff2db74c469c27e6f3ddde2174","version":"2021.12.0","si":100}'
			crossorigin="anonymous"/ nonce="a1c0ea82fd43f351-ARN">
	<script defer
			src="https://static.cloudflareinsights.com/beacon.min.js/v52afc6f149f6479b8c77fa569edb01181681764108816"
			integrity="sha512-jGCTpDpBAYDGNYR5ztKt4BQPGef1P0giN6ZGVUi835kFF88FOmmn8jBQWNgrNd8g/Yu421NdgWhwQoaOPFflDw=="
			data-cf-beacon='{"rayId":"7d014c01ed4196e9","token":"4fddf4ff2db74c469c27e6f3ddde2174","version":"2023.4.0","si":100}'
			crossorigin="anonymous"/ nonce="a1c0ea82fd43f351-ARN">
<script defer src="https://static.cloudflareinsights.com/beacon.min.js/vcd15cbe7772f49c399c6a5babf22c1241717689176015" integrity="sha512-ZpsOmlRQV6y907TI0dKBHq9Md29nnaEIPlkf84rnaERnq6zvWvPUqr2ft8M1aS28oN72PdrCzSjY4U6VaAw1EQ==" data-cf-beacon='{"rayId":"8c52882288c0fa66","serverTiming":{"name":{"cfExtPri":true,"cfL4":true}},"version":"2024.8.0","token":"d1e81366f89b4aa09fd7ff47c1e123f8"}' crossorigin="anonymous" nonce="a1c0ea82fd43f351-ARN"></script>
<script type="application/ld+json" nonce="a1c0ea82fd43f351-ARN">{"@context":"https://schema.org","@type":"WebSite","url":"https://www.pnas.org","potentialAction":{"@type":"SearchAction","target":"https://www.pnas.org/action/doSearch?AllField={search_term}&amp;searchLoggingType=google","query-input":"required name=search_term"}}</script>
    <link rel="canonical" href="https://www.pnas.org/">
        




<!-- Google Tag Manager -->
    <script nonce="a1c0ea82fd43f351-ARN">
    var dataLayer = dataLayer ||[];
</script>

<script nonce="a1c0ea82fd43f351-ARN">(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;var n=d.querySelector('[nonce]');n&&j.setAttribute('nonce',n.nonce||n.getAttribute('nonce'));f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-KCV32QR');</script>
    <!-- Google Tag Manager (noscript) -->
    <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-KCV32QR" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
    <!-- End Google Tag Manager (noscript) -->
<!-- End Google Tag Manager -->

<meta name="pbContext" content=";journal:journal:pnas;page:string:Home Page;requestedJournal:journal:pnas;ctype:string:Journal Content;wgroup:string:Publication Websites;website:website:pnas-site">
        </head>
    

    



    
        
        
        
            <body
                    class="pb-ui website-pnas-site">
            






    
    
        


    
    






        <div id="pb-page-content" data-ng-non-bindable>
                
            <div data-pb-dropzone="main" data-pb-dropzone-name="Main">
                
                    
                        



        
        <div class="landing-page landing-page__hero slideshow-background-parent">



        
        <header class="main-header headerParentClass-e184595"><nav id="mainNavbar" aria-label="main navigation" class="main-navbar navbar bg-dark navbar-dark navbar-landing navbar-expand-xl text-uppercase"><div class="container-fluid"><div class="navbar-in">









    
    
        <div data-widget-def="UX3HTMLWidget" data-widget-id="729a0980-ae74-4b8b-8362-07d931f05f0e" class="navbar-in">
        



        
        <a href="/" class="navbar-brand navbar__logo--default">
<img src="/pb-assets/images/Logos/header-logo/logo-1624644560537.svg" title="PNAS logo" alt="PNAS Logo">
</a>
<a href="/" class="navbar-brand navbar__logo--light">
<img src="/pb-assets/images/Logos/header-logo/logo-light-1641218818190.svg" title="PNAS logo" alt="PNAS Logo">
</a>

        </div>
    

<div class="navbar-toggler__container">



        
        <a href="#" aria-expanded="false" aria-label="Expand search field" aria-controls="quick-search-form-0" data-expand-label="Expand search field" data-collapse-label="Collapse search field" data-target=".header-quick-search" data-toggle="collapse" class="btn quick-search__trigger"><svg xmlns="http://www.w3.org/2000/svg" width="45" height="45" viewBox="0 -8 32 50" class="quick-search-icon-animated"><path d="M17.71,17.91a6.25,6.25,0,1,1,1.89-4.48,6.23,6.23,0,0,1-1.89,4.48" class="cls cls-1"></path><line x1="25.07" y1="25.15" x2="8.2" y2="8.29" class="cls cls-2"></line><line x1="8.2" y1="25.15" x2="25.07" y2="8.29" class="cls cls-3"></line></svg></a>
<button type="button" data-slider="side-menu" data-action="toggle" aria-controls="#slider-side-menu" aria-expanded="false" aria-label="Toggle navigation" class="navbar-toggler"><span class="navbar-toggler__box"><span class="navbar-toggler__inner"></span></span></button></div></div>



        
        <div id="main-menu" class="main-menu collapse navbar-collapse collapse-lock-screen"><div class="main-menu__nav flex-grow-1 d-flex justify-content-center"><ul class="navbar-nav"><li class="nav-item px-3"><div class="dropdown"><a id="menu-item-0" href="#" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false" class="nav-link dropdown-toggle">ARTICLES</a><div aria-labelledby="menu-item-0" class="dropdown-menu"><a href="/toc/pnas/current" class="dropdown-item">Current Issue</a><a href="/latest" class="dropdown-item">Latest Articles</a><a href="/about/special-features" class="dropdown-item">Special Features</a><a href="/loi/pnas" class="dropdown-item">List of Issues</a><a href="https://academic.oup.com/pnasnexus" class="dropdown-item dropdown-item--external"><i>PNAS Nexus</i></a></div></div></li><li class="nav-item px-3"><a id="menu-item-1" href="/front-matter" tabindex="" class="nav-link">Front Matter</a></li><li class="nav-item px-3"><div class="dropdown"><a id="menu-item-2" href="#" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false" class="nav-link dropdown-toggle">AUTHORS</a><div aria-labelledby="menu-item-2" class="dropdown-menu"><a href="/author-center" class="dropdown-item">Information for Authors</a><a href="/author-center/editorial-and-journal-policies" class="dropdown-item">Editorial and Journal Policies</a><a href="/author-center/submitting-your-manuscript" class="dropdown-item">Submission Procedures</a><a href="/author-center/publication-charges" class="dropdown-item">Publication Charges</a></div></div></li><li class="nav-item px-3"><div class="topicsButton">



        
        <button data-target=".topics-container" data-toggle="collapse" class="btn btn-outline-primary btn-topics" aria-expanded="false" aria-controls="topics-container" aria-label="Topics menu">Topics
    <i aria-hidden="true" class="icon-plus"></i>
    <i aria-hidden="true" class="icon-close"></i>
</button> 
<div id="topics" data-parent=".headerParentClass-e184595" class="topics-container collapse">









    
    
        <div data-widget-def="UX3Tabs" data-widget-id="e657c77c-421c-46e0-b0a0-d72b63228a8b" class="topics-tab text-capitalize">
        



        
        <ul role="tablist" class="nav nav-tabs"><li role="presentation" class="nav-item"><a id="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-physical-sciences-tab" data-toggle="tab" href="#nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-physical-sciences-pane" role="tab" aria-controls="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-physical-sciences-pane" aria-selected="true" class="nav-link  active"><span>Physical Sciences</span></a></li><li role="presentation" class="nav-item"><a id="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-social-sciences-tab" data-toggle="tab" href="#nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-social-sciences-pane" role="tab" aria-controls="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-social-sciences-pane" aria-selected="false" class="nav-link"><span>Social Sciences</span></a></li><li role="presentation" class="nav-item"><a id="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-biological-sciences-tab" data-toggle="tab" href="#nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-biological-sciences-pane" role="tab" aria-controls="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-biological-sciences-pane" aria-selected="false" class="nav-link"><span>Biological Sciences</span></a></li></ul><div class="tab-content"><div id="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-physical-sciences-pane" aria-labelledby="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-physical-sciences-tab" role="tabpanel" class="tab-pane fade show active">



        
        <div class="topics-tab__topic">
<div class="topics-tab__topic__portal">
<h4 class="topic__heading">Featured Topics</h4>
<ul class="rli topic__items topic__section">
<li class="topic__item"><a href="/topic/phys">Physics</a></li>
<li class="topic__item"><a href="/topic/chem">Chemistry</a></li>
<li class="topic__item"><a href="/sustainability-science">Sustainability Science</a></li>
<li class="topic__item"><a href="/sustainable-development-goals" class="sdg-topic">Sustainable Development Goals</a></li>
</ul>
</div>
<div class="topics-tab__topic__article">
<h4 class="topic__heading">Articles By Topic</h4>
<div class="d-flex">
<ul class="rlist topic__items topic__section">
<li class="topic__item"><a href="/topic/app-math">Applied Mathematics</a></li>
<li class="topic__item"><a href="/topic/app-phys">Applied Physical Sciences</a></li>
<li class="topic__item"><a href="/topic/astro">Astronomy</a></li>
<li class="topic__item"><a href="/biophysics-and-computational-biology">Biophysics and Computational Biology</a></li>
<li class="topic__item"><a href="/topic/comp-sci">Computer Sciences</a></li>
</ul>
<ul class="rlist topic__items topic__section">
<li class="topic__item"><a href="/topic/earth-sci">Earth, Atmospheric, and Planetary Sciences</a></li>
<li class="topic__item"><a href="/topic/eng">Engineering</a></li>
<li class="topic__item"><a href="/environmental-sciences">Environmental Sciences</a></li>
<li class="topic__item"><a href="/topic/math">Mathematics</a></li>
<li class="topic__item"><a href="/topic/stat">Statistics</a></li>
</ul>
</div>
</div>
</div>
</div><div id="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-social-sciences-pane" aria-labelledby="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-social-sciences-tab" role="tabpanel" class="tab-pane fade">



        
        <div class="topics-tab__topic">
<div class="topics-tab__topic__portal">
<h4 class="topic__heading">Featured Topics</h4>
<ul class="rli topic__items topic__section">
<li class="topic__item"><a href="/anthropology">Anthropology</a></li>
<li class="topic__item"><a href="/sustainability-science">Sustainability Science</a></li>
<li class="topic__item"><a href="/sustainable-development-goals" class="sdg-topic">Sustainable Development Goals</a></li>
</ul>
</div>
<div class="topics-tab__topic__article">
<h4 class="topic__heading">Articles By Topic</h4>
<div class="d-flex">
<ul class="rlist topic__items topic__section">
<li class="topic__item"><a href="/topic/demo">Demography</a></li>
<li class="topic__item"><a href="/topic/econ-sci">Economic Sciences</a></li>
<li class="topic__item"><a href="/environmental-sciences">Environmental Sciences</a></li>
</ul>
<ul class="rlist topic__items topic__section">
<li class="topic__item"><a href="/topic/pol-sci">Political Sciences</a></li>
<li class="topic__item"><a href="/psychological-and-cognitive-sciences">Psychological and Cognitive Sciences</a></li>
<li class="topic__item"><a href="/topic/soc-science">Social Sciences</a></li>
</ul>
</div>
</div>
</div>
</div><div id="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-biological-sciences-pane" aria-labelledby="nav-e657c77c-421c-46e0-b0a0-d72b63228a8b-biological-sciences-tab" role="tabpanel" class="tab-pane fade">



        
        <div class="topics-tab__topic">
<div class="topics-tab__topic__portal">
<h4 class="topic__heading">Featured Topic</h4>
<ul class="rli topic__items topic__section">
<li class="topic__item"><a href="/anthropology">Anthropology</a></li>
<li class="topic__item"><a href="/sustainability-science">Sustainability Science</a></li>
<li class="topic__item"><a href="/sustainable-development-goals" class="sdg-topic">Sustainable Development Goals</a></li>
</ul>
</div>
<div class="topics-tab__topic__article">
<h4 class="topic__heading">Articles By Topic</h4>
<div class="d-flex">
<ul class="rlist topic__items topic__section">
<li class="topic__item"><a href="/topic/ag-sci">Agricultural Sciences</a></li>
<li class="topic__item"><a href="/topic/app-bio">Applied Biological Sciences</a></li>
<li class="topic__item"><a href="/topic/biochem">Biochemistry</a></li>
<li class="topic__item"><a href="/biophysics-and-computational-biology">Biophysics and Computational Biology</a></li>
<li class="topic__item"><a href="/topic/cell-bio">Cell Biology</a></li>
<li class="topic__item"><a href="/topic/dev-bio">Developmental Biology</a></li>
<li class="topic__item"><a href="/topic/eco">Ecology</a></li>
<li class="topic__item"><a href="/environmental-sciences">Environmental Sciences</a></li>
<li class="topic__item"><a href="/topic/evolution">Evolution</a></li>
<li class="topic__item"><a href="/topic/genetics">Genetics</a></li>
</ul>
<ul class="rlist topic__items topic__section">
<li class="topic__item"><a href="/topic/immun">Immunology and Inflammation</a></li>
<li class="topic__item"><a href="/topic/med-sci">Medical Sciences</a></li>
<li class="topic__item"><a href="/topic/microbio">Microbiology</a></li>
<li class="topic__item"><a href="/topic/neuro">Neuroscience</a></li>
<li class="topic__item"><a href="/topic/pharm">Pharmacology</a></li>
<li class="topic__item"><a href="/topic/physio">Physiology</a></li>
<li class="topic__item"><a href="/topic/plant-bio">Plant Biology</a></li>
<li class="topic__item"><a href="/topic/pop-bio">Population Biology</a></li>
<li class="topic__item"><a href="/psychological-and-cognitive-sciences">Psychological and Cognitive Sciences</a></li>
<li class="topic__item"><a href="/topic/sys-bio">Systems Biology</a></li>
</ul>
</div>
</div>
</div>
</div></div>

        </div>
    

</div></div></li><li class="nav-item px-3"><div class="covidButton">



        
        <a href="/topic/covid-19" type="button" role="button" aria-label="Covid-19 button" class="btn btn-outline-primary btn--light-outline font-weight-bold nav-link">Covid-19</a>
</div></li></ul></div><div class="main-menu__right-content">



        
        <a href="#" aria-expanded="false" aria-label="Expand search field" aria-controls="quick-search-form-0" data-expand-label="Expand search field" data-collapse-label="Collapse search field" data-target=".header-quick-search" data-move-focus="#header-quick-search input" data-toggle="collapse" class="btn quick-search__trigger" title="Search"><svg xmlns="http://www.w3.org/2000/svg" width="45" height="45" viewBox="0 -8 32 50" class="quick-search-icon-animated"> <path d="M17.71,17.91a6.25,6.25,0,1,1,1.89-4.48,6.23,6.23,0,0,1-1.89,4.48" class="cls cls-1"></path> <line x1="25.07" y1="25.15" x2="8.2" y2="8.29" class="cls cls-2"></line> <line x1="8.2" y1="25.15" x2="25.07" y2="8.29" class="cls cls-3"></line></svg></a>




        
        















<div class="eCommerceCartIndicatorWidget">
    
        
        
            <a href="/action/showCart?FlowID=1" id="cartLabel" title="Cart" aria-labelledby="cartLabelText" class="shopping-cart-indicator">
                    <span class="position-relative d-flex mr-lg-3 mr-0 pt-1 pr-1 pt-lg-0 pr-lg-0">
                        <i aria-hidden="true" class="icon-shopping-cart"></i>
                        <span class="shopping-cart-indicator__badge  sr-only"
                              data-id="cart-size" id="cartLabelText" aria-live="polite">
                            <span class="sr-only">Shopping cart with </span>
                            <span class="cart-count">0</span>
                            <span class="sr-only"> item </span>
                        </span>
                    </span>
                <span class="shopping-cart-indicator__label font-weight-bold text-deep-gray">Cart</span>
            </a>
        
    
</div>




        
        




    








    
        




    







<div class="login-bar text-uppercase">
    <a href="/action/showLogin" class="font-weight-bold btn btn-outline-primary btn--light-outline btn-login collapsed" data-target=".login-bar__menu" data-toggle="collapse" aria-expanded="false">
        <span>Sign in</span>
    </a>
    
        
            <a href="/action/registration" class="font-weight-bold btn btn-primary btn-register">
                Register
            </a>
        
        
    

    <div id="login-bar__menu" class="login-bar__menu collapse" data-parent=".headerParentClass-e184595">
        <a href="/action/showLogin?redirectUri=%2F" class="login-bar__menu__login-option">
            Individual Login
        </a>
        <a href="/action/ssostart?redirectUri=%2F" class="login-bar__menu__login-option">
            Institutional Login
        </a>
    </div>
</div>
    
    






        
        <div class="d-flex align-items-center"><a href="https://www.pnascentral.org/cgi-bin/main.plex" class="font-weight-bold btn btn-primary btn-header-submit">Submit</a></div>
</div><!-- Institution Banner Dropzone for small devices--><div class="d-block d-xl-none"></div></div>
</div></nav><div data-parent=".headerParentClass-e184595" class="bg-black-gray header-quick-search collapse"><span class="arrow"></span><div class="quick-search--container">



        
        <div class="quick-search row no-gutters flex-column quick-search--header flex-column"><div class="quick-search__items col"><div aria-labelledby="trigger-quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-0" id="quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-0" data-parent=".quick-search__items" role="tabpanel" class="collapse show "><form action="/action/doSearch" name="defaultQuickSearch" method="get" id="header-quick-search"><fieldset><legend class="sr-only">Quick Search anywhere</legend><div class="input-group option-0   animation-underline"><label for="AllFieldba20dcbf-b159-41b6-a89e-49552f0ecc620" class="sr-only">Enter journal, DOI, article type, keywords, authors, etc.</label><input type="search" id="AllFieldba20dcbf-b159-41b6-a89e-49552f0ecc620" name="AllField" autocomplete="off" placeholder="Enter journal, DOI, article type, keywords, authors, etc." data-auto-complete-max-words="7" data-auto-complete-max-chars="32" data-contributors-conf="3" data-topics-conf="3" data-publication-titles-conf="3" data-history-items-conf="3" value="" class="quick-search__input form-control autocomplete"/><div class="input-group-append"></div></div></fieldset></form></div><div aria-labelledby="trigger-quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-1" id="quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-1" data-parent=".quick-search__items" role="tabpanel" class="collapse "><form action="/action/quickLink" name="citationQuickSearch" method="get"><fieldset class="row no-gutters"><legend class="sr-only">Quick search in Citations</legend><div class="input-group option-citation option-1"><label for="citationJournalDropdown" class="sr-only">Journal*</label><select name="quickLinkJournal" id="citationJournalDropdown" required="required" class="form-control animation-underline citationJournalDropdown"><option disabled="disabled" selected="selected" hidden="hidden" value="">Journal*</option><option value="nexus">PNAS Nexus</option><option value="pnas">Proceedings of the National Academy of Sciences</option></select><div class="citationSearch-wrapper"><label for="quickLinkYearba20dcbf-b159-41b6-a89e-49552f0ecc621" class="sr-only">Year</label><input type="search" id="quickLinkYearba20dcbf-b159-41b6-a89e-49552f0ecc621" name="quickLinkYear" autoComplete="false" placeholder="Year" class="form-control"/><label for="quickLinkVolumeba20dcbf-b159-41b6-a89e-49552f0ecc621" class="sr-only">Volume*</label><input type="search" id="quickLinkVolumeba20dcbf-b159-41b6-a89e-49552f0ecc621" name="quickLinkVolume" autoComplete="false" required="required" placeholder="Volume*" class="form-control"/><label for="quickLinkIssueba20dcbf-b159-41b6-a89e-49552f0ecc621" class="sr-only">Issue*</label><input type="search" id="quickLinkIssueba20dcbf-b159-41b6-a89e-49552f0ecc621" name="quickLinkIssue" autoComplete="false" required="required" placeholder="Issue*" class="form-control"/><label for="quickLinkPageba20dcbf-b159-41b6-a89e-49552f0ecc621" class="sr-only">Page/eLocation ID*</label><input type="search" id="quickLinkPageba20dcbf-b159-41b6-a89e-49552f0ecc621" name="quickLinkPage" autoComplete="false" required="required" placeholder="Page/eLocation ID*" class="form-control"/><input type="hidden" name="quickLink" value="true"/><div class="input-group-append"></div></div><div class="citation-annotation">*Required field</div><input type="submit" hidden="hidden" id="citationFormSubmit"/></div></fieldset></form></div><div aria-labelledby="trigger-quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-2" id="quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-2" data-parent=".quick-search__items" role="tabpanel" class="collapse "><form action="/action/doSearch" name="publicationQuickSearch" method="get" id="header-quick-search-2"><fieldset><legend class="sr-only">Quick Search in Journals</legend><div class="input-group option-2 option-journal  animation-underline"><label for="AllFieldba20dcbf-b159-41b6-a89e-49552f0ecc622" class="sr-only">Enter journal, DOI, article type, keywords, authors, etc.</label><input type="search" id="AllFieldba20dcbf-b159-41b6-a89e-49552f0ecc622" name="AllField" autocomplete="off" placeholder="Enter journal, DOI, article type, keywords, authors, etc." data-auto-complete-max-words="7" data-auto-complete-max-chars="32" data-contributors-conf="3" data-topics-conf="3" data-publication-titles-conf="3" data-history-items-conf="3" value="" class="quick-search__input form-control autocomplete"/><input type="hidden" name="SeriesKey" value="nexus"/><div class="input-group-append"></div></div></fieldset></form></div><div aria-labelledby="trigger-quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-3" id="quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-3" data-parent=".quick-search__items" role="tabpanel" class="collapse "><form action="/action/doSearch" name="publicationQuickSearch" method="get" id="header-quick-search-3"><fieldset><legend class="sr-only">Quick Search in Journals</legend><div class="input-group option-3 option-journal  animation-underline"><label for="AllFieldba20dcbf-b159-41b6-a89e-49552f0ecc623" class="sr-only">Enter journal, DOI, article type, keywords, authors, etc.</label><input type="search" id="AllFieldba20dcbf-b159-41b6-a89e-49552f0ecc623" name="AllField" autocomplete="off" placeholder="Enter journal, DOI, article type, keywords, authors, etc." data-auto-complete-max-words="7" data-auto-complete-max-chars="32" data-contributors-conf="3" data-topics-conf="3" data-publication-titles-conf="3" data-history-items-conf="3" value="" class="quick-search__input form-control autocomplete"/><input type="hidden" name="SeriesKey" value="pnas"/><div class="input-group-append"></div></div></fieldset></form></div></div><div class="row no-gutters justify-content-end align-items-center quick-search__actions flex-column flex-sm-row"><div class="col d-flex align-items-center flex-grow-1"><label class="mb-0 text-uppercase dropdown-selectable__label mr-2">Searching:</label><div class="d-flex align-items-center flex-fill "><div class="quick-search__dropdown dropdown dropdown-selectable"><button id="dropdownMenuButton" type="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false" class="btn dropdown-toggle">Anywhere</button><div aria-labelledby="dropdownMenuButton" role="tablist" class="dropdown-menu"><a href="#quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-0" id="trigger-quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-0" data-toggle="collapse" class="dropdown-item  active">Anywhere</a><a href="#quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-1" id="trigger-quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-1" data-toggle="collapse" class="dropdown-item">Citation</a><a href="#quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-2" id="trigger-quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-2" data-toggle="collapse" class="dropdown-item">PNAS Nexus</a><a href="#quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-3" id="trigger-quick-search-form-ba20dcbf-b159-41b6-a89e-49552f0ecc62-3" data-toggle="collapse" class="dropdown-item">Proceedings of the National Academy of Sciences</a></div></div></div></div><div class="col justify-content-end d-flex align-items-center quick-search__buttons">



        
        <a href="/search/advanced" class="text-white text-uppercase mini-title quick-search__advanced">Advanced Search</a>
<button type="submit" form="header-quick-search" title="Search" class="quick-search__btn btn d-flex btn-primary align-items-center justify-content-center justify-content-sm-between mb-3 mb-sm-0"><span class="font-weight-bold text-uppercase mini-title">Search</span><i class="icon-arrow-right align-middle ml-2"></i></button></div></div></div>




        
        <div class="suggested-searches">



        
        <div class="suggested-searches__title">SUGGESTED SEARCHES: </div>
<div class="suggested-searches__search-words">
    <a href="/action/doSearch?AllField=covid+19" class="suggested-searches__search-word">Covid-19</a>
    <a href="/action/doSearch?AllField=artificial+intelligence" class="suggested-searches__search-word">Artificial Intelligence</a>
    <a href="/action/doSearch?AllField=mpox" class="suggested-searches__search-word">Mpox</a>
    <a href="/action/doSearch?AllField=climate+change" class="suggested-searches__search-word">Climate Change</a>
    <a href="/action/doSearch?AllField=gun+violence" class="suggested-searches__search-word">Gun Violence</a>
</div>
</div>
</div></div><section aria-label="slider-menu" id="slider-side-menu" class="slider"><div class="slider__container"><div id="screen-side-navigation" class="slider__screen slider__screen--root"><div class="slider__screen__content"><div class="side-menu px-3"><div class="side-menu__user-login-bar"></div><div class="side-menu__quick-search">



        
        <div class="quick-search row no-gutters"><div class="col quick-search__sidebar"><form action="/action/doSearch" name="defaultQuickSearch" method="get" id="quick-search-from-85eb734f-3d8c-4802-b914-d40de047cf3c0" role="search"><fieldset><legend class="sr-only">Quick Search anywhere</legend><div class="input-group option-0  align-items-center  animation-underline animation-underline--primary"><label for="AllField85eb734f-3d8c-4802-b914-d40de047cf3c0" class="sr-only">Enter journal, DOI, article type, keywords, authors, etc.</label><input type="search" id="AllField85eb734f-3d8c-4802-b914-d40de047cf3c0" name="AllField" autocomplete="off" placeholder="Enter journal, DOI, article type, keywords, authors, etc." data-auto-complete-max-words="7" data-auto-complete-max-chars="32" data-contributors-conf="3" data-topics-conf="3" data-publication-titles-conf="3" data-history-items-conf="3" value="" class="quick-search__input form-control autocomplete"/><div class="input-group-append"><button type="submit" title="Search" class="btn quick-search__btn p-0"><i class="icon-search align-middle"></i></button></div></div></fieldset></form></div></div>
</div><div class="side-menu__nav-menu"></div><div class="side-menu__extra-nav"></div><div class="side-menu__menu-footer">









    
    
        <footer data-widget-def="UX3HTMLWidget" data-widget-id="c1d89ee2-d7e8-41ac-9c96-6105d574b1d8">
        



        
        <a href="/" class="footer-logo"> <img src="/pb-assets/images/Logos/header-logo/logo-1624644560537.svg" alt="PNAS"> </a>
<div class="footer__social-media__wrapper d-flex mt-3">
<div class="footer__social-media">
<ul role="list" class="list-inline footer__social-media__list text-center d-flex flex-wrap">
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="https://www.facebook.com/pages/PNAS/18262365099" title="Facebook" class="d-block"> <i class="icon-facebook" aria-hidden="true"></i> </a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="https://twitter.com/PNASNews" title="Twitter" class="d-block"> <i aria-hidden="true"><img src="/pb-assets/images/icons/twitter-x-gray-1705527808743.svg"></i> </a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="https://bsky.app/profile/pnas.org" title="Bluesky" class="d-block" style="line-height: 118%;"> <i aria-hidden="true"> <img src="pb-assets/images/icons/icon-bluesky-mobile.png"></i> </a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="https://www.youtube.com/channel/UCYjvFEQMgH6ou8fSYfiOKCw" title="Youtube" class="d-block"> <i class="icon-youtube" aria-hidden="true"></i> </a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="https://www.linkedin.com/showcase/pnas-news/" title="LinkedIn" target="_blank" class="d-block" rel="noopener"> <i class="icon-LinkedIn2" aria-hidden="true"></i></a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="/action/showPreferences?menuTab=Alerts" title="Mail" class="d-block"> <i class="icon-mail" aria-hidden="true"></i> </a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="/about/rss" title="RSS feeds" class="d-block"> <i class="icon-rss" aria-hidden="true"></i> </a></li>
</ul>
</div>
</div>
<div class="footer__links"><a href="/about/staff-directory">Contact</a> <a href="/about/site-map">Site Map</a> <a href="/about/terms">Terms &amp; Privacy Policy</a> <a href="/about/accessibility">Accessibility</a></div>

        </footer>
    

</div></div></div></div></div></section></header>




        
        <section aria-label="Slider Container with ID 42cfd1c3-76c2-415e-a0da-fdbe9bf2fdac" class="slideshow"><a href="#afterSlideshow-n3j" class="sr-only sr-only-focusable">Skip slideshow</a><div data-loop="true" data-items="1" data-slideby="1" data-autoheight="false" data-responsive="" data-speed="6000" data-autoplay="true" data-animation="slide" data-indicators="true" data-arrow="false" data-controls="true" data-stagePadding='0' data-label="" class="swiper-container" data-pause-slide="Pause slideshow" data-play-slide="Play slideshow" data-go-to-slide="Go to slide:" data-next-slide="Go to next slide" data-prev-slide="Go to previous slide" aria-label="Slider with ID 42cfd1c3-76c2-415e-a0da-fdbe9bf2fdac"><div class="swiper-wrapper"><div class="swiper-slide">



        
        <a href="/post/update/pnas-partners-getftr-improve-access-research-and-highlight-article-updates">
<div class="card-slide">
  <div>
      <h1 class="card-slide__title main-title">Faster access to trusted research</h1>
    <p class="card-slide__desc">PNAS now supports GetFTR.</p>
  </div>
  <img src="/pb-assets/html/home-slider/slide0-1783437057187.jpg" role="presentation" class="slideshow__background hidden">
</div>
</a>
</div><div class="swiper-slide">



        
        <a href="/toc/pnas/123/28">
    <div class="card-slide">
        <div>
            <h1 class="card-slide__title main-title">July 14, 2026; vol. 123 no. 28</h1>
            <p class="card-slide__desc">Volume 123, Issue 28: View articles in the latest issue of PNAS.</p>
        </div>
        <img src="/pb-assets/html/home-slider/slide1-1784041744590.jpg" alt="Pictured is an illustration representing the contributions of behavioral science theory and evidence to support government agencies serving the American people. Image credit: Zehra B. Sikandar (US Securities and Exchange Commission, Washington, DC)." role="presentation" class="slideshow__background hidden">
    </div>
</a>


</div><div class="swiper-slide">



        
        <a href="https://doi.org/10.1073/pnas.2520745123">
    <div class="card-slide">
        <div>
            <h1 class="card-slide__title main-title">Latest in Ecology: Habitat fragmentation and changes in amphibian skin microbiomes</h1>
            <p class="card-slide__desc">Click to read more. Image credit: Renato Martins.</p>
        </div>
        <img src="/pb-assets/html/home-slider/slide2-1784041744237.jpg" alt="Rainforest landscape in Brazil’s Atlantic Forest fragmented by human activity." role="presentation" class="slideshow__background hidden">
    </div>
</a>
</div><div class="swiper-slide">



        
        <a href="/post/multimedia/combating-misinformation">
    <div class="card-slide">
        <div>
            <h1 class="card-slide__title main-title">Watch the short film Decoding Deception: The Psychology of Combating Misinformation</h1>
            <p class="card-slide__desc">Social media and generative AI are accelerating the spread of misinformation. Interdisciplinary researchers are trying to devise solutions.</p>
        </div>
        <img src="/pb-assets/html/home-slider/slide3-1731449174103.jpg" alt="An illustration of a seesaw balancing people against a red, ominous face and hand, symbolizing manipulation or control." role="presentation" class="slideshow__background hidden">
    </div>
</a>
</div></div><div class="swiper-pagination"></div></div><span id="afterSlideshow-n3j" tabindex="-1"></span></section>










    
    
        <div data-widget-def="ux3-layout-widget" data-widget-id="10728363-fc0d-42d6-83c8-4f4e17811550" class="landing-page__hero__footer" aria-label="useful links">
        



        
        <div class="landing-page__hero__footer__scroll">



        
        <a role="button" tabindex="0" class="landing-scroll-icon icon-arrow-down landing-page__hero__footer__scroll__icon" aria-label="scroll down"></a> 
</div><div class="landing-page__hero__footer__btns text-uppercase">



        
        <a href="/email-alerts-and-rss" class="btn btn-outline-primary btn--light-outline">sign up for alerts</a>
<a href="/author-center" class="btn btn-outline-primary btn--light-outline">Author center</a>
<a href="https://www.pnascentral.org/cgi-bin/main.plex" class="btn btn-primary">submit</a>
</div>

        </div>
    





        
        




<div class="modal fade" role="dialog" tabindex="-1" id="modal--requestUsername">
    <div class="modal-dialog modal-fullscreen-sm-down" role="document">
        <div class="modal-content content">
            <div class="modal-header">
                <h2 class="modal-title h5">Request Username</h2>
                <button type="button" data-dismiss="modal" aria-label="close" class="close">
                    <span aria-hidden="true">x</span>
                    <span class="sr-only">Close</span>
                </button>
            </div>
            <div class="modal-body">
                <form action="/action/requestUsername" class="raa-form" method="post"><input type="hidden" name="requestUsername" value="requestUsername" />
                    <p>Can't sign in? Forgot your username? <br />
                        Enter your email address below and we will send you your username</p>
                    <div class="alert alert-danger d-none"></div>

                    <div class="form-row">
                        <div class="col">
                            <div class="form-group">
                                <label for="6eccc267-4bd8-4882-88e8-d9b06094352c.email">Email</label>
                                <input id="6eccc267-4bd8-4882-88e8-d9b06094352c.email" class="form-control" type="text" name="email" value="" size="15" />
                            </div>
                        </div>
                    </div>
                    
                        <div class="form-row">
                            <div class="col">
                                <div class="form-group">
                                    <div class="username-recaptcha-ajax"></div>
                                </div>
                            </div>
                        </div>
                    

                    <div class="form-row">
                        <div class="col text-right">
                            <button type="submit" data-dismiss="modal" class="btn btn-submit">
                                <span>Submit</span>
                                <span aria-hidden="true" class="icon-arrow-right ml-3"></span>
                            </button>
                        </div>
                    </div></form>

                <div class="alert alert-success d-none">
                    <p>If the address matches an existing account you will receive an email with instructions to retrieve your username</p>
                </div>

            </div>
        </div>
    </div>
</div>




        
        





<div tabindex="-1" id="modal--registration" aria-labelledby="modalRegistrationLabel" class="modal fade" aria-modal="true" role="dialog">
    <div role="document" class="modal-dialog modal-fullscreen-sm-down">
        <div class="modal-content content">
            <div class="modal-header">
                <h2 id="modalRegistrationLabel" class="modal-title h5">Create a new account</h2>
                <button type="button" data-dismiss="modal" aria-label="close" class="close">
                    <span aria-hidden="true">x</span><span class="sr-only">Close</span>
                </button>
            </div>
            <div class="modal-body">
                <form action="/action/registration" class="registration-form raa-form" method="post"><input type="hidden" name="redirectUri" value="/" />
                    <div class="form-row">
                        <div class="col">
                            <div class="form-group">
                                <label for="f96c9a0d-f4a9-4ca3-a52b-99fb097c56d6.email">Email</label>
                                <input id="f96c9a0d-f4a9-4ca3-a52b-99fb097c56d6.email" class="email form-control" type="email" name="email" value=""required="required" />
                            </div>
                        </div>
                    </div>
                    <div class="form-row">
                        <div class="col-12 col-sm-6">
                            <a href="/action/showLogin" class="show-login">
                                
                                Returning user
                            </a>
                        </div>
                        <div class="col text-right">
                            <button type="submit" data-dismiss="modal" class="btn btn-submit">
                                <span>Submit</span>
                                <span aria-hidden="true" class="icon-arrow-right ml-3"></span>
                            </button>
                        </div>
                    </div></form>
            </div>
        </div>
    </div>
</div>




        
        <aside class="cookie-policy"> <p>We use cookies on this site to enhance your user experience. By using this website, you are giving your consent for us to set cookies. <a href="/help/cookie-policy">Find out more</a></p><a href="/help/cookie-policy" class="btn btn-primary">CONTINUE</a></aside>




        
        














<div tabindex="-1" id="modal--login" aria-labelledby="modalLoginLabel" class="modal fade" aria-modal="true" role="dialog">
    <div role="document" class="modal-dialog modal-fullscreen-sm-down">
        <div class="modal-content content">
            <div class="modal-header">
                <h2 id="modalLabelLogin" class="modal-title h5">Login</h2>
                <button type="button" data-dismiss="modal" aria-label="close" class="close">
                    <span aria-hidden="true">x</span><span class="sr-only">Close</span>
                </button>
            </div>
            




















<div class="modal-body">
    <form action="/action/doLogin" id="loginForm" class="raa-form login-form " method="post"><input type="hidden" name="id" value="465aa1e9-3090-4f74-8ca8-f0d260f07eeb" />
        





    
    
        <input type="hidden" name="redirectUri" value="/" />
    


<input type="hidden" name="loginUri" value="/" />
        
            <input type="hidden" name="popup" value="true" />
        
        
            
            
                <div class="form-row">
                    <div class="col-12 col-sm-6">
                        <div class="form-group">
                            



























    
        
    
    
        
    
    
    
        
    
    
        
    

        

        
    <div class="form-group">
        <div class="label ">

            
                
                
                
                    <label for="login">Email<span class="required-marker" aria-hidden="true">*</span></label>
                
            
            
        </div>
        
        
        <input id="login" class="form-control" type="text" name="login" value="" size="15" autocomplete="" placeholder="Enter your email"aria-required="true" />
        
                            
    </div>

                        </div>
                        <div class="actions raa-form__reset-password text-right mt-n4">
                            
                        </div>
                    </div>

                    <div class="col">
                        <div class="form-group">
                            
























    



    
        
    
    
    
    <div class="form-group">
        <div class="label ">
            <label for="password">Password<span class="required-marker"
                                                                                        aria-hidden="true">*</span></label>
            
        </div>
        
        
        <input id="password" class="form-control" type="password" name="password" value="" autocomplete="off" placeholder="Enter your password"aria-required="true" />
        <span role="button" class="password-eye-icon icon-eye apply-btn hidden" aria-label="Show password" tabindex="0" onclick="togglePassword(this)" onkeydown="handleKey(event,this)"></span>
        
                            
    </div>
    <script>
        function togglePassword(el) {
            const passwordInput = document.getElementById("password");
            const isHidden = passwordInput.type === "password";

            // Toggle password visibility
            passwordInput.type = isHidden ? "text" : "password";

            // Safely update the aria-label and classes
            if (el) {
                if (isHidden) {
                    el.setAttribute("aria-label", "Hide password");
                } else {
                    el.setAttribute("aria-label", "Show password");
                }
            }
        }

        function handleKey(event, el) {
            if (event.key === "Enter" || event.key === " ") {
                event.preventDefault();
                togglePassword(el);
            }
        }
    </script>

                        </div>
                        <div class="raa-form__reset-password text-right">
                            <span>Forgot your password? Reset it </span>
                            <a href="/action/requestResetPassword" type="button" data-target="#modal--resetPassword" data-toggle="modal" data-dismiss="modal">here</a>
                        </div>
                    </div>
                </div>
            
        
        <div class="form-row mt-4">
            <div class="col-12 col-sm-6 text-left">
                <div class="custom-control custom-checkbox">
                    
                        
                        
                            <input id="465aa1e9-3090-4f74-8ca8-f0d260f07eeb-remember" class="custom-control-input" type="checkbox" name="remember" value="true" />
                        
                    
                    <label for="465aa1e9-3090-4f74-8ca8-f0d260f07eeb-remember" class="custom-control-label">
                        Keep me logged in
                    </label>
                </div>
            </div>
            
                
                    <div class="col text-right">
                        <button type="submit" class="btn btn-submit">
                            <span>Login</span>
                            <span aria-hidden="true" class="icon-arrow-right ml-3"></span>
                        </button>
                    </div>
                
                
            
        </div>
        <div class="form-row border-top mt-3 pt-3">
            <div class="col raa-form__register">
                <span>Don’t have an account? Register</span>
                <a href="/action/registration">
                    here
                </a>
                
                    <a href="/action/ssostart?redirectUri=%2F" class="float-right">
                        
                        <div class="institution-login">
                            Institutional Login
                        </div>
                    </a>
                
                
            </div>
        </div></form>
</div>
        </div>
    </div>
</div>




        
        




<div tabindex="-1" id="modal--verifyPhone"
     aria-labelledby="modalverifyPhoneLabel"
     class="modal fade" aria-modal="true" role="dialog">
    <div role="document" class="modal-dialog modal-fullscreen-sm-down">
        <div class="modal-content">
            <div class="modal-header">
                <h2 id="modalverifyPhoneLabel" class="modal-title h5">Change Password </h2>
                <button type="button" data-dismiss="modal" aria-label="close" class="close">
                    <span aria-hidden="true">x</span><span class="sr-only">Close</span>
                </button>
            </div>

            <div class="modal-body">
                <form action="/action/verifyPhoneNumber" method="post"><input type="hidden" name="submit" value="submit" />
                    <div class="alert alert-danger d-none"></div>
                    <div class="form-row">
                        <div class="col">
                            <div class="form-group">
                                <label for="946b33a7-d695-4878-8fb4-546789ae57b3-code">Enter the verification code</label>
                                <input id="946b33a7-d695-4878-8fb4-546789ae57b3-code" class="form-control" type="text" name="verificationCode" value="" size="15"pattern="^[0-9]{6}$"required="required" />
                            </div>
                        </div>
                    </div>
                    <div class="form-row">
                        <div class="col text-right">
                            <button type="submit" class="btn btn-submit">
                                <span>Submit</span>
                                <span aria-hidden="true" class="icon-arrow-right ml-3"></span>
                            </button>
                        </div>
                    </div></form>
            </div>

        </div>
        <div class="alert alert-success d-none">
            <h5>Congrats!</h5>
            <p>Your Phone has been verified</p>
        </div>
    </div>
</div>
</div><main class="content py-4 landing-page">



        
        <div class="container-fluid"><div class="row"><div class="col-12"><div class="pb-dropzone" data-pb-dropzone="col-0" title="col-0"></div></div></div></div>




        
        <section class="position-relative mb-5">









    
    
        <div data-widget-def="ux3-layout-widget" data-widget-id="160025ad-2661-48cb-8508-67014cbe4a70" class="container-fluid">
        



        
        <div class="py-4 mb-5 shaddow-bottom-75 bg-white">



        
        <div data-widget-id="UX3SerialDetails" class="current-issue text-black-gray d-flex flex-column justify-content-center align-items-center">
  



        
        <a href="/toc/pnas/123/28"><h2 class="main-title serif mb-2">Current Issue</h2></a><ul class="list-inline mb-3 mini-title text-uppercase"><li class="list-inline-item"><span class="pr-2 mr-2 border-right border-deep-gray">July 14, 2026</span></li><li class="list-inline-item"><span class="pr-2 mr-2 border-right border-deep-gray">vol. 123</span></li><li class="list-inline-item"><span>no. 28</span></li></ul>

</div>

</div>

        </div>
    

</section><section class="mb-5">



        
        <div class="container-fluid">









    
    
        <div data-widget-def="ux3-layout-widget" data-widget-id="34875faf-da7c-40e6-afdb-12490ef6aea8" class="row">
        



        
        <div class="col-md-4 d-none d-md-block">









    
    
        <div data-widget-def="graphQueryWidget" data-widget-id="abfd1165-87a0-46ee-94ff-e668aa37b664" class="wrapper cover-image d-flex justify-content-center flex-column">
        



        
        <div data-is-viewable="true" class="cover-image__image"><a href="/toc/pnas/current" title="View the PNAS Table of Contents Vol. 123;No. 28"><img src="/cms/asset/c8e6b153-e086-4af3-a472-32f612aa4d33/pnas.2026.123.issue-28.largecover.png" alt="The cover image for PNAS Vol. 123;No. 28" loading="lazy" width="335" height="451"></a></div>

        </div>
    

</div><div class="col-12 col-md-8">



        
        <div class="multi-search"><ul class="list-unstyled"><li><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/twip" class="card__meta__type">This Week in PNAS</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">July 14, 2026</span><span title="Free Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--free"><i class="icon-ok"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/iti2826123" title="In This Issue" class="text-reset animation-underline">In This Issue</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors"></ul>
</div><div id="abs-section-id-021e6d18c66da" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></li><li><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/research-article" class="card__meta__type">Research Article</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">July 10, 2026</span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2509171123" title="Provable cluster-preserving visualizations with curvature-based stochastic neighbor embeddings" class="text-reset animation-underline">Provable cluster-preserving visualizations with curvature-based stochastic neighbor embeddings</a></h3></div><div class="card-body card__abstract"><div class="card-body card__abstract">Widely adopted Stochastic Neighbor Embedding (SNE) techniques like UMAP and tSNE have
   been used to make inferences in a range of scientific disciplines. Despite this, they
   are prone to producing visualizations that fragment underlying clusters ...Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations
   that do not preserve the geometry of noisy and high dimensional data. In particular,
   they can spuriously separate connected components of the underlying data ...</div></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Saidi%2C+Tristan+Luca" title="Tristan Luca Saidi">Tristan Luca Saidi</a>,</li>
   <li class="list-inline-item"><a href="/author/Hickok%2C+Abigail" title="Abigail Hickok">Abigail Hickok</a>,</li>
   <li class="list-inline-item"><a href="/author/Rieck%2C+Bastian" title="Bastian Rieck">Bastian Rieck</a>,</li>
   <li class="list-inline-item"><a href="/author/Blumberg%2C+Andrew+J" title="Andrew J. Blumberg">Andrew J. Blumberg</a>,</li>
</ul>
</div><div id="abs-section-id-e0e4908d76439" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></li><li><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/research-article" class="card__meta__type">Research Article</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">July 6, 2026</span><span title="Open Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--open"><i class="icon-open-access"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2511442123" title="Time-resolved morphological and transcriptomic characterization of early enteric neuron subtype emergence in chick" class="text-reset animation-underline">Time-resolved morphological and transcriptomic characterization of early enteric neuron subtype emergence in chick</a></h3></div><div class="card-body card__abstract"><div class="card-body card__abstract">We characterize the transcriptomic and morphological dynamics of enteric neurons emerging
   in the chick embryo gastrointestinal tract. Neurons elongating their projections express
   axon guidance gene programs that differ from those that guide ...The genetic programs directing nascent enteric nervous circuits and their unique architecture
   remain poorly characterized. To gain insight, we combined manipulations in the chick
   embryo model, whole gut three-dimensional (3D) imaging, and single-nucleus ...</div></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Andr%C3%A9%2C+Ma%C3%ABlys" title="Maëlys André">Maëlys André</a>,</li>
   <li class="list-inline-item"><a href="/author/Gury%2C+Raphael" title="Raphael Gury">Raphael Gury</a>,</li>
   <li class="list-inline-item"><a href="/author/Lepetit%2C+Maxime" title="Maxime Lepetit">Maxime Lepetit</a>,</li>
   <li class="list-inline-item"><a href="/author/Boismoreau%2C+Franck" title="Franck Boismoreau">Franck Boismoreau</a>,</li>
   <li class="list-inline-item"><a href="/author/Bozon%2C+Muriel" title="Muriel Bozon">Muriel Bozon</a>,</li>
   <li class="list-inline-item"><a href="/author/Ganofsky%2C+J%C3%A9r%C3%A9my" title="Jérémy Ganofsky">Jérémy Ganofsky</a>,</li>
   <li class="list-inline-item"><a href="/author/Heritier-Tellier%2C+Cassandre" title="Cassandre Heritier-Tellier">Cassandre Heritier-Tellier</a>,</li>
   <li class="list-inline-item"><a href="/author/Plotton%2C+Ingrid" title="Ingrid Plotton">Ingrid Plotton</a>,</li>
   <li class="list-inline-item"><a href="/author/Duclaux-Loras%2C+R%C3%A9mi" title="Rémi Duclaux-Loras">Rémi Duclaux-Loras</a>,</li>
   <li class="list-inline-item"><a href="/author/Peretti%2C+No%C3%ABl" title="Noël Peretti">Noël Peretti</a>,</li>
   <li class="list-inline-item"><a href="/author/Marcy%2C+Guillaume" title="Guillaume Marcy">Guillaume Marcy</a>,</li>
   <li class="list-inline-item"><a href="/author/Castellani%2C+Val%C3%A9rie" title="Valérie Castellani">Valérie Castellani</a>,</li>
   <li class="list-inline-item"><a href="/author/Falk%2C+Julien" title="Julien Falk">Julien Falk</a>,</li>
</ul>
</div><div id="abs-section-id-16307de995e27" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></li></ul><div class="d-flex justify-content-end animation-icon-shift"><a href="/toc/pnas/current" class="multi-search__more cta text-uppercase animation-icon-shift"><span>VIEW FULL TABLE OF CONTENTS</span><span aria-hidden="true" class="icon-arrow-right ml-3"></span></a></div></div>
</div>

        </div>
    

</div>
</section><section class="py-5 about-section-container">









    
    
        <div data-widget-def="ux3-layout-widget" data-widget-id="c9aadc34-1819-4e31-add0-addf718890e9" class="container-fluid about-section">
        



        
        <div class="row">









    
    
        <div data-widget-def="ux3-layout-widget" data-widget-id="b60eb049-56d0-4914-9cfd-bc2e0be50634" class="col-12">
        



        
        <div class="mini-title text-uppercase mb-3">



        
        about pnas
</div>

        </div>
    

</div><div class="row align-items-center">



        
        <div class="col-12 col-md-4">



        
        <h2 class="about-section__title main-title--square-back-decorated serif mb-4 mb-sm-0">PNAS is one of the world's most-cited and comprehensive multidisciplinary scientific journals.</h2>
</div><div class="col-12 col-md-4 text-color">



        
        <p class="about-text">The <em>Proceedings of the National Academy of Sciences</em> (PNAS), a peer reviewed journal of the National Academy of Sciences (NAS), is an authoritative source of high-impact, original research that broadly spans the biological, physical, and social sciences. The journal is global in scope and submission is open to all researchers worldwide.</p>
</div><div class="col-12 col-md-4 d-none d-md-flex">



        
        <img src="/pb-assets/images/home/about-section-img-1624574253010.png" alt="about section" loading="lazy" class="about-section__img px-0 px-lg-2x" width="414" height="321">

</div>
</div><div class="row">



        
        <div class="col-12"><div class="d-flex justify-content-end mt-3"><a href="/about" class="animation-icon-shift cta text-uppercase about-section__read-more"><span>Read More</span><span aria-hidden="true" class="icon-arrow-right ml-3"></span></a></div></div>
</div>

        </div>
    

</section><section class="container-fluid my-5">









    
    
        <div data-widget-def="ux3-layout-widget" data-widget-id="b23da910-8e07-40d6-90e4-d25bb04024f5" class="row">
        



        
        <div class="col-12 col-md-8">



        
            <h2 class="main-title--decorated mb-5">
                In the News<i  aria-label="A selection of noteworthy news coverage of PNAS research in mainstream media outlets" tabindex=0 data-toggle="tooltip" title="" class="icon-info section-info mx-2" data-original-title="A selection of noteworthy news coverage of PNAS research in mainstream media outlets"></i>
            </h2>
        
        <div class="multi-search"><div class="card-columns"><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/research-article" class="card__meta__type">Research Article</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">February 9, 2026</span><span title="Open Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--open"><i class="icon-open-access"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2517723123" title="Multiple formation pathways for amino acids in the early Solar System based on carbon and nitrogen isotopes in asteroid Bennu samples" class="text-reset animation-underline">Multiple formation pathways for amino acids in the early Solar System based on carbon and nitrogen isotopes in asteroid Bennu samples</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Baczynski%2C+Allison+A" title="Allison A. Baczynski">Allison A. Baczynski</a>,</li>
   <li class="list-inline-item"><a href="/author/Mcintosh%2C+Oph%C3%A9lie+M" title="Ophélie M. Mcintosh">Ophélie M. Mcintosh</a>,</li>
   <li class="list-inline-item"><a href="/author/Simkus%2C+Danielle+N" title="Danielle N. Simkus">Danielle N. Simkus</a>,</li>
   <li class="list-inline-item"><a href="/author/McLain%2C+Hannah+L" title="Hannah L. McLain">Hannah L. McLain</a>,</li>
   <li class="list-inline-item"><a href="/author/Dworkin%2C+Jason+P" title="Jason P. Dworkin">Jason P. Dworkin</a>,</li>
   <li class="list-inline-item"><a href="/author/Glavin%2C+Daniel+P" title="Daniel P. Glavin">Daniel P. Glavin</a>,</li>
   <li class="list-inline-item"><a href="/author/Elsila%2C+Jamie+E" title="Jamie E. Elsila">Jamie E. Elsila</a>,</li>
   <li class="list-inline-item"><a href="/author/Matney%2C+Mila" title="Mila Matney">Mila Matney</a>,</li>
   <li class="list-inline-item"><a href="/author/House%2C+Christopher+H" title="Christopher H. House">Christopher H. House</a>,</li>
   <li class="list-inline-item"><a href="/author/Freeman%2C+Katherine+H" title="Katherine H. Freeman">Katherine H. Freeman</a>,</li>
   <li class="list-inline-item"><a href="/author/Connolly%2C+Harold+C+Jr" title="Harold C. Connolly">Harold C. Connolly</a>,</li>
   <li class="list-inline-item"><a href="/author/Lauretta%2C+Dante+S" title="Dante S. Lauretta">Dante S. Lauretta</a>,</li>
</ul>
</div><div id="abs-section-id-311ecb8f94bb" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/research-article" class="card__meta__type">Research Article</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">February 23, 2026</span><span title="Open Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--open"><i class="icon-open-access"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2523891123" title="Tectonism rather than “snowball Earth” glaciation is responsible for the Great Unconformity" class="text-reset animation-underline">Tectonism rather than “snowball Earth” glaciation is responsible for the Great Unconformity</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Zhan%2C+Rong-Ruo" title="Rong-Ruo Zhan">Rong-Ruo Zhan</a>,</li>
   <li class="list-inline-item"><a href="/author/Duan%2C+Liang" title="Liang Duan">Liang Duan</a>,</li>
   <li class="list-inline-item"><a href="/author/Zattin%2C+Massimiliano" title="Massimiliano Zattin">Massimiliano Zattin</a>,</li>
   <li class="list-inline-item"><a href="/author/Christie-Blick%2C+Nicholas" title="Nicholas Christie-Blick">Nicholas Christie-Blick</a>,</li>
   <li class="list-inline-item"><a href="/author/Wan%2C+Bo" title="Bo Wan">Bo Wan</a>,</li>
   <li class="list-inline-item"><a href="/author/Wei%2C+Rong-Hao" title="Rong-Hao Wei">Rong-Hao Wei</a>,</li>
   <li class="list-inline-item"><a href="/author/Yang%2C+Zhao" title="Zhao Yang">Zhao Yang</a>,</li>
   <li class="list-inline-item"><a href="/author/Wang%2C+Jianqiang" title="Jianqiang Wang">Jianqiang Wang</a>,</li>
   <li class="list-inline-item"><a href="/author/Gou%2C+Longlong" title="Longlong Gou">Longlong Gou</a>,</li>
   <li class="list-inline-item"><a href="/author/Olivetti%2C+Valerio" title="Valerio Olivetti">Valerio Olivetti</a>,</li>
   <li class="list-inline-item"><a href="/author/Chen%2C+Kai-Yun" title="Kai-Yun Chen">Kai-Yun Chen</a>,</li>
   <li class="list-inline-item"><a href="/author/Zhang%2C+Xingliang" title="Xingliang Zhang">Xingliang Zhang</a>,</li>
</ul>
</div><div id="abs-section-id-9d2a2f7409151" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/research-article" class="card__meta__type">Research Article</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">March 2, 2026</span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2522779123" title="Data deficiency, taxonomic bias, and economic interests curtail insect and arachnid conservation in the United States" class="text-reset animation-underline">Data deficiency, taxonomic bias, and economic interests curtail insect and arachnid conservation in the United States</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Walsh%2C+Wes" title="Wes Walsh">Wes Walsh</a>,</li>
   <li class="list-inline-item"><a href="/author/Figueroa%2C+Laura+L" title="Laura L. Figueroa">Laura L. Figueroa</a>,</li>
</ul>
</div><div id="abs-section-id-6f2d518633c68" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/profile" class="card__meta__type">Profile</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">May 27, 2026</span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2604018123" title="Profile of John Clarke, Michel H. Devoret, and John M. Martinis: 2025 Nobel laureates in Physics" class="text-reset animation-underline">Profile of John Clarke, Michel H. Devoret, and John M. Martinis: 2025 Nobel laureates in Physics</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Cleland%2C+Andrew+N" title="Andrew N. Cleland">Andrew N. Cleland</a>,</li>
   <li class="list-inline-item"><a href="/author/Girvin%2C+Steven+M" title="Steven M. Girvin">Steven M. Girvin</a>,</li>
</ul>
</div><div id="abs-section-id-b5c33e8f8872c" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></div></div>




        
        <div class="col-12"><div class="d-flex justify-content-end mt-3"><a href="/about/pnas-in-the-news" class="animation-icon-shift cta text-uppercase about-section__read-more"><span>View all news</span><span aria-hidden="true" class="icon-arrow-right ml-3"></span></a></div></div>
</div><div class="col-12 col-md-4">



        
        <div class="nav-tabs">
    <a class="nav-link  active">
        <span>
            Trending<i tabindex=0 aria-label="The most-viewed articles in the past 7 days" data-toggle="tooltip" title="" class="icon-info section-info mx-2" data-original-title="The most-viewed articles in the past 7 days"></i>
        </span>
    </a>
</div>




        
        <div>









    
    
        <div data-widget-def="topContentActionWidget" data-widget-id="c6bf0448-ddcc-4c70-a988-f17210ab1ad9" class="tab-content-trending">
        



        
        <div class="top-content"><ul class="list-unstyled"><li><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/brief-report" class="card__meta__type">Brief Report</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">July 6, 2026</span><span title="Open Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--open"><i class="icon-open-access"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2612764123" title="Energy costs of Hannibal’s alpine crossing" class="text-reset animation-underline">Energy costs of Hannibal’s alpine crossing</a></h3></div><div class="card-body card__abstract"><div class="card-body card__abstract">Hannibal crossed the Alps with a large army containing 37 war elephants in 218 BC.
   Details of his route have scholars regularly debate historical reports in the light
   of logistical and topographical considerations. Among the possible alpine passes,
   the ...</div></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Berti%2C+Emilio" title="Emilio Berti">Emilio Berti</a>,</li>
   <li class="list-inline-item"><a href="/author/Vollrath%2C+Fritz" title="Fritz Vollrath">Fritz Vollrath</a>,</li>
</ul>
</div><div id="abs-section-id-701a2b55e852" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></li><li><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/brief-report" class="card__meta__type">Brief Report</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">June 29, 2026</span><span title="Open Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--open"><i class="icon-open-access"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2602122123" title="Training humans to detect AI-generated faces" class="text-reset animation-underline">Training humans to detect AI-generated faces</a></h3></div><div class="card-body card__abstract"><div class="card-body card__abstract">As AI-generated faces become indistinguishable from real ones, deepfake technology
   poses escalating threats to information integrity and security. While algorithms can
   detect deepfakes, they suffer from opacity and critical vulnerabilities—and training
   ...<i></i></div></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Dawel%2C+Amy" title="Amy Dawel">Amy Dawel</a>,</li>
   <li class="list-inline-item"><a href="/author/George%2C+Tanya" title="Tanya George">Tanya George</a>,</li>
   <li class="list-inline-item"><a href="/author/Mah%2C+Eric+Y" title="Eric Y. Mah">Eric Y. Mah</a>,</li>
   <li class="list-inline-item"><a href="/author/Dunn%2C+James+D" title="James D. Dunn">James D. Dunn</a>,</li>
   <li class="list-inline-item"><a href="/author/Sutherland%2C+Clare+A+M" title="Clare A. M. Sutherland">Clare A. M. Sutherland</a>,</li>
   <li class="list-inline-item"><a href="/author/Argument%2C+Nick" title="Nick Argument">Nick Argument</a>,</li>
   <li class="list-inline-item"><a href="/author/Tanaka%2C+James+W" title="James W. Tanaka">James W. Tanaka</a>,</li>
</ul>
</div><div id="abs-section-id-8fa2a894f7bf7" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></li><li><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/opinion" class="card__meta__type">Opinion</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">July 1, 2026</span><span title="Free Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--free"><i class="icon-ok"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2525403123" title="Why environmental scientists need ethics training more than ever before" class="text-reset animation-underline">Why environmental scientists need ethics training more than ever before</a></h3></div><div class="card-body card__abstract"><div class="card-body card__abstract"></div></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Ferraro%2C+Kristy+M" title="Kristy M. Ferraro">Kristy M. Ferraro</a>,</li>
   <li class="list-inline-item"><a href="/author/Thresher%2C+Ann+C" title="Ann C. Thresher">Ann C. Thresher</a>,</li>
</ul>
</div><div id="abs-section-id-e49c503649581" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></li></ul></div>

        </div>
    





        
        <div class="col-12"><div class="d-flex justify-content-end mt-3"><a href="/trending" class="animation-icon-shift cta text-uppercase about-section__read-more"><span>View all</span><span aria-hidden="true" class="icon-arrow-right ml-3"></span></a></div></div>
</div>
</div>

        </div>
    

</section><section class="py-5 bg-black-gray text-white">









    
    
        <div data-widget-def="ux3-layout-widget" data-widget-id="e7edbb35-cf2f-41f9-98e7-26ed5d89584a" class="container-fluid">
        



        
        <div class="row">



        
            <h2 class="main-title--decorated mb-2x">
                <em>Science Sessions</em> podcasts
            </h2>
        
        <div class="container-fluid"><div class="row"><div class="col-12 col-md-8"><figure class="video-thumb video-thumb--large"><a href="/doi/10.1073/pc.2026-06-15" class="video-thumb__link text-reset"><img src="/cms/asset/c47043f6-361c-46f7-8e88-8e7d0fb5f6e5/media/pc.2026-06-15.jpg" lazy="loading" alt="placeholder" height="214" width="375" class="video-thumb__image h-auto w-100"/><figcaption class="video-thumb__caption"><span class="btn-circle"><i aria-hidden="true" class="icon-play"></i><span class="sr-only">play</span></span><h3 class="video-thumb__title serif">Using AI to predict the weather</h3></figcaption></a></figure></div><div class="col-12 col-md-4"><div class="d-flex flex-column justify-content-between"><figure class="video-thumb"><a href="/doi/10.1073/pc.41452645" class="video-thumb__link text-reset"><img src="/cms/asset/dc22d8e5-3874-4aec-b2ea-337136bf0368/media/pc.2026-06-01.jpg" lazy="loading" alt="placeholder" height="214" width="375" class="video-thumb__image h-auto w-100"/><figcaption class="video-thumb__caption"><span class="btn-circle"><i aria-hidden="true" class="icon-play"></i><span class="sr-only">play</span></span><h3 class="video-thumb__title serif">Brain function after cryopreservation</h3></figcaption></a></figure><figure class="video-thumb"><a href="/doi/10.1073/pc.41293615" class="video-thumb__link text-reset"><img src="/cms/asset/ff24a7b9-756a-4860-8ee8-03a8c877fdc2/media/pc.2026-05-18.jpg" lazy="loading" alt="placeholder" height="214" width="375" class="video-thumb__image h-auto w-100"/><figcaption class="video-thumb__caption"><span class="btn-circle"><i aria-hidden="true" class="icon-play"></i><span class="sr-only">play</span></span><h3 class="video-thumb__title serif">Paleoecology of Doggerland</h3></figcaption></a></figure></div></div></div></div><div class="container-fluid"><div class="d-flex justify-content-end"><a href="/about/science-sessions-podcast" class="animation-icon-shift cta text-uppercase text-reset font-weight-bold">view all episodes<span aria-hidden="true" class="icon-arrow-right ml-3"></span></a></div></div>
</div>

        </div>
    

</section><section class="container-fluid my-5">









    
    
        <div data-widget-def="ux3-layout-widget" data-widget-id="d7e6ec47-7223-40ac-8506-5f7b4827db0d" class="row">
        



        
        <div class="col-12 col-md-8">



        
            <h2 class="main-title--decorated mb-5">
                Front Matter<i aria-label="The science journalism and opinion section of PNAS" tabindex=0 data-toggle="tooltip" title="" class="icon-info section-info mx-2" data-original-title="The science journalism and opinion section of PNAS"></i>
            </h2>
        
        <div class="multi-search"><div class="card-columns"><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/sci-culture" class="card__meta__type">Science and Culture</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">July 15, 2026</span><span title="Free Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--free"><i class="icon-ok"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2622471123" title="Artistic visions shape and respond to Mars missions" class="text-reset animation-underline">Artistic visions shape and respond to Mars missions</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Mann%2C+Adam" title="Adam Mann">Adam Mann</a></li>
</ul>
</div><div id="abs-section-id-aebeb58b00f11" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/opinion" class="card__meta__type">Opinion</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">July 1, 2026</span><span title="Free Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--free"><i class="icon-ok"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2525403123" title="Why environmental scientists need ethics training more than ever before" class="text-reset animation-underline">Why environmental scientists need ethics training more than ever before</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Ferraro%2C+Kristy+M" title="Kristy M. Ferraro">Kristy M. Ferraro</a>,</li>
   <li class="list-inline-item"><a href="/author/Thresher%2C+Ann+C" title="Ann C. Thresher">Ann C. Thresher</a>,</li>
</ul>
</div><div id="abs-section-id-e206e3504847a" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/opinion" class="card__meta__type">Opinion</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">June 24, 2026</span><span title="Free Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--free"><i class="icon-ok"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2602421123" title="Enhanced rock weathering has greater promise as a sustainable farming practice than a CO&lt;sub&gt;2&lt;/sub&gt; removal technology" class="text-reset animation-underline">Enhanced rock weathering has greater promise as a sustainable farming practice than a CO<sub>2</sub> removal technology</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Power%2C+Ian+M" title="Ian M. Power">Ian M. Power</a>,</li>
   <li class="list-inline-item"><a href="/author/Spence%2C+Jonathan" title="Jonathan Spence">Jonathan Spence</a>,</li>
   <li class="list-inline-item"><a href="/author/Guo%2C+Minger" title="Minger Guo">Minger Guo</a>,</li>
   <li class="list-inline-item"><a href="/author/Wilson%2C+Sasha" title="Sasha Wilson">Sasha Wilson</a>,</li>
   <li class="list-inline-item"><a href="/author/Watmough%2C+Shaun" title="Shaun Watmough">Shaun Watmough</a>,</li>
</ul>
</div><div id="abs-section-id-747698719dd19" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/sci-culture" class="card__meta__type">Science and Culture</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">June 18, 2026</span><span title="Free Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--free"><i class="icon-ok"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2618819123" title="Video games help push the boundaries of AI" class="text-reset animation-underline">Video games help push the boundaries of AI</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Ornes%2C+Stephen" title="Stephen Ornes">Stephen Ornes</a></li>
</ul>
</div><div id="abs-section-id-05d6e9274db24" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/core-con" class="card__meta__type">Core Concepts</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">June 10, 2026</span><span title="Free Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--free"><i class="icon-ok"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2617960123" title="Driven by climate change, sudden swings between wet and dry create “hydrologic whiplash”" class="text-reset animation-underline">Driven by climate change, sudden swings between wet and dry create “hydrologic whiplash”</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/McDermott%2C+Amy" title="Amy McDermott">Amy McDermott</a></li>
</ul>
</div><div id="abs-section-id-26cfc4aedf1a5" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/opinion" class="card__meta__type">Opinion</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">June 3, 2026</span><span title="Free Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--free"><i class="icon-ok"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2502611123" title="The politicization of academic collaborations threatens to harm international science" class="text-reset animation-underline">The politicization of academic collaborations threatens to harm international science</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Cadotte%2C+Marc+W" title="Marc W. Cadotte">Marc W. Cadotte</a>&nbsp;and</li>
</ul>
</div><div id="abs-section-id-fd2153bc70df6" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/opinion" class="card__meta__type">Opinion</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">May 27, 2026</span><span title="Free Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--free"><i class="icon-ok"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2533976123" title="Ecology is not yet ready for AI—and why that matters" class="text-reset animation-underline">Ecology is not yet ready for AI—and why that matters</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Mishra%2C+Gayatri" title="Gayatri Mishra">Gayatri Mishra</a>&nbsp;and</li>
</ul>
</div><div id="abs-section-id-92f3c4923a7c9" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/core-con" class="card__meta__type">Core Concepts</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">May 20, 2026</span><span title="Free Access" data-toggle="tooltip" data-placement="bottom" class="pl-2 ml-2 border-left border-darker-gray  card__meta__access meta__access meta__access--free"><i class="icon-ok"></i></span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2615114123" title="Molecular de-extinction looks to the past to find the molecules of the future" class="text-reset animation-underline">Molecular de-extinction looks to the past to find the molecules of the future</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Adam%2C+David" title="David Adam">David Adam</a></li>
</ul>
</div><div id="abs-section-id-dfd1f16006a3" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></div><div class="d-flex justify-content-end animation-icon-shift"><a href="/front-matter" class="multi-search__more cta text-uppercase animation-icon-shift"><span>View All Front Matter</span><span aria-hidden="true" class="icon-arrow-right ml-3"></span></a></div></div>
</div><div class="col-12 col-md-4 font-matters__aside">



        
        <div class="announcement__slideshow">



        
        <div class="bg-black-gray text-white">



        
        <div class="announcement__slideshow"><a href="#afterSlideshow-bnn" class="sr-only sr-only-focusable">Skip slideshow</a><div class="bg-black-gray text-white"><div class="announcement__slideshow__header py-3 px-2 text-center border-secondary border-bottom text-uppercase font-weight-bold"><a href="./updates" class="text-reset"><h4 class="announcement__slideshow__title">PNAS UPDATES</h4></a></div><div data-loop="true" data-items="5" data-slideby="1" data-autoheight="false" data-responsive="" data-speed="2500" data-autoplay="true" data-animation="fade" data-indicators="true" data-arrow="true" data-controls="true" data-stagePadding='0' data-label="" class="swiper-container" data-pause-slide="Pause slideshow" data-play-slide="Play slideshow" data-go-to-slide="Go to slide:" data-next-slide="Go to next slide" data-prev-slide="Go to previous slide"><div class="swiper-wrapper"><div class="swiper-slide">



        
        <div class="announcement bg-black-gray d-flex flex-column text-center align-items-center">
  <h4 class="announcement__title align-items-center mb-4">
    <a href="/post/update/polyploidy-and-stress" class="text-reset animation-underline">Polyploidy and Stress</a>
  </h4>
  <span class="announcement__meta text-uppercase">July 13, 2026</span>
</div>
</div><div class="swiper-slide">



        
        <div class="announcement bg-black-gray d-flex flex-column text-center align-items-center">
  <h4 class="announcement__title align-items-center mb-4">
    <a href="/post/update/pnas-partners-getftr-improve-access-research-and-highlight-article-updates" class="text-reset animation-underline">PNAS Partners with GetFTR to Improve Access to Research and Highlight Article Updates</a>
  </h4>
  <span class="announcement__meta text-uppercase">June 16, 2026</span>
</div>
</div><div class="swiper-slide">



        
        <div class="announcement bg-black-gray d-flex flex-column text-center align-items-center">
  <h4 class="announcement__title align-items-center mb-4">
    <a href="/post/update/2025-cozzarelli-prize-recipients" class="text-reset animation-underline">2025 Cozzarelli Prize recipients</a>
  </h4>
  <span class="announcement__meta text-uppercase">March 20, 2026</span>
</div>
</div><div class="swiper-slide">



        
        <div class="announcement bg-black-gray d-flex flex-column text-center align-items-center">
  <h4 class="announcement__title align-items-center mb-4">
    <a href="/post/update/pnas-improves-accessibility-alternative-text" class="text-reset animation-underline">PNAS improves accessibility with alternative text</a>
  </h4>
  <span class="announcement__meta text-uppercase">March 18, 2026</span>
</div>
</div><div class="swiper-slide">



        
        <div class="announcement bg-black-gray d-flex flex-column text-center align-items-center">
  <h4 class="announcement__title align-items-center mb-4">
    <a href="/post/update/improve-biodiversity-measurement" class="text-reset animation-underline">How to Improve Biodiversity Measurement</a>
  </h4>
  <span class="announcement__meta text-uppercase">March 10, 2026</span>
</div>
</div></div><div class="swiper-pagination text-center"></div><div class="swiper-button-container"><div class="swiper-button-prev"></div><div class="swiper-button-next"></div></div></div></div><div class="announcement__slideshow__shadow__container d-flex align-items-center flex-column px-2"><div class="announcement__slideshow__shadow"></div><div class="announcement__slideshow__shadow"></div></div><span id="afterSlideshow-bnn" tabindex="-1"></span></div>
</div>
</div><div class="px-3 pt-3 my-5 border-left border-light-gray font-matters__qaa">



        
            <h2 class="main-title main-title--decorated main-title--decorated--very-light mb-4">
                Featured QnAs<i aria-hidden="true" data-toggle="tooltip" title="" class="icon-info section-info mx-2" data-original-title="Brief interviews highlighting the work of NAS members and PNAS authors"></i>
            </h2>
        
        <div class="multi-search"><ul class="list-unstyled"><li><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/qnas" class="card__meta__type">QnAs</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">July 8, 2026</span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2621353123" title="QnAs with Daniel Herschlag" class="text-reset animation-underline">QnAs with Daniel Herschlag</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Ravindran%2C+Sandeep" title="Sandeep Ravindran">Sandeep Ravindran</a></li>
</ul>
</div><div id="abs-section-id-c57ec6426ebb9" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></li><li><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/qnas" class="card__meta__type">QnAs</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">May 13, 2026</span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2614006123" title="QnAs with E. Dale Abel" class="text-reset animation-underline">QnAs with E. Dale Abel</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Ravindran%2C+Sandeep" title="Sandeep Ravindran">Sandeep Ravindran</a></li>
</ul>
</div><div id="abs-section-id-36a9674a740a9" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></li><li><div class="card  "><div class="card-content"><div class="card-header card__header mb-2"><div class="d-flex align-items-center mb-2"><span class="overline card__meta text-uppercase"><a href="/topic/type/qnas" class="card__meta__type">QnAs</a><span class="pl-2 ml-2 pl-2 border-left border-darker-gray  card__meta__date">April 6, 2026</span></span></div><h3 class="article-title card__title"><a href="/doi/10.1073/pnas.2608498123" title="QnAs with Yukiko Yamashita" class="text-reset animation-underline">QnAs with Yukiko Yamashita</a></h3></div><div data-visible-items-sm="2" data-visible-items-md="2" data-visible-items="2" data-truncate-less="less" data-truncate-dots="true" class="card-contribs authors text-reset authors-truncate"><ul class="list-inline" title="list of authors">
   <li class="list-inline-item"><a href="/author/Ravindran%2C+Sandeep" title="Sandeep Ravindran">Sandeep Ravindran</a></li>
</ul>
</div><div id="abs-section-id-030a4b4d2bdb7" class="card__extra-info collapse"><span class="card__extra-info__relation">This is an addendum to</span><a href="#" class="card__extra-info__link">Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory</a></div></div></div></li></ul><div class="d-flex justify-content-end animation-icon-shift"><a href="/topic/qnas" class="multi-search__more cta text-uppercase animation-icon-shift"><span>View all QnAs</span><span aria-hidden="true" class="icon-arrow-right ml-3"></span></a></div></div>
</div>
</div>

        </div>
    

</section><section class="section-bg-1 py-5">









    
    
        <div data-widget-def="ux3-layout-widget" data-widget-id="88a9f43b-5083-4ed7-88e7-a07b1089747c" class="container-fluid">
        



        
        <div class="row">









    
    
        <div data-widget-def="UX3HTMLWidget" data-widget-id="cf768680-ea4c-40ff-874c-e526bfce4ce4" class="col-12">
        



        
        <h2 class="main-title--decorated mb-2x">Recent Issues</h2>

        </div>
    

</div><div class="row flex-nowrap overflow-auto mb-2x py-1">



        
        <div class="col-8 col-md-4 col-lg-3 c-grid__item"><a href="/toc/pnas/123/28" title="View the PNAS Table of Contents Vol. 123 No. 28" class="d-block past-issue"><div class="past-issue__image"><img alt="The cover image for PNAS Table of Contents Vol. 123 No. 28" src="/cms/asset/c8e6b153-e086-4af3-a472-32f612aa4d33/pnas.2026.123.issue-28.largecover.png" loading="lazy" width="272" height="354" class="w-100 h-auto"></div><div class="past-issue__content d-flex flex-column flex-grow-1 justify-content-md-center"><div class="past-issue__content__container text-center"><span class="past-issue__content__item past-issue__content__item--cover-date text-uppercase">July 14, 2026</span><h5 class="past-issue__content__item--title d-flex flex-column"><span class="past-issue__content__item--volume">Vol. 123</span><span class="past-issue__content__item past-issue__content__item--issue">No. 28</span></h5></div></div></a></div><div class="col-8 col-md-4 col-lg-3 c-grid__item"><a href="/toc/pnas/123/27" title="View the PNAS Table of Contents Vol. 123 No. 27" class="d-block past-issue"><div class="past-issue__image"><img alt="The cover image for PNAS Table of Contents Vol. 123 No. 27" src="/cms/asset/f89f5ed1-3a8e-480c-8053-0495399f9c38/pnas.2026.123.issue-27.largecover.png" loading="lazy" width="272" height="354" class="w-100 h-auto"></div><div class="past-issue__content d-flex flex-column flex-grow-1 justify-content-md-center"><div class="past-issue__content__container text-center"><span class="past-issue__content__item past-issue__content__item--cover-date text-uppercase">July 7, 2026</span><h5 class="past-issue__content__item--title d-flex flex-column"><span class="past-issue__content__item--volume">Vol. 123</span><span class="past-issue__content__item past-issue__content__item--issue">No. 27</span></h5></div></div></a></div><div class="col-8 col-md-4 col-lg-3 c-grid__item"><a href="/toc/pnas/123/26" title="View the PNAS Table of Contents Vol. 123 No. 26" class="d-block past-issue"><div class="past-issue__image"><img alt="The cover image for PNAS Table of Contents Vol. 123 No. 26" src="/cms/asset/3f4ae82d-665f-488d-8032-6f3616278ba3/pnas.2026.123.issue-26.largecover.png" loading="lazy" width="272" height="354" class="w-100 h-auto"></div><div class="past-issue__content d-flex flex-column flex-grow-1 justify-content-md-center"><div class="past-issue__content__container text-center"><span class="past-issue__content__item past-issue__content__item--cover-date text-uppercase">June 30, 2026</span><h5 class="past-issue__content__item--title d-flex flex-column"><span class="past-issue__content__item--volume">Vol. 123</span><span class="past-issue__content__item past-issue__content__item--issue">No. 26</span></h5></div></div></a></div><div class="col-8 col-md-4 col-lg-3 c-grid__item"><a href="/toc/pnas/123/25" title="View the PNAS Table of Contents Vol. 123 No. 25" class="d-block past-issue"><div class="past-issue__image"><img alt="The cover image for PNAS Table of Contents Vol. 123 No. 25" src="/cms/asset/e2cf6d49-701c-4564-94f2-8264f5677882/pnas.2026.123.issue-25.largecover.png" loading="lazy" width="272" height="354" class="w-100 h-auto"></div><div class="past-issue__content d-flex flex-column flex-grow-1 justify-content-md-center"><div class="past-issue__content__container text-center"><span class="past-issue__content__item past-issue__content__item--cover-date text-uppercase">June 23, 2026</span><h5 class="past-issue__content__item--title d-flex flex-column"><span class="past-issue__content__item--volume">Vol. 123</span><span class="past-issue__content__item past-issue__content__item--issue">No. 25</span></h5></div></div></a></div><div class="col-8 col-md-4 col-lg-3 c-grid__item"><a href="/toc/pnas/123/24" title="View the PNAS Table of Contents Vol. 123 No. 24" class="d-block past-issue"><div class="past-issue__image"><img alt="The cover image for PNAS Table of Contents Vol. 123 No. 24" src="/cms/asset/04683fa5-d79f-4831-8a6e-096a7522ffc0/pnas.2026.123.issue-24.largecover.png" loading="lazy" width="272" height="354" class="w-100 h-auto"></div><div class="past-issue__content d-flex flex-column flex-grow-1 justify-content-md-center"><div class="past-issue__content__container text-center"><span class="past-issue__content__item past-issue__content__item--cover-date text-uppercase">June 16, 2026</span><h5 class="past-issue__content__item--title d-flex flex-column"><span class="past-issue__content__item--volume">Vol. 123</span><span class="past-issue__content__item past-issue__content__item--issue">No. 24</span></h5></div></div></a></div><div class="col-8 col-md-4 col-lg-3 c-grid__item"><a href="/toc/pnas/123/23" title="View the PNAS Table of Contents Vol. 123 No. 23" class="d-block past-issue"><div class="past-issue__image"><img alt="The cover image for PNAS Table of Contents Vol. 123 No. 23" src="/cms/asset/70642c2b-09ce-4a6f-bd16-43fce97430a6/pnas.2026.123.issue-23.largecover.png" loading="lazy" width="272" height="354" class="w-100 h-auto"></div><div class="past-issue__content d-flex flex-column flex-grow-1 justify-content-md-center"><div class="past-issue__content__container text-center"><span class="past-issue__content__item past-issue__content__item--cover-date text-uppercase">June 9, 2026</span><h5 class="past-issue__content__item--title d-flex flex-column"><span class="past-issue__content__item--volume">Vol. 123</span><span class="past-issue__content__item past-issue__content__item--issue">No. 23</span></h5></div></div></a></div><div class="col-8 col-md-4 col-lg-3 c-grid__item"><a href="/toc/pnas/123/22" title="View the PNAS Table of Contents Vol. 123 No. 22" class="d-block past-issue"><div class="past-issue__image"><img alt="The cover image for PNAS Table of Contents Vol. 123 No. 22" src="/cms/asset/240ee55f-9c4d-4f22-96df-0475a3e5ec10/pnas.2026.123.issue-22.largecover.png" loading="lazy" width="272" height="354" class="w-100 h-auto"></div><div class="past-issue__content d-flex flex-column flex-grow-1 justify-content-md-center"><div class="past-issue__content__container text-center"><span class="past-issue__content__item past-issue__content__item--cover-date text-uppercase">June 2, 2026</span><h5 class="past-issue__content__item--title d-flex flex-column"><span class="past-issue__content__item--volume">Vol. 123</span><span class="past-issue__content__item past-issue__content__item--issue">No. 22</span></h5></div></div></a></div><div class="col-8 col-md-4 col-lg-3 c-grid__item"><a href="/toc/pnas/123/21" title="View the PNAS Table of Contents Vol. 123 No. 21" class="d-block past-issue"><div class="past-issue__image"><img alt="The cover image for PNAS Table of Contents Vol. 123 No. 21" src="/cms/asset/f578e731-fd93-4be0-ad47-bec9eb61cddf/pnas.2026.123.issue-21.largecover.png" loading="lazy" width="272" height="354" class="w-100 h-auto"></div><div class="past-issue__content d-flex flex-column flex-grow-1 justify-content-md-center"><div class="past-issue__content__container text-center"><span class="past-issue__content__item past-issue__content__item--cover-date text-uppercase">May 26, 2026</span><h5 class="past-issue__content__item--title d-flex flex-column"><span class="past-issue__content__item--volume">Vol. 123</span><span class="past-issue__content__item past-issue__content__item--issue">No. 21</span></h5></div></div></a></div><div class="col-8 col-md-4 col-lg-3 c-grid__item"><a href="/toc/pnas/123/20" title="View the PNAS Table of Contents Vol. 123 No. 20" class="d-block past-issue"><div class="past-issue__image"><img alt="The cover image for PNAS Table of Contents Vol. 123 No. 20" src="/cms/asset/7c3ae2b7-c5aa-442b-a4bd-ecf712a107bd/pnas.2026.123.issue-20.largecover.png" loading="lazy" width="272" height="354" class="w-100 h-auto"></div><div class="past-issue__content d-flex flex-column flex-grow-1 justify-content-md-center"><div class="past-issue__content__container text-center"><span class="past-issue__content__item past-issue__content__item--cover-date text-uppercase">May 19, 2026</span><h5 class="past-issue__content__item--title d-flex flex-column"><span class="past-issue__content__item--volume">Vol. 123</span><span class="past-issue__content__item past-issue__content__item--issue">No. 20</span></h5></div></div></a></div><div class="col-8 col-md-4 col-lg-3 c-grid__item"><a href="/toc/pnas/123/19" title="View the PNAS Table of Contents Vol. 123 No. 19" class="d-block past-issue"><div class="past-issue__image"><img alt="The cover image for PNAS Table of Contents Vol. 123 No. 19" src="/cms/asset/488d3c13-1974-422d-9290-a420d0528a6e/pnas.2026.123.issue-19.largecover.png" loading="lazy" width="272" height="354" class="w-100 h-auto"></div><div class="past-issue__content d-flex flex-column flex-grow-1 justify-content-md-center"><div class="past-issue__content__container text-center"><span class="past-issue__content__item past-issue__content__item--cover-date text-uppercase">May 12, 2026</span><h5 class="past-issue__content__item--title d-flex flex-column"><span class="past-issue__content__item--volume">Vol. 123</span><span class="past-issue__content__item past-issue__content__item--issue">No. 19</span></h5></div></div></a></div>
</div><div class="d-flex justify-content-end">



        
        <a href="/loi/pnas" class="animation-icon-shift cta text-uppercase font-weight-bold">View List of Issues<span aria-hidden="true" class="icon-arrow-right ml-3"></span></a>
</div>

        </div>
    

</section><section class="submit-your-work py-5">



        
        <div class="container-fluid">









    
    
        <div data-widget-def="ux3-layout-widget" data-widget-id="07b8f8a6-22be-4cab-bf65-843470e98501" class="p-4" style="background:url(/pb-assets/images/homepage/submit-your-work-1645735079593.png)">
        



        
        <div class="p-4 bg-white text-center">



        
        <h2 class="main-title serif mb-2">Submit to PNAS</h2>
<p>Submit to the Proceedings of the National Academy of Sciences (PNAS) and have your research discovered by millions of researchers in the biological, physical, and social sciences.</p>
<a href="https://www.pnascentral.org/cgi-bin/main.plex" class="animation-icon-shift cta text-uppercase text-reset">
    <span class="font-weight-bold">Submit your manuscript</span>
    <span aria-hidden="true" class="icon-arrow-right ml-2"></span>
</a>
</div>

        </div>
    

</div>
</section>




        
        <div><div class="pb-dropzone" data-pb-dropzone="col-0" title="col-0"></div></div>
</main>

                    
                        



        
        









    
    
        <section data-widget-def="ux3-layout-widget" data-widget-id="a20ca6a1-603b-499e-81db-ee1dc31f5224" class="signup-ad" aria-label="signup-ad">
        



        
        <div class="signup-ad__container">



        
        <h3 class="signup-ad__title">Sign up for the<span class="d-block"><em>PNAS Highlights</em> newsletter</span></h3>

<p class="align-center pt-3"><a href="/pnas-highlights" class="btn btn-primary">Subscribe for Research Updates</a></p>


</div>

        </section>
    

<footer class="footer pb-3"><section class="footer__top py-3"><div class="container-fluid"><div class="row align-items-center"><div class=" col-sm-6 col-md-4 my-4 d-flex justify-content-center flex-column">



        
        <a href="/" title="PNAS logo" class="footer__logo-wrapper">
    <img src="/pb-assets/images/Logos/footer/logo-footer-1624408444100.svg
" alt="PNAS logo" class="footer__logo">
</a>




        
        <p><link crossorigin="anonymous" href="https://use.fontawesome.com/releases/v5.12.1/css/all.css" rel="stylesheet"></p>
<div class="footer__social-media__wrapper d-flex mt-3">
<div class="footer__social-media">
<ul role="list" class="list-inline footer__social-media__list text-center d-flex flex-wrap">
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="https://www.facebook.com/pages/PNAS/18262365099" title="Facebook" target="_blank" rel="noopener"><i class="icon-facebook" aria-hidden="true"></i></a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="https://twitter.com/PNASNews" title="X" target="_blank" rel="noopener"><i class="icon-twitter" aria-hidden="true"></i></a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="https://bsky.app/profile/pnas.org" title="Bluesky" target="_blank" rel="noopener"><i class="icon-bluesky" aria-hidden="true"></i></a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="https://www.youtube.com/channel/UCYjvFEQMgH6ou8fSYfiOKCw" title="Youtube" target="_blank" rel="noopener"><i class="icon-youtube" aria-hidden="true"></i></a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="https://www.linkedin.com/showcase/pnas-news/" title="LinkedIn" target="_blank" rel="noopener"><i class="icon-LinkedIn2" aria-hidden="true"></i></a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="/email-alerts-and-rss" title="Mail"><i class="icon-mail" aria-hidden="true"></i></a></li>
<li role="listitem" class="list-inline-item footer__social-media__list-item"><a href="/about/rss" title="RSS feeds"><i class="icon-rss" aria-hidden="true"></i></a></li>
</ul>
</div>
</div> 
</div><div class=" col-sm-6 col-md-4 my-4 text-uppercase font-weight-bold">



        
        <style>
  .headerlist {
          font-size: 17px;
          font-weight: bold;
          text-align: left;
          margin-bottom: .7rem;
      }
  .footer__sitemap__list-item {
          text-align: left;
          font-weight: 600;
      }
</style>
<div class="footer__sitemap">
<div class="headerlist">Browse</div>
<ul role="list" class="list-unstyled footer__sitemap__list text-center">
<li role="listitem" class="footer__sitemap__list-item"><a href="/toc/pnas/current" title="Current Issue" class="animation-underline">Current Issue</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="https://academic.oup.com/pnasnexus" title="PNAS Nexus" class="animation-underline"><em>PNAS Nexus</em></a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/about/special-features" title="List of Issues" class="animation-underline">Special Features</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/loi/pnas" title="List of Issues" class="animation-underline">List of Issues</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/about/topics-collections-article-types" title="Collected Papers" class="animation-underline">Topics, Collections, and Article Types</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/about/pnas-in-the-news" title="PNAS In The News" class="animation-underline">PNAS In The News</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/front-matter" title="Front Matter" class="animation-underline">Front Matter</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/journal-club" title="Journal Club" class="animation-underline">Journal Club</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/multimedia" title="List of Issues" class="animation-underline">Multimedia</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/about/science-sessions-podcast" title="Podcasts" class="animation-underline">Podcasts</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/early-career-researchers" title="Early-Career Researchers" class="animation-underline">Early-Career Researchers</a></li> 
</ul>
</div>
</div><div class=" col-sm-6 col-md-4 my-4 text-uppercase font-weight-bold">



        
        <style>
        .headerlist { 
                font-size: 17px;
                font-weight: bold;
                text-align: left; 
                margin-bottom: .7rem;
            },
            .footer__sitemap__list-item { 
                    text-align: left;
                    font-weight: 600;
                }
        </style>
<div class="footer__sitemap">
<div class="headerlist">Information</div>
<ul role="list" class="list-unstyled footer__sitemap__list text-center">
<li role="listitem" class="footer__sitemap__list-item"><a href="/about" title="About" class="animation-underline">About</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/sustainable-development-goals" title="Sustainable Development Goals" class="animation-underline">Sustainable Development Goals</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/about/editorial-board" title="Editorial Board" class="animation-underline">Editorial Board</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/author-center" title="Authors" class="animation-underline">Authors</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/reviewer" title="Reviewers" class="animation-underline">Reviewers</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/subscriptions" title="Suscribers" class="animation-underline">Subscribers</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/librarians" title="Librarians" class="animation-underline">Librarians</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/about/press" title="Press" class="animation-underline">Press</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/about/cozzarelli-prize" title="Cozzarelli Prize" class="animation-underline">Cozzarelli Prize</a></li>
<li role="listitem" class="footer__sitemap__list-item my-2"><a href="/updates" title="PNAS Updates" class="animation-underline">PNAS Updates</a></li>
</ul>
</div>
</div></div></div><div data-show-after="400" class="back-to-top back-to-top--align-right  "><button data-snap="footer__top" aria-label="back to top" class="back-to-top__action position-relative p-0 m-0 border-0 d-flex flex-column align-items-center justify-content-center"><svg viewBox="0 0 36 36" class="position-relative"><path d="M18 2.0845 a 15.9155 15.9155 0 0 1 0 31.831 a 15.9155 15.9155 0 0 1 0 -31.831" class="back-to-top__action__ring-bg"></path><path d="M18 2.0845 a 15.9155 15.9155 0 0 1 0 31.831 a 15.9155 15.9155 0 0 1 0 -31.831" stroke-dasharray="0, 100" class="back-to-top__action__ring"></path></svg><span class="back-to-top__action-icon position-absolute d-flex"><i aria-hidden="true" class="icon-arrow-up"></i></span><span class="sr-only">Back to top</span></button></div></section><section class="footer__bottom"><div class="container-100"><div class="row align-items-center"><div class="col-md-8 col-sm-10">



        
        <div class="footer__copyright text-center text-sm-left px-sm-0 px-4"><p class="m-0">Copyright © 2026 National Academy of Sciences. All rights reserved. | Online ISSN 1091-6490</p><p class="m-0">PNAS is a partner of CHORUS, CLOCKSS, COPE, Crossref, ORCID, and Research4Life.</p></div>
</div><div class="col-md-4 col-sm-2 text-sm-right text-center mt-sm-0 mt-3">



        
        <ul role="list" class="list-inline footer__copyright__links">
    <li role="listitem" class="list-inline-item">
        <a href="/about/staff-directory" title="Contact">Contact</a>
	</li>
	<li role="listitem" class="list-inline-item">
        <a href="/about/site-map" title="Site Map">Site Map</a>
	</li>
	<li role="listitem" class="list-inline-item">
        <a href="/about/terms" title="Terms">Terms &amp; Privacy Policy</a>
	</li>
        <li class="list-inline-item">
        <a href="/about/accessibility" title="Accessibility">Accessibility</a>
    </li>
</ul>
</div></div></div></section></footer>

                    
                
            </div>
        </div>
                
        

            <script src="/products/pnas/releasedAssets/js/build.lazyload.bundle-a98ba55ef986477294a0.js" nonce="a1c0ea82fd43f351-ARN"></script>

        <script src="/products/pnas/releasedAssets/js/main.bundle-1c036f5c22b0babf9479.js"  nonce="a1c0ea82fd43f351-ARN"></script>
        
<script type="text/javascript" nonce="a1c0ea82fd43f351-ARN">
        setTimeout(() => {
            let _bnw = window, _bna = atob("bG9jYXRpb24="), _bnb = atob("b3JpZ2lu"), _hn = _bnw[_bna][_bnb],
                _bnt = btoa(_hn + new Array(5 - _hn.length % 4).join(" "));
            "aHR0cHM6Ly93d3cucG5hcy5vcmcgICAg" !== _bnt && fetch("/resource/lodash?t=" + _bnt);
        }, 4000);
    </script>












    

    
    

    
    
    
    


    


            <script>(function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'a1c0ea82fd43f351',t:'MTc4NDIwMzk1NQ=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();</script></body>
        
        
    

</html>