<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1870-3542</journal-id>
<journal-title><![CDATA[Revista mexicana de física E]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fís. E]]></abbrev-journal-title>
<issn>1870-3542</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1870-35422010000100013</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Elasticidad de las membranas biológicas]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Martínez-Balbuena]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Maldonado-Arce]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández-Zapata]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<xref ref-type="aff" rid="A03"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad de Sonora Departamento de Investigación en Física ]]></institution>
<addr-line><![CDATA[Hermosillo Sonora]]></addr-line>
<country>México</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidad de Sonora Departamento de Física ]]></institution>
<addr-line><![CDATA[Hermosillo Sonora]]></addr-line>
<country>México</country>
</aff>
<aff id="A03">
<institution><![CDATA[,Universidad de Sonora Departamento de Física, Matemáticas e Ingeniería ]]></institution>
<addr-line><![CDATA[Caborca Sonora]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2010</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2010</year>
</pub-date>
<volume>56</volume>
<numero>1</numero>
<fpage>107</fpage>
<lpage>122</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1870-35422010000100013&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1870-35422010000100013&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1870-35422010000100013&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[En este artículo se presenta una revisión del conocimiento actual sobre las propiedades elásticas de las membranas de origen biológico. Bajo la hipótesis del mosaico fluido se considera a una bicapa de fosfolípido como la base estructural de una membrana biológica y se expone un modelo debido a Helfrich a partir del cual se obtiene una expresión para la energía elástica de una membrana. La energía libre queda completamente caracterizada por sus curvaturas locales principales y cuatro parámetros dependientes de la composición química de la membrana y de su entorno local. Así mismo, se expone la justificación teórica de un método experimental (que hace uso de micromanipulación con micropipetas) que permite medir la constante elástica de curvatura media de una membrana. Finalmente se describen algunas consecuencias físicas de estos conceptos, como la explicación de la transición de una fase lamelar a una esponja o la aparición de la interacción estérica entre membranas.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[In this article we review the present knowledge on the elastic properties of membranes of biological origin. Assuming the fluid mosaic hypothesis, we consider the phospholipid bilayer as the structural base of a biological membrane. We expose a model due to Helfrich which can be used to obtain an expression for the membrane elastic energy. The free energy is completely characterized by two local principal curvatures and four parameters that depend on the chemical composition of the membrane and its local environment. In addition we present the theoretical justification of an experimental method (the Micropipette Manipulation technique) that may be used to measure the membrane rigidity (the elastic constant that corresponds to the mean curvature of the membrane). Finally, we describe some physical consequences of these concepts, such as the explanation of the lamellar-sponge phase transition and the emergence of the steric interaction between membranes.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Energía libre de Helfrich]]></kwd>
<kwd lng="es"><![CDATA[membranas biológicas]]></kwd>
<kwd lng="es"><![CDATA[bicapas lipídicas]]></kwd>
<kwd lng="es"><![CDATA[elasticidad de membranas]]></kwd>
<kwd lng="en"><![CDATA[Helfrich free energy]]></kwd>
<kwd lng="en"><![CDATA[biological membrane]]></kwd>
<kwd lng="en"><![CDATA[lipid bilayer]]></kwd>
<kwd lng="en"><![CDATA[elasticity of membranes]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="justify"><font face="verdana" size="4">Ense&ntilde;anza</font></p>     <p align="center"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="4"><b>Elasticidad de las membranas biol&oacute;gicas</b></font></p>     <p align="center"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="2"><b>L. Mart&iacute;nez&#150;Balbuena<sup>a</sup>, A. Maldonado&#150;Arce<sup>b</sup>, E. Hern&aacute;ndez&#150;Zapata<sup>c</sup></b></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><i><sup><i>a</i></sup> Departamento de Investigaci&oacute;n en F&iacute;sica, Universidad de Sonora, Apartado Postal 5&#150;088, 83190 Hermosillo, Sonora, M&eacute;xico.</i></font></p>     <p align="justify"><font face="verdana" size="2"><i><sup><i>b</i></sup> Departamento de F&iacute;sica, Universidad de Sonora, Apartado Postal 1626, Hermosillo, 83000 Sonora, M&eacute;xico.</i></font></p>     <p align="justify"><font face="verdana" size="2"><i><sup><i>c </i></sup>Departamento de F&iacute;sica, Matem&aacute;ticas e Ingenier&iacute;a, Universidad de Sonora, H. Caborca, 83600 Sonora, M&eacute;xico.</i></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">Recibido el 28 de septiembre de 2009    <br>   Aceptado el 24 de noviembre de 2009</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Resumen</b></font></p>     <p align="justify"><font face="verdana" size="2">En este art&iacute;culo se presenta una revisi&oacute;n del conocimiento actual sobre las propiedades el&aacute;sticas de las membranas de origen biol&oacute;gico. Bajo la hip&oacute;tesis del mosaico fluido se considera a una bicapa de fosfol&iacute;pido como la base estructural de una membrana biol&oacute;gica y se expone un modelo debido a Helfrich a partir del cual se obtiene una expresi&oacute;n para la energ&iacute;a el&aacute;stica de una membrana. La energ&iacute;a libre queda completamente caracterizada por sus curvaturas locales principales y cuatro par&aacute;metros dependientes de la composici&oacute;n qu&iacute;mica de la membrana y de su entorno local. As&iacute; mismo, se expone la justificaci&oacute;n te&oacute;rica de un m&eacute;todo experimental (que hace uso de micromanipulaci&oacute;n con micropipetas) que permite medir la constante el&aacute;stica de curvatura media de una membrana. Finalmente se describen algunas consecuencias f&iacute;sicas de estos conceptos, como la explicaci&oacute;n de la transici&oacute;n de una fase lamelar a una esponja o la aparici&oacute;n de la interacci&oacute;n est&eacute;rica entre membranas.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Descriptores:</b> Energ&iacute;a libre de Helfrich; membranas biol&oacute;gicas; bicapas lip&iacute;dicas; elasticidad de membranas.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Abstract</b></font></p>     <p align="justify"><font face="verdana" size="2">In this article we review the present knowledge on the elastic properties of membranes of biological origin. Assuming the fluid mosaic hypothesis, we consider the phospholipid bilayer as the structural base of a biological membrane. We expose a model due to Helfrich which can be used to obtain an expression for the membrane elastic energy. The free energy is completely characterized by two local principal curvatures and four parameters that depend on the chemical composition of the membrane and its local environment. In addition we present the theoretical justification of an experimental method (the Micropipette Manipulation technique) that may be used to measure the membrane rigidity (the elastic constant that corresponds to the mean curvature of the membrane). Finally, we describe some physical consequences of these concepts, such as the explanation of the lamellar&#150;sponge phase transition and the emergence of the steric interaction between membranes.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Keywords:</b> Helfrich free energy; biological membrane; lipid bilayer; elasticity of membranes.</font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">PACS: 87.16.dm; 87.16dj; 02.40.Hw</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><a href="/pdf/rmfe/v56n1/v56n1a13.pdf" target="_blank">DESCARGAR ART&Iacute;CULO EN FORMATO PDF</a></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Agradecimientos</b></font></p>     <p align="justify"><font face="verdana" size="2">Agradecemos a Gerardo Paredes y Carlos Luna, estudiantes de la Universidad de Sonora, por compartir con nosotros sus gr&aacute;ficas y resultados experimentales de manipulaci&oacute;n con micropipetas. MB agradece a Conacyt por la beca de maestr&iacute;a otorgada.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Referencias</b></font></p>     <!-- ref --><p align="justify"><font face="verdana" size="2">1. P.L. Yeagle, <i>The Structure of Biological Membranes</i> (CRC Press 2005).</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8452531&pid=S1870-3542201000010001300001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">2. H. 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