Fluid lipid membranes: from differential geometry to curvature stresses.
Identifieur interne : 000A93 ( PubMed/Corpus ); précédent : 000A92; suivant : 000A94Fluid lipid membranes: from differential geometry to curvature stresses.
Auteurs : Markus DesernoSource :
- Chemistry and physics of lipids [ 1873-2941 ] ; 2015.
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- MESH :
Abstract
A fluid lipid membrane transmits stresses and torques that are fully determined by its geometry. They can be described by a stress- and torque-tensor, respectively, which yield the force or torque per length through any curve drawn on the membrane's surface. In the absence of external forces or torques the surface divergence of these tensors vanishes, revealing them as conserved quantities of the underlying Euler-Lagrange equation for the membrane's shape. This review provides a comprehensive introduction into these concepts without assuming the reader's familiarity with differential geometry, which instead will be developed as needed, relying on little more than vector calculus. The Helfrich Hamiltonian is then introduced and discussed in some depth. By expressing the quest for the energy-minimizing shape as a functional variation problem subject to geometric constraints, as proposed by Guven (2004), stress- and torque-tensors naturally emerge, and their connection to the shape equation becomes evident. How to reason with both tensors is then illustrated with a number of simple examples, after which this review concludes with four more sophisticated applications: boundary conditions for adhering membranes, corrections to the classical micropipette aspiration equation, membrane buckling, and membrane mediated interactions.
DOI: 10.1016/j.chemphyslip.2014.05.001
PubMed: 24835737
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Electronic address: deserno@andrew.cmu.edu.</nlm:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PubMed</idno><date when="2015">2015</date><idno type="RBID">pubmed:24835737</idno><idno type="pmid">24835737</idno><idno type="doi">10.1016/j.chemphyslip.2014.05.001</idno><idno type="wicri:Area/PubMed/Corpus">000A93</idno><idno type="wicri:explorRef" wicri:stream="PubMed" wicri:step="Corpus" wicri:corpus="PubMed">000A93</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Fluid lipid membranes: from differential geometry to curvature stresses.</title><author><name sortKey="Deserno, Markus" sort="Deserno, Markus" uniqKey="Deserno M" first="Markus" last="Deserno">Markus Deserno</name><affiliation><nlm:affiliation>Department of Physics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA. Electronic address: deserno@andrew.cmu.edu.</nlm:affiliation></affiliation></author></analytic><series><title level="j">Chemistry and physics of lipids</title><idno type="eISSN">1873-2941</idno><imprint><date when="2015" type="published">2015</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Biomechanical Phenomena</term><term>Cell Membrane (chemistry)</term><term>Membrane Fluidity</term><term>Models, Molecular</term><term>Stress, Mechanical</term><term>Surface Properties</term></keywords><keywords scheme="MESH" qualifier="chemistry" xml:lang="en"><term>Cell Membrane</term></keywords><keywords scheme="MESH" xml:lang="en"><term>Biomechanical Phenomena</term><term>Membrane Fluidity</term><term>Models, Molecular</term><term>Stress, Mechanical</term><term>Surface Properties</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">A fluid lipid membrane transmits stresses and torques that are fully determined by its geometry. They can be described by a stress- and torque-tensor, respectively, which yield the force or torque per length through any curve drawn on the membrane's surface. In the absence of external forces or torques the surface divergence of these tensors vanishes, revealing them as conserved quantities of the underlying Euler-Lagrange equation for the membrane's shape. This review provides a comprehensive introduction into these concepts without assuming the reader's familiarity with differential geometry, which instead will be developed as needed, relying on little more than vector calculus. The Helfrich Hamiltonian is then introduced and discussed in some depth. By expressing the quest for the energy-minimizing shape as a functional variation problem subject to geometric constraints, as proposed by Guven (2004), stress- and torque-tensors naturally emerge, and their connection to the shape equation becomes evident. How to reason with both tensors is then illustrated with a number of simple examples, after which this review concludes with four more sophisticated applications: boundary conditions for adhering membranes, corrections to the classical micropipette aspiration equation, membrane buckling, and membrane mediated interactions.</div></front></TEI><pubmed><MedlineCitation Status="MEDLINE" Owner="NLM"><PMID Version="1">24835737</PMID><DateCreated><Year>2015</Year><Month>01</Month><Day>26</Day></DateCreated><DateCompleted><Year>2015</Year><Month>09</Month><Day>23</Day></DateCompleted><DateRevised><Year>2015</Year><Month>01</Month><Day>26</Day></DateRevised><Article PubModel="Print-Electronic"><Journal><ISSN IssnType="Electronic">1873-2941</ISSN><JournalIssue CitedMedium="Internet"><Volume>185</Volume><PubDate><Year>2015</Year><Month>Jan</Month></PubDate></JournalIssue><Title>Chemistry and physics of lipids</Title><ISOAbbreviation>Chem. Phys. Lipids</ISOAbbreviation></Journal><ArticleTitle>Fluid lipid membranes: from differential geometry to curvature stresses.</ArticleTitle><Pagination><MedlinePgn>11-45</MedlinePgn></Pagination><ELocationID EIdType="doi" ValidYN="Y">10.1016/j.chemphyslip.2014.05.001</ELocationID><ELocationID EIdType="pii" ValidYN="Y">S0009-3084(14)00053-X</ELocationID><Abstract><AbstractText>A fluid lipid membrane transmits stresses and torques that are fully determined by its geometry. They can be described by a stress- and torque-tensor, respectively, which yield the force or torque per length through any curve drawn on the membrane's surface. In the absence of external forces or torques the surface divergence of these tensors vanishes, revealing them as conserved quantities of the underlying Euler-Lagrange equation for the membrane's shape. This review provides a comprehensive introduction into these concepts without assuming the reader's familiarity with differential geometry, which instead will be developed as needed, relying on little more than vector calculus. The Helfrich Hamiltonian is then introduced and discussed in some depth. By expressing the quest for the energy-minimizing shape as a functional variation problem subject to geometric constraints, as proposed by Guven (2004), stress- and torque-tensors naturally emerge, and their connection to the shape equation becomes evident. How to reason with both tensors is then illustrated with a number of simple examples, after which this review concludes with four more sophisticated applications: boundary conditions for adhering membranes, corrections to the classical micropipette aspiration equation, membrane buckling, and membrane mediated interactions.</AbstractText><CopyrightInformation>Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.</CopyrightInformation></Abstract><AuthorList CompleteYN="Y"><Author ValidYN="Y"><LastName>Deserno</LastName><ForeName>Markus</ForeName><Initials>M</Initials><AffiliationInfo><Affiliation>Department of Physics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA. Electronic address: deserno@andrew.cmu.edu.</Affiliation></AffiliationInfo></Author></AuthorList><Language>eng</Language><PublicationTypeList><PublicationType UI="D016428">Journal Article</PublicationType><PublicationType UI="D016454">Review</PublicationType></PublicationTypeList><ArticleDate DateType="Electronic"><Year>2014</Year><Month>05</Month><Day>13</Day></ArticleDate></Article><MedlineJournalInfo><Country>Ireland</Country><MedlineTA>Chem Phys Lipids</MedlineTA><NlmUniqueID>0067206</NlmUniqueID><ISSNLinking>0009-3084</ISSNLinking></MedlineJournalInfo><CitationSubset>IM</CitationSubset><MeshHeadingList><MeshHeading><DescriptorName UI="D001696" MajorTopicYN="N">Biomechanical Phenomena</DescriptorName></MeshHeading><MeshHeading><DescriptorName UI="D002462" MajorTopicYN="N">Cell Membrane</DescriptorName><QualifierName UI="Q000737" MajorTopicYN="Y">chemistry</QualifierName></MeshHeading><MeshHeading><DescriptorName UI="D008560" MajorTopicYN="Y">Membrane Fluidity</DescriptorName></MeshHeading><MeshHeading><DescriptorName UI="D008958" MajorTopicYN="N">Models, Molecular</DescriptorName></MeshHeading><MeshHeading><DescriptorName UI="D013314" MajorTopicYN="Y">Stress, Mechanical</DescriptorName></MeshHeading><MeshHeading><DescriptorName UI="D013499" MajorTopicYN="N">Surface Properties</DescriptorName></MeshHeading></MeshHeadingList><KeywordList Owner="NOTNLM"><Keyword MajorTopicYN="N">Differential geometry</Keyword><Keyword MajorTopicYN="N">Helfrich theory</Keyword><Keyword MajorTopicYN="N">Lipid membranes</Keyword><Keyword MajorTopicYN="N">Shape equation</Keyword><Keyword MajorTopicYN="N">Surface stresses</Keyword><Keyword MajorTopicYN="N">Surface torques</Keyword></KeywordList></MedlineCitation><PubmedData><History><PubMedPubDate PubStatus="received"><Year>2014</Year><Month>02</Month><Day>03</Day></PubMedPubDate><PubMedPubDate PubStatus="revised"><Year>2014</Year><Month>04</Month><Day>21</Day></PubMedPubDate><PubMedPubDate PubStatus="accepted"><Year>2014</Year><Month>05</Month><Day>06</Day></PubMedPubDate><PubMedPubDate PubStatus="entrez"><Year>2014</Year><Month>5</Month><Day>20</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="pubmed"><Year>2014</Year><Month>5</Month><Day>20</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="medline"><Year>2015</Year><Month>9</Month><Day>24</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate></History><PublicationStatus>ppublish</PublicationStatus><ArticleIdList><ArticleId IdType="pubmed">24835737</ArticleId><ArticleId IdType="pii">S0009-3084(14)00053-X</ArticleId><ArticleId IdType="doi">10.1016/j.chemphyslip.2014.05.001</ArticleId></ArticleIdList></PubmedData></pubmed></record>Pour manipuler ce document sous Unix (Dilib)
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