Geometric evolution towards the understanding of biomembranes
Titel (Englisch)
Geometric evolution towards the understanding of biomembranes
Kurzbeschreibung (Deutsch)
Biological membranes are a mixture of many different types of lipids and protein components,rnand their relative amount and composition differ between functionally distinctrndomains. The strongly increasing interest in lipid membranes results from the hypothesizedrncoupling of lipid phase segregation in the membrane to fundamental cell biologicalrnprocesses, such as membrane signaling and trafficing. Sub-domains of distinct curvaturernmay have precise biological properties, thus an understanding how lipid componentsrncan dynamically influence to membrane morphology is of utmost importance.rnChanges in lipid composition are assumed to assist or antagonize the membrane curvaturernon one side, but also might respond to the curvature by concentrating in domainsrnof curvature that they prefer on the other side. Strong curvature variations have recentlyrnbeen observed experimentally in giant liposmes, where different lipids segregate accordingrnto their chemical properties and lead to the formation of buds. The strong couplingrnof phase separation and shape dynamics in lipid membranes has also been shownrnnumerically by molecular dynamics and Monte Carlo simulations. Such atomisticrnsimulations however are limited in the accessible length and time scales.rnWith the curvature as one of the crucial incrediences to determine properties of membranesrnit seems natural to model the evolution within a continuum framework. This isrnfurther justified by the different length scales which come into play. The thickness of thernmembrane is in the nm-range, while a typical size of a biomembrane is in the μm-range.rnThis length scale separation allows the biomembrane to be described as an elastic surface, which is the basis for our treatment. Within such a continuum description the observedrnbudding in multicomponent lipid bilayers can be understood, by the possibility tornreduce the line energy associated with the domain boundaries by budding these domains, an additional degree of freedom which is not present for phase separation processes inrnthe bulk. A dynamic simulation of multicomponent biomembranes on a continuum levelrnhowever is until now limited to small deformations or special shapes, which isrndue to the high-order nonlinear terms in the governing equations to describe the phasernseparation and domain formation on evolving surfaces.rnWe propose to study the dynamics of the interactions between membrane structure,rndomain formation and shape deformation within a mathematical model for lipid bilayerrnbiomembranes which will overcome this limitations. A thermodynamically consistentrnmodel will be direved, which mathematically leads to a higher order evolution equationrnon an evolving surface. We will consider various numerical approaches for such problems,rnincluding combined front-tracking and phase-field models, combined level-set and phasefieldrnmodels and fully phase-field model to consider the evolution of the surface combinedrnwith the phase-separation on the surface. All approaches will use adaptive finite elementsrnand multilevel techniques. Parallization furthermore will allow to solve the highly nonlinearrnsystem in 3d in a reasonable amount of time and to answer questions concerningrnthe long time behavior.
Kurzbeschreibung (Englisch)
Biological membranes are a mixture of many different types of lipids and protein components,rnand their relative amount and composition differ between functionally distinctrndomains. The strongly increasing interest in lipid membranes results from the hypothesizedrncoupling of lipid phase segregation in the membrane to fundamental cell biologicalrnprocesses, such as membrane signaling and trafficing. Sub-domains of distinct curvaturernmay have precise biological properties, thus an understanding how lipid componentsrncan dynamically influence to membrane morphology is of utmost importance.rnChanges in lipid composition are assumed to assist or antagonize the membrane curvaturernon one side, but also might respond to the curvature by concentrating in domainsrnof curvature that they prefer on the other side. Strong curvature variations have recentlyrnbeen observed experimentally in giant liposmes, where different lipids segregate accordingrnto their chemical properties and lead to the formation of buds. The strong couplingrnof phase separation and shape dynamics in lipid membranes has also been shownrnnumerically by molecular dynamics and Monte Carlo simulations. Such atomisticrnsimulations however are limited in the accessible length and time scales.rnWith the curvature as one of the crucial incrediences to determine properties of membranesrnit seems natural to model the evolution within a continuum framework. This isrnfurther justified by the different length scales which come into play. The thickness of thernmembrane is in the nm-range, while a typical size of a biomembrane is in the μm-range.rnThis length scale separation allows the biomembrane to be described as an elastic surface, which is the basis for our treatment. Within such a continuum description the observedrnbudding in multicomponent lipid bilayers can be understood, by the possibility tornreduce the line energy associated with the domain boundaries by budding these domains, an additional degree of freedom which is not present for phase separation processes inrnthe bulk. A dynamic simulation of multicomponent biomembranes on a continuum levelrnhowever is until now limited to small deformations or special shapes, which isrndue to the high-order nonlinear terms in the governing equations to describe the phasernseparation and domain formation on evolving surfaces.rnWe propose to study the dynamics of the interactions between membrane structure,rndomain formation and shape deformation within a mathematical model for lipid bilayerrnbiomembranes which will overcome this limitations. A thermodynamically consistentrnmodel will be direved, which mathematically leads to a higher order evolution equationrnon an evolving surface. We will consider various numerical approaches for such problems,rnincluding combined front-tracking and phase-field models, combined level-set and phasefieldrnmodels and fully phase-field model to consider the evolution of the surface combinedrnwith the phase-separation on the surface. All approaches will use adaptive finite elementsrnand multilevel techniques. Parallization furthermore will allow to solve the highly nonlinearrnsystem in 3d in a reasonable amount of time and to answer questions concerningrnthe long time behavior.
Zeitraum
01.05.2007 - 30.04.2014
Art der Finanzierung
Drittmittel
Projektleiter
- Herr Prof. Dr. rer. nat. habil. Axel Voigt
Projektmitarbeiter
- Herr Dipl.-Math. Sebastian Reuther
Finanzierungseinrichtungen
Kooperationspartnerschaft
keine
Relevant für den Umweltschutz
Nein
Relevant für Multimedia
Nein
Relevant für den Technologietransfer
Nein
Schlagwörter
biomembrane, phase separation, geometric evolution, finite element