Specific Adhesion of Membranes: Mapping to an Effective Bond Lattice Gas

We theoretically consider specific adhesion of a fluctuating membrane to a hard substrate via the formation of bonds between receptors attached to the substrate and ligands in the membrane. By integrating out the degrees of freedom of the membrane shape, we show that in the biologically relevant limit specific adhesion is well described by a lattice gas model, where lattice sites correspond to bond sites. We derive an explicit expression for the effective bond interactions induced by the thermal undulations of the membrane. Furthermore, we compare kinetic Monte Carlo simulations for our lattice gas model with full dynamic simulations that take into account both the shape fluctuations of the membrane and reactions between receptors and ligands at bond sites. We demonstrate that an appropriate mapping of the height dependent binding and unbinding rates in the full scheme to rates in the lattice gas model leads to good agreement

Diffusing proteins on a fluctuating membrane: Analytical theory and simulations

Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the membrane shape through its spontaneous curvature and bending rigidity. The lateral motion of the protein may be viewed as diffusion in an effective potential, hence, the effective mobility is always reduced compared to the case of free diffusion. Using a rigorous path-integral approach we derive an analytical expression for the effective diffusion coefficient for small ratios of temperature and bending rigidity, which is the biologically relevant limit. Simulations show very good quantitative agreement with our analytical result. The analysis of the correlation functions contributing to the diffusion coefficient shows that the correlations between the stochastic force of the protein and the response in the membrane shape are responsible for the reduction. Our quantitative analysis of the membrane height correlation spectrum shows an influence of the protein-membrane interaction causing a distinctly altered wave-vector dependence compared to a free membrane. Furthermore, the time correlations exhibit the two relevant timescales of the system: that of membrane fluctuations and that of lateral protein diffusion with the latter typically much longer than the former. We argue that the analysis of the long-time decay of membrane height correlations can thus provide a new means to determine the effective diffusion coefficient of proteins in the membrane.Comment: 12 pages, 8 figure

Hybrid simulations of lateral diffusion in fluctuating membranes

In this paper we introduce a novel method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the inclusion along the membrane. While membrane fluctuations can be expressed in terms of a dynamic equation which follows from the Helfrich Hamiltonian, the dynamics of the diffusing particle is described by a Langevin or Smoluchowski equation. In the latter equations, the curvature of the surface needs to be accounted for, which makes particle diffusion a function of membrane fluctuations. In our scheme these coupled dynamic equations, the membrane equation and the Langevin equation for the particle, are numerically integrated to simulate diffusion in a membrane. The simulations are used to study the ratio of the diffusion coefficient projected on a flat plane and the intramembrane diffusion coefficient for the case of free diffusion. We compare our results with recent analytical results that employ a preaveraging approximation and analyze the validity of this approximation. A detailed simulation study of the relevant correlation functions reveals a surprisingly large range where the approximation is applicable.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.

Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations

We investigate how the dynamics of a single chain influences the kinetics of early stage phase separation in a symmetric binary polymer mixture. We consider quenches from the disordered phase into the region of spinodal instability. On a mean field level we approach this problem with two methods: a dynamical extension of the self consistent field theory for Gaussian chains, with the density variables evolving in time, and the method of the external potential dynamics where the effective external fields are propagated in time. Different wave vector dependencies of the kinetic coefficient are taken into account. These early stages of spinodal decomposition are also studied through Monte Carlo simulations employing the bond fluctuation model that maps the chains -- in our case with 64 effective segments -- on a coarse grained lattice. The results obtained through self consistent field calculations and Monte Carlo simulations can be compared because the time, length, and temperature scales are mapped onto each other through the diffusion constant, the chain extension, and the energy of mixing. The quantitative comparison of the relaxation rate of the global structure factor shows that a kinetic coefficient according to the Rouse model gives a much better agreement than a local, i.e. wave vector independent, kinetic factor. Including fluctuations in the self consistent field calculations leads to a shorter time span of spinodal behaviour and a reduction of the relaxation rate for smaller wave vectors and prevents the relaxation rate from becoming negative for larger values of the wave vector. This is also in agreement with the simulation results.Comment: Phys.Rev.E in prin

Zusammenhang zwischen der Einzelkettendynamik und der Dynamik von Konzentrationsfluktuationen in mehrkomponentigen Polymersystemen

Zusammmenfassung:Um Phasenseparation in binären Polymermischungen zuuntersuchen, werden zwei dynamische Erweiterungen der selbstkonsistenten Feldtheorie (SCFT)entwickelt. Die erste Methode benutzt eine zeitliche Entwicklung der Dichten und wird dynamische selbstkonsistente Feldtheorie (DSCFT) genannt, während die zweite Methode die zeitliche Propagation der effektiven äußeren Felder der SCFT ausnutzt. Diese Methode wird mit External Potential Dynamics (EPD) bezeichnet. Für DSCFT werden kinetische Koeffizienten verwendet, die entweder die lokale Dynamik von Punktteilchen oder die nichtlokale Dynamik von Rouse'schen Polymeren nachbilden. Die EPD-Methode erzeugt mit einem konstanten kinetischen Koeffizienten die Dynamik von Rouse'schen Ketten und benötigt weniger Rechenzeit als DSCFT. Diese Methoden werden für verschiedene Systeme angewendet.Zuerst wird spinodale Entmischung im Volumen untersucht,wobei der Unterschied zwischen lokaler und nichtlokalerDynamik im Mittelpunkt steht. Um die Gültigkeit derErgebnisse zu überprüfen, werden Monte-Carlo-Simulationen durchgeführt. In Polymermischungen, die von zwei Wänden, die beide die gleiche Sorte Polymere bevorzugen, eingeschränkt werden, wird die Bildung von Anreicherungsschichten an den Wänden untersucht. Für dünne Polymerfilme zwischen antisymmetrischen Wänden, d.h. jede Wand bevorzugt eine andere Polymerspezies, wird die Spannung einer parallel zu den Wänden gebildeten Grenzfläche analysiert und der Phasenübergang von einer anfänglich homogenen Mischung zur lokalisierten Phase betrachtet. Des Weiteren wird die Dynamik von Kapillarwellenmoden untersucht.Abstract:To analyse phase separations in binary polymer mixtures twodynamic extensions of self consistent field theory (SCFT)are developed. The first method uses the propagation of the densities in time and is called dynamic self consistent field theory (DSCFT), while the other method regards the time evolution of the external fields of SCFT. This method is called external potential dynamics (EPD). In DSCFT kinetic coefficients are used that model the dynamicsof either point-like particles or of polymers obeying Rousedynamics. The EPD method reproduces Rouse dynamics through aconstant kinetic coefficient and is less time consuming thanDSCFT. Both methods are applied in various systems.First spinodal decomposition in the bulk is investigatedwith the main concern being the difference between local andnonlocal dynamics. To validate the results Monte Carlosimulations are employed. In polymer mixtures between two walls that both attract thesame kind of polymer the formation of enrichment layers isinvestigated. For thin polymer films between antisymmetric walls, i.e.each wall attracts a different kind of polymer, the tensionof an interface parallel to the walls is analysed and theprocess of the phase separation from a homogeneous to thelocalised phase is regarded. Further the dynamics ofcapillary waves is investigated

Two intertwined facets of adherent membranes: membrane roughness and correlations between ligand–receptors bonds

We study equilibrium fluctuations of adherent membranes by means of Langevin simulations in the case when the interaction of the membrane with the substrate is twofold: a non-specific homogeneous harmonic potential is placed at large distances, whereas discrete ligand–receptor interactions occur at short distances from the flat substrate. We analyze the correlations between neighboring ligand–receptor bonds in a regime of relatively strong membrane fluctuations. By comparison with the random distribution of bonds, we find that the correlations between the bonds are always positive, suggesting spontaneous formation of domains. The equilibrium roughness of the membrane is then determined by fluctuations in the number density of bonds within the domains. Furthermore, we show that the excess number of bonds arising due to correlations and the instantaneous roughness of the membrane both follow master curves that depend only on the instantaneous bond density and not on the intrinsic binding strength of the ligand–receptor pair. The master curves show identical trends, further corroborating the link between membrane roughness and bond correlations