Biomedical subjects

W K den Otter

Publications and source records attributed to W K den Otter.

13 recordsLinked to original sources

PubMed2006

Simulations of the dynamics of thermal undulations in lipid bilayers in the tensionless state and under stress.

The relaxation processes of height undulations and density fluctuations in a membrane have been studied by molecular dynamics simulations of a coarse grained amphiphilic bilayer model. We observe a double exponential decay in their time correlations, with relaxation rates in good quantitative agreement with the theory by Seifert and Langer [Europhys. Lett. 23, 71 (1993)]. Intermonolayer friction due to slippage between the two monolayers is shown to be the dominant dissipative mechanism at the high wave numbers, q>10 mum(-1), typically encountered in computer simulations. We briefly discuss the ramifications of the slow undulatory relaxation process for the calculation of bending rigidities from the static undulation structure factors. The relaxation rates are sensitive to the surface tension, and at high elongations an oscillatory contribution is observed in the time correlation of the undulations.

Algorithms↗

PubMed2006

Periodic orientational motions of rigid liquid-crystalline polymers in shear flow.

The collective periodic motions of liquid-crystalline polymers in a nematic phase in shear flow have, for the first time, been simulated at the particle level by Brownian dynamics simulations. A wide range of parameter space has been scanned by varying the aspect ratio L/D between 10 and 60 at three different scaled volume fractions Lphi/D and an extensive series of shear rates. The influence of the start configuration of the box on the final motion has also been studied. Depending on these parameters, the motion of the director is either characterized as tumbling, kayaking, log-rolling, wagging, or flow-aligning. The periods of kayaking and wagging motions are given by T=4.2(Lphi/D)gamma(-1) for high aspect ratios. Our simulation results are in agreement with theoretical predictions and recent shear experiments on fd viruses in solution. These calculations of elongated rigid rods have become feasible with a newly developed event-driven Brownian dynamics algorithm.

Algorithms↗

PubMed2006

Thermal undulations of lipid bilayers relax by intermonolayer friction at submicrometer length scales.

The time correlation functions of the thermal undulations of a lipid membrane have been studied by molecular dynamics simulations of a coarse-grained bilayer model. We observe a double-exponential decay, with relaxation rates in good agreement with the theory by Seifert and Langer, [Europhys. Lett. 23, 71 (1993)]. Intermonolayer friction resulting from local velocity differences between the two monolayers is shown to be the dominant dissipative mechanism for fluctuations with wave lengths below approximately -0.1 microm.

Friction↗

PubMed2006

Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations.

Atomistic molecular dynamics simulations of a lipid bilayer were performed to calculate the free energy of a trans-membrane pore as a function of its radius. The free energy was calculated as a function of a reaction coordinate using a potential of mean constraint force. The pore radius was then calculated from the reaction coordinate using Monte Carlo particle insertions. The main characteristics of the free energy that comes out of the simulations are a quadratic shape for a radius less than about 0.3 nm, a linear shape for larger radii than this, and a rather abrupt change without local minima or maxima between the two regions. In the outer region, a line tension can be calculated, which is consistent with the experimentally measured values. Further, this line tension can be rationalized and understood in terms of the energetic cost for deforming a part of the lipid bilayer into a hydrophilic pore. The region with small radii can be described and understood in terms of statistical mechanics of density fluctuations. In the region of crossover between a quadratic and linear free energy there was some hysteresis associated with filling and evacuation of the pore with water. The metastable prepore state hypothesized to interpret the experiments was not observed in this region.

Computer Simulation↗

PubMed2006

Isotropic-nematic spinodals of rigid long thin rodlike colloids by event-driven Brownian dynamics simulations.

The isotropic-nematic spinodals of solutions of rigid spherocylindrical colloids with various shape anisotropies L/D in a wide range from 10 to 60 are investigated by means of Brownian dynamics simulations. To make these simulations feasible, we developed a new event-driven algorithm that takes the excluded volume interactions between particles into account as instantaneous collisions, but neglects the hydrodynamic interactions. This algorithm is applied to dense systems of highly elongated rods and proves to be efficient. The calculated isotropic-nematic spinodals lie between the previously established binodals in the phase diagram and extrapolate for infinitely long rods to Onsager's [Ann. N. Y. Acad. Sci. 51, 627 (1949)] theoretical predictions. Moreover, we investigate the shear induced shifts of the spinodals, qualitatively confirming the theoretical prediction of the critical shear rate at which the two spinodals merge and the isotropic-nematic phase transition ceases to exist.

Journal Article↗

PubMed2005

Kayaking and wagging of rods in shear flow.

For the first time, we have simulated the periodic collective orientational motions performed by rigid liquid-crystalline polymers with large aspect ratio in the nematic state in shear flow. In order to be able to do so, we developed a new, event-driven Brownian dynamics technique. We present the results of simulations of rods with aspect ratios L/d ranging from 20 to 60 at volume fractions phi given by Lphi/d = 3.5 and 4.5. By studying the path of the director, i.e., the average direction of the rods, we observe kayaking, wagging, flow aligning, and log-rolling type of orbits, depending on the parameters of the simulation and the initial orientation. We find that the tumbling periods depend on Lphi/d and the shear rate but not on the type of motion. Our simulation results qualitatively confirm theoretical predictions and are in good agreement with the experimental measurements of tumbling times of fd viruses.

Journal Article↗

PubMed2005

Area compressibility and buckling of amphiphilic bilayers in molecular dynamics simulations.

The elastic modulus or area compressibility of a membrane is routinely calculated in molecular dynamics simulations as the proportionality constant relating surface tension and projected surface area. Recent studies, however, have revealed a marked system size dependence of these moduli, which we attribute to the neglect of thermal undulations in the area calculation. We discuss several methods, based on the Helfrich model and on numerical triangulation, to remedy this situation, and find a satisfying agreement between them. The Helfrich model also quantitatively describes a buckling transition observed for compressed bilayers.

Compressive Strength↗

PubMed2005

Mechanical properties of surfactant bilayer membranes from atomistic and coarse-grained molecular dynamics simulations.

We use simulations to predict the stability and mechanical properties of two amphiphilic bilayer membranes. We carry out atomistic MD simulations and investigate whether it is possible to use an existing coarse-grained (CG) surfactant model to map the membrane properties. We find that certain membranes can be represented well by the CG model, whereas others cannot. Atomistic MD simulations of the erucate membrane yield a headgroup area per surfactant a(0) of 0.26 nm(2), an elastic modulus K(A) of 1.7 N/m, and a bending rigidity kappa of 5 k(B)T. We find that the CG model, with the right choice for the size and potential well depth of the head, correctly reproduces a(0), kappa, as well as the fluctuation spectrum over the whole range of q values. Atomistic MD simulations of EHAC, on the other hand, suggest that this membrane is unstable. This is indicated by the fact that kappa is of the order of k(B)T, which means that the interface is extremely flexible and diffuse, and K(A) is close to zero, which means that the surface tension is zero. We argue that the CG model can be used if the headgroups are uncharged, dipolar, or effectively dipolar due to headgroup charge screening induced by counterion condensation.

Journal Article↗

PubMed2005

Brownian dynamics simulations of the self- and collective rotational diffusion coefficients of rigid long thin rods.

Recently a microscopic theory for the dynamics of suspensions of long thin rigid rods was presented, confirming and expanding the well-known theory by Doi and Edwards [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] and Kuzuu [J. Phys. Soc. Jpn. 52, 3486 (1983)]. Here this theory is put to the test by comparing it against computer simulations. A Brownian dynamics simulation program was developed to follow the dynamics of the rods, with a length over a diameter ratio of 60, on the Smoluchowski time scale. The model accounts for excluded volume interactions between rods, but neglects hydrodynamic interactions. The self-rotational diffusion coefficients D(r)(phi) of the rods were calculated by standard methods and by a new, more efficient method based on calculating average restoring torques. Collective decay of orientational order was calculated by means of equilibrium and nonequilibrium simulations. Our results show that, for the currently accessible volume fractions, the decay times in both cases are virtually identical. Moreover, the observed decay of diffusion coefficients with volume fraction is much quicker than predicted by the theory, which is attributed to an oversimplification of dynamic correlations in the theory.

Journal Article↗

PubMed2005

Surface viscosity, diffusion, and intermonolayer friction: simulating sheared amphiphilic bilayers.

The flow properties of an amphiphilic bilayer are studied in molecular dynamics simulations, by exposing a coarse grained model bilayer to two shear flows directed along the bilayer surface. The first field, with a vorticity perpendicular to the bilayer, induces a regular shear deformation, allowing a direct calculation of the surface viscosity. In experiments this property is measured indirectly, by relating it to the diffusion coefficient of a tracer particle through the Saffman-Einstein expression. The current calculations provide an independent test of this relation. The second flow field, with a vorticity parallel to the bilayer, causes the two constituent monolayers to slide past one another, yielding the interlayer friction coefficient.

Computer Simulation↗

PubMed2004

Nucleation free energy of pore formation in an amphiphilic bilayer studied by molecular dynamics simulations.

The formation of a pore in a membrane requires a considerable rearrangement of the amphiphilic molecules about to form the bilayer edge surrounding the pore, and hence is accompanied by a steep increase of the free energy. Recent rupture and conductance experiments suggest that this reshuffling process is also responsible for a small energy barrier that stabilizes "prepores" with diameters of less than 1 nm, rendering both the opening and closing of pores an activated process. We use the potential of mean constraint force method to study this free energy profile, as a function of pore radius, in a coarse grained bilayer model. The calculations show that the free energy rises by (15-20) kT during pore opening, making it an extremely rare nucleation event. Although we do not observe a barrier to pore closure, the results do make the existence of such a barrier plausible. For larger pores we find a smooth transition to Litster's model, from which a line tension coefficient of about 3.7 x 10(-11) J m(-1) is deduced.

Journal Article↗

PubMed2004

Simulations of stable pores in membranes: system size dependence and line tension.

Amphiphilic bilayers with a pore were simulated using a coarse grained model. By stretching the bilayer to 70% beyond its equilibrium surface area, we established the phase diagram of pores, identifying regions where pores are stable, metastable, or unstable. A simple theoretical model is proposed to explain the phase diagram, and to calculate the critical and equilibrium relative stretches. Interestingly, these are found to scale with the inverse cubic root of the number of amphiphiles in the bilayer, thus explaining the order of magnitude difference between the simulated and the measured values. Three different methods are used to calculate a line tension coefficient of (3.5-4.0) x 10(-11) J/m, in good agreement with experimental data.

Computer Simulation↗

PubMed2001

Geometric approach to the pressure tensor and the elastic constants.

Expressions are obtained for the pressure tensor in the canonical and the microcanonical ensemble for both isolated and periodic systems, using the same geometric approach to thermodynamic derivatives as has been used previously to define the configurational temperature. The inherent freedom of the method leads to a straightforward proof of the equivalence of atomic and molecular pressures, for short molecules and for molecules exceeding the dimensions of a periodic simulation box. The effect of holonomic constraints on the pressure is discussed. Expressions for the elastic constants are derived in the same manner.

Journal Article↗