Daniel M. Kroll

Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids.

Anterograde Microtubule Transport Drives Microtubule Bending in LLC-PK1 Epithelial Cells

Microtubules (MTs) have been proposed to act mechanically as compressive struts that resist both actomyosin contractile forces and their own polymerization forces to mechanically stabilize cell shape. To identify the origin of MT bending, we directly observed MT bending and F-actin transport dynamics in the periphery of LLC-PK1 epithelial cells. We found that F-actin is nearly stationary in these cells even as MTs are deformed, demonstrating that MT bending is not driven by actomyosin contractility. Furthermore, the inhibition of myosin II activity through the use of blebbistatin results in microtubules that are still dynamically bending. In addition, as determined by fluorescent speckle microscopy, MT polymerization rarely results, if ever, in bending. We suppressed dynamic instability using nocodazole, and we observed no qualitative change in the MT bending dynamics. Bending most often results from anterograde transport of proximal portions of the MT toward a nearly stationary distal tip. Interestingly, we found that in an in vitro kinesin-MT gliding assay, MTs buckle in a similar manner. To make quantitative comparisons, we measured curvature distributions of observed MTs and found that the in vivo and in vitro curvature distributions agree quantitatively. In addition, the measured MT curvature distribution is not Gaussian, as expected for a thermally driven semiflexible polymer, indicating that thermal forces play a minor role in MT bending. We conclude that many of the known mechanisms of MT deformation, such as polymerization and acto-myosin contractility, play an inconsequential role in mediating MT bending in LLC-PK1 cells and that MT-based molecular motors likely generate most of the strain energy stored in the MT lattice. The results argue against models in which MTs play a major mechanical role in LLC-PK1 cells and instead favor a model in which mechanical forces control the spatial distribution of the MT array.

Analysis of Microtubule Curvature

The microtubule cytoskeleton in living cells generate and resist mechanical forces to mediate fundamental cell processes, including cell division and migration. Recent advances in digital fluorescence microscopy have enabled the direct observation of bending of individual microtubules in living cells, which has enabled quantitative estimation of the mechanical state of the microtubule array. Although a variety of mechanisms have been proposed, the precise origins of microtubule deformation in living cells remain largely obscure. To investigate these mechanisms and their relative importance in cellular processes, a method is needed to accurately quantify microtubule bending within living cells. Here we describe a method for quantification of bending, using digital fluorescence microscope images to estimate the distribution of curvature in the microtubule. Digital images of individual microtubules can be used to obtain a set of discrete x-y coordinates along the microtubule contour, which is then used to estimate the curvature distribution. Due to system noise and digitization error, the estimate will be inaccurate to some degree. To quantify the inaccuracy, a computational model is used to simulate both the bending of thermally driven microtubules and their observation by digital fluorescence microscopy. This allows for direct comparison between experimental and simulated images, a method which we call model convolution microscopy. We assess the accuracy of various methods and present a suitable method for estimating the curvature distribution for thermally driven semiflexible polymers. Finally, we discuss extensions of the method to quantify microtubule curvature in living cells.

Dynamic correlations in stochastic rotation dynamics

The dynamic structure factor, vorticity and entropy density dynamic correlation functions are measured for stochastic rotation dynamics (SRD), a particle based algorithm for fluctuating fluids. This allows us to obtain unbiased values for the longitudinal transport coefficients such as thermal diffusivity and bulk viscosity. The results are in good agreement with earlier numerical and theoretical results, and it is shown for the first time that the bulk viscosity is indeed zero for this algorithm. In addition, corrections to the self-diffusion coefficient and shear viscosity arising from the breakdown of the molecular chaos approximation at small mean free paths are analyzed. In addition to deriving the form of the leading correlation corrections to these transport coefficients, the probabilities that two and three particles remain collision partners for consecutive time steps are derived analytically in the limit of small mean free path. The results of this paper verify that we have an excellent understanding of the SRD algorithm at the kinetic level and that analytic expressions for the transport coefficients derived elsewhere do indeed provide a very accurate description of the SRD fluid.

Monte Carlo simulations of complex formation between a mixed fluid vesicle and a charged colloid

Monte Carlo simulations are employed to investigate the ability of a charged fluidlike vesicle to adhere to and encapsulate an oppositely charged spherical colloidal particle. The vesicle contains mobile charges that interact with the colloid and among themselves through a screened electrostatic potential. Both migration of charges on the vesicle surface and elastic deformations of the vesicle contribute to the optimization of the vesicle-colloid interaction. Our Monte Carlo simulations reveal a discontinuous wrapping transition of the colloid as a function of the number of charges on the vesicle. Upon reducing the bending stiffness of the vesicle, the transition terminates in a critical point. At large electrostatic screening length we find a reentrant wrapping-unwrapping behavior upon increasing the total number of charges on the vesicle. We present a simple phenomenological model that qualitatively captures some features of the wrapping transition.

Monte Carlo simulations of a polymer confined within a fluid vesicle

Monte Carlo simulations are employed to study a fluid vesicle that contains a single worm-like polymer chain. The contour length of the polymer is about five times the circumference of the nominally spherical vesicle. We vary the degree of polymer confinement in our simulations by increasing the persistence length of the polymer. The vesicle is represented by a randomly triangulated self-avoiding network that can undergo bending deformations. Upon increasing the persistence length of the polymer beyond the size of the vesicle, we observe a transition of the polymer from an isotropic disordered random conformation to an ordered toroidal coil. Concomitantly, the vesicle adopts an oblate shape to allow for some expansion of the polymer coil inside the vesicle. It is convenient to characterize both polymer and vesicle in terms of the asphericity, a quantity derived from the gyration tensor. At the onset of the polymers ordering transition, the asphericity passes through a minimum for both polymer and vesicle. The increase in vesicle asphericity for a semi-flexible polymer can be understood in terms of ground state energy calculations, either for a simplified representation of the vesicle shape (we specifically discuss a disk shape with a semi-toroidal rim) or involving a full vesicle shape optimization. The asphericity of the polymer coil results from conformational fluctuations and can be rationalized using Odijks deflection length of strongly curved semi-flexible polymers.

Scattering intensity of bicontinuous microemulsions and sponge phases

Monte Carlo simulations of dynamically triangulated surfaces of variable topology are used to investigate the scattering intensities of bicontinuous microemulsions. The bulk scattering intensity is shown to follow the Teubner-Strey expression. The domain size and the correlation length are extracted from the scattering peaks as a function of the bending rigidity, saddle-splay modulus, and surfactant density. The results are compared to earlier theories based on Ginzburg-Landau and Gaussian random field models. The ratio of the two length scales is shown to be well described by a linear combination of logarithmically renormalized bending rigidity and saddle-splay modulus with universal prefactors. This is in contrast to earlier theoretical predictions in which the scattering intensity is independent of the saddle-splay modulus. The equation of state, and the asymptotics of the bulk and film scattering intensities for high and low wave vectors are determined from simulations and compared with theoretical results.

Dynamics of thermally driven capillary waves for two-dimensional droplets

Capillary waves have been observed in systems ranging from the surfaces of ordinary fluids to interfaces in biological membranes and have been one of the most studied areas in the physics of fluids. Recent advances in fluorescence microscopy and imaging enabled quantitative measurements of thermally driven capillary waves in lipid monolayers and bilayers, which resulted in accurate measurements of the line tension in monolayer domains. Even though there has been a considerable amount of work on the statics and dynamics of capillary waves in three dimensions, to the best of our knowledge, there is no detailed theoretical analysis for two-dimensional droplet morphologies. In this paper, we derive the dynamic correlation function for two-dimensional fluid droplets using linear response theory and verify our results using a novel particle-based simulation technique for binary mixtures.