Efficient coarse-grained brownian dynamics simulations for dna and lipid bilayer membrane with hydrodynamic interactions

The coarse-grained molecular dynamics (CGMD) or Brownian dynamics (BD) simulation is a particle-based approach that has been applied to a wide range of biological problems that involve interactions with surrounding fluid molecules or the so-called hydrodynamic interactions (HIs). From simple biological systems such as a single DNA macromolecule to large and complicated systems, for instances, vesicles and red blood cells (RBCs), the numerical results have shown outstanding agreements with experiments and continuum modeling by adopting Stokesian dynamics and explicit solvent model. Finally, when combined with fast algorithms such as the fast multipole method (FMM) which has nearly optimal complexity in the total number of CG particles, the resulting method is parallelizable, scalable to large systems, and stable for large time step size, thus making the long-time large-scale BD simulation within practical reach. This will be useful for the study of a large collection of molecules or cells immersed in the fluids. This dissertation can be divided into three main subjects: (1) An efficient algorithm is proposed to simulate the motion of a single DNA molecule in linear flows. The algorithm utilizes the integrating factor method to cope with the effect of the linear flow of the surrounding fluid and applies the Metropolis method (MM) in [N. Bou-Rabee, A. Donev, and E. Vanden-Eijnden, Multiscale Model. Simul. 12, 781 (2014)] to achieve more efficient BD simulation. More importantly, this proposed method permits much larger time step size than methods in previous literature while still maintaining the stability of the BD simulation, which is advantageous for long-time BD simulation. The numerical results on λ-DNA agree very well with both experimental data and previous simulation results. (2) Lipid bilayer membranes have been extensively studied by CGMD simulations. Numerical efficiencies have been reported in the cases of aggressive coarse-graining, where several lipids are coarse-grained into a particle of size 4 ~ 6 nm so that there is only one particle in the thickness direction. In [H. Yuan et al., Phys. Rev. E, 82, 011905 (2010)], Yuan et al. proposed a pair-potential between these one-particle-thick coarse-grained lipid particles to capture the mechanical properties of a lipid bilayer membrane, such as gel-fluid-gas phase transitions of lipids, diffusion, and bending rigidity. This dissertation provides a detailed implementation of this interaction potential in LAMMPS to simulate large-scale lipid systems such as a giant unilamellar vesicle (GUV) and RBCs. Moreover, this work also considers the effect of cytoskeleton on the lipid membrane dynamics as a model for RBC dynamics, and incorporates coarse-grained water molecules to account for hydrodynamic interactions. (3) An action field method for lipid bilayer membrane model is introduced where several lipid molecules are represented by a Janus particle with corresponding orientation pointing from lipid head to lipid tail. With this level of coarse-grained modeling, as the preliminary setup, the lipid tails occupy a half sphere and the lipid heads take the other half. An action field is induced from lipid-lipid interactions and exists everywhere in the computational domain. Therefore, a hydrophobic attraction energy can be described from utilizing the variational approach and its minimizer with respect to the action field is the so-called screened Laplace equation. For the numerical method, the well-known integral equation method (IEM) has great capability to solve exterior screened Laplace equation with Dirichlet boundary conditions. Finally, one then can obtain the lipid dynamics to validate the self-assembly property and other physical properties of lipid bilayer membrane. This approach combines continuum modeling with CGMD and gives a different perspective to the membrane energy model from the traditional Helfrich membrane free energy

Modeling and Analyzing a Patch of Human Red Blood Cell by Coarse-Grained Particle Method

This thesis consists of three sections. First, some background information and theories about the erythrocyte membrane are provided. Second, a coarse-grained molecular dynamics model for a patch of erythrocyte membrane is built up. Third, the mechanical responses of the patch of red blood cells to diffusion and diffusivity, tension, rupture, and shear-induced pore area are analyzed.The patch of erythrocyte membrane is validated by modeling diffusivity and determining the diffusion coefficient constant. Then, the patch of the coarse-grained erythrocyte membrane is stretched uniformly until rupture. The critical stress/strain from simulation match with those obtained in experiments in laser optical tweezers trapping a bead. Lastly, the pore area of the patch of erythrocyte membrane at the high-stress region is determined over a range of deformations.The purpose of creating the patch of erythrocyte membrane is to reduce computational cost, obtain accurate and detailed answers from our interested regime conditions, and transfer some quantities from nanoscale to mesoscale by solving time and length scale gaps

Molecular Dynamics Simulation of Biomembrane Systems

PhDThe fundamental structure of all biological membranes is the lipid bilayer. At- tributed to the multifaceted features of lipids and its dynamical interaction with other membrane-integrated molecules, the lipid bilayer is involved in a variety of physiological phenomena such as transmembrane transportation, cellular signalling transduction, energy storage, etc. Due to the nanoscale but high complexity of the lipid bilayer system, experimental investigation into many important processes at the molecular level is still challenging. Molecular dynamics (MD) simulation has been emerging as a powerful tool to study the lipid membrane at the nanoscale. Utilizing atomistic MD, we have quantitatively investigated the effect of lamellar and nonlamellar lipid composition changes on a series of important bilayer properties, and how membranes behave when exposed to a high-pressure environment. A series of membrane properties such as lateral pressure and dipole potential pro les are quanti ed. Results suggest the hypothesis that compositional changes, involving both lipid heads and tails, modulate crucial mechanical and electrical features of the lipid bilayer, so that a range of biological phenomena, such as the permeation through the membrane and conformational equilibria of membrane proteins, may be regulated. Furthermore, water also plays an essential role in the biomembrane system. To balance accuracy and efficiency in simulations, a coarse-grained ELBA water model was developed. Here, the ELBA water model is stress tested in terms of temperature- and pressure-related properties, as well as hydrating properties. Results show that the accuracy of the ELBA model is almost as good as conventional atomistic water models, while the computational efficiency is increased substantially

Coarse-grained modelling of blood cell mechanics

This thesis concerns development of mechanically realistic in silico representations of human blood cells using coarse-grained molecular dynamics (CGMD), ultimately building a new model for a lymphocyte-class white blood cell (WBC). This development is approached successively, evaluated through simulation of experimental testing methods common to past in vitro studies on blood cell mechanics. Considering both their biophysical simplicity and the extensive associated literature, the red blood cell (RBC) is first considered. As a foundation, I thus used the CGMD RBC model of Fu et al. [Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS, Fu et al., Comput. Phys. Commun., 210, 193-203 (2017)]. Chapter 3 establishes implementation of this model, and in silico implementations of the three chosen testing methods. In doing so, the first quantitative assessment of the "miniature cell" approach is conducted - being the down-scaling of the physical cell size to make feasible simulation times, as was done in the original article presenting the model. The RBC model is then used as a foundation from which to develop a new whole-cell WBC lymphocyte model. This is approached sequentially. Firstly (Chapter 4), the morphology and mechanics relevant to the existing RBC model are adapted to those of a lymphocyte. As such, a quasi-spherical morphology is induced, and elastic membrane-associated parameters brought in line with the literature on isolated lymphocytes in vitro. A semi-rigid nucleus is then added to the cell interior, again parameterised to produce elastic properties consistent with the literature. These developments produce a cell having macroscopic mechanical properties much more consistent with a WBC, with an "optimal" parameterisation established. After the membrane and nucleus, the entity most influential to the mechanics of nucleated cells (such as WBC) is their complex intracellular actin-based cytoskeleton (CSK). Therefore, Chapter 5 attempts to represent such a system within our new lymphocyte model. This is approached in three successive stages, assessed against recognised CSK mechanical properties, in particular those also common to soft glassy materials. As such, a novel CSK representation is developed, inspired as a discretisation of soft glassy rheology (SGR). It is proposed that the resulting system has characteristics comparable to having undergone a glass-like transition, as relatable to a real CSK. Therefore, the resulting lymphocyte model may lay a foundation for future development towards mechanically accurate representations of other cells - in particular, a circulating tumour cell

Heterogeneous Vesicles with Phases having Different Preferred Curvatures: Shape Fluctuations and Mechanics of Active Deformations

We investigate the mechanics of heterogeneous vesicles having a collection of phase-separated domains with different preferred curvatures. We develop approaches to study at the coarse-grained level and continuum level the role of phase separation, elastic mechanics, and vesicle geometry. We investigate the elastic responses of vesicles both from passive shape fluctuations and from active deformations. We develop spectral analysis methods for analyzing passive shape fluctuations and further probe the mechanics through active deformations compressing heterogeneous vesicles between two flat plates or subjecting vesicles to insertion into slit-like channels. We find significant domain rearrangements can arise in heterogeneous vesicles in response to deformations. Relative to homogeneous vesicles, we find that heterogeneous vesicles can exhibit smaller resisting forces to compression and larger insertion times into channels. We introduce quantitative approaches for characterizing heterogeneous vesicles and how their mechanics can differ from homogeneous vesicles

Effect of electrostatic interactions on biomolecular self-assembly processes

Molecular level self-assembly processes are not only ubiquitous in living cells, but also widely applied in industry to synthesize and fabricate a variety of nanoscale biomaterials. The emergence of ordered aggregates from disordered components typically requires driving forces from electrostatic interactions to hydrophobic-hydrophilic effects. This thesis aims to elucidate the effect of electrostatic interactions, and the intricate balance between electrostatic and hydrophobic interactions in dictating spontaneous self-assembly processes with three case studies covering various types of biomolecules. For the first case study, we have examined the pH-induced polysaccharide hydrogel network formation. The polysaccharide molecule chitosan forms hydrogels composed of water-filled cross-linking polymer chains. The pH-responsive selfassembly behavior of chitosan hydrogel has been utilized in fabricating nanomaterials with a wide range of applications. To investigate the role of electrostatic interactions in the chitosan hydrogel network formation, we have developed a novel coarse-grained (CG) chitosan polymer model that captures the pH-dependent self-assembly behavior. The structural, mechanical, and thermodynamical properties of chitosan polymer hydrogel have been characterized well in the simulations and agree very well with experimental observations. For the second case study, the anticancer peptide folding induced by phospholipid membrane was investigated. Peptide folding in an aqueous environment is a self-assembly process that has been well studied over the years. However, the folding in a membranous environment is complicated by the heterogeneity in phospholipid distributions and membrane-peptide interactions. To provide information about the driving forces behind membrane peptide folding and the effect of lipid composition on folding behavior, my work has combined our recently developed Water-Explicit Polarizable Protein (WEPPRO) and Membrane (WEPMEM) model to explore the driving forces behind model anticancer peptide SVS-1 folding and how they can be affected by changing the membrane composition. For the third case study, we have studied the formation of nanodomains in mixed lipid bilayers. Phospholipid membranes are essential components in animal cells. The heterogeneous distribution of phospholipids on the membrane bilayer plays an important role in cellular structure and function such as signal transduction and membrane fusion. Interactions between a mixture of lipids and different ligands give rise to interesting patterns that are yet to be understood. Model lipid bilayers with a content of anionic lipids have been shown experimentally to be sensitive to the presence of certain ions. Monovalent cation Li+ induces membrane phase transition similarly as Ca2+ and Mg2+, while distinctive from other monovalent cations like Na+ and K+. We have evaluated the role of electrostatics interactions in the sizedependent cation-induced lipid nanodomain formation with binary mixed bilayers composed of zwitterionic and anionic lipids

The ELBA Force Field for Coarse-Grain Modeling of Lipid Membranes

A new coarse-grain model for molecular dynamics simulation of lipid membranes is presented. Following a simple and conventional approach, lipid molecules are modeled by spherical sites, each representing a group of several atoms. In contrast to common coarse-grain methods, two original (interdependent) features are here adopted. First, the main electrostatics are modeled explicitly by charges and dipoles, which interact realistically through a relative dielectric constant of unity (). Second, water molecules are represented individually through a new parametrization of the simple Stockmayer potential for polar fluids; each water molecule is therefore described by a single spherical site embedded with a point dipole. The force field is shown to accurately reproduce the main physical properties of single-species phospholipid bilayers comprising dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylethanolamine (DOPE) in the liquid crystal phase, as well as distearoylphosphatidylcholine (DSPC) in the liquid crystal and gel phases. Insights are presented into fundamental properties and phenomena that can be difficult or impossible to study with alternative computational or experimental methods. For example, we investigate the internal pressure distribution, dipole potential, lipid diffusion, and spontaneous self-assembly. Simulations lasting up to 1.5 microseconds were conducted for systems of different sizes (128, 512 and 1058 lipids); this also allowed us to identify size-dependent artifacts that are expected to affect membrane simulations in general. Future extensions and applications are discussed, particularly in relation to the methodology's inherent multiscale capabilities