Tadashi Ando

Crowding and hydrodynamic interactions likely dominate in vivo macromolecular motion

To begin to elucidate the principles of intermolecular dynamics in the crowded environment of cells, employing Brownian dynamics (BD) simulations, we examined possible mechanism(s) responsible for the great reduction in diffusion constants of macromolecules in vivo from that at infinite dilution. In an Escherichia coli cytoplasm model comprised of 15 different macromolecule types at physiological concentrations, BD simulations of molecular-shaped and equivalent sphere representations were performed with a soft repulsive potential. At cellular concentrations, the calculated diffusion constant of GFP is much larger than experiment, with no significant shape dependence. Next, using the equivalent sphere system, hydrodynamic interactions (HI) were considered. Without adjustable parameters, the in vivo experimental GFP diffusion constant was reproduced. Finally, the effects of nonspecific attractive interactions were examined. The reduction in diffusivity is very sensitive to macromolecular radius with the motion of the largest macromolecules dramatically slowed down; this is not seen if HI dominate. In addition, long-lived clusters involving the largest macromolecules form if attractions dominate, whereas HI give rise to significant, size independent intermolecular dynamic correlations. These qualitative differences provide a testable means of differentiating the importance of HI vs. nonspecific attractive interactions on macromolecular motion in cells.

Chirality in planar cell shape contributes to left-right asymmetric epithelial morphogenesis.

Left-right asymmetry in cell shape is converted to a directional twist of the gut epithelial tube. Some organs in animals display left-right (LR) asymmetry. To better understand LR asymmetric morphogenesis in Drosophila, we studied LR directional rotation of the hindgut epithelial tube. Hindgut epithelial cells adopt a LR asymmetric (chiral) cell shape within their plane, and we refer to this cell behavior as planar cell-shape chirality (PCC). Drosophila E-cadherin (DE-Cad) is distributed to cell boundaries with LR asymmetry, which is responsible for the PCC formation. Myosin ID switches the LR polarity found in PCC and in DE-Cad distribution, which coincides with the direction of rotation. An in silico simulation showed that PCC is sufficient to induce the directional rotation of this tissue. Thus, the intrinsic chirality of epithelial cells in vivo is an underlying mechanism for LR asymmetric tissue morphogenesis.

Biomolecular interactions modulate macromolecular structure and dynamics in atomistic model of a bacterial cytoplasm

Biological macromolecules function in highly crowded cellular environments. The structure and dynamics of proteins and nucleic acids are well characterized in vitro, but in vivo crowding effects remain unclear. Using molecular dynamics simulations of a comprehensive atomistic model cytoplasm we found that protein-protein interactions may destabilize native protein structures, whereas metabolite interactions may induce more compact states due to electrostatic screening. Protein-protein interactions also resulted in significant variations in reduced macromolecular diffusion under crowded conditions, while metabolites exhibited significant two-dimensional surface diffusion and altered protein-ligand binding that may reduce the effective concentration of metabolites and ligands in vivo. Metabolic enzymes showed weak non-specific association in cellular environments attributed to solvation and entropic effects. These effects are expected to have broad implications for the in vivo functioning of biomolecules. This work is a first step towards physically realistic in silico whole-cell models that connect molecular with cellular biology. DOI: http://dx.doi.org/10.7554/eLife.19274.001

Sliding of proteins non-specifically bound to DNA: Brownian dynamics studies with coarse-grained protein and DNA models.

DNA binding proteins efficiently search for their cognitive sites on long genomic DNA by combining 3D diffusion and 1D diffusion (sliding) along the DNA. Recent experimental results and theoretical analyses revealed that the proteins show a rotation-coupled sliding along DNA helical pitch. Here, we performed Brownian dynamics simulations using newly developed coarse-grained protein and DNA models for evaluating how hydrodynamic interactions between the protein and DNA molecules, binding affinity of the protein to DNA, and DNA fluctuations affect the one dimensional diffusion of the protein on the DNA. Our results indicate that intermolecular hydrodynamic interactions reduce 1D diffusivity by 30%. On the other hand, structural fluctuations of DNA give rise to steric collisions between the CG-proteins and DNA, resulting in faster 1D sliding of the protein. Proteins with low binding affinities consistent with experimental estimates of non-specific DNA binding show hopping along the CG-DNA. This hopping significantly increases sliding speed. These simulation studies provide additional insights into the mechanism of how DNA binding proteins find their target sites on the genome.

On the Importance of Hydrodynamic Interactions in Lipid Membrane Formation

Hydrodynamic interactions (HI) give rise to collective motions between molecules, which are known to be important in the dynamics of random coil polymers and colloids. However, their role in the biological self-assembly of many molecule systems has not been investigated. Here, using Brownian dynamics simulations, we evaluate the importance of HI on the kinetics of self-assembly of lipid membranes. One-thousand coarse-grained lipid molecules in periodic simulation boxes were allowed to assemble into stable bilayers in the presence and absence of intermolecular HI. Hydrodynamic interactions reduce the monomer-monomer association rate by 50%. In contrast, the rate of association of lipid clusters is much faster in the presence of intermolecular HI. In fact, with intermolecular HI, the membrane self-assembly rate is 3-10 times faster than that without intermolecular HI. We introduce an analytical model to describe the size dependence of the diffusive encounter rate of particle clusters, which can qualitatively explain our simulation results for the early stage of the membrane self-assembly process. These results clearly suggest that HI greatly affects the kinetics of self-assembly and that simulations without HI will significantly underestimate the kinetic parameters of such processes.

Dynamic simulation of concentrated macromolecular solutions with screened long-range hydrodynamic interactions: Algorithm and limitations

Hydrodynamic interactions exert a critical effect on the dynamics of macromolecules. As the concentration of macromolecules increases, by analogy to the behavior of semidilute polymer solutions or the flow in porous media, one might expect hydrodynamic screening to occur. Hydrodynamic screening would have implications both for the understanding of macromolecular dynamics as well as practical implications for the simulation of concentrated macromolecular solutions, e.g., in cells. Stokesian dynamics (SD) is one of the most accurate methods for simulating the motions of N particles suspended in a viscous fluid at low Reynolds number, in that it considers both far-field and near-field hydrodynamic interactions. This algorithm traditionally involves an O(N(3)) operation to compute Brownian forces at each time step, although asymptotically faster but more complex SD methods are now available. Motivated by the idea of hydrodynamic screening, the far-field part of the hydrodynamic matrix in SD may be approximated by a diagonal matrix, which is equivalent to assuming that long range hydrodynamic interactions are completely screened. This approximation allows sparse matrix methods to be used, which can reduce the apparent computational scaling to O(N). Previously there were several simulation studies using this approximation for monodisperse suspensions. Here, we employ newly designed preconditioned iterative methods for both the computation of Brownian forces and the solution of linear systems, and consider the validity of this approximation in polydisperse suspensions. We evaluate the accuracy of the diagonal approximation method using an intracellular-like suspension. The diffusivities of particles obtained with this approximation are close to those with the original method. However, this approximation underestimates intermolecular correlated motions, which is a trade-off between accuracy and computing efficiency. The new method makes it possible to perform large-scale and long-time simulation with an approximate accounting of hydrodynamic interactions.

Left-right asymmetry is formed in individual cells by intrinsic cell chirality.

Many animals show left-right (LR) asymmetric morphology. The mechanisms of LR asymmetric development are evolutionarily divergent, and they remain elusive in invertebrates. Various organs in Drosophila melanogaster show stereotypic LR asymmetry, including the embryonic gut. The Drosophila embryonic hindgut twists 90° left-handedly, thereby generating directional LR asymmetry. We recently revealed that the hindgut epithelial cell is chiral in shape and other properties; this is termed planar cell chirality (PCC). We previously showed by computer modeling that PCC is sufficient to induce the hindgut rotation. In addition, both the PCC and the direction of hindgut twisting are reversed in Myosin31DF (Myo31DF) mutants. Myo31DF encodes Drosophila MyosinID, an actin-based motor protein, whose molecular functions in LR asymmetric development are largely unknown. Here, to understand how PCC directs the asymmetric cell-shape, we analyzed PCC in genetic mosaics composed of cells homozygous for mutant Myo31DF, some of which also overexpressed wild-type Myo31DF. Wild-type cell-shape chirality only formed in the Myo31DF-overexpressing cells, suggesting that cell-shape chirality was established in each cell and reflects intrinsic PCC. A computer model recapitulating the development of this genetic mosaic suggested that mechanical interactions between cells are required for the cell-shape behavior seen in vivo. Our mosaic analysis also suggested that during hindgut rotation in vivo, wild-type Myo31DF suppresses the elongation of cell boundaries, supporting the idea that cell-shape chirality is an intrinsic property determined in each cell. However, the amount and distribution of F-actin and Myosin II, which are known to help generate the contraction force on cell boundaries, did not show differences between Myo31DF mutant cells and wild-type cells, suggesting that the static amount and distribution of these proteins are not involved in the suppression of cell-boundary elongation. Taken together, our results suggest that cell-shape chirality is intrinsically formed in each cell, and that mechanical force from intercellular interactions contributes to its formation and/or maintenance.

GENESIS 1.1: A hybrid-parallel molecular dynamics simulator with enhanced sampling algorithms on multiple computational platforms

GENeralized‐Ensemble SImulation System (GENESIS) is a software package for molecular dynamics (MD) simulation of biological systems. It is designed to extend limitations in system size and accessible time scale by adopting highly parallelized schemes and enhanced conformational sampling algorithms. In this new version, GENESIS 1.1, new functions and advanced algorithms have been added. The all‐atom and coarse‐grained potential energy functions used in AMBER and GROMACS packages now become available in addition to CHARMM energy functions. The performance of MD simulations has been greatly improved by further optimization, multiple time‐step integration, and hybrid (CPU + GPU) computing. The string method and replica‐exchange umbrella sampling with flexible collective variable choice are used for finding the minimum free‐energy pathway and obtaining free‐energy profiles for conformational changes of a macromolecule. These new features increase the usefulness and power of GENESIS for modeling and simulation in biological research.

Multiple Time Step Brownian Dynamics for Long Time Simulation of Biomolecules

We report a multiple time step algorithm applied to an atomistic Brownian dynamics simulation for simulating the long time scale dynamics of biomolecules. The algorithm was based on the original multiple time step method; a short time step was used to keep faster motions in local equilibrium. When applied to a 28-mer # # ! folded peptide, the simulation gave stable trajectories and the computation time was reduced by a factor of 160 compared to a conventional molecular dynamics simulation using explicit water molecules. We applied it for the folding simulation of a 13-mer ! -helical peptide, giving a successful folding simulation. These results indicate that the Brownian dynamics with the multiple time step algorithm is useful for studies of biomolecular motions by long time simulation.

Free energy landscapes of two model peptides: α-helical and β-hairpin peptides explored with Brownian dynamics simulation

We applied an atomistic Brownian dynamics (BD) simulation with multiple time step method for the folding simulation of a 13-mer α-helical peptide and a 12-mer β-hairpin peptide, giving successful folding simulations. In this model, the driving energy contribution towards folding came from both electrostatic and van der Waals interactions for the α-helical peptide and from van der Waals interactions for the β-hairpin peptide. Although, many non-native structures having the same or lower energy than that of native structure were observed, the folded states formed the most populated cluster when the structures obtained by the BD simulations were subjected to the cluster analysis based on distance-based root mean square deviation of side-chains between different structures. This result indicates that we can predict the native structures from conformations sampled by BD simulation.