Landscape of finite-temperature equilibrium behaviour of curvature-inducing proteins on a bilayer membrane explored using a linearized elastic free energy model

Using a recently developed multiscale simulation methodology, we describe the equilibrium behaviour of bilayer membranes under the influence of curvature-inducing proteins using a linearized elastic free energy model. In particular, we describe how the cooperativity associated with a multitude of protein-membrane interactions and protein diffusion on a membrane-mediated energy landscape elicits emergent behaviour in the membrane phase. Based on our model simulations, we predict that, depending on the density of membrane-bound proteins and the degree to which a single protein molecule can induce intrinsic mean curvature in the membrane, a range of membrane phase behaviour can be observed including two different modes of vesicle-bud nucleation and repressed membrane undulations. A state diagram as a function of experimentally tunable parameters to classify the underlying states is proposed.     

Multiscale molecular dynamics simulations of membrane remodeling by Bin/Amphiphysin/Rvs family proteins

Membrane curvature is no longer thought of as a passive property of the membrane; rather, it is considered as an active, regulated state that serves various purposes in the cell such as between cells and organelle definition. While transport is usually mediated by tiny membrane bubbles known as vesicles or membrane tubules, such communication requires complex interplay between the lipid bilayers and cytosolic proteins such as members of the Bin/Amphiphysin/Rvs(BAR) superfamily of proteins. With rapid developments in novel experimental techniques, membrane remodeling has become a rapidly emerging new field in recent years. Molecular dynamics(MD) simulations are important tools for obtaining atomistic information regarding the structural and dynamic aspects of biological systems and for understanding the physics-related aspects. The availability of more sophisticated experimental data poses challenges to the theoretical community for developing novel theoretical and computational techniques that can be used to better interpret the experimental results to obtain further functional insights. In this review, we summarize the general mechanisms underlying membrane remodeling controlled or mediated by proteins. While studies combining experiments and molecular dynamics simulations recall existing mechanistic models, concurrently, they extend the role of different BAR domain proteins during membrane remodeling processes. We review these recent findings, focusing on how multiscale molecular dynamics simulations aid in understanding the physical basis of BAR domain proteins, as a representative of membrane-remodeling proteins.     

Computer simulations of critical phenomena and phase behaviour of fluids

Computer simulation techniques such as Monte Carlo (MC) and Molecular Dynamics (MD) methods yield numerically exact information (apart from statistical errors) on model systems of classical statistical mechanics. However, a systematic limitation is the restriction to a finite (and often rather small) particle number N (or box linear dimension L, respectively). This limitation is particularly restrictive near critical points (due to the divergence of the correlation length of the order parameter) and for the study of phase equilibria (possibly involving interfaces, droplets, etc.). Starting out with simple lattice gas (Ising) models, finite size scaling analyses have been developed to overcome this limitation. These techniques work for both simple Lennard-Jones fluids and their mixtures, including generalizations to approximate models for quadrupolar fluids such as carbon dioxide, benzene etc. and various mixtures, whose phase behaviour can be predicted. A combination of MC and MD allows the study of dynamic critical phenomena, and specialised techniques (umbrella sampling plus thermodynamic integration) yield the surface free energy of droplets as function of droplet size. Thus, computer simulation has become a versatile and widely applicable tool for the study of fluids.     

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L= 8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at T_c= 3.6403({2}). A convincing finite-size scaling analysis of the model yields υ=0.9995(21), β / υ = 0.12400({17}), γ / υ = 1.75223(22), γ '/υ=1.7555(22), α/υ= 0.00077(420) (scaling) and α / υ = 0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.     

The impact of competition and litter accumulation on germination success in a model of annual plants

A new model of one type of annual plant dynamics is proposed and discussed. The model is based on individual agents Monte Carlo simulations. We take into account, the plant requirements for external resources (sunshine, moisture etc.), competition among plants and the influence of accumulated dead biomass on the plant germination and seed production. We show that the density of plants could have oscillatory character, with periods depending on the rate of biomass reduction. Investigations on the temporal changes in the spatial distribution of plants show some clustering and moreover persistence of patterns during the oscillations. The average number of seeds produced by a plant in a year versus density of plants has a power-law type character. The obtained results are compared with field data and findings in other theoretical models. Agreement with experimental data is found, at least on a qualitative level. We have been also able to add new arguments in the long debate about the existence or not of oscillations in plant dynamics.     

Role of asymmetry in competition for light in a model of annual plants

We propose and discuss a model describing dynamics of annual plants competing with their nearest neighbours for sunlight. The effect of the competition determines the size, or equivalently, the biomass of each plant and the number of seeds it produces. At the end of a period (year) plants distribute their seeds over the sites in the Moore neighbourhood and then die. They leave their biomass in the form of litter, which hinders germination of the seeds.We show that the dynamical behaviour depends crucially on two parameters—litter reduction rate and the plants’ growth rate. Larger litter reduction rate and smaller growth rate lead to the population of few plants, producing more biomass than when more smaller plants are present and the litter reduction rate is low and growth rate is high. We show that asymmetry in the competition, which could favour bigger plants, have rather weak effect on the dynamical behaviour. The distribution of the biomass depends on the asymmetry. When larger plants receive much more sunlight than the smaller ones, the latter are quite often eliminated from the neighbourhood. For weaker asymmetry smaller plants could survive, producing however less biomass than the larger plants.     

Exact and Monte Carlo computations on a lattice model for change of conformation of a polymer

Conformational changes of linear polymers are studied by means of dynamic lattice models. The relaxation rates for the following four parameters describing the conformation of the polymer are studied for various polymer lengths: the square of the end-to-end distance, the square of the radius of gyration, thex component of the end-to-end vector, and the number of windings.In the most realistic models the relaxation rates for the first three of the above-mentioned properties decrease approximately proportional to the square of the number of monomers in agreement with the well-known Rouse model, while the relaxation of the winding number appears to be independent of the polymer length. The long-range interactions due to excluded volume restrictions are found to be of only minor importance compared to the rules presented for the local movements of the polymer segments.The results are obtained by diagonalizing the Markov matrix forn = 3, 4, 5, and 6 and by Monte Carlo simulation forn = 8, 16, 32, 64, and 128, wheren is the number of monomers.     

Effect of a monomeric sequence on the structure of hydrated Nafion in the sandwich model and solvent dynamics in nano-channels: a molecular dynamic study

Molecular dynamics simulations are performed to obtain insight into the structural properties of hydrated Nafion using the sandwich model of the polymer membrane. It is shown that a larger distance between the sulfonate groups of a chain leads to the polymer forming a better inverted micelles structure. Water– and hydronium–polymer interfaces are investigated. Comparing our results with others indicates that, from the perspective of distance, the formation of shells of water and hydronium ions is independent of the model and monomer type, but depends on both if the coordination number is considered. The behaviour of water molecules and hydronium ions is also studied dynamically. Our survey shows that there is an increasing jump in the diffusion coefficient of water at a certain distance between the sulfonate groups of a chain, which then tends to change slightly. Such behaviour is discussed on the basis of density, the available space, as well as the loss of one translational degree of freedom of the water molecules at larger distances. The diffusion coefficient for the hydronium ions was also determined to be much smaller than that for water (by 3.5–6.1 times). The diffusion coefficient of the hydronium ions shows a declining jump at a certain distance between the sulfonate groups of a chain, but the jump is not significant as that for the water molecules.     

Theoretical study on interaction of cytochrome f and plastocyanin complex by a simple coarse-grained model with molecular crowding effect

ABSTRACT

We present a simple coarse-grained model with the molecular crowding effect in solvent to investigate the structure and dynamics of protein complexes including association and/or dissociation processes and investigate some physical properties such as the structure and the reaction rate from the viewpoint of the hydrophobic intermolecular interactions of protein complex. In the present coarse-grained model, a function depending upon the density of hydrophobic amino acid residues in a binding area of the complex is introduced, and the function involves the molecular crowding effect for the intermolecular interactions of hydrophobic amino acid residues between proteins. We propose a hydrophobic intermolecular potential energy between proteins by using the density-dependent function. The present coarse-grained model is applied to the complex of cytochrome f and plastocyanin by using the Langevin dynamics simulation to investigate some physical properties such as the complex structure, the electron transfer reaction rate constant from plastocyanin to cytochrome f and so on. We find that for proceeding the electron transfer reaction, the distance between metals in their active sites is necessary within about 18 Å. We discuss some typical complex structures formed in the present simulation in relation to the molecular crowding effect on hydrophobic interactions.     

Influence of dietary fibre on gluten proteins structure – a study on model flour with application of FT‐Raman spectroscopy

Dietary fibres are regarded as the source of polysaccharides and antioxidants such as polyphenols. However, addition of dietary fibre to bread causes significant reduction in its quality. The bread quality is connected with the structure of gluten proteins. For this reason, Fourier transform Raman spectroscopy was applied to determine changes in structure of gluten proteins modified by seven dietary fibres. The fibres were added to model flour reconstituted with wheat gluten and wheat starch. The model flour was used to provide gluten proteins of definite structure. The obtained results showed that six out of seven fibres caused similar changes in β‐turn structures. The appearance of the band at 1642 cm⁻¹ and the shift toward lower wavenumbers of the band at 1670 cm⁻¹ in the difference spectra indicated hydrogen bonding of carbonyl groups in β‐turns leading to protein folding/aggregation. Addition of fibre preparations caused also changes in conformation of disulfide bridges (S–S), corresponding to transformation to trans‐gauche‐gauche and trans‐gauche‐trans conformations at the expense of the stable gauche‐gauche‐gauche conformation. The S–S bonds in less stable conformations were formed inside the protein complex as well as between protein complexes in the form of β‐structures. Generally, the observed changes in gluten proteins after addition of dietary fibres were results of interactions between fibre polysaccharides and gluten proteins rather than between polyphenols and gluten proteins. Copyright © 2015 John Wiley & Sons, Ltd.