Brownian dynamics computational model of protein diffusion in crowded media with dextran macromolecules as obstacles

The high concentration of macromolecules (i.e., macromolecular crowding) in cellular environments leads to large quantitative effects on the dynamic and equilibrium biological properties. These effects have been experimentally studied using inert macromolecules to mimic a realistic cellular medium. In this paper, two different experimental in vitro systems of diffusing proteins which use dextran macromolecules as obstacles are computationally analyzed. A new model for dextran macromolecules based on effective radii accounting for macromolecular compression induced by crowding is proposed. The obtained results for the diffusion coefficient and the anomalous diffusion exponent exhibit good qualitative and generally good quantitative agreement with experiments. Volume fraction and hydrodynamic interactions are found to be crucial to describe the diffusion coefficient decrease in crowded media. However, no significant influence of the hydrodynamic interactions in the anomalous diffusion exponent is found

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a power-law increase of the MSD, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations, non-gaussian distributions of the displacements, heterogeneous diffusion, and immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like FBM and Langevin equations for visco-elastic media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for identical MSDs. Then, we review the theory underlying common experimental techniques in the presence of anomalous transport: single-particle tracking, FCS, and FRAP. We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where model systems mimic physiological crowding conditions. Finally, computer simulations play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.Comment: review article, to appear in Rep. Prog. Phy

Macromolecular diffusion in crowded media beyond the hard-sphere model

The effect of macromolecular crowding on diffusion beyond the hard-core sphere model is studied. A new coarse-grained model is presented, the Chain Entanglement Softened Potential (CESP) model, which takes into account the macromolecular flexibility and chain entanglement. The CESP model uses a shoulder-shaped interaction potential that is implemented in the Brownian Dynamics (BD) computations. The interaction potential contains only one parameter associated with the chain entanglement energetic cost (Ur). The hydrodynamic interactions are included in the BD computations via Tokuyama mean-field equations. The model is used to analyze the diffusion of a streptavidin protein among different sized dextran obstacles. For this system, Ur is obtained by fitting the streptavidin experimental long-time diffusion coefficient Dlong versus the macromolecular concentration for D50 (indicating their molecular weight in kg mol-1) dextran obstacles. The obtained Dlong values show better quantitative agreement with experiments than those obtained with hard-core spheres. Moreover, once parametrized, the CESP model is also able to quantitatively predict Dlong and the anomalous exponent (a) for streptavidin diffusion among D10, D400 and D700 dextran obstacles. Dlong, the short-time diffusion coefficient (Dshort) and a are obtained from the BD simulations by using a new empirical expression, able to describe the full temporal evolution of the diffusion coefficient

Diffusion in macromolecular crowded media. Monte Carlo simulation of obstructed diffusion vs. FRAP experiments

The diffusion of tracer particles in 3D macromolecular crowded media has been studied using two methodologies, simulation and experimental, with the aim of comparing their results. Firstly, the diffusion of a tracer in an obstructed 3D lattice with mobile and big size obstacles has been analyzed through a Monte Carlo (MC) simulation procedure. Secondly, Fluorescence Recovery after Photobleaching (FRAP) experiments have been carried out to study the diffusion of a model protein (alpha-chymotrypsin) in in vitro crowded solution where two type of Dextran molecules are used as crowder agents. To facilitate the comparison the relative size between the tracer and the crowder is the same in both studies. The results indicate a qualitative agreement between the diffusional behaviors observed in the two studies. The dependence of the anomalous diffusion exponent and the limiting diffusion coefficient with the obstacle size and excluded volume shows, in both cases, a similar tendency. The introduction of a reduced mobility parameter in the simulation model accounting for the short range tracer-obstacle interactions allows to obtain a quantitative agreement between the limiting diffusion coefficient values yielded by both procedures. The simulation-experiment quantitative agreement for the anomalous diffusion exponent requires further improvements. As far as we know, this is the first reported work where both techniques are used in parallel to study the diffusion in macromolecular crowded media

Nonequilibrium Phenomena in Confined Systems

Confined systems exhibit a large variety of nonequilibrium phenomena. In this special issue, we have collected a limited number of papers that were presented during the XXV Sitges Conference on Statistical Mechanics, devoted to "Nonequilibrium phenomena in confined systems". The conference took place in Barcelona from the 6th until the 10th of June 2016 (http://www.ffn.ub.es/~sitges25/), was organized by G. Franzese, I. Latella, D. Reguera, and J.M. Rubi, and gathered more than 60 international scientists in the areas of physics, chemistry, and biology working on confined systems in topics like: Diffusion and entropic transport in confined systems; Ion and polymer translocation; Phase transitions and chemical reactions in confined media; Forces induced by fluctuations in confined systems and Casimir effect; Confined active matter; Macromolecular crowding; and Energy conversion in confinement

Fractal dimension of the trajectory of a single particle diffusing in crowded media

Using Monte Carlo simulations we have modeled the diffusion of a single particle in twoand three-dimensional lattices with different crowding conditions given by distinct obstacles size and density. All registered data emphasize that diffusion process is anomalous and diffusing particle describes fractal trajectories. We have introduced a new time-scale fractal dimension, dm, which is related to the anomalous diffusion exponent, α. This allows us to relate the well-known length-scale fractal dimension of the random walk, dw, to the new one introduced here as a time-scale fractal dimension. Moreover, the 3D simulations consider similar conditions to those used in our previous FRAP experiments in order to reveal the relationship between the length and time-scale fractal dimensions

The Shape of Protein Crowders is a Major Determinant of Protein Diffusion

AbstractAs a model for understanding how molecular crowding influences diffusion and transport of proteins in cellular environments, we combined experimental and theoretical approaches to study the diffusion of proteins in highly concentrated protein solutions. Bovine serum albumin and γ-Globulin were chosen as molecular crowders and as tracers. These two proteins are representatives of the main types of plasma protein and have different shapes and sizes. Solutions consisting of one or both proteins were studied. The self-diffusion coefficients of the fluorescently labeled tracer proteins were measured by means of fluorescence correlation spectroscopy at a total protein concentration of up to 400 g/L. γ-Globulin is found to have a stronger influence as a crowder on the tracer self-diffusion coefficient than Bovine serum albumin. Brownian dynamics simulations show that the excluded volume and the shape of the crowding protein have a significantly stronger influence on translational and rotational diffusion coefficients, as well as transient oligomerization, than hydrodynamic or direct interactions. Anomalous subdiffusion, which is not observed at the experimental fluorescence correlation spectroscopy timescales (>100 μs), appears only at very short timescales (<1 μs) in the simulations due to steric effects of the proteins. We envision that the combined experimental and computational approach employed here can be developed to unravel the different biophysical contributions to protein motion and interaction in cellular environments by systematically varying protein properties such as molecular weight, size, shape, and electrostatic interactions

Efecte del crowding macromolecular en la cinètica de reaccions enzimàtiques catalitzades per oligoproteïnes. El cas del dímer-tetràmer de la LDH.

Treballs Finals de Grau de Química, Facultat de Química, Universitat de Barcelona, Any: 2015, Tutors: Cristina Balcells i Francesc MasA study on the enzyme kinetics of L-lactate dehydrogenase, which catalyses the reduction of pyruvate to lactate oxidizing NADH, is presented. This reaction occurs when a lack of oxygen is present and is related to muscular fatigue. LDH is one of the most important biomarkers of injuries and disease, because it is released during tissue breakdown. General concepts of enzyme kinetics have been reviewed and some models to explain the kinetics of the enzyme have been proposed. L-lactate dehydrogenase is a tetrameric protein, an enzyme formed by four subunits, and the presence of a possible cooperativity, i.e., different affinity in each active centre, must be considered. Besides, macromolecular crowding, the alteration of the behaviour of molecules with the presence of highly concentrated macromolecules, and its possible effects on enzyme kinetics have been presented. A series of experiments, measuring the initial velocity of the reaction by spectrophotometric means and using a stopped-flow methodology, have been performed. The experiments have been carried out varying the pyruvate and the enzyme concentration and working in solution conditions. A series of experiments in crowded media, at high macromolecules concentration, have been performed. The crowded media experiments have been carried out using different obstacle sizes, using dextran polymer to simulate the cellular crowding, and with different enzyme concentrations. A surface plot of initial velocity as a function of substrate and enzyme concentrations, for the solution media data, has been obtained. The data has been fitted to the proposed models and the results have suggested an ideal behaviour without cooperativity. In crowded media, a higher decrease in the reaction velocity has been found when using the bigger dextran and the higher enzyme concentration. An auto-crowding hypothesis, the enzyme acts itself as a crowding agent, is presented to possibly explain the results

Anomalous Diffusion and Non-classical Reaction Kinetics in Crowded Fluids

This thesis investigates the underlying mechanism and the effects of anomalous diffusion in crowded fluids by means of computer simulations. In order to elucidate the mechanism behind crowding-induced subdiffusion we discuss the average shape of tracer trajectories as a potential criterion that allows to reliably discriminate between frequently proposed models. Our simulations show that measurement errors inherent to single particle tracking generally impair the determination of the underlying random process from experimental data. We propose a particle-based model for the crowded cytoplasm that incorporates soft-core repulsion and weak attraction between globular proteins of various sizes. Under these prerequisites simulations reveal transient subdiffusion of proteins. On experimental time scales, however, diffusion is normal indicating that realistic, microscopic models of crowded fluids require further detail of the relevant interactions. In the second part of this thesis, the impact of subdiffusion on biochemical reactions is studied via mesoscopic, stochastic simulations. Due to their compact trajectories subdiffusive reactants get increasingly segregated over time. This results in anomalous kinetics that differs strongly from classical theories. Moreover, for a two-step reaction scheme relying on an intermediate dissociation-association event, subdiffusion can substantially improve the overall productivity because spatio-temporal correlations are exploited with high efficiency