Influences of Excluded Volume of Molecules on Signaling Processes on Biomembrane

We investigate the influences of the excluded volume of molecules on biochemical reaction processes on 2-dimensional surfaces using a model of signal transduction processes on biomembranes. We perform simulations of the 2-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins, and crowders on the cell membrane. The signaling proteins are activated by receptors, and these activated signaling proteins activate target proteins that bind autonomously from the cytoplasm to the membrane, and unbind from the membrane if activated. If the target proteins bind frequently, the volume fraction of molecules on the membrane becomes so large that the excluded volume of the molecules for the reaction and diffusion dynamics cannot be negligible. We find that such excluded volume effects of the molecules induce non-trivial variations of the signal flow, defined as the activation frequency of target proteins, as follows. With an increase in the binding rate of target proteins, the signal flow varies by i) monotonically increasing; ii) increasing then decreasing in a bell-shaped curve; or iii) increasing, decreasing, then increasing in an S-shaped curve. We further demonstrate that the excluded volume of molecules influences the hierarchical molecular distributions throughout the reaction processes. In particular, when the system exhibits a large signal flow, the signaling proteins tend to surround the receptors to form receptor-signaling protein clusters, and the target proteins tend to become distributed around such clusters. To explain these phenomena, we analyze the stochastic model of the local motions of molecules around the receptor.Comment: 31 pages, 10 figure

A Didactic Model of Macromolecular Crowding Effects on Protein Folding

A didactic model is presented to illustrate how the effect of macromolecular crowding on protein folding and association is modeled using current analytical theory and discrete molecular dynamics. While analytical treatments of crowding may consider the effect as a potential of average force acting to compress a polypeptide chain into a compact state, the use of simulations enables the presence of crowding reagents to be treated explicitly. Using an analytically solvable toy model for protein folding, an approximate statistical thermodynamic method is directly compared to simulation in order to gauge the effectiveness of current analytical crowding descriptions. Both methodologies are in quantitative agreement under most conditions, indication that both current theory and simulation methods are capable of recapitulating aspects of protein folding even by utilizing a simplistic protein model

Entropic Tension in Crowded Membranes

Unlike their model membrane counterparts, biological membranes are richly decorated with a heterogeneous assembly of membrane proteins. These proteins are so tightly packed that their excluded area interactions can alter the free energy landscape controlling the conformational transitions suffered by such proteins. For membrane channels, this effect can alter the critical membrane tension at which they undergo a transition from a closed to an open state, and therefore influence protein function \emph{in vivo}. Despite their obvious importance, crowding phenomena in membranes are much less well studied than in the cytoplasm. Using statistical mechanics results for hard disk liquids, we show that crowding induces an entropic tension in the membrane, which influences transitions that alter the projected area and circumference of a membrane protein. As a specific case study in this effect, we consider the impact of crowding on the gating properties of bacterial mechanosensitive membrane channels, which are thought to confer osmoprotection when these cells are subjected to osmotic shock. We find that crowding can alter the gating energies by more than $2\;k_BT$ in physiological conditions, a substantial fraction of the total gating energies in some cases. Given the ubiquity of membrane crowding, the nonspecific nature of excluded volume interactions, and the fact that the function of many membrane proteins involve significant conformational changes, this specific case study highlights a general aspect in the function of membrane proteins.Comment: 20 pages (inclduing supporting information), 4 figures, to appear in PLoS Comp. Bio

Unified regression model of binding equilibria in crowded environments

Molecular crowding is a critical feature distinguishing intracellular environments from idealized solution-based environments and is essential to understanding numerous biochemical reactions, from protein folding to signal transduction. Many biochemical reactions are dramatically altered by crowding, yet it is extremely difficult to predict how crowding will quantitatively affect any particular reaction systems. We previously developed a novel stochastic off-lattice model to efficiently simulate binding reactions across wide parameter ranges in various crowded conditions. We now show that a polynomial regression model can incorporate several interrelated parameters influencing chemistry under crowded conditions. The unified model of binding equilibria accurately reproduces the results of particle simulations over a broad range of variation of six physical parameters that collectively yield a complicated, non-linear crowding effect. The work represents an important step toward the long-term goal of computationally tractable predictive models of reaction chemistry in the cellular environment

Crowding Alone Cannot Account for Cosolute Effect on Amyloid Aggregation

Amyloid fiber formation is a specific form of protein aggregation, often resulting from the misfolding of native proteins. Aimed at modeling the crowded environment of the cell, recent experiments showed a reduction in fibrillation halftimes for amyloid-forming peptides in the presence of cosolutes that are preferentially excluded from proteins and peptides. The effect of excluded cosolutes has previously been attributed to the large volume excluded by such inert cellular solutes, sometimes termed “macromolecular crowding”. Here, we studied a model peptide that can fold to a stable monomeric β-hairpin conformation, but under certain solution conditions aggregates in the form of amyloid fibrils. Using Circular Dichroism spectroscopy (CD), we found that, in the presence of polyols and polyethylene glycols acting as excluded cosolutes, the monomeric β-hairpin conformation was stabilized with respect to the unfolded state. Stabilization free energy was linear with cosolute concentration, and grew with molecular volume, as would also be predicted by crowding models. After initiating the aggregation process with a pH jump, fibrillation in the presence and absence of cosolutes was followed by ThT fluorescence, transmission electron microscopy, and CD spectroscopy. Polyols (glycerol and sorbitol) increased the lag time for fibril formation and elevated the amount of aggregated peptide at equilibrium, in a cosolute size and concentration dependent manner. However, fibrillation rates remained almost unaffected by a wide range of molecular weights of soluble polyethylene glycols. Our results highlight the importance of other forces beyond the excluded volume interactions responsible for crowding that may contribute to the cosolute effects acting on amyloid formation

A Coarse-Grained Biophysical Model of E. coli and Its Application to Perturbation of the rRNA Operon Copy Number

We propose a biophysical model of Escherichia coli that predicts growth rate and an effective cellular composition from an effective, coarse-grained representation of its genome. We assume that E. coli is in a state of balanced exponential steadystate growth, growing in a temporally and spatially constant environment, rich in resources. We apply this model to a series of past measurements, where the growth rate and rRNA-to-protein ratio have been measured for seven E. coli strains with an rRNA operon copy number ranging from one to seven (the wild-type copy number). These experiments show that growth rate markedly decreases for strains with fewer than six copies. Using the model, we were able to reproduce these measurements. We show that the model that best fits these data suggests that the volume fraction of macromolecules inside E. coli is not fixed when the rRNA operon copy number is varied. Moreover, the model predicts that increasing the copy number beyond seven results in a cytoplasm densely packed with ribosomes and proteins. Assuming that under such overcrowded conditions prolonged diffusion times tend to weaken binding affinities, the model predicts that growth rate will not increase substantially beyond the wild-type growth rate, as indicated by other experiments. Our model therefore suggests that changing the rRNA operon copy number of wild-type E. coli cells growing in a constant rich environment does not substantially increase their growth rate. Other observations regarding strains with an altered rRNA operon copy number, such as nucleoid compaction and the rRNA operon feedback response, appear to be qualitatively consistent with this model. In addition, we discuss possible design principles suggested by the model and propose further experiments to test its validity

Three-Dimensional Stochastic Off-Lattice Model of Binding Chemistry in Crowded Environments

Molecular crowding is one of the characteristic features of the intracellular environment, defined by a dense mixture of varying kinds of proteins and other molecules. Interaction with these molecules significantly alters the rates and equilibria of chemical reactions in the crowded environment. Numerous fundamental activities of a living cell are strongly influenced by the crowding effect, such as protein folding, protein assembly and disassembly, enzyme activity, and signal transduction. Quantitatively predicting how crowding will affect any particular process is, however, a very challenging problem because many physical and chemical parameters act synergistically in ways that defy easy analysis. To build a more realistic model for this problem, we extend a prior stochastic off-lattice model from two-dimensional (2D) to three-dimensional (3D) space and examine how the 3D results compare to those found in 2D. We show that both models exhibit qualitatively similar crowding effects and similar parameter dependence, particularly with respect to a set of parameters previously shown to act linearly on total reaction equilibrium. There are quantitative differences between 2D and 3D models, although with a generally gradual nonlinear interpolation as a system is extended from 2D to 3D. However, the additional freedom of movement allowed to particles as thickness of the simulation box increases can produce significant quantitative change as a system moves from 2D to 3D. Simulation results over broader parameter ranges further show that the impact of molecular crowding is highly dependent on the specific reaction system examined

Proteomic Shifts in Embryonic Stem Cells with Gene Dose Modifications Suggest the Presence of Balancer Proteins in Protein Regulatory Networks

Large numbers of protein expression changes are usually observed in mouse models for neurodegenerative diseases, even when only a single gene was mutated in each case. To study the effect of gene dose alterations on the cellular proteome, we carried out a proteomic investigation on murine embryonic stem cells that either overexpressed individual genes or displayed aneuploidy over a genomic region encompassing 14 genes. The number of variant proteins detected per cell line ranged between 70 and 110, and did not correlate with the number of modified genes. In cell lines with single gene mutations, up and down-regulated proteins were always in balance in comparison to parental cell lines regarding number as well as concentration of differentially expressed proteins. In contrast, dose alteration of 14 genes resulted in an unequal number of up and down-regulated proteins, though the balance was kept at the level of protein concentration. We propose that the observed protein changes might partially be explained by a proteomic network response. Hence, we hypothesize the existence of a class of “balancer” proteins within the proteomic network, defined as proteins that buffer or cushion a system, and thus oppose multiple system disturbances. Through database queries and resilience analysis of the protein interaction network, we found that potential balancer proteins are of high cellular abundance, possess a low number of direct interaction partners, and show great allelic variation. Moreover, balancer proteins contribute more heavily to the network entropy, and thus are of high importance in terms of system resilience. We propose that the “elasticity” of the proteomic regulatory network mediated by balancer proteins may compensate for changes that occur under diseased conditions

Macromolecular Crowding Directs Extracellular Matrix Organization and Mesenchymal Stem Cell Behavior

Microenvironments of biological cells are dominated in vivo by macromolecular crowding and resultant excluded volume effects. This feature is absent in dilute in vitro cell culture. Here, we induced macromolecular crowding in vitro by using synthetic macromolecular globules of nm-scale radius at physiological levels of fractional volume occupancy. We quantified the impact of induced crowding on the extracellular and intracellular protein organization of human mesenchymal stem cells (MSCs) via immunocytochemistry, atomic force microscopy (AFM), and AFM-enabled nanoindentation. Macromolecular crowding in extracellular culture media directly induced supramolecular assembly and alignment of extracellular matrix proteins deposited by cells, which in turn increased alignment of the intracellular actin cytoskeleton. The resulting cell-matrix reciprocity further affected adhesion, proliferation, and migration behavior of MSCs. Macromolecular crowding can thus aid the design of more physiologically relevant in vitro studies and devices for MSCs and other cells, by increasing the fidelity between materials synthesized by cells in vivo and in vitro

The Effect of Macromolecular Crowding, Ionic Strength and Calcium Binding on Calmodulin Dynamics

The flexibility in the structure of calmodulin (CaM) allows its binding to over 300 target proteins in the cell. To investigate the structure-function relationship of CaM, we combined methods of computer simulation and experiments based on circular dichroism (CD) to investigate the structural characteristics of CaM that influence its target recognition in crowded cell-like conditions. We developed a unique multiscale solution of charges computed from quantum chemistry, together with protein reconstruction, coarse-grained molecular simulations, and statistical physics, to represent the charge distribution in the transition from apoCaM to holoCaM upon calcium binding. Computationally, we found that increased levels of macromolecular crowding, in addition to calcium binding and ionic strength typical of that found inside cells, can impact the conformation, helicity and the EF hand orientation of CaM. Because EF hand orientation impacts the affinity of calcium binding and the specificity of CaM's target selection, our results may provide unique insight into understanding the promiscuous behavior of calmodulin in target selection inside cells.Comment: Accepted to PLoS Comp Biol, 201