Adaptive coarse-grained Monte Carlo simulation of reaction and diffusion dynamics in heterogeneous plasma membranes

Background: An adaptive coarse-grained (kinetic) Monte Carlo (ACGMC) simulation framework is applied to reaction and diffusion dynamics in inhomogeneous domains. The presented model is relevant to the diffusion and dimerization dynamics of epidermal growth factor receptor (EGFR) in the presence of plasma membrane heterogeneity and specifically receptor clustering. We perform simulations representing EGFR cluster dissipation in heterogeneous plasma membranes consisting of higher density clusters of receptors surrounded by low population areas using the ACGMC method. We further investigate the effect of key parameters on the cluster lifetime.Results: Coarse-graining of dimerization, rather than of diffusion, may lead to computational error. It is shown that the ACGMC method is an effective technique to minimize error in diffusion-reaction processes and is superior to the microscopic kinetic Monte Carlo simulation in terms of computational cost while retaining accuracy. The low computational cost enables sensitivity analysis calculations. Sensitivity analysis indicates that it may be possible to retain clusters of receptors over the time scale of minutes under suitable conditions and the cluster lifetime may depend on both receptor density and cluster size.Conclusions: The ACGMC method is an ideal platform to resolve large length and time scales in heterogeneous biological systems well beyond the plasma membrane and the EGFR system studied here. Our results demonstrate that cluster size must be considered in conjunction with receptor density, as they synergistically affect EGFR cluster lifetime. Further, the cluster lifetime being of the order of several seconds suggests that any mechanisms responsible for EGFR aggregation must operate on shorter timescales (at most a fraction of a second), to overcome dissipation and produce stable clusters observed experimentally. © 2010 Collins et al; licensee BioMed Central Ltd

A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks

<p>Abstract</p> <p>Background</p> <p>The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can <it>simultaneously </it>tackle disparity in time scales <it>and </it>population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo (HyMSMC) method that fills in this void.</p> <p>Results</p> <p>The proposed HyMSMC method blends stochastic singular perturbation concepts, to deal with potential stiffness, with a hybrid of exact and coarse-grained stochastic algorithms, to cope with separation in population sizes. In addition, we introduce the computational singular perturbation (CSP) method as a means of systematically partitioning fast and slow networks and computing relaxation times for convergence. We also propose a new criteria of convergence of fast networks to stochastic low-dimensional manifolds, which further accelerates the algorithm.</p> <p>Conclusion</p> <p>We use several prototype and biological examples, including a gene expression model displaying bistability, to demonstrate the efficiency, accuracy and applicability of the HyMSMC method. Bistable models serve as stringent tests for the success of multiscale MC methods and illustrate limitations of some literature methods.</p

Heterogeneities in EGF receptor density at the cell surface can lead to concave up scatchard plot of EGF binding

AbstractThe mechanism responsible for the concave up nature of the Scatchard plot of epidermal growth factor (EGF) binding on EGF receptor (EGFR) has been a controversial issue for more than a decade. Past efforts to mechanistically simulate the concave up nature of the Scatchard plot of EGF binding have shown that negative cooperativity in EGF binding on an EGFR dimer or inclusion of some external site or binding event can describe this behavior. However, herein we show that heterogeneity in the density of EGFR due to localization in certain regions of the plasma membrane, which has been experimentally reported, can also lead to concave up shape of the Scatchard plot of the EGF binding on EGFR

Computational modeling reveals molecular details of epidermal growth factor binding

BACKGROUND: The ErbB family of receptors are dysregulated in a number of cancers, and the signaling pathway of this receptor family is a critical target for several anti-cancer drugs. Therefore a detailed understanding of the mechanisms of receptor activation is critical. However, despite a plethora of biochemical studies and recent single particle tracking experiments, the early molecular mechanisms involving epidermal growth factor (EGF) binding and EGF receptor (EGFR) dimerization are not as well understood. Herein, we describe a spatially distributed Monte Carlo based simulation framework to enable the simulation of in vivo receptor diffusion and dimerization. RESULTS: Our simulation results are in agreement with the data from single particle tracking and biochemical experiments on EGFR. Furthermore, the simulations reveal that the sequence of receptor-receptor and ligand-receptor reaction events depends on the ligand concentration, receptor density and receptor mobility. CONCLUSION: Our computer simulations reveal the mechanism of EGF binding on EGFR. Overall, we show that spatial simulation of receptor dynamics can be used to gain a mechanistic understanding of receptor activation which may in turn enable improved cancer treatments in the future

Parametric Sensitivity Analysis for Biochemical Reaction Networks based on Pathwise Information Theory

Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space. We develop a sensitivity analysis methodology suitable for complex stochastic reaction networks with a large number of parameters. The proposed approach is based on Information Theory methods and relies on the quantification of information loss due to parameter perturbations between time-series distributions. For this reason, we need to work on path-space, i.e., the set consisting of all stochastic trajectories, hence the proposed approach is referred to as "pathwise". The pathwise sensitivity analysis method is realized by employing the rigorously-derived Relative Entropy Rate (RER), which is directly computable from the propensity functions. A key aspect of the method is that an associated pathwise Fisher Information Matrix (FIM) is defined, which in turn constitutes a gradient-free approach to quantifying parameter sensitivities. The structure of the FIM turns out to be block-diagonal, revealing hidden parameter dependencies and sensitivities in reaction networks

1,2-H- versus 1,2-C-Shift on Sn-Silsesquioxanes

Lewis acidic zeolites such as Sn-Beta catalyze glucose isomerization to fructose via an intramolecular 1,2-H-shift reaction, a key step for converting lignocellulosic biomass into renewable chemicals. Na-exchange of Sn-Beta titrates the neighboring SiOH group in the open Sn site and shifts catalyst selectivity to mannose formed by a 1,2-C-shift reaction. To probe structure/activity relationships in the zeolite, tin-containing silsesquioxanes with (1a) and without (1b) a neighboring SiOH group were recently synthesized and tested. These molecular catalysts are active for glucose conversion, and the presence (absence) of the SiOH favors fructose (mannose) selectivity by intramolecular H(C)-shift reactions. Using density functional theory, we investigated numerous H/C-shift pathways on these tin-silsesquioxane catalysts. On both 1a and 1b, the H-shift reaction occurs through a bidentate binding mode without participation of the SiOH, while the bidentate binding mode is not favored for the C-shift due to steric hindrance. Instead, the C-shift reaction occurs through different concerted reaction pathways, in which an acetylacetonate (acac) ligand interacts with the substrate in the transition state complexes. Favorable H-shift pathways without SiOH participation and acac ligand promotion of the C-shift pathway explain why 1a produces mannose from C-shift reactions instead of exclusively catalyzing H-shift reactions, as the Sn-Beta open site does

Coupled Stochastic Spatial and Non-Spatial Simulations of ErbB1 Signaling Pathways Demonstrate the Importance of Spatial Organization in Signal Transduction

BACKGROUND: The ErbB family of receptors activates intracellular signaling pathways that control cellular proliferation, growth, differentiation and apoptosis. Given these central roles, it is not surprising that overexpression of the ErbB receptors is often associated with carcinogenesis. Therefore, extensive laboratory studies have been devoted to understanding the signaling events associated with ErbB activation. METHODOLOGY/PRINCIPAL FINDINGS: Systems biology has contributed significantly to our current understanding of ErbB signaling networks. However, although computational models have grown in complexity over the years, little work has been done to consider the spatial-temporal dynamics of receptor interactions and to evaluate how spatial organization of membrane receptors influences signaling transduction. Herein, we explore the impact of spatial organization of the epidermal growth factor receptor (ErbB1/EGFR) on the initiation of downstream signaling. We describe the development of an algorithm that couples a spatial stochastic model of membrane receptors with a nonspatial stochastic model of the reactions and interactions in the cytosol. This novel algorithm provides a computationally efficient method to evaluate the effects of spatial heterogeneity on the coupling of receptors to cytosolic signaling partners. CONCLUSIONS/SIGNIFICANCE: Mathematical models of signal transduction rarely consider the contributions of spatial organization due to high computational costs. A hybrid stochastic approach simplifies analyses of the spatio-temporal aspects of cell signaling and, as an example, demonstrates that receptor clustering contributes significantly to the efficiency of signal propagation from ligand-engaged growth factor receptors

Experimental Insights into the Coupling of Methane Combustion and Steam Reforming in a Catalytic Plate Reactor in Transient Mode

The microstructured reactor concept is very promising technology to develop a compact reformer for distributed hydrogen generation. In this work, a catalytic plate reactor (CPR) is developed and investigated for the coupling of methane combustion (MC) and methane steam reforming (MSR) over Pt/Al2O3-coated microchannels in cocurrent and counter-current modes in transient experiments during start-up. A three-dimensional (3D) computational fluid dynamics (CFD) simulation shows uniform velocity and pressure distribution profiles in microchannels. For a channel velocity from 5.1 to 57.3 m/s in the combustor, the oxidation of methane is complete and self-sustainable without explosion, blow-off, or extinction; nevertheless, flashbacks are observed in counter-current mode. In the reformer, the maximum methane conversion is 84.9% in cocurrent mode, slightly higher than that of 80.2% in counter-current mode at a residence time of 33 ms, but at the cost of three times higher energy input in the combustor operating at ∼1000 °C. Nitric oxide (NO) is not identified in combustion products, but nitrous oxide (N2O) is a function of coupling mode and forms significantly in cocurrent mode. This research would be helpful to establish the start-up strategy and environmental impact of compact reformers on a small scale

Dynamics of the Dissociation of Hydrogen on Stepped Platinum Surfaces Using the ReaxFF Reactive Force Field

The dissociation of hydrogen on eight platinum surfaces, Pt(111), Pt(100), Pt(110), Pt(211), Pt(311), Pt(331), Pt(332), and Pt(533), has been studied using molecular dynamics and the reactive force field, ReaxFF. The force field, which includes the degrees of freedom of the atoms in the platinum substrate, was used unmodified with potential parameters determined from previous calculations performed on a training set exclusive of the surfaces considered in this work. The energetics of the eight surfaces in the absence of hydrogen at 0 K were first compared to previous density functional theory (DFT) calculations and found to underestimate excess surface energy. However, taking Pt(111) as a reference state, we found that the trend between surfaces was adequately predicted to justify a relative comparison between the various stepped surfaces. To assess the strengths and weaknesses of the force field, we performed detailed simulations on two stepped surfaces, Pt(533) and Pt(211), and compared our findings to published experimental and theoretical results. In general, the absolute magnitude of reaction rate predictions was low, a result of the force field's tendency to underpredict surface energy. However, when normalized, the simulations show the correct linear scaling with incident energy and angular dependence at collision energies where a direct dissociation mechanism is observed. Because ReaxFF includes all degrees of freedom in the substrate, we carried out simulations aimed at understanding surface-temperature effects on Pt(533). On the basis of the results on Pt(533)/Pt(211), we studied the reaction of hydrogen at normal incidence on all eight surfaces in a range of energies where we anticipated the force field to give reasonable qualitative trends. These results were subsequently fit to a simple linear model that predicts the enhanced reactivity of surfaces containing 111-type atomic steps versus 100-type atomic steps. This model provides a simple framework for predicting high-energy/high-temperature kinetics of complex surfaces not vicinal to Pt(111)