Investigating the effects of molecular crowding on Ca2+ diffusion using a particle-based simulation model.

Calcium ions (Ca(2+)) are an important second messenger in eucaryotic cells. They are involved in numerous physiological processes which are triggered by calcium signals in the form of local release events, temporal oscillations, or reaction-diffusion waves. The diffusive spread of calcium signals in the cytosol is strongly affected by calcium-binding proteins (buffers). In addition, the cytosol contains a large number of inert molecules and molecular structures which make it a crowded environment. Here, we investigate the effects of such excluded volumes on calcium diffusion in the presence of different kinds of buffers. We find that the contributions in slowing down Ca(2+) diffusion coming from buffering and molecular crowding are not additive, i.e., the reduction in Ca(2+) diffusivity due to crowding and buffering together is not the sum of each single contribution. In the presence of Ca(2+) gradients and high affinity mobile buffers the effective diffusion coefficient of Ca(2+) can be reduced by up to 60% in highly crowded environments. This suggests that molecular crowding may significantly affect the shape of Ca(2+) microdomains and wave propagation in cell types with high excluded volume fractions.

Extraction of elementary rate constants from global network analysis of E. coli central metabolism.

BACKGROUND: As computational performance steadily increases, so does interest in extending one-particle-per-molecule models to larger physiological problems. Such models however require elementary rate constants to calculate time-dependent rate coefficients under physiological conditions. Unfortunately, even when in vivo kinetic data is available, it is often in the form of aggregated rate laws (ARL) that do not specify the required elementary rate constants corresponding to mass-action rate laws (MRL). There is therefore a need to develop a method which is capable of automatically transforming ARL kinetic information into more detailed MRL rate constants. RESULTS: By incorporating proteomic data related to enzyme abundance into an MRL modelling framework, here we present an efficient method operating at a global network level for extracting elementary rate constants from experiment-based aggregated rate law (ARL) models. The method combines two techniques that can be used to overcome the difficult properties in parameterization. The first, a hybrid MRL/ARL modelling technique, is used to divide the parameter estimation problem into sub-problems, so that the parameters of the mass action rate laws for each enzyme are estimated in separate steps. This reduces the number of parameters that have to be optimized simultaneously. The second, a hybrid algebraic-numerical simulation and optimization approach, is used to render some rate constants identifiable, as well as to greatly narrow the bounds of the other rate constants that remain unidentifiable. This is done by incorporating equality constraints derived from the King-Altman and Cleland method into the simulated annealing algorithm. We apply these two techniques to estimate the rate constants of a model of E. coli glycolytic pathways. The simulation and statistical results show that our innovative method performs well in dealing with the issues of high computation cost, stiffness, local minima and uncertainty inherent with large-scale non-convex nonlinear MRL models. CONCLUSION: In short, this new hybrid method can ensure the proper solution of a challenging parameter estimation problem of nonlinear dynamic MRL systems, while keeping the computational effort reasonable. Moreover, the work provides us with some optimism that physiological models at the particle scale can be rooted on a firm foundation of parameters generated in the macroscopic regime on an experimental basis. Thus, the proposed method should have applications to multi-scale modelling of the real biological systems allowing for enzyme intermediates, stochastic and spatial effects inside a cell.

Coarse-grained molecular simulation of diffusion and reaction kinetics in a crowded virtual cytoplasm.

We present a general-purpose model for biomolecular simulations at the molecular level that incorporates stochasticity, spatial dependence, and volume exclusion, using diffusing and reacting particles with physical dimensions. To validate the model, we first established the formal relationship between the microscopic model parameters (timestep, move length, and reaction probabilities) and the macroscopic coefficients for diffusion and reaction rate. We then compared simulation results with Smoluchowski theory for diffusion-limited irreversible reactions and the best available approximation for diffusion-influenced reversible reactions. To simulate the volumetric effects of a crowded intracellular environment, we created a virtual cytoplasm composed of a heterogeneous population of particles diffusing at rates appropriate to their size. The particle-size distribution was estimated from the relative abundance, mass, and stoichiometries of protein complexes using an experimentally derived proteome catalog from Escherichia coli K12. Simulated diffusion constants exhibited anomalous behavior as a function of time and crowding. Although significant, the volumetric impact of crowding on diffusion cannot fully account for retarded protein mobility in vivo, suggesting that other biophysical factors are at play. The simulated effect of crowding on barnase-barstar dimerization, an experimentally characterized example of a bimolecular association reaction, reveals a biphasic time course, indicating that crowding exerts different effects over different timescales. These observations illustrate that quantitative realism in biosimulation will depend to some extent on mesoscale phenomena that are not currently well understood.

Accommodating space, time and randomness in network simulation.

Interest in the possibility of dynamically simulating complex cellular processes has escalated markedly in recent years. This interest has been fuelled by three factors: the generally accepted value in understanding living processes as integrated systems; the dramatic increase in computational capability; and the availability of new or improved technology for making the quantitative measurements that are needed to drive and validate cellular simulations. Between the extremes of atom-scale and organism-scale simulation is a vast middle-ground requiring simulation strategies that are capable of dealing with a range of spatial, temporal and molecular abundance scales that are crucial for a comprehensive understanding of integrative cell biology. Although at an early stage, methodological improvements and the development of computational platforms provide some hope that simulations will emerge that can bridge the gap between network models and the true operation of the cell as a complex machine.

A method for the analysis of ginsenosides, malonyl ginsenosides, and hydrolyzed ginsenosides using high-performance liquid chromatography with ultraviolet and positive mode electrospray ionization mass spectrometric detection.

A high-performance liquid chromatographic separation coupled to diode array absorbance and positive mode electrospray mass spectrometric detection has been developed for the analysis of ginsenosides, malonyl ginsenosides, and hydrolyzed ginsenosides in extracts of Asian ginseng (Panax ginseng) and American ginseng (P. quinquefolius). The method is capable of separating, identifying, and quantifying the predominant ginsenosides found in heated alcoholic extracts of Asian and American ginseng roots routinely sold as nutraceuticals. It also separates and identifies the malonyl ginsenosides often found in cold alcoholic extracts of ginseng root and has the potential to quantify these compounds if pure standards are available. Furthermore, it can separate and identify ginsenoside hydrolysis products such as those readily produced in situations mimicking gastric situations, including those used for dissolution studies (i.e., 0.1 N HCl, 37 degrees C).