Accommodating space, time and randomness in network simulation

Potential based, spatial simulation of dynamically nested particles

BACKGROUND

To study cell biological phenomena which depend on diffusion, active transport processes, or the locations of species, modeling and simulation studies need to take space into account. To describe the system as a collection of discrete objects moving and interacting in continuous space, various particle-based reaction diffusion simulators for cell-biological system have been developed. So far the focus has been on particles as solid spheres or points. However, spatial dynamics might happen at different organizational levels, such as proteins, vesicles or cells with interrelated dynamics which requires spatial approaches that take this multi-levelness of cell biological systems into account.

RESULTS

Based on the perception of particles forming hollow spheres, ML-Force contributes to the family of particle-based simulation approaches: in addition to excluded volumes and forces, it also supports compartmental dynamics and relating dynamics between different organizational levels explicitly. Thereby, compartmental dynamics, e.g., particles entering and leaving other particles, and bimolecular reactions are modeled using pair-wise potentials (forces) and the Langevin equation. In addition, forces that act independently of other particles can be applied to direct the movement of particles. Attributes and the possibility to define arbitrary functions on particles, their attributes and content, to determine the results and kinetics of reactions add to the expressiveness of ML-Force. Its implementation comprises a rudimentary rule-based embedded domain-specific modeling language for specifying models and a simulator for executing models continuously. Applications inspired by cell biological models from literature, such as vesicle transport or yeast growth, show the value of the realized features. They facilitate capturing more complex spatial dynamics, such as the fission of compartments or the directed movement of particles, and enable the integration of non-spatial intra-compartmental dynamics as stochastic events.

CONCLUSIONS

By handling all dynamics based on potentials (forces) and the Langevin equation, compartmental dynamics, such as dynamic nesting, fusion and fission of compartmental structures are handled continuously and are seamlessly integrated with traditional particle-based reaction-diffusion dynamics within the cell. Thereby, attributes and arbitrary functions allow to flexibly describe diverse spatial phenomena, and relate dynamics across organizational levels. Also they prove crucial in modeling intra-cellular or intra-compartmental dynamics in a non-spatial manner, and, thus, to abstract from spatial dynamics, on demand which increases the range of multi-compartmental processes that can be captured.

Computational Systems Biology in Cancer: Modeling Methods and Applications

In recent years it has become clear that carcinogenesis is a complex process, both at the molecular and cellular levels. Understanding the origins, growth and spread of cancer, therefore requires an integrated or system-wide approach. Computational systems biology is an emerging sub-discipline in systems biology that utilizes the wealth of data from genomic, proteomic and metabolomic studies to build computer simulations of intra and intercellular processes. Several useful descriptive and predictive models of the origin, growth and spread of cancers have been developed in an effort to better understand the disease and potential therapeutic approaches. In this review we describe and assess the practical and theoretical underpinnings of commonly-used modeling approaches, including ordinary and partial differential equations, petri nets, cellular automata, agent based models and hybrid systems. A number of computer-based formalisms have been implemented to improve the accessibility of the various approaches to researchers whose primary interest lies outside of model development. We discuss several of these and describe how they have led to novel insights into tumor genesis, growth, apoptosis, vascularization and therapy.

ReaDDyMM: Fast interacting particle reaction-diffusion simulations using graphical processing units

ReaDDy is a modular particle simulation package combining off-lattice reaction kinetics with arbitrary particle interaction forces. Here we present a graphical processing unit implementation of ReaDDy that employs the fast multiplatform molecular dynamics package OpenMM. A speedup of up to two orders of magnitude is demonstrated, giving us access to timescales of multiple seconds on single graphical processing units. This opens up the possibility of simulating cellular signal transduction events while resolving all protein copies.

A Complete Pathway Model for Lipid A Biosynthesis in Escherichia coli

Lipid A is a highly conserved component of lipopolysaccharide (LPS), itself a major component of the outer membrane of Gram-negative bacteria. Lipid A is essential to cells and elicits a strong immune response from humans and other animals. We developed a quantitative model of the nine enzyme-catalyzed steps of Escherichia coli lipid A biosynthesis, drawing parameters from the experimental literature. This model accounts for biosynthesis regulation, which occurs through regulated degradation of the LpxC and WaaA (also called KdtA) enzymes. The LpxC degradation signal appears to arise from the lipid A disaccharide concentration, which we deduced from prior results, model results, and new LpxK overexpression results. The model agrees reasonably well with many experimental findings, including the lipid A production rate, the behaviors of mutants with defective LpxA enzymes, correlations between LpxC half-lives and cell generation times, and the effects of LpxK overexpression on LpxC concentrations. Its predictions also differ from some experimental results, which suggest modifications to the current understanding of the lipid A pathway, such as the possibility that LpxD can replace LpxA and that there may be metabolic channeling between LpxH and LpxB. The model shows that WaaA regulation may serve to regulate the lipid A production rate when the 3-deoxy-D-manno-oct-2-ulosonic acid (KDO) concentration is low and/or to control the number of KDO residues that get attached to lipid A. Computation of flux control coefficients showed that LpxC is the rate-limiting enzyme if pathway regulation is ignored, but that LpxK is the rate-limiting enzyme if pathway regulation is present, as it is in real cells. Control also shifts to other enzymes if the pathway substrate concentrations are not in excess. Based on these results, we suggest that LpxK may be a much better drug target than LpxC, which has been pursued most often.

ReaDDy--a software for particle-based reaction-diffusion dynamics in crowded cellular environments

We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.

Enrichment map profiling of the cancer invasion front suggests regulation of colorectal cancer progression by the bone morphogenetic protein antagonist, gremlin-1

The cancer invasion front (CIF), a spatially-recognized area due to the frequent presence of peritumoral desmoplastic reaction, represents a cancer site where many hallmarks of cancer metastasis occur. It is now strongly suggested that the desmoplastic microenvironment holds crucial information for determining tumor development and progression. Despite extensive research on tumor-host cell interactions at CIFs, the exact paracrine molecular network that is hardwired into the proteome of the stromal and cancer subpopulations remains partially understood. Here, we interrogated the signaling pathways and the molecular functional signatures across the proteome of a desmoplastic coculture model system of colorectal cancer progression. We discovered a group of bone morphogenetic protein (BMP) antagonists that coordinates major biological programs in CIFs, including cell proliferation, invasion, migration and differentiation processes. Using a mathematical model of cancer cell progression, coupled to in vitro cell migration assays, we demonstrated that the prominent BMP antagonist gremlin-1 (GREM1) may trigger motility of cancer cell cohorts. Our data collectively demonstrate that the desmoplastic CIFs deploy a microenvironmental signature, based on BMP antagonism, in order to regulate the motogenic fates of cancer cell cohorts invading the adjacent stroma.

Systems biology of complex symptom profiles: capturing interactivity across behavior, brain and immune regulation

As our thinking about the basic principles of biology and medicine continue to evolve, the importance of context and regulatory interaction is becoming increasingly obvious. Biochemical and physiological components do not exist in isolation but instead are part of a tightly integrated network of interacting elements that ensure robustness and support the emergence of complex behavior. This integration permeates all levels of biology from gene regulation, to immune cell signaling, to coordinated patterns of neuronal activity and the resulting psychosocial interaction. Systems biology is an emerging branch of science that sits as a translational catalyst at the interface of the life and computational sciences. While there is no universally accepted definition of systems biology, we attempt to provide an overview of some the basic unifying concepts and current efforts in the field as they apply to illnesses where brain and subsequent behavior are a chief component, for example autism, schizophrenia, depression, and others. Methods in this field currently constitute a broad mosaic that stretches across multiple scales of biology and physiological compartments. While this work by no means constitutes an exhaustive list of all these methods, this work highlights the principal sub-disciplines presently driving the field as well as future directions of progress.

Spatial simulations in systems biology: from molecules to cells

Cells are highly organized objects containing millions of molecules. Each biomolecule has a specific shape in order to interact with others in the complex machinery. Spatial dynamics emerge in this system on length and time scales which can not yet be modeled with full atomic detail. This review gives an overview of methods which can be used to simulate the complete cell at least with molecular detail, especially Brownian dynamics simulations. Such simulations require correct implementation of the diffusion-controlled reaction scheme occurring on this level. Implementations and applications of spatial simulations are presented, and finally it is discussed how the atomic level can be included for instance in multi-scale simulation methods.

Accounting for diffusion in agent based models of reaction-diffusion systems with application to cytoskeletal diffusion

Diffusion plays a key role in many biochemical reaction systems seen in nature. Scenarios where diffusion behavior is critical can be seen in the cell and subcellular compartments where molecular crowding limits the interaction between particles. We investigate the application of a computational method for modeling the diffusion of molecules and macromolecules in three-dimensional solutions using agent based modeling. This method allows for realistic modeling of a system of particles with different properties such as size, diffusion coefficients, and affinity as well as the environment properties such as viscosity and geometry. Simulations using these movement probabilities yield behavior that mimics natural diffusion. Using this modeling framework, we simulate the effects of molecular crowding on effective diffusion and have validated the results of our model using Langevin dynamics simulations and note that they are in good agreement with previous experimental data. Furthermore, we investigate an extension of this framework where single discrete cells can contain multiple particles of varying size in an effort to highlight errors that can arise from discretization that lead to the unnatural behavior of particles undergoing diffusion. Subsequently, we explore various algorithms that differ in how they handle the movement of multiple particles per cell and suggest an algorithm that properly accommodates multiple particles of various sizes per cell that can replicate the natural behavior of these particles diffusing. Finally, we use the present modeling framework to investigate the effect of structural geometry on the directionality of diffusion in the cell cytoskeleton with the observation that parallel orientation in the structural geometry of actin filaments of filopodia and the branched structure of lamellipodia can give directionality to diffusion at the filopodia-lamellipodia interface.

Exploring the spatial and temporal organization of a cell's proteome

To increase our current understanding of cellular processes, such as cell signaling and division, knowledge is needed about the spatial and temporal organization of the proteome at different organizational levels. These levels cover a wide range of length and time scales: from the atomic structures of macromolecules for inferring their molecular function, to the quantitative description of their abundance, and spatial distribution in the cell. Emerging new experimental technologies are greatly increasing the availability of such spatial information on the molecular organization in living cells. This review addresses three fields that have significantly contributed to our understanding of the proteome's spatial and temporal organization: first, methods for the structure determination of individual macromolecular assemblies, specifically the fitting of atomic structures into density maps generated from electron microscopy techniques; second, research that visualizes the spatial distributions of these complexes within the cellular context using cryo electron tomography techniques combined with computational image processing; and third, methods for the spatial modeling of the dynamic organization of the proteome, specifically those methods for simulating reaction and diffusion of proteins and complexes in crowded intracellular fluids. The long-term goal is to integrate the varied data about a proteome's organization into a spatially explicit, predictive model of cellular processes.

Discrete diffusion models to study the effects of Mg2+ concentration on the PhoPQ signal transduction system

Background

The challenge today is to develop a modeling and simulation paradigm that integrates structural, molecular and genetic data for a quantitative understanding of physiology and behavior of biological processes at multiple scales. This modeling method requires techniques that maintain a reasonable accuracy of the biological process and also reduces the computational overhead. This objective motivates the use of new methods that can transform the problem from energy and affinity based modeling to information theory based modeling. To achieve this, we transform all dynamics within the cell into a random event time, which is specified through an information domain measure like probability distribution. This allows us to use the “in silico” stochastic event based modeling approach to find the molecular dynamics of the system.

Results

In this paper, we present the discrete event simulation concept using the example of the signal transduction cascade triggered by extra-cellular Mg²⁺ concentration in the two component PhoPQ regulatory system of Salmonella Typhimurium. We also present a model to compute the information domain measure of the molecular transport process by estimating the statistical parameters of inter-arrival time between molecules/ions coming to a cell receptor as external signal. This model transforms the diffusion process into the information theory measure of stochastic event completion time to get the distribution of the Mg²⁺ departure events. Using these molecular transport models, we next study the in-silico effects of this external trigger on the PhoPQ system.

Conclusions

Our results illustrate the accuracy of the proposed diffusion models in explaining the molecular/ionic transport processes inside the cell. Also, the proposed simulation framework can incorporate the stochasticity in cellular environments to a certain degree of accuracy. We expect that this scalable simulation platform will be able to model more complex biological systems with reasonable accuracy to understand their temporal dynamics.

Designing communicating colonies of biomimetic microcapsules

Using computational modeling, we design colonies of biomimetic microcapsules that exploit chemical mechanisms to communicate and alter their local environment. As a result, these synthetic objects can self-organize into various autonomously moving structures and exhibit ant-like tracking behavior. In the simulations, signaling microcapsules release agonist particles, whereas target microcapsules release antagonist particles and the permeabilities of both capsule types depend on the local particle concentration in the surrounding solution. Additionally, the released nanoscopic particles can bind to the underlying substrate and thereby create adhesion gradients that propel the microcapsules to move. Hydrodynamic interactions and the feedback mechanism provided by the dissolved particles are both necessary to achieve the collective dynamics exhibited by these colonies. Our model provides a platform for integrating both the spatial and temporal behavior of assemblies of "artificial cells," and allows us to design a rich variety of structures capable of exhibiting complex, cooperative behavior. Due to the cell-like attributes of polymeric microcapsules and polymersomes, material systems are available for realizing our predictions.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

Background

We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined.

For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided.

Results

Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa.

Conclusions

We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation

Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally.

Parameter effects on binding chemistry in crowded media using a two-dimensional stochastic off-lattice model

The intracellular environment imposes a variety of constraints on biochemical reaction systems that can substantially change reaction rates and equilibria relative to an ideal solution-based environment. One of the most notable features of the intracellular environment is its dense macromolecular crowding, which, among many other effects, tends to strongly enhance binding and assembly reactions. Despite extensive study of biochemistry in crowded media, it remains extremely difficult to predict how crowding will quantitatively affect any given reaction system due to the dependence of the crowding effect on numerous assumptions about the reactants and crowding agents involved. We previously developed a two dimensional stochastic off-lattice model of binding reactions based on the Green's function reaction dynamics method in order to create a versatile simulation environment in which one can explore interactions among many parameters of a crowded assembly system. In the present work, we examine interactions among several critical parameters for a model dimerization system: the total concentration of reactants and inert particles, the binding probability upon a collision between two reactant monomers, the mean time of dissociation reactions, and the diffusion coefficient of the system. Applying regression models to equilibrium constants across parameter ranges shows that the effect of the total concentration is approximately captured by a low-order nonlinear polynomial model, while the other three parameter effects are each accurately captured by a linear model. Furthermore, validation on tests with multi-parameter variations reveals that the effects of these parameters are separable from one another over a broad range of variation in all four parameters. The simulation work suggests that predictive models of crowding effects can accommodate a wider variety of parameter variations than prior theoretical models have so far achieved.

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.

Stochastic simulation of signal transduction: impact of the cellular architecture on diffusion

The transduction of signals depends on the translocation of signaling molecules to specific targets. Undirected diffusion processes play a key role in the bridging of spaces between different cellular compartments. The diffusion of the molecules is, in turn, governed by the intracellular architecture. Molecular crowding and the cytoskeleton decrease macroscopic diffusion. This article shows the use of a stochastic simulation method to study the effects of the cytoskeleton structure on the mobility of macromolecules. Brownian dynamics and single particle tracking were used to simulate the diffusion process of individual molecules through a model cytoskeleton. The resulting average effective diffusion is in line with data obtained in the in vitro and in vivo experiments. It shows that the cytoskeleton structure strongly influences the diffusion of macromolecules. The simulation method used also allows the inclusion of reactions in order to model complete signaling pathways in their spatio-temporal dynamics, taking into account the effects of the cellular architecture.

Dynamic knowledge representation using agent-based modeling: ontology instantiation and verification of conceptual models

The sheer volume of biomedical research threatens to overwhelm the capacity of individuals to effectively process this information. Adding to this challenge is the multiscale nature of both biological systems and the research community as a whole. Given this volume and rate of generation of biomedical information, the research community must develop methods for robust representation of knowledge in order for individuals, and the community as a whole, to "know what they know." Despite increasing emphasis on "data-driven" research, the fact remains that researchers guide their research using intuitively constructed conceptual models derived from knowledge extracted from publications, knowledge that is generally qualitatively expressed using natural language. Agent-based modeling (ABM) is a computational modeling method that is suited to translating the knowledge expressed in biomedical texts into dynamic representations of the conceptual models generated by researchers. The hierarchical object-class orientation of ABM maps well to biomedical ontological structures, facilitating the translation of ontologies into instantiated models. Furthermore, ABM is suited to producing the nonintuitive behaviors that often "break" conceptual models. Verification in this context is focused at determining the plausibility of a particular conceptual model, and qualitative knowledge representation is often sufficient for this goal. Thus, utilized in this fashion, ABM can provide a powerful adjunct to other computational methods within the research process, as well as providing a metamodeling framework to enhance the evolution of biomedical ontologies.

Stochastic off-lattice modeling of molecular self-assembly in crowded environments by Green's function reaction dynamics

The environment inside a living cell is dramatically different from that found in in vitro models, presenting a problem for computational models of biochemistry that are only beginning to capture these differences. This deviation between idealized in vitro models and more realistic intracellular conditions is particularly problematic for models of molecular self-assembly, but also specifically hard to address because the large sizes and long assembly times of biological self-assembly systems force the use of highly simplified models. We have developed a prototype of a molecular self-assembly simulator based on the Green's function reaction dynamics (GFRD) model to achieve more realistic models of assembly in the crowded conditions of the cell without unduly sacrificing tractability. We tested the model on a simple representation of dimer assembly in a two-dimensional space. Our simulations verify that the model is computationally efficient, provides a realistic quantitative model of reaction kinetics in uncrowded conditions, and exhibits expected excluded volume effects under conditions of high crowding. This work confirms the effectiveness of the GFRD technique for more realistic coarse-grained modeling of self-assembly in crowded conditions and helps lay the groundwork for exploring the effects of in vivo crowding on more complex assembly systems.

Introduction of an agent-based multi-scale modular architecture for dynamic knowledge representation of acute inflammation

Background

One of the greatest challenges facing biomedical research is the integration and sharing of vast amounts of information, not only for individual researchers, but also for the community at large. Agent Based Modeling (ABM) can provide a means of addressing this challenge via a unifying translational architecture for dynamic knowledge representation. This paper presents a series of linked ABMs representing multiple levels of biological organization. They are intended to translate the knowledge derived from in vitro models of acute inflammation to clinically relevant phenomenon such as multiple organ failure.

Results and Discussion

ABM development followed a sequence starting with relatively direct translation from in-vitro derived rules into a cell-as-agent level ABM, leading on to concatenated ABMs into multi-tissue models, eventually resulting in topologically linked aggregate multi-tissue ABMs modeling organ-organ crosstalk. As an underlying design principle organs were considered to be functionally composed of an epithelial surface, which determined organ integrity, and an endothelial/blood interface, representing the reaction surface for the initiation and propagation of inflammation. The development of the epithelial ABM derived from an in-vitro model of gut epithelial permeability is described. Next, the epithelial ABM was concatenated with the endothelial/inflammatory cell ABM to produce an organ model of the gut. This model was validated against in-vivo models of the inflammatory response of the gut to ischemia. Finally, the gut ABM was linked to a similarly constructed pulmonary ABM to simulate the gut-pulmonary axis in the pathogenesis of multiple organ failure. The behavior of this model was validated against in-vivo and clinical observations on the cross-talk between these two organ systems

Conclusion

A series of ABMs are presented extending from the level of intracellular mechanism to clinically observed behavior in the intensive care setting. The ABMs all utilize cell-level agents that encapsulate specific mechanistic knowledge extracted from in vitro experiments. The execution of the ABMs results in a dynamic representation of the multi-scale conceptual models derived from those experiments. These models represent a qualitative means of integrating basic scientific information on acute inflammation in a multi-scale, modular architecture as a means of conceptual model verification that can potentially be used to concatenate, communicate and advance community-wide knowledge.

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.

Insight or illusion? Seeing inside the cell with mesoscopic simulations

The expulsion of material from a cell by fusion of vesicles at the plasma membrane, and the entry of a virus by membrane invagination are complex membrane-associated processes whose control is crucial to cell survival. Our ability to visualize the dynamics of such processes experimentally is limited by spatial resolution and the speed of molecular rearrangements. The increase in computing power of the last few decades enables the construction of computational tools for observing cellular processes in silico. As experiments yield increasing amounts of data on the protein and lipid constituents of the cell, computer simulations parametrized using this data are beginning to allow models of cellular processes to be interrogated in ways unavailable in the laboratory. Mesoscopic simulations retain only those molecular features that are believed to be relevant to the processes of interest. This allows the dynamics of spatially heterogeneous membranes and the crowded cytoplasmic environment to be followed at a modest computational cost. The price for such power is that the atomic detail of the constituents is much lower than in atomistic Molecular Dynamics simulations. We argue that this price is worth paying because mesoscopic simulations can generate new insight into the complex, dynamic life of a cell.

The hard cell: From proteomics to a whole cell model

Proteomics has provided a wealth of data related to the nature of the proteome, including subcellular location, copy number, interaction partners and protein complexes. This raises the question of whether it is feasible to combine these data, together with other data related to overall cellular structure, to construct a static picture of the cell. In this minireview, we discuss these data, and the issues of turning them into whole cell models.

Computational systems biology in drug discovery and development: methods and applications

Computational systems biology is an emerging field in biological simulation that attempts to model or simulate intra- and intercellular events using data gathered from genomic, proteomic or metabolomic experiments. The need to model complex temporal and spatiotemporal processes at many different scales has led to the emergence of numerous techniques, including systems of differential equations, Petri nets, cellular automata simulators, agent-based models and pi calculus. This review provides a brief summary and an assessment of most of these approaches. It also provides examples of how these methods are being used to facilitate drug discovery and development.