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

Multiscale simulation unravel the kinetic mechanisms of inflammasome assembly

In the innate immune system, the host defense from the invasion of external pathogens triggers the inflammatory responses. Proteins involved in the inflammatory pathways were often found to aggregate into supramolecular oligomers, called 'inflammasome', mostly through the homotypic interaction between their domains that belong to the death domain superfamily. Although much has been known about the formation of these helical molecular machineries, the detailed correlation between the dynamics of their assembly and the structure of each domain is still not well understood. Using the filament formed by the PYD domains of adaptor molecule ASC as a test system, we constructed a new multiscale simulation framework to study the kinetics of inflammasome assembly. We found that the filament assembly is a multi-step, but highly cooperative process. Moreover, there are three types of binding interfaces between domain subunits in the ASC^PYD filament. The multiscale simulation results suggest that dynamics of domain assembly are rooted in the primary protein sequence which defines the energetics of molecular recognition through three binding interfaces. Interface I plays a more regulatory role than the other two in mediating both the kinetics and the thermodynamics of assembly. Finally, the efficiency of our computational framework allows us to design mutants on a systematic scale and predict their impacts on filament assembly. In summary, this is, to the best of our knowledge, the first simulation method to model the spatial-temporal process of inflammasome assembly. Our work is a useful addition to a suite of existing experimental techniques to study the functions of inflammasome in innate immune system.

A Multiscale Computational Model for Simulating the Kinetics of Protein Complex Assembly

Proteins fulfill versatile biological functions by interacting with each other and forming high-order complexes. Although the order in which protein subunits assemble is important for the biological function of their final complex, this kinetic information has received comparatively little attention in recent years. Here we describe a multiscale framework that can be used to simulate the kinetics of protein complex assembly. There are two levels of models in the framework. The structural details of a protein complex are reflected by the residue-based model, while a lower-resolution model uses a rigid-body (RB) representation to simulate the process of complex assembly. These two levels of models are integrated together, so that we are able to provide the kinetic information about complex assembly with both structural details and computational efficiency.

Multiscale Modeling of Diffusion in a Crowded Environment

We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space-dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size, and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.

Excluded volume effects in on- and off-lattice reaction-diffusion models

Mathematical models are important tools to study the excluded volume effects on reaction-diffusion systems, which are known to play an important role inside living cells. Detailed microscopic simulations with off-lattice Brownian dynamics become computationally expensive in crowded environments. In this study, the authors therefore investigate to which extent on-lattice approximations, the so-called cellular automata models, can be used to simulate reactions and diffusion in the presence of crowding molecules. They show that the diffusion is most severely slowed down in the off-lattice model, since randomly distributed obstacles effectively exclude more volume than those ordered on an artificial grid. Crowded reaction rates can be both increased and decreased by the grid structure and it proves important to model the molecules with realistic sizes when excluded volume is taken into account. The grid artefacts increase with increasing crowder density and they conclude that the computationally more efficient on-lattice simulations are accurate approximations only for low crowder densities.

A coarse-grained model for the simulations of biomolecular interactions in cellular environments

The interactions of bio-molecules constitute the key steps of cellular functions. However, in vivo binding properties differ significantly from their in vitro measurements due to the heterogeneity of cellular environments. Here we introduce a coarse-grained model based on rigid-body representation to study how factors such as cellular crowding and membrane confinement affect molecular binding. The macroscopic parameters such as the equilibrium constant and the kinetic rate constant are calibrated by adjusting the microscopic coefficients used in the numerical simulations. By changing these model parameters that are experimentally approachable, we are able to study the kinetic and thermodynamic properties of molecular binding, as well as the effects caused by specific cellular environments. We investigate the volumetric effects of crowded intracellular space on bio-molecular diffusion and diffusion-limited reactions. Furthermore, the binding constants of membrane proteins are currently difficult to measure. We provide quantitative estimations about how the binding of membrane proteins deviates from soluble proteins under different degrees of membrane confinements. The simulation results provide biological insights to the functions of membrane receptors on cell surfaces. Overall, our studies establish a connection between the details of molecular interactions and the heterogeneity of cellular environments.

Applying molecular crowding models to simulations of virus capsid assembly in vitro

Virus capsid assembly has been widely studied as a biophysical system, both for its biological and medical significance and as an important model for complex self-assembly processes. No current technology can monitor assembly in detail and what information we have on assembly kinetics comes exclusively from in vitro studies. There are many differences between the intracellular environment and that of an in vitro assembly assay, however, that might be expected to alter assembly pathways. Here, we explore one specific feature characteristic of the intracellular environment and known to have large effects on macromolecular assembly processes: molecular crowding. We combine prior particle simulation methods for estimating crowding effects with coarse-grained stochastic models of capsid assembly, using the crowding models to adjust kinetics of capsid simulations to examine possible effects of crowding on assembly pathways. Simulations suggest a striking difference depending on whether or not a system uses nucleation-limited assembly, with crowding tending to promote off-pathway growth in a nonnucleation-limited model but often enhancing assembly efficiency at high crowding levels even while impeding it at lower crowding levels in a nucleation-limited model. These models may help us understand how complicated assembly systems may have evolved to function with high efficiency and fidelity in the densely crowded environment of the cell.

Reaching new levels of realism in modeling biological macromolecules in cellular environments

An increasing number of studies are aimed at modeling cellular environments in a comprehensive and realistic fashion. A major challenge in these efforts is how to bridge spatial and temporal scales over many orders of magnitude. Furthermore, there are additional challenges in integrating different aspects ranging from questions about biomolecular stability in crowded environments to the description of reactive processes on cellular scales. In this review, recent studies with models of biomolecules in cellular environments at different levels of detail are discussed in terms of their strengths and weaknesses. In particular, atomistic models, implicit representations of cellular environments, coarse-grained and spheroidal models of biomolecules, as well as the inclusion of reactive processes via reaction-diffusion models are described. Furthermore, strategies for integrating the different models into a comprehensive description of cellular environments are discussed.

A new paradigm for the roles of the genome in ssRNA viruses

Recent work with RNA phages and an ssRNA plant satellite virus challenges the widely held view that the sequences and structures of genomic RNAs are unimportant for virion assembly. In the T=3 phages, RNA–coat protein interactions occur throughout the genome, defining the quasiconformers of their protein shells. In the plant virus, there are multiple packaging signals dispersed throughout the genome that overcome electrostatic barriers to protein self-assembly. Both viral coat proteins cause the solution structures of their cognate genomes to collapse into a form that is readily encapsidated in a two-stage assembly process. Such similar behavior in two structurally unrelated viral protein folds implies that this might be a conserved feature of many viral assembly reactions. These results suggest a highly defined structure for the RNA in the virions, consistent with recent structural studies. They also have implications both for subsequent genome release during infection and for the evolution of viral sequences.

Formation of protein complexes in crowded environments--from in vitro to in vivo

Traditionally, biochemical studies are performed in dilute homogenous solutions, which are very different from the dense mixture of molecules found in cells. Thus, the physiological relevance of these studies is in question. This recognition motivated scientists to formulate the effect of crowded solutions in general, and excluded volume in particular, on biochemical processes. Using polymers or proteins as crowders, it was shown that while crowding tends to significantly enhance the formation of complexes containing many subunits, dimerizations are only mildly affected. Computer simulations, together with experimental evidence, indicate soft interactions and diffusion as critical factors that operate in a concerted manner with excluded volume to modulate protein binding. Yet, these approaches do not truly mimic the cellular environment. In vivo studies may overcome this shortfall. The few studies conducted thus far suggest that in cells, binding and folding occur at rates close to those determined in dilute solutions. Obtaining quantitative biochemical information on reactions inside living cells is currently a main challenge of the field, as the complexity of the intracellular milieu was what motivated crowding research to begin with.

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.

Rule-based modeling of signal transduction: a primer

Biological cells accomplish their physiological functions using interconnected networks of genes, proteins, and other biomolecules. Most interactions in biological signaling networks, such as bimolecular association or covalent modification, can be modeled in a physically realistic manner using elementary reaction kinetics. However, the size and combinatorial complexity of such reaction networks have hindered such a mechanistic approach, leading many to conclude that it is premature and to adopt alternative statistical or phenomenological approaches. The recent development of rule-based modeling languages, such as BioNetGen (BNG) and Kappa, enables the precise and succinct encoding of large reaction networks. Coupled with complementary advances in simulation methods, these languages circumvent the combinatorial barrier and allow mechanistic modeling on a much larger scale than previously possible. These languages are also intuitive to the biologist and accessible to the novice modeler. In this chapter, we provide a self-contained tutorial on modeling signal transduction networks using the BNG Language and related software tools. We review the basic syntax of the language and show how biochemical knowledge can be articulated using reaction rules, which can be used to capture a broad range of biochemical and biophysical phenomena in a concise and modular way. A model of ligand-activated receptor dimerization is examined, with a detailed treatment of each step of the modeling process. Sections discussing modeling theory, implicit and explicit model assumptions, and model parameterization are included, with special focus on retaining biophysical realism and avoiding common pitfalls. We also discuss the more advanced case of compartmental modeling using the compartmental extension to BioNetGen. In addition, we provide a comprehensive set of example reaction rules that cover the various aspects of signal transduction, from signaling at the membrane to gene regulation. The reader can modify these reaction rules to model their own systems of interest.

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.

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.