When do diffusion-limited trajectories become memoryless?

Stochastic description of cellular dynamics by the chemical master equation assumes the exponential distribution of intervals between reaction events. Diffusion-limited reactions violate this assumption. Using the example of the target search we investigate the conditions under which a peaked waiting-time distribution can be approximated by the exponential function. We link the steady-state flux and the dynamic property of the diffusion, the mean first-passage time

Detailed simulations of cell biology with Smoldyn 2.1.

Most cellular processes depend on intracellular locations and random collisions of individual protein molecules. To model these processes, we developed algorithms to simulate the diffusion, membrane interactions, and reactions of individual molecules, and implemented these in the Smoldyn program. Compared to the popular MCell and ChemCell simulators, we found that Smoldyn was in many cases more accurate, more computationally efficient, and easier to use. Using Smoldyn, we modeled pheromone response system signaling among yeast cells of opposite mating type. This model showed that secreted Bar1 protease might help a cell identify the fittest mating partner by sharpening the pheromone concentration gradient. This model involved about 200,000 protein molecules, about 7000 cubic microns of volume, and about 75 minutes of simulated time; it took about 10 hours to run. Over the next several years, as faster computers become available, Smoldyn will allow researchers to model and explore systems the size of entire bacterial and smaller eukaryotic cells

Efficient Reactive Brownian Dynamics

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and disassociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion, and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as Reaction-Diffusion Master Equation (RDME) algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction- and diffusion-limited irreversible association in three dimensions. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. We find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.Comment: To appear in J. Chem. Phy

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

Modeling and identification of a gene regulatory network programming erythropoiesis (1)

The development of mature blood cells of distinct lineages from the hematopoietic stem cells (hematopoiesis) involves a progressive restriction of differentiation potential and the establishment of lineage-specific gene expression profiles. The establishment of these profiles relies on lineage-specific transcription factors to modulate the expression of their target genes. This work is embedded in a wider ErasmusMC/CWI collaboration that develops the informatics and mathematics to underpin studies on gene expression regulation by mapping and analyzing the regulatory pathways and networks of transcription factors that control cellular functions (so called 'Gene Regulatory Networks' or 'GRNs'). This project is concerned with the mathematical part and concentrates on a GRN central to erythropoiesis. Among the many housekeeping and tissue-specific genes involved in the differentiation and the commitment of hematopoietic stem cells to erythrocytes (erythropoiesis), we focus on a small pool of genes (Gata-1, Gata-2, Pu.1, EKLF, FOG-1, alpha/beta-globin) known to be critically involved in an intricate but well-less investigated regulatory circuit. Based on the regulatory interactions in the GRN we have developed models in the form of a system to account for the dynamics of gene expression and regulation involved in this process. Because of the lack of information about a significant number of model parameters, our focus is on system identification. In this first report some preliminary results are presented based on synthetic data. However, time series of the levels of all relevant mRNA’s are available from micro-array analysis of G1E cells, a murine cell line which recapitulates erythropoiesis. In the follow-up report a detailed account will be given of the parameter estimation and identifiability analysis with respect to these data. This will eventually allow for a thorough evaluation of the role of various characterized as well as hypothetical regulatory mechanisms. In depth characterization of the necessary expression patterns and gene regulatory interactions responsible for the the set of commitments all along the erythroid lineage is essential to gain fundamental insight into the behaviour of these complex networks and to design further experiments. Ultimately, this may lead to ways to rescue erythroid differentiation in several anemic diseases

Simulation methods for spatiotemporal models of biochemical signaling networks

Cells use signaling networks consisting of multiple interacting proteins to respond to changes in their environment. In many situations, such as chemotaxis, spatial and temporal information must be transmitted through a signaling network. Recent computational studies have emphasized the importance of cellular geometry in signal transduction, but have been limited in their ability to accurately represent complex cell morphologies. We present a finite volume method that addresses this problem. Our method uses Cartesian cut cells in a differential algebraic formulation to handle the complex boundary dynamics encountered in biological systems. The method is second order in space and time. Several models of signaling systems are simulated in realistic cell morphologies obtained from live cell images. We then examine the effects of geometry on signal transduction. External signals can trigger cells to polarize and move in a specific direction. During migration, spatially localized activity of proteins is maintained. To investigate the effects of morphological changes on intracellular signaling, we present a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods to simulate the resulting advection-reaction-diffusion equation. We then show that shape deformations drive a Turing-type system into an unstable regime. The method is also applied to a model of a signaling network in a migrating fibroblast. Determining the signaling mechanisms used by membrane proteins that interact with the cytoskeleton is important for understanding phenomena such as T-cell activation and viral infection. To investigate these interactions, recent experiments have tracked the movements of single lipids and glycosyl-phosphatidylinositol (GPI) anchored protein clusters tagged with 40 nm gold particles. These experiments reveal regions of transient confinement and transient anchorage of the particles. The distribution of transient anchorage release times exhibits a long tail. We developed a stochastic model of the system to explain the transient anchorage release times and the underlying biochemical reaction system

The Role of Heterogeneity During Development and Stem Cell Differentiation

Heterogeneity is an integral property of many biological responses from molecular scales to members of a population of one species. While several recent studies have demonstrated the extent of the underlying heterogeneity on different scales, its origin, regulation, and consequences have not been thoroughly understood. In this dissertation, first we draw a general picture of how heterogeneity accompanies most biological responses from molecular to tissue scale, then we uncover the factors that can cause or contribute to non-uniformity. We explore the regulation of variation of biological systems as well as its consequences and illustrate the pivotal role that molecular, cellular and tissue heterogeneity plays in survival of an organism. First, we seek to elucidate the role of macromolecular crowding in transcription and translation. It is well known that stochasticity in gene expression can lead to differential gene expression and heterogeneity in a cell population. Recent experimental observations by Tan et al. (Nature nanotechnology. 2013 Aug;8(8):602) have improved our understanding of the functional role of macromolecular crowding. It can be inferred from their observations that macromolecular crowding can lead to robustness in gene expression, resulting in a more homogeneous cell population. We introduce a spatial stochastic model to provide insight into this process. Our results show that macromolecular crowding reduces noise (as measured by the kurtosis of the mRNA distribution) in a cell population by limiting the diffusion of transcription factors (i.e. removing the unstable intermediate states), and that crowding by large molecules reduces noise more efficiently than crowding by small molecules. Finally, our simulation results provide evidence that the local variation in chromatin density as well as the total volume exclusion of the chromatin in the nucleus can induce a homogenous cell population. Next we incorporate three-dimensional (3D) conformation of chromosome (Hi-C) and single-cell RNA sequencing data together with discrete stochastic simulation, to explore the role of chromatin reorganization in determining gene expression heterogeneity during development. While previous research has emphasized the importance of chromatin architecture on activation and suppression of certain regulatory genes and gene networks, our study demonstrates how chromatin remodeling can dictate gene expression distribution by folding into distinct topological domains. We hypothesize that the local DNA density during differentiation accentuates transcriptional bursting due to the crowding effect of chromatin. This phenomenon yields a heterogeneous cell population, thereby increasing the potential of differentiation of the stem cells. Finally, we depict the interplay between microRNAs and mRNAs and how this network can regulate human fetal brain development. microRNAs (miRNAs) regulate many cellular events during brain development by interacting with hundreds of mRNA transcripts. However, miRNAs operate non-uniformly upon the transcriptional profile with an as yet unknown logic. Shortcomings in defining miRNA-mRNA networks are limited knowledge of in vivo miRNA targets, and their abundance in single cells. By combining multiple complementary approaches: AGO2-HITS-CLIP, single-cell profiling, and innovative computational analyses using bipartite and co-expression networks, we show that miRNA- mRNA interactions operate as functional modules that often correspond to cell-type identities and undergo dynamic transitions during brain development. These networks are highly dynamic during development and over the course of evolution. One such interaction is between radial glia-enriched ORC4 and miR-2115, a great ape specific miRNA, which appears to control radial glia proliferation rates during human brain development