Survival and proliferation of immature B lymphocytes requires expression and tonic signaling of the pre-B cell receptor (pre-BCR). This low level, ligand-independent signaling is likely achieved through frequent, but short-lived, homo interactions. Tonic signaling is also central in the pathology of precursor B acute lymphoblastic leukemia (B-ALL). In order to understand how repeated, transient events can lead to sustained signaling and to assess the impact of receptor accumulation induced by the membrane landscape, we developed a spatial stochastic model of receptor aggregation and downstream signaling events. Our rule- and agent-based model builds on previous mature BCR signaling models and incorporates novel parameters derived from single particle tracking of pre-BCR on surfaces of two different B-ALL cell lines, 697 and Nalm6. Live cell tracking of receptors on the two cell lines revealed characteristic differences in their dimer dissociation rates and diffusion coefficients. We report here that these differences affect pre-BCR aggregation and consequent signal initiation events. Receptors on Nalm6 cells, which have a lower off-rate and lower diffusion coefficient, more frequently form higher order oligomers than pre-BCR on 697 cells, resulting in higher levels of downstream phosphorylation in the Nalm6 cell line.

True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady-state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here, we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher-dimensional space. We show that the linearized version of the steady-state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1.

The spatio-temporal landscape of the plasma membrane regulates activation and signal transduction of membrane bound receptors by restricting their two-dimensional mobility and by inducing receptor clustering. This regulation also extends to complex formation between receptors and adaptor proteins, which are the intermediate signaling molecules involved in cellular signaling that relay the received cues from cell surface to cytoplasm and eventually to the nucleus. Although their investigation poses challenging technical difficulties, there is a crucial need to understand the impact of the receptor diffusivity, clustering, and spatial heterogeneity, and of receptor-adaptor protein complex formation on the cellular signal transduction patterns. Building upon our earlier studies, we have developed an adaptive coarse-grained Monte Carlo method that can be used to investigate the role of diffusion, clustering and membrane corralling on receptor association and receptor-adaptor protein complex formation dynamics in three dimensions. The new Monte Carlo lattice based approach allowed us to introduce spatial resolution on the 2-D plasma membrane and to model the cytoplasm in three-dimensions. Being a multi-resolution approach, our new method makes it possible to represent various parts of the cellular system at different levels of detail and enabled us to utilize the locally homogeneous assumption when justified (e.g., cytoplasmic region away from the cell membrane) and avoid its use when high spatial resolution is needed (e.g., cell membrane and cytoplasmic region near the membrane) while keeping the required computational complexity manageable. Our results have shown that diffusion has a significant impact on receptor-receptor dimerization and receptor-adaptor protein complex formation kinetics. We have observed an "adaptor protein hopping" mechanism where the receptor binding proteins may hop between receptors to form short-lived transient complexes. This increased residence time of the adaptor proteins near cell membrane and their ability to frequently change signaling partners may explain the increase in signaling efficiency when receptors are clustered. We also hypothesize that the adaptor protein hopping mechanism can cause concurrent or sequential activation of multiple signaling pathways, thus leading to crosstalk between diverse biological functions.

UNLABELLED: Developing a quantitative understanding of intracellular networks requires simulations and computational analyses. However, traditional differential equation modeling tools are often inadequate due to the stochasticity of intracellular reaction networks that can potentially influence the phenotypic characteristics. Unfortunately, stochastic simulations are computationally too intense for most biological systems. Herein, we have utilized the recently developed binomial tau-leap method to carry out stochastic simulations of the epidermal growth factor receptor induced mitogen activated protein kinase cascade. Results indicate that the binomial tau-leap method is computationally 100-1000 times more efficient than the exact stochastic simulation algorithm of Gillespie. Furthermore, the binomial tau-leap method avoids negative populations and accurately captures the species populations along with their fluctuations despite the large difference in their size. AVAILABILITY: http://www.dion.che.udel.edu/multiscale/Introduction.html. Fortran 90 code available for academic use by email. SUPPLEMENTARY INFORMATION: Details about the binomial tau-leap algorithm, software and a manual are available at the above website.

Abstract Summary: We have developed a Mathematica®application package to perform dynamic simulations of the red blood cell (RBC) metabolic network. The package relies on, and integrates, many years of mathematical modeling and biochemical work on red blood cell metabolism. The extensive data regarding the red blood cell metabolic network and the previous kinetic analysis of all the individual components makes the human RBC an ideal ‘model’ system for mathematical metabolic models. The Mathematica package can be used to understand the dynamics and regulatory characteristics of the red blood cell. Availability: The Mathematica package and an example file can be downloaded from http://gcrg.ucsd.edu

BACKGROUND: Genome sequencing and bioinformatics are producing detailed lists of the molecular components contained in many prokaryotic organisms. From this 'parts catalogue' of a microbial cell, in silico representations of integrated metabolic functions can be constructed and analyzed using flux balance analysis (FBA). FBA is particularly well-suited to study metabolic networks based on genomic, biochemical, and strain specific information. RESULTS: Herein, we have utilized FBA to interpret and analyze the metabolic capabilities of Escherichia coli. We have computationally mapped the metabolic capabilities of E. coli using FBA and examined the optimal utilization of the E. coli metabolic pathways as a function of environmental variables. We have used an in silico analysis to identify seven gene products of central metabolism (glycolysis, pentose phosphate pathway, TCA cycle, electron transport system) essential for aerobic growth of E. coli on glucose minimal media, and 15 gene products essential for anaerobic growth on glucose minimal media. The in silico tpi-, zwf, and pta- mutant strains were examined in more detail by mapping the capabilities of these in silico isogenic strains. CONCLUSIONS: We found that computational models of E. coli metabolism based on physicochemical constraints can be used to interpret mutant behavior. These in silica results lead to a further understanding of the complex genotype-phenotype relation.