Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Biological diversity of prokaryotic type IV secretion systems.

Type IV secretion systems (T4SS) translocate DNA and protein substrates across prokaryotic cell envelopes generally by a mechanism requiring direct contact with a target cell. Three types of T4SS have been described: (i) conjugation systems, operationally defined as machines that translocate DNA substrates intercellularly by a contact-dependent process; (ii) effector translocator systems, functioning to deliver proteins or other macromolecules to eukaryotic target cells; and (iii) DNA release/uptake systems, which translocate DNA to or from the extracellular milieu. Studies of a few paradigmatic systems, notably the conjugation systems of plasmids F, R388, RP4, and pKM101 and the Agrobacterium tumefaciens VirB/VirD4 system, have supplied important insights into the structure, function, and mechanism of action of type IV secretion machines. Information on these systems is updated, with emphasis on recent exciting structural advances. An underappreciated feature of T4SS, most notably of the conjugation subfamily, is that they are widely distributed among many species of gram-negative and -positive bacteria, wall-less bacteria, and the Archaea. Conjugation-mediated lateral gene transfer has shaped the genomes of most if not all prokaryotes over evolutionary time and also contributed in the short term to the dissemination of antibiotic resistance and other virulence traits among medically important pathogens. How have these machines adapted to function across envelopes of distantly related microorganisms? A survey of T4SS functioning in phylogenetically diverse species highlights the biological complexity of these translocation systems and identifies common mechanistic themes as well as novel adaptations for specialized purposes relating to the modulation of the donor-target cell interaction.

Biological diversity of prokaryotic type IV secretion systems.

Type IV secretion systems (T4SS) translocate DNA and protein substrates across prokaryotic cell envelopes generally by a mechanism requiring direct contact with a target cell. Three types of T4SS have been described: (i) conjugation systems, operationally defined as machines that translocate DNA substrates intercellularly by a contact-dependent process; (ii) effector translocator systems, functioning to deliver proteins or other macromolecules to eukaryotic target cells; and (iii) DNA release/uptake systems, which translocate DNA to or from the extracellular milieu. Studies of a few paradigmatic systems, notably the conjugation systems of plasmids F, R388, RP4, and pKM101 and the Agrobacterium tumefaciens VirB/VirD4 system, have supplied important insights into the structure, function, and mechanism of action of type IV secretion machines. Information on these systems is updated, with emphasis on recent exciting structural advances. An underappreciated feature of T4SS, most notably of the conjugation subfamily, is that they are widely distributed among many species of gram-negative and -positive bacteria, wall-less bacteria, and the Archaea. Conjugation-mediated lateral gene transfer has shaped the genomes of most if not all prokaryotes over evolutionary time and also contributed in the short term to the dissemination of antibiotic resistance and other virulence traits among medically important pathogens. How have these machines adapted to function across envelopes of distantly related microorganisms? A survey of T4SS functioning in phylogenetically diverse species highlights the biological complexity of these translocation systems and identifies common mechanistic themes as well as novel adaptations for specialized purposes relating to the modulation of the donor-target cell interaction.

High-resolution microarray analysis of chromosome 20q in human colon cancer metastasis model systems

Amplification of human chromosome 20q DNA is the most frequently occurring chromosomal abnormality detected in sporadic colorectal carcinomas and shows significant correlation with liver metastases. Through comprehensive high-resolution microarray comparative genomic hybridization and microarray gene expression profiling, we have characterized chromosome 20q amplicon genes associated with human colorectal cancer metastasis in two in vitro metastasis model systems. The results revealed increasing complexity of the 20q genomic profile from the primary tumor-derived cell lines to the lymph node and liver metastasis derived cell lines. Expression analysis of chromosome 20q revealed a subset of over expressed genes residing within the regions of genomic copy number gain in all the tumor cell lines, suggesting these are Chromosome 20q copy number responsive genes. Bases on their preferential expression levels in the model system cell lines and known biological function, four of the over expressed genes mapping to the common intervals of genomic copy gain were considered the most promising candidate colorectal metastasis-associated genes. Validation of genomic copy number and expression array data was carried out on these genes, with one gene, DNMT3B, standing out as expressed at a relatively higher levels in the metastasis-derived cell lines compared with their primary-derived counterparts in both the models systems analyzed. The data provide evidence for the role of chromosome 20q genes with low copy gain and elevated expression in the clonal evolution of metastatic cells and suggests that such genes may serve as early biomarkers of metastatic potential. The data also support the utility of the combined microarray comparative genomic hybridization and expression array analysis for identifying copy number responsive genes in areas of low DNA copy gain in cancer cells. ^