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.

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.

Spatial and temporal aspects of synaptic plasticity

The notion that changes in synaptic efficacy underlie learning and memory processes is now widely accepted even if definitive proof of the synaptic plasticity and memory hypothesis is still lacking. When learning occurs, patterns of neural activity representing the occurrence of events cause changes in the strength of synaptic connections within the brain. Reactivation of these altered connections constitutes the experience of memory for these events and for other events with which they may be associated. These statements summarize a long-standing theory of memory formation that we refer to as the synaptic plasticity and memory hypothesis. Since activity-dependent synaptic plasticity is induced at appropriate synapses during memory formation, and is both necessary and sufficient for the information storage, we can speculate that a methodological study of the synapse will help us understand the mechanism of learning. Random events underlie a wide range of biological processes as diverse as genetic drift and molecular diffusion, regulation of gene expression and neural network function. Additionally spatial variability may be important especially in systems with nonlinear behavior. Since synapse is a complex biological system we expect that stochasticity as well as spatial gradients of different enzymes may be significant for induction of plasticity. ^ In that study we address the question "how important spatial and temporal aspects of synaptic plasticity may be". We developed methods to justify our basic assumptions and examined the main sources of variability of calcium dynamics. Among them, a physiological method to estimate the number of postsynaptic receptors as well as a hybrid algorithm for simulating postsynaptic calcium dynamics. Additionally we studied how synaptic geometry may enhance any possible spatial gradient of calcium dynamics and how that spatial variability affect plasticity curves. Finally, we explored the potential of structural synaptic plasticity to provide a metaplasticity mechanism specific for the synapse. ^

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.

Development and Characterization of an in vitro Four-species Anaerobic Dental Biofilm Model

Dental caries is the most common chronic disease worldwide. It is characterized by the demineralization of tooth enamel caused by acid produced by cariogenic dental bacteria growing on tooth surfaces, termed bacterial biofilms. Cariogenesis is a complex biological process that is influence by multiple factors and is not attributed to a sole causative agent. Instead, caries is associated with multispecies microbial biofilm communities composed of some bacterial species that directly influence the development of a caries lesion and other species that are seemingly benign but must contribute to the community in an uncharacterized way. Clinical analysis of dental caries and its microbial populations is challenging due to many factors including low sensitivity of clinical measurement tools, variability in saliva chemistry, and variation in the microbiota. Our laboratory has developed an in vitro anaerobic biofilm model for dental carries to facilitate both clinical and basic research-based analyses of the multispecies dynamics and individual factors that contribute to cariogenicity. The rational for development of this system was to improve upon the current models that lack key elements. This model places an emphasis on physiological relevance and ease of maintenance and reproducibility. The uniqueness of the model is based on integrating four critical elements: 1) a biofilm community composed of four distinct and representative species typically associated with dental caries, 2) a semi-defined synthetic growth medium designed to mimic saliva, 3) physiologically relevant biofilm growth substrates, and 4) a novel biofilm reactor device designed to facilitate the maintenance and analysis. Specifically, human tooth sections or hydroxyapatite discs embedded into poly(methyl methacrylate) (PMMA) discs are incubated for an initial 24 hr in a static inverted removable substrate (SIRS) biofilm reactor at 37°C under anaerobic conditions in artificial saliva (CAMM) without sucrose in the presence of 1 X 106 cells/ml of each Actinomyces odontolyticus, Fusobacterium nucleatum, Streptococcus mutans, and Veillonella dispar. During days 2 and 3 the samples are maintained continually in CAMM with various exposures to 0.2% sucrose; all of the discs are transferred into fresh medium every 24 hr. To validate that this model is an appropriate in vitro representation of a caries-associated multispecies biofilm, research aims were designed to test the following overarching hypothesis: an in vitro anaerobic biofilm composed of four species (S. mutans, V. dispar, A. odontolyticus, and F. nucleatum) will form a stable biofilm with a community profile that changes in response to environmental conditions and exhibits a cariogenic potential. For these experiments the biofilms as described above were exposed on days 2 and 3 to either CAMM lacking sucrose (no sucrose), CAMM with 0.2% sucrose (constant sucrose), or were transferred twice a day for 1 hr each time into 0.2% sucrose (intermittent sucrose). Four types of analysis were performed: 1) fluorescence microscopy of biofilms stained with Syto 9 and hexidium idodine to determine the biofilm architecture, 2) quantitative PCR (qPCR) to determine the cell number of each species per cm2, 3) vertical scanning interferometry (VSI) to determine the cariogenic potential of the biofilms, and 4) tomographic pH imaging using radiometric fluorescence microscopy after exposure to pH sensitive nanoparticles to measure the micro-environmental pH. The qualitative and quantitative results reveal the expected dynamics of the community profile when exposed to different sucrose conditions and the cariogenic potential of this in vitro four-species anaerobic biofilm model, thus confirming its usefulness for future analysis of primary and secondary dental caries.

Isolation and characterization of cDNAs encoding novel homeoproteins from chondrocytes

Bone morphogenesis is a complex biological process. The multistep process of chondrogenesis is the most important aspect of endochondral bone formation. To study the mechanisms which control this multistep pathway of chondrogenesis during embryonic development, I started by isolating cDNAs encoding novel transcriptional factors from chondrocytes. Several such cDNAs encoding putative homeoproteins were identified from a rat chondrosarcoma cDNA preparation. I have been concentrating on characterizing two of these cDNAs. The deduced amino acid sequence of the first homeoprotein, Cart-1, contains a prd-type homeodomain. Northern hybridization and RNase protection analysis revealed that Cart-1 RNAs were present at high levels in a well differentiated rat chondrosarcoma tumor and in a cell line derived from this tumor. Cart-1 transcripts were also detected in primary chondrocytes, but not in numerous other cell types except very low levels in testis. In situ hybridization of rat embryos at different stages of development revealed relatively high levels of Cart-1 RNAs in prechondrocytic mesenchymal cells and in early chondrocytes of cartilage primordia. It is speculated that Cart-1 might play an important role in chondrogenesis. The second putative homeoprotein, rDlx, contains a Distal-less-like homeodomain. rDlx RNAs were also present at high levels in the rat chondrosarcoma tumor and in the cell line derived from this tumor. In situ hybridization of rat embryos revealed high levels of rDlx transcripts in the developing cartilages and perichondria of mature cartilages. rDlx transcripts were also detected in a number of nonchondrogenic tissues such as forebrain, otic vesicles, olfactory epithelia, apical ectodermal ridge (AER) of limb buds, the presumptive Auerbach ganglia of gastrointestinal tract. The unique expression pattern of rDlx suggests that it might play important roles in chondrogenesis and other aspects of embryogenesis. ^