Mathematical modeling of the formation of apoptosome in intrinsic pathway of apoptosis.

Caspase-9 is the protease that mediates the intrinsic pathway of apoptosis, a type of cell death. Activation of caspase-9 is a multi-step process that requires dATP or ATP and involves at least two proteins, cytochrome c and Apaf-1. In this study, we mathematically model caspase-9 activation by using a system of ordinary differential equations (an ODE model) generated by a systems biology tool Simpathica-a simulation and reasoning system, developed to study biological pathways. A rudimentary version of "model checking" based on comparing simulation data with that obtained from a recombinant system of caspase-9 activation, provided several new insights into regulation of this protease. The model predicts that the activation begins with binding of dATP to Apaf-1, which initiates the interaction between Apaf-1 and cytochrome c, thus forming a complex that oligomerizes into an active caspase-9 holoenzyme via a linear binding model with cooperative interaction rather than through network formation.

Quantitative analysis of germline mitosis in adult C. elegans.

Certain aspects of the distal gonad of C. elegans are comparable to niche/stem cell systems in other organisms. The distal tip cell (DTC) caps a blind-ended tube; only the distal germ cells maintain proliferation in response to signaling from the DTC via the GLP-1/Notch signaling pathway in the germ line. Fruitful comparison between this system and other stem cell systems is limited by a lack of basic information regarding germ cell division behavior in C. elegans. Here, we explore the spatial pattern of cell division frequency in the adult C. elegans germ line relative to distance from the distal tip. We mapped the positions of actively dividing germline nuclei in over 600 fixed gonad preparations including the wild type and a gain-of-function ligand-responsive GLP-1 receptor mutant with an extended mitotic zone. One particularly surprising observation from these data is that the frequency of cell divisions is lower in distal-most cells-cells that directly contact the distal tip cell body-relative to cells further proximal, a difference that persists in the gain-of-function GLP-1 mutant. These results suggest that cell division frequency in the distal-most cells may be suppressed or otherwise controlled in a complex manner. Further, our data suggest that the presence of an active cell division influences the probability of observing simultaneous cell divisions in the same gonad arm, and that simultaneous divisions tend to cluster spatially. We speculate that this system behaves similarly to niche/stem cell/transit amplifying cell systems in other organisms.

A sense of life: computational and experimental investigations with models of biochemical and evolutionary processes.

We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure, and computational environment for understanding, experimenting with, manipulating, and modifying a diverse set of fundamental biological processes at multiple scales and spatio-temporal modes. The novelty of our research is based on an approach that (i) requires coevolution of experimental science and theoretical techniques and (ii) exploits a certain universality in biology guided by a parsimonious model of evolutionary mechanisms operating at the genomic level and manifesting at the proteomic, transcriptomic, phylogenic, and other higher levels. Our current program in "systems biology" endeavors to marry large-scale biological experiments with the tools to ponder and reason about large, complex, and subtle natural systems. To achieve this ambitious goal, ideas and concepts are combined from many different fields: biological experimentation, applied mathematical modeling, computational reasoning schemes, and large-scale numerical and symbolic simulations. From a biological viewpoint, the basic issues are many: (i) understanding common and shared structural motifs among biological processes; (ii) modeling biological noise due to interactions among a small number of key molecules or loss of synchrony; (iii) explaining the robustness of these systems in spite of such noise; and (iv) cataloging multistatic behavior and adaptation exhibited by many biological processes.

Model building and model checking for biochemical processes.

A central claim of computational systems biology is that, by drawing on mathematical approaches developed in the context of dynamic systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis, and reasoning tools for working biologists to decipher existing data, devise new experiments, and ultimately to understand functional properties of genomes, proteomes, cells, organs, and organisms. In this article, a novel computational tool is described that achieves many of the goals of this new discipline. The novelty of this system involves an automaton-based semantics of the temporal evolution of complex biochemical reactions starting from the representation given as a set of differential equations. The related tools also provide ability to qualitatively reason about the systems using a propositional temporal logic that can express an ordered sequence of events succinctly and unambiguously. The implementation of mathematical and computational models in the Simpathica and XSSYS systems is described briefly. Several example applications of these systems to cellular and biochemical processes are presented: the two most prominent are Leibler et al.'s repressilator (an artificial synthesized oscillatory network), and Curto- Voit-Sorribas-Cascante's purine metabolism reaction model.