Ấn phẩm:
Modeling and Symbolic Analysis of Biological Protein Signaling Networks Using Hybrid Automata
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Recent advances in quantitative biology have created a tremendous opportunity to apply dynamical systems modeling to biological phenomena, and to validate these models using experimental data. Using simulation and analysis, there is immense scope to discover non-intuitive design principles behind biological processes, and successfully predict the effects of changing key variables. Systems biology, defined as the integration of mathematical analysis with experimental biology, has the potential to revolutionize the way biology is done.
Cellular protein signaling networks exhibit complex combinations of both discrete and continuous behaviors. The dynamics that govern the spatial and temporal in-crease or decrease of protein concentrations inside cells are continuous differential equations, while the activation or deactivation of these continuous dynamics are triggered by discrete switches that involve regulating species concentrations reaching given thresholds.
This thesis proposes a hybrid automata framework for modeling such processes; hybrid automata theory being a hierarchical mathematical system that uses differential equations to model continuous dynamics, and discrete event-driven switches to model the governing equations in different modes of operation. In particular, the thesis proposes hybrid models of two interesting intercellular signaling pathways active during embryonic development: the lateral inhibitory Delta-Notch pathway responsible for pattern formation in the embryonic skin of Xenopus laevis, and the Planar Cell Polarity (PCP) signaling pathway in Drosophila melanogaster wings. These models are validated against experimentally observed steady state protein concentration patterns.
A fundamental objective of this work is to analytically compute constraints on the kinetic parameters of the model, for particular biologically observed or interesting steady states to exist. The constraints are computed symbolically, i.e. without having to numerically instantiate the parameters. This is a great advantage in the context of biological processes, where exact numerical parameters cannot often be identified from experimental data, but a range of values, or relative values for the parameters can be obtained. The particular structure of the hybrid automata models developed in this work make symbolic constraint generation computationally tractable.
Another key objective is the computation of initial conditions, or initial protein concentrations, that converge to a particular steady state. The initial conditions can be interpreted as initial biases in the distribution of signaling species that lead to a biologically interesting steady state. This is posed as a backward reachable set computation problem. An abstraction procedure is presented that converts the hybrid automaton into a discrete transition system using symbolic solutions to the differential equations and Lie derivatives to compute transitions between discrete states. The backward reachability problem is then computed on the discrete abstraction, which makes the analysis tractable for large state spaces. The reachability computation is implemented using MATLAB and the quantifier elimination tool QEPCAD and is demonstrated for multiple cell Delta-Notch signaling networks with up to eighteen continuous variables.
Since the computed reachable sets are large, it is difficult to directly interpret them in a biologically meaningful way. To solve this problem, a query algorithm is developed and presented that can be used to test whether a particular protein distribution is guaranteed to converge to a steady state of interest. The use of the query algorithm is demonstrated for the Delta-Notch hybrid model. The thesis concludes with a description of the implementation of the analysis tools on a publicly available systems biology software platform known as Bio-SPICE. A further example, lactose metabolism inside a cell, is described as an illustration of the methods developed in this work; and reachable sets are computed for this model using the tools integrated with Bio-SPICE.
Tác giả
Ghosh, Ronojoy
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Nơi xuất bản
Nhà xuất bản
Stanford University
Năm xuất bản
2005
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Sinh học tính toán , Mablab (Phần mềm máy tính) -- Ứng dụng trong sinh học