(650g) Novel Statechart and Control Theory Based Approaches for Gene Network Modeling

Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells, via the use of a wide spectrum of theoretical and experimental techniques [1]. One of the main thrusts of systems biology is the study of gene networks [2], via top-down and bottom-up approaches [3]. A top-down approach aims at unraveling the complexity of network dynamics without or with little prior knowledge of the network components and the relationships among them [4]. On the other hand, in a bottom-up approach, the dynamics are modeled using selected components and small-scale topologies [5]. The bottom-up approach is closely related to synthetic biology, which focuses on constructing novel, artificial biological networks from modular components. The behavior of gene networks is inherently stochastic [6,7] which renders any modeling effort nontrivial. Furthermore, as the size of a network increases, it becomes prohibitively difficult to predict its dynamic behavior. Another characteristic feature is the existence of nonlinearities in biological networks, which further complicates any modeling approach. Towards analyzing the dynamic behavior of gene networks, a range of mathematical and computational modeling methods have been developed, including Boolean networks, Petri nets, neural networks, ordinary differential equations, and stochastic simulation algorithms [8-9]. These approaches can be further organized into two larger categories: logical and continuous models. In this work, we demonstrate that well-established engineering methods such as statecharts and linear control theory tools can be utilized to model and analyze the dynamics of gene networks [10,11]. Sequential logic-based models are often represented as finite state machines and state diagrams. Nevertheless, these methods are less efficient for large and complex systems, because determining and managing the states and transitions among them can be overwhelming, due to their flat, unstratified structure. We provide a solution to this issue using statecharts. Furthermore, we show that linear control theory, and in particular transfer function (frequency domain) and linear state-space (time domain) methods, can be extremely useful for systems and synthetic biologists towards unraveling the dynamic properties of gene networks. We provide examples of the application of statecharts and linear control theory for the analysis of gene networks and we compare out results to published experimental systems. We illustrate that the use of linear state-space approach enables us to utilize a spectrum of tools available (e.g. Kalman filter) for optimal/robust estimation/control for gene network modeling.

References:

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[11] Shin, Y.J., Bleris, L. G. (2010) Linear Control Theory for Gene Network Modeling. Under Review