An SQP method for general nonlinear programs using only equality constrained subproblems
Mathematical Programming: Series A and B
Quantifying Dynamic Stability of Genetic Memory Circuits
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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The development of gene-regulatory memory circuits provides key understandings of biological information storage and enables new biological applications. Computer models and simulations can provide quantitative analysis and prediction of the behaviors and functions of genetic networks, thereby providing valuable verification and design guidance. In this paper, we model the nonlinear dynamics associated with various chemical reactions in gene-regulatory memory networks using chemical reaction equations. These reaction equations are mapped into a set of electrical-equivalent models and the network is simulated by an extended SPICE-like circuit simulation environment. Furthermore, we address the practical difficulty in direct characterization of network model parameters by developing a simulation-driven Bayesian framework for parameter identification. To ensure the reliable identification of key system properties, we propose a two-step structure-preserving parameter identification approach. The first step infers bistability, the most critical characteristics of a memory device; and the second step is geared towards identifying dynamical properties of the network while maintaining the identified bistability. We demonstrate the proposed approaches through extensive simulations that well agree with established biological understandings and identified networks that recreate measured circuit responses in a statistical sense.