Systems biology aims to develop mathematical models of biological systems by integrating experimental and theoretical techniques. During the last decade, many systems biological approaches that base on genome-wide data have been developed to unravel the complexity of gene regulation. This review deals with the reconstruction of gene regulatory networks (GRNs) from experimental data through computational methods. Standard GRN inference methods primarily use gene expression data derived from microarrays. However, the incorporation of additional information from heterogeneous data sources, e.g. genome sequence and protein-DNA interaction data, clearly supports the network inference process. This review focuses on promising modelling approaches that use such diverse types of molecular biological information. In particular, approaches are discussed that enable the modelling of the dynamics of gene regulatory systems. The review provides an overview of common modelling schemes and learning algorithms and outlines current challenges in GRN modelling.

Gene regulatory network inference: Data integration in dynamic models—A review

The lithium-ion battery is an ideal candidate for a wide variety of applications due to its high energy/power density and operating voltage. Some limitations of existing lithium-ion battery technology include underutilization, stress-induced material damage, capacity fade, and the potential for thermal runaway. This paper reviews efforts in the modeling and simulation of lithium-ion batteries and their use in the design of better batteries. Likely future directions in battery modeling and design including promising research opportunities are outlined.

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Modeling and Simulation of Lithium-Ion Batteries from a Systems Engineering Perspective

Lithium iron phosphate based battery: Assessment of the aging parameters and development of cycle life model

http://www.optimization-online.org/DB_FILE/2012/02/3378.pdf

Non-convex mixed-integer nonlinear programming: A survey

This manuscript introduces ANTIGONE, Algorithms for coNTinuous/Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework. ANTIGONE is the evolution of the Global Mixed-Integer Quadratic Optimizer, GloMIQO, to general nonconvex terms. The purpose of this paper is to show how the extensible structure of ANTIGONE realizes our previously-proposed mixed-integer quadratically-constrained quadratic program and mixed-integer signomial optimization computational frameworks. To demonstrate the capacity of ANTIGONE, this paper presents computational results on a test suite of $$2{,}571$$ 2 , 571 problems from standard libraries and the open literature; we compare ANTIGONE to other state-of-the-art global optimization solvers.

ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations

https://cse.sc.edu/~gatzke/publications/00pse3.pdf

Model based control of a four-tank system

A rigorous decomposition approach to solve separable mixed-integer nonlinear programs where the participating functions are nonconvex is presented. The proposed algorithms consist of solving an alternating sequence of Relaxed Master Problems (mixed-integer linear program) and two nonlinear programming problems (NLPs). A sequence of valid nondecreasing lower bounds and upper bounds is generated by the algorithms which converge in a finite number of iterations. A Primal Bounding Problem is introduced, which is a convex NLP solved at each iteration to derive valid outer approximations of the nonconvex functions in the continuous space. Two decomposition algorithms are presented in this work. On finite termination, the first yields the global solution to the original nonconvex MINLP and the second finds a rigorous bound to the global solution. Convergence and optimality properties, and refinement of the algorithms for efficient implementation are presented. Finally, numerical results are compared with currently available algorithms for example problems, illuminating the potential benefits of the proposed algorithm.

Outer approximation algorithms for separable nonconvex mixed-integer nonlinear programs

Analysis of capacity fade in a lithium ion battery

The problem of estimating the parameters of dynamic models of complex biological systems from time series data is becoming increasingly important. Particular consideration is given to metabolic systems that are formulated as Generalized Mass Action (GMA) models. The estimation problem is posed as a global optimization task, for which novel techniques can be applied to determine the best set of parameter values given the measured responses of the biological system. The challenge is that this task is nonconvex. Nonetheless, deterministic optimization techniques can be used to find a global solution that best reconciles the model parameters and measurements. Specifically, the paper employs branch-and-bound principles to identify the best set of model parameters from observed time course data and illustrates this method with an existing model of the fermentation pathway in Saccharomyces cerevisiae. This is a relatively simple yet representative system with five dependent states and a total of 19 unknown parameters of which the values are to be determined. The efficacy of the branch-and-reduce algorithm is illustrated by the S. cerevisiae example. The method described in this paper is likely to be widely applicable in the dynamic modeling of metabolic networks.

/pdf/identification-of-metabolic-system-parameters-using-global-2o2slj8p7z.pdf

Edward P. Gatzke

Papers

Model based control of a four-tank system

Outer approximation algorithms for separable nonconvex mixed-integer nonlinear programs

Analysis of capacity fade in a lithium ion battery

Identification of metabolic system parameters using global optimization methods

Determination of coalescence kernels for high-shear granulation using DEM simulations