The dynamic behavior of microbial communities can be described by Lotka-Volterra models, which involve highly nonlinear sets of differential and algebraic equations. Estimating parameters for such types of models is computationally challenging. In this work, we demonstrate that state-of-the-art nonlinear programming tools can tackle this class of parameter estimation models . In our framework, we use JuMP (a mathematical programming modeling language) to implement a discrete-time version of the microbial community model, which enables us to compute exact derivative information and to exploit algebraic sparsity. We solve the resulting nonlinear programming problem by using interior-point solvers. We combine these computational capabilities with real experimental data to estimate parameters for a microbial community model. The model under study involves 12 different species and we use over 100 experimental data sets to perform the estimation. The resulting estimation problems contain over 1,000,000 variables and constraints and can be solved in around 10 minutes by using IPOPT. We show that these times can be reduced further by using the parallel solver PIPS-NLP. These favorable solution times enable us to consider additional analysis tasks such as identification of the level sets of the parameter posterior distribution . The proposed computational framework can also be applied more broadly to high-dimensional and nonlinear biological systems models including signaling networks, metabolic pathways, and ecological systems.
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