A Hybrid Parameter Estimation Algorithm for S-System Model of Gene Regulatory Networks

The S-system model is one of the nonlinear differential equation models of gene regulatory networks, and it can describe various dynamics of the relationships among genes. If we successfully infer rigorous S-system model parameters that describe a target gene regulatory network, we can simulate gene expressions mathematically. However, the problem of finding an optimal S-system model parameter is too complex to be solved analytically. Thus, some heuristic search methods that offer approximate solutions are needed for reducing the computational time. In previous studies, several heuristic search methods such as Genetic Algorithms (GAs) have been applied to the parameter search of the S-system model. However, they have not achieved enough estimation accuracy. One of the conceivable reasons is that the mechanisms to escape local optima. We applied an Immune Algorithm (IA) to search for the S-system parameters. IA is also a heuristic search method, which is inspired by the biological mechanism of acquired immunity. Compared to GA, IA is able to search large solution space, thereby avoiding local optima, and have multiple candidates of the solutions. These features work well for searching the S-system model. Actually, our algorithm showed higher performance than GA for both simulation and real data analyses.

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Model-Checking Based Approaches to Parameter Estimation of Gene Regulatory Networks

2014 19th International Conference on Engineering of Complex Computer Systems ◽

10.1109/iceccs.2014.38 ◽

2014 ◽

Author(s):

Andrzej Mizera ◽

Jun Pang ◽

Qixia Yuan

Keyword(s):

Parameter Estimation ◽

Model Checking ◽

Gene Regulatory Networks ◽

Regulatory Networks ◽

Gene Regulatory

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Accuracy of parameter estimation for auto-regulatory transcriptional feedback loops from noisy data

Journal of The Royal Society Interface ◽

10.1098/rsif.2018.0967 ◽

2019 ◽

Vol 16 (153) ◽

pp. 20180967 ◽

Cited By ~ 14

Author(s):

Zhixing Cao ◽

Ramon Grima

Keyword(s):

Parameter Estimation ◽

Gene Regulatory Networks ◽

Regulatory Networks ◽

Moment Closure ◽

Large Protein ◽

Likelihood Approximation ◽

Gene Regulatory ◽

Inference Methods ◽

Closure Method ◽

Transcriptional Feedback

Bayesian and non-Bayesian moment-based inference methods are commonly used to estimate the parameters defining stochastic models of gene regulatory networks from noisy single cell or population snapshot data. However, a systematic investigation of the accuracy of the predictions of these methods remains missing. Here, we present the results of such a study using synthetic noisy data of a negative auto-regulatory transcriptional feedback loop, one of the most common building blocks of complex gene regulatory networks. We study the error in parameter estimation as a function of (i) number of cells in each sample; (ii) the number of time points; (iii) the highest-order moment of protein fluctuations used for inference; (iv) the moment-closure method used for likelihood approximation. We find that for sample sizes typical of flow cytometry experiments, parameter estimation by maximizing the likelihood is as accurate as using Bayesian methods but with a much reduced computational time. We also show that the choice of moment-closure method is the crucial factor determining the maximum achievable accuracy of moment-based inference methods. Common likelihood approximation methods based on the linear noise approximation or the zero cumulants closure perform poorly for feedback loops with large protein–DNA binding rates or large protein bursts; this is exacerbated for highly heterogeneous cell populations. By contrast, approximating the likelihood using the linear-mapping approximation or conditional derivative matching leads to highly accurate parameter estimates for a wide range of conditions.

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