Mathematical modeling and application of genetic algorithm to parameter estimation in signal transduction: Trafficking and promiscuous coupling of G-protein coupled receptors

Dynamic Optimization with Particle Swarms (DOPS): a meta-heuristic for parameter estimation in biochemical models

BACKGROUND

Mathematical modeling is a powerful tool to analyze, and ultimately design biochemical networks. However, the estimation of the parameters that appear in biochemical models is a significant challenge. Parameter estimation typically involves expensive function evaluations and noisy data, making it difficult to quickly obtain optimal solutions. Further, biochemical models often have many local extrema which further complicates parameter estimation. Toward these challenges, we developed Dynamic Optimization with Particle Swarms (DOPS), a novel hybrid meta-heuristic that combined multi-swarm particle swarm optimization with dynamically dimensioned search (DDS). DOPS uses a multi-swarm particle swarm optimization technique to generate candidate solution vectors, the best of which is then greedily updated using dynamically dimensioned search.

RESULTS

We tested DOPS using classic optimization test functions, biochemical benchmark problems and real-world biochemical models. We performed [Formula: see text] = 25 trials with [Formula: see text] = 4000 function evaluations per trial, and compared the performance of DOPS with other commonly used meta-heuristics such as differential evolution (DE), simulated annealing (SA) and dynamically dimensioned search (DDS). On average, DOPS outperformed other common meta-heuristics on the optimization test functions, benchmark problems and a real-world model of the human coagulation cascade.

CONCLUSIONS

DOPS is a promising meta-heuristic approach for the estimation of biochemical model parameters in relatively few function evaluations. DOPS source code is available for download under a MIT license at http://www.varnerlab.org .

A Six-Stage Workflow for Robust Application of Systems Pharmacology

Quantitative and systems pharmacology (QSP) is increasingly being applied in pharmaceutical research and development. One factor critical to the ultimate success of QSP is the establishment of commonly accepted language, technical criteria, and workflows. We propose an integrated workflow that bridges conceptual objectives with underlying technical detail to support the execution, communication, and evaluation of QSP projects.

Parameter estimation using meta-heuristics in systems biology: a comprehensive review

This paper gives a comprehensive review of the application of meta-heuristics to optimization problems in systems biology, mainly focussing on the parameter estimation problem (also called the inverse problem or model calibration). It is intended for either the system biologist who wishes to learn more about the various optimization techniques available and/or the meta-heuristic optimizer who is interested in applying such techniques to problems in systems biology. First, the parameter estimation problems emerging from different areas of systems biology are described from the point of view of machine learning. Brief descriptions of various meta-heuristics developed for these problems follow, along with outlines of their advantages and disadvantages. Several important issues in applying meta-heuristics to the systems biology modelling problem are addressed, including the reliability and identifiability of model parameters, optimal design of experiments, and so on. Finally, we highlight some possible future research directions in this field.

Identification of a model of non-esterified fatty acids dynamics through genetic algorithms: the case of women with a history of gestational diabetes

Elevation in non-esterified fatty acids (NEFA) has been shown to modulate insulin secretion and it is considered as a risk factor for the development of type 2 diabetes. Here we present a method that complements a mathematical model of NEFA kinetics with genetic algorithms for model identification. The complemented strategy allowed to assess parameters of NEFA kinetics and to get insight into their relationship with insulin during oral glucose tolerance tests in women with former gestational diabetes: (i) providing a reliable estimation of the model parameters, (ii) assuring the usability of the model, and (iii) promoting and facilitating its application in a clinical context.

Parameter inference and model selection in signaling pathway models

To support and guide an extensive experimental research into systems biology of signaling pathways, increasingly more mechanistic models are being developed with hopes of gaining further insight into biological processes. In order to analyze these models, computational and statistical techniques are needed to estimate the unknown kinetic parameters. This chapter reviews methods from frequentist and Bayesian statistics for estimation of parameters and for choosing which model is best for modeling the underlying system. Approximate Bayesian computation techniques are introduced and employed to explore different hypothesis about the JAK-STAT signaling pathway.

Autocatalytic loop, amplification and diffusion: a mathematical and computational model of cell polarization in neural chemotaxis

The chemotactic response of cells to graded fields of chemical cues is a complex process that requires the coordination of several intracellular activities. Fundamental steps to obtain a front vs. back differentiation in the cell are the localized distribution of internal molecules and the amplification of the external signal. The goal of this work is to develop a mathematical and computational model for the quantitative study of such phenomena in the context of axon chemotactic pathfinding in neural development. In order to perform turning decisions, axons develop front-back polarization in their distal structure, the growth cone. Starting from the recent experimental findings of the biased redistribution of receptors on the growth cone membrane, driven by the interaction with the cytoskeleton, we propose a model to investigate the significance of this process. Our main contribution is to quantitatively demonstrate that the autocatalytic loop involving receptors, cytoplasmic species and cytoskeleton is adequate to give rise to the chemotactic behavior of neural cells. We assess the fact that spatial bias in receptors is a precursory key event for chemotactic response, establishing the necessity of a tight link between upstream gradient sensing and downstream cytoskeleton dynamics. We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor. The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization. Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response.

Study on correlation of signal molecule genes and their receptor-associated genes with rat liver regeneration

To investigate the effect of signal molecules and their receptor-associated genes on rat liver regeneration (LR) at the transcriptional level, the associated genes were originally obtained by retrieving the databases and related scientific publications; their expression profiles in rat LR were then checked using the Rat Genome 230 2.0 microarray. The LR-associated genes were identified by comparing gene expression difference between partial hepatectomy groups and operation-control groups. A total of 454 genes were proved to be LR related. The genes associated with the seven kinds of signal molecules (steroid hormones, fatty acid derivatives, protein and polypeptide hormones, amino acids and their derivatives, choline, cytokines, and gas signal molecules) were detected to be enriched in a cluster characterized by upregulated expression in LR. The number of genes related to the seven kinds of signal molecules was, in sequence, 63, 27, 100, 102, 16, 166, and 18. The 1027 frequencies of upregulation and 823 frequencies of downregulation in total as well as 42 types of different expression patterns suggest the complex and diverse gene expression changes in LR. It is presumed that signal molecules played an important role in metabolism, inflammation, cell proliferation, growth and differentiation, etc., during rat LR.