Abstract
Construction of quantitative models is a primary goal of quantitative biology, which aims to understand cellular and organismal phenomena in a quantitative manner. In this article, we introduce optimization procedures to search for parameters in a quantitative model that can reproduce experimental data. The aim of optimization is to minimize the sum of squared errors (SSE) in a prediction or to maximize likelihood. A (local) maximum of likelihood or (local) minimum of the SSE can efficiently be identified using gradient approaches. Addition of a stochastic process enables us to identify the global maximum/minimum without becoming trapped in local maxima/minima. Sampling approaches take advantage of increasing computational power to test numerous sets of parameters in order to determine the optimum set. By combining Bayesian inference with gradient or sampling approaches, we can estimate both the optimum parameters and the form of the likelihood function related to the parameters. Finally, we introduce four examples of research that utilize parameter optimization to obtain biological insights from quantified data: transcriptional regulation, bacterial chemotaxis, morphogenesis, and cell cycle regulation. With practical knowledge of parameter optimization, cell and developmental biologists can develop realistic models that reproduce their observations and thus, obtain mechanistic insights into phenomena of interest.
Highlights
REGRESSION ANALYSES FOR IDENTIFYING PARAMETER VALUES BY APPLYING EXPERIMENTAL DATA TO A QUANTITATIVE MODEL The purpose of quantitative biology is to achieve biological discovery through quantitative data analyses and modeling
A quantitative model consists of a set of rules, often expressed by mathematical formulas, which involve a set of parameters governing variables for the rules and initial/boundary conditions
In Section Model selection Using Likelihood, we introduce information criteria, which enable us to solve this problem when used in combination with likelihood
Summary
REGRESSION ANALYSES FOR IDENTIFYING PARAMETER VALUES BY APPLYING EXPERIMENTAL DATA TO A QUANTITATIVE MODEL The purpose of quantitative biology is to achieve biological discovery through quantitative data analyses and modeling. The simplest way to validate a given quantitative model is to test whether an appropriate set of rules and parameters reproduces experimental observations. If it does this successfully, it can be concluded that the model (i.e., the rules and parameter values) is “sufficient” to explain the observations. If the rules adequately represent the true mechanisms underlying the biological process, the identified parameters should reflect the quantitative properties of that process In this way, we can argue that the model (i.e., the rules and the “estimated”parameter values) is sufficient to explain the observations. In Section Model selection Using Likelihood, we introduce information criteria, which enable us to solve this problem when used in combination with likelihood
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