title: Estimating cellular parameters through optimization procedures: elementary principles and applications.
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.
authors.affiliation: Cell Architecture Laboratory, National Institute of Genetics Mishima, Japan ; Department of Genetics, School of Life Science, SOKENDAI (The Graduate University for Advanced Studies) Mishima, Japan ; Transdisciplinary Research Integration Center and Data Centric Science Research Commons, Research Organization of Information and Systems Tokyo, Japan.
authors.forename: Akatsuki
authors.initials: A
authors.lastname: Kimura
authors.affiliation: Quantitative Life Sciences Unit, The Abdus Salam International Centre for Theoretical Physics Trieste, Italy.
authors.forename: Antonio
authors.initials: A
authors.lastname: Celani
authors.affiliation: Transdisciplinary Research Integration Center and Data Centric Science Research Commons, Research Organization of Information and Systems Tokyo, Japan ; Research and Development Center for Data Assimilation, The Institute of Statistical Mathematics Tokyo, Japan ; Research Center for Large-Scale Earthquake, Tsunami and Disaster, Earthquake Research Institute, The University of Tokyo Tokyo, Japan.
authors.forename: Hiromichi
authors.initials: H
authors.lastname: Nagao
authors.affiliation: Department of Biochemistry and Molecular Biology, Colorado State University Fort Collins, CO, USA.
authors.forename: Timothy
authors.initials: T
authors.lastname: Stasevich
authors.affiliation: Department of Mathematical Sciences Based on Modeling and Analysis, School of Interdisciplinary Mathematical Sciences, Meiji University Tokyo, Japan.
authors.forename: Kazuyuki
authors.initials: K
authors.lastname: Nakamura
keywords: likelihood; model selection; parameter optimization; probability density function; quantitative modeling