Abstract
Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem in contemporary systems biology. Conventional methods involve repeatedly solving the ODEs by numerical integration, which is computationally onerous and does not scale up to complex systems. Aimed at reducing the computational costs, new concepts based on gradient matching have recently been proposed in the computational statistics and machine learning literature. In a preliminary smoothing step, the time series data are interpolated; then, in a second step, the parameters of the ODEs are optimized, so as to minimize some metric measuring the difference between the slopes of the tangents to the interpolants, and the time derivatives from the ODEs. In this way, the ODEs never have to be solved explicitly. This review provides a concise methodological overview of the current state-of-the-art methods for gradient matching in ODEs, followed by an empirical comparative evaluation based on a set of widely used and representative benchmark data.
Highlights
The elucidation of the structure and dynamics of biopathways is a central objective of systems biology
We look at the methods of: Campbell and Steele (2012), who carry out parameter inference using adaptive gradient matching and Bsplines interpolation; González et al (2013), who implement a reproducing kernel Hilbert space (RKHS) and penalized maximum likelihood approach in a non-Bayesian fashion; Ramsay et al (2007), who optimize the gradient mismatch, interpolant, and ordinary differential equations (ODEs) parameters using a hierarchical regularization method and penalize the difference between the gradients using B-splines in a non-Bayesian approach; Dondelinger et al (2013), who use adaptive gradient matching with Gaussian processes, inferring the degree of mismatch between the gradients; and Macdonald and Husmeier (2015), who use adaptive gradient matching with Gaussian processes and temper the parameter that controls the degree of mismatch between the gradients
The penalty mismatch parameter γ is inferred rather than tempered
Summary
The elucidation of the structure and dynamics of biopathways is a central objective of systems biology. Depending on the species involved, g may define different types of regulatory interactions, e.g., mass action kinetics, Michaelis–Menten kinetics, allosteric Hill kinetics, etc All of these interactions depend on a vector of kinetic parameters, ρi. The explication of the biopathway dynamics requires the majority of kinetic parameters to be inferred from observed (typically noisy and sparse) time course concentration profiles. In principle, this can be accomplished with standard techniques from machine learning and statistical inference. This can be accomplished with standard techniques from machine learning and statistical inference These techniques are based on first quantifying the difference between predicted and measured time course profiles by some appropriate metric to obtain the likelihood of the data. The parameters are either optimized to maximize the likelihood (or a regularized version thereof), or sampled from a distribution based on the likelihood (the posterior distribution)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
