Estimating kinetic mechanisms with prior knowledge II: Behavioral constraints and numerical tests

Abstract

In their preceding paper, Salari et al. describe a formalism that allows existing knowledge to be enforced into kinetic models. Here, Navarro et al. present a penalty-based optimization mechanism to incorporate arbitrary parameter relationships and constraints that quantify the behavior of the model.

Estimating kinetic mechanisms with prior knowledge I: Linear parameter constraints

“…In fact, the parameter-estimation procedure itself can be designed to enforce prior knowledge, by making it generate parameter values that are in agreement with a set of model constraints. We classify these model constraints in two categories: (1) parameter constraints, discussed in this study, and (2) behavioral constraints, discussed in the companion article ( Navarro et al, 2018 ). A parameter constraint is formulated as an explicit mathematical relationship that involves rate constants or other model parameters.…”

“…The mathematical and computational procedures discussed here for enforcing parameter constraints are limited to linear relationships. However, nonlinear relationships can be enforced using the mechanism developed for behavioral constraints, presented in the second part of this study ( Navarro et al, 2018 ). As illustrated in Fig.…”

“…Although tempting, using inequality relationships to enforce a range constraint on a model parameter is not possible, unfortunately, because it would result in two equality relationships that are redundant. However, this limitation can be overcome through the same mechanism that handles behavioral constraints ( Navarro et al, 2018 ). Furthermore, although inequality constraints add slack variables to the overall set of free parameters, the total number of equality and inequality constraints must still be strictly smaller than the number of model parameters K .…”

“…Any relationship between these parameters can now be enforced, as long as it is linear. Second, as described in the companion article ( Navarro et al, 2018 ), any other types of model constraints, such as range constraints, nonlinear parameter relationships, or model properties and behavior, are handled by applying a penalty to the cost function. Together, the reduction method and the penalty method can handle virtually any type of model constraint that is likely to be encountered in the field.…”

Four ways to fit an ion channel model

“…A tool by Teed and Silva (45) similarly implements a Method 2, but also varies model structure when searching. While some authors prefer manually adjusting model parameters, several optimisation algorithms have also been applied to Method 2, including simulated annealing (45), a Davidon-Fletcher-Powell optimiser (46), subspace trust region methods (40), and the Nelder-Mead downhill simplex method (40, 43).…”