Proteins as fuzzy controllers: Auto tuning a biological fuzzy inference system to predict protein dynamics in complex biological networks

Abstract

Biological systems such as mammalian cell cycle are complex systems consisting of a large number of molecular species interacting in ways that produce complex nonlinear systems dynamics. Discrete models such as Boolean models and continuous models such as Ordinary Differential Equations (ODEs) have been widely used to study these systems. Boolean models are simple and can capture qualitative systems behaviour, but they cannot capture the continuous trends of protein concentrations, while ODE models capture continuous trends but require kinetics parameters that are limited. Further, as systems get larger, complexity of these models becomes an issue for parameterization, analysis and interpretation. Also, molecular systems operate under the conditions of uncertainty and noise and our understanding of molecular processes in general is more at a qualitative level characterised by vagueness, imprecision and ambiguity. Hence, as more data are generated, there is a greater need for simpler data driven methods that can approximate continuous system behaviour while representing vagueness and ambiguity without requiring kinetic parameters. Fuzzy inferencing is one such promising method with the ability to work with qualitative vague/imprecise biological knowledge. In this study, we propose a fuzzy inference system for representing continuous behaviour of proteins and apply to some key proteins in the mammalian cell cycle system. The methods we introduced here is novel to protein interaction systems and cell cycle proteins. Our study proposes a three-stage approach to develop fuzzy protein controllers. In stage one, protein system is studied for interactions. We studied some significant core controllers of mammalian cell cycle and their producers and degraders as presented in a published ODE model. Based on the observations from a dataset generated from it, we developed Fuzzy inference systems (FIS) in the second stage, that involved deriving fuzzy IF-THEN rules and their processing, and manually tuned the FIS to predict the dynamics of individual proteins. In stage three, we employed Particle Swarm Optimisation (PSO) for optimising the FIS to further enhance prediction accuracy. Systems dynamics simulation results of the optimised FIS models were in close agreement with the benchmark ODE model results. The results show that the FIS models provide a close approximation to the comprehensive benchmark model in robustly representing continuous protein dynamics while representing the control of protein behavior in an intuitive and transparent format without requiring kinetic parameters. Therefore, FIS models can be an alternative to ODEs in network modelling. Further, FIS models can be assembled to develop large complex systems without losing information or accuracy.