Parallel Networks to simulate complex multicellular dynamics - A proof of concept with intervertebral disc cell systems

Abstract

BackgroundNetwork models are convenient to represent in a mechanistic way the complexity of cell biological activity. Dynamic simulations of such networks might require approximations of equation parameters through reverse engineering, numerous and costly experimental research, and/or have limited capacity to explore cell responses to chronic, dose-dependent stimulus exposure. Here we present a mechanistic methodology allowing the simulation of interrelated cell responses of multicellular systems to multifactorial stimuli with dose-and time dependent network links. Methodsa mathematical framework to approach systems biology research questions is presented, the Parallel Networks (PN)-Methodology. It consists of a novel concept, where multicellular systems are described as many relatively small feed-forward networks acting in parallel. Each parallel network is calculated through a specifically designed ordinary differential equation (ODE). Through a unique approach to feed the ODE with interrelated parameters, a system of decoupled, analytically resolvable ODE was obtained. ResultsApplied to intervertebral disc multicellular systems, virtual environments of multifactorial stimuli and multiple cell responses simulating daily moving activities, and to microgravity could successfully be created. ConclusionsThe PN-Methodology stands for a one-of-a-kind mathematical methodology to approximate dynamics of complex multicellular systems over long periods of time at low computational costs.