Parallel networks to simulate complex multicellular dynamics – A proof of concept with intervertebral disc cell systems

Background: Network 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. Methods: a 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. Results: Applied 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. Conclusions: The 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.