A Novel Method to Describe and Share Complex Mathematical Models of Cellular Physiology

Abstract

With improved experimental techniques and computational power we have seen an explosion in the complexity of mathematical models of cellular physiology. Modern lumped parameter models integrating cellular electrophysiology, mechanics, and mitochondrial energetics can easily consist of many tens of coupled differential equations requiring hundreds of parameters. The reward of this increase in complexity is improved biophysical realism and an increase in the predictive qualities of the models. One of the most significant challenges with such models is being able to completely describe the model in such a manner that the authors can share the model with collaborators and, potentially, the scientific community at large. In this work we have developed methods and tools for the specification of the complete description of mathematical models of cellular physiology using established community standards combined with some emerging and proposed standards. We term the complete description of the cellular model a 'reference description'. Such a description includes everything from the mathematical equations, parameter definitions, numerical simulations, graphical outputs, and post-processing of simulation outputs. All of these are grouped into a hierarchy of tasks which define the overall reference description structure and provide the documentation glue to enable the presentation of a complete story of the model development and application. Our reference description framework is based primarily on the CellML project, using annotated CellML models as the basis of the model description. Being based on CellML allows the underlying mathematical model to be shared with the community using standard CellML tools, and allows tools capable of interpreting the annotations to present the complete reference description in various manners.