The complexity of biological systems creates challenges for fully understanding their behaviour. This is particularly true for cell migration which requires the co-ordinated activity of hundreds of individual components within cells. Mathematical modelling can help understand these complex systems by breaking the system into discrete steps which can then be interrogated in silico . In this review, we highlight scenarios in cell migration where mathematical modelling can be applied and discuss what types of modelling are most suited. Almost any aspect of cell migration is amenable to mathematical modelling from the modelling of intracellular processes such as chemokine receptor signalling and actin filament branching to larger scale processes such as the movement of individual cells or populations of cells through their environment. Two common ways of approaching this modelling are the use of models based on differential equations or agent-based modelling. The application of both these approaches to cell migration are discussed with specific examples along with common software tools to facilitate the process for non-mathematicians. We also highlight the challenges of modelling cell migration and the need for rigorous experimental work to effectively parameterise a model.

Systems biology is an integrative discipline connecting the molecular components within a single biological scale and also among different scales (e.g. cells, tissues and organ systems) to physiological functions and organismal phenotypes through quantitative reasoning, computational models and high-throughput experimental technologies. Systems biology uses a wide range of quantitative experimental and computational methodologies to decode information flow from genes, proteins and other subcellular components of signaling, regulatory and functional pathways to control cell, tissue, organ and organismal level functions. The computational methods used in systems biology provide systems-level insights to understand interactions and dynamics at various scales, within cells, tissues, organs and organisms. In recent years, the systems biology framework has enabled research in quantitative and systems pharmacology and precision medicine for complex diseases. Here, we present a brief overview of current experimental and computational methods used in systems biology.