Abstract
Movement of cells and tissues is a basic biological process that is used in development, wound repair, the immune response to bacterial invasion, tumour formation and metastasis, and the search for food and mates. While some cell movement is random, directed movement stimulated by extracellular signals is our focus here. This involves a sequence of steps in which cells first detect extracellular chemical and/or mechanical signals via membrane receptors that activate signal transduction cascades and produce intracellular signals. These intracellular signals control the motile machinery of the cell and thereby determine the spatial localization of the sites of force generation needed to produce directed motion. Understanding how force generation within cells and mechanical interactions with their surroundings, including other cells, are controlled in space and time to produce cell-level movement is a major challenge, and involves many issues that are amenable to mathematical modelling.