Predictive numerical models of cellular response to biophysical cues have emerged as a useful quantitative tool for cell biology research. Cellular experiments in silico can augment in vitro and in vivo investigations by filling gaps in what is possible to achieve through 'wet work'. Biophysics-based numerical models can be used to verify the plausibility of mechanisms regulating tissue homeostasis derived from experiments. They can also be used to explore potential targets for therapeutic intervention. In this perspective article we introduce a single cell model developed towards the design of novel biomaterials to elicit a regenerative cellular response for the repair of diseased tissues. The model is governed by basic mechanisms of cell spreading (lamellipodial and filopodial extension, formation of cell-matrix adhesions, actin reinforcement) and is developed in the context of cellular interaction with functionalized substrates that present defined points of potential adhesion. To provide adequate context, we first review the biophysical underpinnings of the model as well as reviewing existing cell spreading models. We then present preliminary benchmarking of the model against published experiments of cell spreading on micro-patterned substrates. Initial results indicate that our mechanistic model may represent a potentially useful approach in a better understanding of cell interactions with the extracellular matrix.