The impact of temporal sampling resolution on parameter inference for biological transport models

Abstract: Imaging data has become widely available to study biological systems at various scales, for example the motile behaviour of bacteria or the transport of mRNA, and it has the potential to transform our understanding of key transport mechanisms. Often these imaging studies require us to compare biological species or mutants, and to do this we need to quantitatively characterise their behaviour. Mathematical models offer a quantitative description of a system that enables us to perform this comparison, but to relate these mechanistic mathematical models to imaging data, we need to estimate the parameters of the models. In this work, we study the impact of collecting data at different temporal resolutions on parameter inference for biological transport models by performing exact inference for simple velocity jump process models in a Bayesian framework. This issue is prominent in a host of studies because the majority of imaging technologies place constraints on the frequency with which images can be collected, and the discrete nature of observations can introduce errors into parameter estimates. In this work, we avoid such errors by formulating the velocity jump process model within a hidden states framework. This allows us to obtain estimates of the reorientation rate and noise amplitude for noisy observations of a simple velocity jump process. We demonstrate the sensitivity of these estimates to temporal variations in the sampling resolution and extent of measurement noise. We use our methodology to provide experimental guidelines for researchers aiming to characterise motile behaviour that can be described by a velocity jump process. In particular, we consider how experimental constraints resulting in a trade-off between temporal sampling resolution and observation noise may affect parameter estimates.