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

Imaging data has become an essential tool to explore key biological questions 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 important 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 mechanistic mathematical models to imaging data, we need to estimate their parameters. In this work we study how collecting data at different temporal resolutions impacts our ability to infer parameters of biological transport models by performing exact inference for simple velocity jump process models in a Bayesian framework. The question of how best to choose the frequency with which data is collected is prominent in a host of studies because the majority of imaging technologies place constraints on the frequency with which images can be taken, and the discrete nature of observations can introduce errors into parameter estimates. In this work, we mitigate 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. Finally, we demonstrate the robustness of our methodology to model misspecification, and then apply our inference framework to a dataset that was generated with the aim of understanding the localization of RNA-protein complexes.Author summary: We consider how the temporal resolution of imaging studies affects our ability to carry out accurate parameter estimation for a stochastic biological transport model. This model provides a mechanistic description of motile behaviour and is often used to interrogate transport processes, such as the motion of bacteria. Parameter inference is necessary to characterise different types of transport and to make predictions about biological behaviour under different conditions. Typically, observations of the transport process, at the level of individual trajectories, are made at discrete times. This can lead to errors in parameter estimation because we do not have complete trajectory information. We present a framework for Bayesian inference for these models of biological transport processes. Using this framework, we study the effects of collecting data more or less frequently, and with varying measurement noise, on what we can learn about the biological system via parameter estimation.