A jump distance based parameter inference scheme for particulate trajectories in biological settings

One type of biological data that needs more quantitative analytical tools is particulate trajectories. This type of data appears in many different contexts and across scales in biology: from the trajectory of bacteria performing chemotaxis to the mobility of ms2 spots within nuclei. Presently, most analyses performed on data of this nature has been limited to mean square displacement (MSD) analyses. While simple, MSD analysis has several pitfalls, including difficulty in selecting between competing models, handling systems with multiple distinct sub-populations, and parameter extraction from limited time-series data. Here, we provide an alternative to MSD analysis using the jump distance distribution (JDD). The JDD resolves several issues: one can select between competing models of motion, have composite models that allow for multiple populations, and have improved error bounds on parameter estimates when data is limited. A major consequence is that you can perform analyses using a fraction of the data required to get similar results using MSD analyses, thereby giving access to a larger range of temporal dynamics when the underlying stochastic process is not stationary. In this paper, we construct and validate a derivation of the JDD for different transport models, explore the dependence on dimensionality of the process, and implement a parameter estimation and model selection scheme. We demonstrate the power of this scheme through an analysis of bacterial chemotaxis data, highlighting the interpretation of results and improvements upon MSD analysis. We expect that our proposed scheme provides quantitative insights into a broad spectrum of biological phenomena requiring analysis of particulate trajectories.