Run-and-tumble motion and differential dynamic microscopy

Abstract

Systems biology focuses on how the biochemical regulations determine the functions of biological systems. Nowadays we are able to test many systems biology hypotheses with synthetic biology, and push the knowledge of biological systems into a new level. Pattern formation and collective motion are important functions for some biological systems, as they help explain the morphogenesis of multicellular organisms. Previous work has shown that patterns can emerge from the regulations of cell motion. However, the precise underlying mechanisms remain an open question.

I attacked this question for E. coli systems. I first investigated the motion of E. coli, which can be described as run-and-tumble motion. It consists of straight runs alternating with frequent random tumbling. The run-and-tumble motion in liquid has been well studied. I revised the previous results, and showed the effect of density-dependent motility regulations on E. coli collective motion. We found density-enhanced motility causes cells to segregate from signals, while density-inhibited motility causes cells to co-migrate with signals. We also found two species with mutual activation of motility can form segregating patterns, while mutual inhibition of motility helps form co-migrating patterns.

However, the environment for E. coli motion is often some polyporous materials, with a lot of obstacles. How the obstacles affect the macroscopic motion of microbes is still an open question. Thus a simplified stochastic model described by master equation had been established to describe cells moving in agar, and lattice Monte-Carlo simulations have been carried out. This model showed the same feature as the observations in experiments that cells with higher tumbling rate can move faster in semi-solid agar, in contrast to the case in liquid. The model suggested the mechanism to be that running cells are more easily blocked by the obstacles, while tumbling events help cells escape from the blocking obstacles.

Another problem in studying motion of E. coli is how to measure their motion in experiments. A novel method called differential dynamic microscopy (DDM), first used to characterize the diffusion of colloids, was adapted to measure parameters of run-and-tumble motion. DDM makes use of the information contained in the auto-correlation function of Fourier transformed time-lapse images, which can be compared with their theoretical predictions for run-and-tumble particles to extract relevant experimental parameters. The difficulty of lacking a mathematical expression of the solution in real time was overcome by a numerical inverse Laplace transform, making use of the classic Weeks' method.

To test this method, data generated from simulations were used, showing that for ideal run-and-tumble particles, both swimming speed and tumbling rate can be measured. Experimental data using AB1157 E. coli\ have been analysed, and the corresponding parameters were measured. The wild type and CheY knock-out strains were compared, and their difference supports the utility of our new development.