Junjiajia Long

What is the best strategy to search in an unknown environment? Navigation with only local information available is a ubiquitous problem in nature, especially when local directional information is unreliable due to limited detection range and accuracy. Facing this challenge, many natural systems, including the chemotactic bacteria Escherichia coli, navigate by registering past information “in memory” and making temporal comparisons to bias their random walk up gradients of signal. In groups, these bacteria can migrate collectively as they consume nutrients to create a gradient that moves along with them, traveling greater distances than a single cell could have. Previously, most research has made simplifying assumptions to reach analytical predictions. Individual memory for signal has been assumed to be short compared to changes in signal so that the past has little effect on present and future behavior. In populations, all individuals have been assumed to be identical. However, cells navigate in all kinds of environments, including ones where their memory is long compared to other time scales, and biological organisms always exhibit phenotypic diversity. Here, we restore these missing components to examine their effects on bacterial navigation. In individual navigation, we show that memory controls the balance between the positive feedback between behavior and sensed signal and the negative feedback of forgetting past signals. When the positive feedback dominates, a cell can quickly turn around after moving in the wrong direction and can extend motion in the right one, achieving “ratchet-like” gradient climbing behavior. In collective migration, we show that the diversity controls the inevitable leakage of cells off the back of the migrating group, which in turn shapes the group’s diversity. During migration, phenotypes that climb gradients too slowly are purged so that the rest of the population stays coherently traveling for longer times. In conclusion, we explicate the role of memory for individuals and the role of diversity for groups, and provide insights on how general biased random walk strategies, from individual to collective behavior, could be exploited.