Spatial information analysis of chemotactic trajectories

During bacterial chemotaxis, a cell acquires information about its environment by sampling changes in the local concentration of a chemoattractant, and then uses that information to bias its motion relative to the source of the chemoattractant. The trajectory of a chemotaxing bacteria is thus a spatial manifestation of the information gathered by the cell. Here we show that a recently developed approach for computing spatial information using Fourier coefficient probabilities, the k-space information (kSI), can be used to quantify the information in such trajectories. The kSI is shown to capture expected responses to gradients of a chemoattractant. We then extend the k-space approach by developing an experimental probability distribution (EPD) that is computed from chemotactic trajectories collected under a reference condition. The EPD accounts for connectivity and other constraints that the nature of the trajectories imposes on the k-space computation. The EPD is used to compute the spatial information from any trajectory of interest, relative to the reference condition. The EPD-based spatial information also captures the expected responses to gradients of a chemoattractant, although the results differ in significant ways from the original kSI computation. In addition, the entropy calculated from the EPD provides a useful measure of trajectory space. The methods developed are highly general, and can be applied to a wide range of other trajectory types as well as non-trajectory data.