Spatial information analysis of chemotactic trajectories

Jan H. Hoh, William F. Heinz, Jeffrey L. Werbin

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)365-381
Number of pages17
JournalJournal of Biological Physics
Issue number2
StatePublished - Mar 2012
Externally publishedYes


  • Chemotaxis
  • Trajectory analysis
  • Trajectory space
  • k-space information

ASJC Scopus subject areas

  • Biophysics
  • Atomic and Molecular Physics, and Optics
  • Molecular Biology
  • Cell Biology


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