### Abstract

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 language | English (US) |
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Pages (from-to) | 365-381 |

Number of pages | 17 |

Journal | Journal of Biological Physics |

Volume | 38 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2012 |

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### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Biological Physics*,

*38*(2), 365-381. https://doi.org/10.1007/s10867-011-9253-5