Information Processing by theE. coli Chemotaxis Network

Sima Setayeshgar, Lin WangIndiana University

Funding: NSF, IU MetaCyt, IU FRSP

AMS Central Sectional MeetingSpecial Session on Applications of Stochastic Processes to Cell

BiologyUniversity of Notre Dame

November 6, 2010

Information Processing by Biochemical Signaling Networks

Biochemical signaling is the most fundamental level of information processing in biological systems, where an external stimulus is measured and converted into a response.

[1] S. M. Block et al. Cell 31, 215-226 (1982) [2] R. C. Hardie et al. Nature 413, 186-193 (2001) [3] M. Postma et al. Biophysical Journal 77, 1811-1823 (1999)

Photon counting in vision[2, 3]

Photon Δ[Ca2+],Δ[Na+],

etc.

Molecule counting in chemotaxis[1]

AttractantΔ[CheY-P]

Response of E. coli to change in external attractant concentration

Response of Drosophila photoreceptor cell to change in photon concentration

Chemotaxis in E.coli

Fluorescently labeled E. coli (from Berg lab)

Physical constants: Cell speed: 20-30 μm/secMean run time: 1 secMean tumble time: 0.1 sec

Dimensions: Body size: 1 μm in length

0.4 μm in radiusFlagellum: 10 μm long

45 nm in diameter

Outline

Information-theoretic analysis of realistic, stochastic computational model of the E. coli chemotaxis network

I. Network filters: integrator, differentiator

II. Input-Output (I/O) relations for Gaussian distributed input signals with fast and slow correlation times

III.Mutual Information (MI) between input signal and motor output

IV.Comparison with minimal network model

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Simulation of Network Response

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Data (from [4])

Simulation

Single motor response:constant stimulus

CheY-P response to step change

[4] E. Korobkova et al. Nature 428, 574 (2004)

Simulation

CheY-P and Motor Response to Input Signal

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Input Signal:

Response:

CW CCW

CCW CW

= 5 M/ = 0.41 = 0.3 s

Network Response: Noise

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Input Signal:

= 5 M/ = 0.41 = 0.3 s

Response:

20 independent simulations w/above input signal

Red: CW CCW transitionsBlue: CCW CW transitions

Input-Output Relations

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Slow Signal

= 3 sec

Fast SignalSpike-Triggered Covariance Analysis (STC)[5],[6]

Construct:

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[5] N. Brenner et al., Neuron (2000)[6] A. L. Fairhall et al., Nature (2001)

where

Left plots: CW CCWRight plots: CCW CW

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(a), (e) Density plots of C

(b), (f) Eigenvalues

(c), (g) Dominant eigenvectors

(d), (h) Dominant eigenvectors, after correction for input signal correlation time

= 5 M/ = 0.41 = 0.3 s

Dimension Reduction

Signal projection onto leading directions:

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v1: “integrator” v2: “differentiator”

I/O Relations:

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Left plots: CW CCWRight plots: CCW CW

= 0.3 s

r(s1)

r(s2)

Rescaling of Input-Output Relations

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Slow Signal: = 3s

Rescaling: normalize input concentration by standard deviation after subtracting mean.

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= 3 M (blue)= 5 M (green)= 7.5 M (magenta)= 10 M (black)

/ = 0.25 (all)

(a), (c) Raw I/O relation

(b), (d) Rescaled

CW CCW CCW CW

I/O relations for inputs with common / collapse!

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Fast Signal = 0.3s

= 3 M (blue)= 5 M (green)= 7.5 M (magenta)= 10 M (black)

/ = 0.41 (all)

(a), (e) Raw I/O relation r(s1)

(b), (f) Rescaled

(c), (g) Raw I/O relation r(s2)

(d), (h) Rescaled

I/O relations for inputs with common / collapse!

Mutual Information

Mutual Information conveyed by dominant filters

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Approximated as

MI: Numerical Results

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Solid points/line: use joint probability distribution with both filtersOpen points/line: treat filters as independent

Observations:•Mutual information is maintained for input signals with common /, independent of over range KD (inactive) < c < KD (active)•Mutual information increases with increasing /.

Summary

• Application of STC analysis to information processing by non-neuronal biochemical sensory system

• Dominant network filters: averaging, differentiating

• Adaptation of network I/O relations to input statistics (,): contrast adaptation

• Mutual Information maintained for signals with the same

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Backup slides

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Backup slides

Chap 6 slow io sameU dif SNov 6, 2010 21S. Setayeshgar - AMS Central Sectional Meeting

Chap 6 slow io dif U same SNov 6, 2010 22S. Setayeshgar - AMS Central Sectional Meeting

Chap 6: Rs_dif U same SNov 6, 2010 23S. Setayeshgar - AMS Central Sectional Meeting

E. coli Chemotaxis Signaling Network

Signal Transduction

Pathway

Motor Response

[CheY-P]

Stimulus

Flagellar Bundling

Motion(Courtesy of Howard Berg lab)

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Chap 6Nov 6, 2010 25S. Setayeshgar - AMS Central Sectional Meeting

Chap 6Nov 6, 2010 26S. Setayeshgar - AMS Central Sectional Meeting

Chap 6Nov 6, 2010 27S. Setayeshgar - AMS Central Sectional Meeting

Minimal Model

Minimal modelNov 6, 2010 28S. Setayeshgar - AMS Central Sectional Meeting

Lin’s chap 7 (minimal model)Nov 6, 2010 29S. Setayeshgar - AMS Central Sectional Meeting

Channel capacity

Lin’s chap 7 minimal model, channel capacityNov 6, 2010 30S. Setayeshgar - AMS Central Sectional Meeting