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