Information Processing by the E. coli Chemotaxis Network
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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
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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
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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
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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
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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
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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
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Input-Output Relations
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Slow Signal
= 3 sec
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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
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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
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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)
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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!
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Mutual Information
Mutual Information conveyed by dominant filters
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Approximated as
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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 /.
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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
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Chap 6 slow io dif U same SNov 6, 2010 22S. Setayeshgar - AMS Central Sectional Meeting
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Chap 6: Rs_dif U same SNov 6, 2010 23S. Setayeshgar - AMS Central Sectional Meeting
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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
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Chap 6Nov 6, 2010 26S. Setayeshgar - AMS Central Sectional Meeting
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Chap 6Nov 6, 2010 27S. Setayeshgar - AMS Central Sectional Meeting
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Minimal Model
Minimal modelNov 6, 2010 28S. Setayeshgar - AMS Central Sectional Meeting
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Lin’s chap 7 (minimal model)Nov 6, 2010 29S. Setayeshgar - AMS Central Sectional Meeting
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Channel capacity
Lin’s chap 7 minimal model, channel capacityNov 6, 2010 30S. Setayeshgar - AMS Central Sectional Meeting