NearPerfect Adaptation in Bacterial Chemotaxis

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Near-Perfect Adaptation in Bacterial Chemotaxis
Yang Yang and Sima Setayeshgar Department of
Physics Indiana University, Bloomington, IN
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Chemotaxis Signal Transduction Network in E. coli
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Robust Perfect Adaptation
From Sourjik et al., PNAS (2002).
Steady state CheY-P / running bias
independent of value constant external stimulus
(adaptation)
Precision of adapation insensitive to changes in
chemotaxis network parameters (robustness)
Adaptation Precison
FRET signal CheY-P
CheR fold expression
Fast response
Slow adaptation
From Alon et al., Nature (1999).
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This Work Outline

• New computational scheme for determining
  conditions and numerical ranges for parameters
  allowing robust (near-)perfect adaptation in the
  E. coli chemotaxis network
• Comparison of results with previous works
• Extension to other modified chemotaxis networks,
  with additional protein components
• Conclusions and future work

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E. coli Chemotaxis Signaling Network
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Approach
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Augmented system
The steady state concentration of proteins in the
network satisfy The steady state concentration
of CheY-P must be independent of stimulus,
s where parameter allows for near-perfect
adaptation. Reaction rates are constant and must
also be independent of stimulus, s
Discretize s in range slow, shigh
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Physical Interpretation of Parameter,
Near-perfect adaptation
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Implementation

• Use Newton-Raphson (root finding algorithm with
  back-tracking), to solve for the steady state of
  augmented system,
• Use Dsode (stiff ODE solver), to verify time-
  dependent behavior for different ranges of
  external stimulus by solving

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Parameter Surfaces
Surface
2D projections
T4 autophosphorylation rate (k10)
LT2 methylation rate (k3c)
LT4 autophosphorylation rate (k10)

• 3lt?lt5
• 1lt?lt3
• 0lt?lt1

T4 demethylation rate (km2)
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Validation
Verify steady state NR solutions dynamically
using DSODE for different stimulus ramps
k3c 5 s-1, k10 101 s-1, km2 6.3e4 M-1s-1
Concentration (µM)
Time (s)
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Violating and Restoring Perfect Adaptation
Step stimulus from 0 to 1e-6M at t250s
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Methylation Rate Autophosphorylation Rate
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Demethylation Rate Autophosphorylation Rate2
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Demethylation Rate/Methylation Rate
Autophosphorylation Rate
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CheB, CheY Phosphorylation Rate
Autophosphorylation Rate
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Diversity of Chemotaxis Systems
In different bacteria, additional protein
components as well as multiple copies of certain
chemotaxis proteins are present.
Eg., Rhodobacter sphaeroides, Caulobacter
crescentus and several rhizobacteria possess
multiple CheYs while lacking of CheZ homologue.
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Two CheY System
Exact adaptation in modified chemotaxis network
with CheY1, CheY2 and no CheZ
Time(s)
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Conclusions

• Successful implementation of a novel method for
  elucidating regions in parameter space allowing
  precise adaptation
• Numerical results for (near-) perfect adaptation
  manifolds in parameter space for the E. coli
  chemotaxis network, allowing determination of
• conditions required for perfect adaptation,
  consistent with previous works
• numerical ranges for unknown or partially known
  kinetic parameters
• Extension to modification of the E. coli
  chemotaxis network, consistent with absence of
  CheZ homologue and presence of multiple CheY
  copies in rhizobacteria

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Future Work