NearPerfect Adaptation in E' coli Chemotaxis Signal Transduction Network

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Near-Perfect Adaptation in E. coli Chemotaxis
Signal Transduction Network
Yang Yang Sima Setayeshgar
Jan, 2007
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E. coli

• lives primary in our intestines
• 1-3 microns long and 1 micron in diameter
• Each cell has 4-6 flagella with approximately
  10-20 microns in length
• Small genome (4288 genes), most of which encode
  proteins
• ease of experimentation, through microscopy and
  genetic analysis
• It is an ideal model organism for understanding
  the behavior of cells at the molecular level from
  the perspectives of several scientific
  disciplines-anatomy, genetics, chemistry and
  physics.

static.howstuffworks.com/gif/cell-ecoli.gif
www.hatetank.dk
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Bacterial Chemotaxis
Increasing attractants or Decreasing repellents
http//www.rowland.harvard.edu/labs/bacteria/index
_movies.html
Run Tumble
E. coli exhibits an important behavioral response
known as chemotaxis - motion toward desirable
chemicals (usually nutrients) and away from
harmful ones - which is also shared by various
other prokaryotic and eukaryotic cells. The
cells motion consists of series of runs
punctuated by tumbles.
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Chemotaxis signal transduction network in E. coli
With approximately 50 interacting proteins , the
network converts an external stimulus into an
internal stimulus which in turn interacts with
the flagella motor to bias the cells motion. It
is used as a well-characterized model system for
the study of properties of (two-component)
cellular signaling networks in general.
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Chemical reactions
Full realistic model
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Perfect adaptation
It is an important and generic property of
signaling systems, where the response returns
precisely to the pre-stimulus level while the
stimulus persists.
Steven M., et al. Journal of bacteriology. 1983
This property allows the system to compensate for
the presence of continued stimulation and to be
ready to respond to further stimuli.
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Robustness
The E. coli chemotaxis signal transduction
network exhibits robust perfect adaptation, where
the concentration of CheYp returns to its
prestimulus value despite large changes in the
values of many of the biochemical reaction rate
constants.
U. Alon et al. Nature,1999
Recent works have highlighted the fact that this
important feature of the network must be robust
to changes in network parameters. In engineered
systems, this property is achieved through
integral feedback control.
Tau-Mu Yi et al. Biophysics,2000
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Motivation
QUESITON The biochemical basis of robustness of
perfect adaptation is not as yet fully
understood.
we develop a novel method for elucidating regions
in parameter space of which the E. coli
chemotaxis network adapts perfectly

• shedding light on biochemical steps and feedback
  mechanisms underlying robustness
• shed light on values of unknown or partially
  known parameters

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Algorithm
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Augmented system
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Implementation

• Dsode (stiff ODE solver), to verify
  Newton-Raphson result for different ranges of
  external stimulus by solving

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Working progress

• Exploring the parameter spaces of E. coli
  chemotaxis signaling transduction network
• Exploring the unknown parameter ranges of
  chemotaxis signaling transduction network which
  has two regulation proteinsCheY1 , CheY2

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Exploring the parameter spaces of E. coli
chemotaxis signaling transduction network

• Exploring pairwise trajectory by setting two
  parameters as unknowns in the augmenting system
• Exploring three dimensional parameter space by
  setting three parameters as unknowns in the
  augmenting system

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Parameter spaces
E .coli
Pairwise result
3d surface result
Relative change of CheYp less than 5 less
than 3 less than 1 pairwise trajectory
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Parameter spaces
E. coli
Pairwise result
3d surface result
Relative change of CheYp less than 5 less
than 3 less than 1 pairwise trajectory
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Parameter spaces
E .coli
Pairwise result
3d surface result
Relative change of CheYp less than 5 less
than 3 less than 1 pairwise trajectory
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Consistency with recent work by Bernardo A. mello
and Yuhai Tu

• In order to hold the perfect adaptation, their
  simulation (perfect
• and near-perfect adaptation in a model of
  bacterial chemotaxis,
• biophysical journal, 2003) shows that
• the phosphorylation rates of CheB(kb) or
  CheY(ky) are proportional to CheA
  autophosphorylation rate(k8-13).
• methylation rates of n1 methylation level
  (k1c-4c) are proportional to demethylation rates
  of n methylation level (km1-m4)

Our simulation of parameter space also shows
linearly or near-linearly relationship as
indicate above although we are using a different
model of the chemotaxis transduction network.
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CheB(kb) and CheY(ky) are proportional to CheA
autophosphorylation rate(k8-13)
The parameter value are normalized to the
literature value( Peter A. S., John S.P. and Hans
G.O. , A model of excitation and adaptation in
bacterial chemotaxis, biochemistry 1997) while
the inset is not since the literature value is
zero for k11.
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k1c/km1, k2c/km2, k3c/km3, k4c/km4 are linearly
related
The parameter value are normalized to the
literature value( Peter A. S., John S.P. and Hans
G.O. , A model of excitation and adaptation in
bacterial chemotaxis, biochemistry 1997).
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Exploring unknown parameter values for signal
transduction network for two CheY system

• Rhodobacter sphaeroides, Caulobacter crescentus,
  and several nitrogen-fixing rhizobacteria have
  multiple cheY which one of the CheY functions as
  the primary motor-binding protein while the
  others work as a phosphatase sink in order to
  compensate the lack of CheZ protein.
• The Two CheY system shows chemotaxis behaviors
  which is similar to E. coli.
• Our work
• Reproduce the key feature of chemotaxis behavior
  in two CheY system by replacing CheZ with CheY2.

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Simulation result for two CheY system
Two CheY

• Modify the augment system by introducing CheY2
  and CheY2 (de-)phosphorylation rates.
• Exploring the parameter values of CheY2
  (de-)phosphorylation rates which can give perfect
  adaptation.

Relative change of CheYp less than 5 less
than 3 less than 1 pairwise trajectory
Other parameter value were set as the literature
value except Kb 1e6 M-1s-1 instead of 8e5
M-1s-1.
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Conclusions

• Successful implementation of the augmented model
  of the chemotaxis signal transduction network in
  E. coli that explicitly takes into account robust
  perfect adaption.
• Preliminary results on projections of robustness
  manifolds in parameter space of E. coli and two
  CheY system

Work in progress
Complete construction of manifolds in parameter
space, allowing insight into parameter
dependence giving rise to robustness
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Future work

• This method should have applicability to other
  cellular signal transduction networks and
  engineered systems that exhibit robust
  homeostasis, such as phototransduction.
• The molecular mechanism underlying light
  adaptation may be discussed in the context of the
  reaction governing the cGMP in the photo receptor
  cytoplasm

Signal flow in visual transduction, Leon Lagnado
and Denis Baylor,Neuron,1992
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• Thanks and comments!

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Physics limitation in signal sensing
25 years ago Berg and Purcell had showed that the
physics limitation of the single celled
organism. The derivation is mainly assumed a
perfect measurement device and they determined
the relative measurement accuracy is But
for multiple and noninterating receptors shaped
as a ring, the formula is derived by Willam and
Sima recently as With know parameter value,
we can get the actual physics limit to
measurements of CheYp concentration corresponds
to

diffusion constant device size average
concentration sampling time
receptor numbers single receptor size
geometric factor of order unity
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Computational models of chemotaxis signal
transduction network