Transcript E. coli - Department of Physics

Optimal Strategy of E. coli Chemotaxis Network: an Information Processing View
Lin Wang and Sima Setayeshgar
Department of Physics, Indiana University, Bloomington, Indiana 47405
P2(n)
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Vertebrate photoreceptor converts external energy (light quanta)
into a change into change of concentration ions.
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Chemotaxis[2]
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E. coli chemotaxis network converts external change of stimulus
into a change into change of concentration protein cheYp.
Molecule
kn(n  n0 )t
p
n0
A 
B
Bi-molecular reaction

A  B 
C
Motion
Physical constants for motion:
Cell speed: 20-30 μm/sec
Mean run time: 1 sec
Mean tumble time: 0.1 sec
kn( n  n0 ) t
2 N AV
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R
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E
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B
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Bp
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Motor response
Number of CheYp molecules as a function of
time. The motor switches state whenever
threshold (red line) is crossed.
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Time [sec]
[5] Carl Jason Morton-Firth et al. 1998 J. Theor. Biol.. 192 117-128
Adaptation to addition /removal of stimuli
Adaptation time to stimulus
Attractant: 30 μM MeAsp.
Adaptation time of E. coli to step-wise
change of [MeAsp] (labeled with
Repellent: 100 μM NiCl2
Aspartate).
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Time [sec]
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x100
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Time [sec]
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Upper:
Gaussian distributed signal
(μ=3 μM, σ2 = μ, τ = 1 sec)
Lower panel:
Response to the input signal.
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 =10
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[Asp]  M
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[Asp]  M
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The preliminary result suggests that E. coli varies its response function under
signals with different statistics. My goal is to understand how signal
transduction pathways, such as the chemotaxis network, may adapt to the
statistics of the fluctuating input so as to optimize the cell’s response. That is,
extract as much information as possible transmitted from the input signal.
S [ P(r )]   P log 2 PdP
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Time [sec]
s: Input signal; P(s): probability distribution of signal
r: response; P(r): probability distribution of response
r(s): I-O relation, mapping s to r.
n: noise;
P(n|r): noise distribution conditioned on response
[5] Naama Brenner et al. (2000) Neuron. 26 695-702
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Simulation result
Adaptation Time [sec]
Response to 10 μM aspartate.
Result: Effect of Correlation Timeτ
Intuitively, the slower the change of signal, the more information biological
system can extract from input signal. In this part, we explore the effect of
correlation time in I/O relation and mutual information transmission.
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Experiment From Howard C. Berg, 1975
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Step Size [ M]
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 Effect of τ in I/O relation
Simulation result
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 Motor CCW and CW intervals
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
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= 0.3 sec
= 0.8
= 1 sec
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CW and CCW intervals [sec]
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Simulation result
Comment on agreement: the simulation results are in good
agreement with experiments, although, the adaptation differ by a
factor of unit in time scale.
Transition.
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[Asp]  M
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 = 1 ( M)
S
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S
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S
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S
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Correlation time of signal [sec]
I/O relation under signals
with different statistics.
(τ = 1 sec)
Focus of Our Work
r
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ltiply100
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1.Signal is binned.
2. response is the average of
responses to signals falls
within each bin.
I  S [ P(r )]   P(r ) S [ P( n | r )]
0 -2
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Experiment From Korobkova et al. 2004
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s r
 Adaptation
 Adaptation time
2
P(r )   P( s)
Fraction
 Adaptation time
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The I/O mutual information rate is calculated by the following equation[6].
Model Validation
Experiment From Block et al. 1982
iontophoretic technique 0.1mM Asp in
pipette. (?? Can not determine the [asp])
Adaptation is an important and generic property of signaling systems,
where the response (e.g. running bias in chemotaxis) returns precisely
to the pre-stimulus level while the stimulus persists. Adaptation
functions from short time scale (impulse) to long time scale
(evolution). It allows the system to compensate for the presence of
continued stimulation and to be ready to respond to further stimuli.
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Result: Mutual Information Equation
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0
Adaptation
[3] Sourjik et al. (2002) PNAS. 99 123-127
[4] Howard C. Berg, (1975) PNAS. 72 71-713
Yp
n: Number of molecules in reaction system
n0: Number of pseudo-molecules
NA: Avogadro constant
p: Probability for a reaction to happen
Δt: Simulation time step
V: Simulation volume
Probability CCW
Flagellar
Bundling
p
 Motor response
Number of CheYp Molecules
Signal
Transduction
Pathway
[CheY-P]
Motor
Response
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Reactions are simulated using Stochsim[5] package, a general platform
for simulating reactions stochastically. Reactions have a probability p
to occur.
Symbols:
 Uni-molecular reaction
k
Stimulus
For now, use number of CheYp molecules as the system output.
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k
Fluorescently labeled E. coli (Berg lab)
Body size:
1 μm in length, 0.4 μm in radius
Flagellum:
10 μm long, 45 nm in diameter
 Adaptation
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 Output of chemotaxis network
NCheYp
 Physical shape of E. coli
The chemotaxis signal transduction
pathway in E. coli – a network of ~50
interacting proteins – converts an external
stimulus (change in concentration of
chemo-attractant / repellent) into an
internal stimulus (change in concentration
of intracellular response regulator, CheYp)
which in turn interacts with the flagella
motor to bias the cell’s motion.
Concentration (μM)
 Simulating reactions
Chemotaxis, motion toward desirable chemicals (usually nutrients)
and away from harmful ones, is achieved through continuous ‘runs’
and ‘tumbles’.
Numerical
Number
Y
[1] Peter B. Detwiler et al. (2000). Biophysical Journal. 79, 2801-2817
[2] Birgit E. Scharf et al. (1998) PNAS. 95, 201-206
 Chemotaxis network
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Table III: Initial Protein Level
Use E. coli chemotaxis network as a prototype to explore the
general information processing principle in biological systems.
E. coli Chemotaxis
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Artificially generate Gaussian distributed time series with correlation time τ.
Information rate (bit)
P1(n)
CheYp
n
N
Table II: Activation Probability
Table I: Signal Transduction Network
 Effect of τ in I/O mutual information
NCheYp
 Parameter values of chemotaxis network
cont.
With this realistic and stochastic numerical implementation that is
consistent with experiments, we explore E. coli chemotaxis network from
an information point of view.
 Input signal
[As]  M
Chemical signaling cascade is the most fundamental information
processing unit in biological systems.
 Photoreceptor[1]

Result: Input-Output Relation
Numerical Implementation
NCheYp
Motivation
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Signals: μ=1 μM, σ2 = μ and τ = 0.1, 0.3, 0.8,
1 sec, respectively.
At τ > 0.8 sec, the response does not change
any more.
(This holds for signals with different mean
values)
Conclusions
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Information transmitted by E. coli chemotaxis
network is plotted as a function of correlation
time of signals, which have different statistic
parameters. With the increasing correlation time,
E. coli is able to extract more information out of
the input signal. Typical impulse response time
of wild-type E. coli is around 1 sec.