Transcript Chemotaxis network - Department of Physics

Optimal Strategy of E. coli Chemotaxis Network from Information Processing View
Lin Wang and Sima Setayeshgar
Department of Physics, Indiana University, Bloomington, Indiana 47405
Focus
Chemical signaling cascade is the most fundamental information
processing unit in biological systems. Generally, it converts an external
stimulus to change in concentration of intracellular signaling molecules.
E. Coli Chemotaxis[3]
Photoreceptor[1,2]
The preliminary result suggests that E. coli varies its response 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.
My focus is to find out an approach to evaluate information transmission
rate and then investigate the role of adaptation.
Photon
Δ[Ca2+]
Ca2+ Fluorescence
Motivation
Attractant
Δ[CheY-P]
Response of E. coli to external attractant.
Yellow: CheY-P relative level.
Response of drosophila photoreceptor
to photon absorption.
Use E. coli chemotaxis network as a prototype to explore the
general information processing principle in biological systems.
Effect of Correlation Time τ
Model Validation
Simulation
Experiment
Adaptation[9]
My first step is to investigate the effect of correlation time τ to the I/O
mutual information rate of the chemotaxis network.
Effect of τ on I/O relation
Response r(s) to signals: μ=1 μM, σ2 = μ, τ =
0.1, 0.3, 0.8, 1 sec, respectively. At τ > 0.8 sec,
the response does not change any more. (This
holds true for signals with different mean
values)
Cell response when exposed to a step change of aspartate from 0 to 0.1 mM
(left), 10 μM (right) beginning at 5 sec.
Numerical Implementation
Adaptation time[10]
Parameter values of chemotaxis network
Effect of τ in I/O mutual information
Table I: Signal Transduction Network
Table II: Activation Probabilities
[1] R. C. Hardie et al. (2001) Nature 413, 186-193
[2] J. Oberwinkler et al. (2000) PNAS 97, 8578-8583
E. coli Chemotaxis
Chemotaxis, motion toward desirable chemicals (usually nutrients) and
away from harmful ones, is achieved through continuous ‘runs’ and
‘tumbles’.
n
P1(n)
P2(n)
0
0.02
0.00291
1
0.17
0.02
2
0.5
0.17
3
0.874
0.5
4
0.997
0.98
The I/O mutual information rate of E. coli
chemotaxis network is plotted as a function
of correlation time τ. The Gaussian
distributed signals used here have means of 1,
3, 5, and 10, respectively.
Transition time to step change of external attractant
Motor CCW and CW intervals[11]
Table III: Initial Protein Levels
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
Chemotaxis network
Stimulus
Numerical
Signal
Transduction
Pathway
[CheY-P]
Motor
Response
Flagellar
Bundling
Motion
From R. M. Berry, Encyclopedia
of Life Sciences
Physical constants for motion:
Cell speed: 20-30 μm/sec
Mean run time: 1 sec
Mean tumble time: 0.1 sec
Uni-molecular reaction
Y
15684
18
Yp
0
0
R
250
0.29
E
6276
-
B
1928
2.27
Bp
0
0
p
kn(n  n0 ) t
n0
Bi-molecular reaction
A  B 
C
k
p
kn( n  n0 ) t
2 N AV
Motor response[6]
Motor response
A simple threshold model is used to model motor
response. The motor switches state whenever
CheY-P trace (blue trace) crosses the threshold
(red line)
Run Bias
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.
Adaptation variation[3]
Adaptation[3]
[5] C. J. Morton-Firth et al. 1998 J. Theor. Biol.. 192 117-128
[6]T. Emonet et al. 2005 Bioinformatics 21 2714-2721
Mutual Information
The average information that observation of Y provide about the signal
X, is I, the mutual information of X and Y[7]. I is at minimum, zero,
when Y is independent of X, while it is at maximum when Y is
completely determined by X. The I/O mutual information rate can be
calculated by the following equation[8].
P(r )   P( s)
s r
[3] Sourjik et al. (2002) PNAS. 99 123-127
[4] H. C. Berg, (1975) PNAS. 72 71-713
Concentration (μM)
Symbols:
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
Adaptation
Attractant: 30 μM aspartate.
Repellent: 100 μM NiCl2
Number
Simulating reactions
Reactions are simulated using Stochsim[5] package, a general platform for
simulating reactions stochastically. Reactions have a probability p to
occur.
k
A 
B
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, CheY-P)
which in turn interacts with the flagella
motor to bias the cell’s motion.
Molecule
Adaptation to various step change
of attractant serine (mM).
I  E[ P (r )]   P (r ) E[ P ( n | r )]
r
E[ P (r )]   P log 2 PdP
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
[7] Spikes, Fred Rieke et al. 1997, p122-123
[8] N. Brenner et al. (2000) Neuron. 26 695-702
Distribution of wild-type E. coli motor CW (grey) and CCW (black) intervals.
Discussion: the simulation results are in good agreement with
experiments, although the adaptation times differ by a small factor.
Effect of varying response
Use r (s1) under input signal s1 (μ1=1 μM, σ12 = μ1, τ1 = 1 sec) to find P(r)
for different input signals, and calculate the mutual information between
r (s1) and sk.
P(r )   P( sk )
s r
The calculated I/O mutual information rate
of E. coli chemotaxis network maximizes
under the condition that the response and the
input signal matches.
[9] S. M. Block et al. 1982 Cell 31 215-226
[10] H. C. Berg et al. 1975 PNAS 72 3235-3239
[11] T. Emonet et al. 2005 Bioinformatics 21 2714-2721
Input-Output Relation
By utilizing this realistic and stochastic numerical implementation, we
explore E. coli chemotaxis network from the standpoint of general
information-processing concepts.
Signal
Conclusions
E. coli
chemotaxis
network
Input signal
Artificially generated Gaussian
distributed time series with
correlation time τ.
1
(s   )2
p( s) 
exp(
)
2
2
2 2
<s(0)s(t)> ~ exp(-t / )
Output
Output
Number of CheY-P molecules
The chemotaxis network is able to extract as much as information
possible once the input signal varies slower relative to the response time
of the chemotaxis network.
Under an input signal with specific statistics, the chemotaxis network
varies its response to optimize the cell’s performance, maximizing the
mutual information between input signal and output response.
Future Work
Use a realistic description of motor to replace the simple threshold
model of motor response.
Take into account the clustering effect among trans-membrane aspartate
receptors to improve the performance of the numerical implementation.
Upper: Gaussian distributed
signal (μ=3 μM, σ2 = μ, τ =
1 sec)
Lower panel: Response to
the input signal.
The response is the
average of responses in
each bin of signal.
I/O relation under signals
with different statistics.
(τ = 1 sec)
Investigate role of adaptation time.