Transcript E. coli

Lin Wang
Advisor: Sima Setayeshgar
Motivation:
Information Processing in Biological
Systems
Chemical signaling cascade is the most fundamental information
processing unit in biological systems.
 Photoreceptor[1]
Vertebrate photoreceptor converts external
energy (light quanta) into a change in
concentration intracellular signaling proteins
( Ca2+?? Vesical release??).
 Chemotaxis[2]
E. coli chemotaxis network converts external
change of stimulus into a change in concentration
of signaling protein CheYp, which controls cell
motile behavior.
Use E. coli chemotaxis network as a prototype to explore the
general information processing principle in biological systems.
[1] Peter B. Detwiler et al. (2000). Biophysical Journal. 79, 2801-2817
[2] Birgit E. Scharf et al. (1998) PNAS. 95, 201-206
Background:
Introduction to Chemotaxis in E. coli
Fluorescently labeled E. coli, from Berg lab
Dimensions:
Body size: 1 μm in length
0.4 μm in radius
Flagellum: 10 μm long
45 nm in diameter
From R. M. Berry, Encyclopedia of Life Sciences
Physical constants:
Cell speed: 20-30 μm/sec
Mean run time: 1 sec
Mean tumble time: 0.1 sec
One of the key features of E. coli chemotaxis
network: Adaptation.
Background:
Adaptation in E. coli Chemotaxis Network
Adaptation is the restoration of pre-stimulus
behavior following a change in external stimulus.
Fig. 1[3]
Adaptation to addition /removal of
stimuli.
Attractant: 30 μM MeAsp.
Repellent: 100 μM NiCl2
YFP/CFP ~ [CheYp]
Fig. 2[4]
The left most curve is the relation
between the adaptation time of E.
coli and step-wise change of
[MeAsp] (1e-2 ~ 1e+4 μM).
Why does E. coli’s response vary?
[3] Sourjik et al. (2002) PNAS. 99 123-127
[4] Howard C. Berg, (1975) PNAS. 72 71-713
Outline
 Modeling E. coli chemotaxis network
 Chemical signal transduction pathway (reactions)
 Numerical implementation of transduction pathway
(stochsim package)
 Couple motor response, output of transduction
pathway, to cell motion
 Preliminary numerical results
 Model validation (excitation and adaptation, motile
behavior, etc)
 Input-output mutual information transmission
 Relates the role of adaptation.
 Future work
Modeling Chemotaxis in E. coli:
Picture of Numerical Implementation
Stimulus
Signal
Transduction
Pathway
Motor
Response
Flagellar
Response (?)
Motion
Chemical Signal Transduction
Pathway
Table I: Signal Transduction Network
Simulating Reactions
We use Stochsim[5] package, a general platform for
simulating reactions using a stochastic method, to simulate
reactions. Reactions have a probabilities p to occur.
 Unimolecular reaction
A 
B
k
 Bimolecular reaction
A  B 
C
k
kn(n  n0 )t
p
n0
p
kn( n  n0 ) t
2 N AV
n: Number of molecules from reaction system
n0: Number of pseudo-molecules
NA: Avogadro constant
p: Probability for a reaction to happen
Δt: Simulation time step
V: Simulation volume
[6] Carl Jason Morton-Firth et al. 1998 J. Theor. Biol.. 192 117-128
Parameters Values for Receptor
Activation
En  En*
En a  En*a
n  [0, 4]
En: methylated receptor complex; activation probability, P1(n)
Ena: ligand-bound receptor complex; activation probability, P2(n)
En*: active form of En
En*a: active form of Ena
Table II: Activation Probabilities
n
P1(n)
P2(n)
0
0.02
0.00291
1
0.1
0.02
2
0.312
0.1
3
0.94
0.345
4
0.997
0.98
Parameters Values for Proteins
Table III:
Initial Numbers of Molecules
Molecule
Number
Concentration (μM)
Y
15684
18
Yp
0
0
R
250
0.29
E
6276
-
B
1928
2.27
Bp
0
0
Reaction Volume: 1.41 x 10-15 liter
Rate constants given above.
Parameter Value for Motor
Response
Table IV: parameters values
Paramter
Value
Literature value
KR
5.9 μM
3~12 μM
KT
1.7 μM
1~7 μM
Kf(0)
1.0E-5 μM
3.35E-4 μM
Kb(0)
1.5E+4 μM
2.2E+4 μM
μ
2.21
1.61
Linda Turner et al. Biophysical Journal (1999),
Philippe Cluzel et al., Science (2000)
From Motor Response to Cell
Motion
 Output of the chemotaxis network is the motor
state which determines the motile behavior.
R  run
T  tumble

v = 20 μm/s
Dr = 0.06205 s-1
Run[6]
t
t+Δt
p( )  2tDr N (0,1)
    1
 
) exp( 
)


p ( ) 
( )
(
 Tumble[7]
α
[6] Zou et al. (2003) Biophys. Journal. 85 2147-2157
[7] Berg and Brown (1972) Nature. 239 500-504
γ=4
μ = -4.6
β = 18.32
Outline
 Modeling E. coli chemotaxis network
 Chemical signal transduction pathway (reactions)
 Numerical implementation of transduction pathway
(stochsim package)
 Couple motor response, output of transduction
pathway, to cell motion
 Preliminary numerical results
 Model validation (excitation and adaptation, motile
behavior, etc)
 Input-output mutual information transmission
 Future work
1
0.5
0
0
10
20
30
40
50
Time [sec]
Fig. 3
E. coli motor response to 10 μM
step-wise change of Asp at t=5 sec.
The motor CCW bias is plotted as a
funcion of time.
Adaptation Time [sec]
Motor CCW Bias
Model Validation:
Step Response and Adaptation Time
100
50
0 -2
10
0
10
Step Size [M]
2
10
Fig. 4
Adaptation time under various
step-wise change of [Asp] from 0
to 0.1, 1, 10, 100, respectively.
Adaptation time is defined as the
motor CCW bias returns to its
pre-stimulus value. (1000 is
running)
Model Validation:
Impulse Response of Wild-type Cell
Motor CCW Bias
1
0.5
0
0
5
10
Time [sec]
Fig. 5
Impulse response of wild-type cell，impulse duration 0.2 sec.
Left: Experimental result from Steven M. Block et all, Cell (1982)
Right: Simulation result (data smoothed)
15
20
Model Validation:
Running & Tumbling Intervals
0
10
-1
Fraction
10
-2
10
-3
10
-4
10
0
5
10
15
20
CCW and CW Interval [sec]
Fig. 6
The distribution of motor CCW and CW events.
Left: korobkova et al., 2004
Right: Simulation results. (Red: CCW events; Black: CW events) (running to get a
better looking result)
I/O Mutual Information:
Preliminary Results
 Construct Input-Output relation.
 Construct a formula to calculate input-output
mutual information.
 Calculate IO information under different signals
if we use the response to a specific signal.
 Investigate the role of correlation time of
signals in input-output information
transmission.
I/O Mutual Information:
Construct Input-output Relation
1500
2
0
0
NCheYp
15
2
4
6
Time [sec]
8
10
x100
1450
1500
1400
1450
 =1
 =3
 =5
 =10
1400
1350
1350
14
13
1550
NCheYp
4
NCheYp
[As]  M
 Artificial signal is presented to the simulation system.
1300
0
2
4
6
Time [sec]
8
Fig. 7
Upper panel: Gaussian
distributed artificial signal
(μ=3 μM,σ2 = 3 μM2,
correlation time 1 sec).
Lower panel: Response
to the input signal.
10
0
2
4
6
[Asp]  M
8
10
Fig. 8

Response delays input by
0.1 sec.

Input signal is binned first.

Find response to input
signal in each bin, then
find the average response.
1300
0
5
10
15
20
[Asp]  M
25
Fig. 9
I-O relation under signals
with different statistics.
The correlation time of the
signals is the same: 1 sec.
Question: What is the role of varying response under different signals.
30
I/O Mutual Information:
Calculation
 The following equation is used to calculate IO
mutual information rate[7].
P(r )   P( s)
s r
I  S [ P(r )]   P(r ) S [ P( n | r )]
r
S [ 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 found as in last slide, mapping s to r.
n: noise;
P(n|r): noise distribution conditioned
on response
[7] Naama Brenner et al. (2000) Neuron. 26 695-702
I/O Mutual Information:
Effect of Correlation Time of Signal
IO information rate (bit)
 The so found response function under an input signal
maximizing information rate under such input.
3
2
1
0
0
5
10
<Signal>  M
15
20
Fig. 10
All signals have correlation time of 1 sec. The response function, r(s), to (3, 3) is
used to transform input signals with different statistical properties to output. The
IO mutual information is calculated. The IO information rate maximizes at (3, 3)
signal, which is the signal that is used to find r(s).
IO Mutual Information:
Effect of Correlation Time of Signal
5
Information rate (bit)
4.5
4
3.5
3
 S = 1 2s = 1 (unit:  M)
 S = 3 2s = 3
2.5
 S = 5 2s = 5
2
1.5
0
 S = 10 2s = 10
0.5
1
1.5
2
2.5
Correlation time of signal [sec]
3
3.5
Fig. 11
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.
Conclusion
Outline
 Modeling E. coli chemotaxis network
 Chemical signal transduction pathway (reactions)
 Motor and flagella response, and cell motion
 Numerical implementation (stochsim package)
 Preliminary numerical results
 Model validation (excitation and adaptation, motile
behavior, etc)
 Input-output mutual information transmission
 Future work
Thank you.