1. Module 2: Robustness in Biochemical Signaling Networks
Complete this
First, design simple reactions show how this worked.
Second, find all reactions and compare the configuration files to those used in Agentcell package.
2/23/07
Indiana University P676

2. Bacterial Chemotaxis
The chemosensory pathway in bacterial chemotaxis and propulsion system it regulates have provided an ideal system for probing the physical principles governing complex cellular signaling and response.
“Hydrogen atom” of biochemical signal transduction networks
Paradigm for two-component receptor-regulated phosphorylation pathways
Accessible for study by structural, biochemical and genetic approaches
2/23/07
Indiana University P676

3. Chemotaxis in E. coli (Courtesy of Howard Berg group) Dimensions:
Specifically, I will talk about modeling chemotaxis in E. coli. As is familiar to this audience, E. coli is the “work horse” of molecular biology. We focus on it from a modeling standpoint because it is well-studied. In particular, the chemotaxis network in E. coli is the best characterized two-component signaling system: all protein components are known and most have been crystallized.
As you know, chemotaxis is the cell’s biased random walk toward attractants and away from repellents. It consists of runs (approximately 50 microns in length) punctuated by tumbles.
Each cell consists of 4-6 flagella. Flagella have an inherent helicity, such that CCW rotation of the flagellar motor leads to bundling of the flagella, which then act as a propeller leading to running motion, and CW rotation of one or more of the flagellar motors leads to the flying apart of the bundle and tumbling motion.
The cell’s response to its environment is through modulation of its mean run time (through modulation of the CW/CCW motor bias), extending it in favorable directions and suppressing it in unfavorable directions.
Dimensions:
Body size: 1 μm in length
0.4 μm in radius
Flagellum: 10 μm long
Physical constants:
Cell speed: μm/sec
Mean run time: 1 sec
Mean tumble time: 0.1 sec
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4. E. coli in Motion From Berg & Brown, Nature (1972). 2/23/07
E. coli in Motion
From Berg & Brown, Nature (1972).
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Indiana University P676

5. Signal Transduction and Behavioral Response
Stimulus
Signal
Transduction
Pathway
[CheY-P]
Motor
Response
In modeling chemotaxis in E. coli, we must describe the signal transduction pathway that converts an external stimulus (attractant or repellent) into an internal response regulator (change in concentration of CheY-P), as well as the motor and flagellar response leading to the cell’s motion.
E. coli’s chemotaxis network is a multiscale network. Some reactions are fast (ligand binding, phosphrylation, and phosphotransfer) while there are other slow reactions (methylation and demethylation), allowing for a memory of the past environment. Adaptation is achieved by balancing the these fast and slow processes.
Flagellar
Bundling
Motion
(Courtesy of Howard Berg lab).
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Indiana University P676

6. Flagellar motor Flagellum Basal part of flagellar motor C-ring
Number of FliM subunits = 34
From Thomas et al. PNAS (1999).
From Cluzel et al. Science (2000).
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Indiana University P676

7. Response to Step Stimulus
From Sourjik et al., PNAS (2002).
From Block et al., Cell (1982).
Fast response
Slow adaptation
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8. Excitation and Adaptation
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9. Precision of Adaptation
Squares: Unstimulated cells
Circles: Cells stimulated at t=0
(Each point represents data from 10s motion of cells.)
Precision of adaptation =
steady state tumbling
frequency of unstimulated cells /
frequency of stimulated cells
From Alon et al. Nature (1999).
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Indiana University P676

10. Robustness of Perfect Adaptation
Precision of adaptation robust to 50-fold change in CheR expression …
…while …
Adaptation time and steady state tumbling frequency vary significantly.
Robustness of perfect adaptation
From Alon et al. Nature (1999).
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Indiana University P676

11. Detailed model of the E. coli chemotaxis network …
Ligand binding (fast)
Phosphorylation (fast)
Methylation (slow)
From Alon et al. Nature (1999).
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Indiana University P676

12. Ligand Binding E: receptor complex a: ligand (eg., aspartate)
Rapid equilibrium:
Rates1:
E: KD = 1.71x10-6 M-1
E*: KD = 12x10-6 M-1
Where are these KD from?
Rapid equilibrium: If a MS is chosen, stochsim will first ‘equilibrate’ any rapid equilibria defined for this complex.
Rate constants1:
kf = 1x109 M-1sec-1
kr = 1x103 sec-1
[1]. Carl Jason et al. 1998
Mention:
In the subsequent slides, the rates are based on the same paper.
Rates:
Biemann & Koshland, 1994 Aspartate receptors of E. coli and Salmonella typhimurium bind ligand with negative and half-of-the sites cooperativity. Biochem. 33,
In viro
In vitro
Barkai: 1.0e09 M-1sec e03 sec-1
Spiro: 7e07 M-1sec sec-1
Possible question:
[1] Morton-Firth et al., J. Mol. Biol. (1999)
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13. Table 1: Activation Probabilities
Receptor Activation
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 1: Activation Probabilities n
P1(n)
P2(n)
0.02 1
0.125 2
0.5 3
0.875 4
0.997
0.98
Rates:
Katherine A. Borkovich, Lisa A. Alex, and Melvin I. Simon, Attenuation of sensory receptor signaling by covalent modification, Proc. Natl. Acad. Sci. USA, 89(1992) 6756
Katherine A. Borkovich, et al. Transmembrand Signal transduction in bacterial chemotaxis involves ligand-depdent activation of phosphate group transfer. Proc. Natl. Acad. Sci. USA, 86(1989) 1208
Determined by in vitro experiment for Tar receptor , 0:2:4 are determined and 1, 3 methyl groups are calculated by linear interpolation.
Ligand-bound Tar receptor, in vitro experiment.
Barkai: unoccupied:
occupied
From Morton-Firth:
Following adaptation to high level aspartate, the average methylation level rises from two to three.
For unoccupide Tar with 3 methyl groups, the probability is calculated
deltaG = -RTln(p/(1-p))
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14. Methylation (1) (2) R: CheR En(a): En, Ena
En(*)(a): En, En*, Ena, En*a
Rate constants:
k1f = 5x106 M-1sec-1
k1r = 1 sec-1
k2f = sec-1
This reaction is in question
En should be inactive, since they assume R only binds to inactive form of En.
Have problem with this slide.
Barkai: 8e07 M-1sec sec sec-1
Spiro: k1r/k1f = 1.7 e-06 M here 0.2 e-06 M use different rates for receptors with different methyl groups.
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Indiana University P676

15. Demethylation (1) (2) Bp: CheB-P En*(a): En*, En*a Rate constants:
k1f = 1x106 M-1sec-1
k1r = 1.25 sec-1
k2f = sec-1
Also have question of the second reaction. Does EnBp changes to inactive form before it can be dephosphrylated. Or both active and inactive form.
Barkai: 8e08 M-1sec sec sec-1
Spiro: dose not given.
Diffusion limited reaction rate:
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16. Autophosphorylation E*: En*, En*a Rate constant: kf = 15.5 sec-1
Personal communication.
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17. CheY Reactions Y: CheY Yp: CheY-P Rate constants:
k1f = 1.24x10-3 sec-1
k1r = 4.5x10-2 sec-1
k2f = sec-1
The second reaction is Yp desphosphorylation by CheZ.
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Indiana University P676

18. CheY Phosphotransfer Rate constants: k1f = 5x106 M-1sec-1
k2f = 20 sec-1
k2r = 5x106 M-1sec-1
k3f = 7.5 sec-1
k3r = 5x106 M-1sec-1
Spiro
Total : 3 e07 M-1sec-1
Second not considered
The first one is assumed to be diffusion-limited reaction.
Association are also assumed to be diffusion-limited. But 5 times 1e06.
Dissociation constant od E-YP is 4 uM. (Li et al. 1995)
Dissociation constant of E-Y is 1.5 uM. (In vitro experiment. stewart)
What is E in the first reaction: All kind of forms of E. En(*)(a)
What is E in the second reaction.
In vitro experiment.
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19. CheB Reactions B: CheB Bp: CheB-P Rate constant: kf = 0.35 sec-1 Spiro
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20. CheB Phosphotransfer Rate constants: k1f = 5x106 M-1sec-1
k2f = 16 sec-1
k2r = 5x106 M-1sec-1
k3f = 16 sec-1
k3r = 5x106 M-1sec-1
3 e 05 M-1s-1
Dissociation constant of EB is 3.2 uM. (Li et al.
Dissociation constant of EpB is assumed to be the same as EB.
Association constant are assumed to be diffusion-limited.
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Indiana University P676

21. Robustness of Receptor Activity to Network Parameters
B-L model:
* simplified model based on
two-state model of
chemoreceptors
* no phosphorylation (!)
* precision of adaptation
defined in terms of receptor
activity
Robustness of perfect adaptation to variations in kinetic rate constants …
… not so for adaptation time.
From Barkai et al. Nature (1997).
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Indiana University P676

22. Next time…
What are the essential features of the BL model allowing robustness of perfect adaption to network parameters (rate constants, total protein concentrations)?
What are the expected variations in these parameters in a population of (clonally identical) cells?
What is integral feedback control and where does it come from?
2/23/07
Indiana University P676