March 8, 2007 March APS Meeting, Denver, CO 1

Near-Perfect Adaptation in Bacterial Chemotaxis

Yang Yang and Sima Setayeshgar

Department of Physics

Indiana University, Bloomington, IN

March 8, 2007 March APS Meeting, Denver, CO 2

Chemotaxis in E. coli

http://www.rowland.harvard.edu/labs/bacteria/index_movies.html

Increasing attractants / decreasing repellent

Run TumbleCourtesy of Howard Berg Lab

March 8, 2007 March APS Meeting, Denver, CO 3

Chemotaxis Signal Transduction Network in E. coli

;

CheB

CheW

CheZ

CheR

CheY

March 8, 2007 March APS Meeting, Denver, CO 4

Robust Perfect Adaptation

March 8, 2007 March APS Meeting, Denver, CO 5

This Work: Outline New computational scheme for determining

conditionsnumerical ranges

for parameters allowing robust (near-)perfect adaptation in the context of the E. coli chemotaxis network

Comparison of results with previous works

Extension to other chemotaxis networks, with additional protein components

Conclusions and future work

March 8, 2007 March APS Meeting, Denver, CO 6

Ligand binding

Methylation

Phosphorylation

)()( )(7/7~5/5

)( CheRLTCheRTL pnkmkkmk

pn

ppnmkmk

ppn

pnckck

pn

CheBTLCheBTL

CheRTLCheRTL

)(14~1

)(

)(14~1

)(

)()(

)()(

PCheBCheB

PCheYCheZCheZCheY

CheBCheRTCheBCheRTL

CheYCheRTCheYCheRTL

ADPCheRTLATPCheRTL

kmbp

kmyp

pnkb

np

nky

np

npkk

n

)()()(

)()()(

)()()()( 9~7

T3 T4T2

T4pT2p T3p

LT3 LT4

LT4p

LT2

LT3pLT2p

phosphorylation

methylation

Liga

nd b

indi

ng

Biochemical Signaling Network

March 8, 2007 March APS Meeting, Denver, CO 7

START with a fine-tuned model of chemotaxis network that:

reproduces key features of experiments

is NOT robust

AUGMENT the model explicitly with the requirements that: steady state value of CheYp

values of reaction rate constants,

are independent of the external stimulus, s, thereby achieving robustness of perfect adaptation.

s

k

F

u

skuFdt

ud

0);;(

: state variables

: reaction kinetics

: reaction constants

: external stimulus

Numerical Scheme

March 8, 2007 March APS Meeting, Denver, CO 8

Decretizing s

into H points

0

||

0);;(

ds

kdds

du

skuFdt

ud

N

02

|2

|

0);;(

)1(

11

11

s

kks

uu

skuFdt

ud

sjss

jm

jm

j

jN

jN

jjj

jlowj

Augmented systemThe steady state concentration of proteins in the network must satisfy:

The steady state concentration of CheYp must satisfy:

At the same time, the reaction rate constants must be independent of stimulus:

: allows for near-perfect adaptation

= CheYp

0ds

kd

0);;( skuFdt

ud

N

N

u

ds

du

||

March 8, 2007 March APS Meeting, Denver, CO 9

Near-perfect Adaptation

ImplementationNewton-Raphson, to solve for the steady state of augmented system:

0

||

0);;(

ds

kdds

du

skuFdt

ud

N

Dsode (stiff ODE solver), to verify Time dependent behavior of proteins for different ranges of external stimulus by solving:

0);;( skuFdt

ud

March 8, 2007 10March APS Meeting, Denver, CO

Pairwise result: 3D surface result:

Relative change of CheYp:• less than 5% and greater than 3%• less than 3% and greater than 1%• less than 1%• pairwise trajectory

E .coli

Auto

phosp

hory

lati

on r

ate

of

T4

(k

10

)

LT2 methylation rate (k3c)

Auto

phosp

hory

lati

on r

ate

of

T4

(k

10

)

T4 demethylation rate (km2)

parameter spaces of E. coli

March 8, 2007 11March APS Meeting, Denver, CO

DSODE solutions for NR parameters set(3)

March 8, 2007 March APS Meeting, Denver, CO 12

1%

k1c : 0.17 s-1 1 s-1

k8 : 15 s-1 12.7 s-1

Violating and restoring perfect adaptation

At 250s, giving step stimulus from 0 to 1e-6M

(1,15)

(1,12.7)

Methylation rate of T2 (k1c)

Auto

phosp

hory

lati

on r

ate

of

T2 (

k8)

March 8, 2007 13March APS Meeting, Denver, CO

Condition 2

Autophosphorylation rate of LT2 (k12)

Meth

yla

tion r

ate

of

LT2

(k

3c)

Autophosphorylation rate of T2 (k8)

Meth

yla

tion r

ate

of

T2

(k1

c)

Autophosphorylation rate of LT3 (k13)

Meth

yla

tion r

ate

of

LT3

(k

4c)

Autophosphorylation rate of T3 (k9)

Meth

yla

tion r

ate

of

T3

(k2

c)

Methylation rate autophosphorylation rate

Condition 2-continue

Autophosphorylation rate of T3 (k9)

Dem

eth

yla

tion r

ate

of

T3

(k

m1)

Autophosphorylation rate of T4 (k10)

Dem

eth

yla

tion r

ate

of

T4

(k

m2)

Autophosphorylation rate of LT3 (k12)

Dem

eth

yla

tion r

ate

of

LT3

(k

m3

)

Autophosphorylation rate of LT4 (k13)

dem

eth

yla

tion r

ate

of

LT4

(k

m4

)

demethylation rate (autophosphorylation rate)2

Condition 4demethylation rate/phosphorylation rate

autophosphorylation rate

T3 autophosphorylation rate

T3

dem

eth

yla

tion

rate

/ T2

meth

yla

tion

ra

te

T4 autophosphorylation rate

T4

dem

eth

yla

tion

rate

/ T3

meth

yla

tion

ra

te

LT3 autophosphorylation rate

T3

dem

eth

yla

tion

rate

/ T2

meth

yla

tion

ra

te

LT4 autophosphorylation rate

LT4

dem

eth

yla

tion

rate

/ LT

3 m

eth

yla

tion

ra

te

Condition 5

*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

CheB

phosp

hory

lati

on

rate

/ lit

era

ture

valu

e

CheY p

hosp

hory

lati

on

rate

/ lit

era

ture

valu

e

(L)Tn autophosphorylation rate / literature value(L)Tn autophosphorylation rate / literature value

● T2● T3● T4● LT3● LT4

● T2● T3● T4● LT3● LT4

Ch

eB

ph

osp

hory

lati

on

rate

LT2 autophosphorylation rate

Ch

eY p

hosp

hory

lati

on

rate

LT2 autophosphorylation rate

CheB, CheY phosphorylation rate autophosphorylation rate

March 8, 2007 March APS Meeting, Denver, CO 18

Two CheY system

•Rhodobacter sphaeroides, Caulobacter crescentus have multiple CheYs while lack of CheZ protein.•Similar chemotaxis behaviors.

Two CheY system

Our work:Reproduce the key feature of chemotaxis behavior in two CheY system by replacing CheZ with CheY2.

Ch

eY1

p (µ

M)

Ch

eY1

p (µ

M)

Time(s) Time(s)

parameter spaces comparison of two and

single CheY case

parameter spaces comparison of two and

single CheY case

parameter spaces comparison of two and

single CheY case

parameter spaces comparison of two and

single CheY case

March 8, 2007 March APS Meeting, Denver, CO 24

Conclusions

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

Work in progress

March 8, 2007 March APS Meeting, Denver, CO 25

Future work• Applying the method to other cellular signal

transduction networks exhibiting robust homeostasis, such as phototransduction

Signal flow in visual transduction, Leon Lagnado and Denis Baylor,Neuron,1992

March 8, 2007 March APS Meeting, Denver, CO 26

Conclusions Successful implementation of a novel method for elucidating regions in parameter space allowing precise adaptation

Preliminary results for two- and three-dimensional projections of (near-) perfect adaptation manifolds in parameter space for the E. coli chemotaxis network, allowing determination of

conditions required for perfect adaptation, consistent with previous works numerical ranges for unknown or partially known kinetic parameters

Extension to modification of the E. coli chemotaxis network, consistent with absence of CheZ homolog and presence of multiple CheY copies in rhizobacteria

March 8, 2007 March APS Meeting, Denver, CO 27

Future Work