March 8, 2007March APS Meeting, Denver, CO1 Near-Perfect Adaptation in Bacterial Chemotaxis Yang Yang and Sima Setayeshgar Department of Physics Indiana University, Bloomington, IN

March 8, 2007March APS Meeting, Denver, CO2 Chemotaxis in E. coli Increasing attractants / decreasing repellent Run Tumble Courtesy of Howard Berg Lab

March 8, 2007March APS Meeting, Denver, CO3 Chemotaxis Signal Transduction Network in E. coli ; CheB CheACheWCheZ CheR CheY

March 8, 2007March APS Meeting, Denver, CO4 Robust Perfect Adaptation

March 8, 2007March APS Meeting, Denver, CO5 This Work: Outline  New computational scheme for determining  conditions  numerical 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, 2007March APS Meeting, Denver, CO6  Ligand binding  Methylation  Phosphorylation T3T4 T2 T4pT2pT3p LT3 LT4 LT4p LT2 LT3pLT2p phosphorylation methylation Ligand binding Biochemical Signaling Network

March 8, 2007March APS Meeting, Denver, CO7  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. : state variables : reaction kinetics : reaction constants : external stimulus Numerical Scheme

March 8, 2007March APS Meeting, Denver, CO8 Decretizing s into H points Augmented system The 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

March 8, 2007March APS Meeting, Denver, CO9 Near-perfect Adaptation

Implementation Newton-Raphson, to solve for the steady state of augmented system: Dsode (stiff ODE solver), to verify Time dependent behavior of proteins for different ranges of external stimulus by solving: March 8, March 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 Autophosphorylation rate of T4 (k10) LT2 methylation rate (k3c) Autophosphorylation rate of T4 (k10) T4 demethylation rate (km2) parameter spaces of E. coli March 8, March APS Meeting, Denver, CO

DSODE solutions for NR parameters set(3) March 8, 2007March APS Meeting, Denver, CO12

9% k 1c : 0.17 s -1  1 s -1 1% k 1c : 0.17 s -1  1 s -1 k 8 : 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)Autophosphorylation rate of T2 (k8) March 8, March APS Meeting, Denver, CO

Condition 2 Autophosphorylation rate of LT2 (k12) Methylation rate of LT2 (k3c) Autophosphorylation rate of T2 (k8) Methylation rate of T2 (k1c) Autophosphorylation rate of LT3 (k13) Methylation rate of LT3 (k4c) Autophosphorylation rate of T3 (k9) Methylation rate of T3 (k2c) Methylation rate autophosphorylation rate

Condition 2-continue Autophosphorylation rate of T3 (k 9 ) Demethylation rate of T3 (k m1 ) Autophosphorylation rate of T4 (k10) Demethylation rate of T4 (k m2 ) Autophosphorylation rate of LT3 (k 12 ) Demethylation rate of LT3 (km3) Autophosphorylation rate of LT4 (k 13 ) demethylation rate of LT4 (km4) demethylation rate (autophosphorylation rate) 2

Condition 4 demethylation rate/phosphorylation rate autophosphorylation rate T3 autophosphorylation rate T3 demethylation rate/ T2 methylation rate T4 autophosphorylation rate T4 demethylation rate/ T3 methylation rate LT3 autophosphorylation rate T3 demethylation rate/ T2 methylation rate LT4 autophosphorylation rate LT4 demethylation rate/ LT3 methylation rate

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 phosphorylation rate / literature value CheY phosphorylation rate / literature value (L)T n autophosphorylation rate / literature value ● T2 ● T3 ● T4 ● LT3 ● LT4 ● T2 ● T3 ● T4 ● LT3 ● LT4 CheB phosphorylation rate LT 2 autophosphorylation rate CheY phosphorylation rate LT 2 autophosphorylation rate CheB, CheY phosphorylation rate autophosphorylation rate

March 8, 2007March APS Meeting, Denver, CO18 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. CheY1 p (µM) Time(s)

parameter spaces comparison of two and single CheY case

March 8, 2007March APS Meeting, Denver, CO24 Conclusions Complete construction of manifolds in parameter space, allowing insight into parameter dependence giving rise to robustness Work in progress

March 8, 2007March APS Meeting, Denver, CO25 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, 2007March APS Meeting, Denver, CO26 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, 2007March APS Meeting, Denver, CO27 Future Work