5/10/2015Yang Yang, Candidacy Seminar1 Near-Perfect Adaptation in Bacterial Chemotaxis Yang Yang and Sima Setayeshgar Department of Physics Indiana University, Bloomington, IN

Bacterial Chemotaxis “Hydrogen atom” of biochemical signal transduction networks Paradigm for two-component receptor-regulated phosphorylation pathways Accessible for study by structural, biochemical and genetic approaches 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.

E. Coli as a Model Organism 5/10/2015Yang Yang, Candidacy Seminar3 Workhorse of molecular biology: Most studied cell in all science: … Small genome(~4300 genes). … Normal lack of pathogenicity … Ease of growth in lab  Basis of recent developements in biotechnology and genetic engineering, including living factory for producing human medicines  Basis for understanding of fundamental cellular processes: … cellular sensory systems, … regulation of gene expression, … cell division, etc.  Size: … 0.5 μm in diameter, … 1.5 μm in length  Cell cycle: … ~ 1 hour

Chemotaxis in E. coli 5/10/2015Yang Yang, Candidacy Seminar4 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 (Courtesy of Howard Berg group)

E. coli in Motion 5/10/2015Yang Yang, Candidacy Seminar5 From Berg & Brown, Nature (1972).

E. coli Flagellar Motor 5/10/2015Yang Yang, Candidacy Seminar6 From R. M. Berry, Encyclopedia of Life Science (2001). From P. Cluzel, et al., Science (2000).

Chemotaxis Signal Transduction Network in E. coli 5/10/2015Yang Yang, Candidacy Seminar 7 Histidine kinase Methylesterase Couples CheA to MCPs Response regulator Methyltransferase Dephosphorylates CheY-P CheB CheA CheW CheZ CheR CheY Signal Transduction Pathway Motor Response [CheY-P] Stimulus Flagellar Bundling Motion Run Tumble

Response to Step Stimulus 5/10/2015Yang Yang, Candidacy Seminar8 Fast responseSlow adaptation From Block et al., Cell (1982). From Sourjik et al., PNAS (2002).

Excitation and Adaptation 5/10/2015Yang Yang, Candidacy Seminar9

Precision of Adaptation 5/10/2015Yang Yang, Candidacy Seminar10 From Alon et al. Nature (1999). Precision of adaptation = steady state tumbling frequency of unstimulated cells / steady state tumbling frequency of stimulated cells Squares: Unstimulated cells Circles: Cells stimulated at t=0 (Each point represents data from 10s motion of cells.)

Robustness of Perfect Adaptation 5/10/2015Yang Yang, Candidacy Seminar11 From Alon et al. Nature (1999). 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

Robust Perfect Adaptation 5/10/2015Yang Yang, Candidacy Seminar Fast responseSlow adaptation From Sourjik et al., PNAS (2002). FRET signal [CheY-P] From Alon et al., Nature (1999). CheR fold expression Adaptation Precison Steady state [CheY-P] / running bias independent of value constant external stimulus (adaptation) Precision of adaptation insensitive to changes in network parameters (robustness) 12

This Work: Outline 5/10/2015Yang Yang, Candidacy Seminar13  New computational scheme for determining conditions and numerical ranges for parameters allowing robust (near-)perfect adaptation in the E. coli chemotaxis network  Comparison of results with previous works  Extension to other modified chemotaxis networks, with additional protein components  Conclusions and future work

E. coli Chemotaxis Signaling Network 5/10/2015Yang Yang, Candidacy Seminar14  Ligand binding  Methylation  Phosphorylation phosphorylation methylation Ligand binding E=F(free form), R(coupling with CheR), B(coupling with CheB p ) E’=F(free form), R(coupling with CheR)  =o(ligand occupied), v(ligand vacuum)  =u(unphosphorylated), p(phosphorylated)

Enzymatic reaction: Where E is the enzyme, S is the substrate, P is the product. A key assumption in this derivation is the quasi steady state approximation, namely that the concentration of the substrate-bound enzyme changes much more slowly than those of the product and substrate. Therefore, it may be assumed that it is in steady state: Michaelis-Menten Kinetics 5/10/2015Yang Yang, Candidacy Seminar15 where K m is the Michaelis Menten Constant (MM constant)

Reaction Rates 5/10/2015Yang Yang, Candidacy Seminar16

Approach … 5/10/2015Yang Yang, Candidacy Seminar17  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 CheY-P  values of reaction rate constants, are independent of the external stimulus, s, thereby explicitly incorporating perfect adaptation. : state variables : reaction kinetics : reaction rates : external stimulus

The steady state concentration of proteins in the network satisfy: The steady state concentration of = [CheY-P] must be independent of stimulus, s: where parameter allows for “near- perfect” adaptation. Reaction rates are constant and must also be independent of stimulus, s: Augmented System 5/10/2015Yang Yang, Candidacy Seminar18 Discretize s in range {s low, s high }

Physical Interpretation of Parameter, : Near-Perfect Adaptation 5/10/2015Yang Yang, Candidacy Seminar19  Measurement of c = [CheY-P] by flagellar motor constrained by diffusive noise Relative accuracy*,  Signaling pathway required to adapt “nearly” perfectly, to within this lower bound (*) Berg & Purcell, Biophys. J. (1977). : diffusion constant (~ 3 µM) : linear dimension of motor C-ring (~ 45 nm) : CheY-P concentration (at steady state ~ 3 µM) : measurement time (run duration ~ 1 second)

 Use Newton-Raphson (root finding algorithm with back-tracking), to solve for the steady state of augmented system,  Use Dsode (stiff ODE solver), to verify time- dependent behavior for different ranges of external stimulus by solving: Implementation 5/10/2015Yang Yang, Candidacy Seminar20

Converting from Guess to Solution 5/10/2015Yang Yang, Candidacy Seminar21 A B Starting from initial guess A, the solution to B is generated. T 3 autophosphorylation rate (k 3a ) Inverse of T 3 MM constant (K 3R -1 ) ● 3%<  <5% ● 1%<  <3% ● 0%<  <1%

Parameter Surfaces 5/10/2015Yang Yang, Candidacy Seminar22 ● 1%<  <3% ● 0%<  <1% Surface 2D projections Inverse of T 1 methylation MM constant (K 1R -1 ) Inverse of T 1 demethylation MM constant(k 1B -1 ) T 1 autophosphorylation rate K 1a Inverse of T 1 methylation MM constant (K 1R -1 )

Slices of 3D Surfaces of Parameter Space 5/10/2015Yang Yang, Candidacy Seminar

Validation 5/10/2015Yang Yang, Candidacy Seminar24 Time (s) Concentration (µM) Verify steady state NR solutions dynamically using DSODE for different stimulus ramps:

Violating and Restoring Perfect Adaptation 5/10/2015 Yang Yang, Candidacy Seminar 25 Step stimulus from 0 to 1e-3M at t=500s (5e+6,10) (1e+6,10) T 3 autophosphorylation rate (k 9 ) CheYp Concentration (µM) Inverse of T 3 MM constant (K 3R -1 ) Time (s)

Conditions for Perfect Adaptation: Kinetic Parameters 5/10/201526Yang Yang, Candidacy Seminar

Inverse of Methylation MM Constant Autophosphorylation Rate 5/10/2015Yang Yang, Candidacy Seminar27 T 0 autophosphorylation rate (k 0a ) Inverse of T 0 MM constant (K 0R -1 ) T 1 autophosphorylation rate (k 1a ) Inverse of T 1 MM constant (K1 R -1 )

Inverse of Methylation MM Constant Autophosphorylation Rate 5/10/2015Yang Yang, Candidacy Seminar28 T 2 autophosphorylation rate (k 2a ) T 3 autophosphorylation rate (k 3a ) Inverse of T 2 MM constant (K 2R -1 ) Inverse of T 3 MM constant (K 3R -1 )

Inverse of Methylation MM Constant Autophosphorylation Rate 5/10/2015Yang Yang, Candidacy Seminar29 LT 0 autophosphorylation rate (k 0al ) LT 1 autophosphorylation rate (k 1al ) Inverse of LT 0 MM constant (K 0LR -1 ) Inverse of LT 1 MM constant (K 1LR -1 )

Inverse of Methylation MM Constant Autophosphorylation Rate 5/10/2015Yang Yang, Candidacy Seminar30 LT 2 autophosphorylation rate (k 2al ) LT 3 autophosphorylation rate (k 3al ) Inverse of LT 2 MM constant (K 2LR -1 ) Inverse of LT 3 MM constant (K 3LR -1 )

Inverse of Demethylation MM Constant Autophosphorylation Rate 5/10/2015Yang Yang, Candidacy Seminar31 T 1 autophosphorylation rate (k 1a ) T 2 autophosphorylation rate (k 2a ) Inverse of T 1 MM constant (K 1B -1 ) Inverse of T 2 MM constant (K 2B -1 )

Inverse of Demethylation MM Constant Autophosphorylation Rate 5/10/2015Yang Yang, Candidacy Seminar32 T 3 autophosphorylation rate (k 3a ) T 4 autophosphorylation rate (k 4a ) Inverse of T 3 MM constant (K 3B -1 ) Inverse of T 4 MIM constant (K 4B -1 )

Inverse of Demethylation MM Constant Autophosphorylation Rate 5/10/2015Yang Yang, Candidacy Seminar33 LT 1 autophosphorylation rate (k 1al ) LT 2 autophosphorylation rate (k 2al ) Inverse of LT 1 MM constant (K 1LB -1 ) Inverse of LT 2 MM constant (K 2LB -1 )

Inverse of Demethylation MM Constant Autophosphorylation Rate 5/10/2015Yang Yang, Candidacy Seminar34 LT 3 autophosphorylation rate (k 12 ) LT 4 autophosphorylation rate (k 13 ) Inverse of LT 3 MM constant (K 2LB -1 ) Inverse of LT 4 MM constant (K 3LB -1 )

Methylation Catalytic Rate/ Demethylation Catalytic Rate = Constant 5/10/2015Yang Yang, Candidacy Seminar35 T 1 demethylation catalytic rate T 1 methylation catalytic rate T 2 demethylation catalytic rate T 2 methylation catalytic rate

Methylation Catalytic Rate/ Demethylation Catalytic Rate = Constant 5/10/2015Yang Yang, Candidacy Seminar36 T 3 demethylation catalytic rate T 2 methylation catalytic rate T 4 demethylation catalytic rate T 3 methylation catalytic rate

Methylation Catalytic Rate/ Demethylation Catalytic Rate = Constant 5/10/2015Yang Yang, Candidacy Seminar37 LT 1 demethylation catalytic rate LT 0 methylation catalytic rate LT 2 demethylation catalytic rate LT 1 methylation catalytic rate

Methylation Catalytic Rate/ Demethylation Catlytic Rate = Constant 5/10/2015Yang Yang, Candidacy Seminar38 LT 3 demethylation catalytic rate LT 2 demethylation catalytic rate LT 4 demethylation catalytic rate LT 3 demethylation catalytic rate

Summary 5/10/2015Yang Yang, Candidacy Seminar39 These conditions are consistent with those obtained in previous works from analysis of a detailed, two-state receptor model *.  The Inverse of Methylation MM constants linearly decrease with Autophosphorylation Rates  The Inverse of Demethylation MM constants linearly increase with Autophosphorylation Rates  The ratio of Methylation catalytic rates and demethylation catlytic rates for the next methylation level is constant for all methylation states * B. Mello et al. Biophysical Journal, (2003).

Conditions in Two-State Receptor Model 5/10/2015Yang Yang, Candidacy Seminar40  Receptor autophosphorylation rates are proportional to the receptor activity:  Only the inactive or active receptors can be methylated or demethylated. The association rates between receptors and CheR or CheB p are linearly related to the receptor activity, whiledissociation rates are independent with . Then the inverse of the methylation or demethylation MM constants are linearly related to the receptor activity:  The ratios between methylation catalytic rates and demethylation catalytic rates for the next methylation level are constant:  The phosphate transfer rates from CheA to CheB or CheY are proportional to receptor activities:

Conditions for Perfect Adaptation: Protein Concentrations

Summary of Protein Concentrations 5/10/2015Yang Yang, Candidacy Seminar42

Relationship Between Protein Concentrations 5/10/2015Yang Yang, Candidacy Seminar43 (M)

Relationship Between Protein Concentrations (cont’d) 5/10/2015Yang Yang, Candidacy Seminar44 (M)

Relationship between Protein Concentrations (cont’d) 5/10/2015Yang Yang, Candidacy Seminar45 (M)

Summary Preliminary observations : CheR concentration is restricted in a narrow small-value region while total receptor and CheY concentration can vary in a wide region. CheR concentration is proportional to the CheB concentration

Diversity of Chemotaxis Systems 5/10/2015Yang Yang, Candidacy Seminar47 Eg., Rhodobacter sphaeroides, Caulobacter crescentus and several rhizobacteria possess multiple CheYs while lacking of CheZ homologue. In different bacteria, additional protein components as well as multiple copies of certain chemotaxis proteins are present. Response regulator Phosphate “sink” CheY1 CheY2

Two CheY System 5/10/2015Yang Yang, Candidacy Seminar48 Exact adaptation in modified chemotaxis network with CheY 1, CheY 2 and no CheZ: CheY1 p (µM) Time(s) Requiring:  Faster phosphorylation/autodephosphorylation rates of CheY 2 than CheY 1  Faster phosphorylation rate of CheB

Conclusions 5/10/2015Yang Yang, Candidacy Seminar49 I.Successful implementation of a novel method for elucidating regions in parameter space allowing precise adaptation II.Numerical results for (near-) perfect adaptation manifolds in parameter space for the E. coli chemotaxis network, allowing determination of i.Conditions required for perfect adaptation, consistent with and extending previous works [1-3] ii.Numerical ranges for experimentally unknown or partially known kinetic parameters I.Extension to modified chemotaxis networks, for example with no CheZ homologue and multiple CheYs [1] Barkai & Leibler, Nature (1997). [2] Yi et al., PNAS (2000). [3] Tu & Mello, Biophys. J. (2003).

Future Work 5/10/2015Yang Yang, Candidacy Seminar50 Extension to other signaling networks  vertebrate phototransduction  mammalian circadian clock allowing determination of a) parameter dependences underlying robustness of adaptation b) plausible numerical values for unknown network parameters

Vertebrate Phototransduction 5/10/2015Yang Yang, Candidacy Seminar51 cGMP: cyclic GMP PDE: cGMP phosphodiesterase GCAP: guanylyl cyclase activating, Ca 2+ binding protein gc: guanylyl cyclase, which synthesis cGMP

Light Adaptation of Phototransduction 5/10/2015Yang Yang, Candidacy Seminar52 An intracellular recording from a single cone stimulated with different amounts of light. Each trace represents the response to a brief flash that was varied in intensity. At the highest light levels, the response amplitude saturates. (Neuroscience, Purves et al., 2001)

Kinetic Model for Vertebrate Phototransduction 5/10/2015Yang Yang, Candidacy Seminar53 Russell D. Hamer, Visual Neuroscience (2000)

Mammalian Circadian Clock 5/10/2015Yang Yang, Candidacy Seminar54  PERs transport CRYs to nucleus  CLOCK and BMAL1 bind together  CLOCK·BMAL1 binds to E box to increase Pers(Crys) transcription rates  E box is the sequence CACGTG of the PER1 and CRY1 genes  PERs bind with kinases CKIε/δ to be phosphorylated  Phosphorylated PERs bind with CRYs  Only phosphorylated PER·CRY· CKIε/δ can enter nucleus  Phosphorylated PER·CRY· CKIε/δ inhibit the ability of CLOCK·BMALI to enhance transcription  Increasing REV-ERB α levels repress BMAL1 transcription  Activator positively regulated BMAL1 transcription From Forger et al., PNAS (2003).

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Checking Dynamics of CheY-P with Solutions 5/10/2015Yang Yang, Candidacy Seminar61 A B C D

Protein Concentration Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar62

Protein Concentration Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar63

Protein Concentration Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar64

Protein Concentration Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar65

Protein Concentration Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar66

Reaction Rates Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar67 T 2 autophosphorylation rate (k 2a ) T 3 autophosphorylation rate (k 3a ) inverse of T 2 MM constant (K 2R -1 ) inverse of T 3 MM constant (K 3R -1 ) Protein concentrations taken from SPO’s Protein concentrations taken from Mello-Tu’s

Reaction Rates Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar68 T 2 autophosphorylation rate (k 2a ) T 3 autophosphorylation rate (k 3a ) inverse of T 2 MM constant (K 2R -1 ) inverse of T 3 MM constant (K 3R -1 ) Protein concentrations taken from SPO’s Protein concentrations taken from Mello-Tu’s

Reaction Rates Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar69 T 1 autophosphorylation rate (k 1a ) T 2 autophosphorylation rate (k 2a ) inverse of T 1 M-M constant (K 1B -1 ) inverse of T 2 M-M constant (K 2B -1 ) Protein concentrations taken from SPO’s Protein concentrations taken from Mello-Tu’s

Reaction Rates Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar70 T 3 autophosphorylation rate (k 3a ) T 4 autophosphorylation rate (k 4a ) inverse of T 3 M-M constant (K 3B -1 ) inverse of T 4 M-M constant (K 4B -1 ) Protein concentrations taken from SPO’s Protein concentrations taken from Mello-Tu’s

Reaction Rates Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar71 LT 1 autophosphorylation rate (k 1al ) LT 2 autophosphorylation rate (k 2al ) inverse of LT 1 MM constant (K 1LB -1 ) inverse of LT 2 MM constant (K 2LB -1 ) Protein concentrations taken from SPO’s Protein concentrations taken from Mello-Tu’s

Reaction Rates Trend Shifting 5/10/2015Yang Yang, Candidacy Seminar72 LT 3 autophosphorylation rate (k 12 ) LT 4 autophosphorylation rate (k 13 ) inverse of LT 3 MM constant (K 2LB -1 ) inverse of LT 4 MM constant (K 3LB -1 ) Protein concentrations taken from SPO’s Protein concentrations taken from Mello-Tu’s

Slices of 3D Surfaces of Parameter Space 5/10/2015Yang Yang, Candidacy Seminar

Slices of 3D Surfaces of Parameter Space 5/10/2015Yang Yang, Candidacy Seminar

Slices of 3D Surfaces of Parameter Space Comparing Pair-Wise Relationship 5/10/2015Yang Yang, Candidacy Seminar75 T 1 autophosphorylation rate (k 1a ) Inverse of T 1 MM constant (K1 R -1 ) T 1 autophosphorylation rate (k 1a ) Inverse of T 1 MM constant (K 1B -1 )

E. coli and Bacteria Chemotaxis 5/10/2015Yang Yang, Candidacy Seminar76 Increasing attractants or Decreasing repellents