1. 1/2/2016Yang Yang, Candidacy Seminar1 Near-Perfect Adaptation in Bacterial Chemotaxis Yang Yang and Sima Setayeshgar Department of Physics Indiana University, Bloomington, IN

4. E. coli and Bacteria Chemotaxis 1/2/2016Yang Yang, Candidacy Seminar4 http://www.rowland.harvard.edu/labs/bacteria/index_movies.html Increasing attractants or Decreasing repellents

5. Chemotaxis Signal Transduction Network in E. coli 1/2/2016Yang Yang, Candidacy Seminar 5 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

6. Robust Perfect Adaptation 1/2/2016Yang 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) 6

7. This Work: Outline 1/2/2016Yang Yang, Candidacy Seminar7  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

8. E. coli Chemotaxis Signaling Network 1/2/2016Yang Yang, Candidacy Seminar8  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)

9. Michaelis-Menten Kinetics 1/2/2016Yang Yang, Candidacy Seminar9 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: where K m is the Michaelis Menten Constant (MM constant) Enzymatic reaction:

10. Reaction Rates 1/2/2016Yang Yang, Candidacy Seminar10

11. Approach … 1/2/2016Yang Yang, Candidacy Seminar11  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

12. 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 1/2/2016Yang Yang, Candidacy Seminar12 Discretize s in range {s low, s high }

13. Physical Interpretation of Parameter, : Near-Perfect Adaptation 1/2/2016Yang Yang, Candidacy Seminar13  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)

14.  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 1/2/2016Yang Yang, Candidacy Seminar14

15. Converting from Guess to Solution 1/2/2016Yang Yang, Candidacy Seminar15 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 )

16. Parameter Surfaces 1/2/2016Yang Yang, Candidacy Seminar16 ● 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 )

17. Validation 1/2/2016Yang Yang, Candidacy Seminar17 Time (s) Concentration (µM) Verify steady state NR solutions dynamically using DSODE for different stimulus ramps:

18. Violating and Restoring Perfect Adaptation 1/2/2016 Yang Yang, Candidacy Seminar 18 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)

19. Conditions for Perfect Adaptation: Kinetic Parameters 1/2/201619Yang Yang, Candidacy Seminar

20. Inverse of Methylation MM Constant Autophosphorylation Rate 1/2/2016Yang Yang, Candidacy Seminar20 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 )

21. Inverse of Methylation MM Constant Autophosphorylation Rate 1/2/2016Yang Yang, Candidacy Seminar21 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 )

22. Inverse of Methylation MM Constant Autophosphorylation Rate 1/2/2016Yang Yang, Candidacy Seminar22 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 )

23. Inverse of Methylation MM Constant Autophosphorylation Rate 1/2/2016Yang Yang, Candidacy Seminar23 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 )

24. Inverse of Demethylation MM Constant Autophosphorylation Rate 1/2/2016Yang Yang, Candidacy Seminar24 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 )

25. Inverse of Demethylation MM Constant Autophosphorylation Rate 1/2/2016Yang Yang, Candidacy Seminar25 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 )

26. Inverse of Demethylation MM Constant Autophosphorylation Rate 1/2/2016Yang Yang, Candidacy Seminar26 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 )

27. Inverse of Demethylation MM Constant Autophosphorylation Rate 1/2/2016Yang Yang, Candidacy Seminar27 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 )

28. Methylation Catalytic Rate/ Demethylation Catalytic Rate = Constant 1/2/2016Yang Yang, Candidacy Seminar28 T 1 demethylation catalytic rate T 1 methylation catalytic rate T 2 demethylation catalytic rate T 2 methylation catalytic rate

29. Methylation Catalytic Rate/ Demethylation Catalytic Rate = Constant 1/2/2016Yang Yang, Candidacy Seminar29 T 3 demethylation catalytic rate T 2 methylation catalytic rate T 4 demethylation catalytic rate T 3 methylation catalytic rate

30. Methylation Catalytic Rate/ Demethylation Catalytic Rate = Constant 1/2/2016Yang Yang, Candidacy Seminar30 LT 1 demethylation catalytic rate LT 0 methylation catalytic rate LT 2 demethylation catalytic rate LT 1 methylation catalytic rate

31. Methylation Catalytic Rate/ Demethylation Catlytic Rate = Constant 1/2/2016Yang Yang, Candidacy Seminar31 LT 3 demethylation catalytic rate LT 2 demethylation catalytic rate LT 4 demethylation catalytic rate LT 3 demethylation catalytic rate

32. Summary 1/2/2016Yang Yang, Candidacy Seminar32 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).

33. Some Conditions in Two-State Receptor Model 1/2/2016Yang Yang, Candidacy Seminar33 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).

34. Conditions for Perfect Adaptation: Protein Concentrations

35. Summary of Protein Concentrations 1/2/2016Yang Yang, Candidacy Seminar35

36. Relationship Between Protein Concentrations 1/2/2016Yang Yang, Candidacy Seminar36 (M)

37. Relationship Between Protein Concentrations (cont’d) 1/2/2016Yang Yang, Candidacy Seminar37 (M)

38. Relationship between Protein Concentrations (cont’d) 1/2/2016Yang Yang, Candidacy Seminar38 (M)

40. Diversity of Chemotaxis Systems 1/2/2016Yang Yang, Candidacy Seminar40 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

41. Two CheY System 1/2/2016Yang Yang, Candidacy Seminar41 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

42. Conclusions 1/2/2016Yang Yang, Candidacy Seminar42 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).

43. Future Work 1/2/2016Yang Yang, Candidacy Seminar43 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

44. Vertebrate Phototransduction 1/2/2016Yang Yang, Candidacy Seminar44 http://www.fz-juelich.de/inb/inb-1/Photoreception/ cGMP: cyclic GMP PDE: cGMP phosphodiesterase GCAP: guanylyl cyclase activating, Ca 2+ binding protein gc: guanylyl cyclase, which synthesis cGMP

45. Light Adaptation of Phototransduction 1/2/2016Yang Yang, Candidacy Seminar45 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)

46. Kinetic Model for Vertebrate Phototransduction 1/2/2016Yang Yang, Candidacy Seminar46 Russell D. Hamer, Visual Neuroscience (2000)

47. Mammalian Circadian Clock 1/2/2016Yang Yang, Candidacy Seminar47 http://www.umassmed.edu/neuroscience/faculty/reppert.cfm?start=0  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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60. 1/2/2016Yang Yang, Candidacy Seminar60 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 )

61. 1/2/2016Yang Yang, Candidacy Seminar61 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 )

62. 1/2/2016Yang Yang, Candidacy Seminar62 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 )

63. 1/2/2016Yang Yang, Candidacy Seminar63 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 )

64. 1/2/2016Yang Yang, Candidacy Seminar64 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 )

65. 1/2/2016Yang Yang, Candidacy Seminar65 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 )