Simple toy models (An experimentalist’s perspective)

1. Simple toy models(An experimentalist’s perspective)

2. Lattice Polymers

3. Lattice Polymers Do they predict absolute folding rates?

4. Lattice Polymers Do they predict relative folding rates?

5. Two-state folding rates kf = 2 x105 s-1 kf = 2 x 10-1 s-1

6. Putative rate-defining criterion Landscape Roughness Energy Gap Collapse Cooperativity

7. Landscape Roughness Bryngelson & Wolynes (1987) PNAS, 84, 7524

8. Kinetics switch from single exponential: A(t) = A0 exp(-t·kf)1/h To stretched exponential: A(t) = A0 exp(-t·kf)1/h When Landscape Roughness Dominates Kinetics Socci, Onuchic & Wolynes (1998) Prot. Struc. Func. Gen.32, 136 Nymeyer, García & Onuchic (1998) PNAS, 95, 5921 Skorobogatiy, Guo & Zuckermann (1998) JCP,109, 2528 Onuchic (1998)PNAS, 95, 5921

9. The energy landscape of protein L h = 0.98  0.08 Gillespie & Plaxco (2000) PNAS, 97, 12014

10. h = 1.04±0.07

11. The pI3K SH3 domain Gillespie & Plaxco (2004) Ann. Rev. Bioch. Biophy, In press

12. The Energy Gap “The necessary and sufficient condition for [rapid] folding in this model is that the native state be a pronounced global minimum [relative to other maximally compact structures].” Sali, Shakhnovich & Karplus (1994) Nature, 369, 248

13. Gap Size Correlates with theFolding Rates of Simple Models Dinner, Abkevich, Shakhnovich & Karplus (1999) Proteins, 35, 34

14. The uniqueness of the native state indicates that it is significantly more stable than any other compact state: the energy gap is generally too large to measure experimentally.

15. An Indirect Test For many simple models, Tm correlates with Energy Gap size 15-mers (B0 = -2.0) r = 0.73 15-mers (B0 = -0.1) r = 0.92 27-mers (B0 = -2.0) r = 0.89 27-mers (B0 = -0.1) r = 0.97 Dinner, Abkevich, Shakhnovich & Karplus (1999) Proteins, 35, 34 Dinner & Karplus (2001) NSB,7, 321

16. Gillespie & Plaxco (2004) Ann. Rev. Bioch. Biophy., In press

17. Collapse cooperativity “The key factor that determines the foldability of sequences is the single, dimensionless parameter s …folding rates are determined by s.”””” Thirumalai & Klimov (1999) Curr. Op. Struc. Biol., 9, 197

19. Thirumalai & Klimov (1999) Curr. Op. Struc. Biol., 9, 197

20. Cytochrome C 

21. Protein Rate Reference Cytochrome C 6400 s-1Gray & Winkler, pers com. Ubiquitin 1530 s-1 Khorasanizadeh et al., 1993 Protein L 62 s-1 Scalley et al., 1997 Lysozyme 37 s-1 Townsley & Plaxco, unpublished Acylphosphatase 0.2 s-1 Chiti et al., 1997 See also: Jaby et al., (2004) JMB, in press

23. Millet, Townsley, Chiti, Doniach & Plaxco (2002) Biochemistry, 41, 321

24. All “foldability” criterion optimal Energy landscapes unmeasurably smooth Energy gaps unmeasurably large All s within error of zero

25. Plaxco, Simons & Baker (1998) JMB, 277, 985

26. When the energy gap dominates folding kinetics, none of a long list of putatively important parameters, including the “number of short- versus long-range contacts in the native state*”, plays any measurable role in defining lattice polymers folding rates. *Sali, Shacknovich & Karplus (1994) “How does a protein fold?” Nature, 369, 248

27. Do subtle, topology-dependent kinetic effects appear only in the absence of confounding energy landscape issues?

28. Go Polymers • Native-centric energy potential • Extremely smooth energy landscape • Topologically complex

29. Topology-dependence of Go folding r = 0.2; p = 0.06

30. The topomer search model The chain is covalent Rates largely defined by native topology Local structure formation is rapid Equilibrium folding is highly two-state

31. Oh, Heeger & Plaxco, unpublished

32. Protein folding is highly two-state Fyn SH3 domain

33. 55 residue protein ∆Gu = -3 kcal/mol Kohn, Gillespie & Plaxco, unpublished

35. 4 residue truncation ∆Gu ~ 2 kcal/mol Kohn, Gillespie & Plaxco, unpublished

36. The Topomer Search Model Makarov & Plaxco (2003) Prot. Sci., 12, 17

38. P(QD)  <K>QD kf = k QD g <K>QD

39. Testing the topomer search model We can test the model if we assume that all sequence- distant residues in contact in the NATIVE STATE must be in proximity in the TRANSITION STATE Sequence-distant: > 4-12 residues Native contact: Ca-Ca < 6 - 8 Å

40. kf QD<K>QD r = 0.88

41. Crowding Effects Gaussian Chains Real Polymers Persistence length Excluded volume

42. kf QD<K>QD/N r = 0.92 Makarov & Plaxco (2003) Prot. Sci., 12, 17

43. “It is also a good rule not to put overmuch confidence in observational results that are put forward until they have been confirmed by theory.”Paraphrasing Sir Arthur Eddington theoretical simulation

44. Minimum requirements for topology-dependent kinetics • Connectivity • Rapid local structure formation • Smooth landscapes • Cooperativity

45. Go polymers are not cooperative

46. -eQ Q(1 - s)/QN + sQ E =

48. s = 2 r = 0.71; p = 10-16

49. s = 3 r = 0.76; p = 10-18 Jewett, Pande & Plaxco(2003) JMB,326, 247 See also: Kaya & Chan (2003) Proteins,52, 524

50. Acknowledgements UCSB Blake Gillespie Lara Townsley Jonathan Kohn Andrew Jewett Horia Metiu UT Austin Dima Makarov Stanford Seb Doniach Ian Millet Vijay Pande Universita di Firenze Fabrizio Chiti NIH, UC BioSTAR, ONR