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Topics to be Covered

Introduction to Protein Folding Mechanism of folding and misfolding GroEL – biological machine (chaperones folding) Molecular motors: Polymer physics and Myosin V motility. Topics to be Covered. Structure Prediction Protein & Enzyme Design Folding Kinetics & Mechanisms

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Topics to be Covered

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  1. Introduction to Protein Folding • Mechanism of folding and misfolding • GroEL – biological machine (chaperones folding) • Molecular motors: Polymer physics and Myosin V motility Topics to be Covered

  2. Structure Prediction Protein & Enzyme Design Folding Kinetics & Mechanisms Crowding& confinement Effects Relation to aggregation Molecular Chaperones Unfolded protein response (UPR) Folding and clearance mechanisms are at the center stage Many Facets of Folding

  3. A Big Protein Folding Problem Length ≈ 220 nm ≈ 700 water Read the Genetic Code; Transcription; Produce Proteins, Function, Degradation A very large protein in water – complex problem indeed! (about 100,000 waters) Size ≈ 22nm

  4. Pictures, Models, Approximations & RealityA bit Philosophy • Rich History in Condensed Matter physics & Soft Matter • (Analytic Theory) • Ising model for magnetic systems (Ni/also biology; 1920) • Spin glasses – Edwards-Anderson model (CuMn alloy; 1975) • Polymer statistics (Flory; 1948) • Liquid Crystals (TMV) (Onsager 1949) • BCS Theory (1956…)

  5. Theory Experiments • Statistical Mechanics (Energy Landscape) • Minimal Models (Lattice/Off-Lattice) • MD Simulations • Bioinformatics (Evolutionary Imprint) Folding Kinetics • Prot Engg (TSE) • SAXS/NMR (DSE) • FAST Folding (T jump; • P JUMP; Rapid Mixing) • SM FRET (Folding/ • unfolding) • LOT/AFM (Force Ramp • Force Quench)

  6. Outline • How far can we go using polymer physics? (no force) • Toy models and generic lessons • Finite size effects: Universal relations • Bringing “specificity” back: Phenomenological Models

  7. How does a chain (necklace with different shape pearls) fold up and how fast? Can things go wrong and then what? Many facets of Protein Folding As structure gets organized Energy gets lowered Minimum Free Energy (water ions cosolvents) Anfinsen over 50 years ago; Nobel Prize 1972 Computational approaches to Biological problems: 2013 Nobel Chemistry

  8. F RNA and some Proteins ΔFiNBA/ΔFij >> 1 I: Gradient to NBA dominates: Most likely event under folding conditions All other transitions less likely. S Page 881 of Textbook Chapter 18

  9. Approximation to Reality! Not all molecules take the same route: Folding is stochastic! At least 4 classes of folding trajectories (Reddy) Another Nobel Protein! (GFP) Complicated Energy Function

  10. Thermodynamics of src-SH3 folding Z. Liu, G. Reddy, E. O’Brien and dt PNAS 2011 Green = Urea Red= MTM predictions Black = Experiments (Baker) ΔGNU[C] = ΔGNU[0] + m[C] m = (1.3 – 1.5) kcal/mol.M Exp. m = 1.5kcal/mol.M Excellent Agreement!

  11. Random Coil (Flory) HIGH T or [C] Characteristic Temperatures in Proteins Rg ≈ aDN0.6 Compact T  T Or [C] Foldable:  = (T - TF)/T small Native State T  TF [CF] Rg ≈ aN N0.33

  12. Estimating Protein Size as a Function of N High denaturant concentration (GdmCl or Urea) Good solvent for polypeptide chain – may be! Flory Theory: F(Rg) ≈ (Rg2/N2) + v(N2/Rgd) (see de Gennes book) Rg ≈ aNνν = 3/(d + 2)

  13. Folded States Globular Proteins • Maximally compact • Largely Spherical • Rg≈ aN N(1/3) • So size of proteins follow polymer laws – surprising!

  14. “Unfolded” Protein Collapse : Rg follows Flory law RgU = 2N0.6 Rg = 3N1/3 Kohn PNAS (05) Folded Dima & dt JPCB (04)

  15. Tetrahymenaribozyme(...difficult) RNA Folding: Tetrahymenaribozyme RNA – Branched polymer Ion valence size shape

  16. RgScaling works for RNA too includingthe ribosome!

  17. Size Dependence of RNA Rg≈ 5.5N(1/3) Fairly decent (due to Hyeon) Exponent may Be larger..analogy To branched polymers Ben Shaul, Gelbart, Knobler

  18. Role of non-native attractions Multiple Folding Nuclei Illustrating Key ideas using Lattice modelsSeems like an Absurd Idea! Fast and slow tracks K. A. Dill Protein Science (1995)

  19. Even simpler Folded lower in energy by one unit Blues Like Each other. They gain one unit of energy Multiple paths! Toy model: Explains protein folding

  20. 4 types of monomers (H, P, +, -) Monomer has 8 beads # of sequences = 48 (amylome) # of conformations on cubic lattice = 1,841 A simple minded approach http://dillgroup.org/#/code HPSandbox

  21. Proteins a lot of choices OP is in the eye of the beholder = N/Rg3 ;  (overlap) “unfolded” (Small,big) Compact non-native (O(1), big) Native (O(1), small) Other Choices Helix/sheet content; Distribution of contacts ……… Macroscopic System Ferromagnetism M Nematic Phases S = P2(cos) Smectic Phases S,tilt angle Spin Glasses: M; qEA Paramagnet M = 0. qEA = 0 Spin Glass M = 0; qEA  0 Ferromanet M  0; qEA  0 Physics dictates OP Order parameter description

  22. Order Parameter Description  = N/Rg3 ;  = Overlap with NBA (0 for NBA) Unfolded (U), Collapsed Globules (CG); Folded (NBA) U:  (small),  Large (“vapor”) CG:  ≈ O(1),  Large (Dense no order “Liquid”) NBA:  ≈ O(1),  Small (Dense order “Solid”) Folding reaction as a phase transition: A rationale N = number of amino acids

  23. Free Energy of Creating a Droplet G(R) ≈ -R3 + R2 Driving force + Opposing Developing a “nucleation” picture What are these forces in proteins? Driving force: Hydrophobic Collapse Burying H bonds Opposing: “Droplet with nonconstant ” Entropy loss due to looping

  24. Tentative Models + Slight refinement Cost of creating a region with NR ordered residues out of N? Rugged Landscape with Many possibilities

  25. GBW(NR)  -f(T)NR + a2NR2/3 NR*  (8a2/3 f(T))3 NR* too large for typical  and f(T) values Some phenomenological Models GGT(NR)  h(h - 1)NR2 + a2NR2/3 NR*  (8a2/h)3/4 NR*  15 or so… Using experimental parameters NR*  27 or so..

  26. Structures near Barrier top or TSE Simulations Folding trajectories to MFN to transition state ensemble (TSE) Moving from one scenario to another – pressure jump…

  27. Refinement (Hiding Ignorance) G(NR)  -1NR + NR + S (loop) •  small barrier (downhill folding) Surface tension cannot be a constant Multiple Folding Nuclei (Structural Plasticity) Multi-domain proteins involve interfaces between globular parts..

  28. Finite Size Effects on FoldingOrder parameters matter

  29. Two points: 1) TF = max in  (suceptibility)  = T(d<>/dh; h = ordering field (analogy to mag system)  is dimensionless  h ~ T (in proteins or [C]) 2) Efficient folding TF  T (collapse Temp; Camacho & dt PNAS (1993)) C controlled by protein DSE at T  TF  T Rg ~ (T/TF)- ~ N (DSE a SAW & manget analogy) T/TF ~ 1/N (Result I) Scaling of C with N (number of aa)

  30. Lattice models Side Chains Finite-size effects on TF T/TF ~ 1/N Li, Klimov & DT Phys. Rev. Lett. (04) Experiments

  31. c= (TF/T) [TF(d<>/dT)] “disp in TF” X “suspectibility” C  N ;  = 1 +  (Universal);   1.2 Result II Scaling of c with NMagnet-Polymer analogy T  TF  T   N

  32. Universality in CooperativityLi, Klimov, dt PRL (04) c ~ N Experiments

  33. Residue-dependent melting Tm-HoltzerEffectConsequences of finite size fm(Tmi) = 0.5 Lattice Models Side Chains Klimov & dt J. Comp. Chemistry (2002)

  34. BBL T large Is the melting temperature Unique? Finite-size effects! Munoz Nature 2006 Holtzer Leucine Zipper Biophys J 1997 -hairpin PNAS 2000 Klimov & dt Udgaonkar Barstar Monnelin

  35. Spread decreases as N decreases….finite-size effects Residue dependent ordering Protein LO’Brien, Brooks & dt Biochemistry (2009)

  36. Summary So Far – Really with little work on acomplex problem • Sizes of single domain proteins (folded and • unfolded) roughly follow Flory’s expectation • Same holds good for RNA folded structures • Nucleation Picture of Folding • Finite size effects – theory matches experiments

  37. Part II: Protein Folding Kinetics Organization of structure Fluctuations due to finite-size effects Changes in distributions at various stages of folding [C] Or T

  38. A Few Questions • Mechanisms of Structural organization • Nature of the Folding Nuclei • Interactions that guide folding (native vs non-native) • Folding rates – dependence on N

  39. Role of non-native attractions Multiple Folding Nuclei Illustrating Key ideas using Lattice modelsSeems like an Absurd Idea! Fast and slow tracks K. A. Dill Protein Science (1995)

  40. Camacho and dt, PNAS (1993) Stages in folding C Random Coil F “Specific Collapse” Native State dt J. de. Physique (1995) F/C  (100 - 1000) C F

  41. Need for Quantitative Models Fernandez, Rief.. Hyeon, Morrison, dt Using mechanical force to trigger folding smFRET trajectories Eaton, Schuler, Haran…

  42. Non-native interactions early (time scales of collapse) in folding; Subsequently native interactions dominate Camacho & dt Proteins 22, 27-40 (1995); Cardenas-Elber (all atom simulations) Dill type HP model Beads on a lattice Native Centric (or Go) models appropriate!

  43. Multiple protein folding nuclei and the transition state ensemble in two‐state proteins Klimov and dt (2001) MC simulations; 600 folding Trajectories; Folding time: A/AGO ≈ 3 LMSC Exact Enumeration Proteins: Structure, Function, and BioinformaticsVolume 43, Issue 4, pages 465-475, 17 APR 2001 DOI: 10.1002/prot.1058http://onlinelibrary.wiley.com/doi/10.1002/prot.1058/full#fig5

  44. Transition State Ensemble: Neural Net Klimov and dt Proteins 2001 ES NSB 2000 Go Equivalent to pfold

  45. Multiple protein folding nuclei and the transition state ensemble in two‐state proteins Multiple Channels Carry Flux to the NBA Multiple Transition States Connecting these Channels Bottom line: To get semi-quantitative results Go-type models May be enough… Proteins: Structure, Function, and BioinformaticsVolume 43, Issue 4, pages 465-475, 17 APR 2001 DOI: 10.1002/prot.1058http://onlinelibrary.wiley.com/doi/10.1002/prot.1058/full#fig9

  46. Folding Rate versus N kF ≈ k0 exp(-Nβ) with β = 0.5 Barriers scale sublinearly with N Proteins: Hydrophobic residues buried In interior (chain compact); Polar and charged residues want solvent exposure (extended states). Frustration between Conflicting requirements. P(ΔG♯) ≈ exp( - (ΔG♯)2/2N) <ΔG♯> ≈ N0.5 (Analogy to glasses)

  47. Fit to Experiments (80 Proteins Dill, PNAS 2012) Reasonable given data from so many different laboratories

  48. Even better for RNA (Hyeon, 2012)

  49. Protein collapse At high [C] is DSE a Flory Coil?It appears that high [C] is a Θ-solvent! O’Brien PNAS 2008 CT =(C - Cm)/C  = 2 + (γ-1)/ν P(x) ~ xexp(-x1/(1-))

  50. 4 types of monomers (H, P, +, -) Monomer has 8 beads # of sequences = 48 (amylome) # of conformations on cubic lattice = 1,841 Toy Model (Is the fibril structure encoded in monomer spectrum) Prot Sci 2002; JCP 2008

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