Transcript N - KIAS
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 Many Facets of Folding 1. Structure Prediction 2. Protein & Enzyme Design 3. Folding Kinetics & Mechanisms 4. Crowding & confinement Effects 5. Relation to aggregation 6. Molecular Chaperones 7. Unfolded protein response (UPR) Folding and clearance mechanisms are at the center stage 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 Pictures, Models, Approximations & Reality A 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…) Folding Kinetics Experiments o Prot Engg (TSE) o SAXS/NMR (DSE) o FAST Folding (T jump; P JUMP; Rapid Mixing) o SM FRET (Folding/ unfolding) o LOT/AFM (Force Ramp Force Quench) Theory Statistical Mechanics (Energy Landscape) Minimal Models (Lattice/Off-Lattice) MD Simulations Bioinformatics (Evolutionary Imprint) 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 Many facets of Protein Folding How does a chain (necklace with different shape pearls) fold up and how fast? Can things go wrong and then what? 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 RNA and some Proteins F ΔFiNBA/ΔFij >> 1 S I: Gradient to NBA dominates: Most likely event under folding conditions All other transitions less likely. Page 881 of Textbook Chapter 18 Approximation to Reality! Another Nobel Protein! (GFP) Not all molecules take the same route: Folding is stochastic! At least 4 classes of folding trajectories (Reddy) Complicated Energy Function 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! Characteristic Temperatures in Proteins Random Coil (Flory) HIGH T or [C] Rg ≈ aDN0.6 Compact T T Or [C] Foldable: = (T - TF)/T small Native State T TF [CF] Rg ≈ aN N0.33 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 ≈ aNν ν = 3/(d + 2) Folded States Globular Proteins • Maximally compact • Largely Spherical • Rg ≈ aN N(1/3) • So size of proteins follow polymer laws – surprising! Protein Collapse : Rg follows Flory law “Unfolded” RgU = 2N0.6 Rg = 3N1/3 Kohn PNAS (05) Folded Dima & dt JPCB (04) RNA Folding: Tetrahymena ribozyme RNA – Branched polymer Tetrahymena ribozyme(...difficult) Ion valence size shape Rg Scaling works for RNA too including the ribosome! 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 Illustrating Key ideas using Lattice models Seems like an Absurd Idea! Role of non-native attractions Multiple Folding Nuclei Fast and slow tracks K. A. Dill Protein Science (1995) 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 A simple minded approach 4 types of monomers (H, P, +, -) Monomer has 8 beads # of sequences = 48 (amylome) # of conformations on cubic lattice = 1,841 http://dillgroup.org/#/code HPSandbox Order parameter description 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 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 ……… Folding reaction as a phase transition: A rationale N = number of amino acids 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”) Developing a “nucleation” picture Free Energy of Creating a Droplet G(R) ≈ -R3 + R2 Driving force + Opposing What are these forces in proteins? Driving force: Hydrophobic Collapse Burying H bonds Opposing: “Droplet with nonconstant ” Entropy loss due to looping Tentative Models + Slight refinement Cost of creating a region with NR ordered residues out of N? Rugged Landscape with Many possibilities Some phenomenological Models GBW(NR) -f(T)NR + a2NR2/3 NR* (8a2/3 f(T))3 NR* too large for typical and f(T) values GGT(NR) h(h - 1)NR2 + a2NR2/3 NR* (8a2/h)3/4 NR* 15 or so… Using experimental parameters NR* 27 or so.. Folding trajectories to MFN to transition state ensemble (TSE) Structures near Barrier top or TSE Simulations Moving from one scenario to another – pressure jump… 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.. Finite Size Effects on Folding Order parameters matter Scaling of C with N (number of aa) 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) Finite-size effects on TF Lattice models Side Chains T/TF ~ 1/N Experiments Li, Klimov & DT Phys. Rev. Lett. (04) Scaling of c with N Magnet-Polymer analogy c= (TF/T) [TF(d<>/dT)] “disp in TF” X “suspectibility” C N ; = 1 + (Universal); 1.2 Result II T TF T N Universality in Cooperativity Li, Klimov, dt PRL (04) c ~ N Experiments Residue-dependent melting Tm-Holtzer Effect Consequences of finite size fm(Tmi) = 0.5 Lattice Models Side Chains Klimov & dt J. Comp. Chemistry (2002) Is the melting temperature Unique? Finite-size effects! T large Holtzer Leucine Zipper Biophys J 1997 Udgaonkar Barstar Monnelin BBL Munoz Nature 2006 -hairpin PNAS 2000 Klimov & dt Residue dependent ordering Protein L O’Brien, Brooks & dt Biochemistry (2009) Spread decreases as N decreases….finite-size effects Summary So Far – Really with little work on a complex 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 Part II: Protein Folding Kinetics Organization of structure Fluctuations due to finite-size effects [C] Or T Changes in distributions at various stages of folding A Few Questions • Mechanisms of Structural organization • Nature of the Folding Nuclei • Interactions that guide folding (native vs nonnative) • Folding rates – dependence on N Illustrating Key ideas using Lattice models Seems like an Absurd Idea! Role of non-native attractions Multiple Folding Nuclei Fast and slow tracks K. A. Dill Protein Science (1995) Stages in folding Camacho and dt, PNAS (1993) C Random Coil dt J. de. Physique (1995) F/C (100 - 1000) C F “Specific Collapse” F Native State Need for Quantitative Models Fernandez, Rief.. Hyeon, Morrison, dt Using mechanical force to trigger folding smFRET trajectories Eaton, Schuler, Haran… 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! 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 Bioinformatics Volume 43, Issue 4, pages 465-475, 17 APR 2001 DOI: 10.1002/prot.1058 http://onlinelibrary.wiley.com/doi/10.1002/prot.1058/full#fig5 Transition State Ensemble: Neural Net Klimov and dt Proteins 2001 Go ES NSB 2000 Equivalent to pfold 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 Proteins: Structure, Function, and Bioinformatics Volume 43, Issue 4, pages 465-475, 17 APR 2001 DOI: 10.1002/prot.1058 http://onlinelibrary.wiley.com/doi/10.1002/prot.1058/full#fig9 Bottom line: To get semi-quantitative results Go-type models May be enough… 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) Fit to Experiments (80 Proteins Dill, PNAS 2012) Reasonable given data from so many different laboratories Even better for RNA (Hyeon, 2012) At high [C] is DSE a Flory Coil? It appears that high [C] is a Θ-solvent! Protein collapse O’Brien PNAS 2008 CT =(C - Cm)/C = 2 + (γ-1)/ν P(x) ~ xexp(-x1/(1-)) Toy Model (Is the fibril structure encoded in monomer spectrum) Prot Sci 2002; JCP 2008 4 types of monomers (H, P, +, -) Monomer has 8 beads # of sequences = 48 (amylome) # of conformations on cubic lattice = 1,841 Structure of “protofilament” + “fibril” Single and double layer Interplay of E+- and EHH a: Monomers parallel b: Monomer alternate c: Double layer d: No fibril compact Optimal growth temp fib = (104 - 10n)F Largest n about 9 Seeding speeds up fibril rate formation Growth rate depends on N* population PN* Depends on sequence Sequence + N* ensemble fibril kinetics monomer landscape encodes structure + growth rate Lifshitz-Slyazov Growth Law Supersaturated solution J. Phys. Chem. Solids (1961) G 0M1/3 Large clusters incorporate small oligomers M Mn* [ PF Fibrils]