FoldingSlide 2Time-scales for foldingKubelka et al (2004)Slide 5Folding, Unfolding, and Re-foldingThermodynamic vs. kinetic control?Levinthal ParadoxSlide 9Two-state foldingSlide 11Slide 12Folding Pathway IntermediatesSlide 14Slide 15Off-pathway intermediatesThe Unfolded “State”Contact OrderF-valuesLattice ModelsSlide 21Slide 22Slide 23Kolinski, Godzik, Skolnick (1993)SICHO (Kolinski and Skolnick, 1998)Reduced-atom modelsMis-folding and Amyloid formationFolding•Anfinsen•cooperativity•time scales, speed range•Levinthal paradox•ensembles•energy landscape; funnel•chaperones•thermodynamics, 15 kcal/mol•denaturation: thermal, chemical•2-state vs. intermediates, phi-values•contact order as a metric of "foldedness"•lattice models (Shakhnovich, Dill, Skolnick)Folding•Anfinsen (1950’s) – showed reversibility of denaturation with urea for RNase A–amino acid sequence encodes struct; thermodynamic hypothesis–exception is chaperones (also role of disulfides, Pro isomerization)•folding is “cooperative”differential scanning calorimetry•cytochrome b562: 5 s•lambda repressor: 0.67 ms•rat IFABP: 33 ms•CRABP 1: 24.5 sec•tryptophan synthase 2-subunit: 992 sec (396 aa)Time-scales for foldingKubelka et al (2004)Galzitskayaet al. (2003)Folding, Unfolding, and Re-folding•at equilibrium, proteins represent an ensemble, with some unfolded (constantly unfolding and refolding)•thermodynamic ensembles (Boltzmann distribution)•can measure with hydrogen-exchange (NMR)–even buried H’s exchange with solvent at some rate–reflects dynamic unfolding/refolding•overall folding rate const vs. kunfold and kfold•equilibrium shifted in direction of GThermodynamic vs. kinetic control?•do folded structures represent true global energy minimum, or just “kinetically accessible” local minima?•what causes slow folding: a high transition-state barrier, or just a large space to search?Levinthal Paradox•How can proteins fold in such a short time?•Number of degrees of freedom: –>2Nres (phi/psi angles), <3*10*Nres (atomic coords) –states: ~3N*3N? (backbone /coil × side-chain rotamers)–how can this large space possibly be sampled to find the global minimum?•intermediates and cooperativity –collapse of hydrophobic core–formation of key secondary structures•folding “pathway”•off-pathway intermediates (local minima) can act as traps and slow-down the folding process•energy landscape funnel•new view: not just one preferred path•many routes lead to min•hydrogen-exchange•natural/fast folding sequence have “minimally frustrated” energy landscapesTwo-state folding•data must fit first-order kinetics•linearity of ln(kf) vs. [denaturant]• G is same whether determined by kinetic vs. thermodynamic (equilibrium) methods•no intermediates (at least not well-defined)•what does the (transient) transition state look like?•molten globule (Ptitsyn): collapsed but not tightly-packed, rapidly fluctuating•stopped-flow hydrogen-exchange shows “native-like” secondary structure signatures (BPTI, -lactalbumin)• T – measure of where transition occurs along reaction coordinate: how “native-like”?•Jackson and Fersht (1991) – chymotrypsin inhibitor 2re-folding(stopped flow)unfolding(fluorescencecurve)3-state:barnase1. 2-state model supported by concordanceof params between thermo. and kinetics2. slope (mF and mU) correlateswith difference in accessiblesurface area between U and F(Myers, Pace, and Scholtz, 1995)3. if Ku=ku/kf and ku=kuH20+mf[GCl] andkf=kfH2O-mu[GCl], then m=mu+mfequilibrium!rates!•thermal denaturationvan 't Hoff equationGibbs-Helmholtz equationPace and Laurents (1989)Method for determining Cp- calorimeter (10% error)- Cp=d(H)/dT from v’Hoff- extrapolate from Gmeasured at differentdenaturant concentrationsbalance between S and HFolding Pathway Intermediates•hard to trap (low populated)•non-linearity in chevrons in plots–due to switch of dominant transition state•intermediate CD spectra, hydrodynamic radius•barnase (Fersht, 2000, PNAS)•Sanchez and Keifhaber (2003) – multiple examples (conditions)•spectrin (Scott and Clarke, 2005)broad transition vs. sequential intermediate states?Lysozyme has both a fast a slow pathway (Keifhaber, 1995) – data fit better by a double-exponential (t1=50ms, t2=420ms)see also Jamin and Baldwin (1996).folding vs. unfolding rates as evidence forintermediates in apomyoglobin•Valerie Daggett–molecular dynamics simulation of folding/unfolding–identification of order of sub-structure formationsimulationsof ubiquitinat 498 Kand 298 KOff-pathway intermediates•BPTI – 3 native disulfide bridges, 14-38, 30-51, and 5-55•other non-native bridges are formed during folding in an oxidizing environment•proper folding follows specific order of formation•making non-native disulfides forms “kinetic traps”•can block free thiols and analyze population; distribution suggests thermodymamically determined (equilibrium?)show picture of interconversion of intermediates...The Unfolded “State”•random coil? (hydrodynamic radius)•backbone, side-chains fully solvated (hydration)•effects of pH, urea...Contact Order•(Plaxco Simons & Baker, 1998)L = length of proteinN = num of contact pairs (side-chain dist < 6A)S = sequence separation1HRC, CO=11.21UBQ, CO=15.11TEN, CO=17.4-values•Fersht AR, Matouschek A, Serrano L. (1992)•a way of studying kinetics and folding intermediates via mutation•if you mutate a residue that is a critical (folded) part of an intermediate structure, you might destabilize it, increasing the barrier, and decreasing the rate of folding•if intermediate is structured and resembles native, then mutation will affect stability of each equally•it intermediate is unfolded, mutation will not affect stability of TS•examples:–Crespo, Simpson, and Searle (2006) – ubiquitin–Bulaj & Goldenberg (2001) - BPTI phi=0no effect on TSphi=1mutation affects TSLattice Models•Sali, Shakhnovich, and Karplus (1994)•Monte Carlo sampling of configurations•simplified interactions: native contact=1, else 0•modeling secondary structure•energy function: sum over all contacts•moves: swap to neighboring site, avoid self-intersection•Metropolis criterion: accept if E<0 or with p>exp(-E/kT)•study which factors determine whether a random sequence will fold
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