Folding • 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
Time-scales for folding • cytochrome b562: 5 ms • lambda repressor: 0.67 ms • rat IFABP: 33 ms • CRABP 1: 24.5 sec • tryptophan synthase b2-subunit: 992 sec (396 aa)
Kubelka et al (2004)
Galzitskaya et 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 DG
Thermodynamic 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 a/b/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 landscapes
Two-state folding • data must fit first-order kinetics • linearity of ln(kf) vs. [denaturant] • DG 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, a-lactalbumin) • bT – measure of where transition occurs along reaction coordinate: how “native-like”?
Jackson and Fersht (1991) – chymotrypsin inhibitor 2 1. 2-state model supported by concordance of params between thermo. and kinetics 2. slope (mF and mU) correlates with difference in accessible surface area between U and F (Myers, Pace, and Scholtz, 1995) 3. if Ku=ku/kf and ku=kuH20+mf[GCl] and kf=kfH2O-mu[GCl], then m=mu+mf 3-state: barnase rates! re-folding (stopped flow) unfolding (fluorescence curve) equilibrium!
van 't Hoff equation • thermal denaturation Gibbs-Helmholtz equation • Pace and Laurents (1989) • Method for determining DCp • - calorimeter (10% error) • DCp=d(DH)/dT from v’Hoff • extrapolate from DG • measured at different • denaturant concentrations balance between DS and DH
Folding 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 for intermediates in apomyoglobin
Valerie Daggett • molecular dynamics simulation of folding/unfolding • identification of order of sub-structure formation simulations of ubiquitin at 498 K and 298 K
Off-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 protein N = num of contact pairs (side-chain dist < 6A) DS = sequence separation 1HRC, CO=11.2 1TEN, CO=17.4 1UBQ, CO=15.1
F-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=0 no effect on TS phi=1 mutation affects TS
Lattice 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 DE<0 or with p>exp(-DE/kT) • study which factors determine whether a random sequence will fold (fast): • short-range vs. long-range contacts (contact order)? • size? secondary structure? hydrophobicity? • presence of a clearly-defined (deep) energy minimum
order parameter for heterogeneity of ensemble (related to entropy) synthetic example of a compact folded polymer ends can’t move
extensions • Dill, HP model: H and P atom types, 2D lattice • off-lattice models
Kolinski, Godzik, Skolnick (1993) • ab initio folding? • Ca’s only, on-lattice model (1.7Å spacing) • side-chains modeled as spheres • statistical side-chain contact potential (eij) • non-directional H-bonds • 4-body side-chain interactions • cooperative coupling
SICHO (Kolinski and Skolnick, 1998) • ab initio folding with a few (~20) restraints (e.g. NMR) • model side-chains centers only (no Ca’s) on-lattice • Monte Carlo moves – multiple groups of atoms • energy function: simplified geometry statistics, contact potentials
Reduced-atom models • Go (1980) model (off-lattice) • Ca’s: beads on a string (bond dist/angle contraints) • good description in Hoang and Cieplak (2000). • energy function includes term for native contacts (springs) • application to mechanical unfolding of titin
Mis-folding and Amyloid formation • aggregation vs. fibril formation • disease processes (20, Alzheimer’s, a-b) • DLS – dynamic light scattering • solid-state crystallography • kinetics (polymerization) • similarity between 2 global minima • “dual-basin” – mis-folded intermediate for GFP • Andrews et al (2008) • http://www.pnas.org/ content/105/34/12283 Dobson (1998)
