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

• 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 folding

Kubelka 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 G

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 /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]• 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 2

re-folding(stopped flow)

unfolding(fluorescencecurve)

3-state:barnase

1. 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+mf

equilibrium!

rates!

• thermal denaturationvan 't Hoff equation

Gibbs-Helmholtz equation

Pace and Laurents (1989)Method for determining Cp

- calorimeter (10% error)- Cp=d(H)/dT from v’Hoff- extrapolate from Gmeasured at differentdenaturant concentrations

balance between S and H

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 forintermediates in apomyoglobin

• Valerie Daggett– molecular dynamics simulation of folding/unfolding– identification of order of sub-structure formation

simulationsof ubiquitinat 498 Kand 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 proteinN = num of contact pairs (side-chain dist < 6A)S = sequence separation

1HRC, CO=11.2 1UBQ, CO=15.1 1TEN, 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 TS

phi=1mutation 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 E<0 or with p>exp(-E/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

ends

can’t move

synthetic example of a compact folded polymer

order parameter for heterogeneityof ensemble (related to entropy)

• 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 (ij)

• 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)• C’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

Dobson (1998)

• aggregation vs. fibril formation• disease processes (20,

Alzheimer’s, a-)• 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