Folding Anfinsen cooperativity time scales, speed range Levinthal paradox ensembles energy...
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Transcript of Folding Anfinsen cooperativity time scales, speed range Levinthal paradox ensembles energy...
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