Folding

1
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)

2
Folding

• Anfinsen (1950s) 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
3
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)

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Kubelka et al (2004)

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Galzitskaya et al. (2003)
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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 Hs exchange with solvent at some
  rate
• reflects dynamic unfolding/refolding
• overall folding rate const vs. kunfold and kfold
• equilibrium shifted in direction of DG

7
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?

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Levinthal Paradox

• How can proteins fold in such a short time?
• Number of degrees of freedom
• gt2Nres (phi/psi angles), lt310Nres (atomic
  coords)
• states 3N3N? (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

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• 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

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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?

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• 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 Kuku/kf and
kukuH20mfGCl and kfkfH2O-muGCl, then
mmumf
3-state barnase
rates!
re-folding (stopped flow)
unfolding (fluorescence curve)
equilibrium!
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van 't Hoff equation

• thermal denaturation

Gibbs-Helmholtz equation

• Pace and Laurents (1989)
• Method for determining DCp
• - calorimeter (10 error)
• DCpd(DH)/dT from vHoff
• extrapolate from DG
• measured at different
• denaturant concentrations

balance between DS and DH
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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?
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Lysozyme has both a fast a slow pathway
(Keifhaber, 1995) data fit better by a
double-exponential (t150ms, t2420ms)
see also Jamin and Baldwin (1996). folding vs.
unfolding rates as evidence for intermediates in
apomyoglobin
15

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

simulations of ubiquitin at 498 K and 298 K
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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...
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The Unfolded State

• random coil? (hydrodynamic radius)
• backbone, side-chains fully solvated (hydration)
• effects of pH, urea...

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Contact Order

• (Plaxco Simons Baker, 1998)

L length of protein N num of contact pairs
(side-chain dist lt 6A) DS sequence separation
1HRC, CO11.2
1UBQ, CO15.1
1TEN, CO17.4
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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

phi0 no effect on TS
phi1 mutation affects TS
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Lattice Models

• Sali, Shakhnovich, and Karplus (1994)
• Monte Carlo sampling of configurations
• simplified interactions native contact1, else 0
• modeling secondary structure
• energy function sum over all contacts
• moves swap to neighboring site, avoid
  self-intersection
• Metropolis criterion accept if DElt0 or with
  pgtexp(-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

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order parameter for heterogeneity of ensemble
(related to entropy)
synthetic example of a compact folded polymer
ends
cant move
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(No Transcript)
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• extensions
• Dill, HP model H and P atom types, 2D lattice
• off-lattice models

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Kolinski, Godzik, Skolnick (1993)

• ab initio folding?
• Cas 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

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SICHO (Kolinski and Skolnick, 1998)

• ab initio folding with a few (20) restraints
  (e.g. NMR)
• model side-chains centers only (no Cas)
  on-lattice
• Monte Carlo moves multiple groups of atoms
• energy function simplified geometry statistics,
  contact potentials

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Reduced-atom models

• Go (1980) model (off-lattice)
• Cas 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

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Mis-folding and Amyloid formation

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