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Entropic and Enthalpic Barriers in Cooperative Protein
FoldingHue Sun CHAN
Departments of Biochemistry, and of Molecular Genetics University of Toronto, Ontario M5S 1A8 Canada
http://biochemistry.utoronto.ca/chan/bch.html
IMA, January 17, 2008
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What do we know from experiments?
Cooperative Folding:
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How does the calorimetric criterion work?
bimodal cooperative folding
unimodal noncooperative folding
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Kinetic manifestation of folding cooperativity: linear chevron plots
Linear folding and unfolding arms imply a linear relationship between log(folding/unfolding rate) and equilibrium stability
Data from Jackson et al., Biochemistry 32:11270 (1993)
chevron rollover is indicative of less cooperative or noncooperative folding
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Do we understand the
Physics of
Generic Protein Properties?
Most current coarse-grained protein chain models do not satisfy experimental cooperativity criteria
Chan et al., Methods Enzymol (2004)
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Clementi et al., JMB (2000); Koga & Takada, JMB (2001); Kaya & Chan, JMB (2003)
Continuum C Go Models
Native-centric local and non-bonded interactions
Langevin dynamics
Thermodynamically quite cooperative
CI2
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Go-model chevron plots have significant chevron rollovers, implying that in many cases Go models are less cooperative than the real proteins they aim to mimick
Jackson & Fersht, Biochemistry (1991)
Kaya & Chan, JMB (2003)
Theory
Experiment
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Even with native biases, pairwise additive coarse-grained interactions do not account for cooperative folding
Better Mesoscopic Principles?
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(local-nonlocal coupling) Kaya & Chan, Proteins
(2003)
‘Many-body’ interactions needed to account for folding cooperativity
A hypothesized cooperative interplay between favorable nonlocal interactions and local conformational preferences
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Testing the local-nonlocal coupling idea by lattice models
a < 1, attentuation factor
Kaya & Chan, Proteins (2003)
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Native Topology (Contact Pattern) Dependent Folding Rates
Plaxco, Simons & Baker, JMB (1998)
Plot from Plaxco et al. Biochemistry (2000)
Can protein chain models capture this trend?
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Kaya & Chan, Proteins (2003); Chan et al., Methods Enzymol (2004)
Many-body interactions in the form of local-nonlocal coupling rationalize topology-dependent folding rates
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Top7, 1qys (93aa) Kuhlman et al., Science (2003)
Scalley-Kim & Baker, JMB (2004); Watters et al., Cell (2007)
Kaya & Chan, Proteins (2003)
Our theoretical perspective was corroborated by experiments:
Cooperativity is likely an evolutionarily selected trait; cooperativity is not a corollary of a protein’s ability to fold
theory
experiment
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Kaya & Chan, Proteins (2003)
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Folding Barriers
entropic & enthalpic components
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Entropic Barriers:
Role of conformational entropic barriers in native topology-dependent folding rates
Wallin & Chan, J Phys Condens Matt (2006)
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Wallin & Chan, J Phys Condens Matt (2006)
Transition-state ensembles:
1div 1pg
b
1imq1wit
‘Transition state’ as conformations around the Q barrier
Q = fractional number
of native contacts
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Wallin & Chan, J Phys Condens Matt (2006); cf. Koga & Takada, JMB (2001)
… found some correlation between model and experimental folding rates, suggesting that the model captures part of the physics
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Wallin & Chan, J Phys Condens Matt (2006)
Entropic barriers:
The topology-folding rate relationship is likely dominated by conformational entropy effect
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lower temperature
Enthalpic barriers:
non-Arrhenius folding rates, positive unfoled-to-transition state enthalpy changes at some temperatures
Does this mean that the folding landscape is not funnel-like?
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H
S
Cp
Thermodynamic Signatures of Protein Folding Kinetics
CI2 “reaction profiles”
25 °C
25 °C
enthalpic barrier
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Desolvation is a likely origin of robust enthalpic barriers to protein folding
Liu & Chan, JMB (2005)
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Liu & Chan, JMB (2005); Phys Biol (2005); cf. Cheung et al., PNAS (2002); Kaya & Chan, JMB (2003)
Desolvation barriers enhance folding/unfolding cooperativity increasing
height of pairwise desolvation barrier leads to …
Higher overall free energy barrier
more linear chevron plots
CI2
CI2
less native fluctuation
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A. Ferguson, Z. Liu & H.S. Chan (2007)
Desolvation barrier effects are a likely contributor to the remarkable diversity in the folding rates of small proteins
simulated folding rates span ~4.5 orders of magnitude
simulated folding rates span ~1.5 orders of magnitude
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…but pairwise desolvation barriers alone are insufficient to account for the thermodynamic signatures of cooperative folding
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Typically, Unfolded-to-Transition-State heat capacity change is negative for protein folding, but …
for the association of small nonpolar solutes in water, heat capacity change is positive around the desolvation free energy barrier.
Length-scale dependence provides a possible probe for cooperativity?
from G at 8 temperatures
Shimizu & Chan, JACS (2001)
TIP4P water model
CP highly non-monotonic
Not well predicted by surface areas
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rnm
r
CH4
Xe
3-body
2-body
Paschek, J Chem Phys 120:6674 (2004)Moghaddam, Shimizu & Chan, JACS (2005)
Hydrophobic interactions among small hydrophobic solutes:
Robust CP > 0 at the desolvation free energy barrier
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Moghaddam, Shimizu & Chan, JACS (2005); Liu & Chan, JMB (2005)
Enthalpic barrier can be significantly higher than the desolvation free energy barrier
temperature dependence of the potential of mean force (PMF)
Enthalpy-Entropy Compensation at Desolvation
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MacCallum, Moghaddam, Chan & Tieleman, PNAS (2007)
Helix association in water as a model for rate-limiting events in protein folding A pair of 20-
residue
poly-alanine or
poly-leucine helices
~3,800 water molecules
Simulated constant-pressure free energy of association (potential of mean force, PMF) at five temperatures
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MacCallum, Moghaddam, Chan & Tieleman, PNAS (2007)
Enthalpic desolvation barriers of ~ 50 kJ/mol comparable to that of protein foldingDramatic enthalpy-entropy compensation at the desolvation step leading to low or non-existent free energy barriers
At 25 deg C,
Enthalpic folding barrier height for
CI2 is ~ 30kJ/mol (Oliveberg et al., 1995)
CspB is ~ 32kJ/mol (Schindler & Schmid, 1996)
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MacCallum, Moghaddam, Chan & Tieleman, PNAS (2007)
Enthalpic barriers caused by steric dewetting
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Recap.:Folding cooperativity implies ‘near-Levinthal’ funnels
Enthalpic barriers can be consistent with funnel-like folding landscapes
?
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Artem Badasyan
Allison Ferguson
Mikael Borg
Huseyin Kaya
Michael Knott
Zhirong Liu
Maria Sabaye Moghaddam
Seishi Shimizu
Stefan Wallin
Co-workers
University of Toronto University of Toronto
Prof. D. Peter Tieleman
Justin MacCallumUniversity of MuensterProf. Erich Bornberg-Bauer
David Vernazobres
Richard Wroe
University of Calgary
Prof. Julie D. Forman-KayProf. Regis Pomes