Basic protein structure and stability VI: Thermodynamics of protein stability

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Basic protein structure and stability
VIThermodynamics of protein stability

• Biochem 565, Fall 2008
• 09/10/08
• Cordes

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Native and denatured states
native state folded state
denatured ensemble unfolded ensemble
single structure or ensemble of very similar
structures compact
many different structures fluctuating not
usually very compact disordered but not a
random coil
For some proteins, but not all, this process is
readily reversible and occurs without populated
intermediate forms--gt two-state folding
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Naive view of folding thermodynamics
DGu
protein becomes less stable at high temp and
unfolds when TDS exceeds DH

• Native (folded)

Denatured (unfolded)
DGu DHu - TDSu
DGu
DHu
0
TDSu


unfolded state more disordered
favorable native state interactions broken
T
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Less naive thermodynamics of unfolding
Free energy of unfolding actually varies in a
more complicated way with T. Enthalpy and entropy
are both temperature dependent. Temperature
dependence is described by the heat capacity DCp.
DHu DHu0 DCp (TT0 )
enthalpy and entropy not temperature independent
DSu DSu0 DCp ln (T/ T0 )
DGu DHu0 TDSu0 DCpT T0 T ln (T/ T0 )
figures into the total free energy as this term
T0 is some arbitrary reference temperature, and
DHu0 and DSu0 are the enthalpy and entropy at
this temperature.
from Becktel Schellman, Biopolymers 26, 1859
(1987).
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Thermodynamic breakdown of unfolding
variation in enthalpy, entropy huge compared to
free energy
TDSu
DHu
slope DCp
this example DHu, 298 35 kcal mol-1 DSu, 298
100 cal mol-1K-1 DCp 1500 cal mol-1K-1
DGu
DCp typically 10-18 cal mol-1K-1 per residue
(large and positive)
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Temperature of maximal stability
point of maximal stability occurs when TDS is
zero (Ts)
below Ts, entropy favors folding folding less
favorable as decrease temp
this line represents zero
above Ts, entropy disfavors folding folding less
favorable as increase temp
from Becktel Schellman, Biopolymers 26, 1859
(1987).
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Stability curves for proteins
Tc --gt cold denaturation temperature--usually
below freezing
proteins typically not very stable 5-20 kcal/mol
at room temp
proteins typically have their maximum stability
near room temp
Tm of a protein --gt temperature at which
folded/unfolded states equally populated--gt DGu
0
proteins with higher heat capacity have tighter,
steeper parabolas (red curve vs. blue)
A protein with a higher room temp stability
could, in principle, have a lower Tm.
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Equation for thermal denaturation
DGu DHu0 TDSu0 DCpT T0 T ln (T/ T0 )
assign Tm as the arbitrary reference temperature
T0
DGu DHu,Tm TDSu,Tm
DCpT Tm T ln (T/ Tm)
DHu,Tm Tm DSu,Tm
DGu, Tm 0 so
DGu DHu,Tm(1 T/ Tm )
DCpT Tm T ln (T/ Tm)
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Amount of unfolded protein as function of T
eqn describing DGu as function of T
DGu DHu,Tm(1 T/ Tm )
DCpT Tm T ln (T/ Tm) Ku exp(-DGu/RT)
U/F fu Ku / (1 Ku )
Keq for unfolding reaction
concentration unfolded and folded
set of nested equations
fraction unfolded
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Heat denaturation curve
basic sigmoidal shape of this curve derives from
the two-state nature of the transition, but its
specific shape will vary with DCp, DH
so if I can somehow measure the folding
transition...
I can in principle extract the DCp, DH and the Tm
by fitting the curve and also get DG at every
temperature.
Tm
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Heat capacity and surface area
from Myers et al. Protein Sci 31, 2138 (1995)
Empirical studies of denaturation of proteins of
known structure show that DCp of unfolding
(y-axis) depends on the DASA (change in
accessible surface area) upon folding (in other
words the amount of surface buried). Note that
proteins with disulfide (open circles) fall below
the curve...why?
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from Myers et al. Protein Sci 31, 2138 (1995)
...and as we have seen the DASA depends upon the
size of the protein, in terms of the number of
residues in the polypeptide chain. This means
that DCp will be fairly predictable for globular
proteins of a given size...on average, its about
14 cal/(mol-K-residue), but it can be as low as
10 or as high as 18.
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Liquid hydrocarbon model for heat capacity

• The dependence of heat capacity of unfolding upon
  surface area burial suggests that it might be
  explained simply as a function of burying the
  chemical groups in the protein side chains and/or
  main chain.
• Indeed, it has been shown that a heat capacity
  change that parallels that observed upon protein
  unfolding also occurs upon dissolution of
  nonpolar solutes in water, so a major contributor
  may simply be the burial of nonpolar groups--this
  is called the liquid hydrocarbon model, which
  essentially explains the heat capacity in terms
  of the resemblance of a protein interior to an
  oil drop.
• However, burial of the amide groups in the
  backbone also has an effect on the heat capacity,
  based on experiments involving dissolution of
  organic amides in water. It is smaller and
  opposite in direction to the effect of burying
  hydrocarbons.

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Heat capacity and burial of surface

• DCp 0.32 DASAnp - 0.14 DASApol

plot showing DASAnp and DASAp for a dozen
proteins of different size
based on dissolution of amide compound solutes in
water--note is opposite in sign.
based on dissolution of hydrocarbon solutes in
water
The relationship above does a pretty good job of
predicting heat capacities of unfolding just by
treating the protein as a collection of nonpolar
and polar solutes. The nonpolar surface area
burial is the dominant effect and determines the
sign of the heat capacity effect, both because
the coefficient is larger and because more
nonpolar than polar surface is buried when
proteins fold.
from Spolar et al. Biochemistry 31, 3947 (1992)
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Chemical denaturants
urea
guanidine (guanidinium)
Molecular dynamics simulations of
urea denaturation suggest that it denatures
proteins by several mechanisms --competes for
backbone hydrogen bonds. --some effect on
solvation of hydrophobic core --affects
dynamics/structure of water, altering the
hydrophobic effect
stronger denaturant than urea also a salt, unlike
urea
See Bennion Daggett, PNAS 100, 5142 (2003).
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Chemical denaturation curve
Cm
fraction unfolded in the transition zone can be
translated into DGu values at each urea
concentration--gt see next slide
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Linear extrapolation to zero / m value
both guanidine urea melt should extrapolate to
same value of DGu H2O here about 4 kcal/mol
DGu DGu H2O m denaturant
urea
m is the slope of the DGu vs. denaturant curve
for urea here, it is 1.8 kcal mol-1 M-1
guanidine
Data are DGu values extracted from fu
in transition zone of melt
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Stability curves determined from melts
pay no attention to this scale-- 7 here is equiv.
to zero.
from transition zones of thermal melts
from chemical denaturation at 3 different temps
from Bowie Sauer Biochemistry 1989, 28, 7139.
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m values correlate with surface area burial, just
like DCp
from Myers et al. Protein Sci 31, 2138 (1995)
notice how proteins with disulfide crosslinks
(open circles) fall below the line...the authors
corrected for this and ultimately came up with
the following equation
m (urea) 0.14 (DASA 995 crosslinks)
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Key points about protein stability

• in general protein native states are weakly
  stable (5-20 kcal/mol) relative to unfolded
  states
• they tend to be maximally stable around room
  temperature, and are subject to both cold and
  heat denaturation, with inversion of sign of both
  the enthalpy and the entropy of unfolding
• large heat capacity change due partly to
  properties of water--large T dependence of
  enthalpy, entropy
• much of the denaturation behavior of proteins can
  be understood in terms of simple burial and
  solvent exposure of nonpolar and polar surface
  area