Transcript Document

Basic protein structure and
stability VI:
Thermodynamics of protein
stability
Biochem 565, Fall 2008
09/10/08
Cordes
Native and denatured states
denatured ensemble
unfolded ensemble
many different structures fluctuating;
not usually very compact;
disordered but not a “random coil”
native state
folded state
single structure or ensemble
of very similar structures;
compact
For some proteins, but not all, this process is readily reversible and occurs
without populated intermediate forms--> “two-state” folding
Naive view of folding thermodynamics
Native
(folded)
DGu
Denatured
(unfolded)
DGu = DHu - TDSu
+
favorable native state
interactions broken
+
protein becomes less stable at
high temp and unfolds when TDS
exceeds DH
DGu
DHu
0
TDSu
unfolded state
more disordered
T
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 (T–T0 )
DSu = DSu0 + DCp ln (T/ T0 )
enthalpy and entropy not
temperature independent
DGu = DHu0 – TDSu0 + DCp[T– 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).
Thermodynamic breakdown of unfolding
2 105
variation in enthalpy, entropy
huge compared to free
energy
5
5
1 10
slope = DCp
u
DG , DH , or T DS , cal/mol
1.5 10
this example:
DHu, 298 = +35 kcal mol-1
DSu, 298 = +100 cal mol-1K-1
DCp = +1500 cal mol-1K-1
5 104
u
u
TDSu
DHu
0
DGu
-5 104
260
280
300
320
340
temperature (K)
360
380DC typically 10-18 cal
p
mol-1K-1 per residue (large
and positive)
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
from Becktel & Schellman,
Biopolymers 26, 1859 (1987).
above Ts, entropy
disfavors folding:
folding less favorable
as increase temp
Stability curves for proteins
Tc --> cold denaturation temperature-usually below
freezing
1 104
proteins typically not very stable:
5-20 kcal/mol at room temp
proteins typically have their
maximum stability near room
temp
5000
Tm of a protein --> temperature
at which folded/unfolded states
equally populated--> DGu = 0
-5000
u
DG , cal/mol
0
-1 10
4
proteins with higher
heat capacity have
tighter, steeper
parabolas (red curve vs.
blue)
-1.5 10 4
260
280
300
320
A protein with a higher room
temp stability could, in
principle, have a lower Tm.
340
temperature (K)
360
380
Equation for thermal denaturation
DGu = DHu0 – TDSu0 + DCp[T– T0 –T ln (T/ T0 )]
assign Tm as the arbitrary
reference temperature T0
DGu = DHu,Tm – TDSu,Tm
+ DCp[T– Tm –T ln (T/ Tm)]
DGu, Tm = 0 so DHu,Tm = Tm DSu,Tm
DGu = DHu,Tm(1 – T/ Tm )
+ DCp[T– Tm –T ln (T/ Tm)]
Amount of
unfolded protein
as function of T
eqn describing DGu
as function of T
DGu = DHu,Tm(1 – T/ Tm )
+ DCp[T– Tm –T ln (T/ Tm)]
Ku = exp(-DGu/RT) = [U]/[F]
Keq for unfolding reaction
fu = Ku / (1 + Ku )
fraction unfolded
concentration unfolded
and folded
set of nested equations
Heat denaturation curve
1
and also get
DG at every
temperature.
0.8
0.6
Tm
0.4
u
I can in
principle
extract the
DCp, DH and
the Tm by
fitting the curve
f (fraction unfolded)
so if I can somehow
measure the folding
transition...
basic sigmoidal shape
of this curve derives
from the “two-state”
nature of the transition,
but its specific shape
will vary with DCp, DH
0.2
0
290
300
310
320
330
temperature (K)
340
350
360
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?
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,
it’s about 14 cal/(mol-K-residue), but it can be as low as 10 or as high as 18.
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.
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 based on dissolution of amide
compound solutes in water--note
of hydrocarbon
is opposite in sign.
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)
Chemical denaturants
O
H2N
NH2
NH2
urea
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
H2N
NH2
guanidine (guanidinium)
stronger denaturant than urea
also a salt, unlike urea
See Bennion & Daggett, PNAS 100, 5142 (2003).
Chemical denaturation curve
1
Cm
fraction unfolded
0.8
0.6
0.4
fraction unfolded in the transition zone
can be translated into DGu values at each
urea concentration--> see next slide
0.2
0
0
1
2
3
4
urea concentration (M)
5
6
Linear extrapolation to zero / m value
both guanidine & urea melt
should extrapolate to same
5
value of DGu H2O here about 4 kcal/mol
4
DGu = DGu H2O + m [denaturant]
2
1
urea
m is the slope of the
u
DG , kcal/mol
3
DGu
0
vs. [denaturant]
curve: for urea here,
it is 1.8 kcal mol-1 M-1
guanidine
-1
-2
y = 3.5627 - 1.7595x R= 0.99781
y = 3.8931 - 2.5989x R= 0.99566
-3
0
0.5
1
1.5
2
2.5
[GdnHCl] or [urea], M
3
3.5
Data are DGu values
extracted from fu in
transition zone of melt
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.
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)
Key points about protein stability
• in general protein native states are weakly stable (520 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