FOLDING & UNFOLDING
Introduction
The process of denaturation and folding are the two opposite ways through
which the specific cellular activity of a protein is created or abolished. The
study of the folding and of the denaturation can give useful information about
the stability of the protein and the identification of the preferred ways to
achieve a specific three-dimensional structure. The prediction of the threedimensional structure of a protein from its amino acid sequence, is perhaps the
not resolved most important issue in the modern structural biology. If there was
a general solution to the problem of folding it would be possible to write a
program for the simulation of the process, avoiding to approach the problem
from the experimental point of view. This chapter will deal with these two
processes which, although opposite in nature, present a number of common
elements. In Figure 1 two states of the same protein, the native and the
denatured state, are represented.
Figura
1.
Equilibrium between the native and the denatured state
The two states have a relatively low difference in energy, implying that the
two states are separated by an high energy activated state, otherwise we would
have a continuous interconversion between the native and the denatured state.
On the other hand it is known that the native state, in physiological conditions,
is fully stable and the conditions must change dramatically to start the process
of denaturation. The transition between the two states can occur through one or
more preferential routes, as shown in Figure 2, with formation of one or more
intermediates.
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Figura 2. Possibile folding pathways
The information contained in the amino acid sequence of the protein is
sufficient to force the protein to reach its three-dimensional structure. This has
been demonstrated in the early'70s, when Anfinsen showed that ribonuclease
could achieve in vitro its three-dimensional structure starting from the
denatured state, once removed the conditions for the denaturation, such as the
presence of urea and reducing agents (Fig. 3). The experiment testified for the
first time that it was possible in vitro to reversibly fold and unfold a protein.
Figura 3. The folding scheme for
ribonuclease
This process, namely the
transition from the denatured to
the native form, in vivo can be
modulated by a series of molecular factors, called chaperons. Indeed, in vivo
there will be proteins that reach the three-dimensional structure regardless of
the interaction with the molecular chaperons, while other ones will find more
convenient to interact with them.
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The folding process is fast
The process of folding is fast, the protein reaches its native state in less than a
few seconds. The process then cannot be completed by sampling all possible
conformations followed by the subsequent choice of the structure with the
lowest energy, since this procedure would require an extremely long time, as
shown in Figure 4.
Figura 4. Time required for the folding of a protein with 150 residues.
Indeed, in a protein of 150 residues where there are only three possible
conformations for each residue and in which the time of interconversion
between the conformations is extremely rapid (one picosecond), the total
number of conformations are 3150 and the time necessary to sample them
would
require 1048 years, a time close to infinite when compared to the time
experimentally necessary. So the choice of the proper conformation is not
through a sampling of all the conformations that can be achieved, but through
one or more preferential routes through which the amino acid sequence will
define the three dimensional structure which is associated to the function.
In Figure 5 ( bottom) a possible outline of the process of folding according
to its reaction coordinate is depicted
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Figura 5. Scheme of the folding process
The symbol U defines the protein in
the denatured state (unfolded), F in the
folded state (folded). These two states
are not too much separated in energy but
between them there is a state T (the
transition), which has a high energy
value. This prevents the native and denatured state to stay in a constant
equilibrium. M is the protein in the molten globule state, a relatively stable
intermediate in the process that goes from U to F, usually characterized by the
presence of secondary structure but the lack of a defined tertiary structure.
The diagram on the top of figure5 shows the decrease of the distribution of
conformations from the denatured protein to the the native form, that, however,
still possess a degree of microheterogeneity.
The protein folding is a cooperative process.
The process of folding is
cooperative, a phenomenon due to
the simultaneous presence of
multiple interactions in a single
molecule.
Let
consider
a
denatured protein where there are
two groups A and B, that can be
in contact via a weak interaction.
Figura 6. The cooperativity for the interaction of two molecules.
The equilibrium constant for the interaction between the two groups in the
denatured protein is given by:.
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KU = KAB[A/B]U
where KAB is the association constant of the two groups when they are on
separate molecules and [A / B] U is the concentration of the two groups in the
denatured protein. The value of [A / B] U ranges from 10-2 to 10-5 M and
depends on the relative position of the two groups within the protein. In the
presence of multiple interactions the value of concentration can change and
thus facilitate or hinder the interaction of groups A and B. If the protein is
completely stretched A and B are far apart, when folded A and B are very
close and therefore the apparent concentration of A and B is much higher.
Basically, the more A and B are close the larger is the apparent concentration
of A and B, increasing their interaction possibility. Consider a protein where
there are four groups A, B, C and D (Fig.6). The groups can exist in a non
interacting, in a partially or fully interacting conformation. The probability of
interaction of A and B will be higher in a partially folded than in the denatured
conformation. Their association constant KAB remains unchanged (because the
groups are always the same), the only thing that changes is the relative
distance of the groups. The ratio [A / B] II / [A / B] U, that is the ratio between
the apparent concentration of A and B in the partially folded state and in the
denatured state represents the cooperativity factor, the factor that facilitates the
interaction between A and B. The apparent concentration of A and B is
increasing as a result of the interaction between C and D as well as in a
symmetric way the interaction of C and D increases as a result of the
interaction between A and B. In the case of a protein, once a number of groups
are beginning to interact with each other, all others have a greater chance to
interact and this means that the process is cooperative.
In the event of multiple interactions the final equilibrium constant between the
total final state (fully interacting groups) and the initial state ( not interacting
state) is given by the following product :
KNET = (KAB[A/B]U) (KCD[C/D]I) (KEF[E/F]III)
The final state will be stable if KNET will be greater than unity. This is easily
understandable considering the presence of multiple groups that can interact
with each other, the initial interaction has an equilibrium constant of 10-4 and
each additional interaction is 10 times stronger than the previous one. The first
interaction will give rise to an equilibrium constant equal to 10-4, the second
one equal to 10-7 (10-4 × 10-3 ), the third one 10-9 (10-4 × 10-3 × 10-2 ) and so
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on. This is because the presence of the first interaction increases the effective
concentration of the latter groups and therefore the second interaction will be
greater by a factor of 10 which is the cooperativity factor. Initially the product
of the various equilibrium constants is always less than one and even the
equilibrium constant of the second, third and fourth term is lower than the
preceeding one. This process continues until the actual concentration of the
interacting groups is such that the equilibrium constant of each interacting
group is greater than unity. From this point onwards KNET starts to increase
for each subsequent interaction, until the value becomes higher than unity,
corresponding to a difference in free energy of zero between the folded and the
unfolded form.
Figure 7 shows the values of equilibrium constants and the corresponding
energy value for a protein in which the equilibrium constant for the first
interaction is 10-4 and any subsequent one is 10 times stronger.
Figura 7. Energetic scheme for the folding of a molecule where each interaction is 10
times stronger than the previous one.
The graph gives rise to a bell curve whose ends represent the completely
denatured and the completely interacting groups respectively. The system is
stable only in these two points and not in the intermediate states.
In Figure 8 the distributions of configurations of a protein during the process
of denaturation for a cooperative (left column) or non-cooperative (right
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column) process are represented. In both cases the protein in the native state is
represented by a distribution of conformations relatively narrow, while the
denatured protein is represented by a broad distribution of conformations. In
the intermediate situation, if the process is cooperative (Fig. 8, left column),
there is an equilibrium between two families of conformations represented by
the native protein and the denatured protein. If the process is not cooperative,
the protein is represented by a broad distribution of conformations, (Fig. 8,
right column). Therefore, the cooperativity of the folding process constrains the
protein to stay, in partially denaturing conditions, in two well-defined
conformations, the native and the denatured state, that are in equilibrium. The
K equilibrium constant is the ratio between the percentage of protein in the
native state over the percentage of protein in the denatured state and will
change varying the external denaturing conditions.
Figura 8. Distribution of the protein conformations for a cooperative (left) and non
cooperative (right) folding process
The presence of an equilibrium between these two forms permits us to
measure the difference in free energy between the native and the denatured
state and to quantitatively measure for each protein how much the native state
is more stable than the denatured one. In fact, for a two states transition K =
[N] / [U] and the difference in free energy ΔG between the native state N and
the denatured state U is given by:.
ΔG = GN – GU = -RTln K
To assess this difference in energy the protein must be denatured in a
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reversibile manner following a parameter diagnostic of the native and of the
denatured state of the protein. This will permit to measure the equilibrium
constant and thus the energy difference between the two states. How can a
protein be denatured? It will be necessary to vary the conditions that maintain
the native state. This can be achieved by varying physical (temperature,
pressure) or chemical parameters (increased concentration of a denaturant
molecule, variation of pH). In fact, the proteins are stable at neutral pH, where
it exists a fair balance between the positive and negative charges of the various
side chains. A change to acidic or alkaline pH creates a large concentration of
negative or positive charges that repel each other leading to the denaturation of
the protein itself.
One method widely used for the denaturation is to add external molecules that
can be divided into two main classes: those that preferentially interact with the
protein (preferential binding) and those that prefer to interact with the solvent
(preferential hydration), as shown in Figure 9. In general, the molecules that
prefer to interact with the solvent are stabilizing factors, while the molecules
that prefer to interact with the surfaces of the protein, in particular with the
non-polar surfaces, are denaturants. Figure 9 shows on the left molecules that
prefer to interact with the protein and on the right molecules that interact
preferentially with the water.
Figura 9.
Distribution
of molecules
preferentially interacting with the protein (left) or with the water (right).
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The two chemical denaturants that are most commonly used are urea and
guanidine chloride, which are able to increase the solubility of both polar and
not polar in a way proportional to the surface accessible to solvent. Figure 10
shows the ΔG of transfer of side chains from water to urea or guanidine
chloride. The ΔG is negative and increases in absolute value with the surface of
the molecule. This means that the side chains prefer to interact with the
denaturant than with water and this is why the protein tends to denature. In
fact, the hydrophobic residues at high urea concentrations do not want to be
buried in the internal part of a protein, but they want to go to the surface to
interact with the denaturant.
Figura 10. Free energy of transfer of the aminoacid side chains from water to a
denaturing agent.
A denaturation curve can be obtained following a parameter, that allows to
distinguish the native and the denatured form, as a function of the
concentration of a denaturing agent. The curve has a sigmoidal shape,
indicative of a cooperative process, as can be seen from Figure 11 where a gel
electrophoresis of cytochrome c in urea gradient is reported.
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Figura 11. Gel electrophoresis
of cytochrome c in urea
gradient
Increasing the urea concentration the protein is more slow as it opens and this
allows you to see a separation of the forms.
In general, the process of denaturation can be efficiently followed by
following a spectroscopic parameter. The emission of fluorescence of a
tryptophan may be a good parameter, if the tryptophan in the native state is
located within the internal region of the protein. The wavelength of emission
of tryptophan depends on its location, being at low wavelength values when it
is in a hydrophobic environment and at high values when it is in a hydrophilic
environment, as when it is denatured. The selected parameter must have very
different characteristics for the protein in the native and in the denatured state.
The measures must be taken after the addition of increasing amounts of the
denaturantand when we are sure that the equilibrium has been reached, in
order to properly assess the percentage of protein molecules in the native and
denatured state at that particular concentration of denaturant. In this way, an
equilibrium constant can be measured and the difference in free energy ΔG
between the native and denatured state can be assessed. After introducing a
defined amount of denaturant concentration (1 M, 2 M), the measurement is
taken and then repeated as a function of time, until there is no change
compared to the previous measurement. This means that the reaction has
reached an equilibrium and the corresponding value can be reported in a graph
(Fig. 12), where the experimental parameters such as absorbance, fluorescence
intensity etc.. are reported as a function of the denaturant concentration. The
obtained curves are sygmoidal confirming that the process is cooperative.
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Figura 12. Denaturation of a protein as a function of the
denaturant concentration
At the beginning and at the end of the graph in
Figure 12, the base line is not perfect though,
initially, 100% of protein is present in solution in
the native state and at the end, 100% of the molecules have been denatured.
The absence of a flat base-line is due to the interaction of the macromolecule
with the denaturant, which can cause a variation of the parameter without a
disruption of the state of the protein. It is interesting to note that the
phenomenon of denaturation occurs in a narrow range of denaturant
concentration or temperature, as shown in Figure 12 and 12b.
Figura 12b. Protein denaturation as a function of temperature.
In this interval the parameter changes rapidly, because its value depends on the
number of molecules that pass from the native to the denatured state. In this
range the protein is not in an undefined state, but the solution contains only two
conformations: the native and the denatured state. The experimental measured
parameter has a value that is given by the linear combination of the
contribution of molecules in the native state plus the contribution of the
molecules in the denatured state. This allows you to measure for each
denaturant concentration an equilibrium constant given by the ratio between
the percentage of molecules in the native and the denatured state. It is in fact
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possibile to write a system of two equations and two unknowns, represented
by the fraction of molecules in native state fF and the fraction in the denatured
state fU (Fig. 13). The sum of the two fractions must be constant and equal to 1
and the experimental parameter y (ie the experimental parameter measured as a
function of the concentration of denaturant) is due to the contribution of the
value of the parameter for the native form yF multiplied by the native fraction
fF and the value for the denatured form yU multiplied by the denatured fraction
fU
Figura 13. The two equations necessary
to work out the free energy difference
between the native and the denatured
state.
The resolution of the system
provides the equilibrium constant K for each value of the concentration of
denaturant, so a constant K1, or a constant K2, K3 for three different urea
concentrations. The differences in free energy ΔG1, ΔG2, ΔG3 corresponding
to these equilibrium constant values can be reported on a graph having as
abscissa the concentration of denaturant and as ordinate the values of free
energy changes. Which is the ΔG value indicative of the energy difference
between the native and the denatured protein? The most appropriate value is
the value that occurs in the absence of denaturant but in these conditions the
protein is in the native state and it is therefore not possible to measure the
equilibrium constant. This value can be obtained by extrapolation. The graph of
the ΔG values as a function of urea concentration is a straight line whose
intercept with the y axis for the value of x = 0 is a good approximation of the
value of the free energy difference between the native and denatured state of
the protein at physiological conditions. In Figure 14 the value is 6 kcal / mol,
corresponding to the contribution of 2 or 3 hydrogen bonds. The two states are
so relatively close in energy that should be in equilibrium, but this does not
happen because they are separated by an intermediate state, the transition state,
that is characterized by a high energy value, so it is necessary to strongly vary
the environmental conditions to denature the protein. The energy difference ΔG
between the native and the denatured state for any globular protein, is of the
same order of magnitude that is typically less than 10 Kcal / mol
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Figura 14. Free energy differente between the native and the denatured state as a
function of urea concentration.
The dependence of the thermodynamic parameters for the native and the
denatured state as a function of temperature shows that the enthalpy and
entropy changes are large and in both cases of the same order of magnitude, of
hundreds of kcal / mol (Fig. 15) . The corresponding free energies are of a few
tens of kcal / mol and the same goes for the free energy difference between the
native and denatured. The graph in Figure 15 shows an example of a protein in
which up to a temperature of 80 ° C the native state is more stable the
denatured one, and after this temperature, the opposite happens.
Figura 15.Dependence on temperature of the
entropic and entalpic parameter
The graph in Figure 16, that shows the
difference in free energy ΔG between the
native and denatured state as a function of
temperature for a series of proteins,
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indicates that each protein has an optimal stability temperature. The graph has a
bell shape, indicating that not all proteins like a very low temperature.
Figura 16. Free energy difference of the
native and denatured state as a function
of temperature.
Qualitative comparison of the stability of a native and mutated protein
In the preceding paragraph it has been shown how to quantitatively assess the
difference in stability between the native and denatured state of a protein
through a reversible denaturation that allows us to assess the relative
thermodynamic parameters. The qualitative measure of the relative stability of
a native protein in comparison to a mutant does not require a reversible
denaturation and informations can be obtained more directly. In this case it is
possible to obtain a scale of relative stability by making an irreversible
denaturation, bringing for example the protein at 100 ° C, maintaining this
temperature for a definite time and then bringing it to room temperature. When
the temperature is increased to 100 ° C, an irreversible denaturation occurs. It is
possibile to measure the percentage of denaturation comparing the activity
before and after the incubation at 100 ° C. This procedure, performed in a
comparative way on both the native and the mutated protein, allows us to
understand whether the mutant is more or less stable than the native protein. In
fact in a graph representing the ln of the activity as function of the incubation
time at high temperature it is possible to assess the speed of the activity loss. In
the graph in Figure 17, the loss of the activity of the mutant represented by
white ball is slower than the native (black dot). This means that the mutation is
a stabilizing mutation, while the mutation represented by the diamond is
destabilizing because the protein is leaking faster the activity. It is enough to
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irreversibly denaturate the proteins to define a level of stability and determine
the stabilizing mutations..
Figura 17. Graph of the ln of the activity as a
function of the incubation time at high
temperature for the native and mutated
samples
If this type of experiment is performed with dimeric or multimeric proteins it
may be useful to do the measurements as a function of enzyme concentration.
In this way you can understand if the path followed during the denaturation is a
transition from the dimeric form directly to the denatured state (DU) or from
the dimer to the monomer and finally to the denatured state (DMU). If the loss
of activity is concentration dependent, it means that the path followed is DMU
because lowering the concentration the monomer-dimer equilibrium is shifted
toward the monomer and the protein tends be more easily denaturated. Instead,
if it is concentration independent, the route followed is DU as the rate of
denaturation doesn’t depend on the -dimer-monomer equilibrium (Fig. 18)..
Figura 18. Rate of the loss of activity as a function
of protein concentration for a dimeric enzyme
following the DMU path.
Stabilizing mutations
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It is possible to make mutations that render the enzymes more stable. Nearly all
consist in the introduction of a new interactions within the folded protein (Fig.
19).
Figura 19. Possibili strategie per stabilizzare le proteine.
A particularly effective strategy is to introduce new disulfide bridges. The
succesfull case, however, are relatively rare because the disulfide bridges have
very specific geometric constraints and it is not so easy to introduce them by
mutagenesis. It is necessary to know the three-dimensional structure of the
protein in order to engineer the cysteines in the right position so that the
disulfide bridge will occur.
Another strategy consists in introducing new residues that form electrostatic
interactions or hydrogen bonds. For example, the introduction of a negative
charge at the N-terminal of an α helix leads to a stabilization due to the
presence of the dipole moment of the helix. The introduction of binding sites
for metal ions is another stabilizing strategy. The resolution of threedimensional structure of thousands of proteins has made possible the
description of many metal sites, the identification of their favorite ligands, the
preferred distance and geometry of this bond and allows the introduction of
specific aminoacids such as histidine, aspartate, cysteine, which are able to
efficiently bind atoms of copper, zinc or other metals and stabilize the protein.
The mutations above described introduce new interactions and thus stabilize
the protein for enthalpic reasons.
The introduction of proline residues and the replacement of glycine residues
instead stabilize the protein for entropic reasons. In fact in the native state both
glycines and prolines have specific values for the Φ and Ψ angles defined by
the constraints of the whole protein. In the denatured state, however, the
glycine can sample a conformational space much higher than proline. This is
due to the fact that the proline has a low conformational freedom, whereas
glycine is the amino acid that has the greatest conformational freedom. Thus, a
protein with a high number of glycines tends towards the denatured state for
entropic reasons, because in the denatured state glycine can play the
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conformational freedom that cannot in the folded state because of the
constraints imposed by the rest of the protein. In particular, substitution of
glycines with prolines, the amino acid characterized by the lowest degree of
conformational freedom, leads to a strong stabilization for entropic reasons.
The effect is produced either by introducing prolines or eliminating glycines.
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