Molecular Crowding Effects on Protein St
Molecular Crowding Effects on Protein
Stability
FLORIN DESPA,a DENNIS P. ORGILL,b AND RAPHAEL C. LEEa
aDepartment
of Surgery, The University of Chicago, Chicago, Illinois 60637, USA
bDepartment
of Surgery, Brigham and Woman’s Hospital, Harvard Medical School,
Boston, Massachusetts 02115, USA
ABSTRACT: The volume fraction occupied by the dry matter of the cell can be
as large as 40%, of which more than half (~60%) are proteins. Thus, cellular
proteins and protein assemblies occupy a large volume that can have a profound effect on their own native-state stabilities and on their unfolding/refolding rates. In addition, macromolecular crowding can change the properties of
a significant fraction of the water in the cell. We review features of the molecular crowding effect which are relevant for describing the microscopic mechanism of thermal injuries.
KEYWORDS: crowding effects; protein denaturation; thermal injury
INTRODUCTION
To a large extent cells are made of proteins, which constitute more than half
(~60%) of the dry weight of the cell.1 Proteins determine the structure of the cell and,
more importantly, they represent the physical apparatus which performs designed
functions in the cell. Specific proteins, such as actin and myosin, are organized in
large macromolecular arrays (e.g., cytoskeleton fibers) and play the essential role in
shaping the cell. Besides proteins, the interior of cells contains several other kinds of
macromolecules like lipids, sugars, and nucleic acids. Because no single macromolecular species may be present at high concentration, but all species taken together occupy a significant fraction of the volume of the medium, such media are referred to
as “crowded.” The volume fraction occupied by the dry matter of the cell (FIG. 1) can
be as large as ϕ = 0.4. The large volume occupied by these crowding agents can have
profound effect on the native state stability and unfolding/refolding rates of cellular
proteins. Molecular crowding is considered as a source of nonspecific interactions
between cellular proteins. Steric repulsion is the most common of all interactions
between macromolecules and is always present in crowded environments, independent of the magnitude of the general electrostatic and hydrophobic interactions.
Because molecules are mutually impenetrable, the presence of a significant volume fraction of macromolecules in the medium is a source of constraints on the
Address for correspondence: Dr. Raphael Lee, Department of Surgery, MC 6035, University
of Chicago, Chicago 60637, IL. Voice: 773-702-6302; fax: 773-702-1634.
[email protected]
Ann. N.Y. Acad. Sci. 1066: 54–66 (2005). © 2005 New York Academy of Sciences.
doi: 10.1196/annals.1363.005
54
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
55
placement of an additional macromolecule. These constraints depend upon the relative sizes, shapes, and concentrations of all macromolecules in that environment.
Volume may be excluded also by the surfaces of “immobile” structures, that is, membranes and large macromolecular assemblies (FIG. 2). Excluded volume effect, as described by Minton and others,2–6 can predict many of the aspects of molecular
crowding in vivo, but other physical factors need to be considered. For instance, a
FIGURE 1. Cell compartments are crowded. Actin filaments, ribosomes, membrane
structures and other macromolecular assemblies occupy a volume fraction which can be as
large as ϕ = 0.4.
FIGURE 2. The volume of certain cellular compartments, though comparable with
protein dimensions, is excluded by membranes and cytoskeleton filaments.
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ANNALS NEW YORK ACADEMY OF SCIENCES
significant outcome of molecular crowding is exerted via diffusion effects on the
process of aggregation of unfolded proteins.7 In addition, interfacial water molecules within a few hydration layers are also a sensor of the cell crowding.8,9 The
physical properties of confined water differ considerably from those corresponding
to bulk water and affect protein–protein interactions.8
In this chapter we will review features of the molecular crowding effect that are
relevant for describing the microscopic mechanism of thermal injuries. For details
regarding various mathematical formulations of the crowding effects, the reader is
directed to the original papers2–7 in the reference list.
NONSPECIFIC INTERACTION AND ENTROPIC EFFECTS
ON PROTEIN STABILITY
Proteins are made from an assortment of 20 very different amino acids, each with
a distinct chemical personality. This leads to specific interactions among the amino
acids (FIG. 3), which are important for the primary and secondary structure, as well
FIGURE 3. The diversity of the chemical constituents of the protein and the properties
of the surrounding media lead to both specific and nonspecific interactions during folding.
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
57
as nonspecific interactions. A nonspecific interaction does not depend strongly upon
details of the primary, secondary, or tertiary structure(s) of the interacting molecules,
but rather upon global properties of the molecules, such as polarity and macromolecular shape, or/and properties of the surrounding environment. Hydrophobic interactions between molecules are promoted by structuring effects of water. Molecular
crowding is a source of nonspecific interactions.
Because of the complexity of these interactions between the protein of interest
and crowding agents (all the other cellular components), it is difficult to predict the
net energetic effect of macromolecular crowding on the protein dynamics.6 Small
molecules (water, amino acids, etc.) alter protein dynamics by short-range site–site
excluded interactions typically over distances of a few angstroms. In contrast, the
range of macromolecular excluded volume interactions can be on the order of tens
of angstroms, which is given by the actual size of globular proteins. By modeling the
crowding particles as hard spheres, Cheung, Klimov, and Thirumalai6 predicted the
changes in the folding of two-state folders (proteins that can be characterized by two
states, folded or unfolded, and have no other intermediate states) by using entropic
arguments. They assume that proteins would prefer to be localized in a region that is
free of the macromolecular objects. The probability to find such a region decreases
at a high fractional volume occupancy f > 0. Therefore, at high values of f, there is
an increased probability that a protein is in its compact form (folded in its native
state). If the protein is compact at large f values, then the entropy change
∆S = S (f > 0) − S (0) < 0
because conformations involving unfolded states are suppressed. Thus, the stability
of the native state of a protein is predicted to increase as f increases.
MOLECULAR CROWDING INCREASES THERMAL STABILITY
OF CELLULAR PROTEINS
Proteins and protein assemblies optimally perform their function when they are
in specific three-dimensional conformations. High temperatures alter these conformations and often lead to irreversible processes (denaturation) which affect the cell
viability and trigger cell death. Because the functional structure of each protein and
organelle is unique, so is its vulnerability to denaturation at high temperatures. Characteristic vulnerability to thermal denaturation of each cellular component can efficiently be characterized by two main thermodynamic parameters, the melting
temperature (Tm) and denaturation enthalpy (∆Hm).10 Tm represents the temperature
at which half of the proteins are denaturated and is the enthalpy of unfolding at this
temperature. Tm and ∆Hm are obtained routinely by calorimetric measurements of
proteins in dilute solutions.11 In the crowded environment of a living cell, the work
required for a protein to unfold is much greater than that required for unfolding in a
dilute solution. Crowding increases usually the value of the melting temperature of
a protein.12,13 Evidence for the increase of Tm due to crowding can be obtained simply by calorimetric measurements of proteins incubated with surfactants. For example, the melting temperature of actin increases by approximately 5°C in the presence
of 100 mg/mL PEG-6000, a nonionic surfactant.14 Minton derived a correction for
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ANNALS NEW YORK ACADEMY OF SCIENCES
the melting temperature of the protein in solution to account for volume exclusion
effects,12
R
∆T m ≅ 2.303 ------------ ∆ log K .
∆H m
(1)
where R is the gas constant, R ⳩ 8.315 JK−1 mol−1. K represents the equilibrium reaction constant defined as the ratio between the unfolding (ku) and folding (kf) rates
of the protein. The above equation states that any isothermal variation of K changes
the temperature at which half of the proteins are denaturated. TABLE 1 displays the
values of the thermodynamic parameters Tm and DHm, as well as the expected values
T *m , T *m = Tm + ∆Tm, for the melting temperatures of these biomolecules in situ. We
can see that crowding effects can substantially increase the thermal stability of the
cellular components. However, the amount of unfolded protein increases dramatically at supraphysiological temperatures. We have shown that,7 at temperatures above
60°C, tissue proteins are most likely denatured, with probabilities approaching unity.
We can infer from TABLE 1 that the lipid bilayer and membrane-bound ATPases
are the proteins most predisposed to thermal denaturation. Therefore, the alteration
of the plasma membrane is likely to be the most significant cause of the tissue necrosis. This hypothesis correlates with the observation that edema is considered to
be the first evidence of thermal injury in tissue. This edema is likely due to early disturbances in the cell membrane or cell membrane ion pumps (NKP). In many cases
it appears that these cells can recover from this injury (i.e., most first-degree burns
heal). Temperatures above the first-degree burn threshold lead to irreversible dam-
TABLE 1. The values of the thermodynamic parameters Tm and ∆Hm as determined
in calorimetric experiments and the expected values T *
m corrected for crowding
effects
T * (°C)
∆H (kJ)
T (°C)
m
Lipid bilayer
Spectrin
NKP
PMCP
SRCP
DNA
RNA
Histone
Cytochrome c
ATP synthase e
F actin
Myosin
Tubulin
ApoCaM
Collagen
290
197.19
490
224
411
314
326
259.83
338.9
539.74
782.41
355.64
627.6
332
289
m
m
41.6
66
54.5
47.4
60
55.5
58.4
47.2
60
57.5
67
53.7
55.8
60
58
45.6
72.8
57
52.8
63.1
59.5
62.3
51.8
63.8
59.8
68.7
57.2
57.8
63.9
62.4
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
59
age to the cell membrane or other macromolecules and yield a critical injury. F actin
seems to be a very stable protein at elevated temperatures, as one can deduce from
TABLE 1. This protein has a low probability of unfolding in the temperature range
corresponding to a second degree burn and is damaged extensively only at higher
temperatures, that is, in a third-degree burn.7 Cells contain also other very thermally
stable proteins, as for example, heat-shock proteins (Hsps). Hsps are assumed to act
as molecular chaperones to assist in refolding denatured proteins. Hsp25 and Hsp27
have a midpoint transition temperature of Tm = 69.9°C,15 which is higher than that
corresponding to F actin, for example. Crowding effects inherently enhance the stability of these proteins, too. One can predict that Hsps can exist in functional form
of 80% even above 75°C. However, above 45°C, the cell membrane breakdown is so
extensive that it is improbable that Hsps occur in high enough concentration to be an
effective protector against cell disruption.7
MOLECULAR CROWDING PLACES GEOMETRICAL RESTRICTIONS
ON THE UNFOLDING OF PROTEINS
Let rg be a measure of the compactness of the protein structure, i.e., the radius of
gyration of a protein (FIG. 4). This rg expands during unfolding excluding volume to
other surrounding proteins. If the increase ∆r of the radius of gyration is in the range
of the protein1 interspace, defined as the mean distance between proteins in solution
[ d = ( 3--4- πn ) – --3- , where n is the protein concentration], the subsequent confinement
would provide stability for adjacent proteins which are in compact, native states. The
self-stabilization effect develops progressively during protein unfolding. The results
are also relevant for describing the stability of proteins in tightly packed fibers and
membranes.16
To understand this effect in a more quantitative way, we can write the apparent
equilibrium constant K of the protein in a crowded environment as7
3
1
∆r
K
-⎞
------ = ⎛ 1 + ------ -------------------⎝
rN 1 – f – 1 ⁄ 3⎠
K0
(2)
where K0 stands for the equilibrium constant of proteins in the ideal case of a dilute
solution, rN is the radial size of the molecule in the native form and f represents the
fractional volume occupancy of the protein,
f
–1 ⁄ 3
⎛ 3 V tot⎞
= ⎜ ------------- ---------⎟
⎝ 4πN p r 3N ⎠
1⁄3
d
≅ ----- ⋅ N p
rN
is the total number of proteins in the particular environment. It is not difficult to observe that any conformational change that increases the volume of a protein
3
4π ⎛ 3
4π
------ r N → ------ ( r N + ∆r ) ⎞
⎠
3⎝
3
changes the protein interspace d. Consequently, d is related to the evolution of the
density distribution of the population in the unfolded state of the protein PU,
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ANNALS NEW YORK ACADEMY OF SCIENCES
FIGURE 4. The compactness of the protein structure in the folded state is different
from that in the unfolded state. rg expands during unfolding, excluding volume to other surrounding proteins.
FIGURE 5. Denaturation of adenylate kinase in time for a temperature history corresponding to a muscle electrical shock injury of 10 kV, 1s hand-to hand contact at the distal
forearm location.7 The self-stabilization occurs owing to steric effects (∆r increases).
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
61
PU = 1 − PN, where PN is the density distribution of the population in the native
state. The above observation leads to the conclusion that the protein unfolding process is progressively inhibited by the conformational changes of proteins that increase their coresponding volumes and shrink the characteristic interspace (d)
between proteins.7 In FIGURE 5 one can observe that, for example, the probability of
distribution of adenylate kinase in the denaturated state (PA) is much lower in a solution in which proteins have a finite volume occupancy (i.e., f = 20%) than in an
ideal case of a dilute solution ( f → 0). The self-stabilization occurs because of steric
effects (∆r increases) induced by the unfolding of a fraction of proteins in solution.
As the volume available per unfolded protein is larger than that corresponding to a
native protein, this will impose geometrical constraints (volume exclusion) on the
proteins in native states, as described above.
A more general approach will describe the unfolding of a protein species i in a
crowd formed by M various other protein species. This shows that the volume exclusion effect leads to a decrease of the equilibrium constant Ki of the protein species i
in a mixture of different protein kinds J.7
UNFOLDING OF THE MOST THERMOLABILE PROTEINS IN A CELL
INCREASES THE STABILITY OF THE
OTHER CELLULAR PROTEINS
The vulnerability to denaturation at high temperatures of various cellular proteins
is different.10 Thus, by increasing the temperature over the physiological level, proteins with low midpoint transitions will unfold first. The excluded volume theory
tells us that the unfolding of these proteins can provide extra stability for the other
proteins in the cell, having presumably higher melting temperatures. Obviously, the
stabilization of proteins with the highest melting point transitions (e.g., proteins
making up the cytoskeleton, such as actin and myosin) is a result of the excluded volume yielded by the unfolding of all the other protein species. The stability of the
most thermolabile proteins in the cell are also affected by molecular crowding, that
is, these proteins have a higher stability in a cell than in a dilute solution. However,
it is unlikely that their dynamics can be influenced at any extent by the unfolding of
the proteins with high melting temperatures.7
DIFFUSION OF THE PROTEINS MODIFIES THE NET EFFECTS OF
MOLECULAR CROWDING
The net outcome of the steric effects on individual proteins can be modified by
diffusional motion of the molecules.4 This is because the driving force in the diffusion process of particles requires the existence of a gradient of concentration, which
makes the crowd to disperse in time. Inherent local fluctuations in the particle density may also alter the steric effects. In addition, the likely presence of direct intermolecular interactions might even reverse the excluded volume effects discussed
above. In this context we recall that protein unfolding leads to an exposure of their
hydrophobic core residues to water. Unfolded protein may stick together to minimize the area of hydrophobic exposure. Therefore, the tendency of aggregation in-
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ANNALS NEW YORK ACADEMY OF SCIENCES
FIGURE 6. If the distance between two unfolded proteins is comparable with the diffusion
length d, then the probability of irreversible aggregation of unfolded proteins increase.
creases with the increase of the population in the unfolded state. However, the rate
of aggregation is limited by the diffusion of the unfolded proteins (FIG. 6). Inherently, crowding in homogeneous solutions of unfolded proteins leads to a rapid irreversible aggregation of those proteins.
The rate of aggregation can be approximated by the inverse of the diffusion time
τi, ka,i = 1/τi. τi for an unfolded molecule of a protein species i relates to its corresponding diffusion coefficient Di by τi = d′2/4Di. Here, Di is an effective diffusion
coefficient which includes a correction due to the restriction on the movement of the
molecules in a crowded environment.7
As discussed above, the aggregation applies only to unfolded proteins. Under
such circumstances, the translational diffusion length d depends on density distribution of the population in the unfolded state of the protein (PU), and on the fractional
volume occupancy of the protein (f).7 In this way, the rate of protein aggregation is
directly related to the extent of crowding.
QUANTITATIVE ESTIMATION OF CROWDING EFFECTS ON
THERMAL DENATURATION OF PROTEINS
As shown above, crowding can substantially affect the transition of a protein between its native (N) and unfolded (U) states via volume exclusion effects. Also,
crowding influences considerably the aggregation (A) of unfolded proteins. To examine the details, one can study the protein transition
k u, i
k a, i
N↔ U → A .
(3)
k f, i
as described by Despa, Orgill and Lee.7 ku,i and kf,i are the unfolding/folding rate coefficients and ka,i denotes the rate constant for the irreversible aggregation. ku,i is a
function of the melting temperature Tm,i and the enthalpy of denaturation ∆Hun,i
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
⎛ ∆H un
T ⎞⎞ .
k u = A exp ⎜ – ------------- ⎛ 1 – -----⎝
⎠⎟
RT
T
⎝
m ⎠
63
(4)
A is a constant which determines the time scale of the unfolding process. This depends, among others, on the coupling of the protein with the solvent.17–20 The backward rate is simply kf,i = ku,i /Κi. Tm,i and ∆Hun,i are derived by calorimetric
measurements of dilute protein solutions. Corrections for crowding effects are incorporated in Ki (see Eq. 2) via volume exclusion and in ka,i by rescaling the translational diffusion length d (see above). This is a model for an experiment in which
temperature is changed with time according to a “temperature history” T(t).7 The approach yields PN,i, PU,i and PA,i, representing the distribution density of the population in the native, unfolded and aggregated state of the protein species i. A suggestive
result is presented in FIGURE 7. Here, one can observe the effects of crowding in a
mixture of proteins (adenylate kinase, creatine kinase, ATP synthase e and cytochrome c) with different thermal stabilities. Steric effects brought by the unfolding
of thermolabile proteins enhance the stability of those proteins in the mixture which
have higher melting points. The top curve represents the denturation of cytochrome
c in a homogeneous solution, while the bottom curve describes the course of denaturation of this protein in a mixture with the other three proteins. A low probability
for aggregation means, implicitly, an increased stability in the native state.
FIGURE 7. Steric effects brought by the unfolding of thermolabile proteins enhance
the stability of those proteins in the mixture that have higher melting points. The time–temperature course is the same as the one used in FIGURE 4. The propensity of unfolded proteins
to aggregate in a homogeneous solution is higher than in a mixture with other three proteins.
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ANNALS NEW YORK ACADEMY OF SCIENCES
MOLECULAR CROWDING AFFECTS THE BEHAVIOR OF
PROTEINS VIA A WATER EFFECT
For a mean protein mass in the cell of ⬃50 kDa, at an assumed protein concentration of 300 mg/mL, the fraction of interfacial water would be about 30% (two layers of interfacial water) to 70% (four layers) of the total water in the cell. Under
circumstances in which macromolecular crowding can change the properties of a
significant fraction of the water in the cell, crowding effects could exert a strong influence on the behavior of smaller solutes as well as on larger macromolecules.
Recent in vivo expriments21 showed that the interfacial water component increases from 23.5% of total water in the control sample to 25% in yeast heat-shocked at
315K and to 30% in yeast cells at 323K. The heat shock, which causes some proteins
to become unfolded in the cell and, therefore, increases molecular crowding, will
change also the hydration of the cell components. An alteration of the properties of
the interfacial water could have a direct influence on a range of cellular functions
and properties.
Physical properties of water confined in microscopic environments differ from
the properties corresponding to bulk water.8 For example, it was shown recently8
that water molecules under hydrophobic confinement move about an order of magnitude slower than those in the bulk, and that the dielectric constant of this water layer is significantly reduced. Water’s high dielectric constant is the reason why it is a
good solvent for ions: it screens their electrical charges and so prevents them from
aggregating. But in the vicinity of hydrophobic residues in a protein chain, the reduction in dielectric constant means that charged residues will interact much more
strongly, potentially helping to fix the protein’s folds in place.
Another example in which the behavior of biomolecules is altered via a water effect is the interaction between hydrophobes. The hydrophobic interaction—the apparent attraction between hydrophobic species in water—is considered a key factor
in maintaining the correct folded conformation of a protein molecule and also the
main cause of protein aggregation. This attraction is thought to result, in a way that
is still imperfectly understood, from changes in the arrangement of hydrogen bonds
between water molecules surrounding a hydrophobe.8,22 This gives rise to a local
polarization of the interfacial water, which is shown to be strong enough to induce
long-range attraction between hydrophobic molecules.
SUMMARY
Proteins are three-dimensional structures with conformations dictated by the
characteristic amino acid sequences. At body temperature, proteins are in native conformations that allow them to perform their designated functions. At supraphysiological temperatures, proteins are driven towards unfolded conformations. Steric
effects increase the stability of the proteins which are in compact, native states. As
each type of protein has its own thermal stability, the unfolding of the most thermolabile proteins will increase the stability of the other proteins. In unfolded conformations, many proteins tend to form stable insoluble aggregates. Aggregation is a
major source of irreversibility of protein unfolding when the temperature returns to
normal. The tendency of aggregation increases with the increase of the population in
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
65
the unfolded state and the rate of aggregation is limited by the diffusion of the unfolded proteins. The net outcome of the steric effects on individual proteins can be
modified by diffusional motion of the molecules.
Understanding the regulation of these processes may lead to clinical strategies for
limiting the devastating development of the injury after the thermal insult of the tissue stopped. Within the computational complexity theory, protein dynamics is defined rigorously as NP harda and, so far, we can simulate exactly the in vitro
structural dynamics only for a very limited pool of proteins. However, the volume of
data sets is often so big that the efficiency of manipulation and extraction of useful
information becomes problematic. Bringing the inherent solvent effects as well as
crowding into play increases the complexity of the problem.
Despite difficulties, studying proteins can advance by a profitable utilization of
recent statistical mechanical treatments of potential energy surfaces17–20 conjoined
with experimental observations on the energetics and stability of proteins.11 Here,
we have reviewed several quantitative analyses of the kinetic stability of cellular
components confronted with the destabilizing effect of irreversible alteration which
are relevant for describing the microscopic mechanism of thermal injuries.
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4. VERKMAN, A.S. 2002. Solute and macromolecule diffusion in cellular aqueous compartments. Trends Biochem. Sci. 27: 27–33.
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of tissue macromolecules and cellular structure in burn injury. Burns 31: 568–577.
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13. ZHANG, S. & C. WANG. 2001. Effects of macromolecular crowding on the refolding of
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15. DUDICH, I.V,, V.P. ZAV’YALOV, W. PFEIL, et al. 1995. Dimer structure as a minimum
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16. YANNAS, I.V., J.F. BURKE, P.L. GORDON, et al. 1980. Design of an artificial skin. II. Control of chemical composition. J. Biomed. Mater. Res. 12: 7–32.
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Stability
FLORIN DESPA,a DENNIS P. ORGILL,b AND RAPHAEL C. LEEa
aDepartment
of Surgery, The University of Chicago, Chicago, Illinois 60637, USA
bDepartment
of Surgery, Brigham and Woman’s Hospital, Harvard Medical School,
Boston, Massachusetts 02115, USA
ABSTRACT: The volume fraction occupied by the dry matter of the cell can be
as large as 40%, of which more than half (~60%) are proteins. Thus, cellular
proteins and protein assemblies occupy a large volume that can have a profound effect on their own native-state stabilities and on their unfolding/refolding rates. In addition, macromolecular crowding can change the properties of
a significant fraction of the water in the cell. We review features of the molecular crowding effect which are relevant for describing the microscopic mechanism of thermal injuries.
KEYWORDS: crowding effects; protein denaturation; thermal injury
INTRODUCTION
To a large extent cells are made of proteins, which constitute more than half
(~60%) of the dry weight of the cell.1 Proteins determine the structure of the cell and,
more importantly, they represent the physical apparatus which performs designed
functions in the cell. Specific proteins, such as actin and myosin, are organized in
large macromolecular arrays (e.g., cytoskeleton fibers) and play the essential role in
shaping the cell. Besides proteins, the interior of cells contains several other kinds of
macromolecules like lipids, sugars, and nucleic acids. Because no single macromolecular species may be present at high concentration, but all species taken together occupy a significant fraction of the volume of the medium, such media are referred to
as “crowded.” The volume fraction occupied by the dry matter of the cell (FIG. 1) can
be as large as ϕ = 0.4. The large volume occupied by these crowding agents can have
profound effect on the native state stability and unfolding/refolding rates of cellular
proteins. Molecular crowding is considered as a source of nonspecific interactions
between cellular proteins. Steric repulsion is the most common of all interactions
between macromolecules and is always present in crowded environments, independent of the magnitude of the general electrostatic and hydrophobic interactions.
Because molecules are mutually impenetrable, the presence of a significant volume fraction of macromolecules in the medium is a source of constraints on the
Address for correspondence: Dr. Raphael Lee, Department of Surgery, MC 6035, University
of Chicago, Chicago 60637, IL. Voice: 773-702-6302; fax: 773-702-1634.
[email protected]
Ann. N.Y. Acad. Sci. 1066: 54–66 (2005). © 2005 New York Academy of Sciences.
doi: 10.1196/annals.1363.005
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DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
55
placement of an additional macromolecule. These constraints depend upon the relative sizes, shapes, and concentrations of all macromolecules in that environment.
Volume may be excluded also by the surfaces of “immobile” structures, that is, membranes and large macromolecular assemblies (FIG. 2). Excluded volume effect, as described by Minton and others,2–6 can predict many of the aspects of molecular
crowding in vivo, but other physical factors need to be considered. For instance, a
FIGURE 1. Cell compartments are crowded. Actin filaments, ribosomes, membrane
structures and other macromolecular assemblies occupy a volume fraction which can be as
large as ϕ = 0.4.
FIGURE 2. The volume of certain cellular compartments, though comparable with
protein dimensions, is excluded by membranes and cytoskeleton filaments.
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ANNALS NEW YORK ACADEMY OF SCIENCES
significant outcome of molecular crowding is exerted via diffusion effects on the
process of aggregation of unfolded proteins.7 In addition, interfacial water molecules within a few hydration layers are also a sensor of the cell crowding.8,9 The
physical properties of confined water differ considerably from those corresponding
to bulk water and affect protein–protein interactions.8
In this chapter we will review features of the molecular crowding effect that are
relevant for describing the microscopic mechanism of thermal injuries. For details
regarding various mathematical formulations of the crowding effects, the reader is
directed to the original papers2–7 in the reference list.
NONSPECIFIC INTERACTION AND ENTROPIC EFFECTS
ON PROTEIN STABILITY
Proteins are made from an assortment of 20 very different amino acids, each with
a distinct chemical personality. This leads to specific interactions among the amino
acids (FIG. 3), which are important for the primary and secondary structure, as well
FIGURE 3. The diversity of the chemical constituents of the protein and the properties
of the surrounding media lead to both specific and nonspecific interactions during folding.
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
57
as nonspecific interactions. A nonspecific interaction does not depend strongly upon
details of the primary, secondary, or tertiary structure(s) of the interacting molecules,
but rather upon global properties of the molecules, such as polarity and macromolecular shape, or/and properties of the surrounding environment. Hydrophobic interactions between molecules are promoted by structuring effects of water. Molecular
crowding is a source of nonspecific interactions.
Because of the complexity of these interactions between the protein of interest
and crowding agents (all the other cellular components), it is difficult to predict the
net energetic effect of macromolecular crowding on the protein dynamics.6 Small
molecules (water, amino acids, etc.) alter protein dynamics by short-range site–site
excluded interactions typically over distances of a few angstroms. In contrast, the
range of macromolecular excluded volume interactions can be on the order of tens
of angstroms, which is given by the actual size of globular proteins. By modeling the
crowding particles as hard spheres, Cheung, Klimov, and Thirumalai6 predicted the
changes in the folding of two-state folders (proteins that can be characterized by two
states, folded or unfolded, and have no other intermediate states) by using entropic
arguments. They assume that proteins would prefer to be localized in a region that is
free of the macromolecular objects. The probability to find such a region decreases
at a high fractional volume occupancy f > 0. Therefore, at high values of f, there is
an increased probability that a protein is in its compact form (folded in its native
state). If the protein is compact at large f values, then the entropy change
∆S = S (f > 0) − S (0) < 0
because conformations involving unfolded states are suppressed. Thus, the stability
of the native state of a protein is predicted to increase as f increases.
MOLECULAR CROWDING INCREASES THERMAL STABILITY
OF CELLULAR PROTEINS
Proteins and protein assemblies optimally perform their function when they are
in specific three-dimensional conformations. High temperatures alter these conformations and often lead to irreversible processes (denaturation) which affect the cell
viability and trigger cell death. Because the functional structure of each protein and
organelle is unique, so is its vulnerability to denaturation at high temperatures. Characteristic vulnerability to thermal denaturation of each cellular component can efficiently be characterized by two main thermodynamic parameters, the melting
temperature (Tm) and denaturation enthalpy (∆Hm).10 Tm represents the temperature
at which half of the proteins are denaturated and is the enthalpy of unfolding at this
temperature. Tm and ∆Hm are obtained routinely by calorimetric measurements of
proteins in dilute solutions.11 In the crowded environment of a living cell, the work
required for a protein to unfold is much greater than that required for unfolding in a
dilute solution. Crowding increases usually the value of the melting temperature of
a protein.12,13 Evidence for the increase of Tm due to crowding can be obtained simply by calorimetric measurements of proteins incubated with surfactants. For example, the melting temperature of actin increases by approximately 5°C in the presence
of 100 mg/mL PEG-6000, a nonionic surfactant.14 Minton derived a correction for
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ANNALS NEW YORK ACADEMY OF SCIENCES
the melting temperature of the protein in solution to account for volume exclusion
effects,12
R
∆T m ≅ 2.303 ------------ ∆ log K .
∆H m
(1)
where R is the gas constant, R ⳩ 8.315 JK−1 mol−1. K represents the equilibrium reaction constant defined as the ratio between the unfolding (ku) and folding (kf) rates
of the protein. The above equation states that any isothermal variation of K changes
the temperature at which half of the proteins are denaturated. TABLE 1 displays the
values of the thermodynamic parameters Tm and DHm, as well as the expected values
T *m , T *m = Tm + ∆Tm, for the melting temperatures of these biomolecules in situ. We
can see that crowding effects can substantially increase the thermal stability of the
cellular components. However, the amount of unfolded protein increases dramatically at supraphysiological temperatures. We have shown that,7 at temperatures above
60°C, tissue proteins are most likely denatured, with probabilities approaching unity.
We can infer from TABLE 1 that the lipid bilayer and membrane-bound ATPases
are the proteins most predisposed to thermal denaturation. Therefore, the alteration
of the plasma membrane is likely to be the most significant cause of the tissue necrosis. This hypothesis correlates with the observation that edema is considered to
be the first evidence of thermal injury in tissue. This edema is likely due to early disturbances in the cell membrane or cell membrane ion pumps (NKP). In many cases
it appears that these cells can recover from this injury (i.e., most first-degree burns
heal). Temperatures above the first-degree burn threshold lead to irreversible dam-
TABLE 1. The values of the thermodynamic parameters Tm and ∆Hm as determined
in calorimetric experiments and the expected values T *
m corrected for crowding
effects
T * (°C)
∆H (kJ)
T (°C)
m
Lipid bilayer
Spectrin
NKP
PMCP
SRCP
DNA
RNA
Histone
Cytochrome c
ATP synthase e
F actin
Myosin
Tubulin
ApoCaM
Collagen
290
197.19
490
224
411
314
326
259.83
338.9
539.74
782.41
355.64
627.6
332
289
m
m
41.6
66
54.5
47.4
60
55.5
58.4
47.2
60
57.5
67
53.7
55.8
60
58
45.6
72.8
57
52.8
63.1
59.5
62.3
51.8
63.8
59.8
68.7
57.2
57.8
63.9
62.4
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
59
age to the cell membrane or other macromolecules and yield a critical injury. F actin
seems to be a very stable protein at elevated temperatures, as one can deduce from
TABLE 1. This protein has a low probability of unfolding in the temperature range
corresponding to a second degree burn and is damaged extensively only at higher
temperatures, that is, in a third-degree burn.7 Cells contain also other very thermally
stable proteins, as for example, heat-shock proteins (Hsps). Hsps are assumed to act
as molecular chaperones to assist in refolding denatured proteins. Hsp25 and Hsp27
have a midpoint transition temperature of Tm = 69.9°C,15 which is higher than that
corresponding to F actin, for example. Crowding effects inherently enhance the stability of these proteins, too. One can predict that Hsps can exist in functional form
of 80% even above 75°C. However, above 45°C, the cell membrane breakdown is so
extensive that it is improbable that Hsps occur in high enough concentration to be an
effective protector against cell disruption.7
MOLECULAR CROWDING PLACES GEOMETRICAL RESTRICTIONS
ON THE UNFOLDING OF PROTEINS
Let rg be a measure of the compactness of the protein structure, i.e., the radius of
gyration of a protein (FIG. 4). This rg expands during unfolding excluding volume to
other surrounding proteins. If the increase ∆r of the radius of gyration is in the range
of the protein1 interspace, defined as the mean distance between proteins in solution
[ d = ( 3--4- πn ) – --3- , where n is the protein concentration], the subsequent confinement
would provide stability for adjacent proteins which are in compact, native states. The
self-stabilization effect develops progressively during protein unfolding. The results
are also relevant for describing the stability of proteins in tightly packed fibers and
membranes.16
To understand this effect in a more quantitative way, we can write the apparent
equilibrium constant K of the protein in a crowded environment as7
3
1
∆r
K
-⎞
------ = ⎛ 1 + ------ -------------------⎝
rN 1 – f – 1 ⁄ 3⎠
K0
(2)
where K0 stands for the equilibrium constant of proteins in the ideal case of a dilute
solution, rN is the radial size of the molecule in the native form and f represents the
fractional volume occupancy of the protein,
f
–1 ⁄ 3
⎛ 3 V tot⎞
= ⎜ ------------- ---------⎟
⎝ 4πN p r 3N ⎠
1⁄3
d
≅ ----- ⋅ N p
rN
is the total number of proteins in the particular environment. It is not difficult to observe that any conformational change that increases the volume of a protein
3
4π ⎛ 3
4π
------ r N → ------ ( r N + ∆r ) ⎞
⎠
3⎝
3
changes the protein interspace d. Consequently, d is related to the evolution of the
density distribution of the population in the unfolded state of the protein PU,
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ANNALS NEW YORK ACADEMY OF SCIENCES
FIGURE 4. The compactness of the protein structure in the folded state is different
from that in the unfolded state. rg expands during unfolding, excluding volume to other surrounding proteins.
FIGURE 5. Denaturation of adenylate kinase in time for a temperature history corresponding to a muscle electrical shock injury of 10 kV, 1s hand-to hand contact at the distal
forearm location.7 The self-stabilization occurs owing to steric effects (∆r increases).
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
61
PU = 1 − PN, where PN is the density distribution of the population in the native
state. The above observation leads to the conclusion that the protein unfolding process is progressively inhibited by the conformational changes of proteins that increase their coresponding volumes and shrink the characteristic interspace (d)
between proteins.7 In FIGURE 5 one can observe that, for example, the probability of
distribution of adenylate kinase in the denaturated state (PA) is much lower in a solution in which proteins have a finite volume occupancy (i.e., f = 20%) than in an
ideal case of a dilute solution ( f → 0). The self-stabilization occurs because of steric
effects (∆r increases) induced by the unfolding of a fraction of proteins in solution.
As the volume available per unfolded protein is larger than that corresponding to a
native protein, this will impose geometrical constraints (volume exclusion) on the
proteins in native states, as described above.
A more general approach will describe the unfolding of a protein species i in a
crowd formed by M various other protein species. This shows that the volume exclusion effect leads to a decrease of the equilibrium constant Ki of the protein species i
in a mixture of different protein kinds J.7
UNFOLDING OF THE MOST THERMOLABILE PROTEINS IN A CELL
INCREASES THE STABILITY OF THE
OTHER CELLULAR PROTEINS
The vulnerability to denaturation at high temperatures of various cellular proteins
is different.10 Thus, by increasing the temperature over the physiological level, proteins with low midpoint transitions will unfold first. The excluded volume theory
tells us that the unfolding of these proteins can provide extra stability for the other
proteins in the cell, having presumably higher melting temperatures. Obviously, the
stabilization of proteins with the highest melting point transitions (e.g., proteins
making up the cytoskeleton, such as actin and myosin) is a result of the excluded volume yielded by the unfolding of all the other protein species. The stability of the
most thermolabile proteins in the cell are also affected by molecular crowding, that
is, these proteins have a higher stability in a cell than in a dilute solution. However,
it is unlikely that their dynamics can be influenced at any extent by the unfolding of
the proteins with high melting temperatures.7
DIFFUSION OF THE PROTEINS MODIFIES THE NET EFFECTS OF
MOLECULAR CROWDING
The net outcome of the steric effects on individual proteins can be modified by
diffusional motion of the molecules.4 This is because the driving force in the diffusion process of particles requires the existence of a gradient of concentration, which
makes the crowd to disperse in time. Inherent local fluctuations in the particle density may also alter the steric effects. In addition, the likely presence of direct intermolecular interactions might even reverse the excluded volume effects discussed
above. In this context we recall that protein unfolding leads to an exposure of their
hydrophobic core residues to water. Unfolded protein may stick together to minimize the area of hydrophobic exposure. Therefore, the tendency of aggregation in-
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ANNALS NEW YORK ACADEMY OF SCIENCES
FIGURE 6. If the distance between two unfolded proteins is comparable with the diffusion
length d, then the probability of irreversible aggregation of unfolded proteins increase.
creases with the increase of the population in the unfolded state. However, the rate
of aggregation is limited by the diffusion of the unfolded proteins (FIG. 6). Inherently, crowding in homogeneous solutions of unfolded proteins leads to a rapid irreversible aggregation of those proteins.
The rate of aggregation can be approximated by the inverse of the diffusion time
τi, ka,i = 1/τi. τi for an unfolded molecule of a protein species i relates to its corresponding diffusion coefficient Di by τi = d′2/4Di. Here, Di is an effective diffusion
coefficient which includes a correction due to the restriction on the movement of the
molecules in a crowded environment.7
As discussed above, the aggregation applies only to unfolded proteins. Under
such circumstances, the translational diffusion length d depends on density distribution of the population in the unfolded state of the protein (PU), and on the fractional
volume occupancy of the protein (f).7 In this way, the rate of protein aggregation is
directly related to the extent of crowding.
QUANTITATIVE ESTIMATION OF CROWDING EFFECTS ON
THERMAL DENATURATION OF PROTEINS
As shown above, crowding can substantially affect the transition of a protein between its native (N) and unfolded (U) states via volume exclusion effects. Also,
crowding influences considerably the aggregation (A) of unfolded proteins. To examine the details, one can study the protein transition
k u, i
k a, i
N↔ U → A .
(3)
k f, i
as described by Despa, Orgill and Lee.7 ku,i and kf,i are the unfolding/folding rate coefficients and ka,i denotes the rate constant for the irreversible aggregation. ku,i is a
function of the melting temperature Tm,i and the enthalpy of denaturation ∆Hun,i
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
⎛ ∆H un
T ⎞⎞ .
k u = A exp ⎜ – ------------- ⎛ 1 – -----⎝
⎠⎟
RT
T
⎝
m ⎠
63
(4)
A is a constant which determines the time scale of the unfolding process. This depends, among others, on the coupling of the protein with the solvent.17–20 The backward rate is simply kf,i = ku,i /Κi. Tm,i and ∆Hun,i are derived by calorimetric
measurements of dilute protein solutions. Corrections for crowding effects are incorporated in Ki (see Eq. 2) via volume exclusion and in ka,i by rescaling the translational diffusion length d (see above). This is a model for an experiment in which
temperature is changed with time according to a “temperature history” T(t).7 The approach yields PN,i, PU,i and PA,i, representing the distribution density of the population in the native, unfolded and aggregated state of the protein species i. A suggestive
result is presented in FIGURE 7. Here, one can observe the effects of crowding in a
mixture of proteins (adenylate kinase, creatine kinase, ATP synthase e and cytochrome c) with different thermal stabilities. Steric effects brought by the unfolding
of thermolabile proteins enhance the stability of those proteins in the mixture which
have higher melting points. The top curve represents the denturation of cytochrome
c in a homogeneous solution, while the bottom curve describes the course of denaturation of this protein in a mixture with the other three proteins. A low probability
for aggregation means, implicitly, an increased stability in the native state.
FIGURE 7. Steric effects brought by the unfolding of thermolabile proteins enhance
the stability of those proteins in the mixture that have higher melting points. The time–temperature course is the same as the one used in FIGURE 4. The propensity of unfolded proteins
to aggregate in a homogeneous solution is higher than in a mixture with other three proteins.
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ANNALS NEW YORK ACADEMY OF SCIENCES
MOLECULAR CROWDING AFFECTS THE BEHAVIOR OF
PROTEINS VIA A WATER EFFECT
For a mean protein mass in the cell of ⬃50 kDa, at an assumed protein concentration of 300 mg/mL, the fraction of interfacial water would be about 30% (two layers of interfacial water) to 70% (four layers) of the total water in the cell. Under
circumstances in which macromolecular crowding can change the properties of a
significant fraction of the water in the cell, crowding effects could exert a strong influence on the behavior of smaller solutes as well as on larger macromolecules.
Recent in vivo expriments21 showed that the interfacial water component increases from 23.5% of total water in the control sample to 25% in yeast heat-shocked at
315K and to 30% in yeast cells at 323K. The heat shock, which causes some proteins
to become unfolded in the cell and, therefore, increases molecular crowding, will
change also the hydration of the cell components. An alteration of the properties of
the interfacial water could have a direct influence on a range of cellular functions
and properties.
Physical properties of water confined in microscopic environments differ from
the properties corresponding to bulk water.8 For example, it was shown recently8
that water molecules under hydrophobic confinement move about an order of magnitude slower than those in the bulk, and that the dielectric constant of this water layer is significantly reduced. Water’s high dielectric constant is the reason why it is a
good solvent for ions: it screens their electrical charges and so prevents them from
aggregating. But in the vicinity of hydrophobic residues in a protein chain, the reduction in dielectric constant means that charged residues will interact much more
strongly, potentially helping to fix the protein’s folds in place.
Another example in which the behavior of biomolecules is altered via a water effect is the interaction between hydrophobes. The hydrophobic interaction—the apparent attraction between hydrophobic species in water—is considered a key factor
in maintaining the correct folded conformation of a protein molecule and also the
main cause of protein aggregation. This attraction is thought to result, in a way that
is still imperfectly understood, from changes in the arrangement of hydrogen bonds
between water molecules surrounding a hydrophobe.8,22 This gives rise to a local
polarization of the interfacial water, which is shown to be strong enough to induce
long-range attraction between hydrophobic molecules.
SUMMARY
Proteins are three-dimensional structures with conformations dictated by the
characteristic amino acid sequences. At body temperature, proteins are in native conformations that allow them to perform their designated functions. At supraphysiological temperatures, proteins are driven towards unfolded conformations. Steric
effects increase the stability of the proteins which are in compact, native states. As
each type of protein has its own thermal stability, the unfolding of the most thermolabile proteins will increase the stability of the other proteins. In unfolded conformations, many proteins tend to form stable insoluble aggregates. Aggregation is a
major source of irreversibility of protein unfolding when the temperature returns to
normal. The tendency of aggregation increases with the increase of the population in
DESPA et al.: MOLECULAR CROWDING AND PROTEIN STABILITY
65
the unfolded state and the rate of aggregation is limited by the diffusion of the unfolded proteins. The net outcome of the steric effects on individual proteins can be
modified by diffusional motion of the molecules.
Understanding the regulation of these processes may lead to clinical strategies for
limiting the devastating development of the injury after the thermal insult of the tissue stopped. Within the computational complexity theory, protein dynamics is defined rigorously as NP harda and, so far, we can simulate exactly the in vitro
structural dynamics only for a very limited pool of proteins. However, the volume of
data sets is often so big that the efficiency of manipulation and extraction of useful
information becomes problematic. Bringing the inherent solvent effects as well as
crowding into play increases the complexity of the problem.
Despite difficulties, studying proteins can advance by a profitable utilization of
recent statistical mechanical treatments of potential energy surfaces17–20 conjoined
with experimental observations on the energetics and stability of proteins.11 Here,
we have reviewed several quantitative analyses of the kinetic stability of cellular
components confronted with the destabilizing effect of irreversible alteration which
are relevant for describing the microscopic mechanism of thermal injuries.
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