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J. Biol. Chem., Vol. 276, Issue 14, 10577-10580, April 6, 2001
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From the Section on Physical Biochemistry, Laboratory of
Biochemistry and Genetics, NIDDK, National Institutes of Health,
Bethesda, Maryland 20892
Detailed knowledge of the rates, equilibria, and
mechanism of biochemical reactions has traditionally been acquired
through experiments conducted on solutions containing low
concentrations (less than about 1 mg/ml) of total protein, nucleic
acid, and/or polysaccharide together with buffer salts, low molecular
weight substrates, and cofactors as required. In contrast, biochemical reactions in living systems take place in media containing
substantially greater total concentrations (50-400 mg/ml) of
macromolecules that may be present in solution and/or in indefinitely
large arrays (e.g. cytoskeletal fibers) (1, 2). 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" (3) and/or "confining" (4) rather than "concentrated," depending upon whether the macrosolutes are soluble and/or structured. Fig.
1 provides a schematic illustration of
crowding and confinement in eukaryotic cytoplasm. In such media,
nonspecific interactions between macrosolutes contribute significantly
to the total free energy of the medium. High concentrations of
"background" macromolecules that do not participate directly in a
particular test reaction have been observed to induce
order-of-magnitude or greater changes in the rates and equilibria of
numerous test reactions (see below). To properly assess the
physiological role of a particular reaction or set of reactions
characterized in vitro, it is important to consider the
possible influence of crowding and/or confinement upon the reaction in
its physiological milieu.
A nonspecific interaction between a pair of macromolecules does
not depend strongly upon details of the primary, secondary, or tertiary
structure(s) of the interacting macromolecules but rather upon global
properties such as net charge, dipole or multipole moment, the polarity
of surface residues, and macromolecular "shape." Nonspecific
interactions may be either repulsive (steric, electrostatic) or
attractive (electrostatic, hydrophobic) and are generally substantially weaker on a pairwise basis than specific interactions between reaction partners.
The concept of "nonspecific interaction" is widely misunderstood.
Many if not most biomedical researchers still regard such interaction
as an artifact of a particular experimental system that interferes with
the acquisition of meaningful data. Strategies such as extrapolation of
results to zero macromolecular concentration are devised for the
reduction or elimination of the influence of nonspecific interaction on
a test reaction. Although such procedures may be appropriate in certain
specific experimental situations, they do not necessarily provide
results that are more meaningful in a biological context. On the
contrary, significant nonspecific interaction is an unavoidable
consequence of crowding and confinement in most or all physiological
fluid media. To understand molecular processes in such media one must
therefore take account of nonspecific interactions rather than attempt
to eliminate them.
The contribution of a particular solute species X to the total
free energy of the system is a function of an effective concentration, called the thermodynamic activity of X, denoted by
ax. Thermodynamics teaches that equilibrium
constants are generally expressed in terms of equilibrium activities
rather than actual concentrations. As a simple example, consider a
protein molecule that may reversibly self-associate to form a dimer.
The equilibrium association constant for this reaction is
K Steric repulsion is the most fundamental of all interactions
between macromolecules in solution and is always present at finite concentration, independent of the magnitude of additional electrostatic or hydrophobic interactions. Because solute molecules are mutually impenetrable, the presence of a significant volume fraction of macromolecules in the medium places constraints on the placement of an
additional molecule of test macrosolute that depend upon the relative
sizes, shapes, and concentrations of all macrosolutes in the medium.
Fig. 2 depicts a region, demarcated by a
square outline, in a solution containing spherical "background"
macrosolutes of radius rb, colored black,
that occupy ~30% of the total volume (vtot)
of the specified region. The available volume (va,T)
is defined to be that part of the volume of the region which may be
occupied by the center of mass of a molecule of a spherical
test species T of radius rt added to the solution. If the test species is very small relative to the background species (Fig. 2A), then the available volume, indicated in
blue, is approximately equal to that part of the total
volume not occupied by the background species, i.e. ~0.7
vtot. However, if the size of the test species
is comparable with (or larger than) the background species (Fig.
2B), the available volume is substantially smaller, as the
center of a molecule of the test species can approach the center of any
background molecule to no less than the distance, denoted by
rC, at which the surfaces of the two molecules contact each other.1 One may
visualize this restriction by drawing a circular shell with radius
rC about each background molecule. Then the volume
available to the test species, indicated by the blue-colored regions in Fig. 2B, is that part of the total
volume which is not occupied by any background molecule or by any
shell. It is evident upon inspection of Fig. 2, A and
B, that the available volume is a sensitive function of the
relative sizes (and shapes) of test and background molecules and the
number density of background molecules.2
Volume may be excluded to a test particle by the surfaces of immobile
structures as well as by individual background macrosolutes (4, 5), as
illustrated in Fig. 3, which depicts a
pore with square
cross-section.3 The center of
a spherical test molecule whose diameter is comparable with the largest
dimension of the pore (Fig. 3B) is excluded from the
pink-colored region, which in this
instance represents a significant fraction of the total volume of the
solution enclosed in the pore.
In a solution of macromolecules interacting exclusively via steric
repulsion there exists an extremely simple relationship between the
effective and actual concentration of each solute species (6),
MINIREVIEW
The Influence of Macromolecular Crowding and
Macromolecular Confinement on Biochemical Reactions in Physiological
Media*
INTRODUCTION
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Fig. 1.
Cartoon of eukaryotic cytoplasm at a
magnification of 1,000,000 ×. The test protein molecule
(red) is in a fluid medium that is crowded by soluble
proteins (green), RNA species (yellow), and
ribosomes (pink) and confined by cytoskeletal fibers
(blue). Modified from Ref. 47 and reproduced with permission
of the copyright holder.
Nonspecific Interaction
Effect of Nonspecific Solute-Solute Interaction upon Chemical
Equilibria
(c2/c
2), where i denotes the ratio of effective to actual
concentrations of species i, termed the activity
coefficient. The activity coefficient has a precise definition in
terms of nonspecific solute-solute interaction, lni = <gi>/kT, where
<gi> denotes the
(composition-dependent) equilibrium average free energy of
nonspecific interaction between a molecule of species i and all of the other macrosolutes present in the medium, k is
the Boltzmann constant, and T is the absolute temperature.
Excluded and Available Volume
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Fig. 2.
Excluded (pink and
black) and available (blue) volume in
a solution of spherical background macromolecules. A,
volume available to a test molecule of infinitesimal size;
B, volume available to a test molecule of size comparable
with background molecules.
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Fig. 3.
Excluded (pink) and
available (blue) volume in a pore of square
cross-section. A, volume available to a test molecule
of infinitesimal size; B, volume available to a test
molecule of size comparable with pore dimensions.
Available Volume, Free Energy, and Chemical Reactivity
i (ai/ci) = (
tot/a,i), where tot and
a,i denote the total volume and volume available to species
i, respectively. The thermodynamic activities of
macromolecules in fluid media may be measured by several
physical-chemical methods. In Fig. 4, the
experimentally measured ratio of the effective to actual concentration
of hemoglobin, under experimental conditions comparable with those
encountered in a red blood cell, is plotted as a function of the actual
concentration. The first remarkable feature of this dependence is its
highly non-linear nature; the effective concentration of hemoglobin
exceeds the actual concentration by a factor of >10 at 200 g/liter and
a factor approaching 100 at 300 g/liter. (For reference, the
concentration of hemoglobin within a normal red blood cell typically
exceeds 300 g/liter.) The second remarkable feature is that the
experimentally measured dependence may be accounted for quantitatively
over the entire concentration range by a simple geometrical model for
available volume, in which each hemoglobin molecule is represented by a rigid spherical particle of radius ~29.5 Å, i.e. a
particle closely resembling a "shrink-wrapped" hemoglobin molecule
(7, 8).
View larger version (24K):
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Fig. 4.
The effect of hemoglobin concentration on its
effective concentration (thermodynamic activity), calculated from
concentration dependence of the osmotic pressure (7).
Inset is a magnification of the low concentration
regime.
The ratio of effective to actual concentration (i.e.
activity coefficient) of a protein within a polymer gel may be
calculated from the extent to which the protein partitions between the
gel and bulk solution (4, 5). In Fig. 5,
this ratio, measured experimentally in a dextran gel occupying about
3% of total solution volume, is plotted for a variety of globular
proteins as a function of molar mass. We note that the dependence of
activity coefficient upon molar mass is reasonably independent of the
identity of the protein, indicating that it is a property primarily of
protein size and is insensitive to small changes in shape or
composition. The solid curve was calculated using
a simple geometrical model for available volume (9), in which each
protein is modeled as a hard spherical particle with a radius
proportional to the cube root of mass, and polymer is modeled as a
random matrix of hard cylindrical rods.
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Estimated Magnitude of Crowding Effects on Association Equilibria |
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We present a simple example of how the difference between activity
and concentration in a crowded medium may qualitatively influence
association
equilibria.4
Consider the dimerization reaction introduced above, with real and
apparent equilibrium constants defined in the first two equations. For
the sake of illustration, we set the molar mass of A equal to 100,000 and assume that both A and
A2 have roughly spherical shape.5 Using the same
geometrical model for excluded volume and the same size and shape
parameters used to fit the data in Fig. 5 (9), the values of
1 and 2 may be estimated to be about
3 × 102 and 1 × 104, respectively,
for a fractional volume occupancy 
of 0.2, and about 1 × 104 and 1 × 106, respectively, for
= 0.3. It follows from the second equation that the
experimentally observed equilibrium constant,
K12, would be expected to exceed
K = 0.2 and ~100 in a medium of
= 0.3. Although this estimate is only qualitative, the large
magnitude of the predicted effect of excluded volume transcends the
crudeness of the theoretical model. Indeed, similar but somewhat more
refined predictions have been confirmed, in some cases quantitatively, by experimental observation (see references in Ref. 11 and in Table
I).
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Effect of Excluded Volume on Macromolecular Association Reaction Rates |
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There are two opposing effects of excluded volume on reaction
rates (12). If the overall rate of the reaction is limited by the rate
with which a transition state complex decays to products, then crowding
would be expected to enhance the relative abundance of the transition
state complex and hence the forward reaction rate. Under these
conditions, the forward rate constant may be increased by up to the
equilibrium enhancement factor, depending upon details of the
particular reaction. However, if the overall rate of the reaction is
limited by the rate with which reactant molecules encounter each other
through diffusional motion, then crowding, which retards diffusional
motion (13, 14), would be expected to lower the forward reaction rate.
In the limit of high fractional volume occupancy, all association
reactions are expected to be diffusion limited and hence slowed by
crowding (11). Hence, depending upon the nature of a particular
reaction, one of two types of behavior may be observed as the
fractional volume occupancy of background molecules increases: the
forward rate for a macromolecular association may decrease
monotonically or may initially increase, pass through a maximum, and
then decrease. A bimodal dependence of reaction rate on crowder
concentration has been observed experimentally (15).
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Macromolecular Reactions Affected by Excluded Volume |
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Macromolecular crowding and/or confinement by background molecules
or structures can in principle affect the equilibrium and kinetics of
any macromolecular reaction in which there exists a significant
difference between the volume excluded to reactants and the volume
excluded to products. Such reactions include self- or
heteroassociation, condensation (crystallization, nucleation-controlled fiber formation), binding of macromolecules to specific surface sites,
nonspecific surface adsorption, and protein isomerization, including
folding/unfolding (4, 10, 11, 16-18). Crowding may also affect
enzyme-catalyzed reactions of small molecules if the mechanism of
catalysis involves significant conformational change of the enzyme (3,
10). Many such effects have indeed been observed experimentally. Most
of the older observations are cited in Ref. 11, and some more recent
observations are listed in Table I.
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Broader Physiological Ramifications |
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In recent years increased attention has been paid to the functioning of ever larger macromolecular assemblies and systems of interacting components, sometimes referred to as molecular machines (19). As larger and more complex systems have come under closer scrutiny, a growing number of biomedical researchers have emphasized the extremely broad ramifications of macromolecular crowding and confinement for biochemistry in the intact cell (see for example Refs. 20-25). It is becoming more widely appreciated that under physiological conditions of crowding or confinement, the size- and shape-dependent reduction of volume available to every species of macromolecule results in major shifts in the rates and equilibria of a broad range of macromolecular reactions relative to those measured in dilute solution. We now recognize that nonspecific interactions, including (but not limited to) steric repulsion, provide a substantial contribution to the free energy balance of a physiological system such as an intact cell or tissue.
It seems likely that the constituent elements of these systems have evolved to function optimally under normal physiological (i.e. crowded and/or confined) conditions and that the proper functioning of the system depends upon maintenance of the free energy balance established under those crowded and/or confined conditions. Excluded volume theory predicts that at the high level of macromolecular fractional volume occupancy characteristic of all living cells (i.e. >0.20-0.30), the reactivity of almost every soluble macromolecular species, dilute as well as concentrated, will depend sensitively upon its available volume, which, in turn, depends sensitively upon the total volume fraction of macromolecules. It follows that relatively small changes in the fractional volume occupancy of the cellular interior are expected to have major effects on the equilibria and kinetics of a broad variety of intracellular reactions (26, 27). These considerations help us to understand two very general properties of living cells. 1) Relatively modest changes of cellular volume in animal cells (i.e. concentration of intracellular macromolecules) are associated with changes in the rates of a broad spectrum of diverse intracellular processes that are much too large to be accounted for on the basis of simple mass action (28). 2) Every type of cell so far examined, from bacterial to human, is equipped with one or more mechanisms (varying widely among different types of cells) for the maintenance or restoration of cellular volume, water content, and/or turgor pressure in response to changes in composition of the extracellular fluid (29).
The examples presented here are only a few of many supporting the
hypothesis that macromolecular crowding and confinement play important
and perhaps essential roles in cell biology and physiology (11, 24,
30-34). Effects of excluded volume in physiological media are of
sufficient magnitude to mandate careful consideration when postulating
a role in vivo for any macromolecular reaction characterized
in vitro.
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ACKNOWLEDGEMENTS |
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I thank the following colleagues for reviewing early drafts of this communication: Damien Hall, Nancy Nossal, Herbert Tabor, Reed Wickner, and especially Steve Zimmerman for incisive comments.
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FOOTNOTES |
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* This minireview will be reprinted in the 2001 Minireview Compendium, which will be available in December, 2001.
To whom correspondence should be addressed: Bldg. 8, Rm. 226, NIH,
Bethesda, MD 20892-0830. Tel.: 301-496-3604; Fax: 301-402-0240; E-mail:
minton@helix.nih.gov.
Published, JBC Papers in Press, February 15, 2001, DOI 10.1074/jbc.R100005200
1 For markedly non-spherical molecules, rC is a function of the mutual orientations of test and background molecules. For approximately spherical molecules, rC may be treated as a constant equal to the sum of the average radii of test and background molecules.
2 Although Fig. 2, A and B, reflects a static distribution of background molecules, these conclusions hold also for a dynamic distribution, assuming equivalence of spatial and time averages.
3 This pore is one possible idealized representation of a small element of volume bounded by large macromolecular assemblies, such as interstices within a lattice of rodlike fibers or lamellar space between adjacent membrane surfaces.
4 A more complete treatment is presented in Ref. 10.
5 Although the dimer is unlikely to be spherical, its deviation from sphericity will not be so large that treatment as an approximate sphere will introduce a qualitative error into the present estimate (10).
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H. Sanabria, Y. Kubota, and M. N. Waxham Multiple Diffusion Mechanisms Due to Nanostructuring in Crowded Environments Biophys. J., January 1, 2007; 92(1): 313 - 322. [Abstract] [Full Text] [PDF]
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 W. Yang and S. M. Musser Nuclear import time and transport efficiency depend on importin {beta} concentration J. Cell Biol., September 25, 2006; 174(7): 951 - 961. [Abstract] [Full Text] [PDF]
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A. P. Minton How can biochemical reactions within cells differ from those in test tubes? J. Cell Sci., July 15, 2006; 119(14): 2863 - 2869. [Abstract] [Full Text] [PDF]
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INTRODUCTION
Nonspecific Interaction