Effects of "Crowding" in Protein Solutions G. B. Rakton Department of Biochemistry. University of Sydney, Sydney, NSW, 2006, Australia
Most biochemists are aware of thermodynamic nonidealitv as something to be avoided. Real molecules are generally recognized as n k i d e a l hecause of their finite size and their electrical charge. Physical studies of macromolecules are therefore usually performed with pure components at concentrations as low as possible within the limits of precision. Nonideal effects are then removed by extrapolation of measured properties to zero concentration, at which point nonidealities vanish ( I ) . Most physiological media, however, are not vanishingly dilute. For example, proteins comprise about 9% (wlv) of plasma, and hemoglobin occupies approx. 33% (wlv) of the erythrocyte cytosol, or 330 g/L (Fig. 1). The mitochondrial matrix may contain proteins a t a total concentration of 500 g/L (Z),and in the cytosol of many cells the protein content may be as high as 200 g/L. Although an individual macromolecular constituent of interest not he~mesent hiah concentrations in a partic. -ma" ~ ~ in~ ular cellor fluid, nevertheless;a substantial fractionof the solution volume mav be occupied by a variety of molecules, both small and large; this typeof solhion has been described as volume-occupied (3). The degree of volume occupancy may affect biochemical equilibria and kinetics markedly. Even in the absence of direct interactions between macromolecules, the ability of macromolecules t o occupy space, and thereby to exclude other molecules from their neighborhoods, can have a profound effect on tertiary structure, quaternary structure, and the kinetics of enzyme-catalyzed reactions. I t has been shown that volume exclusion phenomena in physiological systems can have thermodynamic consequences a t least as great as those of hydrophobic or electrostatic interactions (3). While the heno omen on of macromolecular nonideality has been known for many years and the biological relevance of macromolecular crowding has been demonstrated unequivocally, there is a resounding silence in this area from
the standard biochemistry texthooks. I t is the purpose of this communication t o draw attention to this important but neglected aspect of hiochemistry and cell biology. Volume Exclusion Phenomena
Consider a solution of identical macromolecules (Fig. 2). Since two molecules cannot occupy the same space in solution, each macromolecule will exclude others from its neighborhood. If we consider the simplest case in which the particles are spherical, then the position of each particle is specified completely by the position of its center. The closest two centers can approach is a distance equal to the sum of their radii. Thus, around each molecule is a spherical volume U (the "excluded volume" or "covolume"), from which the centers of all the others are excluded (Fig. 2). If we continue to add more molecules to the solution, the number of ways that it is possible to place each added molecule becomes progressively limited. The space in which the added molecules can he located (i.e., where their centers can he placed) is restricted to the volume of solution from which they are not excluded: the volume outside the shaded regions in Figure 3.
Figure 2. Spherical particles in a solution. The closest approach between two moiecules occurs when their surfaces just touch. The volume U around moiecule A from which the center of molecule B is excluded is a sphere of radius twice Mat of a single molecule. The volume Uis thus eight times Mat of a single molecule.
Figure 1. Representationota slice 20 nm thick through e m r m y t e cyiopiasm. showing the crowded nature. Hemoglobin molecules are represented as spheres. with three layers in view, Uwse toward the back being darker than ttme in front.
Figure 3. On adding en aWitional molecule B to a crowded solution, the center of the added molecule B is restricted to the volume of solution fromwhich it is not excluded, represented by the unshaded areas.
Volume 67
Number 10 October 1990
857
Thus, the more solute particles are present in the solution, the less randomly can they be distributed. As a consequence, the entropy of the solute is less than i t would he in an ideal solution in which the solute molecules occupied no space, and the decrease in entropy leads to an increase in the free energy of the solute. In an ideal solution, the partial molar free energy of a component, i, depends on its concentration: = pp
+ RT in e;
(1)
where u;is the oartial molar free enerev (or "chemical potential") i f t h e ith'component, d i s its cKkniica~potentiaiin the standard state and c is the mold concentration. The increase in free energy arising from volume exclusion can he taken into account through the use of thermodynamic activities rather than concentrations: piba'
= p,O
+ RT h a j = pp + RT In ci + RT In y,
where the respective sums take into account the excluded volume contributions from all two-particle interactions, three-particle interactions and so on. in this form, the concentrations are expressed in molal units, and the u,, are the two-particle "excess excluded volumen" in units of Llmol: = U.. 8, vj (4) where U, is the volume around molecule i from which molecule j is excluded, expressed in units of Llmol, and Vj is the molar volume of molecule j, also in Llmol. Equation 3 corresponds to the virial expansion for the activity coefficient and 858
Journal of Chemical Education
Chemlcal Equlllbrla For chemical reactions the various thermodynamic activities are related through an equilibrium constant. For example, for the isomerization reaction: A a B
(5)
we can write: K = -= .[B]
(2)
where aj is the thermodynamic activity, or effective thermodynamicconcentration. This can in turn be expressed as a; = yicj, where yi is an "activity coefficient" taking into account the deviation from ideal hehavior. We can consider the term R T in yi as a measure of the free energy change per mole of solute due to the nonideality arising from volume exclusion. In ideal solutions, there is no interaction between solute molecules and 7 = 1. In the presence of volume exclusion, the increase in free enerev ... h o.l i e s that r > 1.As a result of the increase in thermodynamic activity, processes that are determined bv the activity will he enhanced. Thus, chemical reactions may be enhanced, osmotic pressure will be increased, the driving force for diffusion will be increased, and sedimentation in a gravitational field will he altered. As an example, the osmotic pressure of hemoglobin rises dramatically with increasing concentration (4); near 320 g/L (the in vivo concentration of hemoglobin within the erythrocyte) the thermodynamic activity of hemoglobin is about 100 times its concentration. I t is for this reason that physical studies are normally carried out in very low concentration and the data extrapolated to zero concentration to yield the ideal values of the measured properties. But in terms of understanding the hehavior within the cell, such information. although often hiehlv and accurate, is by itself - . precise . largkly irrelevant. In order to understand behavior in real solutions we need to he ahle to take account of the excluded volume effects quantitatively. As a general problem, such an approach needs to be ahle t o take account of the exclusion effects, not only due to the molecule under study, but also those arising from the presence of any inert "bystander" molecules, whether large or small, since these will also contribute significantly to the overall degree of volume occupancy in the solution and thereby to the nonideal behavior. Statistical mechanics allows us to describe the activity coefficient of each species in terms of the molal concentrations of all species in the solution and their excluded volumes (5):
.
takes into account all of the interactions between all solute molecules present in the solution. If we consider a homogeneous, relatively dilute solution of spherical particles, the excluded volume per molecule is eight times the volume of an individual molecule, so that even in this least nonideal state, the excluded volume effects can he large. For any other shape the excluded volume is even larger ( 1 , 3 ) .
"A
YB
-
--
F P P
.YB
[A1 YA
-
YA
where K is the thermodynamic equilihrium constant, the square brackets indicate molar concentrations, and Kapp is an apparent equilihrium constant determined by the molar concentrations of the reacting species rather than their activities; i.e.,
Since methods dependent on concentration, such as optical rotation or absorbance, are usually used to follow such reactions experimentally, this apparent constant is the value that is directly measurable. The usual approach in practice is to assume that K can be equated with Kapp; i.e., that the activities can he approximated closely by the concentrations. This implies that the nonideal term, the ratio of the activity coefficients, is unity. This will only he valid for very dilute solutions, or in special cases. For a conformation change in a macromolecule in dilute solution, in the presence of a fixed, relatively larger molar concentration, [PI,of an inert, space-filling molecule, P, the dominant coefficients in eq 3 will he nAp andasp, and as a first approximation: In YE = (UBp- Vp)[Pl @a) I ~ Y=A(Uap - Vp)[Pl
(8b)
whence:
ra = exp((UBp- VdIPl)
(9a)
YA = exp((U~p -
(9b)
Vp)[Pl)
Thus:
YAIYB
= ex~((UAp - UBP)[~])
(10)
Now, if state A is more compact than state B, then Ugp > UAp,and so yAlys < 1; consequently, Kapp < K. This means that the concentration of the compact form, A, is favored in the presence of a space-filling substance, and the effect increases exponentially with the concentration of inert molecule. Experimentally, this prediction has been verified quantitatively by the finding that sucrose a t concentrations near 1 M stahilizes a-chymotrypsin against acid denaturation; the apparent equilibrium constant for denaturation decreased exponentially with sucrose concentration as predicted by eq 10 (6). Association Reactions For a self-association reaction comprising an n-mer in equilihrium with its monomer: nAaC
an equilihrium constant, K, can he written:
(11)
Excluded volume lost on association
Figure 4. LOSS01 volume excluded to an inert solute on self-association of a protein. On forming the dimer from two spherical monomers, there Is a loss of volume excluded to the inert solute, represented by the shaded regions.
Again, if the term involving the activity coefficient ratios is close to unity, the thermodynamic equilibrium constant may be approximated by the apparentconstant based on the concentrations. Ogston and Winzor (7) have examined the validity of this approximation, suggested originally by Adams and Fujita (8)to make tractable analysis of sedimentation equilibrium experiments of self-associating species. For end-to-end association of rods, or for highly charged molecules. the Adams-Fuiita aooroximation vields reliable estimate$ of the thermodyna&k equilibriu& constant. However. for other shapes and other modes of association, and for uncharged molehes, the approximation will fail progressively as the concentration of solute is raised. As is the case for isomerization reactions, the presence of space-filling bystander molecules may make a dominant contribution to the activity coefficient ratio, thereby markedly affecting the apparent equilibrium constant. Consider the dimerization reaction represented in Figure 4. In the presence of a significant concentration of inert bystander molecules, the macromolecules and the inert bystander molecule exclude each other from their neighborhoods. The volume around each dimer of the macromolecule from which the bystander molecules is excluded is somewhat less than twicethe volume around each monomer; the shaded sections shown in Figure 4 represent the excluded volume lost when the molecules associate. In the presence of inert bystander molecules, crowding in the solution is increased, and the available volume is decreased. Le Chatelier's principle states that when a system originally a t equilibrium is perturbed, the system will adjust in a direction so as to oppose the perturbation. So, if we crowd the solution, the system will change to minimize the crowding; i.e., the molecules will associate, thereby reducing the excluded volume (or, alternatively, restoring some of the available solution volume lost through the presence of the bystander). t As was thecase withisomerization. t h e a.o.~ a r e neauilibrium constant, based on the measured concentrations*of species a t eauilibrium. can be expressed auantitativelv in terms of the lois in excluded volume and thk molar concentration of the bystander molecules: In dilute solution. the enzvme ovruvate dehvdroeenase ex. ists as a roughly spherical partiilk of Stokes radius 13 nm. In the oresence of the inert space-filline material ~olvethvlene glych, the enzyme has been reportedio aggregaie tb produce a rather uniform population of larger, roughly spherical clusters that sediment rapidly in the ultracentrifuge. Nichol e t al (9) ascribed this effect to volume exclusion and showed that with plausible estimates of particle geometry the presence of
moderate concentrations of polyethylene glycol could lead to an enhancement of the apparent association constant such that the aggregates were the dominant form of the enzyme present, even though the aggregates would be undetectable in the absence of the polyethylene glycol. In the case of pyruvate dehydrogenase, the number of subunits involved in the aggregate is large andso the excludedvolume lost, consequent upon association, is also large. However, even for a monomer-dimer reaction the effects of solution crowding can be substantial. Minton 13)has cautioned aeainst too facile an intermetation of the results from experiments with polyethylene glycol. which mav exhibit effects bevond simole volume exclusion. ~everthkless,volume exclu~ioneffects have been well documented in mans other cases of enhanced protein selfassociation in the presence of inert, bystande; proteins a t high concentration. For example, myoglobin undergoes weak self-association normally detectable only at conceutrations above 20 g/L. In the presence of other, non-interacting, proteins a t comparable concentration, dilute solutions of myoglohin also show self-association (10). Even small molecules like elvcerol -. and sucrose can have profound effects on association and isomerization (6, 11). While the volume excluded to sucrose around a macromolecule is relatively small, it is the molar concentration that is important in these phenomena, and for a given mass concentration, smaller molecules have a greater molar concentration. Enzyme Klnetlcs In the case of a simple single substrate/single product enzyme-catalyzed reaction, there are potentially several ~ o i &a t which crowdine can operate. If the enzyme can associate to an oligomer with an enzymicactivitvdifferent from that of the monomer. then crowded solutions will favor the oligomer and thereby alter the observed enzvmic activitv. An examde here is elvceraldehyde-3-phosphate dehyd;ogenase, inwhich the enzymic activitv of thetetramer is less than that of the monomer. In the presknce ofother proteins comparable in concentration with that expected intmcellulnrly, the activity of the enzyme is reduced in a manner quantitatively consi&nt with excluded volume effects (12). If the association of enzyme and substrate leads to a more compact ES complex, then crowding effects will enhance c o m ~ l e xformation. lowerine the Michaelis constant.. K,.... ~he'valueof K , miasured under usual kinetic conditions is therefore unlikelv to reflect that in vivo. Initiation of bacterial chromosome replication in vitro requires the inclusion of h i ~ concentrations h of polymers such as polyethylene glycol; this is believed to enhance the interactinn between the DNA and the appropriate enzymes and proteins through crowding effects (13). During catalysis, the transition state may be expanded or contracted. In crowded solutions this will produce a raising or lowering, respectively, of the energy of activation, thereby affecting V,,,.,. The measured V,., for reduction of pyruvate by lactate dehydrogenase was found to increase linearly with concentration of ovalhumin. serum albumin or dextran (Fie. 5) (14),consistent withadecrease in volumeofthe transition state following the binding of NADH. Note that a 5% increase in V,,, is seen with only 0.1 mhl added bystander molecules. Hemoalobin in the red cell is present at approx. 5 mM, potentially Lading to an enhancement of up ti2.5 fold in V,., for the kinetics of lactate dehydrogenase in vivo, compared with values determined in dilute solution. The suhstrate itself may affect enzymic activity through volume exclusion effects when present a t high concentrations. For example, the activity of invertase (Fig. 6 ) shows a marked decrease at high concentrations of the substrate, sucrose, quantitatively consistent with a small expansion of the transition state during catalysis (15). Volume 67 Number 10 October 1990
859
Sucrose conc. ( M)
Conc. inert solute (mM) Figure 5. Increase in V,, forthe reduction of pyruvate by lanate dehydmgsnase In Um presence of ovalbumin (01,serum albumln (0).and dexhan (0). Data from Nichol et al. (14).
Fgwe 6. The enzymlc activlly of iwertase as a function ot ths concenbalion of its ouoahale,aucrose.(01Experimental data: (01Michaella-Menten oehavlor computed from the dataat sucrose concentrationsbelow 90 mM. Data from shearwin and Wlnzor (15).
prospect
nresence of other soace-filline molecules: in Dart, this additional understanding can come from qu&tit&ive studies of volume exclusion nhenomena in well defined model systems. The use of d e x t r k as a model crowding agent cangive an insight into the types of changes to he expected in vivo. Thirdly, we also need to apply methods of measurement to intact biochemical systems, in order to determine the properties and interaction parameters that pertain in vivo; one type of approach that may be of use here is the application of NMR to the study of enzymic reactions, transport phenomena, and exchange reactions in intact cells.
Although i t has been appreciated for a long time that the milieu within cells is highly nonideal, i t is only in recent years that volume exclusion phenomena in biochemical systems have been investigated in earnest (3).It isclear that the presence of relatively high concentrations of space-filling solutes, even those not much larger than water molecules, may alter observed equilibrium constants for reacting systems and may profoundly alter the kinetic parameters of enzyme-catalyzed reactions. Neither the magnitude nor even the direction of some of these effects can be predicted a priori without some knowledee of the chanees in eeometrv of the macromoiecules invoked: V,, for lactate dehydiogenase is increased, while V, for invertase is decreased, through volume exclusion phenomena. Nevertheless, volume exclusion can be used as a tool in kinetic studies of enzymes in the presence of inert polymers such as dextran to reveal such changes in geometry during binding and catalysis. Deeper understanding of the behavior of living cells therefore requires a three-pronged approach. Firstly, we still require a good understanding of the properties and interactions of the components under pseudo- or nearly ideal conditions. Secondly, we need t o understand t h e way t h e measurable properties and interactions are modified by the
LHerature Clted 1. Tanford. C. Physical Chamisfry a/Moemmokcul~~: Wiiey: New York, 1961. 2. Lore. P. Trenda Biochom. Sci. 1980.5.120-122. 3. Minton. A. P. Mol. Cell. Bimhem. 1983.55,llP-140. 4. Adair, G. S. Pmr.Ray.Soe. London S ~ PA. 1928. IM. 573603. 5. Willa,P.R;Nichol,L.W.;Sieren,R.J.Biophya. Chem. 1980,.11,71-82. 6. Winsor, D. J.;Wills, P. R. Biophyz. Chem. 1986.25.243-251, , 7. Ogstan, A. G.; Winror. D. J. J. Phys. Chem 1875.79.2496-25W' 8. A d a m , E. T.; Fujita. H. In Ulfroeenfrifugol Anolysis in Theory and Experiment; Willisma, J. W., Ed.;Academic: New York, 1961; pp 119-128. 9. NlchoLL. W.;Ogstan,A.G.: Willa,P.R.FEBSLeft. l981,126,4&ZO. 10. Wiif. J.;Minton,A.P.Biochim.Biophys.Acfo 1881,670,316322. 11. Sheanvin. K. E.: Wmzor.D. JBiophys. Chern. 1988.31.287.294. 12. Minton. A. P.; Wilf, J. Biochemistry 1981.20, 48214826. 13. Fuller, R. S.;Kaguni. J. M.; Kornbrg,A. Ploc.Not1. Acnd.Sci. USA 1981,78,7370-
.
7374. 14. N ~ C ~ w.; O ISCUII.~.M. ,L. J.; ward.^. 0.;wimor,~. J.AFC~. ~ i ~ ~ h ~ ~was, .~ioph~~. 222,57&581.
15. She&,
K. E.:Winlor, D. J. Arch.Biochem.Biophya. 1988,260,532-539,
1991Award for Excellence in Polymer Education by a High School Chemistry Teacher Allactive high schoolteachers who include polymer chemistry in their curriculum and encourage others to do the same are invited to apply for the 1991Award in Excellence in Polymer Education by a High School Chemistry Teacher. The awards, sponsored by the Joint Polymer Education Committee (PolyEd) of the ACS Polymer Chemistry Division and Polymeric Materials: Science and Engineering Division, honor two national recipients and three honorable mention recipients. The awards recognize the outstanding efforts of high school chemistry teachers who educate youths to be informed citizens and to consider careers in chemistry. Awards are based on the applicants' innovative use of classroom laboratory activitiesto promote understanding of polymer chemistry and its role in the products students use daily and on applicants' outreach activities to encourage other teachers to explore polymer chemistry with their students. Deadline for the 1991awards is January 15,1991. Applications can he obtained by writing to A. M. Sarquis, PolyEd High School Teacher Polymer Awards, Miami University Middletown, Department of Chemistry, 4200 East University Blvd., Middletown, OH 45042.
880
Journal of Chemical Education
