Proc. Natl. Acad. Sci. USA Vol. 89, pp. 10504-10506, November 1992 Physiology

Model for the role of macromolecular crowding in regulation of cellular volume (swelling-activated ion transporters/exduded volume/scaled particle theory) ALLEN P. MINTONt, G. CRAIG COLCLASUREt, AND JOHN C. PARKERt tLaboratory of Biochemical Pharmacology, National Institute of Diabetes, Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892; and tDepartment of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 Communicated by Carl W. Gottschalk, August 3, 1992

ABSTRACT A simple model is proposed to account for Effect of Crowding on the Binding of Macromolecular large increases in transporter-mediated ion flux across cell Ligands to Surface Sites membranes that are elicited by small fractional changes of cell volume. The model is based upon the concept that, as a result Macromolecular reaction rates and equilibria inside living of large excluded volume effects in cytoplasm (macromolecular cells are not governed, in general, by mass-action rate and crowding), the tendency ofsoluble macromolecules to associate equilibrium expressions. Both theory and experiment have with membrane proteins is much more sensitive to changes in shown that the thermodynamic activity of each macromo- cell water content than expected on the basis of simple consid- lecular species in a highly volume-occupied, or crowded, erations of mass action. The model postulates that an ion solution exceeds the activity of that species at an identical transporter may exist in either an active dephosphorylated concentration in an uncrowded fluid (9). The activity coef- state or an inactive phosphorylated state and that the steady- ficient of the ith species, defined as the ratio of thermody- namic activity ai to concentration ci, is denoted by y,. For a state activity of the transporter reflects a balance between the fluid containing a mixture of molecular species that may be rates of phosphatase-catalyzed activation and kinase-catalyzed represented by compact rigid particles, scaled particle theory inactivation. Cell swelling results in the inhibition of kinase (10) provides the approximate relation relative to phosphatase activity, thereby increasing the steady- state concentration of the active form of the transporter. 3 Calculated volume-dependent stimulation of ion flux is com- In j= Ajr0 Ill parable to that observed experimentally. j = Many animal cell types respond to swelling or shrinkage by where ri is the characteristic dimension of the ith species (for activating membrane transporters or synthesizing osmolytes, example, the radius of a quasispherical molecule), and the Aj thereby changing their content of solute and osmotically coefficients are positive-definite functions of the concentra- obliged water and returning toward a normal volume (1). tions and characteristic dimensions of all of the species Although effector mechanisms for these responses have been present in the fluid. extensively investigated, little is known about how cells Cytoplasm contains 20-40%o total protein and thus quali- detect changes in their volume (2). Some believe that a signal fies as a highly crowded medium (11). Zimmerman and Trach of the membrane its (12) recently estimated that in the cytoplasm of Escherichia is generated by deformation and/or coli, the activity coefficient of a hypothetical quasispherical cytoskeletal connections (3), whereas others have suggested protein of radius 30 nm would be between 100 and 1000. For that the volume message arises from changes in the concen- the sake of simplicity, we limit our considerations to eryth- tration of a critical cytosolic solute (4). Jennings and Schulz rocytes, in which volume occupancy effects may be attrib- (4) and Cossins (5) have stressed that since small changes in uted to a single protein, hemoglobin (Mr, 65,000), occupying cell water can result in large changes in permeability, some 30-35% of cytosolic volume. In Fig. 1 we plot the activity sort ofamplification system must exist. We have observed (6, coefficient, estimated via scaled particle theory (10), of a 7) that swelling-induced K-Cl cotransport and shrinkage- dilute quasispherical molecule in a hemoglobin (300 g/liter) induced Na/H exchange in resealed erythrocyte ghosts of solution, as a function ofits molecular weight. It may be seen varying volume and intracellular protein composition corre- that the effect of volume occupancy on the activity coeffi- lated not with volume per se and not with the concentration cients of small solutes (such as simple ions) is minimal. ofany particular intracellular component but rather with total However, volume exclusion by hemoglobin causes the ac- cytosolic protein concentration. We present here a quanti- tivity coefficient of quasispherical proteins with molecular tative model that demonstrates how small dilutions of total weights in the range 50,000-100,000 to approach 10, 100, or cytosolic protein incident to cell swelling can exert nonspe- even 1000. These large numbers reflect the increasing amount cific effects of the required magnitude upon osmolyte trans- ofwork required to "fit" progressively larger solutes into the port rates. The success of this model lends credence to the interstices between hemoglobin molecules in a solution of speculation of Zimmerman and Harrison (8) that "changes in hemoglobin at 300 g/liter. reaction rates due to changes in [macromolecular] crowding The effects of macromolecular crowding upon a variety of provide, in principle, a simple mechanism by which the cell biochemical equilibrium and rate processes have been ex- could sense in its own volume." plored in some detail (9, 14). Consider the simple association changes of a soluble protein L with a surface binding site S. The publication costs of this article were defrayed in part by page charge L + S = LS payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact. The association equilibrium is governed by the constant 10504 Downloaded by guest on September 28, 2021 Physiology: Minton et al. Proc. Natl. Acad. Sci. USA 89 (1992) 10505 4 We further assume that both K and 4 obey Michaelis-Menten kinetics, i.e., 3 / KcsubstrateX Rate = Etotkcat KCsub [5] 1 + Kcsu strate cm2 0 where Etot is the total amount of enzyme (substrate-free and substrate-bound), kcat is the intrinsic turnover rate ofenzyme that is fully saturated with substrate, and the remaining expression represents the fractional saturation of enzyme 0 with substrate, where K is the apparent equilibrium constant 0 1 2 3 4 5 6 for association of enzyme and substrate. For a soluble log Mr enzyme and an immobile substrate (i.e., membrane trans- FIG. 1. Dependence of the activity coefficient (y) of a dilute porter), it follows from Eq. 3 that quasispherical solute in a solution of hemoglobin (300 g/liter) upon the molecular weight (size) of the solute, calculated using equation K= KOYE [6] A3 of ref. 13, with all effective hard particle specific volumes assumed equal to 1.0 ml/g. where KO is the thermodynamic association constant, defined in terms ofactivities, and YE is the activity coefficient offree enzyme. According to this model, K0- aLS - CLSYLS [2] aLas CLYLCSYS RateIA = fOtt1k (1 + K4ci) [7a] where a is activity and c is concentration. It follows that apparent equilibrium constant, defined in terms of conc trations rather than activities, may be given by Kt (1+ KKCAJ [7b] CLS K= = K0F [3] At steady state, the two rates are equal. CLCS / t ( KKC where KOC*KcI/ A~ci\i+c/\ [8] YiLYs where the superscript asterisk indicates a steady-state con- 'YLS centration. Two simplifying postulates are now introduced: Postulate 1. At steady state, the transporter is essentially The last approximate equality follows from the very large size fully inactive, i.e., cI>> CA difference between either S or LS and L (14). The binding Postulate 2. K,*ci>> 1 >> KK c. This postulate is fully isotherm for a single homogeneous class of binding sites is consistent with the preceding postulate. From Eqs. 6 and 8 then given by the Langmuir isotherm and the two preceding postulates, we obtain

/KCL X /KOyLC * totkqcat noecc =- ntotal 1 + KCL) ~to t1 + [4] [9] KOVLCL)L KtotkCpat KK^Y where now and ntotw, respectively, denote the number of sites where yK is the activity coefficient of free kinase. Note that occupied by ligand and the total number of sites (unoccupied there is only one concentration-dependent term in the above plus occupied). expression, namely 7K, and since all species other than hemoglobin are presumed to be dilute, this factor depends Model for Swelling-Induced Activation of a Membrane only on the concentration of hemoglobin. Transporter The transporter is activated by cell swelling in the follow- ing fashion. Let the initial state of the system (erythrocyte) Let us postulate that the activity ofthe transporter is regulated be characterized by a volume V = V0 and a hemoglobin by its degree ofphosphorylation, which, in turn, is controlled concentration CHb = COb. Next, let the cell volume change by two soluble enzymes, kinase K and phosphatase 4. In (via entry of water) to xV0; the hemoglobin concentration accordance with the model ofJennings and coworkers (15, 16), drops to CIb/x. The response to the change between initial we stipulate that the phosphorylated transporter is inactive (1), and final states is defined as and the dephosphorylated transporter is fully active (A).§ c* (final) yj~initial) Y,,(Cob 4 R =- = = [10] Phosphatase c* (initial) eKjfinal) y,(cHbIX) I A (phosphorylated-inactive) In Fig. 2 the normalized transporter-mediated ion flux (R) is (dephosphorylated-active) plotted as a function ofpercent volume increase, for putative kinases of various molecular weights. We infer from this Kinase K model that swelling-induced activation of the transporter arises from swelling-induced inhibition of kinase (dissocia- §This and other simplifying postulates introduced below are not tion of kinase from transporter), in agreement with the necessary; qualitatively similar results can be shown to result from conclusions of Jennings and coworkers (15, 16). a more general analysis (A.P.M., unpublished results). For didactic Activation of volume-sensitive transporters by phosphor- purposes we prefer a specific example to a general treatment. ylation and dephosphorylation, as postulated in the model, Downloaded by guest on September 28, 2021 10506 Physiology: Minton et al. Proc. Natd. Acad. Sci. USA 89 (1992)

x 30 @ catalytic activities of enzymes regulating membrane trans- porters. It predicts sensitivity to volume change comparable 25 to that observed experimentally (4, 19). Although the signal- ing mechanism is probably more complicated than repre- a) 20 4 sented by our simple model and the theoretical calculation of the contribution of macromolecular crowding to thermody- C) 15 namic activity is approximate, the basic principle illustrated here should apply to a variety of swelling or shrinkage- X 10 activated reactions involving enzymes and macromolecular substrates in crowded solutions. II *..'* ~~~~~~~~ ...... 1. Chamberlin, M. E. & Strange, K. (1989) Am. J. Physiol. 257, 0 10 20 30 C159-C173. 2. Sarkadi, B. & Parker, J. C. (1991) Biochim. Biophys. Acta 1071, % volume increase 407-427. 3. Watson, P. A. (1991) FASEB J. 5, 2013-2019. FIG. 2. Dependence of transporter-mediated osmolyte flux upon 4. Jennings, M. L. & Schulz, R. K. (1990) Am. J. Physiol. 259, cell volume, calculated as described in text for a cell containing C960-C%7. hemoglobin (350 g/liter) at initial volume. Activity coefficients were 5. Cossins, A. R. (1991) Nature (London) 352, 667-668. calculated as described in Fig. 1. Individual curves represent effects 6. Colclasure, G. C. & Parker, J. C. (1991) J. Gen. Physiol. 98, calculated by hypothetical kinase molecules having effective molec- 881-892. ular volumes equal to 1/4, 1/2, 1, 2, and 4 times that of hemoglobin 7. Colclasure, G. C. & Parker, J. C. (1992) J. Gen. Physiol. 100, (curves 1-5, respectively). 1-10. 8. Zimmerman, S. B. & Harrison, B. (1987) Proc. Nat!. Acad. Sci. has been surmised from studies with kinase and phosphatase USA 84, 1871-1875. 9. Minton, A. P. (1983) Mol. Cell. Biochem. 55, 119-140. inhibitors. The former inhibit shrinkage-induced activation of 10. Lebowitz, J. L., Helfand, E. & Prestgaard, E. (1965) J. Chem. Na-K-2C1 cotransport whereas the latter inhibit or delay the Phys. 43, 774-779. activation of swelling-induced K-Cl cotransport (16-18). It 11. Fulton, A. B. (1982) Cell 30, 345-347. has been suggested that coordination between shrinking- and 12. Zimmerman, S. B. & Trach, S. 0. (1991) J. Mol. Biol. 222, swelling-activated transporters is controlled by the phos- 599-620. 13. Chatelier, R. C. & Minton, A. P. (1987) Biopolymers 26, 507- phorylation state of a regulatory molecule (5, 19). Influence 524. of macromolecular crowding on phosphorylation of such a 14. Minton, A. P. (1981) Biopolymers 20, 2093-2120. regulator could be treated as an extension of the present 15. Jennings, M. L. & Al-Rohil, N. (1990) J. Gen. Physiol. 95, model. 1021-1040. We emphasize that the effect of macromolecular crowding 16. Jennings, M. L. & Schulz, R. K. (1991) J. Gen. Physiol. 97, on low molecular weight solutes is extremely small (Fig. 1). 799-817. None of the effects described here are incompatible with the 17. Kaji, D. M. & Tsukitani, Y. (1991) Am. J. Physiol. 260, C178-C182. finding that activity coefficients for small ions in cell water 18. Pewitt, E. B., Hegde, R. S., Haas, M. & Palfrey, H. C. (1990) are the same as for ions in extracellular fluid (20). The J. Biol. Chem. 265, 20747-20756. crowding effect is exerted by large molecules on other large 19. Parker, J. C., Colclasure, G. C. & McManus, T. J. (1991) J. molecules. The model presented here provides a simple Gen. Physiol. 98, 869-880. mechanism whereby small changes in cytosolic protein con- 20. Freedman, J. C. & Hoffman, J. F. (1979) J. Gen. Physiol. 74, centration can markedly influence the thermodynamic and 157-185. Downloaded by guest on September 28, 2021