Biophysical Journal Volume 108 February 2015 453–454
453
New and Notable The Fallacy of Misplaced Concreteness John Prausnitz1,* 1 Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California
Cambridge mathematician and Harvard philosopher Alfred North Whitehead provided excellent advice for scientists. He said, ‘‘Seek simplicity but distrust it’’ (1). Scientists who like to explain observed phenomena by reduction, and to model experimental results using (mostly mechanical) models, often follow the first part of Whitehead’s sentence while forgetting the second. For describing the thermodynamic and phase-equilibrium properties of globular-protein solutions, it has been customary to model the protein as a hard sphere bearing an electric charge that depends on the solution’s pH. The charged sphere interacts with other spheres through electrostatic and (London) dispersion forces in a continuous dielectric medium that may contain other globular solutes as well as salt at known ionic strength. Using the concept potential of mean force coupled with hard-sphere perturbation theory, it is then possible to calculate the phase diagram where temperature is plotted against the number density of protein particles in the solution, as shown in Fig. 1. This procedure is similar to the more than 60-year-old DVLO theory for describing the thermodynamic properties of colloid solubilities. Upon making some structural assumptions about globular-protein crystals, it is also possible to calculate liquid-solid as well as liquid-liquid equilibria for protein solutions (2). Numerous publica-
Submitted November 17, 2014, and accepted for publication November 24, 2014. *Correspondence: [email protected] Editor: Nathan Baker. Ó 2015 by the Biophysical Society 0006-3495/15/02/0453/2 $2.00
tions along these lines have appeared in the literature, although comparisons with experiment are rare (2–11). Authors of the extensive literature on the theory of protein solutions have not been inhibited by the many (often drastic) simplifications required to obtain a simple result, perhaps relying on J. H. Hildebrand’s remark (J. H. Hildebrand, University of California, Berkeley, personal communication, 1979) that, when trying to establish a simple theory for a complex phenomenon, it is better to make many, rather than a few, simplifying assumptions because there is a good chance that the errors from some assumptions will be canceled by the errors from some other assumptions. Hildebrand’s remark (J. H. Hildebrand, University of California, Berkeley, personal communication, 1979), coupled with the first part of Whitehead’s advice (1), provide music to the ears of those applied scientists (like me) who want an easy solution to a complex problem. Of course applied scientists know that, in principle, calculations based on colloidal behavior are not really valid for protein solutions and that one should not confuse globular proteins with perturbed hard spheres, as stated in Whitehead’s fallacy of misplaced concreteness, where results from a model are erroneously believed equivalent to reality. Although we may not want to admit it, deep-down we know that the perturbed-hard-sphere theory is not correct for representing the properties of a protein solution. It’s bad, yes, but how bad? Little attention has been given to this question until the pioneering work of Sarangapani et al. (12) published in this issue of the Biophysical Journal. Sarangapani et al. (12) have performed extensive experimental studies of bovine serum albumin (BSA) solutions as a function of pH, ionic strength, and protein concentration at several temperatures. Experimental studies include rheology, neutron scat-
tering, and ultraviolet circular dichroism. These studies, coupled with extensive published data for BSA, show that models based on colloidlike assumptions are in serious error. The authors conclude that proteins are not simple particles of fixed dimension; they are polyelectrolytes whose configurations change with solution conditions, especially with protein concentration. The potential of mean force depends strongly on protein concentration due to changes in the protein’s tertiary structure. The authors present convincing evidence (12) that ‘‘The idealized view in the literature that proteins such as BSA are rigid ellipsoidal colloidal particles, whose size and shape are invariant with protein concentration and pH, is found to be untenable.’’ Protein particles in solution are much more complex than hard spheres in solution even when the properties of hard sphere are adjusted (perturbed) by addition of a variety of interparticle attractive and repulsive forces. Unlike hard spheres, protein particles change size, shape, and extension as solution conditions vary. In an initial effort toward improved understanding, the authors discuss a more realistic interpretation of scattering data than that provided by the conventional method based on colloidlike behavior. To obtain a better understanding of BSA properties in solution, the authors suggest molecular-dynamic simulations. Many (like me) will be secretly unhappy about the demise of the colloidlike theory of globular-protein solutions. Although we knew that this theory was ‘‘sick’’, we hoped that it might ‘‘recover’’. But now, after the report of Sarangapani et al. (12), the colloidlike theory is dead; the Sarangapani group have delivered a coup de graˆce. We can take comfort in the remark of Sarangapani et al. (12) that, while
http://dx.doi.org/10.1016/j.bpj.2014.11.3486
454
Prausnitz tion by nonionic polymer. J. Am. Inst. Chem. Eng. 36:1517. 3. Arzensek, D., D. Kuzman, and R. Podgornik. 2012. Colloidal interactions between monoclonal antibodies in aqueous solutions. J. Colloid Interface Sci. 384:207–216. 4. Bostro¨m, M., F. W. Tavares, ., J. M. Prausnitz. 2006. Effect of salt identity on the phase diagram for a globular protein in aqueous electrolyte solution. J. Phys. Chem. B. 110:24757–24760. 5. W. Kunz, and J. Tsurko, editors. 2010. Thermodynamics of Amino Acid and Protein Solutions. Transworld Research Network, Kerala, India. 6. Liu, H., S. K. Kumar, and F. Sciortino. 2007. Vapor-liquid coexistence of patchy models: relevance to protein phase behavior. J. Chem. Phys. 127:084902–084905. 7. Minton, A. P. 2007. The effective hard particle model provides a simple, robust, and broadly applicable description of nonideal behavior in concentrated solutions of bovine serum albumin and other nonassociating proteins. J. Pharm. Sci. 96:3466– 3469.
FIGURE 1 Cooling line A / B. At a, a solid may form but, because of slow kinetics, it is more likely that precipitation is delayed until b, where a second liquid phase appears. Further cooling produces two metastable liquid phases, d and e. Additional cooling may give four phases, f–i. Because phases f and g are metastable, a true equilibrium gives only phases h and i. Here, s is the protein diameter, r is the protein number density, and Tc is the maximum temperature on the liquid-liquid coexistence curve.
scientifically erroneous, the colloidlike theory may nevertheless be useful for some purposes in biotechnology. Thank you! That’s like saying even a placebo can sometimes cure an illness. While we mourn with sadness, we also owe much thanks to Sarangapani et al. (12) for reminding us that, when describing nature, yes, by all means seek simplicity but, with
Biophysical Journal 108(3) 453–454
respect for complexity, don’t forget to mistrust it. REFERENCES 1. Whitehead, A. N., and B. Russell. 1963. Principia Mathematica Vol. III, 2nd Ed. Cambridge University Press, New York. 2. Mahadevan, H., and C. K. Hall. 1990. Statistical-mechanical model of protein precipita-
8. Minton, A. P. 2008. Effective hard particle model for the osmotic pressure of highly concentrated binary protein solutions. Biophys. J. 94:L57–L59. 9. Piazza, R. 2000. Interactions and phase transitions in protein solutions. Curr. Opin. Colloid Interface Sci. 5:38–43. 10. Stradner, A., H. Sedgwick, ., P. Schurtenberger. 2004. Equilibrium cluster formation in concentrated protein solutions and colloids. Nature. 432:492–495. 11. Tavares, F. W., and J. M. Prausnitz. 2004. Analytic calculation of phase diagrams for solutions containing colloids or globular proteins. Colloid Polym. Sci. 282: 620–632. 12. Sarangapani, P. S., S. D. Hudson, and J. A. Pathak. 2014. Critical examination of the colloidal particle model of globular proteins. Biophys. J. 108:724–737.
453
New and Notable The Fallacy of Misplaced Concreteness John Prausnitz1,* 1 Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California
Cambridge mathematician and Harvard philosopher Alfred North Whitehead provided excellent advice for scientists. He said, ‘‘Seek simplicity but distrust it’’ (1). Scientists who like to explain observed phenomena by reduction, and to model experimental results using (mostly mechanical) models, often follow the first part of Whitehead’s sentence while forgetting the second. For describing the thermodynamic and phase-equilibrium properties of globular-protein solutions, it has been customary to model the protein as a hard sphere bearing an electric charge that depends on the solution’s pH. The charged sphere interacts with other spheres through electrostatic and (London) dispersion forces in a continuous dielectric medium that may contain other globular solutes as well as salt at known ionic strength. Using the concept potential of mean force coupled with hard-sphere perturbation theory, it is then possible to calculate the phase diagram where temperature is plotted against the number density of protein particles in the solution, as shown in Fig. 1. This procedure is similar to the more than 60-year-old DVLO theory for describing the thermodynamic properties of colloid solubilities. Upon making some structural assumptions about globular-protein crystals, it is also possible to calculate liquid-solid as well as liquid-liquid equilibria for protein solutions (2). Numerous publica-
Submitted November 17, 2014, and accepted for publication November 24, 2014. *Correspondence: [email protected] Editor: Nathan Baker. Ó 2015 by the Biophysical Society 0006-3495/15/02/0453/2 $2.00
tions along these lines have appeared in the literature, although comparisons with experiment are rare (2–11). Authors of the extensive literature on the theory of protein solutions have not been inhibited by the many (often drastic) simplifications required to obtain a simple result, perhaps relying on J. H. Hildebrand’s remark (J. H. Hildebrand, University of California, Berkeley, personal communication, 1979) that, when trying to establish a simple theory for a complex phenomenon, it is better to make many, rather than a few, simplifying assumptions because there is a good chance that the errors from some assumptions will be canceled by the errors from some other assumptions. Hildebrand’s remark (J. H. Hildebrand, University of California, Berkeley, personal communication, 1979), coupled with the first part of Whitehead’s advice (1), provide music to the ears of those applied scientists (like me) who want an easy solution to a complex problem. Of course applied scientists know that, in principle, calculations based on colloidal behavior are not really valid for protein solutions and that one should not confuse globular proteins with perturbed hard spheres, as stated in Whitehead’s fallacy of misplaced concreteness, where results from a model are erroneously believed equivalent to reality. Although we may not want to admit it, deep-down we know that the perturbed-hard-sphere theory is not correct for representing the properties of a protein solution. It’s bad, yes, but how bad? Little attention has been given to this question until the pioneering work of Sarangapani et al. (12) published in this issue of the Biophysical Journal. Sarangapani et al. (12) have performed extensive experimental studies of bovine serum albumin (BSA) solutions as a function of pH, ionic strength, and protein concentration at several temperatures. Experimental studies include rheology, neutron scat-
tering, and ultraviolet circular dichroism. These studies, coupled with extensive published data for BSA, show that models based on colloidlike assumptions are in serious error. The authors conclude that proteins are not simple particles of fixed dimension; they are polyelectrolytes whose configurations change with solution conditions, especially with protein concentration. The potential of mean force depends strongly on protein concentration due to changes in the protein’s tertiary structure. The authors present convincing evidence (12) that ‘‘The idealized view in the literature that proteins such as BSA are rigid ellipsoidal colloidal particles, whose size and shape are invariant with protein concentration and pH, is found to be untenable.’’ Protein particles in solution are much more complex than hard spheres in solution even when the properties of hard sphere are adjusted (perturbed) by addition of a variety of interparticle attractive and repulsive forces. Unlike hard spheres, protein particles change size, shape, and extension as solution conditions vary. In an initial effort toward improved understanding, the authors discuss a more realistic interpretation of scattering data than that provided by the conventional method based on colloidlike behavior. To obtain a better understanding of BSA properties in solution, the authors suggest molecular-dynamic simulations. Many (like me) will be secretly unhappy about the demise of the colloidlike theory of globular-protein solutions. Although we knew that this theory was ‘‘sick’’, we hoped that it might ‘‘recover’’. But now, after the report of Sarangapani et al. (12), the colloidlike theory is dead; the Sarangapani group have delivered a coup de graˆce. We can take comfort in the remark of Sarangapani et al. (12) that, while
http://dx.doi.org/10.1016/j.bpj.2014.11.3486
454
Prausnitz tion by nonionic polymer. J. Am. Inst. Chem. Eng. 36:1517. 3. Arzensek, D., D. Kuzman, and R. Podgornik. 2012. Colloidal interactions between monoclonal antibodies in aqueous solutions. J. Colloid Interface Sci. 384:207–216. 4. Bostro¨m, M., F. W. Tavares, ., J. M. Prausnitz. 2006. Effect of salt identity on the phase diagram for a globular protein in aqueous electrolyte solution. J. Phys. Chem. B. 110:24757–24760. 5. W. Kunz, and J. Tsurko, editors. 2010. Thermodynamics of Amino Acid and Protein Solutions. Transworld Research Network, Kerala, India. 6. Liu, H., S. K. Kumar, and F. Sciortino. 2007. Vapor-liquid coexistence of patchy models: relevance to protein phase behavior. J. Chem. Phys. 127:084902–084905. 7. Minton, A. P. 2007. The effective hard particle model provides a simple, robust, and broadly applicable description of nonideal behavior in concentrated solutions of bovine serum albumin and other nonassociating proteins. J. Pharm. Sci. 96:3466– 3469.
FIGURE 1 Cooling line A / B. At a, a solid may form but, because of slow kinetics, it is more likely that precipitation is delayed until b, where a second liquid phase appears. Further cooling produces two metastable liquid phases, d and e. Additional cooling may give four phases, f–i. Because phases f and g are metastable, a true equilibrium gives only phases h and i. Here, s is the protein diameter, r is the protein number density, and Tc is the maximum temperature on the liquid-liquid coexistence curve.
scientifically erroneous, the colloidlike theory may nevertheless be useful for some purposes in biotechnology. Thank you! That’s like saying even a placebo can sometimes cure an illness. While we mourn with sadness, we also owe much thanks to Sarangapani et al. (12) for reminding us that, when describing nature, yes, by all means seek simplicity but, with
Biophysical Journal 108(3) 453–454
respect for complexity, don’t forget to mistrust it. REFERENCES 1. Whitehead, A. N., and B. Russell. 1963. Principia Mathematica Vol. III, 2nd Ed. Cambridge University Press, New York. 2. Mahadevan, H., and C. K. Hall. 1990. Statistical-mechanical model of protein precipita-
8. Minton, A. P. 2008. Effective hard particle model for the osmotic pressure of highly concentrated binary protein solutions. Biophys. J. 94:L57–L59. 9. Piazza, R. 2000. Interactions and phase transitions in protein solutions. Curr. Opin. Colloid Interface Sci. 5:38–43. 10. Stradner, A., H. Sedgwick, ., P. Schurtenberger. 2004. Equilibrium cluster formation in concentrated protein solutions and colloids. Nature. 432:492–495. 11. Tavares, F. W., and J. M. Prausnitz. 2004. Analytic calculation of phase diagrams for solutions containing colloids or globular proteins. Colloid Polym. Sci. 282: 620–632. 12. Sarangapani, P. S., S. D. Hudson, and J. A. Pathak. 2014. Critical examination of the colloidal particle model of globular proteins. Biophys. J. 108:724–737.
