Rush University - Department of Molecular Biophysics and Physiology

Bob Eisenberg’s Recent Work in Physical Chemistry

January 24, 2012

Bob Eisenberg has recently been working mostly in physical chemistry because he rediscovered what has been known for a long time, since the 1800's: the law of mass action is derived and applies to infinitely dilute gases without electrical charge. ONLY in that case are the equilibrium constants chemists are taught actually constant! Otherwise, they vary a great deal, and depend on the concentration of everything in the solution, and the shape of the system, and properties of its boundaries.

Biology occurs in ionic solutions, ionic plasmas in fact, that are charged and not at all dilute. The law of mass action has been consistently misused in this situation because equilibrium and rate constants have been assumed constant. That means that interactions of the ions themselves have been mistakenly attributed to interactions with proteins, channels or enzymes (or binding proteins).[14] Since much of biology is produced by these interactions, the implications are serious and general.

The crucial fact is that equilibrium and rate constants change when the concentrations of EVERY species in a biological 'Ringer' solution is changed and they change a lot. This crucial property of ionic solutions has always been known to experimental physical chemists (i.e., since the 1920's or earlier) but escaped the notice of the key biophysical chemists Edsall [4] and Tanford.[32, 33]

These facts were presented at the Gordon Conference on Water in the summer of 2010 and led to an invitation to write a Frontiers article that appeared on the cover of Chemical Physics Letters.[10] See also [11]. This article was invited by Rich Saykally a physical chemist at University of California at Berkeley and a member of the National Academy of Sciences (USA). At the same time, Mark Ratner and George Schaatz, also members of the National Academy in physical chemistry, invited Bob to write an article showing why the simulations of molecular dynamics have so far not been able to deal with the solutions that life exists in.[9]

The key challenge here is that in ionic solutions everything interacts with everything else and a mathematics is needed that will accommodate interactions in a constrained way without an indefinite number of unknown parameters. The energetic variational method of Chun Liu [3, 20, 22, 25, 27, 28, 30, 31, 34] applied to electrolyte solutions [13 , 21, 23, 24, 26, 29, 30] does this. Mathematical problems that prevented such treatments [18, 19] have been solved by Chun and his community.

The importance of these questions has been recognized by the physical chemistry community, along with the (so far unproven) possibility that the variational method may actually solve problems outstanding for a century or so. Bob was invited to write a long review about how he approaches problems of ions in solution and channels and it has recently appeared.[12] This article was invited by Stuart Rice, a recent recipient of the Wolf Prize and the National Medal of Science.

The physical chemistry community evidently wants to learn more of this variational approach and so nominated Bob to be a Visiting Professor (four months) in the Miller Institute of the University of California at Berkeley and the Department of Chemistry. This position is highly competitive between Departments many of which at Berkeley are among the best anywhere, including Chemistry. Awards have rarely been given to people ‘unqualified’ in their field. (Bob was trained as a biophysicist and has nearly become a biomathematician. He was not trained as a physical chemist.) So it was a pleasant surprise to hear that Bob received the award. It was particularly pleasant in a personal way to have critical thoughts well received by the targets of the criticisms, since the biophysical community in which Bob was raised (Ph.D. in Biophysics, Univ. of London 1965; A.B. summa in Biochemical Sciences, Harvard College, 1963) had not responded kindly to an equally serious criticism published some 25 years ago [1, 2, 5, 6, 7, 8, 15, 16, 17] despite the general acceptance of the criticism nowadays. (The earlier criticism is a subset of the recent work.)


1. Chen, D., L. Xu, A. Tripathy, G. Meissner, and R. Eisenberg, Rate Constants in Channology. Biophys. J., 1997. 73(3): p. 1349-1354.
2. Cooper, K.E., P.Y. Gates, and R.S. Eisenberg, Surmounting barriers in ionic channels. Quarterly Review of Biophysics, 1988. 21: p. 331–364.
3. Doi, M., Gel Dynamics. Journal of the Physical Society of Japan, 2009. 78(2009): p. 052001.
4. Edsall, J. and J. Wyman, Biophysical Chemistry. 1958, NY: Academic Press.
5. Eisenberg, B., Permeation as a Diffusion Process, in Biophysics Textbook On Line "Channels, Receptors, and Transporters", L.J. DeFelice, Editor. 2000, Published in ArXiv as arXiv:0807.0721.
6. Eisenberg, B., Ion Channels as Devices. Journal of Computational Electronics, 2003. 2: p. 245-249.
7. Eisenberg, B., Living Transistors: a Physicist’s View of Ion Channels. available on as q-bio/0506016v2 24 pages, 2005.
8. Eisenberg, B., Engineering channels: Atomic biology. Proceedings of the National Academy of Sciences, 2008. 105(17): p. 6211-6212.
9. Eisenberg, B., Multiple Scales in the Simulation of Ion Channels and Proteins. The Journal of Physical Chemistry C, 2010. 114(48): p. 20719-20733.
10. Eisenberg, B., Mass Action in Ionic Solutions. Chemical Physics Letters, 2011. 511.
11. Eisenberg, B., Life’s Solutions are Not Ideal. Posted on with Paper ID arXiv:1105.0184v1, 2011.
12. Eisenberg, B., Crowded Charges in Ion Channels, in Advances in Chemical Physics. 2010, John Wiley & Sons, Inc. p. 77-223 also available at http:\\ as arXiv 1009.1786v1001.
13. Eisenberg, B., Y. Hyon, and C. Liu, Energy Variational Analysis EnVarA of Ions in Water and Channels: Field Theory for Primitive Models of Complex Ionic Fluids. Journal of Chemical Physics, 2010. 133: p. 104104.
14. Eisenberg, R.S., Channels as enzymes: Oxymoron and Tautology. Journal of Membrane Biology, 1990. 115: p. 1–12. Available on arXiv as
15. Eisenberg, R.S., Computing the field in proteins and channels. J. Membrane Biol., 1996. 150: p. 1–25. Also available on http:\\ as arXiv 1009.2857.
16. Eisenberg, R.S., Atomic Biology, Electrostatics and Ionic Channels., in New Developments and Theoretical Studies of Proteins, R. Elber, Editor. 1996, World Scientific: Philadelphia. p. 269-357. Published in the Physics ArXiv as arXiv:0807.0715.
17. Eisenberg, R.S., From Structure to Function in Open Ionic Channels. Journal of Membrane Biology, 1999. 171: p. 1-24.
18. Finlayson, B.A., The method of weighted residuals and variational principles: with application in fluid mechanics, heat and mass transfer. 1972, New York: Academic Press. 412.
19. Finlayson, B.A. and L.E. Scriven, The Method of Weighted Residuals---a Review. Applied Mechanics Reviews, 1966. 19(9): p. 735-748.
20. Hou, T.Y., C. Liu, and J.-g. Liu, Multi-scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulations. 2009, Singapore: World Scientific Publishing Company.
21. Hyon, Y., B. Eisenberg, and C. Liu, A mathematical model for the hard sphere repulsion in ionic solutions Preprint# 2318 of the reprint series of the Institute for Mathematics and its Applications, 2010. (IMA, University of Minnesota, Minneapolis)
22. Hyon, Y., D.Y. Kwak, and C. Liu, Energetic Variational Approach in Complex Fluids : Maximum Dissipation Principle. Discrete and Continuous Dynamical Systems (DCDS-A), 2010. 26(4: April): p. 1291 - 1304, available at URL: as IMA Preprint Series # 2228.
23. Hyon, Y., Q. Du, and C. Liu, On Some Probability Density Function Based Moment Closure Approximations of Micro-Macro Models for Viscoelastic Polymeric Fluids. Journal of Computational and Theoretical Nanoscience, 2010. 7: p. 756-765.
24. Hyon, Y., B. Eisenberg, and C. Liu, A Mathematical Model for the Hard Sphere Repulsion in Ionic Solutions. Communications in Mathematical Sciences, 2011. 9: p. 459–475 also available as preprint# 2318 (IMA, University of Minnesota, Minneapolis), 2010.
25. Hyon, Y., J.A. Carrillo, Q. Du, and C. Liu, A Maximum Entropy Principle Based Closure Method for Macro-Micro Models of Polymeric Materials. Kinetic and Related Models, 2008. 1(2): p. 171-184.
26. Hyon, Y., J.E. Fonseca, B. Eisenberg, and C. Liu, A New Poisson-Nernst-Planck Equation (PNP-FS-IF) for Charge Inversion Near Walls. Biophysical Journal, 2011. 100(3): p. 578a.
27. Lin, F.-H., C. Liu, and P. Zhang, On a Micro-Macro Model for Polymeric Fluids near Equilibrium. Communications on Pure and Applied Mathematics, 2007. 60: p. 838-866.
28. Liu, C., An Introduction of Elastic Complex Fluids: An Energetic Variational Approach, in Multi-scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulations, T.Y. Hou, Liu, C., Liu, J.-g, Editor. 2009, World Scientific Publishing Company: Singapore.
29. Mori, Y., C. Liu, and R.S. Eisenberg, A model of electrodiffusion and osmotic water flow and its energetic structure. Physica D: Nonlinear Phonomena, 2011. 240(22): p. 1835-1852.
30. Ryham, R., R. Eisenberg, C. Liu, and F. Cohen, A Continuum Variational Approach to Vesicle Membrane Modeling. Biophysical Journal, 2011. 100(3): p. 187a.
31. Sheng, P., J. Zhang, and C. Liu, Onsager Principle and Electrorheological Fluid Dynamics. Progress of Theoretical Physics Supplement No. 175, 2008: p. 131-143.
32. Tanford, C., Physical Chemistry of Macromolecuiles. 1961, New York: Wiley. 710.
33. Tanford, C. and J. Reynolds, Nature's Robots: A History of Proteins. 2001, New York: Oxford. 304 pages
34. Zhang, J., X. Gong, C. Liu, W. Wen, and P. Sheng, Electrorheological Fluid Dynamics. Physical Review Letters, 2008. 101: p. 194503.

PDF download links

Bob Eisenberg's CV

Bob Eisenberg's Recent Work in Physical Chemistry

Channels as Enzymes

Crowded Charges in Ion Channels

Mass Action in Ionic Solutions

Multiple Scales in the Simulation of Ion Channels and Proteins

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