Atomic Biology, Electrostatics, and Ionic Channels RS Eisenberg Department of Molecular Biophysics and Physiology Rush Medical College 1750 West Harrison Street Chicago IL 60612 USA in New Developments and Theoretical Studies of Proteins World Scientific Publishing, Philadelphia 1996 Edited by Ron Elber Published in the arXiv at http://arxiv.org/ with article id: 0807.0715 Headers and footers revised on May 15, 2013. Published in ArXiv as arXiv:0807.0715 Table of Contents MOLECULAR BIOLOGY ................................................................................................ 4 ATOMIC BIOLOGY ......................................................................................................... 6 ELECTRODIFFUSION IN THE OPEN CHANNEL .......................................................... 9 Drift in the Electric Field .............................................................................................................................. 10 Charge in the channel’s pore ..................................................................................................................... 10 Protein’s permanent charge ....................................................................................................................... 11 Distant charge and the trans-membrane potential ..................................................................................... 14 Interfacial charge....................................................................................................................................... 15 Charge at the ends of the channel .............................................................................................................. 16 Induced charge .......................................................................................................................................... 17 Diffusion through Channels ........................................................................................................................... 18 ELECTRODIFFUSION IN MIXED ELECTROLYTES ................................................... 20 MODELS OF PERMEATION ........................................................................................ 24 State Models of Permeation are Inconsistent with the Electric Field .......................................................... 26 MAKING MODELS IN ATOMIC BIOLOGY ................................................................... 30 MOLECULAR DYNAMICS ............................................................................................ 31 Temporal Limitations .................................................................................................................................... 33 Spatial Limitations......................................................................................................................................... 35 Periodic boundary conditions. .................................................................................................................... 36 HIERARCHY OF MODELS OF THE OPEN CHANNEL ............................................... 39 Stochastic Motion of the Channel: Langevin Dynamics ............................................................................... 40 Simulations of the Reaction Path: the Permion ............................................................................................ 42 Langevin Dynamics........................................................................................................................................ 44 CHEMICAL REACTIONS.............................................................................................. 51 - 2 - Published in ArXiv as arXiv:0807.0715 WHAT WAS WRONG? ................................................................................................. 53 BACK TO THE HIERARCHY ........................................................................................ 54 MACROSCOPIC MODELS OF THE CONTINUUM ...................................................... 55 Levels of the hierarchy: Occam’s razor can slit your throat ........................................................................ 56 POISSON-NERNST-PLANCK ( PNP) MODEL ............................................................ 59 Flux Ratios ..................................................................................................................................................... 67 Pumping by Field Coupling ........................................................................................................................... 71 GATING IN CHANNELS OF ONE CONFORMATION .................................................. 74 Gating by Field Switching ............................................................................................................................. 78 Gating Current .............................................................................................................................................. 80 Gating in Branched Channels ....................................................................................................................... 82 Blocking ......................................................................................................................................................... 83 BACK TO THE HIERARCHY: LINKING LEVELS ........................................................ 85 Occupancy...................................................................................................................................................... 85 IS THERE A THEORY? ................................................................................................ 88 At what level will the adaptation be found? .................................................................................................. 89 Simplicity, Evolution, and Natural Function................................................................................................. 89 AFTERWORD ............................................................................................................... 91 ACKNOWLEDGMENT .................................................................................................. 92 REFERENCES .............................................................................................................. 93 - 3 - Published in ArXiv as arXiv:0807.0715 MOLECULAR BIOLOGY The identification and manipulation of the molecules of life is one of the triumphs of man, putting biological systems under his control, embedding them into his technology, allowing the control of many of life’s functions. In the next few years some of the dreams of centuries will become realities, as we learn to control disease and our biological life cycle in ways that only poets and novelists have imagined, by controlling proteins. The triumph of this molecular biology is based on the identification and manipulation of proteins, and of their blueprints, DNA and some kinds of RNA. The technology of molecular biology manufactures these blueprints and thereby allows manipulation and bulk production of the encoded protein. This impressive technology is possible because so many biological functions can be controlled, or influenced, simply by the presence or absence of specific proteins in sufficient amounts. Evolution has used this simple method of control probably because it is easier to make adaptations this way, depending on the mutation and selection of single genes, rather than in other ways that depend on changes in many genes, and therefore occur with much lower probability, if the mutation of each of the genes is independent, as traditionally assumed. If evolution has used this simple mechanism to control many systems, then we can use it too; we can take advantage of this simplicity and govern those systems ourselves, even if we do not understand them. A car can easily be controlled by a driver who knows little of how it works. Similarly, a metabolic pathway governed by a single enzyme can be controlled technologically long before the pathway is known or understood. Molecular biology, as presently practiced, allows the control of biological functions that depend on the concentration of one protein. It will allow less control in systems that depend on the presence and properties of many proteins, although let us hope these are few and far between (for the sake of our own health). The quip is 1 that it will be possible to grow a nervous system long before we understand it! 1because the growth is determined (in all likelihood) by hundreds or a few thousands of genes whereas the function of the mammalian nervous system is determined (potentially) by its some 1013 cells and their multitude of connections. Many of those cells and connections have to be investigated individually to determine how the nervous system functions. The problem is simpler in the much smaller nervous systems of invertebrates, but it is - 4 - Published in ArXiv as arXiv:0807.0715 Molecular biology is also a useful tool for analyzing the function of a protein. Molecular genetics allows the rational manipulation of a protein’s primary (and, perhaps someday, secondary and tertiary) structure, an experimental technique of the greatest importance. But the simple replacement of one amino acid by another (e.g., in site-directed mutagenesis and its congener techniques) cannot tell how the protein works, how that amino acid influences function any more than the simple replacement of the parts of a machine, an automobile for example, will tell