Channels as Enzymes: Oxymoron and Tautology
Channels are Catalysts for Diffusion and in that sense are Enzymes. This idea is useful for the design and interpretation of experiments.
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arXiv subjects
Bob Eisenberg
Publications and source records attributed to Bob Eisenberg.
Life's Solutions are Not Ideal
Life occurs in ionic solutions, not pure water. The ionic mixtures of these solutions are very different from water and have dramatic effects on the cells and molecules of biological systems, yet theories and simulations cannot calculate their properties. I suggest the reason is that existing theories stem from the classical theory of ideal or simple gases in which (to a first approximation) atoms do not interact. Even the law of mass action describes reactants as if they were ideal. I propose that theories of ionic solutions should start with the theory of complex fluids because that theory is designed to deal with interactions from the beginning. The variational theory of complex fluids is particularly well suited to describe mixtures like the solutions in and outside biological cells. When a component or force is added to a solution, the theory derives - by mathematics alone - a set of partial differential equations that captures the resulting interactions self-consistently. Such a theory has been implemented and shown to be computable in biologically relevant systems but it has not yet been thoroughly tested in equilibrium or flow.
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From Structure to Function in Open Ionic Channels
We consider a simple working hypothesis that all permeation properties of open ionic channels can be predicted by understanding electrodiffusion in fixed structures, without invoking conformation changes, or changes in chemical bonds. We know, of course, that ions can bind to specific protein structures, and that this binding is not easily described by the traditional electrostatic equations of physics textbooks, that describe average electric fields, the so-called `mean field'. The question is which specific properties can be explained just by mean field electrostatics and which cannot. I believe the best way to uncover the specific chemical properties of channels is to invoke them as little as possible, seeking to explain with mean field electrostatics first. Then, when phenomena appear that cannot be described that way, by the mean field alone, we turn to chemically specific explanations, seeking the appropriate tools (of electrochemistry, Langevin, or molecular dynamics, for example) to understand them. In this spirit, we turn now to the structure of open ionic channels, apply the laws of electrodiffusion to them, and see how many of their properties we can predict just that way.
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Computing the Field in Proteins and Channels
This is an early but comprehensive review of the PNP Poisson Nernst Planck theory of ion channels. Extensive reference is made to the earlier literature. The starting place for this theory of open channels is a theory of electrodiffusion rather like that used previously to describe membranes. The theory uses Poisson's equation to describe how charge on ions and the channel protein creates electrical potential; it uses the Nernst-Planck equations to describe migration and diffusion of ions in gradients of concentration and electrical potential. Combined, these are also the "drift-diffusion equations" of solid state physics, which are widely, if not universally used to describe the flow of current and the behavior of semiconductors.
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Crowded Charges in Ion Channels
Ions in water are the liquid of life. Life occurs almost entirely in 'salt water'. Water itself (without ions) is lethal to animal cells and damaging for most proteins. Water must contain the right ions in the right amounts if it is to sustain life. Physical chemistry is the language of electrolyte solutions. Physical chemistry and biology are intertwined. Physical chemists and biologists come from different traditions that separated for several decades as biologists described the molecules of life. Communication is not easy between a fundamentally descriptive tradition and a fundamentally analytical one. Biologists have now learned to study well defined systems with physical techniques, of considerable interest to physical chemists. Physical chemists are increasingly interested in spatially inhomogeneous systems with structures on the atomic scale so common in biology. Physical chemists will find it productive to work on well defined systems built by evolution to be reasonably robust, with input output relations insensitive to environmental insults. This article deals with properties of ion channels that in my view can be dealt with by 'physics as usual', with much the same tools that physical chemists apply to other systems. Indeed, I introduce and use a tool of physicists-a field theory (and boundary conditions) based on an energy variational approach developed by Chun Liu-not too widely used among physical chemists. My goal is to provide the knowledge base, and identify the assumptions, that biologists use in studying ion channels, avoiding jargon. Rather simple models of selectivity and permeation in ion channels work quite well in important cases. Those physical models and cases are the main focus of this review because they demonstrate the strong essential link between the traditional treatments of ions in chemical physics, and the biological function of ion channels.
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Self-organized Models of Selectivity in Ca and Na Channels
A simple pillbox model with two adjustable parameters accounts for the selectivity of both DEEA Ca channels and DEKA Na channels in many ionic solutions of different composition and concentration. Only the side chains are different in the model of the Ca and Na channels. Parameters are the same for both channels in all solutions. 'Pauling' radii are used for ions. No information from crystal structures is used in the model. Side chains are grossly approximated as spheres. The predicted properties of the Na and Ca channels are very different. How can such a simple model give such powerful results when chemical intuition says that selectivity depends on the precise relation of ions and side chains? We use Monte Carlo simulations of this model that determine the most stable-lowest free energy-structure of the ions and side chains. Structure is the computed consequence of the forces in this model. The relationship of ions and side chains vary with ionic solution and are very different in simulations of the Na and Ca channels. Selectivity is a consequence of the 'induced fit' of side chains to ions and depends on the flexibility (entropy) of the side chains as well as their location. The model captures the relation of side chains and ions well enough to account for selectivity of both Na channels and Ca channels in the wide range of conditions measured in experiments. Evidently, the structures in the real Na and Ca channels responsible for selectivity are self-organized, at their free energy minimum. Oversimplified models are enough to account for selectivity if the models calculate the 'most stable' structure as it changes from solution to solution, and mutation to mutation.
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Permeation as a Diffusion Process
The paper shows how the diffusive movement of ions through a channel protein can be described as a chemical reaction over an arbitrary shaped potential barrier. The result is simple and intuitive but without approximation beyond the electrodiffusion description of ion movement.
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Understanding Life with Molecular Dynamics and Thermodynamics: Comment on Nature 451, 240-243 (2008)
One of the important challenges facing high resolution molecular dynamics calculations is to reproduce biological functions that occur in the macroscopic world and involve macroscopic variables. Some of these functions can be well described by reduced models, with few parameters, over a wide range of conditions, even though the functions are complex. We are all eager to see how molecular dynamics will accurately estimate the thermodynamic variables that define and control so many macroscopic biological functions.
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Bubble Gating Currents in Ionic Channels
Bubbles in ion channel proteins have been proposed to be the bistable gates that control current flow. Gating currents associated with channel gating would then be an electrical signature of bubble breaking and formation, arising from the change in dielectric coefficient as the bubble breaks or forms. A bubble would have a dielectric coefficient of 1. A filled bubble would have a dielectric coefficient (say) between 30 and 80. Transporters, pumps, and channels would be expected to have gating currents.
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