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.
Introduction. Life is diverse and complex in both structure and function. The variety of animals and structures within animals has been obvious at least since the time of Aristotle (Aristotle, 1961), and so has been the richness of what they can do. For more than two millennia scientists have followed Aristotle's path, trying to understand how structure produces function in biological systems, continually looking at smaller and smaller parts of the systems, trying to make ‗the secrets of life' understandable, and controllable.
Progress along this path has been frustrating scientists for centuries. Every structure seems to be followed by still smaller structures, all important to natural function. But the end of the path can now be seen. Structures smaller than atoms are not directly involved in life’s work, except in so far as electrons carry current and protons control the chemical properties of dissolved molecules. The role of macroscopic quantum coherence in the biological world has intrigued many (Loewenstein, 1999) but is not yet established. The smallest length scale directly relevant to life is that of molecules and their atoms. The magnificent tools of molecular biology make life’s machines (proteins) and blueprints (nucleic acids) experimentally accessible. The machines and blueprints are on the molecular and atomic scale, and not on the length scale of the nucleus, the quark, or (fortunately) the electron.
The other part of the biologists’ quest is to understand how these structures produce function. There, the goal is not in sight yet, although we will argue later in this paper that it may be fairly soon for one type of protein, ionic channels, that have simple structure when open, and use particularly simple physics, that of electrodiffusion.
Understanding the function of any biological systems means understanding how biological systems use physical laws to perform that function. When the biological systems consist of hierarchy upon hierarchy of structures, each itself of considerable complexity, the role of physical laws may be hard to recognize, at least in the form they are used by chemists and physicists. But open ionic channels have such simple structure, they involve so few hierarchical levels in their biological function, that we may be able to understand and solve them in the not too distant future. Fortunately, channels are of great biological importance, so despite their simplicity, they are worth studying.
Before we turn to channels explicitly, I will try the reader’s patience (or ask the impatient reader to skip ahead to the section labeled Working Hypothesis) with some more philosophical remarks about biological complexity, that are meant to show that not all biological systems use physical laws in the simple way they are used by open channels.
Vitalism and Complexity. Hierarchies can and do have qualitatively different properties from their components. The operation of an automobile engine cannot be understood just from the study of the burning of gasoline. The function of an integrated circuit or even transistor cannot be understood solely from the physics of conduction of current by quasiparticles. The nervous system cannot be understood from the physics of ionic conduction.
In each case, knowledge of structure is needed as well as knowledge of underlying physics.
The wiring diagram of the devices is as important as their physics.
The structure and underlying physics are not always enough to understand biological systems of complexity, because the complexity itself adds qualitatively new behaviors not evident in the underlying pieces of the system. While these new behaviors are certainly compatible with the underlying physical laws of the pieces, and in that sense implicit in them, they cannot be uniquely predicted from those underlying laws without a detailed understanding of the relevant hierarchy of structure. In many fewer words: a machine does much more than its parts do separately because its parts are designed to work together to perform a function.
When confronted with biological behaviors for which there is no technological precedent, like the speed with which the human visual system recognizes loved ones in a rain or snowstorm, it is sensible to seek explanations that are not well precedented in chemistry and physics, simply because chemical and physical systems have no such behaviors. It is sensible to seek explanations that arise from the hierarchy of structural complexity. In this quite limited sense, explanations are needed for biological systems that lie outside the laws of physics, as they are usually presented. The explanation must include both the physics and the structure, and, in a certain sense, the purpose of the structure, but it cannot consist only of the structure or only of the physics, at least in my view.
In this quite limited sense, then, vitalism is an appropriate part of biology. Physical laws undoubtedly govern the behavior of these compl
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