Analyses of mechanisms—including selectivity and permeation—of proteins with newly discovered structures are found in most issues of the widely read journals
Scienceand Natureas well as the more specialized journals of molecular and structural biology and biophysics. These analyses of mechanism [219] follow the traditional practice of biochemistry textbooks and are nearly always verbal, without quantitative specification (however, see Ref. [354] that cites Kramers [234] but uses arbitrary rate constants and prefactors without physical discussion). These discussions of the mechanism of protein function are entirely in words, without reference to measurements of function, or graphs or numbers at all. Poetic license has its place but this is not it, at least in my view.
The mechanisms of structural biology usually depend on arbitrary choices of impossible ionic trajectories—impossible because the trajectories never reverse direction, unlike trajectories of real atoms that reverse so often that they travel 0.15 mm before they reach the end of a 1.5 nm channel, as we have just seen. (Indeed, in the Brownian approximation, widely used in simulations of channel motion [111, 218, 293–295, 323, 362–373], trajectories reverse an infinite number of times in any finite time, no matter how small. That is a fundamental property of the stochastic processes mathematicians call Brownian.)
The functional models of structural biology ignore the statistical reality of atomic physics known at least since the time of Maxwell (see history in Ref. [374]) and so are even less helpful than the arrow models of physiologists. They resemble Kekule’s molecular dreams more than physical reality. The simulations of molecular dynamics available now for decades [375] should have provided a visual vaccination against the idea that ions move in smooth slightly curved paths. Roux and coworkers [292] address the issue most directly, in contrast with MacKinnon and coworkers [354], in the same issue of the journalNature. Sadly, a glance at the literature of structural biology shows essentially no “back-and-forth” paths of ions like those that actually characterize atomic motion. Verbal models of smooth paths are nearly always used to describe the “mechanisms” of molecular biology, just as in biochemistry textbooks for what seems to be forever.
The reader may think that these smooth paths should be thought of as average paths. Average paths of course can be smooth, but renaming the paths of struc- tural models begs the question. How are the smooth paths chosen? It is not at all clear how one should average the astronomical number of atomic motions that determine the motion of an ion as it crosses a channel without calculation and theory. Statistical physics and molecular simulations were in fact developed to do that averaging. Modern simulations of ions in channels are beginning to average trajectories successfully and this work may eventually succeed in reaching bio- logical timescales. The other issues of scales are so large, however, that atomic simulations of biological systems seem likely to remain out of reach for a long time, as we discuss at length later in this chapter. The key idea is that all the gaps of scales (see Table I, much later in the paper) must be dealt with simultaneously
TABLE I
Time, Space, and Concentration Scales
Variable Computations Biology Ratio
Time 10−16s, vibrational modes 10−4s, action potential 1012
Space 10−11m, side chains 10−5m, typical cell 106
Solute concentration − 10−11to 5×10 M 5×1012
Volume − − 1018
in a fully atomic simulation, because all those scales exist and are significant to the natural function of ion channels.
Calculations of selectivity or functional properties involve much more than the average paths, of course. They also involve the driving forces (of concentration, electrical, and chemical potential) that send ions through these paths and the “resis- tances” of various forms of friction that result from the motion along these paths. The friction involves collisions, with water, ions, and atoms of the channel pro- tein and even more importantly (I imagine) dissipative electrostatic interactions (dielectric friction) with charged atoms of the protein, water, and solutes within a Debye length or two of the ion itself. The average paths change with experimental conditions and so the friction must as well.
In the real biological case, the number of atomic motions and interactions in- volved are far larger than astronomical. The current flow through a sodium channel during a propagating action potential depends on the electrical potential over a distance of millimeters. All the ions in that region interact and are significant in producing the propagation and waveform of the electrical potential. The number of interactions of some 1019ions is very large indeed.
Verbal descriptions do not deal with these issues at all. But the issues exist whether or not structural biologists choose to discuss them. Statistical physics has been developed over the centuries because words alone cannot account for the properties of inorganic solids and liquids. Indeed, it is hard to see how verbal models can be falsified, or verified, even in principle. They have more characteristics of metaphor and poetry than of science and engineering.
Poetry and metaphor have important places in scientific thinking, as motivators of the guesses that start most scientific work. But the checking that makes the metaphorical guess into science needs to be objective and quantitative if at all possible. Quantitative analysis addressing the known properties of atoms is needed to deal with ions in channels. The molecular mythology of smooth reaction paths in traditional biochemistry textbooks is not useful if we wish to compute and control biological systems the way engineers compute and control inorganic systems. An objective method of computing those smooth paths is needed, that includes the ionic conditions, and boundary conditions, as well as the structure of the protein. Engineers do not use verbal models to design or build things, any more than building contractors do.
Verbal structures fall of their own weight unless buttressed by numbers. But verbal structures can take a long time to fall if words are allowed to replace actual theories that confront specific experimental data.