Using a combination of techniques, including molecular dynamics, time-correlation analysis, stochastic dynamics, and fitting of continuum diffusion theory to electrophysiological data, a characterization is made of thermally driven sodium, water, and D2O motion within the gramicidin A channel. Since the channel contents are constrained to move in a single-file fashion, the motion that corresponds to experimentally measurable rates of permeation of the membrane is the motion of the center of mass of the channel contents. We therefore emphasize channel contents center-of-mass motion in our analysis of molecular dynamics computations. The usual free energy calculation techniques would be of questionable validity when applied to such motion. As an alternative to those techniques, we postulate a periodic sinusoidal free energy profile (related to the periodic structure of the helical channel) and deduce the fluid dynamic diffusion coefficient and the height and spacing of the free energy barriers from the form of the mean-square-deviation function, using stochastic computations. The fluid dynamic friction in each case appears similar to that for aqueous solution. However, the diffusive motions are modulated by a spatially periodic free energy profile with a periodicity characteristic of an L-D pair of amino acids in the gramicidin helix, approximately 1.7 A in the model we use. The barrier height depends on which substance is moving in the channel, but in each case is several times thermal energy. For barriers of this width and height, the motion is intermediate between the low-friction (transition-state) and high-friction (Brownian) limits. Thus, neither of these formalisms that have been used commonly to describe membrane permeation gives an accurate picture of the underlying physical process (although the Brownian description seems closer to correct). The non-Markovian Langevin equation must be solved to describe properly the statistics of the process. The "channel state of matter" characteristic of the channel contents appears to have some properties typical of the solid and some typical of the liquid state. The magnitude of the local friction and nature of the ion solvation are similar to the liquid state, but the periodicities of structure, free energy, and dynamics are somewhat solid-like. The alignment of water dipoles in the channel bears some resemblance to the orientational ordering of a nematic liquid crystal, but unlike a nematic liquid crystal, the waters have a degree of translational order as well. Thus, the "channel state" is not adequately described by analogy to either the solid or liquid states or to liquid crystals but must be dealt with as its own characteristic type of condensed matter.

The electrical behavior of small single frog atrial trabeculae in the double sucrose gap has been investigated. The currents injected during voltage clamp experiments did not behave as predicted from the assumption of spatial uniformity of the voltage across a Hodgkin-Huxley membrane. Much of the difference is due to the geometrical complexities of this tissue. Nonetheless, two transient inward currents have been identified, the faster of which is blocked by tetrodotoxin (TTX). The magnitude of the slower transient varies markedly between preparations but always increases in a given preparation with increase of external calcium. The fast transient current traces, at small to intermediate depolarizations, are often marred by the presence of notches and secondary peaks due most probably to the loss of space clamp conditions. In many preparations these could be removed by reducing the current magnitude through application of a partially-blocking dose of TTX. Conversely, in the preparations whose fast transient was fully blocked by TTX, notches and secondary peaks in the slow transient could by induced through increasing calcium concentration and thereby the slow current magnitude. Previously used techniques for the measurement of the reversal potential of the fast inward transient have been shown to be invalid. In so far as they can be measured, the reversal potentials of the fast and slow inward transient are in the same neighborhood, i.e. around 120 mV from rest. The true values may be quite a bit apart. The total charge flow in the capacitive transient was measured for different sized nodes and preparations. From these data and estimates of plasma membrane area per unit trabecular volume, specific membrane capacitances of around 3 muF/cm2 were calculated for small bundles. The apparent ion current densities on this basis are approximately 1/10 of those measured in axons. The capacitive current occurring in small bundles decayed as the sum of at least three exponential functions of time. On the basis of these data and the anomalously large stable node widths, we suggest a coaxial core model of the preparation with the inner elements in series with an additional large extracellular resistance.

The purpose of this study was to investigate the validity of the MetaMax II portable metabolic measurement system against the Douglas Bag technique. Nine recreationally active male subjects were included in a validation at 100 W, 10 well-trained male subjects at 200 W and 10 well-trained males at 250 W and at maximal exercise (volitional fatigue at a mean workload of 325 W). All testing was performed on an electronically braked bicycle at 60 rpm. At 100 W, the influence on MetaMax II measurements of adding a Douglas Bag breathing valve in series to the MetaMax II was investigated. The oxygen uptake was, for the MetaMax II, at 100 W mean 0.03 l x min (-1) higher (p < 0.01), at 200 W mean 0.02 l x min (-1) (n. s.) lower, at 250 W mean 0.04 l x min (-1) (n. s.) higher, and at 325 W mean 0.11 l x min (-1) (p < 0.05) higher. The carbon dioxide excretion was, for the MetaMax II, at 100 W mean 0.06 l x min (-1) (p < 0.01) lower, at 200 W mean 0.11 l x min (-1) (p < 0.05) lower, at 250 W mean 0.03 l x min (-1) (n. s.) lower, and at 325 W mean 0.16 l x min (-1) (p < 0.05) lower. The addition of a breathing valve in series to the MetaMax II resulted in lower breathing frequency, a higher ventilated tidal volume, and an affected gas measurement validation. In conclusion, the MetaMax II was found to be valid for metabolic gas measurements between 100 and at least 250 W.

This paper deals with the hierarchy of simulation methods and theoretical analysis that may be used in understanding biomolecular function. The hierarchy proceeds from the most detailed and most difficult for large systems and long times-quantum mechanics-to the least detailed and most readily directly applicable to large systems and long times-integrated constitutive theory. Substantial advances in understanding biological systems can come from linking these different hierarchies into integrated comprehensive descriptions of biomolecular function. This paper critically reviews several recent and ongoing studies of biomolecular function in membranes that accomplish this linking. These studies are chosen to illustrate both the power of this approach and possible pitfalls in particular applications. 0 1993 John Hierarchies of Descriptions of Biomolecular SystemsThis section of the paper reviews very briefly a hierarchy of simulation methods and theory used to understand biomolecular function. This review will provide the context for discussing particular studies that link different levels of description to provide a more comprehensive description of biomolecular systems, especially biological membranes, than could be obtained by description at one level alone. Quantum MechanicalThis is the most detailed description, but also the most difficult to utilize for large systems and/or for systems whose behavior must be sampled for long times (more than picoseconds). In addition to directly describing some biomolecular events, it has major value in providing reliable numerical parameters for a coarser level of description: Classical Molecular DynamicsThis level of description depicts biological molecules as a set of charged balls connected by springs. The charge distribution and properties of the springs and the surfaces of the balls are determined by quantum mechanics, but the evolution of the system with time is strictly Newtonian, permitting a relatively efficient simulation