The intent of this paper is to bring up to date an earlier theory of equilibrium selectivity [23, 24], with emphasis on making it applicable to the permeation of membrane channels and carriers, which involve kinetic considerations [8, 56]. We will review critically and unify a number of conceptual advances that have occurred since 1961, particularly the recognition by Hille [56] of how the same energetic principles that describe equilibrium selectivity of binding sites also apply to the peaks of the energy barriers (the so-called selectivity filters) involved in the kinetics of permeation. In the process, the precision of the term selectivity will gradually be increased. We will start with the intuitively simple comparison of effects of one ion versus another. Then we will proceed through more theoretically based classical concepts such as permeability ratios, conductance ratios, and ratios of binding affinities, all of which can be interrelated quite directly in sufficiently simple channels. It will become clear that these concepts lose their crispness and usefulness in multi-barrier channels as a consequence of asymmetry and/or possible multiple occupancy. Our formulation is influenced by a number of useful concepts from classical rate theory [40, 48, 126, 128], where the channel is viewed as having a static energy profile for a given state of ion occupancy; but we will also consider the consequences of viewing the channel as a dynamic structure with a fluctuating energy profile [83, 851. Besides presenting a topical review of selectivity, we have found it necessary to consider two subjects which are so new that they have received little attention as yet in a selectivity context. These are the effects in multi-barrier channels of asymmetry and multiple occupancy. This is because a number of classical concepts, and even ways of thinking about selectivity, are implicitly conditioned by conclusions that have been reached from considerations heretofore largely restricted to channels occupiable by no more than one ion at a time, or to channels with only one significantly rate determining barrier 1, or to channels which are symmetrical. To exemplify the effects of channel asymmetry, we examine in a simple two-barrier one-site model the consequences of asymmetry for reversal potential selectivity. To exemplify the effects of multiple rate-determining barriers, we also examine some implications of the energy profile which can be inferred for the gramicidin channel. In the process of presenting this material, we describe certain relationships between selectivity as seen in different phenomena such as conductance, reversal potential, and binding at least in systems which are simple enough for these classical concepts to retain their utility. This should lead to an understanding of why different measures of selectivity sometimes lead to different apparent selectivities, even in very simple channels. We also will define some guidelines for the applicability of these classical concepts and give some suggestions as to how to define selectivity when they fail, as fail they must, in those biological channels which are asymmetric and/or occupied by more than one ion at a time.

Ionic selectivity revisited: The role of kinetic and equilibrium processes in ion permeation through channels

Numerous physical characterizations clearly demonstrate that the polypentapeptide of elastin (Val1-Pro2-Gly3-Val4-Gly5)n in water undergoes an inverse temperature transition. Increase in order occurs both intermolecularly and intramolecularly on raising the temperature from 20 to 40 degrees C. The physical characterizations used to demonstrate the inverse temperature transition include microscopy, light scattering, circular dichroism, the nuclear Overhauser effect, temperature dependence of composition, nuclear magnetic resonance (NMR) relaxation, dielectric relaxation, and temperature dependence of elastomer length. At fixed extension of the cross-linked polypentapeptide elastomer, the development of elastomeric force is seen to correlate with increase in intramolecular order, that is, with the inverse temperature transition. Reversible thermal denaturation of the ordered polypentapeptide is observed with composition and circular dichroism studies, and thermal denaturation of the crosslinked elastomer is also observed with loss of elastomeric force and elastic modulus. Thus, elastomeric force is lost when the polypeptide chains are randomized due to heating at high temperature. Clearly, elastomeric force is due to nonrandom polypeptide structure. In spite of this, elastomeric force is demonstrated to be dominantly entropic in origin. The source of the entropic elastomeric force is demonstrated to be the result of internal chain dynamics, and the mechanism is called the librational entropy mechanism of elasticity. There is significant application to the finding that elastomeric force develops due to an inverse temperature transition. By changing the hydrophobicity of the polypeptide, the temperature range for the inverse temperature transition can be changed in a predictable way, and the temperature range for the development of elastomeric force follows. Thus, elastomers have been prepared where the development of elastomeric force is shifted over a 40 degrees C temperature range from a midpoint temperature of 30 degrees C for the polypentapeptide to 10 degrees C by increasing hydrophobicity with addition of a single CH2 moiety per pentamer and to 50 degrees C by decreasing hydrophobicity.(ABSTRACT TRUNCATED AT 400 WORDS)

/pdf/entropic-elastic-processes-in-protein-mechanisms-i-elastic-6uj6d0m4y1.pdf

Entropic elastic processes in protein mechanisms. I. Elastic structure due to an inverse temperature transition and elasticity due to internal chain dynamics.

Biologicalfree energy transduction: Living organisms evolved by developing the capacity to utilize energy in one form and to convert it into energy of different forms. How can the principal players in such processes, the proteins and their constituent polypeptides, function in the conversion of one form of energy into another? The set of pairwise free energy transductions, other than photon-driven processes, that can occur in biological systems involve the intensive variables of temperature, pressure, mechanical force, chemical potential and electrochemical potential (see below). What is (or what are) the primary mechanism (or mechanisms) whereby these couplings or transductions can occur? Is it possible that there could be a common mechanism for these seemingly diverse interconversions ranging from the more obvious chemomechanical transduction of muscle contraction to the free energy transductions involved in oxidative phosphorylation?

Free energy transduction in polypeptides and proteins based on inverse temperature transitions.

We have discussed in some detail a variety of experimental studies which were designed to elucidate the conformational and dynamic properties of gramicidin and alamethicin. Although the behavior of these peptides is by no means fully characterized, these studies have already permitted aspects of ion channel activity to be understood in molecular terms. Studies with gramicidin in a variety of organic solutions have revealed conformational heterogeneity of this peptide; at least five major isomers exist, several of which have been characterized in detail using NMR spectroscopy and X-ray crystallography. When added to lipid membranes gramicidin undergoes a further conformational conversion. Although the conformation of gramicidin in membranes is not as well characterized as the solution conformation(s) and an X-ray structure is not yet available, detailed data, particularly from solid-state NMR studies, continue to become available and a right-handed beta 6.3 helical conformation of the peptide backbone is now generally accepted. Two of these beta 6.3 helices joined at their N-termini are believed to form the conducting channel. The conformational behavior of the side-chains of gramicidin in the membrane-bound form is not well established and several NMR, CD, fluorescence and theoretical studies are now focussed on this. Although the side-chains do not directly contact the permeating ions, they can have distinct effects on conductance and selectivity by altering the electrostatic environment sensed by the ion. The dynamics of both side-chain and backbone conformations of gramicidin appear critical to a detailed understanding of the ion transport process in this channel. As the description of the membrane-bound conformation of gramicidin becomes more detailed, simulations of ion transport using computational methods are likely to improve and will further our understanding of the processes of ion transport. As well as internal motion of the backbone and side-chains, gramicidin undergoes rotational and translational motion in the plane of the membrane. These motions do not appear to be essential for the process of ion transport but can affect channel lifetime since lifetime is determined by the rate of association and dissociation of gramicidin monomers. Gramicidin-membrane interactions are also likely to be involved in the frequency of occurrence of channel subconductance states, the frequency of channel flickering and fundamentally in the stability of the membrane-bound gramicidin conformation. Alamethicin forms channels in membranes which are strongly voltage-dependent. The molecular origin of voltage-dependent conductances has been a fundamental problem in biophysics for many years.(ABSTRACT TRUNCATED AT 400 WORDS)

Model ion channels: gramicidin and alamethicin.

https://febs.onlinelibrary.wiley.com/doi/pdf/10.1016/0014-5793%2885%2980702-X

1H-NMR study of gramicidin A transmembrane ion channel: Head-to-head right-handed, single-stranded helices

Thallium ion-induced carbonyl carbon chemical shifts were compared for all of the L-residue-peptide carbonyl carbons of the gramicidin A transmembrane channel. Molecular structures were deduced by using the argument that helically equivalent and equally proximal carbonyls would exhibit essentially equivalent ion-induced chemical shifts. The transmembrane channel was found to be a head-to-head dimer with the structure of a left-handed, single-stranded β-helix.

https://science.sciencemag.org/content/sci/221/4615/1064.full.pdf

Is the Gramicidin A Transmembrane Channel Single-Stranded or Double-Stranded Helix? A Simple Unequivocal Determination

Malonyl gramicidin is incorporated into lysolecithin micelles in a manner which satisfies a number of previously demonstrated criteria for the formation of the transmembrane channel structure. By means of sodium-23 nuclear magnetic resonance, two binding sites are observed: a tight site and a weak site with binding constants of approximately 100m
−1 and 1m
−1, respectively. In addition, off-rate constants from the two sites were estimated from NMR analyses to bek

 off
 ≃3×105/sec andk

 off
 ≃2×107/sec giving, with the binding constants, the on-rate constants,k

 on
 ≃3×107/msec andk

 on
 ≃2×107/m sec. Five different multiple occupancy models with NMR-restricted energy profiles were considered for the purpose of calculating single-channel currents as a function of voltage and concentration utilizing the four NMR-derived rate constants (and an NMR-limit placed on a fifth rate constant for intrachannel ion translocation) in combination with Eyring rate theory for the introduction of voltage dependence. Using the X-ray diffraction results of Koeppe et al. (1979) for limiting the positions of the tight sites, the two-site model and a three-site model in which the weak sites occur after the tight site is filled were found to satisfactorily calculate the experimental currents (also reported here) and to fit the experimental currents extraordinarily well when the experimentally derived values were allowed to vary to a least squares best fit. Surprisingly the “best fit” values differed by only about a factor of two from the NMR-derived values, a variation that is well within the estimated experimental error of the rate constants. These results demonstrate the utility of ion nuclear magnetic resonance to determine rate constants relevant to transport through the gramicidin channel and of the Eyring rate theory to introduce voltage dependence.

The malonyl gramicidin channel: NMR-derived rate constants and comparison of calculated and experimental single-channel currents

Carbon-13 NMR longitudinal relaxation time and line-width studies are reported on the coacervate concentration (about 60% water by weight) of singly carbonyl carbon enriched polypentapeptides of elastin: specifically, (L-Val1-L-[1-13C]Pro2-Gly3-L-Val4-Gly5)n and (L-Val1-L-Pro2-Gly3-L-Val4-[1-13C]Gly5)n. On raising the temperature from 10 to 25 degrees C and from 40 to 70 degrees C, carbonyl mobility increases, but over the temperature interval from 25 to 40 degrees C, the mobility decreases. The results characterize an inverse temperature transition in the most fundamental sense of temperature being a measure of molecular motion. This transition in the state of the polypentapeptide indicates an increase in order of polypeptide on raising the temperature from 25 degrees C to physiological temperature. This fundamental NMR characterization corresponds with the results of numerous other physical methods, e.g., circular dichroism, dielectric relaxation, and electron microscopy, that correspondingly indicate an increase in order of the polypentapeptide both intramolecularly and intermolecularly for the same temperature increase from 25 to 40 degrees C. Significantly with respect to elastomeric function, thermoelasticity studies on gamma-irradiation cross-linked polypentapeptide coacervate show a dramatic increase in elastomeric force over the same interval that is here characterized by NMR as an inverse temperature transition. The temperature dependence of mobility above 40 degrees C indicates an activation energy of the order of 1.2 kcal/mol, which is the magnitude of barrier expected for elasticity.

Carbon-13 NMR relaxation studies demonstrate an inverse temperature transition in the elastin polypentapeptide

Publisher Summary This chapter describes the determination of rate and binding constants and site locations ion interactions at membranous regions of polypeptide sites using nuclear magnetic resonance (NMR). Monitoring a site within the membrane is made difficult by the slow reorientation of the membrane. For interpreting ion correlation times, it is helpful when the reorientation correlation time of the site is long compared to the lifetime of the ion in the channel. The membranous gramicidin channel, the ion correlation time, derived from resonance linewidth analyses, can be interpreted as the ion occupancy time in the channel. The reciprocal of the ion occupancy time becomes the important off-rate constant for an ion leaving the channel. It is suggested that gramicidin channel is a particularly favorable membranous peptide that can function as a proving ground for these NMR approaches to the characterization of ion interactions. The process of substantiating or validating the interpretation or analyses of NMR data on ion interaction with membranous polypeptide is facilitated by the particular characteristics of the gramicidin channel transport and structure.

Ion interactions at membranous polypeptide sites using nuclear magnetic resonance: determining rate and binding constants and site locations.

Publisher Summary This chapter illustrates the capacity to determine meaningful rate constants by means of NMR relaxation studies of spin 7/2 cesium- 133 and allow these approaches to be considered for spin 7/2 calcium-43. Background NMR data are presented for calcium-43, e.g., CaCI 2 concentration dependence and temperature dependence of the longitudinal relaxation time, TI, in D,O, in the presence of phosphatidylcholine lipid and in the presence of phosphatidylcholine lipid plus gramicidin A channels and the transverse relaxation time, T 2 for 100 m M and 1 M CaCI 2 , in the presence and absence of channels. These data allow determination of the off-rate constant for calcium ions leaving the channel binding site to be of the order of 5 x 10 7 /sec. With the binding constant demonstrated here to be about l/M for the site at the mouth of the gramicidin A channel and with the experimental off-rate constant, it becomes apparent that the lack of a calcium ion current is due to a high central barrier arising from the large repulsive image force which occurs when a divalent charge is separated from the lipid dielectric constant by no more than a single layer of polypeptide backbone.

T. L. Trapane

Papers

Is the Gramicidin A Transmembrane Channel Single-Stranded or Double-Stranded Helix? A Simple Unequivocal Determination

The malonyl gramicidin channel: NMR-derived rate constants and comparison of calculated and experimental single-channel currents

Carbon-13 NMR relaxation studies demonstrate an inverse temperature transition in the elastin polypentapeptide

Ion interactions at membranous polypeptide sites using nuclear magnetic resonance: determining rate and binding constants and site locations.

Chapter 4 Ion Interactions with the Gramicidin A Transmembrane Channel: Cesium-133 and Calcium-43 NMR Studies