"Adaptive" behavior of ligand-gated ion channels: constraints by thermodynamics

The calcium-induced calcium release channel of the cardiac sarcoplasmic reticulum has been reported to inactivate in a novel manner (termed "adaptation"), which permits reactivation by exposure to successively higher concentrations of calcium. I examined the limitations placed by thermodynamics on the possible kinetic mechanisms for such behavior. The mechanism suggested by Gyorke and Fill, in which the affinity of a calcium-binding site decreases during adaptation, is not thermodynamically feasible for a passive system, but requires an external input of free energy. Possible sources of such energy are 1) metabolic energy, which is excluded by the fact that adaptation was observed in isolated channels in the absence of ATP, or 2) coupling of ion permeation to gating, for which there is currently no evidence. I derived a general limit on the thermodynamic feasibility of a sequence of channel activations and adaptations, irrespective of channel kinetics, from the requirement that the free energy must decrease during the spontaneous evolution of the system from the state existing immediately after a step increase in [Ca2+] to the state of maximum open probability that follows. The opening of the channel must involve an increase in free energy, which must be compensated by the free energy released by the incremental binding of calcium. This requirement leads to a complicated system of inequalities, which was simplified and manipulated algebraically into the form of a linear programming problem. Numerical solution of this problem showed that the sequence of adaptations of the SR channel observed by Gyorke and Fill requires the presence of at least 10 calcium-binding sites on the channel if it is to occur in the absence of exogenous sources of free energy. This indicates either that a large number of calcium-binding sites participate in the regulation of the SR calcium release channel, or that the existing data are significantly flawed with respect to the low open probability in the resting state, the importance of "calcium spike" artifacts from flash photolysis, or both.     

Kramers' diffusion theory applied to gating kinetics of voltage-dependent ion channels

Kramers' diffusion theory of reaction rates in the condensed phase is considered as an alternative to the traditional discrete-state Markov (DSM) model in describing ion channel gating current kinetics. Diffusion theory can be expected to be particularly relevant in describing high-frequency (>100 kHz) events in channel activation. The generalized voltage sensor of a voltage-dependent ion channel is treated as a Brownian motion particle undergoing spatial diffusion along a one-dimensional energy landscape. Two classes of energy landscapes are considered. The first class contains large barriers, which give rise to gating currents with two distinct time scales: the usual low-frequency decay, which can modeled with a DSM scheme, and a high-frequency component arising from intrastate relaxation. Large depolarizations reduce potential barriers to such a degree that activation rates are diffusion limited, causing the two time scales to merge. Landscapes of the second class are either featureless or contain barriers that are small compared to kT; these are termed "drift landscapes." These landscapes require a larger friction coefficient to generate slow gating kinetics. The high-frequency component that appears with barrier models is not present in pure drift motion. The presence of a high-frequency component can be tested experimentally with large-bandwidth recordings of gating currents. Topics such as frequency domain analysis, spatial dependence of the friction coefficient, methods for determining the adequacy of a DSM model, and the development of physical models of gating are explored.     

Structure and dynamics of hydronium in the ion channel gramicidin A

The effects of the hydronium ion, H(3)0+, on the structure of the ion channel gramicidin A and the hydrogen-bonded network of waters within the channel were studied to help elucidate a possible mechanism for proton transport through the channel. Several classical molecular dynamics studies were carried out with the hydronium in either the center of a gramicidin monomer or in the dimer junction. Structural reorganization of the channel backbone was observed for different hydronium positions, which were most apparent when the hydronium was within the monomer. In both cases the average O-O distance between the hydronium ion and its nearest neighbor water molecule was found to be approximately 2.55 A, indicating a rather strong hydrogen bond. Importantly, a subsequent break in the hydrogen-bonded network between the nearest neighbor and the next-nearest neighbor(approximately 2.7 -3.0 A) was repeatedly observed. Moreover, the carbonyl groups of gramicidin A were found to interact with the charge on the hydronium ion, helping in its stabilization. These facts may have significant implications for the proton hopping mechanism. The presence of the hydronium ion in the channel also inhibits to some degree the reorientational motions of the channel water molecules.     

Cross-linking studies and membrane localization and assembly of radiolabelled large mechanosensitive ion channel (MscL) of Escherichia coli

While the overall energy landscape of a foldable protein can be described by means of a few parameters characterizing its statistical topography, specific energetic terms subtly bias the representative structures giving rise to residue pair correlations as in a liquid. We use a free energy functional incorporating an inhomogeneous pair contact energy along with a contact formation entropy and a cooperativity contribution to determine residue-specific contact probabilities in the denatured state and the transition state ensemble. The predicted "hot residues" for the theoretical transition state ensemble reasonably agree with experiment for chymotrypsin inhibitor 2, and generally a strong correlation exists with the measured kinetic effects of mutating residues not involved in highly solvent-exposed regions.     

Folding thermodynamics of a model three-helix-bundle protein

The calculated folding thermodynamics of a simple off-lattice three-helix-bundle protein model under equilibrium conditions shows the experimentally observed protein transitions: a collapse transition, a disordered-to-ordered globule transition, a globule to native-state transition, and the transition from the active native state to a frozen inactive state. The cooperativity and physical origin of the various transitions are explored with a single "optimization" parameter and characterized with the Lindemann criterion for liquid versus solid-state dynamics. Below the folding temperature, the model has a simple free energy surface with a single basin near the native state; the surface is similar to that calculated from a simulation of the same three-helix-bundle protein with an all-atom representation [Boczko, E. M. & Brooks III, C. L. (1995) Science 269, 393-396].     

Microstructural evolution during liquid phase sintering: Part I. Development of microstructure

During liquid phase sintering, numerous solid-solid particle contacts can be generated by particle motion within the fluid. It is shown that, somewhat surprisingly, Brownian motion can produce such contacts. If such contacts are accompanied by particle adherence, the particles can then subsequently fuse into one (i.e., coalesce) by the liquid state analog of the evaporation-condensation mechanism of sintering. An isolated microstructure will develop if the time for particle coalescence is much less than the time between contacts. A highly skeletal arrangement of particles will form under the converse condition. Using these principles, a “microstructure map” is calculated in which the expected morphology of microstructure (i.e., skeletal or isolated) is related to the solid particle volume fraction, the kinetic and thermodynamic parameters affecting particle coalescence, and the frequency of particle contacts by Brownian motion. Some discussion of the thermodynamic and morphological factors affecting the probability of particle adherence after contact is presented.     

Does conformational free energy distinguish loop conformations in proteins?

Limitations in protein homology modeling often arise from the inability to adequately model loops. In this paper we focus on the selection of loop conformations. We present a complete computational treatment that allows the screening of loop conformations to identify those that best fit a molecular model. The stability of a loop in a protein is evaluated via computations of conformational free energies in solution, i.e., the free energy difference between the reference structure and the modeled one. A thermodynamic cycle is used for calculation of the conformational free energy, in which the total free energy of the reference state (i.e., gas phase) is the CHARMm potential energy. The electrostatic contribution of the solvation free energy is obtained from solving the finite-difference Poisson-Boltzmann equation. The nonpolar contribution is based on a surface area-based expression. We applied this computational scheme to a simple but well-characterized system, the antibody hypervariable loop (complementarity-determining region, CDR). Instead of creating loop conformations, we generated a database of loops extracted from high-resolution crystal structures of proteins, which display geometrical similarities with antibody CDRs. We inserted loops from our database into a framework of an antibody; then we calculated the conformational free energies of each loop. Results show that we successfully identified loops with a "reference-like" CDR geometry, with the lowest conformational free energy in gas phase only. Surprisingly, the solvation energy term plays a confusing role, sometimes discriminating "reference-like" CDR geometry and many times allowing "non-reference-like" conformations to have the lowest conformational free energies (for short loops). Most "reference-like" loop conformations are separated from others by a gap in the gas phase conformational free energy scale. Naturally, loops from antibody molecules are found to be the best models for long CDRs (> or = 6 residues), mainly because of a better packing of backbone atoms into the framework of the antibody model.     

Spectroscopic studies of the interactions of the pyrethroid insecticide fenvalerate with gramicidin

Fenvalerate is a pyrethroid insecticide which interacts with ionic channels. Using circular dichroism technique we have studied the interaction of fenvalerate with gramicidin, a model channel peptide which transports ions. In most organic solvents, gramicidin exists as a double helix except in trifluoroethanol where it exists as a channel forming single stranded beta6.3 helical monomer. In model lipid membranes, under certain experimental conditions, gramicidin exists as a channel forming single stranded beta6.3 helical dimer. Our results show that fenvalerate interacts more with the single stranded beta6.3 helical monomer or dimer than with the double helical form of gramicidin. This was further confirmed by an increase in the rate of gramicidin mediated proton transport in liposomes by fenvalerate, using the pH sensitive fluorophore, pyranine.     

Study of ionic currents across a model membrane channel using Brownian dynamics

Brownian dynamics simulations have been carried out to study ionic currents flowing across a model membrane channel under various conditions. The model channel we use has a cylindrical transmembrane segment that is joined to a catenary vestibule at each side. Two cylindrical reservoirs connected to the channel contain a fixed number of sodium and chloride ions. Under a driving force of 100 mV, the channel is virtually impermeable to sodium ions, owing to the repulsive dielectric force presented to ions by the vestibular wall. When two rings of dipoles, with their negative poles facing the pore lumen, are placed just above and below the constricted channel segment, sodium ions cross the channel. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength does not increase the channel conductance further. When only those ions that acquire a kinetic energy large enough to surmount a barrier are allowed to enter the narrow transmembrane segment, the channel conductance decreases monotonically with the barrier height. This barrier represents those interactions between an ion, water molecules, and the protein wall in the transmembrane segment that are not treated explicitly in the simulation. The conductance obtained from simulations closely matches that obtained from ACh channels when a step potential barrier of 2-3 kTr is placed at the channel neck. The current-voltage relationship obtained with symmetrical solutions is ohmic in the absence of a barrier. The current-voltage curve becomes nonlinear when the 3 kTr barrier is in place. With asymmetrical solutions, the relationship approximates the Goldman equation, with the reversal potential close to that predicted by the Nernst equation. The conductance first increases linearly with concentration and then begins to rise at a slower rate with higher ionic concentration. We discuss the implications of these findings for the transport of ions across the membrane and the structure of ion channels.     

Mechanism of ion permeation in skeletal muscle chloride channels

Voltage-gated Cl- channels belonging to the ClC family exhibit unique properties of ion permeation and gating. We functionally probed the conduction pathway of a recombinant human skeletal muscle Cl- channel (hClC-1) expressed both in Xenopus oocytes and in a mammalian cell line by investigating block by extracellular or intracellular I- and related anions. Extracellular and intracellular I- exert blocking actions on hClC-1 currents that are both concentration and voltage dependent. Similar actions were observed for a variety of other halide (Br-) and polyatomic (SCN-, NO3-, CH3SO3-) anions. In addition, I- block is accompanied by gating alterations that differ depending on which side of the membrane the blocker is applied. External I- causes a shift in the voltage-dependent probability that channels exist in three definable kinetic states (fast deactivating, slow deactivating, nondeactivating), while internal I- slows deactivation. These different effects on gating properties can be used to distinguish two functional ion binding sites within the hClC-1 pore. We determined KD values for I- block in three distinct kinetic states and found that binding of I- to hClC-1 is modulated by the gating state of the channel. Furthermore, estimates of electrical distance for I- binding suggest that conformational changes affecting the two ion binding sites occur during gating transitions. These results have implications for understanding mechanisms of ion selectivity in hClC-1, and for defining the intimate relationship between gating and permeation in ClC channels.     

Dynamic properties of Na+ ions in models of ion channels: a molecular dynamics study

We present simulation results for the effective diffusion coefficients of a sodium ion in a series of model ion channels of different diameters and hydrophobicities, including models of alamethicin, a leucine-serine peptide, and the M2 helix bundle of the nicotinic acetylcholine receptor. The diffusion coefficient, which in the simulations has a value of 0.15(2) A2ps-1 in bulk water, is found to be reduced to as little as 0.02(1) A2ps-1 in the narrower channels, and to about 0.10(5) A2ps-1 in wider channels such as the nicotinic acetylcholine receptor. It is anticipated that this work will be useful in connection with calculations of channel conductivity using such techniques as the Poisson-Nernst-Planck equation, Eyring rate theory, or Brownian dynamics.     

A novel explanation for fluctuations of ion current through narrow pores

Fluctuation of ion current, between a high conductance and a low conductance state, through biological ion channels and pores is assumed to arise from conformational changes between an "open" and a "closed" configuration. Here we offer an additional mechanism that arises from changes in ionization of fixed charges within, or at the mouth of, a channel or pore. Our hypothesis, which is based on measurements of ion selectivity alongside ion current, applies to pores through some synthetic membranes and through channels-such as those created by certain toxins-that remain (at least partially) open in the low conductance state. It may also explain the phenomena of "open channel noise" and "substate behavior" that characterize several endogenous ion channels and should be considered when modeling the behavior of such channels.     

Polylysine decelerates kinetics of negatively charged gramicidin channels as shown by sensitized photoinactivation

Effect of a cationic polymer, poly(L-lysine), on the kinetic properties of ionic channels formed by neutral gramicidin A (gA) and its negatively charged analogue O-pyromellitylgramicidin (OPg) in a bilayer lipid membrane is studied using a method of sensitized photoinactivation. This newly developed method is based on the analysis of transmembrane current transients induced by a flash in the presence of a photosensitizer. It has been shown previously that the time course of the flash-induced current decrease in most cases follows a single exponential decay with an exponential factor (tau, the characteristic time of photoinactivation) that correlates well with the single-channel lifetime. Addition of polylysine does not affect tau for gA channels, but causes a substantial increase in tau for OPg channels. This effect is reversed by addition of polyacrylic acid. The deceleration of the photoinactivation kinetics is ascribed to electrostatic interaction of polylysine with OPg probably resulting in OPg clustering. The latter can stabilize the channel state by reducing the rotational and lateral mobility of OPg monomers and dimers, and thus increase the single channel lifetime.     

金属有机骨架与相变芯材相互作用的分子动力学

金属有机骨架材料（metal-organic frameworks, MOFs）由于具有规整的孔道结构,较高的孔隙率十分适合作为相变材料的载体,从而实现对相变芯材的有效封装。本文采用分子动力学方法,对Cr-MIL-101负载十八烷,十八酸,十八胺和十八醇等不同芯材而构筑的复合相变材料的结构特性进行了研究,主要包括相变芯材和金属有机骨架基材之间的相互作用,芯材在金属有机骨架材料孔道内的扩散特性以及空间分布特性等。研究表明:十八酸和金属有机骨架基体之间的相互作用最强,十八醇和十八胺次之,十八烷最弱,具体体现在相变芯材分子与金属有机骨架材料之间的相互作用能,回转半径,分子动能,自扩散系数以及热容等众多方面,此外,当芯材分子间相互作用和金属有机骨架材料与芯材之间的相互作用达到平衡时,芯材分子在孔道内处于较为自由的状态,有利于扩散的进行,进而有利于芯材的结晶。      

铁液非均质形核的热力学研究

利用电解纯铁,通过高温钼丝炉制备了含有不同种类、不同含量异质核心的试样.利用差热分析方法测定了试样在相同冷却速度条件下的过冷度.从理论上比较了铁液凝固热力学驱动力的不同计算方法及误差,计算了铁液在凝固过程中的热力学驱动力,形核功和临界晶核半径.     

Cation transport: an example of structural based selectivity

Through the high-resolution structure of the gramicidin A channel in lamellar phase lipids and the characterization of specific ion peptide interactions, fundamental principles for ion channel selectivity and conductance efficiency are illustrated with atomic resolution detail. Delocalized cation binding in the first turn of the helix reduces the unfavorable entropy contribution upon binding. Stepwise dehydration minimizes the energy barrier for cation entry and provides valence selectivity in this channel. Three or more water molecules in the monovalent cation binding site result in flexibility in the cation solvation environment causing weak cation size selectivity. Lack of cation induced structural modification avoids the formation of a significant energy barrier, thus permitting efficient cation transport.     

Three-Dimensional Hydrodynamics of Meandering Compound Channels

The velocity field in meandering compound channels with overbank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields using computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. In particular, an accurate computer prediction of the velocity field could benefit studies of channel morphology and pollution transport. In this paper, a meandering channel experiment from the U.K. Flood Channel Facility is simulated using computational fluid dynamics and the predicted velocities compared with the experimental data. Particular attention is paid to the reproduction of the secondary velocities and the helical motion of the water flowing within the main channel. Sensitivity tests of mesh design, discretization scheme, and roughness height are reported, together with the turbulence characteristics of the flow.     

Role of phosphatidylethanolamine lipids in the stabilization of protein-lipid contacts

We have investigated the effect of lipids with phosphatidylethanolamine (PE) head groups on the stabilization of contacts between the tryptophan side chains of gramicidin and the lipid head groups. We initially developed two fluorescence methods that can be correlated to the spontaneous curvature of DOPC/DOPE and DOPC/DOPEme. One is based on bilayer structure and measures the rotational motion of a probe located close to the membrane surface relative to a more deeply-buried probe. The second is based on surface hydration/polarity and measures the emission energy of a polarity-sensitive probe located on the membrane surface. We used these methods to estimate the pseudo-curvature (i.e., curvature obtained by fluorescence measurements) of lipids with dimyristyl chains, and their pressure and temperature dependence. We then investigated the stability of gramicidin tryptophan-lipid contacts in DMPC/DMPE as a function of temperature and pressure. Stability was assessed by tryptophan rotational motion as determined by fluorescence anisotropy, since rotational motion is limited when the indoles are hydrogen bonded to the lipid head groups. The results suggest that the presence of PE lipids destabilizes these contacts due to either their smaller size relative to PC head groups, or their tendency to self-interact. Fluorescence quenching studies support these results.