Microscopic calculation of ion-transport rates in membrane channels

A method, based on rate theory, is described by which transport rates in ion channels can be calculated using only microscopic parameters, such as atomic coordinates, force constants and intermolecular energy parameters. The channel is treated as a system of elastically bound ligands interacting with the ion by coulombic and Lennard-Jones forces. Jump frequencies of the ion are obtained from the potential mean force which represents a thermal average over the different configurations of the ligand system. The method is illustrated by application to a special channel model, helical arrangement of dipolar ligands, which can be tilted toward the channel axis against harmonic restoring force. The jump frequency is found to be a non-monotonous function of ion radius. Furthermore, the ion specificity of the channel strongly depends on whether the ligand system is 'hard' or 'soft', i.e., on the extent to which the interaction with the ion can lead to a reorientation of the ligand groups.     

Chemical dynamic approach to synergetics and instability in biological systems

Based on Haken's theory, self-organization or synergetics is discussed using chemical dynamics to represent an autocatalytic reaction. In a simple case the changes in a self-organizing system are given by a set of two rate equations for a primary and a partial system. When these systems mutually form a feedback loop under the adiabatic condition, the rate equation of self-organization is described by a generalized Gibbs' free energy change delta U (delta x) followed by the reaction. The sign of the parameter k'3 (k0-kex; k0, kex: rate constants with or without an external stimulus) determines the instability of the coupled system in quasi-equilibrium (k'3 approximately greater than 0; k0 greater than kex). When the product exceeds the threshold (k'3 less than 0; k0 less than kex), the system transfers into a new state, or a phase transition appears. Considering the Boltzmann distribution, the transition parameter k'3 is evaluated by an average distribution of the states and the instability is discussed using the reaction velocities vqe and vqe in the quasi-equilibrium state. As an example of this model membrane excitation is discussed briefly.     

A functional NMR for membrane proteins: dynamics,ligand binding,and allosteric modulation

By nature of conducting ions, transporting substrates and transducing signals, membrane channels, transporters and receptors are expected to exhibit intrinsic conformational dynamics. It is therefore of great interest and importance to understand the various properties of conformational dynamics acquired by these proteins, for example, the relative population of states, exchange rate, conformations of multiple states, and how small molecule ligands modulate the conformational exchange. Because small molecule binding to membrane proteins can be weak and/or dynamic, structural characterization of these effects is very challenging. This review describes several NMR studies of membrane protein dynamics, ligand‐induced conformational rearrangements, and the effect of ligand binding on the equilibrium of conformational exchange. The functional significance of the observed phenomena is discussed.     

How lipophilic cannabinergic ligands reach their receptor sites

It is postulated that lipophilic ligands reach their sites of action on membrane-bound functional proteins through fast lateral diffusion across the membrane bilayer. We have shown using NMR experiments that such ligands when incorporated in a membrane system assume a preferred orientation and conformation. While occupying a specific location within the bilayer, these molecules undergo fast lateral diffusion which allows them to engage in productive interactions with their respective protein sites of action. The proposed model is discussed using a group of classical and non-classical cannabinoids as well as the endogenous cannabinoid ligand anandamide.     

Modulation of TRPV2 by endogenous and exogenous ligands: A computational study

Transient receptor potential vanilloid (TRPV) channels play various important roles in human physiology. As membrane proteins, these channels are modulated by their endogenous lipid environment as the recent wealth of structural studies has revealed functional and structural lipid binding sites. Additionally, it has been shown that exogenous ligands can exchange with some of these lipids to alter channel gating. Here, we used molecular dynamics simulations to examine how one member of the TRPV family, TRPV2, interacts with endogenous lipids and the pharmacological modulator cannabidiol (CBD). By computationally reconstituting TRPV2 into a typical plasma membrane environment, which includes phospholipids, cholesterol, and phosphatidylinositol (PIP) in the inner leaflet, we showed that most of the interacting surface lipids are phospholipids without strong specificity for headgroup types. Intriguingly, we observed that the C-terminal membrane proximal region of the channel binds preferentially to PIP lipids. We also modelled two structural lipids in the simulation: one in the vanilloid pocket and the other in the voltage sensor-like domain (VSLD) pocket. The simulation shows that the VSLD lipid dampens the fluctuation of the VSLD residues, while the vanilloid lipid exhibits heterogeneity both in its binding pose and in its influence on protein dynamics. Addition of CBD to our simulation system led to an open selectivity filter and a structural rearrangement that includes a clockwise rotation of the ankyrin repeat domains, TRP helix, and VSLD. Together, these results reveal the interplay between endogenous lipids and an exogenous ligand and their effect on TRPV2 stability and channel gating.     

Group separation of peptides by ligand-exchange chromatography with a Sephadex containing N-(2-pyridylmethyl)glycine

The synthesis of 2-hydroxy-3[N-(2-pyridylmethyl)glycine]propyl Sephadex ether--a new chelating resin--is described. This resin has been employed in the form of its Cu2+ complex to separate peptides, as a group, from alpha-amino acids and NaCl. Ninety-seven ligands of different structures were separated chromatographically at room temperature. It was shown that two structural parameters of the ligands control the separation process, namely, the presence of ligand donor groups and the possibility for them to form chelate rings of suitable size. Separation of peptides from alpha-, gamma-, delta-amino acids, N-acetyl derivatives of amino acids (except N-Ac-Trp), and NaCl is possible if the peptides fulfill the following structural requirements: the peptide molecule must have a free terminal amino group; a carbonyl group (of the peptide linkage) must be situated in the alpha- or beta-position of the free amino group; and the peptide may not contain an imidazole residue (except Gly-Gly-His). A relationship was found between the log k' and the corresponding pKHHL, log KCuCuL, and log KCuBipyCuBipyL values. Interpretation of the different K' values was possible based on the different basicities of the terminal amino groups and on the structures of the different side chains of the peptides.     

Interactions of drugs and toxins with permeant ions in potassium, sodium, and calcium channels

Ion channels in cell membranes are targets for a multitude of ligands including naturally occurring toxins, illicit drugs, and medications used to manage pain and treat cardiovascular, neurological, autoimmune, and other health disorders. In the past decade, the x-ray crystallography revealed 3D structures of several ion channels in their open, closed, and inactivated states, shedding light on mechanisms of channel gating, ion permeation and selectivity. However, atomistic mechanisms of the channel modulation by ligands are poorly understood. Increasing evidence suggest that cationophilic groups in ion channels and in some ligands may simultaneously coordinate permeant cations, which form indispensible (but underappreciated) components of respective receptors. This review describes ternary ligand-metal-channel complexes predicted by means of computer-based molecular modeling. The models rationalize a large body of experimental data including paradoxes in structure-activity relationships, effects of mutations on the ligand action, sensitivity of the ligand action to the nature of current-carrying cations, and action of ligands that bind in the ion-permeation pathway but increase rather than decrease the current. Recent mutational and ligand-binding experiments designed to test the models have confirmed the ternary-complex concept providing new knowledge on physiological roles of metal ions and atomistic mechanisms of action of ion channel ligands.     

How subunits cooperate in cAMP-induced activation of homotetrameric HCN2 channels

Hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels are tetrameric membrane proteins that generate electrical rhythmicity in specialized neurons and cardiomyocytes. The channels are primarily activated by voltage but are receptors as well, binding the intracellular ligand cyclic AMP. The molecular mechanism of channel activation is still unknown. Here we analyze the complex activation mechanism of homotetrameric HCN2 channels by confocal patch-clamp fluorometry and kinetically quantify all ligand binding steps and closed-open isomerizations of the intermediate states. For the binding affinity of the second, third and fourth ligand, our results suggest pronounced cooperativity in the sequence positive, negative and positive, respectively. This complex interaction of the subunits leads to a preferential stabilization of states with zero, two or four ligands and suggests a dimeric organization of the activation process: within the dimers the cooperativity is positive, whereas it is negative between the dimers.     

The FPR2-specific ligand MMK-1 activates the neutrophil NADPH-oxidase,but triggers no unique pathway for opening of plasma membrane calcium channels

Human neutrophils express formyl peptide receptor 1 and 2 (FPR1 and FPR2), two highly homologous G-protein-coupled cell surface receptors important for the cellular recognition of chemotactic peptides. They share many functional as well as signal transduction features, but some fundamental differences have been described. One such difference was recently presented when the FPR2-specific ligand MMK-1 was shown to trigger a unique signal in neutrophils [S. Partida-Sanchez, P. Iribarren, M.E. Moreno-Garcia, et al., Chemotaxis and calcium responses of phagocytes to formyl peptide receptor ligands is differentially regulated by cyclic ADP ribose, J. Immunol. 172 (2004) 1896–1906]. This signal bypassed the emptying of the intracellular calcium stores, a route normally used to open the store-operated calcium channels present in the plasma membrane of neutrophils. Instead, the binding of MMK-1 to FPR2 was shown to trigger a direct opening of the plasma membrane channels. In this report, we add MMK-1 to a large number of FPR2 ligands that activate the neutrophil superoxide-generating NADPH-oxidase. In contrast to earlier findings we show that the transient rise in intracellular free calcium induced by MMK-1 involves both a release of calcium from intracellular stores and an opening of channels in the plasma membrane. The same pattern was obtained with another characterized FPR2 ligand, WKYMVM, and it is also obvious that the two formyl peptide receptor family members trigger the same type of calcium response in human neutrophils.     

On the influence of polyvalent ligands on membrane curvature

The suggestion is made that a polyvalent ligand attached to a membrane will induce a curvature in that membrane which is concave toward the side to which that ligand is bound. This article presents a semiquantitative thermodynamic analysis predicting this effect for a simple system. The criterion for equilibrium of the ligand membrane complex is stated and for the simple system this is calculated for an arbitrary set of parameters. The influence of changes in these parameters is discussed. The energies calculated for this effect are of the order of 0·1 kcal/mol suggesting that for observable effects on curvature an array of such ligands will be needed. Some real systems in which this effect may be playing a role are discussed.     

Parameter dependence of myoglobin-facilitated transport of oxygen in the presence of membranes

Some physicochemical entities involved in the facilitated transport of oxygen along a transport path z1 less than or equal to z less than or equal to zn with membranes impermeable to myoglobin at zi, i = 1,...,n, were identified in an earlier paper [Math. Biosci. 95:209 (1989)]. These entities are the partition between the oxygen and oxymyoglobin flows, the flow transfers taking place near a membrane, and the membrane resistance. Expressions for these entities were obtained that explicitly involve the parameters of the system. In this paper, for the case of prescribed boundary oxygen concentrations x1 and xn, these expressions are incorporated into (i) an explicit representation for the facilitated transport value in terms of the difference, E(x1)-E(xn), between the boundary oxymyoglobin equilibrium values and the sum, gamma, of the membrane resistances, and (ii) a representation for the distribution of the membrane oxygen concentrations xi at zi, i = 2,...,n-1. This makes it possible to analyze the manner in which the facilitated transport depends on the parameters. For a physiological range of parameter values, the facilitated transport was found to increase as either the oxygen-myoglobin association rate constant k', the dissociation rate constant k, the oxygen diffusion coefficient, or the oxymyoglobin diffusion coefficient increases. Thus, the facilitated transport does not depend directly on ratios of chemical and diffusion coefficients. Although the increase in the oxygen diffusion coefficient does not per se affect the chemical conductance, it diminishes the membrane resistance through an interface feature, with a resulting increase in the facilitated transport. For a larger range of values of k' and k, the dependences of the facilitated transport on k' and on k are both biphasic and are similar in shape. However, the mechanisms involved are different: The associated changes in E(x1)-E(xn) and in gamma that result from the increase in k' are opposite to those that result from an increase in k. The use of (i) and (ii) permits, also, discrimination between the different roles of the physicochemical entities involved in a given facilitated transport change. In some cases (e.g., the decreasing phase of the facilitated transport as k' increases), this change depends in an essential manner on a secondary modification of the profile xi, i = 1,...,n, along the transport path.     

A fluctuation analysis study of the development of amiloride-sensitive Na+ transport in the skin of larval bullfrogs (Rana catesbeiana)

In the presence of the Na+ -channel blocker amiloride, the short-circuit current across the skins of bullfrog tadpoles in metamorphic stages XIX-XXIV was subjected to fluctuation analysis. The resulting power spectra contained a Lorentzian component of which the plateau value (S0) decreased while the corner frequency (fc) increased as the mucosal amiloride concentration was increased from 0.5 to 24 microM. From the linear relationship between the fc values and the amiloride concentrations it was possible to determine the binding (k'01) and unbinding (k10) constants for amiloride to its receptor on the Na+ channel. With these parameters as well as short-circuit current and S0 values, the current through the individual Na+ channels (i) was calculated (average 0.58 pA). It did not increase significantly during late metamorphosis. The density of Na+ channels (M) in the apical membrane, on the other hand, increased significantly. It would appear that the increase in short-circuit current which occurs at this time is due primarily to an increase in amiloride-blockable Na+ channels. Unexpectedly, a Lorentzian component could be fitted to power spectra in amiloride-treated skins (stages XIX-XXI) which showed no amiloride-sensitive short-circuit current. Moreover, the typical increase in fc with the amiloride concentration did not occur in these animals.     

Validation of an Allosteric Binding Site of Src Kinase Identified by Unbiased Ligand Binding Simulations

Allostery plays a primary role in regulating protein activity, making it an important mechanism in human disease and drug discovery. Identifying allosteric regulatory sites to explore their biological significance and therapeutic potential is invaluable to drug discovery; however, identification remains a challenge. Allosteric sites are often “cryptic” without clear geometric or chemical features. Since allosteric regulatory sites are often less conserved in protein kinases than the orthosteric ATP binding site, allosteric ligands are commonly more specific than ATP competitive inhibitors. We present a generalizable computational protocol to predict allosteric ligand binding sites based on unbiased ligand binding simulation trajectories. We demonstrate the feasibility of this protocol by revisiting our previously published ligand binding simulations using the first identified viral proto-oncogene, Src kinase, as a model system. The binding paths for kinase inhibitor PP1 uncovered three metastable intermediate states before binding the high-affinity ATP-binding pocket, revealing two previously known allosteric sites and one novel site. Herein, we validate the novel site using a combination of virtual screening and experimental assays to identify a V-type allosteric small-molecule inhibitor that targets this novel site with specificity for Src over closely related kinases. This study provides a proof-of-concept for employing unbiased ligand binding simulations to identify cryptic allosteric binding sites and is widely applicable to other protein–ligand systems.     

Differences between apo and three holo forms of the intestinal fatty acid binding protein seen by molecular dynamics computer calculations

It is commonly believed that binding affinity can be estimated by consideration of local changes of ligand and protein. This paper discusses a set of molecular dynamics simulations of intestinal fatty acid binding protein addressing the protein's response to presence or absence of different ligands. A 5-ns simulation was performed of the protein without a ligand, and three simulations (one 5-ns and two 2-ns) were performed with different fatty acids bound. The results indicate that, although the basic protein structure is unchanged by the presence of the ligand, other properties are significantly affected by ligand binding. For example, zero-time covariance patterns between protein, bound waters, and ligand vary between the different simulations. Moreover, the interaction energies between ligand and specific residues indicate that different ligands are stabilized in different ways. In sum, the results suggest that binding thermodynamics within this system will need to be calculated not from a subset of nearby protein:ligand interactions, but will depend on a knowledge of the motions coupling together water, protein, and ligand.     

The diagram methods for the evaluation of exchange fluxes in membrane transport systems

In this paper theoretical methods for the evaluation of fluxes of ligand exchange processes in a transporter-mediated membrane transport system are studied. The exchange process of a transport system is defined as a set of reactions of the transporters in the membrane that do not result in a complete turnover and must include the following consecutive sequence of steps: the binding of ligands from bath 1 and a subsequent release of bound ligands to bath 2 followed immediately by a binding of ligands from bath 2 and a subsequent release of bound ligands to bath 1. Thus, unlike the ordinary one-way cycles, the completion of an exchange process does not result in a net transport of ligands across the membrane. However, since it exchanges the ligands between the two baths, the exchange process of a transport system is closely related to the operational tracer flux of labelled ligands in the system. In this paper, both the numerical and the analytical procedures for the evaluation of exchange fluxes in any given biochemical diagram are discussed. In particular, we show that the exchange fluxes of a given kinetic diagram, like one-way cycle fluxes, can be expressed analytically in terms of the rate constants of the diagram with the use of either the original diagram or an expanded diagram. The diagram methods presented in this paper should be very useful in analyzing the mechanisms of transporter-mediated transport systems when tracer flux data are available.     

Three's company: two or more unrelated receptors pair with the same ligand

Intercellular communication relies on signal transduction mediated by extracellular ligands and their receptors. Although the ligand-receptor interaction is usually a two-player event, there are selective examples of one polypeptide ligand interacting with more than one phylogenetically unrelated receptor. Likewise, a few receptors interact with more than one polypeptide ligand, and sometimes with more than one coreceptor, likely through an interlocking of unique protein domains. Phylogenetic analyses suggest that for certain triumvirates, the matching events could have taken place at different evolutionary times. In contrast to a few polypeptide ligands interacting with more than one receptor, we found that many small nonpeptide ligands have been paired with two or more plasma membrane receptors, nuclear receptors, or channels. The observation that many small ligands are paired with more than one receptor type highlights the utilitarian use of a limited number of cellular components during metazoan evolution. These conserved ligands are ubiquitous cell metabolites likely favored by natural selection to establish novel regulatory networks. They likely possess structural features useful for designing agonistic and antagonistic drugs to target diverse receptors.     

A note on modeling mechano-chemical transduction with an application to a skin receptor

Strain-sensitive (also called stretch-sensitive) ionic channels are thought to be present in various mechanoreceptors. The gating of these channels is precipitated by mechanical strains, as opposed to the usual activation processes of changes in membrane potential or other ligands. Below we present a class of models for the strain-activated mechanism, compare our approach to one of Sachs and Lecar (1991), and apply the gating mechanism to a model of a specific mechanoreceptor, namely a Pacinian corpuscle neurite model. The simulation experiment suggests the activation energy of the channel depends linearly, rather than nonlinearly, on the (hoop) strain in the receptor membrane.     

Notch ligand endocytosis generates mechanical pulling force dependent on dynamin, epsins, and actin

Notch signaling induced by cell surface ligands is critical to development and maintenance of many eukaryotic organisms. Notch and its ligands are integral membrane proteins that facilitate direct cell-cell interactions to activate Notch proteolysis and release the intracellular domain that directs Notch-specific cellular responses. Genetic studies suggest that Notch ligands require endocytosis, ubiquitylation, and epsin endocytic adaptors to activate signaling, but the exact role of ligand endocytosis remains unresolved. Here we characterize a molecularly distinct mode of clathrin-mediated endocytosis requiring ligand ubiquitylation, epsins, and actin for ligand cells to activate signaling in Notch cells. Using a cell-bead optical tweezers system, we obtained evidence for cell-mediated mechanical force dependent on this distinct mode of ligand endocytosis. We propose that the mechanical pulling force produced by endocytosis of Notch-bound ligand drives conformational changes in Notch that permit activating proteolysis.     

Opening mechanism of a cyclic nucleotide-gated channel based on analysis of single channels locked in each liganded state.

Cyclic nucleotide-gated channels contain four subunits, each with a binding site for cGMP or cAMP in the cytoplasmic COOH-terminal domain. Previous studies of the kinetic mechanism of activation have been hampered by the complication that ligands are continuously binding and unbinding at each of these sites. Thus, even at the single channel level, it has been difficult to distinguish changes in behavior that arise from a channel with a fixed number of ligands bound from those that occur upon the binding and unbinding of ligands. For example, it is often assumed that complex behaviors like multiple conductance levels and bursting occur only as a consequence of changes in the number of bound ligands. We have overcome these ambiguities by covalently tethering one ligand at a time to single rod cyclic nucleotide-gated channels (Ruiz, ML., and J.W. Karpen. 1997. Nature. 389:389-392). We find that with a fixed number of ligands locked in place the channel freely moves between three conductance states and undergoes bursting behavior. Furthermore, a thorough kinetic analysis of channels locked in doubly, triply, and fully liganded states reveals more than one kinetically distinguishable state at each conductance level. Thus, even when the channel contains a fixed number of bound ligands, it can assume at least nine distinct states. Such complex behavior is inconsistent with simple concerted or sequential allosteric models. The data at each level of liganding can be successfully described by the same connected state model (with different rate constants), suggesting that the channel undergoes the same set of conformational changes regardless of the number of bound ligands. A general allosteric model, which postulates one conformational change per subunit in both the absence and presence of ligand, comes close to providing enough kinetically distinct states. We propose an extension of this model, in which more than one conformational change per subunit can occur during the process of channel activation.