Reinterpreting the anomalous mole fraction effect: the ryanodine receptor case study

Electrostatic correlations in electrolytes: Contribution of screening ion interactions to the excess chemical potential

A new theory for the electrostatic component of the chemical potential for homogeneous electrolytes modeled with the primitive model is developed. This Mean Countershell Approximation (MCSA) is an analytic theory derived by including the interactions between the ions' screening clouds. At molar concentrations, these contribute substantially to the excess chemical potential but are absent in classical Debye-Hückel and Mean Spherical Approximation (MSA) theories. Simulations show that the MCSA is highly accurate, including at the low dielectric constants of ionic liquids. While sharing a mathematical framework with the MSA, the MCSA has simpler formulas and is qualitatively more accurate when there is ion size asymmetry.

The ZAR1 resistosome is a calcium-permeable channel triggering plant immune signaling

Nucleotide-binding, leucine-rich repeat receptors (NLRs) are major immune receptors in plants and animals. Upon activation, the Arabidopsis NLR protein ZAR1 forms a pentameric resistosome in vitro and triggers immune responses and cell death in plants. In this study, we employed single-molecule imaging to show that the activated ZAR1 protein can form pentameric complexes in the plasma membrane. The ZAR1 resistosome displayed ion channel activity in Xenopus oocytes in a manner dependent on a conserved acidic residue Glu11 situated in the channel pore. Pre-assembled ZAR1 resistosome was readily incorporated into planar lipid-bilayers and displayed calcium-permeable cation-selective channel activity. Furthermore, we show that activation of ZAR1 in the plant cell led to Glu11-dependent Ca²⁺ influx, perturbation of subcellular structures, production of reactive oxygen species, and cell death. The results thus support that the ZAR1 resistosome acts as a calcium-permeable cation channel to trigger immunity and cell death.

Specific adsorption of trivalent cations in biological nanopores determines conductance dynamics and reverses ionic selectivity

Adsorption processes are central to ionic transport in industrial and biological membrane systems. Multivalent cations modulate the conductive properties of nanofluidic devices through interactions with charged surfaces that depend principally on the ion charge number. Considering that ion channels are specialized valves that demand a sharp specificity in ion discrimination, we investigate the adsorption dynamics of trace amounts of different salts of trivalent cations in biological nanopores. We consider here OmpF from Escherichia coli, an archetypical protein nanopore, to probe the specificity of biological nanopores to multivalent cations. We systematically compare the effect of three trivalent electrolytes on OmpF current-voltage relationships and characterize the degree of rectification induced by each ion. We also analyze the open channel current noise to determine the existence of equilibrium/non-equilibrium mechanisms of ion adsorption and evaluate the extent of charge inversion through selectivity measurements. We show that the interaction of trivalent electrolytes with biological nanopores occurs via ion-specific adsorption yielding differential modulation of ion conduction and selectivity inversion. We also demonstrate the existence of non-equilibrium fluctuations likely related to ion-dependent trapping-detrapping processes. Our study provides fundamental information relevant to different biological and electrochemical systems where transport phenomena involve ion adsorption in charged surfaces under nanoscale confinement.

Modeling the Device Behavior of Biological and Synthetic Nanopores with Reduced Models

Biological ion channels and synthetic nanopores are responsible for passive transport of ions through a membrane between two compartments. Modeling these ionic currents is especially amenable to reduced models because the device functions of these pores, the relation of input parameters (e.g., applied voltage, bath concentrations) and output parameters (e.g., current, rectification, selectivity), are well defined. Reduced models focus on the physics that produces the device functions (i.e., the physics of how inputs become outputs) rather than the atomic/molecular-scale physics inside the pore. Here, we propose four rules of thumb for constructing good reduced models of ion channels and nanopores. They are about (1) the importance of the axial concentration profiles, (2) the importance of the pore charges, (3) choosing the right explicit degrees of freedom, and (4) creating the proper response functions. We provide examples for how each rule of thumb helps in creating a reduced model of device behavior.

The mixture effect on ionic selectivity and permeability of nanotubes

Ion-selective nanotubes have great potential in applications such as ion separation, desalination, and power generation. However, their performance is often limited by the deteriorated selectivity in mixed salt solutions. To reveal the underlying mechanism of the mixture effect on ion transport through nanotubes, we perform molecular dynamics (MD) simulations on ion transport through carbon nanotubes (CNTs) and polymer nanopores with a pore diameter of ∼1 nm and a charge density of -1 e nm^-2. Based on the simulation results, when a single salt solution is replaced by a mixed salt solution, the ionic selectivity drops as the permeability of higher permeable ions decreases much greater than that of lower permeable ions. This is because the adsorption of lower permeable ions on the inner surface of nanotubes blocks the ion flux and increases the entrance barrier to the nanotube, and the adsorption is significantly reduced in the mixed salt solution. Such a reduction results from the occupancy of higher permeable ions on the adsorption sites as they have a higher adsorption tendency albeit weaker adsorption compared with lower permeable ions. These studies will help design the next generation of nanostructures to circumvent the mixture effect and show high permeability and selectivity in real applications.

Energetics of counterion adsorption in the electrical double layer

The energetics of the electrical double layer (EDL) is studied in a systematic way to define how different components of the chemical potential help or hinder cation adsorption at a negatively charged wall. Specifically, the steric (i.e., excluded-volume interactions), mean electrostatic, and screening (i.e., electrostatic correlations beyond the mean field) components were computed using classical density functional theory of the primitive model of ions (i.e., ions as charged, hard spheres in a background dielectric). The reduced physics of the primitive model allows for an extensive analysis over a large parameter space: cation valences +1, +2, and +3, cation diameters 0.15, 0.30, 0.60, and 0.90 nm, bulk concentrations ranging from 1 µM to 1M, and surface charges ranging from 0 to -0.50 C/m². Our results show that all components are necessary to understand the physics of the EDL. The screening component is always significant; for small monovalent cations such as K⁺, it is generally much larger than the steric component, and for multivalent ions, charge inversion cannot occur without it. At moderate surface charges, the screening component makes the electrostatic potential less negative than in classical Poisson-Boltzmann theory, sometimes even positive (charge inversion). At high surface charges, this is overcome by the repulsive potential of the steric component as the first ion layer becomes extremely crowded. Large negative electrostatic potentials counteract this to draw even more cations into the first layer. Although we used an approximate model of the EDL, the physics inherent in these trends appears to be quite general.

Multiscale analysis of the effect of surface charge pattern on a nanopore's rectification and selectivity properties: From all-atom model to Poisson-Nernst-Planck

We report a multiscale modeling study for charged cylindrical nanopores using three modeling levels that include (1) an all-atom explicit-water model studied with molecular dynamics, and reduced models with implicit water containing (2) hard-sphere ions studied with the Local Equilibrium Monte Carlo simulation method (computing ionic correlations accurately), and (3) point ions studied with Poisson-Nernst-Planck theory (mean-field approximation). We show that reduced models are able to reproduce device functions (rectification and selectivity) for a wide variety of charge patterns, that is, reduced models are useful in understanding the mesoscale physics of the device (i.e., how the current is produced). We also analyze the relationship of the reduced implicit-water models with the explicit-water model and show that diffusion coefficients in the reduced models can be used as adjustable parameters with which the results of the explicit- and implicit-water models can be related. We find that the values of the diffusion coefficients are sensitive to the net charge of the pore but are relatively transferable to different voltages and charge patterns with the same total charge.

Selective ion permeation involves complexation with carboxylates and lysine in a model human sodium channel

Bacterial and human voltage-gated sodium channels (Navs) exhibit similar cation selectivity, despite their distinct EEEE and DEKA selectivity filter signature sequences. Recent high-resolution structures for bacterial Navs have allowed us to learn about ion conduction mechanisms in these simpler homo-tetrameric channels, but our understanding of the function of their mammalian counterparts remains limited. To probe these conduction mechanisms, a model of the human Nav1.2 channel has been constructed by grafting residues of its selectivity filter and external vestibular region onto the bacterial NavRh channel with atomic-resolution structure. Multi-μs fully atomistic simulations capture long time-scale ion and protein movements associated with the permeation of Na+ and K+ ions, and their differences. We observe a Na+ ion knock-on conduction mechanism facilitated by low energy multi-carboxylate/multi-Na+ complexes, akin to the bacterial channels. These complexes involve both the DEKA and vestibular EEDD rings, acting to draw multiple Na+ into the selectivity filter and promote permeation. When the DEKA ring lysine is protonated, we observe that its ammonium group is actively participating in Na+ permeation, presuming the role of another ion. It participates in the formation of a stable complex involving carboxylates that collectively bind both Na+ and the Lys ammonium group in a high-field strength site, permitting pass-by translocation of Na+. In contrast, multiple K+ ion complexes with the DEKA and EEDD rings are disfavored by up to 8.3 kcal/mol, with the K+-lysine-carboxylate complex non-existent. As a result, lysine acts as an electrostatic plug that partially blocks the flow of K+ ions, which must instead wait for isomerization of lysine downward to clear the path for K+ passage. These distinct mechanisms give us insight into the nature of ion conduction and selectivity in human Nav channels, while uncovering high field strength carboxylate binding complexes that define the more general phenomenon of Na+-selective ion transport in nature.

Comparison of permeation mechanisms in sodium-selective ion channels

Voltage-gated sodium channels are the molecular components of electrical signaling in the body, yet the molecular origins of Na⁺-selective transport remain obscured by diverse protein chemistries within this family of ion channels. In particular, bacterial and mammalian sodium channels are known to exhibit similar relative ion permeabilities for Na⁺ over K⁺ ions, despite their distinct signature EEEE and DEKA sequences. Atomic-level molecular dynamics simulations using high-resolution bacterial channel structures and mammalian channel models have begun to describe how these sequences lead to analogous high field strength ion binding sites that drive Na⁺ conduction. Similar complexes have also been identified in unrelated acid sensing ion channels involving glutamate and aspartate side chains that control their selectivity. These studies suggest the possibility of a common origin for Na⁺ selective binding and transport.

In silico assessment of the conduction mechanism of the Ryanodine Receptor 1 reveals previously unknown exit pathways

The ryanodine receptor 1 is a large calcium ion channel found in mammalian skeletal muscle. The ion channel gained a lot of attention recently, after multiple independent authors published near-atomic cryo electron microscopy data. Taking advantage of the unprecedented quality of structural data, we performed molecular dynamics simulations on the entire ion channel as well as on a reduced model. We calculated potentials of mean force for Ba2+, Ca2+, Mg2+, K+, Na+ and Cl- ions using umbrella sampling to identify the key residues involved in ion permeation. We found two main binding sites for the cations, whereas the channel is strongly repulsive for chloride ions. Furthermore, the data is consistent with the model that the receptor achieves its ion selectivity by over-affinity for divalent cations in a calcium-block-like fashion. We reproduced the experimental conductance for potassium ions in permeation simulations with applied voltage. The analysis of the permeation paths shows that ions exit the pore via multiple pathways, which we suggest to be related to the experimental observation of different subconducting states.

Simulation of a model nanopore sensor: Ion competition underlies device behavior

We study a model nanopore sensor with which a very low concentration of analyte molecules can be detected on the basis of the selective binding of the analyte molecules to the binding sites on the pore wall. The bound analyte ions partially replace the current-carrier cations in a thermodynamic competition. This competition depends both on the properties of the nanopore and the concentrations of the competing ions (through their chemical potentials). The output signal given by the device is the current reduction caused by the presence of the analyte ions. The concentration of the analyte ions can be determined through calibration curves. We model the binding site with the square-well potential and the electrolyte as charged hard spheres in an implicit background solvent. We study the system with a hybrid method in which we compute the ion flux with the Nernst-Planck (NP) equation coupled with the Local Equilibrium Monte Carlo (LEMC) simulation technique. The resulting NP+LEMC method is able to handle both strong ionic correlations inside the pore (including finite size of ions) and bulk concentrations as low as micromolar. We analyze the effect of bulk ion concentrations, pore parameters, binding site parameters, electrolyte properties, and voltage on the behavior of the device.

Multiscale modeling of a rectifying bipolar nanopore: explicit-water versus implicit-water simulations

In a multiscale modeling approach, we present computer simulation results for a rectifying bipolar nanopore at two modeling levels. In an all-atom model, we use explicit water to simulate ion transport directly with the molecular dynamics technique. In a reduced model, we use implicit water and apply the Local Equilibrium Monte Carlo method together with the Nernst-Planck transport equation. This hybrid method makes the fast calculation of ion transport possible at the price of lost details. We show that the implicit-water model is an appropriate representation of the explicit-water model when we look at the system at the device (i.e., input vs. output) level. The two models produce qualitatively similar behavior of the electrical current for different voltages and model parameters. Looking at the details of concentration and potential profiles, we find profound differences between the two models. These differences, however, do not influence the basic behavior of the model as a device because they do not influence the z-dependence of the concentration profiles which are the main determinants of current. These results then address an old paradox: how do reduced models, whose assumptions should break down in a nanoscale device, predict experimental data? Our simulations show that reduced models can still capture the overall device physics correctly, even though they get some important aspects of the molecular-scale physics quite wrong; reduced models work because they include the physics that is necessary from the point of view of device function. Therefore, reduced models can suffice for general device understanding and device design, but more detailed models might be needed for molecular level understanding.

Dampened activity of ryanodine receptor channels in mutant skeletal muscle lacking TRIC-A

KEY POINTS

The role of trimeric intracellular cation (TRIC) channels is not known, although evidence suggests they may regulate ryanodine receptors (RyR) via multiple mechanisms. We therefore investigated whether Tric-a gene knockout (KO) alters the single-channel function of skeletal RyR (RyR1). We find that RyR1 from Tric-a KO mice are more sensitive to inhibition by divalent cations, although they respond normally to cytosolic Ca²⁺ , ATP, caffeine and luminal Ca²⁺ . In the presence of Mg²⁺ , ATP cannot effectively activate RyR1 from Tric-a KO mice. Additionally, RyR1 from Tric-a KO mice are not activated by protein kinase A phosphorylation, demonstrating a defect in the ability of β-adrenergic stimulation to regulate sarcoplasmic reticulum (SR) Ca²⁺ -release. The defective RyR1 gating that we describe probably contributes significantly to the impaired SR Ca²⁺ -release observed in skeletal muscle from Tric-a KO mice, further highlighting the importance of TRIC-A for normal physiological regulation of SR Ca²⁺ -release in skeletal muscle.

ABSTRACT

The type A trimeric intracellular cation channel (TRIC-A) is a major component of the nuclear and sarcoplasmic reticulum (SR) membranes of cardiac and skeletal muscle, and is localized closely with ryanodine receptor (RyR) channels in the SR terminal cisternae. The skeletal muscle of Tric-a knockout (KO) mice is characterized by Ca²⁺ overloaded and swollen SR and by changes in the properties of SR Ca²⁺ release. We therefore investigated whether RyR1 gating behaviour is modified in the SR from Tric-a KO mice by incorporating native RyR1 into planar phospholipid bilayers under voltage-clamp conditions. We find that RyR1 channels from Tric-a KO mice respond normally to cytosolic Ca²⁺ , ATP, adenine, caffeine and to luminal Ca²⁺ . However, the channels are more sensitive to the inactivating effects of divalent cations, thus, in the presence of Mg²⁺ , ATP is inadequate as an activator. Additionally, channels are not characteristically activated by protein kinase A even though the phosphorylation levels of Ser2844 are similar to controls. The results of the present study suggest that TRIC-A functions as an excitatory modulator of RyR1 channels within the SR terminal cisternae. Importantly, this regulatory action of TRIC-A appears to be independent of (although additive to) any indirect consequences to RyR1 activity that arise as a result of K⁺ fluxes across the SR via TRIC-A.

Permeation Mechanisms in the TMEM16B Calcium-Activated Chloride Channels

TMEM16A and TMEM16B encode for Ca²⁺-activated Cl⁻ channels (CaCC) and are expressed in many cell types and play a relevant role in many physiological processes. Here, I performed a site-directed mutagenesis study to understand the molecular mechanisms of ion permeation of TMEM16B. I mutated two positive charged residues R573 and K540, respectively located at the entrance and inside the putative channel pore and I measured the properties of wild-type and mutant TMEM16B channels expressed in HEK-293 cells using whole-cell and excised inside-out patch clamp experiments. I found evidence that R573 and K540 control the ion permeability of TMEM16B depending both on which side of the membrane the ion substitution occurs and on the level of channel activation. Moreover, these residues contribute to control blockage or activation by permeant anions. Finally, R573 mutation abolishes the anomalous mole fraction effect observed in the presence of a permeable anion and it alters the apparent Ca²⁺-sensitivity of the channel. These findings indicate that residues facing the putative channel pore are responsible both for controlling the ion selectivity and the gating of the channel, providing an initial understanding of molecular mechanism of ion permeation in TMEM16B.

Selecting ions by size in a calcium channel: the ryanodine receptor case study

Many calcium channels can distinguish between ions of the same charge but different size. For example, when cations are in direct competition with each other, the ryanodine receptor (RyR) calcium channel preferentially conducts smaller cations such as Li(+) and Na(+) over larger ones such as K(+) and Cs(+). Here, we analyze the physical basis for this preference using a previously established model of RyR permeation and selectivity. Like other calcium channels, RyR has four aspartate residues in its GGGIGDE selectivity filter. These aspartates have their terminal carboxyl group in the pore lumen, which take up much of the available space for permeating ions. We find that small ions are preferred by RyR because they can fit into this crowded environment more easily.

Sarcoplasmic reticulum K(+) (TRIC) channel does not carry essential countercurrent during Ca(2+) release

The charge translocation associated with sarcoplasmic reticulum (SR) Ca(2+) efflux is compensated for by a simultaneous SR K(+) influx. This influx is essential because, with no countercurrent, the SR membrane potential (Vm) would quickly (<1 ms) reach the Ca(2+) equilibrium potential and SR Ca(2+) release would cease. The SR K(+) trimeric intracellular cation (TRIC) channel has been proposed to carry the essential countercurrent. However, the ryanodine receptor (RyR) itself also carries a substantial K(+) countercurrent during release. To better define the physiological role of the SR K(+) channel, we compared SR Ca(2+) transport in saponin-permeabilized cardiomyocytes before and after limiting SR K(+) channel function. Specifically, we reduced SR K(+) channel conduction 35 and 88% by replacing cytosolic K(+) for Na(+) or Cs(+) (respectively), changes that have little effect on RyR function. Calcium sparks, SR Ca(2+) reloading, and caffeine-evoked Ca(2+) release amplitude (and rate) were unaffected by these ionic changes. Our results show that countercurrent carried by SR K(+) (TRIC) channels is not required to support SR Ca(2+) release (or uptake). Because K(+) enters the SR through RyRs during release, the SR K(+) (TRIC) channel most likely is needed to restore trans-SR K(+) balance after RyRs close, assuring SR Vm stays near 0 mV.

Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

Interacting ions in biophysics: real is not ideal

Ions in water are important throughout biology, from molecules to organs. Classically, ions in water were treated as ideal noninteracting particles in a perfect gas. Excess free energy of each ion was zero. Mathematics was not available to deal consistently with flows, or interactions with other ions or boundaries. Nonclassical approaches are needed because ions in biological conditions flow and interact. The concentration gradient of one ion can drive the flow of another, even in a bulk solution. A variational multiscale approach is needed to deal with interactions and flow. The recently developed energetic variational approach to dissipative systems allows mathematically consistent treatment of the bio-ions Na(+), K(+), Ca(2+), and Cl(-) as they interact and flow. Interactions produce large excess free energy that dominate the properties of the high concentration of ions in and near protein active sites, ion channels, and nucleic acids: the number density of ions is often >10 M. Ions in such crowded quarters interact strongly with each other as well as with the surrounding protein. Nonideal behavior found in many experiments has classically been ascribed to allosteric interactions mediated by the protein and its conformation changes. The ion-ion interactions present in crowded solutions-independent of conformation changes of the protein-are likely to change the interpretation of many allosteric phenomena. Computation of all atoms is a popular alternative to the multiscale approach. Such computations involve formidable challenges. Biological systems exist on very different scales from atomic motion. Biological systems exist in ionic mixtures (like extracellular and intracellular solutions), and usually involve flow and trace concentrations of messenger ions (e.g., 10(-7) M Ca(2+)). Energetic variational methods can deal with these characteristic properties of biological systems as we await the maturation and calibration of all-atom simulations of ionic mixtures and divalents.

Ion correlations in nanofluidic channels: effects of ion size, valence, and concentration on voltage- and pressure-driven currents

The effects of ion-ion and ion-wall correlations in nanochannels are explored, specifically how they influence voltage- and pressure-driven currents and pressure-to-voltage energy conversion. Cations of different diameters (0.15, 0.3, and 0.9 nm) and different valences (+1, +2, and +3) at concentrations ranging from 10(-6) M to 1 M are considered in 50-nm- and 100-nm-wide nanoslits with wall surface charges ranging from 0 C/m(2) to -0.3 C/m(2). These parameters are typical of nanofluidic devices. Ion correlations have significant effects on device properties over large parts of this parameter space. These effects are the result of ion layering (oscillatory concentration profiles) for large monovalent cations and charge inversion (more cations in the first layer near the wall than necessary to neutralize the surface charge) for the multivalent cations. The ions were modeled as charged, hard spheres using density functional theory of fluids, and current was computed with the Navier-Stokes equations with two different no-slip conditions.

Pernicious attrition and inter-RyR2 CICR current control in cardiac muscle

In cardiac muscle cells, ryanodine receptor (RyR) mediated Ca(2+) release from the sarcoplasmic reticulum (SR) drives the contractile apparatus. Spontaneous bouts of inter-RyR Ca(2+) induced Ca(2+) release (CICR) generate an elemental unit of SR Ca(2+) release called a spark. Sparks are localized events that terminate soon after they begin. The local control of sparks is not clearly understood. In this article, we review the potential regulatory role that the changing single RyR Ca(2+) current may play. Moreover, we aggregate RyR data into a working scheme of inter-RyR CICR current control of sparks and a potential inter-RyR CICR termination mechanism that we call pernicious attrition.

Ionic Interactions Are Everywhere

Ionic solutions are dominated by interactions because they must be electrically neutral, but classical theory assumes no interactions. Biological solutions are rather like seawater, concentrated enough so that the diameter of ions also produces important interactions. In my view, the theory of complex fluids is needed to deal with the interacting reality of biological solutions.

Ionizable side chains at catalytic active sites of enzymes

Catalytic active sites of enzymes of known structure can be well defined by a modern program of computational geometry. The CASTp program was used to define and measure the volume of the catalytic active sites of 573 enzymes in the Catalytic Site Atlas database. The active sites are identified as catalytic because the amino acids they contain are known to participate in the chemical reaction catalyzed by the enzyme. Acid and base side chains are reliable markers of catalytic active sites. The catalytic active sites have 4 acid and 5 base side chains, in an average volume of 1,072 Å(3). The number density of acid side chains is 8.3 M (in chemical units); the number density of basic side chains is 10.6 M. The catalytic active site of these enzymes is an unusual electrostatic and steric environment in which side chains and reactants are crowded together in a mixture more like an ionic liquid than an ideal infinitely dilute solution. The electrostatics and crowding of reactants and side chains seems likely to be important for catalytic function. In three types of analogous ion channels, simulation of crowded charges accounts for the main properties of selectivity measured in a wide range of solutions and concentrations. It seems wise to use mathematics designed to study interacting complex fluids when making models of the catalytic active sites of enzymes.

Is ryanodine receptor a calcium or magnesium channel? Roles of K+ and Mg2+ during Ca2+ release

The ryanodine receptor (RyR) is a poorly selective channel that mediates Ca(2+) release from intracellular Ca(2+) stores. How RyR's selectivity between the physiological cations K(+), Mg(2+), and Ca(2+) affects single-channel Ca(2+) current amplitude is examined using a recent model of RyR permeation. It is found that K(+) provides the vast majority of the countercurrent (through RyR itself) that is needed to prevent the sarcoplasmic reticulum (SR) membrane potential from changing and stopping Ca(2+) release. Moreover, intra-pore competition between Ca(2+) and Mg(2+) defines single RyR Ca(2+) current amplitude. Since both [Mg(2+)] and [Ca(2+)](SR) can change during pathophysiological conditions, the RyR unitary Ca(2+) current amplitude during Ca(2+) release may change significantly due to this Ca(2+)/Mg(2+) competition. Compared to the classic action of Mg(2+) on RyR open probability, these Ca(2+) current amplitude changes have as large or larger effects on overall RyR Ca(2+) mobilization. A new aspect of RyR divalent versus monovalent selectivity is also identified where this kind of selectivity decreases as divalent concentration increases.

Current and selectivity in a model sodium channel under physiological conditions: Dynamic Monte Carlo simulations

A reduced model of a sodium channel is analyzed using Dynamic Monte Carlo simulations. These include the first simulations of ionic current under approximately physiological ionic conditions through a model sodium channel and an analysis of how mutations of the sodium channel's DEKA selectivity filter motif transform the channel from being Na(+) selective to being Ca(2+) selective. Even though the model of the pore, amino acids, and permeant ions is simplified, the model reproduces the fundamental properties of a sodium channel (e.g., 10 to 1 Na(+) over K(+) selectivity, Ca(2+) exclusion, and Ca(2+) selectivity after several point mutations). In this model pore, ions move through the pore one at a time by simple diffusion and Na(+) versus K(+) selectivity is due to both the larger K(+) not fitting well into the selectivity filter that contains amino acid terminal groups and K(+) moving more slowly (compared to Na(+)) when it is in the selectivity filter.

Analyzing the components of the free-energy landscape in a calcium selective ion channel by Widom's particle insertion method

The selectivity filter of the L-type calcium channel works as a Ca(2+) binding site with a very large affinity for Ca(2+) versus Na(+). Ca(2+) replaces half of the Na(+) ions in the filter even when these ions are present in 1 μM and 30 mM concentrations in the bath, respectively. The energetics of this strong selectivity is analyzed in this paper. We use Widom's particle insertion method to compute the space-dependent profiles of excess chemical potential in our grand canonical Monte Carlo simulations. These profiles define the free-energy landscape for the various ions. Following Gillespie [Biophys. J. 94, 1169 (2008)], the difference of the excess chemical potentials for the two competing ions defines the advantage that one of the ions has over the other in the competition for space in the crowded selectivity filter. These advantages depend on ionic bath concentrations: the ion that is present in the bath in larger quantity (Na(+)) has the "number" advantage which is balanced by the free-energy advantage of the other ion (Ca(2+)). The excess chemical potentials are decomposed into hard sphere exclusion and electrostatic components. The electrostatic terms correspond to interactions with the mean electric field produced by ions and induced charges as well to ionic correlations beyond the mean field description. Dielectrics are needed to produce micromolar Ca(2+) versus Na(+) selectivity in the L-type channel. We study the behavior of these terms with changes in bath concentrations of ions, charges, and diameters of ions, as well as geometrical parameters such as radius of the pore and the dielectric constant of the protein. Ion selectivity in calcium binding proteins probably has a similar mechanism.

Single ryanodine receptor channel basis of caffeine's action on Ca2+ sparks

Caffeine (1, 3, 7-trimethylxanthine) is a widely used pharmacological agonist of the cardiac ryanodine receptor (RyR2) Ca(2+) release channel. It is also a well-known stimulant that can produce adverse side effects, including arrhythmias. Here, the action of caffeine on single RyR2 channels in bilayers and Ca(2+) sparks in permeabilized ventricular cardiomyocytes is defined. Single RyR2 caffeine activation depended on the free Ca(2+) level on both sides of the channel. Cytosolic Ca(2+) enhanced RyR2 caffeine affinity, whereas luminal Ca(2+) essentially scaled maximal caffeine activation. Caffeine activated single RyR2 channels in diastolic quasi-cell-like solutions (cytosolic MgATP, pCa 7) with an EC(50) of 9.0 ± 0.4 mM. Low-dose caffeine (0.15 mM) increased Ca(2+) spark frequency ∼75% and single RyR2 opening frequency ∼150%. This implies that not all spontaneous RyR2 openings during diastole are associated with Ca(2+) sparks. Assuming that only the longest openings evoke sparks, our data suggest that a spark may result only when a spontaneous single RyR2 opening lasts >6 ms.

Selectivity sequences in a model calcium channel: role of electrostatic field strength

The energetics that give rise to selectivity sequences of ionic binding selectivity of Li(+), Na(+), K(+), Rb(+), and Cs(+) in a model of a calcium channel are considered. This work generalizes Eisenman's classic treatment (Biophys J 2(Suppl. 2):259, 1962) by including multiple, mobile binding site oxygens that coordinate many permeating ions (all modeled as charged, hard spheres). The selectivity filter of the model calcium channel allows the carboxyl terminal groups of glutamate and aspartate side chains to directly interact with and coordinate the permeating ions. Ion dehydration effects are represented with a Born energy between the dielectric coefficients of the selectivity filter and the bath. High oxygen concentration creates a high field strength site that prefers small ions, as in Eisenman's model. On the other hand, a low filter dielectric constant also creates a high field strength site, but this site prefers large ions, contrary to Eisenman's model. These results indicate that field strength does not have a unique effect on ionic binding selectivity sequences once entropic, electrostatic, and dehydration forces are included in the model. Thus, Eisenman's classic relationship between field strength and selectivity sequences must be supplemented with additional information about selectivity filters such as the calcium channel that has amino acid side chains mixing with ions to make a crowded permeation pathway.

Simulations of calcium channel block by trivalent cations: Gd(3+) competes with permeant ions for the selectivity filter

Current through L-type calcium channels (Ca(V)1.2 or dihydropyridine receptor) can be blocked by micromolar concentrations of trivalent cations like the lanthanide gadolinium (Gd(3+)). It has been proposed that trivalent block is due to ions competing for a binding site in both the open and closed configuration, but possibly with different trivalent affinities. Here, we corroborate this general view of trivalent block by computing conductance of a model L-type calcium channel. The model qualitatively reproduces the Gd(3+) concentration dependence and the effect that substantially more Gd(3+) is required to produce similar block in the presence of Sr(2+) (compared to Ba(2+)) and even more in the presence of Ca(2+). Trivalent block is explained in this model by cations binding in the selectivity filter with the charge/space competition mechanism. This is the same mechanism that in the model channel governs other selectivity properties. Specifically, selectivity is determined by the combination of ions that most effectively screen the negative glutamates of the protein while finding space in the midst of the closely packed carboxylate groups of the glutamate residues.

Sieving experiments and pore diameter: it's not a simple relationship

The classic sieving experiment for estimating an ion channel's diameter with successively larger ions is re-examined. Using a very reduced model of a calcium channel, it is shown that sieving experiments measure a combination of three mechanisms: the cross-sectional area available to the sieving ions (the classic interpretation), the exclusion of the sieving ions from a pore crowded with amino acid side chains that protrude into the permeation pathway, and competitive selectivity of the sieving ions with other ions in the bath (even if those are present only at trace concentrations). The latter two can be called sieving-by-crowding because they stem from the excluded volume of the amino acids in the permeation pathway. The model shows that--to a first--order approximation-sieving experiments measure the available volume inside a selectivity filter, rather than the available cross-sectional area. The two are only the same if the narrow part of the pore does not have flexible amino acid side chains interacting directly with the permeant ions; this may be true of potassium channels, but not calcium, sodium, and other channels with "crowded" selectivity filters.

Protein structure and ionic selectivity in calcium channels: selectivity filter size, not shape, matters

Calcium channels have highly charged selectivity filters (4 COO(-) groups) that attract cations in to balance this charge and minimize free energy, forcing the cations (Na(+) and Ca(2+)) to compete for space in the filter. A reduced model was developed to better understand the mechanism of ion selectivity in calcium channels. The charge/space competition (CSC) mechanism implies that Ca(2+) is more efficient in balancing the charge of the filter because it provides twice the charge as Na(+) while occupying the same space. The CSC mechanism further implies that the main determinant of Ca(2+) versus Na(+) selectivity is the density of charged particles in the selectivity filter, i.e., the volume of the filter (after fixing the number of charged groups in the filter). In this paper we test this hypothesis by changing filter length and/or radius (shape) of the cylindrical selectivity filter of our reduced model. We show that varying volume and shape together has substantially stronger effects than varying shape alone with volume fixed. Our simulations show the importance of depletion zones of ions in determining channel conductance calculated with the integrated Nernst-Planck equation. We show that confining the protein side chains with soft or hard walls does not influence selectivity.