BioMOCA—a Boltzmann transport Monte Carlo model for ion channel simulation

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.

End-plate acetylcholine receptor: structure, mechanism, pharmacology, and disease

The synapse is a localized neurohumoral contact between a neuron and an effector cell and may be considered the quantum of fast intercellular communication. Analogously, the postsynaptic neurotransmitter receptor may be considered the quantum of fast chemical to electrical transduction. Our understanding of postsynaptic receptors began to develop about a hundred years ago with the demonstration that electrical stimulation of the vagus nerve released acetylcholine and slowed the heart beat. During the past 50 years, advances in understanding postsynaptic receptors increased at a rapid pace, owing largely to studies of the acetylcholine receptor (AChR) at the motor endplate. The endplate AChR belongs to a large superfamily of neurotransmitter receptors, called Cys-loop receptors, and has served as an exemplar receptor for probing fundamental structures and mechanisms that underlie fast synaptic transmission in the central and peripheral nervous systems. Recent studies provide an increasingly detailed picture of the structure of the AChR and the symphony of molecular motions that underpin its remarkably fast and efficient chemoelectrical transduction.

Web interface for Brownian dynamics simulation of ion transport and its applications to beta-barrel pores

Brownian dynamics (BD) based on accurate potential of mean force is an efficient and accurate method for simulating ion transport through wide ion channels. Here, a web-based graphical user interface (GUI) is presented for carrying out grand canonical Monte Carlo (GCMC) BD simulations of channel proteins: http://www.charmm-gui.org/input/gcmcbd. The webserver is designed to help users avoid most of the technical difficulties and issues encountered in setting up and simulating complex pore systems. GCMC/BD simulation results for three proteins, the voltage dependent anion channel (VDAC), α-Hemolysin (α-HL), and the protective antigen pore of the anthrax toxin (PA), are presented to illustrate the system setup, input preparation, and typical output (conductance, ion density profile, ion selectivity, and ion asymmetry). Two models for the input diffusion constants for potassium and chloride ions in the pore are compared: scaling of the bulk diffusion constants by 0.5, as deduced from previous all-atom molecular dynamics simulations of VDAC, and a hydrodynamics based model (HD) of diffusion through a tube. The HD model yields excellent agreement with experimental conductances for VDAC and α-HL, while scaling bulk diffusion constants by 0.5 leads to underestimates of 10-20%. For PA, simulated ion conduction values overestimate experimental values by a factor of 1.5-7 (depending on His protonation state and the transmembrane potential), implying that the currently available computational model of this protein requires further structural refinement.

Intramembrane proton binding site linked to activation of bacterial pentameric ion channel

Prokaryotic orthologs of eukaryotic Cys-loop receptor channels recently emerged as structural and mechanistic surrogates to investigate this superfamily of intercellular signaling proteins. Here, we examine proton activation of the prokaryotic ortholog GLIC using patch clamp electrophysiology, mutagenesis, and molecular dynamics (MD) simulations. Whole-cell current recordings from human embryonic kidney (HEK) 293 cells expressing GLIC show half-maximal activation at pH 6, close to the pK(a) of histidine, implicating the three native His residues in proton sensing linked to activation. The mutation H235F abolishes proton activation, H277Y is without effect, and all nine mutations of His-127 prevent expression on the cell surface. In the GLIC crystal structure, His-235 on transmembrane (TM) α-helix 2, hydrogen bonds to the main chain carbonyl oxygen of Ile-259 on TM α-helix 3. MD simulations show that when His-235 is protonated, the hydrogen bond persists, and the channel remains in the open conformation, whereas when His-235 is deprotonated, the hydrogen bond dissociates, and the channel closes. Mutations of the proximal Tyr-263, which also links TM α-helices 2 and 3 via a hydrogen bond, alter proton sensitivity over a 1.5 pH unit range. MD simulations show that mutations of Tyr-263 alter the hydrogen bonding capacity of His-235. The overall findings show that His-235 in the TM region of GLIC is a novel proton binding site linked to channel activation.

Brownian dynamics simulations of ion transport through the VDAC

It is important to gain a physical understanding of ion transport through the voltage-dependent anion channel (VDAC) because this channel provides primary permeation pathways for metabolites and electrolytes between the cytosol and mitochondria. We performed grand canonical Monte Carlo/Brownian dynamics (GCMC/BD) simulations to explore the ion transport properties of human VDAC isoform 1 (hVDAC1; PDB:2K4T) embedded in an implicit membrane. When the MD-derived, space-dependent diffusion constant was used in the GCMC/BD simulations, the current-voltage characteristics and ion number profiles inside the pore showed excellent agreement with those calculated from all-atom molecular-dynamics (MD) simulations, thereby validating the GCMC/BD approach. Of the 20 NMR models of hVDAC1 currently available, the third one (NMR03) best reproduces both experimental single-channel conductance and ion selectivity (i.e., the reversal potential). In addition, detailed analyses of the ion trajectories, one-dimensional multi-ion potential of mean force, and protein charge distribution reveal that electrostatic interactions play an important role in the channel structure and ion transport relationship. Finally, the GCMC/BD simulations of various mutants based on NMR03 show good agreement with experimental ion selectivity. The difference in ion selectivity between the wild-type and the mutants is the result of altered potential of mean force profiles that are dominated by the electrostatic interactions.

Single-channel current through nicotinic receptor produced by closure of binding site C-loop

We investigated the initial coupling of agonist binding to channel gating of the nicotinic acetylcholine receptor using targeted molecular-dynamics (TMD) simulation. After TMD simulation to accelerate closure of the C-loops at the agonist binding sites, the region of the pore that passes through the cell membrane expands. To determine whether the structural changes in the pore result in ion conduction, we used a coarse-grained ion conduction simulator, Biology Boltzmann transport Monte Carlo, and applied it to two structural frames taken before and after TMD simulation. The structural model before TMD simulation represents the channel in the proposed "resting" state, whereas the model after TMD simulation represents the channel in the proposed "active" state. Under external voltage biases, the channel in the "active" state was permeable to cations. Our simulated ion conductance approaches that obtained experimentally and recapitulates several functional properties characteristic of the nicotinic acetylcholine receptor. Thus, closure of the C-loop triggers a structural change in the channel sufficient to account for the open channel current. This approach of applying Biology Boltzmann transport Monte Carlo simulation can be used to further investigate the binding to gating transduction mechanism and the structural bases for ion selection and translocation.

Simulation of charge transport in ion channels and nanopores with anisotropic permittivity

Ion channels are part of nature's solution for regulating biological environments. Every ion channel consists of a chain of amino acids carrying a strong and sharply varying permanent charge, folded in such a way that it creates a nanoscopic aqueous pore spanning the otherwise mostly impermeable membranes of biological cells. These naturally occurring proteins are particularly interesting to device engineers seeking to understand how such nanoscale systems realize device-like functions. Availability of high-resolution structural information from X-ray crystallography, as well as large-scale computational resources, makes it possible to conduct realistic ion channel simulations. In general, a hierarchy of simulation methodologies is needed to study different aspects of a biological system like ion channels. Biology Monte Carlo (BioMOCA), a three-dimensional coarse-grained particle ion channel simulator, offers a powerful and general approach to study ion channel permeation. BioMOCA is based on the Boltzmann Transport Monte Carlo (BTMC) and Particle-Particle-Particle-Mesh (P(3)M) methodologies developed at the University of Illinois at Urbana-Champaign. In this paper we briefly discuss the various approaches to simulating ion flow in channel systems that are currently being pursued by the biophysics and engineering communities, and present the effect of having anisotropic dielectric constants on ion flow through a number of nanopores with different effective diameters.

Mechanosensitive channel MscS in the open state: modeling of the transition, explicit simulations, and experimental measurements of conductance

Mechanosensitive channels of small conductance (MscS) are ubiquitous turgor pressure regulators found in many walled cells and some intracellular organelles. Escherichia coli MscS acting as a tension-activated osmolyte release valve shows a nonsaturable conductance (1.2 nS in a 39 mS/cm electrolyte) and weak preference for anions. Pursuing the transition pathways in this channel, we applied the extrapolated motion protocol (cycles of displacements, minimizations, and short simulations) to the previously generated compact resting conformation of MscS. We observed tilting and straightening of the kinked pore-forming TM3 helices during the barrel expansion. Extended all-atom simulations confirmed the stability of the open conformation in the bilayer. A 53° spontaneous axial rotation of TM3s observed after equilibration increased the width and polarity of the pore allowing for stable voltage-independent hydration and presence of both cations and anions throughout the pore. The resultant open state, characterized by a pore 1.6 nm wide, satisfied the experimental conductance and in-plane expansion. Applied transmembrane electric field (±100 to ±200 mV) in simulations produced a flow of both K⁺ and Cl⁻, with Cl⁻ current dominating at higher voltages. Electroosmotic water flux strongly correlated with the chloride current (∼8 waters per Cl⁻). The selectivity and rectification were in agreement with the experimental measurements performed in the same range of voltages. Among the charged residues surrounding the pore, only K169 was found to contribute noticeably in the rectification. We conclude that (a) the barrel expansion involving tilting, straightening, and rotation of TM3s provides the geometry and electrostatics that accounts for the conductive properties of the open pore; (b) the observed regimen of ion passage through the pore is similar to electrodiffusion, thus macroscopic estimations closely approximate the experimental and molecular dynamics-simulated conductances; (c) increased interaction of the opposing ionic fluxes at higher voltages may result in selectivities stronger than measured near the reversal potential.

Steric selectivity in Na channels arising from protein polarization and mobile side chains

Monte Carlo simulations of equilibrium selectivity of Na channels with a DEKA locus are performed over a range of radius R and protein dielectric coefficient epsilon(p). Selectivity arises from the balance of electrostatic forces and steric repulsion by excluded volume of ions and side chains of the channel protein in the highly concentrated and charged (approximately 30 M) selectivity filter resembling an ionic liquid. Ions and structural side chains are described as mobile charged hard spheres that assume positions of minimal free energy. Water is a dielectric continuum. Size selectivity (ratio of Na+ occupancy to K+ occupancy) and charge selectivity (Na+ to Ca2+) are computed in concentrations as low as 10(-5) M Ca2+. In general, small R reduces ion occupancy and favors Na+ over K+ because of steric repulsion. Small epsilon(p) increases occupancy and favors Na+ over Ca2+ because protein polarization amplifies the pore's net charge. Size selectivity depends on R and is independent of epsilon(p); charge selectivity depends on both R and epsilon(p). Thus, small R and epsilon(p) make an efficient Na channel that excludes K+ and Ca2+ while maximizing Na+ occupancy. Selectivity properties depend on interactions that cannot be described by qualitative or verbal models or by quantitative models with a fixed free energy landscape.

Temporal Analysis of Valence & Electrostatics in Ion-Motive Sodium Pump

The present work establishes a unique framework for the simulation study of ion-motive pumps in general and the Na(+)/K(+)-ATPase, or sodium pump, in particular. We shall discuss the implications of electrostatic analysis, valence calculations, and protein cavity data, each carried over data extracted from molecular dynamics simulations, on the structure-function relationship of Na(+)/K(+)-ATPase. These diverse set of tools will be used to investigate atomic-level characteristics that remain undetermined such as ion binding and accessibility.

Ion conduction through MscS as determined by electrophysiology and simulation

The mechanosensitive channel of small conductance (MscS) is a membrane protein thought to act as a safety valve in bacteria, regulating the release of ions and small solutes when gated by membrane tension under challenging osmotic conditions. The influence of voltage on channel activation and the functional state depicted by the available crystal structure of MscS remain debated. Therefore, in an effort to relate electrophysiological measurements on MscS and properties of the MscS crystal conformation, we report here MscS's response to voltage and pressure as determined by patch-clamp experiments, as well as MscS electrostatics and transport properties as determined through all-atom molecular dynamics simulations of the protein embedded in a lipid bilayer, a 224,000-atom system. The experiments reveal that MscS is a slightly anion-selective channel with a conductance of approximately 1 ns, activated by pressure and inactivated in a voltage-dependent manner. On the other hand, the simulations, covering over 200 ns and including biasing electrostatic potentials, show that MscS restrained to the crystal conformation exhibits low conductance; unrestrained it increases the channel radius upon application of a large electrostatic bias and exhibits then ion conduction that matches experimentally determined conductances. The simulated conductance stems mainly from Cl- ions.

Ca2+ selectivity of a chemically modified OmpF with reduced pore volume

We studied an E. coli OmpF mutant (LECE) containing both an EEEE-like locus, typical of Ca(2+) channels, and an accessible and reactive cysteine. After chemical modification with the cysteine-specific, negatively charged (-1e) reagents MTSES or glutathione, this LECE mutant was tested for Ca(2+) versus alkali metal selectivity. Selectivity was measured by conductance and zero-current potential. Conductance measurements showed that glutathione-modified LECE had reduced conductance at Ca(2+) mole fractions <10(-3). MTSES-modified LECE did not. Apparently, the LECE protein is (somehow) a better Ca(2+) chelator after modification with the larger glutathione. Zero-current potential measurements revealed a Ca(2+) versus monovalent cation selectivity that was highest in the presence of Li(+) and lowest in the presence of Cs(+). Our data clearly show that after the binding of Ca(2+) the LECE pore (even with the bulky glutathione present) is spacious enough to allow monovalent cations to pass. Theoretical computations based on density functional theory combined with Poisson-Nernst-Planck theory and a reduced pore model suggest a functional separation of ionic pathways in the pore, one that is specific for small and highly charged ions, and one that accepts preferentially large ions, such as Cs(+).

Electrostatic properties of the mechanosensitive channel of small conductance MscS

The mechanosensitive channel of small conductance (MscS) belongs to a family of membrane proteins that are gated in response to changes in membrane tension, thereby protecting the cell from hypo-osmotic shock. Here we report on passive ion transport simulations of MscS in a POPC bilayer using a coarse-grained particle-based description based on the Boltzmann transport Monte Carlo method. Single channel current-voltage curves are computed over hundreds of nanoseconds for channel conformations derived from all-atom molecular dynamics simulations reaching an overall simulation time of over 5 micros. Channel conformations similar to that of the crystal structure exhibit low conductance, whereas conformations reached after opening the channel by means of steered molecular dynamics simulations match experimentally determined conductances. However, while experiments indicate a slight preference for anionic currents, the simulated channel strongly selects anions over cations and the direction of rectification at high voltages is opposite to what is observed in experiments. Three-dimensional maps of time-averaged ion distribution and equilibrium occupancy profiles constructed from trajectory data indicate separation of anions and cations inside and in the immediate vicinity of the large cytoplasmic domain of MscS, in accordance with earlier molecular dynamics simulations. This separation arises from the distribution of ionizable residues of MscS and suggests a specific, yet unknown, functional purpose.