Dynamics of ions in the selectivity filter of the KcsA channel

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion’s dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications

From Structure to Function in Open Ionic Channels

We consider a simple working hypothesis that all permeation properties of open ionic channels can be predicted by understanding electrodiffusion in fixed structures, without invoking conformation changes, or changes in chemical bonds. We know, of course, that ions can bind to specific protein structures, and that this binding is not easily described by the traditional electrostatic equations of physics textbooks, that describe average electric fields, the so-called `mean field'. The question is which specific properties can be explained just by mean field electrostatics and which cannot. I believe the best way to uncover the specific chemical properties of channels is to invoke them as little as possible, seeking to explain with mean field electrostatics first. Then, when phenomena appear that cannot be described that way, by the mean field alone, we turn to chemically specific explanations, seeking the appropriate tools (of electrochemistry, Langevin, or molecular dynamics, for example) to understand them. In this spirit, we turn now to the structure of open ionic channels, apply the laws of electrodiffusion to them, and see how many of their properties we can predict just that way.Comment: Nearly final version of publicatio

Stochastic Modeling and Simulation of Ion Transport through Channels

Ion channels are of major interest and form an area of intensive research in the fields of biophysics and medicine since they control many vital physiological functions. The aim of this work is on one hand to propose a fully stochastic and discrete model describing the main characteristics of a multiple channel system. The movement of the ions is coupled, as usual, with a Poisson equation for the electrical field; we have considered, in addition, the influence of exclusion forces. On the other hand, we have discussed about the nondimensionalization of the stochastic system by using real physical parameters, all supported by numerical simulations. The specific features of both cases of micro- and nanochannels have been taken in due consideration with particular attention to the latter case in order to show that it is necessary to consider a discrete and stochastic model for ions movement inside the channels

Interacting Ions in Biophysics: Real is not Ideal

Ions in water are important in biology, from molecules to organs. Classically, ions in water are treated as ideal noninteracting particles in a perfect gas. Excess free energy of ion was zero. Mathematics was not available to deal consistently with flows, or interactions with ions or boundaries. Non-classical 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 bio-ions Na, K, Ca 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, channels, and nucleic acids: the number density of ions is often more than 10 M. Ions in such crowded quarters interact strongly with each other as well as with the surrounding protein. Non-ideal behavior has classically been ascribed to allosteric interactions mediated by protein conformation changes. Ion-ion interactions present in crowded solutions--independent of conformation changes of proteins--are likely to change interpretations of 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 (extracellular/intracellular solutions), and usually involve flow and trace concentrations of messenger ions (e.g., 10-7 M Ca2+). Energetic variational methods can deal with these characteristic properties of biological systems while we await the maturation and calibration of all atom simulations of ionic mixtures and divalents

Molecule transport in nanopores with applications to water purification, power generation and disease diagnosis

High performance water transport in nanopores has drawn a great deal of attention in a variety of applications, such as water desalination, power generation and biosensing. A single-layer MoS2 nanopore is shown, here, to possess high water transport rate and strong salt rejection rate making it ideal for water desilation. High water transport enhancement factors in carbon-based nanopores have been reported over the classical Hagen-Poiseuille (HP) equation which does not account for the physics of transport at molecular scale. Instead, comparing the experimentally measured transport rates to that of a theory, that accounts for the microscopic physics of transport, would result in enhancement factors approaching unity. Here, molecular corrections are introduced into HP equation by considering the variation of key hydrodynamical properties (viscosity and friction) with thickness and diameter of pores in ultrathin graphene and finite-length carbon nanotubes (CNTs) using Green-Kubo relations and molecular dynamics (MD) simulations. The corrected HP (CHP) theory, successfully predicts the permeation rates from non-equilibrium MD pressure driven flows. The previously reported enhancement factors over no-slip HP (of the order of 1000) approach unity when the permeations are normalized by the CHP flow rates. In a follow-up study, we revisit Sampson’s theory after more than a century to account for the surface chemistry of nanopores by incorporating slippage and interfacial viscosity variation into the original Sampson’s theory. The HP theory works for flow in infinitely long tubes where end effects are neglected. In 1891, Ralph Allen Sampson came up with a formula, known as Sampson formula, within the fluid mechanics framework to describe flow in an infinitesimally thin orifice. Zeev Dagan, Sheldon Weinbaum and Robert Pfeffer published an article in the Journal of Fluid Mechanics in 1982, where the HP and Sampson formulas were combined to successfully describe flow in circular tubes of finite length. Although the Sampson formula is a powerful theory for end effects, it has been shown to lack accuracy for relatively small-radius pores (e.g., nanopores in single-layer graphene membranes) since it does not account for the molecular interface chemistry. We show that the corrected Sampson’s theory is able to accurately describe flow in ultrathin nanopores when compared to the data from molecular dynamics simulations. Combining our corrected Sampson formula with the HP equation, we can remarkably predict flow in not only ultrathin pores but also finite-length pores such as carbon nanotubes. We also explored the structure and dynamics of aqueous ions in nanopores. At the nanopore interfaces, properties of ions are shown to differ largely from those of predicted by the classical ionic layering models (e.g., Gouy-Chapman electric double layer (EDL)) when the thickness of the nanopore is scaled down to the limit of ultrathin membranes (e.g, single-layer graphene). Here, using extensive molecular dynamics, the structure and dynamics of aqueous ions inside nanopores are studied for different thicknesses, diameters and surface charge densities of carbon-based nanopores (ultrathin graphene and finite-length carbon nanotubes (CNTs)). The ion concentration and diffusion coefficient in ultrathin nanopores show no indication of Stern layer formation (an immobile counter-ionic layer) as the counter-ions and nanopore atoms are weakly correlation with time compared to the strong correlation in thick nanopores. Adsorption constants of counter-ions onto the nanopore surface are shown to be many orders of magnitudes smaller than that of thick nanopores. The vanishing counter-ion adsorption in ultrathin nanopores explains the lack of Stern layer formation leading to fast dynamics of ions with picosecond scale residence times. Finally, we investigated DNA transport through biological nanopores. Distinguishing bases of nucleic acids by passing them through nanopores has so far primarily relied on electrical signals – specifically, ionic currents through the nanopores. However, the low signal-to-noise ratio makes detection of ionic currents difficult. We show that the initially closed Mechano-Sensitive Channel of Large Conductance (MscL) protein pore opens for single stranded DNA (ssDNA) translocation under an applied electric field. As each nucleotide translocates through the pore, a unique mechanical signal is observed – specifically, the tension in the membrane containing the MscL pore is different for each nucleotide. In addition to the membrane tension, we found that the ionic current is also different for the 4 nucleotide types. The initially closed MscL adapts its opening for nucleotide translocation due to the flexibility of the pore. This unique operation of MscL provides single nucleotide resolution in both electrical and mechanical signals

Theoretical and computational studies of the correlated ionic motion in narrow ion channels

An ion channel is a protein with a hole down its middle embedded into the cytoplasmic membrane of a living biological cells. Ion channels facilitate ionic transport across the membrane, thus bridging the intra- and extra-cellular compartments. Properly functioning channels contribute to the healthy state of an organism, making them one of the main targets for pharmaceutical applications. The description and prediction of a channel’s performance --conductivity, selectivity, blocking etc., -- under arbitrary experimental conditions starting from its crystal structure thus appears as an important challenge in contemporary theoretical research. The main obstacle for such description arises from the presence of the multiple non-negligible interactions in the system. These include ion-ion, ion-water, ion-ligands, ion-pore, and other interactions. Their self-consistent consideration is essential in narrow ion channels, where due to inter-ion interactions and atomic confinement, the ions move in a single-file highly-correlated manner. Molecular dynamics, the most detailed computational tool to date, does not allow one routinely to evaluate the properties of such channels, while continuous methods overlook the ion-ion interactions. Therefore, one needs a method that combines atomic details with the ability to estimate ionic currents. This thesis focuses on the classical treatment of ion channels. Namely, a Brownian Dynamics simulation is described where the interactions of the ion with other ions and the channel are incorporated via the multi-ion potential of the mean force (PMF). This allows one to model the channel’s behaviour under various experimental conditions, while preserving the details of the structure and nanoscale interactions with atomic precision. Secondly, we use the concept of a quasiparticle to describe the highly-correlated ionic motion in the selectivity filter of the KcsA channel. We derive the quasiparticle’s effective potential from the multi-ion atomic PMF, thus connecting the quasiparticle’s properties with the nanoscale features of the channel. We also evaluate the rates of transition between different quasiparticles by virtue of the BD simulation. These ingredients comprehensively describe the quasiparticle’s dynamics which hence serves as an intermediary between the crystal structure and the experimentally observed properties of a narrow ion channel. Lastly, an analytical method to describe the ion-solvent interaction is proposed. It incorporates the ion-solvent and ion-lattice radial density functions, and hence automatically accounts for the pore shape, the type of atoms comprising the lattice, the type of solvent, and the ion’s location near the pore entrance. This method paves the way to an analytical decomposition of single-ion PMFs, what is of fundamental importance in predicting the conductive and selective properties of mutated biological ion channels. This method can also find application in designing functionalized artificial nanopores with on-demand transport properties for efficient water desalination

Gating and Permeation of Ion Channels

Recent crystal structures of ClC chloride channels have led to a proposed fast-gating mechanism that couples ion permeation to ion channel gating. This proposed mechanism is studied by pushing the amino acid E148 of StClC out of the path of the proposed permeation path. The resulting structure produces an open state that is similar to the mutant EcClC E148Q structure, a proposed open structure of ClC-type channels. Due to the interaction of the fast-gate with permeating ions, a hybrid methodology is proposed for explicitly simulating the interaction of protein fluctuations with permeating ions. This methodology is used for two model systems and compared to single-ion Potential of Mean Force permeation models methodologies

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field