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

Experimental and Theoretical Brownian Dynamics Analysis of Ion Transport During Cellular Electroporation of E. coli Bacteria

Escherichia coli bacterium is a rod-shaped organism composed of a complex double membrane structure. Knowledge of electric field driven ion transport through both membranes and the evolution of their induced permeabilization has important applications in biomedical engineering, delivery of genes and antibacterial agents. However, few studies have been conducted on Gram-negative bacteria in this regard considering the contribution of all ion types. To address this gap in knowledge, we have developed a deterministic and stochastic Brownian dynamics model to simulate in 3D space the motion of ions through pores formed in the plasma membranes of E. coli cells during electroporation. The diffusion coefficient, mobility, and translation time of Ca$^{2+}$, Mg$^{2+}$, Na$^+$, K$^+$, and Cl$^-$ ions within the pore region are estimated from the numerical model. Calculations of pore's conductance have been validated with experiments conducted at Gustave Roussy. From the simulations, it was found that the main driving force of ionic uptake during the pulse is the one due to the externally applied electric field. The results from this work provide a better understanding of ion transport during electroporation, aiding in the design of electrical pulses for maximizing ion throughput, primarily for application in cancer treatment.Comment: Annals of Biomedical Engineering, 202

Statistical theory of selectivity and conductivity in narrow biological ion channels:studies of KcsA

Biological ion channels are essential for maintaining life, and appear as a seemingly paradoxical combination of both large conductivity and strong selection between ionic species. This process involves many complicated interactions, and their inclusion in a multi-species conduction model remains a fundamental theoretical challenge. In this thesis, we derive the theory of multi-species ionic conduction through narrow biological channels, taking into account ion-ion, ion-water and ion-channel interactions. The theories we derive lead to new results that describe multi-species conduction in and far from equilibrium in KcsA, including the resolution of the conductivity-selectivity paradox. The thesis builds on existing research on the physiological properties and structures of biological ion channels in deriving a first-principles, multi-species statistical and kinetic theory. The development of the statistical theory includes the derivation of the free energy, distribution and partition functions, as well as the statistical properties within the grand canonical ensemble. The conductivity of the channels is also derived using linear response theory and the generalised Einstein relation. The development of the kinetic theory involves the analysis of the transition rates, and the calculation of current and selectivity ratios. The kinetic model is then validated by comparing the theoretical currents with the currents measured experimentally for the Shaker and KcsA potassium channels in five different external data sets. The main results of this thesis are: a derivation of the grand canonical ensemble for narrow channels with multiple binding sites and mixed-species bulk solutions; a derivation of the linear response theory of multi-species conduction in such channels; development of non-equilibrium multi-species kinetic equations, that describe the conductivity; the validation of the kinetic theory through comparison with experimental data sets; and the joint application of these derived theories to the multi-species conduction of KcsA in and far from equilibrium, which demonstrates the resolution of the conductivity-selectivity paradox. These results should be applicable to other narrow voltage-gated ion channels, and can describe multi-species conduction of neutral particles through zeolites

Multi-Scale Computational Studies of Calcium (Ca\u3csup\u3e2+\u3c/sup\u3e) Signaling

Ca2+ is an important messenger that affects almost all cellular processes. Ca2+ signaling involves events that happen at various time-scales such as Ca2+ diffusion, trans-membrane Ca2+ transport and Ca2+-mediated protein-protein interactions. In this work, we utilized multi-scale computational methods to quantitatively characterize Ca2+ diffusion efficiency, Ca2+ binding thermodynamics and molecular bases of Ca2+-dependent protein-protein interaction. Specifically, we studied 1) the electrokinetic transport of Ca2+ in confined sub-µm geometry with complicated surfacial properties. We characterized the effective diffusion constant of Ca2+ in a cell-like environment, which helps to understand the spacial distribution of cytoplasmic Ca2+. 2) the association kinetics and activation mechanism of the protein phosphatase calcineurin (CaN) by its activator calmodulin (CaM) in the presence of Ca2+. We found that the association between CaM and CaN peptide is diffusion-limited and the rate could be tuned by charge density/distribution of CaN peptite. Moreover, we proposed an updated CaM/CaN interaction model in which a secondary interaction between CaN’s distal helix motif and CaM was highlighted. 3) the roles of Mg2+ and K+ in the active transport of Ca2+ by sarco/endoplasmic reticulum Ca2+-ATPase (SERCA) pump. We found that Mg2+ most likely act as inhibitor while K+ as agonist in SERCA’s transport process of Ca2+. Results reported in this work shed insights into various aspects of Ca2+ signaling from molecular to cellular level

Modeling ion and water permeation through narrow biological channels

Standard Poisson-Nernst-Planck (PNP) theory is modified by adding contributions due the Dielectric Self Energy and dynamic relaxation of a protein channel in response to ion permeation. This approach is utilized to predict ionic currents through the Gramicidin A (GA) channel, in which the applicability of conventional continuum theories is questionable. The Potential of Mean Force for K+ and Cl- ions in GA are obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations with a continuum electrostatic calculation of the free energy. The results of our study show that the channel response to the permeating ion produces significant electrostatic stabilization of K+ inside the channel.The local diffusion constant of K+ inside the GA channel has been calculated using four different computational methods based on MD simulations: Mean Square Displacement (MSD), Velocity Autocorrelation Function (FACF), Second Fluctuation Dissipation Theorem (SFDT) and analysis of the Generalized Langevin Equation for a Harmonic Oscillator (GLE-HO). All methods were tested and compared in bulk water and all predicted the correct diffusion constant. Inside GA, MSD and VACF methods were found to be unreliable because they are biased by the systematic force exerted by the channel system. SFDT and GLE-HO methods properly unbias the influence of systematic force and predicted a similar diffusion constant of K+ inside GA, namely, ca. 10 times smaller than in the bulk.A simplified three-dimensional model of ClC chloride channel was constructed to couple the ion permeation to the motion of a glutamate side chain which acts as the putative fast gate. Dynamic Monte Carlo (DMC) simulations were carried out using this model channel to investigate the dependence of the gate closing rate on internal and external chloride concentration as well as the gate charge. Our simulation results were in qualitative agreement with experimental observations and consistent with the "foot-in-the-door" mechanism.Osmotic and diffusion permeabilities of H2O and D2O in Aquaporin 1 (AQP1) were calculated using MD simulations and, subsequently, osmotic permeabilities were measured experimentally. The combined computational and experimental results suggest that D2O permeability through AQP1 is similar to that of water

Computational Studies of Biological Ion Channels

Structural and functional characteristics of three biological ion channels were studied. First, current-voltage characteristics were calculated using non-equilibrium molecular dynamics (NEMD), Brownian Dynamics (BD), and Poisson-Nernst-Planck theory (PNP) for the ion channel alpha-hemolysin, comparing and contrasting the results among each other and experimental values. Results show that all methods produce qualitatively accurate results in terms of selectivity, where quantitave accuracy increases with more atomistic detailed simulation methodology. Results from NEMD simulations show that a specific location within the pore may account for selectivity of the channel, and point mutation of one residue (lys147) would likely result in a change in selectivity. The residue was mutated to serine, structural viability was tested with all-atom molecular dynamics, and PNP and BD calculations of the mutated structure show that selectivity is changed via this mutation. Second, pH dependence of current-voltage characteristics of alpha-hemolysin were studied using PNP and compared to experimental data, applying pH-dependent charge states determined from calculated pKa values for all titratable residues in the structure. Results indicate that altered charge states of both internal and external residues most accurately described experimental data. Third, Poisson-Boltzmann and (PNP) calculations were performed to determine the functional state of the crystallographic structure of the mitochondrial channel VDAC1, finding that the current-voltage properties indicated that structure represents the open conformation of the channel. Calculations were repeated using mutant channel structures, reflecting experimental results showing changes in selectivity. Two proposed gating motions of the channel were explored, with calculated current-voltage results from the gated structures not reflecting experimental changes in current-voltage properties, suggesting that the two proposed gating methods were not correct for this channel. Last, Poisson-Nernst-Planck calculations were performed of the influx of ferrous ions (Fe2+) into human H-ferritin protein. All-atom molecular dynamics simulation was used to determine both the equilibrium pore structure as well as the diffusion constant profile through the channel, using Force-Force Autocorrelation Function methodology. Results show relatively slow (compared to other channels) transit of Fe2+ ions through the channel due to greatly reduced internal diffusion constants (from bulk values) within the ferritin pore as well as low physiological concentration of Fe2+

Physics of Ionic Conduction in Narrow Biological and Artificial Channels

The book reprints a set of important scientific papers applying physics and mathematics to address the problem of selective ionic conduction in narrow water-filled channels and pores. It is a long-standing problem, and an extremely important one. Life in all its forms depends on ion channels and, furthermore, the technological applications of artificial ion channels are already widespread and growing rapidly. They include desalination, DNA sequencing, energy harvesting, molecular sensors, fuel cells, batteries, personalised medicine, and drug design. Further applications are to be anticipated.The book will be helpful to researchers and technologists already working in the area, or planning to enter it. It gives detailed descriptions of a diversity of modern approaches, and shows how they can be particularly effective and mutually reinforcing when used together. It not only provides a snapshot of current cutting-edge scientific activity in the area, but also offers indications of how the subject is likely to evolve in the future