Abstract
Kinetic models of ion channels: from atomic structures to membrane currents Ion channels are transmembrane proteins that regulate the movement of ions across cell membranes. The ion channels-mediated currents are involved in a plethora of biological processes, including cardiac contraction, nerve transmission, and cell homeostasis. Mutations of channels, or their interactions with pharmaceutical molecules, can modify these ion fluxes, with important consequences in numerous diseases, with cardiac arrhythmias and cystic fibrosis being two relevant examples. Thus, there is a great interest in numerical techniques for simulating the activity of ion channels. Nowadays, there are two approaches that are commonly used to model ion channels. The functional properties are usually described by Markov Models (MMs) estimated from experimental data. These MMs reproduce quantitatively the membrane currents, but they do not reveal how channels operate at the atomic level. Conversely, Molecular Dynamics (MD) simulations reproduce the behaviours of proteins at atomic level, but because of the high computational cost, they cannot be routinely used to simulate membrane currents. The aim of this project is to fill the gap between empirical models of membrane currents and atomic simulations of ion channels. Thanks to recent theoretical and computational advancements, it is now possible to estimate MMs directly from MD simulations. Inspired by this possibility, we designed a multiscale algorithm for simulating ion channels. MD simulations will be used to sample the dynamics of channels at atomic scale under different boundary conditions. Then, these atomic trajectories will be used to estimate kinetic models that describe the processes under investigation (e.g. ion conduction and inactivation) by a minimal number of long-lived metastable states and the corresponding transition rates. Thanks to this approach, it will be possible to include atomic details in kinetic simulations that can be directly compared with experimental data on membrane currents. The methods will be tested in two potassium selective channels: KcsA and hERG. KcsA is the prototypical system in the field of atomic simulations of ion channels, and consequently it is an ideal model for testing novel methods. hERG is a crucial channel for the electrical activity of cardiac cells. Electrophysiological experiments of hERG will be performed and compared with kinetic models estimated from MD simulations. The aim of this comparison is to identify the atomic mechanisms responsible for the functional properties of hERG, in particular its peculiar C-type inactivation properties, with important implications for the current understanding of the role of hERG mutations in cardiac arrythmias and for drug-design. More than 20 years after the publication of the first atomic structure of a potassium channel, many questions regarding the mechanisms responsible for the functioning of these proteins are still unanswered. The combination of atomic simulations and experimentally-derived kinetic models developed in this project could contribute to their understanding. In particular, we anticipate that our simulation tools will reveal how the boundary conditions (membrane potentials and ion concentrations) modify the mechanisms of conduction/selectivity, and if these mechanisms differ among K+-channels. Computational models that relate atomic structures to membrane-currents will be useful for predicting the effects of residue mutations, eventually providing a guide to better understand pathogenic mutations, and for the design of ion channels with desired functional characteristics. With respect to C-type inactivation, we will contribute to the current debate on the relation between atomic structures and functional states. In detail, with the combination of simulations and experiments, we anticipate to identify candidate atomic structures for the Na+-conductive state of hERG. Since this Na+-conductive state is related to the early stages of hERG inactivation, understanding the atomic mechanisms responsible for this state transition might help to explain the unusual gating/inactivation properties of hERG. In the wide context of scientific computing, the objective of this project is to estimate macroscopic functional characteristics from atomic structures, which is a Holy Grail in simulations of complex biological systems. Ion channels are optimal candidates to reach this goal for several reasons, namely: (i) experimental atomic structure are available; (ii) functional properties can be measured experimentally at the single-molecule level on the millisecond timescale; (iii) ion channels are “fast” when compared to other biological molecules (ion conduction takes place in the nanosecond timescale, hERG inactivation in the sub-millisecond timescale). These features pose ion channels at the frontiers of scientific-computing, as a class of biological molecules where a direct link between atomic structures and functional properties is possible. While the project focuses on this link between the atomic structure of a protein and its functional characteristics, its real impacts are better understood in the wider context of multiscale simulations in biology and medicine. In this field, the system where multiscale modelling has been more widely adopted is by no doubt the cardiac system. Nowadays, it is possible to define a multiscale model of the cardiac system that incorporates details on the functioning of single protein families. Starting from the Markov Models of the membrane currents estimated from experimental data, it is possible to formulate a model that quantitatively reproduces the electric activity of a cardiac cell. In turn, the cardiac cell models can be incorporated into a mathematical description of the heart that reproduces the electric activity of the entire organ. Models on even higher scales can be used to analyse how changes in the electric activity of the heart impact the electrostatic potentials measured on the body surface. Thus, by a multiscale approach, it is already possible to relate the functional characteristics of a class of membrane proteins to the macroscopic behaviour of the cardiac system. The next step is to extend this multiscale framework down to the atomic scale. This project will contribute to the development of methods for linking the Markov Models of the membrane currents and the atomic characteristics of the membrane proteins responsible for those currents. In this way, it will be possible to create the first mathematical model of an organ that spans the whole spectrum of scales from atoms to macroscopic functional characteristics. These simulations would provide an unprecedented understanding of physiological events, with possible implications to drug-discovery and to the treatment of hereditary diseases. Results The project produced a computational framework that connects atomistic molecular dynamics simulations of ion permeation with channel currents. First, a formalism was developed to calculate ionic current directly from a Markov State Model by combining its transition matrix with a flux matrix that records the charge displaced during each discrete state transition. A current-preserving state-reduction procedure was also introduced, allowing complex permeation trajectories to be represented by compact and mechanistically interpretable kinetic schemes. Applied to the prototypical potassium channel KcsA, the method generated a five-state model that accurately reproduced the current measured directly from the MD trajectories and supported an association–dissociation mechanism in which ion binding at one side of the selectivity filter promotes ion release at the opposite side. This framework was subsequently extended to predict complete current–voltage relationships from simulations performed at only a limited number of membrane potentials. Time-discrete MSMs were converted into continuous-time rate matrices, and the voltage dependence of individual transition rates was described using a rate-theory formulation. Validation on the MthK and KcsA potassium channels showed that the resulting models accurately predicted currents and, more generally, the voltage-dependent populations of the principal ion-occupancy states at membrane potentials not used to construct the models. The analysis also indicated that transitions involving ion movements through the central region of the selectivity filter are strongly voltage dependent, whereas transitions near the extracellular entrance are comparatively insensitive to voltage, consistent with most of the membrane potential drop occurring across the filter core. Overall, the project established an efficient strategy for extrapolating from computationally accessible simulations at high voltages to channel currents and conduction mechanisms under a broader range of conditions, thereby facilitating quantitative comparison between atomistic simulations and electrophysiological measurements.
Dettagli del progetto
Responsabile scientifico: Simone Furini
Strutture Unibo coinvolte:
Dipartimento di Ingegneria dell'Energia Elettrica e dell'Informazione "Guglielmo Marconi"
Contributo totale di progetto: Euro (EUR) 197.866,00
Contributo totale Unibo: Euro (EUR) 97.806,00
Durata del progetto in mesi: 24
Data di inizio
28/09/2023
Data di fine:
28/02/2026
