Nonlinear dynamics of selectivity, conductivity, and gating in biological ion channels

Lead Research Organisation: Lancaster University
Department Name: Physics

Abstract

We propose to investigate the physics of biological ion channels. These natural conducting nanotubes control a vast range of biological functions. Analogous to nano-scale transistors, they are present in the membranes of all biological cells. Moving a finger involves the coordinated operation of billions of ion channels. Half of the metabolic energy consumed by the human brain is used by ion pumps moving K+ and Na+ in and out of nerve cells. Understanding ion channel structure and operation is not only relevant to curing disease, but may also pave the way to bio-computers and their integration with nano-electronics. Channels are extraordinarily complicated devices, built of thousands of atoms, flexible, and filled with ions and water dipoles that adjust their positions to movements of the ions and channel walls. They are very selective and sensitive to external conditions. E.g. the KcsA potassium channel discriminates between K+ and Na+ ions by a factor of 1000, even though they are of the same polarity and Na+ is actually smaller in diameter by 0.4A. Yet channels conduct up to 100 million ions/sec, i.e. almost at the rate of free diffusion, and display very robust performance. Modelling channels is a fundamentally difficult many-body problem with long range interactions and widely-varying timescales, ranging from sub-ps atomic motion to sub-ms gating dynamics. Despite impressive scientific progress, theoretical models of channels are often too simplistic to capture the all-important relationship between structure and function, e.g. traditional models of channel diffusion consider ions as point charges, water as continuous dielectric, and protein as a dielectric with rigid walls - although ion size, hydration, and interaction with protein vibrations in the pore are known to play crucial roles.Our main goal is to develop a novel Brownian dynamics (BD) description of channels by isolating biologically relevant degrees of freedom using molecular dynamics (MD), and to demonstrate theoretically and numerically that protein vibration, ion size and hydration at the selectivity filter, and charge fluctuations (all largely neglected in earlier work), provide leading order contributions to the channel's high conductivity and selectivity between ions of the same polarity. We now propose a full-scale research programme, building on the strong base of: (i) our EPSRC-funded (GR/S86174/01) preliminary project on BD simulations, Poisson-Nernst-Planck and reaction rate theories of ion channels; (ii) the Lancaster group's life-time expertise in non-equilibrium stochastic dynamics; (iii) their long-term collaboration with Rush University Medical College; and (iv) the international distinction and enormous experience of the Warwick group in MD simulation. We will seek a self-consistent explanation of how strong selectivity between alike ions can be combined with high conductivity, stress relaxation and energy dissipation in the channel by developing a novel approach based on a combination of BD and MD simulations. We will also try to establish how coupling to the ion permeation via vibrations of the protein walls changes the energetics and statistics of the gating. Our theoretical and simulation results will be compared with real potassium, calcium, and artificial channel data in collaboration with experimentalists in Oxford, Chicago, Chapel Hill and Groningen.The investigations bring new ideas from non-equilibrium physics to focus on long-standing problems that are of central importance in biology. The work will draw freely on the group's special expertise in nonlinear dynamics, fluctuation theory, coupled oscillators, and their biomedical applications. Even partial success in improving the understanding of conduction in open ion channels will be highly significant, and will more than justify the enterprise.

Publications

10 25 50
 
Description We analysed a generic electrodiffusion model of ion channel, presenting calcium/sodium channels in the very simple form: a water-filled open nanotube with some fixed charge Qf around its middle, where discrete charged ions move stochastically under electrostatic control, using both analytic theory and modelling with self-consistent electrostatic Brownian dynamics. We complemented this mesoscale description with molecular dynamics simulations that take account of individual atoms and provide the parameters needed by the analytic description.
The most important outcome was our discovery and first-principles explanation of an emergent phenomenon in these channels: a periodic sequence of multi-ion calcium conduction-bands and stop-bands as a function of Qf.
We connected this phenomenon with charge discreteness, an electrostatic exclusion principle, and sequential SF neutralisation; hence making an essential step towards our subsequent hypothesis that it arises as a manifestation of Ionic Coulomb blockade, a novel discrete electrostatic phenomenon closely analogous to Coulomb blockade oscillations in quantum dots. In the context of ion channels, this brings an entirely fresh vision of the conduction process.
We have observed ,and explained on a preliminary basis, the splitting of calcium profiles along the SF, a phenomenon that was shown to be connected with ion-ion Coulomb interaction inside the SF. It is directly connected to the multi-ion knock-on mechanism (see below).
Our new model of conduction and selectivity is based on a discrete electrostatics approach, later formulated as Ionic Coulomb blockade. It seems potentially able to account for numerous earlier observations on wild-type channels and their mutants that had hitherto been regarded as mysterious and puzzling, bringing them all together within a consistent, unified, picture.
In addition, we have discovered and theoretically investigated a novel "remote knock-on" mechanism of concerted conduction, which may be responsible for the fast and selective conduction of calcium in the L-type calcium channel.
Exploitation Route In principle, they pave the way to predicting the function of a channel from a knowledge of its structure. Thus there are potential applications wherever ion channels - or artificial nanotubes - need to be designed for particular purposes.
Sectors Education,Healthcare,Other

URL http://www.physics.lancs.ac.uk/research/ionchannel/
 
Description The main impact was the training of a Postdoctoral Research Associate, Dr Rodrigue Tindjong. Since graduation, he has trained for teaching and is now a physics teacher in a school near Preston.
Sector Education
Impact Types Societal,Policy & public services

 
Description Conduction and selectivity between monovalent ions within the potassium channel
Amount £275,830 (GBP)
Funding ID RPG-2017-134 
Organisation The Leverhulme Trust 
Sector Academic/University
Country United Kingdom
Start 10/2017 
End 09/2020
 
Description Ionic Coulomb blockade oscillations and the physical origins of permeation, selectivity, and their mutation transformations in biological ion channels
Amount £1,161,214 (GBP)
Funding ID EP/M015831/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Academic/University
Country United Kingdom
Start 04/2015 
End 09/2018
 
Description Bob Eisenberg 
Organisation Rush University
Department Department of Molecular Biophysics and Physiology
Country United States 
Sector Academic/University 
PI Contribution We have contributed insight into the function of biological ion channels from a physics perspective.
Collaborator Contribution Our partner at Rush University he contributed his unique experience and knowledge of biological ion channels from the perspective of biology an physiology.
Impact Some 21 interdisciplinary joint scientific papers have been published during 2004-2017, all bearing on different aspects of ion channel function. Basically, Lancaster University provided the expertise in physics and Rush University provided expertise in biology and physiology. The main impact of this long-running collaboration has been scientific
 
Description Warwick MD 
Organisation University of Warwick
Department School of Engineering
Country United Kingdom 
Sector Academic/University 
PI Contribution Lancaster University mostly contributed expertise in the analytic theory of biological ion channels, coupled with Brownian dynamics simulations of the permeation process. Lancaster and Warwick each contributed expertise in stochastic nonlinear dynamics
Collaborator Contribution Warwick mostly contributed molecular dynamics simulations of the ion channels. Warwick and Lancaster each contributed expertise in stochastic nonlinear dynamics.
Impact Some 10 Lancaster/Warwick joint scientific papers have been published. the main impact of the joint work has been in scientific progress.
Start Year 2009