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

Lead Research Organisation: University of Warwick
Department Name: Sch of Engineering

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

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Description The project allowed us to make a significant progress in understanding of the key factors regulating activity and properties of the potassium ion channels. During the grant a team has been formed and additional support in the form another EPSRC grant has been secured.

This project has helped to identify a number of fundamental problems related to modelling of ion channel and more widely in modelling biological objects. The problems have been formulated and steps to tackle these problems have been performed.



This research has been conducted by the Warwick University team in collaboration with Lancaster Nonlinear Dynamics group ands with Bob Eisenberg (Rush University, Chicago).



The object of the study was a potassium ion channel KcsA that resembles human K+ channels with respect to the ion permeation and selectivity between potassium and sodium ions. In the central part of the channel, so-called selectivity filter, ions and water molecules move in a single file fashion. The current is regulated by several types of "gates", common to a wide variety of potassium ion channels, which are crucial for physiological functions such as initiation of electrical pulse in excitable cells of the heart. Among these gates, the C-type inactivation involves structural rearrangements in the filter region, and these rearrangements are mostly unknown.



The primary activity of our (Warwick) team was aimed to two objectives of the project:



(i) Investigate the inactivation mechanism and determinants in the protein sequence and in the coupling between permeation and inactivation revealed by several experimental evidences,



(ii) Develop MD simulations of a channel for unambiguously separating all the relevant "slow" variables from the faster motions, so that the former can be represented as a deterministic component and the latter stochastically in terms of Brownian dynamics.



Within the first objective the following results have been obtained:



Inactivation of potassium KcsA has been described and a mechanism of the inactivation has been proposed. The mechanism was confirmed with calculations performed on different mutants widely reported in the literature as having different inactivation probabilities with respect of the wild type. The central role of the aspartate residue located close the external filter entryway has been demonstrated and a strong coupled network of several residues with the aspartate as a hub has been proved being responsible for the state of the filter. Moreover, the aspartate belongs to the motif TXXTXGYGD that highly conserves among potassium ion channels. It has been found that the location of the ions inside the selectivity filter is one of the key components in the inactivation mechanism.



Different residues affecting the filter state are exposed to the extra-cellular bulk. This provides opportunity to control their behaviour and consequently inactivation by binding chemicals, that is to control the inactivation of potassium channels by drugs.

The study of the inactivation mechanism has revealed the existence of several configurations of the selectivity filter with different conducting properties. A conductive configuration has been identified.



Ion permeation in the conducting configuration identified by this research, was studied and a detailed picture of multi-ions conduction was built in the form of multi-dimensional free-energy surface. Several distinct permeation pathways were identified, and it was shown that these pathways are regulated by diffusion of ion from the intracellular region to the cavity. Once the incoming potassium ion reached the cavity the free-energy gradient promotes the permeation with a barrier-less entering of the ion in the filter.



Comparative analysis of sodium and potassium behaviours in the conducting configurations allows us to conclude that a thermodynamically driven selectivity over the two ion species occurs before the entrance of the filter. Additionally it has been shown that a partial knock-on effect can be induced by incoming sodium ions confirming the earlier finding of Lancaster group obtained by using Brownian dynamics model. Sodium's permeation,nevertheless, is unfavoured due to the impossibility of the sodium ion to enter in the filter and finalise the knock-on process.



The key result of the second objective is the existence of 1/f component in ion dynamics. The presence of this component is defined by complex re-arrangements of a large number of residues and bonds. It has been shown that widely-used description of an ion in the selectivity filter as a motion of an over-damped particle in multi-stable potential under action of white Gaussian noise(archetypical over-damped Langevin equation) is not valid. Such description should be based on under-damped particle motion, and Generalised Langevin equation with a memory-kernel, which includes 1/f component, has to be used.



Additionally, a number of results have been obtained in collaboration with Lancaster group for describing noise-induced transitions in multi-stable systems. These results helped to form a comprehensive picture of ion permeation on Brownian dynamics scale, i. e. considering a flow of ions via the channel.



Finally, the project has shown the importance of the presence of an infrastructure for storing and sharing data as well as the necessity of computational resources for data analysis. These components are complementary to high-performance computing facilities used in the course of the project. To develop these components we partially used finance resources initially aimed for travelling.
Exploitation Route Several residues acceptable from extra-cellular environment significantly affect the inactivation. These residues may be controlled by binding chemicals and, consequently, there is an opportunity to control the inactivation of potassium channels by drugs.
Sectors Pharmaceuticals and Medical Biotechnology,Other

 
Description Responsive Mode
Amount £1,500,000 (GBP)
Funding ID EP/M016889/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 04/2015 
End 09/2018