Ionic Coulomb blockade oscillations and the physical origins of permeation, selectivity, and their mutation transformations in biological ion channels

Lead Research Organisation: Lancaster University
Department Name: Physics


We will apply physics to elucidate the operation of biological ion channels including the long-standing problem of how their function emerges from their structure. These natural nanotubes exist in the membranes of all biological cells. They control a vast range of biological functions and are crucially important for life. Just lifting a finger requires the coordinated operation of billions of ion channels. Understanding ion channels is relevant to curing many diseases, and may also provide the future basis for bio-computers and their integration with nano-electronics.

The project promises significant contributions to the EPSRC Physics Grand Challenges (a) "Understanding the Physics of Life" and (b) "Emergence and Physics Far from Equilibrium" - and it has been inspired and encouraged by their associated NetworksPlus.

Channels are extraordinarily complex devices, built of thousands of atoms, and operating under non-equilibrium conditions. They conduct selected ions discretely on "one-by-one" basis. Channels can be very selective, e.g. the calcium channel discriminates between Ca++ and Na+ ions by a factor of 1000, even though they are of almost identical size. Yet a channel conducts almost at the rate of free diffusion, like an open hole. Modelling channels is an innately difficult many-body problem with long range interactions and widely-varying timescales, ranging from ps atomic motion to ms gating dynamics. The detailed structures of some channels are now known, but this knowledge has helped much less than expected/hoped in understanding how they actually work.

Our recent research has involved the analysis of a generic ion channel of very simple form: an open nanotube with some fixed charge around its middle, 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.

One outcome was our discovery of an emergent phenomenon: a periodic sequence of conduction-bands and stop-bands dependent on the fixed charge. We hypothesise that it is a manifestation of Ionic Coulomb blockade, 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. Our new model based on ionic Coulomb blockade seems potentially able to account for numerous earlier observations on wild-type channels and their mutants that have hitherto been regarded as mysterious and puzzling, bringing them together within a consistent, unified, picture.

We now request the funding needed to exploit this scientific break-through. We will develop an analytic model of ionic Coulomb blockade oscillations, accounting for resonant fluctuation-induced permeation. We will validate the model through an experimental investigation of bacterial sodium channels and their mutants, comparing the measurements with model predictions, and seeking evidence for for Ca2+ and Ba2+ conduction bands, stop-bands and selectivity. By extending the ionic Coulomb blockade model to include the discreteness of the hydration shells around the ion, we can expect to account for selectivity between alike ions, i.e. of equal charge like Na+ and K+.

From the perspective of our reduced model based on ionic Coulomb blockade, there is no inherent difference between an ion channel and an artificial charged nanopore. So we expect most of our results to be equally applicable to nanopores, if values of charge and dimensions are adjusted appropriately.

The investigations bring ideas from far-from-equilibrium physics to bear on problems in biology that are also applicable to nanotechnology. The work will draw freely on the consortium's special expertise in experiments on ion channels, nonlinear dynamics, fluctuation theory, and molecular dynamics.

Planned Impact

The expected beneficiaries are: (a) industry, and especially the pharmaceutical industry; (b) the medical profession; and (c) the public. We consider these in turn -


The work proposed is basic research, seeking to understand how biological ion channels function. Nonetheless, the chain leading from discovery to practical benefits in the long term is so clear, and so well established by recent successes, that the case is easy to make. There are two books by Frances Ashcroft FRS ("The Spark of Life: Electricity in the Human Body", Norton, 2012; and "Ion Channels and Disease", New York, Academic Press, 1999) focussed on just this subject.

The path from channel research to public benefit lies mainly in medical progress. There are literally thousands of diseases that result directly from single-molecule defects in ion channel proteins. If the protein can be modified, e.g. by means of a drug, the disease can be cured. For this reason, ion channels are a primary target of the pharmaceutical industry: in many cases, modification of the protein, by drugs or mutation, can cure the disease; in most cases, modification can greatly ameliorate symptoms.

Thus the long-term medical impacts relate to the possibility that a deeper appreciation of the physical mechanisms of permeation will yield better drugs targeted on ion channels (like calcium channel blockers) and a better understanding of diseases related to ion channel dysfunction. In particular our discovery of forbidden gaps is likely to be important.

After being validated and further developed, our model will provide a simple and efficient way to calculate the properties of ion channels from a knowledge of their structure, and vice versa to infer the probable structure from the functionality/dysfunctionality. An understanding of the physical reason for the dysfunction of a particular ion channel is likely to help in the optimisation of treatment.

Another likely path from ion channels to public benefit lies in technology. A wide variety of single molecule sensors is being developed using artificial ion channels as the key devices, including methods to allow cheap and easy reading of DNA sequences. Again, better understanding of how the channels function will almost certainly lead to improved devices. The impact will come from the possibility of calculating and predicting selected nanotube properties from predefined structure/geometry, and vice versa to determine the optimal structure of artificial nanotubes needed to provide the required properties. These possibilities can be used in the exponentially growing industrial applications of nano-filters including artificial ion channels, industrial pollution filters, fast DNA sequencing, and numerous other applications of ion-selective nanotubes.

In the long term, medical practitioners stand to gain from the improved drugs on offer from the pharmaceutical companies. Channelopathies include some of the scourges of mankind (cystic fibrosis, influenza, and diabetes), so that the potential benefits are nontrivial. In other cases, natural properties of ion channels (like the sensitivity of the herg channel to commonly used pharmaceuticals) has profound public health consequences. In still other (frustrating) cases, small changes in the current through a channel, e.g. the calcium current through the CaV L-type calcium channel, can exert a dramatic influence on longevity. Hundreds of thousands of people die each year from cardiac arrhythmias that would be converted to normal rhythms if one could simply double or triple the calcium current through this type of channel.

The public stand to benefit from the proposed research programme : (i) in the longer term, through improved medical treatment and technological possibilities (see above); and (ii) culturally during the research itself from our website and outreach activities.


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Description We have introduced and developed the ionic Coulomb blockade (ICB) model of permeation and selectivity in biological ion channels, providing a fundamental explanation for a range of phenomena that have been observed experimentally in sub-nm artificial nanopores as well as in biological ion channels. Systematic site-directed mutagenesis/patch-clamp studies were performed for the NaChBac bacterial channel in order to vary the negative fixed charge Qf at the selectivity filter (SF) in the range |Qf | = 0-12e. Comparisons of the ICB predictions with experimental results (both our own and those in the literature), Brownian dynamics (BD) simulations, and molecular dynamics (MD) simulations have allowed us to validate the ICB model itself and significantly extend our understanding of permeation and selectivity mechanisms in bacterial channels/mutants. A local-binding extension of the ICB model is being introduced to account for the contribution to selectivity coming from the singular 3D Coulomb terms at the ion-site and from ion-ion electrostatic interactions (complementing the 1D Coulomb interaction already incorporated into the standard ICB model). We have also extended the ICB model by developing an equilibrium statistical theory of the permeation process, and a self-consistent non-equilibrium kinetic model based on this statistical theory. Our extended theory is intended to take explicit account of the ionic radius, the excess chemical potential, the structure of distinct binding sites within the filter, and the non-equilibrium conditions caused by differences in potential or in ionic concentration between the bulk solutions on either side of the channel. The theory also encompasses selectivity between ions of the same valence. All the equations used are derived from first principles.
In more detail -
1. We introduced and described ICB in biological ion channels. ICB is a first-principles electrostatic phenomenon based on charge discreteness and self-energy effects, closely related to its electronic counterpart. We have also described base predictions of ICB (positions of stop and conduction bands, Fermi-Dirac statistical distributions of ions inside the SF, characteristic features of valence selectivity and divalent blockade) providing explanation of several effects of valence selectivity, and allowing direct comparison with experiments.
2. Our systematic site-directed mutagenesis/patch clamp studies of NaChBac bacterial channels, varying the fixed charge Qf, have confirmed the strong dependence of the conductance and selectivity on Qf. We have observed novel phenomenon of systematic Qf-induced shift of Eisenman selectivity sequences to large ionic sizes . That phenomenon is being explained on the basis of an extended ICB model, taking account of quantized dehydration energy.
In doing so we have: (a) trained a post-doctoral researcher in demanding cell biological and electrophysiological techniques, thereby addressing a UK skills gap; and (b) optimised the techniques for establishing heterologous expression of NaChBac and for measuring its activity.
3. We have also generated the extensive data set required for development of the ICB model, including a unique range of mutated NaChBac channels which have structurally different SFs but with similar associated nominal Qf values. Our analysis of the ion permeation properties (covering the full range of both Group I and II metal ions) has highlighted a dependence of ion permeation not only on nominal charge (Qf value), but also on substitution between nominally equally-charged EEEE and DDDD protein residue rings in key SF positions and on their different effective Qf values. That difference appears to be related to different protonation of charged rings which are a key factor of pore architecture.
4. Our development of a novel technique for recording NaChBac channel activity in high Na (500 mM) conditions has enabled us to match the conditions used by our Warwick collaborators in their MD simulations of NaChBac-mediated Na permeation (see ref below). This work was key to validating the MD simulation approach itself. 4.
5. Our preliminary study of stochastic binding in mixed tetramers has pioneered a way of obtaining partially-charged NaChBac mutants able to provide additional tests of the ICB model.
6. We found that the ICB model can explain some characteristic features of divalent blockade of the sodium current in calcium/sodium ion channels, including: (a) the strong exponential dependence of the blockade threshold IC50 on Qf for NaChBac and its mutants; and (b) the Fermi-Dirac shape of monovalent current decay vs divalent ionic concentration. Our explanation of divalent blockade is based on an enhanced ICB model that we are developing, taking account of the concentration of divalent ions. The ICB model was found to be consistent with the experiments.
7. Our ongoing comparison of the ICB model predictions of Na occupancy of the SF in NaChBac channels with MD simulations results are yielding promising results.
8. The ICB Model has led to a putative resolution of the celebrated "EEEE paradox" between mammalian Calcium channels and bacterial Sodium channels, both of which were thought to have the same Qf. We have suggested that an additional charged protein residue contributes to Qf in the case of the mammalian channel, but this idea needs to be tested.
9. The ICB model is being further developed to account for concentration-related effects, including (a) Concentration-dependent shifts of the Coulomb staircase for the SF ionic occupancy. These shifts are found to be consistent with the results of earlier BD simulations. (b) Divalent blockade/anomalous mole fraction effect (AMFE) phenomenon observed in calcium/sodium channels. The predicted AMFE effects are consistent with both mutation experiments and Brownian dynamics simulations.
10. Our ongoing enhancement of the ICB model takes account of the local (singular) 3D Coulomb (hyperbolic potential) term for describing attraction to the binding site (i.e. local-site binding) in addition to 1D Coulomb interaction inside the SF, accounted in standard ICB model. This correction leads to a geometry-dependent shift of the ICB resonant point which allows us to account separately for the influence on conduction and selectivity of the SF radius and the radius of the charged ring.
11. A similar extension of the 3D local Coulomb ion-ion interaction extends the ICB (i.e. 1D Coulomb) explanation of the phenomenon of multi-ion self-organization inside the SF, earlier revealed by Brownian dynamics simulations. Multi-ion self-organization leads to a dynamically multi-site pattern, even in a statically single-site channel, and to self-oscillations of ion occupancy inside the SF. These oscillations can lead to resonance in multi-site channels (e.g. the KcsA potassium channel), giving rise to potential energy patterns leading to strong selectivity enhancement. We are trying to connect these results to the corresponding results obtained by MD simulations of NaChBac.
12. Application of the statistical mechanics theory of permeation to the KcsA potassium channel has placed into context several earlier ideas, including the "snug fit" and "knock-on" conditions, and the Eisenman selectivity relations.
13. We have provided a first-principles resolution of a long-standing paradox: how can the potassium selectivity filter conduct K+ ions at nearly the rate of free diffusion while selecting them over (smaller) Na+ ions almost 1,000-fold? Our explanation involves derivation of an effective grand canonical ensemble of ions in the SF and leads to an analytic expression for its conductivity that takes account of multi-particle interactions. It also shows that the Eisenman-type selectivity equation for ions of equal valence, observed experimentally in earlier work, follows automatically from the condition of diffusion-limited conductivity.
Exploitation Route The ICB model can be applied by anybody interested in understanding the conduction properties of natural ion channels, or in designing mutants or artificial channels with specific properties. For example -

1. Our ICB model has already been applied successfully (paper in Nature Materials) by a group in Switzerland to explain current-voltage curves for sub-nm Mo2S artificial nanopores.

2. Eventually the improved understanding of ion channel selectivity mechanisms could lead to the creation of new drugs.

3. By analysing the mutations underlying the role of the potassium channel in cancer, to we can hope to identify therapeutic targets in cancer patients

The work is paving the way towards a general theory that will enable prediction of the conduction properties of different ions though different channel structures; correspondingly, it should eventually become possible to design the structure needed to exhibit a desired set of features.
Sectors Education,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology

Description In cultural and educational contexts, e.g. in giving talks is schools and to parties of school students visiting the Department, on several occasions.
First Year Of Impact 2016
Sector Education
Impact Types Cultural

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 Charity/Non Profit
Country United Kingdom
Start 10/2017 
End 09/2020
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