Using quantum calculations to study potassium ion channels

Voltage-gated potassium ion channels open and close depending on voltages across the cell membrane, exclusively transporting potassium ions. They are key in important biological processes. Alisher Kariev and Michael Green, from The City College of the City University of New York, have studied ion channels using quantum calculations, and found that proton motion is responsible for channel gating; this result is controversial, and is challenging the common perception of how these channels operate.

Potassium ion channels are an incredibly important component of life. Not only are they found in all cells, they are also part of essentially all organisms – even a virus has been found with a potassium channel. Malfunctioning channels lead to a range of diseases, called channelopathies. One key biological process they are involved with are action potentials, which occur in excitable cells such as nerve cells.

Action potentials play a key role in the contraction of the heart and neuron signalling. The opening of sodium ion channels kicks off the action potential in neurons, causing a more positive charge of the inside of the cell due to an influx of positive sodium ions, known as depolarisation. When the inside of the cell becomes positive enough, these channels close, and potassium channels open. As these channels respond to changes in cell membrane potential, they are referred to as voltage gated. The voltage-gated potassium channels cause positive potassium ions to flood out of the cell, returning it to its resting charge. These channels have shown a preference for potassium ions over sodium ions of 1000:1, with a selectivity filter in their narrow pores to weed out anything in the cell that is not potassium.

Gating methods

Voltage-gated potassium channels are tetramers, meaning they are made up of four subunits. These four identical subunits span the cell membrane and form a square with the potassium pore in the middle. Each subunit has a voltage sensing domain (VSD), with four transmembrane (membrane-spanning) segments, plus two that combine to make an eight-segment pore. The gate is a section at the surface of the pore inside the cell that allows ions to pass when open, and prevents ion passage when closed.

“Gating by protons is a controversial model, but it is supported by calculations and re-interpretation of the data.”

But how does the gate open and close? There are standard models of gating which explain the process as follows: there is positive charge on the fourth transmembrane segment of the VSD, S4. When the membrane polarises, reaching around -70 mV, in most gating models, S4 is supposed to be pulled toward the gate, closing it. When the membrane depolarises and approaches 0, S4 is said to pull up and away, opening it.

Dr Alisher Kariev and Prof Michael Green, from The City College of the City University of New York, have carried out quantum calculations on sections of the channel. These suggest an alternate mechanism: S4 does not move, but positively charged protons in fact account for the brief gating current that precedes channel opening. The open structure of the channel is known from X-ray studies, but the closed structure has yet to be determined – so far, no structural method has succeeded in finding the structure with applied voltage.

The difference in gating methods is crucial. The common model was originally derived from substituting (mutating) an internal amino acid and reacting it with an external reagent. Since the side from which the reaction occurs changes with membrane depolarisation, it was assumed that a charged transmembrane segment moved across the membrane. Other mutations are more difficult to interpret on the common model, and quantum calculations by Kariev and Green have shown how these fit with this new model of gating. Most important, they have pointed out how the reaction with the original mutant does not prove that S4 moves.

In a 2019 paper, Kariev and Green examined how voltage closes the voltage-gated potassium channel. They started their quantum calculations from the X-ray structure of the open human potassium channel Kv1.2. Their results did not agree with the standard model of how the potassium channel functions, but they do agree with experimental results.

The key question was whether S4 actually moves in response to voltage changes to gate the channel (see figure 1). Some of their quantum calculations were done with S4 free to move, and the results, unlike commonly held beliefs, showed no protein backbone movement. However, protons did move – and in newer unpublished work, they propose two paths of protons from the end of S4 to the gate when the membrane is polarised, where the protons can close the gate, with essentially no protein backbone motion. Computations are continuing to test whether the paths function as hypothesised.

In the completed calculations on the VSD, Kariev and Green included 70 amino acids from the voltage sensing domain, as well as 24 water molecules. Their calculations showed protons being transferred along the voltage-sensing domain. To close the channel, protons must move through the VSD from outside to inside the cell, with the entire system acting cooperatively to facilitate this. From looking at 10 amino acids directly involved in the transport of these protons, they discerned one primary path for the protons to travel, and at least one other alternate path within the VSD.

Selectivity and rectification

The selectivity filter of the ion channel allows potassium ions through, but not others like sodium (see figure 2). This is key for the channel to fulfil its purpose. There is a specific sequence of amino acids in the selectivity filter of practically all voltage-gated potassium channels: TTVGYG. T stands for threonine, V stands for valine, Y stands for tyrosine, and G stands for glycine. Interactions with these amino acids are key in the ion selection process, a fact backed up by how consistently this pattern appears in potassium channels through half a billion years of evolution.

In a preprint in bioRxiv in March 2020, Kariev and Green discussed the selectivity filter using the same X-ray structure. They focused on a section found in each of the four domains, spanning from the upper section of the pore cavity to the second of four energy minimum positions the ion sees as it passes through the filter.

They found that the four sets of two threonines (the TT in the TTVGYG sequence), located where the ion transfers to the selectivity filter from the cavity, played a key role in selecting for potassium ions, taking over solvation of the potassium ion. Sodium ions were not solvated in a manner that allowed them to enter the selectivity filter. They were asymmetrically placed inside the pore, bound more strongly on one side than the other, failing to be solvated by one pair of threonines, whereas potassium ions remained on the pore axis, effectively in contact with all four sets of threonines.

In a standard model of potassium ion channel pore conductivity, each potassium ion pushes the one in front of it forward, called a knock-on mechanism. The question is why this does not result in the entering ion being pushed back. The mechanism that the quantum calculations gave the researchers resembled a ratchet and pawl, with two of the threonine hydroxyls alternately hydrogen bonding to water in the selectivity filter, then opening to admit another ion, with the water above preventing the previous ion from going backwards. While the ions and water that is transported with the ion through the pore do interact, the actual molecular detail, as revealed by the quantum calculation, suggests a considerable modification of the earlier form of the model.

“These studies suggest water and the conserved amino acids have the key role in ion conduction in the pore.”

Using quantum calculations to study the potassium ion channel

Kariev and Green chose to study the function of this channel using quantum calculations, rather than the more common molecular dynamics simulation (MD). Ab initio MD (MD using quantum calculations) exists, but has been too demanding of computer resources to be much use in ion channel calculations.

A number of advantages of quantum calculations are cited, and it is claimed that MD calculation results do not seem appropriate for ion channels. For example, the water basket below the selectivity filter has not been reported by MD, but was found by quantum calculation. Also, channels open and close tens of thousands of times over their lifetime. Most MD calculations do not consider the channel returning to its starting position. In contrast, quantum calculations do. With quantum calculations, charges on atoms and bond orders can be determined in the calculation, rather than fixed a priori, and the energies are more accurate. Hydrogen bonds can also be approximated much better using quantum calculations. Quantum mechanics, unlike almost all MD, also correctly calculates the transfer of charge between atoms as they approach, or move apart, and this is critical for the correct determination of the properties of the water, the protein, and the way these interact. Interactions leading to charge transfer among neighbouring molecules depend on relative orientations of the molecules, as well as distances, and quantum calculations get these correct automatically. Normal MD calculations cannot make changes in charge; MD that allows for “polarisation”, which includes at least some charge transfer, comes at the cost of loss of the ability to do the very large calculations that are the most important advantage of MD.

However, quantum calculations also have limitations. One reason is that these calculations give the structure of the channel protein at 0 Kelvin, or absolute zero, where molecular motion is essentially stopped, whereas MD takes place at room temperature. Therefore, quantum calculations neglect the channel’s vibrations. The surroundings of the channel could impact function. Quantum calculations can only cover a fraction of the channel; hence, they may miss some of these effects. There is a limit of around 1000 atoms for each quantum calculation, while MD may include 100,000. This is determined by present computer capacity – with much more powerful computers now being developed (exascale computing), these limitations should disappear, or at least be greatly ameliorated.

Fewer research groups have used quantum calculations than MD to study ion channels, in part due to these limitations and also the large amount of computer resources they consume. The Kariev and Green calculations seem to be the most extensive ion channel quantum calculations so far.

These quantum calculations account for much of the behaviour of the channel in relation to the ions. For gating, it produces a model which differs completely from the most common models. For conductivity, it adds considerable detail. This suggests the most productive approach to understanding the function of channels is likely to be quantum calculations.

References

• Kim, D. M., & Nimigean, C. M. (2016). Voltage-Gated Potassium Channels: A Structural Examination of Selectivity and Gating. Cold Spring Harbor perspectives in biology, 8(5), a029231. Available at: https://doi.org/10.1101/cshperspect.a029231
• Kariev, A., & Green, M. (2019). Quantum Calculation of Proton and Other Charge Transfer Steps in Voltage Sensing in the Kv1.2 Channel. The Journal Of Physical Chemistry B, 123(38), 7984-7998. Available at: https://doi.org/10.1021/acs.jpcb.9b05448
• Kariev, A., & Green, M. (2020). The Role of Ion Transition from the Pore Cavity to the Selectivity Filter in the Mechanism of Selectivity and Rectification in the Kv1.2 Potassium Channel: Transfer of Ion Solvation from Cavity Water to the Protein and Water of the Selectivity Filter. bioRxiv, 2020.03.16.994194. Available at: https://doi.org/10.1101/2020.03.16.994194

Research Objectives

Prof Green and Dr Kariev study ion transitions in voltage-gated sodium and potassium channels.

Funding

This research used resources of the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science Facility, and the Scientific Data and Computing Center, a component of the Computational Science Initiative, at Brookhaven National Laboratory under Contract No. DE-SC0012704, and resources at the High Performance Computation facility at City University of New York. Other funding was provided by the corresponding author.

Bio

Michael E. Green is Professor Emeritus of Chemistry, The City College of the City University of New York.

Alisher M. Kariev Alisher M. Kariev is Research associate at the Department of Chemistry and Biochemistry, The City College of the City University of New York.

Contact

E: [email protected]
W: https://www.ccny.cuny.edu/profiles/michael-green

Using quantum calculations to study potassium ion channels