Quantum Coherence in Ion Channels: An Alternating Electric Field Could Put the Idea to the Test

Abstract

The selectivity filter of a potassium channel passes about 100 million ions per second while still turning sodium away at a ratio of at least 10,000 to 1. The researchers proposed quantum coherence as a hypothesis, pointing out that the matter wavelength of a potassium ion (about 0.05 nm) is within a factor of five of the spacing of the potential inside the filter (about 0.24-0.25 nm), and that a calculated tunneling probability multiplied by the ion's trapping frequency gives a throughput approaching the measured conduction rate. As the key test of that hypothesis they proposed a resonance effect: when the channel is driven by an alternating electric field, the current should fall sharply at particular driving conditions, a phenomenon called dynamic localization that classical rate equation models cannot produce. [Quantum Biology Society] Every process in a living organism, from nerve signaling to muscle contraction, passes at some point through a protein tunnel called an ion channel. Potassium channels are among the most impressive of them. In the bacterial KcsA channel, an open gate lets through about 100 million potassium ions (K⁺) per second, close to the physical limit set by diffusion. At the same time it turns away sodium ions (Na⁺), which are similar in size, at a ratio of better than 10,000 to 1. The classical account explains this selectivity through the attraction between the ion and the filter, the repulsion between ions, and the fact that potassium pays a smaller energy penalty than sodium for shedding its hydration shell. But there is a physical tension in that picture: the thermal fluctuations of the backbone atoms that form the filter are large compared with the small difference in size between potassium and sodium, which has prompted calls to re-examine the traditional explanation. Alipasha Vaziri of the Howard Hughes Medical Institute's Janelia Farm Research Campus in the United States and Martin B. Plenio of the Institute of Theoretical Physics at Ulm University in Germany brought a quantum mechanical yardstick to this dilemma in a 2010 paper in New Journal of Physics (vol. 12, article 085001). The significance of the work lies not in asserting that quantum coherence definitely exists inside an ion channel, but in raising its possible existence as a hypothesis and designing a concrete way to test it experimentally. The authors were explicit that they are not arguing for macroscopic quantum states across the brain: any coherence they expect is a protein level phenomenon confined to subnanometer distances and picosecond times. ■ A Filter That Passes 100 Million Ions a Second and Sorts Them 10,000 to 1 The selectivity filter of the KcsA channel is a narrow tube about 0.3 nm across and about 1.2 nm long. Amino acid chains reaching in from four subunits form its walls, with the oxygen atoms of carbonyl groups lined up pointing into the pore. Sets of these oxygens lie in a plane and form binding sites where an ion can briefly rest. The passage is so narrow that a potassium ion, normally surrounded by eight water molecules, has to shed that entire hydration shell before it can enter. Inside the tube, potassium ions and water molecules move in single file, alternating with one another. Numerical calculations of the free energy of ion conduction find two configuration paths that are nearly degenerate in energy, separated by only about 2 kcal/mol, and x-ray diffraction data support this picture, revealing two equally represented arrangements of water and potassium in the filter, known as the 1,3 and 2,4 states. The binding sites are spaced about 0.24 nm apart, and the height of the barrier an ion must cross rises and falls between about 1.7 and 8 kBT (roughly 1-5 kcal/mol) depending on whether a given site is occupied and on the thermal vibrations of the protein. ■ Can an Ion Behave Like a Wave? At this point the authors offer two quantum mechanical estimates. The first turns on the idea of a matter wave. At room temperature the de Broglie wavelength of a potassium ion works out to about 0.05 nm, within a factor of five of the periodic spacing of the potential inside the filter (0.24-0.25 nm). That leaves room, they suggest, for the ion to behave like a wave striking a kind of diffraction grating as it crosses the periodic energy barriers. The second is quantum tunneling. The probability that a potassium ion passes through a barrier rather than over it comes out at about 7×10⁻⁵. Assuming the ion rattles against the barrier inside its binding site roughly 10¹² times per second, the product of the two gives a transmission rate approaching the observed figure of about 100 million ions per second. The system interacts strongly with its surroundings, however, so coherence cannot survive indefinitely. The authors' rough estimate puts the decoherence time, the interval over which the quantum state is destroyed, at 10⁻⁹-10⁻⁸ seconds, comparable to the expected tunneling times, and they identify the stretching vibration of the carbonyl groups as the main culprit. The protein structure that guides the ion is, paradoxically, also the source of the noise that scrambles its quantum state. ■ The Fingerprint of Coherence: A Sharp Drop in Current Under an Alternating Field The paper's central contribution is its proposal for measuring that coherence directly. The authors focus on what happens when an external alternating (ac) electric field is applied to shake the energy levels of the channel periodically. If the strength of the applied field is scanned while the driving frequency is held fixed, the ion current falls off sharply at particular values, a resonance effect known as dynamic localization, with the positions of the dips set jointly by the frequency and the strength of the drive. The principle is that when the shaking is mistimed, the probability waves describing the ion's possible routes interfere destructively, so the ion fails to advance and is trapped where it is. What matters is that this resonance can never appear in a classical rate equation model, in which the process is described purely in terms of probabilities: a classical model has no phase to interfere with in the first place, and the current would be essentially independent of the strength of the driving field. Conversely, as noise grows and quantum dephasing deepens, the resonances become shallower. Measuring the depth of the valley into which the current falls therefore offers a quantitative gauge of how much quantum coherence survives inside the channel. ■ Experimental Feasibility The tool the authors propose for the test is a modification of patch clamping, the electrophysiology technique long in routine use in biophysics. Using an excised patch, a steady ionic current is established by the difference in potassium concentration across the membrane (90 mM against 3 mM); an ac field at around 100 MHz is then superimposed and the resulting change in current is observed. The largest obstacle is the capacitive current induced by the fast ac field. At around 3 μA it is a million times larger than the picoampere (pA) ionic current the experiment is trying to measure. The authors set out practical ways around this: lock-in detection that exploits the difference in timing between the two currents, circuits that introduce negative capacitance as compensation, chambers built around artificial lipid bilayers, and nitrogen vacancy (NV) centers in diamond, nanoscale sensors recently developed for recording picoampere currents in biological systems. ■ Significance and Outlook The lasting value of this paper is that it takes quantum coherence in ion channels, until then an abstract speculation, and brings it into the realm of a physical prediction that can actually be verified or falsified with a current measurement. The authors themselves acknowledge that the model behind their calculations simplifies the formidable complexity of a real channel, and that ion conduction is a many body phenomenon, so more rigorous simulations and experiments must follow. Indeed, in the years since the 2010 proposal, more skeptical calculations of how long coherence can be maintained have appeared, and the debate, along with the experimental challenge, remains open. Whichever way the answer falls, the paper stands as an important marker in biophysics for supplying an experimental blueprint for judging how far the machinery of life is classical and where it begins to be quantum. #QuantumBiology #IonChannel #PotassiumChannel #SelectivityFilter #QuantumCoherence #Decoherence #KcsA #QuantumTunneling #MatterWave #Electrophysiology https://arxiv.org/abs/1006.3892