Fig. 1: Ion coherence in the transport dynamics of the KcsA channel.

a Transmembrane voltage dependence of the K⁺ ion distribution. Left: Simulation system of the KcsA channel. The KcsA protein (cyan) is embedded in a phospholipid bilayer membrane (green) in the presence of solution molecules (gray). Middle and right: Transmembrane voltage (V) dependence of the K⁺ ion distribution. The Filter+ region is introduced for covering the S1’, S1, S2, S3 and S4 peaks at a voltage of V = 100 mV. b Typical picosecond-scale z-coordinate trajectories of confined K⁺ ion oscillation and an ion moving out of the channel at the transmembrane voltage of 100 mV. The black, red, green and blue curves indicate the trajectories of the K1, K2, K3 and K4 ions, respectively. Top: Oscillation waveforms of confined ions in Filter+ along the channel axis. The peak locations (solid gray lines) per oscillating trajectory are almost the same as those of other trajectories, and a similar case also occurs in the trough locations (dotted gray lines), indicating that the oscillation phases of confined K⁺ ions match each other, i.e., coherent oscillation. Bottom: Ion transfer trajectories. The four ions simultaneously move up of ~2 Å during δ = 0 ps to 7 ps, the ions K1 and K4 separately move up ~2 Å during δ = 118 ps to 177 ps, and the K1 ion moves out of channel after δ = 177 ps. c Multitimescale evolution of the coherence-associated ion transport dynamics of the KcsA channel. Top: Typical picosecond-scale trajectory of the ion coherence degree α_F+. Middle and bottom: Typical nanosecond- (middle) and microsecond- (bottom) scale trajectories of the ion coherence degree (black) and transport events (red). The dashed green line represents the time location of transport event occurrence. The green curve denotes the distribution probability of α_F+, which has two peaks at 0.267 and 0.141, respectively, indicating two kinds of coherence states for the ions confined in the KcsA Filter + .