Thermal fluctuations set fundamental limits on ion channel function

Abstract

Voltage-gated ion channels are essential for propagating signals in neurons. Each channel senses the local membrane potential created by nearby ions. Fluctuations in these ions introduce two fundamental noise sources: (i) shot noise, from the discreteness of ionic charge, and (ii) Johnson-Nyquist noise, from long-wavelength thermal fluctuations of the electric field. We show that, for an individual channel, shot noise dominates and sets an intrinsic limit to voltage sensing. On the $10$ $μ$s timescales relevant to channel gating, this limit corresponds to an accuracy of about $10$ mV -- close to measured channel sensitivities. When signals from many channels are aggregated, Johnson-Nyquist noise eventually overtakes shot noise and bounds the total information that can be sensed from the environment. This transition occurs at an ion channel density of $< 1$ channel/$μ$m$^2$ for slow signals and around $10^2-10^4$ channels/$μ$m$^2$ for signals with $10$ $μ$s timescales, both of which are within the range of experimentally-measured densities for somas and axon initial segments, respectively. These results provide design principles for single-channel architecture and collective sensing and suggest that neuronal computation is ultimately constrained by thermal fluctuations.

Figures (7)

• Figure 1: Charge sensed by ion channels is generated by a discrete distribution of ions. The ion channel senses charge in a region of width $\sigma$ and height $h$. It is embedded in a membrane of thickness $d$.
• Figure 2: Numerical analysis of fluctuations for the parameters in Table \ref{['tab:parameters']}. (A) Scaling of signal-to-noise ratio with sensor height $h$. Dashed lines represent the unique optimal heights. (B) Comparison of fluctuations to shot noise. Values are shown at the optimal height $h^*(\sigma, d)$. The dashed line represents the analytical prediction of where the two contributions are equal. (C) Comparison of fluctuations to Johnson-Nyquist noise.
• Figure 3: Communication scheme in the soma. A time-dependent current is injected from a source. This signal propagates through the charge density field $\lambda$ and is sensed by $N$ ion channels distributed throughout the sphere. In the spherical integrals, vectors on the sphere correspond to ${\bf x} \coloneqq (R \sin(\theta) \cos(\phi), R \sin(\theta) \sin(\phi), R \cos(\theta))$ and the area element is $ds({\bf x}) \coloneqq R^2 \sin(\theta) \, d\theta \, d\phi$.
• Figure 4: Saturation of the $N$-channel signal-to-noise ratio $\text{SNR}_N(\omega)$ to the whole-cell signal-to-noise ratio $\text{SNR}_{\text{cell}}(\omega)$ for the parameters in Table \ref{['tab:parameters']} and $\omega = \tau_{\text{leak}}^{-1}$.
• Figure S1: Communication scheme for two far away ion channels. The sender channel injects current at the membrane, while the output channel makes a local measurement of charge.