Thermal Noise Sets a Limit on Nerve Signals express
A neuron listens to the electric world like a sensitive microphone. Its 'ears' are ion channels in the membrane: they open in response to voltage, created by the flow of charged particles. But interference is inevitable in this flow. First, shot noise makes itself known: each ion, darting through a channel, delivers a microscopic thump, like a rare raindrop on a tin roof. For a single channel, this limits accuracy to about 10 millivolts.
When the signal is gathered from hundreds of channels, the shot impacts average out, but another menace emerges — thermal noise, the incessant trembling of molecules driven by heat. This background hum never fades and sets the ultimate limit on the neuron’s sensitivity. It’s striking that the transition from one noise to the next occurs precisely at the channel densities observed in real neurons. In the axon hillock, where speed is vital, there are hundreds of times more channels than on the cell body — nature economizes resources, operating on the razor’s edge of physical laws.
Original abstract
as written by the authors arXiv:2604.03538
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 $$10$$ $$\mu$$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/$$\mu$$m$$^2$$ for slow signals and around $$10^2-10^4$$ channels/$$\mu$$m$$^2$$ for signals with $$10$$ $$\mu$$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.
The crossover from shot noise to thermal noise dominance occurs at channel densities that strikingly mirror those measured in real neurons. In the axon hillock, where transmission speed counts, there are hundreds of times more channels than on the cell body.