From Berg-Purcell precision bounds to clock-limited information capacity

Physical limits to chemical sensing are traditionally expressed as Berg-Purcell bounds on estimation accuracy.

Whether these bounds also limit the total amount of information a molecular receptor can transmit has remained unclear, despite the fact that cellular signaling performance is naturally quantified in bits rather than precision alone.

Here we derive an explicit link between Berg-Purcell-type sensing limits and the information capacity of a single two-state receptor, yielding a compact expression that separates contributions from concentration range, receptor copy number, and averaging time.

We show that, in the ideal fixed-time occupancy model, diffusion-limited sampling alone does not define a finite global information bound: with a perfectly specified integration window and unbounded input range, information capacity grows without bound with dynamic range, albeit slowly.

A finite saturation arises when time integration is treated as an explicit physical resource.

Finite timing precision yields a clock-limited bound on information capacity, and in the high-occupancy regime information transmission crosses over from diffusion-limited to clock-limited behavior.

Together, these results establish a receptor-level information bound in bits that is finite once constraints on timing precision are taken into account.