Thermodynamic Uncertainty Relation for Biomolecular Processes

Biomolecular systems like molecular motors or pumps, transcription and translation machinery, and other enzymatic reactions, can be described as Markov processes on a suitable network. We show quite generally that, in a steady state, the dispersion of observables, like the number of consumed or produced molecules or the number of steps of a motor, is constrained by the thermodynamic cost of generating it. An uncertainty $\epsilon$ requires at least a cost of $2k_{B}T/{\epsilon }^2$ independent of the time required to generate the output.

Figure 1

Multicyclic network of states for an enzyme $E$ that can bind substrates $S_1$ and $S_2$, and produces $P$. The solid (dashed) cycle represents the first (second) cycle in Eq. (23).