Universal lower bound on the free-energy cost of molecular measurements

The living cell uses a variety of molecular receptors to read and process chemical signals that vary in space and time. We model the dynamics of such molecular level measurements as Markov processes in steady state, with a coupling between the receptor and the signal. We prove exactly that, when the signal dynamics is not perturbed by the receptors, the free energy consumed by the measurement process is lower bounded by a quantity proportional to the mutual information. Our result is completely independent of the receptor architecture and dependent on signal properties alone, and therefore holds as a general principle for molecular information processing.

Figure 1

The signal and receptor state spaces are embedded in their physical environments (upper and lower boxes, respectively). The signal transition rates $w^{\alpha ,\beta }$ are independent of the receptor, while the receptor transition rates $w_{i,j}^{\alpha }$ depend on the current signal state.

Figure 2

(a) Single ligand-receptor binding model, with states $(\alpha ,i)$, where the first entry represents the absence ($·$) or presence ($•$) of a ligand, and the second entry represents whether the receptor is unbound ($\cup$) or bound. The arrows represent transitions with the rates written alongside. (b) For this model we have generated the data by numerically diagonalizing the transition matrix. The logarithm is in natural base. The parameters are $w_u=1,w_e=0.01$. The dotted lines are the analytical bounds from (5), which are clearly validated. The triangles represent $\dot{{\sigma }_y}$, which diverge with increasing $w_m$, as opposed to $I_{\text{ss}}$ (boxes) which saturate at large $w_m$.