Fig. 3.

The regulatory circuit of the GPCRs can act as a logarithmic sensor. (A) Upon activation by ligand (c), the receptor (R) changes conformation and activates a G protein (T), which then break into an α and a $\beta \gamma$ subunit. The α subunit is responsible for downstream signaling, after which, it recombines with a $\beta \gamma$ subunit and recover the pool of G proteins. (B) Activity of the GPCR system, (i.e., the concentration of ${\widehat{\alpha }}_{GTP}$) is logarithmically tuned by $\frac{k_6}{k_4}$, the effective allosteric constant in the system. The logarithmic tuning breaks down when $k_4$ is much slower than $k_6$. In this plot, $k_1=1,k_2=10,k_3=10,k_5=50,k_6=.01,$ and $k_4\mathrm{\in }\left[{10}^{-2},{10}^2\right]$.