Fig. 3.

Complementary shapes demonstrate the capacity of programmable interactions. (A) Each shape $x_i$ is made of L vertical bars of different heights and has a corresponding binding partner $y_i$ shaped exactly as its complement; interactions are mediated via depletant particles of diameter d, and each adjoining bar can change by a maximum amount of δ. (B) Mutual information as a function of N, the number of lock–key pairs, showing a capacity of 7.8 bits ($L=10$, $d=0.2\hspace{0.5em}\mu \text{m}$, $\delta =1\hspace{0.5em}\mu \text{m}$, $\overline{s}=-10\hspace{0.17em}{k}_{B}T$). (C) Increasing L increases the on-target binding strength $\left|s\right|$ (blue), but has little effect on off-target binding strength $\left|\overline{w}\right|$ (black), unlike with colors (Fig. 2C). (C, Inset) Capacity scales linearly with L. Allowing translations has no effect on $\left|\overline{s}\right|$, but increases $\left|\overline{w}\right|$ (black, dashed line) and therefore decreases C (red, dashed line). ($d=0.07\hspace{0.5em}\mu \text{m}$, $\delta =1\hspace{0.5em}\mu \text{m}$, $\mathit{ϵ}=1\hspace{0.17em}{k}_{B}T$). (D) Fixing $\overline{s}=-10\hspace{0.17em}{k}_{B}T$, the capacity can be increased by increasing δ: When $\delta /d$ is small, on-target keys are indistinguishable from off-target keys, and so capacity is small. Increasing δ decreases the crosstalk, and capacity increases accordingly.