Fig. S5.

(A) Model lock, with a spherical cavity of radius r_l cut off at angle θ. When a key is not bound, depletant particles are excluded from the volume between the lock and the dashed line. This excluded volume, originally $d\Omega r_l^2$, can be decreased via key binding inside the cavity. (B) Full calculation for the change in excluded volume V_exc as a function of $r_k$. The maximal change, and therefore the most energetically favorable radius for binding, occurs when $r_k=r_l$. Here $r_l=3$ and $\theta =\pi /2$. (C) When $r_k\ll r_l$, the excluded volume is just given by the contact area of the two spheres. Black, lock; red, key. Dashed lines indicate the respective excluded volumes when the lock and key are separated. (D) When $r_k$ approaches $r_l$, the intersection with the plane must be taken into account. Black, lock; red, key. The vertical line indicates the plane through the opening of the lock. Dashed lines indicate the respective excluded volumes when the lock and key are separated.