  Depletion interactions are thought to significantly contribute to the
organization of intracellular structures in the crowded cytosol. The strength
of depletion interactions depends on physical parameters like the depletant
number density and the depletant size ratio. Cells are known to dynamically
regulate these two parameters by varying the copy number of proteins of a wide
distribution of sizes. However, mammalian cells are also known to keep the
total protein mass density remarkably constant, to within 0.5% throughout the
cell cycle. We thus ask how the strength of depletion interactions varies when
the total depletant mass is held fixed, a.k.a. fixed-mass depletion. We answer
this question via scaling arguments, as well as by studying depletion effects
on networks of reconstituted semiflexible actin $\textit{in silico}$ and
$\textit{in vitro}$. We examine the maximum strength of the depletion
interaction potential $U^*$ as a function of $q$, the size ratio between the
depletant and the matter being depleted. We uncover a scaling relation $U^*
\sim q^{-\zeta}$ for two cases: fixed volume fraction $\phi$ and fixed mass
density $\rho$. For fixed volume fraction, we report $\zeta < 0$. For the fixed
mass density case, we report $\zeta > 0$, which suggests the depletion
interaction strength increases as the depletant size ratio is increased. To
test this prediction, we prepared our filament networks at fixed mass
concentrations with varying sizes of the depletant molecule poly(ethylene
glycol) (PEG). We characterize the depletion interaction strength in our
simulations via the mesh size. In experiments, we observe two distinct actin
network morphologies, which we call weakly bundled and strongly bundled. We
identify a mass concentration where different PEG depletant sizes leads to
weakly bundled or strongly bundled morphologies...[more in main text].
