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Depletion interactions are thought to significantly contribute to theorganization of intracellular structures in the crowded cytosol. The strengthof depletion interactions depends on physical parameters like the depletantnumber density and the depletant size ratio. Cells are known to dynamicallyregulate these two parameters by varying the copy number of proteins of a widedistribution of sizes. However, mammalian cells are also known to keep thetotal protein mass density remarkably constant, to within 0.5% throughout thecell cycle. We thus ask how the strength of depletion interactions varies whenthe total depletant mass is held fixed, a.k.a. fixed-mass depletion. We answerthis question via scaling arguments, as well as by studying depletion effectson networks of reconstituted semiflexible actin $\textit{in silico}$ and$\textit{in vitro}$. We examine the maximum strength of the depletioninteraction potential $U^*$ as a function of $q$, the size ratio between thedepletant and the matter being depleted. We uncover a scaling relation $U^*\sim q^{-\zeta}$ for two cases: fixed volume fraction $\phi$ and fixed massdensity $\rho$. For fixed volume fraction, we report $\zeta < 0$. For the fixedmass density case, we report $\zeta > 0$, which suggests the depletioninteraction strength increases as the depletant size ratio is increased. Totest this prediction, we prepared our filament networks at fixed massconcentrations with varying sizes of the depletant molecule poly(ethyleneglycol) (PEG). We characterize the depletion interaction strength in oursimulations via the mesh size. In experiments, we observe two distinct actinnetwork morphologies, which we call weakly bundled and strongly bundled. Weidentify a mass concentration where different PEG depletant sizes leads toweakly bundled or strongly bundled morphologies...[more in main text].

Morphological Control of Bundled Actin Networks Subject to Fixed-Mass Depletion