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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]., Comment: 21 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2205.01864

The actin cytoskeleton is a semiflexible biopolymer network whose morphology is controlled by a wide range of biochemical and physical factors. Actin is known to undergo a phase transition from a single-filament state to a bundled state by the addition of polyethylene glycol (PEG) molecules in sufficient concentration. While the depletion interaction experienced by these biopolymers is well-known, the effect of changing the molecular weight of the depletant is less well understood. Here, we experimentally identify a phase transition in solutions of actin from networks of filaments to networks of bundles by varying the molecular weight of PEG polymers, while holding the concentration of these PEG polymers constant. We examine the states straddling the phase transition in terms of micro and macroscale properties. We find that the mesh size, bundle diameter, persistence length, and intra-bundle spacing between filaments across the line of criticality do not show significant differences, while the relaxation time, storage modulus, and degree of bundling change between the two states do show significant differences. Our results demonstrate the ability to tune actin network morphology and mechanics by controlling depletant size, a property which could be exploited to develop actin-based materials with switchable rigidity., Comment: 22 pages, 10 figures. Authors James Clarke and Francis Cavanna contributed equally; Changes: Added modeling work, extended dynamic light scattering analysis