Mechanical cues affect a number of important biological processes in metazoan cells, such as migration, proliferation, and differentiation. Many of these processes are mediated by the cytoskeleton, an intracellular network of protein filaments that provides mechanical rigidity to the cell and drives cellular shape change. In particular, actin, a very highly conserved and abundant cytoskeletal protein, forms filaments that, when organized by a large and diverse group of actin-binding and regulatory proteins, self-assemble into dynamic and mechanically complex networks. The actin filament itself is polymorphic, with a structure and a set of mechanical properties that are modulated by the binding of regulatory proteins. Both the structure and the mechanical properties of actin filaments play an important role in determining the mechanical properties, architecture, and dynamics of the subcellular structure that result from self-assembly. We sought to investigate an important unanswered question: how do mechanical constraints help regulate the assembly of an actin network? This dissertation focuses on branched actin networks, which play a key force-generating role in the formation of membrane protrusions, in endocytosis, and in several types of intracellular motility. These networks are nucleated by the Arp2/3 complex and display adaptive behavior in response to compressive forces. They consist of Y-shaped branches formed by a pre-existing filament, the Arp2/3 complex bound to its side, and a new actin filament nucleated by the Arp2/3 complex. To investigate how the architecture of these networks is shaped by mechanical constraints, such as compressive forces arising from the resistance of cellular membranes to deformation, we devised a methodology for mechanically constraining single actin filaments while new branches are nucleated from their sides by the Arp2/3 complex. Branch nucleation on individual filaments was imaged with two-color fluorescence microscopy using a protocol that distinguishes constrained mother filaments from freshly nucleated daughter filaments. Combining this two-color assay with quantitative analysis of filament curvature, we show that filamentous actin serves in a mechanosensitive capacity itself, by biasing the location of actin branch nucleation in response to filament bending. We observed preferential branch formation by the Arp2/3 complex on the convex face of the curved filament. At radii of curvature of 1 micrometer, we observed approximately twice as many branches on the convex face as on the concave face. In the cellular context, where actin filaments tend to make a ~35 degree angle with the normal to the membrane, this observation suggests that compressive forces that bend actin filament tips away from the membrane would result in an enhancement of branching nucleated on the membrane-facing convex face of each filament. This effect constitutes a novel mechanism by which branched actin networks may be oriented toward membranes, as observed in vivo. Furthermore, in the context of a limited branching zone near the membrane, which is expected from the known biochemistry of the process, orientation of new branches toward the membrane also leads to an increase in network density in response to force, which has been documented in experiments with motility of bacteria in cytoplasmic extract. To explain the biased nucleation of branches on curved actin filaments, we propose a fluctuation gating model in which filament binding or branch nucleation by Arp2/3 occur only when a sufficiently large, transient, local curvature fluctuation causes a favorable conformational change in the filament. Using Monte Carlo simulations of a discretized worm-like chain model of the actin filament immobilized on a surface like the filaments in the constrained branching assay, we show that the fluctuation gating model can quantitatively account for our experimental data. Expanding the scope of the simulations beyond the in vitro experiment, we hypothesize that the curvature fluctuations of filaments in the cell may be modulated by the architecture of the actin network to which they belong. To test this hypothesis, we computationally explore how three types of mechanical constraints - buckling or bending of a filament end by a hard wall, bundling of filaments by a crosslinking protein, and uniaxial tension applied to a single filament - affect local curvature fluctuations. We find that bending of simulated filaments by a hard wall can significantly alter curvature fluctuations, the magnitude of which can be approximately calculated by the simple geometry of filament bending at the barrier. On the other hand, crosslinking of simulated actin filaments with crosslinking elements of physiologically relevant stiffness has surprisingly little effect on the small-scale local curvature fluctuations. Similarly, enclosure of a simulated filament bundle in a tube does not significantly affect curvature of filaments on the nanometer scale. Tension, however, in the range of 100 pN, does have a marked effect on curvature fluctuations in our simulations, suggesting that any interactions of actin-binding proteins with actin filaments that depend on bending fluctuations may be modulated by tension. This has been observed in several recent experiments, suggesting that the effects of tension on the biochemical interactions regulating actin network assembly and disassembly warrant further study. Overall, the results presented here demonstrate how filament curvature can alter the interaction of cytoskeletal filaments with regulatory proteins, suggesting that direct mechanotransduction by actin may serve as a general mechanism for organizing the cytoskeleton in response to force.