Colloidal suspensions, consisting of particles of nano to micron scale dispersed in a medium, experience interparticle interactions that profoundly impact the macroscopic properties of soft materials, including stability, structure formation, and dynamics. A mechanism to dynamically tune these interactions can provide new avenues for self assembly and material processing. However, while traditional colloidal interactions have been well understood, it has been theoretically challenging to develop frameworks for nonequilibrium systems where interactions are dynamically evolving on the order of colloidal timescales.

In this thesis, I combine theoretical, experimental, and computational efforts to understand out-of-equilibrium colloidal interactions that are modulated by external stimuli. These nonequilibrium interactions result from microscopic relaxation timescales which are intrinsic to the colloidal system and may be controlled to vary suspension-level properties such as viscosity and morphology. First, as a proof of concept, I demonstrate precise control of dynamic pair interactions using surface-mobile polymer-coated colloids that are inspired by biological cell membranes. I show that entropically-driven surface rearrangement of polymers at colloidal contact interfaces enable an effective, dynamic interaction which is controllable over a range of pico-Newton forces and seconds timescales. Later in the thesis, I extend the theoretical framework to attractive colloids and show that polymer entropic effects regulate structure formation and phase stability in the context of colloidal self assembly. Unlike traditional interactions, we show that surface-mobile polymers act as dynamic surfactants and allow colloids to acquire anisotropic shape throughout the assembly process. Microscopic polymer distributions impose unique geometric constraints between colloids that precisely control their packing in lamellar, string, and vesicle superstructures. Then, to understand the material properties of the suspension, I develop a first-principle framework that captures the multiscale coupling between microscopic timescales and macroscopic transport properties. Using microrheology in a bidisperse suspension as a case study, we demonstrate that effective depletion interactions between driven colloids are sensitive to particle timescales out of equilibrium and cannot be predicted by equilibrium-based pair potentials. We show that the interplay between Brownian relaxation timescales of different species plays a critical role in governing the viscosity of multi-component suspensions. Finally, in the context of biological systems, I use Brownian Dynamics simulations and polymer theory to investigate crowding effects on reconstituted and living cell membranes and characterize spatial heterogeneities. Overall, several systems are presented which exhibit multiscale, nonequilibrium interactions, and a framework connecting local dynamics to macroscopic material properties is developed.

Many living systems, such as bacteria or eukaryotic cells, utilize self-propulsion to enhance transport, find nutrients, or avoid threats. However, cells often inhabit complex and heterogeneous spaces---e.g. gels and tissues in the body, or soil sediments in the environment---that impede rapid transport. Additionally, many biologically and industrially relevant complex materials are opaque and difficult to characterize, indicating the need for adequate computational and analytical models to guide experimental efforts.

In this dissertation, I utilize theory and simulation to study the structure and motion of microscopic self-propelled (or active) species in confinement, including bacteria, synthetic swimmers, and cytoskeletal filaments. Active matter systems are inherently nonequilibrium and traditional theories of Brownian motion in porous media fail to accurately describe the swimmers' dispersion. Active particles accumulate along boundaries due to their self-propulsion, even in the absence of attractive interactions. This mechanism traps the active particles at regions of high concavity, coupling the diffusivity of the swimmer to the microstructure of the confining walls.

I then extend these theories to study the motion of anisotropic active particles (like cytoskeletal filaments or rod-shaped bacteria) in the presence of soft confinement. I develop a Smoluchowski model that demonstrates the connection between the long-time self-diffusivity and active rod nematic order. Finally, I use these results to examine the partitioning of bacteria in an aqueous two-phase system, and the nematic ordering of F-actin filaments on topographically patterned channels.