Microswimmers are objects that are able to propel themselves actively in fluid environments. The typical motion of bacteria such as E. coli can be described by the run-and-tumble model, which consists of successive relatively straight runs in conjunction with erratic changes of the swimming direction known as tumbles. The process of diffusion of microswimmers in porous media is crucial in many biological and environmental systems, and their motility is critical for processes such as bioinfection, bioremediation and biodegradation. In this thesis, the diffusion of microswimmers in porous media is studied numerically based on the run-and-tumble model. The results show that an increase in volume fraction of the obstacles comprising the porous medium leads to a decrease in effective long-time diffusivity. In cases where obstables are allowed to overlap, the diffusivity drops even more dramatically with volume fraction than in the case of no overlap. The effect of varying the range of pillar dimensions is also studied. In the case of overlapping pillars, it is found that the diffusivity increases slightly when the domain is filled with

This thesis is devoted to understanding the effect of inter-particle interactions, external fields and confinement in active suspensions. Active suspensions, such as a bath of swimming micro-organisms, have microstructural elements which are motile and exert active stresses on the suspending fluid. The internally generated stresses in active suspensions lead to an intrinsic coupling between the swimmer configurations and the immersing fluid.

The first theme of the thesis focuses on hydrodynamically driven self-organization in active suspensions. We first study the dynamics of concentrated active suspensions in a 3D periodic domain using a coupled Smoluchowski-Stokes kinetic model and discover novel instabilities for both rear-actuated (pusher) and front-actuated (puller) swimmers, characterized by giant number density fluctuations, due to the coupled effects of hydrodynamic and steric interactions. Next, we incorporate chemotactic run-and-tumble effects in the kinetic model to study the dynamics in thin films of aerotactic bacteria. A transition to chaotic dynamics beyond a critical film thickness is reported, in agreement with experiments, and shown to be a consequence of the coupling between aerotactic response of bacteria and hydrodynamic disturbance flows.

The second theme focuses on the sole interplay between motility and confinement in dilute suspensions, ignoring the effect of inter-particle interactions. First, we investigate the dynamics of a confined suspension of Brownian swimmers using a simple kinetic model by prescribing a no-flux condition on the probability distribution function of particle configurations and explain several peculiar dynamics reported in experiments, viz., wall accumulation, as well as upstream swimming, centerline depletion and shear-trapping when a pressure-driven flow is imposed. Next, we calculate the swim pressure of non-Brownian run-and-tumble spherical swimmers using a kinetic model based on coupled bulk/surface probability density functions.

The third theme focuses on the effect of confinement on active self-organization. We discover a symmetry-breaking phase-transition to a spontaneous flowing state with net fluid pumping beyond a critical concentration in a strongly confined channel. The framework for studying confined active suspensions is also extended to explore geometric control of active self-organization in circular and other complex domains.

Active fluids, such as suspensions of swimming microorganisms, have been shown to spontaneously create flow. Controlling active flows could provide advantages for those designing microfluidic devices. Therefore, we looked into geometric control of active fluids confined in a ring. Primarily focusing on the effect on bacterial flow, we used a sawtooth perturbation to determine factors useful in guiding and controlling active flows. It was found that the amplitude, asymmetry, and size of the sawtooth affected the total bacterial flow created by the geometry. Additionally, optimization methods were developed to determine a shape that creates maximum bacterial flux.

Mammalian sperm cells manage locomotion by the movement of their flagella. Dynein motors inside the flagellum consume energy from ATP to exert active sliding forces between microtubule doublets, thus creating bending waves along the flagellum and enabling the sperm cell to swim in a viscous medium. Recently, a model has been proposed for the planar nonlinear beating of the flagellum under clamped and hinged boundary conditions, where spontaneous oscillations emerged from the coupling of dynein motor kinetics with deformations. In a new framework combining slender-body theory and the boundary element method, we extend this model to study the free swimming of sperm cells with arbitrary head shapes, considering the effects of non-local hydrodynamic interactions between head and flagellum. The model is shown to produce realistic beating patterns and swimming trajectories, which we analyze as a function of sperm number and motor activity. Remarkably, we find that the swimming velocity does not vary monotonically with motor activity, but instead displays two local maxima corresponding to distinct modes of swimming.

Elastic filaments subjected to hydrodynamic forcing are a common class of fluid-structure interaction problems. In biology, they are crucial to cytoskeletal motions of the cell, the locomotion of micro-organisms, and mucal transport. In engineering, they are often the source of non-Newtonian rheological properties and a variety of complex fluid behavior such as hydrodynamic instabilities and chaotic mixing. At the heart of many of these dynamics is the competition between an elastic backbone and viscous forces acting to deform it, tangled with the anisotropic shape of such filaments as well as slowly decaying hydrodynamic interactions in a Stokesian fluid. In this work, we use slender-body theory for low-Reynolds-number hydrodynamics to address theoretically and computationally a few such problems of physical and biological significance. We first describe the tumbling of polymers in shear flow and the suppression of thermal fluctuations in extensional flow. A theory for the stretch-coil transition of semiflexible polymers is also developed. We then turn to the transport properties of semiflexible filaments in a flow setup that mimics some of the dynamics of biological polymers in motility assays. Thermal fluctuations frequently trap polymers within vortical cells, and are shown to lead to subdiffusive transport at long times. The mechanism behind this anomalous feature and the subtle role of flexibility is emphasized. Then we focus on the sedimentation of flexible filaments. In the weakly flexible regime, a multiple-scale asymptotic expansion is used to obtain expressions for filament shapes and peculiar trajectories. In the highly flexible regime, we show that a filament sedimenting along its long axis is susceptible to a buckling instability. Our predictions are corroborated by detailed numerical simulations. Finally, we look at suspensions of sedimenting elastic fibers, emphasizing the role of filament shape, flexibility, and long-ranged hydrodynamic interactions. We develop a mean-field theory for such a suspension, and its stability to perturbations of fiber concentration is analytically explored. Detailed numerical simulations are also performed to verify these predictions and elucidate the microstructural mechanisms tied to the growth or suppression of this instability.

The central theme of the dissertation is to understand physical principles underlying the dynamical self-organization of the genome in the cell across different length and time scales. The inherently multiscale and out-of equilibrium nature of chromatin dynamics and compaction in the strongly heterogeneous nucleus has been addressed in this work. The large-scale organization of chromatin – the functional form of DNA – is critical to transcription during which ATP-powered enzymes such as RNA polymerases must physically access specific genes within a tightly-packed, micron-scale nucleus. In differentiated cell nuclei, two major chromatin compartments -- heterochromatin and euchromatin -- are spatially segregated, with transcriptionally active euchromatin loosely packed while mostly silent genes are compacted into heterochromatin. Through the lens of an active polymer model of chromosomes using Brownian dynamics simulations based on a boundary integral formulation, along with a kernel-independent fast multipole method, we investigate how large heterochromatic regions form and segregate through complex interactions with euchromatin. Our model consists of a system of long flexible bead-spring polymers representing chromosomes, which are confined to a spheroidal nucleus and composed of alternating segments of active euchromatin and silent heterochromatin immersed in a viscous solvent. Our simulations are applied to analyze the role of euchromatic activity on nuclear dynamics and pattern formation, and demonstrate that active stresses and resulting nucleoplasmic flows serve to enhance heterochromatin segregation and compaction by promoting interactions and subsequent crosslinking between distant genomic segments.

Moving to nano-scale organization, we also analyzed the dynamics of DNA loop extrusion in the presence of the active motor proteins known as structural maintenance of chromosomes (SMC) complexes, of which condensin and cohesin are two important examples. These complexes have been observed to translocate along chromatin in a force-dependent directed manner to form loops via a process known as "loop extrusion" using the energy obtained from the hydrolysis of ATP. In this work, we elucidated the role played by hydrodynamic interactions, the active response of the motors and chain mechanics in assisting loop extrusion under different parameter regimes. The model accounts for the structural features and dynamics of the motor proteins. Furthermore, studies with active polymer in an unconfined environment elucidated the role of activity and hydrodynamics in the self induced coil-stretch transition. This `active coil–stretch transition' is reminiscent of the transition exhibited by passive flexible polymers in externally applied extensional flows, but is internally driven by dipolar activity in the present case. Discussions of the simulation findings are complemented with a simple kinetic model for an active trimer. Our modeling efforts complemented and informed some of the experimental observations providing deeper insight into the mechanisms behind the genome organization.