The transport of cargo across the nuclear membrane is highly selective and accomplished by a poorly understood mechanism involving hundreds of nucleoporins lining the inside of the nuclear pore complex (NPC). Currently, there is no clear picture of the overall structure formed by this collection of proteins within the pore, primarily due to their disordered nature and uncertainty regarding the properties of individual nucleoporins. We first study the defining characteristics of the amino acid sequences of nucleoporins through bioinformatics techniques, although bioinformatics of disordered proteins is especially challenging given high mutation rates for homologous proteins and that functionality may not be strongly related to sequence. Here we have performed a novel bioinformatic analysis, based on the spatial clustering of physically relevant features such as binding motifs and charges within disordered proteins, on thousands of FG motif containing nucleoporins (FG nups). The biophysical mechanism by which the critical FG nups regulate nucleocytoplasmic transport has remained elusive, yet our analysis revealed a set of highly conserved spatial features in the sequence structure of individual FG nups, such as the separation, localization, and ordering of FG motifs and charged residues along the protein chain. These sequence features are likely conserved due to a common functionality between species regarding how FG nups functionally regulate traffic, therefore these results constrain current models and eliminate proposed biophysical mechanisms responsible for regulation of nucleocytoplasmic traffic in the NPC which would not result in such a conserved amino acid sequence structure. Additionally, this method allows us to identify potentially functionally analogous disordered proteins across distantly related species.

To understand the physical implications of the sequence features on structure and dynamics of the nucleoporins, we performed coarse-grained simulations of nucleoporins to understand their individual polymer properties. Our results indicate that different regions or blocks of an individual NPC protein can have distinctly different forms of disorder and that this property appears to be a conserved functional feature, consistent with the results of our physical bioinformatic analysis. Further simulations of grafted rings of FG nups mimicking the in vivo geometry of the NPC were performed and supplemented with polymer brush modeling to understand how aggregates of FG nups regulate transport in vivo. We found that the block structure at the individual protein level in terms of polymer properties is critical to the formation of a unique higher-order polymer brush architecture that can exist in distinct morphologies depending on the effective interaction energy between the phenylalanine glycine (FG) domains of different nups. Because the interactions between FG domains may be modulated by certain forms of transport factors, our results indicate that transitions between brush morphologies that correspond to open and closed states could play an important role in regulating transport across the NPC, suggesting novel forms of gated transport across membrane pores with wide biomimetic applicability in our Diblock Copolymer Brush Gate model.

Previous experimental research has concluded that FG nups from S. cerevisiae are present in a bimodal distribution, with the ”Forest Model” classifying FG nups as either diblock polymer like ”trees” or single block polymer like ”shrubs.” Our simulation and polymer brush modeling results indicated that the function of the tree FG nups in the Diblock Copolymer Brush Gate (DCBG) model is to form a higher-order polymer brush architecture which can open and close to regulate transport across the NPC. Here we perform coarse grained simulations of the shrub FG nups which confirm that they have a single block polymer structure rather than the diblock structure of tree nups. Our molecular simulations also demonstrate that these single block FG nups are likely compact collapsed coil polymers, implying that shrubs are generally localized to their grafting location within the NPC. We find that adding a layer of shrub FG nups to the DCBG model increases the range of cargo sizes which are able to translocate the pore through a cooperative effect involving shrub and tree nups. This effect can explain the puzzling connection between shrub FG nup deletion mutants in S. cerevisiae and the resulting failure of certain large cargo transport through the NPC. Facilitation of large cargo transport via single block and diblock FG nup cooperativity in the nuclear pore could provide a model mechanism for designing future biomimetic pores of greater applicability. In summary, this dissertation presents a cohesive body of research that uses a combination of techniques including bioinformatics, coarse grained molecular modeling, and polymer brush theory to understand the properties of individual FG nups and how they behave in aggregate, strongly constraining possible biophysical mechanisms which may play a role in regulating traffic through the NPC. Our results are observed across different species and are consistent with many experimental observations which have been reported. Finally, our DCBG model for NPC function provides testable predictions for future experimental investigation and provides a foundation for the design and commercialization of biomimetic pores for filtering applications in vitro and industrial use.

This dissertation studies the late-time critical behavior of interacting many- particle systems. Two examples of such systems considered here are Brownian vicious walks with long-range interactions and vicious L´evy flights. In the first example we consider distinct groups of independent diffusive particles interacting by means of a long ranged potential that decays in d dimensions with distance r as r−d−s such that the process is terminated upon the intersection of any two trajectories of particles in the spatio-temporal plane. The main characteristics of this system are the survival and reunion probabilities defined, respectively, as the probability that no trajectories intersect up to time t and the probability that all trajectories meet each other exactly at time t. We employ methods of renormalized field theory to show that these quantities decay as t−® and t(N−1)d/2−2®, respectively, where N is total number of particles. We calculate, for the first time, the exponent ® for all values of parameters s and d to first order in the double expansion in " = 2−d and ± = 2 − d − s. We show that there are several regions in the s − d plane cor- responding to different scalings for survival and reunion probabilities. Furthermore, we calculate the leading logarithmic corrections, for the first time. In the second example we study the statistics of encounters of L´evy flights by introducing the concept of vicious L´evy flights - distinct groups of walkers performing independent L´evy flights with the process terminating upon the first encounter between walkers of different groups. We show that the probability that the process survives up to time t decays as t−® at late times. We compute ® up to the second order in "-expansion, where " = ¾ − d, ¾ is the L´evy exponent and d is the spatial dimension. For d = ¾, we find the exponent of the logarithmic decay exactly. Theoretical values of the exponents are confirmed by numerical simulations.

Collective motion is a widespread phenomenon in nature where individuals actively propel themselves, gather together and move as a group. Some examples of collective motion are bird flocks, fish schools, bacteria swarms, cell clusters, and crowds of people. Many models seek to understand the effects of activity in collective systems including things such as environmental disorder, density, and interaction details primarily at infinite size limits and with uniform populations. In this dissertation I investigate the effects of finite sizes and behavioral heterogeneity as it exists in nature. Behavioral heterogeneity can originate from several different sources. Mixed populations of individuals can have inherently different behaviors such as mutant bacteria, injured fish, or agents that prefer individualistic behavior over coordinated motion. Alternatively, agents may modify their own behavior based on some local environmental dependency, such as local substrate, or density.

In cases such as mutant cheaters in bacteria or malfunctioning drones in swarms, mixed populations of behaviorally heterogeneous agents can be modelled as arising in the form of aligning and non-aligning agents. When this kind of heterogeneity is introduced, there is a critical carrying capacity of non-aligners above which the system is unable to form a cohesive ordered group. However, if the cohesion of the group is relaxed to allow for fracture, the system will actively sort out non-aligning agents the system will exist at a critical non-aligner fraction. A similar heterogeneity could result in a mixture of high and low noise individuals. In this case there is also a critical carry capacity beyond which the system is unable to reach an ordered state, however the nature of this transition depends on the model details.

Agents which are part of an ordered collective may vary their behavior as the group changes environments such as a flock of birds flying into a cloud. Using a unique model of a flock where the group behaves as a rigid disk reveals interesting behaviors as the system crosses a boundary between interfaces. The collective rotates and reorients or becomes stuck on the boundary as it crosses. I also investigate the effects of variable behavior depending on local density, and find that a frustration driven transient rotational phase arises in clusters where agents with low local density move faster than those with high local density as in cell clusters. All together I have shown that behavioral heterogeneity in collective motion can lead to unique phases and behaviors that are not seen in their homogeneous counterparts.

Bacteria, eukaryotic cells, multicellular organisms, animals, and even humans forage to find resources such as food. Foraging involves random search processes, and it has been shown that trajectories of many types of foragers resemble random walks. It is also known that solitary foragers can change their foraging strategy to maximize their encounter rate or search efficiency. While there has been much work done on foraging individually, less is known about foraging in groups. Members of a group can cooperate to find resources like herds of Mongolian gazelles, or compete with each other like tigers. The effect of cooperation and competition on foraging patterns is not yet fully understood. In this dissertation, we aim to increase our understanding by focusing on two specific cases - (i) efficient foraging strategies for territorial competitors and (ii) cooperative foraging in cell clusters. Many animals such as albatrosses are known to exhibit foraging patterns where the distances they travel in a given direction are drawn from a heavy-tailed Levy distribution. However, in nature, there also exist situations where multiple foragers interact with each other competitively. To understand the effects of competition, we develop a stochastic agent-based simulation that models competitive foraging among territorial individuals by incorporating a territory of a certain size around each forager which is not accessible by other competitors. While competition is common, many living organisms such as bees, school of fish, and caterpillars collaborate with each other to complete a task. Such collaboration extends to the cellular scale. Multicellular aggregates such as cell clusters and tissues exhibit collective migration with complex emergent behaviors that are critical for function and very different from the behavior of the constituent single cells. We focus on the chemotaxis of clusters of malignant lymphocytes, responsible for the metastases of lymphomas by using an agent-based model.

Stochastic transport is a widely studied phenomenon among physicists. This includes diffusive processes like Brownian motion which have helped describe numerous systems ranging from the spreading of dye molecules in a liquid to the spreading of human populations. Transport behavior can be affected by properties such as the local curvature of a surface or the dynamics of a network on which the transport takes place. A quantitative characterization of these factors is critical for a deeper understanding of transport in such cases and is of much interest to the study of random walk theory, stochastic processes, and anomalous diffusion in general. In this dissertation, we aim to accomplish this aim by focusing on two specific cases - (i) anomalous diffusion of a random walker on curved surfaces and (ii) transport of cargo on dynamic filament networks.Levy walks are a class of anomalous diffusion studied in Euclidean space. In many cases of interest, transport takes place on surfaces with non-zero Gaussian curvature. We take the first steps towards studying how surface curvature affects anomalous transport described by Levy walk statistics. We develop a computational model to simulate Levy walks along geodesics in Euclidean, spherical, and hyperbolic spaces. By comparing our numerical results to a Taylor expansion of the mean-squared displacement (MSD) in powers of curvature around the Euclidean case, we can establish the validity of a generalized expression for MSD of anomalous diffusion with curvature corrections. The transport of cargo within cells is a critical physiological process. Many new studies consider the impact on transport of the morphology of the networks of filaments. One aspect that has received less attention is the growth/shrinkage and dynamic turnover of these networks. We study transport of cargo carried by myosin motors on dynamic actin network. Use a stochastic simulation model accounting for both active and passive transport and incorporate the dynamics of the actin network. We show how treadmilling speed of actin filament affect cargo transport, motor attachment/detachment rates and network density. We show the existence of filament dynamics in physiological regimes that optimize cargo transport and how it can be tuned.

Intracellular transport in eukaryotic cells is a process in which cargo, carrying various materials and attached to molecular motors, moves around the cell. The cargos' transport consists of phases of passive, diffusion-based transport in the bulk cytoplasm and active, motor-driven transport along filaments that make up the cell's cytoskeleton. Because of it's role in the active phase of transport, the cytoskeletal geometry is an important factor. In this dissertation, we consider network parameters such as filament length, number, polarization direction, and location and examine their effect on the transport process. This can be achieved by computationally determining cargo transport through simulation and numerical analysis techniques.

We present this research by first demonstrating an approach that evolves a distribution of cargos in time using numerical integration. To do this, we use two coupled differential equations that enforce the distribution movement on and off filaments. An interesting finding here is that the distribution can become ``trapped" at what we consider intermediate filament lengths.

Although we mostly use a simplified model where normal diffusion governs the passive phase of transport, we also consider the effects of incorporating anomalous subdiffusion in the bulk. This means that the entire transport process can be described as anomalously diffusive, with the active transport phase being superdiffusive and the passive transport phase being subdiffusive. One thing we found by taking this approach is that filament length, rather than filament number, has a greater influence on the domination of overall superdiffusive transport at relatively early times compared to the domination of subdiffusive transport at later times. We were able to extend this observation to model the biphasic release of insulin out of cells in which there is a large spike in insulin release, followed by a slower, more sustained release.

In the final chapter, we consider the possibility of cargos capable of switching to different filaments. If multiple motors are attached to a cargo, it can switch from one filament to another, provided one is nearby. In this phase of our research, we took real images of networks of microtubule bundles and extracted network parameters from them in order to run our simulations. We compared our simulation data, where cargos had different switching probabilities, with experimental data, where cargos had different numbers of motors, and were able to draw a correlation between cargo switching probability and motor number. The network images and the experimental data were provided by our collaborator, Professor Jennifer Ross at UMass, Amherst.

The escape rate of asteroids, chemical reaction rates, and fluid mixing rates are all examples of chaotic transport rates in dynamical systems. A Monte Carlo simulation can be used to compute such rates, for example using a model consisting of a system of ODEs or PDEs. The set of trajectories in a chaotic system can be highly complex, and a Monte Carlo simulation often requires millions or billions of trajectories to properly sample the state space and compute accurate transport rates. We study methods of computing transport rates using a smaller number trajectories by studying the structure of the state space or phase space. One way to analyze chaotic phase spaces is to compute symbolic dynamics, which is the labeling of trajectories based on a partitioning of the space. The symbolic dynamics of the system can be represented as a network consisting of a set of partition elements, the nodes, and the allowed transitions between them, the edges. In a Hamiltonian system, for example, a partition element represents a region of phase space, and edges connect pairs of nodes between which transport is allowed in time. A firm grasp of the symbolic dynamics results in the ability to compute important transport rates, including the topological entropy and the escape rate.

One way to compute symbolic dynamics is using invariant manifolds which can divide the state space into pieces. The collection of stable and unstable invariant manifolds is known as a heteroclinic tangle, and the topology of the intersections of stable and unstable manifolds in the tangle encodes information about restrictions on the dynamics. The question we address is How can symbolic dynamics computed from invariant manifolds reduce the number of trajectories required to compute transport rates? In addition, we ask and try to address what useful information does the topology of invariant manifolds tell us about a system that is not apparent from direct or Monte Carlo computation of transport rates? An essential tool in computing the transport rates will be the computation of periodic orbits and using a function called the spectral determinant.

We study several examples of understanding phase space and computing chaotic transport rates using a technique called Homotopic Lobe Dynamics (HLD), which is an automated technique to compute accurate partitions and symbolic dynamics for maps by using the topological forcing by intersections of stable and unstable manifolds of a few anchor periodic orbits. We have applied the HLD technique to analyze and compute transport rates in three systems. In a two-dimensional, double-gyre-like cavity flow that models a microfluidic mixer, we accurately compute the topological entropy over a range of parameter value. In the Hénon map, we use periodic orbits computed from HLD to compute multiexponential decay rates from different zones. In the hydrogen atom in parallel electric and magnetic fields, we use periodic orbits computed from HLD to compute the ionization rate over a range of electron energy where the system exhibits a ternary horseshoe. In each system, computations of transport rates over ranges of parameter value using HLD provided considerable improvements upon previous attempts to compute the same rates.

While foraging phenomena have historically been a focus of ecology, they can be described as search processes carried out by one or multiple agents in a landscape characterised by a resource distribution. As a result, tools from statistical physics can be used to study foraging phenomena. The integration of statistical physics as a set of tools to both describe patterns observed in foraging processes and understand the underlying mechanisms that give rise to these patterns has enabled the development of robust theory as well as the expansion of the scope of foraging to include applications in intracellular processes, human cognitive behaviour, and even robotics.

Treating foraging processes as undertakings by a single foraging agent in a resource environment has laid the foundation for a significant amount of our understanding of foraging. However, these approaches fail to capture the complexities of real foraging phenomena which arise from the fact that foraging agents do not exist independent of their environment. The logical first order step to rectify this is to consider foraging processes carried out by multiple interacting agents. This dissertation describes complex, emergent phenomena in three different systems resulting from interactions between multiple foraging agents.

First, I present a minimal, one-dimensional analytical model that describes emergent pattern formation in a community of phototactic bacteria moving towards a directional light source. During phototaxis---essentially, foraging for light---interactions between individual bacteria result in emergent community-level spatial organisation, leading to the formation of finger-like projections at the propagating front. We developed a one-dimensional analytical model which describes the dynamics of this pattern formation and predicts critical parameters that limit finger formation. This model also predicts the loss of instabilities in mutant phenotypes lacking a key photoreceptor.

Second, I present a framework to use foraging theory to investigate the dynamics of vocal interactions between human infants and their adult caregivers. By analysing day-long recordings of infant and caregiver vocalisations in naturalistic settings over the infants' first year, we demonstrated support for the hypothesis that infants and their adult caregivers are foraging in an acoustic space for sounds that have social value. Our findings also provide evidence that vocal interactions between infants and caregivers modify these foraging patterns.

Finally, I present a computational model to study the diversity of foraging strategies employed by terrestrial carnivore predators. Mammalian carnivores' foraging strategies include hunting, scavenging, and kleptoparasitism (stealing). However, despite the prevalence of literature on predator-prey systems, the factors that result in the deployment of these strategies and their effects on predator-prey systems are not well understood. In this study, we use an energetics approach to investigate how a focal predator's interactions with potential prey and other predators constrain the use of these strategies. Our results predict the dependence of predator foraging strategy on predator energetics as well as the body sizes of the focal predator, prey, and potential competitors. In particular, our predictions for the boundaries between hunting and alternative foraging strategies (scavenging and stealing) show remarkable agreement with observational data. By employing dimensional reduction, we are also able to accurately describe the phase transition from a state where the focal predator relies predominantly on hunting to a state where the focal predator largely relies on scavenging and stealing.