Mathematical Models and Simulations of Phototaxis and Cancer Immune Interactions

The macroscopic dynamics created by complex systems of microscopic cells can be better understood using mathematical modeling. In this dissertation, we study the dynamics of two different biological systems: phototaxis exhibited by cyanobacterium Synechocystis sp. and cancer immune interactions as affected by the protein B7-H1. Synechocystis sp., a common unicellular freshwater cyanobacterium, has been used as a model organism to study phototaxis, i.e. motion in the direction of a light source. This microorganism displays a number of additional characteristics such as delayed motion, surface dependence, and a quasi-random motion, where cells move in a seemingly disordered fashion instead of in the direction of the light source. These unexplained motions are thought to be modulated by local interactions between cells. In this work, we formulate a model of local interactions between phototactic cells in order to study the structure of their quasi-random motion. We present a stochastic dynamic particle system modeling interacting phototactic cells. We extend our model of local interactions to include global forcing due to light. We also add an activation process of cells as they become affected by the presence of light. We study the parameter space of our model by deriving a system of ordinary differential equations that describe the dynamics of the system in one dimension. The simulations of our model are consistent with experimentally observed phototactic motion. The second part of this dissertation focuses on the surface protein B7-H1. This protein, also called PD-L1 and CD274, is found on carcinomas of the lung, ovary, colon and melanomas but not on most normal tissues. B7-H1 has been experimentally determined to be an anti-apoptotic receptor on cancer cells, where B7-H1-positive cancer cells have been shown to be immune resistant, and in vitro experiments and mouse models have shown that B7-H1-negative tumor cells are significantly more susceptible to being repressed by the immune system. We derive a mathematical model for studying the interaction between cytotoxic T cells and tumor cells as affected by B7-H1. By integrating experimental data into the model, we isolate the parameters that control the dynamics and obtain insights on the mechanisms that control apoptosis

Modeling and Optimization of Dynamical Systems in Epidemiology using Sparse Grid Interpolation

Infectious diseases pose a perpetual threat across the globe, devastating communities, and straining public health resources to their limit. The ease and speed of modern communications and transportation networks means policy makers are often playing catch-up to nascent epidemics, formulating critical, yet hasty, responses with insufficient, possibly inaccurate, information. In light of these difficulties, it is crucial to first understand the causes of a disease, then to predict its course, and finally to develop ways of controlling it. Mathematical modeling provides a methodical, in silico solution to all of these challenges, as we explore in this work. We accomplish these tasks with the aid of a surrogate modeling technique known as sparse grid interpolation, which approximates dynamical systems using a compact polynomial representation. Our contributions to the disease modeling community are encapsulated in the following endeavors. We first explore transmission and recovery mechanisms for disease eradication, identifying a relationship between the reproductive potential of a disease and the maximum allowable disease burden. We then conduct a comparative computational study to improve simulation fits to existing case data by exploiting the approximation properties of sparse grid interpolants both on the global and local levels. Finally, we solve a joint optimization problem of periodically selecting field sensors and deploying public health interventions to progressively enhance the understanding of a metapopulation-based infectious disease system using a robust model predictive control scheme

Numerical modeling of F-.Actin bundles interacting with cell membranes

Actin is one of the most aboundant proteins in eukaryotic cells, where it forms a dendridic network (cytoskeleton) beneath the cell membrane providing mechanical stability and performing fundamental tasks in several functions, including cellular motility. The first step in cell locomotion is the protrusion of a leading edge, for which a significant deformation of the membrane is required: this step relies essentially on the forces generated by actin polymerization pushing the plasma membrane outward. Different types of structures can emerge from the plasma membrane, like lamellipodia (quasi-2d actin mesh) and filopodia (parallel actin bundles). The main topic of the research project is the dynamics of bundles of parallel actin filaments growing against barriers, either rigid (a wall) or flexible (a membrane). In the first part of the thesis, the dynamic behavior of bundles of actin filaments growing against a loaded wall is investigated through a generalized version of the standard multi filaments Brownian Ratchet model in which the (de)polymerizing filaments are treated not as rigid rods but as semi-flexible discrete wormlike chains with a realistic value of the persistence length. A Statistical Mechanics framework is built for bundles of actin filaments growing in optical trap apparatus (harmonic external load) and several equilibrium properties are derived from it, like the maximum force that the filaments can exert (stalling force) or the number of filaments in contact with the wall. Besides, Stochastic Dynamic simulations are employed to study the non-equilibrium relaxation of the bundle of filaments growing in the same optical trap apparatus, interpreting the system evolution by a suitable Markovian approach. Thanks to the observed time scale separation between the wall motion and the filament size relaxation, the optical trap set-up allows to extract the full velocity-load curve V(F) -- the velocity at which the obstacle moves when subject to the combined action of the polymerizing filaments and the external load F -- from a single experiment. The main finding is the observation of a systematic evolution of steady non-equilibrium states over three regimes of bundle lengths L. A first threshold length Λ marks the transition between the rigid dynamic regime (L Λ), where the velocity V(F,L) is an increasing function of the bundle length L at fixed load F, the enhancement being the result of an improved level of work sharing among the filaments induced by flexibility. A second critical length corresponds to the beginning of an unstable regime characterized by a high probability to develop escaping filaments which start growing laterally and thus do not participate anymore to the generation of the polymerization force. This phenomenon prevents the bundle from reaching at this critical length the limit behavior corresponding to Perfect Load Sharing. In the second part of the thesis, filaments growing against a flexible, deformable membrane are studied by means of Langevin dynamics simulations; the membrane is discretized into a dynamically triangulated network of tethered beads, while the filaments are described as chains of bonded monomers. Both the monomers in the filaments and the membrane beads, which interact with each other via a purely repulsive potential, are followed in space and time integrating its equations of motion with a second order accurate scheme. The elastic properties of the membrane are studied in detail via several methods, showing an unprecedentent level of agreement among them. The onset of filopodial protrusions is observed for N>1 filaments growing from beneath the membrane and pushing it upwards, with a velocity which is systematically larger for flexible filaments than for rigid ones. Since filaments are wrapped by the membrane in the protrusion, escaping filaments are not predicted nor observed in this case

Computing Interpretable Representations of Cell Morphodynamics

Shape changes (morphodynamics) are one of the principal ways cells interact with their environments and perform key intrinsic behaviours like division. These dynamics arise from a myriad of complex signalling pathways that often organise with emergent simplicity to carry out critical functions including predation, collaboration and migration. A powerful method for analysis can therefore be to quantify this emergent structure, bypassing the low-level complexity. Enormous image datasets are now available to mine. However, it can be difficult to uncover interpretable representations of the global organisation of these heterogeneous dynamic processes. Here, such representations were developed for interpreting morphodynamics in two key areas: mode of action (MoA) comparison for drug discovery (developed using the economically devastating Asian soybean rust crop pathogen) and 3D migration of immune system T cells through extracellular matrices (ECMs). For MoA comparison, population development over a 2D space of shapes (morphospace) was described using two models with condition-dependent parameters: a top-down model of diffusive development over Waddington-type landscapes, and a bottom-up model of tip growth. A variety of landscapes were discovered, describing phenotype transitions during growth, and possible perturbations in the tip growth machinery that cause this variation were identified. For interpreting T cell migration, a new 3D shape descriptor that incorporates key polarisation information was developed, revealing low-dimensionality of shape, and the distinct morphodynamics of run-and-stop modes that emerge at minute timescales were mapped. Periodically oscillating morphodynamics that include retrograde deformation flows were found to underlie active translocation (run mode). Overall, it was found that highly interpretable representations could be uncovered while still leveraging the enormous discovery power of deep learning algorithms. The results show that whole-cell morphodynamics can be a convenient and powerful place to search for structure, with potentially life-saving applications in medicine and biocide discovery as well as immunotherapeutics.Open Acces

THE ROLE OF THE CYTOSKELETON IN 3D CANCER CELL MIGRATION

Arp2/3 is a protein complex that nucleates actin filament assembly in the lamellipodium in adherent cells crawling on planar two-dimensional (2D) substrates. However, in patho-physiological situations, cell migration typically occurs within a three-dimensional (3D) environment and little is known about the role of Arp2/3 and associated proteins in 3D cell migration. Using time resolved live-cell imaging and a fibrosarcoma cell line, HT1080, commonly used to study cell migration, we find that the Arp2/3 complex and associated proteins N-WASP, WAVE1, Cortactin, and Cdc42 regulate 3D cell migration. This regulation is caused by formation of multi-generation dendritic protrusions, which mediate traction forces on the surrounding matrix and effective cell migration. The primary protrusions emanating directly from the cell body and prolonging the nucleus form independent of Arp2/3 and dependent on focal adhesion proteins FAK, talin, and p130Cas. The Arp2/3 complex, N-WASP, WAVE1, Cortactin, and Cdc42 regulate the secondary protrusions branching off from the primary protrusions. In 3D matrices, fibrosarcoma cells as well as migrating breast, pancreatic, and prostate cancer cells do not display lamellipodial structures. This study characterizes the unique topology of protrusions made by cells in a 3D matrix and show that these dendritic protrusions play a critical role in 3D cell motility and matrix deformation. The relative contribution of these proteins to 3D migration is significantly different from their role in 2D migration. Microtubules have long been targeted to control tumor growth and, more recently, metastatic disease, for which a critical step is the local invasion of tumor cells into the 3D collagen-rich stromal matrix. To migrate in collagen matrices human fibrosarcoma and breast cancer cells exploit the dynamic formation of highly branched protrusions, which are composed of a microtubule-filled core surrounded by actin filaments that is largely absent in the same cells flattened on 2D substrates. Microtubule plus-end tracking protein EB1 and microtubule-associated motor protein dynein critically modulate 3D cell migration, not by regulating vesicular trafficking, but by regulating both speed and persistence through regulation of protrusion branching itself regulated by differential assembly dynamics of microtubules in the protrusions. These proteins do not regulate conventional 2D migration. An important consequence of the prominent role of microtubules in 3D migration is that the treatment of fibrosarcomas by commonly used cancer drug paclitaxel, which stabilizes microtubules, is dramatically more effective in 3D than in 2D, uniformly and completely blocking 3D cell migration. This work reveals the central role that microtubule dynamics plays in cell migration in more pathologically relevant 3D collagen matrices and suggests that cancer drugs targeting microtubule dynamics to mitigate migration should be further tested in 3D microenvironments. Cell migration through three-dimensional (3D) extra-cellular matrices is critical to the normal development of tissues and organs and in disease processes, yet adequate analytical tools to characterize 3D migration are lacking. We quantified the migration patterns of individual fibrosarcoma cells on 2D substrates and in 3D collagen matrices and found that 3D migration does not follow a random walk. Both 2D and 3D migration feature a non-Gaussian, exponential mean cell velocity distribution, which we show is primarily a result of cell-to-cell variations. Unlike in the 2D case, 3D cell migration is anisotropic: velocity profiles display different speed and self-correlation processes in different directions, rendering the classical persistent random walk (PRW) model of cell migration inadequate. By incorporating cell heterogeneity and local anisotropy to the PRW model, 3D cell motility is predicted over a wide range of matrix densities, which identifies density-independent emerging migratory properties. This analysis also reveals the unexpected robust relation between cell speed and persistence of migration over a wide range of matrix densities

3D Organization of Eukaryotic and Prokaryotic Genomes

There is a complex mutual interplay between three-dimensional (3D) genome organization and cellular activities in bacteria and eukaryotes. The aim of this thesis is to investigate such structure-function relationships. A main part of this thesis deals with the study of the three-dimensional genome organization using novel techniques for detecting genome-wide contacts using next-generation sequencing. These so called chromatin conformation capture-based methods, such as 5C and Hi-C, give deep insights into the architecture of the genome inside the nucleus, even on a small scale. We shed light on the question how the vastly increasing Hi-C data can generate new insights about the way the genome is organized in 3D. To this end, we first present the typical Hi-C data processing workflow to obtain Hi-C contact maps and show potential pitfalls in the interpretation of such contact maps using our own data pipeline and publicly available Hi-C data sets. Subsequently, we focus on approaches to modeling 3D genome organization based on contact maps. In this context, a computational tool was developed which interactively visualizes contact maps alongside complementary genomic data tracks. Inspired by machine learning with the help of probabilistic graphical models, we developed a tool that detects the compartmentalization structure within contact maps on multiple scales. In a further project, we propose and test one possible mechanism for the observed compartmentalization within contact maps of genomes across multiple species: Dynamic formation of loops within domains. In the context of 3D organization of bacterial chromosomes, we present the first direct evidence for global restructuring by long-range interactions of a DNA binding protein. Using Hi-C and live cell imaging of DNA loci, we show that the DNA binding protein Rok forms insulator-like complexes looping the B. subtilis genome over large distances. This biological mechanism agrees with our model based on dynamic formation of loops affecting domain formation in eukaryotic genomes. We further investigate the spatial segregation of the E. coli chromosome during cell division. In particular, we are interested in the positioning of the chromosomal replication origin region based on its interaction with the protein complex MukBEF. We tackle the problem using a combined approach of stochastic and polymer simulations. Last but not least, we develop a completely new methodology to analyze single molecule localization microscopy images based on topological data analysis. By using this new approach in the analysis of irradiated cells, we are able to show that the topology of repair foci can be categorized depending the distance to heterochromatin