2019 Summer REU Program

Project 1 (Mentor: Dr. Jared Barber): Characterizing interactions between pairs of cells in tube/vessel flow: Blood is composed of mainly red blood cells (45%) and plasma. As blood flows through vessels, cells near walls are pushed towards the vessel center by wall interactions but pushed away from the vessel center by interactions with other cells. These competing effects have a primary role in how cells are distributed across the vessel which, in turn, affect distribution of other important quantities like oxygen. We have developed a two-dimensional computational model of red blood cell motion to use to consider how two isolated cells interact near vessel walls. The project, based on past work, will be to use the model to consider different types of interactions that pairs of cells undergo in this environment, how flexibility and vessel width affect the strength of these interactions, and the implications of such findings on red blood cell distribution across the vessel lumen.

Project 2 (Mentor: Dr. Julia Arciero): The role of blood flow regulation and oxygen transport in glaucoma: Dysfunctional blood flow regulation and impaired oxygenation of the retina have been identified as potential factors contributing to glaucoma.  In this project, students will adapt a theoretical model to simulate flow regulation in a heterogeneous retinal arteriolar network obtained from confocal microscopy images.  Blood flow regulation will be modeled using the length-tension characteristics of vascular smooth muscle that are assumed to depend on myogenic, shear-dependent, and conducted metabolic responses.  Oxygen transport will be simulated in the vasculature and surrounding tissue using a Green’s function model that allows for a non-uniform network structure.  The impact of the regulatory mechanisms will be assessed by simulating responses independently and in combination.  Overall, this model will allow for spatial predictions of tissue oxygenation in the retina, which is an important feature for identifying hypoxic regions in a realistic, heterogeneous retinal vascular network and for providing insight into glaucoma risk factors.

Project 3 (Mentor: Dr. Jared Barber): Using a computational model to investigate breast cancer cell translocation: Breast cancer deaths are usually not due to the site of primary infection but rather by metastases at other locations. Preventing breast cancer cells from entering blood vessels (intravasation), traveling to other potential tumor sites (translocation), and migrating into the tissues at those sites (extravasation) could help mitigate the effects of cancer on the estimated 3.5 million people with a history of breast cancer. Experiments suggest that prevention of these metastatic events can depend on cell physical properties such as elastic and viscous coefficients as well as physical forces acting on the cells that can instigate mechanotransduction of cellular processes such as apoptosis, division, and others. To study these physical properties and forces, we have constructed a mechanical model of an individual cancer cell in a microfluidic device. The project is to investigate the numerical stability of our model by considering the numerical stability associated with a couple of simpler problems. Numerical stability corresponds with the step size one can take when running a simulation which corresponds with the overall speed with which one can produce a simulation. Understanding what parameters significantly affect the numerical stability of our model will help us as we calibrate and improve the current model so that we can use it to investigate how cell properties and mechanotransduced processes may contribute to the metastatic potential of breast cancer cells.

Project 1 (Mentors: Dr. Simon Garnier (NJIT), Dr. Jason Graham (U of Scranton)): Models of pattern formation and decision making in slime mold: In a complex and dynamic world, how do you navigate your environment when you do not possess a brain, or even the beginnings of a nervous system? From bacteria and immune cells to fungi and plants, the large majority of living beings face this problem every day. Nevertheless our knowledge of decision-making mechanisms is mostly limited to those of neuronal animals, and in particular vertebrates. The goal of this project is for students to explore with University of Scranton Associate Professor Jason Graham and NJIT Associate Professor Simon Garnier the navigational abilities of a non-neuronal model organism: the slime mold Physarum polycephalum. Using models of morphogenesis, the students will study (1) how external and internal stimuli modify the morphology of this giant cell as it moves through its environment and (2) how this morphological changes result in the integration of noisy and contradictory information during decision-making by P. polycephalum. The students will also compare their results to experimental data collected by Garnier’s lab as part of an IOS NSF-funded research effort. The results of this work will help understand information processing in organisms without a brain, thereby advancing our comprehension of the emergence of cognitive processes in biological systems.

Project 2 (Mentors: Dr. Anand U. Oza): Hydrodynamic interactions in animal schools and flocks: The complexity and beauty of fish schools and bird flocks have long fascinated scientists, as their complex collective dynamics are readily observed in nature. Recent experiments have suggested a hydrodynamic function for orderly formations in schools and flocks, but hydrodynamic interactions between fast-moving animals remain poorly understood. The goal of this project is for students to develop and analyze a mathematical model for schooling and flocking that accounts for the vortices shed by flapping wings. The model accounts for the temporally nonlocal hydrodynamic interactions between constituents, wherein the forces between bodies at a given time depend on their past positions and velocities. The project will combine mathematical analysis and computation to shed light on the role of hydrodynamics in stabilizing schooling formations, and the potential speed and energetic benefits of such formations.

Project 3 (Mentor: Dr. Enkeleida Lushi): Coupled dynamics of predator and prey plankton: Bdellovibrio bacteriovorus (BV) is a predator bacterial species found in the environment and within the human gut which preys and hunts other pathogen bacteria like Escherichia coli, Pseudomonas aeruginosa and Staphylococcus aureus. Due to this remarkable ability, it is suggested that BV may serve as a biocontrol agent and a living antibiotic. We will explore a simple mathematical model of BV sensing and hunting pathogen bacteria with various shapes and surface attachment properties, to explore how BV proliferates whether it manages to eradicate a pathogen colony.

Project 1 (Mentor: Dr. Chuan Xue): Mathematical models for intracellular transport: A biological cell is like a city, and it has an internal transportation system that connects different parts of the cell. Nearly all cellular functions rely on the active transport of various cargoes, including proteins and organelles, inside the cell. Microtubules are long, dynamic polymers that serve as highway tracks for intracellular transport. Kinesin and dynein are motor proteins that move cargoes back and forth along microtubules. Disruptions of intracellular transport in nerve cells can cause local swelling of the axon, similar to a traffic jam that we see in real life, leading to nerve cell degeneration in severe situations. These phenomena have been found in many neurodegenerative diseases, such as ALS, Alzheimer’s and Parkinson’s. In this project, we will use mathematical models to investigate how intracellular traffic is regulated under normal conditions and how intracellular traffic jams arise under abnormal conditions. Sponsored in part by NSF CAREER Award 1553637.

Project 2 (Mentors: Dr. Oksana Chkrebtii, Dr. Amir Asiaeetaheri): Approximate Inference of Cancer Progression Network from Cross-sectional Data: We are interested in modeling the way cancer progresses. The observations that we usually have are outcomes of life long gain of genetic aberrations and therefore it is very challenging to use them to reverse engineer the sequence of events that caused cancer. For each type of cancer, genetic aberrations will progress differently and understanding the order of such events are of interest for early detection and targeted therapy. We assume that there is an underlying network structure (summarized by a directed acyclic graph, or DAG) that determines the order of events. We then assume that sample patient cancers are generated probabilistically by the DAG. Realization of the underlying progression network in each patient is different, which results in various clones. We have developed a probabilistic engine that generates aberrations for different clones and returns the superposition of those aberrations as a synthetic sample. This model is written in terms of several unknown parameters, and a primary goal of this project is to simultaneously infer the cancer progression network and parameters of the sample generating engine from cross-sectional samples.

Project 3 (Mentors: Dr. Adrian Lam, Dr. Rachidi Salako): Phytoplankton Competition in Water Columns: Human activities have accelerated the eutrophication of many freshwater lakes and coastal ecosystems, including Lake Erie in the US and the Baltic Sea in Europe, causing harmful algal blooms (HABs) to emerge. This phenomenon can be explained by the competitive reversal between diatoms and cyanobacteria (or blue-green algae). Several ways of mitigating the phenomenon, involving physical mixing of the lake, has proved effective. In this project we will use a spatial model to study the competition dynamics among multiple phytoplankton species, to better understand HABs, and to weigh the cost and benefit of each mitigating method. This project will have a numerical component using Matlab programming, and an analysis component based on simplified models.

Project 4 (Mentors: Dr. Adrian Lam, Dr. Rachidi Salako): Spreading Phenomena of Interacting Species with Multiple Speeds: While the spreading of a single species in an unoccupied habitat is well understood, the question has been largely open in case of multiple species. The latter question has the potential to explain, for instance, the spreading of plant species in the de-glaciated North American continent after the last ice-age. In this project we will use the Lotka-Volterra model to study how multiple species spread into an empty habitat with multiple spreading speeds, and to recover the different speeds from model parameters. This project will have a numerical component using Matlab programming, and an analysis component based on simplified models.