Mathematical Biology

List of researchers in CAMS working on problems related to Mathematical Biology: Booth, Bose, Bukiet, Dhar, Elmer, Georgieva, Goldman, Golowasch, Khan, Lott, Matveev, Miura, Muratov, Nadim, Perez, Raymond, Russel, Tao, Wang, Yoo.

Mathematical Biology broadly refers to the branch of mathematics that is devoted to the study of biological processes. Historically, applications have arisen in a number of disparate areas such as population ecology, pattern formation, blood flow in mammals, and nerve impulse propagation in the central nervous system. More recently, there has been quite a bit of emphasis on the intersection of mathematics with developmental biology, neurophysiology, and especially genomics. Moreover, mathematicians are applying their modeling and analytical skills to the study of various diseases, such as diabetes, Parkinson's disease, multiple sclerosis, Alzheimer's disease, and HIV-AIDS. The kinds of mathematics needed to describe and address problems in these areas of Mathematical Biology are quite vast and include dynamical systems, partial differential equations, fluid dynamics, mechanics, and statistics, to name only a few. Researchers in Mathematical Biology at NJIT have strong interdisciplinary research program since most of them have active collaborations with experimentalists. This group of Mathematical Biologists is the largest in a department of mathematics in North America.

A primary focus of the Mathematical Biology group is in experimental, computational, and mathematical Neuroscience. The experimental research in neuroscience within CAMS is headed up by Jorge Golowasch and Farzan Nadim. Both researchers run labs in which they conduct experiments on various aspects of the crustacean stomatogastric nervous system (STNS). The main focus of Nadim's research is to understand how synaptic dynamics, such as short-term depression and facilitation contribute to the generation and control of oscillatory neuronal activity. Experiments in Nadim's lab involve characterizing the synaptic dynamics in the STNS and studying the contributions of these dynamics, through mathematical modeling, to the output from the biological network. Using both electrophysiological and computational tools, Golowasch studies mechanisms of neuronal plasticity and homeostasis of the ionic currents that determine the excitability and electrical activity of neurons and simple neural networks in the STNS. Currently, he also is screening several neuropeptides for their possible involvement in trophic regulation of dissociated adult neurons in cultured and in long term organotypical culture. These neuropeptides are known to have short-term neurmodulatory effects.

Various aspects of Computational and Mathematical neuroscience are being studied by Victor Matveev, Louis Tao, Amitabha Bose, and Robert Miura. Matveev studies mechanisms responsible for short-term synaptic plasticity. He is particularly interested in understanding the role of residual calcium in synaptic facilitation. Tao is primarily interested in the modeling and analysis of the dynamics of neuronal networks, with application to visual cortex and other large-scale cortical networks. He focuses on developing analytical techniques to study networks in simplified settings and on identifying possible biological functions of emergent network dynamics. Bose is interested in developing mathematical techniques to understand the role of short-term synaptic plasticity in producing multi-stable periodic solutions within neuronal networks. He is also interested in developing models for persistent localized activity in excitatory networks. Miura has worked extensively on modeling and analysis of models for electrical activity in excitable cells, including neurons and pancreatic beta-cells. He is currently working on mathematical models for spreading depression, a slowly propagating chemical wave in the cortex of various brain structures, which has been implicated in migraine with aura. Also, he is working on developing a theory for the formation of glass microelectrodes, which are used daily in electrophysiology laboratories around the world.

In the area of Developmental Biology, Cyrill Muratov is interested in developing models that describe the patterning events leading to the formation of dorsal appendages during Drosophila egg development. He studies a system of coupled reaction-diffusion equations driven by a localized input and characterizes the oocyte phenotype by the number of peaks in the signaling pattern.

Dan Goldman and Sheldon Wang use techniques of fluid dynamics to study various biological phenomenon. The research of Dan Goldman is centered on developing a flexible, efficient and highly realistic computational model for simulating microvascular blood flow and oxygen delivery. His model has been used to study both steady-state and time-dependent oxygen delivery, which is of primary interest for understanding physiological functioning. Current studies use this model to understand blood flow and oxygen transport during sepsis at the onset of exercise. Sheldon Wang is developing new immersed boundary/continuum methods which will provide a platform for effective modeling of highly deformable shells/beams and solids immersed in biological fluids. These methods will facilitate further research in multi-scale and multi-physics coupling of complex fluid-solid systems with microscopic models.

Chris Raymond is interested in mathematical modeling for immunocolloid labeling. In this process, colloidal metal particles are conjugated to ligand molecules which bind to the molecule of interest, commonly a receptor molecule on a cell surface. With experimental and mathematical collaborators, he is developing mathematical models for the immunocolloid labeling process with the goal of optimizing the choice of experimentally adjustable parameters to maximize labeling efficiency.

The rest of this page contains links to examples of the research projects that have been recently considered by the CAMS members. The links to individual faculty web pages that contain more information can be found at the top of this page.