Theoretical and Computational Studies of Nonequilibrium Phenomena.
Complex phenomena occurring under far from equilibrium conditions are ubiquitous in nature. But in contrast to equilibrium statistical mechanics, no standard approach exists for describing nonequilibrium phenomena. My main research interest lies in the development of mathematical models and computational techniques for studying nonequilibrium phenomena, particularly in the areas of condensed matter physics and biology.
My research in the area of condensed matter physics has been directed towards the development and application of scaling theory, Kinetic Monte Carlo (KMC) and rate equations to study the kinetics of aggregation, the evolution of thin film morphology and the kinetic roughening of surfaces and interfaces. The specific projects that I have been interested in range from understanding the fractal morphology and kinetics of colloidal aggregation to the dynamics of fluid interfaces in porous media and from the formation and evolution of submonolayer islands to the growth and roughening of multilayer thin films by chemical vapor deposition and molecular beam epitaxy (MBE).
In biology, my efforts have focused on two areas: (1) molecular transport and (2) Age-related Macular Degeneration (AMD), which is the leading cause of blindness caused by aging.
(1) Cellular transport processes are carried out by molecules called molecular motors. Examples include Myosin that is responsible for muscle contraction, Kinesin that carries cargo inside cells along microtubules, Dynein that produces the axonemal beating of cilia and flagella, and Dynamin that helps separate the clathrin buds from the plasma membrane. Molecular motors are biological nanoscale machines that are responsible for the conversion of energy into mechanical transport. For example, many protein-based molecular motors convert the chemical free energy created by the hydrolysis of ATP to mechanical work. The key characteristic of molecular motors is that they operate in the thermal bath, an environment where there are significant fluctuations due to thermal noise. For this reason, molecular motors are modeled with the stochastic Fokker-Planck equation or Brownian particles moving in a fluctuating asymmetric potential called the "ratchet". Using ratchet models we have studied both overdamped and inertial ratches. A significant aspect of our findings has been the elucidation of the chaotic behavior in driven inertial ratchets in the presence of quenched noise.
(2) Age-related macular degeneration (AMD) is the leading cause of blindness in adults over the age of 60. The underlying cause appears to be premature dysfunction of the retinal pigment epithelium (RPE), a monolayer responsible for most of the maintenance functions of the neurosensory retina. The "Dry" form of AMD occurs as a deposit called drusen forms and atrophies the RPE. Drusen are formed by the deposition of a retinal waste product called lipofuscin. This process causes the RPE to separate from its underlying basement membrane, which accounts for approximately 10% of the cases of severe visual loss in AMD. In the "Wet" or exudative AMD the growth and penetration of abnormal choroidal neovascularization into the weakened RPE causes additional complications including retinal edema, subretinal serous exudation, and eventual scarring of the overlying retina. The new vessels are fragile and often lead to subretinal hemorrhage, further compromising retinal function. Wet AMD accounts for 90% of the cases of severe visual loss in AMD.
Treatment for AMD is highly limited due to a lack of understanding of the key steps in the initiation and progression of the disease. Currently, we are working on understanding the molecular causes of AMD, most specifically the physicochemical mechanisms involved in choroidal neovascularization -- a complex and multifaceted process that involves angiogenesis, growth and penetration of new vasculature into an elastic collagenous layer called the Bruch's membrance. The goal of this research is to develop effective mathematical models and Kinetic Monte Carlo (KMC) simulations that can provide reliable testing grounds for sorting out the variety of hypotheses that have been advanced from clinical studies regarding the underlying mechanisms leading to both dry and wet AMD.