Nonequilibrium models in statistical physics Our group has a longstanding interest in applying paradigmatic models of stochastic processes to biophysics and materials science. Of particular interest are interacting particles systems such as exclusion processes and zero-range processes. We are exploring how results from these models can be extended to describe the salient features of processes such as mRNA translation, ligand-receptor kinetics, and nucleosome repositioning.
Mechanisms of viral entry We are developing models, in conjunction with experimental efforts by others, to describe entry pathways of enveloped viruses. Recent experiments have demonstrated the ubiquity of multiple entry pathways, including direct virus-cell fusion and endocytosis. We have constructed kinetic models describing the competition between the fusion and endocytosis pathways. Kinetic receptor/coreceptor engagement models are being developed to account for stoichiometry and surface diffusion.
Membrane biophysics The mechanics and dynamics of lipid membranes play a key role cell function. However, the richness in their function derives from their interactions with embedded membrane proteins, the surrounding cytoskeleton, and other particles. My group has developed and carefully analyzed mathematical models describing membrane protein-protein interactions, adhesion-mediated endocytosis, and membrane delamination from cytoskeleton.
Stochastic models of molecular motors We have studied a number of novel mathematical models for nontraditional molecular motors. These include motors that promote nucleosome repositioning and motors driven by track hydrolysis. Systems of current interest are DNA polymerase and reverse transcriptase, and how they synchronize and error correct.
Electrostatics and electrokinetics The goal of this research is to use variational methods to solve particular problems in electrostatics and electrokinetics. We have derived an effective Young-Dupre equation describing the contact angle of an electrolytic droplet in contact with an ionizable surface. We have also found the lowest order solution in the infinitely conducting fluid limit of electrokinetic flow across nanopore. This electrokinetic flow can affect the capture rate of charge macromolecules to the pore in unexpected ways.
Nucleosome structure and dynamics Nucleosomes are proteins about which DNA is wrapped. Their binding on DNA can preclude access by other processing enzymes such as those involved in transcription. The relatively simple structure of nucleosomes on DNA allows us to develop simplified physical models.
Cornea mechanics and fluid-solid interactions in the eye The measurement of intraocular pressure (IOP), considered a key risk factor in the development of glaucoma, is typically measured using very crude indentation devices that are calibrated to a single model system. Individual characteristics are not accounted for and the measured, apparent IOP may be different from the true IOP. We are developing the appropriate shell theory to account for the effects of corneal bending forces on IOP measurement. Another interesting aspect of this problem is how anterior fluid flow affects the measured IOP.
