Frontiers in Mathematical Biology

Advanced Boundary-Integral Methods for Biomolecule Analysis and Design

Jaydeep Bardhan

Rush University Medical Center
[SLIDES]

Many important biological phenomena can be understood using partial-differential equations (PDEs) such as the Poisson equation in electrostatics. Fast computer simulation methods are essential modeling tools for these problems, because few complex biological systems can be studied analytically. In this talk, I will use protein electrostatics as a case study to illustrate how applied math dramatically increases the power of seemingly problem-specific physical insights, yielding powerful new simulation algorithms applicable to a much wider range of problems across bioengineering and science. For example, fast electrostatic algorithms originally developed for molecular engineering can be applied in clinically important problems such as the analysis of electroencephalography (EEG) data, as well as other physics including hydrodynamics (Stokes flow). Other modeling advances allow sophisticated multiscale theories to be computed just as quickly as popular, simpler (less accurate) models. These fast methods enable important new research towards resolving long-standing problems in biophysics, such as pH-dependent protein function. Furthermore, by developing these techniques we enable faster and more accurate calculations ranging from sub-atomic length scales to the macroscopic ones critical for biomedical applications.