6/17(Thu)
09:10?09:30 In Chan Kim Orientation
09:30?12:00 Chi-Ok Hwang Scientific computing and computational science
13:10?16:00 In Chan Kim Random walk and Diffusion
6/18(Fri)
09:10?11:00 Chi-Ok Hwang Monte Carlo methods and their applications
11:10-12:00 In Chan Kim Effective property of composite material
13:10?16:00 Chulung Lee Stochastic process, MDP and random walk
6/21(Mon)
09:10?12:00 Michael Mascagni Introduction to Monte Carlo method
13:10?16:00 Michael Mascagni Introduction to random number generation
6/22(Tue)
09:10?11:00 Michael Feig Solvation in general
11:10?13:00 Michael Feig Introduction to the implicit solvent method
14:10?16:00 Guowei Wei Solving the PB equation with interface techniques
6/23(Wed)
09:10?11:00 Michael Mascagni General Monte Carlo methods for PDEs
11:10?13:00 Guowei Wei Differential geometry approach to determine biomolecular surfaces
14:10?16:00 Michael Mascagni Using Monte Carlo method to solve PDEs from bioelectrostatics
6/24(Thu)
09:10?11:00 Guowei Wei Multiscale solvation model I ? Lagrangian formulation
11:10?13:00 Michael Feig Solute-solvent boundaries and heterogeneous environments
14:10?16:00 Michael Feig Empirical approximations of PB (GB etc.)
6/25(Fri)
09:10?11:00 Guowei Wei Multiscale salvation model II ? Nanofluids and biosensors
11:10?13:00 Michael Feig Applications of Implicit Solvent and practical issues with MD
A major feature of biological science in the 21st century will be its transition from phenomenological and deive
science to quantitative science. Revolutionary opportunities have emerged for theoretically driven advances in
biological research. Rigorous, quantitative, and atomic scale deion of complex biological systems is a grand
challenge. Under physiological conditions, most biological processes occur in water, which consists of 65-90%
human cell weight. Explicit deion of biomolecules and their aqueous environment, including solvent, co-solutes,
and mobile ions, is prohibitively expensive. Therefore, multiscale analysis is an attractive and sometimes
indispensable approach. In a series of lectures, I will discuss a number of multiscale models for biomolecular
systems.
In Lecture One, I will discuss Poisson-Boltzmann (PB) equation based implicit solvent model. The PB model treats
the solvent as a macroscopic continuum while admitting a microscopic atomic deion for the biomolecule. It has
been widely used for electrostatic solvation analysis, pH and pKa estimation, electrostatic map, electrostatic force
calculation, and molecular dynamics. The derivation of the PB equation from the free energy functional will be
discussed. Electrostatic force expressions will be given.
In Lecture Two, I will further discuss a mathematical interface approach for obtaining highly accurate solutions of the
Poisson-Boltzmann (PB) equation. A solvent-solute interface is assumed in the implicit solvent models. Rigorous
solution of the PB equation requires the enforcement of interface jump conditions. Due to the complexity of the
biomolecular interfaces, it is very challenging to implement the interface jump conditions. A matched interface and
boundary (MIB) method has been developed in my group to obtain second-order accurate electrostatic potentials for
protein and other biomolecules. A Green function approach has also been developed to overcome the difficulty of
handling singular charges in the PB model.
In Lecture Three, I will introduce a differential geometry based multiscale solvation model. This model utilizes
differential geometry theory of surfaces for coupling microscopic and macroscopic scales at an equal footing. The
biomolcule of interest is described by discrete atomic and quantum mechanical variables. While the aquatic
environment is described by continuum hydrodynamic variables. I will derive coupled geometric flow and Poisson-
Boltzmann (PB) equations for describing biomolecular surfaces and electrostatic potentials, respectively. The free
energies of biomolecular surface, mechanical work, solvent-solute interface and electrostatic interactions are
optimized in this model. Another multiscale model includes the quantum mechanics deion of the electron density
of (part of) the solute molecule in the salvation analysis. This is needed in refining charge force fields and in
chemical binding analysis.
Applications are considered to biomolecular solvation analysis, virus surface construction and proton transport in
membrane proteins.
In Lecture Four, I will discuss the two different formulations of the multiscale salvation model. One is the Eulerian
formulation and the other is the Lagrangian formulation. The latter has a few utilities/advantages. First, it provides an
essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of
biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many
existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian
representation does not need to resort to artificially enlarged van der Waals radii as required by the Eulerian
representation in solvation analysis. However, it may encounter difficulty in surface merging and break up. For this
reason, the Eulerian formulation is used in practical computations. I will discuss inter-conversion of these two
formalisms.
In Lecture Five, I will introduce more differential geometry based multiscale models. One of these models is originated
from microfluidic and nanofluidic systems, which require the deion of solvation, fluid flows, and molecular
mechanics. We derive the coupled geometric flow equation, Navier-Stokes (NS) equation, generalized Poisson-
Boltzmann (PB) equation and molecular dynamics to describe the dynamics of nanofluidic systems. Finally, we
discuss models for the analysis of nano-biosensors. The Nernst-Planck equation is incorporated into our fluid-
electro-and geometric systems to describe the drift and diffusion of ions over the nanopores. Applications will be
discussed to protein folding, ion channels, micro/nanofluidic devices, and nano-bio sensors.
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