컨퍼런스
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2010 NIMS Summer School "Stochastic/Multiscale Methods and their Applications"

**발표자**김인찬, 황치옥**기간**2010-06-17 ~ 2010-06-25**장소**숭실대학교

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.