Overview:Electrostatics + Basic Forces

Overview:Methods for the Generation and Analysis of Macromolecular Simulations

Electric potential, a quick review

Maxwell's Equations

Multipole Expansion

Gauss’ Law: Electrostatics

Dipole Derivation

Polariz-ation

Dielectric const.

Polarity vs. Polarizability

VDW Forces: Start by Deriving Dipole-Dipole Energy

Average Dipole-Dipole Interaction Energy

Dipole-induced dipole Energy

VDW Foces: Induced dipole-induced dipole

Packing ~ VDW force

Close-packing is Default

Small Packing Changes Significant

Different Sets of Radii

Molecular Mechanics:Simple electrostatics

H-bonds subsumed by electrostatic interactions

Bond Length Springs

Bond angle, More Springs

Torsion angle

Potential Functions

Sum up to get total energy

Energy Scale of Interactions

Elaboration on the Basic Protein Model

Goal: ModelProteins and Nucleic Acidsas Real Physical Molecules

Ways to Move Protein on its Energy Surface

Steepest Descent Minimization

Multi-dimensional Minimization

Other Minimization Methods

Adiabatic mapping

Molecular Dynamics

Molecular Dynamics (cont)

Phase Space Walk

ExamplePhaseSpaceWalk

Monte Carlo

Monte Carlo (cont)

MC vs/+ MD

Moving Molecules Rigidly

Typical Systems: Water v. Argon

Typical Systems: DNA + Water

Typical Systems: Protein + Water

Practical Aspects: simulation cycle I

Practical Aspects: simulation cycle II

Sample Protein Parameters (toph19.pro)

Sample Protein Parameters (toph19.pro)

Sample Protein Parameters (param19.pro)

Sample Protein Parameters (param19.pro)

Sample Protein Parameters (param19.pro)

Sample Protein Parameters (param19.pro)

Periodic Boundary Conditions

Average over simulation

Timescales

D & RMS

Number Density

Number Density (cont)

Major Protein Simulation Packages

Molecular Biophysics & Biochemistry 400a/700a (Advanced Biochemistry)

The Handouts

The Handouts II

Outline

Practical Aspects: simulation cycle I

Practical Aspects: simulation cycle II

Major Protein Simulation Packages

Moving Molecules Rigidly

Simulation, Part II:Analysis: What can beCalculated from Simulation?

Average over simulation

Energy and Entropy

Application of Simulation:Thermodynamic Cycles

Number Density

Number Density (cont)

Measurement of Dynamic Quantities I

Measurement of Dynamic Quantities II

D & RMS

Observed RMS values

Other Things to Calculate

Monitor Stability of Specific Hydrogen Bonds

Energy Landscapes and Barriers Traversed in a Simulation

Timescales

Electrostatics Revisited:the Poisson-Boltzmann Equation

Poisson-Boltzmann equation

Simplifications of the Poisson-Boltzmann equation

Protein on a Grid

Demand Consistency on the Grid

Adding a Dielectric Boundary into the Model

Electrostatic Potential of Thrombin

Increasing Ionic Strength

Increasing Dielectric

pKa shifts

pKa continued I

pKa continued II

Water Simulationand Hydrophobicity

Simulating Liquid Water

Periodic Boundary Conditions

Tetrahedral Geometry of Water

HydrophobicityArises Naturallyin Simulation

Different Behavior of Water around Hydrophobic and Hydrophilic Solutes

Consequences of Hydrophobic Hydration and “Clathrate” Formation

Ways of Rationalizing Packing

PPT Slide

PPT Slide

Water around Hydrophobic Groups on protein surface is more Compressible

Interaction Between Water and the Protein Surface

Simple Two Helix System

Second Solvent Shell:Water v LJ Liquid

Water vs. Ar (Helical Project-ions)

Hydration Surface

Water Participates in Protein Unfolding

Simplified Simulation

Simplification

Simplified Protein: Lattice Models

Off-lattice Discrete State Models

How Well Do Lattice Structures Match Real Protein Structure?

How well does the off-lattice model fit?

Simplified Solvent

Review -- Basic Forces

Review -- Simulation

Demos

References

References 2

References

References 2