Kobe-Brown Simulation Summer School 2015 Project: DPD Simulation of a Membrane
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1 Kobe-Brown Simulation Summer School 2015 Project: DPD Simulation of a Membrane Clark Bowman Karen Larson Yuji Funaki Ross Parker Tae Woo Kim
2 Week 1: Introduction to Molecular Dynamics (MD) Computer simulation of a large number of particles Trajectories of particles are determined by solving Newton s laws numerically Simulation proceeds in discrete time steps
3 Goal of Week 1 Write a two-dimensional MD simulation of liquid argon from scratch using C++! Forces calculated using Lennard-Jones (LJ) potential Velocity Verlet method used for numerical integration Experiment with different boundary conditions (periodic, reflecting, no-slip)
4 Lennard-Jones Potential Lennard-Jones Potential Image:
5 Force Calculation: Pairwise Forces
6 Force Calculation: Cell List Method
7 Force Calculation: Neighbor List Method
8 Boundary Conditions Periodic Reflecting No-slip
9 Testing the Code: Flow in a Pipe 3D rectangular channel with no-slip walls Channel filled with LJ fluid Uniform force along channel due to pressure gradient (Poiseuille flow) Parabolic velocity profile?
10 Week 2: Dissipative Particle Dynamics (DPD) Particle simulator like Molecular Dynamics Coarse-graining: model groups of atoms as single beads Reduced complexity allows simulating larger systems while still modeling flows Image:
11 Goal of Week 2 Simulate a 3D bilipid membrane with DPD and study its properties! Method: LAMMPS particle simulator same algorithms as Week 1, but parallel/optimized Means: Brown CCV Computing Cluster Oscar Teraflops across 7,632 Intel Xeon E5 cores Images: lammps.sandia.gov
12 DPD Force Equation In MD, only force was due to LJ pairwise interactions DPD has three forces: Conservative force (soft repulsion), Dissipative force (viscous resistance), Random force (thermostat) New forces compensate for coarse-graining to yield similar mechanics
13 Creating a DPD Bilipid Membrane Built out of lipids: Blue = hydrophilic head particles Red = hydrophobic tail particles Harmonic (spring) bonds Initialize on cubic lattice
14 Tunable Parameters to Achieve Stability Structure of lipids (e.g., number of tail beads) Dimensions of lattice for initialization (e.g., space between lipids) Spacing between two halves of membrane Conservative coefficient and dissipative coefficient for different types of beads (water, heads, tails)
15 Exploring DPD Parameters For water, = 25.0 and = 4.5 (Groot, Warren 1997) For lipid heads and tails:???
16 Exploring DPD Parameters (End Result)
17 Simulation 1: Pinned Membrane Pin (fix in place) corners of membrane Subject membrane to uniform orthogonal force What shape is formed? Record extent of deflection for different forces At what force does the membrane break?
18 Forces and Membrane Breaking
19 Simulation 2: Density Difference Numerical density: 10.0 Numerical density: 3.0 Increase fluid density on one side of membrane Reflecting walls keep sides separate How does the membrane move?
20 Final Distance Traveled by Membrane
21 Membrane Position Over Time
22 Project Recap Week 1 MD implemented from scratch in C++ Simulation: Flow in a Pipe Week 2 DPD model of a membrane in LAMMPS (project goal) Simulation: Pinned Membrane Simulation: Density Difference
23 Thank you for your attention!
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