Simulation of Self-Assembly of Ampiphiles Using Molecular Dynamics

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Simulation of Self-Assembly of Ampiphiles Using
Molecular Dynamics

• Reza Banki, Misty Davies, Haneesh Kesari
• Final Project Presentation ME346
• Stanford University

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Overview

• Introduction and Background
• Methodology
• Bead Spring Model
• Potential Models
• Implementation
• Results
• Conclusions and Future Work

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Introduction

• Ampiphiles--large molecule with one or more
  hydrophilic head groups and hydrophobic tail
  groups
• Lipids, fat molecules which create cell
  membranes and micelles, do so because they are
  ampiphiles

Images from Nielsen and Klein
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Motivation

• Cell membranes are composed of lipids
• Drug delivery
• Protobiological evolution
• Nanomechanical Synthesis by Self-Assembly

library.thinkquest.org/.../cell_membranes.html
mrsec.uchicago.edu/Nuggets/Nanostructures/
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Bead and Spring Model

• Replace hydrophilic head groups with one kind
  of bead and hydrophobic tail groups with
  another kind of bead. Water as a third kind of
  bead.
• Model bond interactions within the lipid as
  springs

Top image from Nielsen and Klein Bottom image
www.ahd.tudelft.nl/frank/showcase.html
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Potential Models LJ 6-12

• Used for all unbonded non-hydrophobic reactions
• h?h
• t?t
• w?w
• h?w

www.lsbu.ac.uk/water/models.html
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Potential Models LJ 9

• Used for all unbonded hydrophobic (purely
  repulsive) reactions
• h?t
• t?w

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Potential Models Bond
Top image www.ahd.tudelft.nl/frank/showcase.html
Bottom image from Goetz and Lipowsky
Stretching and bending energies in the bonds
(modeled as springs)
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Implementation makelipids

• Created as a function within MD
• Allows for creation of lipids with multiple
  heads, multiple number of beads per tail, and
  allows you to specify which heads are connected
  to tails
• Each lipid is randomly placed, and then water
  molecules are created based on specified density
  and concentration.
• System is relaxed using CG method to begin
  simulation at equilibrium

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Implementation Connectivity
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• Each bead is assigned an index corresponding to a
  row in an array that lists neighbor beads that it
  is connected to. The columns of the array
  identify the structure and the bead type.
• Also identifies which lipid each bead belongs to.
  This allows the entire molecule to be moved
  across a periodic boundary for visualization.

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Implementation lennard_jones_bond

• Created as a function within MD
• Calculates bond and bending energies for bonded
  particles (LJ potentials for bonded particles are
  neglected.)
• Calculates appropriate LJ potential energy for
  unbonded particles.
• Calculates and sums forces between particles
  within the cutoff radius (used same cutoff radius
  for all particles). Uses neighbor list
  implementation within MD

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Results Current Model

• Used molecules with completely flexible tails
  (ht4) and semi-rigid tails (HT4)
• ?0.006 particles/Å3
• Cs0.069, 0.208, 0.347, 0.417
• LxLy40Å, Lz50Å
• ?t0.001ps, total simulation time100ps
• ?03.321e-24 kJ
• ?3.33 Å, ?rep1.05 ?
• rc2.5 ?
• kbond5000 ?0 /sqrt(?), kbend50 ?0

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Results Conjugate Gradient

• Conjugate gradient failed more often for higher
  densities. Current model approximately 1/3 the
  density of the desired model.
• Conjugate gradient converged much more slowly for
  HT4.
• Much faster simulation times than those reported
  in previous simulations may be due to conjugate
  gradient creating excellent initial conditions.

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Results 0.069 Concentration
ht4
HT4
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Results 0.208 Concentration
ht4
HT4
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Results 0.347 Concentration
ht4
HT4
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Results 0.417 Concentration
ht4
HT4
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Conclusions

• Using very simple models for the molecular
  structures and for the potential interactions it
  is possible to simulate lipid self-assembly
• More complicated structures are formed with
  higher lipid concentration
• Bending potentials assist aggregate formation
• Relaxation may speed total simulation times
• CG Relaxation may not be suitable for high
  density simulations

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Suggestions for Future Work

• Implement bending energies in bonds between heads
• Implement a function that allows for more than
  one kind of lipid
• Model the different masses of each
  particle--instead of using the average
• Implement a detection algorithm to determine the
  time of self-assembly and to place the center of
  mass of the structure at the center of the
  simulation cell for visualization
• Implement a DPD model so that water molecules do
  not have to be simulated--this may allow CG to
  relax higher density simulations