1. Simulation of Self-Assembly of Ampiphiles Using Molecular Dynamics
Reza Banki, Misty Davies, Haneesh Kesari
Final Project Presentation ME346
Stanford University

2. Overview Introduction and Background Methodology Implementation
Bead & Spring Model
Potential Models
Implementation
Results
Conclusions and Future Work

3. 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

4. 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/

5. 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:

6. Potential Models: LJ 6-12
Used for all unbonded non-hydrophobic reactions
hh
tt
ww
hw

7. Potential Models: LJ 9
Used for all unbonded hydrophobic (purely repulsive) reactions
ht
tw

8. Potential Models: Bond
Top image:
Bottom image from Goetz and Lipowsky
Potential Models: Bond
Stretching and bending energies in the bonds (modeled as springs)

9. 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

10. Implementation: Connectivity6
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. 5 7 8 1 9 2 10 3 4

11. 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++

12. Results: Current Model
Used molecules with completely flexible tails (ht4) and semi-rigid tails (HT4)
=0.006 particles/Å3
Cs=0.069, 0.208, 0.347, 0.417
Lx=Ly=40Å, Lz=50Å
t=0.001ps, total simulation time=100ps
0=3.321e-24 kJ
=3.33 Å, rep=1.05 
rc=2.5 
kbond=5000* 0 /sqrt(), kbend=50* 0

13. 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.

14. Results: 0.069 Concentration
ht4
HT4

15. Results: 0.208 Concentration
ht4
HT4

16. Results: 0.347 Concentration
ht4
HT4

17. Results: 0.417 Concentration
ht4
HT4

18. 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

19. 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