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

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

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

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/

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

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

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

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

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

Implementation: Connectivity 6 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

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++

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

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.

Results: 0.069 Concentration ht4 HT4

Results: 0.208 Concentration ht4 HT4

Results: 0.347 Concentration ht4 HT4

Results: 0.417 Concentration ht4 HT4

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

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