Modeling molecular motion: complex adaptive thermodynamic

The Glotzer Group @ University of Michigan

Mmm: cats!Modeling molecular motion:

complex adaptive thermodynamic simulations

Eric JankowskiGlotzer Group

CSAAW talk 1-19-2007


A tale of two talks:

• ABM’s and potential energy minimization: can “learning” be used to speed up simulations?

• Self-assembly and switchability: can we figure out what properties particles need to robustly assemble a desired structure?


Nanoscale simulation

• Want to predict what structures will form, given a set of particles and interactions

• Want to ask “How do I assemble __?”

• Many methods to do this: molecular dynamics, Brownian dynamics

• If all you care about is equilibrium structure, then Monte Carlo is method of choice


Monte Carlo basics

• Find free energy minima by randomly changing configurations in a smart way

• Uphold detailed balance

• P(A)*P(A->B)=P(B)*P(B-A)

• Ensures that the chain of states moves towards equilibrium, and stays there


Agent-based modeling

• Bread and butter for many CSCS students

• Strength is in hypothesis testing

• Simple premise:

• Define agents, interactions

• Define environment

• See what happens!


Ratner et al.

• Model designed to simulate charged molecules such as polymers.

• Agents are “Tetris” pieces made up of three types of cells.

Ratner, Troisi, Wong 2004Note, cell colors not equivalent

Interaction energies:


Learning algorithm

• Goal is to bias energetically favorable structures

• Particles form clusters with most attractive neighbor

• These clusters are sorted by size

• Best energy for each cluster size is recorded


Learning algorithm

• Cluster energies are checked against tabulated values

• If they are the best cluster of that size, they move as a cluster

• If not, the cluster breaks up into individual particles


Ratner’s results

• Learning algorithm finds energy minimizing structures in fewer time steps than Monte Carlo

• Finds better structures (energy 15% lower)

Ratner, Troisi, Wong 2004


...but there are some problems

• No discussion of temperatures

• Critical for comparing energies

• Disobeys detailed balance

• Clock cycles/real time, not timesteps, are the performance indicator

• Does learning speed up a cluster Monte Carlo code?


Investigate effect of learning

• Reproduce Ratner’s system, compare cluster Monte Carlo with and without learning

• What to look for:

• Best structure in each simulation

• How long it took to find the structure


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Maximum Cluster Size

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Results

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Discussion

• Learning doesn’t help

• Prevents “almost as good” clusters

• Different learning schemes could do better, but they’re all non-physical

• ABM’s good for exploring systems that aren’t understood

Learning No learning


Future work

• Make a better learning algorithm, compare clock cycles

• Use a genetic algorithm to search configuration space

• Explore 3D systems

• Add “state” variables, and keep learning Markovian

• Chat with the man himself


Lattice + 2D = 2plane

• Real systems are often far from equilibrium

• What about systems of particles with adaptive interactions?

• Want to figure out what properties a set of particles needs to form a target structure: transistor, synthetic capsid, spiraling swarm


Why model switchable cubes?

• Experimentalists improving control over particle morphology

• Switchable surfaces have been developed

• Base model for proteins, nanobots, not-so-nano bots

Au

Obare & MurphyNano Letters, 2001

Kotov, Pre-print

Y particle


Inspiration: Poulton et al.

• Model a system of homogenous agents whose states can switch

• Like proteins or nanoparticles that change shape or charge when something binds to it

Poulton et al, 2005.


The idea:

• Make a Brownian dynamics simulation of cubes

• Make the cubes switchable

• Pick some nice structures to form

• Use a GA to find rule sets that make them

• Tell experimentalists what they need to do

• Throw fistfuls of money in the air


The Simulation

• Approximate cubes with 14 spheres

• “face” spheres can change their interaction potentials

• Choice of interaction potentials important


Changing faces

• Rules encoded as strings

• Positive=1, Negative=-1, Neutral=0, “don’t care” = #

• (#,0,-1,#,#,#)@(#,#,1,#,#,#)->(#,#,#,#,#,1) means “if my 2nd face is neutral, 3rd is negative, and a positive face is stuck to my third face, change my 6th face to positive”

• Easy to manipulate, large rule space (68 billion rules, way more combinations of rules)


What to make?

• The letter “T”

• A box

• A cycling swarm

• The snag: defining a fitness function for each structure


Computational Challenges

• Say it takes 3 hours to run a million time steps

• Need to run ~50 simulations per GA generation

• Need to run lots of GA generations...


In the meantime...

• Very interesting to look at how adaptive particles behave

• Use some Intelligent Design to make some basic structures

• Can use same ideas, applied to interaction potentials


The end, kinda

• ABM’s can be very useful in studying molecular self-assembly

• Should be used to model the way you think things might behave

• Lots to be learned, so this is just the beginning of the story

Documents

Modeling molecular motion: complex adaptive thermodynamic