Amélie Chatelain presents a new method called NEWMA (No prior knowledge Exponentially Weighted Moving Average) to detect conformational changes in molecular dynamics simulations. NEWMA uses optical or CPU-based random features to analyze trajectories without prior knowledge. It was shown to outperform existing methods like diffusion maps in detecting changes in SARS-CoV-2 simulations, with optical random features providing faster computation. Future work includes using reinforcement learning to guide molecular dynamics simulations.

1. How Optical Random Features can be used to
Accelerate SARS-CoV-2 Molecular Dynamics Studies
Amélie Chatelain
contact@lighton.ai
Paris - Women in Machine Learning and Data Science - 22.04.2020

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My background: from neutrinos to photons
[Chatelain, Volpe, 2018]
Ph. D. in theoretical physics
linkedin.com/in/amelie-chatelain/
Travelling around ... Paris Rive Gauche
Master ICFP in
theoretical
physics at ENS
LightOn AI Research Team

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LightOn AI Research Team
Larger Scale
Faster Computation
Better Energy Efficiency
Optical Processing Unit (OPU)
Now available on
Pay-per-use or for Research
For more information: cloud.lighton.ai

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Molecular Dynamics (MD) and conformational changes
Molecular Dynamics (MD): follow trajectories of atoms
Fluctuations ~fs
Transitions ~μs, up to msFreeenergy
Collective Variable
A billion timesteps!
→ Methods to enhance sampling.
[Trstanova, Leimkuhler, Lelievre, 2019]

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Enhanced Sampling Methods
Example: metadynamics [Laio, Gervasio, 2008]

6. How to identify collective variables?
Diffusion maps

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Diffusion Maps – General Method
Nonlinear dimensionality reduction technique
dimension N dimension k, k < N
[Coifman, Lafon, Lee, Maggioni, Nadler, Warner, Zucker, 2005]
Diffusion
matrix
Stochastic
matrix
Diffusion
coordinates
diagonalisenormalise normalise

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Diffusion Maps – Illustration: the swiss-roll
Bonus Pearson’s correlation coefficients → relevant physical coordinates
●
Diffusion Coordinate 2 → ϕ
●
Diffusion Coordinate 3 → z
[Marsland, 2009]
x
y
z
Diffusion Coordinate 2
DiffusionCoordinate3

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Diffusion Maps: application to MD trajectories
[Trstanova, Leimkuhler, Lelievre, 2019]
Conformational changes
Issues:
(1) Memory footprint
(2) Hyperparameters
(3) User-defined threshold
(4) Compute time [ ]
F F F
F
Produced
by MD
Diffusion Maps
algorithm
Eigenvalues Change in
→ change of
conformation
Metadynamics
(or other)
Collective
variables
Diffusion
coordinates

10. Do we really have to compute & extract the
eigenvalues of the diffusion matrix every m
timesteps?
Maybe not...

11. Do we really have to compute & extract the
eigenvalues of the diffusion matrix every m
timesteps?
→ NEWMA!

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Online change-point detection – EWMA
Statistics Function of
time series
→ Change pointIf
In-control value Threshold
→ Requires prior knowledge of the dataset
Exponentially Weighted Moving Average for series of points

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Introducing NEWMA
→ No prior knowledge
: random features
→ CPU: Random Fourier Features (RFF),
or FastFood (FF)
[Rahimi, Recht, 2007] [Sarlós, Smola, 2013]
→ optically: RP on Aurora OPU
[Keriven, Garreau, Poli, 2018]
Change point if:
Adaptive threshold

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A new strategy for sampling!

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Applying NEWMA to MD trajectories: SARS-CoV-2
[Cespugli, Durmaz, Steinkellner, Gruber, 2020]
Comparison with changes computed with the diffusion maps algorithm.

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Applying NEWMA to MD trajectories: SARS-CoV-2
[DE Shaw Research, 2020]
Comparison with changes observed in video produced by Anton
https://youtu.be/HFkPq-l2EEY

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Applying NEWMA to MD: performances comparison
OPU vs. CPU for random projections: faster and lower memory footprint

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Take away message
●
NEWMA: great way to detect conformational changes in molecular
dynamics simulations.
●
Optical random features: particularly adapted to this task.
●
Future work: reinforcement learning for molecular dynamics.
[Shin, Tran, Takemura, Kitao, Terayama, Tsuda, 2019]

19. Thank you for your attention!

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Acknowledgments & References

We would like to thank Žofia Trsťanová for useful discussions and insights on her work.

Alessandro Laio and Francesco L. Gervasio. In: Reports on Progress in Physics 71.12, 2008.
ISSN:00344885. DOI: 10.1088/0034–4885/71/12/126601.

Zofia Trstanova, Ben Leimkuhler, and Tony Lelièvre. 2019. arXiv: 1901.06936.

R.R. Coifman, S. Lafon, A.B. Lee, M. Maggioni, B. Nadler, F. Warner, and S.W Zucker. In:
PNAS.102(21):7426–7431, 2005. DOI: 10.1073/pnas.0500334102

Nicolas Keriven, Damien Garreau, and Iacopo Poli. 2018. arXiv: 1805.08061.

A. Rahimi, and B. Recht. In Advances in Neural Information Processing Systems (NIPS),
2007.
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Q. V. Le, T. Sarlós, and A. J. Smola. In: International Conference on Machine Learning
(ICML), volume 28, 2013.

Marco Cespugli, Vedat Durmaz, Georg Steinkellner, and Christian C. Gruber. 2020. DOI:
10.6084/m9.figshare.11764158.v2

D. E. Shaw Research, "Molecular Dynamics Simulations Related to SARS-CoV-2," D. E. Shaw
Research Technical Data, 2020.http://www.deshawresearch.com/resources_sarscov2.html

Lindorff-Larsen, Piana, Dror, Shaw. In: Science 28 Oct 2011, Vol. 334, Issue 6055, pp. 517–
520. DOI: 10.1126/science.1208351