Accelerating SARS-CoV-2 Molecular Dynamics Studies with Optical Random Features

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Viruses -- or more generally, biomolecular systems -- are made of atoms which constantly fluctuate. However, they can occasionally undergo large-scale structural variations, called conformational changes. We explore detecting online these transitions in numerical simulations: this is a key to analyse and improve on drug discovery and design.

Science

Accelerating SARS-CoV-2 Molecular Dynamics
Studies with Optical Random Features
Amélie Chatelain
amelie@lighton.ai
Paris - Women in Machine Learning and Data Science - 22.04.2020

22.04.2020 2
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

22.04.2020 3
LightOn AI Research Team
Reducing compute time and energy consumption
Optical Processing Unit (OPU)

22.04.2020 4
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]

22.04.2020 5
Enhanced Sampling Methods
Example: metadynamics [Laio, Gervasio, 2008]

Diffusion Maps to Identify Collective Variables

22.04.2020 8
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

22.04.2020 9
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

22.04.2020 10
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

NEWMA to Detect Conformational Changes in
Molecular Dynamics

22.04.2020 13
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 .

22.04.2020 14
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:
Adaptative threshold

22.04.2020 15
A new strategy for sampling!

22.04.2020 17
Applying NEWMA to MD trajectories: SARS-CoV-2
[DE Shaw Research, 2020]
Comparison with changes observed in video produced by Anton
+ match changes observed using the diffusion maps algorithm

22.04.2020 18
Applying NEWMA to MD: performances comparison
OPU vs. CPU for random projections: faster and lower memory footprint

22.04.2020 19
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]

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7. 22.04.2020 8 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

8. 22.04.2020 9 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

9. 22.04.2020 10 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. NEWMA to Detect Conformational Changes in Molecular Dynamics

11. 22.04.2020 13 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 .

12. 22.04.2020 14 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: Adaptative threshold

13. 22.04.2020 15 A new strategy for sampling!

14. 22.04.2020 17 Applying NEWMA to MD trajectories: SARS-CoV-2 [DE Shaw Research, 2020] Comparison with changes observed in video produced by Anton + match changes observed using the diffusion maps algorithm

15. 22.04.2020 18 Applying NEWMA to MD: performances comparison OPU vs. CPU for random projections: faster and lower memory footprint

16. 22.04.2020 19 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]

17. Thank you for your attention!

Accelerating SARS-CoV-2 Molecular Dynamics Studies with Optical Random Features

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