1. Deep learning enhanced Markov State Models (MSMs)
Wei Wang
Feb 20, 2019

2. Outline General protocol of building MSM Challenges with MSM VAMPnets
Time-lagged auto-encoder

3. Revisit the protocol of building MSM

4. Need a lot of expertise in biology & machine learning
Wang, Cao, Zhu, Huang WIREs Comput. Mol. Sci., e1343, (2017)

5. Criterion to choose a model: slowest dynamics
Choose the MSM that best captures the slowest transitions of the system
Wang, Cao, Zhu, Huang WIREs Comput. Mol. Sci., e1343, (2017)

6. Choose the one with slowest transition
Timescales (μs)
Da, Pardo, Xu, Zhang, Gao, Wang, Huang,  Nature Communications., 7, 11244, (2016)

7. Perform this cumbersome work: search
Propose good clustering algorithms & features
Parametric search using good strategies

8. Challenges: parametric space is too large: Collective Variable (CV)
Need to propose good features

9. Challenges: parametric space is too large: CV
Need to propose good features

10. Challenges: parametric space is too large: CV
Need to propose good features, otherwise will worsen the clustering stage
Truth
tICA
Wehmeyera and Noe, J. Chem. Phys. 148, (2018)

11. Challenges: parametric space is too large: clustering
Zhang et al., Methods in Enzymology, 578,  (2016)

12. Essence of these operations
Linearlly/Nonlinearlly transform the protein configurations into the state vectors: 𝒙 𝑡 𝟑𝑵 → 𝑝 1 , 𝑝 2 ,…, 𝑝 𝑀 , 𝑗=1 𝑀 𝑝 𝑀 =1
(1, 0, 0, 0)
(0, 0, 1, 0)
Husic and Pande, J. Am. Chem. Soc. 2018, 140, 2386−2396

13. Deep learning can greatly help: powerful
In the mathematical theory of artificial neural networks, the universal approximation theorem states that a feed-forward network with a single hidden layer containing a finite number of neurons can approximate continuous functions on compact subsets of Rn, under mild assumptions on the activation function.
Deep learning has been widely applied in numerous fields
Dog: 0.99
Cat: 0.01

14. Deep learning can greatly help MSM
Dog: 0.99
Cat: 0.01
Macro1: 0.990
Macro2: 0.005
Macro3: 0.005

15. Outline General protocol of building MSM Challenges with MSM VAMPnets
Time-lagged auto-encoder

16. VAMPnets for deep learning of molecular kinetics
VAMPnets: employ the variational approach for Markov processes (VAMP) to develop a deep learning framework for molecular kinetics using neural networks, encodes the entire mapping from molecular coordinates to Markov states, thus combining the whole data processing pipeline in a single end-to-end framework.
coordinates
state vector
Related to the implied timescale plot, maximize it
Noe et al., 9, 5, 2018, Nature Communications

17. Understanding VAMPnets
The basic structure of neural network
What is VAMP score

18. Basic structure of neural network

19. Where can we get the weights?
Forward propagation
Where can we get the weights?

20. Backpropagation to update the weights
Define a objective function 𝜖= 𝑖 𝑦 𝑡𝑟𝑢𝑒 − 𝑦 𝑝𝑟𝑒𝑑 2
Weights are updated following the largest gradient direction

21. Backpropagation to update the weights

22. Backpropagation to update the weights
In VAMPnets, it is VAMP-2 score
Define a objective function 𝜖= 𝑖 𝑦 𝑡𝑟𝑢𝑒 − 𝑦 𝑝𝑟𝑒𝑑 2
Weights are updated following the largest gradient direction

23. VAMP-2 score: objective function
𝜒(𝑥): state vector, e.g., 𝜒 𝑥 =(0,1,0) if x belongs to state 2
Noe et al., 9, 5, 2018, Nature Communications

24. VAMP-2 score: related to TPM
Sum of eigenvalues of T(𝜏) 2
Related to the implied timescale plot, we want to maximize it
𝜒(𝑥): state vector, e.g., 𝜒 𝑥 =(0,1,0) if x belongs to state 2
Noe et al., 9, 5, 2018, Nature Communications

25. VAMPnets: example on alanine dipeptide
Try to lump to 6 states
Output: 6 probabilities
10 heavy atoms
xyz for 10 heavy atoms
Noe et al., 9, 5, 2018, Nature Communications

26. VAMPnets: example on alanine dipeptide
Visualizing the outputs (soft assignments)
Once we have the state vectors, we can calculate TPM, and get the kinetics
Noe et al., 9, 5, 2018, Nature Communications

27. Comparison with traditional way to build MSM
Advantages
No need to worry about features to do tICA and the clustering algorithms
Inputs are simple: aligned trajectories
Find the variationally optimal one
Disadvantages
Easy to overfit the data
Easy to be trapped in local optimal
Alanine dipeptide
Noe et al., 9, 5, 2018, Nature Communications

28. Outline General protocol of building MSM Challenges with MSM VAMPnets
Time-lagged auto-encoder

29. Other application of deep learning in MSM: CV
Improve PCA/tICA through nonlinear transformation trained by (time-lagged) auto-encoder
PCA/tICA: find the direction that maximizes the variance/time- lagged covariance matrix.

30. PCA: minimizing reconstruction error

31. PCA: Linear version of auto-encoder
Original data
Reconstructed data
 Wehmeyer and Noe, J. Chem. Phys. 148, (2018)

32. Improving tICA using time-lagged auto-encoder
D,E are constant matrix in tICA
Current frame
Next frame
 Wehmeyer and Noe, J. Chem. Phys. 148, (2018)

33. Improving tICA using time-lagged auto-encoder
D,E are constant matrix in tICA
𝝉=𝟑
 Wehmeyer and Noe, J. Chem. Phys. 148, (2018)

34. Time-lagged autoencoder improves over tICA
Villin
 Wehmeyer and Noe, J. Chem. Phys. 148, (2018)

35. Summary
Deep learning improves MSM in reducing the number of prior knowledge
However, deep learning may overfit the data when our sampling is not enough