Robert McGibbon
2016-03-01 (print)
Chapter 1 is a bespoke introduction to MD and MSMs
Chapter 2 is adapted from 2013-mcgibbon-kdml (ref. 37).
Chapter 3 is adapted from 2014-mcgibbon-hmm (ref. 92).
Chapter 4 is adapted from 2015-ratematrix (ref. 120).
Chapter 5 is adapted from 2014-mcgibbon-bic (ref. 162).
Chapter 6 is adapted from 2015-mcgibbon-gmrq (ref. 214).
Chapter 7 is adapted from 2016-sparsetica.
Chapter 8 is adapted from 2015-mdtraj.
Show References| Num | Entry | Why |
|---|---|---|
| 37 | 2013-mcgibbon-kdml | |
| 92 | 2014-mcgibbon-hmm | |
| 120 | 2015-ratematrix | |
| 162 | 2014-mcgibbon-bic | |
| 214 | 2015-mcgibbon-gmrq |
Christian Schwantes
2015-05-01 (print)
Section 1.2 is adapted from 2015-schwantes-ktica (ref. 27) and 2014-mcgibbon-bic (ref. 28).
Chapter 2 is adapted from 2014-mcgibbon-bic (ref. 28).
Chapter 3 is adapted from 2013-schwantes-tica (ref. 73).
Chapter 4 is adapted from 2016-schwantes-nug2 (ref. 122).
Chapter 5 is adapted from 2015-schwantes-ktica (ref. 27).
Chapter 6 is supposed to have been submitted for publication.
Show References| Num | Entry | Why |
|---|---|---|
| 27 | 2015-schwantes-ktica | |
| 28 | 2014-mcgibbon-bic | |
| 28 | 2014-mcgibbon-bic | |
| 73 | 2013-schwantes-tica | |
| 122 | 2016-schwantes-nug2 | |
| 27 | 2015-schwantes-ktica |
Kyle Beauchamp
2013-09-01 (print)
Christian R. Schwantes; Diwakar Shukla; Vijay S. Pande
2016-04-01 (print)
Biophysical Journal (Biophys. J.). 110, 8, 1716-1719. doi:10.1016/j.bpj.2016.03.026
They find an intermediate in 2011-larsen-folding NuG2 trajectories that is a register shift that was missed before tICA+MSM.
Robert T. McGibbon; Vijay S. Pande
2015-07-21 (print)
The Journal of Chemical Physics (J. Chem. Phys.). 143, 3, 034109. doi:10.1063/1.4926516
msm-theory
Robert T. McGibbon; Vijay S. Pande
2015-03-28 (print)
The Journal of Chemical Physics (J. Chem. Phys.). 142, 12, 124105. doi:10.1063/1.4916292
msm-theory variational
Christian R. Schwantes; Vijay S. Pande
2015-02-10 (print)
Journal of Chemical Theory and Computation (J. Chem. Theory Comput.). 11, 2, 600-608. doi:10.1021/ct5007357
They introduce kernel tICA as an extension to tICA. This is useful to get non-linear solutions to the tICA equation. They claim you can estimate eigenprocesses without building an MSM.
They briefly introduce the transfer operator. They introduce the variational principle of conformation dynamics per 2011-prinz (ref. 25). They introduce tICA as maximizing the autocorrelation. They say that solutions to tICA are the same as solutions to the variational problem per 2013-noe-tica (ref. 28). Linearity makes them crude solutions.
They explain that a natural approach to introduce non-linearity is to expand the original representation into a higher dimensional space and do tICA there. They say this is impractical. The expanded space probably has to be huge. You can perform analysis in the big representation without explicitly representing it by using the "kernel trick". They reproduce an example of the kernel trick from 1998-scholkopf-kernel-pca (ref. 39).
They re-write the tICA problem only in terms of inner products so you can apply the kernel trick. They introduce normalization. They choose a gaussian kernel. They simulate a four-well potential, muller potential, alanine dipeptide, and fip35ww. They need to do MLE cross validation over parameters (kernel width and regularization strength).
This uses so much RAM! Huge matrices to solve (that scale with the amount of data!!)
Show References| Num | Entry | Why |
|---|---|---|
| 21 | 2014-msm-perspective | Data needs analysis |
| 25 | 2011-prinz | Details of transfer operator approach. |
| 33 | 2001-schutte-variational | Details of transfer operator approach. |
| 34 | 2013-noe-variational | "It was shown that a variational principle can be derived for the eignvalues of the transfer operator." The autocorelation of a function is less than the autocorrelation of the first dynamical eigenfunction of the transfer operator. This is used to argue that you don't have to estimate the operator itself. Just estimate its eigenfunctions |
| 35 | 2014-nuske-variational | "Successfully constructed estimates of the top eigenfunctions in the span of a prespecified library of basis functions." Contrast with this work, which "does not require a predefined basis set" |
| 22 | 2013-schwantes-tica | Citing tICA |
| 28 | 2013-noe-tica | solutions to tica provide estimates of the slowest eigenfunctions of the transfer operator. |
| 36 | doi:10.1103/PhysRevLett.72.3634 | Citing tICA |
| 37 | doi:10.1162/neco.2006.18.10.2495 | Citing tICA |
| 39 | 1998-scholkopf-kernel-pca | Used to introduce ther kernel trick. |
msm-theory
C. R. Schwantes; R. T. McGibbon; V. S. Pande
2014-09-07 (print)
The Journal of Chemical Physics (J. Chem. Phys.). 141, 9, 090901. doi:10.1063/1.4895044
Very good perspective on the importance of analysis (particularly MSM analysis) for understanding large, modern MD datasets. Money quote: "we believe that quantitative analysis has increasingly become a limiting factor in the application of MD"
msm-theory perspective
Robert T. McGibbon; Christian R. Schwantes; Vijay S. Pande
2014-06-19 (print)
The Journal of Physical Chemistry B (J. Phys. Chem. B). 118, 24, 6475-6481. doi:10.1021/jp411822r
This is before 2015-mcgibbon-gmrq GRMQ cross-validation. They explicitly find the volume of voronoi cells (in low number of tIC space) to find a likelihood. They use AIC/BIC to find the number of states to use. Finding volumes is tough and you still can't compare across protocols (so you can basically only scan number of states or clustering method), but! this was the first paper to seriously suggest using a smaller number of states to avoid overfitting.
msm cross-validation
Feliks Nüske; Bettina G. Keller; Guillermo Pérez-Hernández; Antonia S. J. S. Mey; Frank Noé
2014-04-08 (print)
Journal of Chemical Theory and Computation (J. Chem. Theory Comput.). 10, 4, 1739-1752. doi:10.1021/ct4009156
This paper is largely redundant with 2013-noe-variational (ref. 65). They cite it as such: "Following the recently introduced variational principle for metastable stochastic processes,(65) we propose a variational approach to molecular kinetics."
They perform their variational approach on 2- and 10-alanine in addition to 1D potentials.
This comes after tICA and cites 2013-schwantes-tica (ref. 57) and 2013-noe-tica (ref. 58) in the intro, but does nothing further with it. In particular, they don't note that tICA is just another choice of basis set.
They cite their error paper 2010-msm-error (ref. 55).
Show References| Num | Entry | Why |
|---|---|---|
| 65 | 2013-noe-variational | |
| 57 | 2013-schwantes-tica | |
| 58 | 2013-noe-tica | |
| 55 | 2010-msm-error |
msm-theory variational
Robert T. McGibbon; Vijay S. Pande
2013-07-09 (print)
Journal of Chemical Theory and Computation (J. Chem. Theory Comput.). 9, 7, 2900-2906. doi:10.1021/ct400132h
Learn scaling of coordinates to better approximate kinetics? Redundant with tICA.
Guillermo Pérez-Hernández; Fabian Paul; Toni Giorgino; Gianni De Fabritiis; Frank Noé
2013-07-07 (print)
The Journal of Chemical Physics (J. Chem. Phys.). 139, 1, 015102. doi:10.1063/1.4811489
The Noe group introduces tica concomitantly with 2013-schwantes-tica. They use the variational approach from 2013-noe-variational to derive the tICA equation. They cite a 2001 book about independent component analysis.
msm-theory tica
Christian R. Schwantes; Vijay S. Pande
2013-04-09 (print)
Journal of Chemical Theory and Computation (J. Chem. Theory Comput.). 9, 4, 2000-2009. doi:10.1021/ct300878a
The Pande group introduces tica concomitantly with 2013-noe-tica. This paper uses PCA as inspiration and cites signal processing literature.
msm-theory tica
Frank Noé; Feliks Nüske
2013-01-01 (print)
Multiscale Modeling & Simulation (Multiscale Model. Simul.). 11, 2, 635-655. doi:10.1137/110858616
I think the point of this versus 2014-nuske-variational is to be "protein agnostic". They allude to proteins, but say this is more general. Their example is a double-well potential.
They introduce the propogator formalism and stipulate that dynamics can be seperated into "fast" and "slow" components. In contrast to a quantum mechanics Hamiltonian, we don't know the propogator here. You have to infer it from data.
They claim the error bound derived in 2010-msm-error (ref. 34) is not constructive, whereas this method *is* constructive.
Math section heavily cites 2010-msm-error (ref. 34).
They adapt the Rayleigh variational principle from quantum mechanics, and cite 1989-szabo-ostlund-qm (ref. 43). They show that the autocorrelation of the true first dynamical eigenfunction is its eigenvalue, and an estimate of the first dynamical eigenfunction necessarily has a smaller eigenvalue. This sets the variational bound. In terms of names that don't seem to be used now that we're in the future: the Ritz method is for when you have no overlap integrals (e.g. MSMs) and the Roothan-Hall method is for when you do (tICA).
They put it to the test on a double well potential. They use indicator basis functions to make an MSM; hermite basis functions so they still have no overlap integrals, but smooth functions; and gaussian basis functions (with overlap integrals). This must have come before tICA because there is no mention made of it, even though it would fit in nicely.
Show References| Num | Entry | Why |
|---|---|---|
| 34 | 2010-msm-error | |
| 34 | 2010-msm-error | |
| 43 | 1989-szabo-ostlund-qm |
msm-theory variational
Jan-Hendrik Prinz; Hao Wu; Marco Sarich; Bettina Keller; Martin Senne; Martin Held; John D. Chodera; Christof Schütte; Frank Noé
2011-05-07 (print)
The Journal of Chemical Physics (J. Chem. Phys.). 134, 17, 174105. doi:10.1063/1.3565032
Fantastic in-depth intro to MSMs. Figure 1 in this paper is necessary for understanding eigenvectors. This defines and relates the propogator and transfer operator. This shows how we compute timescales from eigenvectors. This discusess state decomposition error and shows that many states are needed in transition regions.
quote: it is clear that a “sufficiently fine” partitioning will be able to resolve “sufficient” detail 2010-msm-error.
Cites 2004-nina-msm for use of the term "MSM".
msm-theory review
Marco Sarich; Frank Noé; Christof Schütte
2010-01-01 (print)
Multiscale Modeling & Simulation (Multiscale Model. Simul.). 8, 4, 1154-1177. doi:10.1137/090764049
msm-theory
Tobias Blaschke; Pietro Berkes; Laurenz Wiskott
2006-10-01 (print)
Neural Computation (Neural Comput.). 18, 10, 2495-2508. doi:10.1162/neco.2006.18.10.2495
Ch. Schütte; W. Huisinga; P. Deuflhard
2001-01-01 (print)
Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems (Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems). 191-223. doi:10.1007/978-3-642-56589-2_9
Full treatment of transfer operator / propagator and build an MSM for a small RNA chain.
msm-theory
Bernhard Schölkopf; Alexander Smola; Klaus-Robert Müller
1998-07-01 (print)
Neural Computation (Neural Comput.). 10, 5, 1299-1319. doi:10.1162/089976698300017467
L. Molgedey; H. G. Schuster
1994-06-06 (online)
Physical Review Letters (Phys. Rev. Lett.). 72, 23, 3634-3637. doi:10.1103/PhysRevLett.72.3634
Attila Szabo; Neil S. Ostlund
1989-01-01 (print)
Cited by 2013-noe-variational for Rayleigh variational method.
qm
Robert McGibbon; Bharath Ramsundar; Mohammad Sultan; Gert Kiss; Vijay Pande
32, 2, 1197-1205.
Use hidden markov models instead of discrete state MSMs.