A kernel-based approach to molecular conformation analysis

We present a novel machine learning approach to understanding conformation dynamics of biomolecules. The approach combines kernel-based techniques that are popular in the machine learning community with transfer operator theory for analyzing dynamical systems in order to identify conformation dynamics based on molecular dynamics simulation data. We show that many of the prominent methods like Markov State Models, EDMD, and TICA can be regarded as special cases of this approach and that new efficient algorithms can be constructed based on this derivation. The results of these new powerful methods will be illustrated with several examples, in particular the alanine dipeptide and the protein NTL9. I. INTRODUCTION The spectral analysis of transfer operators such as the Perron-Frobenius or Koopman operator is by now a well-established technique in molecular conformation analysis These slow transitions are critical for a better understanding of the functioning of peptides and proteins. Since these operators are infinite-dimensional, they are typically projected onto a space spanned by a set of predefined basis functions. The advantage of the former is that the size of the resulting eigenvalue problem depends only on the size of the feature space, but not on the size of the training data set (this corresponds to EDMD or VAC). However, this approach can in general not be applied to the typically high-dimensional systems prevalent in molecular dynamics due to the curse of dimensionality and furthermore requires an explicit feature space representation, i.e., an explicit basis of the approximation space. For the kernel-based variant, the size of the eigenvalue problem is independent of the number of basis functions--and thus allows for implicitly infinitedimensional feature spaces--, but depends on the size of the training data set (this corresponds to kernel EDMD or kernel TICA). Kernel-based methods thus promise increased performance and accuracy in transfer operatorbased conformation analysis.