Folding a small protein using harmonic linear discriminant analysis

Abstract

Many processes of scientific importance are characterized by time scales that extend far beyond the reach of standard simulation techniques. To circumvent this impediment a plethora of enhanced sampling methods has been developed. One important class of such methods relies on the application of a bias that is function of a set of collective variables specially designed for the problem under consideration. The design of good collective variables can be challenging and thereby constitutes the main bottle neck in the application of these methods. To address this problem, recently we have introduced Harmonic Linear Discriminant Analysis, a method to systematically construct collective variables. The method uses as input information on the metastable states visited during the process that is being considered, information that can be gathered in short unbiased MD simulations, to construct the collective variables as linear combinations of a set of descriptors.Here, to scale up our examination of the method's efficiency, we applied it to the folding of Chignolin in water. Interestingly, already before any biased simulations were run, the constructed one dimensional collective variable revealed much of the physics that underlies the folding process. In addition, using it in Metadynamics we were able to run simulations in which the system goes from the folded state to the unfolded one and back, where to get fully converged results we combined Metadynamics with Parallel Tempering. Finally, we examined how the collective variable performs when different sets of descriptors are used in its construction.

Perturbation of ACE2 Structural Ensembles by SARS-CoV-2 Spike Protein Binding

“… 51 , 52 This has been recently used to analyze molecular simulations, 33 , 53 including to determine collective variables for enhanced sampling simulations. 54 , 55 As there are only two classes during training here (“apo” and “complex”), the analysis yields only one LDA vector. Projection of a structure onto this vector yields a single scalar, which in this case assesses whether the structure is “apo-like” or “complex-like”.…”

Data-Driven Molecular Dynamics: A Multifaceted Challenge

“…The method was further generalized to a multiclass problem (MC-HLDA) in order to treat more than two states simultaneously [103]. The obtained CV space was proven to be effective for reconstructing the free energy surface of chemical reactions through metadynamics, but was unable to lead to a converged free energy surface when a more complex problem like the folding of chignolin was considered [104]. Finally, we mention that other supervised ML methods other than LDA (like support vector machines, and logistic regression) have also been employed for the automatic detection of CVs for MD/ML resampling [105].…”

Computational methods for exploring protein conformations

“…The first few eigenvectors of the correlation matrix, which represent the leading high-variance modes, can be used as CVs [ 59 ]. More recently, h armonic l inear d iscriminant a nalysis (HLDA) has been used to obtain CVs that are linear combinations of a small set of user-specified descriptors thought to be capable of discriminating between metastable states, based on short unbiased simulations of each state [ 60 ]. Combination of HLDA with neural networks allows compression of a larger number of descriptors into a lower-dimensional space [ 61 ].…”