Discovering Collective Variables of Molecular Transitions via Genetic Algorithms and Neural Networks

Abstract

With the continual improvement of computing hardware and algorithms, simulations have become a powerful tool for understanding all sorts of (bio)molecular processes. To handle the large simulation data sets and to accelerate slow, activated transitions, a condensed set of descriptors, or collective variables (CVs), is needed to discern the relevant dynamics that describes the molecular process of interest. However, proposing an adequate set of CVs that can capture the intrinsic reaction coordinate of the molecular transition is often extremely difficult. Here, we present a framework to find an optimal set of CVs from a pool of candidates using a combination of artificial neural networks and genetic algorithms. The approach effectively replaces the encoder of an autoencoder network with genes to represent the latent space, i.e., the CVs. Given a selection of CVs as input, the network is trained to recover the atom coordinates underlying the CV values at points along the transition. The network performance is used as an estimator of the fitness of the input CVs. Two genetic algorithms optimize the CV selection and the neural network architecture. The successful retrieval of optimal CVs by this framework is illustrated at the hand of two case studies: the well-known conformational change in the alanine dipeptide molecule and the more intricate transition of a base pair in B-DNA from the classic Watson–Crick pairing to the alternative Hoogsteen pairing. Key advantages of our framework include the following: optimal interpretable CVs, avoiding costly calculation of committor or time-correlation functions, and automatic hyperparameter optimization. In addition, we show that applying a time-delay between the network input and output allows for enhanced selection of slow variables. Moreover, the network can also be used to generate molecular configurations of unexplored microstates, for example, for augmentation of the simulation data.

Sequence dependence of transient Hoogsteen base-pairing in DNA

“…S2). Our profiles are validated by: 1) the previous result for the CAA sequence reported in [36]; 2) the consistent WCFto-HG free-energy difference between our inside and outside calculations; and 3) the relatively favored HG base pairing for the TAA sequence, which agrees with experimental evidence about the effect of A•T steps [21]. We run ∼ 7 ns with twelve walkers to calculate each free-energy profile; placing our total runtime to obtain the inside and outside profiles of one sequence at ∼ 168 ns.…”

“…The attractors successfully keep the paths separated, with the inside ones near θ = 0 and the outside ones flipping toward the major groove. The free-energy profile for the CAA sequence compares well to our results from [23] and [36], which consider only the 3' direction of rotation. To simplify the analysis of the numerous free-energy profiles, in Fig.…”

“…We use two CVs: the base opening pseudodihedral angle θ, as defined in [15], which has been repeatedly proven effective to bias base flipping [5,16,23]; and the base rolling pseudo-dihedral angle χ , as defined in [23], which is a correction to the glycosidic torsion χ to prevent sugar rotation. The fitness of these two CVs has been discussed in [36]. A value of χ = 0 rad implies a mid-rotated A16 with its 6-ring pointing in the 3' direction, while χ = ±π implies that the A16 6-ring points toward the 5' direction.…”

Force Field Dependent DNA Breathing Dynamics: A Case Study of Hoogsteen Base Pairing in A6-DNA

“…26 This highly stable extra-helical conformation is inconsistent with the conventional idea about the stability of DNA, and provokes further discussion on the accuracy of force fields in describing the base pairing intermediates and transition pathways. Path sampling studies by Vreede et al 29 and Hooft et al 30 also revealed that partial opening of the A-T base pair is necessary for the conformational switching, but no stable open base paired intermediate conformation was observed.…”

Explaining reaction coordinates of alanine dipeptide isomerization obtained from deep neural networks using Explainable Artificial Intelligence (XAI)

“…Machine learning models have been widely utilized to determine the dominant CVs from trajectories obtained using MD simulations. [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71] Furthermore, a feasible application is the nonlinear regression based on a deep neural network (DNN), which is expected to have a performance beyond that of the LR in searching for an appropriate RC. 67,72,73 In particular, nonlinear functions of a DNN with hidden layers will provide richer expressions when the number of CVs is drastically increased in the system of interest.…”