A Machine-Learning Protocol for Ultraviolet Protein-Backbone Absorption Spectroscopy under Environmental Fluctuations

A simple approach to rotationally invariant machine learning of a vector quantity

Unlike with the energy, which is a scalar property, machine learning (ML) prediction of vector or tensor properties poses the additional challenge of achieving proper invariance (covariance) with respect to molecular rotation. For the energy gradients needed in molecular dynamics (MD), this symmetry is automatically fulfilled when taking analytic derivative of the energy, which is a scalar invariant (using properly invariant molecular descriptors). However, if the properties cannot be obtained by differentiation, other appropriate methods should be applied to retain the covariance. Several approaches have been suggested to properly treat this issue. For nonadiabatic couplings and polarizabilities, for example, it was possible to construct virtual quantities from which the above tensorial properties are obtained by differentiation and thus guarantee the covariance. Another possible solution is to build the rotational equivariance into the design of a neural network employed in the model. Here, we propose a simpler alternative technique, which does not require construction of auxiliary properties or application of special equivariant ML techniques. We suggest a three-step approach, using the molecular tensor of inertia. In the first step, the molecule is rotated using the eigenvectors of this tensor to its principal axes. In the second step, the ML procedure predicts the vector property relative to this orientation, based on a training set where all vector properties were in this same coordinate system. As the third step, it remains to transform the ML estimate of the vector property back to the original orientation. This rotate-predict-rotate (RPR) procedure should thus guarantee proper covariance of a vector property and is trivially extensible also to tensors such as polarizability. The RPR procedure has an advantage that the accurate models can be trained very fast for thousands of molecular configurations, which might be beneficial where many training sets are required (e.g., in active learning). We have implemented the RPR technique, using the MLatom and Newton-X programs for ML and MD, and performed its assessment on the dipole moment along MD trajectories of 1,2-dichloroethane.

Universal machine learning for the response of atomistic systems to external fields

Machine learned interatomic interaction potentials have enabled efficient and accurate molecular simulations of closed systems. However, external fields, which can greatly change the chemical structure and/or reactivity, have been seldom included in current machine learning models. This work proposes a universal field-induced recursively embedded atom neural network (FIREANN) model, which integrates a pseudo field vector-dependent feature into atomic descriptors to represent system-field interactions with rigorous rotational equivariance. This "all-in-one" approach correlates various response properties like dipole moment and polarizability with the field-dependent potential energy in a single model, very suitable for spectroscopic and dynamics simulations in molecular and periodic systems in the presence of electric fields. Especially for periodic systems, we find that FIREANN can overcome the intrinsic multiple-value issue of the polarization by training atomic forces only. These results validate the universality and capability of the FIREANN method for efficient first-principles modeling of complicated systems in strong external fields.

Machine Learning Spectroscopy Using a 2-Stage, Generalized Constituent Contribution Protocol

A corrected group contribution (CGC)-molecule contribution (MC)-Bayesian neural network (BNN) protocol for accurate prediction of absorption spectra is presented. Upon combination of BNN with CGC methods, the full absorption spectra of various molecules are afforded accurately and efficiently-by using only a small dataset for training. Here, with a small training sample (<100), accurate prediction of maximum wavelength for single molecules is afforded with the first stage of the protocol; by contrast, previously reported machine learning (ML) methods require >1,000 samples to ensure the accuracy of prediction. Furthermore, with <500 samples, the mean square error in the prediction of full ultraviolet spectra reaches <2%; for comparison, ML models with molecular SMILES for training require a much larger dataset (>2,000) to achieve comparable accuracy. Moreover, by employing an MC method designed specifically for CGC that properly interprets the mixing rule, the spectra of mixtures are obtained with high accuracy. The logical origins of the good performance of the protocol are discussed in detail. Considering that such a constituent contribution protocol combines chemical principles and data-driven tools, most likely, it will be proven efficient to solve molecular-property-relevant problems in wider fields.

Characterizing viral samples using machine learning for Raman and absorption spectroscopy

Machine learning methods can be used as robust techniques to provide invaluable information for analyzing biological samples in pharmaceutical industries, such as predicting the concentration of viral particles of interest in biological samples. Here, we utilized both convolutional neural networks (CNNs) and random forests (RFs) to predict the concentration of the samples containing measles, mumps, rubella, and varicella-zoster viruses (ProQuad®) based on Raman and absorption spectroscopy. We prepared Raman and absorption spectra data sets with known concentration values, then used the Raman and absorption signals individually and together to train RFs and CNNs. We demonstrated that both RFs and CNNs can make predictions with R2 values as high as 95%. We proposed two different networks to jointly use the Raman and absorption spectra, where our results demonstrated that concatenating the Raman and absorption data increases the prediction accuracy compared to using either Raman or absorption spectrum alone. Additionally, we further verified the advantage of using joint Raman-absorption with principal component analysis. Furthermore, our method can be extended to characterize properties other than concentration, such as the type of viral particles.

Machine learning recognition of protein secondary structures based on two-dimensional spectroscopic descriptors

Protein secondary structure discrimination is crucial for understanding their biological function. It is not generally possible to invert spectroscopic data to yield the structure. We present a machine learning protocol which uses two-dimensional UV (2DUV) spectra as pattern recognition descriptors, aiming at automated protein secondary structure determination from spectroscopic features. Accurate secondary structure recognition is obtained for homologous (97%) and nonhomologous (91%) protein segments, randomly selected from simulated model datasets. The advantage of 2DUV descriptors over one-dimensional linear absorption and circular dichroism spectra lies in the cross-peak information that reflects interactions between local regions of the protein. Thanks to their ultrafast (∼200 fs) nature, 2DUV measurements can be used in the future to probe conformational variations in the course of protein dynamics.

Global Fold Switching of the RafH Protein: Diverse Structures with a Conserved Pathway

It is generally believed that a protein's sequence uniquely determines its structure, the basis for a protein to perform biological functions. However, as a representative metamorphic protein, RfaH can be encoded by a single amino acid sequence into two distinct native state structures. Its C-terminal domain (CTD) either takes an all-α-helical configuration to pack tightly with its N-terminal domain (NTD), or the CTD disassociates from the NTD, transforms into an all-β-barrel fold, and further attaches to the ribosome, leaving the NTD exposed to bind RNA polymerases. Therefore, the RfaH protein couples transcription and translation processes. Although previous studies have provided a preliminary understanding of its function, the full course of the conformational change of RfaH-CTD at the atomic level is elusive. We used teDA2, a feature space-based enhanced sampling protocol, to explore the transformation of RfaH-CTD. We found that it undergoes a large-scale structural rearrangement, with characteristic spectra as the fingerprint, and a global unfolding transition with a tighter and energetically moderate molten globule-like nucleus formed in between. The formation of this nucleus limits the possible intermediate conformations, facilitates the formation of secondary and tertiary structures, and thus ensures the efficiency of transformation. The key features along the transition path disclosed from this work are likely associated with the evolution of RfaH, such that encoding a single sequence into multiple folds with distinct biological functions is energetically unhindered.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.

Accurate Machine Learning Prediction of Protein Circular Dichroism Spectra with Embedded Density Descriptors

A data-driven approach to simulate circular dichroism (CD) spectra is appealing for fast protein secondary structure determination, yet the challenge of predicting electric and magnetic transition dipole moments poses a substantial barrier for the goal. To address this problem, we designed a new machine learning (ML) protocol in which ordinary pure geometry-based descriptors are replaced with alternative embedded density descriptors and electric and magnetic transition dipole moments are successfully predicted with an accuracy comparable to first-principle calculation. The ML model is able to not only simulate protein CD spectra nearly 4 orders of magnitude faster than conventional first-principle simulation but also obtain CD spectra in good agreement with experiments. Finally, we predicted a series of CD spectra of the Trp-cage protein associated with continuous changes of protein configuration along its folding path, showing the potential of our ML model for supporting real-time CD spectroscopy study of protein dynamics.