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

Abstract

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.

Figure 1

(a) NMA structure and protein structure. (b) Valence molecular orbitals and two electronic transitions of the peptide bond which are n → π* or π → π* transitions. (c) Machine learning protocol for predicting protein CD spectra.

Figure 2

ML prediction of the electric and magnetic transition dipole moments of peptide bonds. (a) Correlation plots of the TDDFT and ML predicted electric transition dipole moments of the n → π* and π → π* transitions using CM with GBR. (b) Correlation plots of the TDDFT and ML predicted magnetic transition dipole moments of the n → π* and π → π* transitions using CM with GBR. (c) Same as (a) but using EANN. (d) Same as (b) but using EANN.

Figure 3

Experimental (black curves) and ML predicted (red curves) CD spectra of different types proteins. Intensity is scaled to have the same maximum intensity for each panel.

Figure 4

(a) Experimental (black curves) and ML predicted (red curves) CD spectra. The ML predictions are based on 1000 MD configurations. (b) The ML predicted CD spectra of the Trp-cage protein along its folding path (S1 → S100, S1: the original unfolded structure, S25: slightly folded along with the decrease of coil content, S50: folding faster and helical elements appear, S75: a cage formed with the rapid increase of α-helix, S100: the final stably folded structure). All spectra are averaged over 100 MD conformations for each state.