[Paper Review] Elucidating the role of hydrogen bonding in the optical spectroscopy of the solvated green fluorescent protein chromophore: using machine learning to establish the importance of high-level electronic structure

Michael S. Chen, Yuezhi Mao+6 more|arXiv (Cornell University)|May 26, 2023

Photoreceptor and optogenetics researchNeuroscience3 citations

TL;DR

This study introduces a data-efficient transfer learning framework to train machine learning models for predicting high-level excited-state energy gaps of the solvated green fluorescent protein (GFP) chromophore using only 400 EOM-CCSD calculations. The method reveals that accurate modeling of hydrogen bonding effects—particularly the chromophore’s sensitivity to environmental electric fields—requires high-level electronic structure theory, as EOM-CCSD better reproduces the broadened experimental absorption spectrum than TDDFT.

ABSTRACT

Hydrogen bonding interactions with chromophores in chemical and biological environments play a key role in determining their electronic absorption and relaxation processes, which are manifested in their linear and multidimensional optical spectra. For chromophores in the condensed phase, the large number of atoms needed to simulate the environment has traditionally prohibited the use of high-level excited-state electronic structure methods. By leveraging transfer learning, we show how to construct machine-learned models to accurately predict high-level excitation energies of a chromophore in solution from only 400 high-level calculations. We show that when the electronic excitations of the green fluorescent protein chromophore in water are treated using EOM-CCSD embedded in a DFT description of the solvent, the optical spectrum is correctly captured and that this improvement arises from correctly treating the coupling of the electronic transition to electric fields, which leads to a larger response upon hydrogen bonding between the chromophore and water.

Motivation & Objective

• To address the computational challenge of simulating chromophore optical spectra in condensed phases with high-level electronic structure methods.
• To overcome the high cost of EOM-CCSD calculations in large solvated systems by developing a data-efficient machine learning strategy.
• To determine whether high-level electronic structure methods are necessary to correctly capture the influence of hydrogen bonding on the GFP chromophore’s optical properties.
• To evaluate the role of nuclear quantum effects and solvent dynamics in spectral broadening and red shifts.
• To compare the predictive power of TDDFT versus EOM-CCSD in modeling linear and 2D electronic spectra of the GFP chromophore in water.

Proposed method

• Employ transfer learning to initialize a machine learning model for EOM-CCSD energy gaps using gradients from lower-level TD-CAM-B3LYP calculations on 300 configurations.
• Train a direct machine learning model on 400 embedded EOM-CCSD energy gaps for the GFP chromophore in water, using both chromophore-only and full solvent-inclusive configurations.
• Use a hidden-solvent ML approach to model chromophore geometry dependence before extending to indirect-solvent models incorporating solvent atom positions.
• Apply the trained models to compute linear absorption spectra and 2D electronic spectra (2DES) using cumulant-based methods on equilibrium ground-state trajectories.
• Compare spectral predictions from EOM-CCSD and TD-CAM-B3LYP models to experimental data, focusing on peak positions, widths, and dynamic Stokes shifts.
• Include nuclear quantum effects (NQEs) via ab initio path integral molecular dynamics to assess their impact on spectral broadening and red shifts.

Experimental results

Research questions

• RQ1 Can transfer learning reduce the number of high-level EOM-CCSD calculations needed to train accurate machine learning models for chromophore excitation energies?
• RQ2 Does EOM-CCSD better reproduce the experimental absorption spectrum of the anionic GFP chromophore in water than TDDFT, particularly in terms of peak width and position?
• RQ3 What is the role of hydrogen bonding in modulating the chromophore’s electronic transition energy and its sensitivity to electric fields in solution?
• RQ4 How do nuclear quantum effects influence the excitation energy distribution and spectral broadening in the GFP chromophore in water?
• RQ5 To what extent does the dynamic Stokes shift in 2D electronic spectra differ between EOM-CCSD and TDDFT due to varying sensitivity to environmental electric fields?

Key findings

• The transfer learning protocol required only 400 high-level EOM-CCSD calculations—10 times fewer than previous methods—enabling efficient training of accurate ML models.
• The EOM-CCSD-based ML model produced a linear absorption spectrum with a full width at half maximum (FWHM) of 0.55 eV, closely matching the experimental breadth, whereas TDDFT predicted a narrower peak (0.35 eV).
• The EOM-CCSD model predicted a peak maximum at 2.94 eV, in excellent agreement with experiment, while TDDFT underestimated the red shift and predicted a peak at 2.75 eV.
• The improved spectral agreement with experiment for EOM-CCSD arises from a more accurate description of the chromophore’s sensitivity to environmental electric fields, particularly from hydrogen bonding with water.
• Including nuclear quantum effects in EOM-CCSD simulations led to a further red shift of the absorption maximum, shifting the peak to 2.85 eV and improving agreement with experiment.
• In 2D electronic spectra, the EOM-CCSD model showed a significantly more pronounced dynamic Stokes shift, with ground state bleach and stimulated emission peaks well-separated by 50 fs, unlike the overlapping peaks in the TDDFT model even at 100 fs.