Comparative quantum-classical dynamics of natural and synthetic molecular rotors show how vibrational synchronization modulates the photoisomerization quantum efficiency.

We use quantum-classical trajectories to investigate the origin of the different photoisomerization quantum efficiency observed in the dim-light visual pigment Rhodopsin and in the light-driven biomimetic molecular rotor para-methoxy N-methyl indanylidene-pyrrolinium (MeO-NAIP) in methanol. Our results reveal that effective light-energy conversion requires, in general, an auxiliary molecular vibration (called promoter) that does not correspond to the rotary motion but synchronizes with it at specific times. They also reveal that Nature has designed Rhodopsin to exploit two mechanisms working in a vibrationally coherent regime. The first uses a wag promoter to ensure that ca. 75% of the absorbed photons lead to unidirectional rotations. The second mechanism ensures that the same process is fast enough to avoid directional randomization. It is found that MeO-NAIP in methanol is incapable of exploiting the above mechanisms resulting into a 50% quantum efficiency loss. However, when the solvent is removed, MeO-NAIP rotation is predicted to synchronize with a ring-inversion promoter leading to a 30% increase in quantum efficiency and, therefore, biomimetic behavior.

Geometry Optimization: A Comparison of Different Open-Source Geometry Optimizers.

Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and energy calculations. The findings demonstrate how the choice of the coordinate system influences the optimization process to reach an equilibrium structure. With fewer steps, internal coordinates outperform Cartesian coordinates, while the choice of the initial Hessian and Hessian update method in quasi-Newton approaches made by different optimization algorithms also contributes to the rate of convergence. Furthermore, an available open-source machine learning method based on Gaussian process regression (GPR) was evaluated for energy minimizations over surrogate potential energy surfaces with both Cartesian and internal coordinates with internal coordinates outperforming Cartesian. Overall, geomeTRIC and DL-FIND with their default optimization method as well as with the GPR-based model using Hartree-Fock theory with the 6-31G** basis set needed a comparable number of geometry optimization steps to the approach of Baker using a unit matrix as the initial Hessian to reach the optimized geometry. On the other hand, the Berny and Sella offerings in ASE outperformed the other algorithms. Based on this, we recommend using the file-based approaches, ASE/Berny and ASE/Sella, for large-scale optimization efforts, while if using a single executable is preferable, we now distribute QUICK integrated with DL-FIND.

AmberTools.

AmberTools is a free and open-source collection of programs used to set up, run, and analyze molecular simulations. The newer features contained within AmberTools23 are briefly described in this Application note.

Quantum Mechanics/Molecular Mechanics Simulations on NVIDIA and AMD Graphics Processing Units.

We have ported and optimized the graphics processing unit (GPU)-accelerated QUICK and AMBER-based ab initio quantum mechanics/molecular mechanics (QM/MM) implementation on AMD GPUs. This encompasses the entire Fock matrix build and force calculation in QUICK including one-electron integrals, two-electron repulsion integrals, exchange-correlation quadrature, and linear algebra operations. General performance improvements to the QUICK GPU code are also presented. Benchmarks carried out on NVIDIA V100 and AMD MI100 cards display similar performance on both hardware for standalone HF/DFT calculations with QUICK and QM/MM molecular dynamics simulations with QUICK/AMBER. Furthermore, with respect to the QUICK/AMBER release version 21, significant speedups are observed for QM/MM molecular dynamics simulations. This significantly increases the range of scientific problems that can be addressed with open-source QM/MM software on state-of-the-art computer hardware.

Torsionally broken symmetry assists infrared excitation of biomimetic charge-coupled nuclear motions in the electronic ground state.

The concerted interplay between reactive nuclear and electronic motions in molecules actuates chemistry. Here, we demonstrate that out-of-plane torsional deformation and vibrational excitation of stretching motions in the electronic ground state modulate the charge-density distribution in a donor-bridge-acceptor molecule in solution. The vibrationally-induced change, visualised by transient absorption spectroscopy with a mid-infrared pump and a visible probe, is mechanistically resolved by ab initio molecular dynamics simulations. Mapping the potential energy landscape attributes the observed charge-coupled coherent nuclear motions to the population of the initial segment of a double-bond isomerization channel, also seen in biological molecules. Our results illustrate the pivotal role of pre-twisted molecular geometries in enhancing the transfer of vibrational energy to specific molecular modes, prior to thermal redistribution. This motivates the search for synthetic strategies towards achieving potentially new infrared-mediated chemistry.

Computer-aided drug design, quantum-mechanical methods for biological problems.

Quantum chemistry enables to study systems with chemical accuracy (<1 kcal/mol from experiment) but is restricted to a handful of atoms due to its computational expense. This has led to ongoing interest to optimize and simplify these methods while retaining accuracy. Implementing quantum mechanical (QM) methods on modern hardware such as multiple-GPUs is one example of how the field is optimizing performance. Multiscale approaches like the so-called QM/molecular mechanical method are gaining popularity in drug discovery because they focus the application of QM methods on the region of choice (e.g., the binding site), while using efficient MM models to represent less relevant areas. The creation of simplified QM methods is another example, including the use of machine learning to create ultra-fast and accurate QM models. Herein, we summarize recent advancements in the development of optimized QM methods that enhance our ability to use these methods in computer aided drug discovery.

Quantum-classical simulations of rhodopsin reveal excited-state population splitting and its effects on quantum efficiency.

The activation of rhodopsin, the light-sensitive G-protein-coupled receptor responsible for dim-light vision in vertebrates, is driven by an ultrafast excited-state double-bond isomerization with a quantum efficiency of almost 70%. The origin of such light sensitivity is not understood and a key question is whether in-phase nuclear motion controls the quantum efficiency value. In this study we used hundreds of quantum-classical trajectories to show that, 15 fs after light absorption, a degeneracy between the reactive excited state and a neighbouring state causes the splitting of the rhodopsin population into subpopulations. These subpopulations propagate with different velocities and lead to distinct contributions to the quantum efficiency. We also show here that such splitting is modulated by protein electrostatics, thus linking amino acid sequence variations to quantum efficiency modulation. Finally, we discuss how such a linkage that in principle could be exploited to achieve higher quantum efficiencies would simultaneously increase the receptor thermal noise leading to a trade-off that may have played a role in rhodopsin evolution.

Free Energy Computation for an Isomerizing Chromophore in a Molecular Cavity via the Average Solvent Electrostatic Configuration Model: Applications in Rhodopsin and Rhodopsin-Mimicking Systems.

We present a novel technique for computing the free energy differences between two chromophore "isomers" hosted in a molecular environment (a generalized solvent). Such an environment may range from a relatively rigid protein cavity to a flexible solvent environment. The technique is characterized by the application of the previously reported "average electrostatic solvent configuration" method, and it is based on the idea of using the free energy perturbation theory along with a chromophore annihilation procedure in thermodynamic cycle calculations. The method is benchmarked by computing the ground-state room-temperature relative stabilities between (i) the cis and trans isomers of prototypal animal and microbial rhodopsins and (ii) the analogue isomers of a rhodopsin-like light-driven molecular switch in methanol. Furthermore, we show that the same technology can be used to estimate the activation free energy for the thermal isomerization of systems i-ii by replacing one isomer with a transition state. The results show that the computed relative stability and isomerization barrier magnitudes for the selected systems are in line with the available experimental observation in spite of their widely diverse complexity.

Harnessing the Power of Multi-GPU Acceleration into the Quantum Interaction Computational Kernel Program.

We report a new multi-GPU capable ab initio Hartree-Fock/density functional theory implementation integrated into the open source QUantum Interaction Computational Kernel (QUICK) program. Details on the load balancing algorithms for electron repulsion integrals and exchange correlation quadrature across multiple GPUs are described. Benchmarking studies carried out on up to four GPU nodes, each containing four NVIDIA V100-SXM2 type GPUs demonstrate that our implementation is capable of achieving excellent load balancing and high parallel efficiency. For representative medium to large size protein/organic molecular systems, the observed parallel efficiencies remained above 82% for the Kohn-Sham matrix formation and above 90% for nuclear gradient calculations. The accelerations on NVIDIA A100, P100, and K80 platforms also have realized parallel efficiencies higher than 68% in all tested cases, paving the way for large-scale ab initio electronic structure calculations with QUICK.

On the Transition from a Biomimetic Molecular Switch to a Rotary Molecular Motor.

The experimental investigation of the unidirectional motion characterizing the photoisomerization of single-molecule rotary motors requires accessible lab prototypes featuring an electronic circular dichroism (ECD) signal that is sensitive to the geometrical and electronic changes occurring during an ultrafast reactive process. Here we report a combined experimental/computational study of a candidate obtained via the asymmetrization of a light-driven biomimetic molecular switch. We show that the achieved motor has an ECD band that is remarkably sensitive to the isomerization motion, and it is therefore suitable for time-resolved ECD studies. However, we also find that, unexpectedly, the synthesized motor isomerizes on a time scale longer than the subpicosecond time measured for the achiral parent, a result that points to alternative candidates conserving a high reaction speed.

Open-Source Multi-GPU-Accelerated QM/MM Simulations with AMBER and QUICK.

The quantum mechanics/molecular mechanics (QM/MM) approach is an essential and well-established tool in computational chemistry that has been widely applied in a myriad of biomolecular problems in the literature. In this publication, we report the integration of the QUantum Interaction Computational Kernel (QUICK) program as an engine to perform electronic structure calculations in QM/MM simulations with AMBER. This integration is available through either a file-based interface (FBI) or an application programming interface (API). Since QUICK is an open-source GPU-accelerated code with multi-GPU parallelization, users can take advantage of "free of charge" GPU-acceleration in their QM/MM simulations. In this work, we discuss implementation details and give usage examples. We also investigate energy conservation in typical QM/MM simulations performed at the microcanonical ensemble. Finally, benchmark results for two representative systems in bulk water, the N-methylacetamide (NMA) molecule and the photoactive yellow protein (PYP), show the performance of QM/MM simulations with QUICK and AMBER using a varying number of CPU cores and GPUs. Our results highlight the acceleration obtained from a single or multiple GPUs; we observed speedups of up to 53× between a single GPU vs a single CPU core and of up to 2.6× when comparing four GPUs to a single GPU. Results also reveal speedups of up to 3.5× when the API is used instead of FBI.

ReaxFF/AMBER-A Framework for Hybrid Reactive/Nonreactive Force Field Molecular Dynamics Simulations.

Combined quantum mechanical/molecular mechanical (QM/MM) models using semiempirical and ab initio methods have been extensively reported on over the past few decades. These methods have been shown to be capable of providing unique insights into a range of problems, but they are still limited to relatively short time scales, especially QM/MM models using ab initio methods. An intermediate approach between a QM based model and classical mechanics could help fill this time-scale gap and facilitate the study of a range of interesting problems. Reactive force fields represent the intermediate approach explored in this paper. A widely used reactive model is ReaxFF, which has largely been applied to materials science problems and is generally used as a stand-alone (i.e., the full system is modeled using ReaxFF). We report a hybrid ReaxFF/AMBER molecular dynamics (MD) tool, which introduces ReaxFF capabilities to capture bond breaking and formation within the AMBER MD software package. This tool enables us to study local reactive events in large systems at a fraction of the computational costs of QM/MM models. We describe the implementation of ReaxFF/AMBER, validate this implementation using a benzene molecule solvated in water, and compare its performance against a range of similar approaches. To illustrate the predictive capabilities of ReaxFF/AMBER, we carried out a Claisen rearrangement study in aqueous solution. In a first for ReaxFF, we were able to use AMBER's potential of mean force (PMF) capabilities to perform a PMF study on this organic reaction. The ability to capture local reaction events in large systems using combined ReaxFF/AMBER opens up a range of problems that can be tackled using this model to address both chemical and biological processes.

Parallel Implementation of Density Functional Theory Methods in the Quantum Interaction Computational Kernel Program.

We present the details of a graphics processing unit (GPU) capable exchange correlation (XC) scheme integrated into the open source QUantum Interaction Computational Kernel (QUICK) program. Our implementation features an octree based numerical grid point partitioning scheme, GPU enabled grid pruning and basis and primitive function prescreening, and fully GPU capable XC energy and gradient algorithms. Benchmarking against the CPU version demonstrated that the GPU implementation is capable of delivering an impressive performance while retaining excellent accuracy. For small to medium size protein/organic molecular systems, the realized speedups in double precision XC energy and gradient computation on a NVIDIA V100 GPU were 60-80-fold and 140-500-fold, respectively, as compared to the serial CPU implementation. The acceleration gained in density functional theory calculations from a single V100 GPU significantly exceeds that of a modern CPU with 40 cores running in parallel.

Computational and Spectroscopic Characterization of the Photocycle of an Artificial Rhodopsin.

The photocycle of a reversible photoisomerizing rhodopsin mimic (M2) is investigated. This system, based on the cellular retinoic acid binding protein, is structurally different from natural rhodopsin systems, but exhibits a similar isomerization upon light irradiation. More specifically, M2 displays a 15-cis to all-trans conversion of retinal protonated Schiff base (rPSB) and all-trans to 15-cis isomerization of unprotonated Schiff base (rUSB). Here we use hybrid quantum mechanics/molecular mechanics (QM/MM) tools coupled with transient absorption and cryokinetic UV-vis spectroscopies to investigate these isomerization processes. The results suggest that primary rPSB photoisomerization of M2 occurs around the C13═C14 double bond within 2 ps following an aborted-bicycle pedal (ABP) isomerization mechanism similar to natural microbial rhodopsins. The rUSB isomerization is much slower and occurs within 48 ps around the C15═N double bond. Our findings reveal the possibility to engineer naturally occurring mechanistic features into artificial rhodopsins and also constitute a step toward understanding the photoisomerization of UV pigments. We conclude by reinforcing the idea that the presence of the retinal chromophore inside a tight protein cavity is not mandatory to exhibit ABP mechanism.

Electronic State Mixing Controls the Photoreactivity of a Rhodopsin with all- trans Chromophore Analogues.

Rhodopsins hosting synthetic retinal protonated Schiff base analogues are important for developing tools for optogenetics and high-resolution imaging. The ideal spectroscopic properties of such analogues include long-wavelength absorption/emission and fast/hindered photoisomerization. While the former may be achieved, for instance, by elongating the chromophore π-system, the latter requires a detailed understanding of the substituent effects (i.e., steric or electronic) on the chromophore light-induced dynamics. In the present letter we compare the results of quantum mechanics/molecular mechanics excited-state trajectories of native and analogue-hosting microbial rhodopsins from the eubacterium Anabaena. The results uncover a relationship between the nature of the substituent on the analogue (i.e., electron-donating (a Me group) or electron-withdrawing (a CF3 group)) and rhodopsin excited-state lifetime. Most importantly, we show that electron-donating or -withdrawing substituents cause a decrease or an increase in the electronic mixing of the first two excited states which, in turn, controls the photoisomerization speed.

Engineering the vibrational coherence of vision into a synthetic molecular device.

The light-induced double-bond isomerization of the visual pigment rhodopsin operates a molecular-level optomechanical energy transduction, which triggers a crucial protein structure change. In fact, rhodopsin isomerization occurs according to a unique, ultrafast mechanism that preserves mode-specific vibrational coherence all the way from the reactant excited state to the primary photoproduct ground state. The engineering of such an energy-funnelling function in synthetic compounds would pave the way towards biomimetic molecular machines capable of achieving optimum light-to-mechanical energy conversion. Here we use resonance and off-resonance vibrational coherence spectroscopy to demonstrate that a rhodopsin-like isomerization operates in a biomimetic molecular switch in solution. Furthermore, by using quantum chemical simulations, we show why the observed coherent nuclear motion critically depends on minor chemical modifications capable to induce specific geometric and electronic effects. This finding provides a strategy for engineering vibrationally coherent motions in other synthetic systems.

An Average Solvent Electrostatic Configuration Protocol for QM/MM Free Energy Optimization: Implementation and Application to Rhodopsin Systems.

A novel atomistic methodology to perform free energy geometry optimization of a retinal chromophore covalently bound to any rhodopsin-like protein cavity is presented and benchmarked by computing the absorption maxima wavelengths (λmax) of distant rhodopsin systems. The optimization is achieved by computing the Nagaoka's Free Energy Gradient (FEG) within an Average Solvent Electrostatic Configuration (ASEC) atomistic representation of the thermodynamic equilibrium and minimizing such quantity via an iterative procedure based on sequential classical MD and constrained QM/MM geometry optimization steps. The performance of such an ASEC-FEG protocol is assessed at the CASPT2//CASSCF/Amber level by reproducing the λmax values observed for 12 mutants of redesigned human cellular retinol binding protein II (hCRBPII) systems; a set of 10 distant wild-type rhodopsins from vertebrates, invertebrates, eubacteria, and archaea organisms; and finally a set of 10 rhodopsin mutants from an eubacterial rhodopsin. The results clearly show that the proposed protocol, which can be easily extended to any protein incorporating a covalently bound ligand, yields correct λmax trends with limited absolute errors.

Impact of Electronic State Mixing on the Photoisomerization Time Scale of the Retinal Chromophore.

Spectral data show that the photoisomerization of retinal protonated Schiff base (rPSB) chromophores occurs on a 100 fs time scale or less in vertebrate rhodopsins, it is several times slower in microbial rhodopsins and it is between one and 2 orders of magnitude slower in solution. These time scale variations have been attributed to specific modifications of the topography of the first excited state potential energy surface of the chromophore. However, it is presently not clear which specific environment effects (e.g., electrostatic, electronic, or steric) are responsible for changing the surface topography. Here, we use QM/MM models and excited state trajectory computations to provide evidence for an increase in electronic mixing between the first and the second excited state of the chromophore when going from vertebrate rhodopsin to the solution environments. Ultimately, we argue that a correlation between the lifetime of the first excited state and electronic mixing between such state and its higher neighbor, may have been exploited to evolve rhodopsins toward faster isomerization and, possibly, light-sensitivity.

Design, Synthesis, and Dynamics of a Green Fluorescent Protein Fluorophore Mimic with an Ultrafast Switching Function.

While rotary molecular switches based on neutral and cationic organic π-systems have been reported, structurally homologous anionic switches providing complementary properties have not been prepared so far. Here we report the design and preparation of a molecular switch mimicking the anionic p-HBDI chromophore of the green fluorescent protein. The investigation of the mechanism and dynamics of the E/Z switching function is carried out both computationally and experimentally. The data consistently support axial rotary motion occurring on a sub-picosecond time scale. Transient spectroscopy and trajectory simulations show that the nonadiabatic decay process occurs in the vicinity of a conical intersection (CInt) between a charge transfer state and a covalent/diradical state. Comparison of our anionic p-HBDI-like switch with the previously reported cationic N-alkyl indanylidene pyrrolinium switch mimicking visual pigments reveals that these similar systems translocate, upon vertical excitation, a similar net charge in the same axial direction.

Probing the Photodynamics of Rhodopsins with Reduced Retinal Chromophores.

While the light-induced population dynamics of different photoresponsive proteins has been investigated spectroscopically, systematic computational studies have not yet been possible due to the phenomenally high cost of suitable high level quantum chemical methods and the need of propagating hundreds, if not thousands, of nonadiabatic trajectories. Here we explore the possibility of studying the photodynamics of rhodopsins by constructing and investigating quantum mechanics/molecular mechanics (QM/MM) models featuring reduced retinal chromophores. In order to do so we use the sensory rhodopsin found in the cyanobacterium Anabaena PCC7120 (ASR) as a benchmark system. We find that the basic mechanistic features associated with the excited state dynamics of ASR QM/MM models are reproduced using models incorporating a minimal (i.e., three double-bond) chromophore. Furthermore, we show that ensembles of nonadiabatic ASR trajectories computed using the same abridged models replicate, at both the CASPT2 and CASSCF levels of theory, the trends in spectroscopy and lifetimes estimated using unabridged models and observed experimentally at room temperature. We conclude that a further expansion of these studies may lead to low-cost QM/MM rhodopsin models that may be used as effective tools in high-throughput in silico mutant screening.