Multiscale biomolecular simulations in the exascale era.

The complexity of biological systems and processes, spanning molecular to macroscopic scales, necessitates the use of multiscale simulations to get a comprehensive understanding. Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations are crucial for capturing processes beyond the reach of classical MD simulations. The advent of exascale computing offers unprecedented opportunities for scientific exploration, not least within life sciences, where simulations are essential to unravel intricate molecular mechanisms underlying biological processes. However, leveraging the immense computational power of exascale computing requires innovative algorithms and software designs. In this context, we discuss the current status and future prospects of multiscale biomolecular simulations on exascale supercomputers with a focus on QM/MM MD. We highlight our own efforts in developing a versatile and high-performance multiscale simulation framework with the aim of efficient utilization of state-of-the-art supercomputers. We showcase its application in uncovering complex biological mechanisms and its potential for leveraging exascale computing.

Polarizable Embedding Potentials through Molecular Fractionation with Conjugate Caps Including Hydrogen Bonds.

Polarizable embedding (PE) refers to classical embedding approaches, such as those used in quantum mechanics/molecular mechanics (QM/MM), that allow mutual polarization between the quantum and classical regions. The quality of the embedding potential is critical to provide accurate results, e.g., for spectroscopic properties and dynamical processes. High-quality embedding-potential parameters can be obtained by dividing the classical region into smaller fragments and deriving the parameters from ab initio calculations on the fragments. For solvents and other systems composed of small molecules, the fragments can be individual molecules, while a more complicated fragmentation procedure is needed for larger molecules, such as proteins and nucleic acids. One such fragmentation strategy is the molecular fractionation with conjugate caps (MFCC) approach. As is widely known, hydrogen bonds play a key role in many biomolecular systems, e.g., in proteins, where they are responsible for the secondary structure. In this work, we assess the effects of including hydrogen-bond fragmentation in the MFCC procedure [MFCC(HB)] for deriving the embedding-potential parameters. The MFCC(HB) extension is evaluated on several molecular systems, ranging from small model systems to proteins, directly in terms of molecular electrostatic potentials and embedding potentials and indirectly in terms of selected properties of chromophores embedded in water and complex protein environments.

Polarizable Embedding without Artificial Boundary Polarization.

We present a fully self-consistent polarizable embedding (PE) model that does not suffer from unphysical boundary polarization. This is achieved through the use of the minimum-image convention (MIC) in the induced electrostatics. It is a simple yet effective approach that includes a more physically accurate description of the polarization throughout the molecular system. Using PE with MIC (PE-MIC), we shed new light on the limitations of commonly employed cutoff models, such as the droplet model, when used in PE calculations. Specifically, we investigate the effects of the unphysical polarization at the outer boundary by comparing induced dipoles and the associated electrostatic potentials, as well as some optical properties of solute-solvent and biomolecular systems. We show that the magnitude of the inaccuracies caused by the unphysical polarization depends on multiple parameters: the nature of the quantum subsystem and of the environment, the cutoff model and distance, and the calculated property.

MiMiCPy: An Efficient Toolkit for MiMiC-Based QM/MM Simulations.

MiMiC is a highly flexible, extremely scalable multiscale modeling framework. It couples the CPMD (quantum mechanics, QM) and GROMACS (molecular mechanics, MM) codes. The code requires preparing separate input files for the two programs with a selection of the QM region. This can be a tedious procedure prone to human error, especially when dealing with large QM regions. Here, we present MiMiCPy, a user-friendly tool that automatizes the preparation of MiMiC input files. It is written in Python 3 with an object-oriented approach. The main subcommand PrepQM can be used to generate MiMiC inputs directly from the command line or through a PyMOL/VMD plugin for visually selecting the QM region. Many other subcommands are also provided for debugging and fixing MiMiC input files. MiMiCPy is designed with a modular structure that allows seamless extensions to new program formats depending on the requirements of MiMiC.

Induction effects on the absorption maxima of photoreceptor proteins.

Multiscale simulations have been established as a powerful tool to calculate and predict excitation energies in complex systems such as photoreceptor proteins. In these simulations the chromophore is typically treated using quantum mechanical (QM) methods while the protein and surrounding environment are described by a classical molecular mechanics (MM) force field. The electrostatic interactions between these regions are often treated using electrostatic embedding where the point charges in the MM region polarize the QM region. A more sophisticated treatment accounts also for the polarization of the MM region. In this work, the effect of such a polarizable embedding on excitation energies was benchmarked and compared to electrostatic embedding. This was done for two different proteins, the lipid membrane-embedded jumping spider rhodopsin and the soluble cyanobacteriochrome Slr1393g3. It was found that the polarizable embedding scheme produces absorption maxima closer to experimental values. The polarizable embedding scheme was also benchmarked against expanded QM regions and found to be in qualitative agreement. Treating individual residues as polarizable recovered between 50% and 71% of the QM improvement in the excitation energies, depending on the system. A detailed analysis of each amino acid residue in the chromophore binding pocket revealed that aromatic residues result in the largest change in excitation energy compared to the electrostatic embedding. Furthermore, the computational efficiency of polarizable embedding allowed it to go beyond the binding pocket and describe a larger portion of the environment, further improving the results.

Deciphering the Spectral Tuning Mechanism in Proteorhodopsin: The Dominant Role of Electrostatics Instead of Chromophore Geometry.

Proteorhodopsin (PR) is a photoactive proton pump found in marine bacteria. There are two phenotypes of PR exhibiting an environmental adaptation to the ocean's depth which tunes their maximum absorption: blue-absorbing proteorhodopsin (BPR) and green-absorbing proteorhodopsin (GPR). This blue/green color-shift is controlled by a glutamine to leucine substitution at position 105 which accounts for a 20 nm shift. Typically, spectral tuning in rhodopsins is rationalized by the external point charge model but the Q105L mutation is charge neutral. To study this tuning mechanism, we employed the hybrid QM/MM method with sampling from molecular dynamics. Our results reveal that the positive partial charge of glutamine near the C14 -C15 bond of retinal shortens the effective conjugation length of the chromophore compared to the leucine residue. The derived mechanism can be applied to explain the color regulation in other retinal proteins and can serve as a guideline for rational design of spectral shifts.

Wavefunction-Based Electrostatic-Embedding QM/MM Using CFOUR through MiMiC.

We present an interface of the wavefunction-based quantum chemical software CFOUR to the multiscale modeling framework MiMiC. Electrostatic embedding of the quantum mechanical (QM) part is achieved by analytic evaluation of one-electron integrals in CFOUR, while the rest of the QM/molecular mechanical (MM) operations are treated according to the previous MiMiC-based QM/MM implementation. Long-range electrostatic interactions are treated by a multipole expansion of the potential from the QM electron density to reduce the computational cost without loss of accuracy. Testing on model water/water systems, we verified that the CFOUR interface to MiMiC is robust, guaranteeing fast convergence of the self-consistent field cycles and optimal conservation of the energy during the integration of the equations of motion. Finally, we verified that the CFOUR interface to MiMiC is compatible with the use of a QM/QM multiple time-step algorithm, which effectively reduces the cost of ab initio MD (AIMD) or QM/MM-MD simulations using higher level wavefunction-based approaches compared to cheaper density functional theory-based ones. The new wavefunction-based AIMD and QM/MM-MD implementations were tested and validated for a large number of wavefunction approaches, including Hartree-Fock and post-Hartree-Fock methods like Møller-Plesset, coupled-cluster, and complete active space self-consistent field.

Efficient Open-Source Implementations of Linear-Scaling Polarizable Embedding: Use Octrees to Save the Trees.

We present open-source implementations of the linear-scaling fast multipole method (FMM) within the polarizable embedding (PE) model for efficient treatment of large polarizable environments in computational spectroscopy simulations. The implementations are tested for accuracy, efficiency, and usability on model systems as well as more realistic biomolecular systems. We explain how FMM parameters affect the calculation of molecular properties and show that PE calculations employing FMM can be carried out in a black-box manner. The efficiency of the linear-scaling approach is demonstrated by simulating the UV/vis spectrum of a chromophore in an environment of more than 1 million polarizable sites. Our implementations are interfaced to several open-source quantum chemistry programs, making computational spectroscopy simulations within the PE model and FMM available to a large variety of methods and a broad user base.

Harmonic Infrared and Raman Spectra in Molecular Environments Using the Polarizable Embedding Model.

We present a fully analytic approach to calculate infrared (IR) and Raman spectra of molecules embedded in complex molecular environments modeled using the fragment-based polarizable embedding (PE) model. We provide the theory for the calculation of analytic second-order geometric derivatives of molecular energies and first-order geometric derivatives of electric dipole moments and dipole-dipole polarizabilities within the PE model. The derivatives are implemented using a general open-ended response theory framework, thus allowing for an extension to higher-order derivatives. The embedding-potential parameters used to describe the environment in the PE model are derived through first-principles calculations, thus allowing a wide variety of systems to be modeled, including solvents, proteins, and other large and complex molecular environments. Here, we present proof-of-principle calculations of IR and Raman spectra of acetone in different solvents. This work is an important step toward calculating accurate vibrational spectra of molecules embedded in realistic environments.

The Impact of Retinal Configuration on the Protein-Chromophore Interactions in Bistable Jumping Spider Rhodopsin-1.

Bistable rhodopsins have two stable forms that can be interconverted by light. Due to their ability to act as photoswitches, these proteins are considered as ideal candidates for applications such as optogenetics. In this work, we analyze a recently crystalized bistable rhodopsin, namely the jumping spider rhodopsin-1 (JSR1). This rhodopsin exhibits identical absorption maxima for the parent and the photoproduct form, which impedes its broad application. We performed hybrid QM/MM simulations to study three isomers of the retinal chromophore: the 9-cis, 11-cis and all-trans configurations. The main aim was to gain insight into the specific interactions of each isomer and their impact on the absorption maximum in JSR1. The absorption spectra were computed using sampled snapshots from QM/MM molecular dynamics trajectories and compared to their experimental counterparts. The chromophore-protein interactions were analyzed by visualizing the electrostatic potential of the protein and projecting it onto the chromophore. It was found that the distance between a nearby tyrosine (Y126) residue plays a larger role in the predicted absorption maximum than the primary counterion (E194). Geometric differences between the isomers were also noted, including a structural change in the polyene chain of the chromophore, as well as changes in the nearby hydrogen bonding network.

Frontiers in Multiscale Modeling of Photoreceptor Proteins.

This perspective article highlights the challenges in the theoretical description of photoreceptor proteins using multiscale modeling, as discussed at the CECAM workshop in Tel Aviv, Israel. The participants have identified grand challenges and discussed the development of new tools to address them. Recent progress in understanding representative proteins such as green fluorescent protein, photoactive yellow protein, phytochrome, and rhodopsin is presented, along with methodological developments.

Polarizable Density Embedding for Large Biomolecular Systems.

We present an efficient and robust fragment-based quantum-classical embedding model capable of accurately capturing effects from complex environments such as proteins and nucleic acids. This is realized by combining the molecular fractionation with conjugate caps (MFCC) procedure with the polarizable density embedding (PDE) model at the level of Fock matrix construction. The PDE contributions to the Fock matrix of the core region are constructed using the local molecular basis of the individual fragments rather than the supermolecular basis of the entire system. Thereby, we avoid complications associated with the application of the MFCC procedure on environment quantities such as electronic densities and molecular-orbital energies. Moreover, the computational cost associated with solving self-consistent field (SCF) equations of the core region remains unchanged from that of purely classical polarized embedding models. We analyze the performance of the resulting model in terms of the reproduction of the electrostatic potential of an insulin monomer protein and further in the context of solving problems related to electron spill-out. Finally, we showcase the model for the calculation of one- and two-photon properties of the Nile red molecule in a protein environment. Based on our analyses, we find that the combination of the MFCC approach with the PDE model is an efficient, yet accurate approach for calculating molecular properties of molecules embedded in structured biomolecular environments.

Accuracy of Molecular Simulation-Based Predictions of koff Values: A Metadynamics Study.

The koff values of ligands unbinding to proteins are key parameters for drug discovery. Their predictions based on molecular simulation may under- or overestimate experiment in a system- and/or technique-dependent way. Here we use an established method-infrequent metadynamics, based on the AMBER force field-to compute the koff of the ligand iperoxo (in clinical use) targeting the muscarinic receptor M2. The ligand charges are calculated by either (i) the Amber standard procedure or (ii) B3LYP-DFT. The calculations using (i) turn out not to provide a reasonable estimation of the transition-state free energy. Those using (ii) differ from experiment by 2 orders of magnitude. On the basis of B3LYP DFT QM/MM simulations, we suggest that the observed discrepancy in (ii) arises, at least in part, from the lack of electronic polarization and/or charge transfer in biomolecular force fields. These issues might be present in other systems, such as DNA-protein complexes.

Dalton Project: A Python platform for molecular- and electronic-structure simulations of complex systems.

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

The DIRAC code for relativistic molecular calculations.

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

Two-Photon Absorption Cross-Sections in Fluorescent Proteins Containing Non-canonical Chromophores Using Polarizable QM/MM.

Multi-photon absorption properties, particularly two-photon absorption (2PA), of fluorescent proteins (FPs) have made them attractive tools in deep-tissue clinical imaging. Although the diversity of photophysical properties for FPs is wide, there are some caveats predominant among the existing FP variants that need to be overcome, such as low quantum yields and small 2PA cross-sections. From a computational perspective, Salem et al. (2016) suggested the inclusion of non-canonical amino acids in the chromophore of the red fluorescent protein DsRed, through the replacement of the tyrosine amino acid. The 2PA properties of these new non-canonical chromophores (nCCs) were determined in vacuum, i.e., without taking into account the protein environment. However, in the computation of response properties, such as 2PA cross-sections, the environment plays an important role. To account for environment and protein-chromophore coupling effects, quantum mechanical/molecular mechanical (QM/MM) schemes can be useful. In this work, the polarizable embedding (PE) model is employed along with time-dependent density functional theory to describe the 2PA properties of a selected set of chromophores made from non-canonical amino acids as they are embedded in the DsRed protein matrix. The objective is to provide insights to determine whether or not the nCCs could be developed and, thus, generate a new class of FPs. Results from this investigation show that within the DsRed environment, the nCC 2PA cross-sections are diminished relative to their values in vacuum. However, further studies toward understanding the 2PA limit of these nCCs using different protein environments are needed.

Molecular Basis of CLC Antiporter Inhibition by Fluoride.

CLC channels and transporters conduct or transport various kinds of anions, with the exception of fluoride, which acts as an effective inhibitor. Here, we performed sub-nanosecond DFT-based QM/MM simulations of the E. coli anion/proton exchanger ClC-ec1 and observed that fluoride binds incoming protons within the selectivity filter, with excess protons shared with the gating glutamate E148. Depending on E148 conformation, the competition for the proton can involve either a direct F-/E148 interaction or the modulation of water molecules bridging the two anions. The direct interaction locks E148 in a conformation that does not allow for proton transport, and thus inhibits protein function.

Avoiding Electron Spill-Out in QM/MM Calculations on Excited States with Simple Pseudopotentials.

QM/MM calculations of electronic excitations with diffuse basis sets often have large errors due to spill-out of electrons from the quantum subsystem. The Pauli repulsion of the electrons by the environment has to be included to avoid this. We propose transferable atomic all-electron pseudopotentials that can readily be combined with most MM force fields to avoid electron spill-out. QM/MM excitation energies computed with time-dependent Hartree-Fock and the algebraic diagrammatic construction through second-order are benchmarked against supermolecular calculations to validate these new pseudopotentials. The QM/MM calculations with pseudopotentials give accurate results that are stable with augmentation of the basis set with diffuse functions. We show that the largest contribution to residual deviations from full QM calculations is caused by the missing London dispersion interaction.

Cost-Effective Potential for Accurate Polarizable Embedding Calculations in Protein Environments.

The fragment-based polarizable embedding (PE) model combined with an appropriate electronic structure method constitutes a highly efficient and accurate multiscale approach for computing spectroscopic properties of a central moiety including effects from its molecular environment through an embedding potential. There is, however, a comparatively high computational overhead associated with the computation of the embedding potential, which is derived from first-principles calculations on individual fragments of the environment. To reduce the computational cost associated with the calculation of embedding potential parameters, we developed a set of amino acid-specific transferable parameters tailored for large-scale PE-based calculations that include proteins. The amino acid-based parameters are obtained by simultaneously fitting to a set of reference electric potentials based on structures derived from a backbone-dependent rotamer library. The developed cost-effective polarizable protein potential (CP3) consists of atom-centered charges and isotropic dipole-dipole polarizabilities of the standard amino acids. In terms of reproduction of electric potentials, the CP3 is shown to perform consistently and with acceptable accuracy across both small tripeptide test systems and larger proteins. We show, through applications on realistic protein systems, that acceptable accuracy can be obtained by using a pure CP3 representation of the protein environment, thus altogether omitting the cost associated with the calculation of embedding potential parameters. High accuracy comparable to that of the full fragment-based approach can be achieved through a mixed description where the CP3 is used only to describe amino acids beyond a threshold distance from the central quantum part.