Generalized QM/MM Force Matching Approach Applied to the 11-cis Protonated Schiff Base Chromophore of Rhodopsin

Simulation of Linear and Cyclic Alkanes with Second-Order Møller-Plesset Perturbation Theory through Adaptive Force Matching

Predicting ensemble properties, such as density and heat of vaporization, of small hydrocarbons is challenging due to the dispersion-dominated weak interactions between these molecules. With the adaptive force matching (AFM) method, the bonded and short-range nonbonded interactions are fitted to second-order Møller-Plesset perturbation theory (MP2) references computed with the def2-TZVP basis set. The dispersion is modeled using symmetry adapted perturbation theory (SAPT) at MP4 accuracy using the def2-TZVPD basis set. A new charge matrix decomposition technique is described to obtain partial charges in AFM. Although the models developed do not have any empirical parameters, several properties of the resulting models are compared with experiments as validations. The density, heat of vaporization, pressure dependence of density, diffusion constants, and surface tensions all show quantitative agreement with experiments. Although the density shows a very small systematic error, which could be due to missing three-body dispersion, the heat of vaporization agrees with experiments of within 0.5%. The paper shows that AFM can be used as a reliable tool to enable simulations at post-Hartree-Fock quality at the cost of molecular mechanics force fields.

Specific zinc binding to heliorhodopsin

Heliorhodopsins (HeRs), a recently discovered family of rhodopsins, have an inverted membrane topology compared to animal and microbial rhodopsins. The slow photocycle of HeRs suggests a light-sensor function, although the actual function remains unknown. Although HeRs exhibit no specific binding of monovalent cations or anions, recent ATR-FTIR spectroscopy studies have demonstrated the binding of Zn²⁺ to HeR from Thermoplasmatales archaeon (TaHeR) and 48C12. Even though ion-specific FTIR spectra were observed for many divalent cations, only helical structural perturbations were observed for Zn²⁺-binding, suggesting a possible modification of the HeR function by Zn²⁺. The present study shows that Zn²⁺-binding lowers the thermal stability of TaHeR, and slows back proton transfer to the retinal Schiff base (M decay) during its photocycle. Zn²⁺-binding was similarly observed for a TaHeR opsin that lacks the retinal chromophore. We then studied the Zn²⁺-binding site by means of the ATR-FTIR spectroscopy of site-directed mutants. Among five and four mutants of His and Asp/Glu, respectively, only E150Q exhibited a completely different spectral feature of the α-helix (amide-I) in ATR-FTIR spectroscopy, suggesting that E150 is responsible for Zn²⁺-binding. Molecular dynamics (MD) simulations built a coordination structure of Zn²⁺-bound TaHeR, where E150 and protein bound water molecules participate in direct coordination. It was concluded that the specific binding site of Zn²⁺ is located at the cytoplasmic side of TaHeR, and that Zn²⁺-binding affects the structure and structural dynamics, possibly modifying the unknown function of TaHeR.

Microsolvation Effects in the Spectral Tuning of Heliorhodopsin

Heliorhodopsins (HeR) are a new category of heptahelical transmembrane photoactive proteins with a covalently linked all-trans retinal. The protonated Schiff base (PSB) nitrogen in the retinal is stabilized by a negatively charged counterion. It is well-known that stronger or weaker electrostatic interactions with the counterion cause a significant spectral blue- or red-shift, respectively, in both microbial and animal rhodopsins. In HeR, however, while Glu107 acts as the counterion, mutations of this residue are not directly correlated with a spectral shift. A molecular dynamics analysis revealed that a water cluster pocket produces a microsolvation effect on the Schiff base, compensating to various extents the replacement of the native counterion. Using a combination of molecular dynamics and quantum mechanical/molecular mechanics (QM/MM), we study this microsolvation effect on the electronic absorption of the retinylidene Schiff base chromophore of HeR.

ParaMol: A Package for Automatic Parameterization of Molecular Mechanics Force Fields

The ensemble of structures generated by molecular mechanics (MM) simulations is determined by the functional form of the force field employed and its parameterization. For a given functional form, the quality of the parameterization is crucial and will determine how accurately we can compute observable properties from simulations. While accurate force field parameterizations are available for biomolecules, such as proteins or DNA, the parameterization of new molecules, such as drug candidates, is particularly challenging as these may involve functional groups and interactions for which accurate parameters may not be available. Here, in an effort to address this problem, we present ParaMol, a Python package that has a special focus on the parameterization of bonded and nonbonded terms of druglike molecules by fitting to ab initio data. We demonstrate the software by deriving bonded terms' parameters of three widely known drug molecules, viz. aspirin, caffeine, and a norfloxacin analogue, for which we show that, within the constraints of the functional form, the methodologies implemented in ParaMol are able to derive near-ideal parameters. Additionally, we illustrate the best practices to follow when employing specific parameterization routes. We also determine the sensitivity of different fitting data sets, such as relaxed dihedral scans and configurational ensembles, to the parameterization procedure, and discuss the features of the various weighting methods available to weight configurations. Owing to ParaMol's capabilities, we propose that this software can be introduced as a routine step in the protocol normally employed to parameterize druglike molecules for MM simulations.

Quantum Mechanical and Molecular Mechanics Modeling of Membrane-Embedded Rhodopsins

Computational chemistry provides versatile methods for studying the properties and functioning of biological systems at different levels of precision and at different time scales. The aim of this article is to review the computational methodologies that are applicable to rhodopsins as archetypes for photoactive membrane proteins that are of great importance both in nature and in modern technologies. For each class of computational techniques, from methods that use quantum mechanics for simulating rhodopsin photophysics to less-accurate coarse-grained methodologies used for long-scale protein dynamics, we consider possible applications and the main directions for improvement.

Retinal isomerization and water-pore formation in channelrhodopsin-2

Channelrhodopsin-2 (ChR2) is a light-sensitive ion channel widely used in optogenetics. Photoactivation triggers a trans-to-cis isomerization of a covalently bound retinal. Ensuing conformational changes open a cation-selective channel. We explore the structural dynamics in the early photocycle leading to channel opening by classical (MM) and quantum mechanical (QM) molecular simulations. With QM/MM simulations, we generated a protein-adapted force field for the retinal chromophore, which we validated against absorption spectra. In a 4-µs MM simulation of a dark-adapted ChR2 dimer, water entered the vestibules of the closed channel. Retinal all-trans to 13-cis isomerization, simulated with metadynamics, triggered a major restructuring of the charge cluster forming the channel gate. On a microsecond time scale, water penetrated the gate to form a membrane-spanning preopen pore between helices H1, H2, H3, and H7. This influx of water into an ion-impermeable preopen pore is consistent with time-resolved infrared spectroscopy and electrophysiology experiments. In the retinal 13-cis state, D253 emerged as the proton acceptor of the Schiff base. Upon proton transfer from the Schiff base to D253, modeled by QM/MM simulations, we obtained an early-M/P2390-like intermediate. Rapid rotation of the unprotonated Schiff base toward the cytosolic side effectively prevents its reprotonation from the extracellular side. From MM and QM simulations, we gained detailed insight into the mechanism of ChR2 photoactivation and early events in pore formation. By rearranging the network of charges and hydrogen bonds forming the gate, water emerges as a key player in light-driven ChR2 channel opening.

Multiscale Methods in Drug Design Bridge Chemical and Biological Complexity in the Search for Cures

Drug action is inherently multiscale: it connects molecular interactions to emergent properties at cellular and larger scales. Simulation techniques at each of these different scales are already central to drug design and development, but methods capable of connecting across these scales will extend understanding of complex mechanisms and the ability to predict biological effects. Improved algorithms, ever-more-powerful computing architectures and the accelerating growth of rich datasets are driving advances in multiscale modeling methods capable of bridging chemical and biological complexity from the atom to the cell. Particularly exciting is the development of highly detailed, structure-based, physical simulations of biochemical systems, which are now able to access experimentally relevant timescales for large systems and, at the same time, achieve unprecedented accuracy. In this Perspective, we discuss how emerging data-rich, physics-based multiscale approaches are of the cusp of realizing long-promised impact in the discovery, design and development of novel therapeutics. We highlight emerging methods and applications in this growing field, and outline how different scales can be combined in practical modelling and simulation strategies.

Molecular Dynamics Simulations with Quantum Mechanics/Molecular Mechanics and Adaptive Neural Networks

Direct molecular dynamics (MD) simulation with ab initio quantum mechanical and molecular mechanical (QM/MM) methods is very powerful for studying the mechanism of chemical reactions in a complex environment but also very time-consuming. The computational cost of QM/MM calculations during MD simulations can be reduced significantly using semiempirical QM/MM methods with lower accuracy. To achieve higher accuracy at the ab initio QM/MM level, a correction on the existing semiempirical QM/MM model is an attractive idea. Recently, we reported a neural network (NN) method as QM/MM-NN to predict the potential energy difference between semiempirical and ab initio QM/MM approaches. The high-level results can be obtained using neural network based on semiempirical QM/MM MD simulations, but the lack of direct MD samplings at the ab initio QM/MM level is still a deficiency that limits the applications of QM/MM-NN. In the present paper, we developed a dynamic scheme of QM/MM-NN for direct MD simulations on the NN-predicted potential energy surface to approximate ab initio QM/MM MD. Since some configurations excluded from the database for NN training were encountered during simulations, which may cause some difficulties on MD samplings, an adaptive procedure inspired by the selection scheme reported by Behler [ Behler Int. J. Quantum Chem. 2015 , 115 , 1032 ; Behler Angew. Chem., Int. Ed. 2017 , 56 , 12828 ] was employed with some adaptions to update NN and carry out MD iteratively. We further applied the adaptive QM/MM-NN MD method to the free energy calculation and transition path optimization on chemical reactions in water. The results at the ab initio QM/MM level can be well reproduced using this method after 2-4 iteration cycles. The saving in computational cost is about 2 orders of magnitude. It demonstrates that the QM/MM-NN with direct MD simulations has great potentials not only for the calculation of thermodynamic properties but also for the characterization of reaction dynamics, which provides a useful tool to study chemical or biochemical systems in solution or enzymes.

Implications of short time scale dynamics on long time processes

This review provides a comprehensive overview of the structural dynamics in topical gas- and condensed-phase systems on multiple length and time scales. Starting from vibrationally induced dissociation of small molecules in the gas phase, the question of vibrational and internal energy redistribution through conformational dynamics is further developed by considering coupled electron/proton transfer in a model peptide over many orders of magnitude. The influence of the surrounding solvent is probed for electron transfer to the solvent in hydrated I-. Next, the dynamics of a modified PDZ domain over many time scales is analyzed following activation of a photoswitch. The hydration dynamics around halogenated amino acid side chains and their structural dynamics in proteins are relevant for iodinated TyrB26 insulin. Binding of nitric oxide to myoglobin is a process for which experimental and computational analyses have converged to a common view which connects rebinding time scales and the underlying dynamics. Finally, rhodopsin is a paradigmatic system for multiple length- and time-scale processes for which experimental and computational methods provide valuable insights into the functional dynamics. The systems discussed here highlight that for a comprehensive understanding of how structure, flexibility, energetics, and dynamics contribute to functional dynamics, experimental studies in multiple wavelength regions and computational studies including quantum, classical, and more coarse grained levels are required.

Theoretical description of protein field effects on electronic excitations of biological chromophores

Photoinitiated phenomena play a crucial role in many living organisms. Plants, algae, and bacteria absorb sunlight to perform photosynthesis, and convert water and carbon dioxide into molecular oxygen and carbohydrates, thus forming the basis for life on Earth. The vision of vertebrates is accomplished in the eye by a protein called rhodopsin, which upon photon absorption performs an ultrafast isomerisation of the retinal chromophore, triggering the signal cascade. Many other biological functions start with the photoexcitation of a protein-embedded pigment, followed by complex processes comprising, for example, electron or excitation energy transfer in photosynthetic complexes. The optical properties of chromophores in living systems are strongly dependent on the interaction with the surrounding environment (nearby protein residues, membrane, water), and the complexity of such interplay is, in most cases, at the origin of the functional diversity of the photoactive proteins. The specific interactions with the environment often lead to a significant shift of the chromophore excitation energies, compared with their absorption in solution or gas phase. The investigation of the optical response of chromophores is generally not straightforward, from both experimental and theoretical standpoints; this is due to the difficulty in understanding diverse behaviours and effects, occurring at different scales, with a single technique. In particular, the role played by ab initio calculations in assisting and guiding experiments, as well as in understanding the physics of photoactive proteins, is fundamental. At the same time, owing to the large size of the systems, more approximate strategies which take into account the environmental effects on the absorption spectra are also of paramount importance. Here we review the recent advances in the first-principle description of electronic and optical properties of biological chromophores embedded in a protein environment. We show their applications on paradigmatic systems, such as the light-harvesting complexes, rhodopsin and green fluorescent protein, emphasising the theoretical frameworks which are of common use in solid state physics, and emerging as promising tools for biomolecular systems.

Polarizable Embedding Density Matrix Renormalization Group

The polarizable embedding (PE) approach is a flexible embedding model where a preselected region out of a larger system is described quantum mechanically, while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures in complex molecular environments. We investigate various embedding potentials for the well-studied first excited state of water with active spaces that correspond to a full configuration-interaction treatment. Moreover, we study the environment effect on the first excited state of a retinylidene Schiff base within a channelrhodopsin protein. For this system, we also investigate the effect of dynamical correlation included through short-range density functional theory.

Toward Determining ATPase Mechanism in ABC Transporters: Development of the Reaction Path-Force Matching QM/MM Method

Adenosine triphosphate (ATP)-binding cassette (ABC) transporters are ubiquitous ATP-dependent membrane proteins involved in translocations of a wide variety of substrates across cellular membranes. To understand the chemomechanical coupling mechanism as well as functional asymmetry in these systems, a quantitative description of how ABC transporters hydrolyze ATP is needed. Complementary to experimental approaches, computer simulations based on combined quantum mechanical and molecular mechanical (QM/MM) potentials have provided new insights into the catalytic mechanism in ABC transporters. Quantitatively reliable determination of the free energy requirement for enzymatic ATP hydrolysis, however, requires substantial statistical sampling on QM/MM potential. A case study shows that brute force sampling of ab initio QM/MM (AI/MM) potential energy surfaces is computationally impractical for enzyme simulations of ABC transporters. On the other hand, existing semiempirical QM/MM (SE/MM) methods, although affordable for free energy sampling, are unreliable for studying ATP hydrolysis. To close this gap, a multiscale QM/MM approach named reaction path-force matching (RP-FM) has been developed. In RP-FM, specific reaction parameters for a selected SE method are optimized against AI reference data along reaction paths by employing the force matching technique. The feasibility of the method is demonstrated for a proton transfer reaction in the gas phase and in solution. The RP-FM method may offer a general tool for simulating complex enzyme systems such as ABC transporters.

Fighting Cancer with Transition Metal Complexes: From Naked DNA to Protein and Chromatin Targeting Strategies

Many transition metal complexes have unique physicochemical properties that can be efficiently exploited in medicinal chemistry for cancer treatment. Traditionally, double-stranded DNA has been assumed to be the main binding target; however, recent studies have shown that nucleosomal DNA as well as proteins can act as dominant molecular binding partners. This has raised new questions about the molecular determinants that govern DNA versus protein binding selectivity, and has offered new ways to rationalize their biological activity and possible side effects. To address these questions, molecular simulations at an atomistic level of detail have been used to complement, support, and rationalize experimental data. Herein we review some relevant studies-focused on platinum and ruthenium compounds-to illustrate the power of state-of-the-art molecular simulation techniques and to demonstrate how the interplay between molecular simulations and experiments can make important contributions to elucidating the target preferences of some promising transition metal anticancer agents. This contribution aims at providing relevant information that may help in the rational design of novel drug-discovery strategies.

Excited States and Photochemistry of Chromophores in the Photoactive Proteins Explored by the Combined Quantum Mechanical and Molecular Mechanical Calculations

A photoactive protein usually contains a unique chromophore that is responsible for the initial photoresponse and functions of the photoactive protein are determined by the interaction between the chromophore and its protein surroundings. The combined quantum mechanical and molecular mechanical (QM/MM) approach is demonstrated to be a very useful tool for exploring structures and functions of a photoactive protein with the chromophore and its protein surroundings treated by the QM and MM methods, respectively. In this review, we summarize the basic formulas of the QM/MM approach and emphasize its applications to excited states and photoreactions of chromophores in rhodopsin protein, photoactive yellow protein, and green fluorescent protein.

Developing accurate molecular mechanics force fields for conjugated molecular systems

A rapid method to parameterize the intramolecular component of classical force fields is proposed and applied to a molecular semiconductor, oligomers of conjugated polymers and a biological chromophore.

Reaction Path Force Matching: A New Strategy of Fitting Specific Reaction Parameters for Semiempirical Methods in Combined QM/MM Simulations

We present a general strategy of reparametrizing semiempirical (SE) methods against ab initio (AI) methods for combined quantum mechanical and molecular mechanical (QM/MM) simulations of specific chemical reactions in condensed phases. The resulting approach, designated Reaction Path Force Matching (RP-FM), features cycles of sampling configurations along a reaction path on an efficient SE/MM potential energy surface (PES) and adjusting specific reaction parameters (SRPs) in the SE method such that the atomic forces computed at the target AI/MM level are reproduced. Iterative applications of the RP-FM cycle make possible achieving the accuracy of AI/MM simulations without explicitly sampling the computationally expensive AI/MM PES. The bypassed sampling, nevertheless, is implicitly accomplished through the aid of the efficient SE-SRP/MM PES, on which the target-level reaction path is expected to be obtained upon convergence. We demonstrate the effectiveness of the RP-FM procedure for a symmetric proton transfer reaction in the gas phase and in solution. The remarkable agreements between the RP-FM optimized SE-SRP methods and the target AI method on various properties, including energy profiles, potential of mean force free energy profiles, atomic forces, charge populations, and solvation effects, suggest that RP-FM can be used as an efficient and reliable strategy for simulating condensed-phase chemical reactions.