Dissociation Energies via Embedding Techniques.

Due to the large number of interactions, evaluating interaction energies for large or periodic systems results in time-consuming calculations. Prime examples are liquids, adsorbates, and molecular crystals. Thus, there is a high demand for a cheap but still accurate method to determine interaction energies and gradients. One approach to counteract the computational cost is to fragment a large cluster into smaller subsystems, sometimes called many-body expansion, with the fragments being molecules or parts thereof. These subsystems can then be embedded into larger entities, representing the bigger system. In this work, we test several subsystem approaches and explore their limits and behaviors, determined by calculations of trimer interaction energies. The methods presented here encompass mechanical embedding, point charges, polarizable embedding, polarizable density embedding, and density embedding. We evaluate nonembedded fragmentation, QM/MM (quantum mechanics/molecular mechanics), and QM/QM (quantum mechanics/quantum mechanics) embedding theories. Finally, we make use of symmetry-adapted perturbation theory utilizing density functional theory for the monomers to interpret the results. Depending on the strength of the interaction, different embedding methods and schemes prove favorable to accurately describe a system. The embedding approaches presented here are able to decrease the interaction energy errors with respect to full system calculations by a factor of up to 20 in comparison to simple/unembedded approaches, leading to errors below 0.1 kJ/mol.

Electric Field Gradient Calculations for Ice VIII and IX Using Polarizable Embedding: A Comparative Study on Classical Computers and Quantum Simulators.

We test the performance of the polarizable embedding variational quantum eigensolver self-consistent field (PE-VQE-SCF) model for computing electric field gradients with comparisons to conventional complete active space self-consistent-field (CASSCF) calculations and experimental results. We compute quadrupole coupling constants for ice VIII and ice IX. We find close agreement of the quantum-computing PE-VQE-SCF results with the results from the classical PE-CASSCF calculations and with experiment. Furthermore, we observe that the inclusion of the environment is crucial for obtaining results that match the experimental data. The calculations for ice VIII are within the experimental uncertainty for both CASSCF and VQE-SCF for oxygen and lie close to the experimental value for ice IX as well. With the VQE-SCF, which is based on an adaptive derivative-assembled problem-tailored (ADAPT) ansatz, we find that the inclusion of the environment and the size of the different basis sets do not directly affect the gate counts. However, by including an explicit environment, the wavefunction and therefore the optimization problem become more complicated, which usually results in the need to include more operators from the operator pool, thereby increasing the depth of the circuit.

Divergences in classical and quantum linear response and equation of motion formulations.

Calculating molecular properties using quantum devices can be performed through the quantum linear response (qLR) or, equivalently, the quantum equation of motion (qEOM) formulations. Different parameterizations of qLR and qEOM are available, namely naïve, projected, self-consistent, and state-transfer. In the naïve and projected parameterizations, the metric is not the identity, and we show that it depends on redundant orbital rotations. This dependency may lead to divergences in the excitation energies for certain choices of the redundant orbital rotation parameters in an idealized noiseless setting. Furthermore, this leads to a significant variance when calculations include statistical noise from finite quantum sampling.

The variational quantum eigensolver self-consistent field method within a polarizable embedded framework.

We formulate and implement the Variational Quantum Eigensolver Self Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding (PE), thereby extending PE to the regime of quantum computing. We test the resulting algorithm, PE-VQE-SCF, on quantum simulators and demonstrate that the computational stress on the quantum device is only slightly increased in terms of gate counts compared to regular VQE-SCF. On the other hand, no increase in shot noise was observed. We illustrate how PE-VQE-SCF may lead to the modeling of real chemical systems using a simulation of the reaction barrier of the Diels-Alder reaction between furan and ethene as an example.

Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra.

Quantum-mechanical (QM) and classical embedding models approximate a supermolecular quantum-chemical calculation. This is particularly useful when the supermolecular calculation has a size that is out of reach for present QM models. Although QM and classical embedding methods share the same goal, they approach this goal from different starting points. In this study, we compare the polarizable embedding (PE) and frozen-density embedding (FDE) models. The former is a classical embedding model, whereas the latter is a density-based QM embedding model. Our comparison focuses on solvent effects on optical spectra of solutes. This is a typical scenario where super-system calculations including the solvent environment become prohibitively large. We formulate a common theoretical framework for PE and FDE models and systematically investigate how PE and FDE approximate solvent effects. Generally, differences are found to be small, except in cases where electron spill-out becomes problematic in the classical frameworks. In these cases, however, atomic pseudopotentials can reduce the electron-spill-out issue.

Mechanism behind Polysorbates' Inhibitory Effect on P-Glycoprotein.

Much effort has been invested in the search for modulators of membrane transport proteins such as P-glycoprotein (P-gp) to improve drug bioavailability and reverse multidrug resistance in cancer. Nonionic surfactants, a class of pharmaceutical excipients, are known to inhibit such proteins, but knowledge about the exact mechanism of this inhibition is scarce. Here, we perform multiscale molecular dynamics simulations of one of these surfactants, polysorbate 20 (PS20), to reveal the behavior of such compounds on the molecular level and thereby discover the molecular mechanism of the P-gp inhibition. We show that the amphiphilic headgroup of PS20 is too hydrophobic to partition in the water phase, which drives the binding of PS20 to the amphiphilic drug-binding domain of P-gp and thereby causes the inhibition of the protein. Based on our findings, we conclude that PS20 primarily inhibits P-gp through direct binding to the drug-binding domain (DBD) from the extracellular leaflet.

Substituted 9-Diethylaminobenzo[a]phenoxazin-5-ones (Nile Red Analogues): Synthesis and Photophysical Properties.

Nile Red is a benzo[a]phenoxazone dye containing a diethylamino substituent at the 9-position. In recent years, it has become a popular histological stain for cellular membranes and lipid droplets due to its unrivaled fluorescent properties in lipophilic environments. This makes it an attractive lead for chemical decoration to tweak its attributes and optimize it for more specialized microscopy techniques, e.g., fluorescence lifetime imaging or two-photon excited fluorescence microscopy, to which Nile Red has never been optimized. Herein, we present synthesis approaches to a series of monosubstituted Nile Red derivatives (9-diethylbenzo[a]phenoxazin-5-ones) starting from 1-naphthols or 1,3-naphthalenediols. The solvatochromic responsiveness of these fluorophores is reported with focus on how the substituents affect the absorption and emission spectra, luminosity, fluorescence lifetimes, and two-photon absorptivity. Several of the analogues emerge as strong candidates for reporting the polarity of their local environment. Specifically, the one- and two-photon excited fluorescence of Nile Red turns out to be very responsive to substitution, and the spectroscopic features can be finely tuned by judiciously introducing substituents of distinct electronic character at specific positions. This new toolkit of 9-diethylbenzo[a]phenoxazine-5-ones constitutes a step toward the next generation of optical molecular probes for advancing the understanding of lipid structures and cellular processes.

Computational and photophysical characterization of a Laurdan malononitrile derivative.

The malononitrile group is considered one of the strongest natural electron-withdrawing groups in a chemist's arsenal. However, surprisingly little is known about how this group functions in push-pull fluorophores. In a recent computational study, we reported that replacing the ketone group of the traditional push-pull dye Laurdan with a malononitrile group significantly improves the optical properties while retaining the membrane behavior of the parent molecule Laurdan. Motivated by these results, we report here the synthesis and photophysical characterization of the said compound, 6-(1-undecyl-2,2-dicyanovinyl)-N,N-dimethyl-2-naphthylamine (CN-Laurdan). To our surprise, this new CN-Laurdan probe is found to be much less bright than the parent Laurdan due to a large drop in the fluorescence quantum yield. Using computational methods, we determine that the origin of this low quantum yield is related to the existence of a non-radiative decay pathway related to a rotation of the malononitrile moiety, suggesting that the molecule could nonetheless function very well as a molecular rotor. We confirm experimentally that CN-Laurdan functions as a molecular rotor by measuring the quantum yield in methanol/glycerol mixtures of increasing viscosity. Specifically, we found a consistent increase in the quantum yield across the entire range of tested viscosities.

Mechanistic Insight into Lipid Binding to Yeast Niemann Pick Type C2 Protein.

Niemann Pick type C2 (NPC2) is a small sterol binding protein in the lumen of late endosomes and lysosomes. We showed recently that the yeast homologue of NPC2 together with its binding partner NCR1 mediates integration of ergosterol, the main sterol in yeast, into the vacuolar membrane. Here, we study the binding specificity and the molecular details of lipid binding to yeast NPC2. We find that NPC2 binds fluorescence- and spin-labeled analogues of phosphatidylcholine (PC), phosphatidylserine, phosphatidylinositol (PI), and sphingomyelin. Spectroscopic experiments show that NPC2 binds lipid monomers in solution but can also interact with lipid analogues in membranes. We further identify ergosterol, PC, and PI as endogenous NPC2 ligands. Using molecular dynamics simulations, we show that NPC2's binding pocket can adapt to the ligand shape and closes around bound ergosterol. Hydrophobic interactions stabilize the binding of ergosterol, but binding of phospholipids is additionally stabilized by electrostatic interactions at the mouth of the binding site. Our work identifies key residues that are important in stabilizing the binding of a phospholipid to yeast NPC2, thereby rationalizing future mutagenesis studies. Our results suggest that yeast NPC2 functions as a general "lipid solubilizer" and binds a variety of amphiphilic lipid ligands, possibly to prevent lipid micelle formation inside the vacuole.

One- and two-photon solvatochromism of the fluorescent dye Nile Red and its CF3, F and Br-substituted analogues.

The solvatochromic fluorophore Nile Red, 9-diethylamino-5H-benzo[a]phenoxazine-5-one, is one of the most commonly used stains to enhance contrast of lipid-rich areas of microscopic biosamples. Quite surprisingly, relatively little is known about the spectrally-resolved two-photon absorption (2PA) properties of this dye despite its promising features for two-photon microscopy of biological matter. For this reason, the two-photon solvatochromism of Nile Red still remains an uncharted territory as well. Also, no study has yet reported on how electron-withdrawing substituents attached to the Nile Red backbone affect its solvatochromic properties and two-photon brightness. In this paper, we demonstrate how solvent polarity influences the one- and two-photon absorption spectra of Nile Red as well as its fluorescence parameters, and we present new analogues that contain -CF3, -F and -Br substituents on its eastern side. Two-photon excited fluorescence experiments in a broad spectral range (780-1240 nm) and electronic structure calculations show that both the nature and location of the substituent have particular influence on the strength of 2PA, peaking in all cases at approx. 860 and 1050 nm. 2PA cross sections are higher at 1050 nm than at 860 nm, which suggests that Nile Red and its analogues are best suited for two-photon imaging employing excitation in the NIR-II optical transparency window of biological tissues.

Modeling the Sterol-Binding Domain of Aster-A Provides Insight into Its Multiligand Specificity.

Intracellular transport of cholesterol and related sterols relies to a large degree on nonvesicular mechanisms, which are only partly understood at the molecular level. Aster proteins belonging to the Lam family of sterol transfer proteins have recently been identified as important catalysts of nonvesicular sterol exchange between the plasma membrane (PM) and endoplasmic reticulum (ER). Here, we used a range of computational tools to study the molecular mechanisms underlying sterol binding as well as multisterol ligand specificity of Aster-A. Our study focused primarily on gaining atomistic insight into the bound ligand-protein complex and was, on this basis, performed in the absence of any membrane. Molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) calculations provide a rationale for the experimentally found ranking of binding affinities of various sterols to Aster-A. In particular, the polarity of the sterols and the length of their alkyl chain could be identified as being critical determinants of ligand affinity. A Gibbs free energy decomposition identified a charged residue, Glu444, at the base of the binding pose as an important control point for sterol binding. Removing its net charge via protonation was found to cause significant changes to the environment surrounding this residue. In addition, the protonation of Glu444 was found to be paralleled by a large redistribution of molecular flexibility in the Aster domain. This finding was supplemented by multiple branched adaptive steered molecular dynamics (MB-ASMD) simulations by which we defined a possible molecular path for sterol release and demonstrated the importance of Glu444 in this process.

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.

Rational design of novel fluorescent analogues of cholesterol: a "step-by-step" computational study.

In this paper we show a theoretical rational design approach on a series of intrinsically fluorescent analogues of cholesterol (FLACs), called polyene-sterols (P-sterols), followed by a step-by-step selection of potential candidates, employing, sequentially, state-of-the-art quantum mechanical (QM) computations of the optical properties (single- and multiphoton absorption electronic spectroscopies and emission), molecular dynamics (MD) simulations in model membranes, and multiscale approaches (polarizable embedding). This selection converged to a promising candidate that shows simultaneously interesting single- and multiphoton absorption properties as well as emitting properties and good abilities to mimic cholesterol order effects in model membranes.

Color Tuning in Bovine Rhodopsin through Polarizable Embedding.

Bovine rhodopsin is among the most studied proteins in the rhodopsin family. Its primary activation mechanism is the photoisomerization of 11-cis retinal, triggered by the absorption of a UV-visible photon. Different mutants of the same rhodopsin show different absorption wavelengths due to the influence of the specific amino acid residues forming the cavity in which the retinal chromophore is embedded, and rhodopsins activated at different wavelengths are, for example, exploited in the field of optogenetics. In this letter, we present a procedure for systematically investigating color tuning in models of bovine rhodopsin and a set of its mutants embedded in a membrane bilayer. Vertical excitation energy calculations were carried out with the polarizable embedding potential for describing the environment surrounding the chromophore. We show that polarizable embedding outperformed regular electrostatic embedding in determining both the vertical excitation energies and associated oscillator strengths of the systems studied.

Importance of Polarizable Embedding for Absorption Spectrum Calculations of Arabidopsis thaliana Cryptochrome 1.

Cryptochromes are essential flavoproteins for circadian rhythms and avian magnetoreception. Flavin adenine dinucleotide (FAD), a chromophore within cryptochromes, absorbs blue light, initiating electron transfer processes that lead to a biological signaling cascade. A key step in this cascade is the formation of the FAD semiquinone radical (FADH•), characterized through a specific red-light absorption. The absorption spectra of FADH• in cryptochromes are, however, significantly different from those recorded for the cofactor in solution, primarily due to protein-induced shifts in the absorption peaks. This study employs a multiscale approach, combining molecular dynamics (MD) simulations with quantum mechanical/molecular mechanical (QM/MM) methodologies, to investigate the influence of protein dynamics on embedded FADH• absorption. We emphasize the role of the protein's polarizable environment in the shaping of the absorption spectrum, crucial for accurate spectral predictions in cryptochromes. Our findings provide valuable insights into the absorption process, advancing our understanding of cryptochrome functioning.

Understanding the Red Shift in the Absorption Spectrum of the FAD Cofactor in ClCry4 Protein.

It is still a puzzle that has not been entirely solved how migratory birds utilize the Earth's magnetic field for biannual migration. The most consistent explanation thus far is rooted in the modulation of the biological function of the cryptochrome 4 (Cry4) protein by an external magnetic field. This phenomenon is closely linked with the flavin adenine dinucleotide (FAD) cofactor that is noncovalently bound in the protein. Cry4 is activated by blue light, which is absorbed by the FAD cofactor. Subsequent electron and proton transfers trigger radical pair formation in the protein, which is sensitive to the external magnetic field. An important long-lasting redox state of the FAD cofactor is the signaling (FADH•) state, which is present after the transient electron transfer steps have been completed. Recent experimental efforts succeeded in crystallizing the Cry4 protein from Columbia livia (ClCry4) with all of the important residues needed for protein photoreduction. This specific crystallization of Cry4 protein so far is the only avian cryptochrome crystal structure available, which, however, has great similarity to the Cry4 proteins of night migratory birds. The previous experimental studies of the ClCry4 protein included the absorption properties of the protein in its different redox states. The absorption spectrum of the FADH• state demonstrated a peculiar red shift compared to the photoabsorption properties of the FAD cofactor in its FADH• state in other Cry proteins from other species. The aim of this study is to understand this red shift by employing the tools of computational microscopy and, in particular, a QM/MM approach that relies on the polarizable embedding approximation.

Simulating X-ray Absorption Spectroscopy in Challenging Environments: Methodological Insights from Water-Solvated Ammonia and Ammonium Systems.

Core-electron excitations in solvated systems, influenced by solvent geometry and hydrogen bonding, make X-ray absorption spectroscopy (XAS) a valuable tool for assessing solvent-solute interactions. However, calculating XAS spectra with electronic-structure methods has proven challenging due to a delicate interplay between correlation and solvation effects. This study provides a computational procedure for XAS modeling in solvated systems, with water-solvated ammonia and ammonium systems serving as probes. Exploring methodological challenges, we investigate explicit embedding models, specifically the polarizable embedding family, including polarizable density embedding and extended polarizable density embedding. Our linear-response time-dependent density functional theory (LR-TDDFT) XAS calculations reveal the efficiency of this approach, with extended polarizable density embedding emerging as a robust improvement over polarizable density embedding. Contrary to some recent literature, our study challenges the belief that LR-TDDFT cannot accurately describe XAS spectra of ammonia and ammonium solvated in water.

Ratiometric fluorescence nanoscopy and lifetime imaging of novel Nile Red analogs for analysis of membrane packing in living cells.

Subcellular membranes have complex lipid and protein compositions, which give rise to organelle-specific membrane packing, fluidity, and permeability. Due to its exquisite solvent sensitivity, the lipophilic fluorescence dye Nile Red has been used extensively to study membrane packing and polarity. Further improvement of Nile Red can be achieved by introducing electron-donating or withdrawing functional groups. Here, we compare the potential of derivatives of Nile Red with such functional substitutions for super-resolution fluorescence microscopy of lipid packing in model membranes and living cells. All studied Nile Red derivatives exhibit cholesterol-dependent fluorescence changes in model membranes, as shown by spectrally resolved stimulated emission depletion (STED) microscopy. STED imaging of Nile Red probes in cells reveals lower membrane packing in fibroblasts from healthy subjects compared to those from patients suffering from Niemann Pick type C1 (NPC1) disease, a lysosomal storage disorder with accumulation of cholesterol and sphingolipids in late endosomes and lysosomes. We also find small but consistent changes in the fluorescence lifetime of the Nile Red derivatives in NPC1 cells, suggesting altered hydrogen-bonding capacity in their membranes. All Nile Red derivatives are essentially non-fluorescent in water but increase their brightness in membranes, allowing for their use in MINFLUX single molecule tracking experiments. Our study uncovers the potential of Nile Red probes with functional substitutions for nanoscopic membrane imaging.

Quantum Mechanical Versus Polarizable Embedding Schemes: A Study of the Xray Absorption Spectra of Aqueous Ammonia and Ammonium.

The X-ray absorption spectra of aqueous ammonia and ammonium are computed using a combination of coupled cluster singles and doubles (CCSD) with different quantum mechanical and molecular mechanical embedding schemes. Specifically, we compare frozen Hartree-Fock (HF) density embedding, polarizable embedding (PE), and polarizable density embedding (PDE). Integrating CCSD with frozen HF density embedding is possible within the CC-in-HF framework, which circumvents the conventional system-size limitations of standard coupled cluster methods. We reveal similarities between PDE and frozen HF density descriptions, while PE spectra differ significantly. By including approximate triple excitations, we also investigate the effect of improving the electronic structure theory. The spectra computed using this approach show an improved intensity ratio compared to CCSD-in-HF. Charge transfer analysis of the excitations shows the local character of the pre-edge and main-edge, while the post-edge is formed by excitations delocalized over the first solvation shell and beyond.

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".