Assessment of Embedding Schemes in a Hybrid Machine Learning/Classical Potentials (ML/MM) Approach.

Machine learning (ML) methods have reached high accuracy levels for the prediction of in vacuo molecular properties. However, the simulation of large systems solely through ML methods (such as those based on neural network potentials) is still a challenge. In this context, one of the most promising frameworks for integrating ML schemes in the simulation of complex molecular systems are the so-called ML/MM methods. These multiscale approaches combine ML methods with classical force fields (MM), in the same spirit as the successful hybrid quantum mechanics-molecular mechanics methods (QM/MM). The key issue for such ML/MM methods is an adequate description of the coupling between the region of the system described by ML and the region described at the MM level. In the context of QM/MM schemes, the main ingredient of the interaction is electrostatic, and the state of the art is the so-called electrostatic-embedding. In this study, we analyze the quality of simpler mechanical embedding-based approaches, specifically focusing on their application within a ML/MM framework utilizing atomic partial charges derived in vacuo. Taking as reference electrostatic embedding calculations performed at a QM(DFT)/MM level, we explore different atomic charges schemes, as well as a polarization correction computed using atomic polarizabilites. Our benchmark data set comprises a set of about 80k small organic structures from the ANI-1x and ANI-2x databases, solvated in water. The results suggest that the minimal basis iterative stockholder (MBIS) atomic charges yield the best agreement with the reference coupling energy. Remarkable enhancements are achieved by including a simple polarization correction.

Short hydrogen bonds enhance nonaromatic protein-related fluorescence.

Fluorescence in biological systems is usually associated with the presence of aromatic groups. Here, by employing a combined experimental and computational approach, we show that specific hydrogen bond networks can significantly affect fluorescence. In particular, we reveal that the single amino acid L-glutamine, by undergoing a chemical transformation leading to the formation of a short hydrogen bond, displays optical properties that are significantly enhanced compared with L-glutamine itself. Ab initio molecular dynamics simulations highlight that these short hydrogen bonds prevent the appearance of a conical intersection between the excited and the ground states and thereby significantly decrease nonradiative transition probabilities. Our findings open the door to the design of new photoactive materials with biophotonic applications.

Dissipative Equation of Motion for Electromagnetic Radiation in Quantum Dynamics.

The dynamical description of the radiative decay of an electronically excited state in realistic many-particle systems is an unresolved challenge. In the present investigation electromagnetic radiation of the charge density is approximated as the power dissipated by a classical dipole, to cast the emission in closed form as a unitary single-electron theory. This results in a formalism of unprecedented efficiency, critical for ab initio modeling, which exhibits at the same time remarkable properties: it quantitatively predicts decay rates, natural broadening, and absorption intensities. Exquisitely accurate excitation lifetimes are obtained from time-dependent DFT simulations for C^{2+}, B^{+}, and Be, of 0.565, 0.831, and 1.97 ns, respectively, in accord with experimental values of 0.57±0.02, 0.86±0.07, and 1.77-2.5 ns. Hence, the present development expands the frontiers of quantum dynamics, bringing within reach first-principles simulations of a wealth of photophysical phenomena, from fluorescence to time-resolved spectroscopies.

Spectroscopy in Complex Environments from QM-MM Simulations.

The applications of multiscale quantum-classical (QM-MM) approaches have shown an extraordinary expansion and diversification in the last couple of decades. A great proportion of these efforts have been devoted to interpreting and reproducing spectroscopic experiments in a variety of complex environments such as solutions, interfaces, and biological systems. Today, QM-MM-based computational spectroscopy methods constitute accomplished tools with refined predictive power. The present review summarizes the advances that have been made in QM-MM approaches to UV-visible, Raman, IR, NMR, electron paramagnetic resonance, and Mössbauer spectroscopies, providing in every case an introductory discussion of the corresponding methodological background. A representative number of applications are presented to illustrate the historical evolution and the state of the art of this field, highlighting the advantages and limitations of the available methodologies. Finally, we present our view of the perspectives and open challenges in the field.

Fluorescence Quantum Yields in Complex Environments from QM-MM TDDFT Simulations: The Case of Indole in Different Solvents.

Fluorescence is commonly exploited to probe microscopic properties. An important example is tryptophan in protein environments, where variations in fluorescence quantum yield, and in absorption and emission maxima, are used as indicators of changes in the environment. Modeling the fluorescence quantum yield requires the determination of both radiative and nonradiative decay constants, both on the potential energy surface of the excited fluorophore. Furthermore, the inclusion of complex environments implies their accurate representation as well as extensive configurational sampling. In this work, we present and test various methodologies based on time-dependent density functional theory (TDDFT) and quantum mechanics/molecular mechanics (QM/MM) dynamics that take all of these requirements into account to provide a quantitative prediction of the effect of the environment on the fluorescence quantum yield of indole, a tryptophan fluorophore. This investigation paves the way for applications to the realistic spectroscopic characterization of the local protein environment of tryptophan from computer simulations.

Electron transport in real time from first-principles.

While the vast majority of calculations reported on molecular conductance have been based on the static non-equilibrium Green's function formalism combined with density functional theory (DFT), in recent years a few time-dependent approaches to transport have started to emerge. Among these, the driven Liouville-von Neumann equation [C. G. Sánchez et al., J. Chem. Phys. 124, 214708 (2006)] is a simple and appealing route relying on a tunable rate parameter, which has been explored in the context of semi-empirical methods. In the present study, we adapt this formulation to a density functional theory framework and analyze its performance. In particular, it is implemented in an efficient all-electron DFT code with Gaussian basis functions, suitable for quantum-dynamics simulations of large molecular systems. At variance with the case of the tight-binding calculations reported in the literature, we find that now the initial perturbation to drive the system out of equilibrium plays a fundamental role in the stability of the electron dynamics. The equation of motion used in previous tight-binding implementations with massive electrodes has to be modified to produce a stable and unidirectional current during time propagation in time-dependent DFT simulations using much smaller leads. Moreover, we propose a procedure to get rid of the dependence of the current-voltage curves on the rate parameter. This method is employed to obtain the current-voltage characteristic of saturated and unsaturated hydrocarbons of different lengths, with very promising prospects.

Mechanism of cysteine oxidation by peroxynitrite: An integrated experimental and theoretical study.

Since peroxynitrite was identified as a pathophysiological agent it has been implicated in a great variety of cellular processes. Particularly, peroxynitrite mediated oxidation of cellular thiol-containing compounds such as Cys residues, is a key event which has been extensively studied. Although great advances have been accomplished, the reaction is not completely understood at the atomic level. Aiming to shed light on this subject, we present an integrated kinetic and theoretical study of the oxidation of free Cys by peroxynitrite. We determined pH-independent thermodynamic activation parameters, namely those corresponding to the reaction between the reactive species: Cys thiolate and peroxynitrous acid. We found a pH-independent activation energy of 8.2 ± 0.6 kcal/mol. Simulations were performed using state of the art hybrid quantum-classical (QM-MM) molecular dynamics simulations. Our results are consistent with a SN2 mechanism, with Cys sulfenic acid and nitrite anion as products. The activation barrier is mostly due to the alignment of sulfur's thiolate atom with the oxygen atoms of the peroxide, along with the concomitant charge reorganization and important changes in the solvation profile. This work provides an atomic detailed description of the reaction mechanism and a framework to understand the environment effects on peroxynitrite reactivity with protein thiols.

The carbonyl-lock mechanism underlying non-aromatic fluorescence in biological matter.

Challenging the basis of our chemical intuition, recent experimental evidence reveals the presence of a new type of intrinsic fluorescence in biomolecules that exists even in the absence of aromatic or electronically conjugated chemical compounds. The origin of this phenomenon has remained elusive so far. In the present study, we identify a mechanism underlying this new type of fluorescence in different biological aggregates. By employing non-adiabatic ab initio molecular dynamics simulations combined with a data-driven approach, we characterize the typical ultrafast non-radiative relaxation pathways active in non-fluorescent peptides. We show that the key vibrational mode for the non-radiative decay towards the ground state is the carbonyl elongation. Non-aromatic fluorescence appears to emerge from blocking this mode with strong local interactions such as hydrogen bonds. While we cannot rule out the existence of alternative non-aromatic fluorescence mechanisms in other systems, we demonstrate that this carbonyl-lock mechanism for trapping the excited state leads to the fluorescence yield increase observed experimentally, and set the stage for design principles to realize novel non-invasive biocompatible probes with applications in bioimaging, sensing, and biophotonics.

Remodelling the surface of thioredoxin from Escherichia coli by grafting an iron-binding site from the CyaY protein family.

In this work, we have designed and generated a Fe(III)-binding protein with thiol oxidoreductase activity. The consensus iron-binding motif EExxED from the frataxin protein family was grafted on a model peptide and on the surface of thioredoxin (TRX) from E. coli. We investigated metal interactions with a family of peptides containing the motif EExxED or altered versions obtained by removing negatively charged residues: EExxEx, xExxED, and xExxEx. The interaction of the metal ion with the peptides was studied by circular dichroism, and our results indicated that the motif EExxED retained its functional properties and also that this motif is able to bind Ga(III) and Al(III). The interaction of the grafted TRX with iron(III) was investigated by NMR, showing that the motif was functional in the context of the protein structure, and also the binding of two equivalents of Fe(III) per TRX molecule was stable in a non-chelating neutral buffer. Protein conformation, stability, and enzymatic activity were studied by applying experimental and computational approaches. Interestingly, the thiol oxidoreductase activity was modulated by interaction with Ga(III), a Fe(III) mimetic ion. Furthermore, the design of functional proteins with both functions, oxidoreductase activity and metal-ion binding ability, should consider the reorganisation of the electrostatic network. Similarly, studying the crosstalk and electrostatic balance among different metal-binding sites may be critical.

Non-Aromatic Fluorescence in Biological Matter: The Exception or the Rule?

While in the vast majority of cases fluorescence in biological matter has been attributed to aromatic or conjugated groups, peptides associated with neurodegenerative diseases, such as Alzheimer's, Parkinson's, or Huntington's, have been recently shown to display an intrinsic visible fluorescence even in the absence of aromatic residues. This has called the attention of researchers from many different fields, trying to understand the origin of this peculiar behavior and, at the same time, motivating the search for novel strategies to control the optical properties of new biophotonic materials. Today, after nearly 15 years of its discovery, there is a growing consensus about the mechanism underlying this phenomenon, namely, that electronic interactions between non-optically active molecules can result in supramolecular assemblies that are fluorescent. Despite this progress, many aspects of this phenomenon remain uncharted territory. In this Perspective, we lay down the state-of-the-art in the field highlighting the open questions from both experimental and theoretical fronts in this fascinating emerging area of non-aromatic fluorescence.

Gain of local structure in an amphipathic peptide does not require a specific tertiary framework.

In this work, we studied how an amphipathic peptide of the surface of the globular protein thioredoxin, TRX94-108, acquires a native-like structure when it becomes involved in an apolar interaction network. We designed peptide variants where the tendency to form alpha-helical conformation is modulated by replacing each of the leucine amino acid residues by an alanine. The induction of structure caused by sodium dodecyl sulfate (SDS) binding was studied by capillary zone electrophoresis, circular dichroism, DOSY-NMR, and molecular dynamics simulations (MDS). In addition, we analyzed the strength of the interaction between a C18 RP-HPLC matrix and the peptides. The results presented here reveal that (a) critical elements in the sequence of the wild-type peptide stabilize a SDS/peptide supramolecular cluster; (b) the hydrophobic nature of the interaction between SDS molecules and the peptide constrains the ensemble of conformations; (c) nonspecific apolar surfaces are sufficient to stabilize peptide secondary structure. Remarkably, MDS shed light on a contact network formed by a limited number of SDS molecules that serves as a structural scaffold preserving the helical conformation of this module. This mechanism might prevail when a peptide with low helical propensity is involved in structure consolidation. We suggest that folding of peptides sharing this feature does not require a preformed tightly-packed protein core. Thus, the formation of specific tertiary interactions would be the consequence of peptide folding and not its cause. In this scenario, folding might be thought of as a process that includes unspecific rounds of structure stabilization guiding the protein to the native state.

Reaction Path Analysis from Potential Energy Contributions Using Forces: An Accessible Estimator of Reaction Coordinate Adequacy.

The calculation of potential energy and free-energy profiles along complex chemical reactions or rare event processes is of great interest because of their importance for many areas in chemistry, molecular biology, and material science. One typical way to generate these profiles is to add a bias potential to modify the energy surface, which can act on a selected degree of freedom in the system. However, in these cases, the quality of the result is strongly dependent on the selection of the degree of freedom over which this bias potential acts. The present work introduces a simple method for the analysis of the degree of freedom selected to describe a chemical process. The proposed methodology is based on the decomposition of contributions to the potential energy profiles by the integration of forces along a reaction path, which allows evaluating the different contributions to the energy change. This could be useful for discriminating the contributions to the energy arising from different regions of the system, which is particularly useful in systems with complex environments that must be represented using hybrid quantum mechanics/molecular mechanics schemes. Furthermore, this methodology allows in generating a quick and simple analysis of the degree of freedom which is used to describe the potential energy profile associated with the reactive process. This is computationally more accessible than the corresponding free-energy profile and can therefore be used as a simple estimator of reaction coordinate adequacy.

Transport and Spectroscopy in Conjugated Molecules: Two Properties and a Single Rationale.

In the context of electron dynamics simulations, when the charge density of a molecule is subject to a perturbation in the form of a short electric field pulse, density fluctuations develop in time. In the absence of dissipation, these oscillations continue indefinitely, reflecting the resonances of the electronic system; as a matter of fact, from the Fourier transform of the time dependent dipole arising from them, the absorption spectrum of the molecule can be calculated. Since these oscillations are the result of the electrons moving through the molecular structrure, it seems plausible that they carry information on the transport properties of the system. This is the idea explored in the present article for the case of conjugated polymers. Specifically, we depart from a nonequilibrium state with the charge concentrated on the ends of the molecule, and estimate the currents flowing back and forth during the evolution of electron dynamics simulations. These show that the charge oscillates between the sides of the polymer with the predominance of a frequency that is coincident with one of the main bands in the absorption spectrum, which can be ascribed to a charge transfer transition. Thus, from the charge transfer band frequency appearing in the absorption spectrum, the molecular conductance of a conjugated molecule can be calculated. Also interestingly, we find that, while a perturbation excites all resonances of an electronic system, the form in which this perturbation is applied can be manipulated to determine the relative manifestation of the response. The electric field pulse excites all resonances according to the transition dipole moment and is then appropriate to produce the absorption spectrum. A charge separated initial state, however, specifically stimulates the charge transfer mode and is then suitable to calculate transport properties. This allows us to propose a simple approach to obtain molecular conductances and tunneling decay constants in agreement with results from much more demanding electronic structure techniques.

Bond or cage effect: how nitrophorins transport and release nitric oxide.

Most blood-sucking insects possess salivary proteins which, upon injection into the victim's tissue, help them improve their feeding. One group of these salivary proteins takes advantage of the vasodilator properties of NO to perform this task. These proteins are the so-called nitrophorins (NPs). NPs are heme proteins that store and transport NO, which, when released in the victim's tissue, produces vasodilation and inhibition of blood coagulation. It has been proposed that NO binds tightly to NP at a low pH of around 5.6 and that once NPs are injected in the victims tissue, at a pH of approximately 7.4, a conformational change occurs which lowers NO affinity, allowing it to be released. In this work we have studied the NO release mechanism of NP4 at a molecular level using state of the art computer simulation techniques. We have used molecular dynamics (MD) simulations to study NP4 conformational dynamics at both pH values 5.6 and 7.4 and computed the corresponding free energy profile for NO release using a multiple steering molecular dynamics scheme. We also have used hybrid quantum mechanical/molecular mechanics (QM/MM) techniques to analyze the heme-NO structure and the Fe-NO bond strength in the different NP4 conformations. Our results provide the molecular basis to explain that NO escape from NP4 is determined by differential NO migration rates and not by a difference in the Fe-NO bond strength. In contrast to most heme proteins that control ligand affinity by modulating the bond strength to the iron, NP4 has evolved a cage mechanism that traps the NO at low pH and releases it upon cage opening when the pH rises.

Chemical Reactivity and Spectroscopy Explored From QM/MM Molecular Dynamics Simulations Using the LIO Code.

In this work we present the current advances in the development and the applications of LIO, a lab-made code designed for density functional theory calculations in graphical processing units (GPU), that can be coupled with different classical molecular dynamics engines. This code has been thoroughly optimized to perform efficient molecular dynamics simulations at the QM/MM DFT level, allowing for an exhaustive sampling of the configurational space. Selected examples are presented for the description of chemical reactivity in terms of free energy profiles, and also for the computation of optical properties, such as vibrational and electronic spectra in solvent and protein environments.

Role of Core Electrons in Quantum Dynamics Using TDDFT.

The explicit simulation of time dependent electronic processes requires computationally onerous routes involving the temporal integration of motion equations for the charge density. Efficiency optimization of these methods typically relies on increasing the integration time-step and on the reduction of the computational cost per step. The implicit representation of inner electrons by effective core potentials-or pseudopotentials-is a standard practice in localized-basis quantum-chemistry implementations to improve the efficiency of ground-state calculations, still preserving the quality of the output. This article presents an investigation on the impact that effective core potentials have on the overall efficiency of real time electron dynamics with TDDFT. Interestingly, the speedups achieved with the use of pseudopotentials in this kind of simulation are on average much more significant than in ground-state calculations, reaching in some cases a factor as large as 600×. This boost in performance originates from two contributions: on the one hand, the size of the density matrix, which is considerably reduced, and, on the other, the elimination of high-frequency electronic modes, responsible for limiting the maximum time-step, which vanish when the core electrons are not propagated explicitly. The latter circumstance allows for significant increases in time-step, that in certain cases may reach up to 3 orders of magnitude, without losing any relevant chemical or spectroscopic information.

Theoretical Insights into the Reaction and Inhibition Mechanism of Metal-Independent Retaining Glycosyltransferase Responsible for Mycothiol Biosynthesis.

Understanding enzymatic reactions with atomic resolution has proven in recent years to be of tremendous interest for biochemical research, and thus, the use of QM/MM methods for the study of reaction mechanisms is experiencing a continuous growth. Glycosyltransferases (GTs) catalyze the formation of glycosidic bonds, and are important for many biotechnological purposes, including drug targeting. Their reaction product may result with only one of the two possible stereochemical outcomes for the reacting anomeric center, and therefore, they are classified as either inverting or retaining GTs. While the inverting GT reaction mechanism has been widely studied, the retaining GT mechanism has always been controversial and several questions remain open to this day. In this work, we take advantage of our recent GPU implementation of a pure QM(DFT-PBE)/MM approach to explore the reaction and inhibition mechanism of MshA, a key retaining GT responsible for the first step of mycothiol biosynthesis, a low weight thiol compound found in pathogens like Mycobacterium tuberculosis that is essential for its survival under oxidative stress conditions. Our results show that the reaction proceeds via a front-side SNi-like concerted reaction mechanism (DNAN in IUPAC nomenclature) and has a 17.5 kcal/mol free energy barrier, which is in remarkable agreement with experimental data. Detailed analysis shows that the key reaction step is the diphosphate leaving group dissociation, leading to an oxocarbenium-ion-like transition state. In contrast, fluorinated substrate analogues increase the reaction barrier significantly, rendering the enzyme effectively inactive. Detailed analysis of the electronic structure along the reaction suggests that this particular inhibition mechanism is associated with fluorine's high electronegative nature, which hinders phosphate release and proper stabilization of the transition state.

A helix-coil transition induced by the metal ion interaction with a grafted iron-binding site of the CyaY protein family.

Iron-protein interactions are involved in electron transfer reactions. Alterations of these processes are present in a number of human pathologies; among them, in Friedreich's ataxia, in which a deficiency of functional frataxin, an iron-binding protein, leads to progressive neuromuscular degenerative disease. The putative iron-binding motif of acidic residues EExxED was selected from the first α-helical stretch of the frataxin protein family and grafted onto a foreign peptide scaffold corresponding to the C-terminal α-helix from E. coli thioredoxin. The resulting grafted peptide named GRAP was studied by applying experimental (circular dichroism, isothermal titration calorimetry, capillary zone electrophoresis, thermal denaturation, NMR) and computational approaches (docking, molecular dynamics simulations). Although isolated GRAP lacks a stable secondary structure in solution, when iron is added, the peptide acquires an α-helical structure. Here we have shown that the designed peptide is able to specifically bind Fe(3+) with a moderate affinity (KD = 1.9 ± 0.2 µM) and a 1 : 1 stoichiometry. Remarkably, the GRAP/Fe(3+) interaction is entropically driven (ΔH° = -1.53 ± 0.03 kcal mol(-1) and TΔS° = 6.26 kcal mol(-1)). Experiments and simulations indicate that Fe(3+) interacts with the peptide through three acidic side chains, inducing an α-helical conformation of the grafted motif. In addition, the acidic side chains involved undergo significant conformational rearrangements upon binding, as judged by the analysis of MDs. Altogether, these results contribute to an understanding of the iron-binding mechanisms in proteins and, in particular, in the case of human frataxin.

GPU Accelerated Implementation of Density Functional Theory for Hybrid QM/MM Simulations.

The hybrid simulation tools (QM/MM) evolved into a fundamental methodology for studying chemical reactivity in complex environments. This paper presents an implementation of electronic structure calculations based on density functional theory. This development is optimized for performing hybrid molecular dynamics simulations by making use of graphic processors (GPU) for the most computationally demanding parts (exchange-correlation terms). The proposed implementation is able to take advantage of modern GPUs achieving acceleration in relevant portions between 20 to 30 times faster than the CPU version. The presented code was extensively tested, both in terms of numerical quality and performance over systems of different size and composition.

QM-MM Investigation of the Reaction of Peroxynitrite with Carbon Dioxide in Water.

We have investigated the reaction of peroxynitrite with carbon dioxide in aqueous solution by means of combined quantum-classical (QM-MM) molecular dynamics simulations. In our QM-MM scheme, the reactant was modeled using density functional theory with a Gaussian basis set, and the solvent was described using the mean-field TIP4P force field. The free energy profile of this reaction has been computed using umbrella sampling and multiple steering molecular dynamics (MSMD) schemes. Umbrella sampling methods turned out to be much more efficient than MSMD schemes, due to the possibility of employing a combination of classical and QM-MM thermalization schemes. We found the presence of a significant barrier in the free energy profile associated with the reaction in solution, which is not present in vacuum, that may be ascribed to the significant charge redistribution upon reaction and the concomitant solvation pattern changes.