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A theoretical-computational approach is presented to characterize the temperature-dependent thermodynamics of protein folding. Making use of the Quasi-Gaussian Entropy (QGE) theory and temperature exchanged molecular dynamics (TREMD) simulations, a complete picture of the folding thermodynamics can be obtained. The strategy is applied to analyze the folding thermodynamics of a β -hairpin peptide, Peptide 1, the folding process of which was experimentally characterized by means of infrared spectroscopy. The results provided by the approach here presented very well reproduce the experimental results, showing that the methodology can be successfully utilized to investigate the thermodynamics of folding processes in a wide temperature range. [ABSTRACT FROM AUTHOR]

In this study, we present an extension of the theoretical-computational approach developed in our group and based on molecular dynamics simulations, quantum chemical calculations, perturbed matrix method, and essential dynamics analysis for taking into account the cybotactic effect in the computational modeling of absorption spectra of molecular systems in condensed phase. The low-energy UV-Vis spectra of para-nitroaniline in water, methanol, and in the presence of a zwitterionic micelle have been computationally addressed and compared to the experimental data. The approach, considering all the systematic errors deriving from the intrinsic limitations of the computational setup (force field, quantum chemical calculations, and the approximations of the method), satisfactorily reproduces the experimental spectral shifts and peaks shapes and provides a promising tool of investigation for reproducing spectral observables of very complex systems. [ABSTRACT FROM AUTHOR]

A benchmark biochemical reaction is here theoretically investigated by means of a perturbative approach in order to model each reaction step. The reaction is the flavin-indole electron transfer, involving also a spin-state relaxation of the ionic complex. The whole reaction path is modeled and the kinetics of the process is studied. The dipolar interaction between the two radicals is explicitly considered during the dynamic evolution of the system in order to investigate the proper conditions for the triplet-to-singlet transition to occur. [ABSTRACT FROM AUTHOR]

Graphical abstract: Ferrocene electronic spectra are calculated in solution with an original methodology. Results, in good agreement with experimental data, indicate that solvent nature does not heavily affect UV-spectra but is relevant for redox potential. Display Omitted Highlights: [•] The UV–Vis spectra of Ferrocene in different solvents have been calculated. [•] The Ferrocene/Ferricinium couple redox potential in the same solvents. [•] Change of the solvent only affect the redox potential. [ABSTRACT FROM AUTHOR]

Abstract: Firefly luciferin and its oxidated form, oxyluciferin, are two heterocyclic compounds involved in the enzymatic reaction, catalyzed by redox proteins called luciferases, which provides the bioluminescence in a wide group of arthropods. Whereas the electronic absorption spectra of d-luciferin in water at different pHs are known since 1960s, only recently reliable experimental electronic spectra of oxyluciferin have become available. In addition oxyluciferin is involved in a triple chemical equilibria (deprotonation of the two hydroxyl groups and keto-enol tautomerism of the 4-hydroxythiazole ring), that obligates to select during an experiment a predominant species, tuning pH or solvent polarity besides introducing chemical modifications. In this study we report the absorption spectra of luciferin and oxyluciferin in each principal chemical form, calculated by means of perturbed matrix method (PMM), which allowed us to successfully introduce the effect of the solvent on the spectroscopic absorption properties, and compare the result with available experimental data. [Copyright &y& Elsevier]

The free-energy profile and the classical kinetics of the heme carbomonoxide binding−unbinding reaction have been derived by means of a theoretical method for the separated chains of human (HbA) and Trematomus newnesi major component (HbTn) hemoglobin. The results reveal that the α- and β-chains of HbA have similar values of kinetic constants for the dissociation of the Fe−CO state, in agreement with experimental data. Comparisons of the present findings with the data obtained for the α- and β-chains of HbTn and with theoretical and experimental results previously collected on myoglobin provide a detailed picture of this important biochemical reaction in globins. The sequence and structural differences among the globins are not reflected in meaningful variations in the rate of CO dissociation. These data support the conclusion that the differences observed for the reaction with CO of globins, if any, involve the rate of ligand migration to the solvent, rather than the Fe−CO complex formation/rupture. Furthermore, our results agree with the recent discovery that globin family proteins exhibit common dynamics, thus confirming the observation that the dynamic properties of proteins are strongly related to their overall architecture. [ABSTRACT FROM AUTHOR]

Abstract: The unfolded- and folded-state infrared (IR) spectra of peptides studied to date show a common pattern, i.e., the amide I peak of the unfolded state is typically shifted toward higher frequencies with respect to the folded peak. Here, we study by means of a theoretical–computational method, the Perturbed Matrix Method (PMM), the IR spectra in the amide I region of two -hairpin peptides. The computed spectra are in good agreement with the experimental ones, thus providing an explanation of the physical origin underlying the differences of the unfolded- and folded-state spectra. [Copyright &y& Elsevier]

Abstract: In this letter we use X-ray scattering data of liquid water, as obtained by different experimental and theoretical-computational procedures, to address the problem of quantitative modeling of the scattering signal in liquids. In particular we investigate the accuracy of well optimized water models in reproducing top level X-ray experimental results and compare experimental data variations with the ones given by different theoretical-computational models. Results show that the experimental scattering data have an intrinsic noise which is comparable to the deviations of the theoretical-computational signals, hence suggesting that no reliable refinement based on scattering data is possible for such models. [Copyright &y& Elsevier]

Intramolecular charge transfer (ICT) of gaseous π-conjugated oligo-phenyleneethynylenes (OPE) induced by a homogeneous applied electric field has been theoretically investigated using a combined approach integrating molecular dynamics (MD) simulations and Perturbed Matrix Method calculations. In line with recent investigations, our results indicate the peculiar role of conformational transitions on OPE electronic properties which reflects on a strong temperature effect on ICT. Electron transfer reactions inducing chemical alteration on OPE, also taken into account in this study, revealed extremely important for explaining non-linear ICT effects and probably plays a central role in the mechanisms underlying molecular transport junctions. Our study further points out the necessity of using MD-based approach for modelling molecular electronics, even when relatively rigid molecular systems are concerned. [ABSTRACT FROM AUTHOR]

Recent work has shown that the nature of hydration of pure hydrophobic surfaces changes with the length scale considered: water hydrogen-bonding networks adapt to small exposed hydrophobic species, hydrating or ‘wetting’ them at relatively high densities, whereas larger hydrophobic areas are ‘dewetted’ [Chandler D (2005), Nature 29:640-647]. Here we determine whether this effect is also present in peptides by examining the folding of a β-hairpin (the 14-residue amyloidogenic prion protein H1 peptide), using microsecond time-scale molecular dynamics simulations. Two simulation models are compared, one explicitly including the water molecules, which may thus adapt locally to peptide configurations, and the other using a popular continuum approximation, the generalized Born/surface area implicit solvent model. The results obtained show that, in explicit solvent, peptide conformers with high solvent-accessible hydrophobic surface area indeed also have low hydration density around hydrophobic residues, whereas a concomitant higher hydration density around hydrophilic residues is observed. This dewetting effect stabilizes the fully folded β-hairpin state found experimentally. In contrast, the implicit solvent model destabilizes the fully folded hairpin, tending to cluster hydrophobic residues regardless of the size of the exposed hydrophobic surface. Furthermore, the rate of the conformational transitions in the implicit solvent simulation is almost doubled with respect to that of the explicit solvent. The results suggest that dehydration-driven solvent exposure of hydrophobic surfaces may be a significant factor determining peptide conformational equilibria. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we address the problem of the role and relevance of the aqueous environment configurational sampling on acetone electronic properties: the (vertical) absorption spectrum and corresponding excitation Helmholtz free energy. By comparing the results obtained by applying the perturbed matrix method (PMM) on molecular dynamics (MD) trajectories of different sampling efficiency, we specifically quantify the effects of the phase space sampling on acetone vertical electronic excitations. Results confirm that PMM provides an accurate and physically consistent description of the electronic excitation processes and show the crucial importance of an extended configurational sampling of the solvent environment in order to obtain a reliable (chromophore) absorption behaviour. [Copyright &y& Elsevier]

Abstract: By means of principle component analysis of the local density fluctuations, as revealed by molecular dynamics simulations, we obtain detailed information on the relevant local density fluxes and corresponding spatial patterns. [Copyright &y& Elsevier]

The Azotobacter vinelandii rhodanese is a 31 kDa sulfurtransferase protein that catalyzes the transfer of sulfur atom from thiosulfate to cyanide in the detoxification process from cyanide and is able to insert sulfur atom in the iron–sulfur cluster. A study of the uniformly 15N isotopic labeling by high resolution NMR, before obtaining the backbone sequential assignment, has been carried out. The sulfur loaded and the sulfur discharged forms of the enzyme show very similar HSQC spectra with a good spectral dispersion. Few resonances show changes in chemical shift between the two forms. Relaxation parameters T1, T2 and 1H–15N NOE of all amide nitrogen atoms, as well as isotope exchange kinetics, show that the two forms exhibit the same global correlation time and hydrodynamic properties. In parallel, essential dynamics studies show that formation and discharging of catalytic cysteine persulfide group has no significant impact on the overall conformation of the protein. These results, taken together, give a clearcut answer to the question if the catalytic mechanism of the enzyme involves a change in the conformation and/or in the mutual orientation of the two domains. On the contrary these results clearly indicate that upon the catalytic mechanism the two domains of the protein behave as a unique fold. [Copyright &y& Elsevier]

A theoretical-computational procedure, recently proposed for modelling Vibrational Energy Relaxation (VER) processes of a molecule (Quantum Center, QC) embedded in a complex atomic-molecular system, is extended and applied for analyzing in detail the features of the QC density matrix (DM) temporal evolution. The results, obtained using aqueous azide ion as a case study, show the total lack of coherence in the DM, when the system is prepared to be initially in a pure vibrational eigenstate. This finding is fully in line with the statistical interpretation of the process typically adopted also in the experimental studies where the relaxation processes are all described within the typical schemes of chemical kinetics. Consistently, when the initial vibrational state corresponds to an eigenstate mixture, although initially coherent, the DM relaxes to a fully incoherent condition with a mean lifetime related to the one of the diagonal elements relaxation. These specific DM features turn out to be essentially governed by the thermal equilibrium condition of the atomic-molecular classical coordinates which drive the ensemble of the quantum-trajectories toward the observed statistical regime. Finally, from the analysis of a single long timescale quantum vibrational trajectory it also clearly emerges its ergodic behaviour., (© 2024 Wiley-VCH GmbH.)

In a recent paper, we proposed a scheme to describe the relaxation mechanism of the excited Indole in aqueous solution, involving the fluctuations among the diabatic electronic states 1 L b , 1 L a and 1 πσ ∗ . Such a theoretical and computational model reproduced accurately the available experimental data at room temperature. Following these results, in the present work, we model the complex temperature dependence of the fluorescence properties of Indole in aqueous solution, with results further validating the proposed relaxation scheme. This scheme is able to explain the temperature effects on the fluorescence behavior indicating the water fluctuations as the main cause of (i) the stabilization of the dark state ( 1 πσ ∗ ) and (ii) the increase in temperature of the kinetics of the irreversible transition towards such a state., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier B.V. All rights reserved.)

The hydrolysis of the phosphodiester bond is an important chemical reaction involved in several biological processes. Here, we study the cleavage of this bond by means of a theoretical-computational method in a model system, the dineopentyl phosphate. By such an approach, we reconstructed the kinetics and related thermodynamics of this chemical reaction along an isochore. In particular, we evaluated the kinetic constants of all the reaction steps within a wide range of temperatures, mostly corresponding to conditions where no experimental measures are available due to the extremely slow kinetics. Our results, in good agreement with the experimental data, show the robustness of our theoretical-computational methodology which can be easily extended to more complex systems., (© 2024 Wiley-VCH GmbH.)

In this paper, we apply a theoretical model for fluid state thermodynamics to investigate simulated water in supercooled conditions. This model, which we recently proposed and applied to sub- and super-critical fluid water [Zanetti-Polzi et al., J. Chem. Phys. 156(4), 44506 (2022)], is based on a combination of the moment-generating functions of the enthalpy and volume fluctuations as provided by two gamma distributions and provides the free energy of the system as well as other relevant thermodynamic quantities. The application we make here provides a thermodynamic description of supercooled water fully consistent with that expected by crossing the liquid-liquid Widom line, indicating the presence of two distinct liquid states. In particular, the present model accurately reproduces the Widom line temperatures estimated with other two-state models and well describes the heat capacity anomalies. Differently from previous models, according to our description, a cluster of molecules that extends beyond the first hydration shell is necessary to discriminate between the statistical fluctuation regimes typical of the two liquid states., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

In this paper, we reconstruct in detail the dynamics of the emitting electronic excited state of aqueous indole, investigating its relaxation mechanism and kinetics to be related to the time-dependent fluorescence signal. Taking advantage of the results shown in a very recent paper, we were able to model the relaxation process in solution in terms of the transitions between two gas-phase singlet electronic states ( 1 L a and 1 L b ), subsequently irreversibly relaxing to the gas-phase singlet dark state ( 1 πσ*). A comparison of the results with the available experimental data shows that the relaxation mechanism we obtain by our theoretical-computational model is reliable, reproducing rather accurately all the experimental observables.

The electronic circular dichroism (ECD) spectra of aqueous d-glucose and d-galactose were modeled using a theoretical-computational approach combining molecular dynamics (MD) simulations and perturbed matrix method (PMM) calculations, hereafter termed MD-PMM. The experimental spectra were reproduced with a satisfactory accuracy, confirming the good performances of MD-PMM in modeling different spectral features in complex atomic-molecular systems, as already reported in previous studies. The underlying strategy of the method was to perform a preliminary long timescale MD simulation of the chromophore followed by the extraction of the relevant conformations through essential dynamics analysis. On this (limited) number of relevant conformations, the ECD spectrum was calculated via the PMM approach. This study showed that MD-PMM was able to reproduce the essential features of the ECD spectrum (i.e., the position, the intensity, and the shape of the bands) of d-glucose and d-galactose while avoiding the rather computationally expensive aspects, which were demonstrated to be important for the final outcome, such as (i) the use of a large number of chromophore conformations; (ii) the inclusion of quantum vibronic coupling; and (iii) the inclusion of explicit solvent molecules interacting with the chromophore atoms within the chromophore itself (e.g., via hydrogen bonds).

(1) Background: the theoretical modelling of reactions occurring in liquid phase is a research line of primary importance both in theoretical-computational chemistry and in the context of organic and biological chemistry. Here we present the modelling of the kinetics of the hydroxide-promoted hydrolysis of phosphoric diesters. (2) Method: the theoretical-computational procedure involves a hybrid quantum/classical approach based on the perturbed matrix method (PMM) in conjunction with molecular mechanics. (3) Results: the presented study reproduces the experimental data both in the rate constants and in the mechanistic aspects (C-O bond vs. O-P bond reactivity). The study suggests that the basic hydrolysis of phosphodiesters occurs through a concerted ANDN mechanism, with no formation of penta-coordinated species as reaction intermediates. (4) Conclusions: the presented approach, despite the approximations, is potentially applicable to a large number of bimolecular transformations in solution and therefore leads the way to a fast and general method to predict the rate constants and reactivities/selectivities in complex environments.

Quantum mechanical/molecular mechanics (QM/MM) methods are important tools in molecular modeling as they are able to couple an extended phase space sampling with an accurate description of the electronic properties of the system. Here, we describe a Python software package, called PyMM, which has been developed to apply a QM/MM approach, the perturbed matrix method, in a simple and efficient way. PyMM requires a classical atomic trajectory of the whole system and a set of unperturbed electronic properties of the ground and electronic excited states. The software output includes a set of the most common perturbed properties, such as the electronic excitation energies and the transitions dipole moments, as well as the eigenvectors describing the perturbed electronic states, which can be then used to estimate whatever electronic property. The software is composed of a simple and complete command-line interface, a set of internal input validation, and three main analyses focusing on (i) the perturbed eigenvector behavior, (ii) the calculation of the electronic absorption spectrum, and (iii) the estimation of the free energy differences along a reaction coordinate.

A theoretical-computational procedure based on the quasi-Gaussian entropy (QGE) theory and molecular dynamics (MD) simulations is proposed for the calculation of thermodynamic properties for molecular and supra-molecular species in the gas phase. The peculiarity of the methodology reported in this study is its ability to construct an analytical model of all the most relevant thermodynamic properties, even within a wide temperature range, based on a practically automatic sampling of the entire conformational repertoire of highly flexible systems, thereby bypassing the need for an explicit search for all possible conformers/rotamers deemed relevant. In this respect, the reliability of the presented method mainly depends on the quality of the force field used in the MD simulations and on the ability to discriminate in a physically coherent way between semi-classical and quantum degrees of freedom. The method was tested on six model systems (n-butane, n-butane, n-octanol, octadecane, 1-butyl-3-methylimidazolium hexafluorophosphate and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic pairs), which, being experimentally characterized and already addressed by other theoretical-computational methods, were considered as particularly suitable to allow us to evaluate the method's accuracy and efficiency, bringing out advantages and possible drawbacks. The results demonstrate that such a physically coherent yet relatively simple method can represent a further valid computational tool that is alternative and complementary to other extremely efficient computational methods, as it is particularly suited for addressing the thermodynamics of gaseous systems with a high conformational complexity over a large range of temperature.

In this paper, we extend the previously described general model for charge transfer reactions, introducing specific changes to treat the hopping between energy minima of the electronic ground state (i.e., transitions between the corresponding vibrational ground states). We applied the theoretical-computational model to the charge transfer reactions in DNA molecules which still represent a challenge for a rational full understanding of their mechanism. Results show that the presented model can provide a valid, relatively simple, approach to quantitatively study such reactions shedding light on several important aspects of the reaction mechanism.

We characterize the folding-unfolding thermodynamics of two mutants of the miniprotein Trp-cage by combining extended molecular dynamics simulations and an advanced statistical-mechanical-based approach. From a set of molecular dynamics simulations in an explicit solvent performed along a reference isobar, we evaluated the structural and thermodynamic behaviors of a mesophilic and a thermophilic mutant of the Trp-cage and their temperature dependence. In the case of the thermophilic mutant, computational data confirm that our theoretical-computational approach is able to reproduce the available experimental estimate with rather good accuracy. On the other hand, the mesophilic mutant does not show a clear two-state (folded and unfolded) behavior, preventing us from reconstructing its thermodynamics; thus, an analysis of its structural behavior along a reference isobar is presented. Our results show that an extended sampling of these kinds of systems coupled to an advanced statistical-mechanical-based treatment of the data can provide an accurate description of the folding-unfolding thermodynamics along a reference isobar, rationalizing the discrepancies between the simulated and experimental systems., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)

We propose in this paper a theoretical model for fluid state thermodynamics based on modeling the fluctuation distributions and, hence, the corresponding moment generating functions providing the free energy of the system. Using the relatively simple and physically coherent gamma model for the fluctuation distributions, we obtain a complete theoretical equation of state, also giving insight into the statistical/molecular organization and phase or pseudo-phase transitions occurring under the sub- and super-critical conditions, respectively. Application to sub- and super-critical fluid water and a comparison with the experimental data show that this model provides an accurate description of fluid water thermodynamics, except close to the critical point region where limited but significant deviations from the experimental data occur. We obtain quantitative evidence of the correspondence between the sub- and super-critical thermodynamic behaviors, with the super-critical water pseudo-liquid and pseudo-gas phases being the evolution of the sub-critical water liquid and gas phases, respectively. Remarkably, according to our model, we find that for fluid water the minimal subsystem corresponding to either the liquid-like or the gas-like condition includes an infinite number of molecules in the sub-critical regime (providing the expected singularities due to macroscopic phase transitions) but only five molecules in the super-critical regime (coinciding with the minimal possible hydrogen-bonding cluster), thus suggesting that the super-critical regime be characterized by the coexistence of nanoscopic subsystems in either the pseudo-liquid or the pseudo-gas phase with each subsystem fluctuating between forming and disrupting the minimal hydrogen-bonding network.

The stationary and time-dependent infrared spectrum (IR) of the CO stretching mode (ν CO ) in carboxymyoglobin (MbCO), a longstanding problem of biophysical chemistry, has been modeled through a theoretical-computational method specifically designed for simulating quantum observables in complex atomic-molecular systems and based on a combined application of long time scale molecular dynamics simulations and quantum-chemical calculations. This study is basically focused on two aspects: (i) the origin of the stationary IR substates (termed as A 0 , A 1 , and A 3 ) and (ii) the modeling and the interpretation of the ν CO energy relaxation. The results, strengthened by a more than satisfactory agreement with the experimental data, concisely indicate that (i) the conformational His64-FeCO relevant substates, i.e., characterized by the formation-disruption of the H-bond between the above moieties, are the main responsible of the presence of two distinct and well separated ( A 0 and A 1 / A 3 ) spectroscopic regions; (ii) the characteristic bimodal shape of the A 1 / A 3 spectral region, according to our model, is the result of the fluctuation of the electric field pattern as provided by the protein-solvent framework perturbing the bound His64-CO-Heme complex; and (iii) the electric field pattern, in conjunction with the relatively high density of MbCO vibrational states, is also the main determinant of the ν CO energy relaxation, characterizing its kinetic efficiency.

The most intriguing hypothesis explaining many water anomalies is a metastable liquid-liquid phase transition (LLPT) at high pressure and low temperatures, experimentally hidden by homogeneous nucleation. Recent infrared spectroscopic experiments showed that upon addition of hydrazinium trifluoroacetate to water, the supercooled ionic solution undergoes a sharp, reversible LLPT at ambient pressure, possible offspring of that in pure water. Here, we calculate the temperature-dependent signature of the OH-stretching band, reporting on the low/high density phase of water, in neat water and in the same experimentally investigated ionic solution. The comparison between the infrared signature of the pure liquid and that of the ionic solution can be achieved only computationally, providing insight into the nature of the experimentally observed phase transition and allowing us to investigate the effects of ionic compounds on the high to low density supercooled liquid water transition. We show that the experimentally observed crossover behavior in the ionic solution can be reproduced only if the phase transition between the low- and high-density liquid states of water is coupled to a mixing-unmixing transition between the water component and the ions: at low temperatures, water and ions are separated and the water component is a low density liquid. At high temperatures, water and ions get mixed and the water component is a high-density liquid. The separation at low temperatures into ion-rich and ion-poor regions allows unveiling the polyamorphic nature of liquid water, leading to a crossover behavior resembling that observed in supercooled neat water under high pressure.

Here, we present the theoretical-computational modeling of the oxidation properties of four DNA nucleosides and nucleotides and a set of dinucleotides in solutions. Our estimates of the vertical ionization energies and reduction potentials, close to the corresponding experimental data, show that an accurate calculation of the molecular electronic properties in solutions requires a proper treatment of the effect of the environment. In particular, we found that the effect of the environment is to stabilize the oxidized state of the nucleobases resulting in a remarkable reduction-up to 6.6 eV-of the energy with respect to the gas phase. Our estimates of the aqueous and gas-phase vertical ionization energies, in good agreement with photoelectron spectroscopy experiments, also show that the effect on the reduction potential of the phosphate group and of the additional nucleotide in dinucleotides is rather limited.

The ionization state of titratable amino acids strongly affects proteins structure and functioning in a large number of biological processes. It is therefore essential to be able to characterize the p K a of ionizable groups inside proteins and to understand its microscopic determinants in order to gain insights into many functional properties of proteins. A big effort has been devoted to the development of theoretical approaches for the prediction of deprotonation free energies, yet the accurate theoretical/computational calculation of p K a values is recognized as a current challenge. A methodology based on a hybrid quantum/classical approach is here proposed for the computation of deprotonation free energies. The method is applied to calculate the p K a of formic acid, methylammonium, and methanethiol, providing results in good agreement with the corresponding experimental estimates. The p K a is also calculated for aspartic acid and lysine as single residues in solution and for three aspartic/glutamic acids inside a well-characterized protein: hen egg white lysozyme. While for small molecules the method is able to deal with multiple protonation states of all titratable groups, this becomes computationally very expensive for proteins. The calculated p K a values for the single amino acids (except for the zwitterionic aspartic acid) and inside the protein display a systematic shift with respect to the experimental values that suggests that the fine balance between hydrophobic and polar interactions might be not accurately reproduced by the usual classical force-fields, thus affecting the computation of deprotonation free energies. The calculated p K a shifts inside the protein are in good agreement with the corresponding experimental ones (within 1 p K a unit), well reproducing the p K a changes due to the protein environment even in the case of large p K a shifts.

Here we present a computational approach based on molecular dynamics (MD) simulation to study the dependence of the protein hydration-shell density on the size of the protein molecule. The hydration-shell density of eighteen different proteins, differing in size, shape and function (eight of them are antifreeze proteins), is calculated. The results obtained show that an increase in the hydration-shell density, relative to that of the bulk, is observed (in the range of 4-14%) for all studied proteins and that this increment strongly correlates with the protein size. In particular, a decrease in the density increment is observed for decreasing protein size. A simple model is proposed in which the basic idea is to approximate the protein molecule as an effective ellipsoid and to partition the relevant parameters, i.e. the solvent-accessible volume and the corresponding solvent density, into two regions: inside and outside the effective protein ellipsoid. It is found that, within the model developed here, almost all of the hydration-density increase is located inside the protein ellipsoid, basically corresponding to pockets within, or at the surface of the protein molecule. The observed decrease in the density increment is caused by the protein size only and no difference is found between antifreeze and non-antifreeze proteins.

Infrared (IR) spectroscopy is commonly utilized for the investigation of protein structures and protein-mediated processes. While the amide I band provides information on protein secondary structures, amino acid side chains are used as IR probes for the investigation of protein reactions, such as proton pumping in rhodopsins. In this work, we calculate the IR spectra of the solvated aspartic acid, with both zwitterionic and protonated backbones, and of a capped form, i.e. mimicking the aspartic acid residue in proteins, by means of molecular dynamics (MD) simulations and the perturbed matrix method (PMM). This methodology has already proved its good modeling capabilities for the amide I mode and is here extended to the treatment of protein side chains. The computed side chain vibrational signal is in very good agreement with the experimental one, well reproducing both the peak frequency position and the bandwidth. In addition, the MD-PMM approach proposed here is able to reproduce the small frequency shift (5-10 cm -1 ) experimentally observed between the protonated and zwitterionic forms, showing that such a shift depends on the excitonic coupling between the modes localized on the side chain and on the backbone in the protonated form. The spectrum of the capped form, in which the amide I band is also calculated, agrees well with the corresponding experimental spectrum. The reliable calculation of the vibrational bands of carboxyl-containing side chains provides a useful tool for the interpretation of experimental spectra.

In this paper we report the description, implementation and application of a kinetic model designed for describing the Covid-19 epidemic spread in Italy and Germany in the period between February and June 2020 coinciding with the beginning of the statistical regime of the epidemic spread and the application of restrictive government measures aimed at its containment. The model, which makes use of a limited number of parameters, in spite of its simplicity is able of capturing the essential physical features of the epidemic spread highlighting the essential role of the restrictive measures and in particular the timeliness of their application for the containment of the most dramatic consequences. This work also confirms how the epidemic spread, if considered during its statistical-regime evolution, can be properly described - and hence probably better understood - using languages and methodologies typically adopted for chemical processes, such as the Mass Action Law and Chemical Kinetics., (Copyright: © 2016 by Fabrizio Serra editore, Pisa · Roma.)

Here we present a theoretical-computational study of the thermodynamics and kinetics of an aqueous Trp-cage, a 20-residue long miniprotein. The combined use of accurate molecular dynamics simulations rigorously reconstructing the proper isobar of the system and a sound statistical-mechanical model provides a quantitative description of the temperature dependence of the relevant physical-chemical properties and insights into the detailed mechanisms regulating the folding-unfolding properties.

In this paper we show how it is possible to treat the quantum vibrational relaxation of a chromophore, embedded in a complex atomic-molecular environment, via the explicit solution of the time-dependent Schroedinger equation once using a proper separation between quantum and semiclassical degrees of freedom. The rigorous theoretical framework derived, based on first principles and making use of well defined approximations/assumptions, is utilized to construct a general model for the kinetics of the vibrational relaxation as obtained by the direct evaluation of the density matrix for all the relevant quantum state transitions. Application to (deuterated) N-methylacetamide (the typical benchmark used as a model for the amino acids) shows that the obtained theoretical-computational approach captures the essential features of the experimental process, unveiling the basic relaxation mechanism involving several vibrational state transitions.

Some years ago we developed a theoretical-computational hybrid quantum/classical methodology, the Perturbed Matrix Method (PMM), to be used in conjunction with molecular dynamics simulations for the investigation of chemical processes in complex systems, that proved to be a valuable tool for the simulation of relevant experimental observables, e.g., spectroscopic signals, reduction potentials, kinetic constants. In typical PMM calculations the quantum sub-part of the system, the quantum centre, is embedded into an external perturbing field providing a perturbation operator explicitly calculated up to the dipolar terms. In this paper we further develop the PMM approach, beyond the dipolar terms in the perturbation operator expansion, by including explicitly the quadrupolar terms and/or by expanding the perturbation operator on each atom of the quantum centre. These different levels of the perturbation operator expansion, providing different levels of theory, have been tested by calculating three different spectroscopic observables: the spectral signal of liquid water and aqueous benzene due to the lowest energy electronic excitation and the infrared amide I band of aqueous trans-N-methylacetamide. All the systems tested show that, even though the previous PMM level of theory is already capable of reproducing the main features of the spectral signal, the higher levels of theory improve the quantitative reproduction of the spectral details.

For small molecule reaction kinetics, computed reaction coordinates often mimic experimentally measured observables quite accurately. Although nowadays simulated and measured biomolecule kinetics can be compared on the same time scale, a gap between computed and experimental observables remains. Here we directly compared temperature-jump experiments and molecular dynamics simulations of protein folding dynamics using the same observable: the time-dependent infrared spectrum. We first measured the stability and folding kinetics of the fastest-folding β-protein, the GTT35 WW domain, using its structurally specific infrared spectrum. The relaxation dynamics of the peptide backbone, β-sheets, turn, and random coil were measured independently by probing the amide I' region at different frequencies. Next, the amide I' spectra along folding/unfolding molecular dynamics trajectories were simulated by accurate mixed quantum/classical calculations. The simulated time dependence and spectral amplitudes at the exact experimental probe frequencies provided relaxation and folding rates in agreement with experimental observations. The calculations validated by experiment yield direct structural evidence for a rate-limiting reaction step where an intermediate state with either the first or second hairpin is formed. We show how folding switches from a more homogeneous (apparent two-state) process at high temperature to a more heterogeneous process at low temperature, where different parts of the WW domain fold at different rates.

In this paper we present a theoretical-computational methodology specifically aimed at describing processes involving internal conversion or intersystem crossing, from atomistic (semiclassical) simulations and, hence, very suitable for treating complex atomic-molecular systems. The core of the presented approach is the evaluation of the diabatic perturbed energy surfaces of a portion of the whole system, treated at the quantum level and therefore preventively selected, in semi-classical interaction with the atomic-molecular environment. Subsequently, the estimation of the coupling between the diabatic surfaces and the inclusion of the obtained observables within a properly designed kinetic model allows the reconstruction of the whole phenomenology directly comparable to the experimental (typically kinetic) data. Application to two systems has demonstrated that the proposed approach can represent a valuable tool, somewhat complementary to other methods based on explicit quantum-dynamical approaches, for the theoretical-computational investigations of large and complex atomic-molecular systems., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

We present here the calculation of the absorption spectrum of riboflavin in acetonitrile and dimethyl sulfoxide using a hybrid quantum/classical approach, namely the perturbed matrix method, based on quantum mechanical calculations and molecular dynamics simulations. The calculated spectra are compared to the absorption spectrum of riboflavin previously calculated in water and to the experimental spectra obtained in all three solvents. The experimentally observed variations in the absorption spectra upon change of the solvent environment are well reproduced by the calculated spectra. In addition, the nature of the excited states of riboflavin interacting with different solvents is investigated, showing that environment effects determine a recombination of the gas-phase electronic states and that such a recombination is strongly affected by the polarity of the solvent inducing significant changes in the absorption spectra., (Copyright © 2017 Elsevier B.V. All rights reserved.)

Cyclin-dependent kinases (CDKs) are enzymes involved in crucial cellular processes. Their biological activity is directly linked to their high conformational variability, which involves large protein conformational rearrangements. We present here the application of an enhancing sampling technique to the study of conformational transitions between the open and closed state of CDKs. The analysis of the conformational intermediates supports the idea that the process is regulated by two important protein regions, which sequentially rearrange in order to allow the protein to reach its final conformation. Furthermore, the two paths involve additional (minor) protein rearrangements which are specific to the paths. Our results show that our procedure can provide reasonable transition pathways between the two protein forms at a very reduced computational cost. The robustness and the simplicity of our approach make it of general application to describe virtually any macromolecular conformational transitions.

A combined theoretical-experimental study of the hyperchromic effect as occurring in the denaturation of a double stranded polyA-polyT is presented. Our theoretical/computational procedure allows us to reproduce the essential features of the experimental spectra and to characterize those molecular interactions responsible for the changes in the UV absorbance. We found that although excitonic intrastrand interactions strongly affect the absorbance, they are almost fully maintained in the single-stranded DNA. Our data indicate that hyperchromic effect originates from the higher delocalization of the excitonic states in the denaturated DNA with respect to the double-stranded conformation.

Infrared spectroscopy has long provided a means to estimate the secondary structure of proteins and peptides. In particular, the vibrational spectra of the amide I' band have been widely used for this purpose as the frequency positions of the amide I' bands are related to the presence of specific secondary structures. Here, we calculate the amide I' IR spectra of polylysine in aqueous solution in its three secondary structure states, i.e., α-helix, β-sheet, and random coil, by means of a mixed quantum mechanics/molecular dynamics (QM/MD) theoretical-computational methodology based on the perturbed matrix method (PMM). The computed spectra show a good agreement with the experimental ones. Although our calculations confirm the importance of the excitonic coupling in reproducing important spectral features (e.g., the width of the absorption band), the frequency shift due to secondary-structure changes is also well reproduced without the inclusion of the excitonic coupling, pointing to a role played by the local environment. Concerning the β-conformation spectrum, which is characterized by a double-peak amide I' band due to excitonic coupling, our results indicate that it does not correspond to a generic antiparallel β-sheet (e.g., of the typical size present in native proteins) but is rather representative of extended β-structures, which are common in β-aggregates. Moreover, we also show that the solvent has a crucial role in the shape determination of the β-conformation amide I' band and in particular in the disappearance of the high-frequency secondary peak in the case of small sheets (e.g., 6-stranded)., (© 2012 American Chemical Society)

Quantitative characterization of quantum states in complex molecular systems is a rather complicated task because of the necessity of maintaining the pure quantum definition of a state interacting with a configurationally complex molecular environment. Unfortunately, many of the "observables" that are of interest for a chemist, typically dealing with "complex objects", belong to the above class and their theoretical modeling may represent a hard task. In this respect, we have developed a new theoretical methodology, "perturbed matrix method", essentially based on the perturbation theory whose main aim is the characterization of the quantum states of a predefined portion of a complex molecular system, e.g., a solute, classically interacting with the environment, e.g., the solvent. This method has been used in this study to systematically characterize, for the first time and in conjunction with experimental observations, the intrinsic nature of pyrene whose vibrational and electronic states are highly sensitive to the nature of molecular environment. More precisely, pyrene shows a strong alteration of spectral intensities upon modification of polarity of the solvent. This property has been extensively used in many experimental studies and has been interpreted in the present study by characterizing pyrene electronic states as fluctuating states strictly connected to the polarity and the fluctuations of the surrounding medium. A correct theoretical modeling has been also obtained and commented for the vertical transitions in different media and also for the vibronic structure for the first transition in water.

By using multiple (independent) molecular dynamics (MD) trajectories (about 500 ns in total) of photolized carbon monoxide (CO) within solvated myoglobin, a quantitative description of CO migration and corresponding kinetics is obtained. MD results combined with previously reported quantum mechanical calculations on the CO-heme binding-unbinding reaction step in myoglobin allowed construction of a detailed quantitative model, shedding light on the kinetic mechanism and relevant steps of CO migration and geminate binding. Finally, the obtained (unbiased) theoretical-computational model is critically compared with the available computational and experimental data for myoglobin in solution.