Modeling quantum vibrational excitations in condensed-phase molecular systems

On the Statistical Regime, Coherence versus Incoherence and Ergodicity of Quantum Vibrational Trajectories in Soft Condensed Molecular Systems

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.

Alternative Fast and Slow Primary Charge-Separation Pathways in Photosystem II

Photosystem-II (PSII) is a multi-subunit protein complex that harvests sunlight to perform oxygenic photosynthesis. Initial light-activated charge separation takes place at a reaction centre consisting of four chlorophylls and two pheophytins. Understanding the processes following light excitation remains elusive due to spectral congestion, the ultrafast nature, and multi-component behaviour of the charge-separation process. Here, using advanced computational multiscale approaches which take into account the large-scale configurational flexibility of the system, we identify two possible primary pathways to radical-pair formation that differ by three orders of magnitude in their kinetics. The fast (short-range) pathway is dominant, but the existence of an alternative slow (long-range) charge-separation pathway hints at the evolution of redundancy that may serve other purposes, adaptive or protective, related to formation of the unique oxidative species that drives water oxidation in PSII.

A Simplified Treatment for Efficiently Modeling the Spectral Signal of Vibronic Transitions: Application to Aqueous Indole

In this paper, we introduce specific approximations to simplify the vibronic treatment in modeling absorption and emission spectra, allowing us to include a huge number of vibronic transitions in the calculations. Implementation of such a simplified vibronic treatment within our general approach for modelling vibronic spectra, based on molecular dynamics simulations and the perturbed matrix method, provided a quantitative reproduction of the absorption and emission spectra of aqueous indole with higher accuracy than the one obtained when using the existing vibronic treatment. Such results, showing the reliability of the approximations employed, indicate that the proposed method can be a very efficient and accurate tool for computational spectroscopy.

Stationary and Time-Dependent Carbon Monoxide Stretching Mode Features in Carboxy Myoglobin: A Theoretical-Computational Reappraisal

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 A₀, A₁, and A₃) 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 (A₀ and A₁/A₃) spectroscopic regions; (ii) the characteristic bimodal shape of the A₁/A₃ 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.

A computational insight into the relationship between side chain IR line shapes and local environment in fibril-like structures

Infrared spectroscopy is a widely used technique to characterize protein structures and protein mediated processes. While the amide I band provides information on proteins' secondary structure, amino acid side chains are used as infrared probes for the investigation of protein reactions and local properties. In this paper, we use a hybrid quantum mechanical/classical molecular dynamical approach based on the perturbed matrix method to compute the infrared band due to the C=O stretching mode of amide-containing side chains. We calculate, at first, the infrared band of zwitterionic glutamine in water and obtain results in very good agreement with the experimental data. Then, we compute the signal arising from glutamine side chains in a microcrystal of the yeast prion Sup35-derived peptide, GNNQQNY, with a fibrillar structure. The infrared bands obtained by selective isotopic labeling of the two glutamine residues, Q4 and Q5, of each peptide were experimentally used to investigate the local hydration in the fibrillar microcrystal. The experimental spectra of the two glutamine residues, which experience different hydration environments, feature different spectral signals that are well reproduced by the corresponding calculated spectra. In addition, the analysis of the simulated spectra clarifies the molecular origin of the experimentally observed spectroscopic differences that arise from the different local electric field experienced by the two glutamine residues, which is, in turn, determined by a different hydrogen bonding pattern.

A Not Obvious Correlation Between the Structure of Green Fluorescent Protein Chromophore Pocket and Hydrogen Bond Dynamics: A Choreography From ab initio Molecular Dynamics

The Green Fluorescent Protein (GFP) is a widely studied chemical system both for its large amount of applications and the complexity of the excited state proton transfer responsible of the change in the protonation state of the chromophore. A detailed investigation on the structure of the chromophore environment and the influence of chromophore form (either neutral or anionic) on it is of crucial importance to understand how these factors could potentially influence the protein function. In this study, we perform a detailed computational investigation based on the analysis of ab-initio molecular dynamics simulations, to disentangle the main structural quantities determining the fine balance in the chromophore environment. We found that specific hydrogen bonds interactions directly involving the chromophore (or not), are correlated to quantities, such as the volume of the cavity in which the chromophore is embedded and that it is importantly affected by the chromophore protonation state. The cross-correlation analysis performed on some of these hydrogen bonds and the cavity volume, demonstrates a direct correlation among them and we also identified the ones specifically involved in this correlation. We also found that specific interactions among residues far in the space are correlated, demonstrating the complexity of the chromophore environment and that many structural quantities have to be taken into account to properly describe and understand the main factors tuning the active site of the protein. From an overall evaluation of the results obtained in this work, it is shown that the residues which a priori are perceived to be spectators play instead an important role in both influencing the chromophore environment (cavity volume) and its dynamics (cross-correlations among spatially distant residues).

Multiresolution continuous wavelet transform for studying coupled solute-solvent vibrations via ab initio molecular dynamics

Vibrational analysis in solution and the theoretical determination of infrared and Raman spectra are of key importance in many fields of chemical interest. Vibrational band dynamics of molecules and their sensitivity to the environment can also be captured by these spectroscopies in their time dependent version. However, it is often difficult to provide an interpretation of the experimental data at the molecular scale, such as molecular mechanisms or the processes hidden behind them. In this work, we present a theoretical-computational protocol based on ab initio molecular dynamics simulations and a combination of normal-like (generalized) mode analysis of solute-solvent clusters with a wavelet transform, for the first time. The case study is the vibrational dynamics of N-methyl-acetamide (NMA) in water solution, a well-known model of hydration of peptides and proteins. Amide modes are typical bands of peptide and protein backbone, and their couplings with the environment are very challenging in terms of the accurate prediction of solvent induced intensity and frequency shifts. The contribution of water molecules surrounding NMA to the composition of generalized and time resolved modes is introduced in our vibrational analysis, showing unequivocally its influence on the amide mode spectra. It is also shown that such mode compositions need the inclusion of the first shell solvent molecules to be accurately described. The wavelet analysis is proven to be strongly recommended to follow the time evolution of the spectra, and to capture vibrational band couplings and frequency shifts over time, preserving at the same time a well-balanced time-frequency resolution. This peculiar feature also allows one to perform a combined structural-vibrational analysis, where the different strengths of hydrogen bond interactions can quantitatively affect the amide bands over time at finite temperature. The proposed method allows for the direct connection between vibrational modes and local structural changes, providing a link from the spectroscopic observable to the structure, in this case the peptide backbone, and its hydration layouts.

Modeling amino-acid side chain infrared spectra: the case of carboxylic residues

Infrared (IR) spectroscopy is commonly utilized for the investigation of protein structures and protein-mediated processes.

Modelling vibrational relaxation in complex molecular systems

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.

Evidence of a Thermodynamic Ramp for Hole Hopping to Protect a Redox Enzyme from Oxidative Damage

Redox proteins and enzymes are at risk of irreversible oxidative damage from highly oxidizing intermediates generated in the active site in the case of unsuccessful functional reaction. Chains of tyrosine and/or tryptophan residues have been recently proposed to provide protection to the active site and the whole protein by delivering oxidizing equivalents (holes) out of the protein via a multistep hopping mechanism. In the present work we use a hybrid quantum/classical theoretical-computational methodology based on the perturbed matrix method and on molecular dynamics simulations to calculate the oxidation potential difference along a chain of tyrosine and tryptophan residues in a human redox enzyme of major importance, a superoxide dismutase, which acts as antioxidant defense. We show that the hole hopping is thermodynamically favored along such a chain and that the hopping propensity is strongly affected by the protein environment and in particular by the active site and its second coordination sphere.

A quantitative connection of experimental and simulated folding landscapes by vibrational spectroscopy

We break the barrier between simulation and experiment by comparing identical computed and experimental infrared observables.

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.

Extending the perturbed matrix method beyond the dipolar approximation: comparison of different levels of theory

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.

Parallel folding pathways of Fip35 WW domain explained by infrared spectra and their computer simulation

We present a calculation of the amide I' infrared (IR) spectra of the folded, unfolded, and intermediate states of the WW domain Fip35, a model system for β-sheet folding. Using an all-atom molecular dynamics simulation in which multiple folding and unfolding events take place we identify six conformational states and then apply perturbed matrix method quantum-mechanical calculations to determine their amide I' IR spectra. Our analysis focuses on two states previously identified as Fip35 folding intermediates and suggests that a three-stranded core similar to the folded state core is the main source of the spectroscopic differences between the two intermediates. In particular, we propose a hypothesis for why folding via one of these intermediates was not experimentally observed by IR T-jump.