Vibrational relaxation in simulated two-dimensional infrared spectra of two amide modes in solution

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.

Direct Observation of Intrachain Hydrogen Bonds in Aqueous Hyaluronan

We use two-dimensional infrared spectroscopy to study the interactions between the amide and carboxylate anion groups of hyaluronan polymers at neutral pH. The spectra reveal the presence of intrachain hydrogen bonds between the amide and carboxylate anion groups in aqueous solution. We determine the relative orientation of the amide and carboxylate anion groups when forming this hydrogen bond and quantify the fraction of amide groups that participate in hydrogen bonding. We find that a variation of the pH and/or temperature has a negligible effect on this fraction, whereas the persistence length of the hyaluronan chains and the associated viscosity of hyaluronan solutions are known to change significantly. We conclude that the hydrogen bonding between the amide and carboxylate anion groups does not significantly contribute to the chain rigidity of hyaluronan polymers.

Hydrophobic Collapse in N-Methylacetamide-Water Mixtures

Aqueous N-methylacetamide solutions were investigated by polarization-resolved pump–probe and 2D infrared spectroscopy (2D IR), using the amide I mode as a reporter. The 2D IR results are compared with molecular dynamics simulations and spectral calculations to gain insight into the molecular structures in the mixture. N-Methylacetamide and water molecules tend to form clusters with “frozen” amide I dynamics. This is driven by a hydrophobic collapse as the methyl groups of the N-methylacetamide molecules cluster in the presence of water. Since the studied system can be considered as a simplified model for the backbone of proteins, the present study forms a convenient basis for understanding the structural and vibrational dynamics in proteins. It is particularly interesting to find out that a hydrophobic collapse as the one driving protein folding is observed in such a simple system.

Simple Quantum Dynamics with Thermalization

In this paper, we introduce two simple quantum dynamics methods. One is based on the popular surface-hopping method, and the other is based on rescaling of the propagation on the bath ground-state potential surface. The first method is special, as it avoids specific feedback from the simulated quantum system to the bath and can be applied for precalculated classical trajectories. It is based on the equipartition theorem to determine if hops between different potential energy surfaces are allowed. By comparing with the formally exact Hierarchical Equations Of Motion approach for four model systems we find that the method generally approximates the quantum dynamics toward thermal equilibrium very well. The second method is based on rescaling of the nonadiabatic coupling and also neglect the effect of the state of the quantum system on the bath. By the nature of the approximations, they cannot reproduce the effect of bath relaxation following excitation. However, the methods are both computationally more tractable than the conventional fewest switches surface hopping, and we foresee that the methods will be powerful for simulations of quantum dynamics in systems with complex bath dynamics, where the system-bath coupling is not too strong compared to the thermal energy.

Hybrid quantum/classical simulations of the vibrational relaxation of the amide I mode of N-methylacetamide in D2O solution

Hybrid quantum/classical molecular dynamics (MD) is applied to simulate the vibrational relaxation (VR) of the amide I mode of deuterated N-methylacetamide (NMAD) in aqueous (D(2)O) solution. A novel version of the vibrational molecular dynamics with quantum transitions (MDQT) treatment is developed in which the amide I mode is treated quantum mechanically while the remaining degrees of freedom are treated classically. The instantaneous normal modes of the initially excited NMAD molecule (INM(0)) are used as internal coordinates since they provide a proper initial partition of the system in quantum and classical subsystems. The evolution in time of the energy stored in each individual normal mode is subsequently quantified using the hybrid quantum-classical instantaneous normal modes (INM(t)). The identities of both the INM(0)s and the INM(t)s are tracked using the equilibrium normal modes (ENMs) as templates. The results extracted from the hybrid MDQT simulations show that the quantum treatment of the amide I mode accelerates the whole VR process versus pure classical simulations and gives better agreement with experiments. The relaxation of the amide I mode is found to be essentially an intramolecular vibrational redistribution (IVR) process with little contribution from the solvent, in agreement with previous theoretical and experimental studies. Two well-defined relaxation mechanisms are identified. The faster one accounts for ≈40% of the total vibrational energy that flows through the NMAD molecule and involves the participation of the lowest frequency vibrations as short-life intermediate modes. The second and slower mechanism accounts for the remaining ≈60% of the energy released and is associated to the energy flow through specific mid-range and high-frequency modes.

Modeling the vibrational dynamics and nonlinear infrared spectra of coupled amide I and II modes in peptides

The amide vibrational modes play an important role in energy transport and relaxation in polypeptides and proteins and provide us with spectral markers for structure and structural dynamics of these macromolecules. Here, we present a detailed model to describe the dynamic properties of the amide I and amide II modes and the resulting linear and nonlinear spectra. These two modes have large oscillator strengths, and their mutual coupling plays an important role in their relaxation. Using first-principles calculations of NMA-d(7) and a dipeptide in a fluctuating bath described by molecular dynamics simulations, we model the frequencies of the local vibrations as well as the coupling between them. Both the coherent couplings and the fluctuations induced by contact with their environment are taken into account. We apply the resulting model of interacting fluctuating oscillators to study the collective vibrations and the partially coherent transport of vibrational energy through a model α-helix. We find that the instantaneous vibrations are delocalized over a few (up to four) amide units, while the coherences in the helix survive for 0.5-1 ps, leading to coherent transport on a similar time scale.

Amide I'-II' 2D IR spectroscopy provides enhanced protein secondary structural sensitivity

We demonstrate how multimode 2D IR spectroscopy of the protein amide I' and II' vibrations can be used to distinguish protein secondary structure. Polarization-dependent amide I'-II' 2D IR experiments on poly-l-lysine in the beta-sheet, alpha-helix, and random coil conformations show that a combination of amide I' and II' diagonal and cross peaks can effectively distinguish between secondary structural content, where amide I' infrared spectroscopy alone cannot. The enhanced sensitivity arises from frequency and amplitude correlations between amide II' and amide I' spectra that reflect the symmetry of secondary structures. 2D IR surfaces are used to parametrize an excitonic model for the amide I'-II' manifold suitable to predict protein amide I'-II' spectra. This model reveals that the dominant vibrational interaction contributing to this sensitivity is a combination of negative amide II'-II' through-bond coupling and amide I'-II' coupling within the peptide unit. The empirically determined amide II'-II' couplings do not significantly vary with secondary structure: -8.5 cm(-1) for the beta sheet, -8.7 cm(-1) for the alpha helix, and -5 cm(-1) for the coil.

Waiting time dynamics in two-dimensional infrared spectroscopy

We review recent work on the waiting time dynamics of coherent two-dimensional infrared (2DIR) spectroscopy. This dynamics can reveal chemical and physical processes that take place on the femto- and picosecond time scale, which is faster than the time scale that may be probed by, for example, nuclear magnetic resonance spectroscopy. A large number of chemically relevant processes take place on this time scale. Such processes range from forming and breaking hydrogen bonds and proton transfer to solvent exchange and vibrational population transfer. In typical 2DIR spectra, multiple processes contribute to the waiting time dynamics and the spectra are often congested. This makes the spectra challenging to interpret, and the aid of theoretical models and simulations is often needed. To be useful, such models need to account for all dynamical processes in the sample simultaneously. The numerical integration of the Schrodinger equation (NISE) method has proven to allow for a very general treatment of the dynamical processes. It accounts for both the motional narrowing resulting from solvent-induced frequency fluctuations and population transfer between coupled vibrations. At the same time, frequency shifts arising from chemical-exchange reactions and changes of the transition dipoles because of either non-Condon effects or molecular reorientation are included in the treatment. This method therefore allows for the disentanglement of all of these processes. The NISE method has thus far been successfully applied to study chemical-exchange processes. It was demonstrated that 2DIR is not only sensitive to reaction kinetics but also to the more detailed reaction dynamics. NISE has also been applied to the study of population transfer within the amide I band (CO stretch) and between the amide I and amide II bands (CN stretch and NH bend) in polypeptides. From the amide I studies, it was found that the population transfer can be used to enhance cross-peaks that act as structural markers for beta-sheet structure in proteins. From the amide I/II investigation, it was found that the amide II band and the hydrogen-bond stretch vibration are important parts of the relaxation pathway for the amide I vibration. With the development of simple approximations, it becomes possible to apply the NISE method even to very big systems, such as the OH stretch of bulk water, which can only be described well when large numbers of coupled vibrations are taken into account.

Simulation of vibrational energy transfer in two-dimensional infrared spectroscopy of amide I and amide II modes in solution

Population transfer between vibrational eigenstates is important for many phenomena in chemistry. In solution, this transfer is induced by fluctuations in molecular conformation as well as in the surrounding solvent. We develop a joint electrostatic density functional theory map that allows us to connect the mixing of and thereby the relaxation between the amide I and amide II modes of the peptide building block N-methyl acetamide. This map enables us to extract a fluctuating vibrational Hamiltonian from molecular dynamics trajectories. The linear absorption spectrum, population transfer, and two-dimensional infrared spectra are then obtained from this Hamiltonian by numerical integration of the Schrodinger equation. We show that the amide I/amide II cross peaks in two-dimensional infrared spectra in principle allow one to follow the vibrational population transfer between these two modes. Our simulations of N-methyl acetamide in heavy water predict an efficient relaxation between the two modes with a time scale of 790 fs. This accounts for most of the relaxation of the amide I band in peptides, which has been observed to take place on a time scale of 450 fs in N-methyl acetamide. We therefore conclude that in polypeptides, energy transfer to the amide II mode offers the main relaxation channel for the amide I vibration.

Two-dimensional infrared population transfer spectroscopy for enhancing structural markers of proteins

We propose the possibility of using vibrational population transfer to enhance the structural markers for protein motifs that occur in two-dimensional infrared spectroscopy. We demonstrate the potential of this method by calculating the spectrum of the trpzip2 beta-hairpin peptide, a system that is small enough to allow accurate simulation of its two-dimensional infrared spectra, including vibrational population transfer induced by a fluctuating solvent. The results show that under selected experimental conditions, in particular by using perpendicular polarization and finite waiting times, the cross peaks that constitute the well-known Z-shape marker for beta-sheet structure in two-dimensional spectra are strongly enhanced. This enhancement is shown to result from vibrational population transfer. It should be possible to use the same technique for enhancing cross peaks in other structures and generally improve structure determination by two-dimensional infrared spectroscopy. The simulated population transfer times are in good agreement with those observed in experiments on typical proteins.