Coherent Multidimensional Vibrational Spectroscopy of Biomolecules: Concepts,Simulations, and Challenges

Good vibrations : The vibrational response of complex molecules to sequences of infrared pulses provides novel femtosecond snapshots of their structure and dynamics. This technique, which is the optical analogue of multidimensional NMR spectroscopy, gives correlation plots of motions during controlled time intervals between pulses that are applied to study protein folding, chirality, hydrogen‐bonding, phospholipid membranes, and chemical exchange.

     

Constrained thermal denaturation of DNA under fixed linking number

A DNA molecule with freely fluctuating ends undergoes a sharp thermal denaturation transition upon heating. However, in circular DNA chains and some experimental setups that manipulate single DNA molecules, the total number of turns (linking number) is constant at all times. The consequences of this additional topological invariant on the melting behaviour are nontrivial. Below, we investigate the melting characteristics of a homogeneous DNA where the linking number along the melting curve is preserved by supercoil formation in duplex portions. We obtain the mass fraction and the number of loops and supercoils below and above the melting temperature. We also argue that a macroscopic loop appears at T _c and calculate its size as a function of temperature.     

Correlated hydrogen bonding fluctuations and vibrational cross peaks in N-methyl acetamide: simulation based on a complete electrostatic density functional theory map

The coherent nonlinear response of the entire amide line shapes of N-methyl acetamide to three infrared pulses is simulated using an electrostatic density functional theory map. Positive and negative cross peaks contain signatures of correlations between the fundamentals and the combination state. The amide I-A and I-III cross-peak line shapes indicate positive correlation and anticorrelation of frequency fluctuations, respectively. These can be ascribed to correlated hydrogen bonding at C[double bond]O and N-H sites. The amide I frequency is negatively correlated with the hydrogen bond on carbonyl C[double bond]O, whereas the amide A and III are negatively and positively correlated, respectively, with the hydrogen bond on amide N-H.     

Simulation protocols for coherent femtosecond vibrational spectra of peptides

Two algorithms for simulating the response of peptides to sequences of IR pulses are developed and applied to N-methyl acetamide (NMA) and a 17 residue alpha-helical peptide (YKKKH17) in D(2)O. A fluctuating vibrational-exciton Hamiltonian for the amide I mode is constructed from molecular dynamics trajectories. Coupling with the environment is described using a density functional theory electrostatic map. The cumulant expansion of Gaussian fluctuation incorporates motional narrowing due to fast frequency fluctuations and is adequate for NMA and for isotopically labeled bands in large peptides. Real-space truncation of the scattering matrix of the nonlinear exciton equations significantly reduces the computational cost, making it particularly attractive for slow fluctuations in large globular proteins.     

Stochastic simulation of chemical exchange in two dimensional infrared spectroscopy

The stochastic Liouville equations are employed to investigate the combined signatures of chemical exchange (two-state jump) and spectral diffusion (coupling to an overdamped Brownian oscillator) in the coherent response of an anharmonic vibration to three femtosecond infrared pulses. Simulations reproduce the main features recently observed in the OD stretch of phenol in benzene.     

Coherent control of cross-peaks in chirality-induced two-dimensional optical signals of excitons

Polarization tuning of the interference of chirality-induced tensor components is used to simulate the suppression of diagonal peaks and amplification of cross peaks in femtosecond two-dimensional photon echo signals of excitons in a chiral porphyrin dimer. Superpositions of various tensor components which generate the optimized signals are constructed using a genetic learning algorithm. Exciton couplings and bath correlations may be extracted from these highly resolved signals.     

Geometry and Excitation Energy Fluctuations of NMA in Aqueous Solution with CHARMM, AMBER, OPLS, and GROMOS Force Fields: Implications for Protein Ultraviolet Spectra Simulation

EPR experiments carried out at various temperatures for partially hydroxylated nanocrystalline MgO exposed to atomic hydrogen reveal that the entrapped electrons arising from spontaneous dissociation of hydrogen atoms exhibit an antiferromagnetic ordering. The measured magnetic data is found to be compatible with a phenomenological model of interacting paramagnetic centres at high temperature, and with a Pauli like behaviour below a certain temperature. This is further corroborated with density functional calculations of the effective magnetic coupling parameter for Heisenberg model between entrapped electrons on suitable embedded cluster models of MgO nanocrystals.     

On the impact and the separation approximations in the theory of multiphoton interactions ivith thermally perturbed systems

Criteria are provided for the factorization of thermal averages incuring in the calculation of cross-sections for several-photon processes, into produc