Temperature dependence of optical dephasing in an organic polymer glass (PMMA) from 300 K to 30 K

Mixed Quantum-Classical Liouville Equation Treatment of Electronic Spectroscopy of Condensed Systems: Harmonic and Anharmonic Electron-Phonon Coupling

This Review integrates the use of electronic optical response function theory and the mixed quantum-classical (MQC) Liouville equation (MQCLE), thereby leading to electronic spectroscopy in MQC media. It further sheds light on the applicability, utility, and efficiency of the mixed quantum-classical dynamics (MQCD) formalism, which starts off with the MQCLE, in probing spectroscopy and dynamics of condensed systems, whereby quantum mechanics and classical mechanics are combined systematically. The author has been exploring and implementing MQCD to investigate electron-phonon coupling effects on electronic dephasing in harmonic and anharmonic systems by calculating linear and nonlinear optical transition analytically and numerically dipole moment time correlation functions in an MQC environment, thereby presenting an in depth spectral profile analysis and their shape and symmetry. The distinctive capability of the MQC time correlation functions is that ergodicity and stationarity properties are inherently satisfied as part of the mixed quantum-classical dynamics (MQCD) framework, unlike classical correlation functions. While some research groups have applied MQCLE to calculate vibrational spectra to study hydrogen-bonded complexes in a MQC environment and other groups calculated Optical response function to probe electron transfer dynamics using the basis mapping technique, the approach, purpose, rigor, applications, and path to the end results reported herein are different. Finally, the same framework is employed to study dissipative systems in the MQC limit, whereby the zero-phonon line adopts the correct width and eliminates its asymmetry. While the full quantum mechanical model, like the multimode Brownian oscillator (MBO) model, yields the correct width and inaccurate shape in the low-temperature limit, the MQCD formalism seems to produce an accurate zero-phonon profile. Nonlinear optical signals are also reviewed in MQC media to show the applicability and utility of this approach. The vibronic optical response functions developed here will account for geometry change, frequency change, and anharmonicity upon electronic excitation to accurately probe electronic dephasing, electron-phonon coupling, shape, and symmetry of profiles and present differences and similarities to the MBO model on pure electronic dephasing. Frequency change and anharmonicity are vitally crucial for accurately assessing electron-phonon coupling upon electronic excitation. This is an additional unique result obtained by the author to further demonstrate the applicability and utility of this approach over other approximation schemes in probing electronic dephasing including that of the MBO model.

Nonequilibrium dynamics of photoinduced forward and backward electron transfer reactions

The biological functions of photoenzymes are often triggered by photoinduced electron transfer (ET) reactions. An ultrafast backward ET (BET) reaction follows the initial photoinduced forward ET (FET), which dissipates the energy of absorbed photons and terminates the biological function in vain. Based upon our previous works, we reasoned that the dynamics of the BET is coupled with that of the FET and other local motions. In this work, the dynamics of the FET and BET is modeled as the master equation of the reduced density operator of a three-state system coupled with a classical harmonic reservoir. The coupling of the FET and BET is reflected in the time-evolution of the charge-transfer state's population, which is generated by a source, the reaction flux for the FET, and annihilated by a sink, the reaction flux for the BET. Surprisingly, numerical simulations show that when the BET is in the Marcus normal region, the BET can be accelerated by nonequilibrium local motions and becomes faster than what is predicted by the Marcus theory. The experimental confirmation of this novel dynamics would provide qualitative evidence for nonequilibrium effects on ultrafast ET dynamics. Additionally, the effects of quantum vibrational modes on the dynamics are discussed. This work can help understand the dynamical interactions between the chain of ultrafast reactions and the complex local environmental motions, revealing the physical nature underlying biological functions.

Adaptive mutations alter antibody structure and dynamics during affinity maturation

While adaptive mutations can bestow new functions on proteins via the introduction or optimization of reactive centers, or other structural changes, a role for the optimization of protein dynamics also seems likely but has been more difficult to evaluate. Antibody (Ab) affinity maturation is an example of adaptive evolution wherein the adaptive mutations may be identified and Abs may be raised to specific targets that facilitate the characterization of protein dynamics. Here, we report the characterization of three affinity matured Abs that evolved from a common germline precursor to bind the chromophoric antigen (Ag), 8-methoxypyrene-1,3,6-trisulfonate (MPTS). In addition to characterizing the sequence, molecular recognition, and structure of each Ab, we characterized the dynamics of each complex by determining their mechanical response to an applied force via three-pulse photon echo peak shift (3PEPS) spectroscopy and deconvoluting the response into elastic, anelastic, and plastic components. We find that for one Ab, affinity maturation was accomplished via the introduction of a single functional group that mediates a direct contact with MPTS and results in a complex with little anelasticity or plasticity. In the other two cases, more mutations were introduced but none directly contact MPTS, and while their effects on structure are subtle, their effects on anelasticity and plasticity are significant, with the level of plasticity correlated with specificity, suggesting that the optimization of protein dynamics may have contributed to affinity maturation. A similar optimization of structure and dynamics may contribute to the evolution of other proteins.

Ultrafast solvation dynamics and charge transfer reactions in room temperature ionic liquids

In this perspective, we review the recent studies concerning the liquid structure and solvation dynamics of ionic liquids, and their influence upon electron transfer and charge transfer reactions.

Protein dynamics and the diversity of an antibody response

The immune system is remarkable in its ability to produce antibodies (Abs) with virtually any specificity from a limited repertoire of germ line precursors. Although the contribution of sequence diversity to this molecular recognition has been studied for decades, recent models suggest that protein dynamics may also broaden the range of targets recognized. To characterize the contribution of protein dynamics to immunological molecular recognition, we report the sequence, thermodynamic, and time-resolved spectroscopic characterization of a panel of eight Abs elicited to the chromophoric antigen 8-methoxypyrene-1,3,6-trisulfonate (MPTS). Based on the sequence data, three of the Abs arose from unique germ line Abs, whereas the remaining five comprise two sets of siblings that arose by somatic mutation of a common precursor. The thermodynamic data indicate that the Abs recognize MPTS via a variety of mechanisms. Although the spectroscopic data reveal small differences in protein dynamics, the anti-MPTS Abs generally show similar levels of flexibility and conformational heterogeneity, possibly representing the convergent evolution of the dynamics necessary for function. However, one Ab is significantly more rigid and conformationally homogeneous than the others, including a sibling Ab from which it differs by only five somatic mutations. This example of divergent evolution demonstrates that point mutations are capable of fixing significant differences in protein dynamics. The results provide unique insight into how high affinity Abs may be produced that bind virtually any target and possibly, from a more general perspective, how new protein functions are evolved.

Three-pulse photon echo peak shift spectroscopy as a probe of flexibility and conformational heterogeneity in protein folding

We investigate the equilibrium unfolding of Zn-cytochrome c in guanidine hydrochloride by three-pulse photon echo peak shift (3PEPS) spectroscopy. Unexpectedly, the measurements reveal that inhomogeneous broadening of the sample at the midpoint of the denaturation is larger than that of either native or unfolded states. To interpret this finding, we present simulations of the peak shift for both two-state and three-state unfolding models. Both the denaturant concentration dependence of the asymptotic peak shift (APS) and the wavelength dependence of the APS at the midpoint of the denaturation are different for the two models. Our data are consistent with two-state unfolding.

Exploring the energy landscape of antibody-antigen complexes: protein dynamics, flexibility, and molecular recognition

The production of antibodies that selectively bind virtually any foreign compound is the hallmark of the immune system. While much is understood about how sequence diversity contributes to this remarkable feat of molecular recognition, little is known about how sequence diversity impacts antibody dynamics, which is also expected to contribute to molecular recognition. Toward this goal, we examined a panel of antibodies elicited to the chromophoric antigen fluorescein. On the basis of isothermal titration calorimetry, we selected six antibodies that bind fluorescein with diverse binding entropies, suggestive of varying contributions of dynamics to molecular recognition. Sequencing revealed that two pairs of antibodies employ homologous heavy chains that were derived from common germline genes, while the other two heavy chains and all six of the light chains were derived from different germline genes and are not homologous. Interestingly, more than half of all the somatic mutations acquired during affinity maturation among the six antibodies are located in positions unlikely to contact fluorescein directly. To quantify and compare the dynamics of the antibody-fluorescein complexes, three-pulse photon echo peak shift and transient grating spectroscopy were employed. All of the antibodies exhibited motions on three distinct time scales, ultrafast motions on the <100 fs time scale, diffusive motions on the picosecond time scale, and motions that occur on time scales longer than nanoseconds and thus appear static. However, the exact frequency of the picosecond time scale motion and the relative contribution of the different motions vary significantly among the antibody-chromophore complexes, revealing a high level of dynamic diversity. Using a hierarchical model, we relate the data to features of the antibodies' energy landscapes as well as their flexibility in terms of elasticity and plasticity. In all, the data provide a consistent picture of antibody flexibility, which interestingly appears to be correlated with binding entropy as well as with germline gene use and the mutations introduced during affinity maturation. The data also provide a gauge of the dynamic diversity of the antibody repertoire and suggest that this diversity might contribute to molecular recognition by facilitating the recognition of the broadest range of foreign molecules.

Efficient Simulation of Three-Pulse Photon-Echo Signals with Application to the Determination of Electronic Coupling in a Bacterial Photosynthetic Reaction Center

A time-nonlocal quantum master equation coupled with a perturbative scheme to evaluate the third-order polarization in the phase-matching direction k(s) = -k(1) + k(2) + k(3) is used to efficiently simulate three-pulse photon-echo signals. The present method is capable of describing photon-echo peak shifts including pulse overlap and bath memory effects. In addition, the method treats the non-Markovian evolution of the density matrix and the third-order polarization in a consistent manner, thus is expected to be useful in systems with rapid and complex dynamics. We apply the theoretical method to describe one- and two-color three-pulse photon-echo peak shift experiments performed on a bacterial photosynthetic reaction center and demonstrate that, by properly incorporating the pulse overlap effects, the method can be used to describe simultaneously all peak shift experiments and determine the electronic coupling between the localized Q(y) excitations on the bacteriopheophytin (BPhy) and accessory bateriochlorophyll (BChl) in the reaction center. A value of J = 250 cm(-1) is found for the coupling between BPhy and BChl.

Measuring Electronic Coupling in the Reaction Center of Purple Photosynthetic Bacteria by Two-Color, Three-Pulse Photon Echo Peak Shift Spectroscopy

One- and two-color, three-pulse photon echo peak shift spectroscopy (1C and 2C3PEPS) was used to estimate the electronic coupling between the accessory bacteriochlorophyll (B) and the bacteriopheophytin (H) in the reaction center of the purple photosynthetic bacterium Rhodobacter sphaeroides as approximately 170 +/- 30 cm-1. This is the first direct experimental determination of this parameter; it is within the range of values found in previously published calculations. The 1C3PEPS signal of the Qy band of the bacteriochlorophyll B shows that it is weakly coupled to nuclear motions of the bath, whereas the 1C3PEPS signal of the Qy band of the bacteriopheophytin, H, shows that it is more strongly coupled to the bath, but has minimal inhomogeneous broadening. Our simulations capture the major features of the data with the theoretical framework developed in our group to separately calculate the response functions and population dynamics.

Appearance of intramolecular high-frequency vibrations in two-dimensional, time-integrated three-pulse photon echo data

An alternative experimental outline to measure homodyne detected three-pulse photon-echo data is presented. The novel experimental approach allowing for online monitoring and correction of experimental timing and stability is discussed in detail using the paradigm system of Nile blue in alcohol solution. It is shown that excellent signal-to-noise ratios together with high reproducibility of the data can be routinely achieved. We report in detail on the appearance of high-frequency intramolecular vibrations in the two-dimensional three-pulse photon-echo data and suggest that besides the conventionally discussed three-pulse photon-echo peak-shift the width of the integrated echo signal as a function of population time contains identical and easily accessible information on high-frequency intramolecular vibrations. A comparison of experimental data with theoretical modeling is performed showing that the observed echo-width oscillations are in line with predictions of the Brownian oscillator model.

AID-initiated purposeful mutations in immunoglobulin genes

Exposure brings risk to all living organisms. Using a remarkably effective strategy, higher vertebrates mitigate risk by mounting a complex and sophisticated immune response to counter the potentially toxic invasion by a virtually limitless army of chemical and biological antagonists. Mutations are almost always deleterious, but in the case of antibody diversification there are mutations occurring at hugely elevated rates within the variable (V) and switch regions (SR) of the immunoglobulin (Ig) genes that are responsible for binding to and neutralizing foreign antigens throughout the body. These mutations are truly purposeful. This chapter is centered on activation-induced cytidine deaminase (AID). AID is required for initiating somatic hypermutation (SHM) in the V regions and class switch recombination (CSR) in the SR portions of Ig genes. By converting C --> U, while transcription takes place, AID instigates a cascade of mutational events involving error-prone DNA polymerases, base excision and mismatch repair enzymes, and recombination pathways. Together, these processes culminate in highly mutated antibody genes and the B cells expressing antibodies that have achieved optimal antigenic binding undergo positive selection in germinal centers. We will discuss the biological role of AID in this complex process, primarily in terms of its biochemical properties in relation to SHM in vivo. The chapter also discusses recent advances in experimental methods to characterize antibody dynamics as a function of SHM to help elucidate the role that the AID-induced mutations play in tailoring molecular recognition. The emerging experimental techniques help to address long-standing conundrums concerning evolution-imposed constraints on antibody structure and function.

Ultrafast Excited-State Excitation Dynamics in a Quasi-Two-Dimensional Light-Harvesting Antenna Based on Ruthenium(II) and Palladium(II) Chromophores

A detailed study on the excited-state-excitation migration taking place within the tetranuclear complex [{(tbbpy)(2)Ru(tmbi)}(2){Pd(allyl)}(2)](PF(6))(2) (tbbpy = 4,4'-di-tert-butyl-2,2'-bipyridine and tmbi = 5,6,5',6'-tetramethyl-2,2'-bibenzimidazolate) is presented. The charge transfer is initiated by the photoexcitation into the lowest metal-to-ligand charge-transfer (MLCT) band of one of the peripheral ruthenium(II) chromophores and terminates on the central structurally complex Pd(2) (II)(allyl)(2) subunit. Thus, the system under investigation can be thought of as a functional model for the photosynthesis reaction center in plants. The kinetic steps involved in the overall process are inferred from femtosecond time-resolved transient-grating kinetics recorded at spectral positions within the regions of ground-state bleach and transient absorption. The kinetics features a complex non-exponential time behavior and can be fitted to a bi-exponential rise (tau(1)> or =200 fs, tau(2) approximately 1.5 ps) and a mono- or bi-exponential decay, depending on the experimental situation. The data leads to the formulation of a model for the intramolecular excitation-hopping ascribing intersystem crossing and subsequent cooling as the two fastest observed processes. Following these initial steps, charge transfer from the ruthenium to the central complex Pd(2)(allyl)(2) moiety is observed with a characteristic time constant of 50 ps. A 220-ps component that is observed in the ground-state recovery only is attributed to excitation equilibration between the two identical Pd(allyl) chromophores.

Photon echo spectroscopy of porphyrins and heme proteins: Effects of quasidegenerate electronic structure on the peak shift decay

Three pulse photon echo peak shift spectroscopy and transient grating measurements on Zn-substituted cytochrome c, Zn-tetraphenylporphyrin, and Zn-protoporphyrin IX are reported. The effects of protein conformation, axial ligation, and solvent are investigated. Numerical simulations of the peak shift and transient grating experiments are presented. The simulations employed recently derived optical response functions for square-symmetric molecules with doubly degenerate excited states. Simulations exploring the effects of excited-state energy splitting, symmetric and asymmetric fluctuations, and excited-state lifetime show that the time scales of the peak shift decay in the three-level system largely reflect the same dynamics as in the two-level system. However, the asymptotic peak shift, which is a clear indicator of inhomogeneous broadening in a two-level system, must be interpreted more carefully for three-level systems, as it is also influenced by the magnitude of the excited-state splitting. The calculated signals qualitatively reproduce the data.

Photoinduced intramolecular charge separation in a polymer solid below the glass transition temperature

Photoinduced intramolecular charge separation (CS) in a polar polymer glass, cyanoethylated pullulan (CN-PUL), was studied below the glass transition temperature (Tg=395 K). A series of three carbazole (Cz: donor)-cyclohexane (S: spacer)-acceptor (A: acceptor) molecules (Cz-S-A) was used as intramolecular donor-acceptor dyads. The photoinduced CS rate was evaluated by the fluorescence decay measurement at temperatures from 100 to 400 K. The CS rate (kCS) increased above 200 K even far below Tg where micro-Brownian motions of the whole polymer chain are frozen. Below 200 K, on the other hand, kCS showed weak dependence on temperature. The temperature dependence of kCS is discussed in terms of the dielectric relaxation time of the polymer matrix. Consequently, CS below Tg was well explained by a thermally nonequilibrium electron transfer (ET) formula above 200 K and by a two-mode quantum-mechanical ET formula below 200 K. The increase in kCS above 200 K is mainly caused by a thermally activated low-frequency matrix mode originating from the side-chain relaxation of polar cyano groups. The weak temperature dependence of kCS can be explained by a nuclear-tunneling effect caused by a high-frequency matrix mode (variant Planck's over 2piomegH=250 cm-1) and an intramolecular vibrational mode (variant Planck's over 2piomegaQ=1300 cm-1). The high-frequency mode of the polymer matrix was attributed to a vibrational or librational motion of polar groups in the CN-PUL glassy solid.

Enhancement and Suppression of Vibrational Coherence in Degenerate Four-Wave-Mixing Signal Generated from Dye-Doped Polymer Films

Vibrational coherence in the degenerate four-wave-mixing (DFWM) signal generated from polymer films doped with a dye, oxazine 4 (Ox4), at 10 K was investigated. It was found that the amplitudes of some low-frequency oscillations (<400 cm(-1)) were enhanced when the delay between the first and second femtosecond pulses was set out of phase with the oscillation period. Frequency and reorganization energy dependence was investigated by computer simulation based on the response function formalism which considers all the possible Liouville space pathways for the DFWM signal. It was revealed that low-frequency oscillations with weak coupling to the optical transition can be enhanced in the stimulated photon echo signal compared to the transient grating signal.

Stimulated emission three-pulse photo-echo peakshift: A mixed pump–probe and photon-echo technique for studying excited-state dynamics

A novel four-pulse photon-echo technique for exploring condensed phase dynamics at different parts of the excited-state potential energy surface is presented. In contrast to traditional three-pulse photon-echo signals, the introduction of a fourth pump pulse allows the use of photon-echo techniques to probe excited-state phenomena. Here, a "proof of principle" experiment is presented where the excited-state solvent dynamics of the coumarin 153 chromophore dissolved in methanol is explored. The fluctuations of the stimulated emission transition is probed, in contrast to the ground-state absorption transition explored in traditional echo measurements. Distinctly different excited-state dynamics, in contrast to ground-state signals, is observed and discussed.

Optical linear response function with linear and diagonal quadratic electron-vibration coupling in mixed quantum-classical systems

Optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed phase systems is derived. The linear response function is derived using Kapral's formalism of statistical mechanics in mixed quantum-classical systems. Our mixed quantum-classical linear dipole moment correlation function J(t) is compared with the full quantum J(t) [Y. J. Yan and S. Mukamel, J. Chem. Phys. 85, 5908 (1986)] in the high temperature limit. Model calculations and discussion of our results are presented. Various formulas of Franck-Condon factors for both linear and quadratic coupling are discussed.

Energy transfer in photosystem I of cyanobacteria Synechococcus elongatus: model study with structure-based semi-empirical Hamiltonian and experimental spectral density

We model the energy transfer and trapping kinetics in PSI. Rather than simply applying Förster theory, we develop a new approach to self-consistently describe energy transfer in a complex with heterogeneous couplings. Experimentally determined spectral densities are employed to calculate the energy transfer rates. The absorption spectrum and fluorescence decay time components of the complex at room temperature were reasonably reproduced. The roles of the special chlorophylls (red, linker, and reaction center, respectively) molecules are discussed. A formally exact expression for the trapping time is derived in terms of the intrinsic trapping time, mean first passage time to trap, and detrapping time. The energy transfer mechanism is discussed and the slowest steps of the arrival at the primary electron donor are found to contain two dominant steps: transfer-to-reaction-center, and transfer-to-trap-from-reaction-center. The intrinsic charge transfer time is estimated to be 0.8 approximately 1.7 ps. The optimality with respect to the trapping time of the calculated transition energies and the orientation of Chls is discussed.