Conformation and electronic population transfer in membrane-supported self-assembled porphyrin dimers by 2D fluorescence spectroscopy

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. I. Response function theory

Fluorescence-encoded infrared (FEIR) spectroscopy is an emerging technique for performing vibrational spectroscopy in solution with detection sensitivity down to single molecules. FEIR experiments use ultrashort pulses to excite a fluorescent molecule's vibrational and electronic transitions in a sequential, time-resolved manner, and are therefore sensitive to intervening vibrational dynamics on the ground state, vibronic coupling, and the relative orientation of vibrational and electronic transition dipole moments. This series of papers presents a theoretical treatment of FEIR spectroscopy that describes these phenomena and examines their manifestation in experimental data. This first paper develops a nonlinear response function description of Fourier-transform FEIR experiments for a two-level electronic system coupled to multiple vibrations, which is then applied to interpret experimental measurements in the second paper [L. Whaley-Mayda et al., J. Chem. Phys. 159, 194202 (2023)]. Vibrational coherence between pairs of modes produce oscillatory features that interfere with the vibrations' population response in a manner dependent on the relative signs of their respective Franck-Condon wavefunction overlaps, leading to time-dependent distortions in FEIR spectra. The orientational response of population and coherence contributions are analyzed and the ability of polarization-dependent experiments to extract relative transition dipole angles is discussed. Overall, this work presents a framework for understanding the full spectroscopic information content of FEIR measurements to aid data interpretation and inform optimal experimental design.

Two-dimensional fluorescence excitation spectroscopy: A novel technique for monitoring excited-state photophysics of molecular species with high time and frequency resolution

We propose a novel UV/Vis femtosecond spectroscopic technique, two-dimensional fluorescence-excitation (2D-FLEX) spectroscopy, which combines spectral resolution during the excitation process with exclusive monitoring of the excited-state system dynamics at high time and frequency resolution. We discuss the experimental feasibility and realizability of 2D-FLEX, develop the necessary theoretical framework, and demonstrate the high information content of this technique by simulating the 2D-FLEX spectra of a model four-level system and the Fenna-Matthews-Olson antenna complex. We show that the evolution of 2D-FLEX spectra with population time directly monitors energy transfer dynamics and can thus yield direct qualitative insight into the investigated system. This makes 2D-FLEX a highly efficient instrument for real-time monitoring of photophysical processes in polyatomic molecules and molecular aggregates.

Double-quantum spectroscopy of dense atomic vapors: Interplay between Doppler and self-broadenings

In this article, we present a simulation study of the linear and nonlinear spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus on double quantum spectroscopy, which directly probes dipole-dipole interactions. By explicitly including thermal velocity, we show that temperature has an important impact on the self-broadening mechanisms of the linear and nonlinear spectra. We also provide analytical expressions for the response functions in the short time limit using the two-body approximation, which shows that double quantum spectroscopy for atomic vapors directly probes the transition amplitude of the electronic excitation between two atoms. We also propose an expression for the double quantum spectrum that includes the effect of Doppler broadening, and we discuss the effect of density on the spectrum. We show that when Doppler broadening is negligible compared to self-broadening, the double quantum spectrum scales with the atomic density, while when Doppler broadening dominates, it scales as the square of the density.

Unifying Nonlinear Response and Incoherent Mixing in Action-2D Electronic Spectroscopy

Action-detection has expanded the scope and applicability of 2D electronic spectroscopy, while posing new challenges for the unambiguous interpretation of spectral features. In this context, identifying the origin of cross-peaks at early waiting times is not trivial, and incoherent mixing is often invoked as an unwanted contribution masking the nonlinear signal. In this work, we elaborate on the relation between the nonlinear response and the incoherent mixing contribution by analyzing the action signal in terms of one- and two-particle observables. Considering a weakly interacting molecular dimer, we show how cross-peaks at early waiting times, reflecting exciton-exciton annihilation dynamics, can be equivalently interpreted as arising from incoherent mixing. This equivalence, on the one hand, highlights the information content of spectral features related to incoherent mixing and, on the other hand, provides an efficient numerical scheme to simulate the action response of weakly interacting systems.

Temperature-dependent local conformations and conformational distributions of cyanine dimer labeled single-stranded-double-stranded DNA junctions by 2D fluorescence spectroscopy

DNA replication and the related processes of genome expression require binding, assembly, and function of protein complexes at and near single-stranded (ss)-double-stranded (ds) DNA junctions. These central protein-DNA interactions are likely influenced by thermally induced conformational fluctuations of the DNA scaffold across an unknown distribution of functionally relevant states to provide regulatory proteins access to properly conformed DNA binding sites. Thus, characterizing the nature of conformational fluctuations and the associated structural disorder at ss-dsDNA junctions is critical for understanding the molecular mechanisms of these central biological processes. Here, we describe spectroscopic studies of model ss-dsDNA fork constructs that contain dimers of "internally labeled" cyanine (iCy3) chromophore probes that have been rigidly inserted within the sugar-phosphate backbones of the DNA strands. Our combined analyses of absorbance, circular dichroism, and two-dimensional fluorescence spectroscopy permit us to characterize the local conformational parameters and conformational distributions. We find that the DNA sugar-phosphate backbones undergo abrupt successive changes in their local conformations-initially from a right-handed and ordered DNA state to a disordered splayed-open structure and then to a disordered left-handed conformation-as the dimer probes are moved across the ss-dsDNA junction. Our results suggest that the sugar-phosphate backbones at and near ss-dsDNA junctions adopt specific position-dependent local conformations and exhibit varying extents of conformational disorder that deviate widely from the Watson-Crick structure. We suggest that some of these conformations can function as secondary-structure motifs for interaction with protein complexes that bind to and assemble at these sites.

Time-Domain Vibrational Action Spectroscopy of Cryogenically Cooled, Messenger-Tagged Ions Using Ultrafast IR Pulses

Herein, we present the initial steps toward developing a framework that will enable the characterization of photoinitiated dynamics within large molecular ions in the gas phase with temporal and energy resolution. We combine the established techniques of tag-loss action spectroscopy on cryogenically trapped molecular ions with ultrafast vibrational spectroscopy by measuring the linear action spectrum of N₂-tagged protonated diglycine (GlyGlyH⁺·N₂) with an ultrafast infrared (IR) pulse pair. The presented time-domain data demonstrate that the excited-state vibrational populations in the tagged parent ions are modulated by the ultrafast IR pulse pair and encoded through the messenger tag-loss action response. The Fourier transform of the time-domain action interferograms yields the linear frequency-domain vibrational spectrum of the ion ensemble, and we show that this spectrum matches the linear spectrum collected in a traditional manner using a frequency-resolved IR laser. Time- and frequency-domain interpretations of the data are considered and discussed. Finally, we demonstrate the acquisition of nonlinear signals through cross-polarization pump-probe experiments. These results validate the prerequisite first steps of combining tag-loss action spectroscopy with two-dimensional IR spectroscopy for probing dynamics in gas-phase molecular ions.

Multidimensional electronic spectroscopy in high-definition-Combining spectral, temporal, and spatial resolutions

Over the past two decades, coherent multidimensional spectroscopies have been implemented across the terahertz, infrared, visible, and ultraviolet regions of the electromagnetic spectrum. A combination of coherent excitation of several resonances with few-cycle pulses, and spectral decongestion along multiple spectral dimensions, has enabled new insights into wide ranging molecular scale phenomena, such as energy and charge delocalization in natural and artificial light-harvesting systems, hydrogen bonding dynamics in monolayers, and strong light-matter couplings in Fabry-Pérot cavities. However, measurements on ensembles have implied signal averaging over relevant details, such as morphological and energetic inhomogeneity, which are not rephased by the Fourier transform. Recent extension of these spectroscopies to provide diffraction-limited spatial resolution, while maintaining temporal and spectral information, has been exciting and has paved a way to address several challenging questions by going beyond ensemble averaging. The aim of this Perspective is to discuss the technological developments that have eventually enabled spatially resolved multidimensional electronic spectroscopies and highlight some of the very recent findings already made possible by introducing spatial resolution in a powerful spectroscopic tool.

Optical two-dimensional coherent spectroscopy of many-body dipole-dipole interactions and correlations in atomic vapors

Many-body interactions and correlations in atomic ensembles are fundamental in understanding many-body effects such as collective and emergent phenomena and also play an important role in various atom-based applications. Optical two-dimensional coherent spectroscopy (2DCS) provides a powerful tool to measure many-body interactions and correlations. Here, we present the study of many-body dipole-dipole interactions and correlations in potassium and rubidium atomic vapors by using double-quantum and multi-quantum 2DCS. The results show that double-quantum 2DCS provides sensitive and background-free detection of weak dipole-dipole interaction between atoms with a mean separation up to about 16 μm, and multi-quantum 2DCS can excite and detect multi-atom states (Dicke states) with up to eight correlated atoms. The technique of optical 2DCS can provide a new approach to study many-body physics in atomic ensembles and can be potentially implemented to measure many-body effects in cold atoms and other atomic/molecular systems.

Two-dimensional spectroscopy beyond the perturbative limit: The influence of finite pulses and detection modes

Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required.

Automatic Feynman diagram generation for nonlinear optical spectroscopies and application to fifth-order spectroscopy with pulse overlaps

Perturbative nonlinear optical spectroscopies are powerful methods to understand the dynamics of excitonic and other condensed phase systems. Feynman diagrams have long provided the essential tool to understand and interpret experimental spectra and to organize the calculation of spectra for model systems. When optical pulses are strictly time ordered, only a small number of diagrams contribute, but in many experiments, pulse-overlap effects are important for interpreting results. When pulses overlap, the number of contributing diagrams can increase rapidly, especially with higher order spectroscopies, and human error is especially likely when attempting to write down all the diagrams. We present an automated Diagram Generator (DG) that generates all the Feynman diagrams needed to calculate any nth-order spectroscopic signal. We characterize all perturbative nonlinear spectroscopies by their associated phase-discrimination condition as well as the time intervals where pulse amplitudes are nonzero. Although the DG can be used to automate impulsive calculations, its greatest strength lies in automating finite pulse calculations where pulse overlaps are important. We consider third-order transient absorption spectroscopy and fifth-order exciton-exciton interaction 2D (EEI2D) spectroscopy, which are described by six or seven diagrams in the impulsive limit, respectively, but 16 or 240 diagrams, respectively, when pulses overlap. The DG allows users to automatically include all relevant diagrams at a relatively low computational cost, since the extra diagrams are only generated for the inter-pulse delays where they are relevant. For EEI2D spectroscopy, we show the important effects of including the overlap diagrams.

Efficient numerical method for predicting nonlinear optical spectroscopies of open systems

Nonlinear optical spectroscopies are powerful tools for probing quantum dynamics in molecular and nanoscale systems. While intuition about ultrafast spectroscopies is often built by considering impulsive optical pulses, actual experiments have finite-duration pulses, which can be important for interpreting and predicting experimental results. We present a new freely available open source method for spectroscopic modeling, called Ultrafast Ultrafast (UF²) spectroscopy, which enables computationally efficient and convenient prediction of nonlinear spectra, such as treatment of arbitrary finite duration pulse shapes. UF² is a Fourier-based method that requires diagonalization of the Liouvillian propagator of the system density matrix. We also present a Runge-Kutta-Euler (RKE) direct propagation method. We include open system dynamics in the secular Redfield, full Redfield, and Lindblad formalisms with Markovian baths. For non-Markovian systems, the degrees of freedom corresponding to memory effects are brought into the system and treated nonperturbatively. We analyze the computational complexity of the algorithms and demonstrate numerically that, including the cost of diagonalizing the propagator, UF² is 20-200 times faster than the direct propagation method for secular Redfield models with arbitrary Hilbert space dimension; it is similarly faster for full Redfield models at least up to system dimensions where the propagator requires more than 20 GB to store; and for Lindblad models, it is faster up to Hilbert space dimension near 100 with speedups for small systems by factors of over 500. UF² and RKE are part of a larger open source Ultrafast Software Suite, which includes tools for automatic generation and calculation of Feynman diagrams.

Signatures of exciton dynamics and interaction in coherently and fluorescence-detected four- and six-wave-mixing two-dimensional electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) can be realized in increasing nonlinear orders of interaction with the electric field, bringing new information about single- and multi-particle properties and dynamics. Furthermore, signals can be detected both coherently (C-2DES) and by fluorescence (F-2DES), with fundamental and practical differences. We directly compare the simultaneous measurements of four- and six-wave mixing C-2DES and F-2DES on an excitonic heterodimer of squaraine molecules. Spectral features are described in increasing orders of nonlinearity by an explicit excitonic model. We demonstrate that the four-wave-mixing spectra are sensitive to one-exciton energies, their delocalization and dynamics, while the six-wave-mixing spectra include information on bi-exciton and higher excited states including the state energies, electronic coupling, and exciton-exciton annihilation. We focus on the possibility to extract the dynamics arising from exciton-exciton interaction directly from the six-wave-mixing spectra. To this end, in analogy to previously demonstrated fifth-order coherently detected exciton-exciton-interaction 2DES (EEI2D spectroscopy), we introduce a sixth-order fluorescence-detected EEI2D spectroscopy variant.

Fluorescence-detected Fourier transform electronic spectroscopy by phase-tagged photon counting

Fluorescence-detected Fourier transform (FT) spectroscopy is a technique in which the relative paths of an optical interferometer are controlled to excite a material sample, and the ensuing fluorescence is detected as a function of the interferometer path delay and relative phase. A common approach to enhance the signal-to-noise ratio in these experiments is to apply a continuous phase sweep to the relative optical path, and to detect the resulting modulated fluorescence using a phase-sensitive lock-in amplifier. In many important situations, the fluorescence signal is too weak to be measured using a lock-in amplifier, so that photon counting techniques are preferred. Here we introduce an approach to low-signal fluorescence-detected FT spectroscopy, in which individual photon counts are assigned to a modulated interferometer phase ('phase-tagged photon counting,' or PTPC), and the resulting data are processed to construct optical spectra. We studied the fluorescence signals of a molecular sample excited resonantly by a pulsed coherent laser over a range of photon flux and visibility levels. We compare the performance of PTPC to standard lock-in detection methods and establish the range of signal parameters over which meaningful measurements can be carried out. We find that PTPC generally outperforms the lock-in detection method, with the dominant source of measurement uncertainty being associated with the statistics of the finite number of samples of the photon detection rate.

Coherently and fluorescence-detected two-dimensional electronic spectroscopy: direct comparison on squaraine dimers

Optical two-dimensional electronic spectroscopy (2DES) is now widely utilized to study excitonic structure and dynamics of a broad range of systems, from molecules to solid state. Besides the traditional experimental implementation using phase matching and coherent signal field detection, action-based approaches that detect incoherent signals such as fluorescence have been gaining popularity in recent years. While incoherent detection extends the range of applicability of 2DES, the observed spectra are not equivalent to the coherently detected ones. This raises questions about their interpretation and the sensitivity of the technique. Here we directly compare, both experimentally and theoretically, four-wave mixing coherently and fluorescence-detected 2DES of a series of squaraine dimers of increasing electronic coupling. All experiments are qualitatively well reproduced by a Frenkel exciton model with secular Redfield theory description of excitation dynamics. We contrast the spectral features and the sensitivities of both techniques with respect to exciton energies, delocalization, coherent and dissipative dynamics, and exciton-exciton annihilation. Discussing the fundamental and practical differences, we demonstrate the degree of complementarity of the techniques.

Rapid multiple-quantum three-dimensional fluorescence spectroscopy disentangles quantum pathways

Coherent two-dimensional spectroscopy is a powerful tool for probing ultrafast quantum dynamics in complex systems. Several variants offer different types of information but typically require distinct beam geometries. Here we introduce population-based three-dimensional (3D) electronic spectroscopy and demonstrate the extraction of all fourth- and multiple sixth-order nonlinear signal contributions by employing 125-fold (1⨯5⨯5⨯5) phase cycling of a four-pulse sequence. Utilizing fluorescence detection and shot-to-shot pulse shaping in single-beam geometry, we obtain various 3D spectra of the dianion of TIPS-tetraazapentacene, a fluorophore with limited stability at ambient conditions. From this, we recover previously unknown characteristics of its electronic two-photon state. Rephasing and nonrephasing sixth-order contributions are measured without additional phasing that hampered previous attempts using noncollinear geometries. We systematically resolve all nonlinear signals from the same dataset that can be acquired in 8 min. The approach is generalizable to other incoherent observables such as external photoelectrons, photocurrents, or photoions.

Long range dipole-dipole interaction in low-density atomic vapors probed by double-quantum two-dimensional coherent spectroscopy

Optical double-quantum two-dimensional coherent spectroscopy (2DCS) was implemented to probe interatomic dipole-dipole interactions in both potassium and rubidium atomic vapors. The dipole-dipole interaction was detected at densities of 4.81×10⁸ cm ^-3 and 8.40×10⁹ cm ^-3 for potassium and rubidium, respectively, corresponding to a mean interatomic separation of 15.8 μm or 3.0×10⁵ a ₀ for potassium and 6.1 μm or 1.2×10⁵ a ₀ for rubidium, where a ₀ is the Bohr radius. The experimental results confirm the long range nature of the dipole-dipole interaction, which is critical for understanding many-body physics in atoms/molecules. The long range interaction also has implications in atom-based applications involving many-body interactions. Additionally, we demonstrated that double-quantum 2DCS is sufficiently sensitive to probe dipole-dipole interaction at densities that can be achieved with cold atom in a magneto-optical trap, paving the way for double-quantum 2DCS studies of cold atoms and molecules. The method can also open a new avenue to study long-range interactions in solid state systems such as quantum dots and color centers in diamonds.

Before Förster. Initial excitation in photosynthetic light harvesting

Electronic 2D spectroscopy allows nontrivial quantum effects to be explored in unprecedented detail. Here, we apply recently developed fluorescence detected coherent 2D spectroscopy to study the light harvesting antenna 2 (LH2) of photosynthetic purple bacteria. We report double quantum coherence 2D spectra which show clear cross peaks indicating correlated excitations. Similar results are found for rephasing and nonrephasing signals. Analysis of signal generating quantum pathways leads to the conclusion that, contrary to the currently prevailing physical picture, the two weakly coupled pigment rings of LH2 share the initial electronic excitation leading to quantum mechanical correlation between the two clearly separate absorption bands. These results are general and have consequences for the interpretation of initially created excited states not only in photosynthesis but in all light absorbing systems composed of weakly interacting pigments where the excitation transfer is commonly described by using Förster theory. Being able to spectrally resolve the nonequilibrium dynamics immediately following photoabsorption may provide a glimpse to the systems' transition into the Förster regime.

Measuring local conformations and conformational disorder of (Cy3)2 dimer labeled DNA fork junctions using absorbance, circular dichroism and two-dimensional fluorescence spectroscopy

The sugar-phosphate backbone of DNA near single-stranded (ss)-double-stranded (ds) junctions likely fluctuates within a broad distribution of conformations to permit the proper binding of genome regulatory proteins that function at these sites. In this work we use absorbance, circular dichroism (CD), and two-dimensional fluorescence spectroscopy (2DFS) to study the local conformations and conformational disorder within chromophore-labeled DNA constructs. These constructs employ dimers of the fluorescent chromophore Cy3 that are site-specifically incorporated into the sugar-phosphate backbones of DNA strands at ss-ds DNA fork junctions. We show that these data can be analyzed to determine the local conformations of the (Cy3)2 dimer, and the degree of conformational disorder. Our analysis employs an essential-state Holstein-Frenkel Hamiltonian model, which takes into account the internal electronic-vibrational motions within each Cy3 chromophore, and the resonant electronic interaction that couples the two chromophores together. Our results suggest that this approach may be applied generally to understand local backbone conformation and conformational disorder at ss-ds DNA fork junctions.

Coherent two-dimensional electronic mass spectrometry

Coherent two-dimensional (2D) optical spectroscopy has revolutionized our ability to probe many types of couplings and ultrafast dynamics in complex quantum systems. The dynamics and function of any quantum system strongly depend on couplings to the environment. Thus, studying coherent interactions for different environments remains a topic of tremendous interest. Here we introduce coherent 2D electronic mass spectrometry that allows 2D measurements on effusive molecular beams and thus on quantum systems with minimum system–bath interaction and employ this to identify the major ionization pathway of 3d Rydberg states in NO₂. Furthermore, we present 2D spectra of multiphoton ionization, disclosing distinct differences in the nonlinear response functions leading to the ionization products. We also realize the equivalent of spectrally resolved transient-absorption measurements without the necessity for acquiring weak absorption changes. Using time-of-flight detection introduces cations as an observable, enabling the 2D spectroscopic study on isolated systems of photophysical and photochemical reactions.

Multidimensional spectroscopy is a powerful tool in exploring photo-induced dynamics and electron coupling processes in molecules. Here the authors demonstrate coherent two-dimensional electronic mass spectrometry on molecular beams and its application to photoionization studies of the NO₂ molecule.

Temperature-dependent conformations of exciton-coupled Cy3 dimers in double-stranded DNA

Understanding the properties of electronically interacting molecular chromophores, which involve internally coupled electronic-vibrational motions, is important to the spectroscopy of many biologically relevant systems. Here we apply linear absorption, circular dichroism, and two-dimensional fluorescence spectroscopy to study the polarized collective excitations of excitonically coupled cyanine dimers (Cy3)₂ that are rigidly positioned within the opposing sugar-phosphate backbones of the double-stranded region of a double-stranded (ds)-single-stranded (ss) DNA fork construct. We show that the exciton-coupling strength of the (Cy3)₂-DNA construct can be systematically varied with temperature below the ds-ss DNA denaturation transition. We interpret spectroscopic measurements in terms of the Holstein vibronic dimer model, from which we obtain information about the local conformation of the (Cy3)₂ dimer, as well as the degree of static disorder experienced by the Cy3 monomer and the (Cy3)₂ dimer probe locally within their respective DNA duplex environments. The properties of the (Cy3)₂-DNA construct we determine suggest that it may be employed as a useful model system to test fundamental concepts of protein-DNA interactions and the role of electronic-vibrational coherence in electronic energy migration within exciton-coupled bio-molecular arrays.

Fluorescence-Detected Two-Quantum and One-Quantum-Two-Quantum 2D Electronic Spectroscopy

We demonstrate two-quantum (2Q) coherent two-dimensional (2D) electronic spectroscopy using a shot-to-shot-modulated pulse shaper and fluorescence detection. Broadband collinear excitation is realized with the supercontinuum output of an argon-filled hollow-core fiber, enabling us to excite multiple transitions simultaneously in the visible range. The 2Q contribution is extracted via a three-pulse sequence with 16-fold phase cycling and simulated employing cresyl violet as a model system. Furthermore, we report the first experimental realization of one-quantum-two-quantum (1Q-2Q) 2D spectroscopy, offering less congested spectra as compared with the 2Q implementation. We avoid scattering artifacts and nonresonant solvent contributions by using fluorescence as the observable. This allows us to extract quantitative information about doubly excited states that agree with literature expectations. The high sensitivity and background-free nature of fluorescence detection allow for a general applicability of this method to many other systems.

Recent advances in multidimensional ultrafast spectroscopy

Multidimensional ultrafast spectroscopies are one of the premier tools to investigate condensed phase dynamics of biological, chemical and functional nanomaterial systems. As they reach maturity, the variety of frequency domains that can be explored has vastly increased, with experimental techniques capable of correlating excitation and emission frequencies from the terahertz through to the ultraviolet. Some of the most recent innovations also include extreme cross-peak spectroscopies that directly correlate the dynamics of electronic and vibrational states. This review article summarizes the key technological advances that have permitted these recent advances, and the insights gained from new multidimensional spectroscopic probes.

Using Multiorder Time-Correlation Functions (TCFs) To Elucidate Biomolecular Reaction Pathways from Microsecond Single-Molecule Fluorescence Experiments

Recent advances in single-molecule fluorescence imaging have made it possible to perform measurements on microsecond time scales. Such experiments have the potential to reveal detailed information about the conformational changes in biological macromolecules, including the reaction pathways and dynamics of the rearrangements involved in processes, such as sequence-specific DNA "breathing" and the assembly of protein-nucleic acid complexes. Because microsecond-resolved single-molecule trajectories often involve "sparse" data, that is, they contain relatively few data points per unit time, they cannot be easily analyzed using the standard protocols that were developed for single-molecule experiments carried out with tens-of-millisecond time resolution and high "data density." Here, we describe a generalized approach, based on time-correlation functions, to obtain kinetic information from microsecond-resolved single-molecule fluorescence measurements. This approach can be used to identify short-lived intermediates that lie on reaction pathways connecting relatively long-lived reactant and product states. As a concrete illustration of the potential of this methodology for analyzing specific macromolecular systems, we accompany the theoretical presentation with the description of a specific biologically relevant example drawn from studies of reaction mechanisms of the assembly of the single-stranded DNA binding protein of the T4 bacteriophage replication complex onto a model DNA replication fork.

Ultrafast Relaxation Dynamics of Photoexcited Zinc-Porphyrin: Electronic-Vibrational Coupling

Cyclic tetrapyrroles are the active core of compounds with crucial roles in living systems, such as hemoglobin and chlorophyll, and in technology as photocatalysts and light absorbers for solar energy conversion. Zinc-tetraphenylporphyrin (Zn-TPP) is a prototypical cyclic tetrapyrrole that has been intensely studied in past decades. Because of its importance for photochemical processes the optical properties are of particular interest, and, accordingly, numerous studies have focused on light absorption and excited-state dynamics of Zn-TPP. Relaxation after photoexcitation in the Soret band involves internal conversion that is preceded by an ultrafast process. This relaxation process has been observed by several groups. Hitherto, it has not been established if it involves a higher lying "dark" state or vibrational relaxation in the excited S2 state. Here we combine high time resolution electronic and vibrational spectroscopy to show that this process constitutes vibrational relaxation in the anharmonic S2 potential.

Ultrafast decoherence dynamics govern photocarrier generation efficiencies in polymer solar cells

All-organic-based photovoltaic solar cells have attracted considerable attention because of their low-cost processing and short energy payback time. In such systems the primary dissociation of an optical excitation into a pair of photocarriers has been recently shown to be extremely rapid and efficient, but the physical reason for this remains unclear. Here, two-dimensional photocurrent excitation spectroscopy, a novel non-linear optical spectroscopy, is used to probe the ultrafast coherent decay of photoexcitations into charge-producing states in a polymer:fullerene based solar cell. The two-dimensional photocurrent spectra are interpreted by introducing a theoretical model for the description of the coupling of the electronic states of the system to an external environment and to the applied laser fields. The experimental data show no cross-peaks in the twodimensional photocurrent spectra, as predicted by the model for coherence times between the exciton and the photocurrent producing states of 20 fs or less.

Fifty years of DNA "breathing": Reflections on old and new approaches

The coding sequences for genes, and much other regulatory information involved in genome expression, are located 'inside' the DNA duplex. Thus the "macromolecular machines" that read-out this information from the base sequence of the DNA must somehow access the DNA "interior." Double-stranded (ds) DNA is a highly structured and cooperatively stabilized system at physiological temperatures, but is also only marginally stable and undergoes a cooperative "melting phase transition" at temperatures not far above physiological. Furthermore, due to its length and heterogeneous sequence, with AT-rich segments being less stable than GC-rich segments, the DNA genome 'melts' in a multistate fashion. Therefore the DNA genome must also manifest thermally driven structural ("breathing") fluctuations at physiological temperatures that should reflect the heterogeneity of the dsDNA stability near the melting temperature. Thus many of the breathing fluctuations of dsDNA are likely also to be sequence dependent, and could well contain information that should be "readable" and useable by regulatory proteins and protein complexes in site-specific binding reactions involving dsDNA "opening." Our laboratory has been involved in studying the breathing fluctuations of duplex DNA for about 50 years. In this "Reflections" article we present a relatively chronological overview of these studies, starting with the use of simple chemical probes (such as hydrogen exchange, formaldehyde, and simple DNA "melting" proteins) to examine the local stability of the dsDNA structure, and culminating in sophisticated spectroscopic approaches that can be used to monitor the breathing-dependent interactions of regulatory complexes with their duplex DNA targets in "real time."

Ultrafast Spectroscopy with Photocurrent Detection: Watching Excitonic Optoelectronic Systems at Work

While ultrafast spectroscopy with photocurrent detection was almost unknown before 2012, in the last 3 years, a number of research groups from different fields have independently developed ultrafast electric probe approaches and reported promising pilot studies. Here, we discuss these recent advances and provide our perspective on how photocurrent detection successfully overcomes many limitations of all-optical methods, which makes it a technique of choice when device photophysics is concerned. We also highlight compelling existing problems and research questions and suggest ways for further development, outlining the potential breakthroughs to be expected in the near future using photocurrent ultrafast optical probes.

Electric Dipole Transition Moments and Solvent-Dependent Interactions of Fluorescent Boron-Nitrogen Substituted Indole Derivatives

Fluorescent analogues of the indole side chain of tryptophan can be useful spectroscopic probes of protein-protein and protein-DNA interactions. Here we present linear dichroism and solvent-dependent spectroscopic studies of two fluorescent analogues of indole, in which the organic C═C unit is substituted with the isosteric inorganic B-N unit. We studied the so-called "external" BN indole, which has C2v symmetry, and the "fused" BN indole with Cs symmetry. We performed a combination of absorption and fluorescence spectroscopy, ultraviolet linear dichroism (UV-LD) in stretched poly(ethylene) (PE) films, and quantum chemical calculations on both BN indole compounds. Our measurements allowed us to characterize the degree of alignment for both molecules in stretched PE films. We thus determined the orientations and magnitudes of the two lowest energy electric dipole transition moments (EDTMs) for external BN indole, and the two lowest energy EDTMs for fused BN indole within the 30 000-45 000 cm(-1) spectral range. We compared our experimental results to those of quantum chemical calculations using standard density functional theory (DFT). Our theoretical predictions for the low-energy EDTMs are in good agreement with our experimental data. The absorption and fluorescence spectra of the external and the fused BN indoles are sensitive to solvent polarity. Our results indicate that the fused BN indole experiences much greater solvation interactions with polar solvents than does the external BN indole.

Temperature-dependent conformations of a membrane supported zinc porphyrin tweezer by 2D fluorescence spectroscopy

We studied the equilibrium conformations of a zinc porphyrin tweezer composed of two carboxylphenyl-functionalized zinc tetraphenyl porphyrin subunits connected by a 1,4-butyndiol spacer, which was suspended inside the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) liposomes. By combining phase-modulation two-dimensional fluorescence spectroscopy (2D FS) with linear absorbance and fluorimetry, we determined that the zinc porphyrin tweezer adopts a mixture of folded and extended conformations in the membrane. By fitting an exciton-coupling model to a series of data sets recorded over a range of temperatures (17-85 °C) and at different laser center wavelengths, we determined that the folded form of the tweezer is stabilized by a favorable change in the entropy of the local membrane environment. Our results provide insights toward understanding the balance of thermodynamic factors that govern molecular assembly in membranes.

Fifth-order three-dimensional electronic spectroscopy using a pump-probe configuration

We present the theoretical details and experimental demonstration of fifth-order three-dimensional (3D) electronic spectroscopy using a pump-probe beam geometry. This is achieved using a pulse shaper and appropriate phase cycling schemes. We show how 8-step and 27-step phase cycling schemes can measure purely absorptive 3D spectra as well as 3D spectra for the individual fifth-order processes that contribute to the purely absorptive spectrum. 3D spectra as a function of two separate controllable waiting time periods can be obtained. The peak shapes and positions of the peaks in the experimental measurement correspond well to theory.

Solution conformation of 2-aminopurine (2-AP) dinucleotide determined by ultraviolet 2D fluorescence spectroscopy (UV-2D FS)

We have observed the conformation-dependent electronic coupling between the monomeric subunits of a dinucleotide of 2-aminopurine (2-AP), a fluorescent analog of the nucleic acid base adenine. This was accomplished by extending two-dimensional fluorescence spectroscopy (2D FS) - a fluorescence-detected variation of 2D electronic spectroscopy - to excite molecular transitions in the ultraviolet (UV) regime. A collinear sequence of four ultrafast laser pulses centered at 323 nm was used to resonantly excite the coupled transitions of 2-AP dinucleotide. The phases of the optical pulses were continuously swept at kilohertz frequencies, and the ensuing nonlinear fluorescence was phase-synchronously detected at 370 nm. Upon optimization of a point-dipole coupling model to our data, we found that in aqueous buffer the 2-AP dinucleotide adopts an average conformation in which the purine bases are non-helically stacked (center-to-center distance R₁₂ = 3.5 Å ± 0.5 Å, twist angle θ₁₂ = 5° ± 5°), which differs from the conformation of such adjacent bases in duplex DNA. These experiments establish UV-2D FS as a method for examining the local conformations of an adjacent pair of fluorescent nucleotides substituted into specific DNA or RNA constructs, which will serve as a powerful probe to interpret, in structural terms, biologically significant local conformational changes within the nucleic acid framework of protein-nucleic acid complexes.

Electronic transition moments of 6-methyl isoxanthopterin--a fluorescent analogue of the nucleic acid base guanine

Fluorescent nucleic acid base analogues are important spectroscopic tools for understanding local structure and dynamics of DNA and RNA. We studied the orientations and magnitudes of the electric dipole transition moments (EDTMs) of 6-methyl isoxanthopterin (6-MI), a fluorescent analogue of guanine that has been particularly useful in biological studies. Using a combination of absorption spectroscopy, linear dichroism (LD) and quantum chemical calculations, we identified six electronic transitions that occur within the 25 000–50 000 cm⁻¹ spectral range. Our results indicate that the two experimentally observed lowest-energy transitions, which occur at 29 687 cm⁻¹ (337 nm) and 34 596 cm⁻¹ (289 nm), are each polarized within the plane of the 6-MI base. A third in-plane polarized transition is experimentally observed at 47 547 cm⁻¹ (210 nm). The theoretically predicted orientation of the lowest-energy transition moment agrees well with experiment. Based on these results, we constructed an exciton model to describe the absorption spectra of a 6-MI dinucleotide–substituted double-stranded DNA construct. This model is in good agreement with the experimental data. The orientations and intensities of the low-energy electronic transitions of 6-MI reported here should be useful for studying local conformations of DNA and RNA in biologically important complexes.

Compressed Sensing for Multidimensional Spectroscopy Experiments

Compressed sensing is a processing method that significantly reduces the number of measurements needed to accurately resolve signals in many fields of science and engineering. We develop a two-dimensional variant of compressed sensing for multidimensional spectroscopy and apply it to experimental data. For the model system of atomic rubidium vapor, we find that compressed sensing provides an order-of-magnitude (about 10-fold) improvement in spectral resolution along each dimension, as compared to a conventional discrete Fourier transform, using the same data set. More attractive is that compressed sensing allows for random undersampling of the experimental data, down to less than 5% of the experimental data set, with essentially no loss in spectral resolution. We believe that by combining powerful resolution with ease of use, compressed sensing can be a powerful tool for the analysis and interpretation of ultrafast spectroscopy data.