Photoinduced Processes in Riboflavin: Superposition of ππ*−nπ* States by Vibronic Coupling, Transfer of Vibrational Coherence, and Population Dynamics under Solvent Control

Emission of Protonated Riboflavin Induced by Inhibition of Out-of-plane Vibration in a Rigid Polymer Network

Chromophores incorporated into rigid polymer matrices may exhibit novel photophysical properties distinct from those in liquid solutions. In this work, we explored the decay path of the second ππ* state (2ππ*) of riboflavin in poly(vinyl alcohol) (PVA) solutions and films with various acidities. Highly efficient internal conversion from 2ππ* to the lowest ππ* state (1ππ*) induced by slight in-plane motion is demonstrated in all PVA solutions and films, irrespective of environmental acidity and rigidification. Ground-state protonation of riboflavin occurs in the highly acidic PVA film, and this cationic species emits fluorescence around 460 nm, in contrast to the ultrafast nonradiative relaxation in aqueous solution. The emission is demonstrated to originate from the 2ππ* state rather than the 1ππ* state. The 2ππ*-1ππ* internal conversion of protonated riboflavin is demonstrated to be induced by out-of-plane motion and impeded in a rigid PVA network, resulting in the anti-Kasha fluorescence.

Electronic, optical and charge transport properties of Zn-porphyrin-C60 MOFs: a combined periodic and cluster modeling

Density functional theory (DFT) calculations were performed on the 5,15 meso-positions of nine porphyrin-containing MOFs; Zn2(TCPB)-(NMe2-ZnP); (H4TCPB = 1,2,4,5-tetrakis(4-carboxyphenyl)benzene), (NMe2-ZnP = [5,15-bis[(4-pyridyl)-ethynyl]-10,20-bis-(dimethylamine) porphinato]zinc(II)) functionalized with nitrogen-, oxygen-, and sulfur-containing groups to study their effects on the electronic, optical and transport properties of the materials. The properties of these materials have also been investigated by encapsulating fullerene (C60) in their pores (C60@MOFs). The results indicate that the guest C60 in the MOF generates high photoconductivity through efficient porphyrin/fullerene donor-acceptor (D-A) interactions, which are facilitated by oxygen and sulfur functionalities. DFT calculations show that C60 interacts favorably in MOFs due to negative Eint values. Encapsulated C60 molecules modify the electronic band structure, affecting the conduction band and unoccupied states of MOFs corresponding to C60 p orbitals. TD-DFT calculations show that incorporating C60 promotes D-A interactions in MOFs, leading to charge transfer in the near-infrared and visible photoinduced electron transfer (PET) from porphyrins to C60. Nonequilibrium Green's function-based calculations for MOFs with sulfur group, with and without C60, performed using molecular junctions with Au(111)-based electrodes show increased charge transport for the doped MOF. These insights into tuning electronic/optical properties and controlling charge transfer can aid in the design of new visible/near-infrared MOF-based optoelectronic devices.

Determining Excited-State Absorption Properties of a Quinoid Flavin by Polarization-Resolved Transient Spectroscopy

As important naturally occurring chromophores, photophysical/chemical properties of quinoid flavins have been extensively studied both experimentally and theoretically. However, little is known about the transition dipole moment (TDM) orientation of excited-state absorption transitions of these important compounds. This aspect is of high interest in the fields of photocatalysis and quantum control studies. In this work, we employ polarization-associated spectra (PAS) to study the excited-state absorption transitions and the underlying TDM directions of a standard quinoid flavin compound. As compared to transient absorption anisotropy (TAA), an analysis based on PAS not only avoids diverging signals but also retrieves the relative angle for ESA transitions with respect to known TDM directions. Quantum chemical calculations of excited-state properties lead to good agreement with TA signals measured in magic angle configuration. Only when comparing experiment and theory for TAA spectra and PAS, do we find deviations when and only when the S0 → S1 of flavin is used as a reference. We attribute this to the vibronic coupling of this transition to a dark state. This effect is only observed in the employed polarization-controlled spectroscopy and would have gone unnoticed in conventional TA.

Shining a Spotlight on Methyl Groups: Photochemically Induced Dynamic Nuclear Polarization Spectroscopy of 5-Deazariboflavin and Its Nor Analogs

5-Deazaflavins are analogs of naturally occurring flavin cofactors. They serve as substitutes for natural flavin cofactors to investigate and modify the reaction pathways of flavoproteins. Demethylated 5-deazaflavins are potential candidates for artificial cofactors, allowing us to fine-tune the reaction kinetics and absorption characteristics of flavoproteins. In this contribution, demethylated 5-deazariboflavin radicals are investigated (1) to assess the influence of the methyl groups on the electronic structure of the 5-deazaflavin radical and (2) to explore their photophysical properties with regard to their potential as artificial cofactors. We determined the proton hyperfine structure of demethylated 5-deazariboflavins using photochemically induced dynamic nuclear polarization (photo-CIDNP) spectroscopy, as well as density functional theory (DFT). To provide context, we compare our findings to a study of flavin mononucleotide (FMN) derivatives. We found a significant influence of the methylation pattern on the absorption properties, as well as on the proton hyperfine coupling ratios of the xylene moiety, which appears to be solvent-dependent. This effect is enhanced by the replacement of N5 by C5-H in 5-deazaflavin derivatives compared to their respective flavin counterparts.

Comparing ultrafast excited state quenching of flavin 1,N6-ethenoadenine dinucleotide and flavin adenine dinucleotide by optical spectroscopy and DFT calculations

Flavins are photoenzymatic cofactors often exploiting the absorption of light to energize photoinduced redox chemistry in a variety of contexts. Both flavin adenine dinucleotide (FAD) and flavin mononucleotide (FMN) are used for this function. The study of these photoenzymes has been facilitated using flavin analogs. Most of these analogs involve modification of the flavin ring, and there is recent evidence that adenine (Ade)-modified FAD can affect enzyme turnover, but so far this has only been shown for enzymes where the adenine and flavin rings are close to each other in a stacked conformation. FAD is also stacked in aqueous solution, and its photodynamics are quite different from unstacked FAD or FMN. Oxidized photoexcited FAD decays rapidly, presumably through PET with Ade as donor and Fl* as acceptor. Definitive identification of the spectral signatures of Ade^∙+ and Fl^∙- radicals is elusive. Here we use the FAD analog Flavin 1,N⁶-Ethenoadenine Dinucleotide (εFAD) to study how different photochemical outcomes depend on the identity of the Ade moiety in stacked FAD and its analog εFAD. We have used UV-Vis transient absorption spectroscopy complemented by TD-DFT calculations to investigate the excited state evolution of the flavins. In FAD*, no radicals were observed, suggesting that FAD* does not undergo PET. εFAD* kinetics showed a broad absorption band that suggests a charge transfer state exists upon photoexcitation with evidence for radical pair formation. Surprisingly, significant triplet flavin was produced from εFAD* We hypothesize that the dipolar (ε)Ade moieties differentially modulate the singlet-triplet energy gap, resulting in different intersystem crossing rates. The additional electron density on the etheno group of εFAD supplies better orbital overlap with the flavin S₁ state, accelerating charge transfer in that molecule.

Modulating catalytic activity of a modified flavin analogue via judicially positioned metal ion toward aerobic sulphoxidation

This manuscript describes the synthesis, spectroscopic and crystallographic characterization of a cadmium complex of 10-propoylisoalloxazine-7-carboxylic acid (Flc-Cd). Catalytic activity of Flc-Cd towards aerobic sulphoxidation reaction was investigated in the presence of l-ascorbic acid as the reducing agent. Notably the neutral un-metalated flavin analogue did not show any significant catalytic activity. The design strategy for Flc provides a close proximity of the metal centre to the flavin core without compromising the catalytic site thereby assisting the product formation when compared to unmetallated Flc. Minor enantioselectivity is also observed in cases where unsymmetrical sulphides were used; indicative of the possible involvement of chiral l-ascorbic acid in the intermediate formation.

Design and synthesis of a catalytically efficient metal-flavin complex toward aerobic sulphoxidation was achieved via judicially positioning the metal ion near the catalytic site thereby assisting the intermediate formation.

Electronic nature and structure of aggregates of riboflavin molecules

Aggregation process of riboflavin molecules in binary mixtures: water - dioxane, water - DMSO, and ethanol - isobutanol, were investigated using spectroscopic methods and quantum-chemical calculation. It was shown that at a constant concentration of riboflavin and different ratios of binary mixtures, a deformation of the electronic absorption spectra with a hypochromic effect is observed. The observed changes are caused by the formation of a hydrogen bond and dipole-dipole interaction between riboflavin molecules, which is accompanied by a shift and resonance splitting of excited electronic levels.

UV-visible absorption spectrum of FAD and its reduced forms embedded in a cryptochrome protein

Cryptochromes are a class of flavoproteins proposed as candidates to explain magnetoreception of animals, plants and bacteria. The main hypothesis is that a biradical is formed upon blue-light absorption by flavin adenine dinucleotide (FAD). In a protein milieu, the oxidized form of FAD can be reduced, leading to four redox derivative forms: anionic and neutral semi-reduced radicals, and anionic and neutral fully reduced forms. All these forms have a characteristic electronic absorption spectrum, with a strong vibrational resolution. Here, we carried out a normal mode analysis at the electrostatic embedding QM/MM level of theory to compute the vibrationally resolved absorption spectra of the five redox forms of FAD embedded in a plant cryptochrome. We show that explicitly accounting for vibrational broadening contributions to electronic transitions is essential to reproduce the experimental spectra. In the case of the neutral radical form of FAD, the absorption spectrum is reproduced only if the presence of a tryptophan radical is considered.

Femtosecond-to-nanosecond dynamics of flavin mononucleotide monitored by stimulated Raman spectroscopy and simulations

Flavin mononucleotide (FMN) belongs to the large family of flavins, ubiquitous yellow-coloured biological chromophores that contain an isoalloxazine ring system. As a cofactor in flavoproteins, it is found in various enzymes and photosensory receptors, like those featuring the light-oxygen-voltage (LOV) domain. The photocycle of FMN is triggered by blue light and proceeds via a cascade of intermediate states. In this work, we have studied isolated FMN in an aqueous solution in order to elucidate the intrinsic electronic and vibrational changes of the chromophore upon excitation. The ultrafast transitions of excited FMN were monitored through the joint use of femtosecond stimulated Raman spectroscopy (FSRS) and transient absorption spectroscopy encompassing a time window between 0 ps and 6 ns with 50 fs time resolution. Global analysis of the obtained transient visible absorption and transient Raman spectra in combination with extensive quantum chemistry calculations identified unambiguously the singlet and triplet FMN populations and addressed solvent dynamics effects. The good agreement between the experimental and theoretical spectra facilitated the assignment of electronic transitions and vibrations. Our results represent the first steps towards more complex experiments aimed at tracking structural changes of FMN embedded in light-inducible proteins upon photoexcitation.

The sacrificial inactivation of the blue-light photosensor cryptochrome from Drosophila melanogaster

Drosophila melanogaster cryptochrome functions as the primary blue-light receptor that mediates circadian photo entrainment. Absorption of a photon leads to reduction of the protein-bound FAD via consecutive electron transfer along a conserved tryptophan tetrad resembling the signalling state required for conformational changes and induction of subsequent signalling cascades. However, how the initial photochemistry and subsequent dark processes leading to downstream signalling are linked to each other at the molecular level is still poorly understood. Here, we investigated in detail the initial photochemical events in DmCRY by time-resolved and stationary absorption spectroscopy combined with quantum chemical and molecular dynamics calculations. We resolved the early events along the conserved tryptophan tetrad and the final deprotonation of the terminal tryptophanyl radical cation. These initial events lead to conformational changes, such as the known C-terminal tail release, Trp decomposition, and finally FAD release providing evidence that DmCRY does not undergo a photocycle. We propose that light is a negative regulator of DmCRY stability even under in vitro conditions where the proteasomal machinery is missing, that is in line with its biological function, i.e. entrainment of the circadian clock.

Enhancement of the lasing efficiency of vitamin B2 in a highly polar organic solvent via DNA-lipid complex

We experimentally demonstrated a green liquid laser at the wavelength of 570 nm, utilizing the optical gain of vitamin B₂ in a highly polar organic solvent, and proposed an efficient method to enhance its lasing efficiency by adding DNA-lipid complex (DNA-CTMA) in the solution. Optical properties of vitamin B₂ in the hexafluoro-2-propanol solvents were investigated by adding various amounts of DNA-CTMA in terms of the UV-visible absorbance, the visible emission, and the fluorescence lifetime. A Fabry-Perot cavity was built to obtain the laser oscillation at 570 nm using a pulsed pump source at the wavelength of 450 nm, 5 ns pulse duration, and 10 Hz repetition rate. By adding DNA-CTMA, both the output power and slope efficiency were enhanced along with a significant reduction of the lasing threshold pump power. The proposed scheme could open new potential for highly efficient biolasers.

Absorption and luminescence spectroscopy of mass-selected flavin adenine dinucleotide mono-anions

We report the absorption profile of isolated Flavin Adenine Dinucleotide (FAD) mono-anions recorded using photo-induced dissociation action spectroscopy. In this charge state, one of the phosphoric acid groups is deprotonated and the chromophore itself is in its neutral oxidized state. These measurements cover the first four optical transitions of FAD with excitation energies from 2.3 to 6.0 eV (210-550 nm). The S₀ → S₂ transition is strongly blue shifted relative to aqueous solution, supporting the view that this transition has a significant charge-transfer character. The remaining bands are close to their solution-phase positions. This confirms that the large discrepancy between quantum chemical calculations of vertical transition energies and solution-phase band maxima cannot be explained by solvent effects. We also report the luminescence spectrum of FAD mono-anions in vacuo. The gas-phase Stokes shift for S₁ is 3000 cm^-1, which is considerably larger than any previously reported for other molecular ions and consistent with a significant displacement of the ground and excited state potential energy surfaces. Consideration of the vibronic structure is thus essential for simulating the absorption and luminescence spectra of flavins.

On the nature of solvatochromic effect: The riboflavin absorption spectrum as a case study

We present here the calculation of the absorption spectrum of riboflavin in acetonitrile and dimethyl sulfoxide using a hybrid quantum/classical approach, namely the perturbed matrix method, based on quantum mechanical calculations and molecular dynamics simulations. The calculated spectra are compared to the absorption spectrum of riboflavin previously calculated in water and to the experimental spectra obtained in all three solvents. The experimentally observed variations in the absorption spectra upon change of the solvent environment are well reproduced by the calculated spectra. In addition, the nature of the excited states of riboflavin interacting with different solvents is investigated, showing that environment effects determine a recombination of the gas-phase electronic states and that such a recombination is strongly affected by the polarity of the solvent inducing significant changes in the absorption spectra.

Ultrafast Spectroscopic Dynamics of Quinacrine-Riboflavin Binding Protein Interactions

Redox active cofactors play a dynamic role inside protein binding active sites because the amino acids responsible for binding participate in electron transfer (ET) reactions. Here, we use femtosecond transient absorption (FsTA) spectroscopy to examine the ultrafast ET between quinacrine (Qc), an antimalarial drug with potential anticancer activity, and riboflavin binding protein (RfBP) with a known K_d = 264 nM. Steady-state absorption reveals a ∼ 10 nm red-shift in the ground state when QcH₃²⁺ is titrated with RfBP, and a Stern-Volmer analysis shows ∼84% quenching and a blue-shift of the QcH₃²⁺ photoluminescence to form a 1:1 binding ratio of the QcH₃²⁺-RfBP complex. Upon selective photoexcitation of QcH₃²⁺ in the QcH₃²⁺-RfBP complex, we observe charge separation in 7 ps to form ¹[QcH_{3_red}^•+-RfBP^•+], which persists for 138 ps. The FsTA spectra show the spectroscopic identification of QcH_{3_red}^•+, determined from spectroelectrochemical measurements in DMSO. We correlate our results to literature and report lifetimes that are 10-20× slower than the natural riboflavin, Rf-RfBP, complex and are oxygen independent. Driving force (ΔG) calculations, corrected for estimated dielectric constants for protein hydrophobic pockets, and Marcus theory depict a favorable one-electron ET process between QcH₃²⁺ and nearby redox active tyrosine (Tyr) or tryptophan (Trp) residues.

Ultrafast 2D-IR spectroelectrochemistry of flavin mononucleotide

We demonstrate the coupling of ultrafast two-dimensional infrared (2D-IR) spectroscopy to electrochemistry in solution and apply it to flavin mononucleotide, an important cofactor of redox proteins. For this purpose, we designed a spectroelectrochemical cell optimized for 2D-IR measurements in reflection and measured the time-dependent 2D-IR spectra of the oxidized and reduced forms of flavin mononucleotide. The data show anharmonic coupling and vibrational energy transfer between different vibrational modes in the two redox species. Such information is inaccessible with redox-controlled steady-state FTIR spectroscopy. The wide range of applications offered by 2D-IR spectroscopy, such as sub-picosecond structure determination, IR band assignment via energy transfer, disentangling reaction mixtures through band connectivity in the 2D spectra, and the measurement of solvation dynamics and chemical exchange can now be explored under controlled redox potential. The development of this technique furthermore opens new horizons for studying the dynamics of redox proteins.

Water-soluble cationic poly(β-cyclodextrin-co-guanidine) as a controlled vitamin B2delivery carrier

Vitamin B₂(VB₂) is effectively incorporated into novel water-soluble cationic β-cyclodextrin (β-CD) polymers in order to improve its physiochemical properties.

Ultrafast excited-state deactivation of flavins bound to dodecin

Dodecins, a group of flavin-binding proteins with a dodecameric quaternary structure, are able to incorporate two flavins within each of their six identical binding pockets building an aromatic tetrade with two tryptophan residues. Dodecin from the archaeal Halobacterium salinarum is a riboflavin storage device. We demonstrate that unwanted side reactions induced by reactive riboflavin species and degradation of riboflavin are avoided by ultrafast depopulation of the reactive excited state of riboflavin. Intriguingly, in this process, the staggered riboflavin dimers do not interact in ground and photoexcited states. Rather, within the tetrade assembly, each riboflavin is kept under the control of the respective adjacent tryptophan, which suggests that the stacked arrangement is a matter of optimizing the flavin load. We further identify an electron transfer in combination with a proton transfer as a central element of the effective excited state depopulation mechanism. Structural and functional comparisons of the archaeal dodecin with bacterial homologs reveal diverging evolution. Bacterial dodecins bind the flavin FMN instead of riboflavin and exhibit a clearly different binding pocket design with inverse incorporations of flavin dimers. The different adoption of flavin changes photochemical properties, making bacterial dodecin a comparably less efficient quencher of flavins. This supports a functional role different for bacterial and archaeal dodecins.

New insights into the ultrafast photophysics of oxidized and reduced FAD in solution

The ultrafast photophysics of oxidized and reduced flavin adenine dinucleotide (FAD) in aqueous solution was studied by broadband UV-vis femtosecond transient absorption spectroscopy. We observed that oxidized FAD (FAD(ox)) in solution readily aggregates at submillimolar concentration. Upon excitation of FAD(ox), three excited-state lifetimes were found and assigned to three different species: the closed (stacked) conformation of the monomer (∼5.4 ps), the open (extended) conformation of the monomer (∼2.8 ns), and the dimer (∼27 ps). In the case of the stacked conformation of the monomer, we show that intramolecular electron transfer from the adenine to the isoalloxazine ring occurs with a time constant of 5.4 ps and is followed by charge recombination on a faster time scale, namely, 390 fs. We additionally demonstrate that deprotonated reduced flavin (FADH(-)) undergoes biphotonic ionization under high excitation fluence and dissociates into a hydrated electron and the neutral semiquinone radical FADH(•).

Synthesis, structure and photophysical properties of a flavin-based platinum(II) complex

We synthesized a thiosemicarbazone-functionalized flavin (Fl-(H)TSC: 2-[2-(3,4-dihydro-7,8-dimethyl-2,4-dioxobenzo[g]pteridin-10(2H)-yl)ethylidene]-hydrazinecarbothioamide) and its Pt(II) complex [Pt(Fl-TSC)(2)], and characterized it using X-ray diffraction, UV-visible absorption and luminescence spectroscopy. X-ray structural analysis for [Pt(Fl-TSC)(2)] revealed that the structure of the isoalloxazine part was almost the same as that in lumiflavin (7,8,10-trimethylisoalloxazine), and the thiosemicarbazone moiety acted as a bidentate ligand to form a PtS(2)N(2) planar conformation. UV-visible absorption and luminescence spectra of these compounds were very similar to those of riboflavin, but the emission intensity and the lifetime decreased considerably. Theoretical calculations suggested that the charge-separated state (Fl˙(-)-TSC˙(+)) contributed to the faster quenching from the (1)π-π* emission state.

(TD-)DFT calculation of vibrational and vibronic spectra of riboflavin in solution

The photophysics and photochemistry of flavin molecules are of great interest due to their role for the biological function of flavoproteins. An important analysis tool toward the understanding of the initial photoexcitation step of flavins is electronic and vibrational spectroscopy, both in frequency and time domains. Here we present quantum chemical [(time-dependent) density functional theory ((TD-)DFT)] calculations for vibrational spectra of riboflavin, the parent molecule of biological blue-light receptor chromophores, in its electronic ground (S(0)) and lowest singlet excited states (S(1)). Further, vibronic absorption spectra for the S(0) --> S(1) transition and vibronic emission spectra for the reverse process are calculated, both including mode mixing. Solvent effects are partially accounted for by using a polarizable continuum model (PCM) or a conductor-like screening model (COSMO). Calculated vibrational and electronic spectra are in good agreement with measured ones and help to assign the experimental signals arising from photoexcitation of flavins. In particular, upon photoexcitation a loss of double bond character in the polar region of the ring system is observed which leads to vibronic fine structure in the electronic spectra. Besides vibronic effects, solvent effects are important for understanding the photophysics of flavins in solution quantitatively.

Fluorescence decay dynamics of flavin adenine dinucleotide in a mixture of alcohol and water in the femtosecond and nanosecond time range

Fluorescence decays of flavin adenine dinucleotide (FAD) that is a typical autofluorescent species in cells and tissues have been measured in a mixture of alcohol and water in the femtosecond and nanosecond time range. The fluorescence lifetimes of both the stacked conformation between the isoalloxazine and adenine moieties in close proximity and the extended open conformation in water are affected by the addition of alcohol. The nanosecond fluorescence lifetime of the open conformation increases with decreasing dielectric constant of the medium, contributing to the enhancement of the fluorescence intensity of FAD in less dielectric media. The fluorescence lifetime of the open conformation is also affected by medium viscosity, suggesting that the photoexcited open conformation is quenched by the dynamic interaction between the two aromatic rings. The fluorescence component decaying in tens of picoseconds is attributed to the stacked conformation that shows the efficient fluorescence quenching due to the intramolecular electron transfer. The picosecond fluorescence lifetime of the stacked conformation increases with decreasing dielectric constant, suggesting the shift of the distribution of the stacked conformation to a longer intramolecular distance between the two aromatic rings in less dielectric media. The pre-exponential factor of the picosecond decaying component relative to that of the nanosecond one decreases with the increase of the alcohol concentration in the femtosecond time-resolved fluorescence, which demonstrates the increase in the population of the open conformation with the reduction of the dielectric constant. The possibility to evaluate the polar environment in a cell by the fluorescence lifetime of FAD is discussed based on the results obtained.

Influence of the LOV domain on low-lying excited states of flavin: a combined quantum-mechanics/molecular-mechanics investigation

The ground and low-lying excited states of flavin mononucleotide (FMN) in the light, oxygen, and voltage sensitive (LOV) domain of the blue-light photosensor YtvA of Bacillus subtilis were studied by means of combined quantum-mechanical/molecular-mechanical (QM/MM) methods. The FMN cofactor (without the side chain) was treated with density functional theory (DFT) for the geometry optimizations and a combination of DFT and multireference configuration interaction (MRCI) for the determination of the excitation energies, while the protein environment was represented by the CHARMM force field. In addition, several important amino acid side chains, including the reactive cysteine residue, were included in the QM region in order to probe their influence on the spectral properties of the cofactor in two protein conformations. Spin-orbit coupling was taken into account employing an efficient, nonempirical spin-orbit mean-field Hamiltonian. Our results reveal that the protein environment of YtvA-LOV induces spectral shifts for the (pi pi*) states that are similar to those in aqueous solution. In contrast, the blue shifts of the (n pi*) states are smaller in the protein environment, enabling a participation of these states in the decay processes of the optically bright S(1) state. Increased spin-orbit coupling between the initially populated S(1) state and the T(1) and T(2) states is found in YtvA-LOV as compared to free lumiflavine in water. The enhanced singlet-triplet coupling is brought about partially by configuration interaction with (n pi*) states at the slightly out-of-plane distorted minimum geometry. In addition, an external heavy-atom effect is observed when the sulfur atom of the nearby cysteine residue is included in the QM region, in line with experimental findings.