Regioselective and solvent-dependent photoisomerization induced internal conversion in red fluorescent protein chromophore analogues

Photophysical properties of three red fluorescent protein (RFP) chromophore analogues are reported here. The three RFP chromophore analogues differ in the additional conjugation present in the RFP chromophore. The three chromophores do not exhibit any solvent effect in both absorption and fluorescence spectra. The photoirradiation experiments and recording of 1H NMR before and after irradiation on one of the three RFP model chromophores show isomerization of the (Z,E) diastereomer to the (E,E) diastereomer. Calculation of S0 and S1 potential energy curves shows the preference for isomerization through the exocyclic C[double bond, length as m-dash]C bond with Z-stereochemistry, thus corroborating the experimental results. The computational studies also suggest that torsional motion along the exocyclic C[double bond, length as m-dash]C bond pushes the molecules to a conical intersection, thus paving the pathway for radiationless deactivation.

Orthopalladated imidazolones and thiazolones: synthesis, photophysical properties and photochemical reactivity

The reaction of Pd(OAc)2 with (Z)-5-arylidene-4-(4H)-imidazolones (2a-e) and (Z)-4-arylidene-5(4H)-thiazolones (3a-e) in trifluoroacetic acid results in the corresponding orthopalladated dinuclear complexes (4a-e, imidazolones; 11a-d, thiazolones) with trifluoroacetate bridges through regioselective C-H activation at the ortho position of the 4-arylidene group. Compound 4e, which contains an imidazolone substituted at 2- and 4-positions of the arylidene ring with methoxide groups and exhibits strong push-pull charge transfer, is an excellent precursor for the synthesis of fluorescent complexes with green yellowish emission and remarkable quantum yields. Breaking the bridging system with pyridine yields the mononuclear complex 5e (ΦF = 5%), while metathesis of trifluoroacetate ligands with chloride leads to the dinuclear complex 6e, also a precursor of fluorescent complexes by breaking the chloride bridging system with pyridine (7e, ΦF = 7%), or by substitution of chloride ligands with pyridine (8e, ΦF = 15%) or acetylacetonate (9e, ΦF = 2%). In addition to notable photophysical properties, dinuclear complexes 4 and 11 also exhibit significant photochemical reactivity. Thus, irradiation of orthopalladates 4a-c and 11a-c in CH2Cl2 with blue light (465 nm) proceeds via [2 + 2] photocycloaddition of the CC double bonds of imidazolone and thiazolone ligands, yielding the corresponding cyclobutane-bridging diaminotruxillic derivatives 10a-c and 12a-c, respectively.

What Happens to a Pyrrole Hemithioindigo Photoswitch Trapped in a Fluorescent Protein?

Artificial molecular photoswitches that can be reversibly controlled into different configurations by external light stimulation have broad application prospects in various fields, such as materials and chemical biology. Among them, the pyrrole hemithioindigo (PHT) photoswitch has a geometric structure similar to that of the fluorescent protein chromophore. What happens when the chromophore is replaced by PHT, and does it achieve similar functions to the original one? To answer these questions, we carried out ONIOM(QM/MM) and classical molecular dynamics studies on the photoisomerization mechanism and spectroscopic properties of PHT in the fluorescent protein. The results showed that in the protein environment, the fate of excited PHT is governed by the competition between fluorescence emission and hula-twist isomerization. Due to the strong steric hindrance effects caused by the interlacing residues in the protein that restrict the PHT conformation transformation, the cis-to-trans isomerization process of PHT needs to overcome a barrier of at least 4.9 kcal/mol; thus, fluorescence emission is more dominant in competition. It is also found that the intermolecular interaction between LYS67 and the carbonyl oxygen of PHT has a significant effect on the fluorescence emission. These results revealed the photochemical reaction mechanism of a light-driven molecular switch in the fluorescent protein and provided further theoretical support for the field of chemical biology.

Fluorescence Amplification of Unsaturated Oxazolones Using Palladium: Photophysical and Computational Studies

Weakly fluorescent (Z)-4-arylidene-5-(4H)-oxazolones (1), Φ_PL < 0.1%, containing a variety of conjugated aromatic fragments and/or charged arylidene moieties, have been orthopalladated by reaction with Pd(OAc)₂. The resulting dinuclear complexes (2) have the oxazolone ligands bonded as a C^N-chelate, restricting intramolecular motions involving the oxazolone. From 2, a variety of mononuclear derivatives, such as [Pd(C^N-oxazolone)(O₂CCF₃)(py)] (3), [Pd(C^N-oxazolone)(py)₂](ClO₄) (4), [Pd(C^N-oxazolone)(Cl)(py)] (5), and [Pd(C^N-oxazolone)(X)(NHC)] (6, 7), have been prepared and fully characterized. Most of complexes 3-6 are strongly fluorescent in solution in the range of wavelengths from green to yellow, with values of Φ_PL up to 28% (4h), which are among the highest values of quantum yield ever reported for organometallic Pd complexes with bidentate ligands. This means that the introduction of the Pd in the oxazolone scaffold produces in some cases an amplification of the fluorescence of several orders of magnitude from the free ligand 1 to complexes 3-6. Systematic variations of the substituents of the oxazolones and the ancillary ligands show that the wavelength of emission is tuned by the nature of the oxazolone, while the quantum yield is deeply influenced by the change of ligands. TD-DFT studies of complexes 3-6 show a direct correlation between the participation of the Pd orbitals in the HOMO and the loss of emission through non-radiative pathways. This model allows the understanding of the amplification of the fluorescence and the future rational design of new organopalladium systems with improved properties.

Multiple Photoisomerization Pathways of the Green Fluorescent Protein Chromophore in a Reversibly Photoswitchable Fluorescent Protein: Insights from Quantum Mechanics/Molecular Mechanics Simulations

Herein, we have employed a combined CASPT2//CASSCF approach within the quantum mechanics/molecular mechanics (QM/MM) framework to explore the early time photoisomerization of rsEGFP2 starting from its two OFF trans states, i.e., Trans1 and Trans2. The results show similar vertical excitation energies to the S₁ state in their Franck-Condon regions. Considering the clockwise and counterclockwise rotations of the C11-C9 bond, four pairs of the S₁ excited-state minima and low-lying S₁/S₀ conical intersections were optimized, based on which we determined four S₁ photoisomerization paths that are essentially barrierless to the relevant S₁/S₀ conical intersections leading to efficient excited-state deactivation to the S₀ state. Most importantly, our work first identified multiple photoisomerization and excited-state decay paths, which must be seriously considered in the future. This work not only sheds significant light on the primary trans-cis photoisomerization of rsEGFP2 but also aids in the understanding of the microscopic mechanism of GFP-like RSFPs and the design of novel GFP-like fluorescent proteins.

Mapping the Complete Photocycle that Powers a Large Stokes Shift Red Fluorescent Protein

Large Stokes shift (LSS) red fluorescent proteins (RFPs) are highly desirable for bioimaging advances. The RFP mKeima, with coexisting cis- and trans-isomers, holds significance as an archetypal system for LSS emission due to excited-state proton transfer (ESPT), yet the mechanisms remain elusive. We implemented femtosecond stimulated Raman spectroscopy (FSRS) and various time-resolved electronic spectroscopies, aided by quantum calculations, to dissect the cis- and trans-mKeima photocycle from ESPT, isomerization, to ground-state proton transfer in solution. This work manifests the power of FSRS with global analysis to resolve Raman fingerprints of intermediate states. Importantly, the deprotonated trans-isomer governs LSS emission at 620 nm, while the deprotonated cis-isomer's 520 nm emission is weak due to an ultrafast cis-to-trans isomerization. Complementary spectroscopic techniques as a table-top toolset are thus essential to study photochemistry in physiological environments.

Generation and direct observation of a triplet arylnitrenium ion

Nitrenium ions are important reactive intermediates in both chemistry and biology. Although singlet nitrenium ions are well-characterized by direct methods, the triplet states of nitrenium ions have never been directly detected. Here, we find that the excited state of the photoprecursor partitions between heterolysis to generate the singlet nitrenium ion and intersystem crossing (ISC) followed by a spontaneous heterolysis process to generate the triplet p-iodophenylnitrenium ion (np). The triplet nitrenium ion undergoes ISC to generate the ground singlet state, which ultimately undergoes proton and electron transfer to generate a long-lived radical cation that further generates the reduced p-iodoaniline. Ab Initio calculations were performed to map out the potential energy surfaces to better understand the excited state reactivity channels show that an energetically-accessible singlet-triplet crossing lies along the N-N stretch coordinate and that the excited triplet state is unbound and spontaneously eliminates ammonia to generate the triplet nitrenium ion. These results give a clearer picture of the photophysical properties and reactivity of two different spin states of a phenylnitrenium ion and provide the first direct glimpse of a triplet nitrenium ion.

Nitrenium ions are highly electrophilic reactive intermediates of formula R−N−R+, nitrogen analogue of carbenes. Here the authors report the detection of a triplet nitrenium ion using time-resolved spectroscopic methods and ab initio computations, allowing a glimpse at the properties and behavior of this important class of intermediates.

Generalized Ab Initio Nonadiabatic Dynamics Simulation Methods from Molecular to Extended Systems

Nonadiabatic dynamics simulation has become a powerful tool to describe nonadiabatic effects involved in photophysical processes and photochemical reactions. In the past decade, our group has developed generalized trajectory-based ab initio surface-hopping (GTSH) dynamics simulation methods, which can be used to describe a series of nonadiabatic processes, such as internal conversion, intersystem crossing, excitation energy transfer and charge transfer of molecular systems, and photoinduced nonadiabatic carrier dynamics of extended systems with and without spin-orbit couplings. In this contribution, we will first give a brief introduction to our recently developed methods and related numerical implementations at different computational levels. Later, we will present some of our latest applications in realistic systems, which cover organic molecules, biological proteins, organometallic compounds, periodic organic and inorganic materials, etc. Final discussion is given to challenges and outlooks of ab initio nonadiabatic dynamics simulations.

An Eight-State Molecular Sequential Switch Featuring a Dual Single-Bond Rotation Photoreaction

Typical photoswitches interconvert between two different states by simple isomerization reactions, which represents a fundamental limit for applications. To expand the switching capacity usually different photoswitches have to be linked together leading to strong increase in molecular weight, diminished switching function, and less precision and selectivity of switching events. Herein we present an approach for solving this essential problem with a different photoswitching concept. A basic molecular switch architecture provides precision photoswitching between eight different states via controlled rotations around three adjacent covalent bonds. All eight states can be populated one after another in an eight-step cycle by alternating between photochemical Hula-Twist isomerizations and thermal single-bond rotations. By simply changing solvent and temperature the same switch can also undergo a different cycle instead interconverting just five isomers in a selective sequence. This behavior is enabled through the discovery of an unprecedented photoreaction, a one-photon dual single-bond rotation.

Theoretical Study of the Photoisomerization Mechanism of All-Trans-Retinyl Acetate

The compound 9-cis-retinyl acetate (9-cis-RAc) is a precursor to 9-cis-retinal, which has potential application in the treatment of some hereditary diseases of the retina. An attractive synthetic route to 9-cis-RAc is based on the photoisomerization reaction of the readily available all-trans-RAc. In the present study, we examine the mechanism of the photoisomerization reaction with the use of state-of-the-art electronic structure calculations for two polyenic model compounds: tEtEt-octatetraene and tEtEtEc-2,6-dimethyl-1,3,5,7,9-decapentaene. The occurrence of photoisomerization is attributed to a chain-kinking mechanism, whereby a series of S₁/S₀ conical intersections associated with kinking deformations at different positions along the polyenic chain mediate internal conversion to the S₀ state, and subsequent isomerization around one of the double bonds. Two other possible photoisomerization mechanisms are taken into account, but they are rejected as incompatible with simulation results and/or the available spectroscopic data.

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.

Excited State Electronic Interconversion and Structural Transformation of Engineered Red-Emitting Green Fluorescent Protein Mutant

Red fluorescent proteins with a large Stokes shift offer a limited autofluorescence background and are used in deep tissue imaging. Here, by introducing the free amino group in Aequorea victoria, the electrostatic charges of the p-hydroxybenzylidene imidazolinone chromophore of green fluorescent protein (GFP) have been altered resulting in an unusual, 85 nm red-shifted fluorescence. The structural and biophysical analysis suggested that the red shift is due to positional shift occupancy of Glu222 and Arg96, resulting in extended conjugation and a relaxed chromophore. Femtosecond transient absorption spectra exhibited that the excited state relaxation dynamics of red-shifted GFP (rGFP) (τ4 = 234 ps) are faster compared to the A. victoria green fluorescent protein (τ4 = 3.0 ns). The nanosecond time-resolved emission spectra of rGFP reveal the continuous spectral shift during emission by a solvent reorientation in the chromophore. Finally, the molecular dynamics simulations revealed the rearrangement of the hydrogen bond interactions in the chromophore vicinity, reshaping the symmetric distribution of van der Waals space to fine tune the GFP structure resulting from highly red-shifted rGFP.

White-light generation from all-solution-processed OLEDs using a benzothiazole–salophen derivative reactive to the ESIPT process

ESIPT for white-light generation from all-solution-processed OLEDs.

Role of Gln222 in Photoswitching of Aequorea Fluorescent Proteins: A Twisting and H-Bonding Affair?

Reversibly photoswitchable fluorescent proteins (RSFPs) admirably combine the genetic encoding of fluorescence with the ability to repeatedly toggle between a bright and dark state, adding a new temporal dimension to the fluorescence signal. Accordingly, in recent years RSFPs have paved the way to novel applications in cell imaging that rely on their reversible photoswitching, including many super-resolution techniques such as F-PALM, RESOLFT, and SOFI that provide nanoscale pictures of the living matter. Yet many RSFPs have been engineered by a rational approach only to a limited extent, in the absence of clear structure-property relationships that in most cases make anecdotic the emergence of the photoswitching. We reported [ Bizzarri et al. J. Am Chem Soc. 2010 , 102 , 85 ] how the E222Q replacement is a single photoswitching mutation, since it restores the intrinsic cis-trans photoisomerization properties of the chromophore in otherwise nonswitchable Aequorea proteins of different color and mutation pattern (Q-RSFPs). We here investigate the subtle role of Q222 on the excited-state photophysics of the two simplest Q-RSFPs by a combined experimental and theoretical approach, using their nonswitchable anacestor EGFP as benchmark. Our findings link indissolubly photoswitching and Q222 presence, by a simple yet elegant scenario: largely twisted chromophore structures around the double bond (including hula-twist configurations) are uniquely stabilized by Q222 via H-bonds. Likely, these H-bonds subtly modulate the electronic properties of the chromophore, enabling the conical intersection that connects the excited cis to ground trans chromophore. Thus, Q222 belongs to a restricted family of single mutations that change dramatically the functional phenotype of a protein. The capability to distinguish quantitatively T65S/E222Q EGFP ("WildQ", wQ) from the spectrally identical EGFP by quantitative Optical Lock-In Detection (qOLID) witnesses the relevance of this mutation for cell imaging.

Direct evidence for hula twist and single-bond rotation photoproducts

Photoisomerization reactions are quintessential processes driving molecular machines and motors, govern smart materials, catalytic processes, and photopharmacology, and lie at the heart of vision, phototaxis, or vitamin production. Despite this plethora of applications fundamental photoisomerization mechanisms are not well understood at present. The famous hula-twist motion—a coupled single and double-bond rotation—was proposed to explain proficient photoswitching in restricted environments but fast thermal follow-up reactions hamper identification of primary photo products. Herein we describe an asymmetric chromophore possessing four geometrically distinct diastereomeric states that do not interconvert thermally and can be crystallized separately. Employing this molecular setup direct and unequivocal evidence for the hula-twist photoreaction and for photoinduced single-bond rotation is obtained. The influences of the surrounding medium and temperature are quantified and used to favor unusual photoreactions. Based on our findings molecular engineers will be able to implement photo control of complex molecular motions more consciously.

Photoisomerization mechanisms govern important (bio)catalytic reactions and lie at the core of many functional materials. Here, the authors report a molecular setup that allows for the direct and separate observation of three fundamental photoreactions, namely the hula twist, single-bond rotation, as well as double-bond isomerization.

Ultrafast action chemistry in slow motion: atomistic description of the excitation and fluorescence processes in an archetypal fluorescent protein

We report quantum mechanical/molecular mechanical non-adiabatic molecular dynamics simulations on the electronically excited state of green fluorescent protein mutant S65T/H148D. We examine the driving force of the ultrafast (τ < 50 fs) excited-state proton transfer unleashed by absorption in the A band at 415 nm and propose an atomistic description of the two dynamical regimes experimentally observed [Stoner Ma et al., J. Am. Chem. Soc., 2008, 130, 1227]. These regimes are explained in terms of two sets of successive dynamical events: first the proton transfers quickly from the chromophore to the acceptor Asp148. Thereafter, on a slower time scale, there are geometrical changes in the cavity of the chromophore that involve the distance between the chromophore and Asp148, the planarity of the excited-state chromophore, and the distance between the chromophore and Tyr145. We find two different non-radiative relaxation channels that are operative for structures in the reactant region and that can explain the mismatch between the decay of the emission of A* and the rise of the emission of I*, as well as the temperature dependence of the non-radiative decay rate.

Mispacking and the Fitness Landscape of the Green Fluorescent Protein Chromophore Milieu

The autocatalytic maturation of the chromophore in green fluorescent protein (GFP) was thought to require the precise positioning of the side chains surrounding it in the core of the protein, many of which are strongly conserved among homologous fluorescent proteins. In this study, we screened for green fluorescence in an exhaustive set of point mutations of seven residues that make up the chromophore microenvironment, excluding R96 and E222 because mutations at these positions have been previously characterized. Contrary to expectations, nearly all amino acids were tolerated at all seven positions. Only four point mutations knocked out fluorescence entirely. However, chromophore maturation was found to be slower and/or fluorescence reduced in several cases. Selected combinations of mutations showed nonadditive effects, including cooperativity and rescue. The results provide guidelines for the computational engineering of GFPs.

Thermal Isomerization Mechanism in Dronpa and Its Mutants

The photoswitching speed of the reversibly switchable fluorescent proteins (RSFPs) from the family of green fluorescent proteins (GFPs) changes upon mutation which is of direct importance for various high-resolution techniques. Dronpa is one of the most used RSFPs. Its point mutants rsFastLime (Dronpa V157G) and rsKame (Dronpa V157L) exhibit a striking difference in their photoswitching speed. Here the QM/MM on-the-fly string method is used in order to explore the details of the thermal isomerization mechanism. The four principal ways in which isomerization may occur have been scrutinized for each of the three proteins. It has been shown that thermal isomerization occurs via a one-bond-flip mechanism in all three proteins, although, in rsKame, where the chromophore is constrained more, the activation free energy difference between hula-twist and one-bond-flip is significantly smaller. Functional mode analysis has been applied to examine the motions of the amino acids during the isomerization. It clearly identifies the importance of Val/Leu 157 as well as the amino acids in the α-helix during the isomerization.

Excited-State Proton-Transfer-Induced Trapping Enhances the Fluorescence Emission of a Locked GFP Chromophore

The chemical locking of the central single bond in core chromophores of green fluorescent proteins (GFPs) influences their excited-state behavior in a distinct manner. Experimentally, it significantly enhances the fluorescence quantum yield of GFP chromophores with an ortho-hydroxyl group, while it has almost no effect on the photophysics of GFP chromophores with a para-hydroxyl group. To unravel the underlying physical reasons for this different behavior, we report static electronic structure calculations and nonadiabatic dynamics simulations on excited-state intramolecular proton transfer, cis–trans isomerization, and excited-state deactivation in a locked ortho-substituted GFP model chromophore (o-LHBI). On the basis of our previous and present results, we find that the S₁ keto species is responsible for the fluorescence emission of the unlocked o-HBI and the locked o-LHBI species. Chemical locking does not change the parts of the S₁ and S₀ potential energy surfaces relevant to enol–keto tautomerization; hence, in both chromophores, there is an ultrafast excited-state intramolecular proton transfer that takes only 35 fs on average. However, the locking effectively hinders the S₁ keto species from approaching the keto S₁/S₀ conical intersections so that most of trajectories are trapped in the S₁ keto region for the entire 2 ps simulation time. Therefore, the fluorescence quantum yield of o-LHBI is enhanced compared with that of unlocked o-HBI, in which the S₁ excited-state decay is efficient and ultrafast. In the case of the para-substituted GFP model chromophores p-HBI and p-LHBI, chemical locking hardly affects their efficient excited-state deactivation via cis–trans isomerization; thus, the fluorescence quantum yields in these chromophores remain very low. The insights gained from the present work may help to guide the design of new GFP chromophores with improved fluorescence emission and brightness.

Emission shaping in fluorescent proteins: role of electrostatics and π-stacking

We obtained the fluorescence spectrum of the GFP with trajectory simulations, and revealed the role of the protein sidechains in emission shifts.

Toward Computationally Designed Self-Reporting Biosensors Using Leave-One-Out Green Fluorescent Protein

Leave-one-out green fluorescent protein (LOOn-GFP) is a circularly permuted and truncated GFP lacking the nth β-strand element. LOO7-GFP derived from the wild-type sequence (LOO7-WT) folds and reconstitutes fluorescence upon addition of β-strand 7 (S7) as an exogenous peptide. Computational protein design may be used to modify the sequence of LOO7-GFP to fit a different peptide sequence, while retaining the reconstitution activity. Here we present a computationally designed leave-one-out GFP in which wild-type strand 7 has been replaced by a 12-residue peptide (HA) from the H5 antigenic region of the Thailand strain of H5N1 influenza virus hemagglutinin. The DEEdesign software was used to generate a sequence library with mutations at 13 positions around the peptide, coding for approximately 3 × 10(5) sequence combinations. The library was coexpressed with the HA peptide in E. coli and colonies were screened for in vivo fluorescence. Glowing colonies were sequenced, and one (LOO7-HA4) with 7 mutations was purified and characterized. LOO7-HA4 folds, fluoresces in vivo and in vitro, and binds HA. However, binding results in a decrease in fluorescence instead of the expected increase, caused by the peptide-induced dissociation of a novel, glowing oligomeric complex instead of the reconstitution of the native structure. Efforts to improve binding and recover reconstitution using in vitro evolution produced colonies that glowed brighter and matured faster. Two of these were characterized. One lost all affinity for the HA peptide but glowed more brightly in the unbound oligomeric state. The other increased in affinity to the HA peptide but still did not reconstitute the fully folded state. Despite failing to fold completely, peptide binding by computational design was observed and was improved by directed evolution. The ratio of HA to S7 binding increased from 0.0 for the wild-type sequence (no binding) to 0.01 after computational design (weak binding) and to 0.48 (comparable binding) after in vitro evolution. The novel oligomeric state is composed of an open barrel.

Theoretical Computer-Aided Mutagenic Study on the Triple Green Fluorescent Protein Mutant S65T/H148D/Y145F

Green fluorescent protein (GFP) mutant S65T/H148D has been proposed to host a photocycle that involves an excited-state proton transfer between the chromophore (Cro) and the Asp148 residue and takes place in less than 50 fs without a measurable kinetic isotope effect. It has been suggested that the interaction between the unsuspected Tyr145 residue and the chromophore is needed for the ultrafast sub-50 fs rise in fluorescence. To verify this, we have performed a computer-aided mutagenic study to introduce the additional mutation Y145F, which eliminates this interaction. By means of QM/MM molecular dynamics simulations and time-dependent density functional theory studies, we have assessed the importance of the Cro-Tyr145 interaction and the solvation of Asp148 and shown that in the triple mutant S65T/H148D/Y145F a significant loss in the ultrafast rise of the Stokes-shifted fluorescence should be expected.

Complete Proton Transfer Cycle in GFP and Its T203V and S205V Mutants

Proton transfer is critical in many important biochemical reactions. The unique three-step excited-state proton transfer in avGFP allows observations of protein proton transport in real-time. In this work we exploit femtosecond to microsecond transient IR spectroscopy to record, in D₂O, the complete proton transfer photocycle of avGFP, and two mutants (T203V and S205V) which modify the structure of the proton wire. Striking differences and similarities are observed among the three mutants yielding novel information on proton transfer mechanism, rates, isotope effects, H-bond strength and proton wire stability. These data provide a detailed picture of the dynamics of long-range proton transfer in a protein against which calculations may be compared.