Detailed characterization of the solution kinetics and thermodynamics of biotin, biocytin and HABA binding to avidin and streptavidin

The high affinity (KD ~ 10−15 M) of biotin for avidin and streptavidin is the essential component in a multitude of bioassays with many experiments using biotin modifications to invoke coupling. Equilibration times suggested for these assays assume that the association rate constant (kon) is approximately diffusion limited (109 M-1s-1) but recent single molecule and surface binding studies indicate that they are slower than expected (105 to 107 M-1s-1). In this study, we asked whether these reactions in solution are diffusion controlled, which reaction model and thermodynamic cycle describes the complex formation, and if there are any functional differences between avidin and streptavidin. We have studied the biotin association by two stopped-flow methodologies using labeled and unlabeled probes: I) fluorescent probes attached to biotin and biocytin; and II) unlabeled biotin and HABA, 2-(4’-hydroxyazobenzene)-benzoic acid. Both native avidin and streptavidin are homo-tetrameric and the association data show no cooperativity between the binding sites. The kon values of streptavidin are faster than avidin but slower than expected for a diffusion limited reaction in both complexes. Moreover, the Arrhenius plots of the kon values revealed strong temperature dependence with large activation energies (6–15 kcal/mol) that do not correspond to a diffusion limited process (3–4 kcal/mol). Accordingly, we propose a simple reaction model with a single transition state for non-immobilized reactants whose forward thermodynamic parameters complete the thermodynamic cycle, in agreement with previously reported studies. Our new understanding and description of the kinetics, thermodynamics, and spectroscopic parameters for these complexes will help to improve purification efficiencies, molecule detection, and drug screening assays or find new applications.

Introduction this study, we asked whether the association rate constants (k on ) for B 7 binding to AV and SAV are truly diffusion controlled, what the association model and thermodynamic cycle that describe the reaction process are, and if there are any functional differences between AV and SAV. In this sense, we analyzed the k on for B 7 binding to AV and SAV by two stopped-flow (SF) methodologies employing fluorescent dye labeled-and unlabeled-B 7 derivatives. In the first case, the association reactions were monitored with two sensing modalities: fluorescence change, F(t), and corrected fluorescence anisotropy, rF(t), under pseudo-first-order conditions as a function of temperature, concentration, and pH with the help of three dye-labeled B 7 probes: 1) biotin-4-fluorescein (BFl), 2) Oregon green 488 biocytin (BcO), and 3) biotinylated DNA labeled at the 3' end with fluorescein (B 7 -DNA ds � Fl-3') (Fig 1). The functional cofactor form of B 7 is biocytin (Bc) which is formed through an amide linkage between the ε-amine of lysine and carboxyl group of B 7 . Modified BcO contains a significantly longer linker with respect to BFl which allows analysis of a potential steric effect in the association process, as has been reported elsewhere [40].
We also studied the effect of AV glycosylation by enzymatically removing the carbohydrate motif to compare the respective association rates with those of the untreated AV, SAV and analogous probes in other studies [20,[36][37][38][39]. To track bound tetrameric species that appeared after SF mixing at pseudo-first order reaction conditions, we show that the binding polynomial distribution (Z) allows us to know the fraction of unbound protein, and protein bounds to one, two, three and four B 7 molecules. Thus, we make a distinction of the AV and SAV complexes using a simple filling model AB n where A is either AV or SAV, and "n" is the total available number of binding sites occupied by the dye-labeled B 7 probes and not the Hill number associated with cooperative binding.
For the second methodology, using a relaxation kinetics approach, the association reactions of unlabeled B 7 were monitored in SF instrumentation by tracking the absorbance changes of an AV-HABA complex as B 7 replaces bound HABA [41]. The presence of ligand stabilizes the avidin tetramer. AV-HABA relaxation experiments were used to determine if stabilizing the tetramer affects the association rate constants and cooperativity.
Global fitting of the kinetic traces and reported calorimetry values allowed us to test reaction models and discriminate the most probable reaction mechanism, as carried out in previous studies [42][43][44][45]. Consequently, the respective activation energies calculated by Arrhenius plots of association rates allowed the acquisition of the forward thermodynamic parameters toward the transition state: enthalpy (E a forward or ΔH ǂ, forward ), entropy (ΔS ǂ, forward ) and Gibbs energy (ΔG ǂ, forward ) of AV and SAV activated complexes. The forward thermodynamic data is in excellent agreement with the backwards thermodynamic values calculated with the dissociation rate constants (k off ) reported by N. M. Green in his seminal work [35]. Additionally, we explain the nature of the second dissociation phase first observed and correctly neglected by Green as a bimolecular "displacement" rate constant (k displacement off ), in addition to the detection of the documented unimolecular "replacement" rate constant (k replacement off ) [26,35] which is used to establish the well-known dissociation constant, K D , as the most stable complex in nature.
Furthermore, we studied the changes in fluorescence lifetime (τ), quantum yield (QY), dynamic quantum yield (F), dye emitting fraction (1-S) and steady state anisotropy (r ss ) of the fluorescent probes before and after complex formation. These spectroscopic properties provide indications of the chemical environment surrounding the B 7 binding pocket in AV and SAV and have important relevance in fluorescence assay detection limits as the signal to noise ratio can be improved by carefully choosing linker length and fluorescent probe.  Fig 1) was purchased from Biotium, Inc. (Hayward, Ca). The 3' end labeled fluorescein top strand with a modified biotinylated d-thymine at position 6 in the following sequence: 5'-GGGAA(biotin-dT)AACTTGGC � Fl-3' (Fig 1) and the respective complement (5'-GCCAAGTTATTCCC-3') were made by Tri-Link Biotechnologies, Inc. (San Diego, CA), and were both HPLC and PAGE purified. The sequences retain the G/C (base pairs) ends and fluorescein identical to those characterized extensively in our previous studies [42,44,46]. The biotinylated 14mer duplex (B 7 -DNA ds � Fl) was formed with 5-10X excess complement and incubated for at least 20 min.

Materials
Protein and active site concentrations. The AV and SAV concentrations were determined with the HABA colorimetric assay of Green [40] for which absorbance measurements, with total protein at 280 nm (1.54 = 1 mg/ml) and HABA at 500 nm (35500 M -1 cm -1 bound, 480 M -1 cm -1 unbound) were made with a Cary 300 Bio UV-Vis spectrophotometer (Varian Inc., Palo Alto, CA). The occupancy of the dye-labeled probes on the AV and SAV tetramer ("p") was obtained with the expansion version of the normalized partition function, Z = (p + q + x) 4 . In considering the totality of binding sites in the AV and SAV tetramer, let "p" denote the fraction of total sites occupied by B 7 ligands (or HABA), "q" the fraction that are unoccupied and are available for binding, and "x" the fraction that are unavailable. The normalized partition function that describes the mole fractions of the various possible AV and SAV tetrameric species is given by Z = (p + q + x) 4 ; where "x", from the HABA assay for AV, was found to be 0.185 (or 18.5%), and q = 1-p-x. Knowing the total concentration of binding sites from UV protein absorbance and Green's methodology [40], and determining "x", results in the maximum value of "p" that will be reached in reacting tetramers with a B 7 analog. Expansion of Z provides the mole fractions of the various species in solution, and in decreasing order in terms of probe occupancy, are: p 4 + 4p 3 q + 4p 3 x + 6p 2 q 2 + 6p 2 x 2 + 12p 2 qx + 4pq 3 + 4px 3 + 12pq 2 x + 12pqx 2 + q 4 + x 4 + 4q 3 x + 4qx 3 + 6q 2 x 2 which totals 1. This development assumes completely random occupancy of probe and inactive sites characterized by "x". The species containing one bound probe have "p" raised to the first power; those with two bound probes have "p" raised to the second power, and so on.
All of the following protein concentrations are presented on a binding site basis, thus in the case of the HABA association reactions for AV were measured at 23.0 ± 0.1˚C with a concentration of 87 μM HABA and 7.7 μM AV. The AV-HABA relaxation reactions were conducted with a preformed AV-HABA complex made up of 200 μM HABA and 10 μM AV, flowed against varying amounts of B 7 from 100 μM up to 4000 μM for a [HABA]/[B 7 ] ratio that ranged from 0.05 to 2.
Association stopped-flow kinetics. These reactions were carried out in a buffered solution of 10 mM Tris-HCl, 100 mM KCl, 2.5 mM MgCl 2 and 1 mM CaCl 2 at pH 8 and only AV-BcO reactions included pH 9 and 10. The concentrations, after mixing, were of 20 nM of dye-labeled B 7 probe and 260 nM, 520 nM or 1040 nM of AV; and 200 nM, 300 nM, 400 nM or 800 nM of SAV at temperatures of 10, 15, 20 and 25˚C. The deglycosylation of AV (for comparative association reactions) was carried out using the provided standard protocol with endoglycosidase H [47], both with and without incubation of a denaturant solution (2% SDS and 1M 2-mercaptoethanol).
Dissociation reactions of dye-labeled biotin complexes. Biotin dissociation was determined using labelled biotin (BcO and BFl) displaced by unlabeled biotin using minimally occupied and fully occupied binding sites. In the minimally occupied measurements, SAV is prepared with less than one site on average occupied by labelled biotin (AB 1 ), using 800 nM SAV and 40 nM of BcO or BFl. For saturated SAV-labelled biotin (AB 4 ) complexes, equimolar binding sites and labelled ligand were prepared, 40 nM SAV and 40 nM of BcO or BFl. The AB 1 complexes were challenged in displacement experiments with several concentrations of unlabeled B 7 (1500 nM, 1750 nM, 2000 nM and 2500 nM) at 20 ± 0.1˚C. In AB 1 , SAV had 760 nM in open sites, therefore the total challenging B 7 concentrations were 740 nM, 990 nM, 1240 nM and 1740 nM, respectively. Additional measurements at 27 ± 0.1˚C using 1300 nM, 1500 nM, 1750 nM, 2000 nM and 3000 nM biotin were completed. The 40 nM AB 4 complexes were challenged with unlabeled B 7 concentrations of 400 nM (10X) and 1600 nM (40X) at 20 ± 0.1˚C. The dissociation reactions of AV complexes were carried out with a preformed complex of 20 nM BFl or BcO and 260 nM AV for a filling model of AB 1 and challenged with unlabeled B 7 at 2,000 nM.
Spectroscopic properties. The lifetimes (τ), steady state anisotropies (r ss ), time-resolved anisotropies (r t ) and quantum yields (QY) of the complexes (at 20 ± 0.1˚C and pH 8) were collected with a dye-labeled B 7 probe concentration of 20-40 nM and 1040-2080 nM of either protein (AV or SAV) to ensure that only one binding site in the tetramer was filled with a ligand (AB 1 filling model).

Methodologies
The following experiments were carried out by at least six times, unless indicated, and the reported errors correspond to the standard deviation.
Steady-state anisotropy (r ss ). The r ss measurements were collected using the Giblin-Parkhurst modification of the Wampler-Desa method as described previously [48]. The fluorescence signal was detected in a model A-1010 Alphascan fluorimeter (Photon Technologies, Inc., Birmingham, NJ) equipped with an R928 PMT (Hamamatsu, Bridgewater, NJ). The excitation was provided by an Ar + ion laser (Coherent Innova 70-4 Argon, Santa Clara, CA) at 488 nm and 5-10 mW of power incident on the sample. A photoelastic modulator (PEM-80; HINDS International, Inc., Portland, OR) was placed between the laser source and the sample compartment with a retardation level of 1.22π, and the PEM stress axis orientated 45˚with respect to the E vector of the laser beam. Two signals were acquired with the PEM alternating between "on" and "off" positions for 10 seconds and the data fitted to a least squared straight line to minimize noise. A minimum of six of these independent measurements were averaged to acquire the r ss values. The fluorimeter G factor was determined using a film polarizer and analyzer with an excitation at 488 nm provided by a xenon arc lamp (model A1010, Photon Technologies Inc, Princeton, NJ). The dissociation reactions of dye-labeled B 7 and protein complexes were monitored by fluorescence changes and were also collected in the fluorimeter described above.
Fluorescence lifetimes (τ) and time-dependent anisotropy decays (r t ). The lifetimes were collected in a FluoTime100 fluorescence spectrometer (PicoQuant, GmbH, Berlin, Germany) with the excitation light source provided by a picosecond pulsed diode laser (Pico-Quant, GmbH, Berlin, Germany) at 470 nm and 20 MHz. The emission was collected at 520 nm through a non-fluorescing 520 nm interference filter (Oriel Corp., Stratford, CT) followed by a liquid filter of 1cm path length containing 24 mM acetate buffered dichromate at pH 4, between the sample and detector to eliminate traces of excitation light [42]. The fluorescence decays were fit by a nonlinear least-squares minimization based on the Marquardt algorithm embedded in the Fluofit software (PicoQuant GmbH). Twenty-eight decays were collected per sample, the decays were grouped in four sets, consisting of seven sample decays and one Instrument Response Function, IRF, for deconvolution proposes. The decay sets were globally fitted to mono-or bi-exponential decay models that were discriminated using the statistical parameter χ 2 . The r t data were acquired with the fluorimeter described above equipped with a polarizer and an analyzer to acquire the parallel VV(t) and perpendicular VH(t) decays. The PicoQuant G factor was calculated according to: G = R HV(t)dt/ R HH(t)dt, where HV(t) and HH(t) were the decays collected with the emission polarizer selecting vertical and horizontal E-vector passing orientations, respectively, and the excitation polarizer set at horizontally position.
Quantum yields (QY). The QY values were obtained by using a reference fluorophore of known quantum yield and were calculated according to Parker and Rees [49,50], where the reference dye was fluorescein in 0.1N sodium hydroxide solution [46]. The emission fluorescence scans were collected from 480 nm to 700 nm with the excitation light set at 460 nm provided by the xenon arc lamp described above. These measurements were made on the AB 1 complexes at high protein concentration.
Intrinsic lifetime (τ˚), dynamic quantum yield (F) and fraction of non-statically quenched molecules (1-S). These calculations have been described elsewhere [46] and were acquired for the AB 1 complexes. The HABA association reaction for AV was carried out under pseudo-first order conditions on a micro absorbance SF instrument [51] equipped with a xenon arc lamp (described above) and a monochromator (model 82-410, Jarrel-Ash, Waltham, Mass.) set at 500 nm.
Relaxation kinetics of unlabeled biotin reacting with the AV-HABA complexes. The relaxation experiments were prepared at concentrations in which HABA occupies all sites (AV-HABA 4 ). Biotin replaces HABA relative to the k off of the dye as shown for the first step (Eq 1) and then repeated for all sites. Having greater affinity, B 7 occupies all sites at the end of the reaction and the measured k on is related to the affinities of the ligand bound protein.
The reaction is monitored by the HABA absorbance changes at 500 nm as it is replaced by unlabeled B 7 ; yielding the relaxation constant of the reaction (Relaxation, Eq 2) which contains information of the B 7 association rate constant of the open binding site, k AVÀ HABA3 1 to form a full saturated complex (AV-HABA 4 ) and the dissociation rate of that full complex, k AVÀ HABA4 to yield a complex with three HABA molecules (AV-HABA 3 ). In the subsequent steps, B 7 replaces HABA as the ligand but the release of HABA creates an unoccupied site that remains in the same state. In summary, the experiment was designed to acquire the pseudo-first order association rate constant of B 7 binding (k B on ) to the solely free binding site in a complex occupied by three HABA molecules (AV-HABA 3 ). ) and the respective slope: m ¼ k AVÀ HABA3 The exponential decays were analyzed by the method of Foss [52]. There was no departure from simple first order decay in the relaxation, justifying the use of the following model and equations.
Association reactions of dye-labeled biotin and AV (or SAV). The reactions were collected with the SF instrument, described previously [53,54]. The fluorescence signal was collected through a 520 nm interference filter (Oriel Corp., Stratford, CT) with a detector time constant and SF dead time of 1 μs and 1 ms, respectively. The excitation light was provided by the Coherent Ar + ion laser (described above) at 488 nm with 15-10 mW of incident power on the reaction cuvette. The laser source was followed by the photo-elastic modulator described above with the axis oriented 45 o with respect to the electric vector of the incident light and with the half-wave modulation (50 kHz) set for 488 nm excitation. The demodulation circuitry following the photomultiplier provided a DC(t) and a rectified AC(t) which were converted to digital data by a high-speed digitizer (PCI-5122) from National Instruments (Austin, TX) with 14-bit resolution and 100 MHz bandwidth, through channels 0 and 1. The data acquisition was controlled by LabVIEW (Vr 8) software at a collection rate of 6120 data points/second and stored in spreadsheets. The AC(t) and DC(t) data were baseline corrected before obtaining the signal ratio (Eq 4) as a function of time (ρ t ).
The constant A Gain is the instrumental amplitude gain and was evaluated by solving ρ(t) using the known steady state anisotropy (r ss ) of the complexes which is equivalent to the r(t) at t = 1; and H, obtained from the equivalent grating factor (G) for the filters and photo multiplier tubes in the SF. For the probes used in here G was 0.82 and H = (1-G)/(1+G) = 0.099. Knowing A gain and H, the AC(t) and DC(t) signals can be solved for r(t) and F(t) (Eqs 4 and 5) and the normalized fluorescence, FðtÞ, and corrected fluorescence anisotropy, rFðtÞ [55], were obtained when Fð0Þ and rFð0Þ were scaled to 1 at t = 0.
The FðtÞ (Eq 6) is equivalent to (I || ) + 2 (I ? ) and proportional to quantum yield (QY i ), molar absorptivity (ε i ) and to the formation or disappearance of the emitting species X i (t); and rFðtÞ including the steady state anisotropies (r ss ) of each fluorescent species (Eq 7) [55].
Biotin association reaction model for AV and SAV. The possible reaction models were discriminated by the squared residuals of the observed and calculated association traces of both fluorescence and anisotropy fluorescence signals, FðtÞ and rFðtÞ, respectively. For the BFl and BcO probes, the association reactions were very well described by the simplest possible model (Eq 8) with single association rate constants (k on ).
In the case of the B 7 -DNA ds � Fl, the association reaction model was complemented by a second k on which resulted in a system of two parallel reactions (Eq 9). In both cases, the backward reaction is not significant during the 5-8 sec required for the B 7 association binding.
Dissociation reactions of the complexes. The dissociation reactions were followed by fluorescence changes, FðtÞ, in the fluorimeter and laser setup described above and tuned to 488 nm under discontinuous excitation to prevent photobleaching distortion. The signal was best fitted to the following dissociation model (Eq 10), in which the dye labeled complex dissociates into the labeled B 7 probe (BFl or BcO) and the respective protein (AV or SAV).
Time-resolved anisotropy (r t ). The r t values were calculated according to Eq 11 where the pre-exponential "f" corresponds to the slow phase that derives from the lifetime of the global motion (τ G ) [56] which was fitted within a range of expected correlation time for the complex size [57]; consequently, facilitating resolution of the fast correlation lifetime (τ p ) and the corresponding pre-exponential (1-f).
The f parameter was constrained to the observed r ss (Eq 12) whereFðtÞ (Eq 13) is normalized (α 1 + α 2 = 1) and derived from the observed fluorescence decays of the complex [58]. WhereF In a simple model, the transition moment is assumed to wobble within a cone of semi-apical angle O [59], where the cone axis is normal to the surface of a sphere that corresponds to the macromolecule. The angle O is calculated from Eq 14.
Results and discussion

Active avidin binding sites
The avidin and streptavidin proteins are tetramers in solution. If the binding of the ligand is positively cooperative, differences in k on for initial and final binding steps could be significant; therefore, the comparison of initial binding by nonliganded AV and final binding by liganded AV is necessary. Measurement of the initial binding rate requires ligand free AV, but endogenous ligand could potentially interfere. In fact, AV preparations often present about 20% of the inactive sites for the binding of any B 7 analogs, either because they contain endogenous B 7 [40], or perhaps the existence of damaged binding sites in some of them, e.g., tryptophan oxidation [60]. To acquire accurate k on values, the actual available binding site concentration for each sample was measured by HABA colorimetric assays in relation with absorbance at 280 nm. Accordingly, the percentage of available active sites of AV and SAV were 81.5 ± 1.0% and 94.0 ± 1.0% with respect to total protein, respectively, which were in excellent agreement with the 82% and 95% reported by the commercial source (Sigma Aldrich and CalBiochem). The SF apparatus provided rapid thorough mixing of the probes with AV and SAV allowing measurement of the full reaction. The issue of rapid mixing vs. more conventional titrations was treated previously [51]. In the SF association measurements, the dye-labeled B 7 probes were sub-stoichiometric to determine the initial binding rates (e.g. 20 nM of BFl, BcO and B 7 -DNA ds � Fl vs. 260 nM, 520 nM and 1040 nM in binding sites basis). Limiting the ligand also reduced several potential measurement artifacts including FRET self-transfer, and contact interference including probe fluorescence quenching by contact interactions [61] in the AB 2 , AB 3 or AB 4 complexes; especially for the BcO which has a longer linker [62]. Using the binding polynomial for the 20 nM probe after mixing, and 638 nM in total sites for the intermediate AV concentration which corresponds to 520 nM in available sites, the mole fraction of species with a single bound probe is 0.114, that with two bound probes is 0.0055, and with three bound probes is 0.0001, so at most, only 0.55% of the molecules with bound AV contain two probes; for 1040 nM available sites, the value drops to 0.15% (S1 File). With limited occupancy, the association reactions acquired the dye-labeled B 7 probes reflect the binding to the first binding site in the tetramer for the SF experiments. The unlabeled B 7 relaxation kinetic experiment was designed to observe the binding at the final site, as discussed below.

Association rate constants (k on ) of biotin binding to avidin
Dye-labeled biotin association rate constants by stopped-flow methodology. The fluorescence FðtÞ and corrected anisotropy association binding traces, rFðtÞ, properly monitored the association reactions, as they yielded equivalent k on values (Table 1) and presented the best optimal fit residuals (Fig 2). In contrast, the anisotropy signal, rðtÞ, lagged behind FðtÞ and rFðtÞ since changes in the quantum yield (QY) of the involved fluorescence species distort the kinetic traces [55]. These three types of association binding traces were acquired with discontinuous excitation that circumvented photobleaching (Fig 3) allowing the detection of all nonphotobleaching rate constants. Consequently, the k on values of AV showed linear concentration dependence (Fig 4) and strong temperature dependence when using the BcO ( Fig 5) and BFl ( Table 2) probes. Notably, a reduction in the k on of~10% was observed with each pH unit increment (from 8 to 10) which may derive from titration of the hydrogen bonding of asparagine and tyrosine in the binding pocket [32].
Unlabeled biotin association rate constants by relaxation kinetics methodology. The experiment consisted in challenging a pre-saturated AV-HABA complex with B 7 (Fig 6) to measure the association rate of the final "relaxed" binding sites which yielded a k B on of 5.3 ± 0.9 × 10 6 M -1 s -1 (at pH 8 and 23˚C) which is slightly slower than the 7.8 ± 0.4 × 10 6 M -1 s -1 acquired with BcO (Arrhenius plot, 23˚C and pH 8) indicating non-cooperativity (or slightly negative) for binding site association rates. The HABA dissociation rate constant of the AV-HABA 4 complex was not rate limiting (k AVÀ HABA4 À 1 = 6.23 ± 0.11 s -1 ) and the HABA association rate for the final site was k AVÀ HABA3 1 = 5.1 ± 0.1 × 10 5 M -1 s -1 which results in a AV-HABA equilibrium constant of K D AV-HABA = 12.2 ± 0.3 × 10 −6 M similar to that reported by Green [60] at pH 8 which supports the quality of our relaxation kinetic experiment. Non-cooperative biotin binding to avidin sites. The association reactions that used the fluorescent probes BFl and BcO monitored the 1 st available binding site, as they were carried out at pseudo-first order, at very high protein concentration with low occupancy for the AB 1 filling model, as discussed above. In contrast, the relaxation kinetic methodology scrutinized the unlabeled B 7 binding to the unoccupied site while the 3 remaining sites were filled with HABA, this process can be thought as the binding of B 7 to the 4 th binding site. Therefore, the data obtained with dye-labeled B 7 probes and unlabeled B 7 should report the binding rates to The association reactions were acquired with BcO (20 nM) binding to AV at several temperatures, protein concentrations and pH 8.The FðtÞ and rFðtÞ signals were equivalent as they tracked in the errors the association process of dye-labeled B 7 binding to the proteins under pseudo-first order conditions. https://doi.org/10.1371/journal.pone.0204194.t001 Detailed characterization of avidin, strepavidin, and ligands the 1 st and 4 th sites. Since these two values only diverge by 32% we believe that there is not significant cooperativity nor an intrinsic difference in any of the AV sites. If a protein has two forms, denoted as relaxed (R) and tense (T), the HABA bound ligand can hold the AV protein in the R-state [63]. In the relaxation experiments, all the bound HABA gets replaced by dyelabeled B 7 (BFl or BcO), but all the sites rest in the R-state; therefore, there is not switching from T to R. This is the same as hemoglobin bound to (HbO 2 ) flowed against CO, where O 2 gets replaced by CO but is not biphasic because no T-state is present [63,64]. As B 7 binding to AV and SAV is non-cooperative, the HABA replacement is a pseudo first order measure of the B 7 association rate and should be the same or close to the association rate of the dye-labeled B 7 flowed against empty AV or SAV. Our values differed only by 32% for these two approaches.

Comparisons with other AV-B kinetic studies.
Comparisons with other AV-B 7 kinetic studies were carried out at the closest possible condition; thus, at 25˚C and pH 8, the BFl and BcO association rate constants, k on , were 3.8X and 7.4X slower than the 7 × 10 7 M -1 s -1 reported by N. M. Green [35] (at 25˚C and pH 5), respectively. However, a larger uncertainty is expected for the latter experiment because it was not carried out using rapid mixing techniques forcing the usage of very low ( 14 carbon) B 7 concentrations (picomolar range) to timely stop the reaction and quantify the un-reacted probe. Consequently, Green's experiment was an extremely tedious task that was carried out, only once and at one temperature. On the other hand, a more recent association rate constant of 2.0 ± 0.3 × 10 6 M -1 s -1 was obtained in a FðtÞ were optimal, and (D) rðtÞ signal is ill-fitted. The k on of rðtÞ was 40% slower than the other two and showed the worst residuals due to changes in QY [55]. The corresponding normalization signals are: rF t ð Þ ¼ ½rFð0Þ À rFðtÞ�=½rFð0Þ À rFð1Þ�; F t ð Þ ¼ FðtÞ Fð0Þ ¼ ½FðtÞ À rFð1Þ�=½rFð0Þ À rFð1Þ� and rðtÞ ¼ ½rð0Þ À rðtÞ�=½rð0Þ À rð1Þ�.
https://doi.org/10.1371/journal.pone.0204194.g002 Detailed characterization of avidin, strepavidin, and ligands Surface Plasmon Resonance (SPR) study [20] at 20˚C and pH 7.4 in HEPES buffer. This independent k on value was~9X and~5X slower than the ones acquired by us for BFl and BcO, respectively. Nevertheless, it has been previously acknowledged that the SPR results are, controversially, too low to be accurate [20,39], due to fixation of one of the reactants to the chip, generally AV or SAV.
Effect of AV glycosylation on the biotin binding kinetics. The AV protein has a glycan attached to asparagine 17 at each tetrameric subunit which is composed of four or five mannoses and three N-acetylglucosamines [65]. These sugar modifications are typically removed to improve crystallization but the glycan effect on the association binding rate of B 7 was previously unknown. Interestingly, after enzymatic removal of the carbohydrates, the k on values of the de-glycosylated AV matched those of natural glycosylated AV for the dye-labeled B 7 probes: e.g., 3.7 ± 0.3 × 10 −6 M -1 s -1 vs. 3.9 ± 0.3 × 10 −6 M -1 s -1 of BcO binding to de-glycosylated AV and untreated AV at 15˚C, respectively. A previous study already suggested that the sugar chain is not required for B 7 binding [65] and now we confirm that AV glycosylation has no influence on the association rate constants.

Association reaction of unlabeled and dye-labeled biotin binding to streptavidin
Dye-labeled biotin association reactions to SAV. The SAV-B 7 association reactions presented temperature (Fig 4C and 4D) and linear concentration dependence (Fig 5C and 5D) and were faster than those of acquired with AV for both dye-labeled probes. For instance, BFl and BcO at 25˚C, presented k on values when binding to SAV that were 4X and 3.2X faster than those observed when binding to AV, respectively. However, the temperature dependence was weaker than that observed for AV which indicated a profound difference in the binding site properties of these two proteins, as reveled by an Arrhenius plot (see 3.9 Thermodynamic Parameters). Thus, SAV should be a more robust system for purification applications as variations on the temperature incubation protocols have less negative significant effects in the yield.
Comparisons with other SAV-B 7 association kinetic studies. An independent SF study tracked the binding of unlabeled B 7 by fluorescence quenching of the tryptophan (Trp) of SAV, yielding a k on of 7.5 ± 0.6 × 10 7 M -1 s -1 (at 25˚C and pH 7) [39] which was in excellent agreement with 7.5 ± 0.2 x 10 7 M -1 s -1 for the BFl probe (at 25˚C and pH 8). This finding strongly indicates that the attached dyes are innocuous and dependably monitor the B 7 binding to SAV and presumably to AV. In addition, the absence of any detectable intermediate in the association reaction in both cases is remarkable, since we monitored the initial binding of B 7 and SAV using the fluorescence change and fluorescence anisotropy signals, and the independent tryptophan-quenching experiments observed the final docking of B 7 near the Trp [39]. Conversely, there is another independent Surface Plasma Resonance (SPR) study of immobilized B 7 binding to SAV that yielded a slower k on of 5.1 × 10 6 M -1 s -1 at 4˚C [66], which was~5X slower than our 2.6 × 10 7 M -1 s -1 at 4˚C, calculated by an Arrhenius plot (ln k on vs 1/ T) of the BFl data. Similarly to AV, we believe that the SPR methodology for the B 7 and AVlike protein kinetics [20,39] was modified by the immobilization of one reactant, either B 7 or protein, to the chip.

Biotinylated and dye-labeled DNA duplex association reaction to AV and SAV
Association rate constants of B 7 attached to biotin-DNA ds � Fl. The biotinylated 14-mer duplex association kinetics showed a biphasic behavior with two temperature and concentration dependent rate constants ( Table 2, Fig 7) when reacting with both AV and SAV. The biphasic association rate constants, k on1 and k on2 , summed to approximately 70% of the total reaction amplitude. The remaining~30% was assigned to a third-rate constant (0.02 ± 0.01 s -1 ) that presented neither temperature nor concentration dependence; therefore, it has been assigned to the readjustments of the Fl dye after being displaced by both proteins. The k on1 and k on2 association rate constants of SAV were 3.4X and 1.8X faster than the corresponding rate constants of AV (Fig 8) as observed with the BFl and BcO probes, confirming the differences in the AV and SAV binding pockets.
Comparisons with other biotinylated DNA kinetic studies. An independent FRET study monitored the reaction of B 7 attached to the 5' end of a 46 nucleotide duplex DNA binding to SAV [38]. The reaction also showed two rate constants at pH 8, but at unspecified temperature, pre-exponentials and errors. To make a comparison, we have chosen SAV data at 20˚C whose association rate constant, k on1 , of 4.6 ± 0.8 × 10 7 M -1 s -1 was in excellent agreement with the 4.5 × 10 7 M -1 s -1 reported by the mentioned study. In the case of our k on2 of 2.3 ± 0.1 × 10 6 M -1 s -1 , it was in good agreement with the second rate of 3.0 × 10 6 M -1 s -1 of that independent study. The agreement in the data validates our findings which imply that B 7 attached internally to DNA (or at the 5' end) will have two rate constants, one enhanced and other diminished probably due to unfavorable orientation according to the reaction models discussed below.

Significance of the association rate constants
The B 7 binding to AV and SAV (at 25˚C) were, respectively, between 54-714X and 13-400X slower than 10 9 M -1 s -1 as expected for a diffusion limited process [67]. On the other hand, the k on values of SAV were 3-4X faster than AV's despite the similarity of the AV and SAV binding sites in the crystal structures (Fig 8). Our deglycosylation experiments indicate that the Detailed characterization of avidin, strepavidin, and ligands disparity in the k on values between both SAV and AV proteins cannot be explained by the presence or absence of the carbohydrate motif on the AV but can be explained by the intermolecular interactions of the aminoacids in the binding pocket and the B 7 ring.

Association reactions of biotin vs. biocytin to SAV and AV
In our study, the association rates were acquired with B 7 and Bc probes, BFl and BcO; respectively, in which Biocytin presents a longer carbon linker. Interestingly, these k on values only differed by 2-fold (Table 1), from 10˚C to 25˚C, when reacting with AV. It is important to clarify that the association rates were not enhanced by the electrostatic attraction of the negative charged probes (BFl and BcO) and the positive AV [32]; since, the association rates of those two probes binding to neutral SAV differed also by~2 fold as observed for AV. The dissociation constants, K D , of AV-B 7 and AV-Bc were reported to be 10 −13 and 10 −15 M, respectively, differing by 100-fold [40]. Consequently, this 100-fold difference, if accurate, must be caused by a difference of 50-fold in the k off , dissociation rate constants which is discussed below.

Dissociation kinetics
The dissociation reactions of the AV-B 7 and SAV-B 7 complexes have been described as passive unimolecular "replacements" (k replacement off ) with units of reciprocal seconds (s -1 ) and values of 9 × 10 −8 s -1 [35] and 2.4 × 10 −6 s -1 [68], respectively. However, we have also observed bimolecular "displacement" off-rate constants (k displacement off ) with M -1 s -1 units for the SAV-BcO , ΔS ǂ, Forward and ΔG ǂ, Forward ) were acquired from global fitting of the rate constants [42,45] for the most probable model which resulted in a simple reaction with a transition state without intermediates. In the case of the B 7 -DNA duplex, the reaction model was a two-serial reaction model also with one transition state without intermediates. The nature of the serial reaction is probably caused by two B 7 populations with different spatial orientations. a The probes were BFl, BcO, and B 7 attached to a nucleotide in a 14-mer DNA duplex and the respective complex with AV and SAV. The k on values were averaged from data in Table 1 c Calculated from an Arrhenius plot. d The pre-exponentials (in parenthesis) of k on1 and k on2 were renormalized after removing a third process associated with remaining photobleaching.
https://doi.org/10.1371/journal.pone.0204194.t002 complexes (AB 1 and AB 4 ) that were strongly dependent on B 7 concentration ( Fig 9A) and temperature (Fig 9B). These reactions had~79% of the total release amplitude, in contrast to the 5% when BFl was used ( Fig 9C); therefore, the longer "tail" of the BcO facilitated the displacement for SAV-BcO; and in the case of the SAV-BFl, the electrostatic interactions between negative charged Fl and positive charge SAV prevented the displacement, as observed elsewhere [69]. Thus, longer linkers and neutral dye molecules and proteins are features that can be exploited to increase purification yields. This new information can find important applications in affinity chromatography purification based on SAV and longer "tail" or tethers that will help to increase the release of the product and enhance efficiency. On the contrary, we could not detect neither displacement nor replacement in AV-BFl and AV-BcO complexes since the reaction is very slow (S3 Fig). Thus, in 1966, Green N. determined heroically the k replacement off for AV-B7 in 9 × 10 −8 s -1 for a half-life of 90 days [35] which could not be detected by us since our fluorescence anisotropy methodology is not suitable.

Biotin reaction models of AV and SAV
Reaction model of BFl and BcO binding to AV and SAV. The SF traces of B 7 binding to AV and SAV were best fitted by a simple association model, A + B Ð C. A single rate constant, k on (Eq 8), could be fit with no intermediates or evidence of cooperativity considering that the dissociation reaction was not significant for the first 5-8 sec after mixing. More elaborate mechanisms have been reported [70,71]. For example, A + B Ð C Ð D has been proposed for polystyrene SAV coated particles (6.5 nM) reacting with a fluorescein labeled B 7 probe (1.8 nM and 17.5 nM), whose linker resembles our BcO probe. This model required fitting of two dissociation and two association rate constants with the extra equilibrium attributed to two  (Table 4). reasons: 1) The interference of the dye structures into the neighboring site due to multiple occupancies on the tetramer [61] and 2) to possible inhibitory steric interactions caused by high density of SAV sites on the surface of the polystyrene particles. Interestingly, a similar model was used to analyze a pull-off study carried out by Scanning Force Microscopy for 1 (k on1 ) and 2.2 (k on2 ); 3 SAV-BcO (red triangles); 4 AV-BFl (purple circles); 5 AV-B 7 -DNA ds � Fl (green circles): 5.1 (k on1 ) and 5.2 (k on2 ); 6 AV-BcO (red circles): 6.1 at pH 8, 6.2 at pH 9 (orange circles), 6.3 at pH 10 (yellow circles). The data points were plotted in semi-logarithm (ln k on vs 1/T) for clarity. https://doi.org/10.1371/journal.pone.0204194.g008 Detailed characterization of avidin, strepavidin, and ligands AV-B complex with immobilized AV in which two events of 20-40 pico-newtons and 40-80 pico-newtons were assigned to the presence of an intermediate [72]. Categorically, we have avoided these experimental complications by following the reaction at pseudo first order to ensure that our probes occupied only one binding site of AV and SAV in solution (non-immobilized), as discussed above. However, when considering a particular AV or SAV bioassay, one must consider that the surface matrix complexity, the multiple orientations of B 7 , and the modifications of the AV-like proteins can modify the dissociation mechanism with respect to those observed in solution by us.
Reaction model of biotin-DNA ds � Fl binding to AV and SAV. The B 7 binding kinetics, when attached to DNA, was best described by two parallel reactions (Eq 9) with two independent association rate constants that showed no evidence of intermediates in solution. The preexponentials of the rate constants were temperature dependent (Table 2) suggesting the presence of two B 7 populations with different orientations with respect to the DNA and responsible for the measured k on1 and k on2 rate constants. Thus, at 25˚C, the measured values of k on1 for both AV and SAV were only 20-40% slower than rate constants acquired with BFl, which suggests that B 7 on the DNA was positioned in a favorable orientation that enhances the association reaction. On the other hand, the slower k on2 rate constant is associated with an unfavorable orientation of the second B 7 population which could be partially intercalated in the stacked nucleotides.

Thermodynamic parameters
The forward activation energies (E a forward or ΔH ǂ,forward ) of the B 7 binding to AV and SAV were~6.0 and~14 kcal/mol, respectively; and they were in good agreement with early estimations of 10-12 kcal/mol for the displacement of water molecules from the binding pocket [60]. These values were larger than the 3-4 kcal/mol [35,73] characteristic of a diffusion limited reaction (which requires also association rate constants in the order of 10 9 M -1 s -1 while our fastest values were in the order of~1.9 × 10 7 M -1 s -1 and~7.5 × 10 7 M -1 s -1 , at 25˚C for AV-BFl and SAV-BFl, respectively). Hence, the association reaction is not diffusion controlled in the range of experimental work carried by us. Interestingly, the B 7 binding process for both proteins share the same k on at 52.1˚C (calculated by Arrhenius plot), and binding of B 7 ligand enhances thermal stability of the proteins shifting from 75˚C to 112˚C for SAV and from 84˚C to 117˚C for AV [74]. Remarkably, the difference of forward and reverse activation energies (E a forward -E a backward ), calculated with Arrhenius plots of the association and dissociation rate constants, respectively; matched, within the error, the reaction enthalpy (ΔH˚R xn ) calculated by calorimetry (Table 3, Fig 10A). The same argument holds for the Gibbs free energy (ΔG ǂ, forward -ΔG ǂ, backwards ) and entropy (ΔS ǂ, forward -ΔS ǂ, backwards ), and the calorimetric ΔG˚R xn and ΔS˚R xn values have been Detailed characterization of avidin, strepavidin, and ligands calculated by others (see references in Table 3, Fig 10B and 10C); Thus, the forward thermodynamic parameters obtained in this study completed nicely the thermodynamics cycles, thus making very compelling arguments in favor of the proposed simple reaction model (Eq 8), which has a single transition state ( ǂ ) but no intermediate. The positive nature of ΔE a forward and ΔS ǂ, forward toward the transition state can be explained as the energy required to remove water molecules and displace the protein's β3-β4 loop [32,75] with an increment of the overall Detailed characterization of avidin, strepavidin, and ligands disorder, ΔS ǂ . A comparative analysis of the transition state ( ǂ ) for the AV-B and SAV-B complexes reveals that the former has a larger ΔE a forward and ΔS ǂ,forward (Table 3, Fig 10, red line) than the latter (Table 3, Fig 10, green line) which implies that binding sites of AV are deeper and less accessible resulting in slower association rate constants and larger activation energy with respect to B 7 binding to SAV.
unbound probes, with the exception of the B 7 -DNA ds � Fl complexes with AV and SAV that were blue-shifted 3 nm by the presence of both proteins. This can be explained by fluorescein (Fl) interactions with DNA ds before binding to AV and SAV which is later displaced to the solution in the complex. In the particular case of the absorbance spectrum of SAV-BFl, it was highly distorted (S1 Fig) owing to the shifting of the Fl -2 /Fl -1 equilibrium by charge transfer [79]; since, we detected the corresponding 4.1 ns and 3.0 ns lifetimes (τ). The time-resolved fluorescence of B 7 -DNA ds � Fl complexes of SAV and AV proteins (S1 Table) had two lifetimes decays of 0.72 (± 0.01) ns and 3.78 (± 0.01) ns, and 2.29 (± 0.02) ns and 4.08 (± 0.01) ns, respectively; whose exponentials were not affected by temperature suggesting the existence of the two Fl positions on the DNA which make a compelling argument for the parallel reaction model (Eq 9) with two reacting populations: (Biotin-DNA ds � Fl) 1 and (Biotin-DNA ds � Fl) 2 . The deconvolution of the SF binding traces was completed using the steady-state anisotropy (r ss ) whose AV values were larger than SAV attributable to a larger molecular weight and to the presence of the carbohydrate motif for the former. Significantly, the quantum yields (QY) of the complexes were in excellent agreement with all the binding association amplitude changes. Thus, in the case of the B 7 -DNA ds � Fl reactions, the traces had shifted directions ( Fig  7) since there are opposite quenching interactions when SAV and AV complex are formed. The quantum yield, of the free probe B 7 -DNA ds � Fl was QY = 0.22 ± 0.01 (Table 4) incremented up to 0.36 ± 0.01 for the AV-B 7 -DNA ds � Fl complex and decreased to 0.18 ± 0.01 for the SAV-B 7 -DNA ds � Fl complex. This effect is caused by the bulkier nature of the AV with respect to SAV that allows further displacement of Fl from the 3' end toward the solution environment resulting in the increase of the QY for the B 7 -DNA ds � Fl-AV. The (S) and (1-S) are, respectively, the static and non-statically quenched dye populations. The latter always decrease with the complex formation with respect to the unbound free probes; however, the fluorescence information pertained to the self-revealing population whose cone angles (O) of~50˚pointed out that the dye probe was fairly free to rotate (Fig 11) in the complexes. On the other hand, the presence of quenching did not affect the accuracy of association rate values, as the rates obtained in the independent SAV tryptophan-quenching study [39] and our data were in perfect agreement.

Conclusions
In the presented study, we calculated the association rate constants of B 7 binding to AV and SAV with dye-labeled B 7 probes and unlabeled B 7 . We concluded that attached fluorescent probes did not alter the association rates and no binding cooperativity was observed when comparing the initial (unoccupied) and final (occupied) binding rates. The fluorescence, FðtÞ, and corrected anisotropy signals, rFðtÞ, of the dye-labeled B 7 probes provided truthful binding traces contrary to the uncorrected anisotropy signal, rðtÞ, due to changes in the QY of the participating reacting species. The B 7 association rate constants of SAV are several times faster than AV and the glycan chain of the latter does not play a role in the B 7 binding association and neither explains the difference in the k on values between these two proteins. Thus, we conclude that the main differences in reaction speeds are likely related to the accessibility to the binding pocket in solution, and due to the open form in the shorter loop in SAV (residue 45 to 52, 8 residues) [81] in comparison with the AV's 12-residue loop L2-L3 (residue [35][36][37][38][39][40][41][42][43][44][45][46] [89].  Detailed characterization of avidin, strepavidin, and ligands Also, the variation in requirements for an induced fit could explain larger activation energy and entropic increment for AV compared to the SAV in the overall thermodynamics of the reaction. Interestingly, the overall reaction free energy changes are equivalent. The association rate constant for BcO, in which the tag is attached to a longer linker of biocytin, is~2X faster than B 7 with the shorter linker (BFl) for both proteins. The difference of 100X in K D of AV complex with B 7 and biocytin can be explained by differences in the dissociation process rather than the association rate constants. The B 7 binding to AV and SAV is not diffusion limited as larger than 3 kcal/mol activation energies were calculated with Arrhenius plots of the rate constants, and those rates were two orders of magnitude slower (on averagẽ 10 7 M -1 s -1 ) than the 10 9 M -1 s -1 required for diffusion limited reactions. The forward thermodynamic parameters of B 7 binding to AV and SAV complemented nicely the thermodynamic cycles with data obtained with independent calorimetric studies and dissociation kinetics elsewhere. Thus, the most probable reaction model is the one without a chemical intermediate and a single transition state in solution, but it could be more elaborate on support matrices, such as in chip assays.
The spectroscopic properties indicated very compact complexes with high dye mobility for all the probes, BFl, BcO and B 7 -DNA ds � Fl. We report for the first time a bimolecular displacement rate constant value for the SAV-BcO complex when challenged by unlabeled B 7 and this displacement of the B 7 with the longer linker (biocytin) in the BcO; this suggests that the repair and reconditioning of enriched B 7 -avidin-like surfaces is possible if long linkers are used. Early observations of affinity variations depending on the linker lengths for similar dye-labeled B 7 probes have been showed in incubation anisotropy titrations [90] but the paper did not systematically study the rate constants at various conditions (Tables 1 and 2) and multiple spectroscopic values (Table 4) of the probes as carried out here.
The AV and SAV complexes are highly thermally stable at 112˚C and 117˚C [74]; respectively, and a possible application of dye-labeled B 7 and AV-like complex could be in Dye-Sensitized Solar Cells (DSSC) [91,92] as the photon harvesting dye can be displaced when damaged. The protein can be attached covalently to the n-type material (e.g. TiO 2 ) and the charge-transfer molecule to B 7 (e.g., porphyrins, chlorophylls, ruthenium-complexes, coumarins or indoline dyes [93]), with the advantage of regeneration capabilities, as damaged dye can be reconditioned or replaced by another dye type on the tetramer attached surface (Fig 9A). This technique could be simpler than switchable mutants of avidin for regenerative biosensors reported elsewhere [94,95]. The spectroscopic properties of these dye-labeled B 7 and AV-like complexes are vital for detection methods based on polarization, fluorescence, anisotropy and Fluorescence Resonance Energy Transfer (FRET) systems because static, dynamic quenching and rotational constraints of the fluorescent probes reduce the detection limits by decreasing the signal to noise ratios [96] and producing artifacts. The information here presented will be valuable to improve new nano-technological applications of B 7 and AV-like protein systems.