Improved 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 to 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 they are slower than expected (105 to 107 M−1s−1). In this study, we asked whether these reactions in solution are diffusion controlled, what reaction model and thermodynamic cycle described the complex formation, and the 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. 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). The data suggest that the avidin binding sites are deeper and less accessible than those of streptavidin. 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.

ABSTRACT: The high affinity (K D ~ 10 -15 M) of biotin to 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 (k on ) is approximately diffusion limited (10 9 M -1 s -1 ) but recent single molecule and surface binding studies indicate they are slower than expected (10 5 to 10 7 M -1 s -1 ). In this study, we asked whether these reactions in solution are diffusion controlled, what reaction model and thermodynamic cycle described the complex formation, and the 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. Native avidin and streptavidin are homotetrameric and the association data show no cooperativity between the binding sites. The k on 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 k on 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). The data suggest that the avidin binding sites are deeper and less accessible than those of streptavidin. 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.
The extremely high affinity of biotin (B 7 , vitamin H) for avidin (AV) and streptavidin (SAV) is widely exploited in biotechnology and biochemistry in a vast array of applications. 1,2 It has been used in molecular biology as markers to identify functional moieties in proteins, receptors 3 and the development of bioprocessing affinity chromatography columns for the recovery of highly valued biomolecules. 4 More recently, advances in the characterization of these complexes have allowed the development of highly specific immunoassays, biosensors, and "omic" tools for disease identification and its molecular mechanism elucidation. 5-8 Furthermore, B 7 and avidin-like interactions can be exploited for imaging purposes in the development of assays in vivo and realtime visualization of intracellular or other type of biological processes 9,10 and nanoscale drug delivery systems of small molecules, proteins, vaccines, monoclonal antibodies, and nucleic acids. 11 SAV and B 7 are used in a Fluorescence Resonance Energy Transfer (FRET) 12 systems for drug High Throughput Screening (HTS) applications, commercially know as Homogeneous Time-Resolved Fluorescence (HTRF). 13-15 Furthermore, it has been suggested that these proteins function in nature as antimicrobial agents by depleting B 7 or sequestering bacterial and viral DNA, 16,17 and questions concerning their biological importance increase as new avidin-like proteins are discovered. For example, rhizavidin was discovered from proteobacterium Rhizobium etli, 18,19 tamavidin from the basidiomycete fungus Pleurotus cornucopiae, 20 xenavidin from the frog Xenopus tropicalis, 21 bradavidin from Bradyrhizobium japonicum, 22,23 and other AV related proteins have been isolated from chicken, Gallus gallus. [24][25][26][27][28] The monomers of AV and SAV are eight stranded anti-parallel beta-barrels with several aromatic residues forming the biotin binding site at one end of the barrel. 29 Two monomers lie parallel to each other forming a dimer with an extensive interface and two dimers associate forming the k on for B 7 binding to AV and SAV by two stopped-flow (SF) methodologies employing fluorescent dye labeled-and unlabeled-B 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) biotin-DNA ds *Fl-3' (Figure 1). The functional cofactor form of B 7 is biocytin (Bc) which is formed through an amide linkage between the amine of lysine and carboxyl group of biotin. 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. 37 We also studied the effect of AV glycosylation by removing, enzymatically, the carbohydrate motif to compare the respective association rates with those of the untreated AV, SAV and analogous probes in other studies. 20,[33][34][35][36] We show that the binding polynomial distribution (Z) of the dye-labeled B 7 complexes to track bound tetrameric species that appeared after SF mixing at pseudo first order conditions corresponding to high excess protein levels. 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 was monitored in SF instrumentation by tracking the absorbance changes of an AV-HABA complex as B 7 replaces bound HABA. 38 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 by some of us in previous studies. [39][40][41][42] 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 ∆H ǂ, forward ), entropy (∆S ǂ, forward ) and Gibbs energy (∆G 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. 32 Additionally, we explain the nature of the second dissociation phase first observed and correctly neglected by Green as a bimolecular "displacement" rate constant ( ), in addition to the detection of the documented unimolecular "replacement" rate constant ( ) 26,32 which is used to establish the wellknown dissociation constant, K D , as the most stable complex in nature.
Furthermore, we studied the changes in fluorescence lifetime (), quantum yield (QY), dynamic quantum yield (), dye emitting fraction (1-S) and steady state anisotropy (r ss ) of the fluorescent probes before and after complex formation. These spectroscopic properties give 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 careful choosing linker length and fluorescent probe. The biotinylated 14mer duplex (biotin-DNA ds *Fl) was formed with 5-10X excess complement and incubated for at least 20 min.

2.1.2.
The protein and active site concentrations of AV and SAV were determined with the HABA colorimetric assay of Green 37 for which absorbance measurements, with total protein at 280 nm (1.54 = 1 mg/ml) and HABA at 500 nm (35.5 mM bound, 0.48 mM 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, 37 and determining "x", gives one the maximum value of "p" that will be reached in reacting tetramers with a B 7 analog. Expansion of Z gives 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. International, Inc., Portland, OR) was placed between the laser source and the sample compartment with a retardation level of 1.22, and with 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 and at least 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. The sets were globally fitted to mono-or bi-exponential decay models that were discriminated using the statistical parameter  2 . The r t data was 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:

Fluorescence lifetimes () and time
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 for horizontally polarized excitation.

Quantum yields (QY)
were obtained by using a reference fluorophore of known quantum yield and were calculated according to Parker and Rees,46,47 where the reference dye was fluorescein in 0.1N sodium hydroxide solution. 38 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. form a full saturated complex (AV-HABA 4 ) and the dissociation rate of that full complex, , to yield a complex with three HABA molecules (AV-HABA 3 ). In subsequent steps, biotin replaces HABA as the ligand but the release of HABA creating an unoccupied site remains the same treating the reaction on a per monomer basis. The experiment was designed to acquire the pseudo first order association rate constant of B 7 binding ( ) to the R-state binding site in a complex occupied by HABA molecules (AV-HABA 4 ). ) and the respective slope: . The exponential 1/ decays were analyzed by the method of Foss. 49 There was no departure from simple first order decay in the relaxation, justifying the use of the following simple model and equations.
2.2.6. The association reactions of dye-labeled biotin and AV (or SAV) were collected with a SF instrument, described previously. 50,51 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 s 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 (Eqn. 4) as a function of time ( t ).
Eqn. 4 The constant A Gain is the instrumental amplitude gain and was evaluated by solving (t) using the known steady state anisotropy (r ss ) of the complexes which is equivalent to the r(t) at t= ; and H, obtained from the equivalent grating factor (G) for the filters and photo multiplied tubes in the SF. The (Eqn. 6) is equivalent to (I  ) + 2 (I  ) and proportional to quantum yield (QY i ), molar ( ) absorptivity ( i ) and to the formation or disappearance of the emitting species X i (t); and ( ) including the steady state anisotropies (r ss ) of each fluorescent species (Eqn. 7). 52 The biotin association reaction model for AV and SAV was discriminated by the squared residuals of the observed and calculated association traces of both fluorescence and anisotropy fluorescence signals, and , respectively. For the labeled biotin probes: BFl ( ) ( ) and BcO probes, the association reactions were very well described by the simplest possible model (Eqn. 8) with single association rate constants (k on ).
In the case of the biotin-DNA ds *Fl, the association reaction model was complemented by second k on which resulted in a system of two parallel reactions (Eqn. 9). In both cases, the backward reaction is not significant during the 5-8 sec required for the biotin association binding.
The dissociation reactions of the complexes were followed by fluorescence changes, , in the fluorimeter and laser setup described above and tuned to 488 nm under F(t) discontinuous excitation to prevent photobleaching distortion. The signal was best fitted to the following dissociation model (Eqn. 10), in which the dye labeled complex dissociates into the labeled B 7 probe (BFl or BcO) and the respective protein (AV or SAV).

2.2.9.
Time-resolved anisotropy ( ) was calculated according to Eqn. 11 where the preexponential "f " corresponds to the slow phase that derives from the lifetime of the global motion ( G ) 53 which was fitted within a range of expected correlation time for the complex size; 54 consequently, facilitating resolution of the fast correlation lifetime ( p ) and the corresponding preexponential (1-f ).

(
) and derived from the observed fluorescence decays of the complex. 55 1 + 2 = 1 In a simple model, the transition moment is assumed to wobble within a cone of semi-apical angle , 56 where the cone axis is normal to the surface of a sphere that corresponds to the macromolecule. The angle  is calculated from Eqn. 14.

3.1
Active avidin binding sites: Avidin and streptavidin are tetramers in solution. If the binding of ligand is positively cooperative, differences in k on for initial (T-state) and final (R-state) binding steps could be significant and therefore comparison of initial binding by unliganded avidin and final binding by liganded avidin is necessary. Measurement of the initial binding rate requires ligand free avidin 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 , 37 or perhaps existence of damaged binding sites in some of them, e.g., tryptophan oxidation. 57 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 ± 0.5 % 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. 48 In the SF association measurements, the dye-labeled B 7 probes were sub-stoichiometric to determine the initial (T-state) binding rates (e.g. 20 nM of BFl, BcO and biotin-DNA ds *Fl vs. 260 nM, 520 nM and 1040 nM in binding sites basis). Limiting the ligand also reduces several potential measurement artifacts including FRET self-transfer, and contact interference including probe fluorescence quenching by contact interactions 58 in the AB 2 , AB 3 or AB 4 complexes; especially for the BcO which has a longer linker. 59 Using the binding polynomial for the 20 nM probe after mixing, and for the intermediate AV concentration, 638 nM in total sites, 520 nM in available sites, the mole fraction of species with a single bound probe is 0.114, that with two bound is 0.0055, with three bound is 0.00012, so at most, only 4.6 % of the molecules with bound AV contain two probes; for 1040 nM available sites, the value drops to 2.3 %. With limited occupancy, the association reactions acquired the dye-labeled B 7 probes reflect the binding to the first binding site (T-state) in the tetramer for the SF experiments. Unlabeled B 7 relaxation kinetic experiment was designed to observe the binding at the final site (R-state), as discussed below.

3.2
Association rate constants (k on ) of biotin binding to apo-avidin:

Dye-labeled biotin association rate constants by stopped-flow methodology.
The fluorescence and corrected anisotropy association binding traces, , properly monitored ( ) ( ) the association reactions, as they yielded equivalent k on values (Table 1) and presented the best optimal fit residuals ( Figure 2). In contrast to the anisotropy signal, , that lagged behind  (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. 29  AV-HABA = 12.2  0.3  10 -6 M similar to that reported by Green 57 at pH 8 which support the quality of our relaxation kinetic experiment.

3.2.3
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 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 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, high (R) and low (T) affinity, 60 the HABA bound ligand will hold the AV protein in the R-state. In the relaxation experiments, all the bound HABA get replaced by dye-labeled B 7 (BFl or BcO) but all the sites are R-state meaning that there is not switching from T to R. This is the same as HbO 2 flowed against CO, where O 2 gets replaced by CO but not biphasic because no T-state is present. 60,61 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 as should be the same or close to the association rate of the dye-labeled B 7 flowed against empty AV or SAV, and our values differed only by 32% for these two approaches.

3.2.4
Comparisons with other AV-B kinetic studies were carried out at the possible closest condition; thus, at 25 C and pH 8, the BFl and BcO association rate constants, k on , were 3.8 and 7.4  slower than the 7  10 7 M -1 s -1 reported by N. M. Green 32 (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 stop the reaction timely 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 Surface Plasmon Resonance study (SPR) 20 at 20 C and a pH 7.4 in HEPES buffer. This independent k on value was ~9 and ~5  slower than the ones acquired by us for BFl and BcO, respectively. Nevertheless, it has been acknowledged previously that the SPR results are, controversially, too low to be accurate. 20,36 due to fixation to the chip of one of the reactants, generally AV or SAV.

Effect of AV glycosylation on the biotin binding kinetics: AV has a glycan attached
to asparagine 17 at each tetrameric subunit which is composed of four or five mannoses and three N-acetylglucosamines. 62 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 with 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 62 and now we confirm that AV glycosylation has no influence on the rate constants.

Association reaction of unlabeled and dye-labeled biotin binding to streptavidin:
3.3.1 Dye-labeled biotin association reactions to SAV presented temperature ( Figure 4C and 4D) and linear concentration dependence ( Figure 5C and 5D). In comparison, at 25 C, the k on values of SAV were 4X and 3.2X faster than those observed for B 7 binding to AV when reacting with BFl and BcO, respectively. However, the temperature dependence was weaker than that observe for AV which indicated a profound difference in the binding site properties of these two proteins. Thus, SAV should be a more robust system for purification applications as variations on the temperature incubation protocols has less negative significant effects in the yield.

Comparisons with other SAV-B 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) 36 which was in excellent agreement with 7.5 ± 0.2 x 10 7 M -1 s -1 for the BFl probe (at 25 ºC 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 tryptophanquenching study the final docking of B 7 near the Trp. Conversely, there is another independent Surface Plasma Resonance (SPR) study of immobilized B 7 binding to SAV that yielded a slower k on of 5.13  10 6 M -1 s -1 at 4°C, 63 which was ~5X slower than our 2.6  10 7 M -1 s -1 at 4 ºC, calculated by an Arrhenius plot (ln k on vs 1/T) of the BFl data. Similarly to AV, we believe that SPR methodology for the B 7 and AV-like protein kinetics 20,36 are modified by the immobilization of one reactant, either B 7 or protein, to the chip.

3.4.1
The association rate constants of biotin attached to our biotin-14mer ds *Fl. In case of biotinylated 14mer duplex showed a biphasic behavior with two temperature and concentration dependent rate constants (Table 2, Figure 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 ( Figure 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. 35 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 ºC whose association rate constant, k on1 , of 4.59  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 2.33  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.

3.5
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. 64 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 (Figure 8). Our deglycosylation experiments indicate that the 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 for true collective interactions of the aminoacids in the binding pocket and the biotin ring.

Biotin vs. Biocytin:
In our study, the association rates were acquired with B 7 and Bc probes, BFl and BcO; respectively, in which Biocytin present a longer carbon linker; however, the values only differed by 2-fold (Table 1), from 10 ºC to 25 ºC, 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; 29 since, the association rates of those two probes binding to neutral SAV differed also by ~2 fold as observed for AV. The dissociation constant, K D , of AV-B and AV-Bc were reported to be 10 -13 and 10 -15 M, respectively, differing by 100-fold. 37 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 and SAV-B complexes had been described as passive unimolecular "replacements" ( ) with units of reciprocal seconds (s -1 ) and values of 9  10 -8 s -1 32 and 2.4  10 -6 s -1 , 65 respectively. However, we have also observed a bimolecular "displacement" off-rate constants ( ) with M -1 s -1 units for the SAV-BcO complexes (AB 1 and AB 4 ) that were strongly dependent of B 7 concentration ( Figure   9A) and temperature ( Figure 9B). These reactions had ~79% of the total release amplitude, in contrast to the 5% when BFl was used ( Figure 9C); therefore, the longer "tail" of the BcO facilitated the displacement, a feature that can be exploited to increase purification yields. Also, the process is protein dependent, as it was not observed for the AV complexes. Significantly, 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.

Biotin reaction models to AV and SAV:
3.8.1 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 single rate constant, A + B ⇌C k on (Eqn. 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 mechanism have been reported 66,67 . For example, has been proposed for polystyrene A + B ⇌C⇌D SAV coated particles (6.5 nM) reacting with a fluorescein labeled biotin probe (1.75 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 reasons: 1) The interference of the dye structures into the neighboring site due to multiple occupancies on the tetramer 58 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 pulloff study carried out by Scanning Force Microscopy for 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 intermediated. 68 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 surface matrix complexity and multiple orientation of the B 7 and 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 was best described by
two parallel reactions (Eqn. 9) with two independent association rate constants that showed no evidence of intermediates in solution and whose pre-exponentials were temperature dependent (Table 2) indicating 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 value of k on1 for both AV and SAV were 20-40 % slower than rate constants acquired with BFl indicating that biotin on the DNA was positioned in a favorable orientation that enhance the reaction. On the other hand, the slower k on2 rate constant is associated with an unfavorable orientation of the second B 7 population.

Thermodynamic Parameters:
The forward activation energies (E a forward or H 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 estimation of 10 -12 kcal/mol for the displacement of water molecules from the binding pocket. 57 These values were larger than the 3-4 kcal/mol 32,69 characteristic of a diffusion limited reaction (which requires also association rate constants in the order of 10 9 M -1 s -1 and 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 mainly that the binding of B 7 ligand enhances thermal stability of the proteins shifting from 75 ºC to 112 ºC for SAV and from 84 ºC to 117 ºC for AV. 70 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 (∆H Rxn ) calculated by calorimetry (Table 3,  (Table 3, Figure 10, red line) than the latter (Table 3, Figure 10, green line) which implies that binding sites of AV are deeper and less accessible resulting in a slower association rate constants, k on , and larger activation energy with respect to biotin binding to SAV.
The fluorescence spectroscopic parameters. The absorbance and emission peaks of all the dyelabeled B 7 complexes (Table 4) were red shifted a few nanometers (Supporting Information, Figure  S1 and S2) with respect to the unbound probes, with the exception of the biotin-DNA ds *Fl complexes with AV and SAV that were blue-shifted 3 nm by the presence of both proteins. This can be explained due to fluorescein (Fl) interactions with DNA ds before binding to AV and SAV and later displaced toward the solution in the complex. In the particular case of the absorbance spectrum of SAV-BFl, it was highly distorted (Supporting Information, Figure  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 traces, which is particularly important for the biotin-DNA ds *Fl reactions, whose traces had shifted directions The (S) and (1-S) are, respectively, the emitting and statically quenched dye populations. The latter always increased with the complex formation with respect to the unbound free probes; thus, the fluorescence information pertained to the self-revealing population whose cone angles () of ~50 pointed out that the dye probe was fairly free to rotate (Figure 11) in the complexes. On the other hand, the presence of (1-S) did not affect the accuracy of association rate values, as the rates obtained in the independent SAV tryptophan-quenching study 36 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, , and corrected ( ) anisotropy signals, , of the dye-labeled B 7 probes provided truthful binding traces contrary ( ) to the uncorrected anisotropy signal, , 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 is likely related to structural aspects of the binding sites. A deeper pocket in AV would be filled with more water molecules requiring more energy to break the hydrogen bonds. Also, the variation in requirements for induced fit could explain in 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 biotin 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 all of those rates were two orders of magnitude slower (on average ~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        Table 2. Association rate constants (k on ) and thermodynamic values of the dye-labeled biotin binding to AV and SAV. a The probes were BFl, BcO, and biotin attached to a nucleotide in a 14-mer DNA duplex. The thermodynamic values were acquired from global fitting of the rate constants 39,42 for the most probable model which resulted in simple reaction with a transition state without intermediates. In case of biotin-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 orientation.
b The k on were averaged from data in Table 1 c Calculated from an Arrhenius plot.  a According to the best fitting model with one transition state and non-intermediates. The forward and reverse rate constants were used to calculate, with Arrhenius plots, the respective forward and backward activation energies, E a forward and E a backwards , respectively. The difference of these activation energies results in ∆E (column 4) which were equivalent to an averaged ∆Hº Rxn (column 1) of multiple independent calorimetry studies. Similarly, analysis was carried out for reaction Gibbs free energy (∆G Rxn ) and entropy (∆S Rxn ).
b Column 4 is the subtraction of column 2 minus column 3 and should be equivalent to experimental reaction values obtained from multiple studies thus confirming the accuracy of the proposed model. h The absorbance spectrum of the SAV-BFl complex (Supporting Information, Figure S1) and the detection of the corresponding lifetimes of 3.0 and 4.1 ns 85,86 indicates the presence of both Fl 1and Fl 2-, respectively. 72 We used these reported lifetimes to calculate the pre-exponentials values (α) of each fluorescent species in the SAV-BFl complex. The intrinsic lifetime of Fl 1was calculated by dividing the lifetime (3.0 ns) over the absolute quantum yield (0.37). 43 We calculated the (1-S) Fl 1by assuming that (1-S) Fl 2is that of AV-BFl (with contains only Fl 2-) and solving the following equation: , where C is the concentration,  is the molar absorptivity  a According to the best fitting model with one transition state and non-intermediates. The forward and reverse rate constants were used to calculate, with Arrhenius plots, the respective forward and backward activation energies, E a forward and E a backwards , respectively. The difference of these activation energies results in ∆E (column 4) which were equivalent to an averaged ∆Hº Rxn (column 1) of multiple independent calorimetry studies. Similarly, analysis was carried out for reaction Gibbs free energy (∆G Rxn ) and entropy (∆S Rxn ).
b Column 4 is the subtraction of column 2 minus column 3 and should be equivalent to experimental reaction values obtained from multiple studies thus confirming the accuracy of the proposed model.  h The absorbance spectrum of the SAV-BFl complex (Supporting Information, Figure S1) and the detection of the corresponding lifetimes of 3.0 and 4.1 ns 85,86 indicates the presence of both Fl 1and Fl 2-, respectively. 72 We used these reported lifetimes to calculate the pre-exponentials values (α) of each fluorescent species in the SAV-BFl complex. The intrinsic lifetime of Fl 1was calculated by dividing the lifetime (3.0 ns) over the absolute quantum yield (0.37). 43 We calculated the (1-S) Fl 1by assuming that (1-S) Fl 2is that of AV-BFl (with contains only Fl 2-) and solving the following equation: , where C is the concentration,  is the molar absorptivity    elucidated by collecting the reaction with continuous (black) and discontinuous (dashed color) laser illumination, where in the latter case the beam was blocked during the times denoted by dashes and the sample was illuminated only during time intervals around 10 s. The slow photobleaching rate constant varied from 6  10 -3 to 1  10 -2 s -1 , and was laser power dependent.     Arrhenius plot (ln k on vs 1/T) of the association rate constants plotted in semi-logarithm for clarity. Temperature dependence of the biotin association reaction at pH 8 (unless otherwise specified) for: 1 SAV-BFl (purple triangles); 2 SAV-biotin-DNA ds *Fl (green triangles): 2.1 (k on1 ) and 2.2 (k on2 ); 3 SAV-BcO (red triangles); 4 AV-BFl (purple circles); 5 AV-biotin-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).     (Table 3). Arrhenius plots of the temperature dependent association and dissociation rate constants were used to calculate the E a forward and E a backwards , respectively.