Bioconjugate Chem. 2006, 17, 501−506
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Kinetics of Amine Modification of Proteins George P. Smith† Division of Biological Sciences, Tucker Hall, University of Missouri, Columbia, Missouri 65211-7400. Received October 14, 2005; Revised Manuscript Received December 23, 2005
A simple kinetic model for coupling small molecules such as biotin to proteins with amine-reactive reagents such as N-hydroxysuccinimide esters is developed. It predicts the reagent concentration required to modify a protein at a given concentration to a specified number of modified amines per molecule. By optimizing the model’s three adjustable kinetic parameters, its predictions can be brought into close agreement with empirical data for modification of IgG, serum albumin, and other proteins over a wide range of protein and reagent concentrations. Data for modification of one protein can be used to approximate the results for modification of another protein with the same reagent under the same reaction conditions.
INTRODUCTION A typical protein has numerous surface-exposed R- and -amino groups; in their unprotonated form they are strong nucleophiles that can be efficiently modified by a number of electrophilic reagents under mild, non-denaturing conditions to yield stable adducts. Although it sometimes happens that a few modifiable amino groups lie in or near functional sitessfor example, the antigen-binding sites of an antibodysmany more lie elsewhere on the surface of the molecule. Random modification of a few of these groups with small molecules is therefore unlikely to functionally inactivate more than a small fraction of the molecules. For these reasons, amine modification has become the most commonly used method of coupling small groups such as biotin or fluorescent dyes to proteins (reviewed in ref 1). To exploit this simple coupling technology fully, it is necessary to control the level of amine modification. Increasing the number of coupled groups per protein molecule far beyond the required number unnecessarily incurs the risk of inactivating a significant fraction of the target proteins. The purpose of this paper is to help researchers achieve this goal by developing a simple mathematical model of modification kinetics. It is obviously desirable that the reaction solution be as free as practicable of competing nucleophiles such as primary and secondary amines, but depletion of the reagent by hydrolysis is inevitable in aqueous solution, at a rate that depends on the particular reagent, pH, temperature, and buffer composition. In this regard, the protein itself must be considered a buffer component, quite apart from its modifiable amines. Proteindependent hydrolysis would include futile modifications (e.g., of histidine) leading to unstable adducts that are rapidly hydrolyzed to regenerate the original nucleophile. In light of these considerations, hydrolysis will be divided into two additive components: a protein-independent component, the rate of which is independent of protein concentration; and a proteindependent component, the rate of which is proportional to protein concentration, which is assumed to be effectively constant throughout the course of the reaction even though the content of modifiable amines diminishes. Figure 1 shows a typical modification reaction, which will serve as an exemplar in this work: biotinylation with the N-hydroxysuccinimide (NHS) ester NHS-PEO4-biotin. Nucleophilic attack on the activated carbonyl by a protein amino †
Telephone (573) 882-3344; e-mail
[email protected].
Figure 1. Modification of protein amines with the N-hydroxysuccinimide (NHS) ester, NHS-PEO4-biotin. The electrophilic carbonyl carbon attacked by the nucleophile (protein amine or water) is printed in bold type.
group displaces the NHS leaving group and couples the biotincontaining moiety to the protein through a stable amide bond. Competing with this modification reaction is hydrolysis, which releases the NHS leaving group and a nonreactive carboxyl. Despite their name, amine-reactive reagents are not entirely selective for amines. In particular, free (non-disulfide-bonded) cysteine thiols in their unprotonated form are stronger nucleophiles and, if accessible on the protein surface, are readily modified by most amine-reactive reagents. The resulting thio adducts are generally much more susceptible than amine adducts to nucleophilic attack by neighboring nucleophiles on the protein itself or by nucleophilic solutes, but in the absence of such nucleophiles can be sufficiently stable in aqueous solution to be operationally indistinguishable from amine adducts. For the sake of simplicity in what follows the term “amine” will be used to refer to all stably modifiable nucleophiles, even though in some cases a few thiols or other nucleophilic groups might be included.
10.1021/bc0503061 CCC: $33.50 © 2006 American Chemical Society Published on Web 02/16/2006
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Smith
EXPERIMENTAL PROCEDURES Biotinylation. Immunoglobulin G (IgG) was purified by protein G chromatography from human serum after prior solvent/detergent (SD) treatment essentially as described (2) and by protein A chromatography from rabbit serum with and without SD treatment. The IgGs were dialyzed against phosphatebuffered saline (PBS), pH 7.2 (0.15 M NaCl, 0.1 M NaH2PO4, pH adjusted to 7.2 with NaOH), and quantified spectrophotometrically, assuming an absorbance of 1.4 at 280 nm for a 1 mg/mL solution (3) and a molecular mass of 150 kDa. Bovine serum albumin (BSA; Sigma Chemical Co., St. Louis, MO; catalog no. A7906) was dissolved in water at a concentration of 726 µM, as determined spectrophotometrically assuming a molar extinction coefficient of 44 022 at 280 nm. In each of 16 reactions, 1 mg of human IgG was reacted with various concentrations of NHS-PEO4-biotin reagent in final volumes ranging from 100 µL to 7.1 mL. To accomplish this, the protein was diluted in PBS, pH 7.2, to a calculated volume slightly less than the final volume; a 2 mg (3.4 µmol) portion of the reagent (No-Weigh NHS-PEO4-biotin; Pierce Chemical Co., Rockford, IL) was dissolved in 100 µL of dimethyl sulfoxide and diluted to the desired concentration in PBS, pH 7.2; working as rapidly as feasible, the diluted reagent was pipetted into the reaction vessels in sufficient volumes to give the desired final volumes and reagent concentrations; the vessels were vortexed immediately and incubated overnight (16-20 h) at room temperature. After the addition of PBS, pH 7.2, to the biotinylated IgG (Bio-IgG) samples as necessary to bring the total volume to 7.1 mL, they were concentrated to ∼50 µL by four concentration cycles on centrifugal ultrafiltration devices with a molecular mass cutoff of 30 kDa (Centricon; Millipore Corp., Bellerica, MA) and freed of uncoupled biotin by four cycles of dilution with 1.8 mL of TBS, pH 8 (0.15 M NaCl, 50 mM Tris-HCl, pH 8.0) and concentration to ∼50 µL on the same ultrafiltration devices. The final Bio-IgG retentates (in ∼50 µL) were diluted with 400 µL of TBS, pH 8, and quantified spectrophotometrically; the yield of Bio-IgG was ∼80% of the starting IgG. Reactions with rabbit IgG and BSA were carried out similarly. Measuring Biotinylation Level. Most biotin assays rely on competition between the analyte (the biotin to be quantified) and another ligand for binding to avidin or streptavidin. Proteincoupled biotins, unlike free biotins, cannot react freely with all four biotin-binding sites on a tetrameric avidin or streptavidin molecule because of steric hindrance. Moreover, multivalent biotinylation can lead to formation of aggregates with uncertain effects on the results. These uncertainties can be reduced if the biotin analyte is released from the protein by acid hydrolysis or proteolytic digestion prior to quantitation (1, 4, 5). The biotinylation levels reported here were measured by inhibition ELISA after first digesting the biotinylated protein extensively with proteinase K and filtering the digest through a centrifugal ultrafiltration device with a molecular mass cutoff well below the size of intact proteinase K (molecular mass ) 27 kDa). In 2.2 mL microtubes, 2 µL of SDS/DTE (5% SDS, 10 mM dithioerythritol in TBS, pH 8) was mixed with 16 µL of TBS, pH 8, containing a known amount (∼30 µg) of biotinylated protein; after heating to 95-100 °C for 5 min, cooling to room temperature, and brief centrifugation to drive condensation to the bottom, 2 µL of 20 mg/mL proteinase K stock solution [a 1:1 v/v mixture of glycerol and 40 mg/mL proteinase K in 0.3 M NaCl, 0.1 M N-(2-hydroxyethyl)piperazine-N′-(2-ethanesulfonic acid), pH adjusted to 7.5 with NaOH; stored at -20 °C] was added (enzyme/substrate weight ratio ) 1.3), and the tube was incubated at 50 °C for 30 min. After brief centrifugation, the digests were heated to 95-100 °C for 5 min, briefly centrifuged again, diluted with 1.8 mL of TBS, pH 7.5 (0.15
Figure 2. Biotin quantitation by inhibition ELISA. Analyte (filtered protein K-digested Bio-IgG) and biotin standard at known concentrations were tested for the ability to inhibit binding of an alkaline phosphatase conjugate of streptavidin (AP-SA) to biotinylated BSA immobilized on ELISA wells, as described in the text. All ELISA signals from a given ELISA dish were fitted to an empirical equation of the form y ) B + S/[1 + (mc/C)N], where y ) predicted ELISA signal (dependent variable), c ) concentration of biotin or Bio-IgG inhibitor (independent variable), m ) modification level (number of biotins per molecule; m ) 1 for the biotin standard; m ) a single positive number for all dilutions of a given Bio-IgG analyte), and B, S, C, and N are unknown “nuisance” parameters assumed to be constant for all 96 wells of a single ELISA dish. The modification level m for each Bio-IgG analyte and the four nuisance parameters were adjusted to minimize the root-mean-squared (RMS) deviation of the empirically measured ELISA signals from the theoretical ELISA signals predicted by the above equation. ELISA signals >35 mOD/min were excluded as being less accurate and informative than lower signals. On a semilogarithmic plot like the one shown, all curves of ELISA signal y as a function of inhibitor concentration c will have the same shape, but will be shifted to the left relative to the curve for the biotin standard (m ) 1) by the increment log(m). The optimal value of m determined in this way for a given Bio-IgG sample was taken as the estimate of its biotinylation level. The modification levels for biotinylated proteins other than Bio-IgG were determined similarly.
M NaCl, 50 mM Tris-HCl, pH 7.5), and filtered through a Centricon ultrafiltration device with a molecular mass cutoff of 10 kDa. A less extensive proteinase K digestion of biotinylated protein (enzyme/substrate weight ratio ) 0.02; 37 °C for 24 h) is sufficient to release the bulk of the biotin in the form of free biotin and much of the remainder as small biotinylated peptide fragments (5). In accord with that finding, a pilot experiment in which fluoresceinated IgG and BSA were digested and filtered in the same way as our biotinylated proteins showed quantitative recovery of fluorescence in the filtrate and no detectable retention in the retentate (data not shown). Inhibition ELISA (detailed in the next paragraph) quantifies the ability of the analytes (filtered proteinase K digests) and of a free biotin standard to block binding of an alkaline phosphatase conjugate of streptavidin (AP-SA; Jackson ImmunoResearch Laboratories, West Grove, PA) to immobilized biotin in the wells of a 96-well ELISA dish. To minimize the effects of steric hindrance on the association rate, the AP-SA was preincubated with analyte or biotin for 30 min before being loaded into the biotin-coated wells. The wells of the ELISA dish were first coated overnight at 4 °C with 200 µL of TBS, pH 7.5, containing nonbiotinylated BSA at 100 µg/mL and biotinylated BSA (Sigma; nominally 10 biotins/molecule) at 2 µg/mL. Meanwhile, using TBS/Tween (TBS, pH 7.5, supplemented with 0.5% v/v Tween 20) as diluent, serial dilutions of a free biotin standard at concentrations ranging from 1.95 to 100 nM and of the proteinase K filtrates equivalent to biotinylated protein concentrations ranging from 0.2 to 45 nM were set up. In the wells of a round-bottom 96well dish (not the ELISA dish) were mixed 50 µL portions of the biotin and filtrate dilutions and 150 µL portions of a 200
Bioconjugate Chem., Vol. 17, No. 2, 2006 503
Kinetics of Amine Modification of Proteins Table 1. Derivation of Equation 1
variables (units in parentheses) t ) time since the start of the modification reaction (s) a ) a(t) ) concentration of unmodified (but modifiable) amines remaining at time t (µM) A ) initial concentration of modifiable amines before any modification (µM); A ) a(0) P ) concentration of protein (µM) M ) number of modifiable amines per protein molecule (dimensionless); A ) P × M m ) m(t) ) number of modified amines per protein at time t (dimensionless); m(t) ) [A - a(t)]/P ) M - a(t)/P; m(0) ) 0 r ) r(t) ) concentration of amine-modifying reagent remaining at time t (µM) R ) initial concentration of reagent before modification or hydrolysis (µM); R ) r(0) km ) second-order modification rate constant (µM-1 s-1) kh ) first-order protein-independent hydrolysis rate constant (s-1) Q ) second-order protein-dependent hydrolysis rate constant (µM-1 s-1) differential equations from the mass-action law da/dt ) - kmar dr/dt ) - kmar - (kh + QP)r dividing the second equation by the first yields an easily solved differential equation relating r to a: dr/da ) 1 + [(kh + QP)/km](1/a) eq 1 of the text is the solution to this equation when the reaction goes to completion (r ) 0)
ng/mL dilution of AP-SA (also in TBS/Tween diluent); the dish was incubated for 30 min at room temperature. As that incubation was ending in the round-bottom dish, the ELISA dish was washed with a plate washer and 150 µL portions were pipetted from the wells of the round-bottom dish into the corresponding wells of the ELISA dish, which was incubated for 30 min at room temperature to allow AP-SA to bind the immobilized biotinylated BSA. The ELISA dish was washed extensively on a plate washer, and the wells were filled with 150 µL portions of substrate solution: a fresh mixture of 20 mL of 1 M diethanolamine, pH adjusted to 9.8 with HCl, 20 µL of 1 M MgCl2, and 200 µL of 50 mg/mL p-nitrophenyl phosphate (stored at -20 °C). The difference between the optical density (OD) at 405 and that at 490 nm was read at 3 min intervals over a 57 min period on a kinetic plate reader at room temperature to obtain a slope (mOD/min) for each well (1 mOD corresponds to an OD of 1/1000), which was taken as the ELISA signal; for slopes up to at least 50 mOD/min, time dependence is linear, with correlation coefficients usually exceeding 0.995. Figure 2 shows an example of an inhibition ELISA with the filtered proteinase K digest of a Bio-IgG sample. As can be seen in the graph, the equivalent Bio-IgG concentration required to reach a given level of inhibition was 2.12 times lower than the concentration of free biotin required to reach the same inhibition level; the modification level of this Bio-IgG sample is therefore estimated at 2.12 biotins/molecule. Duplicate measurements (on separate ELISA dishes) with all biotinylated protein samples gave closely similar numbers with few exceptions. The inhibition data for the free biotin standard in Figure 2 deviate slightly but systematically from the theoretical curve, indicating that protein-derived biotins are not entirely equivalent kinetically to free biotins. A plausible explanation is that a few biotins remain coupled to small peptide fragments even after extensive proteinase K digestion, as noted above (5). Such peptide-coupled biotins may well bind streptavidin with somewhat altered kinetics compared to free biotin because of steric hindrance, thus accounting for the slight deviations in Figure 2. Still, there is no reason to believe such peptides are so abundant and so kinetically different from biotin as to lead to large errors in biotin content estimates. Complete acid hydrolysis has been advocated as a method for releasing all protein-coupled biotin in the form of free biotin (5); however, as measured by inhibition ELISA, that method yielded only 66% as much biotin from a Bio-IgG sample as did proteinase K digestion, possibly because some biotin was destroyed or altered in the acid (6). In any case, modest errors in biotin level (on the order of 33%, say) are seldom of practical importance and do not undermine
the conclusions of this papersespecially if, as seems likely, they apply proportionally across all samples (see below under eq 2).
RESULTS AND DISCUSSION Mathematical Model. If one makes the simplifying assumptions that all amines react independently and identically, depletion of the target amines and amine-reactive reagent from their respective initial concentrations is described by the differential equations in Table 1. At completion of the reaction those equations have the solution
[
R) m-
)]
(
kh Q m m ln 1 P - ln 1 km M km M
(
)
(1)
where M ) total number of modifiable amines per protein molecule, m ) average number of amines modified per protein molecule at completion of the reaction, R ) reagent concentration, P ) protein concentration, km ) second-order modification rate constant, kh ) first-order protein-independent hydrolysis rate constant, and Q ) second-order protein-dependent hydrolysis rate constant (derivation in Table 1). According to eq 1, the reagent concentration R required to achieve a given modification level m is a linear function of the protein concentration P, with slope [m - (Q/km) ln(1 - m/M)] and intercept -(kh/km)ln(1 - m/M) (both expressions are always positive, because the logarithm is negative). It is obvious from this expression that the ratio of reagent to protein, R/P, is not an adequate description of reaction conditions, contrary to common practice in protein chemistry. Indeed, in circumstances when the intercept term of eq 1 dominates, either because the protein concentration P is low or because protein-independent hydrolysis is relatively fast compared to modification, the reagent concentration required is independent of protein concentration. To fully describe the conditions of a modification reaction, therefore, both the reagent concentration R and the protein concentration P must be individually specified (along with buffer composition and pH, temperature, and time of reaction). In most applications, the fraction of available amines modified m/M will be small (less than ∼20%, say), in which circumstances -ln(1 - m/M) ≈ m/M and eq 1 can be approximated by
R≈
[(
1+
)
]
kh Q m P+ m when , 1 kmM kmM M
(2)
In a typical modification reaction, therefore, the reagent concentration R required to achieve modification level m at fixed
504 Bioconjugate Chem., Vol. 17, No. 2, 2006
protein concentration P will be nearly proportional to m. In these circumstances, proportional errors in measuring m lead only to the same proportional errors in R. The mass-action law that underlies eq 1 is silent on the values of the three kinetic parameters Q/km, kh/km, and Msor, when eq 2 applies, the two parameters Q/kmM and kh/kmM. Those parameter values must be estimated empirically by adjusting their values to optimize the fit of eq 1 (or eq 2) to experimentally measured modification levels. It is vital that those experimental measurements span a wide range of protein concentrations, because modification at a single protein concentration is essentially governed by a single proportionality constantsthe quantity in square brackets in eq 2sand cannot be used to constrain two or three separate parameters. Biotinylation as an Example of Amine Modification. Conjugating biotin to proteins opens up a wealth of techniques that exploit the extremely rapid and stable binding of biotin to avidin and streptavidin (reviewed in refs 1 and 7). For most of these purposes, a modification level of 2-3 biotins per molecule is fully sufficient and stands very little chance of interfering with the biological activity of most modified proteins. Biotinylation of human IgG with NHS-PEO4-biotin (Figure 1) will serve as the chief example of amine modification in this paper. Sixteen human IgG samples at concentrations ranging from 0.953 to 67.6 µM (from 143 µg/mL to 10.1 mg/mL) were biotinylated overnight at room temperature with NHS-PEO4biotin at various concentrations in PBS, pH 7.2, and freed of uncoupled biotin as described under Experimental Procedures. The biotin contents of the resulting biotinylated IgGs (Bio-IgGs) were quantified by proteinase K digestion and duplicate inhibition ELISA as described under Experimental Procedures. The measured biotinylation levels m were fitted to eq 1 by adjusting the kinetic parameters to optimize agreement with the data. A series of four biotinylation reactions with BSA were likewise fitted to eq 1, yielding an independent set of optimal parameter values. In Figure 3 those optimized IgG and BSA parameter values (reported in the caption) are used to plot the predicted reagent concentration R required to achieve various modification levels m as a function of protein concentration P (IgG in the upper part of the graph, BSA in the lower part); in a linear plot these isomodification contours would be straight lines, as explained above under eq 1. Superimposed on the theoretical contour curves are the data on which they are based. For each biotinylation reaction, the open symbol marks the actual concentrations of protein and reagent, whereas the associated horizontal bars plot the reagent concentration R that according to eq 1 would theoretically be required to achieve the biotinylation levels m actually measured for that sample (one bar for each of the duplicate determinations). The closeness of the bars to each other testifies to the excellent reproducibility of the biotin determinations; the closeness of the bars to their corresponding open symbols testifies to the excellent fit between the observed data and the theoretical calculations over a wide range of protein and reagent concentrations. Also included in the upper part of Figure 3 (but not considered in optimizing the IgG parameter values) are four reactions with rabbit IgG; here, too, the observed biotinylation levels closely match the predictions of eq 1. This graph illustrates dramatically how eq 1 allows results of a handful of pilot experiments to be parlayed into reliable projections covering a broad continuous range of concentrations of the same protein and the same reagent under the same reaction conditions. As Figure 3 shows, eq 1 (or, when applicable, its corollary eq 2) applies in form to biotinylation of both IgG and BSA, although the optimal parameter values are different for the two proteins as will be detailed in the next subsection. It is probable that eq 1 will likewise apply in form to almost any amine
Smith
Figure 3. Graph of NHS-PEO4-biotin concentration R required to biotinylate human and rabbit IgGs (upper part) and BSA (lower part) to various modification levels m as a function of protein concentration P. The theoretical curves are iso-modification contours for m ) 1-11, calculated according to eq 1 (IgG) or eq 2 (BSA) with the following optimized parameter values: kh/km ) 2274 µM, Q/km ) 25.60, and M ) 128.9 accessible amines per molecule for IgG; and kh/kmM ) 24.1 µM per accessible amine and Q/kmM ) 0 for BSA. The open symbols plot the protein and reagent concentrations for each reaction; the associated pair of horizontal bars represent the duplicate results for that reaction, as explained in the text.
modification reaction that goes to completion, because it appeals only to basic principles of mass action that successfully describe the great majority of chemical interconversions. In accord with this supposition, for example, Larson et al. (8) found that the degree of modification of IgG at constant concentration with amine-reactive poly(ethylene glycol) (PEG) polymer chains was directly proportional to the concentration of the PEGylating reagent, as predicted by eq 2. The mathematical model’s most vulnerable assumption is kinetic homogeneity of the accessible aminess, but it is not necessary for that assumption to be literally true for eq 1 to be empirically useful: all that is required is that there exist compromise values of the parameters that give a reasonable approximation to the overall kinetic behavior of the amines. Equation 1 may be much less successful if extended to high degrees of modification, when the homogeneity assumption would be more severely challenged, but in most applications calling for the kinetic predictability afforded by eq 1, only modest modification levels are of practical interest. The ratio [(Q/kmM)P)/((kh/km)M] ) QP/kh gauges the relative contribution of protein-dependent and protein-independent hydrolysis to consumption of the reagent. For IgG that ratio reaches 0.75 at the highest IgG concentrations P, when hydrolysis as a whole is relatively unimportant compared to modification, but declines proportionally at lower IgG concentrations as hydrolysis comes to dominate. For BSA the ratio vanishes altogether. The data therefore do not support the existence of a significant protein-dependent route for hydrolysis of NHS-PEO4-biotin. When protein-mediated hydrolysis is negligible and the modification level m is modest compared to the total number of
Bioconjugate Chem., Vol. 17, No. 2, 2006 505
Kinetics of Amine Modification of Proteins Table 2. Dependence of the Kinetic Parameters of Equation 1 on Reagent, Protein, and Reaction Conditions and Sensitivity of Predictions of Equation 1 to Variations in Those Parametersa expected dependence of parameter on parameter
reagent
protein
conditions
sensitivity of reaction kinetics to variations in parameter
kh km M
strong strong weak
strong strong strong
strong strong strong
Q
strong
none none proportional to amines? proportional to MW?
strong
weak
a
See text for details.
accessible amines M, eq 2 reduces further to the single-parameter approximation
(
R≈ P+
)
kh QP m m when , 1 and ,1 kmM M kh
(3)
It is entirely possible that protein-dependent hydrolysis may be much more important for amine-reactive reagents other than NHS-PEO4-biotin, howeversparticularly when the reactive function is something other than an NHS ester. It is evident from Figure 3 that at the lowest protein concentrations P explored the curves are nearly horizontal because consumption of reagent by modification of protein amines or protein-mediated hydrolysis is negligible compared to consumption by non-protein-mediated hydrolysis. In those circumstances eq 3 further simplifies to the approximation
R≈
( )
(
)
kh kh m Q m when , 1 and 1 + P, kmM M kmM kmM
(4)
and it is not necessary to know the protein concentration accurately to modify it to a specified level. This case underscores the inadequacy of reagent/protein ratio R/P alone as a description of the conditions of a modification reaction, as emphasized in the previous subsection (Mathematical Model). Applicability to Different Proteins, Reagents, and Conditions. The three parameters of eq 1 are composed of four fundamental parameters that arise directly from the underlying kinetic model and that respond in different ways to changes in the protein, reagent, and reaction conditions (pH, buffer composition, and temperature). The parameters kh and km, respectively, gauge the susceptibility of the reagent to proteinindependent hydrolysis and its intrinsic reactivity with an accessible amine; they are therefore specific to the reagent but independent of the protein. In contrast, M gauges the total number of accessible amines on the protein molecule; it is therefore specific to the protein and may also depend somewhat on the reagent to the degree that the reagent’s structure affects its access to amines. For a given reagent M should vary roughly in proportion to the total number of amines, although of course there will be excursions from this trend because of variations in protein shape and other properties. Finally, Q parametrizes the rate of protein-dependent hydrolysis and, in general, may depend on both reagent and protein. This mode of hydrolysis is presumably due to various surface groups on the protein, and because the nature of those groups is unknown, the best guess is that Q for a given reagent is roughly proportional to total protein molecular mass. All four fundamental parameters might depend strongly on pH and temperature, but probably only weakly on buffer composition provided no strong nucleophiles are included. These theoretical dependencies are summarized in the second, third, and fourth columns of Table 2. The last
column of the table summarizes the sensitivity of reaction kinetics (R as calculated from eq 1) to variation in the four kinetic parameters. The value of each parameter was halved and doubled relative to its optimal value for the IgG data, keeping the other three parameters constant, and the resulting overall deviations from the original values of R were scored. This sensitivity analysis reveals that halving or doubling Q changes the theoretical predictions of eq 1 only slightly, reflecting the finding that protein-dependent hydrolysis is minor or nonexistent (see above). In contrast, halving or doubling the other three parameters drastically changes the predictions of eq 1 in at least some circumstances. Because eq 1 is based on an oversimplification of the true kinetic situation (particularly the simplifying assumption that all modifiable amines are kinetically homogeneous), the parameter values that optimize the fit to actual data may represent compromise values in which the theoretical dependencies in Table 2 are somewhat blurred. For example, the optimal value of the parameter M for IgG in Figure 3, 129 modifiable amines per molecule, certainly cannot be interpreted literally, in that it greatly exceeds the number of accessible IgG amines [∼30 as determined at saturating concentrations of another NHS ester, N-succinimidyl S-acetylthioacetate (1)], and indeed exceeds the total number of amines in a typical IgG (∼90). Because the conditions of eq 2 apply to a good approximation for most of the IgG reactions, the overall fit of eq 1 to the IgG data can evidently be improved by exaggerating the value of M substantially while keeping the ratios Q/kmM and kh/kmM roughly the same. The improvement is slight: the best fit to the data with M fixed at 30 is nearly as good as the overall best fit. Despite these reservations to the theoretical parameter dependencies, though, it is reasonable to accept them as first approximations in extrapolating results from one combination of protein, reagent, and reaction conditions to another. For instance, whatever the discrepancy between the optimal value of M for IgG and that protein’s actual content of modifiable amines, when one is extrapolating from IgG to other proteins, it is reasonable to assume that M scales as the total amine content to a first approximation. The BSA data in Figure 3 provide an opportunity to test the validity of such projections. Because BSA has 44% of the molecular mass and 66.7% of the total amine content of IgG, parameters kh/kmM and Q/kmM for biotinylation of BSA are projected to be (kh/km)/M ≈ 2274/0.667 × 129 ) 26.4 µM per accessible amine and (Q/km)/M ≈ (0.44 × 25.6)/(0.667 × 129) ) 0.13 per accessible amine. Actual results for BSA biotinylation optimally fit values of 24.1 and 0 for those parameters, respectively (Figure 3 caption). The agreement for the first parameter (24.1 predicted, 26.5 observed) is quite close, whereas the discrepancy for the second (0.13 predicted, 0 observed) is of little significance because protein-dependent hydrolysis seems to be very minor. By the same token, the observed BSA modification levels were only 11-19% higher than those projected on the basis of the IgG results. The BSA data thus suggest that results for modification of one protein can be used to make reasonable predictions about modification of another with the same reagent under the same reaction conditions. Such extrapolationssespecially if supported by a handful of additional proteinssare of great practical usefulness because they bypass the need for preliminary investigation of modification kinetics for each new protein to be modified (provided great precision is not required). For modifications such as biotinylation that are difficult to quantify accurately (see Experimental Procedures), a great deal of effort can thereby be saved. For proteins in very short supply, valuable material can be spared. It remains to be ascertained if other additional useful generalizations will emerge from further investigation with additional reagents, proteins, and reaction conditions.
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ACKNOWLEDGMENT Robert Davis provided excellent technical assistance in this work, which was supported by U.S. National Institutes of Health Grant GM41478 to the author and National Cancer Institute Center Grant P50-CA-10313-01 to Wynn A. Volkert.
LITERATURE CITED (1) Hermanson, G. T. (1996) Bioconjugate Techniques; Academic Press, San Diego, CA. (2) Kouzmitcheva, G. A., Petrenko, V. A., and Smith, G. P. (2001) Identifying diagnostic peptides for Lyme disease through epitope discovery. Clin. Diagn. Lab. Immunol. 8, 150-160. (3) Mandy, W. J., and Nisonoff, A. (1963) Effect of reduction of several disulfide bonds on the properties and recombination of univalent fragments of rabbit antibody. J. Biol. Chem. 238, 206-213.
Smith (4) Bayer, E. A., and Wilchek, M. (1990) Protein biotinylation. Methods Enzymol. 184, 138-160. (5) Rao, S. V., Anderson, K. W., and Bachas, L. G. (1997) Determination of the extent of protein biotinylation by fluorescence binding assay. Bioconjugate Chem. 8, 94-98. (6) Mock, D. M., Mock, N. I., and Langbehn, S. E. (1992) Biotin in human milk: methods, location, and chemical form. J. Nutr. 122, 535-545. (7) Wilchek, M., and Bayer, E. A., Eds. (1990) AVidin-Biotin Technology. Methods in Enzymology; Vol. 184, Academic Press, New York. (8) Larson, R. S., Menard, V., Jacobs, H., and Kim, S. W. (2001) Physicochemical characterization of poly(ethylene glycol)-modified anti-GAD antibodies. Bioconjugate Chem. 12, 861-869. BC0503061
