Transition-state theory and secondary forces in antigen-antibody complexes

Transition-State Theory and Secondary Forces in Antigen-Antibody Complexes Mark E. Mummert and Edward W. Voss, Jr. Dept. of Microbiology, University of Illinois at Urbana-Champaign, Urbana, IL 61801

I. Introduction Secondary forces, defined as those interactions exhibited outside of the classically defined antibody active site, have been demonstrated to modulate the conformation and free energy of binding of antifluorescein antibodies (1-3). Figure 1 defines and distinguishes primary from secondary interactive components. The ability of the epitopic environment to influence antibody binding has obvious immunological ramifications. Dissection of those interactions that influence the overall dynamic and thermodynamics of a given protein system is of general importance in understanding interfacial protein chemistry. The antifluorescein system is advantageous for evaluating and quantitating interfacial chemistry. Binding of fluorescein ligand in the antifluorescein active site results in bathochromic shifts of the ligand's absorption spectrum and a decrease in both the fluorescence quantum yield and lifetime. These properties allow sensitive spectral and kinetic measurements to be made (4). Changes in the spectral and kinetic properties of a given antifluorescein antibody upon interacting with fluorescein attached to a carrier molecule compared to fluorescein (devoid of carrier residues) thus provides important information about secondary force directed perturbations. Placement of the fluorescein moiety in various environments is easily achieved due to the availability of the highly reactive isothiocyanate derivative of fluorescein. Evaluations of secondary interactive components have been discussed (5-8). In general, the delineation between primary and secondary interactive components have been vague (9). An important advantage of the fluorescein system is that the ligand fills the active site (10-12) which has been conclusively demonstrated by X-ray crystallographic results for the monoclonal antifluorescein antibody (mAb) 4-4-20 (13-15). Thus, interactions with carrier residues associated with the ligand-carrier complex are by necessity outside of the primary interactions. An understanding of interfacial protein chemistry requires evaluation of the thermodynamics of the system under investigation as well as the energetic barriers responsible for the observed kinetics and affinity. Due to the kinetic methodology available for the antifluorescein system, the energetic barriers for complex decomposition TECHNIQUES IN PROTEIN CHEMISTRY VIII Copyright © 1997 by Academic Press All rights of reproduction in any form reserved.

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Mark E. Mummert and Edward W. Voss, Jr. Antibody variable domains

Carrier environment (highly charged protein or lipid membrane)

Figure 1. Schematic representation differentiating primary and secondary interactions. Secondary interactions are the result of interactions between regions surrounding the mouth of the active site and regions of the carrier environment surrounding the ligand. A highly charged protein or lipid interface represents an example of substrate exerting secondary effects.

can be evaluated (Figure 2). It is important to note that the kinetic measurements can be conducted in solution under near physiological conditions. Thus, the results obtained can be extrapolated to biological situations. In this report, we summarize the results of a study in which the energetic barriers of several protein/complex decompositions were analyzed utilizing transition-state theory. In essence, fluorescein 5-isothiocyanate was covalently linked to a variety of synthetic peptides and allowed to bind with the well defined high affinity 4-4-20 mAb. Differences in the rates of decomposition were measured at 275 K and 291 K and the height of energetic barriers calculated using classical transition-state analysis (16).

n. Methods and Materials A. Monoclonal anti-fluorescein antibody 4-4-20 mAb 4-4-20 was produced in ascitic fluid from pristane treated Balb/c mice and affinity purified using a fluorescein Sepharose 4B adsorbent (17,18). B. Peptide synthesis for use as carriers Peptides of different chemical composition acetylated in the amino-terminal position were synthesized using an Applied Biosystem model 430A peptide synthesizer at the University of Illinois Genetic Engineering Facility (Urbana, DL) employing solid-phase F-moc chemistry with standard amino acid protecting groups. The generic peptide design was as follows: Ac-NH-(X)6-K-(X)6-COOwhere Ac-NH denotes the acetylated a-amino group, X represents glutamate or arginine, and K is the central lysine residue available for FITC (I) derivatization. Peptides were desalted and purity verified by RP-HPLC. Purified peptides were analyzed by mass spectrometry to verify composition.

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Second Transition Stat*

Reaction Coordinate

Figure 2. Two dimensional reaction coordinate depicting the interaction of mAb 4-4-20 with homologous ligand. The x-axis is arbitrarily assigned reaction progression while the y-axis is the chemical potential. The height of the chemical potential barriers dictates the rate of the reaction. The encounter complex was included based on kinetic considerations (19). Monofluoresceinated peptides were synthesized by adding an equimolar concentration of FITC(I) to peptides. The reaction was adjusted to a pH of 10.3 with K2CO3 and incubated at ambient temperature overnight. The resulting reaction mixture was resolved over a P-2 column (Bio-Rad) equilibrated in 0.1 M phosphate, pH 8.0 to remove unreacted fluorescein from the peptides. Fluorescently labeled peptides were analyzed by thin layer chromatography with water saturated methyl ethyl ketone as the solvent system. C. Determination of unimolecular rate constants Ligand dissociation rates were determined at 275 K and 291 K utilizing the methodology and analysis as described in detail by (19). This technique provides an essentially unidirectional displacement of the fluorescein/antibody complex. D. Calculation of transition-state thermodynamic parameters All calculations have been described in detail elsewhere (3). Transition-state equations can be found in most elementary physical chemistry texts or in the classical work of Wynne-Jones and Eyring (16). III. Results A. Monofluoresceinated peptides Thin layer chromatographic analyses of monofluoresceinated peptides indicated a single fluorescent band for each of the labeled peptides. RF values were 0.90, 0.85, 0.83 and 0.76 for FDS, D12KF1, R6D6KF1 and R12KF1 respectively.

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Table L Comparative unimolecular rate constants at 275 K and 291 K for the interaction of FDS and monofluoresceinated peptides with mAb 4-4-20 Ligand

k.i^

k.^i,

^Ab^Asi

FDS

1.63(±0.02)xl0-4

1.92(iO.09)xl0-3

11.8

D12KF1

3.52(±O.62)xl0-3

1.06(±0.19)xl0-l

30.1

R6D6KF1

6.96(±1.02)xl0-3

I.15(dt0.42)xl0-1

16.5

R12KR

6.79(±0.25)xlO-3

6.08(±0.81)xl0"2

8.9

k.ia = unimolecular rate constant at 275 K k_n, = unimolecular rate constant at 291 K

B. Affinity of mAb 4-4-20 with various ligands In previous studies (2), the affinity constants (Ka) for the interaction of mAb 4-420 with fluorescein and monofluoresceinated peptides were measured at 275 K. The affinities of mAb 4-4-20 for FDS, D12KH, R12KF1 and R6D6KF1 were 3.14x10^° M'\ 1.49x10^ M"^ 7.49x10^ M^^ and 7.55x10^ M \ respectively. C. Unimolecular rate constants Unimolecular rate constants for decay of the mAb 4-4-20/fluorescein complex and mAb 4-4-20/monofluoresceinated peptide complexes were determined at 275 K and 291 K. The 16 K differential resulted in significant changes in the individual decay rates of the various complexes. The largest change with temperature was with the mAb 4-420/D12KF1 complex (30.1-fold), while the smallest change was with R12KF1 (8.9-fold). Importantly, the R6D6KF1 ligand resulted in an approximate average (16.5 -fold) of the poly anionic (D12KF1) and polycationic (R12KF1) environments. Table 1 summarizes these results. D. Relationship between enthalpy and entropy Table 2 summarizes the calculated transition state thermodynamic parameters (AH", AS" and AG"). The secondary effects that resulted from the carrier molecule caused an apparent enhancement in AH" and AS" relative to fluorescein devoid of carrier residues. The enhanced values of AS" offset the enhanced AH" with the net effect of lowering the overall energetic barriers (AG") of the 4-4-20/monofluoresceinated complexes relative to the 4-4-20/fluorescein complex (Table 3).

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Table IL Comparative thermodynamic transition-state parameters and transition-state equilibria for the interaction of mAb 4-4-20 with FDS and monofluoresceinated peptides at 275 K Ligand

AH^

AS^

AC"

K^

FDS

+23.96±0.06

+0.0110.00

+20.8210.07

2.84x10-^7

D12Kn

+33.28+1.95

+0.0510.00

+19.1511.95

6.03x10-^6

R6D6KF1

+27.3213.36

+0.0310.00

+18.7713.36

1.21x10-1^

R12KF1

N.A.

N.A.

N.A.

N.A.

AH^ = transition-state enthalpy (kcal/mol) AS"^ = transition-state entropy (kcal/mol/K) K"^ = transition-state equilibrium (dimensionless) N.A. = not applicable; does not conform to the theoretical assumptions of transition-state theory

E. K values Values for the transmission coefficient (K) at 275 K were 1.00, 1.02, 1.00 and 0.58 for FDS, D12KF1, R6D6KF1 and R12KF1, respectively. Transition-state theory assumes unity for K. Deviations of K from unity indicated poor approximation of the various transition-state thermodynamic parameters. Thus all complex decays were adequately described by transition-state theory, except for the R12KF1 peptide.

IV. Discussion Understanding those components that influence the interfacial binding properties in protein/protein and protein/ligand interactions is of basic importance in protein chemistry. In this report, we have defined a system that should allow the dissection of those chemical properties that influence primary interactions via an evaluation of the transition-state thermodynamic components. It is important to realize fundamental assumptions made in the calculations. At the temperatures utilized in these experiments (275 K and 291 K), it was assumed that complexes moved over energetic barriers with standard Arrhenius motion. Deviations from Ahrrenius motion (e.g., tunneling) usually result as a consequence of low temperature (20-22). It is also important to realize that the values calculated for AH^, AS"" and /SG^ are the upper limits of the system, since solvent was considered as a part of the system (23). This study suggested that secondary forces of the mAb 4-4-20 /monofluoresceinated peptide complexes modulated binding interactions via increased transition-state enthalpic and entropic contributions. The net result was a decreased energetic barrier that allowed modulation of the previously reported affinity constants of mAb 4-4-20 for the monofluoresceinated peptides due to variation of the unimolecular rate constant (2).

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Table i n . Comparative differences in thermcxlynaniic transition-state parameters of monofluoresceinated peptides with respect to FDS at 275 K

Ligand

AAH^

AAS''

AAC

D12KF1

+9.32±1.95

•K).04±0.00

-1.67±1.95

R6D6KF1

+3.36±3.36

0.02±0.00

-2.05±3.36

R12KF1

N.A.

N.A.

N.A.

AAIT^ = change in transition-state enthalpy with respect to FDS (kcal/mol) AAS'^ = change in transition-state entropy with respect to FDS (kcal/mol/K) AAG^ = change in transition-state free energy with respect to FDS (kcal/mol) N.A. = not applicable

Increased values of AH" and AS" for the mAb 4-4-20/monofluoresceinated peptide complexes relative to the mAb 4-4-20/fluorescein complex decay were interpreted as resulting from inclusion of the carrier peptides. Increased enthalpic contributions may have resulted from actual binding interactions between the surface accessible complementarity determining regions (CDRs) surrounding the mouth of the antibody active site and the amino acids of the peptides. Whitlow et al. (15) reported that a significant percentage of the amino acids that compose the mAb 4-4-20 CDRs were solvent accessible when fluorescein was in the active site. The increased values for AH" also may have been due to differences in hydration of the antibody complexes. Enhanced AS" values for the antibody/peptide complexes may have been a result of the greater rotational, translational and vibrational degrees of freedom as the complexes decayed relative to the mAb 4-4-20/fluorescein complex. As in the AH" argument, hydration may also be an important factor to consider. Hydration has been shown to significantly influence the free energy of binding (14). We interpreted the inability of transition-state theory to predict the decay of the mAb 4-4-20/R12KF1 complex to be a result of differential conformational changes. Deviations of K from unity are a direct result of the inertial (solvent coupling) and diffusive (intramolecular dynamic) regimes (24-27). The frictional coefficient in both of these regimes dictates the value of K (24,25). Both inertial and diffusive regimes modulate K in proteins (27-29). We therefore proposed that the mAb 4-4-20/R12KF1 complex could not be evaluated by transition-state theory due to inertial and/or diffusive regimes. We conceived that the secondary forces dictated by R12KF1 resulted in greater perturbation of the antibody variable domains than the secondary forces dictated by either D12KF1 or R6D6KF1. It was postulated that the greater van der Waals volume for arginine (R~148 A^) as opposed to aspartic acid (D~91 A^) resulted in greater variable domain atomic coordinate displacement and thus enhanced frictional components. In conclusion, the antifluorescein system provides a reasonable model with which to evaluate interfacial interactions utilizing transition-state theory. Evaluations like those presented herein provide means to develop mechanistic models to describe interfacial interaction from an energetic barrier viewpoint.

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