Thermodynamic analysis to assist in the design of recombinant antibodies.

This critical review examines the thermodynamics of binding of bivalent antibodies (IgG and IgE) to soluble ligands with two or more binding moieties joined covalently (multivalent ligands) and to surfaces functionalized with multiple identical ligands. Given the prevalence of antibodies in nature, the goal of this paper is to begin to understand what aspects of bivalent antibodies are important relative to their monovalent counterparts (Fab). We provide a brief introduction to the thermodynamic parameters of importance to bivalent binding, guidance as to which of these parameters are most useful for the comparison of disparate systems, and a re-examination of binding studies of bivalent antibodies from the literature. For all of the cases we examined, the intramolecular free energy of binding (ΔG°intra) was less favorable than the intermolecular free energy (ΔG°inter). The effective molarity (EM) and the ratio of the free energies of intramolecular and intermolecular binding (ΔG°intra/ΔG°inter) are tools to assess the particular contribution of intramolecular binding to the thermodynamics of bivalent association. The paper concludes with guidance to the reader on what to consider when designing experiments to study bivalent systems.

Dependence of avidity on linker length for a bivalent ligand-bivalent receptor model system.

This paper describes a synthetic dimer of carbonic anhydrase, and a series of bivalent sulfonamide ligands with different lengths (25 to 69 Å between the ends of the fully extended ligands), as a model system to use in examining the binding of bivalent antibodies to antigens. Assays based on analytical ultracentrifugation and fluorescence binding indicate that this system forms cyclic, noncovalent complexes with a stoichiometry of one bivalent ligand to one dimer. This dimer binds the series of bivalent ligands with low picomolar avidities (K(d)(avidity) = 3-40 pM). A structurally analogous monovalent ligand binds to one active site of the dimer with K(d)(mono) = 16 nM. The bivalent association is thus significantly stronger (K(d)(mono)/K(d)(avidity) ranging from ~500 to 5000 unitless) than the monovalent association. We infer from these results, and by comparison of these results to previous studies, that bivalency in antibodies can lead to associations much tighter than monovalent associations (although the observed bivalent association is much weaker than predicted from the simplest level of theory: predicted K(d)(avidity) of ~0.002 pM and K(d)(mono)/K(d)(avidity) ~ 8 × 10(6) unitless).

Selective precipitation and purification of monovalent proteins using oligovalent ligands and ammonium sulfate.

This paper describes a method for the selective precipitation and purification of a monovalent protein (carbonic anhydrase is used as a demonstration) from cellular lysate using ammonium sulfate and oligovalent ligands. The oligovalent ligands induce the formation of protein-ligand aggregates, and at an appropriate concentration of dissolved ammonium sulfate, these complexes precipitate. The purification involves three steps: (i) the removal of high-molecular-weight impurities through the addition of ammonium sulfate to the crude cell lysate; (ii) the introduction of an oligovalent ligand and the selective precipitation of the target protein-ligand aggregates from solution; and (iii) the removal of the oligovalent ligand from the precipitate by dialysis to release the target protein. The increase of mass and volume of the proteins upon aggregate formation reduces their solubility, and results in the selective precipitation of these aggregates. We recovered human carbonic anhydrase, from crude cellular lysate, in 82% yield and 95% purity with a trivalent benzene sulfonamide ligand. This method provides a chromatography-free strategy of purifying monovalent proteins--for which appropriate oligovalent ligands can be synthesized--and combines the selectivity of affinity-based purification with the convenience of salt-induced precipitation.

Mechanism of the hydrophobic effect in the biomolecular recognition of arylsulfonamides by carbonic anhydrase.

The hydrophobic effect--a rationalization of the insolubility of nonpolar molecules in water--is centrally important to biomolecular recognition. Despite extensive research devoted to the hydrophobic effect, its molecular mechanisms remain controversial, and there are still no reliably predictive models for its role in protein-ligand binding. Here we describe a particularly well-defined system of protein and ligands--carbonic anhydrase and a series of structurally homologous heterocyclic aromatic sulfonamides--that we use to characterize hydrophobic interactions thermodynamically and structurally. In binding to this structurally rigid protein, a set of ligands (also defined to be structurally rigid) shows the expected gain in binding free energy as hydrophobic surface area is added. Isothermal titration calorimetry demonstrates that enthalpy determines these increases in binding affinity, and that changes in the heat capacity of binding are negative. X-ray crystallography and molecular dynamics simulations are compatible with the proposal that the differences in binding between the homologous ligands stem from changes in the number and organization of water molecules localized in the active site in the bound complexes, rather than (or perhaps in addition to) release of structured water from the apposed hydrophobic surfaces. These results support the hypothesis that structured water molecules--including both the molecules of water displaced by the ligands and those reorganized upon ligand binding--determine the thermodynamics of binding of these ligands at the active site of the protein. Hydrophobic effects in various contexts have different structural and thermodynamic origins, although all may be manifestations of the differences in characteristics of bulk water and water close to hydrophobic surfaces.

Fluoroalkyl and alkyl chains have similar hydrophobicities in binding to the "hydrophobic wall" of carbonic anhydrase.

The hydrophobic effect, the free-energetically favorable association of nonpolar solutes in water, makes a dominant contribution to binding of many systems of ligands and proteins. The objective of this study was to examine the hydrophobic effect in biomolecular recognition using two chemically different but structurally similar hydrophobic groups, aliphatic hydrocarbons and aliphatic fluorocarbons, and to determine whether the hydrophobicity of the two groups could be distinguished by thermodynamic and biostructural analysis. This paper uses isothermal titration calorimetry (ITC) to examine the thermodynamics of binding of benzenesulfonamides substituted in the para position with alkyl and fluoroalkyl chains (H(2)NSO(2)C(6)H(4)-CONHCH(2)(CX(2))(n)CX(3), n = 0-4, X = H, F) to human carbonic anhydrase II (HCA II). Both alkyl and fluoroalkyl substituents contribute favorably to the enthalpy and the entropy of binding; these contributions increase as the length of chain of the hydrophobic substituent increases. Crystallography of the protein-ligand complexes indicates that the benzenesulfonamide groups of all ligands examined bind with similar geometry, that the tail groups associate with the hydrophobic wall of HCA II (which is made up of the side chains of residues Phe131, Val135, Pro202, and Leu204), and that the structure of the protein is indistinguishable for all but one of the complexes (the longest member of the fluoroalkyl series). Analysis of the thermodynamics of binding as a function of structure is compatible with the hypothesis that hydrophobic binding of both alkyl and fluoroalkyl chains to hydrophobic surface of carbonic anhydrase is due primarily to the release of nonoptimally hydrogen-bonded water molecules that hydrate the binding cavity (including the hydrophobic wall) of HCA II and to the release of water molecules that surround the hydrophobic chain of the ligands. This study defines the balance of enthalpic and entropic contributions to the hydrophobic effect in this representative system of protein and ligand: hydrophobic interactions, here, seem to comprise approximately equal contributions from enthalpy (plausibly from strengthening networks of hydrogen bonds among molecules of water) and entropy (from release of water from configurationally restricted positions).

Using covalent dimers of human carbonic anhydrase II to model bivalency in immunoglobulins.

This paper describes the development of a new bivalent system comprising synthetic dimers of carbonic anhydrase linked chemically through thiol groups of cysteine residues introduced by site-directed mutagenesis. These compounds serve as models with which to study the interaction of bivalent proteins with ligands presented at the surface of mixed self-assembled monolayers (SAMs). Monovalent carbonic anhydrase (CA) binds to benzenesulfonamide ligands presented on the surface of the SAM with K(d)(surf) = 89 nM. The synthetic bivalent proteins--inspired by the structure of immunoglobulins--bind bivalently to the sulfonamide-functionalized SAMs with low nanomolar avidities (K(d)(avidity,surf) = 1-3 nM); this difference represents a ~50-fold enhancement of bivalent over monovalent association. The paper describes dimers of CA having (i) different lengths of the covalent linker that joined the two proteins and (ii) different points of attachment of the linker to the protein (either near the active site (C133) or distal to the active site (C185)). Comparison of the thermodynamics of their interactions with SAMs presenting arylsulfonamide groups demonstrated that varying the length of the linker between the molecules of CA had virtually no effect on the rate of association, or on the avidity of these dimers with ligand-presenting surfaces. Varying the point of attachment of the linker between monomeric CA's also had almost no effect on the avidity of the dimers, although changing the point of attachment affected the rates of binding and unbinding. These observations indicate that the avidities of these bivalent proteins, and by inference the avidities of structurally similar bivalent proteins such as IgG, are unexpectedly insensitive to the structure of the linker connecting them.

Mathematical model for determining the binding constants between immunoglobulins, bivalent ligands, and monovalent ligands.

This paper analyzes the equilibria between immunoglobulins (R(2)), homo-bifunctional ligands (L(2)), monovalent ligands (I), and their complexes. We present a mathematical model that can be used to estimate the concentration of each species present in a mixture of R(2), L(2), and I, given the initial conditions defining the total concentration of R(2), L(2), I, and four dissociation constants (K(d)(inter), K(d)(intra), K(d)(mono), and α). This model is based on fewer assumptions than previous models and can be used to describe exactly a broad range of experimental conditions. A series of curves illustrates the dependence of the equilibria upon the total concentrations of receptors and ligands, and the dissociation constants. We provide a set of guidelines for the design and analysis of experiments with a focus on estimating the binding constants from experimental binding isotherms. Two analytical equations relate the conditions for maximum aggregation in this system to the binding constants. This model is a tool to quantify the binding of immunoglobulins to antigens and a guide to understanding and predicting the experimental data of assays and techniques that employ immunoglobulins.

Heterogeneous films of ionotropic hydrogels fabricated from delivery templates of patterned paper.

The use of delivery templates makes it possible to fabricate shaped, millimeter-thick heterogeneously patterned films of ionotropic hydrogels. These structures include two-dimensional (2-D) patterns of a polymer cross-linked by different ions (e.g., alginic acid cross-linked with Ca2+ and Fe3+) and patterns of step gradients in the concentration of a single cross-linking ion. The delivery templates consist of stacked sheets of chromatography paper patterned with hydrophobic barriers (waterproof tape, transparency film, or toner deposited by a color laser printer). Each layer of paper serves as a reservoir for a different solution of cross-linking ions, while the hydrophobic barriers prevent solutions on adjacent sheets from mixing. Holes cut through the sheets expose different solutions of cross-linking ions to the surface of the templates. Films with shaped regions of hydrogels cross-linked by paramagnetic ions can be oriented with a bar magnet. Variations in the concentrations of cations used to cross-link the gel can control the mechanical properties of the film: for single alginate films composed of areas cross-linked with different concentrations of Fe3+, the regions cross-linked with high concentrations of Fe3+ are more rigid than regions cross-linked with low concentrations of Fe3+. The heterogeneous hydrogel films can be used to culture bacteria in various 2-D designs. The pattern of toxic and nontoxic ions used to cross-link the polymer determines the pattern of viable colonies of Escherichia coli within the film.

Exact analysis of ligand-induced dimerization of monomeric receptors.

This paper analyzes the equilibria involved in the dimerization of monomeric receptors with homo-bifunctional ligands. We provide analytical expressions that can be used to estimate the concentration of each species present in a mixture of homo-bifunctional ligand and monomeric proteins, given initial conditions defining the total concentration of bivalent ligand [L2]0, the total concentration of protein [P]0, one dissociation constant Kd, and a parameter to account for cooperativity alpha. We demonstrate that the fraction of protein present in a complex of two proteins and one bivalent ligand (P x L2 x P) is maximized at [L2]0 = Kd/2 + [P]0/2.

Photoaffinity labeling with 8-azidoadenosine and its derivatives: chemistry of closed and opened adenosine diazaquinodimethanes.

The reactive intermediate produced upon photolysis of 8-azidoadenosine was studied by chemical trapping studies, laser flash photolysis with UV-vis and IR detection, and modern computational chemistry. It is concluded that photolysis of 8-azidoadenosine in aqueous solution releases the corresponding singlet nitrene which rapidly tautomerizes to form a closed adenosine diazaquinodimethane in less than 400 fs. A perbenzoylated derivative of 8-azidoadenosine cannot undergo this tautomerization, and instead, it fragments upon photolysis to form an opened adenosine diazaquinodimethane. The singlet nitrene is too short-lived to be observed and, thus, to relax to the lowest triplet state or to become covalently attached to targeted biological macromolecules. The pivotal closed adenosine diazaquinodimethane, the product of nitrene tautomerization, has a lifetime of ca. 1 min or longer in water and in HEPES buffer at ambient temperature. However, this intermediate reacts rapidly with good nucleophiles such as amines, thiols, and phenolates, and significantly more slowly with weak nucleophiles such as alcohols and water. On the basis of these studies, it is clear that the closed adenosine diazaquinodimethane, and not the singlet or triplet nitrene, is the pivotal reactive intermediate involved in photolabeling and cross-linking studies using the 8-azidoadenosine family of photoaffinity labeling reagents.

DNA photocleavage and biological activity of a pyrene dihydrodioxin.

A pyrene dihydrodioxin has been synthesized, shown to bind to duplex DNA by intercalation, and cleave the phiX 174 supercoiled plasmid upon irradiation with UV light. This compound also exhibits cytotoxic activity at the micromolar range in a number of human cancer cell lines.

Thermal and photochemistry of a pyrene dihydrodioxin (PDHD) and its radical cation: a photoactivated masking group for ortho-quinones.

Pyrene dihydrodioxins (1 and 2) have been synthesized and shown to be effective photochemical blocking groups for pyrene-4,5-dione (3). The mechanism of quinone release proceeds through the formation of a remarkably stable radical cation. Direct evidence is provided that this radical cation is not only thermally labile but also photochemically labile, and that both pathways lead to quinone extrusion. Once initiated with UV light, the pyrene quinone product serves as an electron-transfer photosensitizer for the further release of quinone with visible light.