HyPare (automatically claculates the impact of mutations on a per-resiude basis for all resiudes of a protein-protein interaction. 

An affinity pair is a pair of two molecules that mutually bind with high specificity. For many affinity pairs, mutual binding occurs through formation of multiple non-covalent bonds such as hydrogen bonds, electrostatic bonds, polarization interactions, Van der Waals forces and hydrophobic interactions. Although any one such non-covalent bond is relatively weak, the sum of the contributions of many such non-covalent bonds is such that the attraction (the affinity) between the two molecules making up the affinity pair is very strong. For example, peptides and proteins have a conformation that is in a large measure determined by non-covalent interactions such as internal hydrogen bonds between protonatable groups (e.g., secondary and/or tertiary structure). The degree of protonation of a molecule is in large part determined by the availability of proteins in the environment (most often an aqueous solution, but also others such as gells) in which the molecule is found. In such caes, the affinity pair is characterized as having a pH-dependent affinity. The pH of the environment in which the affinity pair is found influences the degree to which the affinity pair is bound or dissociated by determining the affinity of the affinity pair by influencing the conformation of one or both of the members of the affinity pair and by influencing the degree of protonation of the functional groups through which the members of the afffinity pair bind.

The rate of association of a protein complex is a function of an intrinsic basal rate of the magnitude of electrostatic steering. (Shaul, Proteins: Structure, function, and bioinfomatics, 60: 341-352 (2005). 

The iteraction between an antibdoy and its antigen can be disrupted by high salt concentrations, extremes of pH, detergents, and sometimes by competition with high concentraitons of the pure epitope itself. The binding is therefore a reversible noncovlaent interaction.  High salt concentrations and extremes of pH disrupt antigen-antibody binding by weakening electrostatic interactions and/or hydrogen bonds.  Electrostatic interactions cocur between charged amino acid side chains, as in salt bridges. Interactions also occur between electric dipoles, as in hydrogen bonds, or can involved short-range van der Waals forces. This principle is employed in the purification of antigens using affintiy columns of immobilized antibodies. The contribution of each of these forces to the overall interaction depends on the particular antibody and antigen involved. In the igh affinity complex ofhen-egg-white lysozyme with another antibody, HyDel5, two salt bridges between two basic arginines on the surface of the lysozyme interact with two glutamic acids, one each from the VH CDR1 and CDR2 loops. Lysozymes that lack one of the two arginine residues show a 1000 fold decrease in affinity. (Walport, Immunobiology: The immune system in health and disease. 5th edition, New York, Garland Science, 2001). 

Mathematical Terms used to described Binding Affinity

One common type of affinity pair is an antibody/antigen pair. Affinity, when made in reference to the binding of an antibody to an antigen, refers to the interaction of the two molecules. It represents the balance etween the ease with which an interaction occurs and the probability that the complex will dissociate and can be written as Ab+Ag AbAg or written another, Ka = Ka/Kd = [AbAg]/[Ab/Ag] where ka and kd are the association and dissociation rate constants and Ka is the equilibrium (affinity) constant.

Association constant, KA, can also be used to express affinity and equals 1/KD and has units of (mol/liter)-1 (or M-1).  An antibody is considered to exhibit a high affinity for its antigen when its affinity constant (Ka) is greater or equal to say 10 to the 9 and to exhibit a low affinity when its Ka is about equal to or less than 10 to 8. (Bartholomew, WO 83/03678)

Avidity: is the measure of the strenght of binding between an antigen binding molecule and the pertinent antigen. Avidity is related to both the affinity between an antigenic determinant and its antigen binding site on the antigen binding molecule and the number of pertinent binding sites present on the antigen binding molecule.

Dissociation constant KD: is commonly used for affinity and has units of mol/liter (or M). The KD for biological interactions which are considered meaningful (e.g., specific) are typically in the range of 10-10M (0.1 nM) to 10-5M (10000 nM). The stronger an interaction is, the lower is its KD. The KD can also be expressed as the ratio of the dissociation rate constant of a complex, denoted as Koff, to the rate of its association, denoted Kon (so that KD=Koff/Kon and KA=Kon/Koff. The off-rate Koff has units s-1 (where s is the SI unit notation of second).

KD is the equilibrium dissociation constant, a ratio of Koff/Kon, between the antibody and its antigen. KD and affinity are inversely related. The KD value relates to the concentration of antibody and so the lower of the KD value (lower concentration) and thus the higher the affinity of the antibody. Most antibodies have KD values in the low micromolar (10^) to nanomolar (10-7 to 10-9) range High affinity antibodies generally considered to be in the low nanomolar range (10-9) with very high affinity antibodies being in the picomolar (10-12) range. (“KD value: a quantitative measurement of antibody affinity: A guide to KD value and antibody affinity”  (abcam.com)

The dissociation constant, Kd, is the inveser of the association constant above. 

 Unpredictability of Function even with same Binding Affintiy

Competitive Inhibition:

The high degree of uncertainty in the field is illustrated by co-pending US application 14/195,458, which is published US 2014/0186348. At ¶173, the ‘348 application teaches that a biotinylated Quidel P2 binds properdin with the same strength of affinity as that of NM9401. However, binding of Quidel P2 to properdin is not inhibited by NM9401 or humanized NM9401, suggesting that even though the affinities of NM9401 and Quidel P2 are substantially similar (i.e., the specific binding to properdin), the “function of these antibodies is not the same”

Dependence of Binding Affinity on pH

The pH dependence of the affinity of an affinity pair and consequence pH dependence on the degree of binding of an affinity pair has been used, for example, for affinity chromatography in the isolation of antibodies. A specific antigen is immobilized on a matrix to make a stationary phase. An eluent including the desired antibody, that together with the immobilized antigen constitutes an affinity pair, is passed along the sationary phase when the pH of the solution is such that the affinity of the affinity pair is high. Due to the high affinity and the high specificity of the affinity pair, only the antibody binds to the stationary phase. The stationary phase is washed with a washing buffer so as to wash away undersired molecules while the antibody remains bound to the stationary phase. Subsequently, the bound antibodies are released form the stationary phase with an elution solution having a pH where the affinity of the affinity pair is low. The affinity pair dissociates and the antibody is isolated.

What Structural Parts of an Antibody determine binding affinity

Importance of Framework Region: 

Binding affinity can even be due to the framework region. Bansal discloses an anti-properdin humanized antibody which had higher affinity than its murine counterpat. This difference in affinity must be due to the differences in the framework regions because this was the only meaningful differences between the humanized antibody and its murine counterpart. ((US 14/195,458, paragraph 175).

it is now well-establisehd and documented that non-CDRs residues may play an important role in teh binding affinity of the antibdoy to its antigen, either by making direct contact with the antigen, by affecting the stability or flexibility of the antibody or its antigen binding loops, or by strcuturing the CDR loop itself. Indeed, the residues form the framework regions can modulate the conformation of CDRs and thus affect the bidning affinity. (Dondeliner “Understanding the significance and implications of antibody numbering and anitgen-binding surface/residue definition” Frontiers in Immunology Volumne 9, 2018)

Xiang (J. Mol. Biol. (1995) 253, 385-390) discloses that structural analysis derived from the crystallographic study of the chimeric B72.3 antibody showed that some heavy chain framework residues having atomic interactions with heavy-chain CDR residues may direclty affect the conformation of CDR loops. For example an alanine resiude at H71 provides room for packing CDR2/CDR1 and lysine reisudes at H73 and H93 contribue a salt-bridge to aspartic acid at H55 in CDR2 and hydrogen bond to the carbonyl group at H96 ion CDR3, respectively. Xian analysed the contribution fo these framework residues by site directed mutagenesis, and determined the affintiy of these mutant chimeric antibodies for the TAG72 antigen and found that a single amino acid substitution of alanine by phenylalanine at H71 or lysin by isoleucine at H93, significantly reduced the binding affinity for TAG72 antigen.

Wells (“Antibody humanization using monovalent phage display” 212(16), 1996) discloses that addiiton to the immunogenicity of rodent mAbs when administered to humans, further limitations arise form weak recruitment of effector function and rapid clearance from serum. However, simple grafting of CDR sequences often yields humanized antibodies that bind antigen much more weakly than the parent murine mAb, and decreases in affinity of up to several hundrefold have been reported. As a means of simplifying antibody humanization, a number of different approaches have been developed. A common method is to select the human fraemwork most homologous in sequence to that of the murine antibody of interest. In this way, the number of mismatches between the humanized and parent murine framework is minimized, and it becomes less likely that a key framework residue will need to be replaced. However, even a single incorrect framework residue can have a dramatic effect on antigen binding. 

In some cases, transplanting hypervariable loops form rodent antibodies into human frameworks is sufficient to transfer high antigne binding affinity, whereas in other cases it has been necessary to also replace one or several framework region residues. For a given antibody, a small number of FR residues are anticipated to be important for antigen binding. First there are a few FR residues that directly contact antigen in crystal structures of antibody-antigen complexes. Second, a number of FR reisdues have been proposed as critically affecting the conformaiton of particular CDRs and thus their contribution to antigen binding. (Shepard, “Humanization of an anti-p185HER2 antibody for human cancer therapy” Proc. Natl. Acad. Sci. USA, 89, pp. 4285-4289, May 1992).

A third step in a typical CDR grafting protocol is to define mutations that will restore or prevent affinity losses. A substantial body of evidence indicates that the number of back mutations and the type of amino acid resplacements to introduce into the humanized antibody in order to restore binding depend on each particular case. Thus, back mutations should be carefully designed based on the sturcture or a model of the humanized antibody and tested experimentally. (Fransson “Humanization of antibodies” Frontiers in Bioscience 13, 1619-1633, 2008)

Importance of Constant Region 

A central dogma in immunology is that antibody specificty is a function of the variable (V) region. However serological analysis of IgG1, IgG2a and IgG2b switch variants of murine mAb 3E5 IgG3 with identical V domains revealed apparent specificity differences for Cryptococcus neoformans glucuronoxylomanna (GXM). V region identical Abs have also been reported to manifest differences in the magnitude of binding to Ag, fine specificity and idiotypic regocognition thus challening this central immunological dogma. (Torres, “The immunoglobulin Heavy chain constant region affects kinetic and thermodynamic parameters of antibody variable region interactions with antigen” The American Society for Biochemistry and Molecular Biology, Inc., 2007). 

Mccloskey (Immunology 1996 88:169-173) discloses that although antibody affinity is primarily determined by immunoglobulin variable region structure, human IgG antibodies of the four subclasses specific for the same antigen have been shown to differ in their affinity. 

Studies have shown that there are allosteric effects during the recognition process of antibody-antigen recognition. Interestingly, the constant domain also plays an essential role in antigen recognition. Zhao’s work on solanuzumab and crenezumab showed that antibodies with identical variable comain, but different constant domain have significantly different affinities when binding to Abeta species. (Zhao, “In silico methods in antibody design” Antibodies, 2018)

Importance of the amino acid sequence of the antigen for binding (small alterations can prevent binding) and Function (different antibodies can bind same antigen but not with same function):

Bansal (US 14/195,458, published as US 2014/0186348) disclose at #173 that a biotinylated Quidel P2 binds properdin with the same strengh of affinity as that of NM9401. Howeever, binding of Quidel P2 to properdin is not inhibited by NM9401 or humanized NM9401, suggesting that even though the affinities of NM9401 and Quidel P2 are substantially similar (i.e., the specific binding to properdin), the function of these antibodies is not the same. 

Chen (EMBO Journal 14(12) pp. 2784-2794, 1995) discloses introducing identical mutations into the CDR2 of two anti-phosphocholine antibodies, T15 and D16, which share the same germline VH gene sequence. T15 predominates in the primary responses and does not undergo affinity maturation. D16 is representative of antibodies that co-dominate in memory responces and do undergo affinity maturation. Both antibodies were equally susceptible to loss mutations, but only D16 was capable of affinity maturation. Since both antibodies use the same VH gene segment but diferent DJ and L chain genes, it is the combination of gene segments that appears to govern the capacity for improvement. A single mutaiton of Glu H58 to Gln (M161) has drmatically different effects in T15 and D16 with a loss of PC protein binding in the D16 mutant but little change in the T15 mutant. 

D’Angelo (“Many routes to an antibody heavy-chain CDR3: necessary, yet insufficient, for specific binding” Frontiers in Immunology March 2018, 9(395) discloses many different HCDR3s can be identified with a target-specific antiobdy population after in vitro selection. For each identified HCDR3, a number of different antibodies bearing differences elsewhere can be found. In such selected populations all antiobdies with the same HCDR3 recognize the target, albeit at different affinities. In constract, within unselected populations, the majority of antibodies with the same HCDR3 sequence do not bind the target. In one HCDR3 examined, all terget specific antiobdies were dervied from the same VDJ rearrangement, while non-binidng antiobdies with the same HCDR3 were dervied form many different V and D gene rearrangements. In conclusion, the same HCDR3 can be generated by many different rearrangements, but specific target binding is an outcome of unique rearrangements and VL pairing: the HCDR3 is necessary, albeit insufificient for specific antibody binding. 

Holers (US2006/0292141) discloses that mAb 1379 both binds and inhibits mouse and human factor B. In contrast, a mAb designated 624 can bind both mouse and human factor B, but does not inhibit the human AP. As revealed in a competition assay, antibodies 624, 691 and 1231 do not block binding by 1379 and thus must bind the protein at a different site, explaining why they bind factor B without inhibiting its function in vitro. However, antibodies 395, 1322 and 1060 are competitive inhibitors of 1379. Epitope mapping was also used to demonstrat that 1379 binds to factor B within the third short consensus repeat (SCR) domain, and the antibody prevented formation of the C3bBb complex. Experiments also demonstrated that the introduction of certain alanine substitutions into SCRs 2nad 3 of human factor B, but not SCR1, reuslted in the loss or substantial loss of binding of the 1379 antibody to factor B. 

Lederman (“A single amino acid substitution in a common African allele of the CD4 molecule ablates binding of the monoclonal antibody, OKT4” Molecular Immunology 28(11), 1171-1181, 1991) discloses that a arginine to tryptophan substitution at amino acid 240 ablates the binding of a mAb to CD4. 

Margolies (“A single engineered amino acid substitution changes antibody fine specificity” J Immunol 152(1); 146-52) discloses that a single amino acid replacement at position 35 in the H chain of an unmutated Ab with specificity for p-azophenylarsonate (Ars) confers specificity for the structurall related hapten p-azophenylsulfonate (Sulf) while abolishing specificity for Ars. The resutls support the potentail of Ab engineering to alter antigen specificity. 

Importance of different VDJ/VD combinations and Small differences in amino acid sequence:

Specific recognized of a given antigen can be achieved by many different VDJ/VD combinations in the adaptable naitve immune receptor repertoire. For example cyrstal structures of two distinct dodecapeptides in complex with two different germline mAb showed that while the two germline mAbs recognized overlapping epitopes, they did so in different topologies. The peptide structures differed, and the two paratopes attained discrete conofrmations, leading to different surface topoligies, in a mode that can be described as adjustable locks and flexible keys. 

Edward (J. Mol. Biol. (2003) 334, 103-118) disclose using pahge display to demonstrate the extraordinary capacity of the human antibody repertories. Over 1000 antibodies, all different in amino acid sequence were generated to a single protein, B-lymphocyte stimulator (BLyS) . The panel fo antibodies was highly diverse as shown by the extensive heavy and light chain germline usage. A high level of sequence diversity was observed in the VHCDR3 domains with 568 different amino acid sequences identified. When studies in a biochemical assay, about 40% of the antibodies inhibited the binding of BLyS to its receptors on B-cell lines. The most potent antibodies inhibited BLyS binding with sub-nanomlolar IC50 values and with sub-nanomolar affinities. 

Ferrara (“Recombinant renewable polyclonal antibodies” mAbs 7:1, 32-41) disclose high quality recombinant polyclonal antibodies, in which hundreds of different antibodies all directed toward a target of interest can be generated in vitro by combining phage and yeast display. By carrying out 2 rounds of phage display, Ferrara captured antibodies shwoing some reactivity for the target. This reduced the diversity to 105-106 which was compatible with yeast display cloning and allowed further precise sorting to restrict reactivity to those clones recognizing the target of interest. The diversity of the polyclonals after selection was assessed by sequencing, with analysis restricted to the HCDR3 becasue of read lenght limitations. The number of different HCDR3s selected against the test antigens ranged from 74 to 460, which the actual number of different antibodies likely to be significantly higher when different VL chains and additional VH mutations are taken into account. 

Small numbers of substitutions in antibodies, such as those presumably introduced by somatic mutations, may in some situations be effective in altering antigen-binding specificity. Rudikoff Proc Natl Acad Sci USA, 79(6), 1982, 1979-83) showed that a single substitution in the CDR region resulted in loss in binding activity.

Computational Design of Antibodies that bind with High Affinity

Poosarla “Computational de novo design of antibodies binding to a peptide with high affinity” Biotechnology and Bioengineering, 114(6), 2017) disclose the application of a ocmputational framework called OptMAVEn combined with molecular dynamics to de novo design of antibodies. The reference antibody as a single chain antiboy (scFC) that recognized a dodecapaptide. Five de novo deisgned scFVS sharing less than 75% sequence similarity to all exisisting natural antibody seuqnces were gnereated using OptMAVEn and their binidng to the dodecapeptide was characterized. Among them, three scFCS showed binding affintiy to the dodecapeptide at the nM level. The de novo designed scFvs exitied considerably dieverse modeled binding modes with the dodecapaptide. 

Experimental Techniques used to measure affinity: 

The affinity of a molecular interaction between two molecules can be measured via different techniques such as surface plasmon resonance biosensor technique where one molecule is immobilized on the biosensor chip and the other molecule is passed over the immobilized molecule under flow conditions. Another approach may be the 2-step ELISA proecdure of Friguet (J.Immunol. Methods, 77, 305-19, 1985).

Methods to Engineer Antibodies with better Affinity

Available X-ray crystallographic data and energy calculations indicate that only a fraction of the substantial contact surface between the Ab and protein antigens contribue significanlty to affinity. Thus, the remaining contact surface presents multiple opportunities to develop additional high affinity contacts. (Balint “Antibody engineering by parsimonious mutagenesis” Gene, 137 (1993) 109-118)

Parsimonius mutagenesis: (Balint “Antibody engineering by parsimonious mutagenesis” Gene, 137 (1993) 109-118) idscloses a computer assisted method for oligodeoxyribonucleotide directed scanning mutageneis, called parsimonious mutagenesis, where all 3 CDR genes can be simultaneously and throughly searched for improved variants in libraries.