# A3. Dimerization and Multiple Binding Sites - Biology

In the previous examples, we considered the case of a macromolecule M binding a ligand L at a single site, as described in the equation below:

[M + L ightleftharpoons ML ]

where

[K_d = dfrac{[M][L]}{[ML]}. label{1}]

We saw that the binding curves ((ML) vs. (L) or (Y) vs. (L) are hyperbolic, with a (K_d = L) at half maximal binding.

A special, yet common example of this equilibrium occurs when a macromolecule binds itself to form a dimer, as shown below:

[ M + M ightleftharpoons M^2 = D ]

where (D) is the dimer, and where

[K_d = dfrac{[M][M]}{[D]} = dfrac{[M]^2}{[D]} label{11} ]

At first glance you would expect a graph of ([D]) vs. ([M]) to be hyperbolic, with the (K_d) again equaling the ([M]) at half-maximal dimer concentration. This turns out to be true, but a simple derivation is in order since in the previous derivation, it was assumed that (M_o) was fixed and (L_o) varied. In the case of dimer formation, (M_o), which superficially represents both (M) and (L) in the earlier derived expression, are both changing.

One again a mass balance expression for (M_o) can be written:

[[M_o] = [M] + 2[D] label{12}]

where the coefficient 2 is necessary since their are 2 M in each dimer.

More generally, for the case of formation of trimers (Tri), tetramers (Tetra), and other oligomers,

[ [M_o] = [M] + 2[D] + 3[Tri] + 4[Tetra] + : .... label{13} ]

Rearranging Equation ef{12} and solving for (M) gives

[[M] = [M_o] -2[D] label{14}]

Substituting Equation ef{14} into the (K_d) expression (Equation ef{1}) gives

[K_d = dfrac{(M_o-2D)(M_o-2D)}{D} ]

where can be rearranged into quadratic form:

[4D2 - (4M_o+K_d)D + (M_o)^2 = 0 label{15} ]

which is of the form (y = ax^2+bx+c). Solving the quadratic equation gives ([D]) at any given ([M_o]). A value (Y), similar to fractional saturation, can be calculated, where (Y) is the fraction of total possible (D), which can vary from 0-1.

[Y = dfrac{2[D]}{[M_o]} label{16}]

A graph of (Y) vs (M_o) with a dimerization dissociation constant (K_d = 25, mu M), is shown below.

Figure 1: Saturation binding curve for dimerization of a macromolecule

Note that the curve appears hyperbolic with half-maximal dimer formation occurring at a total (M) concentration (M_o = K_d). Also note, however, that even at (M_o = 1000 ,mu M), which is 40x (K_d), only 90% of the total possible (D) is formed ((Y = 0.90)). For the simple

[M + L <=> ML]

equilibrium, if (L_o) = 40x the (K_d) and (M_o ll L_o), then

[ Y = dfrac{L}{K_d+L} = dfrac{L}{(L/40)+L} = 0.976 ]

The aggregation state of a protein monomer is closely linked with its biological activity. For proteins that can form dimers, some are active in the monomeric state, while others are active as a dimer. High concentrations, such as found under conditions when protein are crystallized for x-ray structure analysis, can drive proteins into the dimeric state, which may lead to the false conclusion that the active protein is a dimer. Determination of the actual physiological concentration of ([M_o]) and (K_d) gives investigators knowledge of the (Y) value which can be correlated with biological activity. For example, interleukin 8, a chemokine which binds certain immune cells, exists as a dimer in x-ray and NMR structural determinations, but as a monomer at physiological concentrations. Hence the monomer, not the dimer, binds its receptors on immune cells. Viral proteases (herpes viral protease, HIV protease) are active in dimeric form, in which the active site is formed at the dimer interface.

Another Special Case: Binding of L to 2 sites with different Kds

Check out the interactive graph to see how the relative sizes of the Kds affect it.

Wolfram Mathematica CDF Player - Binding of L to 2 Sites (free plugin required)

## Comparative integromics on FZD7 orthologs: conserved binding sites for PU.1, SP1, CCAAT-box and TCF/LEF/SOX transcription factors within 5'-promoter region of mammalian FZD7 orthologs

Canonical WNT signals are transduced through Frizzled (FZD) family receptor and LRP5/LRP6 co-receptor to upregulate MYC, CCND1, FGF20, JAG1, WISP1 and DKK1 genes, while non-canonical WNT signals are transduced through FZD family receptor and PTK7/ROR2/RYK co-receptor to activate RHOA/RHOU/RAC/CDC42, JNK, PKC, NFAT and NLK signaling cascades. FZD7, expressed in the normal gastrointestinal tract, is upregulated in esophageal cancer, gastric cancer, colorectal cancer, and hepatocellular carcinoma. Here, chimpanzee FZD7 and cow Fzd7 genes were identified and characterized by using bioinformatics (Techint) and human intelligence (Humint). Chimpanzee FZD7 and cow Fzd7 genes were identified within NW_001232110.1 and AC173037.2 genome sequences, respectively. Chimpanzee FZD7 and cow Fzd7 showed 100% and 97.2% total-amino-acid identity with human FZD7. All of the nine amino-acid residues substituted between human FZD7 and human FzE3 were identical to those of human FZD7 in chimpanzee, cow, mouse and rat FZD7 orthologs. Functional analyses using FzE3 with multiple cloning artifacts and/or sequencing errors are invalid. FZD7 orthologs were seven-transmembrane proteins with extracellular Frizzled domain, leucine zipper motif around the 5th transmembrane domain, and cytoplasmic DVL- and PDZ-binding motifs. Ser550 and Ser556 of FZD7 orthologs were putative aPKC phosphorylation sites. Dimerization and Ser550/556 phosphorylation were predicted as regulatory mechanisms for the signaling through FZD7. Transcriptional start site of human FZD7 gene was 735-bp upstream of NM_003507.1 RefSeq 5'-end. In addition to gastrointestinal cancer, hepatocellular cancer and pancreatic cancer, human FZD7 mRNAs were expressed in blastocysts, undifferentiated embryonic stem (ES) cells, ES-derived endodermal progenitors, ES-derived neural progenitors, fetal cochlea, retinal pigment epithelium, olfactory epithelium, regenerating liver, and multiple sclerosis. Comparative genomics analyses revealed that the binding sites for PU.1, SP1/Krüppel-like, CCAAT-box, and TCF/LEF/SOX transcription factors were conserved among 5'-promoter regions of mammalian FZD7 orthologs.

## Antibiotic binding releases autoinhibition of the TipA multidrug-resistance transcriptional regulator

Investigations of bacterial resistance strategies can aid in the development of new antimicrobial drugs as a countermeasure to the increasing worldwide prevalence of bacterial antibiotic resistance. One such strategy involves the TipA class of transcription factors, which constitute minimal autoregulated multidrug resistance (MDR) systems against diverse antibiotics. However, we have insufficient information regarding how antibiotic binding induces transcriptional activation to design molecules that could interfere with this process. To learn more, we determined the crystal structure of SkgA from Caulobacter crescentus as a representative TipA protein. We identified an unexpected spatial orientation and location of the antibiotic-binding TipAS effector domain in the apo state. We observed that the α6-α7 region of the TipAS domain, which is canonically responsible for forming the lid of antibiotic-binding cleft to tightly enclose the bound antibiotic, is involved in the dimeric interface and stabilized via interaction with the DNA-binding domain in the apo state. Further structural and biochemical analyses demonstrated that the unliganded TipAS domain sterically hinders promoter DNA binding but undergoes a remarkable conformational shift upon antibiotic binding to release this autoinhibition via a switch of its α6-α7 region. Hence, the promoters for MDR genes including tipA and RNA polymerases become available for transcription, enabling efficient antibiotic resistance. These insights into the molecular mechanism of activation of TipA proteins advance our understanding of TipA proteins, as well as bacterial MDR systems, and may provide important clues to block bacterial resistance.

Keywords: DNA-binding protein TipA activation mechanism antibiotic resistance autoinhibition crystal structure drug resistance multidrug resistance (MDR) structure biology transcription promoter transcription regulation transcriptional regulator.

### Conflict of interest statement

Conflict of interest —The authors declare no conflicts of interest with the contents of this article.

The authors declare no conflicts of interest with the contents of this article

## Biochemistry - Binding Proteins

It describes the effectiveness with which a ligand and protein may bind.

The smaller the Kd value the stronger the binding because Kd = P L/PL, the greater the Kd the weaker the binding.

The cellular response is a type of immune response that involves use of T lymphocytes where they themselves can rid of an antigen.

These sites are referred to as epitopes.

The variable domain is used for epitope recognition on an antibody.

It possesses high avidity meaning that a single binding event can lead to another binding event between the antigen more readily to occur.

For example, the Fab region with a single site for epitope recognition and binding has a given affinity.

In IgG with 2 binding sites it has a 100 fold greater binding.

Because an antibody may not be effective for a tumour cell for example, but we know that it goes directly to a tumour and only to a tumour cell

In free heme Fe2+ can bind oxygen but it can also be converted into Fe 3+ (which can't bind O2), so we must bind heme to something.

The 4 pyrrole rings' nitrogens form 4 out of the 6 possible coordination bonds that Fe2+ can form.

The proximal histidine
Involved in bond formation with the iron which allows it to position the heme / iron in a given way that aids in oxygen binding

It has to be able to release oxygen at low oxygen concentrations (i.e. the concentration of oxygen in the muscles)

Myoglobin has to be able to effectively bind oxygen even at low concentrations (i.e. in the muscles)

It only releases oxygen when the concentration is very low (i.e. when it needs to and is deep in the tissue where conc. of oxygen is significantly low)

This is because at low conc of oxygen there isn't very significant binding of the oxygen molecule, however at very high concentrations of oxygen there is significant binding.

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## Structures of the active HER2/HER3 receptor complex reveal dynamics at the dimerization interface induced by binding of a single ligand

The Human Epidermal Growth Factor Receptor 2 (HER2) and HER3 form a potent pro-oncogenic heterocomplex upon binding of growth factor neuregulin-1β (NRG1β) 1–3 . The mechanism by which HER2 and HER3 interact remains unknown in the absence of any structures of the complex. We isolated the NRG1β-bound near full-length HER2/HER3 dimer and obtained a 2.9Å cryo-electron microscopy (cryo-EM) reconstruction of the extracellular domain module which reveals unexpected dynamics at the HER2/HER3 dimerization interface. We show that the dimerization arm of NRG1β-bound HER3 is unresolved likely because the apo HER2 monomer fails to undergo a ligand-induced conformational change needed to establish a HER3 dimerization arm binding pocket. In a second structure of an oncogenic extracellular domain mutant of HER2, S310F, we observe a compensatory interaction with the HER3 dimerization arm that stabilizes the dimerization interface. We show that both HER2/HER3 and HER2-S310F/HER3 retain the capacity to bind to the HER2-directed therapeutic antibody, trastuzumab, but the mutant complex does not bind to pertuzumab. Our 3.5Å structure of the HER2-S310F/HER3/NRG1β/trastuzumab Fragment antigen binding (Fab) complex shows that the receptor dimer undergoes a conformational change to accommodate trastuzumab. Thus, like oncogenic mutations, therapeutics exploit the intrinsic dynamics of the HER2/HER3 heterodimer. The unique features of a singly liganded HER2/HER3 heterodimer underscore the allosteric sensing of the ligand occupancy by the dimerization interface and explain why extracellular domains of HER2 do not homo-associate via canonical active dimer interface.

## Point mutations in dimerization motifs of the transmembrane domain stabilize active or inactive state of the EphA2 receptor tyrosine kinase

The EphA2 receptor tyrosine kinase plays a central role in the regulation of cell adhesion and guidance in many human tissues. The activation of EphA2 occurs after proper dimerization/oligomerization in the plasma membrane, which occurs with the participation of extracellular and cytoplasmic domains. Our study revealed that the isolated transmembrane domain (TMD) of EphA2 embedded into the lipid bicelle dimerized via the heptad repeat motif L(535)X3G(539)X2A(542)X3V(546)X2L(549) rather than through the alternative glycine zipper motif A(536)X3G(540)X3G(544) (typical for TMD dimerization in many proteins). To evaluate the significance of TMD interactions for full-length EphA2, we substituted key residues in the heptad repeat motif (HR variant: G539I, A542I, G553I) or in the glycine zipper motif (GZ variant: G540I, G544I) and expressed YFP-tagged EphA2 (WT, HR, and GZ variants) in HEK293T cells. Confocal microscopy revealed a similar distribution of all EphA2-YFP variants in cells. The expression of EphA2-YFP variants and their kinase activity (phosphorylation of Tyr(588) and/or Tyr(594)) and ephrin-A3 binding were analyzed with flow cytometry on a single cell basis. Activation of any EphA2 variant is found to occur even without ephrin stimulation when the EphA2 content in cells is sufficiently high. Ephrin-A3 binding is not affected in mutant variants. Mutations in the TMD have a significant effect on EphA2 activity. Both ligand-dependent and ligand-independent activities are enhanced for the HR variant and reduced for the GZ variant compared with the WT. These findings allow us to suggest TMD dimerization switching between the heptad repeat and glycine zipper motifs, corresponding to inactive and active receptor states, respectively, as a mechanism underlying EphA2 signal transduction.

Keywords: Alternative Dimerization Cell Surface Receptor Eph Receptor Flow Cytometry Membrane Proteins Protein Domains Receptor Tyrosine Kinase Transmembrane Domain.

© 2014 by The American Society for Biochemistry and Molecular Biology, Inc.

## DISCUSSION

This study has used confocal microscopy in conjunction with a rapid-exchange perfusion system to investigate cooperative interactions resulting from homodimerization of A1-ARs or A3-ARs at the surface of live cells. In contrast to the A1-AR, highly cooperative interactions between competitive ligands were observed at the A3-AR. These effects could be decreased significantly on coexpression of A3-AR GFP with the non-ligand-binding A3(N250A)-AR YFP , suggesting that the cooperativity between competitive ligands arises as a result of interactions between A3-ARs at the cell surface. Kinetic data were subsequently fit to a dynamic mathematical model of constitutive dimerization to allow, for the first time, quantification of the interactions between competitive ligands at a homodimeric GPCR in live cells.

Within classical GPCR pharmacology, ligands are defined by two system-independent properties, affinity and intrinsic efficacy. However, recent studies have identified GPCR ligand binding and signaling profiles that do not conform to this theoretical framework. The discovery of allosteric ligands and functionally selective orthosteric ligands introduced the phenomenon of probe dependence and, as such, the requirement for careful consideration of the tracer ligand and functional assays employed when screening for drug candidates ( 6 ). Additional layers of complexity are introduced when describing ligand binding and intracellular signaling events at GPCR dimers or higher order oligomers. Homomeric and heteromeric interactions between GPCRs have the potential to be dependent on probe, receptor density, and tissue. However, these system-dependent properties of GPCR-GPCR interactions may also represent potential novel therapeutic avenues for developing drug candidates that modulate GPCR intracellular signaling with greater functional and/or spatiotemporal selectivity ( 12 ).

To date, the majority of studies investigating GPCR dimerization in live cells have employed techniques such as resonance energy transfer (RET) or BiFC. Within the adenosine receptor family, BiFC between YFP fragments suggest that both the A1-AR and the A3-AR can form homomeric complexes (Fig. 2 and ref. 38 ). Although BiFC and RET between GPCRs can be very powerful in detecting receptor proximity in live cells, when used alone, these methods cannot establish the pharmacological or physiological consequences of GPCR-GPCR interactions. Cooperative interactions must be present for GPCR dimerization to have an influence on ligand binding and/or function however, few studies have investigated this phenomenon in live cells ( 11 , 12 ). Quantification of probe-dependent co-operativity factors can provide a mechanistic framework within which to understand the influence of dimerization on ligand-GPCR interactions and, as such, develop structure-activity relationships for ligands interacting across a dimer interface.

Investigation of the dissociation kinetics of a tracer ligand in the absence and presence of a second ligand represents a sensitive method to detect cooperative interactions between two topographically distinct binding sites. The fluorescent adenosine derivative ABA-X-BY630 used within this study has been well characterized previously ( 33 , 39 ). At both CHO-A1 and CHO-A3 cells, ABA-X-BY630 retained the ability to stimulate calcium mobilization and ERK1/2 phosphorylation in a concentration-dependent manner. The association and dissociation specific binding kinetics of ABA-X-BY630 concentrations within the nanomolar range follow a monoexponential association and decay respectively. Together, these results suggest that, similar to endogenous adenosine, ABA-X-BY630 acts as a classical orthosteric agonist at both the A1-AR and A3-AR. The nonselective adenosine receptor antagonist XAC and the nonselective adenosine receptor agonists NECA and adenosine had varying influences on the dissociation of ABA-X-BY630, at the A1-AR and A3-AR. At the A3-AR, each of the nonselective ligands mediated a >9-fold enhancement in ABA-X-BY630 dissociation (Fig. 5A). In contrast, at the A1-AR, each of the ligands mediated a small,

1.5-fold, increase in ABA-X-BY630 dissociation (Fig. 5B). The influence of competitive ligands on ABA-X-BY630 dissociation at the A3-AR cannot reflect ABA-X-BY630 rebinding under conditions of infinite dilution or A3-AR sequestration from the cell surface. This is because the combination of ABA-X-BY630 association alone and ABA-X-BY630 dissociation in the presence of a saturating concentration of antagonist do not conform to the rules of simple mass action that is, the observed association rate is slower than the dissociation rate. Furthermore, the significant difference between the A1-AR and A3-AR must be receptor specific, as the fluorescent ligand, competitive ligands, and cell background remain constant. Interestingly, cooperative interactions are unlikely to be a consequence of high receptor density, as the receptor expression is

4-fold greater in A1-CHO cells as compared to A3-CHO cells.

Cooperative interactions at the A3-AR receptor between ABA-X-BY630 and NECA could be inhibited in a concentration-dependent manner by the presence of the non-ligand-binding mutant A3-AR at the cell surface. These experiments involved cotransfection of A3-AR GFP and A3(N250A)-AR YFP into CHO cells. Spectral unmixing of confocal images represented a robust method to separate the fluorescence resulting from simultaneously excited GFP and YFP. Within a field of view, GFP/YFP fluorescence intensity ratios varied greatly from cell to cell. As such, single-cell analysis of cooperative interactions were determined for cells where the only variable was the ratio of A3AR GFP to A3(N250A)AR YFP . Increasing the proportion of A3(N250A)-AR YFP at the cell surface, which likely correlates with an increase of A3-AR GFP /A3(N250A)-AR YFP dimers, mediated a progressive decrease in the cooperativity between ABA-X-BY630 and NECA. Allosteric interactions within a monomeric receptor should not be influenced by the presence of a nonbinding mutant receptor. The observed decrease in cooperativity in the presence of A3(N250A)-AR YFP suggests the existence of A3-AR YFP /A3(N250A)-AR YFP dimers and no influence of the non-ligand-binding protomer on the ligand-binding protomer. These results support the suggestion that in CHO-A3 cells, the observed allosteric interactions are being mediated across an A3-AR homomeric complex.

The similar effects of agonists and antagonists with respect to the increase in ABA-X-BY630 dissociation from the A3-AR are consistent with a number of previous studies describing homomeric and heteromeric interactions and suggest that cooperative interactions across a dimeric GPCR interface do not necessarily require receptor activation ( 11 , 12 ). A recent study at the dopamine D2 receptor, investigating the downstream signaling consequences of GPCR-GPCR interactions, observed opposing cooperative interactions between agonist-agonist and agonist-inverse agonist binding to the D2 receptor homodimer ( 42 ). In contrast to dopamine D2 receptor homdimers, cooperativity at adenosine A3 receptor homodimers does not correlate with ligand efficacy. However, given the complex allosteric nature of GPCR homomers and heteromers, it is perhaps not surprising that allosteric interactions can vary depending on the receptor, probe, and tissue investigated.

To quantify allosteric interactions, a mechanistic framework is required. The general aim of mathematical modeling within GPCR pharmacology is to develop a model that can describe allosteric interactions adequately using a minimum number of parameters. The simplest model describing allosteric modulation of ligand affinity at constitutive heterodimers is the ternary complex model. In the case of constitutive homodimerization, the ternary complex model must be extended to allow simultaneous occupancy of the homodimer by 2 molecules of the same ligand. Within this model, binding is dependent on the affinity of the ligand for both the free and singularly occupied homodimer. When describing the binding of 2 structurally different ligands, the simple model of constitutive GPCR homodimerization is extended, now described by 2 affinity constants and 3 cooperativity factors. A kinetic version of constitutive GPCR homodimerization was derived within these studies to quantify cooperative interactions between competitive ligands at A3-AR homodimers. Within this model, the assumption that A3-ARs exist as constitutive homodimers is consistent with previous studies suggesting that GPCRs are born, function, and die as dimers ( 43 , 44 ). The receptor homodimerization model yields analytical solutions for bound fractions as functions of the binding parameters and ligand concentrations, and also of time for the dynamic systems. A relatively inexpensive computational parameter estimation routine could therefore be employed to obtain ligand rate constant and cooperativity estimates. Interactions between simultaneously bound homodimeric A3-AR sites were generally found to be negatively cooperative. Analysis of kinetic data represents a high content approach to investigating GPCR-GPCR interactions. Furthermore, kinetic analysis of GPCR pharmacology may represent a more physiologically relevant approach to understanding endogenous ligand-binding events that are rarely at equilibrium within the body.

An unexpected observation within these studies is the contrasting influence of nonselective ligands on the dissociation kinetics of ABA-X-BY630 from the A1-AR as compared to the A3-AR. The A3-AR is more rapidly desensitized when compared to the other members of the AR ( 45 ). Enhanced dissociation on 2 molecules of adenosine binding to an A3-AR homodimer may reflect an additional physiological mechanism to reduce the residence time of the endogenous adenosine at pathophysiologically high concentrations. With respect to drug discovery, increased A3-AR expression within a number of different types of tumor cells has been suggested to have a role in cell proliferation and migration. As such, if A3-AR homomerization is receptor density and/or tissue dependent, ligands that distinguish between A3-AR monomers and homomers may represent a novel therapeutic strategy for selective targeting of tumor cells in the treatment of cancer ( 46 ).

The A3-AR is a potential novel therapeutic target for a number of conditions, including inflammatory disorders and cancer ( 46 , 47 ). This study has identified and quantified novel homomeric interactions between native A3-ARs. The kinetic and mathematical approach used within this study represents a powerful method to detect and interpret cooperative interactions between allosteric and/or orthosteric ligands. An additional advantage of this approach is that it is readily amenable to study interactions between endogenously expressed GPCRs within a physiological context.