Tinkering with Binding Polynomials in Isothermal Titration Calorimetry

Isothermal titration calorimetry (ITC) has become the preferred experimental technique for characterizing intermolecular interactions between biological molecules. Among the several advantages, the use of natural non-labeled molecules and the determination of the complete thermodynamic profile for the interaction in solution remain as the primary features that have promoted ITC to the forefront of experimental biophysics. The experimental design in ITC may range from studying a simple direct binary macromolecule-ligand interaction to studying the homotropic or heterotropic cooperative effect between ligands when interacting with a given macromolecule. The theory of the binding polynomial has proven to be an appropriate unifying framework for handling the complexities that can be encountered when studying macromolecule-ligand interactions, though it has been deemed troublesome. The goal of this chapter is to provide a quite simple and widely available set of training experiments aimed at mastering the formalism of the binding polynomial applied to isothermal titration calorimetry.

Exploring the complete mutational space of the LDL receptor LA5 domain using molecular dynamics: linking SNPs with disease phenotypes in familial hypercholesterolemia

Familial hypercholesterolemia (FH), a genetic disorder with a prevalence of 0.2%, represents a high-risk factor to develop cardiovascular and cerebrovascular diseases. The majority and most severe FH cases are associated to mutations in the receptor for low-density lipoproteins receptor (LDL-r), but the molecular basis explaining the connection between mutation and phenotype is often unknown, which hinders early diagnosis and treatment of the disease. We have used atomistic simulations to explore the complete SNP mutational space (227 mutants) of the LA5 repeat, the key domain for interacting with LDL that is coded in the exon concentrating the highest number of mutations. Four clusters of mutants of different stability have been identified. The majority of the 50 FH known mutations (33) appear distributed in the unstable clusters, i.e. loss of conformational stability explains two-third of FH phenotypes. However, one-third of FH phenotypes (17 mutations) do not destabilize the LR5 repeat. Combining our simulations with available structural data from different laboratories, we have defined a consensus-binding site for the interaction of the LA5 repeat with LDL-r partner proteins and have found that most (16) of the 17 stable FH mutations occur at binding site residues. Thus, LA5-associated FH arises from mutations that cause either the loss of stability or a decrease in domain's-binding affinity. Based on this finding, we propose the likely phenotype of each possible SNP in the LA5 repeat and outline a procedure to make a full computational diagnosis for FH.

Calcium-dependent antigen binding as a novel modality for antibody recycling by endosomal antigen dissociation

The pH-dependent antigen binding antibody, termed a recycling antibody, has recently been reported as an attractive type of second-generation engineered therapeutic antibody. A recycling antibody can dissociate antigen in the acidic endosome, and thus bind to its antigen multiple times. As a consequence, a recycling antibody can neutralize large amounts of antigen in plasma. Because this approach relies on histidine residues to achieve pH-dependent antigen binding, which could limit the epitopes that can be targeted and affect the rate of antigen dissociation in the endosome, we explored an alternative approach for generating recycling antibodies. Since calcium ion concentration is known to be lower in endosome than in plasma, we hypothesized that an antibody with antigen-binding properties that are calcium-dependent could be used as recycling antibody. Here, we report a novel anti-interleukin-6 receptor (IL-6R) antibody, identified from a phage library that binds to IL-6R only in the presence of a calcium ion. Thermal dynamics and a crystal structure study revealed that the calcium ion binds to the heavy chain CDR3 region (HCDR3), which changes and possibly stabilizes the structure of HCDR3 to make it bind to antigen calcium dependently (PDB 5AZE). In vitro and in vivo studies confirmed that this calcium-dependent antigen-binding antibody can dissociate its antigen in the endosome and accelerate antigen clearance from plasma, making it a novel approach for generating recycling antibody.

The closed conformation of the LDL receptor is destabilized by the low Ca(++) concentration but favored by the high Mg(++) concentration in the endosome

The LDL receptor (LDLR) internalizes LDL and VLDL particles. In the endosomes, it adopts a closed conformation important for recycling, by interaction of two modules of the ligand binding domain (LR4-5) and a β-propeller motif. Here, we investigate by SPR the interactions between those two modules and the β-propeller. Our results indicate that the two modules cooperate to bind the β-propeller. The binding is favored by low pH and by high [Ca(++)]. Our data show that Mg(++), at high concentration in the endosome, favors the formation of the closed conformation by replacing the structuring effect of Ca(++) in LR5. We propose a sequential model of LDL release where formation of the close conformation follows LDL release.

An explicit formulation approach for the analysis of calcium binding to EF-hand proteins using isothermal titration calorimetry

We present an improved and extended version of a recently proposed mathematical approach for modeling isotherms of ligand-to-macromolecule binding from isothermal titration calorimetry. Our approach uses ordinary differential equations, solved implicitly and numerically as initial value problems, to provide a quantitative description of the fraction bound of each competing member of a complex mixture of macromolecules from the basis of general binding polynomials. This approach greatly simplifies the formulation of complex binding models. In addition to our generalized, model-free approach, we have introduced a mathematical treatment for the case where ligand is present before the onset of the titration, essential for data analysis when complete removal of the binding partner may disrupt the structural and functional characteristics of the macromolecule. Demonstration programs playable on a freely available software platform are provided. Our method is experimentally validated with classic calcium (Ca(2+)) ion-selective potentiometry and isotherms of Ca(2+) binding to a mixture of chelators with and without residual ligand present in the reaction vessel. Finally, we simulate and compare experimental data fits for the binding isotherms of Ca(2+) binding to its canonical binding site (EF-hand domain) of polycystin 2, a Ca(2+)-dependent channel with relevance to polycystic kidney disease.

Low-density lipoprotein receptor is a calcium/magnesium sensor - role of LR4 and LR5 ion interaction kinetics in low-density lipoprotein release in the endosome

The low-density lipoprotein receptor (LDLR) captures circulating lipoproteins and delivers them in the endosome for degradation. Its function is essential for cholesterol homeostasis, and mutations in the LDLR are the major cause of familiar hypercholesterolemia. The release of LDL is usually attributed to endosome acidification. As the pH drops, the affinity of the LDLR/LDL complex is reduced, whereas the strength of a self-complex formed between two domains of the receptor (i.e. the LDL binding domain and the β-propeller domain) increases. However, an alternative model states that, as a consequence of a drop in both pH and Ca(2+) concentration, the LDLR binding domain is destabilized in the endosome, which weakens the LDLR/LDL complex, thus liberating the LDL particles. In the present study, we test a key underlying assumption of the second model, namely that the lipoprotein binding repeats of the receptor (specifically repeats 4 and 5, LR4 and LR5) rapidly sense endosomal changes in Ca(2+) concentration. Our kinetic and thermodynamic analysis of Ca(2+) and Mg(2+) binding to LR4 and LR5, as well as to the tandem of the two (LR4-5), shows that both repeats spontaneously release Ca(2+) in a time scale much shorter than endosomal delivery of LDL, thus acting as Ca(2+) sensors that become unfolded under endosomal conditions. Our analysis additionally explains the lower Ca(2+) affinity of repeat LR4, compared to LR5, as arising from a very slow Ca(2+) binding reaction in the former, most likely related to the lower conformational stability of apolipoprotein LR4, compared to apolipoprotein LR5, as determined from thermal unfolding experiments and molecular dynamics simulations.

Membrane partitioning of the pore-forming domain of colicin A. Role of the hydrophobic helical hairpin

The colicins are bacteriocins that target Escherichia coli and kill bacterial cells through different mechanisms. Colicin A forms ion channels in the inner membranes of nonimmune bacteria. This activity resides exclusively in its C-terminal fragment (residues 387-592). The soluble free form of this domain is a 10 α-helix bundle. The hydrophobic helical hairpin, H8-H9, is buried inside the structure and shielded by eight amphipathic surface helices. The interaction of the C-terminal colicin A domain and several chimeric variants with lipidic vesicles was examined here by isothermal titration calorimetry. In the mutant constructions, natural sequences of the hydrophobic helices H8 and H9 were either removed or substituted by polyalanine or polyleucine. All the constructions fully associated with DOPG liposomes including the mutant that lacked helices H8 and H9, indicating that amphipathic rather than hydrophobic helices were the major determinants of the exothermic binding reactions. Alanine is not specially favored in the lipid-bound form; the chimeric construct with polyalanine produced lower enthalpy gain. On the other hand, the large negative heat capacities associated with partitioning, a characteristic feature of the hydrophobic effect, were found to be dependent on the sequence hydrophobicity of helices H8 and H9.

Applications of isothermal titration calorimetry in pure and applied research--survey of the literature from 2010

Isothermal titration calorimetry (ITC) is a biophysical technique for measuring the formation and dissociation of molecular complexes and has become an invaluable tool in many branches of science from cell biology to food chemistry. By measuring the heat absorbed or released during bond formation, ITC provides accurate, rapid, and label-free measurement of the thermodynamics of molecular interactions. In this review, we survey the recent literature reporting the use of ITC and have highlighted a number of interesting studies that provide a flavour of the diverse systems to which ITC can be applied. These include measurements of protein-protein and protein-membrane interactions required for macromolecular assembly, analysis of enzyme kinetics, experimental validation of molecular dynamics simulations, and even in manufacturing applications such as food science. Some highlights include studies of the biological complex formed by Staphylococcus aureus enterotoxin C3 and the murine T-cell receptor, the mechanism of membrane association of the Parkinson's disease-associated protein α-synuclein, and the role of non-specific tannin-protein interactions in the quality of different beverages. Recent developments in automation are overcoming limitations on throughput imposed by previous manual procedures and promise to greatly extend usefulness of ITC in the future. We also attempt to impart some practical advice for getting the most out of ITC data for those researchers less familiar with the method.

Structure of complement C6 suggests a mechanism for initiation and unidirectional, sequential assembly of membrane attack complex (MAC)

The complement membrane attack complex (MAC) is formed by the sequential assembly of C5b with four homologous proteins as follows: one copy each of C6, C7, and C8 and 12-14 copies of C9. Together these form a lytic pore in bacterial membranes. C6 through C9 comprise a MAC-perforin domain flanked by 4-9 "auxiliary" domains. Here, we report the crystal structure of C6, the first and longest of the pore proteins to be recruited by C5b. Comparisons with the structures of the C8αβγ heterodimer and perforin show that the central domain of C6 adopts a "closed" (perforin-like) state that is distinct from the "open" conformations in C8. We further show that C6, C8α, and C8β contain three homologous subdomains ("upper," "lower," and "regulatory") related by rotations about two hinge points. In C6, the regulatory segment includes four auxiliary domains that stabilize the closed conformation, inhibiting release of membrane-inserting elements. In C8β, rotation of the regulatory segment is linked to an opening of the central β-sheet of its clockwise partner, C8α. Based on these observations, we propose a model for initiation and unidirectional propagation of the MAC in which the auxiliary domains play key roles: in the assembly of the C5b-8 initiation complex; in driving and regulating the opening of the β-sheet of the MAC-performin domain of each new recruit as it adds to the growing pore; and in stabilizing the final pore. Our model of the assembled pore resembles those of the cholesterol-dependent cytolysins but is distinct from that recently proposed for perforin.

Nanomechanics of the cadherin ectodomain: "canalization" by Ca2+ binding results in a new mechanical element

Cadherins form a large family of calcium-dependent cell-cell adhesion receptors involved in development, morphogenesis, synaptogenesis, differentiation, and carcinogenesis through signal mechanotransduction using an adaptor complex that connects them to the cytoskeleton. However, the molecular mechanisms underlying mechanotransduction through cadherins remain unknown, although their extracellular region (ectodomain) is thought to be critical in this process. By single molecule force spectroscopy, molecular dynamics simulations, and protein engineering, here we have directly examined the nanomechanics of the C-cadherin ectodomain and found it to be strongly dependent on the calcium concentration. In the presence of calcium, the ectodomain extends through a defined ("canalized") pathway that involves two mechanical resistance elements: a mechanical clamp from the cadherin domains and a novel mechanostable component from the interdomain calcium-binding regions ("calcium rivet") that is abolished by magnesium replacement and in a mutant intended to impede calcium coordination. By contrast, in the absence of calcium, the mechanical response of the ectodomain becomes largely "decanalized" and destabilized. The cadherin ectodomain may therefore behave as a calcium-switched "mechanical antenna" with very different mechanical responses depending on calcium concentration (which would affect its mechanical integrity and force transmission capability). The versatile mechanical design of the cadherin ectodomain and its dependence on extracellular calcium facilitate a variety of mechanical responses that, we hypothesize, could influence the various adhesive properties mediated by cadherins in tissue morphogenesis, synaptic plasticity, and disease. Our work represents the first step toward the mechanical characterization of the cadherin system, opening the door to understanding the mechanical bases of its mechanotransduction.