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).

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.

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.

Partitioning microfluidic channels with hydrogel to construct tunable 3-D cellular microenvironments.

Accurate modeling of the cellular microenvironment is important for improving studies of cell biology in vitro. Here, we demonstrate a flexible method for creating a cellular microenvironment in vitro that allows (i) controlled spatial distribution (patterning) of multiple types of cells within three-dimensional (3-D) matrices of a biologically derived, thermally curable hydrogel (Matrigel) and (ii) application of gradients of soluble factors, such as cytokines, across the hydrogel. The technique uses laminar flow to divide a microchannel into multiple subchannels separated by microslabs of hydrogel. It does not require the use of UV light or photoinitiators and is compatible with cell culture in the hydrogel. This technique makes it possible to design model systems to study cellular communication mediated by the diffusion of soluble factors within 3-D matrices. Such factors can originate either from secretions of neighboring cells patterned within the microchannel, or from an external source -- e.g., a solution of growth factors injected into a subchannel. This method is particularly useful for studying cells such as those of the immune system, which are often weakly adherent and difficult to position precisely with standard systems for cell culture. We demonstrated this application by co-culturing two types of macrophage-like cells (BAC1.2F5 and LADMAC cell lines) within spatially separated regions of a slab of hydrogel. This pair of cell lines represents a simple model system for intercellular communication: the LADMAC cells produce colony-stimulating factor 1 (CSF-1), which is required by the BAC cells for survival.

Patterning micron-sized features in a cross-linked poly(acrylic acid) film by a wet etching process.

This paper describes a photolithographic method to create sub-micron-scale patterns of cation-cross-linked poly(acrylic acid) (CCL-PAA). PAA can be cross-linked with a wide range of metal cations-including, but not limited to, Ag, Ca, Pd, Al, La, and Ti. Upon patterning a positive photoresist (diazonaphthoquinone-novolac resin) on a film of CCL-PAA, the exposed regions of CCL-PAA were etched by either an aqueous NaOH or EDTA solution. The initial cross-linking cation could be exchanged for a second cation that could not be patterned photolithographically. We used these patterned films of CCL-PAA i) to host and template the reduction of metallic cations to metallic nanoparticles, and ii) to fabricate porous, low- dielectric substrates.

Position along the nasal/temporal plane affects synaptic development by adult photoreceptors, revealed by micropatterning.

In retinal degeneration, death of photoreceptors causes blindness. Repair of the retina by transplanting photoreceptors has resulted in limited functional connectivity between transplanted and host neurons. We hypothesize that absence of appropriate biological cues, specifically positional (retinotopographic) cues, reduces synaptogenesis. Here we use micropatterning to test whether regional origin affects the early synaptic development of photoreceptors. Right and left retinas from salamanders were first labelled with dextran tetramethyl-rhodamine and fluorescein, respectively, bisected into nasal (N)/temporal (T) or dorsal (D)/ventral (V) halves, individually dissociated, mixed, and cultured for 1 week. Origin of cells was identified by the fluorescent label. Interactions between photoreceptors and neighboring (target) cells were assessed by the number of neuritic contacts with a presynaptic swelling (varicosity). Randomly-plated photoreceptors showed no preference for cellular origin, likely due to multiple potential interactions available to each cell. To reduce cell-cell interactions, culture substrate was patterned using a microfluidic device with 10 µm-wide channels separated by 200 µm, thus allowing only 1-2 targets per photoreceptor. In patterned cultures, 36.89% of N rod cells contacted T targets but only 27.42% of N rod cells contacted N targets; similarly 35.05% of T rod cells contacted N cells but only 17.08% contacted T cells. Thus, opposite regions were more permissive of contact. However, neither cone nor D/V rod cells showed preferences for positional origin of targets. In conclusion, micropatterning demonstrated that neuritic differentiation by rod cells depends on retinotopographic cues along the nasal/temporal plane, suggesting that transplanting rod cells of known positional origin will increase transplant success.

Subtle Interplay between synaptotagmin and complexin binding to the SNARE complex.

Ca²âº-triggered neurotransmitter release depends on the formation of SNARE complexes that bring the synaptic vesicle and plasma membranes together, on the Ca²âº sensor synaptotagmin-1 and on complexins, which play active and inhibitory roles. Release of the complexin inhibitory activity by binding of synaptotagmin-1 to the SNARE complex, causing complexin displacement, was proposed to trigger exocytosis. However, the validity of this model was questioned based on the observation of simultaneous binding of complexin-I and a fragment containing the synaptotagmin-1 C2 domains (C2AB) to membrane-anchored SNARE complex. Using diverse biophysical techniques, here we show that C2AB and complexin-I do not bind to each other but can indeed bind simultaneously to the SNARE complex in solution. Hence, the SNARE complex contains separate binding sites for both proteins. However, total internal reflection fluorescence microscopy experiments show that C2AB can displace a complexin-I fragment containing its central SNARE-binding helix and an inhibitory helix (Cpx26-83) from membrane-anchored SNARE complex under equilibrium conditions. Interestingly, full-length complexin-I binds more tightly to membrane-anchored SNARE complex than Cpx26-83, and it is not displaced by C2AB. These results show that interactions of N- and/or C-terminal sequences of complexin-I with the SNARE complex and/or phospholipids increase the affinity of complexin-I for the SNARE complex, hindering dissociation induced by C2AB. We propose a model whereby binding of synaptotagmin-1 to the SNARE complex directly or indirectly causes a rearrangement of the complexin-I inhibitory helix without inducing complexin-I dissociation, thus relieving the inhibitory activity and enabling cooperation between synaptotagmin-1 and complexin-I in triggering release.

Adhesive-tape soft lithography for patterning mammalian cells: application to wound-healing assays.

This paper introduces a benchtop method for patterning mammalian cells-i.e., for culturing cells at specific locations-on planar substrates. Compared with standard cell culture techniques, which do not allow the control of what areas of a monolayer are populated by one type of cell or another, techniques of cell patterning open new routes to cell biology. Researchers interested in cell patterning, however, are often times hindered by limited access to photolithographic capabilities. This paper shows how cells can be patterned easily with sub-millimeter precision using a non-photolithographic technique that is based on the use of office adhesive tape and poly(dimethylsiloxane) (PDMS). This method is fast (~4 h to go from a layout to have the cells patterned in the shape of such layout) and only requires materials and tools readily available in a conventional biomedical laboratory. A wound-healing assay is presented here that illustrates the potential of the technique (which we call tape-based soft lithography) for patterning mammalian cells and studying biologically significant questions such as collective cellular migration.

Density-based diamagnetic separation: devices for detecting binding events and for collecting unlabeled diamagnetic particles in paramagnetic solutions.

This paper describes the fabrication of a fluidic device for detecting and separating diamagnetic materials that differ in density. The basis for the separation is the balance of the magnetic and gravitational forces on diamagnetic materials suspended in a paramagnetic medium. The paper demonstrates two applications of separations involving particles suspended in static fluids for detecting the following: (i) the binding of streptavidin to solid-supported biotin and (ii) the binding of citrate-capped gold nanoparticles to amine-modified polystyrene spheres. The paper also demonstrates a microfluidic device in which polystyrene particles that differ in their content of CH2Cl groups are continuously separated and collected in a flowing stream of an aqueous solution of GdCl3. The procedures for separation and detection described in this paper require only gadolinium salts, two NdFeB magnets, and simple microfluidic devices fabricated from poly(dimethylsiloxane). This device requires no power, has no moving parts, and may be suitable for use in resource-poor environments.

Fabrication of large-area patterned nanostructures for optical applications by nanoskiving.

Cost-effective and convenient methods for fabrication of patterned metallic nanostructures over the large (mm2) areas required for applications in photonics are much needed. In this paper, we demonstrate the fabrication of arrays of closed and open, loop-shaped nanostructures by a technique (nanoskiving) that combines thin-film deposition by metal evaporation with thin-film sectioning. These arrays of metallic structures serve as frequency-selective surfaces at mid-infrared wavelengths. Experiments with structures prepared using this technique demonstrate that a closed-looped structure has a single dominant resonance regardless of the polarization of the incident light, while open structures have resonances that are anisotropic with respect to the polarization of the electric field. Finite-difference time-domain (FDTD) simulations reproduce the scattering spectra of these frequency-selective surfaces, provide an explanation of the wavelength of the experimentally observed resonances, and rationalize their polarization dependence based on the patterns of current induced in the nanostructures.

Fabrication of high-aspect-ratio metallic nanostructures using nanoskiving.

This communication describes the fabrication of gold structures (for example, rings) with wall thickness of 40 nm, and with high aspect ratios up to 25. This technique combines thin-film deposition of metal on a topographically patterned epoxy substrate, with nanometer-scale sectioning using a microtome in a plane parallel to the patterned substrate. The dimensions of the metal structures are determined by the thickness of the metal film and the thickness of the epoxy sections. The shape of the resulting nanostructure is defined by the cross section of the original template.