Fundamental Determinants of the Accuracy of Equilibrium Constants for Affinity Complexes.

The equilibrium constant of a chemical reaction is arguably the key thermodynamic parameter in chemistry; we naturally expect that equilibrium constants are determined accurately. The majority of equilibrium constants determined today are those of binding reactions that form affinity complexes, such as protein-protein, protein-DNA, and protein-small molecule. There is growing awareness that the determination of equilibrium constants for highly stable affinity complexes may be very inaccurate. However, fundamental (i.e., method-independent) determinants of accuracy are poorly understood. Here, we present a study that explicitly shows what the accuracy of equilibrium constants of affinity complexes depends on. This study reveals the critical importance of the choice of concentration of interacting components and creates a theoretical foundation for improving the accuracy of the equilibrium constants. The predicted influence of concentrations on accuracy was confirmed experimentally. The results of this fundamental study provide instructive guidance for experimentalists independently on the method they use.

Bulk Affinity Assays in Aptamer Selection: Challenges, Theory, and Workflow.

Selection of oligonucleotide aptamers involves consecutive rounds of affinity isolation of target-binding oligonucleotides from a random-sequence oligonucleotide library. Every next round produces an aptamer-enriched library with progressively higher fitness for tight binding to the target. The progress of enrichment can only be accurately assessed with bulk affinity assays in which a library is mixed with the target and one of two quantitative parameters, the fraction of the unbound library (R) or the equilibrium dissociation constant (Kd), is determined. These quantitative parameters are used to help researchers make a key decision of either continuing or stopping the selection. Despite the importance of this decision, the suitability of R and Kd for bulk affinity assays has never been studied theoretically, and researchers rely on intuition when choosing between them. Different approaches used for bulk affinity assays expectedly hinder comparative analyses of selections. Our current work has two goals: to give bulk affinity assays a thorough theoretical consideration and to propose a scientifically justified and practical bulk-affinity-assay approach. We postulate a formal criterion of suitability: a quantitative parameter must satisfy the principle of superposition. R satisfies this principle, while Kd does not, suggesting R as a theoretically preferable parameter. Further, we propose a solution for two limitations of R: its dependence on target concentration and narrow dynamic range. Finally, we demonstrate the use of this algorithm in both computer-simulated and experimental aptamer selection. This study sets a cornerstone in the theory of bulk affinity assays, and it provides researchers with a scientifically sound and instructive approach for conducting bulk affinity assays.

Transient Incomplete Separation of Species with Close Diffusivity to Study the Stability of Affinity Complexes.

Large molecules can be generically separated from small ones, though partially and temporarily, in a pressure-driven flow inside a capillary. This transient incomplete separation has been only applied to species with diffusion coefficients different by at least an order of magnitude. Here, we demonstrate, for the first time, the analytical utility of transient incomplete separation for species with close diffusion coefficients. First, we prove in silico that even a small difference in diffusivity can lead to detectable transient incomplete separation of species. Second, we use computer simulation to prove that such a separation can be used for the reliable determination of equilibrium dissociation constant (Kd) of complexes composed of similar-sized molecules. Finally, we demonstrate experimentally the use of this separation for the accurate determination of Kd value for a protein-aptamer complex. We conclude that "accurate constant via transient incomplete separation" (ACTIS) can serve as a reference method for affinity characterization of protein-aptamer binding in solution.

Quantitative Characterization of Partitioning in Selection of DNA Aptamers for Protein Targets by Capillary Electrophoresis.

Partitioning of protein-DNA complexes from protein-unbound DNA is a key step in selection of DNA aptamers. Conceptually, the partitioning step is characterized by two parameters: transmittance for protein-bound DNA (binders) and transmittance for unbound DNA (nonbinders). Here, we present the first study to reveal how these transmittances depend on experimental conditions; such studies are pivotal to the effective planning and control of selection. Our focus was capillary electrophoresis (CE), which is a partitioning approach of high efficiency. By combining a theoretical model and experimental data, we evaluated the dependence of transmittances of binders and nonbinders on the molecular weight of the protein target in two modes of CE-based partitioning: nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) and ideal-filter capillary electrophoresis (IFCE). Our data suggest that as the molecular weight of the protein target decreases: (i) the transmittance for binders remains close to unity in NECEEM but decreases drastically in IFCE and (ii) the transmittance for nonbinders increases orders of magnitude in NECEEM but remains relatively stable at a very low level in IFCE. To determine the optimal CE conditions for a given size of protein target, a balance between transmittances of binders and nonbinders must be reached; such a balance would ensure the collection of binders of sufficient purity and quantity. We conclude that, as a rule of thumb, IFCE is preferable for large-size protein targets while NECEEM should be the method of choice for small-size protein targets.

Template Instrumentation for "Accurate Constant via Transient Incomplete Separation".

Accurate Constant via Transient Incomplete Separation (ACTIS) is a new method for finding the equilibrium dissociation constant Kd of a protein-small molecule complex based on transient incomplete separation of the complex from the unbound small molecule in a capillary. This separation is caused by differential transverse diffusion of the complex and the small molecule in a pressure-driven flow. The advection-diffusion processes underlying ACTIS can be described by a system of partial differential equations allowing for a virtual ACTIS instrument to be built and ACTIS to be studied in silico. The previous in silico studies show that large variations in the fluidic system geometry do not affect the accuracy of Kd determination, thus, proving that ACTIS is conceptually accurate. The conceptual accuracy does not preclude, however, instrumental inaccuracy caused by run-to-run signal drifts. Here we report on assembling a physical ACTIS instrument with a fluidic system that mimics the virtual one and proving the absence of signal drifts. Furthermore, we confirmed method ruggedness by assembling a second ACTIS instrument and comparing the results of experiments performed with both instruments in parallel. Despite some unintentional differences between the instruments (caused by tolerances in sizes, positions, etc.) and noticeable differences in their respective separagrams, we found that the Kd values determined for identical samples with these instruments were equal. Conclusively, the fluidic system presented here can serve as a template for reliable ACTIS instrumentation.

Empirical predictor of conditions that support ideal-filter capillary electrophoresis.

Ideal-filter CE (IFCE) is a method for the selection of affinity binders for protein targets from oligonucleotide libraries, for example, random-sequence oligonucleotide libraries and DNA-encoded libraries, in a single step of partitioning. In IFCE, protein-oligonucleotide complexes and unbound oligonucleotides move in the opposite directions, facilitating very high efficiency of their partitioning. For any given protein target and oligonucleotide library, protein-oligonucleotide complexes and unbound oligonucleotides move in the opposite directions only for a limited range of EOF mobilities, which, in turn, corresponds to a limited range of pH and ionic strength values of the running buffer. Rational design of IFCE-based partitioning requires a priori knowledge of this range of pH and ionic strength values, and here we introduce an approach to predict this range for a given type of the running buffer. The approach involves measuring EOF mobilities for a relatively wide range of pH and ionic strength (I) values and finding an empirical predictor function that related the EOF mobility with pH and ionic strength. In this work, we developed a predictor function for a running buffer (Tris-HCl) that is commonly used in CE-based partitioning of affinity binders for protein targets. This predictor function can be immediately used for the rational design of IFCE-based partitioning in this running buffer, while the described approach will be used to develop predictor functions for other types of running buffer if needed.