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.

How to Develop and Prove High-Efficiency Selection of Ligands from Oligonucleotide Libraries: A Universal Framework for Aptamers and DNA-Encoded Small-Molecule Ligands.

Screening molecular libraries for ligands capable of binding proteins is widely used for hit identification in the early drug discovery process. Oligonucleotide libraries provide a very high diversity of compounds, while the combination of the polymerase chain reaction and DNA sequencing allow the identification of ligands in low copy numbers selected from such libraries. Ligand selection from oligonucleotide libraries requires mixing the library with the target followed by the physical separation of the ligand-target complexes from the unbound library. Cumulatively, the low abundance of ligands in the library and the low efficiency of available separation methods necessitate multiple consecutive rounds of partitioning. Multiple rounds of inefficient partitioning make the selection process ineffective and prone to failures. There are continuing efforts to develop a separation method capable of reliably generating a pure pool of ligands in a single round of partitioning; however, none of the proposed methods for single-round selection have been universally adopted. Our analysis revealed that the developers' efforts are disconnected from each other and hindered by the lack of quantitative criteria of selection quality assessment. Here, we present a formalism that describes single-round selection mathematically and provides parameters for quantitative characterization of selection quality. We use this formalism to define a universal strategy for development and validation of single-round selection methods. Finally, we analyze the existing partitioning methods, the published single-round selection reports, and some pertinent practical considerations through the prism of this formalism. This formalism is not an experimental protocol but a framework for correct development of experimental protocols. While single-round selection is not a goal by itself and may not always suffice selection of good-quality ligands, our work will help developers of highly efficient selection approaches to consolidate their efforts under an umbrella of universal quantitative criteria of method development and assessment.

Determination of the Equilibrium Constant and Rate Constant of Protein-Oligonucleotide Complex Dissociation under the Conditions of Ideal-Filter Capillary Electrophoresis.

Ideal-filter capillary electrophoresis (IFCE) allows selection of protein binders from oligonucleotide libraries in a single step of partitioning in which protein-bound and unbound oligonucleotides move in the opposite directions. In IFCE, the unbound oligonucleotide does not reach the detector, imposing a problem for finding the equilibrium constant ( Kd) and rate constant ( koff) of protein-oligonucleotide complex dissociation. We report a double-passage approach that allows finding Kd and koff under the IFCE conditions, i.e. near-physiological pH and ionic strength. First, a plug of the protein-oligonucleotide equilibrium mixture passes to the detector in a pressure-driven flow, allowing for both the complex and free oligonucleotide to be detected as a single first peak. Second, the pressure is turned off and the voltage is applied to reverse the migration of only the complex which is detected as the second peak. The experiment is repeated with a lower voltage consequently resulting in longer travel time of the complex to the detector, greater extent of complex dissociation, and the decreased area of the second peak. Finally, the peak areas are used to calculate the values of Kd and koff. Here we explain theoretical and practical aspects of the double-passage approach, prove its validity quantitatively, and, demonstrate its application to determine Kd and koff for an affinity complex between a protein and its DNA aptamer. The double-passage approach for finding Kd and koff of protein-oligonucleotide complexes under the IFCE conditions is a perfect complement for IFCE-based selection of protein binders from oligonucleotide libraries.

Ideal-filter capillary electrophoresis: A highly efficient partitioning method for selection of protein binders from oligonucleotide libraries.

Selection of affinity ligands for protein targets from oligonucleotide libraries currently involves multiple rounds of alternating steps of partitioning of protein-bound oligonucleotides (binders) from protein-unbound oligonucleotides (nonbinders). We have recently introduced ideal-filter capillary electrophoresis (IFCE) for binder selection in a single step of partitioning. In IFCE, protein-binder complexes and nonbinders move inside the capillary in the opposite directions, and the efficiency of their partitioning reaches 109 , i.e., only one of a billion molecules of nonbinders leaks through IFCE while all binders pass through. The condition of IFCE can be satisfied when the magnitude of the mobility of EOF is smaller than that of the protein-binder complexes and larger than that of nonbinders. The efficiency of partitioning in IFCE is 10 million times higher than those of solid-phase-based methods of partitioning typically used in selection of affinity ligands for protein targets from oligonucleotide libraries. Here, we provide additional details on our justification for IFCE development. We elaborate on electrophoretic aspects of the method and define the theoretical range of EOF mobilities that support IFCE. Based on these theoretical results, we identify an experimental range of background electrolyte's ionic strength that supports IFCE. We also extend our interpretation of the results and discuss in-depth IFCE's prospective in practical applications and fundamental studies.

Ideal-Filter Capillary Electrophoresis (IFCE) Facilitates the One-Step Selection of Aptamers.

Selection of aptamers from oligonucleotide libraries currently requires multiple rounds of alternating steps of partitioning of binders from nonbinders and enzymatic amplification of all collected oligonucleotides. Herein, we report a highly practical solution for reliable one-step selection of aptamers. We introduce partitioning by ideal-filter capillary electrophoresis (IFCE) in which binders and nonbinders move in the opposite directions. The efficiency of IFCE-based partitioning reaches 109 , which is ten million times higher than that of typical solid-phase partitioning methods. One step of IFCE-based partitioning is sufficient for the selection of a high-affinity aptamer pool for a protein target. Partitioning by IFCE promises to become an indispensable tool for fast and robust selection of binders from different types of oligonucleotide libraries.

Predicting efficiency of NECEEM-based partitioning of protein binders from nonbinders in DNA-encoded libraries.

Nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) is an affinity method for separating binder-target complexes from nonbinders by gel-free CE. NECEEM is a promising high-efficiency method for partitioning protein binders from nonbinders in DNA-encoded libraries (DEL), such binders are used as "hits" in drug development. It is important to be able to predict the efficiency of NECEEM-based partitioning, which is the efficiency of collecting binders while removing nonbinders for a specific protein and a specific DEL with a minimum of empirical information. Here, we derive and study the dependence of efficiency of NECEEM-based partitioning on electrophoretic mobilities of the protein and the DNA moiety in DEL compounds. Our derivation is based upon a previously found relation between the electrophoretic mobility of protein-binder complex and measured electrophoretic mobilities of the protein and unbound DEL and their estimated sizes. The derivation utilizes the assumption of Gaussian shapes of electrophoretic peaks and the approximation of the efficiency of partitioning by the background of nonbinders - a fraction of nonbinders, which elutes along with protein-binder complexes. Our results will serve as a guiding tool for planning the NECEEM-based partitioning of protein binders from non-binders in DELs. In particular, it can be used to estimate a minimum number of rounds of partitioning required for the desired level of DEL enrichment.