Estimation of statistical binding properties of ligand population during in vitro selection based on population dynamics theory

• We made a theory of a population dynamics during in vitro selection.
• We proposed a novel method to estimate binding properties of the population.
• Particularly, the probability density of binding free energy in the population.
• Estimation is based on experimental measurements and theoretical analysis.
• The validity of our method was confirmed by several computer simulations.

During in vitro selection process, it is very valuable to monitor the binding properties of the ligand population in real time, particularly the population average of the association constant in the population. If this monitoring can be realized, the selection process can be controlled in a rational way. In this paper, we present a simple method to estimate the binding properties of the ligand population during in vitro selection. The framework of the method is as follows. First, the number of all the collected ligand molecules, which are eluted after incubation and washing, is measured. Ideally, this number corresponds to the number of all the ligand molecules bound with the target–receptor or other materials in a test tube. This measurement is performed through several successive rounds of selection. Second, the measured numbers of molecules are subjected to a theoretical analysis, based on the mathematical theory of population dynamics in the selection process. Then, we can estimate the probability density of the binding free energy in the ligand population. The validity of our method was confirmed by several computer simulations based on a physicochemical model.

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