Mathematical consideration of massive estimation of dissociation rate constant for genotype–phenotype linking molecules bound to targets through washing/selection and next-generation sequencing

As one of methods for in vitro selection, a flow reactor type washing/selection system seems to be effective, where a ligand library is composed of “genotype–phenotype linking molecules”. In this system, high affinity ligands are selected by their respective “residual ratio” given by $exp(-k_{\mathrm{off}}\times t)$, where $k_{\mathrm{off}}$ is the dissociation rate constant and $t$ is the washing time. In this paper, we mathematically considered the following possibility. When the washing/selection dynamics obeys the residual ratio $exp(-k_{\mathrm{off}}\times t)$ deterministically and mole fraction measurement for sampled sequences by next-generation sequencing (NGS) is performed ideally, the “relative value” of $k_{\mathrm{off}}$ for each of high-ranking sequences can be estimated simultaneously. In addition to these, when the residual ratio for the whole ligand population is measured correctly, the “absolute value” for each sequence can be estimated. We deduced formulas to present the relative and absolute estimates, and mathematically analyzed the effect of fluctuations in the number of NGS reads on the estimates in details. These were confirmed by numerical simulations.