Subtractive SELEX against two heterogeneous target samples: Numerical simulations and analysis

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Abstract

Systematic evolution of ligands by exponential (SELEX) is a revolutionary technology that integrates combinatorial chemistry with high throughput screening to generate from synthesized nucleic acid ligand libraries the high affinity nucleic acid ligands (aptamers) for interesting targets. Recently, the SELEX experiments have advanced from targeting the ligand libraries by a single purified target to multiple heterogeneous target samples. Having the potential of bringing enormous technical and economical advantages to drug discovery, the new application suffers from unpredictable performances. To gain an insight of the new method, we develop a computer model to numerically analyze the subtractive SELEX alternatively against two distinct heterogeneous samples of unknown targets. The model features the discretization of ligand library, the ligand–target binding equilibrium equations, and the separation efficiency of bound and unbound ligands in experiments. By computer simulations, we investigate how aptamers for desired targets embedded in undefined target mixtures are generated under different experimental conditions. We find the iterative screening scheme is fundamentally capable of developing desired aptamers. On the other hand, target sample configuration and separation efficiency may all together significantly diversify the screening dynamics and results.

Introduction

Systematic evolution of ligands by exponential (SELEX) enrichment or in vitro selection is a nucleic acid-based combinatorial chemistry technique that generates high affinity nucleic acid ligands (aptamers) for proteins or other biological targets [1], [2]. In a typical SELEX experiment, a library of more than 1013 different single-stranded nucleic acid ligands is prepared and incubated with a purified target in a binding buffer. Following a partition process that separates bound and unbound ligands at the binding equilibrium, the target-binding ligands are selected and amplified by the polymerase chain reaction (PCR). The amplified ligands are then put through the same series of experimental steps. The operation cycle repeats several times until the library is enriched with aptamers. Aptamers generated by the SELEX experiments also exhibit the binding specificity to distinguish between similar targets such as homologous proteins [3], [4]. Since its development in early 1990s, the scheme has been applied for finding new aptamers for a variety of biological targets with potential diagnostic and therapeutic values [5], [6], [7], [8], [9].

The power of SELEX arises from its ability of generating aptamers without knowing the target structures. Conventional SELEX experiments screen nucleic acid libraries against purified targets. However, purifying a target implies knowing some properties of the target. In the meantime, a few reports [10], [11], [12] indicate that the SELEX experiments can develop aptamers by screening the ligand library against complex target mixtures (the complex SELEX). The generation of aptamers for complex targets opens the possibility of screening the huge amount of pharmaceutically interesting targets in a highly parallel manner. More interestingly, by modifying the protocol of complex SELEX, the experimentalists may develop aptamers for targets embedded in target mixtures for which purification would be difficult, or targets even not known (e.g., the tumor-associated antigens on tumor cells are widely assumed to exist but it is not known what these antigens are). For example, assume that there are two distinct biological samples that contain protein targets. In the experiment, the nucleic acid ligands are incubated with one sample to extract the bound ligands at the binding equilibrium. The extracted ligands are then incubated with the other sample, and the bound ligands are extracted and amplified to form a new library. It is comprehensible that the two-sample complex SELEX experiment may generate aptamers for targets existing in both target samples in some rounds of screening. Another example is the two-sample subtractive SELEX. In the experiment, the ligands are incubated with one sample (the subtractive target sample) to remove the bound ligands from the library. The unbound ligands are selected and incubated with the other sample (the selective target sample). The target-binders are then extracted and amplified for a new round of screening. The goal of the experiment is to develop aptamers for some targets that are in the selective target sample without being in the subtractive target sample. In both examples, aptamers are developed for conceptually specified targets (e.g., proteins that are common or unique in target samples). We illustrate the two-sample SELEX protocols in Fig. 1. Recently, Wang et al. [13] reported a cell-based subtractive SELEX experiment in which DNA aptamers binding to differentiated cells but not regular cells are selected. In the experiment, parental PC12 cells were mixed with the random single-stranded DNA library to remove their binders prior to the selection of ligands for differentiated PC12 cells. The library was enriched with aptamers binding only to differentiated PC12 cells in several rounds of screening. In general, one must know the behaviors of the experiment in a rather wide range of experimental conditions to make the two-sample SELEX useful.

As the SELEX technology advances, theories have been developed to understand the sophisticated experimental basics [14], [15], [16]. Vant-Hull et al. [16] first modeled and numerically analyzed the complex SELEX. To facilitate the computation, they conceptually discretized the library into subpools of ligands with similar affinities for any target in the target mixture. Since the computer memory required for simulations grows exponentially with targets by this way of subpooling (see more detailed discussion in Section 4), they restricted their investigations primarily to experiments with a couple of targets. Their simulated results were therefore insufficient to shed light on the SELEX experiments if the target samples are highly complex (e.g., samples from crude cell extracts of Escherichia coli may contain more than hundreds of target proteins). To assess the complex SELEX against many targets, Chen et al. [17] defined and utilized the characteristic affinity of ligand for targets to discretize the ligand library. By a computer model built with their ligand subpools, they simulated the complex SELEX against up to a few hundred targets. In this work, we generalize the modeling strategy by Chen et al. for the two-sample experiments. We develop a new computer model applicable for simulating the two-sample SELEX against complex target samples. Due to the page limitation, and the parallelism of two-sample complex SELEX and subtractive SELEX, we will present the modeling and numerical analysis for the latter only. Although published data on the subtractive SELEX hardly exist, we incorporate the target binding property of the initial ligand library, the target abundance, and the efficiency of separating bound and unbound ligands during the experiment into our model as they have shown importance for one-sample experiments. We examine by simulations the effects of these factors on subtractive SELEX against complex target samples with randomly generated heterogeneous configurations.

The paper is organized as follows. Section 2 presents the modeling of subtractive SELEX, computational algorithm, and simulation specifications. Section 3 presents simulation results and analysis. This is followed by remarks in Section 4. Among other comments, we compare the current approach with that of Vant-Hull et al., and validate our simulations. Some results used in the main part of the paper are derived in the Appendix A.

Section snippets

Discretization of ligand library

In the subtractive SELEX, a huge random nucleic acid library (>1013 different sequences) is prepared and incubated alternatively with two distinct target samples S1,S2 to select ligands for conceptually specified desired targets. Let ω be a nucleic acid ligand in the library, and Pj, where j=1,,M, be targets from either of S1 or S2. Assume both subtraction and selection of ligands are carried out through the ligand–target binding equilibrium process: ω+PjωPj. The mechanism of formation of

The evolution of ligands in the subtractive SELEX

We first demonstrate the evolution of ligands in the subtractive SELEX experiment in Fig. 2. In the simulation, S1 contains seven targets, and S2 contains nine targets. The fractions of Pj in S1,S2 are randomly assigned as in Table 1. As there are M=10 distinct targets from the two samples, Ltot is subdivided into Lijtot with i,j=1,,10. These partial subpools are represented by squares in the basis of bar-plots. We note that ligands in squares of each row (subpool) have approximately equal

Discussion

The subtractive SELEX is a methodology with the potential of generating aptamers for conceptually specified targets embedded in target mixtures. Vant-Hull et al. simulated the subtractive SELEX experiments by pooling ligands with similar affinities for any target in target samples into subpools. For example, if there are two targets Pj, j=1,2, from S1 or S2, and for each Pj the ligands are divided into 10 groups {ω:ξi-1kj(ω)<ξi}, i=1,,10, the ligands are then pooled into 102 subpools liitot={

Acknowledgment

This research was supported by grants of National Science Council, Taiwan (NSC 93-2115-M-005-007) to Chi-Kan Chen.

Chi-Kan Chen received his Ph.D. degree in 1998 from the University of Utah. He worked as a postdoctoral research fellow at the University of Utah, a visiting assistant professor at Brigham Young University, and an assistant professor at the University of Central Arkansas. He is currently an assistant professor at National Chung Hsing University in Taiwan. His research areas include the application of mathematical modeling and computational methods to biosciences, statistical machine learning

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    At last, our stochastic simulation approach can be used to analyze more complicated SELEX experiments, e.g., the subtractive SELEX [24], and, with possible minor modifications, address problems in other areas where the evolution principles are implemented on huge populations against multiple targets.

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Chi-Kan Chen received his Ph.D. degree in 1998 from the University of Utah. He worked as a postdoctoral research fellow at the University of Utah, a visiting assistant professor at Brigham Young University, and an assistant professor at the University of Central Arkansas. He is currently an assistant professor at National Chung Hsing University in Taiwan. His research areas include the application of mathematical modeling and computational methods to biosciences, statistical machine learning and its application, and time-evolution differential equations and their applications. He is the author who has made the actual contribution to this paper, and with whom all questions about this paper should correspond.

Tzy-Ling Kuo received her M.S. degree from National Cheng Kung University in Taiwan. She is a graduate student on her Ph.D. program at National Chung Hsing University in Taiwan.

Po-Chou Chan received his M.S. degree from National Chung Hsing University in Taiwan. He is an instructor at Central Taiwan University of Science and Technology in Taiwan.

Lung-Ying Lin received his Ph.D. degree from Chicago University. He is a professor at Central Taiwan University of Science and Technology in Taiwan.

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