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Exploring Sequence Space to Identify Binding Sites for Regulatory RNA-Binding Proteins
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A mathematical analysis of multiple-target SELEX.

Yeon-Jung Seo1, Shiliang Chen, Marit Nilsen-Hamilton

  • 1Department of Mathematics, Iowa State University, Ames, IA 50011, USA. syeonj@iastate.edu

Bulletin of Mathematical Biology
|January 16, 2010
PubMed
Summary

Systematic Evolution of Ligands by Exponential Enrichment (SELEX) is a method for isolating nucleic acids with specific binding properties. This study analyzes multi-target SELEX, revealing conditions for predictable outcomes and suggesting single-target SELEX may be more effective.

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Area of Science:

  • Biochemistry
  • Molecular Biology
  • Computational Biology

Background:

  • SELEX (Systematic Evolution of Ligands by Exponential Enrichment) is a powerful technique for isolating nucleic acid ligands with specific biochemical activities.
  • Mathematical models have been developed to analyze SELEX, including multi-target variations.

Purpose of the Study:

  • To analyze the mathematical behavior of multi-target SELEX as a dynamical system.
  • To characterize the limiting states of multi-target SELEX and their dependence on initial conditions.
  • To identify conditions ensuring convergence to a unique subset of nucleic acids.

Main Methods:

  • Revisiting and analyzing the mathematical framework of Vant-Hull et al. (1998) for multi-target SELEX.
  • Modeling the process as a discrete dynamical system.
  • Deriving a structure condition on the affinity matrix for predictable convergence.

Main Results:

  • The iteration scheme for multi-target SELEX is shown to be convergent.
  • A simplified algorithm is presented.
  • A structure condition on the affinity matrix guarantees convergence to a unique subset of nucleic acids, dependent on initial conditions and overall association constant.

Conclusions:

  • The effectiveness of multi-target SELEX may be limited compared to single-target SELEX unless specific thermodynamic properties are understood.
  • The study provides a mathematical framework for understanding and potentially optimizing multi-target SELEX processes.
  • Predictable outcomes in multi-target SELEX depend on specific structural properties of the target affinity matrix.