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The Importance of Thermodynamic Equilibrium for High Throughput Gene Expression Arrays

Gyan Bhanot^*, Yoram Louzoun, Jianhua Zhu and Charles DeLisi

^* Institute for Advanced Study, Princeton, New Jersey 08540 and Computational Biology Center, IBM Research, Yorktown Heights, New York 10598; Department of Molecular Biology, Princeton University, Princeton, NJ 08540; and Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215

Correspondence: Address reprint requests to Gyan V. Bhanot, IBM Research, T. J. Watson Research Center, 347 Dodds Lane, Princeton, NJ 08540. Tel.: 609-497-0241; E-mail: gyan{at}us.ibm.com, gyanbhanot{at}hotmail.com.

We present an analysis of physical chemical constraints on the accuracy of DNA micro-arrays under equilibrium and nonequilibrium conditions. At the beginning of the article we describe an algorithm for choosing a probe set with high specificity for targeted genes under equilibrium conditions. The algorithm as well as existing methods is used to select probes from the full Saccharomyces cerevisiae genome, and these probe sets, along with a randomly selected set, are used to simulate array experiments and identify sources of error. Inasmuch as specificity and sensitivity are maximum at thermodynamic equilibrium, we are particularly interested in the factors that affect the approach to equilibrium. These are analyzed later in the article, where we develop and apply a rapidly executable method to simulate the kinetics of hybridization on a solid phase support. Although the difference between solution phase and solid phase hybridization is of little consequence for specificity and sensitivity when equilibrium is achieved, the kinetics of hybridization has a pronounced effect on both. We first use the model to estimate the effects of diffusion, crosshybridization, relaxation time, and target concentration on the hybridization kinetics, and then investigate the effects of the most important kinetic parameters on specificity. We find even when using probe sets that have high specificity at equilibrium that substantial crosshybridization is present under nonequilibrium conditions. Although those complexes that differ from perfect complementarity by more than a single base do not contribute to sources of error at equilibrium, they slow the approach to equilibrium dramatically and confound interpretation of the data when they dissociate on a time scale comparable to the time of the experiment. For the best probe set, our simulation shows that steady-state behavior is obtained in a relaxation time of 12–15 h for experimental target concentrations (10^-13 - 10^-14)M, but the time is greater for lower target concentrations in the range (10^-15–10^-16)M. The result points to an asymmetry in the accuracy with which up- and downregulated genes are identified.

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