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. 2005 Nov;89(5):2950-9.
doi: 10.1529/biophysj.104.058552. Epub 2005 Aug 26.

Competitive hybridization kinetics reveals unexpected behavior patterns

Ying Zhang  1 , Daniel A Hammer, David J Graves
Affiliations

Competitive hybridization kinetics reveals unexpected behavior patterns

Ying Zhang et al. Biophys J. 2005 Nov.

Abstract

Although the kinetics of hybridization between a soluble polynucleotide and an immobilized complementary sequence have been studied by others, it is almost universally assumed that the interaction between each probe/target pair can be treated as a separate event. This simplifies the mathematics considerably, but it can give a false picture of the extent of hybridization that one achieves at equilibrium as well as the relative quantities of each hybridized pair during the approach to equilibrium. Here we solve the relevant kinetics equations simultaneously using Mathematica as a simulation language. Among the interesting results of this study are that, for certain circumstances, the relative ratio of incorrect to correct hybrids can change dramatically with time; that the relative abundances of two pairs are not what one would expect based on their equilibrium dissociation constants; that the volume of a wash solution after hybridization can have a large effect on results; and the fact that a short wash is typically better than a long one. We show that an optimum wash time exists for a given set of conditions. In addition, the ratio of soluble to insoluble (spotted) molecules can influence results substantially. Finally, the true levels of rare transcripts can be masked by the presence of highly abundant ones. Code is supplied to enable others to study conditions beyond those presented in this article.

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Figures

FIGURE 1
FIGURE 1
(a) Time course for competitive hybridization for correct hybrids (CA) and incorrect hybrids (CB). Forward rate constants are equal to 1 and reverse constants are 0.01 and 0.1 respectively. (b) Similar plot but with forward and reverse constants for CB increased threefold. Note that in this latter case the incorrect hybrid can temporarily exceed the correct hybrid in concentration, although the eventual result is the same as in a.
FIGURE 2
FIGURE 2
(a) Time course for washing hybrids CA and CB with 100 times the initial hybridization volume using clean solution. (b) Note that an optimum time (maximum CA/CB ratio) exists for washing. Extended washing removes C from CA as well as from the incorrect CB. (c) For the case given by row 4 in Table 2, the CA/CB ratio changes from unfavorable to favorable before returning to an unfavorable value again at long times.
FIGURE 3
FIGURE 3
Time course for washing of hybridized species at 10,000 times the initial hybridization volume. Times shorter than the optimal value of 63 may be useful to prevent too much of the correct hybrid CA from dissociating.
FIGURE 4
FIGURE 4
Time course for a system with two soluble and two insoluble polynucleotides. C1 is the complement of A and C2 of B. However, C1 and cross-hybridize with B and C2 with A. Although only B hybrids are shown, the constants used are symmetrical so that C2B represents C1A and C1B represents C2A as well. (a) Results from the constants given in Table 3, row 1. (b) Results for Table 3, row 10.
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