Breakdown of thermodynamic equilibrium for DNA hybridization in microarrays

Test experiments of hybridization in DNA microarrays show systematic deviations from the equilibrium isotherms. We argue that these deviations are due to the presence of a partially hybridized long-lived state, which we include in a kinetic model. Experiments confirm the model predictions for the intensity vs free-energy behavior. The existence of slow relaxation phenomena has important consequences for the specificity of microarrays as devices for the detection of a target sequence from a complex mixture of nucleic acids.

Figure 1

Plot of $I/c$ as a function of $\Delta \Delta G$ for four different experiments at concentrations $c=2$, 10, 50 and 250 pM. The hybridization time is of 17 h. The “collapse” of the four data sets into a single curve demonstrates that $I\propto c$ in the whole intensity range. Deviations from the equilibrium isotherm $I\propto e^{-\Delta G/RT}$ are observed at high intensities. Inset: plot of each individual concentration.

Figure 2

Plot of intensity vs $\Delta \Delta G$ four experiments at different times with a 30-mer target and $c=50\text{pM}$. Dashed lines have slope $1/RT$, dotted lines have slope $\gamma /RT$ with $\gamma =0.32$. Solid lines are obtained from the solution of Eqs. (2, 3) using as parameters $k_1={10}^5{\text{M}}^{-1}{\text{s}}^{-1}$, $k_2=1{\text{s}}^{-1}$, $\gamma =0.32$, and $\Delta G_{\text{PM}}=-14.5\text{kcal}/\text{mol}$.

Figure 3

As in Fig. 2 for a target sequence of length 25. The target concentration is $c=500\text{pM}$.

Figure 4

The three-state model for hybridization in DNA microarrays is specified by the four rate constants.