nomenon known as cross-hybridization. For an optimal functioning of the microarrays it is then desirable to work under equilibrium conditions [8]. Several parameters may influence the relaxation time as temperature, salt and buffer conditions. The experimental setup discussed in this paper provides a good test of equilibrium (single line vs. broken line in a I vs. ΔΔ G plot) and can be used to investigate the best working conditions for hybridization. We thank Karen Hollanders (VITO) for help with the experiments. We acknowledge financial support from Re- search Fundation – Flanders (FWO) G.0311.08 and from KULeuven OT/07/034A. Δ G$_{PM}$ , as the method of Ref. [3] does not provide abso- lute Δ G for a sequence but only ΔΔ G , i.e. differences in free energies with respect to a perfect match hybridiza- tion. In addition, in the fit we adjusted the constant A ( I = Aθ$_{2}$ ) as we note in the experimental data a global decrease of the intensity scale. This is probably due to some degradation of the fluorophores or of the target and probe strands (as depurination, the loss of purines, which alters the binding energies of the involved strands). The overall decrese in intensity occurs both for the 25-mer and the 30-mer sequences. In the latter the effect is somewhat stronger, especially at longer hybridization times. Eq. (7) predicts that the relaxation time is a function of Δ G , Δ G ′ and k$_{2}$ . We can use this equation to compare the ratio between the times for a L = 30 and L = 25 tar- gets. Consider the same probe sequence hybridizing to the two targets. Assuming Δ G $^{′}$( L = 30) ≈ Δ G $^{′}$( L = 25) and using as estimate of the difference in binding en- ergies between Δ G ( L = 30) − Δ G ( L = 25) ≈ − 2 . 5 kcal/mol [17], we get from Eq. (7) a decrease of a factor exp(2 . 5 /RT ) ≈ 40 in the relaxation time. In addition one also expects k$_{2}$ ( L = 25) > k$_{2}$ ( L = 30) which decreases the relaxation time even further. The similarities be- tween Fig. 2(c) and Fig. 3(a) suggest that the relaxation time ratio between 25-mers and 30-mers is approximately 25, which is the same order of magnitude just obtained from Eq. (7). Since typical biological experiments in- volve target strands of lengths 30-50, the breakdown of equilibrium shown here may occur in many different mi- croarrays platforms and in biological experiments, and could involve even longer relaxation times. Summarizing: We showed that hybridization in DNA microarrays under standard conditions is characterized by relaxation times which may largely exceed the ex- perimental time. In the non equilibrium regime the intensities are distributed as e − γ Δ $^{G/RT}$, with γ < 1. This is equivalent to introducing an effective tempera- ture T$_{eff}$ = T/γ > T . Interestingly effective temperatures were used as adjustable phenomenological parameters to fit biological microarray data [6, 9]. This work provides an insight on the origin of these. The breakdown of equilibrium implies lower specificity of the microarrays as devices for the detection of a de- sired sequence from a complex mixture. To see this con- sider a probe at the microarray surface and two sequences at equal concentration in solution: one perfect matching with the probe and one with a mismatch. In the equilib- rium regime the two sequences hybridize to the probe with a probability ratio e (Δ G$_{PM}$ − Δ G$_{MM}$ ) /RT ≈ 0 . 05, where we have used a typical value Δ G$_{MM}$ − Δ G$_{PM}$ ≈ 2 kcal/mol [3] and a temperature of T = 65 ◦ C. In the nonequilibrium regime, due to the presence of a factor γ < 1 in the exponential the ratio is about 0 . 4 (tak- ing γ = 0 . 32). Therefore in the non-equilibrium regime a significant fraction of a measured signal may be due to hybridization to non-complementary targets, a phe- [19] G. A. Held, G. Grinstein, and Y. Tu, Nucleic Acids Res. 34 , e70 (2006); C. J. Burden, Y. Pittelkow and S. R. Wilson, J. Phys.: Cond. Matt. 18 , 5545 (2006). [18] C. R. Cantor and P. R. Schimmel, Biophysical Chemistry, part III: The behavior of biological Macromolecules (W. H. Freeman and Company, 1980). [17] We estimated Δ G PM ( L = 30) = − 14 . 5kcal/mol from the fits of Fig. 2, using extensivity we expect Δ G PM ( L = 25) ≈ 0 . 83Δ G PM ( L = 30) = − 12 kcal/mol [16] M. Glazer et al., Anal. Biochem. 358 , 225 (2006). [15] M. F. Hagan and A. K. Chakraborty, J. Chem. Phys. 120 , 4958 (2004). [14] A. W. Peterson, R. J. Heaton, and R. M. Georgiadis, Nucleic Acids Res. 29 , 5163 (2001). [13] We note that the slope in the non-equilibrium regime of Fig. 1(a) is somewhat smaller than that of (b,c,d). This is probably due to the protocol followed: at time t = 0 both the solution containing the target molecules and the array are at room temperature. They are then placed into an oven for the duration of the experiment at a temperature T = 65 ◦ C. 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