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given sequence and the perfect match (PM) sequence. It is calculated from the nearest-neighbor parameters ob- tained from the analysis of microarray data, as discussed in Ref. [3] (the nearest-neighbor model assumes that Δ G can be written as a sum of dinucleotide terms [1]). Fig- ure 1 shows that the intensity is proportional to the con- centration for four orders of magnitude in I . In the low c limit, equilibrium thermodynamics predicts that 

where A sets the intensity scale, R is the gas con- stant and T the temperature. Eq. (1) is obtained from the c → 0 limit of the Langmuir isotherm (which was used in microarray data analysis [6–10]), but also from isotherms in which electrostatic effects are taken into ac- count [11] (electrostatic effects were experimentally ob- served at low ionic strengths [12]). In the latter Δ G con- tains a contribution from electrostatic interactions. For both isotherms, in the I ∝ c regime one expects a linear dependence of log I on Δ G (or ΔΔ G ). Fig. 1 shows that the experimental data are only in partial agreement with Eq. (1), which is drawn as a dashed line in the figure. 

We then extended the analysis at different hybridiza- tion times. Figure 2 shows a plot of I vs. ΔΔ G for a 30-mer target at four different times and for a concen- tration of 50 pM (the 17 h hybridization data are those already shown in Fig. 1). Once the desired hybridization time has been reached the experiment is stopped, the microarray washed and scanned to measure the emitted fluorescence from every spot. Experiments at different hybridization times thus require different slides. As the hybridization time increases, a larger fraction of the data aligns along a line with a slope 1 /RT , which shows that 

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the observed deviations from Eq. (1) are due to the break- down of thermodynamic equilibrium. Surprisingly, full equilibrium has not been reached here even after 86h. In Fig. 2(b,c,d) the data for log I align along two slopes: in the equilibrium regime the slope is 1 /RT (Eq. (1)), in the non-equilibrium regime the slope is smaller and appears to be constant in the course of time [13]. Hy- bridization data for the shorter target sequence (25-mer) are shown in Fig. 3. The agreement with Eq. (1) is over three orders of magnitude in the intensity scale at times > 3h. Hence equilibration is much faster for the shorter sequences. The experimental setup allows a detection of non-equilibrium effects as deviation from the 1 /RT line without the need, in principle, of a time series analysis. 

Hybridization of oligonucleotides in solution is usually described as a two state process. However, as will be shown, a two-state process cannot be reconciled with the experimental data shown in Fig. 2. During manufactur- ing the probes are tethered to the surface and can form a dense layer that slows down hybridization. Some of these effects have been discussed in Refs.[14, 15]. The typical distance between probes is 10 nm, and the length of a fully stretched 30-mer duplex is 10 nm and its thick- ness of 2 nm. Probe sequences in the experiment have also a poly(A) 30-mer spacer (see Table I). Therefore a single target molecule can interact with more than one probe. Taking this into account, we have extended the two state hybridization model with an additional inter- mediate state (Fig. 4). Indicating with θ$_{1}$ and θ$_{2}$ , the fraction of partially and fully hybridized probes on a mi- croarray spot, the kinetics of these reactions is given by 

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where c is the target concentration in solution and k$_{1}$ , 

