Breakdown of thermodynamic equilibrium for DNA hybridization in microarrays J. Hooyberghs, 1, 2, 3 M. Baiesi, 2 A. Ferrantini, 2 and E. Carlon 2 $^{1}$Flemish Institute for Technological Research (VITO), Boeretang 200, B-2400 Mol, Belgium $^{2}$Institute for Theoretical Physics, KULeuven, Celestijnenlaan 200D, B-3001 Leuven $^{3}$Hasselt University, Campus Diepenbeek, B-3590 Diepenbeek, Belgium (Dated: August 20, 2018) Test experiments of hybridization in DNA microarrays show systematic deviations from the equi- librium 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. PACS numbers: 87.15.v, 82.39.Pj arXiv:1001.2428v1 [q-bio.BM] 14 Jan 2010 DNA hybridization (the binding of two strands to form a double helix) in bulk solution has been extensively stud- ied in the past [1]. In this letter we discuss hybridization in DNA microarrays. Microarrays are high throughput devices which have been widely used to measure the ac- tivity of genes at a genome wide level. In a microarray singled stranded DNAs are arrayed on a solid substrate in spots, each containing a specific sequence. Hybridization takes place between surface-bound sequences (referred to as probes ) and sequences in solution ( targets ) carrying a fluorophore. The amount of hybridized target is obtained from the emitted fluorescence from a given spot. Al- though hybridization in microarrays has attracted some interest in recent years its physical properties are still poorly understood (for reviews on the topic see, e.g., [2]). We demonstrate here that, contrary to a widespread be- lief, in DNA microarrays equilibration times may largely exceed typical experimental times. These claims are based on experimental results and are corroborated by the analysis of a kinetic model. FIG. 1: Plot of I/c as a function of ΔΔ 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 ∝ c in the whole intensity range. Deviations from the equilibrium isotherm I ∝ e − Δ G/RT are observed at high intensities. Inset: plot of each individual concentration. TABLE I: Target and probe sequences used in the experi- ments. All sequences have a 5’ to 3’ orientation. Target se- quences have a 20-mer poly(A) stretch attached to their 3’ end, which terminates with a Cy3 fluorophore. Probes have a 30-mer poly(A) stretch at their 3’ end, which is covalently linked to the microarray surface. Target sequences in solution 1. CTTTGTCGAGCTGGTATTTGGAGAACACGT 2. TCGAGCTGGTATTTGGAGAACACGT Probes at the microarray surface PM ACGTGTTCTCCAAATACCAGCTCGACAAAG 1MM ACGTGATCTCCAAATACCAGCTCGACAAAG ACGTGCTCTCCAAATACCAGCTCGACAAAG ACGTGGTCTCCAAATACCAGCTCGACAAAG . . . 2MM ACGTGATCTCCCAATACCAGCTCGACAAAG . . . The experimental setup is shown in Table I and ex- tends that of Ref. [3]. A single sequence is present in solution: either a 30-mer or a 25-mer. The surface probe sequences are perfect matching, with one or two mis- matches. The mismatches can be of different nature and they are at different positions along the sequence [4]. In total there are 1006 different probe sequences [3]. Cus- tom arrays containing spots with the probe sequences of Table I were purchased from Agilent Technologies. We used 15K slides which accommodate 15 replicas of the 1006 sequences. The analysis is performed on the me- dian intensities over the replicas. The standard Agilent protocol (except for target fragmentation) and Agilent buffers [5] were used. The temperature is 65 ◦ C. Figure 1 shows a plot of I/c (the intensity divided by the target concentration) vs. ΔΔ G for four experiments at different concentrations using the setup of Table I (for the 30-mer target). The variable ΔΔ G ≡ Δ G$_{PM}$ − Δ G is the difference in hybridization free energies between a -7 -6 -5 -4 -3 -2 -1 0 10 0 10 1 10 2 10 3 10 4 10 5 I -7 -6 -5 -4 -3 -2 -1 0 G (kcal/mol) 10 0 10 1 10 2 I/c slope 1/RT PM