The differences between hybridiza- tion signals for probe pairs corresponding to the same gene. (A) Expression levels (signal from a spot divided by the total signal from the microarray) after hybridizing cDNA targets from mouse cerebral cortex or thymus overnight. (B) Signal ratios for pairs of probes to mutual genes in cerebral cortex and in thymus. (C) Signal ratios between cerebral cortex and thymus for each probe, deduced from panel A. Values are from three independent microarray experiments. 

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... the considered probe-target. Equation 2 is true also in case of diffusion-limited kinetics in spite of a different interpretation of effective rate constants (14). It is well known that the forward rate constants k ass are very similar for perfect match (perf) and for mismatch (mism) duplexes, while reverse rate constants k diss may differ considerably (9,15,16). Typically, k diss (perf) << k diss (mism), indicating that perfect duplexes are much more stable than mismatch duplexes formed upon cross-hybridization (16,17). Thus, the equilibration time τ is longer for perfect duplexes than for mismatch duplexes (see Equation 2 and Reference 9). It was shown both theoretically (10,18) and experimentally (19) that at early stages of hybridization the highest concentration species dominate (either specific or non-specific), while at later stages the highest affinity species displace non-specific binding. Considerable amount of cross-hybridization (non- specific binding) is present under non- equilibrium conditions (9,20). The possible formation of secondary structures in the probes and in the targets can influence both the rate and the extent of hybridization. The kinetic effects of secondary structures are documented in a number of studies (21,22). To model the on-chip hybridization kinetics, we used oligonucleotide targets that were strictly complementary to the oligonucleotide probes immobilized on the NeuroTrans microarray. The linear dependence (Eq. 2) of the hybridization rate (1/ τ ) on target concentration c allows to measure k diss and K and then to deduce τ at the cDNA target concentrations used during gene expression experiment. Thermodynamic stability of the hybridized duplexes was estimated in a separate experimental study. Oligonucleotides listed in Table 1 were spotted onto custom microarrays. These microarrays were hybridized with Texas Red-labeled 50-mer oligonucelotide targets complementary to immobilized probes until equilibrium was reached. Rather high oligonucleotide target concentration (10 nM) was chosen to ensure fast attainment of hybridization equilibrium. Hybridization was performed in the same buffer as the one used for cDNA hybridization. On- chip melting of the duplexes was then recorded. Normalized melting curves are shown in Figure 2. Equilibrium melting temperatures (T m ) obtained by fitting the theoretical equation for the occupation level (12): to experimentally obtained melting curves are represented in Table 2. However, the similarity of melting curves observed in the thermodynamic experiments does not guarantee the identity of hybridization kinetics. An example using the experimental data for the probe pair 22-23 is represented in Figure 3. Figure 3A shows the difference in on-chip normalized kinetic curves for probes 22 and 23 recorded at target concentrations 0.05, 0.1, 0.25, and 1 nM. The dependence of hybridization signal ratios between probes 22 and 23 on time is represented in Figure 3B. At high target concentrations (1 nM), the equilibration time was short, and the final value of the ratio between probe 22 and probe 23 was close to 1 (Figure 3B). For lower target concentrations (0.1 and 0.25 nM), because of the difference in hybridization kinetics between probes 22 and 23, at the beginning of hybridization, the signal ratio was high, especially at concentration 0.1 nM. However, when approaching equilibrium, the ratio decreased to smaller values close to 1. At the lowest target concentration (0.05 nM) even after 50,000 s of hybridization, the ratio 22/23 was only approaching 1 (Figure 3B). For a detailed study of the kinetic effects, we have measured the on-chip hybridization kinetics of Texas Red- labeled 50-mer oligonucleotide targets at four concentrations: 0.05, 0.1, 0.25, and 1 nM. Results of fitting (K and k diss values) are listed in Table 2. These experiments allowed the calculation of τ as well as the modeling of hybridization kinetic curves at any target concentration. As an example we simulated the kinetic curves for 0.01 and 0.005 nM target concentrations, using Equation 1, and K and k values listed in The discrepancy between hybrid- ization signals obtained from different probes corresponding to the same gene is a problem for gene expression analysis. Except for the well-known alternative splicing and stable secondary conformation of cDNA targets, some other factors could influence micro- array expression results. To analyze these factors we performed thermo- stability study and analysis of on-chip hybridization kinetics at four concen- trations of complementary oligonucel- otide targets: 1, 0.25, 0.1, and 0.05 nM. Theoretical analysis applied to our on- chip kinetics data allowed estimation of kinetic behavior at target concentrations corresponding to cDNA concentrations in gene expression experiments. The probes selected for the study showed high hybridization signals as well as a significant difference between probes corresponding to the same gene (Figure 1). Figure 1B indicates at least a 2-fold difference in the hybridization signals for each pair of probes in cerebral cortex and/or thymus. When the difference is the same for both tissues, it is most probably caused by different secondary structures of the probes or/and of the targets. Such a case makes no confusion in the interpretation of the expression data. However, several probe pair ratios were found to differ in cerebral cortex and thymus (probes 3-4, 7-8, 7-9, 14-15, 18-19, 20-21, 22- 23, 28-29) (Figure 1B). This entailed a difference in expression level ratios between cerebral cortex and thymus depending on the probe (Figure 1C). This difference could be due to the presence or absence of alternative transcripts in cerebral cortex or thymus that would correspond to one probe or to the other. Indeed probes from pairs 19- 18, 20-21, 22-23, and 29-28 map either to different exons or to alternative 5 ′ or 3 ′ untranslated regions (UTRs) in two databases (www.ensembl.org; genome. ewha.ac.kr). However, for pairs 3-4, 14- 15, and 27-28, the two probes mapped to the same transcript. Alternatively, the observed tissue-dependent variations in signal ratios between two probes corresponding to the same gene could result from differences in hybridization kinetics at different cDNA target concen- trations. In addition, kinetic properties of the probes could be different within the same microarray. Thus, if a gene is highly expressed, hybridization signals at the end of the experiment may reach saturation levels. In this condition, signal ratio between oligonucleotide pairs will only depend on the equilibrium binding constant K of on-chip duplex formation (see above). However, for low-copy genes, hybridization signals might be rather far from saturation, and thus hybridization signal ratios will depend on the hybridization time and target concentration. To illustrate this, we performed on-chip kinetics analysis at different target concentrations and modeled the behavior of the duplexes. We first analyzed the temperature stability of on-chip formed duplexes. The experimental data (Figure 2) demon- strate that thermodynamic stability of the duplexes, including also the enthalpy Δ H of duplex formation, reflected by the shape of the melting curves, is similar for all immobilized probes tested. The minor differences observed cannot explain the difference in hybridization signals of oligonucle- otide probes belonging to the same gene. In addition, the experimental data confirmed the correct design of oligonucleotide probes and the absence of degradation of either probes or targets. However, the similarity of melting curves does not guarantee the identity of hybridization kinetics. Indeed, probes 22 and 23 have similar melting curves but different hybridiza- tions curves (Figure 3, A and B). This suggests that signal ratios between the two probes depend on target concen- tration and hybridization time. Based on the kinetic data obtained at higher concentrations of targets using Equations 1 and 2, it was possible to model the kinetics behavior of the duplexes at target concentrations corre- sponding to real cDNA hybridization experiments. DNA target concentration in biological samples was estimated using the data of Reference 23. Approximately 10 μ g RNA are typically used for microarray experiments. This amount corresponds to RNA quantities contained in 10 6 cells. The copy number of single genes in a cell varies from 1 to 10 4 , and the efficiency of reverse transcription is about 20 % (24). Thus, the expected concentration of cDNA in 20 μ L hybridization solution is 10 -14 to 10 -10 M. Unfortunately, the on-chip kinetic measurements at concentrations lower than 5 × 10 -11 M (0.05 nM) are hardly feasible because the fluorescent hybridization signals are too low as compared with the fluorescence of the hybridization solution. Thus, according to Equation 2, using the linear depen- dence of 1/ τ value measured at concen- trations 0.05, 0.1, and 0.25 nM, we can estimate the K and k diss values for each probe-target pair (Figure 4 and Table 2). Based on these data, we were able to extrapolate the kinetics behavior at low target concentrations after 15 h hybrid- ization and at saturation (Figure 5, A and B). Figure 4 shows that 15 h (54,000 s) hybridization time was not always sufficient for reaching at least 70 % of maximal hybridization signal, especially at 0.005 nM target concentration (probes 6, 12 14, 18, 23, and 28). Obviously, for target concentration below 0.005 nM, the hybridization kinetics would be even slower. Thus, one can expect that after hybridization times used in classical experiments (roughly 15 h), the majority of hybridization signals is rather far from saturation level. While at equilibrium (saturated signals) a decrease in target concen- tration leads to an increase of the absolute value of the hybridization signal ratio (Figure 5B), at non-equilibrium conditions (15 h of hybridization), ...