Brush Effects on DNA Chips: Thermodynamics, Kinetics and Design Guidlines

In biology experiments, oligonucleotide microarrays are contacted with a solution of long nucleic acid (NA) targets. The hybridized probes thus carry long tails. When the surface density of the oligonucleotide probes is high enough, the progress of hybridization leads to the formation of a polyelectrolyte brush due to mutual crowding of the NA tails. The free energy penalty associated with the brush modifies both the hybridization isotherms and the rate equations: the attainable hybridization is lowered significantly as is the hybridization rate. While the equilibrium hybridization fraction, $x_{eq}$, is low, the hybridization follows a Langmuir type isotherm, $x_{eq}/(1-x_{eq}) = c_t K$ where $c_t$ is the target concentration and $K$ is the equilibrium constant smaller than its bulk value by a factor $(n/N)^{2/5}$ due to wall effects where $n$ and $N$ denote the number of bases in the probe and the target. At higher $x_{eq}$, when the brush is formed, the leading correction is $x_{eq}/(1-x_{eq}) = c_t K \exp [ - const' (x_{eq}^{2/3} - x_B^{2/3})]$ where $x_B$ corresponds to the onset of the brush regime. The denaturation rate constant in the two regimes are identical. However, the hybridization rate constant in the brush regime is lower, the leading correction being $\exp [- const' (x^{2/3} - x_B^{2/3})]$.