Fig. 5.

Theoretical prediction (Eq. 8) for specificity as a function of the probe density. Specificity is defined as a ratio $f_{\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}\mathrm{t}}/f_{\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}\mathrm{t}}$ between the number of bound probes to “target” DNA ($\mathrm{\Delta }G=-8k_{\mathrm{B}}T$) and to “nontarget” DNA ($\mathrm{\Delta }G=-7k_{\mathrm{B}}T$). The blue (“short target”) curves are in the monovalent-binding regime ($k=1$ in ref. 8), while the red curves describe binding of “long targets” in the multivalent-binding regime ($k=10$). Here we have assumed that that target size scales with target length (or multiplicity) as $l_t\left(k\right)=k^{\nu }{l}_{t|k=1}$ with the self-avoiding walk scaling exponent $\nu =0.588$ and that the target concentration is $c_t=10^{-6}{c}_0/k$.