  Despite tremendous potential of highly sensitive electronic detection of
bio-molecules by nanoscale biosensors for genomics and proteomic applications,
many aspects of experimentally observed sensor response (S) are unexplained
within consistent theoretical frameworks of kinetic response or electrical
screening. In this paper, we combine analytic solutions of Poisson-Boltzmann
and reaction-diffusion equations to show that the electrical response of
nanobiosensor varies logarithmically with the concentration of target
molecules, time, the salt concentration, and inversely with the fractal
dimension of sensor surface. Our analysis provides a coherent theoretical
interpretation of wide variety of puzzling experimental data that have so far
defied intuitive explanation.
