The probing of processes below micrometer length scales requires new types of nanosensors for a nanosensor to be useful the interplay between theory and experiments is crucial for accessing the fundamental physical and chemical parameters of interest. In this talk two different theoretical nanosensor problems are investigated.
(I) Utilizing fluorophore-quencher dressed DNA constructs for nanosensing applications: An important feature of double-stranded DNA is the ease with which its component strands can come apart and rejoin without damaging the chemical structure of the two single-strands. It has been demonstrated recently, by fluorescence correlation methods, that the fluctuations of DNA-bubbles (the DNA breathing) can be explored on the single molecule level using fluorophore-quencher dressed DNA constructs (Ref. ). We have developed a new discrete dynamical description of the DNA breathing dynamics in terms of a master equation (Ref. ). Employing recent experimental DNA stability data we calculate and experimentally measurable quantities such as the autocorrelation function of a fluorophore-quencher labeled basepair and the distribution of DNA bubble relaxation times these quantities are found to be depend on temperature, NaCl concentration, and DNA sequence, allowing for possible nanosensor applications. Good agreement with the experimental results in Ref.  is found.
(II) Tagged particle motion in 1d systems (single-file diffusion): Excluded volume effects (i.e. particles cannot pass each other) are pronounced in a system of diffusing particles in one dimension. Of particular interest is the diffusive motion of a tagged particle (experimentally accessible through fluorescent labeling techniques) in such a system it has been found previously (theoretically and experimentally) that the mean square displacement for a tagged particle scales as t^(1/2) (single-file diffusion), rather than t as for unconstrained diffusion. The prefactor in front of the t^(1/2) depends in a specific way on the concentration of particles, thereby allowing for the the tagged particle to serve as a nanosensor. The result above is valid for an infinite system we have recently investigated (Ref. ) the case of N diffusing excluding particles in a "box" of FINITE size, and find that the t^(1/2) behaviour then represents a quasiasymptotic regime, whereas for very long times a (non-trivial) equilibrium distribution for the tagged particle position is reached. In a wider perspective, the use of labeled particles is of much use for studying biological systems therefore understanding how the motion of such particles correlate with its environment is the key for being able to use these particles as nanosensors in a quantitative fashion.
 G. Altan-Bonnet, A. Libchaber and O. Krichevsky, Phys. Rev. Lett. 90, 138101 (2003).
 T. Ambjornsson, S.K. Banik, O. Krichevsky and R. Metzler, Phys. Rev. Lett. 97, 128105 (2006).
 L. Lizana and T. Ambjornsson, in preparation.