way of detecting a transition from the c to the ot state the o state which is not associated with the target contributes to a u201c background fluorescence u201d the equations below describe mathematically the corresponding coupled equilibria the four input parameters are the initial looped probe concentration p 0 initial target concentration t 0 and the relevant equilibrium constants in the most general situation the target is permitted to interact not only with the open but also directly with the closed state of the looped probe in a displacement reaction so as to form a probe target complex for molecular beacon probes in solution u2014 beacons in contrast to the looped probes considered here are designed to form a probe target complex by way of the loop sequence and thus do not impose molecular stringency u2014 bonnet et al reported a mathematical model applicable under conditions of excess target see bonnet et al proc natl acad sci usa vol 96 pp 6171 6176 may 1999 biophysics here we consider the more general situation i e that there is usually low concentration of target and excess probe in assays using solid phase immobilized probes to detect targets in solution consider first looped probes exposed to targets the probes capable of adopting one of three states i a duplex state associated with target ii a closed state the complementary stem subsequences forming a duplex and iii an open state for example in the form of an open random coil prevalent for example at high.