We study the operation of a system where quantum dot (QD) and point contact (PC) defined in a two-dimensional electron gas of a high-mobility GaAs/AlGaAs heterostructure are capacitively coupled to each other and to metallic single electron transistor (SET). The charge state of the quantum dot can be probed by the point contact or single electron transistor. These can be used for sensitive detection of terahertz radiation. In this work, we explore an electrostatic model of the system. From the model, we determine the sensitivity of the point contact and the single electron transistor to the charge excitation of the quantum dot. Nearly periodic oscillations of the point contact conductance are observed in the vicinity of pinch-off voltage. They can be attributed to Coulomb blockade effect in a quasi-1D channel because of unintentional formation of small quantum dot. The latter can be a result of fluctuations in GaAs quantum well thickness.