In this study, the biophysical factors underlying the irregular spike patterns produced by neurons in the neocortex, whose cause and function are not fully understood yet, are investigated. In the experimental studies in the literature, it has been proposed that neocortical neurons are subject to high background activity. Thereby, the postsynaptic cortical neuron, used in the study, is modeled as a single-compartment neuron which receives random inputs from a large number of excitatory presynaptic neurons. Furthermore, synaptic transmission lines in the model are designed to include the short-term synaptic depression mechanism. In order to examine the regularity of spike trains in postsynaptic neuron having fix and adaptive threshold, the coefficient of variation of interspikes intervals are computed. The obtained results show that short-term synaptic depression and adaptive threshold mechanisms might be candidate mechanisms explaining the irregular firings in cortical neurons.