The bursting of action potential and sparse activity are ubiquitously observed in the brain. Although the functions of these activity modes remain to be understood, it is expected that they play a critical role in information processing. In addition, the functional role of retrograde signalling in neural systems is under intensive research. Therefore, we propose a bio-inspired neural network that is capable of demonstrating these activity modes as well as shifting themselves from normal to bursting or sparse modes by changing model parameter values. Accordingly, we model diffused retrograde signalling with different activity patterns in dendrites and presynaptic neurons. Using in a three-layered spiking neural network, simulation studies are conducted using different conditions and parameter values to find factors underlying the change in firing rate of output neurons. Our findings propose the application of retrograde signalling as a known synaptic mechanism for the development of artificial neural systems to encode environmental information by different spiking modes.