The hedgehog signaling cascade generates highly diverse, fine-tuned responses in response to the external stimulus by the sonic hedgehog (SHH) protein. This is required for the flawless functioning of the cell, its development, survival and proliferation; maintained through production of Glioma protein (GLI) and transcriptional activation of its target genes. Any change in the behavior of GLI response by ectopic expression of SHH or mutations in the core pathway components may cause serious consequences in the cell fate through rapid, uncontrolled and elevated production of GLI. Here, we present a simple but extensive computational model that considers the detailed reaction mechanisms involved in the hedgehog signal transduction and provides a detailed insight into regulation of GLI. For the first time, by explicit involvement of suppressor of fused (SUFU) and Hedgehog interacting protein (HHIP) reaction kinetics in the model, we try to demonstrate the vital importance of HHIP and SUFU in maintaining the graded response of GLI in response to SHH. By performing parameter variations, we capture the conversion of a graded response of GLI to an ultrasensitive switch under SUFU-deficient conditions that might predispose abnormal embryonic development and the irreversible switching response of GLI that corresponds to signal-independent pathway activation observed in cancers. © 2015 World Scientific Publishing Company.