Beneficial and deleterious mutations change an organism's fitness but the distribution of these mutational effects on fitness are unknown. Several experimental, theoretical, and computational studies have explored this question but are limited because of experimental restrictions, or disconnect with physiology. Here we attempt to characterize the distribution of fitness effects (DFE) due to mutations in a cellular regulatory motif. We use a simple mathematical model to describe the dynamics of gene expression in the lactose utilization network, and use a cost-benefit framework to link the model output to fitness. We simulate mutations by changing model parameters and computing altered fitness to obtain the DFE. We find beneficial mutations distributed exponentially, but distribution of deleterious mutations seems far more complex. In addition, we find neither the starting fitness, nor the exact location on the fitness landscape, affecting these distributions qualitatively. Lastly, we quantify epistasis in our model and find that the distribution of epistatic effects remains qualitatively conserved across different locations on the fitness landscape. Overall, we present a first attempt at exploring the specific statistical features of the fitness landscape associated with a system, by using the specific mathematical model associated with it.