In our previous work, we have designed and implemented a synthetic metabolic pathway for 1,2,3-trichloropropane (TCP) biodegradation in Escherichia coli. Significant effects of metabolic burden and toxicity exacerbation were observed on single cell and population levels. Deeper understanding of mechanisms underlying these effects is extremely important for metabolic engineering of efficient microbial cell factories for biotechnological processes. In this paper, we present a novel mathematical model of the pathway. The model addresses for the first time the combined effects of toxicity exacerbation and metabolic burden in the context of bacterial population growth. The model is calibrated with respect to the real data obtained with our original synthetically modified E. coli strain. Using the model, we explore the dynamics of the population growth along with the outcome of the TCP biodegradation pathway considering the toxicity exacerbation and metabolic burden. On the methodological side, we introduce a unique computational workflow utilising algorithmic methods of computer science for the particular modelling problem.