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An unstructured model is developed to describe the growth and product formation behavior of a recombinant yeast Saccharomyces cerevisiae using beta-galactosidase as a model protein. The model shows good agreement with the experimental data over a range of conditions. It also accurately predicts the effect of growth rate on yield coefficient and gene expression. The simplicity and accuracy of the model make it suitable for designing and implementing control and optimization strategies for the production of recombinant proteins at large scale.