A Linear Mixed Effects Model for Evaluating Synthetic Gene Circuits

A significant advancement in synthetic biology is the development of synthetic gene circuits with predictive Boolean logic. However, there is no universally accepted or applied statistical test to analyze the performance of these circuits. Many basic statistical tests fail to capture the predicted logic (OR, AND, etc.) and most studies neglect statistical analysis entirely. As synthetic gene circuits shift toward advanced applications, primarily in computing, biosensing, and human health, it is critical to standardize the statistical methods used to evaluate gate success. Here, we propose the application of a linear mixed effects model to analyze and quantify genetic Boolean logic gate performance. First, we analyzed 144 currently published Boolean logic gates for trends and used unsupervised machine learning (k-means clustering) to validate the statistical model. Next, we utilized the model to generate estimates for the fixed effect of the ON state, β, as a general descriptor of the Boolean nature of a circuit and used Monte Carlo simulations to recommend sample sizes for evaluating gate performance. Finally, we examined β as a holistic metric for circuit performance using a series of nested repressor OR gates with intentionally degraded performance. We observed a linear correlation between β and the predicted translation rate, highlighting the use of β for the forward design of new Boolean gates. In summary, we utilized a linear mixed effects model to describe synthetic gene circuits and determined that the fixed effect, β, is an appropriate descriptor of gate behavior that can be used to statistically evaluate performance.