A Linear Mixed Effects Model for Evaluating Synthetic Gene Circuits

One 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 account for the predicted logic (OR, AND, etc.), and many 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 emergent trends with unsupervised machine learning (k-means clustering). We then simulated data representative of the centroid of each k-means cluster. Next, we utilized a linear mixed effects model to estimate the Boolean nature of a circuit, where the fixed effect β represents the difference between the ON and OFF states, and the random effect is the input grouping (i.e.,+/-, +/+). We first validated this model on the simulated data and used Monte Carlo simulations to recommend sample sizes for evaluating gate performance. We then evaluated point estimates of the fixed effect, β̂, as a holistic metric for circuit performance using a series of nested repressor OR gates with intentionally degraded performance. We observed an association between β̂ and the predicted translation rate, and used β̂ to guide the design of a 3-input gate, highlighting the potential use of this modeling approach for the forward design of new Boolean gates. Finally, we extended our analysis to multi-input (>2) and multi-output gates, emphasizing that the linear mixed effects model can be applied for higher-order logic. In summary, we utilized a linear mixed effects model to evaluate synthetic gene circuits and determined that point estimates of the fixed effect, β̂, are appropriate descriptors of gate behavior that can be used to statistically evaluate performance.