Biosensors exploiting communication within genetically engineered bacteria are becoming increasingly important for monitoring environmental changes. Currently, there are a variety of mathematical models for understanding and predicting how genetically engineered bacteria respond to molecular stimuli in these environments, but as sensors have miniaturized towards microfluidics and are subjected to complex time-varying inputs, the shortcomings of these models have become apparent. The effects of microfluidic environments such as low oxygen concentration, increased biofilm encapsulation, diffusion limited molecular distribution, and higher population densities strongly affect rate constants for gene expression not accounted for in previous models. We report a mathematical model that accurately predicts the biological response of the autoinducer N-acyl homoserine lactone-mediated green fluorescent protein expression in reporter bacteria in microfluidic environments by accommodating these rate constants. This generalized mass action model considers a chain of biomolecular events from input autoinducer chemical to fluorescent protein expression through a series of six chemical species. We have validated this model against experimental data from our own apparatus as well as prior published experimental results. Results indicate accurate prediction of dynamics (e.g., 14% peak time error from a pulse input) and with reduced mean-squared error with pulse or step inputs for a range of concentrations (10 μM–30 μM). This model can help advance the design of genetically engineered bacteria sensors and molecular communication devices.
C.R.F., B.K.H., and J.P.B. are grateful for funding by the National Science Foundation (CISE 1110947). C.R.F. acknowledges funding by the National Science Foundation (EHR 0965945), NIH Single Cell Grant 1 R01 EY023173, NIH Computational Neuroscience Training Grant (DA032466-02), Georgia Tech Translational Research Institute for Biomedical Engineering & Science (TRIBES) Seed Grant Awards Program, Georgia Tech Fund for Innovation in Research and Education (GT-FIRE), Wallace H. Coulter Translational/Clinical Research Grant Program and support from Georgia Tech through the Institute for Bioengineering and Biosciences Junior Faculty Award, Technology Fee Fund, Invention Studio, and the George W. Woodruff School of Mechanical Engineering. C.M.A. and W.S. acknowledge the National Science Foundation Graduate Fellowship Program, without which this work would not be possible. P.S. is grateful for the National Science Foundation's National Nanotechnology Infrastructure Network (NNIN) Summer Research Experience for Undergraduates (REU) program that funded his participation in this research, and M.H. is thankful for the Georgia Tech President's Undergraduate Research Award and Undergraduate Research Opportunities Program that supported her contributions.
The authors declare no competing financial interest or conflict of interest in this work.
B. Experimental setup
III. RESULTS AND DISCUSSION
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