1. An Empirical Investigation of Delayed Growth Response in Escherichia coli Nariman Ghoochan Jerald D. Hendrix Sean Ellermeyer Department of Biological and Physical Sciences Department of Mathematics Kennesaw State University

2. Overview Continuous culture of bacteria can be achieved in a chemostat Chemostat: A broth culture system in which fresh nutrient is continuously added at a constant rate (and used broth is removed at the same rate)

3. Basic Chemostat System

4. Our Chemostat System

5. Overall Objectives of Our Work To develop and refine mathematical models that predict the growth of bacteria in continuous culture To test the predictions of the models under a variety of experimental conditions

6. Mathematical Models of Continuous Bacterial Culture Factors that affect bacterial population growth in continuous culture:  Relationship between the organism’s growth rate and the limiting nutrient concentration  The amount of bacteria produced per unit mass of nutrient (yield)  Concentration of limiting nutrient in the feed  Flow rate and vessel volume

7. Mathematical Models of Continuous Bacterial Culture The classic model (Monod model) of continuous culture:  Is a set of differential equations  That predict changes in bacterial concentration and limiting nutrient concentration over time.  The Monod model assumes that the bacterial growth rate responds instantaneously to a change in nutrient concentration

8. Mathematical Models of Continuous Bacterial Culture The Monod model is given in the equations:

9. Mathematical Models of Continuous Bacterial Culture We have modified the Monod model to account for a delayed response of growth rate to a change in nutrient concentration We have determined a preliminary fit of this model to continuous culture of E. coli 23716, under conditions of limiting glucose concentration

10. Mathematical Models of Continuous Bacterial Culture Our delayed response model:

11. Experimental Details E. coli 23716  Grown in Davis minimal broth with glucose as the limiting nutrient and sole carbon source  Starter (batch) culture in chemostat vessel grown to early stationary phase  Continuous culture in Virtis chemostat (1500 ml) at 37°C, with stirring and aeration  Flow rate of 3 ml/min, with varying glucose concentrations in the feed  Bacterial concentration determined by measuring A 425. The absorbance measurements were calibrated and converted to dry mass equivalents (g/L)

12. Results: Estimation of  m & K h  m :  Estimated by determining the growth rate of 23716 in excess glucose (0.2%) in batch culture in the reaction vessel K h :  Estimated by determining the growth rate in a series of glucose concentrations (0.005 – 0.1% glucose)

13. Results: Estimation of  m & K h

32. Conclusions Using the empirically-estimated value of  = 20 min:  Good fit of the predictions of the time- delay model with experimental data (using Y = 0.28)  Very little difference between predictions of the time delay and Monod models

33. Conclusions Using the value of  = 360 min:  Good fit of the predictions of the time- delay model with experimental data (using Y = 0.49)  Large differences between predictions of the time delay and Monod models

34. Continuing Research Is there a short or a long time delay during chemostat runs? Analysis of glucose concentration over time Analysis of model with a different limiting nutrient (e.g., with a tryptophan auxotroph) Isolation of “time delay” mutants with varying  values