An Empirical Investigation of Delayed Growth Response in Escherichia col i

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 A425. The absorbance measurements were calibrated and converted to dry mass equivalents (g/L)

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

13. Results: Estimation of m & Kh

14. Results: Estimation of m & Kh

15. Results: Estimation of m & Kh

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