1.018 – 7.30J Population Growth in Chemostats – Lecture Notes Steady State, resource-limited growth Jaques Monod (1950s) Wanted to look at the effects of a limited nutrient on the growth rate of bacteria Noticed . . . [S3] [S2] [S] = Substrate (Nutrient) ln N Concentration [S1] Slope = r (growth rate) Time Hypothesized . . . SKSrrs+=maxrmaxr But could not get good data here. Ks [S] Needed system with constant low supply of nutrients Chisholm1.018 – 7.30J Chemostat Theory System in which a fresh supply of nutrients is fed to a culture of constant volume at a fixed rate, and the contents of the culture are withdrawn at the same rate. Si, f S,f SsssS S,N, Q Assumptions - Completely Mixed - Inflow = Outflow - One limiting Nutrient in Influent Medium Units cells /L L L/hr μg/L μg/L μg/cell cells/μg hr-1 hr Constants & Variables N = Cell Concentration V = Volume of Culture f = Flow Rate Si = Influent Limiting Nutrient Concentration S = Residual Concentration in Vessel Q = Cell Quota Y = Yield Coefficient = 1/Q Dilution Rate D = f/V Residence Time = 1/D1.018 – 7.30J Analysis of a Chemostat Change in Cell Concentration = Growth – Washout “Births” – “Deaths”DNrNdtdN−=Mass Balance in steady-state . . . 0=dtdN and Dr= [hr-1] rQNDSDSdtdSi−−=in steady-state . . . 0=dtdS and QSSNi−=and, by hypothesis and observation: SKSrrs+=max1.018 – 7.30J Remember . . . We have control over D and Si. Given (for steady-state assumption): Dr=QSSNi−=SKSrrs+=maxWhat happens when we change D? What happens when we change Si? (assuming a constant Q) (knowing that D is fixed) (knowing S is fixed for a given r) “washout” Si high Si med N Si low D=r rmaxWhy does a chemostat always reach a steady-state? If r < D Cells will be washed out and N ↓ S ↑, r ↑, until r = D If r > D Cells will get too dense and N ↑, S ↓, r ↓ until r = D Think about it carefully . . . Question: What will the output of cells per unit time look like as a function of D for a given Si?MIT OpenCourseWare http://ocw.mit.edu 1.018J / 7.30J Ecology I: The Earth Fall 2009 For information about citing these materials or our Terms of Use, visit: