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Industrial Microbiology INDM 4005 Lecture 8 20/02/04

Industrial Microbiology INDM 4005 Lecture 8 20/02/04. Lecture 8. Biotechnological Processing Bacterial Kinetics. Questions for today:. 1. What is meant by doubling time of a bacterial culture? 2. What is specific growth rate? 2. What is the Monod equation? 3. What is a chemostat?

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Industrial Microbiology INDM 4005 Lecture 8 20/02/04

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  1. Industrial Microbiology INDM 4005 Lecture 820/02/04

  2. Lecture 8 Biotechnological Processing Bacterial Kinetics

  3. Questions for today: • 1. What is meant by doubling time of a bacterial culture? • 2. What is specific growth rate? • 2. What is the Monod equation? • 3. What is a chemostat? • 4. What is dilution rate? • 5. What is the relationship between substrate concentration and specific growth rate?

  4. Overview (Lecture Objectives) (a) Bacterial growth (b) Growth kinetics and equations (c) Batch and continuous growth kinetics

  5. Growth in batch culture • Growth in batch cultures is split into several distinct phases • E.g of a closed culture system

  6. Bacterial growth Most bacterial cells reproduce asexually by binary fission. This involves several stages: (i) increasing cell size (growth) (ii) DNA replication, and (iii) division (septum formation)

  7. Generation Time: Time required for a cell population to double DNA DNA Replication Cell Elongation Septum Formation Cell Separation One generation 12 9 3 6 Generation time

  8. Bacterial growth 2N 1N N time • The time taken for a microbial population to double in number is called the doubling time. The time taken for a single cell to divide is called the generation time • The mean generation time of a population is equal to the doubling time. • Doubling time is a measure of growth rate a short doubling time implies a fast growth rate. DT

  9. Use of generation time to compare growth of different bacteria Microorganism Temp oC Generation Time B. stearothermophilus 40 11 min Escherichia coli 40 20 min S. aureus 37 28 min P. aeroginosa 37 36 min Lactobacillus acidophilus 37 75 min M. tuberculosis 37 720 min

  10. Stationary Phase Death Phase Exponential Phase Lag Phase

  11. For a batch process, the rate of cell growth in the exponential phase is given by: dx = μx dt x is the concentration of cells (biomass in g/L) μ is the specific growth rate of the cells t = time in hrs This equation is valid under conditions of balanced growth, which is when the cell composition remains constant. During the exponential growth phase, cell growth is not limited by nutrient concentrations and µ equals µmax. However, during the deceleration phase the specific growth rate of the cells depend on the concentration of limiting substrate. In this case, µ can be calculated using the Monod expression:

  12. On Integration xt = x0emt x0 = original biomass concentration xt = biomass concentration after time t e = base of the natural logarithm On taking natural logarithms ln xt = lnx0 + mt

  13. Bacterial growth • If we consider a bacterium growing under ideal conditions in which the numbers of cells exactly doubles in every generation, the population size after a known number of generations can be calculated... When the initial population size is N0 after one generation N1 = 2 x N0 after two generations N2 = 2 x 2 N0 = 22N0 after three generations N3 = 2 x 22N0 = 23N0 etc… .: after n-generations Nn = 2n N0

  14. Geometric progression 24 23 22 21 1 2 4 8 16

  15. The Mathematics of Growth No = the initial population number Nt = the population at time t n = the number of generations at time t Nt = No x 2n There is a direct relationship between the number of cells originally in a culture and the number present after exponential growth.

  16. Growth starting with a single cell Time Generation 2n Population Nt log10 Nt number (No x 2n) 0 0 20 = 1 1 0.000 20 1 21 = 2 2 0.301 40 2 22 = 4 4 0.602 60 3 23 = 8 8 0.903 80 4 24 = 16 16 1.204 100 5 25 = 32 32 1.505 120 6 26 = 64 64 1.806

  17. The Mathematics of Growth Nt = N0 x 2n Expressed as n n = logNt - logN0 log 2 n = 3.3(logNt - logN0) If you know the initial (No) and final (Nt) number of cells then you can calculate n, the number of generations.

  18. The Mathematics of Growth n = 3.3 (log Nt - log N0) Example: Nt = 107, N0 = 103 n = 3.3 (7-3) n = 13.2 generations If you know n, the number of generations, and t, the growth time, then you can calculate td, the generation time.

  19. The Mathematics of Growth The generation time (td) is calculated as td = t n t = number of hours of exponential growth n= number of generations If n = 15.5 and t = 31 then td = 2 hours

  20. Estimation of generation time from a bacterial growth curve 1 x 108 8 x 107 5 x 107 4 x 107 2 x 107 1 x 107 Population Doubles in 2 hrs T = 2 n = 1 td = t/n = 2hrs Slope = 0.15 Cells /ml 2 hours Generation time 1 2 3 4 5

  21. Gradient = m

  22. Growth Rate Constant K • Growth rate is often expressed as a value (k), equivalent to the number of doublings per unit time. • k is usually expressed as generations per hour • If t/d = 2 hours then K = 0.5 generations per hr k = LogNt - LogN0 / 0.301 t

  23. Monod Equation • The decrease in growth rate and cessation of growth may be described by the relationship between m and the residual growth limiting substrate m max S m = Ks + s s = residual substrate concentration (g/L) Ks = substrate utilisation constant whenm is halfm max (g/L) m max = maximum specific growth per hour

  24. The relationship between substrate concentration and specific growth rate mmax 1/2 mmax S>>Ks then m = mmax Ks = 1.0 g/L

  25. ks • Bacteria with a high affinity for substrate has a low Ks and vice versa • The higher the affinity the less growth is affected until substrate levels are very low

  26. Yield Coefficient • Important in optimising batch fermentations Defined as x = Yx/ s(S- Sr) x = biomass concentration (g/L) Yx/ s = yield coefficient (g biomass/g substrate utilised) S = initial substrate concentration (g/L) Sr = residual substrate concentration (g/L)

  27. Continuous Growth Kinetics • Start as batch fermentations but exponential growth can be extended by addition of fresh broth • Reactor is continuously stirred and constant volume is maintained • Steady state conditions exist • The rate of addition of fresh broth controls growth

  28. Continuous Growth Kinetics D = F V D = dilution rate (per hour) F = flow (L/h) V = reactor volume (L)

  29. Continuous Growth Kinetics Under steady state conditions dx rate of growth rate of loss dt in reactor from reactor (washout) or dx dt - = Under steady state conditions rate of growth = rate of loss hence dx/dt = 0 therefore mx = Dx andm = D =mx - Dx

  30. Continuous Growth Kinetics • At fixed flow rates and dilution rates the specific growth rate is dependant on the operating dilution rate • For any given dilution rate under steady-state conditions the residual substrate concentration in the reactor can be predicted by substituting D for m in the Monod equation mmaxSr D = Ks + sr where Sr is the steady-state residual concentration in the reactor at a fixed dilution rate

  31. Critical dilution rate • The dilution rate at which x = zero is termed the critical dilution rate Dcrit • Dcrit is affected by the constants mmax and Ks and the variable Sr, the largerSr the closerDcrit tommax

  32. Growth of a microorganism in continuous chemostat culture Low Ks value Dcrit critical dilution rate

  33. Growth of a microorganism in continuous chemostat culture High Ks value

  34. Effect of increased initial substrate concentration on the steady-state biomass and residual substrate concentrations in a chemostat x at Sr3 x at Sr2 x at Sr1 Sr3 Sr2 Sr1 Steady state residual substrate concentration X = steady state cell concentration s = steady state residual substrate concentration Sr = Initial substrate concentration

  35. mmaxSr D = Ks + sr Rearranging gives: D (Ks + Sr) = mmax Sr dividing by Sr then gives: DKs + D = mmax Sr Hence: DKs mmax - D Consequently, the residual substrate concentration in the reactor is controlled by the dilution rate Sr =

  36. Chemostat / Turbidostat • Chemostat Device for maintaining a bacterial population in the exponential growth phase by controlling nutrient input and cell removal. • Turbidostat The concentration of cells is kept constant by controlling the flow of medium such that the turbidity of the culture is kept within certain limits

  37. Summary Bacterial kinetics; 1. We have looked at the growth kinetics of homogeneous unicellular suspension cultures 2. We have examined growth in batch and continuous cultures 3. Examined how cell growth is controlled by substrate levels 4. Monod showed that growth rate is a hyperbolic function of the concentration of rate limiting substrate 5. Understand the relationship between substrate concentration and specific growth rate 6. How Ks the saturation constant effects cell growth

  38. Conclusion • This lecture introduced bacterial growth kinetics in relation to fermentation • It outlined how bacterial growth and fermentation efficiency are controlled

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