Reaction Engineering

1. Reaction Engineering

3. Batch culture: exponential phase (balanced growth) Exponential phase = log-phase Maximum growth rates μmax „midexponential“: bacteria often used for functional studies Max growth rate -> smallest doubling time

5. MichaelisMenten Kinetics Used when microbe population is constant = non-growing (or short time spans) Derivable from first principles (enzyme-substrate binding rates and equilibria expressions) Parameter determination methods used for Monod calculations (i.e. Lineweaver Burke)

7. Monod Growth Kinetics • Relates specific growth rate, m, to substrate concentration • Empirical---no theoretical basis—it just “fits”! • Have to determine mmax and Ks in the lab • Each m is determined for a different starting S

8. MichaelisMenten Kinetic expression derived (theoretical) Constant enzyme pool Free enzymes Non-growing microbes v vs. S where v is velocity Km is half saturation constant MichaelisMenten vs. Monod • Monod • Empirical expression • Growth • Enzyme concentration increases with time • Relates microbial growth rate constant to S • μvs S • Ks is half saturation constant

9. MichaelisMenten vs. Monod Parameters (vmax or μmax; Ks or Km) are determined by linearization (e.g. Lineweaver Burke model) or nonlinear curve fitting. Relationship between dependent variable and S determined experimentally, in the lab Range of S Set conditions (T, chemistry, enzyme or microbe) Measure the v or μ for each S Plot v or μ vs. S; analyze data for parameter estimation

10. Determining Monod parameters Double reciprocal plot (Lineweaver Burke) Commonly used Caution that data spread are often insufficient Other linearization (Eadie Hofstee) Less used, better data spread Non-linear curve fitting More computationally intensive Progress-curve analysis (for substrate depletion) Less lab work (1 curve), more uncertainty

11. It applies where μ ǂ 0 -> exponential growth (μ = μmax ) + transition into stationary Where Monod Growth Kinetics Applies • KS is the half-saturation coefficient [mg/L] Monod kinetics -> “Substrate depletion kinetics”

12. Substrate Depletion Kinetics Y Yield coefficients Since And Monod applies!! Then And Where k = • k is the maximum substrate utilization rate [sec-1] • KS is the half-saturation coefficient [mg/L]

13. Substrate Depletion Kinetics Substrate consumption rates have often been described using ‘Monod kinetics’ -> Substrate controls growth Kinetics S is the substrate concentration [mg/L] X is the biomass concentration [mg/ L] k is the maximum substrate utilization rate [sec-1] KS is the half-saturation coefficient [mg/L]

14. Stoichiometric Coefficients for Growth Yield coefficients, Y, are defined based on the amount of consumption of another material. Because ΔS changes with growth condition, YX/S is not a constant

15. Monod Growth Kinetics mixed order S >> KS S << KS 1 3 2 mmax m, 1/hr S, mg/L Expontential growth μ = μmax Stationary phase μ = 0

16. Depletion Kinetics mixed order S >> KS S << KS 1 3 2 1. Zero-order region,S >> KS, the equation can be approximated by μ = μmax -> exponential growth 2. Center region, Monod “mixed order” kinetics must be used -> transition from exponential growth to stationary growth caused by [S] limitation 3. First-order region, S << KS, the equation can be approximated as μ = μmaxS/Ks -> transition from exponential growth to stationary growth caused by [S] limitation Just before stationary phase starts (stationary phase μ = 0) mmax m, 1/hr S, mg/L • k is the maximum substrate utilization rate [sec-1] • KS is the half-saturation coefficient [mg/L]

17. Modeling Substrate Depletion Three common assumptions Monod kinetics applies (mid range concentrations) -> “Substrate depletion kinetics” First-order decay (low concentration of S, applicable to many natural systems) Zero-order decay (substrate saturated) μ =μmax -> exponential growth

18. Growth and Production Kinetic Cellular growth rate Monod approximation Yield factor Substrate Utilization Product Formation (Beginning of Stationary Phase)

19. Factors Determining Kinetics Rate per microbe, which depends on Species Substrates Environmental factors Total numbers of microbes

20. Quantification of Microbes in the Environment Culture-based (limited: 2000 species vs. 13,000 species of bacteria in soil by DNA-based methods Counting colony forming units (CFUs) Activity assays: need cell or biomass count to normalize Culture-independent Direct Counts General fluorescent stain, like acridine orange or SYBR gold Counting cells in FISH assay Biomass assays Quantification of an element like C or N Chloroform fumigation / incubation or direct extraction Total protein or DNA

21. Fermentation Technology -> Why is it important to know the kinetics of the reaction in the fermenter?

22. Fermentation Technology -> What is going on in a fermenter? -> How to control the process in a fermenter?

28. Stochiometric Coefficients

29. Mass Balance

30. Example -> Too complex !!!!

31. -> Blackbox effect substrates + cells → extracellular products + more cells ( ∑S + X → ∑P + nX)

32. Model to describe what is going on in a Bio-reactor Monod’s model -> S depletion • Mass balance : depentend on reactor type -> S, P, X • Growth Kinetics: -> Monod model (substrate depleting model) -> Describes what happens in the reactor in steady state (constant conditions)

34. Primary metabolic products Secondary metabolic products

35. Microbial Products 1. Growth associated products : products appear simultaneoulsy with cells in culture qp is the specific rate of product formation (mg product per g biomas per hours 2. Non-growth associated products : products appear during stationary phase of batch growth 3. Mixed-growth associated products : products appear during slow growth and stationary phase

36. Biotechnological processes of growing microorganisms in a bioreactor Mass Balance: Fin = Fout = 0 Fin≠ 0; Fout = 0 Fin = Fout≠ 0 V= const. V increases V = const.

37. Mass balance : depentend on reactor type -> S, P, X • Growth Kinetics: -> Monod model (substratedepleting model) -> Describeswhathappens in the reactor in steadystate(constantconditions) Model to describe what is going on in a Bio-reactor 1. Mass Ballance: In – Out + Reaction = Accumulation Biomass: FX0 - FX + ∫r dV = dn/dt dn/dt = d(XV)/dt r = dX/dt = µ X dn/dt=V (dX/dt) + X (dV/dt) 2. Monod Kinetics: 3. Steady state: dX/dt = 0 (NOT for Batch reactor!!!)

38. V= const. Batch Reactor Closed Well-mixed Constant volume -> substrate growth limiting factor Mass Balance - Biomass: n = mole Acc = dn/dt Verbal: In – Out + Reaction = Accumulation dn/dt = d(XV)/dt = (dX/dt) V Math: 0 0 r V dX/dt V Rearrange: r V = dX/dt V -> Substrate concentration controls growth rate Growth Growth

39. Growth and Production Kinetic in Batch Cellular growth rate Monod approximation Yield factor Substrate Utilization Product Formation (Beginning of Stationary Phase)

40. Biotechnological processes of growing microorganisms in a bioreactor Mass Balance: Fin = Fout = 0 Fin≠ 0; Fout = 0 Fin = Fout≠ 0 V= const. V increases V = const.