Calculating coefficient kinetics in bioprocessing

How to calculate coefficient growth kinetics of microorganisms undergoing lag , log and exponential phase.

1. Maintenance Coefficient Dr S Venkat Kumar B.Tech ., M.E., Ph.D., FRSB., Vellore Institute of Technology (VIT)

2. Maintenance Coefficient The maintenance coefficient is a measure of the amount of substrate consumed by a cell for functions other than the production of new biomass. Cell consume substrate from the external environment and channel it into different metabolic pathways. Some substrate may be directed into growth and product synthesis and some is used to generate energy for maintenance activities. Substrate requirement for maintenance is different for different organism and culture conditions. The specific rate of substrate uptake for maintenance activities is known as maintenance coefficient , m . A maintenance coefficient is used to describe the specific rate of substrate uptake for cellular maintenance, or m s = - [ dS / dt ] /X Unit of maintenance coefficient , m . is kg substrate (kg biomass) -1 S -1

3. Mode of operation of Bioreactors Operation modes : Batch Fed batch Continuous

4. Batch operation of a mixed reactor Batch processes operate in closed systems; substrate is added at the beginning of the process and products removed only at the end. Reactors with neither input nor output of liquid are classified as batch. The liquid volume in batch reactor is considered constant Most commercial bioreactors are mixed vessels operated in batch The cost of running a batch reactor depends on the time taken to achieve the desired product concentration or level of substrate conversion; operating costs are reduced if the reaction is completed quickly

5. Batch operation of a mixed reactor Mass balance on cells in a well mixed batch fermenter is Where, M  mass of component A in the vessel  mass flow rate of A entering the reactor  mass flow rate of A leaving R G  mass rate of generation of A by reaction R C mass rate of consumption

6. Cell Culture Mass balance on cells in a well mixed batch fermenter is Cell do not flow into or out of the vessel, Mass of cells (M) = cell conc.(x) X liquid volume(V) M= xV Mass of cell growth R G = r x V r x  Volumetric rate of growth = µ(x) R G = µ(x) V If cell death occurs in reactor alongside growth R c = r d V r d  Volumetric rate of cell death = k d (x) K d  specific death constant R c = k d (x) V

7. (µ - k d )x µ in batch reactor remains approximately constant and equal to µ max for most of the growth period If the rate of cell death is negligible compared to growth, k d << µ max, above equation reduce to x= x o e t t b = ln Time required to achieve cell density x f starting from cell density x  

8. Batch culture time can also be related to substrate conversion and product concentration using expressions for rates of substrate uptake and product formation Mass balance equation to the growth-limiting substrate in batch fermentation. M i =M o =0 (substrate does not flow into or out of the reactor) M= sV R G = 0 (substrate is not generated) R C = r s V (Volumetric rate of substrate uptake multiplied by liq vol ) r s depends on whether extracellular product is formed by the culture and the relation between product synthesis and energy coupled with energy metabolism Y xs is the true biomass yield from substrate, q p is the specific rate of product formation, Y ps is the true product yield from substrate and m s is the maintenance coefficient.

9. Substituting all in the mass balance equation, ; For µ equal to µ max and V constant, Integrated directly with initial condition s=s o at t= 0

10. If no product is formed or if production is directly linked with energy metabolism, rate of substrate consumption does not contain product synthesis In addition, maintenance requirements can be neglected

11. To obtain an expression for batch culture time as a function of product concentration , apply mass balance equation to the product M i =M o = M= pV (p is the product concentration) Rc = 0 (product is not consumed) R G = r p V (r p is Volumetric rate of product formation) For all types of product r p = q p x q p is the specific rate of product formation R G = r p V= q p xV Applying all these in mass balance equation

12. If q p is constant, the above equation can be integrated directly with initial condition p=p o at t=0 Equation for batch culture time as a function of the final product concentration p f :

13. Problem Zymomonas mobilis is used to convert glucose to ethanol in a batch fermenter under anaerobic conditions. The yield of biomass from substrate is 0.06 g g -1 ; Y PX is 7.7 g g - 1 . The maintenance coefficient is 2.2 g g -1 h - 1 ; the specific rate of product formation is 1.1 h - 1 . The maximum specific growth rate of Z. mobilis is approximately 0.3 h - 1 . 5 g bacteria are inoculated into 50 litres of medium containing 12 g L - 1 glucose. Determine batch culture times required to: (a) produce 10 g biomass; (b) achieve 90% substrate conversion; and (c) produce 100 g ethanol.

14. Thank you