Microbial Growth – Overview of terms: exponential growth u td productivity

1. Growth - Overview Microbial Growth –Overview of terms: exponential growth u td productivity Substrate limitation of metabolism Link between metabolism and growth

2. Growth - Overview • Microbial Growth I • Energy metabolism overview: glycolysis, TCA cycle, respiration chain, ATP synthase • Growth medium components, energy, carbon, nitrogen, phosphorus sources , minerals, trace elements, buffer • Growth rate, specific growth rate, exponential growth, semilog plot, maximum and total productivity, lag phase

3. Growth - Overview • Microbial Growth II – • Substrate limitation • Michaelis Menten model of substrate dependent substrate uptake rate vmax, km • The yield coefficient connects the Michaelis Menten Model to the Monod model of substrate dependent growth rate, umax, ks • Yield coefficient measurements • Yield coefficient is not constant • Maintenance coefficient • Pirt model contains 4 growth constants, ms, Ymax

4. Growth - Overview • Microbial Growth III – • Maintenance coefficient • Microbial Growth IV • Growth in batch culture • Microbial Growth V • Chemostat • Microbial Growth VI • Determining growth constants • Biomass retention

5. 1 Growth Medium Ingredients 1.1 The rationale of media recipes Bacterial cells typically grow by cell division into two daughter cells. To do this they require a suitable growth medium. Growth media recipes in the literature vary widely and it can be confusing to students to discriminate between essential ingredients and replaceable ones. Rather than blindly following recipes, it would be more useful for microbiologists to be able to design own media, or to modify or optimise exiting media. For this it is useful to understand the generic microbial growth requirements. The ingredients of a typical growth medium satisfy a number of principal needs of growing cells by providing a source of Energy, carbon, nitrogen, phosphate, sulfur, minerals, trace elements, vitamins, growth factors, buffer capacity. 1.2 Energy source Microbial growth (assimilation) is an endergonic process and requires energy input for the conversion of ingredients from the growth medium into biomass. This energy is derived from the energy source component of the growth medium. Typically an energy source consists of a suitable electron donor and electron acceptor. It is the transfer of electrons from the electron donor (a redox couple that of a more negative potential than that of the electron accepting redox couple) to the acceptor that liberates energy which is conserved as ATP. The ATP is typically generated during this electron transfer via electron transport phosphorylation (electron carriers, electron transport chain, proton gradient, ATP synthase). For most bacteria the electron donor is an organic compound being oxidised to CO2 and the electron acceptor is oxygen, which is supplied by allowing air access to the growht container (e.g. petri dishes or shake flasks). However many bacteria use inorganic reduced chemical species as the electron donor, such as ferrous iron, sulfide, ammonia, or hydrogen gas which supply electrons by being oxidised to ferric iron, sulfate, nitrite or protons, respectively. Electron accepting species alternative to oxygen are can be ferric iron, nitrate, sulfate, CO2, etc. which accept electrons by being reduced to ferrous iron, N2, sulfide and methane respectively. When supplying specific electron acceptors it needs to be considered that the presence of multiple potential electron acceptors can cause mutual inhibition. For example the presence of oxygen inhibits the reduction of nitrate, sulfate and CO2 while the presence of nitrate inhibits the reduction of sulfate and CO2. The use of external electron acceptors other than oxygen is still a respiration (anaerobic respiration). If a suitable electron donor and electron acceptor is provided this enables the bacteria to generate ATP by harnessing the energy liberated from the flux of electrons from electron donor to electron acceptor.

6. 1.3 Carbon source The carbon source for microbial growth is typically an organic compound and is often identical to the electron donor. For example an aerobic bacterium growing by oxidising sugar to CO2 for ATP generation will also use the same sugar as a starting material for biomass synthesis. The sugar may be partly degraded via glycolysis to pyruvate or even to Acetyl-CoA to use parts of the TCA cycle for biomass synthesis purposes (compare to pathway of glutamate formation later in this text). The ratio of carbon that is used as energy source (catabolism, dissimilation) or as carbon source for biomass synthesis (anabolism, assimilation) determines the bacterial yield coefficient. Aerobic bacteria degrading a sugar use about 40 to 50% of the carbon for assimilation and the rest for energy generation. Hence a yield coefficient of 0.4 to 0.5 (g of microbial cells formed per g or carbon source used) is commonly observed. In rare but interesting cases no formal carbon source needs to be provided to the growth medium. This is the case for autotrophic bacteria. Similar to plants and algae, autotrophic bacteria use CO2 as the carbon source which can be obtained from the air supply. However the additional supply of CO2 via a bicarbonate buffer (HCO3-+ H+  H2CO3  CO2 + H2O) helps the growth of autotrophs by minimising CO2 limiting conditions. Examples of autotrophic bacteria with industrial and environmental significance include: nitrifying bacteria that use NH3 as electron acceptor and Fe2+ and sulfur oxidising bacteria. These bacteria of the genera Nitrosomonas and Thiobacillus are used for nitrogen removal from wastewater and bioleaching of ores respectively. 1.4 Nitrogen source Nitrogen is next to carbon, hydrogen and oxygen (the latter two are sourced from water) the quantitative most important element. Nitrogen is needed for the synthesis of enzymes and other proteins. In minimal media it is typically supplied as ammonium or nitrate salts, in rich media it is supplied as an organic nitrogen source (e.g. part of yeast extract or peptone based media). With nitrate as the nitrogen source the bacteria need to first reduce the nitrate to ammonia (assimilative nitrate reduction) followed by ammonia assimilation into biomass. Some bacteria are capable of using the relatively inert (triple bond) N2 from air as the nitrogen source. Hence selective media for such nitrogen fixing bacteria do not include any nitrogen source.

7. 1.3 Phosphate source The next most important element for microbial growth is phosphorous. In contrast to the other elements in biomass, phosphorus does not undergo oxidation or reduction and stays in its phosphate status (hence phosphate source). Phosphate needs to be present in all microbial growth media, without it growth cannot occur. Phospholipids and ATP are two examples of essential phosphate containing cell components. Rich media produced from biomass hydrolysates (e.g. yeast extract or peptone) contain organic phosphate compounds. Many media use manifold more phosphate than necessary for biosynthetic purposes (e.g. about 50 mM). Here phosphate serves as the buffer species for pH control. While phosphate buffers are typically recommended to be added in two components, the more acidic phosphate (KH2PO4) and the more basic phosphate (K2HPO4) to result in a precise pH of the final media, it can also be provided by other phosphate sources followed by adjustment of the pH to a precise setpoint by any suitable acid or base. This pH adjustment will result in producing the same ratio of hydrogen and dihydrogen phosphate as suggested by the original recipe. 1.4 Sulfur source Sulfur is needed for protein synthesis and hence essential to all growth media. For aerobic media sulfur is added as sulfate, which the bacteria reduce (assimilatory sulfate reduction) to sulfide prior to assimilation into amino acids. Alternative sulfur sources are sulfide (for anaeroboic media) or organic sulfur sources such as yeast extract or cysteine.

8. OUR- Growth medium for microbes Components of Growth Medium: Energy source (electron donor and acceptor) C-source (e.g. sugar) N-source (e.g. NaNO3) P-source (e.g. KH2PO4) other minerals (e.g. Na+Mg+, SO42-, Trace elements (e.g. Co, Mn, Fe, etc) Vitamins (e.g. cyanocobalamin) Buffer (e.g. carbonate or phosphate buffer)

9. Growth- Overview of Energy Metabolism =Dissimilation simplifying FAD and ATP genration in TCA glucose glucolysis TCA cycle 1 ATP  3 H+ ATP synthase 2 ATP + 12 NADH Cell Overall: 38 ATP allowing growth ETC each NADH  9 H+ O2

10. Growth- Simplified Scheme of Energy preservation as ATP Important Quantities: ATP-synthase: 3H+  1 ATP ETC: 1 NADH  3*3 = 9 H+ 2 NADH reduce 1 O2 1 NADH = 2 electron equivalents 1 O2 accepts 4 electron equivalents glycolysis: 1 glucose  12 NADH 1 glucose  12*9=108 H+ = 36 ATP + 2 ATP from glycolysis via substrate level phosphorylation = 38 ATP

11. Growth- Simplified Scheme of Energy preservation as ATP Minor corrections not needed for exams: During TCA cycle not only NADH is produced but also FAD. FAD translocates only 2 H+ rather than 3  hence 2 less ATP. However TCA also generates 2 ATP not mentioned in simplified balance.

12. Growth- Exponential Multiplication by binary fission: 0 min 30 min 60 min 1, 2, 4, 8, 16, 32 → exponential

13. Growth- Exponential (split… split… split ) The resulting seqeunce in numbers is exponential ( 2, 4, 8, 16, 32)

14. Growth- Exponential (split… split… split ) • The resulting sequence in numbers is exponential ( 1,2, 4, 8, 16, 32). • Not only the biomass (X) increases exponentially but also the rate at which it is produced (calculate from above) • growth rate is NOT constant in batch culture (similar to OTR not being constant) • needed: a constant that describes the speed of binary fission (similar to kLa in oxygen transfer) Plotting the growth rate as a function of time will reveal

15. Xt = Xoeμt Integration gives ln(Xt) = ln(Xo) + μt Take ln of both sides μ = (In(Xt) – In(Xo)) t Thus: dX/dt X , dX/dt = factor • X ˜ μ indicates how much more biomass is produced per biomass present (g/h/g) = (h-1) Growth- Exponential (split… split… split ) Not only biomass (X) increases exponentially, but also the rate at which it is produced. The proportionality factor is μ the specific growth rate dX/dt = μ * X (g/L.h) (h-1) (g/L)

16. not examinable: dX/dt = μ * X dx = u *n X * dt dx/X = u * dt ∫dx/x = ∫ udt ∫1/x * dx = ∫ udt lnx = ut +c x = e ut+c x = e ut *ec for t= 0: x=xo xo = e ut *ec Hence: x = e ut *xo

17. InXt – ln Xo μ = t In 8 – In 2 = 90 min 2.77 – 0.693 = 90 min 2.077 = 90 min In 2 0.69 μ 1.38 h-1 Growth- Estimation of u from single interval = 0.023 min-1 = 1.3847 h-1 Doubling time = = = 0.5 h

18. Growth- Estimation of doubling time from semilog plot When plotting the log of cell mass versus time a straight line is obtained. The slope of the line reveals the doubling time. The specific growth rate can be calculated from the doubling time by: Advantage of plot: averaging out, avoiding outliers

19. Growth- Limitation and growth phases • Growth in batch culture can not continue forever • Typical industrial growth curve incl.: • preparation time (clean, sterilise, fill) • lag phase • log phase • stationary phase • decay phase X (g/L) Time (h)

20. Growth- Limitation and growth phases lag log

21. Growth- Productivity in industrial batch cultures Most important to industry:productivity of the process (g.L-1.h-1). Productivity is the overall product (here biomass X) concentration produced per time required. The process can be stopped for maximum productivity or maximum product concentration (total productivity) Choice depends on cost of operation and product maximum productivity X (g/L) total productivity Time (h)

22. Growth- Substrate Limitation In most environmental and many industrial bioprocesses (e.g. chemostat), the growth rate is limited by substrate availability. Substrate uptake rate at different substrate concentrations is important (limitation and saturation of substrate) substrate saturation Substrate (g/L) substrate limitation Time (h)

23. Growth- Substrate Limitation Substrate uptake rate at different substrate concentrations is important substrate saturation v (g/L/h) substrate limitation Substrate (g/L)

24. S v = vmax ------- kM S + Growth- Michaelis Menten model What is the relationship between substrate concentration (S) and its uptake rate (v) ? vmax (h-1) v (h-1) substrate limitation Described by Michaelis-Menten kinetics (standard biochemistry knowledge) S (g/L) kM Growth- Michaelis Menten model

25. Growth- Relationship between Michaelis Menten kinetics and and Monod kinetics Michalis Menten Model: predicts substrate uptake fromsubstrate concentration Monod Model: predicts specific growth rate from substrate concentration Under substrate limitation:  Substrate concentration  Substrate uptake rate (SUR)  ATP production rate  rate of producing new cells (u) Growth- Michaelis Menten model

26. S v = vmax ------- kM S + Growth- Michaelis Menten model What is the relationship between substrate concentration (S) and its uptake rate (v) ? µmax (h-1) µ (h-1) substrate limitation Described by Michaelis-Menten kinetics (standard biochemistry knowledge) S (g/L) kS Growth- Michaelis Menten model

27. S v = vmax ------- kM S + Growth- Relationship between Michaelis Menten kinetics and and Monod kinetics • What is the relationship between specific growth rate (µ) and specific substrate uptake rate (v) • Relationship is given by the • yield coefficient Y (g of X formed • per g of S degraded). • v= substrate uptake rate (SUR) • but can also be OUR • Note: unlike µmax and kS, Y is • not a true growth constant. • kS and kM are equivalent µ = Y * v S µ = Y * vmax -------- kS S + Growth- Michaelis Menten model

28. µmax (h-1) µ (h-1) substrate limitation kS Substrate (g/L) Substrate limitation of microbial growth The two curves are described by two properties: The maximum specific growth rate obtained with no substrate limitation (umax (h-1)) and the half saturation constant (Michaelis Menten constat), giving the substrate concentratation at which half of the maximum u is reached (ks (g/L)). Growth- Michaelis Menten model

29. S µ = µmax * ---------- kS S + Substrate limitation of microbial growth Typically there are low and high substrate specialists and ecological “substrate niches” for the specialists to outcompete each other µ (h-1) kS Substrate (g/L) kS Growth- Michaelis Menten model

30. S µ = µmax * ---------- kS S + Substrate limitation of microbial growth µmax (h-1) To be most competitive against other microbes a low ks value and a high umax value are important. This simplified growth model only uses 2 out of 4 growth constants. µ (h-1) substrate limitation kS Substrate (g/L) Growth- Michaelis Menten model

31. S µ = µmax * ---------- kS S + Substrate limitation of microbial growth There is also room for medium substrate “allround” specialists µ (h-1) kS Substrate (g/L) kS Growth- Michaelis Menten model

32. S µ = µmax * ---------- kS S + Substrate limitation of microbial growth With the same ks the organism with a higher µmaxwill always win. µ (h-1) kS Substrate (g/L) Growth- Michaelis Menten model

33. S µ = µmax * ---------- kS S + Substrate limitation of microbial growth With the same same umax the organism with a lower ks will always win. µ (h-1) kS Substrate (g/L) Growth- Michaelis Menten model

34. Conclusions – substrate limitation • Substrate limitation slows down metabolism • Slowed metabolism slows growth (how? via Y!) • The limitation effect can be quantified (S/(S+kS)) • The quantifier term has values between 0 and 1 • e.g. if S=kS then u is half of umax • different microbes have different kS • competition between microbes is determined by kS and umax • What is missing -- maintenance, death, Ymax Growth- Michaelis Menten model

35. μmax • S μ = ks + S Microbial Growth Comparison of μmax and kS for competition under Substrate limitation Which of the two growth constants influences to a larger extent The growth of an organism under substrate limitation (substrate Concentration approaches zero) Approach 1. For S approaching zero the μmax term approaches zero. Thus it appears that μ would be mainly influenced by kS (Textbook explanation). Growth- Michaelis Menten model

36. Microbial Growth Comparison of μmax and kS for competition under Substrate limitation Approach 2. Question is doubling of μmax (strain A) or halving of kS (strain B) having a larger effect on μ? μmax(B) • S μmax(A) • S μ(B) = μ(A) = ks(B) + S ks(A) + S To compare growth rate of strain A and B: μ(A) = μ(B) μmax(A) • S μmax(B) • S = ks(A) + S ks(B) + S μmax(A) μmax(B) = ks(A) + S ks(B) + S Growth- Michaelis Menten model

37. 2 1 = 1 + 0.1 0.5 + 0.1 1.82 > 1.67 At all substrate concentrations μmax is more important than kS Growth- Michaelis Menten model

38. Microbial Growth Dependence of Biomass concentration on substrate used (Yield Coefficient) - Intro Final X in several batch cultures with increasing [S] X (g/L) Substrate Concentration (g/L) Substrate inhibition Growth ceased because of endproduct inhibition Growth ceased because of lack of substrate Growth- Yield Coefficient

39. Microbial Growth Dependence of Biomass concentration on substrate used (Yield Coefficient) - Intro In the absence of inhibition the biomass formed is correlated to the substrate used (X) X (g/L) The correlation factor is the Yield Coefficent (dimensionless, X/S) [S] (g/L) Typical Y for aerobes on glucose: 0.4 to 0.5 Growth- Yield Coefficient

40. Microbial Growth Yield Coefficient – Role in Establishing Correct Mass Balance The biomass yield coefficient is essential to establish a complete mass balance in a fermentation: E.g. Substrate + Oxygen → Products + Biomass The empirical formula for biomass must be known: CH1.8O0.5N0.2 Growth- Yield Coefficient

41. E.g. Gluconate degradation by Klebsiella Ideal biocatalyst a. By resting Cells (non growing): 1 gluconate → 1.5 acetate + 0.5 ethanol + 2 formate b. By growing cells: 1 gluconate + 0.174 NH3 + 0.04 H2O → 1.4 acetate + 0.3 ethanol + 1.7 formate + 0.87 CH1.8O0.5N0.2 Thus: Growing cells incorporate 14.5 % of carbon from Gluconate into cell growth resulting in increased acetate/ethanol ratio. Growth- Yield Coefficient

42. Microbial Growth Significance of Special Yield Coefficients X (g/L) • Only works for same substrate, pathway YS = S (g/L) X (g/L) Molar yield coefficient S (mol/L) • Works only for aerobes and for same • ATP/O2 X (g/L) YO2 = O2 (mol/L) + works for unknown or complex substrates (e.g. cornsteep liquor, wastes Growth- Yield Coefficient

43. Microbial Growth Significance of Special Yield Coefficients Similar to YO2 but works also for other electron acceptors X (g/L) Ye = Mole of reducing equivalents respired Works also for fermenting Bacteria, and unknown Substrates and pathways X (g/L) YkJ = kJ of heat of combustion For scientific purposes under N or P limitation X (g/L) YN, YP = Mole of N or P Growth- Yield Coefficient

44. Microbial Growth YATP X (g/L) YATP = Mole of ATP • + completely comparable between different physiological types • + can compare efficiency of growth for aerobes and anaerobes • requires knowledge about how much ATP is gained • Note: Moles of ATP generated can be estimated • for many pathways: • e.g. glycolysis to pyruvate 2 ATP • consumption of 1 mole of O2 ~ 2 NADH ~ 4 electrons  6 ATP • For rich media where all cell building blocks are provided • (e.g. Yeast Extract): YATP = 10.5 g/mol Growth- Yield Coefficient

45. Microbial Growth YATP Comparison of YS and YATP for glucose fermenting bacteria YATP gX/ mol ATP ATP Yield (mol ATP/ mol substance) YS Organism Streptococcus lactis 19.5 2 9.8 Lactobacillus plantarum 18.5 2 9.4 Saccharomyces cerevisiae 18.5 2 9.4 Zymomonas mobilis 9 1 9 Aerobacter aerogenes 29 3 9.6 E. coli 26 3 8.6 The literature valuefor YATP is given as 10.5 g biomass/ mol ATP (Baushop and Elsden 1960) Growth- Yield Coefficient

46. Microbial Growth Calculation and Inconsistencies of YATP • ATP gained per mole of substrate can be estimated for • bacteria growing in rich media from Ys if the YATP is known • (e.g. 10.5 g/ATP) • E.g. If Ys = 21 g/mole of substrate → about 2 mole of ATP • generated per mol of substrate • Although the YATP is more consistent than any other way of • expressing the yield coefficient it can also vary: • Not constant for all microbes (4.7 to 21) in rich media • Experimental YATP < theoretical YATP (30 g/mol ATP) • Low YATP on minimal media • YATP dependent on growth conditions (ease of life) • ↑ temperature → ↓ YATP (thermal denaturation of proteins) • Unsuitable growth conditions → ↓ YATP • Likely Reason for less cells formed: Higher ATP usage for cell maintenance rather than cell growth  Maintenance coefficient Growth- Yield Coefficient

47. Microbial Growth Maintenance Coefficient • 1 mole of ATP generated during catabolism allows • • theoretically → synthesis of 32 g cells • • in praxis → 10.5 g cells • The maintenance coefficient (ms) is the reason for • 2/3 being “wasted” • Substrate transport into cell (e.g. against diffusion gradient) • Osmotic work • Motility • Intracellular pH • Replacement of thermally denatured proteins (↑ T → ↑ ms) • Leakage of H+ ions across membrane (uncoupling) • ms influences Y, μ and the metabolic activity of the cells and • is thus important to be considered in bioprocesses. S (mg) ms = X (mg) • time (h) Growth- maintenenace

48. Effect of Maintenance Coefficient on Growth Rate What is maintenance coefficient? The energy supply rate needed to maintain the life functions of a non growing cell. Units? strictly speaking: mol ATP/ cell/ h mostly used: g substrate / g biomass / h = (h-1) Growth- maintenenace

49. Effect of Maintenance Coefficient on Growth Rate • What does the maintenance coefficient (mS) affect? • ms is the reason for Y not being constant. • ms   Y hence”: • ms   u (compare slide) • Why? Because some substrate is taken up just for maintenance, not for growth. • Effect is more apparent in slow growing cultures than in fast growing cultures. • Slow growing cultures can have a very low Y . mS (gS/gX/h) * Ymax (gX/gS) = Decay rate (h-1) Growth- maintenenace

50. Effect of maintenance coefficient on growth rate Effect of mS on Y? Y is the observed yield coefficient. The maximum yield coefficient Ymax is approached only when u = umax Ymax is one of four growth constants Ymax Y (gX/ gS)) Specific Growth rate u (h-1) Growth- maintenenace