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Growth - Overview Microbial Growth –Overview of terms: exponential growth u td productivity Substrate limitation of metabolism Link between metabolism and growth And 22 Growth - Overview Microbial Growth I 1) Energy metabolism overview: glycolysis, TCA cycle, respiration chain, ATP synthase 2) Growth medium components, energy, carbon, nitrogen, phosphorus sources , minerals, trace elements, buffer 3) Growth rate, specific growth rate, exponential growth, semilog plot, maximum and total productivity, lag phase And 33 Growth - Overview Microbial Growth II – 1) Substrate limitation 2) Michaelis Menten model of substrate dependent substrate uptake rate vmax, km 3) The yield coefficient connects the Michaelis Menten Model to the Monod model of substrate dependent growth rate, umax, ks 4) Yield coefficient measurements 5) Yield coefficient is not constant 6) Maintenance coefficient 7) Pirt model contains 4 growth constants, ms, Ymax And 44 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 And 55 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. And 66 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. And 77 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. And 88 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) And 99 Growth- Overview of Energy Metabolism =Dissimilation simplifying FAD and ATP genration in TCA glucose glucolysis TCA cycle 2 ATP + 12 NADH 1 ATP 3 H+ Cell ETC each NADH 9 H+ O2 ATP synthase Overall: 38 ATP allowing growth And 1010 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 And 1111 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. And 1212 Growth- Exponential Multiplication by binary fission: 0 min 30 min 60 min 1, 2, 4, 8, 16, 32 → exponential And 1313 Growth- Exponential (split… split… split ) The resulting seqeunce in numbers is exponential ( 2, 4, 8, 16, 32) And 1414 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 And 1515 Growth- Exponential (split… split… split ) Not only biomass (X) increases exponentially, but also the rate at which it is produced. Thus: dX/dt ˜ X , dX/dt = factor • X The proportionality factor is μ the specific growth rate dX/dt = μ * X (g/L.h) Integration gives Take ln of both sides (h-1) (g/L) Xt = Xoeμt ln(Xt) = ln(Xo) + μt μ = (In(Xt) – In(Xo)) t μ indicates how much more biomass is produced And 1616 -1 per biomass present (g/h/g) = (h ) 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 Growth- Estimation of u from single interval InXt – ln Xo μ= t = In 8 – In 2 90 min 2.77 – 0.693 = 90 min = 2.077 90 min = 0.023 min-1 = 1.3847 h-1 Doubling time = In 2 μ = 0.5 h = 0.69 1.38 h-1 And 1818 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 And 1919 Growth- Limitation and growth phases Growth in batch culture can not continue forever Typical industrial growth curve incl.: X (g/L) Time (h) preparation time (clean, sterilise, fill) lag phase log phase stationary phase decay phase And 2020 Growth- Limitation and growth phases lag log And 2121 Growth- Productivity in industrial batch cultures Most important to industry:productivity of the process (g.L-1.h-1). maximum productivity X (g/L) total productivity 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) Time (h) Choice depends on cost of operation and product And 2222 Growth- Substrate Limitation substrate saturation Substrate (g/L) substrate limitation Time (h) 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) And 2323 Growth- Substrate Limitation substrate saturation v (g/L/h) Substrate uptake rate at different substrate concentrations is important substrate limitation Substrate (g/L) And 2424 Growth- Michaelis Menten model What is the relationship between substrate concentration (S) and its uptake rate (v) ? vmax (h-1) v (h-1) v = vmax substrate limitation kM S (g/L) S ------S + kM Described by MichaelisMenten kinetics (standard biochemistry knowledge) And 2525 Growth- Michaelis Menten model 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) And 2626 Growth- Michaelis Menten model End of Lec1 on Growth And 2727 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) And 2828 Growth- Michaelis Menten model Growth- Michaelis Menten model µ (h-1) What is the relationship between substrate concentration (S) and its uptake rate (v) ? µmax (h-1) v = vmax substrate limitation kS S (g/L) S ------S + kM Described by MichaelisMenten kinetics (standard biochemistry knowledge) And 2929 Growth- Michaelis Menten model 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 v = vmax S ------S + kM µ=Y*v S µ = Y * vmax -------S + kS And 3030 Growth- Michaelis Menten model Substrate limitation of microbial growth The two curves are described by two properties: µmax (h-1) The maximum specific growth rate obtained with no substrate limitation (umax (h-1)) substrate limitation kS and the half saturation constant (Michaelis Menten constat), giving the substrate concentratation at which half of the maximum u is reached (ks (g/L)). S (g/L) And 3131 Growth- Michaelis Menten model Substrate limitation of microbial growth S µ = µmax * ---------S + kS µ (h-1) Typically there are low and high substrate specialists and ecological “substrate niches” for the specialists to outcompete each other kS kS Substrate (g/L) And 3232 Growth- Michaelis Menten model Substrate limitation of microbial growth S µ = µmax * ---------S + kS µmax (h-1) substrate limitation kS S (g/L) 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. And 3333 Growth- Michaelis Menten model Substrate limitation of microbial growth S µ = µmax * ---------S + kS µ (h-1) There is also room for medium substrate “allround” specialists kS kS Substrate (g/L) And 3434 Growth- Michaelis Menten model Substrate limitation of microbial growth S µ = µmax * ---------S + kS µ (h-1) With the same ks the organism with a higher µmax will always win. kS Substrate (g/L) And 3535 Growth- Michaelis Menten model Substrate limitation of microbial growth S µ = µmax * ---------S + kS µ (h-1) With the same same umax the organism with a lower ks will always win. kS Substrate (g/L) And 3636 Growth- Michaelis Menten model 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 And 3737 Growth- Michaelis Menten model 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. μmax • S μ= ks + S For S approaching zero the μmax term approaches zero. Thus it appears that μ would be mainly influenced by kS (Textbook explanation). And 3838 Growth- Michaelis Menten model 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 ks(A) + S = μmax(B) • S ks(B) + S μmax(A) ks(A) + S = μmax(B) ks(B) + S And 3939 Growth- Michaelis Menten model 2 1 + 0.1 = 1.82 > 1 0.5 + 0.1 1.67 At all substrate concentrations μmax is more important than kS And 4040 Growth- Michaelis Menten model 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) Growth ceased Substrate Growth ceased inhibition because of because of lack endproduct of substrate inhibition And 4141 Growth- Yield Coefficient 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 And 4242 Growth- Yield Coefficient Microbial Growth- Yield Coefficient Y Microbial processes not only turn substrate to products Because of Y there will be new biomass formed: Resulting for aerobic processes in the following E.g. Substrate + Oxygen → Products + Biomass An empirical formula for biomass can be given as: CH1.8O0.5N0.2 Formula just an approximation and varies with different microbes. Formula is useful to establish carbon or electron balance for bioprocesses (e.g. BioProSim) And 4343 Growth- Yield Coefficient E.g. Gluconate degradation by Klebsiella a. By resting Cells (non growing): Ideal biocatalyst 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. And 4444 Growth- Yield Coefficient Microbial Growth YS = Significance of Special Yield Coefficients X (g/L) - Only works for same substrate, pathway S (g/L) X (g/L) S (mol/L) Molar yield coefficient -Works only for aerobes and for same X (g/L) ATP/O2 YO2 = O2 (mol/L) + works for unknown or complex substrates (e.g. cornsteep liquor, wastes And 4545 Growth- Yield Coefficient Microbial Growth Significance of Special Yield Coefficients Ye = X (g/L) Mole of reducing equivalents respired Similar to YO2 but works also for other electron acceptors X (g/L) YkJ = kJ of heat of combustion X (g/L) YN, YP = Mole of N or P Works also for fermenting Bacteria, and unknown Substrates and pathways For scientific purposes under N or P limitation And 4646 Growth- Yield Coefficient Microbial Growth YATP YATP = X (g/L) 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 And 4747 Growth- Yield Coefficient Microbial Growth YATP Comparison of YS and YATP for glucose fermenting bacteria YATP ATP Yield YS Organism gX/ (mol ATP/ mol substance) mol ATP Streptococcus lactis 19.5 2 9.8 Lactobacillus plantarum 18.5 2 9.4 Saccharomyces cerevisiae 18.5 Zymomonas mobilis 9 Aerobacter aerogenes 29 E. coli 26 2 1 3 3 9.4 9 9.6 8.6 The literature valuefor YATP is given as 10.5 g biomass/ mol ATP (Baushop and Elsden 1960) And 4848 Growth- Yield Coefficient 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: 1. Not constant for all microbes (4.7 to 21) in rich media 2. Experimental YATP < theoretical YATP (30 g/mol ATP) 3. Low YATP on minimal media 4. YATP dependent on growth conditions (ease of life) 5. ↑ temperature → ↓ YATP (thermal denaturation of proteins) 6. Unsuitable growth conditions → ↓ YATP 7. Likely Reason for less cells formed: Higher ATP usage for cell maintenance rather than cell growth Maintenance coefficient And 4949 Growth- Yield Coefficient 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” 1. Substrate transport into cell (e.g. against diffusion gradient) 2. Osmotic work 3. Motility 4. Intracellular pH 5. Replacement of thermally denatured proteins (↑ T → ↑ ms) 6. Leakage of H+ ions across membrane (uncoupling) S (mg) ms = X (mg) • time (h) ms influences Y, μ and the metabolic activity of the cells and And 5050 is thus important to be considered in bioprocesses. Growth- maintenenace 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) And 5151 Growth- maintenenace 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) And 5252 Growth- maintenenace Effect of maintenance coefficient on growth rate Effect of mS on Y? Ymax Y (gX/ gS)) Y is the observed yield coefficient. The maximum yield coefficient Ymax is approached only when u = umax Specific Growth rate u (h-1) Ymax is one of four growth constants And 5353 Growth- maintenenace Effect of maintenance coefficient on growth rate mS and Ymax can be combined: mS (gS/gX/h) * Ymax (gX/gS) = Decay rate (h-1) The Pirt equation of growth includes all four growth constants: S µ = µmax * -------- mS *Ymax S + kS And 5454 Growth- maintenenace Effect of maintenance coefficient on growth rate ms the respiration u = (v – mS) *Ymax S u = ( vmax * -------- - mS) * Ymax S + kS activity used to just stay alive S µ = Ymax * vmax * -------- - mS *Ymax S + kS S µ = µmax * -------- - mS *Ymax S + kS substrate uptake And 5555 Growth- maintenenace Effect of Maintenance Coefficient (mS) on growth Rate ignoring mS S µ = µmax * ---------S + kS µ (h-1) 0 S(g/L) including mS S µ = µmax * -------- - mS *Ymax S + kS And 5656 Effect of Maintenance Coefficient (mS) on growth Rate Sm = critical substrate concentration growth is zero µ (h-1) mS.kS.Ymax sm= -----------------umax- ms.Ymax 0 S(g/L) Sm And 5757 Growth- maintenenace Effect of Maintenance Coefficient (mS) on growth Rate The negative specific growth rate (µ) observed in the absence of substrate (when S = 0) (cells are starving, causing loss of biomass over time) µ (h-1) 0 S(g/L) is the decay rate mS*Ymax - mS*Ymax And 5858 Points about ms • ms more heat produced (e.g. uncoupler) • when S= 0 and u is negative (decay rate) then any oxygen uptake is via endogenous respiration. And 5959 Growth- maintenenace