Mikrobielles Wachstum

Wie wachsen Mikroorganismen in der Natur?

Exponentielles Wachstum und Diauxie

• Ziel der Vorlesung:• Verständnis darüber wie Mikroorganismen

in der Natur leben (nicht im Labor)• Kläranlage, Boden, Sedimente,

Grundwasser

Exponentielles Wachstum• Baks wachsen durch Verdopplung• 20 → 21 → 22 → 23 → … → 2n

• N = N0 x 2n

• log N = log N0 + n log 2• n = (log N - log N0) / log 2• Erweitern um 1/t = 1/(t1 – t2)• Teilungsrate ν = n/t = (log N - log N0) / t x lg 2• D.h. bei einer Verdopplung (N = 2 N0)• ν = n/t = (log 2 N0 - log N0) / log 2 x t• (log 2 + log N0 - log N0) / log 2 x t• log 2 / log 2 x t = 1/td = Verdopplungszeit oder

Generationszeit Tafelbild log-Wachstum

Wachstumsrate und Ertrag• Biomasse X = Zellzahl mal BM/ Zelle• Wachstumsrate µ = dX/dt x 1/X• Integration: X = X0 x e(µ x t)

• Eine Verdopplung: 2 X0 = X0 x e(µ x td)

• 2 = e(µ x td)

• ln 2 = µ x td• µ = ln 2 /td• = 0,693/td• = 0,693 x ν

• Ertrag:• dX/dt = -Y dS/dt• Y = Ertragskoeffizient

Exponentielles Wachstum im Batch

Exponentielles Wachstum von Einzellern. Arithmetische (blau) und halblogarithmische (rot) Auftragung der Zellzahl gegen die Zeit

Idealisierte Wachstumskurve einer Bakterienkultur

Exponentielles Wachstum bei zwei oder mehr Substraten: Diauxie

Monod Growth Model

Monod equation: µ = µmaxS/(KS+ S)Where: µ = dX/dt x 1/X0 [1/t] = growth rate at substrate concentration S µmax = maximum attainable growth rate [1/t]KS = substrate affinity or Monod constant [mg/L] = substrate concentration where µ = 1/2 µmax

Monod Growth Model

Monod equation: µ = µmaxS/(KS+ S)Wenn S >> Ks geht (Ks+ S) gegen S und µ = µmax S/ S bzw. µ = µmax

Wenn S<< Ks geht (Ks+ S) gegen Ks und µ = µmax S/ Ks

Modified Monod: Incorporation of Cell Maintenance

For S << Ks the measured cell growth rate µ is actually lower than the effective growth rate on account of cell death in all phasesµ = (µmax [S])/(Ks + [S]) – bWhere b is the maintenance rate, or death rate. This term also represents the minimum growth rate necessary to maintain the microbial population, i.e. where the growth rate is equal to the cell death rate. Smin is the substrate concentration at which the cell growth rate equals zero

Zuverlässigkeit der Parameter

Entnommen aus Kovarova , MMBR, 1998

Kinetic Adaptation Strategies: Oligotrophy and Copiotrophy

• Early observations on the kinetic properties of microbial populations resulted in a definition of oligotrophy and copiotrophy, based on a number of characteristics, such as Ks, and and Smin

• The argument is that oligotrophs can take advantage of low carbon fluxes on account of their low Ks

Distribution of affinity constant values

Lineares Wachstum und Chemostat

The Monod Chemostat Model

Xi, Si, Ci

Xe, Se, Ce

Xe, Se, Ce

Verdünnungsrate D

= Wachstumsrate µ

Biomassedichte X hängt nur von der Substratkonzentration Si am Einfluss ab

dX/dt = -Y dS/dt

Y = Ertragskoeffizient

Relation Between D, S, X and Cell Production Rate(1) when D 0: S 0 and X = Y Si

i.e. this situation is similar to a batch reactor system where all the feed substrate is consumed by the cells(2) when D --> µmax: X decreases and S increases

i.e. the dilution rate is too high for complete consumption of S(3) when D = µmax : dX/dt = 0 only steady state solution : X = 0

loss of cells or WASHOUT occurs at D > Dmax

Restkonzentrationen

• Die Restkonzentration hängt u.a. von der Wachstumsgeschwindigkeit ab:

– Je geringer µ desto geringer S– Deshalb brauchen wie in der Kläranlage die

Schlammrückführung.1) Wir Verringern µ enorm und erzielen geringeres

Biomassewachstum weil wir näher an den Erhaltungsstoffwechsel herankommen

2) Wir verringern die Restkonzentration S weil die Wachstumsrate µ kleiner wird

Restkonzentrationen im Chemostat

Entnommen aus Kovarova-Kovar and Egli, MMBR, 1998

Entwicklung der Restkonzentration im Chemostaten in Abhängigkeit der

Verdünnungsrate

Gibt es im Chemostaten Diauxie?

• Wie müsste die aussehen?

Substratmischungen im Chemostaten

FIG. 5. Mixed-substrate kinetics during growth of E. coli in carbon-limited culture. (a) Growth with mixtures of glucose, fructose, and galactose at a dilution rate of 0.3 h21. Data from reference 145. (b) Growth with mixtures of glucose and 3-PPA at a dilution rate (D) of 0.6 h21. All the mixtures were designed in such a way that the total biomass concentration was always approximately 45 mg liter21 (dry weight). Data from reference 137. Adapted from reference 138. Entnommen aus Kovarova, MMBR, 1998

Substratgemische und Wachstum

Legende zu Folie Substratgemisch• FIG. 6. Effect of enzyme regulation on the relationship between specific substrate

consumption rate and steady-state substrate concentration (note the link between panels a and d, panels b and e, and panels c and f). (a) Steady-state concentrations of glucose and galactose in chemostat cultures of E. coli growing under carbon-controlled conditions at a constant dilution rate (D 5 0.3 h21) with different glucose-galactose mixtures in the feed. The total sugar concentration in the inflowing medium was always 10 mg liter21, and the composition of glucose-galactose is given in weight proportions. Data from reference 148. (b) Regulated catabolic enzyme level. Concentrations of 3-PPA during growth of E. coli in carbon-controlled chemostat cultures with different mixtures of 3-PPA and glucose at constant dilution rate are shown (D 5 0.3 h21). The shaded area indicates the range from 0 mg of 3-PPA liter21 up to the apparent threshold concentration below which the 3-PPA was not utilized (i.e., the same residual concentrations [h] as those in medium feed were measured). Once induced, 3-PPA was utilized down to concentrations (n) that were lower than those required to trigger induction. Data from reference 134. (c) Steady-state methanol concentration (n) and specific activity of alcohol oxidase (h) in the yeast Kloeckera sp. strain 2201 during simultaneous utilization of glucose-methanol mixtures in carbon-controlled chemostat culture at a constant dilution rate (D 5 0.14 h21). The specific activity of alcohol oxidase is given in micromoles per milligram of protein per minute. Adapted from references 63 and 64. (d to f) Different enzyme expression patterns (the details of the meaning of the numbers are discussed in the text). It is assumed that the consumption kinetics of a microbial culture for a substrate can be described by a Monod-type relationship. qmax(ind) and qmax(rep) are the maximum specific substrate consumption rates under fully induced and repressed conditions, respectively.

Limitierende Stoffe in Gemischen

FIG. 7. Influence of the molar ratio of glucose to ammonium in the feed medium on the steady-state concentration of glucose (E) and ammonium (n) in chemostat cultures of Klebsiella pneumoniae at dilution rates of 0.2 h21 (a) and 0.4 h21 (b). The shaded area indicates the dual carbon- and nitrogen-limited zone. Adapted from reference 214. Entnommen aus Kovarova, MMBR, 1998.

Bedeutung für die Natur?

Bedeutung für die Natur?

• Permanente Substratlimitierung• Festkörperreaktor• Kaum Wachstum• Folgt ev., dass in der Natur alles

gleichzeitig ablaufen sollte.