Transcript Mikrobielles_Wachstum_Muna

Mikrobielles Wachstum
Wie wachsen Baks 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
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Baks wachsen durch Verdopplung
2 0 → 2 1 → 22 → 2 3 → … → 2n
N = N0 x 2 n
lgN = lg N0 + n lg 2
n = (lgN - lg N0) / lg 2
Erweitern um t = (t1 – t2)
Teilungsrate ν = n/t = (lgN - lg N0) / lg 2 x t
D.h. bei einer Verdopplung (N = 2 N0)
ν = n/t = (lg 2 N0 - lg N0) / lg 2 x t
(lg 2 + Lg N0 - lg N0) / lg 2 x t
lg 2 / lg 2 x t = 1/td = Verdopplungszeit oder
Generationszeit
Wachstumsrate und Ertrag
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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
Idealisierte Wachstumskurve einer Bakterienkultur
Exponentielles Wachstum von Einzellern.
Arithmetische (blau) und halblogarithmische (rot)
Auftragung der Zellzahl gegen die Zeit
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.
Wenn S<< Ks
geht (Ks+ S) gegen Ks und µ = µmax S/ Ks
µ = µmax
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
phases
µ = (µmax [S])/(Ks + [S]) – b
Where 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
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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
Verdünnungsrate D
Xi, Si, Ci
= Wachstumsrate µ
Biomassedichte X hängt
nur von der
Substratkonzentration Si
am Einfluss ab
Xe, Se, Ce
dX/dt = -Y dS/dt
Y = Ertragskoeffizient
Xe, Se, Ce
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
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Die Restkonzentration hängt u.a. von der
Wachstumsgeschwindigkeit ab:
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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
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
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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 carboncontrolled conditions at a constant dilution rate (D 5 0.3 h21) with different glucosegalactose 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?
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Permanente Substratlimitierung
Festkörperreaktor
Kaum Wachstum
Folgt ev., dass in der Natur alles
gleichzeitig ablaufen sollte.