Download Microbial growth stoichiometry “fundamentals”

Quantification of Microbial Rates
Consumption or Production
Micro-organism
N-source
Biomass
Product
Heat
Substrate
O2
H2O
#1_Rates
H+
HCO3-
Marc Deront (Sirous Ebrahimi)
1
Fundamentals of microbial growth stoichiometry
• Composition of biomass
• Anabolism
• Maintenance
• Catabolism
• Coupled anabolism + Maintenance / catabolism
• Microbial growth stoichiometry using conservation principles
• Degree of reduction
• Stoichiometric calculations in undefined chemical systems
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
2
Biomass Composition
Molecules
Elements
Proteins
30-60%
C
40-50%
Carbohydrates
5-30%
H
7-10%
Lipids
5-10%
O
20-30%
DNA
1%
N
5-10%
RNA
5-15%
P
1- 3%
Ash
3-10%
Ash (P, K+, Mg2+, etc)
Typical biomass composition formula
(CHON :49% 7% 33% 11%)
MW =1∗12+1.8∗1+0.5∗16+0.2∗14 =24.6
C1H1.8O0.5N0.2P0.01
MW =24.6 gr/C-mole
1 kg dry biomass contains e.g. 5% ash  950 gr organic matter
= 950 gr / (24.6 gr/C-mole)
= 38.62 C-mole biomass
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
3
Anabolism
From C-source (e.g. glucose) + (…)
Σ of all reactions …
Amino acids
 Proteins
 Sugars
 Carbohydrates
 Fatty acids
 Lipids
 Nucleotides
 DNA RNA
______________________________
gives the  Anabolic reaction
(..) C-source + (..) N-source + (..) P-source + (..) Energy

1
C1H1.8O0.5N0.2P0.01 + (..) H2O + (..) H+ + (..) HCO3-
For Anabolism, Thermodynamic Energy is needed
for biomass growth and synthesis.
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
Note: No electron
acceptor is required,
only energy!
4
Maintenance
Micro-organism
(Self) Restoration of :
• Leakage processes
• Degradation processes
Protein
degraded
Thermodynamic Energy is required
for Maintenance.
Pump out
Leakage of
ions, etc.
Energy
Membrane
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
5
Catabolism
Catabolism generates the energy required for Anabolism & Maintenance
Catabolic reaction consists of a red/ox reaction, between 2 couples
• electron donor couple
• electron acceptor couple
1 glucose + (..) O2  (..) HCO3– +(..) H+ + (..) H2O
• e_donor couple: glucose / HCO3–(soluble CO2)
Oxidation: “C” Oxid. nb (0) (+4)
• e_acceptor couple: O2 / H2O
C6H12O6 + 6 O2  6 CO2 + 6 H2O + Energy
Reduction: “O” Oxid. nb (0)  (-2)
1 glucose  (..) ethanol + (..) HCO3– +(..) H+ + (..) H2O
• e_donor couple: glucose / HCO3–
• e_acceptor couple: HCO3– / ethanol
 Gibbs Energy (kJ) produced
− ΔGCat.reaction
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
6
Anabolism/Catabolism coupling
Growth system definition
electron donor (D)
+
electron acceptor (A)
Catabolism
oxidized donor
+
reduced acceptor
Biomass (X)
C1H1.8O0.5N0.2
Energetically
Coupled
Maintenance
Anabolism
•
•
•
•
•
C-source
N-source
H2O
HCO3−
H+
Catabolism provides energy to Anabolism and Maintenance
Note: C-source and electron donor are often the same compound (but not always)
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
7
Coupled Anabolism/Catabolism
C-source (Anabolism) and electron-donor (Catabolism) are often the same (e.g. organic
substrate)
Only a fraction of the substrate, used as C-source, ends in biomass.
The other part is catabolized as electron donor to provide Energy for Anabolism and
Maintenance requirements
 Concept of Yield
of Biomass on Substrate YSX
YSX =
produced biomass (X)
̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶̶ ̶ ̶ ̶
consumed substrate (S)
YSX is the result of anabolic/catabolic coupling
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
8
Global growth equation
As Catabolism provides energy to Anabolism and Maintenance
YSX is the result of
anabolic/catabolic coupling
The global growth equation is the result of the catabolic reaction
(Energy) and anabolic reaction (Biomass).
−
1
YSX
Substrate + (..) electron acceptor + (..) N-source(e.g.NH4+)
+ (..) H2O + (..) HCO3− + (..) H+ + 1 C1H1.8O0.5N0.2
+ (..) oxidized substrate + (..) reduced acceptor
Note: A + B  C + D ≈ – A –B + C +D (= 0)
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
9
Stoichiometry of general growth equation
1
−
YSX
Substrate + (..) electron acceptor + (..) N-source(e.g.NH4+)
+ (..) H2O + (..) HCO3− + (..) H+ + 1 C1H1.8O0.5N0.2
+ (..) oxidized substrate + (..) reduced acceptor
• N-source, and Biomass are always present with H2O, HCO3-, H+ are partner
elements (from medium)
• Substrate often acts as electron-donor and C-source
• Only substrate and electron-acceptor are case specific
• Most often only 1 measured yield is available e.g. biomass yield on substrate YSX
YSX unit [C-mole of biomass /mole consumed substrat ]
What about the stoichiometric coefficients ?
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
10
Stoichiometry of global growth equation
1
−
YSX
Substrate + (..) electron acceptor + (..) N-source(e.g.NH4+)
+ (..) H2O + (..) HCO3− + (..) H+ + 1 C1H1.8O0.5N0.2
+ (..) oxidized substrate + (..) reduced acceptor
• By convention Biomass stoichiometric coefficient is always 1
• Often catabolic reaction end products are H2O, CO2 which are taken into account
through partner elements …
• If YSX unit [C-mole of biomass / mole substrate] is available
 Only 5 coefficients are required to determine the global growth equation
With Conservation principles - Balances
These coefficients can be determined over atomic element (C, H, O and N)
balances and charge (+, −) balance
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
11
Example global growth stoichiometry
Aerobic growth on oxalate 1/3
Establish the global growth equation for aerobic growth of Pseudomonas oxalaticus on oxalate
(C2O42-, 88 g/mole), and NH4+ as N-source. The measured biomass yield is 0.0506 gram TSS
biomass per gram oxalate (C2O42− ). Biomass has 5% ash.
C-source:
N-source for biomass:
Catabolism:
• Electron donor couple:
• Electron acceptor couple:
Oxalate
NH4+
Oxalate / CO2
O2 / H2 O
1- Convert Biomass yield YSX 0.0506 [gTSS. gOxal.-1] in [C-mole X / mole oxalate]
Note: 1 C_mole X = 24.6 g Biomass [VSS]
0.95 gVSS 1 C-mole X
88 g oxal.
YSX = 0.0506 [gTSS/g oxal.] × ———— × ————— × ————
gTSS
24.6 gVSS
mole oxal.
C-mole X
YSX = 0.172 —————
 Observed growth yield of Biomass over substrate
mole oxal.
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
12
Example global growth stoichiometry
Aerobic growth on oxalate 2/3
2- Set up the global stoichiometric
growth equation
f C2O42−+ a NH4++ b H+ + c O2 + d H2O + 1 C1H1.8O0.5N0.2 + e HCO3a.
Use YSX value
to calculate f coefficient:
-1
-1
mole oxal.
f = —— = ——— = - 5.815 ————
Ysx
0.172
C-mole X
b. How many unknown coeff. and how many conservation equations?
5 unknowns (a, b, c, d, e)
5 conservation balances (C, H, O, N, charge)
c. Set up the conservation balances
C
2.f + 1 + e = 0
H
4.a + b +2.d + 1.8 + e = 0
O
4.f + 2.c + d + 0.5 + 3.e = 0
N
a + 0.2 = 0
d. Solve for a, e, b, d, c (with f = -5.815)
Charge -2.f +a + b – e = 0
- 5.81 C2O42− - 0.2 NH4+ - 1.86 O2 - 0.8 H+ − 5.41 H2O + 1 C1H1.8O0.5N0.2 + 10.63 HCO3#2_Stoichio
Marc Deront (Sirous Ebrahimi)
13
Example global growth stoichiometry
Aerobic growth on oxalate 3/3
Global Growth reaction
- 5.81 C2O42− - 0.2 NH4+ - 1.86 O2 - 0.8 H+ − 5.41 H2O + 1 C1H1.8O0.5N0.2 + 10.63 HCO3Catabolic reaction
to provide Energy
Catabolism of growth
consumes:
1.86 mole O2
and
3.71 mole Oxal.
− 1 C2O42− − 0.5 O2 − H2O + 2 HCO3− (for 1 mole oxalate)
− 3.71 C2O42− − 1.86 O2 − 3.71 H2O + 7.43 HCO3−
Anabolic reaction = Global Growth reaction – Catabolic reaction
For substrate : 5.81 Global_Growth - 3.71 Catabolisme  2.1 mole available/used for Anabolism
2−
+
+
- 2.1 C2O4 - 0.2NH4 - 0.8 H -1.7 H2O + 1 C1H1.8O0.5N0.2 + 3.2 HCO3
3.71
Catabolism fraction: —— = 64%
5.81
#2_Stoichio
−
Note: No electron
acceptor is required,
only energy!
2.1
Anabolism fraction: —— = 36%
5.81
Marc Deront (Sirous Ebrahimi)
14
Example global growth stoichiometry
Anaerobic growth on glucose 1/3
Establish the global growth reaction for anaerobic growth on glucose C6H1206 with
ethanol C2H60 as product and NH4+ as N-source. The measured biomass yield is
YSX = 0.123 g VSS biomass / g glucose
C-source:
N-source for biomass:
Catabolism:
• Electron donor couple:
• Electron acceptor couple:
Glucose
NH4+
Glucose / CO2
CO2 / Ethanol
1- Convert Biomass yield YSX 0.123[gVSS. gGlucose.-1] in [C-mole X / mole Glucose]
Note: 1 mole Glucose = 180 g
1 C-mole X
180 g Glucose
YSX = 0.123 [gVSS/g glucose] × ————— × ——————
24.6 gVSS
mole Glucose.
C-mole X
YSX = 0.9 ——————
 Observed growth yield of Biomass over substrate
mole Glucose
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
15
Example global growth stoichiometry
Anaerobic growth on glucose 2/3
2- Set up the global stoichiometric growth equation
f C6H12O6+ a NH4++ b H+ + c H2O + d C2H6O+ e HCO3- + 1 C1H1.8O0.5N0.2
a.
Use YSX value
to calculate f coefficient:
-1
-1
mole Glucose
f = —— = ——— = - 1.11 ————
Ysx
0.9
C-mole X
b. How many unknown coeff. and how many conservation equations?
5 unknowns (a, b, c, d, e)
5 conservation balances (C, H, O, N, charge)
c. Set up the conservation balances
C
6.f + 2.d + e + 1 = 0
H
12.f + 4.a + b + 2.c + 6.d + e + 1.8 = 0
O
6.f + c + d + 3.e + 0.5 = 0
N
a + 0.2 = 0
d. Solve for a, e, b, d, c (with f = -1.11)
Charge a + b – e = 0
-1.11 C6H12O6 -0.2 NH4++ 2.12 H+ -1.47 H2O +1.87 C2H6O +1.92 HCO3- + 1 C1H1.8O0.5N0.2
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
16
Example global growth stoichiometry
Anaerobic growth on glucose 3/3
Global Growth reaction
-1.11 C6H12O6 - 0.2 NH4++ 2.12 H+ -1.47 H2O +1.87 C2H6O +1.92 HCO3- + 1 C1H1.8O0.5N0.2
Catabolic reaction
to provide Energy
− 1C6H12O6 + 2C2H6O + 2HCO3- + 2H+ − 2H2O (for 1mole glucose)
Catabolism of growth
− 0.93C6H12O6 +1.87C2H6O +1.87 HCO3- +1.87 H+ −1.87 H2O
consumes:
0.93 mole Glucose
produces:
1.87 mole Ethanol.
Anabolic reaction = Global Growth reaction – Catabolic reaction
For substrate : 1.11 Global_Growth – 0.93 Catabolisme  0.18 mole available/used for Anabolism
- 0.18 C6H12O6 - 0.2 NH4+ + 1 C1H1.8O0.5N0.2 + 0.05 HCO3- + 0.25 H+ +0.40 H2O
0.93
Catabolism fraction: —— = 84%
1.11
#2_Stoichio
0.18
Anabolism fraction: —— = 16%
1.11
Marc Deront (Sirous Ebrahimi)
17
Stoichiometry of general growth equation
−
1
YSX
Substrate + (..) electron acceptor + (..) N-source(e.g.NH4+)
+ (..) H2O + (..) HCO3− + (..) H+ + 1 C1H1.8O0.5N0.2
+ (..) oxidized substrate + (..) reduced acceptor
• Energetic coupling of Catabolism / Anabolism determine YSX Biomass yield
over substrate [C_mole X / mole S]
• If YSX is known coefficients are given from C, H, O, N and Charges conservative
balances !
• As Global
Growth = Anabolism + Catabolism
• Catabolic and Anabolic substrate fractions are given by the electron acceptor
stoichiometry of Global Growth Reaction
#2_Stoichio
Marc Deront (Sirous Ebrahimi)
18