1. Engineering of Biological Processes Lecture 3: Yields and stoichiometry
Mark Riley, Associate Professor
Department of Ag and Biosystems Engineering
The University of Arizona, Tucson, AZ
2007

2. Objectives: Lecture 3 Biosynthetic processes (anabolic)
Case studies - cholesterol
Stoichiometry and modeling cellular requirements
"You are what you eat"

3. Stoichiometry Provides information on fundamental constraints
Substrate conversion to product
Cell mass from substrate

4. Yields and yield coefficients
Mass based = “kg” of this from “kg” of that
Y (output / input)
Y x/s
Y p/s
Y ATP/O2
Ymx/s maximal yield of cell mass from substrate

5. Yield Overall Instantaneous YIELD Ratio of rates Ratio of yields
Theoretical = Y
Observed = Y’
YIELD

6. Cell metabolism
Y’ lactate / glucose = ranges from 2 to 0 based on environment
The basic reaction is:
Glucose + 2 Pi + 2 ADP → 2 Lactate + 2 ATP + 2 H2O

7. Yield of cell mass from substrate Y x/s
Glucose [g/L]
Bacterial
dry cell weight
[mg/L]
Slope = dX/dS
7 (mg/L) / (g/L)

8. Aerobic Yx/s=58 mg/mol Anaerobic Yx/s=22 mg/mol Bacterial
Glucose [mM]
Bacterial
dry cell weight
[g/L]
Aerobic
Yx/s=58 mg/mol
Anaerobic
Yx/s=22 mg/mol

9. Cell composition
CHxOyNz

10. In a very simplistic interpretation of metabolism, the following applies:
Cells + medium + O2 (sometimes) → more cells + product + CO2 + H2O
Medium contains sugars, amino acids, cofactors and the elements in the previous table.

11. Stoichiometric calculations
Based on 1 mole of C in the input
CHmOn + a O2 + b NH3 →
c CHaObNd + dH2O + eCO2
This is normalized to 1 mole of C. Could also be normalized to 1 mole of the C source compound
Perform elemental balances to determine the unknown values of the cofactors

12. Example C6H12O6 + a O2 + b NH3 → c C4.4H7.3O1.2N0.86 + dH2O + eCO2
2/3 of the glucose C goes to biomass
What are the stoichiometric coefficients, and Yx/s, Yx/O2?
MWglucose = 180
MWcell = 89.62
MWoxygen = 32
MWammonia = 17

13. Generalized growth reaction
C6H12O6 + a NH3 + b O2 → a CH1.8O0.5N0.2 +
b CHxOyNz + gCO2 + dH2O
Normalized to 1 mole of carbon source compound
Where a, b, a, b, g, d, x, y, z depend on the type of cell involved.
a, b, a, b, g, d, are stoichiometric coefficients
When little info is available about cell composition, use an approximated cell composition of CH1.8O0.5N0.2
This yields a MW of a cell ~ 24.6

14. Generalized growth reaction
C6H12O6 + a NH3 + b O2 → a CH1.8O0.5N0.2 +
b CHxOyNz + gCO2 + dH2O
g of cells from g of glucose

15. Lack of information
Unfortunately, the elemental balances often do not provide enough information to completely solve for the stoichiometric coefficients.

16. Respiratory quotient RQ = YCO2/O2 Molar basis
Moles of CO2 produced from moles of O2
Provides information on the metabolic state of the cell
A high RQ means that much CO2 is produced and hence the metabolism is operating at high efficiency

17. c CHaObNd + d CHxOyNz + eH2O + fCO2
Aerobic metabolism
CHmOn + a O2 + b NH3 →
c CHaObNd + d CHxOyNz + eH2O + fCO2
RQ = ?

18. Degree of reduction Electron balance
= # of available electrons / g of atomic C
Or, this can be described as:
= # of available electrons / # of C’s
Provides another independent equation

19. Degree of reduction C = 4 H = 1 N = -3 O = -2 P = 5 S = 6
CO2 = +4 (C) + -2 (O) = 0
C6H12O6 = 6(4) + 12(1) + 6(-2) = 24
g = 24 / 6 (# carbon atoms) = 4
C2H5OH = 2(4) + 6(1) + (-2) = 12
g = 12 / 2 (# carbon atoms) = 6

20. Example – yeast grown on glucose
C6H12O NH3 + 3 O2 →
0.48 CH1.8O0.5N CO H2O
To grow yeast to 50 g/L in a 100,000 L reactor, determine:
a) mass of glucose and ammonia required
b) O2 required
c) Yx/s and YX/O2
MWglucose = 180
MWcell = 24.6
MWoxygen = 32
MWammonia = 17

21. HW #1 questions
What kind of cell would you use to produce androstenedione? Your answer should describe the attributes of such a cell (don't just state, "a cell that produces andro"). An answer longer than 4 sentences is too much.
Producing cholesterol is an energy intensive process. How much energy (in terms of # of ATP molecules) is consumed in producing one cholesterol molecule from a source of glucose?