Transcript Yields and stoichiometry

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
Objectives: Lecture 3
• Biosynthetic processes (anabolic)
•
Case studies - cholesterol
• Stoichiometry and modeling cellular
requirements
• "You are what you eat"
Stoichiometry
• Provides information on fundamental
constraints
– Substrate conversion to product
– Cell mass from substrate
Yields and yield coefficients
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•
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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
Yield
• Overall
• Instantaneous
• Ratio of rates
• Ratio of yields
• Theoretical = Y
• Observed = Y’
YIELD
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
•Yield of cell mass from substrate
Y x/s
Bacterial
dry cell weight
[mg/L]
Slope = dX/dS
7 (mg/L) / (g/L)
Glucose [g/L]
Aerobic
Yx/s=58 mg/mol
Bacterial
dry cell weight
[g/L]
Anaerobic
Yx/s=22 mg/mol
Glucose [mM]
Cell composition
Dry weight vs. wet weight
70% of the composition is water
CHxOyNz
Dry weight consists of:
Element
E. coli
Yeast
C
O
N
H
P
S
K
Na
Others
50%
20%
14%
8%
3%
1%
1%
1%
<1%
50%
34%
8%
6%
1%
<1%
<1%
<1%
<1%
• 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.
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
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
MWoxygen
MWammonia
= 89.62
= 32
= 17
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
Generalized growth reaction
C6H12O6 + a NH3 + b O2 → a CH1.8O0.5N0.2 +
b CHxOyNz + gCO2 + dH2O
Yx s
24.6a

180
g of cells from g of glucose
Lack of information
• Unfortunately, the elemental balances
often do not provide enough information
to completely solve for the stoichiometric
coefficients.
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
Aerobic metabolism
• CHmOn + a O2 + b NH3 →
• c CHaObNd + d CHxOyNz + eH2O + fCO2
• RQ = ?
Degree of reduction
• Electron balance
g = # of available electrons / g of atomic C
g Or, this can be described as:
g = # of available electrons / # of C’s
• Provides another independent equation
Degree of reduction
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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
Example – yeast grown on glucose
• C6H12O6 + 0.48 NH3 + 3 O2 →
 0.48 CH1.8O0.5N0.2 + 3.12CO2 + 4.32H2O
• To grow yeast to 50 g/L in a 100,000 L reactor, determine:
•
a) mass of glucose and ammonia required
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b) O2 required
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c) Yx/s and YX/O2
MWglucose
MWcell
MWoxygen
MWammonia
= 180
= 24.6
= 32
= 17
HW #1 questions
1) 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.
2) 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?