Engineering of Biological Processes Lecture 3: Yields and stoichiometry

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Engineering of Biological ProcessesLecture 3
Yields and stoichiometry

• Mark Riley, Associate Professor
• Department of Ag and Biosystems Engineering
• The University of Arizona, Tucson, AZ
• 2007

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Objectives Lecture 3

• Biosynthetic processes (anabolic)
• Case studies - cholesterol
• Stoichiometry and modeling cellular requirements
• "You are what you eat"

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Stoichiometry

• Provides information on fundamental constraints
• Substrate conversion to product
• Cell mass from substrate

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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

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Yield

• Overall
• Instantaneous
• Ratio of rates
• Ratio of yields
• Theoretical Y
• Observed Y

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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
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• Yield of cell mass from substrate
• Y x/s

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Cell composition
CHxOyNz
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• 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.

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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

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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
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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

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Generalized growth reaction
C6H12O6 a NH3 b O2 ? a CH1.8O0.5N0.2 b
CHxOyNz gCO2 dH2O
g of cells from g of glucose
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Lack of information

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

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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

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Aerobic metabolism

• CHmOn a O2 b NH3 ?
• c CHaObNd d CHxOyNz eH2O fCO2
• RQ ?

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Degree of reduction

• Electron balance
• of available electrons / g of atomic C
• Or, this can be described as
• of available electrons / of Cs
• Provides another independent equation

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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

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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
• b) O2 required
• c) Yx/s and YX/O2

MWglucose 180 MWcell 24.6 MWoxygen
32 MWammonia 17
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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?