Engineering of Biological Processes

Lecture 3: Yields and stoichiometry

Mark Riley, Associate ProfessorDepartment of Ag and Biosystems

EngineeringThe 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

• 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

Glucose [g/L]

Bacterial dry cell weight

[mg/L]Slope = dX/dS7 (mg/L) / (g/L)

•Yield of cell mass from substrate

Y x/s

Glucose [mM]

Bacterial dry cell weight

[g/L]

AerobicYx/s=58 mg/mol

AnaerobicYx/s=22 mg/mol

Cell compositionDry weight vs. wet weight

70% of the composition is water

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%

CHxOyNz

• 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 CHON + 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 C4.4HO1.2N + dH2O + eCO2

• 2/3 of the glucose C goes to biomass

• What are the stoichiometric coefficients, and Yx/s, Yx/O2?

MWglucose = 180MWcell = 89.62MWoxygen = 32MWammonia = 17

Generalized growth reaction• C6H12O6 + a NH3 + b O2 → CH1.8O0.5N0.2 +

CHxOyNz + CO2 + H2O

• Normalized to 1 mole of carbon source compound• Where a, b, , x, y, z depend on the type of cell

involved. • a, b, 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

180

6.24Y sx

C6H12O6 + a NH3 + b O2 → CH1.8O0.5N0.2 +

CHxOyNz + CO2 + H2O

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 CHON + d CHxOyNz + eH2O + fCO2

• RQ = ?

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

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 = 24 / 6 (# carbon atoms) = 4

• C2H5OH = 2(4) + 6(1) + (-2) = 12 = 12 / 2 (# carbon atoms) = 6

Example – yeast grown on glucose

• C6H12O6 + 0.48 NH3 + 3 O2 →

CH1.8O0.5N0.2 + CO2 + 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 = 180MWcell = 24.6MWoxygen = 32MWammonia = 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?