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 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 YIELD 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 Glucose [g/L] Bacterial dry cell weight [mg/L] Slope = dX/dS 7 (mg/L) / (g/L)

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

Cell composition 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 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 = 89.62 MWoxygen = 32 MWammonia = 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 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

c CHaObNd + d CHxOyNz + eH2O + fCO2 Aerobic metabolism CHmOn + a O2 + b NH3 → c CHaObNd + 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 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 b) O2 required c) Yx/s and YX/O2 MWglucose = 180 MWcell = 24.6 MWoxygen = 32 MWammonia = 17

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?