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Biochemical Stoichiometry n  Cell growth and product synthesis are complex processes

n  overall kinetics and stoichiometry of thousands of intracellular reactions

n  Initial process design deals with comparison of potential substrates

n  cell yield mass n  product yield n  evolution of heat n  waste generation

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Concept of Yield Coefficient n  Quantifies efficiency of conversion of substrate to cell mass/cell

number n  Cell yield coefficient, YX/S , defined as

n  Cell yield coefficient is rate of change of cell concentration with respect to substrate concentration

x

S

xi

Si

tangent at Si(or xi) gives observed Yx/S

Y dxdSx S/ =

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Commonly used Yield Coefficients n  YX/S - growth yield on substrate n  YP/S - product yield on substrate n  YX/O2

- growth yield on oxygen n  YX/ATP - growth yield per mole ATP generated n  YH - g cell synthesised per unit heat evolution n  RQ - respiratory quotient

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True Yield vs Observed Yield n  Substrate consumption channeled into making more cell mass, for

maintenance purposes and product synthesis n  Ignoring product synthesis,

rate of substrate consumption = rate of substrate consumed for growth + rate of substrate utilized in maintenance Rate of substrate consumption = Rate of substrate used for growth =

= (recall that ) Rate of substrate used for maintenance = where m is maintenance coefficient, ie.

dSdt( )

( )/

dSdx

dxdt

Yx

growth

x S true

1µ dx

dtx= µ

mx

mxdSdt

=1

5

⇒ = +

= +

= +

dSdt

xY

mx

xdSdt Y

m

Y Ym

x S true

x S true

x S obs x S true

µ

µ µ

µ

( )

( )

( ) ( )

/

/

/ /

1 1

1 1

Hence, only if substrate utilized for maintenance can be ignored that

obsSxtrueSx YY )()( // =

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Summary of Yield Factors for Aerobic Growth

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ATP Yields for Anaerobic Growth

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Heat Generation by Microbial Growth

n  50-60% of energy stored in carbon and energy source liberated as heat during aerobic metabolism

n  In absence of maintenance, heat evolution directly related to growth

n  Estimation of heat-removal requirements essential for proper reactor design

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Yield on Heat Evolution (YH) Substrate YH (g cell/kcal)Malate 0.30Acetate 0.21Glucose 0.42Methanol 0.12Ethanol 0.18Isopropanol 0.074n-Paraffins 0.16Methane 0.061

•  Hydrocarbons produce more heat than partially oxygenated substrates •  More reduced substrates imply greater heat removal demands

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hlmmolOQhlkcalQ

QQ

O

H

OH

−=

−=

=

//

12.0

22

2