Chemical Kinetics and Cell Growth in Bioprocessing

Chemical Kinetics

Study of reaction rates and mechanisms.

Reaction Kinetics

Speed of reactants converting to products.

Rate of Reaction

Change in concentration over time.

Irreversible Reaction

Reaction that proceeds in one direction only.

Mass Balance

Equation accounting for mass changes in reactions.

Volumetric Rate

Rate of reaction per unit volume.

Zero-Order Kinetics

Rate independent of reactant concentration.

First-Order Kinetics

Rate proportional to reactant concentration.

Rate Constant (k)

Specific constant for reaction rate.

Enzyme-Substrate Complex

Intermediate formed during enzyme reactions.

Michaelis-Menten Kinetics

Model describing enzyme-catalyzed reactions.

Vmax

Maximum rate of an enzyme-catalyzed reaction.

Concentration (C)

Amount of substance per unit volume.

Reaction Rate Equation

Mathematical expression for reaction rate.

Activation Energy

Energy required to initiate a reaction.

Closed System

No mass exchange with surroundings.

Rate of Change

Speed at which concentration varies.

Substrate (S)

Reactant in an enzyme-catalyzed reaction.

Product (P)

Substance formed from a chemical reaction.

Reactants (A, B)

Starting materials in a chemical reaction.

Consumption Rate

Rate at which reactants are used up.

Production Rate

Rate at which products are formed.

Initial Condition

Starting concentration at time t=0.

E

Enzyme in a catalyzed reaction.

S

Substrate that is converted to product.

P

Product formed from substrate reaction.

Vmax

Maximum reaction velocity (mol l-1 min-1).

[S]

Substrate concentration (mol l-1 or mol m-3).

r

Reaction rate (mol l-1 min-1).

Km

Michaelis constant (mol m-3).

kcat

Catalytic constant or turnover number.

e

Enzyme concentration in reaction.

Zero-order reaction

Rate independent of substrate concentration.

First-order reaction

Rate depends on substrate concentration.

Michaelis-Menten equation

V = Vmax[S] / (Km + [S]).

Substrate saturation

Condition when [S] exceeds Km.

Enzyme-substrate complex

Intermediate formed during enzyme catalysis.

Rate constant

k, typically first-order (time-1).

Experimental data

Used to determine Michaelis-Menten parameters.

Trendline fitting

Method to extract parameters from plotted data.

Graph plotting

Visual representation of reaction rates versus substrate.

Reaction velocity

Speed of product formation over time.

Enzyme kinetics

Study of reaction rates involving enzymes.

Catalysis

Process of accelerating a chemical reaction.

Reaction mechanism

Stepwise process of substrate conversion to product.

Monod equation

Describes cell growth rate in bioreactors.

Specific growth rate (𝜇)

Rate of cell growth per time unit (s-1).

Maximum growth rate (𝜇max)

Highest specific growth rate achievable (s-1).

Substrate concentration ([S])

Concentration of substrate in solution (mol m-3).

Michaelis constant (𝐾+)

Substrate concentration at half Vmax (mol m-3).

Rate of reaction (rB)

Speed of enzymatic reaction (mol l-1 min-1).

Maximum velocity (Vmax)

Maximum reaction rate achievable (mol m-3 s-1).

Lag phase

Initial phase where cells acclimatize and grow in size.

Exponential phase

Rapid cell division and biomass increase occurs.

Stationary phase

Growth rate equals death rate; toxins accumulate.

Death phase

Cell numbers decline exponentially due to toxins.

Acceleration phase

Transition from lag to rapid growth phase.

Decline phase

Growth slows before entering stationary phase.

Growth rate (r@)

Rate of biomass increase over time.

Biomass

Total mass of living cells in culture.

Primary metabolites

Compounds produced during exponential growth phase.

Secondary metabolites

Compounds produced during stationary phase, often pharmaceuticals.

Toxin accumulation

Build-up of harmful by-products during growth.

Enzymatic processes

Biochemical reactions catalyzed by enzymes in cells.

Nutrient consumption

Utilization of resources for cell growth.

Bioreactor

Controlled environment for cultivating microorganisms.

Growth curve

Graphical representation of cell growth phases.

Growth rate (𝑟@)

Rate of biomass increase over time.

Biomass production

Amount of biological material generated.

Initial concentration (𝑋)

Starting amount of cells in culture.

Specific growth rate (𝜇)

Rate constant for cell growth per concentration.

Doubling time (𝑡Z)

Time required for cell concentration to double.

First-order kinetics

Reaction rate proportional to concentration.

Cell concentration (𝑥)

Amount of cells per volume unit.

Exponential growth phase

Rapid increase in cell number.

Lag phase

Initial period of adaptation before growth.

Stationary phase

Growth rate equals death rate, no net increase.

Death phase

Decline in cell number due to unfavorable conditions.

Turbidity meter

Device measuring microbial density via light scattering.

Monod equation

Model relating growth rate to substrate concentration.

Substrate concentration ([S])

Amount of nutrient available for cell growth.

Maximum growth rate (𝜇max)

Highest specific growth rate achievable.

Half-saturation constant (𝐾+)

Substrate concentration at half maximum growth rate.

Linear kinetics

Growth model assuming constant rate over time.

Reaction order

Determines how growth rate changes with concentration.

Slope of ln 𝑥 vs. 𝑡

Represents specific growth rate (𝜇).

Separation of variables

Mathematical method for solving differential equations.

Exponential growth equation

Describes growth as a function of time.

Homologue of Lineweaver-Burk equation

Used to calculate Monod parameters from experimental data.