Simulation Of Bioprocess ERT 315/4

Bioreaction Stoichiometry, Thermodynamics, and Kinetics

Stoichiometry -the basis for quantitative analysis of chemical and biochemical reactions -used to relate the relative quantities of the reactants with product that are formed -for single reactions, stoichiometric coefficients are well defined Example 1: vAA+vBB vCC vi: the stoichiometric coefficient for species i v is positive for the products and negative for the reactants The stoichiometric coefficients is the simplest ratio of the number of moles of reactant and product species involved in reaction

Stoichiometry Example 2: Hydrolysis of penicillin G to 6-inopenicillanic acid using penicillin acrylase Penicillin G salt + H2O Phenylacetate + 6-aminopenicillanic acid The stoichiometric coefficients for this reaction are all 1. Confirmed by checking elemental and charge balance,which is fulfilled for this reaction

Example 3 Dehydrogenase of formate -If two reactions are coupled, a stoichiometric amount of formate has to be fed to the reactor. The overall stoichiometry of this reaction is: Trimethylpyruvate + Ammonium + Formate L-tert-Leucine + Water + Carbon dioxide -The oxidized product carbon dioxide is eventually released into the gas phase, which has to be considered in the process model -In process modelling, the net reaction can be treated as a single reaction -the amount of NADH required is not determined by the stoichiometry because it only needed in catalytic amounts

A complete, well-defined stoichiometric equation can be set up for a whole set of biochemical reactions, e.g ethanol formation by yeast starting from glucose. This represents the net result of many coupled biochemical reactions which utilize multi-co-factors C6H12O6 2CO2 +2C2H6O Glucose 2Carbon dioxide + 2 Ethanol From the reaction: -the associated of yeast biomass is neglected -Yeast biomass is the catalyst for the formation of ethanol from glucose, and produce from glucose and other nutrients during fermentation -The rate and overall yield of ethanol will be influenced by the amount of yeast made but the stoichiometry for ethanol from glucose entering this reaction pathway is not effected

ΣvSjCSjCHSjHOSjONSjN + vO2 ΣvPjCPjCHPjHOPjONPjN +vCO2 + vH2OH2O Biomass synthesis: -a complex process requiring the elements carbon, nitrogen, oxygen, sulfur, phosphorus, calcium, iron, magnesium, etc. -For many complex biological reaction, not all elementary reaction and their contributions to the overall observed reaction stoichiometru. -The general case foe fermentation is usually approximated by an overall reaction equation: Substrates + O2 Products + CO2 + H2O ΣvSjCSjCHSjHOSjONSjN + vO2 ΣvPjCPjCHPjHOPjONPjN +vCO2 + vH2OH2O where, j: substrate or product, such as metabolites or biomasss,is given by a general formula, Ns and Np: the numbers of substrates and products, vSj and vPj: stoichiometric coefficients NS NS j=1 j=1 -recommended to formulate all equations in terms of C-moles, e.g. CH2O0.5 for ethanol to allow general fermentation balance on a molar basis (a mole of cells) and to indicate the Relative magnitudes of the stoichiometric coefficients from elemental balancing. C: ΣvSjSjC-ΣvPjPjC-vCO2=0 H: ΣvSjSjH-ΣvPjPjH -2vH2O=0 O: ΣvSjSjO+2vO2-ΣvPjPjO-vCO2 -2vH2O=0 N: ΣvSjSjN – ΣvPjPjN=0

-In a complex media, used yield coefficients derived from experimental data -Yields: variables, used to relate ratio between various consumption and production rates of mass and energy: assumed to be time- independent and are calculated on an overall basis -Examples: Biomass yield coefficients on substrate (YX/S): YX/S = amount of biomass produced/total amount of substrate consumed =ΔX/ΔS Energy yield coefficients: YQ/O2=amount of heat released/amount of oxygen consumed Carbon substrate consumed: YQ/S=amount of heat released/amount of substrate consumed

Thermodynamics ΔH = Σvi ΔHFi = Σvi ΔHCi -Two major important thermodynamics characteristics for the description of biochemical in process modeling: heat of reaction and thermodynamic equilibrium -heat of reaction: -the amount of heat to be removed by appropriate cooling since most biological reactions are run isothermally -determines by reaction enthalpies, ΔH, that can be calculated from the heats of Formation or heats of combustion: ΔH = Σvi ΔHFi = Σvi ΔHCi where, ΔHFi : the heat of component i, ΔHCi: the heat of combustion of component i having coefficient vi -can be determined experimentally from calorimetric measurement -negative for exothermic reaction and positive for endothermic reactions by convention -Thermodynamic equilibrium: i. Chemical equilibrium: defined by the equilibrium constant vAA+vBB vCC K=CvC/AvABvB ii. Gibbs Free Energy: ΔG is related to reaction enthalpy, ΔH and reaction entropy ΔS, ΔG0= ΔH0-TΔS0 The equilibrium constant is related to Gibbs Free Energy of a reaction by: ΔG0=-RT lnK, R is universal gas constant

Kinetics vs=vmax S KM+S+S2/K1 -the time needed for a desired conversion and therefore reactor size and associated investment costs -determine reaction selectivity -major kinetics process that was needed in process design: Enzyme kinetics, whole-cell kinetics -Enzyme kinetics: -follow Michaelis-Menten-type kinetics with first-order dependency in the higher, concentration range: Where Vmax: the maximum rate, S: substrate concentration, Km: saturation constant describing the affinity of enzyme -equation of substrate-inhibition kinetics caused by allosteric effects is:                       vs=vmax S KM+S+S2/K1 Where K1: inhibition constant, at high substrate concentration, rate is decreased proportionally with 1/S

where kd: deactivation constant, E: enzyme concentration -example of product inhibition: vs=vmax S KM+S+P/K1 -first-order reaction rate process of denaturation or deactivation of the biocatalyst: rd=-kdE where kd: deactivation constant, E: enzyme concentration -Whole-cell kinetics: -more complex than the individual enzymatic reaction -a typical growth curve is depicted below where substrate concentration and the Logarithm of biomass concentration are plotted against time S A: lag phase B: exponential C: Stationary D: Death -cellular growth is autocatalytic in nature and is often observed to be exponential, which is described in a batch reactor by: dX/dt=µmaxX, integration yield, X = X0eµmaxt X0: the initial biomass concentration

Km: substrate concentration of half maximum rate -exponential growth is characterized by the maximum specific growth rate µmax which is in turn dependent on the environmental conditions of the process -lag phases can be avoided or controlled by careful, reproducible pre-cultivation -substrate limitation can be described by Monod-type kinetics: µ =µmax S KM+S where, S:concentration of limiting substrate, µmax:maximum specific growth rate, Km: substrate concentration of half maximum rate -Typical kinetic patterns of growth and product formation: X B A P X,P X,P X,P C Time Time Time -most production processes operate only until the stationary growth phase (A) -production can starts already during growth but is prolonged into stationary phase (B) -production also occurs only in late phase of cultivation in which growth has slowed to a low rate (C)

Modeling and Simulation Of Bioprocesses

Modeling steps Define goal & process boundaries Collect data (internal and external) Define bioreactors Identity process flow diagram (unit operations + streams) Define unit operation models Perform simulations Make inventory analysis and assessments

Goal definition and model boundaries: -it is crucial to define the modeling goal right at the beginning -includes the final product specification (define not only molecule but also the necessary purity and other specifications), the plant size (derived either from a volume and number of fermenters or from an expected annual production), the biocatalyst and the model boundaries Data mining: -collect the necessary data Data source Possible difficulties Own experiments Previous project of a similar process Literature Patents Expert opinions Own estimates Scale, existence/availability Transferability, outdated information Accuracy, up-to-dateness, transferability Accuracy, (legal) usability Actual availability, range of opinions validation Bioreaction model: -from the collected data and the general bioprocess knowledge, the reaction equations and conditions are derived -first, list the raw materials. Next, determined the parameters like yields, fermentation time, final product concentration,by-product formation etc.

Process Flow diagram and unit operation: -Identify the process flow diagram (PFD) -Define all unit procedures and the process streams of the model -every unit operation has to be described in a model and the model parameters have to be defined Documentation: -addressed every model contains assumptions, estimates, and simplifications, influence on individual steps and the overall performance in an uncertainty analysis -created the model and finally transferred into suitable software where simulation are performed

Simulation steps Define process flow diagram Complete material database Define scale and process mode Define input streams Define reaction model Define unit operation parameters Solve material and energy balance Validate results, troubleshooting Scheduling Define and validate economic parameters