Unit 4 Metabolic Stoichiometry and Energetics PDF

UNIT IV METABOLIC STOICHIOMETRY AND ENERGETICS Unit-4 : Fundamentals of Biological Engineering Material and energy balances for reactive and non-reactive systems; Stoichiometry of growth and product formation; Degree of reduction, electron balance and theoretical oxygen...

UNIT IV METABOLIC STOICHIOMETRY AND ENERGETICS Unit-4 : Fundamentals of Biological Engineering Material and energy balances for reactive and non-reactive systems; Stoichiometry of growth and product formation; Degree of reduction, electron balance and theoretical oxygen demand, Determination of stoichiometric coefficients, Theoretical prediction of yield coefficients, Conductive and convective heat transfer; Overall heat transfer coefficient, Bio-thermodynamics. 1  STOICHIOMETRIC OF CELL GROWTH STOICHIOMETRY OF PRODUCT FORMATION 2  Stoichiometry of cell growth Cell growth is a fundamental process in microbiology and biotechnology, involving increasing cell mass and numbers over time. The stoichiometry of cell growth refers to the quantitative relationships between the consumption of nutrients and the production of biomass and byproducts during microbial growth. Cell growth and product formation are complex processes reflecting the overall kinetics and stoichiometry of the thousands of intracellular reactions observed within a cell. Atoms of carbon, nitrogen, hydrogen, oxygen, and other elements are rearranged in the cell's metabolic processes, but the total amounts of each element incorporated into cell material are equal to the amounts received from the environment. Further, the amount of some metabolic product formed or the amount of heat released by cell growth is often proportional to the amount of substrate consumption or formation of another product. 3 4 5  The complexity of the reactions can be represented by rigorous material balance constraints as well as approximate, empirical stoichiometric considerations These stoichiometric considerations have broad implications in biochemical technology ranging from growth medium formulation to computer control and cooling requirements in bioreactors. Also, as in reactor analysis in general, knowledge of stoichiometric relationships is critical in formulating bioreactor material balances and making most effective and systematic use of reaction kinetics. 6  Medium Formulation and Yield Factors Cell growth involves the consumption of substrates, which provide energy and raw materials required to synthesize additional cell mass. Medium formulation is more complicated for the following reasons (i) Some substrate elements are released in products not assimilated into cell material (ii) Rate limitations, as well as stoichiometric limitations, must be considered (iii) Specific nutrients may be limiting or specific products may be inhibitory due to the metabolic properties of a particular cell strain. It is necessary to consider both stoichiometry and kinetics when formulating a strategy for simplifying the stoichiometric representation of cell growth and product formation. The number of nutrient components in the medium is typically very large, and we cannot in practice, include all of them in our considerations either of process stoichiometry or of process kinetics. The rational simplification of the system's description based upon identifying certain key, limiting compounds or elements. The stoichiometric relationship is also potentially useful for bioreactor monitoring: measurement of substrate concentration implies a corresponding estimate of the cell concentration if initial values of both quantities are known. 7  Product Formation Stoichiometry A variety of metabolic end products is released into the growth medium or accumulated intracellularly. The pertinent stoichiometries for product formation may be classified into the following four classes; the first three correspond to the fermentations classification formulated by Elmer L. Gaden, Jr. in 1995. 1. The main product appears as a result of primary energy metabolism. Eg. Ethanol production during the anaerobic growth of yeast 2. The main product arises indirectly from energetic metabolism Eg of citric acid formation during aerobic mold cultivation 3. The product is a secondary metabolite. Eg. Penicillin production in aerated mold culture 4. Biotransformation. The product is obtained from substrate through one or more reactions catalyzed by enzymes in the cells. Eg. Steroid hydroxylation 8  Class 1 processes have a relatively simple stoichiometric description. Product appears in relatively constant proportions as cell mass accumulates and substrate is consumed. Here, substrate utilization, cell mass synthesis, and product formation are linked as in a simple, single chemical reaction. CHmOn + aO2 + bNH3 -------- cCHαOβNδ + dH20 + eCO2 + f CHxOy Nz For class 2 situations, the simple stoichiometry does not apply. Product formation is not necessarily proportional to substrate utilization or cell mass increase. Representation of the stoichiometry in such a case requires an independent reaction equation for product formation. 9  The stoichiometric descriptions appropriate for classes 3 and 4 cases depend on the particular substrates and products involved. Product formation in these cases is typically completely uncoupled from cell growth. Secondary metabolite accumulation is dictated by kinetic regulation and activity of the cells Examination of product formation stoichiometry offers several useful insights for engineering analysis. One application is an estimation of the upper bound for product yields. These numbers can be very useful in preliminary economic analysis. 10 ELEMENTAL BALANCE, DEGREE OF REDUCTION SUBSTRATE AND BIOMASS 11  Elemental Balances Cell growth and metabolic activities are similarly described as a simple chemical reaction. It is also necessary to establish a definite formula for dry cell matter. The elemental composition of certain strains of microorganism is defined by an empirical formula CHαOβNδ The general biochemical reaction for biomass production is based on consumption of organic substrate as shown below. Substrate oxidation is simplified in the following biochemical oxidation CHmOn + aO2 + bNH3 -------- cCHαOβNδ + dH20 + eCO2 CHmOn - 1 mole of carbohydrate CHαOβNδ - 1 mole of cellular material 12  CHmOn + aO2 + bNH3 -------- cCHαOβNδ + dH20 + eCO2 Elemental balances on C, H, O, and N yield the following equation, C: 1=c+e H: m+3b=cα+2d 1 O: n+2a=cβ+d +2e N: b=cδ Respiratory quotient, 2 Equation 1 and 2 constitute five equations for 5 unknowns a, b, c, d, e. With the measured value of RQ, these equations can be solved to determine the stoichiometry coefficients.  Degree of Reduction The degree of reduction is equal to the valency of the element. The degree of reduction of some key elements C=4; H=1; N=-3; O=-2; P=5 And S=6 The degree of reduction of any element in a compound is equal to the valence of the element 14 Examples for calculating the degree of reduction Methane (CH4): 1(4) + 4(1) =8; γ=8/1=8 Glucose (C6H12O6): 6(4) +12(1) +6(-2) =24; γ=24/6=4 Ethanol (C2H5OH): 2(4) +6(1) +1(-2) =12; γ=12/2=6 The high degree of reduction indicates a low degree of oxidation. Consider the aerobic process of a single extracellular product CHmOn+aO2+bNH3-------- cCHαOβNδ+dCHxOyNz+eH20+fCO2 The degree of reduction of substrate, biomass, and product are γs=4+m-2n γb=4+α-2β-3δ γp=4+x-2y-3z The degree of reduction of CO2, NH3, and H2O is 0.  ELECTRON BALANCE YIELD COEFFICIENT OF BIOMASS AND PRODUCT FORMATION 16  Electron Balance CwHxOyNz + aO2 + bHgOhNi ---- cHαOβNδ + dH2O + eCO2 + fCjHkOlNm Electron Balance : wγs – 4a = cγb + fjγp a = (wγs - cγb - fjγp)/4 Maximum Possible Yield 4a/ wγs + cγb/ wγs + fjγp/ wγs = 1 ξ + ξb + ξp = 1 Maximum Biomass Yield ξb = 1 ξb = cγb/ wγs cmax = wγs/γb Maximum Product Yield ξp = 1 ξp = fjγp/ wγs fmax = wγs/jγp An energy balance for aerobic growth is Qocγb+Qodγp= Qoγs-Qo4a biomass product substrate oxygen Where Qo—heat evolved per equivalent of available electrons transferred to oxygen If Qo is constant, cγb+dγp= γs-4a 1= cγb/γs +dγp/γs+4a/γs 1= ξb+ ξp+ ξ Where, ξ is the fraction of available electrons in the organic substrate that is transferred to oxygen, ξb is the fraction of available electrons incorporated into the biomass ξp is the fraction of available electrons incorporated into the extracellular product.  Yield Coefficients Yield coefficients based on other substrates or product formation may be defined as: Yield coefficient Yx/s= -∆X/∆S Apparent Yield coefficient Yx/o2 = -∆X/∆O2 Observed Yield coefficient Yp/s= -∆P/∆S Theoretical Yield coefficient Y x/s = Yx/ATP N Where Yx/ATP = Moles of Biomass produced / Moles of ATP generated And N = Moles of ATP produced / gram of substrate consumed. Maintenance coefficient For continuous culture, M (based on the substrate) = kd/ Ym x/s Where kd is the first order rate constant. Overall Yield Coefficient Ym x/s = maximum biomass produced per gram of substrate consumed when maintenance is not considered. 19 Ykcal = Moles of Biomass produced / Kcal of heat evolved in fermentation.  True or Stoichiometric or theoretical yield = (total mass or mole of product formed) /(mass or moles of reactant used to form that particular product) Observed or apparent yield = (mass or moles of product present) /(total mass or moles of reactant consumed) YX/S = mass or moles of biomass produced per unit mass or moles of substrate consumed. YP/S = mass or moles of product formed per unit mass or moles of substrate consumed. YP/X = mass or moles of product formed per unit mass or moles of biomass. YX/O = mass or moles of biomass formed per unit mass or moles of oxygen consumed. YCO2/S = mass or moles of CO2 formed per unit mass or moles of substrate consumed. RQ = moles of CO2 formed per mole of O2 consumed applied only for balanced growth. For continuous culture, M (based on substrate) = kd/ Ym x/s Where kd is the first order rate constant Overall Yield Coefficient Ym x/s = maximum biomass produced per gram of substrate consumed when maintenance is not considered 20  Problems 1. Assume that experimental measurement for a certain organism has shown that cells can convert 2/3 w/w of the substrate carbon (alkane or glucose) to biomass. a) Calculate the stoichiometric coefficient for the following biochemical reaction: Hexadecane: C16H34+aO2+bNH3--------------- cC4.4H7.3N0.86O1.2+dH2O+eCO2 Glucose: C6H12O6+aO2+bNH3--------------- cC4.4H7.3N0.86O1.2+dH2O+eCO2 b) Calculate yield coefficient Y x/s and Y x/o2 for both reactions. Solution: Hexadecane reaction: C-balance : Amt. of carbon in 1 mole of substrate = 16x12=192g. Amt. of carbon converted in biomass = 192 x 2/3 = 128g. Amt. of carbon in biomass = 12x4.4c=52.8g. 128g=52.8c g c=128/52.8=2.424 Amt. of carbon converted to CO2 = 192-128=64g 12xe=64 e=5.33g N-balance : b=0.86c b=2.0846 H-balance : 34+3b=7.3c+2d d=11.27 O-balance : 2a=1.2c+d+2e a=12.42 a=12.42; b=2.0846; c=2.424; d=11.27; e=5.33 Y x/s = (c x Molecular wt. of biomass)/Molecular wt. of substrate Molecular wt. of biomass = 4.4(12)+7.3+0.86(14)+1.2(16) = 91.34g Molecular wt. of substrate = 16(12)+34 = 226g Y x/s = 2.424 x 91.34 / 226 =0.9796 g of biomass/g of substrate. Y x/o2 = (c x Molecular wt. of biomass)/(a x Molecular wt. of oxygen) Y x/o2 = (2.424 x 91.34) / (12.42 x 32) = 0.5566 g of biomass/g of O2  Exercise Problems 2. The growth of Saccharomyces cerevisiae on glucose under anaerobic conditions can be described by the following overall reaction, C6H12O6 + βNH3 0.59CH1.74N0.2O0.45 + 0.43C6H8O3 + 0.036H2O + 1.54CO2 + 1.3C2H5OH a) Determine Y x/s, Y ethanol/s, Y CO2/S, Y C6H8O3/s b) Determine the coefficient β 3. Aerobic growth of bacteria on ethanol described by the following overall reaction: C2H5OH + aO2+bNH3--------------- cC5H7NO2+dH2O+eCO2 a) Determine coefficients a,b,c,d and e where RQ =0.66 b) Determine Y x/s and Y x/o2  4. Aerobic degradation of benzoic acid by a mixed culture of icroorganism can be described by the following overall reaction: C6H5COOH + aO2+bNH3--------------- cC5H7NO2 + dH2O + eCO2 a) Determine coefficients a,b,c,d and e where RQ=0.9 b) Determine Y x/s and Y x/o2 c) Determine the degree of reduction of substrate and bacteria. 5. Aerobic degradation of an organic compound by a mixed culture of MO in wastewater can be represented by the following overall reaction: C3H6O3 + aO2+bNH3--------------- cC5H7NO2 + dH2O + eCO2 a) Determine coefficients a,b,c,d, and e if Y x/s = 0.4 g of dry wt. cells/g of substrate b) Determine Y x/o2 ,Y x/s c)Determine the degree of reduction of substrate and bacteria. d)Determine the RQ of the organism.  6. Biological denitrification of nitrate-containing wastewater can be described by: NO3- + aCH3OH + H+ --- bC5H7NO2 + dH2O + eCO2 a)Determine coefficients a,b,c,d, and e if Y x/s = 0.5 g of dry wt.cells/g of N b) Determine the degree of reduction of bacteria and methanol. ENERGETIC ANALYSIS OF MICROBIAL GROWTH AND PRODUCT FORMATION 27  Microorganisms carry out oxidation-reduction reactions in order to obtain energy for growth and cell maintenance. The amount of energy released per electron equivalent on an electron donor oxidized varies considerably from reaction to reaction Cell maintenance has energy requirements for activities such as cell movement and repair of cellular proteins that decay because of normal resource recycling or through interactions with toxic compounds. When cells grow rapidly in the presence of nonlimiting concentrations of all factors required for growth, cells make the maximum investment of energy for synthesis. However, when an essential factor, such as the electron-donor substrate, is limited in concentration, then a larger portion of the energy obtained from substrate oxidation must be used for cell maintenance. 28 29  The net yield of cells decreases with a decrease in substrate utilization rate. The net yield becomes zero when the energy supplied through substrate utilization equals m, the maintenance energy. Under these conditions, all energy released is used just to maintain the integrity of the cells. If the substrate available for the microorganisms decreases further, food is insufficient to maintain the microorganisms, and they go into net decay. 30  Conversely, when substrate and all other required factors are unlimited in amount, the rate of substrate utilization will be at its maximum, and the net yield, Yn, will approach the true yield, Y. Over the years, many approaches have been taken to describe how the true yield relates to the energy released from electron–donor oxidation. Although no unified approach for relating growth to reaction energetics is yet widely accepted, a method based on electron equivalents and differentiating between the energy portion of an overall biological reaction and the synthesis portion has proven useful. 31 OXYGEN TRANSFER IN AEROBIC CULTURES 32 OTR (Oxygen Transfer Rate) No2 = kLa (C*-CL) Where, kL is the oxygen transfer coefficient (cm/h) a is the gas-liquid interfacial area (cm2/cm3) kLa is the volumetric oxygen transfer coefficient (h-1) C* is saturated DO concentration (mg/l) CL is the actual DO concentration in the broth (mg/l) No2 is the rate of oxygen transfer (mg O2/l.h) Oxygen Uptake Rate Where qo2 is the specific rate of oxygen consumption (mg O2/g dw cells.h), YX/o2 is the yield coefficient on oxygen (g dw cells/g O2), X is cell concentration (g dw cells/l). When oxygen transfer is the rate-limiting step, oxygen consumption equals the oxygen transfer rate. If the maintenance requirement of O2 is negligible compared to growth, then µgX/ (YX/o2) = kLa(C*-CL) or dX/dt= (YX/o2) kLa(C*-CL)  Theoretical Oxygen Demand Oxygen demand is an important parameter in bioprocessing, as oxygen is often the limiting substrate in aerobic fermentations. Oxygen demand is represented by the stoichiometric coefficient in Eqs (1) and (2). Oxygen requirement is related directly to the electrons available for transfer to oxygen; the oxygen demand can therefore, be derived from an appropriate electron balance. When product synthesis occurs, as represented by Eq. (2), the electron balance is (Eq. 3): (1) (2) (3) 35  where fp is the stoichiometric coefficient for the product. Product synthesis introduces one extra unknown stoichiometric coefficient to the equation; thus, an additional relationship between coefficients is required. This is usually provided as another experimentally determined yield coefficient, the product yield from the substrate, YPS: As mentioned above with regard to biomass yields, we must be sure that the experimental system used to measure YPS conforms to Eq. (2). Eq. (2) does not hold if product formation is not directly linked with growth; accordingly it cannot be applied for secondary-metabolite production such as penicillin fermentation, or for biotransformations such as steroid hydroxylation which involve only a small number of enzymes in cells. In these cases, independent reaction equations must be used to describe growth and product synthesis. 36  where γp is the degree of reduction of the product. Rearranging gives: (4) Eq. (4) is a very useful equation. It means that if we know which organism (γ B)' substrate (wand γs) and product (j and γp,) are involved in cell culture, and the yields of biomass (c) and product (f), we can quickly calculate the oxygen demand. Of course we could also determine a by solving for all the stoichiometric coefficients of Eq. (2)) allows more rapid evaluation and does not require that the quantities of NH3, CO2 and H20 involved in the reaction be known. 37  From Eqn. 3, The fractional allocation of available electrons in the substrate can be written as: (5) In Eq. (5), the first term on the right-hand side is the fraction of available electrons transferred from substrate to oxygen, the second is the fraction of available electrons transferred to biomass, and the third is the fraction of available electrons transferred to the product. This relationship can be used to obtain upper bounds for biomass and product yields from the substrate. 38 HEAT EVOLUTION IN AEROBIC CULTURE 39  Heat Generation by Microbial Growth About 40% to 50% of the energy stored in a carbon and energy source is converted to biological energy (ATP) during aerobic metabolism, and the rest of the energy is released as heat. For actively growing cells, the maintenance requirement is low, and heat evolution is directly related to growth. The heat generated during microbial growth can be calculated using the heat of combustion of the substrate and of cellular material. A schematic of an enthalpy balance for microbial utilization of substrate is presented in the following figure. The heat of combustion of the substrate is equal to the sum of metabolic heat and the heat of combustion of the cellular material where, is the heat of combustion of the substrate (kJ/g substrate), Yx/s is the substrate yield coefficient(g cell/g substrate), is the heat of combustion of cells(kJ/g cells),and 1/YH is the metabolic heat evolved per gram of cell mass produced(kJ/g cells). and can be determined from the combustion of substrate and cells.  The total rate of heat evolution in a batch fermentation is QGr = VLµnet x 1/YH Where VL is the liquid volume (I) and X is the cell concentration (g/l). In aerobic fermentations, the rate of metabolic heat evolution can roughly be correlated to the rate of oxygen uptake, since oxygen is the final electron acceptor. QGr = 0.12QO2 Here QGr is in units of kcal/h,while QO2 is in millimoles of O2/h. Metabolic heat released during fermentation can be removed by circulating cooling water through a cooling coil or cooling jacket in the fermenter. Often, temperature control is an important limitation of reactor design. The ability to estimate heat-removal requirements is essential to proper reactor design. 42 BIOTHERMODYNAMICS 43  Thermodynamics is the quantitative study of the energy G transductions in living organisms, the pathways, and functions of the chemical processes. In biotechnology, the development of thermodynamic analysis has two fundamental concepts underlying most quantitative theories and calculations in engineering sciences, these being balances (e.g., mass, elemental, energy, momentum) and kinetics (e.g., momentum and mass transfer, reaction and growth kinetics). The resulting lack of basic data concerning biomolecular properties, thermodynamic equilibrium position, formulation of driving forces, and energy efficiency relations in biotechnology is one among several reasons why the development and design of biotechnological processes is still today in many cases carried out in an essentially empirical fashion and why bioprocesses often are not as thoroughly optimized as many chemical processes. The thermodynamic analysis should be able to predict whether the growth of a given type of cells or a specified type of metabolic reaction is feasible and under what conditions. On the basis of such analyses, it ought to be possible to estimate key parameters of biotechnological cultures roughly and thus to address the economic viability of the process before 44 even performing experiments. 45  Fundamentals of Biothermodynamics The continuous heat generation by microbial cultures could also be used as a basis for an online monitoring of microbial activity and metabolism. If the temperature increase in the cooling water, its flow rate, and the other relevant energy exchange terms such as agitation and evaporation rates were measured systematically, the heat dissipation rate of the cellular culture could quantitatively be monitored online in industrial fermenters. 46 The First Law and energy balances In microbial growth, the growth reaction may be formulated as a so-called macrochemical equation with fixed stoichiometry. A typical example reads: where S, A, X, and P represent the carbon and energy source, an electron acceptor, the newly grown biomass, and a catabolic waste product, respectively. YX/S denotes the biomass yield on the carbon and energy source (C-mol of biomass / C-mol of S), Yi/X the other yields. Based on below equation, it is possible to (i) predict heat dissipation rates for live cultures, or conversely to (ii) use measured heat dissipation rates to determine the enthalpy of growth, rHX, or to (iii) observe the biological activity, i.e., rX, on-line. 47  where Q represents the heat signal. Ve and CPe stand for the entering molar flow rate and the mean heat capacity of the mixture respectively, and rHX represents the heat of reaction, and rX denotes its rate (C-mol m3 s-1). To measure heat dissipation Q, a calorimetric technique has to be applied to the bioreactor. 48  The temperature TR in the reaction vessel itself is measured very accurately. The control algorithm continuously adapts the temperature TJ so that TR remains at its set point value. The different TR - TJ is a measure for the heat flow rate transferred to the jacket (W) and may be used to determine the Q according to the below equation: 49  Gibbs energy transduction from energy-yielding to biosynthetic reactions The dissipation of energy in the form of heat was directly measured in a reaction calorimeter and compared with predictions from an energy balance. The Gibbs energy dissipation was evaluated based on the observed stoichiometry. 50  In formulating the biosynthetic reaction it was assumed that all of the substrate is catabolized first and biomass then synthesized from catabolic products. For these investigations, the enthalpy and the Gibbs energy of reaction had to be evaluated based on their definition: The stoichiometric coefficients are defined by the yield factors and must be determined experimentally. The enthalpies and Gibbs energies of combustion were known from thermodynamic tables. The heat of combustion for dried biomass was determined by direct measurements in a combustion calorimeter. 51