Substrate limiting

Starting from an inoeulum, at t = 0, and an initial quantity of limiting substrate at t = 0, the biomass will grow after a short lag phase and will eonsume substrate. The growth rate slows as the substrate eoneentration deereases, and beeomes zero when all the substrate has been eonsumed. Simultaneously, the biomass eoneentration initially inereases slowly, then faster until it levels off when the substrate beeomes depleted. Figure 11-21 shows a sketeh of a bateh fermenter. 

The multi-stream multi-stage system is a valuable means for obtaining steady-state growth when, in a simple chemostat, the steady-state is unstable eg when the growth-limiting substrate is also a growth inhibitor. This system can also be used to achieve stable conditions with maximum growth rate, an achievement that is impossible in a simple chemostat (substrate-limited continuous culture). 

Biomass feedback refers to increasing the concentration of biomass in the culture vessel. This is achieved by fitting some device, either internally or externally, to the continuous culture which retains or returns biomass to the vessel. The main advantage of biomass feedback is that the maximum output rate of biomass (and products) in the vessel with a given medium can be increased. This is particularly useful when the growth-limiting substrate is unavoidably dilute, for example if substrate has low solubility or has to be limited because of the formation of an inhibitory product. 

Applications of peroxide formation are underrepresented in chiral synthetic chemistry, most likely owing to the limited stability of such intermediates. Lipoxygenases, as prototype biocatalysts for such reactions, display rather limited substrate specificity. However, interesting functionalizations at allylic positions of unsaturated fatty acids can be realized in high regio- and stereoselectivity, when the enzymatic oxidation is coupled to a chemical or enzymatic reduction process. While early work focused on derivatives of arachidonic acid chemical modifications to the carboxylate moiety are possible, provided that a sufficiently hydrophilic functionality remained. By means of this strategy, chiral diendiols are accessible after hydroperoxide reduction (Scheme 9.12) [103,104]. 

Substrate Consumption. Consumption of substrates and generation of products can be described using empirical yield coefficients. Yields are usually based on the amount of limiting substrate that has been consumed. Thus, Ypjs denotes the mass of product produced per mass of substrate consumed, and Yxts denotes... 

There may be a limiting substrate concentration required for induction of the appropriate catabolic enzyme. At low substrate concentrations the necessary enzymes wonld simply not be synthesized, and this could be the determining factor in some circumstances (Janke 1987). 

The oxidative cleavage of alkenes is a common reaction usually achieved by ozonolysis or the use of potassium permanganate. An example of NHC-coordina(ed Ru complex (31) capable of catalysing the oxidative cleavage of alkenes was reported by Peris and co-workers (Table 10.9) [44]. Despite a relatively limited substrate scope, this reaction reveals an intriguing reactivity of ruthenium and will surely see further elaboration. 

Here the single limiting substrate is taken to be oxygen. 

Oin experimental technique of choice in many cases is reaction calorimetry. This technique relies on the accurate measurement of the heat evolved or consumed when chemical transformations occur. Consider a catalytic reaction proceeding in the absence of side reactions or other thermal effects. The energy characteristic of the transformation - the heat of reaction, AH i - is manifested each time a substrate molecule is converted to a product molecule. This thermodynamic quantity serves as the proportionality constant between the heat evolved and the reaction rate (eq. 1). The heat evolved at any given time during the reaction may be divided by the total heat evolved when all the molecules have been converted to give the fractional heat evolution (eq. 2). When the reaction under study is the predominant source of heat flow, the fractional heat evolution at any point in time is identical to the fraction conversion of the limiting substrate. Fraction conversion is then related to the concentration of the limiting substrate via eq. (3). 

The temporal reaction heat flow data may be graphically manipulated to reveal the overall second order dependence in a quantitative manner. Reaction heat flow is converted to reaction rate using eq. (1), and the concentration of the limiting substrate 5 may be calculated according to eq. (3). From these calculations we may constract the plot in Figure 50.2b of reaction rate vs. [5]. The reaction is known to be first order in both [5] and [6] these plots reveal the curvature typical of overall second order kinetics. 

In this section we shall use the standard notation employed by biochemical engineers and industrial microbiologists in presenting the material. Thus if we denote by Xv the viable cell (cells/L) or biomass (mg/L) concentration, S the limiting substrate concentration (mmol/L) and P the product concentration (immol/L) in the bioreactor, the dynamic component mass balances yield the following ODEs for each mode of operation ... 

The limiting substrate (glucose) concentration is denoted by S. There are four parameters pmax is the maximum specific growth rate, Ks is the saturation constant for S, kd is the specific death rate and Y is the average yield coefficient (assumed constant). 

Tong, C. C., and Fan, L. S., Concentration Multiplicity in a Draft Tube Fluidized-Bed Bioreactor Involving Two Limiting Substrates, Biotechnol. Bioeng., 31 24 (1988)... 

A dynamic model has been developed to simulate the behavior of a Pseudomonas sp. 0X1 biofilm reactor for phenol and azo-dye conversion during the aerobic-anaerobic cyclic operation. Phenol and oxygen were considered as the limiting substrates for growth kinetics. 

A continuous fermenter is operated at a series of dilution rates though at constant, sterile, feed concentration, pH, aeration rate and temperature. The following data were obtained when the limiting substrate concentration was 1200 mg/1 and the working volume of the fermenter was 9.8 1. Estimate the kinetic constants Km, //, and kd as used in the modified Monod equation ... 

Substrate-limited growth in terms of reduced availability of both the electron donor and the electron acceptor is common in wastewater of sewer systems. Based on the concept of Michaelis-Menten s kinetics for enzymatic processes, Monod (1949) formulated, in operational terms, the relationship between the actual and the maximal specific growth rate constants and the concentration of a limiting substrate [cf. Equation (2.14)] ... 

These second-order nonlinear differential equations have no explicit solution but can be solved numerically. The limiting substrate for the biofilm transformations is the one that penetrates the shortest distance into the biofilm. Equations (2.26) and (2.27) are, thereby, reduced to an equation corresponding to Equation (2.20). If the limiting substrate cannot be identified, approximations based on Equation (2.25) can be developed. 

Fig. 1.23 Specific growth rate versus limiting substrate concentration according to the Monod relation.

Starting from an inoculum (X at t=0) and an initial quantity of limiting substrate, S at t=0, the biomass will grow, perhaps after a short lag phase, and will consume substrate. As the substrate becomes exhausted, the growth rate will slow and become zero when substrate is completely depleted. The above general balances can be applied to describe the particular case of a batch fermentation (constant volume and zero feed). Thus,... 

Where p = specific growth rate, p max = maximum specific growth rate, X = microorganism concentration, S= growth limiting substrate concentration, and Ks= half saturation coefficient for hydrolysis. 

The relationship between reaction velocity and enzyme concentration (in the absence of self-association of the enzyme) should also be adjusted such that reaction rate is linearly related to catalyst concentration, [Etotai]- Initial rates typically fail to obtain if [Etotai] = 0-01 [Ajmitiai where [Ajinitiai is the initial substrate concentration. As a general rule, the substrate concentration will not have changed more than 5-10% of its value over the initial rate phase of the reaction. This rule-of-thumb applies only to thermodynamically favorable reactions, and investigators are well advised to limit substrate consumption to well below 5%. 

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