Mathematical Model for Microbial Metabolism

Ultrasound Assisted Microbial Desulfurization

5.3.2 Mathematical Model for Microbial Metabolism

The time profiles of product (HBP) formation and substrate consumption were fitted to Haldane kinetics model as suggested by Caro et al. (2007):

[ ] [ ] [ ]

max

2 o o

o

m o

I

V S

V

K S S K

=

+ +

.

Various notations are: Vmax – maximum reaction velocity or rate of product formation, Km – Michaelis constant, KI – inhibition constant, Vo – initial velocity of the reaction, So – initial substrate concentration. Haldane substrate inhibition kinetic model assumes that the enzyme has two binding sites for the substrate S. First site is a catalytic site that can produce a product, P; and the second is a non-catalytic site that

can produce a product at reduced rate or may not produce any product at all. Binding of substrate to catalytic site results in E⋅S complex formation (E+S←→E S⋅ ⁾, while binding of two substrate molecules to both catalytic and non-catalytic site results in formation of complex S⋅E⋅S (E+S←→E S⋅ +S←→S E S⋅ ⋅ ⁾. Haldane kinetic model makes three assumptions: (1) binding of substrate to catalytic site precedes the binding to non-catalytic site, (2) no product forms through S⋅E⋅S complex (or the kinetic constant of product formation through S⋅E⋅S complex is zero), and (3) rapid equilibrium for the E⋅S complex formation in reaction: E+S←→E S⋅ . KI is the dissociation equilibrium for the reaction: S E S⋅ ⋅ ←→ + ⋅S E S. An inspection of the Haldane kinetic expression reveals that reaction velocity goes to zero for excess substrate concentration [S] for which the double binding of substrate to enzyme predominates resulting in non-productive S⋅E⋅S complex. The parameters Km, KI and Vmax in the Haldane kinetic expression have physical significance. Low value of Km signifies greater affinity of enzyme towards substrate. High value of KI signifies lesser tendency of enzyme towards substrate binding to non-catalytic site. Finally, high value of reaction velocity Vmax indicates fast splitting of E⋅S complex into the products. Comparative evaluation of these parameters or constants for different experimental categories employing different experimental conditions gives a mechanistic account of the influence of ultrasound on biodesulfurization process.

Numerical values of the three parameters of Haldane kinetics model can be determined by measuring initial reaction velocities of DBT oxidation for three initial substrate concentrations, and solving the Haldane kinetic equation with these values.

It should be noted that biodesulfurization of DBT occurs through four steps that involves four enzymes (DszA, DszB, DszC, Flavin reductase). The physiological

characteristics of each enzyme, and hence, their response to the different experimental conditions, could be distinct from other. The biodesulfurization rate calculated using time profiles reduction in concentration of DBT or increase in concentration of the final product HBP is a manifestation of the overall or gross kinetics of all enzymatic reactions in the metabolic pathway. The numerical values of parameters of Haldane kinetic model fitted to DBT reduction profile are, thus, representative of the “lumped”

or “consolidated” physiology of all enzymes involved in the desulfurization metabolism.

5.4. R

ESULTS AND

D

ISCUSSION 5.4.1 Preliminary Experiments

Effect of organic (O)/aqueous (A) volume ratio: The effect of O/A volume ratio on reduction on DBT (for initial DBT concentration of 0.54 mM or 100 ppm) is depicted in Fig. 5.2.A. The maximum degradation of DBT occurs for volume ratio of 1:1 for both mechanical stirring and sonication. This result can be explained as follows: the extent of DBT reduction depends on two factors, viz. the cell density or population in the reaction mixture and the interfacial area between organic and aqueous phase.

Microbial cell concentration (or population) in the reaction mixture reduces for higher O/A volume ratio (or lower fraction of water containing microbial cells in total reaction mixture). While for lower O/A ratio (or higher fraction of aqueous phase in reaction mixture), the extent of emulsification in reaction mixture is reduced. The cause leading to this effect could be high surface tension (and hence interfacial tension) of water due to which toluene does not get dispersed properly in the continuous aqueous phase. In case of sonication, another factor that also contributes to lower dispersion of toluene in aqueous phase is relatively lesser intensity of acoustic

(or shock) waves emitted by cavitation bubbles in water – as explained in greater detail in section on simulations results. The best combination of microbial cell population and interfacial area (or emulsification) is obtained for phase ratio of 1:1, which is reflected in the highest DBT oxidation.

Optimization of amount of immobilized support: The optimum amount of immobilized support in the reaction mixture (for both mechanical agitation and sonication) was determined by varying the number of cubes of polyurethane foam added to reaction mixture. Results shown in Fig. 5.2.B reveal that the highest DBT oxidation was achieved for 2 cubes for both mechanical shaking and sonication system. Lesser cubes reduce the microbial cell population in the reaction medium.

Large numbers of cubes in the reaction mixture hinder convection as well as emulsification in reaction mixture. Net result of both of these causes is reduction in DBT oxidation.

Effect of surfactant: β–CD acts as a phase transfer agent for DBT as it forms complexes with DBT that have high solubility in the aqueous phase. The percentage reduction of DBT obtained for different concentration of β–CD is shown in Fig.

5.2.C. The highest DBT oxidation was observed for 20 ppm concentration of β–CD for both free and immobilized cells. At high concentration (> 30 ppm), the surfactant molecules can competitively adsorb on the water-toluene interface along with microbial cells. This effect can hinder access of microbial cells to the DBT molecules that are transported across the interface. This effect is more marked for free cells than the immobilized cells, which are already adsorbed on the polyurethane support and do not compete with surfactant for adsorption on interface.