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In this study, the entrapment of amyloglucosidase from Aspergillus niger into dipalmitoylphosphatidylcholine …

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Mathematical models
- Amyloglucosidase enzymatic reactivity inside lipid vesicles

The kinetics of amyloglucosidase from different sources has been extensively investigated [14-16]. Process conditions, including temperature, pH, chain length of the starch, and starch concentration, have been found to influence the rate constants.

The rate of starch consumption by amyloglucosidase can generally be expressed in a Michaelis-Menten form with competitive product inhibition [15]:


where S is substrate concentration (mg mL-1), Vmax (mg mL-1 min-1) the maximum rate of reaction, Km (mg mL-1) the Michaelis-Menten constant, G product concentration (mg ml-1), and Ki (mg mL-1) the inhibition constant.

AMG-containing lipid vesicles were first proposed for use in enzyme-replacement therapy [17]. A quantitative understanding of enzyme reactions in vesicles is crucial to understanding the enzyme performance and mass transfer limitation [18]. An AMG-containing vesicle system is schematically illustrated in Figure 1. Starch diffuses from the bulk aqueous phase, permeates across the dipalmitoylphosphatidylcholine (DPPC) bilayer shell of the liposome into the vesicle's aqueous lumenal phase (interior), where the enzymatic hydrolysis reaction is catalyzed by entrapped AMG. The flux of starch from the external phase into the aqueous interior is assumed to follow Fick's first law of diffusion [19,20]. The mass balance for starch in the bulk solution is expressed in Equation 2.


where [S]outside and [S]insideare the substrate (starch) concentration outside and inside the vesicles at time t, respectively. Kc is mass transfer coefficient. Once the vesicle surface area and volume are determined, permeability coefficient (Ps) for the substrate can be calculated [18].

The mass balance inside vesicle can be expressed in Equation 3.


Michaelis-Menten kinetics with competitive product inhibition (Eq. 1) can be applied to describe the rate of enzymatic reaction (v) inside the vesicles (Eq. 4).


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