# Biomod/2014/UANL/KineticModel

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# Kinetic model

A mathematical model will help describe the behavior of the reactions that develop inside the reactor

The following reactions are proposed to describe the system:

The Michaelis-Menten equation is prefered as it describes better the selected reactions. It is represented by the following symbols:

Where:

Sustrates: S1 is uric acid y S2 is peroxyde.

Enzymes: E1 is uricase and E2 is catalase.

W: water

O: diatomic oxygen

P1 : products (allantoin and carbon dioxide)

ES1 and ES2 : enzyme - substrate complex

These are the substrate's reaction rates:

These are the enzyme-substrate’s net reaction rates:

Enzymes does not get consumed so the concentrations (Et) remain constant and equal to the sum of the free enzyme E plus the substrate-enzyme complex ES*.

The equations above can be rearranged to show the rates of reaction using measurable variables:

Assuming excess water and oxygen, equations (7) and (8) can be rewritten as:

Where :

Maximun rates of reaction for each enzyme are represented as Vmax and the following equations are obtained:

Where:

Reverting the equation (11):

The graphic shows that equation (13) has the shape of a straight line. Its intersection with the Y axis is the maximum velocity’s inverse and the slope is Michaelis constant divided over the maximum velocity. This graphic is known as Lineweaver-Burk. The diagram allow to find some parameters of the Michaelis -Menten equation like Vmax y Km

It can be found on available literature that the relation between uric acid and uricase has a Km = 16.2mmol/min and a Vmax = 0.025mmol/min. at pH=7.0 and 350C.

Considering the nanoreactor as a batch reactor, isothermal and with a constant pH, mol balances can be defined as:

Combining equations (11) and (12) with (14) and (15) respectively, the next result is obtained:

Where:

Equations (16) and (17) have the shape of a straight line, so intersection with the Y axis and slope should be easily found taking into account conversion and time of reaction. The Vmax and Km can be mathematically obtained.

## References:

PRASHANT PRADHAN1*, J. G. (2008). A Facile Microfluidic Method for Production of Liposomes. ANTICANCER RESEARCH.

Bo Yu*, †. R. (2009). Microfluidic Methods for Production of Liposomes. Methods Enzymol , 5-6.
M.E. Lanioa†, M. L.-L. (2009). Las vesículas liposomales: obtención, propiedades y aplicaciones potencialesen la biomedicina. Rev. Cub. Física , 23-30.

Hairul Hisham Hamzah1, 3. Z. (2013). Spectrophotometric Determination of Uric Acid in Urine Based-Enzymatic . J Anal Bioanal Tech , 4.

Fogler, H. S. (1999). Elements of Quemical Reaction Engineering (Third Edition ed.). New Jersey, E.U.A.: Prentice-Hall.