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Using fractional differential equations to model the Michaelis-Menten reaction in a 2-d region containing obstacles

Farah Aini Abdullah^*

 
ABSTRACT:     Features inside living cells are complex and crowded, and in such complex environments diffusion processes exhibit three different behaviours; Fickian diffusion, subdiffusion, and superdiffusion. This study aims to investigate the phenomenon of subdiffusion, which occurs when there is molecular crowding, by proposing a new continuous spatial model involving fractional differential equations. The anomalous diffusion parameter is introduced to represent the spatial crowdedness in the media. The equations are solved numerically using an implicit fractional trapezoidal method. Simulations applied to the particular case of the Michaelis-Menten reaction demonstrate that, as a result of anomalous diffusion or a crowded situation in low dimensional biological media, kinetics are of the fractal type. The model also predicts that increasing obstacle density results in reactant segregation, which is similar to that observed in in vivo conditions in cells.

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* Corresponding author, E-mail: farahaini@usm.my

Received 1 Mar 2010, Accepted 2 Nov 2010