Mathematical model for fragmentation of bacterial inclusion bodies

Abstract

Bacterial inclusion bodies are microscopic, ovoid-shaped aggregates of insoluble protein. Under protease exposure a digestion process is produced that reveals a variable fragmentation rate, not compatible with a surface restricted erosion of body particles, or an uniform sensibility to the fragmentation agent. The modelling and fitting of experimental data is performed in two steps. (a) Due to poor estimation of protein amounts only first derivatives can be numerically evaluated, and a non-linear first-order fragmentation model is adopted. Although it is a very good approximation for intermediate points, the asymtotic behaviour of the solution is inconsistent with the fragmentation process. (b) The solution of previous kinetic modelling is used to compute higher-order derivatives in intermediate points and to adopt a higher-order lineal model for the overall interval with protein fragmentation. The resulting model consists in a superposition of Poisson processes associated with several populations of protein with different fragmentation resistance. Numerical estimation of model constants is also described and discussed. In particular, an iterative method of weighted least squares is used in order to obtain minimum variance parameters.