Mathematical modelling of hepatopancreatic digestive cell of the blue mussel
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The lysosomal system of the hepatopancreatic digestive cell of the mussel (Mytilus sp.) is critical in intracellular food degradation, toxic responses and internal cellular turnover. Mathematical and numerical models are developed to simulate the responses of this system to varying conditions, dietary and toxicological. The model evolution encompasses: inclusion of glycogen/lipid storage forms; extrapolation to include nitrogen metabolism; development of rate of endocytosis and food signal; increased functionality of endo/lysosomes; shift to protein/carbohydrate/lipid based model; and the incorporation of the cost of normal Sanction and replacement of damaged components. Control is asserted through control of cytosolic concentrations: the intial assumption of constant carbon concentration is shown to be unacceptable for later models. A control algorithm is developed which regulates cell volume by the ratio of proteinaceous material to energy forms. Endocytosis is shown to be the main determinant behind routine cellular behaviour. Observed phasic behaviour of the digestive tubules is incorporated into the cellular behavioural pattern. A probability-based model for the rate of endocytosis is developed. Increased autophagy as the sole response to toxic injury is found to be inadequate to explain observed responses. It is proposed to complement this response with impairment of lysosomal efficiency to explain this inadequacy. Toxic injury is implemented through an increase in the rates of damage to cellular components. Within the lysosome this leads to a reduction in the concentration of digestive enzymes inhibiting lysosomal performance and, in conjunction with the enhanced autophagy due to increased cytosolic damage, invoking the lysosomal swelling commonly observed.
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