A constitutive model for the remodelling erythrocyte membrane skeleton during the active invasion by the malaria merozoite

Malaria merozoites phosphorylate erythrocyte membrane proteins to breach the membrane during invasion. This study aimed to develop a constitutive model for erythrocyte membrane phosphorylation that reduces the membranes elastic modulus and resistance to merozoite invasion. The hyperelastic Mooney Rivlin constitutive model was adapted by adding an exponential term to represent the mechanical effect of erythrocyte membrane phosphorylation. The modified algorithm was verified with the unmodified Mooney Rivlin model for the intact erythrocyte membrane and used to predict erythrocyte membrane stress for equi-biaxial membrane strain up to 1.1 for different severity of phosphorylation damage. The stability of the damage model was assessed using the Drucker criterion for equi-biaxial strain up to 2.0. Strain and stress predicted with the developed damage model and the Mooney Rivlin model agreed for the intact erythrocyte membrane. The membrane stress at a strain of 1.1 decreased by 42% for minor and 95% for severe erythrocyte membrane damage. The stability strain threshold of the damage model was 1.98 for minor and 1.19 for severe membrane damage. The developed model can represent different degrees of erythrocyte membrane damage through phosphorylation by a malaria merozoite. The model will enable in silico investigations of the invasiveness of malaria merozoites.