No abstract

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 membrane's 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.

The invasion of a merozoite into an erythrocyte by membrane wrapping is a hallmark of malaria pathogenesis. The invasion involves biomechanical interactions whereby the merozoite exerts actomyosin-based forces to push itself into and through the erythrocyte membrane while concurrently inducing biochemical damage to the erythrocyte membrane. Whereas the biochemical damage process has been investigated, the detailed mechanistic understanding of the invasion mechanics remains limited. Thus, the current study aimed to develop a mathematical model describing the mechanical factors involved in the merozoite invasion into an erythrocyte and explore the invasion mechanics. A shell theory model was developed comprising constitutive, equilibrium and governing equations of the deformable erythrocyte membrane to predict membrane mechanics during the wrapping of an entire non-deformable ellipsoidal merozoite. Predicted parameters include principal erythrocyte membrane deformations and stresses, wrapping and indentation forces, and indentation work. The numerical investigations considered two limits for the erythrocyte membrane deformation during wrapping (4% and 51% areal strain) and erythrocyte membrane phosphorylation (decrease of membrane elastic modulus from 1 to 0.5 kPa). For an intact erythrocyte, the maximum indentation force was 1 and 8.5 pN, and the indentation work was 1.92 x10-18 and 1.40 x10-17 J for 4% and 51% areal membrane strain. Phosphorylation damage in the erythrocyte membrane reduced the required indentation work by 50% to 0.97 x10-18 and 0.70 x10-17 J for 4% and 51% areal strain. The current study demonstrated the developed model's feasibility to provide new knowledge on the physical mechanisms of the merozoite invasion process that contribute to the invasion efficiency towards the discovery of new invasion-blocking anti-malaria drugs.