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 × 10-18 and 1.40 × 10-17 J for 4% and 51% areal membrane strain. Phosphorylation damage in the erythrocyte membrane reduced the required indentation work by 50% to 0.97 × 10-18 and 0.70 × 10-17 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.
Keywords: Malaria; Mathematical model; Phosphorylation; Red blood cell; Spectrin network.
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