Bending Energy Schemes for Discrete-Spring-Network Structural Modelling of Red Blood Cells

Area of Science:

• Biophysics
• Computational Biology
• Cellular Mechanics

Background:

• Red blood cells (RBCs) exhibit significant structural deformation and shape variability (e.g., stomatocytes, discocytes, echinocytes) influenced by physiological conditions and external factors.
• Discrete-spring-network models are crucial for simulating RBC structural mechanics, but their accuracy depends on the numerical treatment of bending energy.
• Existing models using bending energy schemes (BES) A and B have shown limitations in predicting accurate RBC shapes and behaviors.

Purpose of the Study:

• To compare the accuracy of three distinct bending energy schemes (BES A, B, and C) in predicting red blood cell (RBC) shapes using discrete-spring-network models.
• To evaluate the performance of each BES in simulating both simple membrane bending and complex equilibrium RBC shape transitions.
• To identify the most accurate and robust BES for future RBC structural modeling.

Main Methods:

• Development and application of discrete-spring-network models for RBC structural simulation.
• Implementation and comparison of three bending energy schemes: BES A (Kantor and Nelson formulations), BES B (Jülicher spring-based curvature), and BES C (Jülicher node-based curvature).
• Testing the schemes using flat membrane models (stiff and soft) and enclosed vesicle/RBC models to predict shape sequences (e.g., stomatocyte-discocyte-echinocyte).

Main Results:

• Bending energy schemes A and B demonstrated limitations, underestimating bending deformation and failing to capture critical necking behavior necessary for accurate complex shape prediction.
• BES A and BES B exhibited inaccuracies in predicting equilibrium vesicle and RBC shapes, including the characteristic shape sequence.
• BES C proved accurate and robust, generating predicted RBC shapes that closely matched observed biological forms.

Conclusions:

• Bending energy scheme C is superior to schemes A and B for simulating red blood cell (RBC) structural mechanics and shape prediction.
• BES C accurately captures complex RBC deformations and transitions, outperforming existing methods.
• BES C is recommended as the preferred method for all future discrete-spring-network RBC structural modeling.