## 2 Methods
### Evolution of Coarse-Grained (CG)-RBC Membrane Model Parameters during In-Vitro Storage  
The CG-RBC membrane model is composed of a triangular surface of \(N_{t}\) triangles representing \(N_{V}\) cytoskeletal actin junctions and \(N_{S}\) spectrin links. The model predicts the minimum free energy state of the RBC membrane, which is the equilibrium RBC morphology at the given reference conditions (e.g., cell surface area (\(A_{0}\)), cell volume (\(V_{0}\)), reference bilayer-leaflet-area-difference (\(\Delta A_{0}\)) and reference total-membrane-curvature (\(C_{0}\))). The CG-RBC membrane model is briefly reviewed in Appendix A: CG-RBC Membrane Model, whereas detailed description and discussion on the model development and shape predictions of the discocyte, echinocyte I, echinocyte II, echinocyte III and sphero-echinocyte, are available in [PERSON] et al. [76]. [PERSON] et al. [76] presents the numerical predictions of stomatocyte-discocyte-echinocyte morphology transformations of a healthy RBC under stomatocytogenic and echinocytogenic shape-transforming conditions, and the corresponding model parameters and constraint coefficients for discocyte, echinocyte I, echinocyte  
Figure 1: Evolution of RBC morphology during in-vitro storage duration. The morphology index (\(MI\)) corresponding to each RBC morphology is presented. II, echinocyte III and sphero-echinocyte morphologies are summarised in Appendix B: Prediction of Discocyte, Echinocyte I, Echinocyte II, Echinocyte III and Sphero-Echinocyte RBC Morphologies. The CG-RBC membrane model requires appropriate adjustments to compensate for the evolution of RBCs during in-vitro storage. Therefore, the numerical evolution of the membrane shear modulus (\(\mu(t)\)), bending modulus (\(\kappa(t)\)), cell surface area (\(A_{0}(t)\)), cell volume (\(V_{0}(t)\)), reference bilayer-leaflet-area-difference (\(\Delta A_{0}(t)\)) and reference total-membrane-curvature (\(C_{0}(t)\)), is determined as a function of in-vitro storage time. The CG-RBC membrane model parameters mentioned in Appendix B: Prediction of Discocyte, Echinocyte I, Echinocyte II, Echinocyte III and Sphero-Echinocyte RBC Morphologies, were adopted as the analogous RBC properties at day 0 of in-vitro storage, and the corresponding membrane shear modulus (\(\mu(t_{0})\)), bending modulus (\(\kappa(t_{0})\)), cell surface area (\(A_{0}(t_{0})\)), and cell volume (\(V_{0}(t_{0})\)) were established accordingly. The evolution of the CG-RBC membrane \(\mu(t)\) and \(\kappa(t)\) during in-vitro storage is presented in the Figure 2a and 2b, respectively. The estimation of \(\mu(t)\) is based on the experimentally observed evolution of RBC membrane Young's modulus by [PERSON] et al. [8], and it is assumed that the evolution of Young's modulus during in-vitro storage is comparable to that of the membrane shear modulus. Young's modulus is one of the key indicators of cell membrane mechanical integrity, and thereby the cell stiffness [8]. However, the storage lesion affects the Young's modulus. It can be observed (refer to Figure 3 of [PERSON] et al. [8]) that the Young's modulus of RBC membranes is approximately constant up to 20 days of in-vitro storage, and increases rapidly during days 20 to 25, where it remains approximately constant during the period of days 26 to 42. This behaviour is comparable with the evolution of RBC morphology during in-vitro storage. The evolution of \(\mu(t)\) was determined in agreement with the outline of the evolution of RBC membrane Young's modulus, and is presented in Figure 2a, where the evolution of \(\mu(t)\) during storage was assumed to be directly proportional to that of the Young's modulus (i.e., Young's modulus \(\propto~{}\mu\)). It can be observed that \(\mu(t)\) increases rapidly during the transition period, and reaches a value which is nearly 2.6 times higher than \(\mu(t_{0})\). These observations agree with available experimental results [18; 38].