## Appendix A CG-RBC Membrane Model  
The CG-RBC membrane model is composed of \(N_{V}\) vertices to represent the cytoskeletal actin junctional complexes, which form a 2D triangulated surface of \(N_{t}\) triangles. The \(N_{S}\) adjacent vertex-vertex connections represent the cytoskeletal spectrin links. The free-energy of the CG-RBC membrane model (\(E\)) takes into account the elastic energy of the cytoskeletal spectrin network (\(E_{\textit{Stretching}}\)), bending resistance of the lipid-bilayer (\(E_{\textit{Bending}}\)), and constraints of fixed total surface area (\(E_{\textit{Surface-area}}\)) and enclosed volume (\(E_{Volume}\)). A BCM-based membrane bending energy approach [88; 89; 90; 91] was implemented via bilayer-leaflet-area-difference constraint (\(E_{\textit{Area-difference}}\)) to achieve the stomatocyte, discocyte and echinocyte morphologies at corresponding reference bilayer-leaflet-area-difference (\(\Delta A_{0}\)). In addition, the total-membrane-curvature constraint (\(E_{\textit{Total-curvature}}\)) was implemented to achieve numerically consistent RBC morphologies at corresponding reference total-membrane-curvature (\(C_{0}\)). Therefore, \(E\) is given by,  
\[E=E_{\textit{Stretching}}+E_{\textit{Bending}}+E_{\textit{Surface-area}}+E_{ Volume}+E_{\textit{Area-diff\,ference}}+E_{\textit{Total-curvature}} \tag{1}\]  
\(E_{\textit{Stretching}}\) was estimated based on the coarse-graining approach by [PERSON] et al. [58], and is given by,  
\[E_{\textit{Stretching}}=\sum_{j\;\epsilon\;\text{ln}\_{N_{S}}}\left[\frac{k_ {B}\;T\;l_{\textit{max}}}{4\;p}\;\frac{3x_{j}^{3}-2x_{j}^{3}}{1-x_{j}}+\frac{ k_{p}}{(m-1)\;l_{j}^{m-1}}\right], \tag{2}\]  
where \(k_{B}\) is the Boltzmann constant, \(T\) is the absolute temperature, \(l_{\textit{max}}\) is the maximum extension of \(\hat{\textit{\emph  
\(j^{th}\) link having \(l_{j}\) length, and \(m\) is an exponent such that \(m>1\). The experimentally estimated membrane shear modulus (\(\mu_{0}\)) of a healthy RBC lies between 4-12 \(\mu\)Nm\({}^{-1}\)[58; 68], and can be determined as below for the CG-RBC membrane model [58]. \[\mu_{0}=\frac{\sqrt{3}\,k_{B}\,T}{4\,p\,l_{max}\,x_{0}}\left[\frac{x_{0}}{2\, \left(1-x_{0}\right)^{3}}-\frac{1}{4\,\left(1-x_{0}\right)^{2}}-\frac{1}{4} \right]+\frac{\sqrt{3}\,k_{p}\,\left(m+1\right)}{4\,l_{0}^{m+1}}\,, \tag{11}\]  
where \(l_{0}\) is the equilibrium length of the \(j^{th}\) link, and defined as \(x_{0}=l_{0}/l_{max}\). \(E_{Bending}\) of the lipid-bilayer for a zero spontaneous curvature is estimated by  
\[E_{Bending}=2\,\kappa\,\sum\
olimits_{j\,\epsilon\,\,1..N_{S}}\frac{M_{j}^{2 }}{\Delta A_{j}}, \tag{12}\]  
where \(\kappa\) is the membrane bending modulus, \(M_{j}\) is the membrane curvature at the \(j^{th}\) link, and \(\Delta A_{j}\) is the membrane surface area associated with the \(j^{th}\) link. \(M_{j}\) and \(\Delta A_{j}\), corresponding to the triangle-pair composed of \(T1\) and \(T2\) triangles that share the \(j^{th}\) link, are estimated as follows;  
\[M_{j}=\frac{1}{2}\,l_{j}\,\theta_{j}, \tag{13}\]  
\[\Delta A_{j}=\frac{1}{3}\,\left(A_{T1}+A_{T2}\right), \tag{14}\]  
where \(\theta_{j}\) is the angle between outward normal vectors to the triangles \(T1\) and \(T2\), and \(A_{T1}\) and \(A_{T2}\) are the planer area associated with \(T1\) and \(T2\), respectively. \(\theta_{j}\) is defined such that the concave arrangement of \(T1\) and \(T2\) corresponds to a positive \(\theta_{j}\), whereas the convex arrangement corresponds to a negative \(\theta_{j}\), and results in positive or negative \(M_{j}\), respectively.