## Appendix D Implementation of Optical Tweezers Stretching  
The optical tweezers stretching forces were implemented on the CG-RBC membrane model-predicted equilibrium RBC morphologies. Assuming rigid body conditions, the centre of mass of the whole cell and its three-principal axes of inertia were determined for each RBC morphology. The total stretching force (\(F^{ext}\)) was applied on \(N_{+}=a\)\(N_{V}\) vertices, whereas \(-F^{ext}\) is applied on \(N_{-}=a\)\(N_{V}\) vertices along the principal axis of inertia [39, 58] (refer to Figure 10). \(N_{+}\) and \(N_{-}\) are the vertices that locate within the circular region of radius \(d_{\text{C}}/2\) on the initial spherical geometry, and from the 2 vertices (\(i_{X_{max}}\) and \(i_{X_{min}}\)) on the furthest ends of the equilibrium cell shape along the principal axis of inertia [3]. \(d_{\text{C}}\) is the contact diameter between the cell membrane and the attached silica beads. The vertex fraction \(a\) corresponds to \(d_{\text{C}}\) and is given by \(a=\pi\,d_{\text{C}}^{2}/(4\,A_{0})\). Therefore, \(f_{i}^{ext}\) is applied on the \(i^{th}\) vertex, such that;  
\[f_{i}^{ext}=\begin{cases}\begin{array}{ccc}F^{ext}/N_{+},&i\,\in\,N_{+}\\ -\,\,F^{ext}/N_{-},&i\,\in\,N_{-}\\ 0,&i\,\
otin\,(N_{+}\,\cup\,N_{-})\end{array}\end{cases}, \tag{11}\]  
Figure 10: Optical tweezers stretching implementation on the discocyte cell; (**a**) identification of \(i_{X_{max}}\) and \(i_{X_{min}}\) vertices, (**b**) identification of \(N_{+}\) vertices, and (**c**) contact region between the RBC membrane and binding silica beads.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**RBC Volume (\(\mu\)m\({}^{3}\))**} \\ \cline{2-10}
**Day \#** & \multicolumn{2}{c}{**Discocyte**} & \multicolumn{2}{c}{**Echinocyte I**} & \multicolumn{2}{c}{**Echinocyte II**} & \multicolumn{2}{c}{**Echinocyte III**} & \multicolumn{2}{c}{**RBC**} \\ \cline{2-10}  & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** & **Mean** \\ \hline
2 & 106.98 & 24.19 & 96.40 & 22.27 & 113.27 & 17.74 & 84.78 & 13.73 &
\begin{tabular}{c} 99.51 \\ \(\pm\) 22.68 \\ \end{tabular} \\ \hline
7 & 77.15 & 19.88 & 86.39 & 21.73 & 81.69 & 22.75 & 97.06 & 23.51 &
\begin{tabular}{c} 85.03 \\ \(\pm\) 22.98 \\ \end{tabular} \\ \hline
21 & 89.95 & 19.88 & 91.62 & 18.73 & 92.62 & 24.61 & 99.38 & 20.72 &
\begin{tabular}{c} 92.47 \\ \(\pm\) 20.78 \\ \end{tabular} \\ \hline
28 & 77.33 & 18.31 & 79.96 & 15.96 & 90.53 & 24.04 & 87.18 & 16.38 &
\begin{tabular}{c} 83.25 \\ \(\pm\) 19.24 \\ \end{tabular} \\ \hline
48 & 76.20 & 20.38 & 69.32 & 25.61 & 69.97 & 22.96 & 82.00 & 24.92 &
\begin{tabular}{c} 73.87 \\ \(\pm\) 24.39 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 11: Measurements of cell volume of RBC morphologies of three donors during 48 days of in-vitro storage in SAGM additive solution ([PERSON], personal communication, 10 October 2018). Mean represents the mean values whereas SD represents the standard deviation.  
\(F^{ext}\) was gradually applied on the cell via regular force increments of \(\Delta F^{ext}\), where the cell is provided with sufficient time to converge to the equilibrium stretched state after each force increment. The equilibrium stretched cell state was determined at equivalent \(A_{0}\), \(A_{k0}\), \(V_{0}\), \(\Delta A_{0}\) and \(C_{0}\) for stomatocyte, discocyte and echinocyte cell shapes and at corresponding \(F^{ext}\). The resultant force and motion of \(i^{th}\) membrane vertex was determined according to Equations (A11) and (A12) for \(F^{ext}\) external force, and the equilibrium cell state was determined. The axial diameter (\(D_{A}\)) was measured along the principal axis of inertia\({}^{3}\), whereas the transverse diameter (\(D_{T}\)) was measured along the principal axis of inertia\({}^{2}\) of the equilibrium stretched cell state at \(F^{ext}\). Refer to Figure 19 for a graphical representation of \(D_{A}\) and \(D_{T}\).