## 3 Results and Discussion
### Evolution of Deformation Behaviour of RBCs during In-Vitro Storage
Therefore, the discocyte morphology at \(0\leq\ t<20\) has a similar \(\mu(t)\) and \(\kappa(t)\), and the sphero-echinocyte morphology at \(26\leq\ t<42\) has a similar \(\mu(t)\) and \(\kappa(t)\) as well. However, the cell surface area and volume gradually decrease throughout the storage. Therefore, the observed increment of \(EI\) for the similar morphology can be attributed to the loss of cell surface area and volume. The results indicate that the stored RBCs have acceptable deformability during \(0\leq\ t<24\) up to echinocyte II morphology. However, echinocyte III and sphero-echinocyte morphologies during \(24\leq\ t\leq 42\) have degraded deformability, and contribute to poor quality and viability of RBCs at prolonged storage. Influence of Cytoskeletal Actin Junctional Defects during In-Vitro Storage on RBC Morphology and Deformability  
The ATP depletion during in-vitro RBC storage can lead to cytoskeletal protein defects such that the connections between the cytoskeletal spectrin network and the lipid-bilayer are disrupted [32; 68; 82]. RBCs with defective vertical interactions between the lipid-bilayer and the cytoskeleton can lose the unsupported membrane area contributing to membrane vesiculation. In this section, the influence on the equilibrium cell shape and its deformation behaviour is investigated for stored RBCs with defects in the membrane proteins that cause disruption in the vertical interactions between the cytoskeleton and the lipid-bilayer. The protein defects in the vertical interaction are presented in the CG-RBC membrane model by broken connections of spectrin links at randomly selected actin junctional complexes. Loss of vertical connectivity at the actin junctional complexes (\(A_{Vertical}\)) from 0% to 25% was introduced to the CG-RBC membrane model such that the spectrin links attached to these defective actin junctional complexes do not contribute to the cytoskeletal stretching response. Therefore, the elastic energy of the cytoskeleton (\(E_{Stretching}\)) for a cell membrane with loss of vertical connectivity between cytoskeleton and lipid-bilayer, is given by  
\[E_{Stretching}=\sum_{j=1}^{N_{S}}\left\{ \begin{array}{cc}\left[\frac{k_{B} \ T_{max}}{4\ p}\frac{3x_{j}^{3}-2x_{j}^{3}}{1-x_{j}}+\frac{k_{p}}{(m-1)\ \frac{k_{p}}{j}-1}\right],&j\
otin S_{A_{Vertical}}\\ 0,&j\in S_{A_{Vertical}}\end{array} \right\} \tag{8}\]  
where \(S_{A_{Vertical}}\) indicates the spectrin links attached to defective actin junctional complexes. \(k_{B}\) is the Boltzmann constant, \(T\) is the absolute temperature, \(l_{max}\) is the maximum extension of \(j^{th}\) link, \(p\) is the persistence length and \(k_{p}\) is the power function coefficient. \(x_{j}\) is defined as \(x_{j}=l_{j}/l_{max}\) for the \(j^{th}\) link having \(l_{j}\) length, and \(m\) is an exponent such that \(m=2\). The cytoskeletal spectrin network of \(A_{Vertical}=0,1,10\) and 25 (%) of defective vertical interactions at randomly selected actin junctional complexes is presented in Figure 8.  
The equilibrium cell shapes and membrane spicules become irregular with the severity of membrane defects (i.e., increase of \(A_{Vertical}\)). The equilibrium cell shapes of day 42 sphero-echinocytes with \(A_{Vertical}=0\%\) and 25% subjected to optical tweezers stretching forces of \(F^{ext}=0\) and 200 pN are presented in Figure 9.  
Figure 8: The cytoskeletal spectrin network having (a) 0%, (b) 1%, (c) 10% and (d) 25% of defective vertical interactions (\(A_{Vertical}\)) at randomly selected actin junctional complexes. Spicules with sharp projections can be observed (refer to Figure 9) in the presence of \(A_{Vertical}\)-especially if the actin junctional defects and spicule tips coincide together. At higher \(A_{Vertical}\)-the unsupported lipid-bilayer forms sharp projections as it can easily contribute to \(\Delta A_{0}(t)\) and \(C_{0}(t)\) in the absence of a cytoskeletal stretching response.