<i>Mechanics of Spectrin As a Stiff Polymer</i>

Introduction:We applied a semi-flexible polymer statistical mechanics theory to predict the mechanics of spectrin tetramer as a stiff polymer in the red blood cells. Previous experimental imaging data showed that the spectrin tetramer was a straight polymer rather than a random coil due to each linker region consisting of a continuous alpha helix. Topological models such as the Chinese Finger Trap model was proposed. However, the development of a mechanical model for spectrin based on these topological propositions as a stiff polymer was not achieved. This has led to previous theoretical treatments of spectrin as flexible polymer chain models, such as freely-jointed chain and worm-like chain, even though recent observations of spectrin suggest that it would be more phenomenologically accurate to treat spectrin as a stiff polymer. By predicting the local persistence lengths using all-atom molecular dynamics simulations of a full-length spectrin tetramer, we found that its persistence length was indeed larger than its contour length. After fitting the parameters of semi-flexible models based on simulations, we found that this new model could predict the mechanics of spectrin network in the red blood cells more accurately than previous flexible polymer models.Materials and Methods:We applied the semi-flexible polymer theory by Blundell and Terentjev to predict the force-extension curve of the spectrin tetramer as a stiff polymer. To calculate the local persistence length of the spectrin tetramer, we applied NAMD to carry out all-atom molecular dynamics simulations of full-length spectrin tetramers predicted by Alpha-Fold. Then, by coarse-graining this all-atom model, we developed a bead-string model to calculate the force-extension curve. Specifically, we measured the equilibrium force imparted on the endpoints of the spectrin tetramer for different ratios of the distance between the endpoints relative to the sum of the equilibrium lengths of the bonds of the molecule. We then constructed the constitutive model of the spectrin network based on the predicted force-extension curve and spectrin length/orientation distributions obtained from experimental imaging. Finally, continuum models using finite element method and boundary element method were used to predict the biconcave shape, tank-treading motion, and micropipette aspiration of a red blood cell with the spectrin network.Results, Conclusions, and Discussions:First, using the semi-flexible polymer model, we show that the shear modulus of the spectrin network decreases with the temperature, consistent with experimental measurements, rather than increasing with temperature as predicted by the entropic flexible polymer model. Second, the initial shear modulus of the spectrin network predicted by the Blundell-Terentjev theory and the updated copy numbers from proteomic data is consistent with experimental measurement. Third, we predicted the biconcave shape by volume deflation and simulated the tank-treading motion of RBCs with a preserved biconcave shape. Finally, we compared the deformation-dependent mechanical properties inferred from micropipette aspiration using both flexible and semi-flexible polymer theories. These results might completely change the picture of the traditional spectrin mechanics.