Non-uniform distribution of myosin-mediated forces governs red blood cell membrane curvature through tension modulation

The biconcave disk shape of the mammalian red blood cell (RBC) is unique to the RBC and is vital for its circulatory function. Due to the absence of a transcellular cytoskeleton, RBC shape is determined by the membrane skeleton, a network of actin filaments cross-linked by spectrin and attached to membrane proteins. While the physical properties of a uniformly distributed actin network interacting with the lipid bilayer membrane have been assumed to control RBC shape, recent experiments reveal that RBC biconcave shape also depends on the contractile activity of nonmuscle myosin IIA (NMIIA) motor proteins. Here, we use the classical Helfrich-Canham model for the RBC membrane to test the role of heterogeneous force distributions along the membrane and mimic the contractile activity of sparsely distributed NMIIA filaments. By incorporating this additional contribution to the Helfrich-Canham energy, we find that the RBC biconcave shape depends on the ratio of forces per unit volume in the dimple and rim regions of the RBC. Experimental measurements of NMIIA densities at the dimple and rim validate our prediction that (a) membrane forces must be non-uniform along the RBC membrane and (b) the force density must be larger in the dimple than the rim to produce the observed membrane curvatures. Furthermore, we predict that RBC membrane tension and the orientation of the applied forces play important roles in regulating this force-shape landscape. Our findings of heterogeneous force distributions on the plasma membrane for RBC shape maintenance may also have implications for shape maintenance in different cell types. Author summary The spectrin-actin network of the membrane skeleton plays an important role in controlling specialized cell membrane morphology. In the paradigmatic red blood cell (RBC), where actin filaments are present exclusively in the membrane skeleton, recent experiments reveal that nonmuscle myosin IIA (NMIIA) motor contractility maintains the RBC biconcave disk shape. In this study, we have identified criteria for micron-scale distributions of NMIIA forces at the membrane required to maintain the biconcave disk shape of an RBC in the resting condition. Supported by experimental measurements of RBC NMIIA distribution, we showed that a heterogeneous force distribution with a larger force density at the dimple is able to capture the experimentally observed biconcave morphology of an RBC with better accuracy compared to previous models that did not consider the heterogeneity in the force distribution. Furthermore, we showed that the biconcave geometry of the RBC is closely regulated by the effective membrane tension and the direction of applied forces on the membrane. These findings can be generalized to any force-mediated membrane shape, providing insight into the role of actomyosin forces in prescribing and maintaining the morphology of different cell types.