The relation between the rod-like inner structures and the shapes of the cells

Abstract

The shapes of the cells with simple rod-like inner structures are studied theoretically. Since the cell with inner structure can be bent, the possibility of non-axisymmetric shapes is considered. The equilibrium shape of the cell, obtained by minimizing the sum of the membrane bending energy and the bending energy of the rod, depends on the ratio between the bending constant of the membrane and the bending rigidity of the polymer rod. The dependence of the cell shape on the length of the rod and on the difference between inner and outer membrane layer areas is presented.

Confined filaments in soft vesicles – the case of sickle red blood cells

“…The filament length and bending energy are also scaled by ρ s and 8πκ b , respectively. As noted earlier [8] the important parameters in this model are the dimensionless ratios (k B T l p /κ b ρ s ), ∆a 0 and the reduced filament lengthl = L/ρ s . Note, that for a free WLC the only relevant parameter is l p /L, but here in the confined case, all lengths have been rescaled by ρ s which is connected to the area of the RBC.…”

“…Analytical calculations reported in the context of vesicle tubulation [6,8,9] are variational in nature: the structure of the deformed vesicle was assumed to be that of two cylindrical membrane tubes attached to a central ellipsoidal vesicle. The structural parameters like the major and minor axes of the vesicle and the length and radius of the tubes are determined by minimizing the total free energy of the system, often subject to fixed area and fixed volume constraints.…”

“…Qualitatively, when the total length of two tubes is same as that of a single tube (of the same radius), the energy difference should be the cost of one kink at the base of the tube. We note that in variational calculations [6,8,9] the two tube conformation was assumed apriori. Experiments in Ref [6] with MT filaments showed a reentrant transition for the vesicle shape: tube → collapsed → tube, as the MT bundle grew in length.…”

Confined filaments in soft vesicles - case of sickle red blood cells

“…This is despite the obvious dissimilarity that phospholipid vesicles when pushed from inside by MT filaments, develop tubular protrusions, which is not seen in RBC sickling. We will show that the same model can be used for both the problems, albeit in a different region of the parameter space.Analytical calculations reported in the context of vesicle tubulation [6,8,9] are variational in nature: the structure of the deformed vesicle was assumed to be that of two cylindrical membrane tubes attached to a central ellipsoidal vesicle. The structural parameters like the major and minor axes of the vesicle and the length and radius of the tubes are determined by minimizing the total free energy of the system, often subject to fixed area and fixed volume constraints.…”