Tubular membrane structures

In presented chapter we focus on the equilibrium shapes of tubular lipid membranes. These shapes are determined using Helfrich model of bending elasticity together with several geometrical constraints (reduced volume and projected length). By varying the constraints, four distinct nonperiodic types of shapes were found: (i) snake-like and (ii) helical structures, (iii) tubes with a spherical body, and (iv) tubes with a discoidal body. The shapes share a common tubular characteristic and can be, depending on their detailed morphology, identified as volume, surface area, or length reservoirs. We present the equilibrium shapes by using numerical computation and by employing simplified analytical models. The validity and accuracy of both approaches is thoroughly presented and the full phase diagram is constructed. Finally, our theoretical results are compared to the previous theoretical and experimental research with a special emphasis on the intercellular biological structures.