Phenomenology Based Multiscale Models as Tools to Understand Cell Membrane and Organelle Morphologies

Abstract

An intriguing question in cell biology is “how do cells regulate their shape?” It is commonly believed that the observed cellular morphologies are a result of the complex interaction among the lipid molecules (constituting the cell membrane), and with a number of other macromolecules, such as proteins. It is also believed that the common biophysical processes essential for the functioning of a cell also play an important role in cellular morphogenesis. At the cellular scale—where typical dimensions are in the order of micrometers—the effects arising from the molecular scale can either be modeled as equilibrium or non-equilibrium processes. In this chapter, we discuss the dynamically triangulated Monte Carlo technique to model and simulate membrane morphologies at the cellular scale, which in turn can be used to investigate several questions related to shape regulation in cells. In particular, we focus on two specific problems within the framework of isotropic and anisotropic elasticity theories: namely, (i) the origin of complex, physiologically relevant, membrane shapes due to the interaction of the membrane with curvature remodeling proteins, and (ii) the genesis of steady state cellular shapes due to the action of non-equilibrium forces that are generated by the fission and fusion of transport vesicles and by the binding and unbinding of proteins from the parent membrane.

Biophysics of membrane curvature remodeling at molecular and mesoscopic lengthscales

“…As for Δℱ, we compute the relative internal energies with respect to the membrane state with $C_{false\Vert }^0=0$. All internal energies increase with an increase in both | $C_{false\Vert }^0$| and also as a function of the coupling parameter λ ; the latter has been shown explicitly in [185]. The dominant contribution is from equation (8), the anisotropic elastic energy, which is explicitly coupled to $C_{false\Vert }^0$.…”

Mem3DG: modeling membrane mechanochemical dynamics in 3D using discrete differential geometry

“…These models, owing to the ease of in silico experimentation, have become an important tool for generating and testing hypotheses (53,54). These mechanics models and associated simulations have been used to provide intuition on the mechanical requirements for forming and maintaining complex cellular membrane shapes (55)(56)(57)(58)(59)(60)(61)(62)(63).…”