An efficient method for oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics

In this paper, a novel numerical technique, the first-order Smooth Composite Chebyshev Finite Difference method, is presented. Imposing a first-order smoothness of the approximation polynomial at the ends of each subinterval is originality of the method. Both round-off and truncation error analyses of the method are performed beside the convergence analysis. Diffusion of oxygen in a spherical cell including nonlinear uptake kinetics is solved by using the method. The obtained results are compared with the existing methods in the literature and it is observed that the proposed method gives more reliable results.

Microtubule-based actin transport and localization in a spherical cell

The interaction between actin filaments and microtubules is crucial for many eukaryotic cellular processes, such as, among others, cell polarization, cell motility and cellular wound healing. The importance of this interaction has long been recognized, yet very little is understood about both the underlying mechanisms and the consequences for the spatial (re)organization of the cellular cytoskeleton. At the same time, understanding the causes and the consequences of the interaction between different biomolecular components are key questions for in vitro research involving reconstituted biomolecular systems, especially in the light of current interest in creating minimal synthetic cells. In this light, recent in vitro experiments have shown that the actin-microtubule interaction mediated by the cytolinker TipAct, which binds to actin lattice and microtubule tips, causes the directed transport of actin filaments. We develop an analytical theory of dynamically unstable microtubules, nucleated from the centre of a spherical cell, in interaction with actin filaments. We show that, depending on the balance between the diffusion of unbound actin filaments and propensity to bind microtubules, actin is either concentrated in the centre of the cell, where the density of microtubules is highest, or becomes localized to the cell cortex.

The evolution of spherical cell shape; progress and perspective

Bacterial cell shape is a key trait governing the extracellular and intracellular factors of bacterial life. Rod-like cell shape appears to be original which implies that the cell wall, division, and rod-like shape came together in ancient bacteria and that the myriad of shapes observed in extant bacteria have evolved from this ancestral shape. In order to understand its evolution, we must first understand how this trait is actively maintained through the construction and maintenance of the peptidoglycan cell wall. The proteins that are primarily responsible for cell shape are therefore the elements of the bacterial cytoskeleton, principally FtsZ, MreB, and the penicillin-binding proteins. MreB is particularly relevant in the transition between rod-like and spherical cell shape as it is often (but not always) lost early in the process. Here we will highlight what is known of this particular transition in cell shape and how it affects fitness before giving a brief perspective on what will be required in order to progress the field of cell shape evolution from a purely mechanistic discipline to one that has the perspective to both propose and to test reasonable hypotheses regarding the ecological drivers of cell shape change.