Location of the axon initial segment assembly can be predicted from neuronal shape.

The axon initial segment (AIS) is located at the proximal axon demarcating the boundary between axonal and somatodendritic compartments. The AIS facilitates the generation of action potentials and maintenance of neuronal polarity. In this study, we show that the location of AIS assembly, as marked by Ankyrin G, corresponds to the nodal plane of the lowest-order harmonic of the Laplace-Beltrami operator solved over the neuronal shape.

Motility of an autonomous protein-based artificial motor that operates via a burnt-bridge principle.

Inspired by biology, great progress has been made in creating artificial molecular motors. However, the dream of harnessing proteins - the building blocks selected by nature - to design autonomous motors has so far remained elusive. Here we report the synthesis and characterization of the Lawnmower, an autonomous, protein-based artificial molecular motor comprised of a spherical hub decorated with proteases.

Time Fractional Fisher-KPP and Fitzhugh-Nagumo Equations.

A standard reaction-diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with modelling assumptions such as the law of mass action for well-mixed systems. In formulating a reaction-subdiffusion equation, it is not sufficient to know the reaction rate equation.

Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains.

Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a one-dimensional domain that is evolving. The model equations, which have been derived from generalized continuous time random walks, can incorporate complexities such as subdiffusive transport and inhomogeneous domain stretching and shrinking.

Division plane placement in pleomorphic archaea is dynamically coupled to cell shape.

One mechanism for achieving accurate placement of the cell division machinery is via Turing patterns, where nonlinear molecular interactions spontaneously produce spatiotemporal concentration gradients. The resulting patterns are dictated by cell shape. For example, the Min system of Escherichia coli shows spatiotemporal oscillation between cell poles, leaving a mid-cell zone for division.