Unicellular algal growth: A biomechanical approach to cell wall dynamics

We present a model for unicellular algal growth as motivated by several experiments implicating the importance of calcium ions and ``loosening'' enzymes in morphogenesis. A growing cell at rest in a diffusive calcium solution is viewed as an elastic shell on short timescales. For a given turgor pressure, we calculate the stressed shapes of the wall elements whose elastic properties are determined by Young's modulus and the thickness of the wall. The local enzyme concentration then determines the rate at which the unstressed shape of a wall element relaxes toward its stressed shape. The local wall thickness is calculated from the calcium-mediated addition of material and thinning due to elongation. We use this model to calculate growth rates for small perturbations to a circular cell. We find an instability related to modulations of the wall thickness, leading to growth rates which peak at a finite wave number.Comment: 5 pages, 2 embedded figure

Properties of Cooperatively Induced Phases in Sensing Models

A large number of eukaryotic cells are able to directly detect external chemical gradients with great accuracy and the ultimate limit to their sensitivity has been a topic of debate for many years. Previous work has been done to understand many aspects of this process but little attention has been paid to the possibility of emergent sensing states. Here we examine how cooperation between sensors existing in a two dimensional network, as they do on the cell's surface, can both enhance and fundamentally alter the response of the cell to a spatially varying signal. We show that weakly interacting sensors linearly amplify the sensors response to an external gradient while a network of strongly interacting sensors form a collective non-linear response with two separate domains of active and inactive sensors forming what have called a "1/2-state" . In our analysis we examine the cell's ability to sense the direction of a signal and pay special attention to the substantially different behavior realized in the strongly interacting regime.Comment: 8 pages, 5 figure