contour map principal curvatures postview

#CONTOUR MAP PRINCIPAL CURVATURES POSTVIEW HOW TO#

also found that forcing cells that lack a cell wall into a rod shape caused the MreB filaments bound to the cell membrane to orient and circle around the rod. The MreB filaments in the bulges move in an oriented way, helping them to generate the rod shape. However, spherical bacteria can regenerate into rods from small surface ‘bulges’. As a result, the filaments in rod-shaped cells orient and move around the rod, while in spherical bacteria they move in all directions. show that the filaments sense the shape of a bacterium by orienting along the direction of greatest curvature. Using a technique called total internal reflection microscopy to study how MreB filaments move across bacteria cells, Hussain, Wivagg et al.

#CONTOUR MAP PRINCIPAL CURVATURES POSTVIEW HOW TO#

But how do the MreB filaments know how to move around the circumference of the rod, instead of moving in any other direction? Together, these filament-enzyme complexes rotate around the cell to build and reinforce the cell wall in a hoop-like manner. This protein forms filaments that bind to the bacteria’s cell membrane and associate with the enzymes that build the cell wall. One protein required to form the rod shape is called MreB. The cell wall often determines which of a variety of shapes – such as rods or spheres – the bacteria grow into. Many bacteria are surrounded by both a cell membrane and a cell wall – a rigid outer covering made of sugars and short protein chains. We propose that the coupling of MreB filament alignment to shape-reinforcing peptidoglycan synthesis creates a locally-acting, self-organizing mechanism allowing the rapid establishment and stable maintenance of emergent rod shape. We observed that spherical cells regenerate into rods in a local, self-reinforcing manner: rapidly propagating rods emerge from small bulges, exhibiting oriented MreB motion. Together, this demonstrates MreB orients along the greatest principal membrane curvature, a conclusion supported with biophysical modeling. Stationary filaments orient within protoplasts, and purified MreB tubulates liposomes in vitro, orienting within tubes. MreB motion is isotropic in round cells, and orientation is restored when rod shape is externally imposed. To understand how oriented MreB motion arises, we altered the shape of Bacillus subtilis. Membrane-associated MreB filaments move around the rod circumference, helping to insert cell wall in the radial direction to reinforce rod shape. MreB is essential for rod shape in many bacteria. Given a surface $z = f(x,y)$, where $f(x,y)$ is a continuous bivariate function,

computed directly from scattered points using interpolation function with suitable properties.

derivation based on differential geometry.

Measure geometric properties at any point of the elevation surface

alternative: 8 triangles connecting grid center with neighboring ones.

sum of 3D triangle areas, depending on the direction of the diagonal: minimum and maximum surface.

can be applied as global or zonal metrics.

where $dx.dy$ is grid cell area, $dz = z_0-z_i$, is cell value difference, $z_0$ is constant, plane or curved surface.

Volume - integral approximated as sum of cuboids:.

Process-based parameters quantify cumulative results of processes (flow, solar radiation, wetness).

Point geometry parameters quantify geometry at each point of the surface: gradient, curvatures.

Quantify property for entire surface or its subregion: volume, surface area, fractal dimension, roughness Derived from discrete representation of $z=f(x,y)$.computing parameters from noisy data, level of detail.methods for slope, aspect and curvatures using polynomial and spline approximation.first and second order point parameters.

summary parameters: volumes, surface areas.GIS/MEA582 Geospatial Modeling and Analysis Geomorphometry II: Basic topographic analysis

Contour map principal curvatures postview