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SO ENDS this first of two weekends focused on patterning in the cone shell family. Fortunately, there are so outstanding virtual collections of cone shells, making actual collections by enthusiasts a thing of the past. These are an enormous source of pattern configurations, beautifully curated, for the mathematician or biologist to study without plundering the reefs. https://lnkd.in/d8vCADd View in LinkedIn

MORPHOGEN MODELS. “Therefore, in principle, morphogen models could have been used instead of the neural model. From a practical viewpoint, however, this would be considerably more difficult because a separate morphogen model is required for each shell pattern, whereas the neural model has a single set of parameters that are varied to match each pattern.” https://lnkd.in/dwfZQzE View in LinkedIn

THE COMPROMISE. “From a theoretical viewpoint, morphogen models can be viewed as an approximation to the neural net model when the range of communication between neurons is short.” https://lnkd.in/dwfZQzE View in LinkedIn

NATURE OF PATTERNING. “Structural studies provide strong evidence that shell patterns are a neurosecretory phenomenon rather than a diffusing morphogen phenomenon.” https://lnkd.in/dwfZQzE View in LinkedIn

LATERAL INHIBITION. “Somewhat surprisingly, the regions of parameter space that correspond to cone shell patterns are fairly restricted and almost always require that the effective spatial interaction be lateral inhibition. When we chose parameters outside this range, we produced shell patterns that do not correspond to any known species.” https://lnkd.in/dwfZQzE View in LinkedIn

BETWEEN NOISE AND CHAOS. “Fig. 3. (A) Both noise and chaos generate within-species pattern diversity. a, Three real C. crocatus shells. b, Three shells generated with 1% noise only. c, Three shells generated with slightly different initial conditions, but no noise. d, Three shells with both 1% noise and slightly different initial conditions. (B) Two examples of “unknown” patterns having too-wide inhibition fields. https://lnkd.in/dwfZQzE View in LinkedIn

THE PIGMENT CYCLE. “The pigment secreting cells have a sigmoidal stimulus response curve. Feedback occurs as the current pigment deposition becomes part of the input to the sensory cells for the next secretion bout.” https://lnkd.in/dwfZQzE View in LinkedIn

SPACE AND TIME FILTERS. “The spatial filter, shown in top and perspective views, has the form of a Mexican hat, in which excitatory activity stimulates a surrounding inhibitory field. The temporal filter that implements delayed inhibition is half a Mexican hat. It generates a refractory period following a period of activity. “ https://lnkd.in/dwfZQzE View in LinkedIn

SHELL SPACETIME. “Time represents the pigmentation pattern that was laid down in previous bouts, whereas space is the dimension along the growing edge of the cell. The resulting filtered activity is passed through nonlinearities for excitation and inhibition, and this net activity drives the secretory cells that lay down the new pigmented shell material.” https://lnkd.in/dwfZQzE View in LinkedIn

PATTERN GENERATION. “Fig 1. (C) Simple pattern on a Conus shell and how the model extrapolates the previous pattern to produce the current day's pigment secretion. The pigmentation pattern is read by the sensory cells in the mantle. This activity is then passed through the space–time filter of neural activation and inhibition.” https://lnkd.in/dwfZQzE View in LinkedIn