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Cornea patch formation

by Jerry Rhee (Submitted: 12/23/2009)

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WHAT IS IT?

This is a work-in-progress that seeks to understand how mosaic patches in mouse corneas arrange themselves into spirals. In part, it seeks to demonstrate the limitations of the current "stem-cell model", which argues that the pattern results from preferential placement of stem cells at the periphery, coupled to centripetal migration.

The yellow represents the parts of the mouse cornea that do not contain labeled clones, i.e., there are cells there but they are not visible. The white ring around the periphery is the limbus, a putative stem cell niche. The dark blue circles within the ring represent stem cells that serve as the sole provider of new "mosaic cells" (leaf shape, a representative cluster of ~16 cells) that ultimately migrate towards the center. Pacemaker cells have the same shape but they are red and have independent adjustable controllers. The cells move based on their ability to respond to a chemical that are secreted periodically by the population. Their rhythm can be entrained but only during a window when they are not secreting.

The rules were inspired by coupled-oscillator and Dictyostelium literature.

HOW IT WORKS

Cells are assigned an intrinsic energy variable (energy-level) that decreases with each tick according to the age-rate. Once that number reaches 0, the cell disappears/dies. Cells are replenished only through a constant stream of new daughters provided by stem cells.

The migration direction is initially recognized by mosaic cells through a patch value that is coupled to the chemical value secreted by both mosaics and pacemakers.

Mosaic cells move based on three parameters: sniff-angle, value-threshold and sniff-distance. Sniff-angle represents the angle the mosaic cell can sense a value. Value-threshold represents the amount necessary to respond. Sniff-distance is the number of patches ahead the mosaic cell can sense.

The primary difference between mosaics and pacemakers is that they have independent adjustable parameters for cycle and secretion length. Although there is no restriction in this model, pacemakers are generally believed to have a faster cycle.

HOW TO USE IT

NUMBER: sets the number of initial mosaic population

STEM-NUMBER: sets the number of initial stemcells population

SNIFF-ANGLE: sets the degree cone-angle with respect to current heading moving cells detect chemical. Also determines the angle the cell will turn after it determines the
highest concentration value.

SNIFF-DISTANCE: sets the point distance from current position cell can detect chemical

ENERGY-LEVEL: sets the initial amount of energy cells possess. This number is spread out over a range so that cells don't die all at once.

AGE-RATE: sets the rate at which cells lose energy.

DRAW-FRAME: draws a wire-frame for assigning positions

CLEAR-FRAME: clears drawings

PARALLELS: sets the number of parallel wires to be drawn

MERIDIANS: sets the number of meridian lines to be drawn

DRAW-SQUARE-FRAME: draws square vertical and horizontal tangents to parallel lines for estimating fractal dimension using a box counting method.

CHEMICAL-CONCENTRATION: sets the amount of chemical secreted with each tick

EVAP-RATE: sets the rate at which chemical is lost

SNIFF-THRESHOLD: sets the amount of chemical required to attract cell movement

FLASHES-TO-RESET: sets the minimum number of secreting neighboring cells required to reset the clock

CYCLE-LENGTH: sets the length of one period

FLASH-LENGTH: sets the duration during cycle in which cells are secreting, which is also the time in which they are refractory to resetting of their cycle.

COUNT-BOXES: reports the number of boxes that cover the periphery.

PACEMKR-RATIO: sets a proportional value with respect to the NUMBER slider to genereate pacemakers cells from the extant mosaic population.

PACEMAKER-LENGTH: sets the period of the pacemaker cell

PACEMAKER-FLASH: sets the duration a pacemaker is secreting

ON-OFF SHOW-CELLS?: gives choice as to whether you want the cells to be visible.

TOTAL-CELL-CLUSTERS: gives a report of how many cell clusters are present.

THINGS TO NOTICE

How do cells behave at the periphery?
How do cells behave near the center?

THINGS TO TRY

Try different values to synchronize flashes. How do combinations affect the turtles' movement, formation and shape of clumps?

Try to figure out a way to change the shape of the chemical concentration curve near the center. How does this affect the shape of cell clusters.

What effect does sniff-angle have?

What effect does lowering chemical concentration to 0 have?

EXTENDING THE MODEL

Try adding some adhesion rules. What effect will this have?
How about changing the shape of the cornea (changing value)?

RELATED MODELS

Ants use a similar idea of creatures that both drop chemical and follow the gradient of the chemical.

Synchrony and movement algorithms were borrowed from the Firefly model.

CREDITS AND REFERENCES

This model was developed at the MIT Media Lab using CM StarLogo. See Resnick, M. (1994) "Turtles, Termites and Traffic Jams: Explorations in Massively Parallel Microworlds." Cambridge, MA: MIT Press. Adapted to StarLogoT, 1997, as part of the Connected Mathematics Project. Adapted to NetLogo, 2000, as part of the Participatory Simulations Project.

To refer to this model in academic publications, please use: Wilensky, U. (1997). NetLogo Slime model. http://ccl.northwestern.edu/netlogo/models/Slime. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 1997 Uri Wilensky. All rights reserved. See http://ccl.northwestern.edu/netlogo/models/Slime for terms of use.

Goodwin BC, Cohen MH. (1969). A phase-shift model for the spatial and temporal organization of developing systems. J Theor Biol. 25(1):49-107.

Dallon JC, Othmer HG. (1997). A discrete cell model with adaptive signalling for aggregation of Dictyostelium discoideum. Philos Trans R Soc Lond B Biol Sci. 352(1351):391-417.

Buck, John. (1988). Synchronous Rhythmic Flashing of Fireflies. The Quarterly Review of Biology, September 1988, 265 - 286.

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