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Title: Code and accompanying input data for simulating lateral inhibition on motionless cell packing Open Access Deposited

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Methodology
  • Numerical solutions of lateral inhibition on disordered cell packing: Starting with a Voronoi tessellation of uniformly (randomly) distributed points, we generated large, disordered, periodic cell packings (e.g., 20,000 total cells) via vertex model simulations with equal tensions on all edges. We model dynamics of individual cell fates on the static cell packing according to the model described in Corson et al., but do not include noise in the dynamics (D=0). Since we changed some aspects of the model, including the external signaling gradient and the noise in fate, we describe the model below for the sake of clarity. The fate of cell i, u_i, evolves as: τ (du_i)/dt=f(u_i,s_i )-u_i where s_i is the signal each cell receives from other cells as well as from any external gradients. We interpret the u=1 fate as the UV cone spectral subtype and the u=0 fate to be other spectral subtypes. Also, f(u,s) is sigmoidal: f(u,s)≡f(u-s)=σ[2(u-s)]=((1+tanh⁡(2(2(u-s))) ))/2 . The signal that cell i receives, s_i, includes an external, time-dependent signal s_0 (x,t) as well as signals from neighboring cells in a distance-dependent manner. s_i=s_0 (x_i,t)+∑_j〖c_ij D^* (u_j ) 〗 The external signal provided to the cells has the following form: s_0 (x,t)=S_0 σ((x-vt)/(ϵ√(A_0 )))≡S_0 ((1+tanh⁡(2(x-vt)/(ϵ√(A_0 ))))/2) where S_0=1 and v=l/4τ and ϵ=1/50. τ is the timescale for cell fate dynamics, and l is the characteristic cell-cell signaling range. The distance-dependent coupling constant c_ij between cell i and cell j is of the form: c_ij=e^(-〖d_ij〗^2/(2l^2)), where d_ij is the distance between the centroids of cell i and cell j. No cell signals to itself directly: c_ii=0. A cell of fate u_j produces signal D^* (u_j )=a(u_j )D(u_j ). The ligand level of cell j, D(u_j ), is directly proportional to the fate u_j. The ligand activity of cell j, called a(u_j ), is of the form: a(u_j )=a_0+(3u^3)/(1+u^2 ) a_1. The constants a_0 and a_1 are 0.05 and 0.95, respectively. To explore the effects of cell-cell signaling range on the final fate pattern, we systemically change the signaling range l from l=3.0√(A_0 ) to l=1.75√(A_0 ) to l=√(A_0 ), where A_0 is the mean cell area. All cells are initially in the u=0 state. The sigmoidal signaling front, sharper than the characteristic cell size, starts at left side of the packing (x=0 at t=0) and moves to the right. In the wake of the front, individual cells differentiate into the u≈1 fate, inhibiting their neighbors from adopting the u≈1 fate within the specified cell-cell signaling range. We solve the differential equations for cell fates using ode45 (MATLAB 2016B, MathWorks).
Description
  • This dataset includes an example cell packing (containing ~20,000 cells). This example cell packing is the same cell packing in Supplementary Figure 11. The Corson_PBC_Square_Sweep_func.m is the main function for simulating lateral inhibition on this (and other) example packings. Please see readme for which simulation parameters may be tuned within this lateral inhibition function.
Creator
Depositor
  • nunley@umich.edu
Contact information
Discipline
Funding agency
  • National Institutes of Health (NIH)
  • National Science Foundation (NSF)
Keyword
Citations to related material
  • Nunley, H., Nagashima, M., Martin, K., Gonzalez, A. L., Suzuki, S. C., Norton, D. A., Wong, R. O. L., Raymond, P. A., & Lubensky, D. K. (2020). Defect patterns on the curved surface of fish retinae suggest a mechanism of cone mosaic formation. PLOS Computational Biology, 16(12), e1008437. https://doi.org/10.1371/journal.pcbi.1008437
  • Corson F, Couturier L, Rouault H, Mazouni K, Schweisguth F. Self-organized Notch dynamics generate stereotyped sensory organ patterns in Drosophila. Science. 2017 May 5;356(6337):eaai7407. doi: 10.1126/science.aai7407. Epub 2017 Apr 6. PMID: 28386027.
  • Hayden Nunley, Mikiko Nagashima, Kamirah Martin, Alcides Lorenzo Gonzalez, Sachihiro C. Suzuki, Declan Norton, Rachel O. L. Wong, Pamela A. Raymond, David K. Lubensky. Defect patterns on the curved surface of fish retinae suggest mechanism of cone mosaic formation. bioRxiv 806679; doi: https://doi.org/10.1101/806679
Resource type
Last modified
  • 11/18/2022
Published
  • 10/19/2020
Language
DOI
  • https://doi.org/10.7302/1jy3-s163
License
To Cite this Work:
Nunley, H., Nagashima, M., Martin, K., Lorenzo Gonzalez, A., Suzuki, S. C., Norton, D. A., Wong, R. O. L., Raymond, P. A., Lubensky, D. K. (2020). Code and accompanying input data for simulating lateral inhibition on motionless cell packing [Data set], University of Michigan - Deep Blue Data. https://doi.org/10.7302/1jy3-s163

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In Collection:

Files (Count: 6; Size: 5.69 MB)

Thumbnailthumbnail-column Title Original Upload Last Modified File Size Access Actions
readme_lateral_inhibition.txt 2020-10-15 2020-10-15 962 Bytes Open Access
20000cellsrelaxed_Out.txt 2020-09-29 2020-09-29 5.66 MB Embargo
Corson_PBC_Square_Sweep_func.m 2020-09-29 2020-09-29 11.2 KB Embargo
MakePBC_Corson.m 2020-09-29 2020-09-29 1.98 KB Embargo
Plot_Corson_Defects_Square_Sweep.m 2020-09-29 2020-09-29 4.08 KB Embargo
ReadSimulationOutput_Corson.m 2020-09-29 2020-09-29 8.82 KB Embargo

Code and accompanying input data for simulating lateral inhibition on motionless cell
packing

Corson_PBC_Square_Sweep_func.m is the main function
% WITHIN THIS FUNCTION, ONE CAN CHANGE THE SIGNALLING RANGE via signalling_range_factor
% One can also include noise in initial conditions if one would like

20000cellsrelaxed_Out.txt is the input function used for the simulation examples in the
paper.

Plot_Corson_Defects_Square_Sweep.m is the function that plots the simulation results…
with a Delaunay triangulation (respecting periodic boundary conditions) and
seven-coordinated particles

All other functions are helper functions.

To Cite this Work:
Nunley, H., Nagashima, M., Martin, K., Lorenzo Gonzalez, A., Suzuki, S., Norton, D.,
Wong, R., Raymond, P., Lubensky, D. Code and accompanying input data for simulating
lateral inhibition on motionless cell packing [Data set]. University of Michigan -
Deep Blue. https://doi.org/10.7302/1jy3-s163

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