Work Description

Date: 21 April, 2025

------------------------------------------------------------------------------------------------

Dataset Title: Dataset of cell layers on micro-patterned substrates compost of posts

------------------------------------------------------------------------------------------------

Dataset Contact: Xufeng Xue [email protected]

------------------------------------------------------------------------------------------------

Dataset Creators:
Name: Xufeng Xue
Email: [email protected]
Institution: Cincinnati Children's Hospital Medical Center Division of Developmental Biology and UC Department of Pediatrics
ORCID: https://orcid.org/0000-0002-9379-8589

Name: Yubing Sun
Email: [email protected]
Institution: University of Massachusetts (Amherst) Department of Mechanical and Industrial Engineering
ORCID: https://orcid.org/0000-0002-6831-3383

Name: Hayden Nunley
Email: [email protected]
Institution: University of Michigan Biophysics Program
ORCID: https://orcid.org/0000-0002-4634-9422

Name: Agnes M. Resto Irizarry
Email: [email protected]
Institution: University of Michigan Department of Mechanical Engineering
ORCID: https://orcid.org/0000-0002-2292-6029

Name: Ye Yuan
Email: [email protected]
Institution: University of Michigan Department of Mechanical Engineering
ORCID: https://orcid.org/0000-0001-9641-9102

Name: Koh Meng Aw Yong
Email: [email protected]
Institution: University of Michigan Department of Mechanical Engineering
ORCID: https://orcid.org/0000-0001-6295-9645

Name: Yi Zheng
Email: [email protected]
Institution: Syracuse University Department of Biomedical and Chemical Engineering
ORCID: https://orcid.org/0000-0002-2685-3680

Name: Shinuo Weng
Email: [email protected]
Institution: Johns Hopkins University Department of Mechanical Engineering
ORCID: https://orcid.org/0000-0001-7932-913X

Name: Yue Shao
Email: [email protected]
Institution: Tsinghua University Department of Engineering Mechanics
ORCID: https://orcid.org/0000-0001-7548-3551

Name: David K. Lubensky
Email: [email protected]
Institution: University of Michigan Department of Physics and Biophysics Program
ORCID: https://orcid.org/0000-0002-4619-116X

Name: Lorenz Studer
Email: [email protected]
Institution: Memorial Sloan-Kettering Institute Developmental Biology Program and Center of Stem Cell Biology
ORCID: https://orcid.org/0000-0003-0741-7987

Name: Jianping Fu
Email: [email protected]
Institution: University of Michigan Department of Mechanical Engineering, Department of Biomedical Engineering, Department of Cell and Developmental Biology
ORCID: https://orcid.org/0000-0001-9629-6739

------------------------------------------------------------------------------------------------

Funding: CMMI 1917304 (NSF), DGE 1256260 (NSF), DMR 2243624 (NSF), 597491-RWC and 1764421 (Simons Foundation/SFARI, NSF), CMMI 1129611 (NSF), CBET 1149401 (NSF), CMMI 1662835 (NSF), 12SDG12180025 (American Heart Association)

------------------------------------------------------------------------------------------------

Key Points:
- We performed experiments with stem cell colonies on micro-patterned substrates as an in vitro model for an important cell fate decision in vivo. The substrate to which cells adhere is composed of micro-posts, and the displacements of the micro-posts allow for the estimation of cell-substrate forces.
- We generated both bright-field and fluorescence images for each colony. The bright-field image shows the approximate area of the cell colony, while the fluorescence image shows the tops of the micro-posts.
- We developed a method and corresponding code to segment each micro-post and to estimate corresponding centroids. We used the observed positions of micro-post tops and their estimated undisplaced positions to calculate forces -- using the independently known spring constant of the posts. A GUI allows the user to check the post segmentation and correct centroids by clicking.
- We concluded that the cells at the colony center are less contractile than other cells in the colony. We also inferred that the colony is not just composed of two domains (center and outer) with different mechanical properties but is seemingly composed of three domains (center, intermediate, outer).
- These measurements motivate our mathematical model in which the outermost (edge) cells are more contractile than the rest and bias their neighbors to differentiate to the more contractile fate. The innermost cells are of the approximately non-contractile cell fate.

------------------------------------------------------------------------------------------------

Research Overview:
In an earlier study (Xue et al. Nature Materials 2018), stem cells differentiated into one of two cell types, neural plate border (NPB) or neural plate (NP), in vitro. This previous study demonstrated that this differentiation is likely mechanics-guided. Part of this demonstration was measurements of the displacement of microposts under the cell layer as the cells differentiate. These measurements suggested that the NPB cells are more contractile than NP cells. In a follow-up study (linked to this dataset), we quantitatively analyzed these data to demonstrate even further that the NPB cells are mechanically different than the NP cells and that the post displacement profile is not explained by a model of a cell layer with uniform mechanical properties. This analysis motivated the mathematical model -- for this cell colony system -- that we proposed and analyzed.

------------------------------------------------------------------------------------------------

Methodology:
Embryonic stem cells were seeded on micro-patterned substrates, and uniformly supplied chemical media induced differentiation of these stem cells into one of two cell fates, either neural plate (NP) or neural plate border (NPB), in a spatially patterned way with the NP forming a circular domain near the colony center. The substrate is composed of micro-posts to which the cells adhere. The cell layer displaces the posts as it contracts, and the displacement can be used to infer cell-substrate forces. We image the tops of the posts, segment the posts, and compare their observed positions to their undeformed positions. By concentrically averaging radial post displacements, we fit these post data to the results of physical models. These fits of data to models inform a mathematical model of the patterning process.

------------------------------------------------------------------------------------------------

Date Coverage: 2017-2024 (Date range includes dates of experimental data acquisition (2017-2018), and subsequent development and use of analysis code for manuscript preparation (2019-2024)).
Instrument and/or Software specifications: See Methods for experimental instruments, code written in MATLAB

------------------------------------------------------------------------------------------------

There are two zipped folders: high density control.zip and my_code_PMA_01_24_2020.zip.

high density control.zip contains images for estimating post displacements and thus cell-substrate forces for differentiating colonies. The images ending in '_c2.TIF' are those used for estimating positions of post tips, while the images ending in '_c1.TIF' are bright-field images.
Each image title begins with: '072015 force high density d1-XXXX' where XXXX is the index of the image.
There are 42 colonies images (84 total images because of two channels).
Each pixel is 0.3115 um x 0.3115 um.
Please note that in Xue et al. Nature Materials 2018, the control condition in Fig. 2A,C and in Fig. S9, S10 corresponds to these data. All post data in the follow-up modeling study are from these same control data.

my_code_PMA_01_24_2020.zip is the code for analyzing the post displacements. compute_forces_on_posts.m is the main function for this analysis (see below). Below is a summary of the code in this folder:
Raw pattern images contains example raw data and image/experimental details
- Raw pattern images/High density_Brightfield.TIF is an example bright-field image at the control cell density (same density as in high density control.zip).
- Raw pattern images/High density_DiI.TIF is an example fluorescence image of the tops of micro-posts at control cell density.
- Raw pattern images/lattice_vector_estimate.mat store the estimate of the lattice vectors of the array of micro-posts.
- Raw pattern images/low density_Brightfield.TIF is an example bright-field image at a low cell density (different from the density in high density control.zip).
- Raw pattern images/low density_DiI.TIF is an example fluorescence image of the tops of micro-posts at low cell density.
- Raw pattern images/zeiss_20x_1x1_hex.mat stores details of the microscope, post dimensions (in pixels) and pixel size.

helper_code contains relevant helper functions. See description below.
- helper_code/estimate_lattice_vector_for_posts.m refines an initial estimate for the lattice vectors for the array of posts based on an example post image.
- helper_code/fixaflat_func.m is used to segment the top of each post.
- helper_code/objfun.m is an objective function which is optimized in helper_code/estimate_lattice_vector_for_posts.m to estimate lattice vectors for array of posts.
- helper_code/select_post.m is used by mPADs-automated to crop around a post (region-of-interest around post).

functions_for_fitting contains functions that are useful for fitting post displacements to physical models.
- functions_for_fitting/fit_for_contractile_outer_cell.m is used to fit concentrically averaged radial post displacements to a model of the cell layer with only two domains of differing mechanical properties. Both have same localization lengths, but different contractility's.
- functions_for_fitting/fit_for_inner_coupled_to_middle.m is used to fit concentrically averaged radial post displacements to a model of the cell layer with only two domains of differing mechanical properties. Both localization length and contractilities can differ.
- functions_for_fitting/fit_for_inner_coupled_to_middle_simplified.m is used to fit concentrically averaged radial post displacements to a model of the cell layer with only two domains of differing mechanical properties. Both localization length and contractilities can differ. The inner domain is assumed to have an infinite localization length (i.e., larger than the inner domain size).
- functions_for_fitting/fit_three_domains.m is used to fit concentrically averaged radial post displacements to a model of the cell layer with only three domains of differing mechanical properties. Innermost domain has localization length l1, intermediate and outer domain have localization length l2. Contractility can differ across all three domains.
- functions_for_fitting/one_domain_fcn_special.m is used to fit to a model of the cell layer as one uniform mechanical domain.
- functions_for_fitting/simulate_disk_special.m directly simulates displacements in a disk with three domains (instead of using closed form solutions). This can be used to fit to concentrically averaged radial post displacements.
- functions_for_fitting/simulate_strip_special.m directly simulates displacements in a stripe geometry (quasi-1D, infinite and symmetric along y) with three domains (instead of using closed form solutions). This can be used to fit to concentrically averaged post displacements.
- functions_for_fitting/two_domain_fcn_special.m is used to consider a mechanical model of a disk with two domains, each with its own localization length and contractility.

functions_for_averaging contains a function used for concentrically averaging radial post displacements.
- functions_for_averaging/average_displacement_within_concentric_ring.m computes the concentrically averaging radial post displacements within windows of size concentric_length.

functions_for_analyzing_fits contains a couple of helper functions for analyzing fits to post displacements.
- functions_for_analyzing_fits/calculate_stress_from_fit.m calculates stress (both radial and hoop) profile based on parameters from fit. You have a disk (2D poisson ratio nu and radius r0) with two regions: region at center (1) with localization length l1 and target volume change p1, region at edge (2) with localization length l2 and target volume change p2.
- functions_for_analyzing_fits/compute_r_squared.m computes an R^2 value by comparing concentrically averaged redial posts displacement and the corresponding model fit.

- fixaflat_umbrella_func.m locates the center of a reference post and calls fixaflat_func to fit a function to the post top.

extract_relevant_info contains a few functions for using the fit function in matlab to fit simple functional dependences to concentrically averaged radial post displacements. Also, generates a plot to compare model to data.
- extract_relevant_info/extract_relevant_info_from_fit_besseli.m fits a simple BesselI function
- extract_relevant_info/extract_relevant_info_from_fit_disk.m fits to simulate_disk_special function.
- extract_relevant_info/extract_relevant_info_from_full_fit.m fits to fit_three_domains function.

- compute_forces_on_posts.m is the main function for estimating post displacements from the image of the top of micro-posts. Note that this includes a GUI for fixing uncertain/incorrect post detections. Below is a description of inputs and outputs:
INPUTS:
% top_image_name -- name of DiI image (.TIF)
% bottom_image_name -- name of brightfield image (.TIF)
% should_rotate_vectors -- should I rotate initial estimates of lattice vectors for post locations?
% FOR THE TWO BELOW, if there is a region of the image that is not useful (like a big bright spot), exclude posts within that region.
% x_range_rejected_by_user
% y_range_rejected_by_user
OUTPUTS:
% pixel_um -- pixel size in um
% radial_distance_vector -- vector of radial distance from undeflected posts tips and center of colony
% dot_product_post_displacement -- dot product of local radial vector and post displacement for all posts in colony

------------------------------------------------------------------------------------------------

Related publication(s):
Hayden Nunley, Xufeng Xue, Jianping Fu, David K. Lubensky bioRxiv 2021.04.30.442205; doi: https://doi.org/10.1101/2021.04.30.442205
Xue X, Sun Y, Resto-Irizarry A.M. et al. Mechanics-guided embryonic patterning of neuroectoderm tissue from human pluripotent stem cells. Nature Mater 17, 633–641 (2018). https://doi.org/10.1038/s41563-018-0082-9

------------------------------------------------------------------------------------------------

Use and Access:
This data set is made available under a Creative Commons Public Domain license (CC BY-NC 4.0).

------------------------------------------------------------------------------------------------

To Cite Data:
Nunley, H., Xue, X., Sun, Y., Resto-Irizarry, A. M., Yuan, Y., Yong, K. M. A., Zheng, Y., Weng, S., Shao, Y., Lubensky, D. K., Studer, L., Fu, J. Dataset of cell layers on micro-patterned substrates compost of posts [Data set], University of Michigan - Deep Blue Data. https://doi.org/10.7302/2kbj-1y73