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Simulating Organogenesis in COMSOL Multiphysics®: Tissue Patterning with Directed Cell Migration

One unified mathematical framework, patterns in 1D/2D/3D, faster than Turing. 🧵 Thread: bsky.app/profile/iber... 📄 Paper: 10.1016/j.newton.2026.100557 ⚙️COMSOL: www.comsol.com/paper/simula...

comsol.com

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Thrilled to see our #DCM paper out in @cp-newton.bsky.social! 🎉 How do cells self-organize into complex patterns so quickly during development? We show that #directed #cell #migration — chemotaxis, durotaxis, differential adhesion — is a surprisingly fast & versatile patterning engine. 🧵👇

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Determinants of the Transition Zone Width of Morphogen Readouts

Smaller cells widen the #transition #zone. The tradeoff between morphogen gradient precision and transition zone sharpness may explain why epithelial cell diameters don't shrink further in developing tissues. 🧵 Thread: bsky.app/profile/iber... 📄 Paper: www.biorxiv.org/content/10.6...

biorxiv.org

In tissue patterning, cell fate boundaries often form transition zones with mixed or gradual fates rather than sharp demarcations. Traditionally, such zones in morphogen-driven systems were attributed...

#MorphoGrad runs the simulations behind several of our papers on morphogen gradient precision. Here's what we found: 👇

🔧 What can #MorphoGrad do? ✅ 1D & 2D reaction–diffusion in cell-based epithelial geometries ✅ Cell-to-cell variability in diffusion, production & degradation ✅ Parameter sweeps & statistical analysis ✅ Gradient variability & positional error ✅ GUI for non-coders Built for robustness & precision.

MorphoGrad: A MATLAB toolbox for simulating steady-state morphogen gradients under cell-to-cell variability

🧰 New tool alert! ⚙️ #MorphoGrad, an open-source toolbox for simulating reaction–diffusion systems in 1D and 2D tissues, with cell-to-cell parameter heterogeneity & graphical user interface. No heavy coding required. Explore complex morphogen gradient models interactively. doi.org/10.1016/j.xp...

cell.com

Studying morphogen gradient-based tissue patterning in silico while accounting for biological variability remains challenging. Here, we present a MATLAB-based protocol for simulating steady-state morp...

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Dagmar Iber & CoBi @iberd.bsky.social · 28/05/2026

✅ Open source ✅ Gradient-based optimisation via backpropagation ✅ Works on tissues too large to fully image ✅ Applied to 5 mouse epithelial tissues 💡 The ratio of apical to lateral surface tension predicts cell shape across epithelial subtypes: single parameter yields broad morphological diversity

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Dagmar Iber & CoBi @iberd.bsky.social · 28/05/2026

🔬⚙️💻 Excited to share #OptiCell3D, our new image-based framework for inferring cell mechanical properties with high precision from 3D microscopy. www.biorxiv.org/content/10.6... #ComputationalBiology #CellBiology #Biophysics #OpenSource

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Dagmar Iber & CoBi @iberd.bsky.social · 20/03/2026

For the science, see our Tweetorial 🧵: bsky.app/profile/iber... Kudos to the @ethz.ch Animal Facility for championing transparency! 🙏 #3Rs #AnimalWelfare #LungDevelopment #COPD

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Dagmar Iber & CoBi @iberd.bsky.social · 20/03/2026

We're fully committed to 3Rs: ♻️ Replace – comp models & simulations go beyond what animal data alone could reveal 📉 Reduce – just 7 pregnant females (severity degree 0) & reuse of 20-year-old datasets instead of new experiments 🔬 Refine – SkelePlex & our pipeline extract max insight from min data

Dagmar Iber & CoBi @iberd.bsky.social · 20/03/2026

The @ethz.ch Animal Facility featured our work on how the lung gets its energy-efficient shape and how it remodels in disease like COPD 🐭🫁 — as part of their spotlight on responsible animal research. 🧵(1/4)

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Many processes influence boundary sharpness and placement: gene regulatory interactions, spatial averaging, cell sorting to name a few. Our analysis shows that cellular readout noise is the main determinant of boundary sharpness, i.e. #TZW. Preprint: doi.org/10.64898/202... 🧵 6/6

doi.org

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By matching simulations with measurement of #TZW & #positional #error, we inferred kinetic and readout noise levels - and found them in the reported range. This further supports that reliable long-range morphogen patterning is feasible with physiological noise levels: x.com/DagmarIber/s... 🧵 5/6

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We uncover a trade-off regarding cell size: • Larger cells yield sharper boundaries (smaller #TZW) • Smaller cells reduce variability in boundary position between embryos (lower positional error) The measured cell size in the neural tube perfectly balances boundary sharpness and precision. 🧵 4/6

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Our theoretical & computational analysis shows that #TZW is primarily set by #noise in the #cellular #readout process, not by fluctuations in the morphogen gradient itself. For exponential gradients, a noisy readout threshold naturally yields a position-independent TZW. 🧵 3/6

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According to prevailing theory, transition zones should widen exponentially with distance from the morphogen source, due to stochastic effects at low morphogen copy numbers. #Contrary, we find that #TZW remains about #constant, independent of readout position and developmental timepoint. 🧵 2/6

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What determines the sharpness of cell fate boundaries in gradient-based patterning? We quantified #transition #zone #widths (TZW) across seven progenitor domain boundaries spanning the entire dorsal-ventral axis of the developing #mouse #neural #tube. Preprint: doi.org/10.64898/202... 🧵 1/6

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doi.org

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Dagmar Iber & CoBi @iberd.bsky.social · 05/11/2025

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Paper & poster are available on the COMSOL conference website: www.comsol.com/paper/direct...

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Reposted by Dagmar Iber & CoBi

SIB Swiss Institute of Bioinformatics @sib.swiss · 18/09/2025

"Within the competition to bring this field to a new level, SimuCell3D is remarkable and will mark a clear evolution of the topic." 🥁That’s what the committee said about this #SIBRemarkableOutputs 2024 👉Discover the output: tinyurl.com/53arz2rz @iberd.bsky.social

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Dagmar Iber & CoBi @iberd.bsky.social · 12/09/2025

The goal: make it easier for others to reproduce and extend these models within COMSOL. We hope this serves as a generalizable reference for simulating collective cell behavior and pattern formation. arxiv.org/pdf/2509.08930

arxiv.org

Dagmar Iber & CoBi @iberd.bsky.social · 12/09/2025

This complements our earlier work introducing the DCM model 👉 bsky.app/profile/iber... That previous paper focused on the biological questions and mathematical framework. Here, we focus on the practical COMSOL #PIDE implementation: setup, BCs, 1D–3D, and Lagrangian reformulation for growth.

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Dagmar Iber & CoBi @iberd.bsky.social · 12/09/2025

Out now: Simulating Organogenesis in #COMSOL: Tissue Patterning with Directed Cell Migration We provide a detailed walkthrough of how to implement #DCM partial integro-differential equation models - enabling accessible simulations of tissue patterning and morphogenesis. arxiv.org/pdf/2509.08930

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Dagmar Iber & CoBi @iberd.bsky.social · 25/08/2025

Our paper "Morphogen gradients can convey position and time in growing tissues" is now out in Newton ‪@cp-newton.bsky.social‬ Quite fitting to see this novel idea that morphogen gradients not only encode position, but can also time & synchronise development over long distances out in a new journal.

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📌 Summary: • #DCM is a rapid, robust mechanism for developmental pattern formation • COMSOL FEM implementation makes DCM models numerically accessible • #DCM patterning parameter ranges and timeframes • Pattern Orientation via attraction anisotropy or directed tissue growth 👇Thread 🧵(10/11)

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2. Dynamic #attraction #zones Spatially varying cell attraction that changes with tissue growth can guide migrating cells, leading to precise large-scale patterning. This mimics how tissues form rings, bands, or layered structures in vivo. 👇Thread 🧵(9/11)

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We identify two mechanisms for guiding pattern orientation: 1. #Anisotropic #attraction Cells pulling or migrating more strongly in one direction form aligned stripe-like patterns—e.g., during directional tissue growth. 👇Thread 🧵(8/11)

#DCM naturally leads to unoriented patterns—spots, labyrinths—similar to Turing-like systems. But biological tissues often require oriented patterns to fulfill specific functions. Can DCM produce stripes, too? 👇Thread 🧵(7/11)

Three key parameters drive the emergence and morphology of patterns: • Initial density of motile cells • Intercellular attraction strength • Cell sensing radius 👇Thread 🧵(6/11)

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Simulations and linear stability analysis allowed us to find #critical #conditions for pattern formation and predict #patterning #speed. We show under which conditions #DCM can realistically pattern tissues in development. 👇Thread 🧵(5/11)

We developed a mathematical framework that represents a wide range of #DCM cues, e.g., chemotaxis, durotaxis, haptotaxis & a general Finite Element Method #FEM: 👉 1D, 2D, 3D 👉 arbitrary geometries & boundary conditions 👉 isotropic & anisotropic interactions 👉 fast, large-scale simulations 🧵(4/11)

To study #DCM, both discrete and continuum models have been used. But: 👉 Discrete models are computationally expensive. 👉 Continuum models have required custom Finite Volume Method #FVM implementations—until now. 👇Thread 🧵(3/11)

During embryonic development, cellular tissues transition from uniform starting conditions into robust spatial patterns. #DCM offers a particularly fast and versatile route to spontaneously symmetry breaks and pattern formation without tissue buckling. 🧵(2/11)