Position-based Dynamics
for Multicellular Systems
with
Adhesion Memory
Steffen Plunder
Kyoto University
Institute for the Advanced Study of Human Biology
ACMB-JSMB2025
Minisymposium MS08
Contents
Modelling of Plithotaxis via adhesion memory
Effect of realistic repolarisation delays
Position-based Dynamics (PBD)
Motivation:
What happens after EMT?
Modelling:
The challenge of syncronisation with polarisation delays
Mathematics: Numerical method
(outlook)
A Volterra-equation for adhesive memory
Extension of PBD for an integral equation
Movivation:
What happens after epithelial-to-mesenchymal transitions?
EMT:
cells change from stable/skin-like phenotype
to migratory phenotype (e.g. migrating cancer cells)
Movivation:
What happens after epithelial-to-mesenchymal transitions?
PhD: Modelling of EMT in...
Neural Crest
(Embryogenesis
)
SP, Cathy Danesin, Bruno Glise, Marina A. Ferreira,
Sara Merino-Aceituno, and Eric Theveneau.
“Modelling Variability and Heterogeneity of EMT Scenarios
Highlights Nuclear Positioning and Protrusions as Main Drivers of Extrusion.”
Nature Communications
, 2024
Mouse Primitive Streak
(Gastrulation)
Despin-Guitard, Evangéline, Viviane S. Rosa, Steffen Plunder, Navrita Mathiah,
Kristof Van Schoor, Eliana Nehme, Sara Merino-Aceituno, et al.
“Non-Apical Mitoses Contribute to Cell Delamination during Mouse Gastrulation.”
Nature Communications
2024
Drosophila Eye-Antenna
(Oncogenesis)
Mira-Osuna, Marta, SP, Eric Theveneau, and Roland Le Borgne.
“The Directionality of Collective Cell Delamination Is Governed
by Tissue Architecture and Cell Adhesion in a Drosophila Carcinoma Model.”
bioRxiv
, 2024
Movivation:
What happens after epithelial-to-mesenchymal transitions?
How do the cells migrate through the basal matrix?
Extracellular Matrix:
- dense network of collagen fibers
Known mechanisms:
- cell can degrade the basal matrix
- migration through created gaps
in small to large groups
Part I
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First approach:
Obstacle model
Many difficult modelling
questions:
- how do single cells move?
- how do pairs of cells move?
- behaviour in clusters?
Too complex!
Foundations of cellular motion
Agent-based Model
bias?
see talk by Antoine Diez
11th (Friday), 10:10am, Room 6
cell-cell adhesion
cell-matrix adhesion
polarity dynamics
Focus today:
Different polarity dynamics!
(n = 1) Individual cell dynamics:
Run & Tumble
Change polarity after (randomized) time-intervals:
(n = 2) Pairwise interactions:
Contact Inhibition of Locomotion
CIL: ~cells collide, stick together for a while and repolarize
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(from a random rice field in Nara)
(n = 2) Pairwise interactions:
Contact Inhibition of Locomotion
Scarpa, Elena, Alice Roycroft, Eric Theveneau, Emmanuel Terriac, Matthieu Piel, and Roberto Mayor.
“A Novel Method to Study Contact Inhibition of Locomotion Using Micropatterned Substrates.”
Biology Open
, 2013
Key biological aspect
for our model:
The time of collision is slow,
aorund 5 minutes!
(n = 2) Pairwise interactions:
Contact Inhibition of Locomotion
hard radius
soft radius
Cell-cell
contact
model
(n = 2) Pairwise interactions:
Contact Inhibition of Locomotion
In our model, CIL affects first the set of adhesive bonds!
set of
adhesive bonds
...then we
change the
polarity
vector
(n = 2) Pairwise interactions:
Contact Inhibition of Locomotion
Note:
Most parameters so far are
inverable from videos!
Question:
Is this enough for collective migration?
Woods, Mae L., Carlos Carmona-Fontaine, Chris P. Barnes,
Iain D. Couzin, Roberto Mayor, and Karen M. Page.
“Directional Collective Cell Migration Emerges
as a Property of Cell Interactions.”
PLOS ONE
, 2014
Yes!
We can replicate
their model!
But it fails once we impose
realistic CIL duration!
Takeaway:
Repolarisation duration / adhesion memory
shows that something is missing for collective cell migration!
(n > 2) Behaviour in clusters
Possible mechanisms of migration:
Chemotaxis / Durotaxis / Haptotaxis / Mechanotaxis / ...
(it's a large field)
Buttenschön, Andreas, and Leah Edelstein-Keshet.
“Bridging from Single to Collective Cell Migration:
A Review of Models and Links to Experiments.”
PLOS Computational Biology
, 2020
Our pick: Plithotaxis
Trepat, Xavier, and Jeffrey J. Fredberg.
“Plithotaxis and Emergent Dynamics in Collective Cellular Migration.”
Trends in Cell Biology 21, no. 11 (November 1, 2011)
The collective tendency for each cell comprising the sheet to steer
along the local orientation of maximal principal intercellular stress, or,
equivalently, minimal intercellular shear stress, is called plithotaxis
source: WikiData
(n > 2)
Adhesive memory + Plithotaxis
Dynamic creating and
breakage of bonds
Force dependent duration of stable protrusions
Dynamic waiting times:
Overview
Movies
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(see https://steffenpl.github.io/research/projects/cell-migration-model/)
Force gradient controls
repolarisation speed
A chaotic but robuts model for self-organisation
Benchmark(s):
Confinement is a requirement for self-organisation
Conclusion
Adding realistic repolarisation delays
(CIL: 5min, Plithotaxis: ~10 - 45min)
affects the ability for collective migration.
Our model recapitulates appearance of stress gradient
and common behaviour
(need for convienment, group speeds fits experimental data, ...)
Future plans:
Experimental evidence by inhibiting cell's ability to
sense mechanical stress / increase duration of repolarisation.
a short break...
math incoming in 3... 2... 1...
Part II
Numerics for
non-overlap
...an easy method
for situations like this
...a veryyy short introduction on simulation
with inequality constraints
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The
idea
behind Position-based Dynamics (PBD)
ODEs with inequality constraints:
Possible numerical discretisation (Moreau's sweeping process):
S
Key insight:
Projection errors (for non-convex sets)
are not linear in the distance to a set
!
First-order PBD converges
Instead of (expensive)
iterative method
for projection:
Pairwise non-overlap
PBD:
SP, and Sara Merino-Aceituno.
“Convergence Proof for First-Order Position-Based Dynamics:
An Efficient Scheme for Inequality Constrained ODEs.”
arXiv
, 2023
computational cost
Consistency (in a susc sense) + stability = convergence.
Thm. (SP, Sara Merino, arxiv, 2023)
Thm. (SP, Sara Merino, arxiv, 2023)
The full theorem is a bit technical...
Other models
Bacteria model
from Michéle Romanos
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Anisotropic repulsion
from Claudia Wytrzens,
Sara Merino-Aceituno
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Neural tube
with Eric Theveneau,
Sara Merino-Aceituno
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Conclusion
Satisfying inequality conditions in
first-order dynamical systems is not that hard!
S
Key insight:
Projection errors (for non-convex sets)
are not linear in the distance to a set
!
Next steps:
Application of PBD to Volterra-type integral equation
Repolarisation (during CIL and in clusters) depends on
existing cytoskeleton and cell-matrix adhesion
matrix
attachment
location
(from the past)
current
position
Next steps:
Application of PBD to Volterra-type integral equation
matrix
Going multicellular:
Introduce non-overlap
PBD-style
Thank you!
Collaborators
Sara Merino-Aceituno
Eric Theveneau
Vuk Milisic
+ many coauthors, colleagues and friends
Funding
22H05110 (PI: Seirin Lee)
Grant-in-Aid for Transformative Research Areas (A)
JP24K16962 (PI: SP)
Grant-in-Aid for Early-Career Scientists
WWTF (Vienna Science and Technology Fund)
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