Understanding collective phenomena in multicellular systems
through agent-based models

Franziska Matthäus, FIAS & Goethe University Frankfurt,
Department of Computer Science and Mathematics, Frankfurt, Germany0Research Overview

Multi-cellular systems exhibit a range of behaviors
that can be studied using agent-based approaches;
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Collective phenomena
Self-organization & pattern formation
Structure – function relationshipmechano-chemical regulation
Active vs. passive mechanisms in biological systems

Goal:
The identification of simple principles of complex behavior:
How does local information generate global structure?
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Applications in Life Sciences

2D / 3D time-lapse microscopy data
Wound healing(with AK Windbergs, FB 14)
Skin patterning(With D. Headon, Roslin Institute, UK)
Organoid dynamics(with AK Stelzer, FB 15)
Development(with AK Stelzer, FB 15, J. Rainger& D. Headon, Roslin Institute, UK)3

Applications in Life Sciences

2D / 3D time-lapse microscopy data
Wound healing(with AK Windbergs, FB 14)
Skin patterning(With D. Headon, Roslin Institute, UK)
Organoid dynamics(with AK Stelzer, FB 15)
Development(with AK Stelzer, FB 15, J. Rainger& D. Headon, Roslin Institute, UK)3

Applications in Life Sciences

2D / 3D time-lapse microscopy data
Wound healing(with AK Windbergs, FB 14)
Skin patterning(With D. Headon, Roslin Institute, UK)
Organoid dynamics(with AK Stelzer, FB 15)
Development(with AK Stelzer, FB 15, J. Rainger& D. Headon, Roslin Institute, UK)3

Applications in Life Sciences

2D / 3D time-lapse microscopy data
Wound healing(with AK Windbergs, FB 14)
Skin patterning(With D. Headon, Roslin Institute, UK)
Organoid dynamics(with AK Stelzer, FB 15)
Development(with AK Stelzer, FB 15, J. Rainger& D. Headon, Roslin Institute, UK)

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Agent-based modeling toolkit

3Agent-based Modeling Toolkit

Position,Velocity

ForcesCentroid position adhesion/repulsion07)= 5 6),& + 1 + 9(2)02GrowthDivision

Environment

Shape

Polarity

Force potential
random motion!(#) = &2 ( ) !"# $!$! − ) !# $!$! ,0,# < -#%# ≥ -#%&∈(Active migration
01 1=5 6),& − 1
02 4
&∈(

mechanotransduction, persistence, friction
Forces7) − 7&
6 = !+ ( !(||7) − 7& ||)||7) − 7& ||Cell neighborhood via Gabriel net(distance based) or Delaunay triangulation

Repulsion
0Adhesion
rc4

Agent-based Modeling Toolkit

Position,
Velocity

ForcesGrowthDivision

Environment

Pressure-dependent cell growth

Polarity

Shape

Repulsion
0Adhesion
rc5

Agent-based Modeling Toolkit

Position,
Velocity

ForcesGrowthDivision

Environment

Polarity

Shape

Division (rule-based):•a second cell centroid is placed in close proximity to the mother centroid•optional: both cell radii are reduced for volume preservation: !! =•local mechanics automatically adjusts position of new cells,

1/2 & !"

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Agent-based Modeling Toolkit

Position,Velocity

ForcesGrowthDivision

Environment

Polarity

Shape

Chemical environment:§ Spatio-temporal dynamics of compounds given by systems of partial differential equations§ Sensing and production of chemicals: coupling off-lattice positions to numerical grid
§ Active motion term extended by chemotaxis

This results in hybrid discrete-continuous models!

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Agent-based Modeling Toolkit

Position,
Velocity

ForcesGrowthDivision

Environment

Polarity

Shape

Spin-dependent force potential

Nissen et al., eLife, 20188Agent-Based Modeling Toolkit

Position,Velocity

ForcesGrowthDivision

Environment

Polarity

Nielsen et al., iScience, 2020

Shape

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Quantiative Data is Needed for Model Design

How do we 'inform' the models?

To develop the structure of the model(which processes to include) we needhypotheses/relations (qualitative data)

To parametrize the models
we need quantitative data

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Instance segmentation (mask_rcnn) [M. Pereyra]

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Object identification
4D linking

movement

2D Annotation
training & prediction& shape analysis
Segmentation & tracking

3D linking

12Movement Analysis – 2D/3D PIV [M. Pereyra]
Many advantages:

Particle image velocimetry (PIV)

Velocity field

PIV

Cross-correlation:

Fast, robust, reliable
No problem with cell clusters
No segmentation needed
No staining needed

Features:
Currently fastest 3D PIV package available

quickPIV

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C++

OpenPIV (Python)quickPIV

2D

63 ms

160.81 ms

50.42 ms

3D--

59.72 s18.09 s§
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Cross-correlation
Peak sub-voxel approximation
Multi-pass
Filtering & Post-processing
Spatial & temporal averaging
Similarity-selective averaging
Mappings
Pseudo-Trajectories

Pereyra et al., BMC Bioinformatics, 2021, Glover et al., PLoS Biol, 2017; Stichel et al., NPJSBA, 2017; Müller et al., J Pathol, 201513

Example: Dynamics of Pancreas Organoids

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Pancreas organoid dynamics [T. Liebisch, M. Kurtz]

Pancreas Organoid Dynamics, Stelzer Lab
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Size oszillations [T. Liebisch, M. Kurtz]

Volume16

Scaling law for dependence of size oscillation events on cell division dynamics
Volume-area relationship for spherical objects:
Production rate of substances is proportional to cell number:
Osmotic pressure depens on concentration and volume:
Surface is proportional to cell count, i.e.,, therefore

This yields
Rupture happens if pressure increases. Constant pressure requires
This is given when
Constant cell division rate

exponential increase

faster than quadratic growth

Linear increase in cell number for division rate decreasing as

expect ruptures

expect no ruptures
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Agent-based model reproduces organoid dynamics [T. Liebisch, M. Kurtz, L. Ramirez]

Position,
Velocity

ForcesDivision

Environment

Polarity- ! includes cell polarity or bending potential- cell division included- dynamics of secretion of osmotically active substance- osmotic pressure

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Agent-based model confirms scaling law
Further validation using bright-field pipeline
Experiment

ExperimentSimulation    



Simulation   







    



Hof et al., BMC Biology, 2021

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Further Dynamics: Rotation!! = 1!! = 0- active migration / acceleration$%1= ' (" ) + %" − %$&!

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(Almost) Full Virtual SystemPosition
Velicity

ForcesGrowthDivisionEnvironment

Polarity

Shape21Migration

Hof et al., BMC Biology, 2021

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What do we learn from these simulations?

Cell division dynamics

volume oscillations

SizeFusions

Rotation

Luminar structures

Polarity

Migration

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Summary / Outlook / Challenges

Take Home message:
Agent-based models are useful in determining regulatory processes and biophysicalprinciples underlying collective phenomena in multicellular systems.
Efficiency / Scaling:
Stochastic simulations are computationally expensive
Current efforts: increase parallelization / GPU implementation
Parameter estimation:
Requires summary statistics / large number simulations for every parameter set
Current efforts: explore AI approaches (simulation-based inference)
Vision: direct parameter estimation using original data (no summary statistics)
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Acknowledgements
Cellular Bioinformatics Group
Camile Fraga Delfino Kunz (PhD)
Tim Liebisch (PhD)Zoë Lange (PhD)
Marc Pereira Marí (PhD)
Armin Drusko (PhD)
Dr. Kai Kopfer (Postdoc)
Katharina Becker (Master)Marina Kurtz (Master)
Judith Massmann (Bachelor)
Lars Dingeldein (Bachelor)
Melanie Mösser (Lab rotation)
Danica Hagen (Lab rotation)
Lucas Fein (Lab rotation)
Alexis Mergez (Internship)

FundingNational Collaborations
E. Vargas (FIAS)
T. Sokolowski (FIAS)
M. Kaschube (FIAS)
E.H.K. Stelzer (GU, FB 15)
M. Windbergs (GU, FB 14)
A. Frangakis (GU, FB 13)
A. Gerisch (TU Darmstadt)

German Research Council
High performance computer

International Collaborations
D. Headon (Roslin Institute Edinburgh)
J. Rainger (Roslin Institute Edinburgh)
K. Painter (Heriot Watt Edinburgh)
J. Sharpe (EMBL Barcelona)

Exhibition at the night of Science & now

THANK YOU FOR YOUR ATTENTION

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