CompuCell3D Workshop: Module 5.3: Cluster size distribution of cells disseminating from a primary tumor

Mrinmoy Mukherjee

Center for Theoretical Biological Physics

Northeastern University

Boston, MA

Friday, August 5th, 2022

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• Please submit questions/concerns/suggestions via zoom chat
• Workshop will be live-streamed, recorded, and distributed

Support: NIH NIBIB-U24EB028887, NIGMS-R01GM122424, NSF-2120200, NSF-2000281, NSF-1720625, NIGMS-R01GM076692, NIGMS-R01GM077138, NSF PHY-1935762, PHY-2019745

https://doi.org/10.1371/journal.pcbi.1009011 November 10, 2021

Metastasis : EMT (Epithelial Plasticity)

Tam et al. Nature Medicine (2013)

EMT : binary transition?

The Core EMT genetic circuit : Coexistense of multiple phenotypes

Lu et al. PNAS (2013)

Stable hybrid state

Robustness with more complete circuit

Huang et al. PLoS Comp Bio (2017)

Many hybrid states

Beyond computational modeling

Puram et al. Molecular and Cellular Oncology (2018)

Jolly et al. Oncotarget (2016), Jolly et al. Mol Oncol (2017)

Hybrid cells move collectively

Head and neck tumors (single cell RNA-seq)

Partial EMT : CTC

Nieto et al. Cell (2016)

CTC Cluster size distribution

Kozminsky et al. Adv. Sci. (2019)

CTC clusters :

• 2-10 cells large
• Formed before entering the circulation
• Made of hybrid cells (more metastatic potential, more stem like)
• Worst patient survival
• Resist cell death in circulation
• Heterogeneous

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CTC Clusters

Aceto et al. Cell (2014)

Bocci et al. Cancer Res (2019)

Computational Model (CompuCell3D)

Assumptions and model implementation:

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• Choose a circular tumor of fixed # of cells in 2D
• Assume that the EMT (partial) has already happened. Choose 60% Epithelial (E) cells and 40% Hybrid (H) cells randomly in the tumor
• Mechanical properties of the cell : E – more adhesive, less motile; H – less adhesive, more motile
• We will control the adhesiveness the cells by contact energy terms
• Motility of the cells –1) diffusive motility (cell membrane fluctuation or temperature), 2) active motility (external potential)
• Hybrid (H) cells will form the clusters

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Goal:

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1. Set up a model in CC3D describing both the single cell and cluster of cells dissemination from a tumor
2. Calculate the cluster size distribution
3. Compare with the CTC cluster size distributions from patient data

E : red cells

H : green cells

m : black (medium)

Parameters

Fluctuation amplitudes:

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Initial Configuration:

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Set up a simulation wizard with 1) Python+XML, 2) Dimension: x=y=200, z=1; Boundary condition: x,y Periodic ; Lattice type: Square; Neighbor order=2; Initial cell layout: Blob, 3) Cell types : Medium, E, H, 4) Select Contact, VolumeFlex, SurfaceFlex (5.3.2.1)

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Area and perimeter:

Fixed :

Contact energies:

Test these two cases :

Cells with diffusive motility

How to get the cluster dissemination?

Pinning of H cells at higher values of E-H contact energies

Cells with active motility (collective migration)

Extra term in the Hamiltonian through ExternalPotential Plugin:

μ denotes the motile force acting on the center of mass of the cells

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describes the direction of polarity of the cells, which is updated by the rule:

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𝜏 is the persistence time of cell polarity, and is the velocity of a cell’s center of mass

Implementation in CC3D:

XML file -> incorporate the ExternalPotential plugin

update the polarity rule in python

Kabla et al. JRSC Interface (2012)

displacement

pbc correction

velocity

Other parameters (5.3.2.2)

Fix persistence time of cell polarity 𝜏 = 50 (What will be the effect of smaller 𝜏 ?)

Try different values of μ = 30, 40, 60

No dissemination

Larger clusters

Smaller clusters

Velocity map

Calculating the cluster size (see 5.3.2.3)

Time series of average cluster size:

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Take a bigger simulation box of x, y dimension = 1000 to avoid frequent collision between clusters.

mcs=50000

Scaling relation

Fraction of H cells released

Average cluster size

Cluster size distributions

Shape driven cluster size

cortical tension is negative

cortical tension is positive

Shape of clusters

Heterogeneity of cell types in the clusters

Consider two types of hybrid cells with different degree of EMT

High μ cell acts as a leader cell and can help to disseminate cells with very low motility

Analogous to experimental cases where non-cancerous cells like fibroblasts can help to release the cells with lower motility (more epithelial like).

Cluster size distributions

1) For , single cells or very small clusters in the medium are largely composed of the cells with lower motility, opposite to the intuition that cells with higher motility produce smaller clusters.

2) Cells with higher motility guide the primary dissemination of the cells with lower motility.

3) Cells with higher motility maintain the larger clusters by leaving behind the smaller clusters composed of cells with lower motility (smaller cluster: more epithelial like, larger cluster: more mesenchymal like).

4) CTCs to be relatively more mesenchymal compared to the primary tumor, as found in the case of Stage II-III breast cancer (GSE111842).

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Exercise 1 : Calculate the effect of heterogeneity in H cell-medium surface tension

at fixed motility μ.

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Exercise 2 : Calculate the size distributions when the motility of all the H cells drawn

from a distribution.

You can find all the answers and the code in the paper Mukherjee et al. PLoS Comp Biol (2021)

Other problems

Other necessary components to add in the system :

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1. Rate of EMT (gene regulatory network)
2. ECM (density, orientation)

Acknowledgements

Prof. Herbert Levine, Northeastern University, USA

Dr. Dapeng (Max) Bi, Northeastern University, USA

Dr. Mohit Kumar Jolly, Indian Institute of Science, India

CompuCell3D Community

Support: NIH NIBIB-U24EB028887, NIGMS-R01GM122424, NSF-188553, NSF-186890, NSF-1720625, NIGMS-R01GM076692, NIGMS-R01GM077138, NSF PHY-1935762, PHY-2019745

A spectrum of EMT states