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Phenotype divergence and cooperation in isogenic multicellularity and in cancer

Frank Alvarez, Jean Clairambault

TL;DR

It is shown how cancer impacts two of the main mechanisms that pushed forward the emergence of multicellularity: phenotype divergence in cell differentiation and between-cell cooperation, and how both mechanisms appear to be reversed in tumour cell populations.

Abstract

We discuss the mathematical modelling of two of the main mechanisms which pushed forward the emergence of multicellularity: phenotype divergence in cell differentiation, and between-cell cooperation. In line with the atavistic theory of cancer, this disease being specific of multicellular animals, we set special emphasis on how both mechanisms appear to be reversed, however not totally impaired, rather hijacked, in tumour cell populations. Two settings are considered: the completely innovating, tinkering, situation of the emergence of multicellularity in the evolution of species, which we assume to be constrained by external pressure on the cell populations, and the completely planned-in the body plan-situation of the physiological construction of a developing multicellular animal from the zygote, or of bet hedging in tumours, assumed to be of clonal formation, although the body plan is largely-but not completely-lost in its constituting cells. We show how cancer impacts these two settings and we sketch mathematical models for them. We present here our contribution to the question at stake with a background from biology, from mathematics, and from philosophy of science.

Phenotype divergence and cooperation in isogenic multicellularity and in cancer

TL;DR

It is shown how cancer impacts two of the main mechanisms that pushed forward the emergence of multicellularity: phenotype divergence in cell differentiation and between-cell cooperation, and how both mechanisms appear to be reversed in tumour cell populations.

Abstract

We discuss the mathematical modelling of two of the main mechanisms which pushed forward the emergence of multicellularity: phenotype divergence in cell differentiation, and between-cell cooperation. In line with the atavistic theory of cancer, this disease being specific of multicellular animals, we set special emphasis on how both mechanisms appear to be reversed, however not totally impaired, rather hijacked, in tumour cell populations. Two settings are considered: the completely innovating, tinkering, situation of the emergence of multicellularity in the evolution of species, which we assume to be constrained by external pressure on the cell populations, and the completely planned-in the body plan-situation of the physiological construction of a developing multicellular animal from the zygote, or of bet hedging in tumours, assumed to be of clonal formation, although the body plan is largely-but not completely-lost in its constituting cells. We show how cancer impacts these two settings and we sketch mathematical models for them. We present here our contribution to the question at stake with a background from biology, from mathematics, and from philosophy of science.
Paper Structure (18 sections, 2 theorems, 44 equations, 2 figures)

This paper contains 18 sections, 2 theorems, 44 equations, 2 figures.

Table of Contents

  1. Biological and evolutionary-developmental background
  2. Being or not teleological: the two settings considered
  3. The atavistic theory of cancer
  4. Why and how does multicellularity fail in cancer?
  5. A narrative of long-term evolution and cancer, freely exposed to the fire of philosophy of science
  6. Cell differentiation and phenotype divergence
  7. Heterogeneity and plasticity with respect to what?
  8. Long-term evolution as genetic adaptation of the body plan in animals
  9. A nonlocal phenotype-structured cell population model
  10. What this model tackles and what it leaves unexplained
  11. Cooperation
  12. Tinkered cooperation in the emergence of multicellularity vs. directed cooperation in constituted multicellular animals
  13. Prisoner's dilemma and reciprocity
  14. First case: The unbalanced scenario: ($\varepsilon_{11}\varepsilon_{21}\neq\varepsilon_{12}\varepsilon_{22}$)
  15. Second case: The balanced scenario ($\varepsilon_{11}\varepsilon_{21}=\varepsilon_{12}\varepsilon_{22}$)
  16. ...and 3 more sections

Key Result

Proposition 1

Consider a couple $(p_0,q_0)$ and the value $e=\varepsilon_{11}\varepsilon_{21}-\varepsilon_{12}\varepsilon_{22}$.

Figures (2)

  • Figure 1: Phenotype divergence and loss of plasticity. On these cartoon-like figures, one can follow the progressive distancing of an initial cell population arbitrarily set at $z=(0.25, 0.25, 0.5)$, submitted to an advection gradient that tends to split the cell population into two subpopulations migrating towards the two extreme points $(0,1)$ and $(1,0)$ of the domain $\Omega$, while the plasticity variable $\theta$ decreases towards $0$.
  • Figure 2: Left panel: Several initial configurations of cooperation probabilities. Right panel: Limiting values of the sequences $(p_k,q_k)$ associated to initial values showcased on the previous figure.

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof