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Version of Record: November 9, 2020
Accepted Manuscript: October 16, 2020

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Enrico Sandro Colizzi

Renske MA Vroomans

Roeland MH Merks

(2020)
Evolution of multicellularity by collective integration of spatial information

eLife 9:e56349.

https://doi.org/10.7554/eLife.56349
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Figures
Videos
Tables
Additional files

21 figures, 7 videos, 1 table and 1 additional file

Figures

Figure 1

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Model description.

(a) Adhesion between two cells is mediated by receptors and ligands (represented by a bitstring, see Hogeweg, 2000). The receptor of one cell is matched to the ligand of the other cell and vice …

Figure 2

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The eco-evolutionary setup of the model.

(a) A population of $N = 200$ cells moves by chemotaxis towards the peak of the gradient, which in this season is located at the left boundary of the grid. (b) At the end of the season, cells divide, the …

Figure 3

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A group of cells performs chemotaxis efficiently in a noisy shallow gradient.

(a) Distance of the centre of mass of $N = 50$ cells from the peak of the gradient as a function of time, for different values of $γ \in [- 4, 6]$ (five independent runs for each value), together with the average …

Figure 4

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Indivdual cell trajectories are noisy, also within a cluster.

(a) The movement of a single cell. (b) Typical movement of a cluster of strongly adhering cells, and of the cells inside the cluster. Cells are placed on the right of the field and move towards …

Figure 5

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The evolution of multicellularity.

(a) Multicellularity ( $γ > 0$ ) rapidly evolves in a population of $N = 200$ cells with $τ_{s} = 10^{5}$ . (b) Multicellularity only evolves when seasons are sufficiently long $τ_{s} \geq 50 * 10^{3}$ ; unicellular strategies evolve when seasons are …

Figure 6

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Interference competition between adhering and non-adhering cells explains evolutionary bistability.

We let a simulation run for $τ_{s} = 30 \times 10^{3}$ MCS and then record the distance from the peak of the gradient, for two different populations of cells - one non-adhering (in red, $γ = - 4$ ) and one adhering (in blue, $γ = 6$ ), …

Appendix 1—figure 1

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Diffusion exponent approximation.

(a) We log-log transformed the data (the shaded area is the relative error $Var (MSD (Δ t)) / MSD (Δ t)$ ). (b) We fitted a polynomial function to the data, then took the derivative of the polynomial function. (**c,d**) …

Appendix 1—figure 2

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The speed of a cluster towards the peak of the gradient saturates with larger cluster sizes.

For each cluster size, we ran five independent simulations. Each dot corresponds to one simulation. Their average (per cluster size) generates the line. All other parameters as in main text.

Appendix 1—figure 3

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The flow field of a cluster of cells with and without gradient.

(a) With chemoattractant gradient. (b) Without chemoattractant gradient. In both cases $N = 50$ cells with $γ = 6$ are placed at the centre of the field (All other parameters as in main text).

Appendix 1—figure 4

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Chemotaxis of a rigid cluster.

(a) $τ_{p} = 5$ . (b) $μ_{p} = 0.5$ . In both cases $N = 50$ cells with $γ = 6$ are placed on the right of the field and move towards higher concentration of the gradient (the semicircle indicates the resource location, where the …

Appendix 1—figure 5

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Collective vs. individual chemotaxis for different values of persistence strength $μ_{p} \in [0, 10]$ .

The plots show the displacement over time of the centre of mass of a single cell (indigo) and that of a cluster of 50 cells (green). Note that the x axis is different in different plots. The value …

Appendix 1—figure 6

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Collective vs. individual chemotaxis for different values of chemotactic strength $μ_{χ} \in [0.1, 5]$ .

The plots show the displacement over time of the centre of mass of a single cell (indigo) and that of a cluster of 50 cells (green). The value of $μ_{χ}$ used in main text is indicated by the Default …

Appendix 1—figure 7

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Large cells perform chemotaxis more efficiently than clusters of small cells.

Each line corresponds to one simulation with a given combination of number of cells N and cell size $A_{T}$ , and shows the distance of the centre of mass of the cluster of cells from the peak of the …

Appendix 1—figure 8

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Simple algorithm for segment extraction.

(a) Visual explanation of the algorithm, with a cartoon representation of a cell track with cell positions recorded at regular time intervals. Images 1-4 represent subsequent stages of the …

Appendix 2—figure 1

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Surface tension distribution for a population of cells that evolve adhesion, compared to the distribution of adhesion strength for randomly generated ligands and receptors.

The data for adhering cells are taken from the same simulation used for main text Figure 5a, over 10 seasons after reaching evolutionary steady state with $τ_{s} = 100^{3}$ MCS. Black: all vs. all surface tension …

Appendix 2—figure 2

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The evolution of multicellularity (and uni-cellularity) for different values of persistent migration strength $μ_{p} \in [1, 5]$ .

For $μ_{p} = 1$ , the inset shows the surface tension for $τ_{s} > 200 \times 10^{3}$ MCS. All other parameters and initialisation are as in main text Figure 5a.

Appendix 2—figure 3

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The evolution of multicellularity (and uni-cellularity) for different values of chemotactic strength $μ_{χ} \in [0.5, 2]$ .

All other parameters and initialisation are as in main text Figure 5a.

Appendix 2—figure 4

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The evolution of multicellularity (and uni-cellularity) when resources are spread for a chemoattractant gradient that decreases parallel from resources distributed on the entire side of the lattice.

All other parameters and initialisation are as in main text Figure 5.

Appendix 2—figure 5

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The evolution of multicellularity (and uni-cellularity) with a steep, noiseless gradient ( $k_{χ} = 10$ , $p_{χ = 0} = 0$ ).

All other parameters and initialisation are as in main text Figure 5.

Appendix 3—figure 1

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Emergence of collective behaviour and evolution of multicellularity are robust to changing the mechanism of chemotaxis.

(a) The emergence of collective chemotaxis when individual cells cannot sense the gradient; (b) the evolution of multicellularity (and uni-cellularity) under these conditions. $μ_{CIL}$ - the strength of …

Appendix 4—figure 1

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The evolution of multicellularity (and uni-cellularity) when adhesion is costly.

Different lines correspond to the evolutionary steady state at different season duration $τ_{s}$ for different values of costs c_m, as indicated in the figure. All other parameters and initialisation are …

Videos

Video 1

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posterframe for video — Inefficient chemotaxis of a single cell.

Video 2

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Video 3

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Video 4

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Video 5

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Video 6

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Video 7

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Tables

Table 1

Parameters.

Parameter	Explanation	Values
$L^{2}$	lattice size	500 × 500 lattice sites
T	Boltzmann temperature	16 AUE
$λ$	cell stiffness	5.0 AUE/[lattice site]²
$A_{T}$	cell targetarea	50 lattice sites
Cell adhesion
$J_{α}$	minimum J value between cells	4 AUE/[lattice site length]
$J_{α}^{'}$	minimum J value between cell and medium	8 AUE/[lattice site length]
$ν$	length of receptor and ligand bitstring	24 bits
$ν^{'}$	length ligand bitstring for medium adhesion	six bits
Cell migration and chemotaxis
$μ_{p}$	strength of persistent migration	3.0 AUE
$τ_{p}$	duration of persistence vector	50 MCS
$μ_{χ}$	strength of chemotaxis	1.0 AUE
$k_{χ}$	scaling factor chemoattractant gradient	1.0 molecules/[lattice site length]
$p_{χ = 0}$	probability of zero value (’hole’) in gradient	0.1 [lattice site]⁻¹
Evolution
N	population size	200 cells
$τ_{s}$	duration of season	5 × 10³ - 150 × 10³ MCS
h_d	distance from gradient peak where fitness is $\frac{1}{2}$	50 [lattice site length]
$μ_{R, I}$	receptor and ligand mutation probability	0.01 per bit, per replication

AUE: Arbitrary Units of Energy (see Hamiltonian in Model Section); lattice site: unit of area; lattice site length: unit of distance; MCS: Monte Carlo Step (unit of time).

Additional files

Transparent reporting form: https://cdn.elifesciences.org/articles/56349/elife-56349-transrepform-v2.docx
Download elife-56349-transrepform-v2.docx

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Open citations (links to open the citations from this article in various online reference manager services)

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Figures

Model description.

The eco-evolutionary setup of the model.

A group of cells performs chemotaxis efficiently in a noisy shallow gradient.

Indivdual cell trajectories are noisy, also within a cluster.

The evolution of multicellularity.

Interference competition between adhering and non-adhering cells explains evolutionary bistability.

Diffusion exponent approximation.

The speed of a cluster towards the peak of the gradient saturates with larger cluster sizes.

The flow field of a cluster of cells with and without gradient.

Chemotaxis of a rigid cluster.

Collective vs. individual chemotaxis for different values of persistence strength $μ_{p} \in [0, 10]$ .

Collective vs. individual chemotaxis for different values of chemotactic strength $μ_{χ} \in [0.1, 5]$ .

Large cells perform chemotaxis more efficiently than clusters of small cells.

Simple algorithm for segment extraction.

Surface tension distribution for a population of cells that evolve adhesion, compared to the distribution of adhesion strength for randomly generated ligands and receptors.

The evolution of multicellularity (and uni-cellularity) for different values of persistent migration strength $μ_{p} \in [1, 5]$ .

The evolution of multicellularity (and uni-cellularity) for different values of chemotactic strength $μ_{χ} \in [0.5, 2]$ .

The evolution of multicellularity (and uni-cellularity) when resources are spread for a chemoattractant gradient that decreases parallel from resources distributed on the entire side of the lattice.

The evolution of multicellularity (and uni-cellularity) with a steep, noiseless gradient ( $k_{χ} = 10$ , $p_{χ = 0} = 0$ ).

Emergence of collective behaviour and evolution of multicellularity are robust to changing the mechanism of chemotaxis.

The evolution of multicellularity (and uni-cellularity) when adhesion is costly.

Videos

Inefficient chemotaxis of a single cell.

Chemotaxis of a cluster of adhering cells.

Inefficient chemotaxis of a cluster of non-adhering cells.

The same cluster of adhering cells.

Video of an evolutionary simulation, starting with neutrally adhering cells ( $γ = 0$ ).

Over time a population of non-adhering cells spread throughout the lattice, when seasons are short.

Over time a population of adhering cells ends up in the centre of the lattice when seasons are short.

Tables

Parameters.

Additional files

Transparent reporting form

Download links

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Share this article

Cite this article

Model description.

The eco-evolutionary setup of the model.

A group of cells performs chemotaxis efficiently in a noisy shallow gradient.

Indivdual cell trajectories are noisy, also within a cluster.

The evolution of multicellularity.

Interference competition between adhering and non-adhering cells explains evolutionary bistability.

Diffusion exponent approximation.

The speed of a cluster towards the peak of the gradient saturates with larger cluster sizes.

The flow field of a cluster of cells with and without gradient.

Chemotaxis of a rigid cluster.

Collective vs. individual chemotaxis for different values of persistence strength μp∈[0,10]<math id="inf251"><mrow><msub><mi>μ</mi><mi>p</mi></msub><mo>∈</mo><mrow><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo stretchy="false">]</mo></mrow></mrow></math>.

Collective vs. individual chemotaxis for different values of chemotactic strength μχ∈[0.1,5]<math id="inf254"><mrow><msub><mi>μ</mi><mi>χ</mi></msub><mo>∈</mo><mrow><mo stretchy="false">[</mo><mn>0.1</mn><mo>,</mo><mn>5</mn><mo stretchy="false">]</mo></mrow></mrow></math>.

Large cells perform chemotaxis more efficiently than clusters of small cells.

Simple algorithm for segment extraction.

Surface tension distribution for a population of cells that evolve adhesion, compared to the distribution of adhesion strength for randomly generated ligands and receptors.

The evolution of multicellularity (and uni-cellularity) when resources are spread for a chemoattractant gradient that decreases parallel from resources distributed on the entire side of the lattice.

Emergence of collective behaviour and evolution of multicellularity are robust to changing the mechanism of chemotaxis.

The evolution of multicellularity (and uni-cellularity) when adhesion is costly.

Inefficient chemotaxis of a single cell.

Chemotaxis of a cluster of adhering cells.

Inefficient chemotaxis of a cluster of non-adhering cells.

The same cluster of adhering cells.

Video of an evolutionary simulation, starting with neutrally adhering cells (γ=0<math id="inf98"><mrow><mi>γ</mi><mo>=</mo><mn>0</mn></mrow></math>).

Over time a population of non-adhering cells spread throughout the lattice, when seasons are short.

Over time a population of adhering cells ends up in the centre of the lattice when seasons are short.

Parameters.

Transparent reporting form

Collective vs. individual chemotaxis for different values of persistence strength $μ_{p} \in [0, 10]$ .

Collective vs. individual chemotaxis for different values of chemotactic strength $μ_{χ} \in [0.1, 5]$ .

Video of an evolutionary simulation, starting with neutrally adhering cells ( $γ = 0$ ).