# Comparative dynamics of female germ cell populations : insight from imaging and multiscale modeling

Frédérique Clément, Romain Yvinec

► To cite this version:

Frédérique Clément, Romain Yvinec. Comparative dynamics of female germ cell populations : insight from imaging and multiscale modeling. Journées INRAE-INRIA 2023, Jul 2023, Nancy, France. hal-04194047

HAL Id: hal-04194047

https://hal.inrae.fr/hal-04194047

Submitted on 1 Sep 2023

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Comparative dynamics of female germ cell populations :
insight from imaging and multiscale modeling

Frédérique Clément, Romain Yvinec

Journées INRAE-INRIA, 04-05 Juillet 2023
- Collaborative background

- Biological background

- Available and future data

- Modeling questions and approaches
◎ EPC CNRS-INRAE-INRIA MUSCA

MUltiSCAle population dynamics for physiological systems
CRI Saclay - MaiAGE - PRC

◎ Projet GinFiz ANSES 2020

Gonadal aromatase inhibition and other toxicity pathways leading to Fecundity Inhibition in Zebrafish:
from initiating events to population impacts
collaboration INERIS (Rémy Beaudouin) + Laboratoire de Physiologie et Génomique des Poissons (LPGP, Violette Thermes)

◎ Projet IMMO Digit-Bio INRAE 2021

Imagerie et modélisation multi-échelles pour la compréhension de la dynamique ovarienne chez le poisson
collaboration LPGP

◎ AAPG ANR CES 45 OVOPAUSE 2022

Dynamics and regulation of female germ cell populations: understanding aging through population
dynamics models
collaboration LPGP + INSERM
Comparative vertebrate oogenesis (1)

<figure><img src="image_2.png" /></figure>

Germ cell cysts

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

Meiotic arrest

<figure><img src="image_6.png" /></figure>

Primordial Follicles

Activation

<figure><img src="image_7.png" /></figure>

Quiescent Follicles (QF)

Primary Follicles

<figure><img src="image_8.png" /></figure>

Postnatal Age

<figure><img src="image_9.png" /></figure>

Follicle formation

Growing Follicles (GF)

Ovulation

<figure><img src="image_10.png" /></figure>

N. follicles

Antral Follicles

Postnatal Age

Cavitation Maturation

proliferation

<figure><img src="image_11.png" /></figure>

Secondary Follicles

N. follicles

Postnatal Age

<figure><img src="image_12.png" /></figure>

Germinal Cradle

Follicle formation

Meiotic arrest

Meiosis

<figure><img src="image_13.png" /></figure>

Oocyte stage I and II

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

Oocyte stage III and IV

Quiescent Follicles (QF)

<figure><img src="image_16.png" /></figure>

Oocyte maturity

Growth Vitellogenesis

Growing Follicles (GF)

<figure><img src="image_17.png" /></figure>

Oocyte stage V to VIII

Spawning

<figure><img src="image_18.png" /></figure>

Oocyte stage IX and X

Growth Maturation

<figure><img src="image_19.png" /></figure>
Comparative vertebrate oogenesis (2)

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<table><thead><tr><th></th><th>Mitosis<br>Bipotential</th><th>Meiotic entry<br>Ovary differentiation</th><th>Mitosis arrested at Prophase I<br>Ovary growth, maturation and maintenance</th></tr></thead><tbody><tr><td>0 dpf</td><td>10 dpf</td><td>13-14 dpf</td><td>21-30 dpf</td></tr><tr><td>PGC<br>6-11 µm</td><td>oogonia<br>10-20 µm</td><td>Stage IA,<br>7-20 µm</td><td>Stage IB<br>20-140 µm</td></tr><tr><td></td><td></td><td>Primary growth stage</td><td>Cortical alveolus stage<br>Virollogenesis stage</td></tr><tr><td></td><td></td><td></td><td>Maturation stage</td></tr><tr><td></td><td></td><td></td><td>Ovulation stage</td></tr></tbody></table>

Li & Ge Mol Cell Endocrinol. 2020

<figure><img src="image_22.png" /></figure>
## Population scale

* Kinetics of oocyte pool exhaustion / intensity of oocyte pool renewal

* Shaping of the oocyte (size/maturation) distribution

* Contribution of direct and indirect interactions within the oocyte population
Management of oocyte resources / Driving of ovarian cyclicity

## Oocyte/follicle scale

* Coupled dynamics between germ cells and somatic cells

* Mechanisms underlying the proper sequence of morphogenetic events

## Preserving the ovarian resources

* Ovarian aging

* Reproductive fitness
# Knowledge driven modeling approaches (Mammals)

Embedding cell biology/developmental biology/endocrine information

<figure><img src="image_23.png" /></figure>

Cordeiro et al. Biol. Reprod. 2015
# Knowledge driven modeling approaches (Mammals)

Embedding cell biology/developmental biology/endocrine information

<figure><img src="image_24.png" /></figure>
<figure><img src="image_25.png" /></figure>

<table><thead><tr><th></th><th>Transition</th><th>Rate</th></tr></thead><tbody><tr><td>Birth (reserve)</td><td>(X<sup>ε</sup>, Y<sup>ε</sup>) → (X<sup>ε</sup> + ε, Y<sup>ε</sup>)</td><td>r<sub>0</sub>(Y<sup>ε</sup>) / ε X<sup>ε</sup></td></tr><tr><td>Maturation (reserve)</td><td>(X<sup>ε</sup>, Y<sup>ε</sup>) → (X<sup>ε</sup> - ε, Y<sup>ε</sup> + e<sub>1</sub>)</td><td>λ<sub>0</sub>(Y<sup>ε</sup>) / ε X<sup>ε</sup></td></tr><tr><td>Death (reserve)</td><td>(X<sup>ε</sup>, Y<sup>ε</sup>) → (X<sup>ε</sup> - ε, Y<sup>ε</sup>)</td><td>μ<sub>0</sub>(Y<sup>ε</sup>) / ε X<sup>ε</sup></td></tr><tr><td>Maturation, i ∈ [1, d-1]</td><td>(X<sup>ε</sup>, Y<sup>ε</sup>) → (X<sup>ε</sup>, Y<sup>ε</sup> - e<sub>i</sub> + e<sub>i+1</sub>)</td><td>λ<sub>i</sub>(Y<sup>ε</sup>) / ε Y<sup>ε</sup><sub>i</sub></td></tr><tr><td>Death, i ∈ [1, d]</td><td>(X<sup>ε</sup>, Y<sup>ε</sup>) → (X<sup>ε</sup>, Y<sup>ε</sup> - e<sub>i</sub>)</td><td>μ<sub>i</sub>(Y<sup>ε</sup>) / ε Y<sup>ε</sup><sub>i</sub></td></tr></tbody></table>
<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>
<figure><img src="image_28.png" /><figcaption>Model selection, parameter identifiability, perturbation prediction</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>OVARY</figcaption></figure>

Primary growth (PG)

Zhang et al. Mol. Cell. Endocrinol. 2020

Secondary growth (SG)

<figure><img src="image_30.png" /></figure>

Nakamura et al. Science 2010
<figure><img src="image_31.png" /></figure>
<table><thead><tr><th>Parameters</th><th>Interpretation</th><th>Output</th><th>Interpretation</th></tr></thead><tbody><tr><td>λ<sub>0</sub></td><td>Cradle exit rate</td><td>ρ<sub>0</sub></td><td>number of cells in the cradle</td></tr><tr><td>r<sub>0</sub></td><td>Cradle renewal rate</td><td>ρ</td><td>size density from stage III to IX</td></tr><tr><td>λ</td><td>growth speed from stage III to IX</td><td>ρ<sub>1</sub></td><td>number of stage X oocytes</td></tr><tr><td>W<sub>i</sub></td><td>"quantity" of hormone i secreted</td><td></td><td></td></tr></tbody></table>

$$ \left\{ \begin{array}{l} \frac{d}{dt}\rho_0(t) = r_0(\rho_0)\rho_0(t) - \lambda_0(W_{AMH}(t))\rho_0(t), \quad t > 0 \\ \lim_{x \to 0}(\lambda\rho) = \lambda_0\rho_0(t), \quad \text{sur } [0, +\infty) \\ \partial_t\rho + \partial_x(\lambda(x, W_{AMH}, W_{E2}, W_{DHP})\rho) = 0, \quad x \in [0, 1], \quad t > 0 \\ \frac{d}{dt}\rho_1(t) = \lim_{x \to 1}(\lambda\rho) - \text{spawn}(t), \quad t > 0 \\ W_i(t) = \int_0^1 \omega_i(x)\rho(t, x)dx, \quad i \in \{AMH, E2, DHP\} \end{array} \right. $$
<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /></figure>

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

30

40

110

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>

130

<figure><img src="image_40.png" /></figure>

160

<figure><img src="image_41.png" /></figure>

190

<figure><img src="image_42.png" /></figure>

260

Inputs : 3D ovarian imaging / Automatic follicle segmentation and classification

Outputs : age/space-varying distribution in size/class of the total population of ovarian follicles
<figure><img src="image_43.png" /><figcaption>Mean follicular density by stage</figcaption></figure>

<figure><img src="image_44.png" /></figure>
$$ \begin{cases} \bar{\rho}(0) = r \\ \partial_x(\lambda(x)\bar{\rho}) = 0, \quad x \in [0, 1] \end{cases} $$

Hormonal interactions cannot be deduced from purely stationary data, yet we can infer the size-dependent oocyte growth speed.

<figure><img src="image_45.png" /><figcaption>$\bar{\rho}$, linear stationary problem</figcaption></figure>

<figure><img src="image_46.png" /></figure>
# Ongoing/ future directions

Stochastic and deterministic models of structured populations with nonlinear and nonlocal terms

* Wellposedness / stationary solutions

* Inverse problems

* Structuring variable(s)
  Coupling with cell dynamics models on the
  single-follicle level
  Spatial distribution

* Physics-based modeling (morphogenesis)

<figure><img src="image_47.png" /><figcaption>ρ(t,.) at different time of the simulation</figcaption></figure>

<figure><img src="image_48.png" /></figure>