From 759cbf0114e6ca80961dbb19d664544066acdc33 Mon Sep 17 00:00:00 2001
From: Guillaume Gay <guillaume@damcb.com>
Date: Sat, 5 Dec 2020 11:19:16 +0100
Subject: [PATCH] Update paper.md (#214)

* adds figure details, adds 3D in figure
---
 doc/illus/Figure1.png |  Bin 0 -> 140568 bytes
 doc/illus/Figure1.svg | 2304 +++++++++++++++++++++++++++++++++++++++++
 paper.md              |   18 +-
 3 files changed, 2310 insertions(+), 12 deletions(-)
 create mode 100644 doc/illus/Figure1.png
 create mode 100644 doc/illus/Figure1.svg

diff --git a/doc/illus/Figure1.png b/doc/illus/Figure1.png
new file mode 100644
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diff --git a/paper.md b/paper.md
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--- a/paper.md
+++ b/paper.md
@@ -30,26 +30,20 @@ bibliography: paper.bib
 The `tyssue` Python library seeks to provide a unified interface to implement bio-mechanical models of living tissues. It's main focus is on vertex based epithelium models. `tyssue` allows to model the mechanical behavior of 2D, apical 3D or full 3D epihelia based on the numerical resolution of the equations of motion for the mesh vertices. Biological process are modeled through changes in the topological and dynamical properties of the mesh. `tyssue` is a modular library. Starting with the same tissue geometry, the choice of constraints, energy potential terms and parameters increases the possibility to answer different biological questions and easily explore mechanical hypotheses.
 </div>
 
-
-<center>
-![figure1](doc/illus/figure1.jpg  "figure1")
-</center>
-
-
 # Statement of Need
 <div align="justify">
 
 Tissue remodelling is a complex process integrating a large number of input such as gene expression pattern, cell adherent properties, cell mechanics. It can be difficult to manipulate specific aspects genetically. It can even be hard to simply capture, when the process takes only few minutes. Furthermore, morphogenesis is inherently a mechanical process. To execute complex morphogenetic movements, epithelia are driven by in-plane forces, like constriction of apical cell surface [@Heer:2017], and/or out-plane forces, such as the apico-basal cable in apoptotic cell [@Monier:2015, @Gracia:2019] or lateral tension [@Sherrard:2010, @Sui:2018]. Modeling those process help us understand how tissue acquires their shape, in complement of the experimental systems, and beyond their limitations. Several vertex models have been developed in the past few years to describe the physics of epithelia (for a review, see [@Alt:2017]), and common features can be identified.
 
-The `tyssue` library defines tissue as meshes. A vertex model defines a tissue as an assembly of vertices and edges, which can form polygonal face (in 2D) or polyhedron (in 3D). For now, we assume that cell junction are straight lines. In `tyssue`, each edge is split, so that every face is limited by oriented "half-edges" (**figure2 A**), in a structure identical to the [Linear Cell Complex](https://doc.cgal.org/latest/Linear_cell_complex/index.html) in the CGAL library. The library implements concepts and mechanisms common to all vertex models, for both topological and mechanical aspects.
+The `tyssue` library defines tissue as meshes. A vertex model defines a tissue as an assembly of vertices and edges, which can form polygonal face (in 2D) or polyhedron (in 3D)  (see figure 1 B),. For now, we assume that cell junction are straight lines. In `tyssue`, each edge is split, so that every face is limited by oriented "half-edges" (see figure 1 A), in a structure identical to the [Linear Cell Complex](https://doc.cgal.org/latest/Linear_cell_complex/index.html) in the CGAL library. The library implements concepts and mechanisms common to all vertex models, for both topological and mechanical aspects.
 
 ### Topology
 
 Common cellular process are implemented in our library such as cell elimination, division or rearangements. We implemented those processes based on previous works.
 
-Cell division is modeled as the splitting of a cell by a straight line (or plane in 3D) [@Brodland:2002], the angle and position of the division plane can be decided.
+Cell division is modeled as the splitting of a cell by a straight line (or plane in 3D) [@Brodland:2002], the angle and position of the division plane can be decided (see Figure 1 C, right pannel).
 
-Changes in cell neighbours - also called rearangements - happen when the size of the boundary between two neighboring cells passes below a certain threshold length in 2D (type 1 transition), or area in 3D (I-H or H-I transition)  [@Okuda:2015]. In that case, the linked vertices fuse and are separated again, witch can lead to a change in the local topology.
+Changes in cell neighbours - also called rearangements - happen when the size of the boundary between two neighboring cells passes below a certain threshold length in 2D (type 1 transition), or area in 3D (I-H or H-I transition)  [@Okuda:2015]. In that case, the linked vertices fuse and are separated again, witch can lead to a change in the local topology  (see Figure 1 C, left pannel).
 
 Cell elimination happens when a cell area (volume) reaches a low threshold. When this happens, cell starts to loose contact with neighboring cells through series of rearangements. Once the cell is reduced to a triangle (in 2D) or a tetrahedron (in 3D) the remaining vertices are merged to create a new vertex.
 
@@ -62,14 +56,14 @@ In `tyssue`, the dynamical behavior of an epithelium is described by solving the
 
 Honda et al. assume that cell movements respond to mechanical forces in an overdamped manner and the vertices are driven by the sum of interfacial tension on cell boundaries and the resistance force against the deformation of cells ([@Honda:1978], [@Honda:1983]). The `EulerSolver` class in `tyssue` allows to simulate such an overdamped movement.
 
-Interactions in the epithelium are described as potentials depending on the mesh geometry, as described in Farhadifar et al., who showed that a 2D epithelium geometry and topology can be faithfully repoduced by finding the quasi-static equilibrium of an energy depending on cell areas and junction lengths [@Farhadifar:2007]. The `QSSolver` class allows to solve this gradient descent problem. 
+Interactions in the epithelium are described as potentials depending on the mesh geometry, as described in Farhadifar et al., who showed that a 2D epithelium geometry and topology can be faithfully repoduced by finding the quasi-static equilibrium of an energy depending on cell areas and junction lengths [@Farhadifar:2007]. The `QSSolver` class allows to solve this gradient descent problem.
 
-More recently, Bi et al. focused his work on tissue rigidity which allows or not cell displacement in an epithelium, based on the relation between area and perimeter of a cell [@Bi:2015]. In `tyssue`, it is easy to define custom terms of the potential, through an object oriented model "factory" design, and use them to solve either the overdamped or gradient descent problem. 
+More recently, Bi et al. focused his work on tissue rigidity which allows or not cell displacement in an epithelium, based on the relation between area and perimeter of a cell [@Bi:2015]. In `tyssue`, it is easy to define custom terms of the potential, through an object oriented model "factory" design, and use them to solve either the overdamped or gradient descent problem.
 
 This way, it is easy to test various combinations of energy terms and find those that best fit the observed _in vivo_ dynamics.
 
 <center>
-![figure2](doc/illus/figure2.jpg  "figure2")
+![figure 1: overview of epithelium representations in tyssue](doc/illus/Figure1.png  "Figure 1")
 </center>
 
 Documentation of the `tyssue` Python library can be found [here](https://tyssue.readthedocs.io/en/latest/). Notebook introduction to how to use `tyssue` library can be found [here](https://github.com/DamCB/tyssue-demo).