# ERC SyG PEPS: Deliverables

## Aim 1

- A mathematical framework to model systems using a continuous space

- theoretical (mathematical) work on how to describe a model in continuous space (e.g., a measure space along a network of trajectory) to replace simple ODE compartment models.
- An efficient software that simulates / solves such models.

- the single-cell time machine: an novel assay that adds methylation marks on the DNA of transcribed genes during a pulse that can then be later read out, along with the transcriptome at sampling time, days to weeks later, so that we know each cell's transcriptional state at two widely separated time points.

- the wet-lab protocol for the assay
- data from using the assay on mice and zebrafish
- a software tool to analyse such data, published as open source software package
- the analysis on our data

- the QuCI system:
- an analysis of the sc-omics data from above (Scenic/MarkovChain) to get suitable protein marker candidates to detect specific stages along the trajectory progressing, with good resolution
- the above will be refined with help of reporter-lines aimed at identifying "hidden-signaling" modules
- Generate mouse or fish lines with such markers (QuCi)
- 4D imaging data validating that the progression can be seen
- LOF experiments aimed at interfering with regulators of progression throughout differen trajectories CRISPR/small molecule/morpholinos
- refinement of our model using these data

## Aim 2

- Data from Rabid-Seq
- Data from Exome-transfer-Seq
- Analysis of all these data using, e.g., graph-based penalized regression as in Theiss's paper
- Hence extension of that work from image-based to barcode-transfer-based data
- Prediction of cells' sensitivity to specific signals at specific stages
- Validation of these predictions using 4D imaging and the QuCI system
- Establishments of gene signatures showing that cells have received a specific signal (e.g., by driving a GFP from a signalling sensitive promotor)
- Cartana to predic trajectory regulators from Aim 1 and integrated with connectome knowledge
- MOdeling dynamics of the system from read interactions as a second layer adding to model coming from Aim 1

## Aim 3

Establishment of models to describe the data found so far; specifically
- extension of lattice models to capture spatial heterogeneity (??) in fish
- extension of these models to account for the fish's overall growth
- establishment of continuous models (using framework from Aim 1) for mouse
- comparison of these models with compartment models (ODE) and with PDE models
- use of the models to study robustness (homeostasis maintenance / stability) under perturbation
- validation of the latter using imaging
- comparison of interaction between length scales
- simulation of localized changes in model parameters, and experimental verification with localized perturbations ("inormation spreading from clones")
- ditto for transient changes