Waddle -- Waddington's epigenetic landscape

We provide different tools and methods in Julia to
(1) simulate, explore and analyse the landscape for a given model and
(2) visualise the landscape of certain genes or gene combinations (after applying dimensionality reduction) given a single-cell data set.

Motivation

The Waddington or epigenetic landscape provides a theoretical framework for cell development and differentiation. A figure and citation from Waddington's original paper [1]:

Workflow

Mathematical introduction on stochastic models and landscape formation:

The cell development process can be described by a general stochastic model.

How do we get from a stochastic system to an epigenetic landscape?

• Some stochastic systems can be expressed in terms of a potential.
• Potential functions are similar to epigenetic landscapes.

Optional input: SBML file

Stabiltiy analysis

Different ways to simulate the landscape:

(1) Probability Flux Method (PFM)

(2) Kernel Density Estimation (KDE)

(3) Action-based method (ABM)

Landscapes from single-cell data

Dimensionality Reduction (DR)

Different dimensionality reduction methods are used, ia linear methods such as PCA, SVD, PPCA as well as non-linear methods such as Kernel PCA, MDS, ICA.

Authors

• Felicia Burtscher -- burfel
• Lucas Ducrot -- lucasducrot
• Madeleine Hall -- mgh17
• Luis Torada --lt2216

Acknowledgments

• JuliaDiffEq and its contributors
• JuliaPlots and its contributors

• Our supervisor Prof Michael PH Stumpf for advice and guidance
• The members of the Theoretical Systems Biology Group at IC London, especially Rowan Brackston and Ivan Croydon Veleslavov, for their help and expertise in both the topic and Julia
• Suhail A Islam for fixing technical issues
• Prof Michael Sternberg and others involved in conducting and overseeing the MSc in Bioinformatics and Theoretical Systems Biology at IC London

References

[1] Waddington CH: Organisers and Genes. 1940, Cambridge, UK: Cambridge University Press