A Stochastic Model of Cell Differentiation B. Laforge LPNHE Paris, Université Paris VI Presentation based on: Modeling embryogenesis and cancer: An approach based on an equilibrium between the autostabilization of stochastic gene expression and the interdependence of cells for proliferation Prog. Biophys. Mol. Biol. 2005 Sep;89(1):93-120 B.L., D. Guez,M. Martinez M, JJ. Kupiec Simulation de modèles sélectifs de la différenciation cellulaire. PhD Thesis of J. Glisse, Université Pierre et Marie Curie–Paris 6, janvier 2009 Directed by JJ. Kupiec and B.L.

Why a physicist doing simulation in Biology ? We all understand the organisation of the universe and its components through a representation : biology needs a theory ! We have to understand if and how we could have a unified representation of physical and biological processes. It is not coherent to assume that physics is governed by stochastics processes while biology is based on information theory I am convinced that organisation is really the result of different dynamics occuring inside the system and at its vicinity. Simulation is the only way to adress this question on a general basis.

Emergence also occurs in physics I don’t think we need non linear processes or chaotic systems to have not trivial organisation, competition between Internal dynamics and outside constraints are enough

The Darwinian Model of Cell differentiation Darwinian Model of Cell Identification Lot of experimental data demon-strate a stochastic component in gene expression  e.g. see review in Nat. Rev. Genet. 2005 Jun;6(6):451-64. Need to build a model of molecular biology processes incorporating that phenomenology random event A B No specific signal Stochastic gene expression - Homogeneity postulated Cellular interactions stabilise cell phenotype - Predicts intrinsic variability By simulation : test intrinsic properties of the Darwinian model to create organised tissues

Description of the model Two cell types A and B grow in a 2D matrix A and B change their phenotype randomly A cells synthesize a molecules whereas B cells synthesize b molecules. a and b molecules diffuse following Fick’s Laws 3 matrices are used to hold cells and (a,b) densities

In each cell, at each simulation step 1) a and b molecules are synthesized 2) a and b are degraded 3) a and b diffuse in the environment (Fick’s laws) 4) Cell Identification (A or B) is stochastically determined. The switching probabilities depend on a or b molecules densities Stochastic to Deterministic behaviour Autostabilisation : the cell is stabilised by its own product Interstabilisation : the cell is stabilised by the molecules produced by the other cell type

Inter and auto stabilisation effects Interstabilisation (small clusters) Autostabilisation (large areas)

2nd model + 1st model in autostabilisation mode Interdependance for proliferation : A (resp. B) cells metabolise a certain quantity of b (resp. a) molecules to survive and proliferate a and b molecules can be seen as pleiotropic growth factors

Results - An invariant bi-layer structure can be obtained with lateral finite growth :  no stop signal but equilibrium ! -Two symmetric gradients of a and b molecules are also created transversally to the bi-layer. - ‘‘embryo mortality’’ is bound to the intrinsic stochastic nature of the model cell death increases the bi-layer formation probability  could explain an evolutionary origin of apoptosis !

Di-layer formation is conserved What happens in 3D ? Di-layer formation is conserved

Some details on few important properties of the model - Molecular Gradient structuration - Cell death function in living organisms Impact of the stochasticity on organism Development What happens when the equilibrium is disrupted ?

Gradients and bilayer are formed at the same time

We could have systems where gradients do not preexist before the structure as stated by position information theory

Simulation Parameters

Stochasticity and Structure Formation kinetics Limited stochasticity Very stochastic Deterministic step b = 0.1 b = 0.5 b = 4.0 Limited stochasticity provide early bilayer formation with lower formation time fluctuation : ☺ selective advantage for organism ruled by such dynamics

Stochasticity and Structure Formation efficiency 29 * 75 * 1000 = 2 175 000 simulations

Stochasticity and Structure Formation efficiency

Number of simulations

% of success vs stochasticity

Effect of cell death on the probability to produce a structure

Stochasticity and Structure Formation efficiency

Change of a parameter disrupt the equilibrium Suggest a new mechanism for control of cell proliferation

Change of a parameter (here L) disrupt the Equilibrium Suggest a new mecanism for cancer

Conclusion The selective model has to be modified : Differentiation and tissues organisation could result from an equilibrium between stochastic gene expression, autostabilisation of phenotypes and interdependence for proliferation. Genetic program could be replaced by an Dynamic Equilibrium Principle Stochasticity gives a better structuration in our model Cell apoptosis can be seen as a consequence of double level of selection of organisms better structured with “apoptosis” cells This model suggest a new mechanism for the control of cell proliferation

Backup Slides

Darwinian Model of Cell Identification Cell differentiation Models Deterministic Cell differentiation Darwinian Model of Cell Identification Kupiec, 1981 random event Information A signal triggers differentiation Cell stability is assumed Heterogeneity is postulated No prediction of intrinsic variability A B No specific signal Stochastic gene expression - Homogeneity postulated Cellular interactions stabilise cell phenotype - Predicts intrinsic variability By simulation : test intrinsic properties of the Darwinian model to create organised tissues

Remove autostabilisation organisation properties and finite growth lost

Remove interdependence for proliferation organisation properties and finite growth lost

Bi-layer structure production A-E : Growth phase E-F : Stabilisation

Results - An invariant bi-layer structure can be obtained with lateral finite growth :  no stop signal but equilibrium ! -Two symmetric gradients of a and b molecules are also created transversally to the bi-layer. - Simulations produce individuals with common property (bi-layer)  Definition of a species ! - cell death increases the bi-layer formation probability (selective origin of apoptosis !) - ‘‘embryo mortality’’ is bound to the intrinsic stochastic nature of the modèle