Publications

2019

1. Percolation in bipartite Boolean networks and its role in sustaining life

   Ryan Hannam, Reimer Kühn, and Annibale, Alessia

   J. Phys. A Math. Theor. J. Phys. A Math. Theor 2019

   Abs

   Boolean networks are popular models for gene regulation, where genes are regarded as binary units, that can be either expressed or not, each updated at regular time intervals according to a random Boolean function of its neighbouring genes. Stable gene expression profiles, corresponding to cell types, are regarded as attractors of the network dynamics. However, the random character of gene updates does not allow to link explicitly the existence of attractors to the biological mechanism with which genes interact. We propose a bipartite Boolean network approach which integrates genes and regulatory proteins (i.e. transcription factors (TFs)) into a single network, where interactions incorporate two fundamental aspects of cellular biology, i.e. gene expression and gene regulation, and the resulting dynamics is highly non-linear. Since any finite stochastic system is ergodic, the emergence of an attractor structure, stable under noisy conditions, requires a giant component in the bipartite graph. By adapting graph percolation techniques to directed bipartite graphs, we are able to calculate exactly the region, in the network parameters space, where a cell can sustain steady-state gene expression profiles, in the absence of inhibitors, and we quantify numerically the effect of inhibitors. Results show that for cells to sustain a steady-state gene expression profile, TFs should typically be small protein complexes that regulate many genes. This condition is crucial for cell reprogramming and remarkably well in line with biological facts.

2017

1. Cell reprogramming modelled as transitions in a hierarchy of cell cycles

   Ryan Hannam, Alessia Annibale, and Kühn, Reimer

   J. Phys. A Math. Theor. 2017

   Abs

   We construct a model of cell reprogramming (the conversion of fully differentiated cells to a state of pluripotency, known as induced pluripotent stem cells, or iPSCs) which builds on key elements of cell biology viz. cell cycles and cell lineages. Although reprogramming has been demonstrated experimentally, much of the underlying processes governing cell fate decisions remain unknown. This work aims to bridge this gap by modelling cell types as a set of hierarchically related dynamical attractors representing cell cycles. Stages of the cell cycle are characterised by the configuration of gene expression levels, and reprogramming corresponds to triggering transitions between such configurations. Two mechanisms were found for reprogramming in a two level hierarchy: cycle specific perturbations and a noise induced switching. The former corresponds to a directed perturbation that induces a transition into a cycle-state of a different cell type in the potency hierarchy (mainly a stem cell) whilst the latter is a priori undirected and could be induced, e.g. by a (stochastic) change in the cellular environment. These reprogramming protocols were found to be effective in large regimes of the parameter space and make specific predictions concerning reprogramming dynamics which are broadly in line with experimental findings.