Using State Space Exploration to Determine How Gene Regulatory Networks Constrain Mutation Order in Cancer Evolution

Cancer develops via the progressive accumulation of somatic mutations, which subvert the normal operation of the gene regulatory network of the cell. However, little is known about the order in which mutations are acquired in successful clones. A particular sequence of mutations may confer an early selective advantage to a clone by increasing survival or proliferation, or lead to negative selection by triggering cell death. The space of allowed sequences of mutations is therefore constrained by the gene regulatory network. Here, we introduce a methodology for the systematic exploration of the effect of every possible sequence of oncogenic mutations in a cancer cell modelled as a qualitative network. Our method uses attractor identification using binary decision diagrams and can be applied to both synchronous and asynchronous systems. We demonstrate our method using a recently developed model of ER-negative breast cancer. We show that there are differing levels of constraint in the order of mutations for different combinations of oncogenes, and that the effects of ErbB2/HER2 over-expression depend on the preceding mutations

A protein phosphatase network controls the temporal and spatial dynamics of differentiation commitment in human epidermis

AbstractEpidermal homeostasis depends on a balance between stem cell renewal and terminal differentiation. The transition between the two cell states, termed commitment, is poorly understood. Here we characterise commitment by integrating transcriptomic and proteomic data from disaggregated primary human keratinocytes held in suspension for up to 12h to induce differentiation. We find that cell detachment induces a network of protein phosphatases. The pro-commitment phosphatases – including DUSP6, PPTC7, PTPN1, PTPN13 and PPP3CA – promote differentiation by negatively regulating ERK MAPK and positively regulating AP1 transcription factors. Their activity is antagonised by concomitant upregulation of DUSP10. Boolean network modelling of phosphatase interactions identifies commitment as an inherently unstable biological switch between the stem and differentiated cell states. Furthermore, phosphatase expression is spatially regulated both in vivo and in vitro. We conclude that an auto-regulatory phosphatase network maintains epidermal homeostasis by controlling the onset and duration of commitment.</jats:p

Stochastic hybrid systems in cellular neuroscience

We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing the basic theory of stochastic hybrid systems, including various approximation schemes in the fast switching (weak noise) limit. In subsequent sections, we consider various applications of stochastic hybrid systems, including stochastic ion channels and membrane voltage fluctuations, stochastic gap junctions and diffusion in randomly switching environments, and intracellular transport in axons and dendrites. Finally, we describe recent work on phase reduction methods for stochastic hybrid limit cycle oscillators