Generalized binomial Tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise

The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol.2, 117–E (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various τ-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial τ- DSSA method that extends the τ-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial τ-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.

Inhibition of activated fibroblast growth factor receptor 2 in endometrial cancer cells induces cell death despite PTEN abrogation

KRAS activation and PTEN inactivation are frequent events in endometrial tumorigenesis, occurring in 10% to 30% and 26% to 80% of endometrial cancers, respectively. Because we have recently shown activating mutations in fibroblast growth factor receptor 2 (FGFR2) in 16% of endometrioid endometrial cancers, we sought to determine the genetic context in which FGFR2 mutations occur. Analysis of 116 primary endometrioid endometrial cancers revealed that FGFR2 and KRAS mutations were mutually exclusive, whereas FGFR2 mutations were seen concomitantly with PTEN mutations. Here, we show that shRNA knockdown of FGFR2 or treatment with a pan-FGFR inhibitor, PD173074, resulted in cell cycle arrest and induction of cell death in endometrial cancer cells with activating mutations in FGFR2. This cell death in response to FGFR2 inhibition occurred within the context of loss-of-function mutations in PTEN and constitutive AKT phosphorylation, and was associated with a marked reduction in extracellular signal-regulated kinase 1/2 activation. Together, these data suggest that inhibition of FGFR2 may be a viable therapeutic option in endometrial tumors possessing activating mutations in FGFR2, despite the frequent abrogation of PTEN in this cancer type.