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.

Osteopontin is a downstream effector of the PI3-kinase pathway in melanomas that is inversely correlated with functional PTEN

The tumor suppressor PTEN antagonizes phosphatidylinositol 3-kinase (PI3K), which contributes to tumorigenesis in many cancer types. While PTEN mutations occur in some melanomas, their precise mechanistic consequences have yet to be elucidated. We sought to identify novel downstream effectors of PI3K using a combination of genomic and functional tests. Microarray analysis of 53 melanoma cell lines identified 610 genes differentially expressed (P<0.05) between wild-type lines and those with PTEN aberrations. Many of these genes are known to be involved in the PI3K pathway and other signaling pathways influenced by PTEN. Validation of differential gene expression by qRT-PCR was performed in the original 53 cell lines and an independent set of 18 melanoma lines with known PTEN status. Osteopontin (OPN), a secreted glycophosphoprotein that contributes to tumor progression, was more abundant at both the mRNA and protein level in PTEN mutants. The inverse correlation between OPN and PTEN expression was validated (P<0.02) by immunohistochemistry using melanoma tissue microarrays. Finally, treatment of cell lines with the PI3K inhibitor LY294002 caused a reduction in expression of OPN. These data indicate that OPN acts downstream of PI3K in melanoma and provides insight into how PTEN loss contributes to melanoma development.