To introduce in a simple way the
To introduce in a simple way the variability in the concentration of the proteins involved in the process, and to consider possible stochastic effects due to possible finite sizes of the populations involved in the problem, the dynamics of each cell is studied using the Gillespie’s algorithm (Gillespie, 1976, Gillespie, 2007) (for a detailed description of the algorithm see Appendix A. Moreover, HC 067047 are placed in a lattice trying to mimic the collective behaviour of a tumor in a tissue.
/bf In each cell the algorithm stops when the concentration of caspase-3 reaches 10 nM (Albeck et al., 2008) and in this case the cell is considered dead. Moreover, to activate the extrinsic pathway in a given cell we consider the status of the neighbourhood of this cell. In particular how many surrounding cells were death of alive at time t. The intuition is that if neighbours cells are death the local environment may turn toxic to an otherwise healthy cell. This toxic environment induces the activation of the extrinsic pathway. In practice, we consider as neighbours of cell i it’s nearest and next-nearest neighbours in a square lattice (in practice 8 neighbours) and assumed that when more than two neighbours of a cell are dead the extrinsic pathway is activated increasing automatically the concentration of DISC from 0 to 50nM (Table 3).
The Gillespie’s algorithm was implemented in the Graphic Processing Units (GPU), using the CUDA (Compute Unified Device Architecture) extension to the C programming language developed by nVidia (Kirk and Wen-Mei, 2016). The simulations where performed on a PC with an Intel i7 processor with 8 cores and a GeForce GTX 550 graphic card with 192 processors. The simulations of 20 × 20 cell matrices run in about 2.3 min and the 100 × 100 in 1 h. The software is available through the authors upon request.
Results and discussion
Acknowledgements The research on this paper was financially supported by the Physics Faculty at Havana University. The authors thanks ICTP Associate Program through which part of this work was carried out during N. Lopez visit in 2016.
Introduction The PI3K/AKT pathway is important for cell signaling pathway and mediates a wide range of cellular functions, such as survival, proliferation, migration and differentiation (Yang et al., 2012). It is well known that phosphatidylinositol 3-kinase (PI3K), a crucial regulatory factor in the PI3K/AKT pathway, can be activated by various environmental stimuli (Lee, 2009). Following the changes that occur upon PI3K activation, phosphoinositide-dependent protein kinase-1 (PDK1) recruits protein kinase B (AKT) to the plasma membrane and activates the kinase (Tang et al., 2015, Paez and Sellers, 2003). Apoptosis, a type of programmed cell death, is an important mechanism that regulates organism growth, cell senescence and tissue homeostasis. Moreover, the PI3K/AKT pathway, via activation of caspases and the Bcl-2 family, tightly regulates it (Numata et al., 2011, Guo et al., 2015). Excessive apoptosis may overwhelm cellular clearance mechanisms and contribute to a reduction in disease in several tumour cell types (Di Serio et al., 2008, Li et al., 2011, Wang et al., 2014). However, excessive apoptosis induced by noxious risk factors can, alternatively, cause disease (Guo et al., 2012). Recent studies indicated that many noxious environmental stimuli could cause serious damage, inducing apoptosis in cells via the PI3K/AKT pathway (Zhao and Zhang, 2017, Sarkar and Sil, 2014, Zhang et al., 2017). Fluoride is one of the essential trace elements for life, and is widely present in food and water. Fluoride, in low concentrations, contributes to the growth and development of skeletal tissues, such as bones and teeth (Gu et al., 2016, Zhou et al., 2015). However, excessive fluoride can damage the liver (Zhou et al., 2015, Zhan et al., 2006), thyroid (Wang et al., 2009, Ge et al., 2005), kidney (Wasana et al., 2015, Chen et al., 2015), brain (Dec et al., 2017, Ge et al., 2006) and reproductive tissues (Zhou et al., 2013, Sun et al., 2010), which seriously affects the normal structures and physiological functions of the body. Several studies reported that excessive fluoride could induce cell apoptosis in HL-60 cells (Anuradha et al., 2000), ameloblasts (Wang et al., 2016) and MC3T3-E1 cells (Gu et al., 2016). In the present study, to measure the toxicity of fluoride in C2C12 cells and investigate the involvement of the PI3K/AKT pathway, a model of fluoride-induced C2C12 cells was established. The C2C12 cell structures, ultrastructure and levels of apoptosis were measured by microscopy, cell activity was measured by MTT method, and the mRNA and protein expression levels were assayed by real-time PCR and western blotting.