br Conflicts of interest br Introduction Photodynamic Therap

Conflicts of interest
Introduction Photodynamic Therapy (PDT) is a technique used for the treatment of several malignant and non malignant diseases (Akimoto, 2016, Keyal, Bhatta, Wang, 2016, Morton, Szeimies, Sidoroff, Wennberg, Basset-Seguin, Calzavara-Pinton, Gilaberte, Hofbauer, Hunger, Karrer, Lehmann, Piaserico, Ulrich, Braathen, European Dermatology Forum, 2015, Olsen, Hodak, Anderson, Carter, Henderson, Cooper, Lim, 2016). The basic principle consists on applying a photosensitizer (PS), preferentially localized in the tumor, that is activated by light of an specific wavelength. The interaction between the photosensitizer, the incident light and the molecular oxygen present in the tissue generates Reactive Oxygen Species (ROS) that are the main responsible for immediate cell death through necrosis. Furthermore, there is a consensus in the scientific and medical community that apoptosis and autophagy are also mechanisms for cell death induced by PDT (Buytaert et al., 2007). Necrosis is the preferential mode of cell death when high doses of PDT are used, and is morphologically characterized by cellular swelling and a rapid loss of plasma membrane integrity. Apoptosis is triggered by mild or low doses of light and photosensitizer (Agostinis, Berg, Cengel, Foster, Girotti, Gollnick, Hahn, Hamblin, Juzeniene, Kessel, Korbelik, Moan, Mroz, Nowis, Piette, Wilson, Golab, 2011, Buytaert, Dewaele, Agostinis, 2007) and is characterized by the reduction of cell volume, L-703,664 succinate sale condensation, nuclear fragmentation and formation of apoptotic bodies that are engulfed by neighbouring phagocytes (Vanden Berghe et al., 2015). The role of autophagy in PDT cell death is more controversial, but in general it is considered that it may as well promote cell death by digesting essential cellular components (Kessel, 2012). In reference Lopez et al. (2016) we studied the reactions leading to the enhancement of ROS in a tumor when it is treated with a photosensitizer and illuminated with incident light. We were able to calculate the cumulative singlet oxygen concentration in each cell ,(1O2), and to characterize the necrosis induced by PDT in a model tumor. Our results also indicated that in the regions of the tumor that are less illuminated, usually far from the surface of the tumor, the concentration of (1O2) is not high enough to induce necrosis and only medium or small damages may occur in the cell structures (Lopez et al., 2016). In this case, experiments suggest (Agostinis et al., 2011) that apoptosis should be the main mechanism responsible of cell death. We are aware that, as in many other problems in Systems Biology, the lack of proper experimental data is one of the main limitations in the process of model building and testing. In our case in particular, and although several studies have made efforts to accurately measure the expression of apoptosis-relevant proteins (Bentele, Lavrik, Ulrich, Stösser, Heermann, Kalthoff, Krammer, Eils, 2004, Lindner, Concannon, Boukes, Cannon, Llambi, Ryan, Boland, Kehoe, McNamara, Murray, et al., 2013, Passante, Würstle, Hellwig, Leverkus, Rehm, 2013, Rehm, Huber, Dussmann, Prehn, 2006), the determination of these protein quantities lacks of accepted and established methodological standards and is subject to considerable heterogeneity. However we used, whenever possible in our model, initial conditions and parameters determined directly from experiments, or inferred from experimental results as can be seen in Tables 1–3.
Model and methods Apoptosis is a programmed cell killing process that occurs in cells (Alberts et al., 2014). In particular, it is reported (Agostinis et al., 2011) to be one of the main mechanisms of cell death after PDT. If a cell does not die by necrosis immediately after the Photodynamic Therapy, apoptosis is the next dominant process for cell death. Moreover, the literature is generous in models of caspase pathways of apoptosis. Some of them are based on ordinary differential equations (Aldridge, Haller, Sorger, Lauffenburger, 2006, Bentele, Lavrik, Ulrich, Stösser, Heermann, Kalthoff, Krammer, Eils, 2004, Eissing, Conzelmann, Gilles, Allgwer, Bullinger, Scheurich, 2004, Hua, Cornejo, Cardone, Stokes, Lauffenburger, 2005, Ooi, Ma, 2013) while others are stochastic, either based on the Gillespie’s algorithm or in constructing a Monte Carlo simulation from first principles (Eißing, Allgöwer, Bullinger, 2005, Raychaudhuri, 2010, Raychaudhuri, Willgohs, Nguyen, Khan, Goldkorn, 2008, Skommer, Brittain, Raychaudhuri, 2010). The models are designed to study phenomena as diverse as the death-receptor mediated apoptosis (Aldridge, Haller, Sorger, Lauffenburger, 2006, Bentele, Lavrik, Ulrich, Stösser, Heermann, Kalthoff, Krammer, Eils, 2004, Eissing, Conzelmann, Gilles, Allgwer, Bullinger, Scheurich, 2004, Hua, Cornejo, Cardone, Stokes, Lauffenburger, 2005, Ooi, Ma, 2013), the mitochondria-mediated apoptosis (Legewie, Blüthgen, Herzel, 2006, Zhang, Brazhnik, Tyson, 2009) or the connection between extrinsic and intrinsic pathways of apoptosis (Albeck, Burke, Spencer, Lauffenburger, Sorger, 2008, Bagci, Vodovotz, Billiar, Ermentrout, Bahar, 2006, Harrington, Ho, Ghosh, Tung, 2008, Kutumova, Zinovyev, Sharipov, Kolpakov, 2013, Nakabayashi, Sasaki, 2006, Stucki, Simon, 2005).