RESUMO

We analyzed a quantitative multiscale model that describes the epigenetic dynamics during the growth and evolution of an avascular tumor. A gene regulatory network (GRN) formed by a set of ten genes that are believed to play an important role in breast cancer development was kinetically coupled to the microenvironmental agents: glucose, estrogens, and oxygen. The dynamics of spontaneous mutations was described by a Yule-Furry master equation whose solution represents the probability that a given cell in the tissue undergoes a certain number of mutations at a given time. We assumed that the mutation rate is modified by a spatial gradient of nutrients. The tumor mass was simulated by means of cellular automata supplemented with a set of reaction diffusion equations that described the transport of microenvironmental agents. By analyzing the epigenetic state space described by the GRN dynamics, we found three attractors that were identified with cellular epigenetic states: normal, precancer and cancer. For two-dimensional (2D) and three-dimensional (3D) tumors we calculated the spatial distribution of the following quantities: (i) number of mutations, (ii) mutation of each gene and, (iii) phenotypes. Using estrogen as the principal microenvironmental agent that regulates cell proliferation process, we obtained tumor shapes for different values of estrogen consumption and supply rates. It was found that he majority of mutations occurred in cells that were located close to the 2D tumor perimeter or close to the 3D tumor surface. Also, it was found that the occurrence of different phenotypes in the tumor are controlled by estrogen concentration levels since they can change the individual cell threshold and gene expression levels. All results were consistently observed for 2D and 3D tumors.

Assuntos

Neoplasias da Mama , Humanos , Feminino , Neoplasias da Mama/genética , Neoplasias da Mama/metabolismo , Proliferação de Células/genética , Difusão , Separação Celular , Estrogênios

RESUMO

We carried out Monte Carlo simulations in the N,Π,T ensemble of a Langmuir monolayer coarse-grained molecular model. Considering that the hydrophilic groups can be ionized by modulating acid-base interactions, here we study the phase behavior of a model that incorporates the short-range steric and long-range ionic interactions. The simulations were carried out in the reduced temperature range 0.1≤T*<4.0, where there is a competition of these interactions. Different order parameters were calculated and analyzed for several values of the reduced surface pressure in the interval, 1≤Π*≤40. For most of the surface pressures two directions of molecular tilt were found: (i) towards the nearest neighbor (NN) at low temperatures, T*<0.7, and most of the values of Π* and (ii) towards next-nearest neighbors (NNN) in the temperature interval 0.7≤T*<1.1 for Π*<25. We also found the coexistence of the NN and NNN at intermediate temperatures and Π*>25. A low-temperature reentrant disorder-order-disorder transition in the positions of the molecular heads and in the collective tilt of the tails was found for all the surface pressure values. It was also found that the molecular tails arranged forming "rotating patterns" in the temperature interval, 0.5