Cavitation of tumoral basement membrane as onset of cancer invasion and metastasis: physics of oncogenic homeorhesis via nonlinear mechano-metabolomics

We investigate the catalytic reactions model used in cell modeling. The reaction kinetics is defined through the energies of different species of molecules following a random independent distribution. The related statistical physics model has three phases and these three phases emerge in the dynamics: fast dynamics phase, slow dynamic phase and ultra-slow dynamic phase. The phenomenon we found is rather general, and does not depend on the details of the model. We assume as a hypothesis that the transition among these phases (glassiness degrees) is related to cancer. The imbalance in the rate of processes between key aspects of the cell (gene regulation, protein-protein interaction, metabolical networks) creates a change in the fine tuning among these key aspects, affects the logics of the cell and initiates cancer. It is probable that cancer is a change of phase resulting from increased and deregulated metabolic reactions. Copyright c © EPLA, 2012 Introduction. – When observing the life on the ground of statistical physics of complex systems we see a hierarchial level of organization and modularity. How can we describe the “good, natural” relations between different parts of complex system? In statistical physics we describe different systems through different order parameters, and in equilibrium different parts of the system have the same temperature. For the stability of the system, it is reasonable to assume the similarity of order parameters at different hierarchy levels and parts (modules) of the system. There is a good similarity with the no-arbitrage condition in financial markets [1] where different stocks that can fluctuate in equilibrium have only identical order parameters, defined as a ratio of driven and diffusion motions. The Random Energy Model (REM) [2] and related complexity (replica symmetry breaking) order parameters [3] work starting from the proteins [4] till quantum chromo-dynamics and strings; therefore we assume that the cell organization and cancer should not be exclusions, and there is a possibility that REM-related ideas can work there. Using the known results of REM, we will prove that the phase structure of (a)E-mail: saakian@yerphi.am the chemical reaction network kinetics is related with the probabilistic distributions of different chemicals in the steady-state distribution. Then we will speculate about the origin of the cancer using similar complexity ideas. One of the main ideas for cell modeling is to consider the dynamical models with network structure [5–7]. One can realize this program studying the network of catalytic reactions, identifying the phenotype of the cell with the attractor of the nonlinear system of differential equations. While constructing the kinetic constants, it is advantageous to have a detailed balance condition. The density of different chemical components change according to the kinetic constants, and the latter are defined through the energies of that components. We are following [8]. There are M chemical components. The transformation between chemicals Xi and Xj is catalyzed by some component xc, so it has a rate ki,jxcxi Thus, we can write a set of equations [8]: