A Modified Ising Model of Barabási-Albert Network with Gene-type Spins

• DOI: 10.48550/arxiv.1908.06872
• Publication Date: 2019-01-01
• Authors: Jeyashree Krishnan; Reza Torabi; Edoardo Di Napoli; Andreas Schuppert
• Keywords: info:eu-repo/classification/ddc/570; 0301 basic medicine; Statistical Mechanics (cond-mat.stat-mech); FOS: Physical sciences; Models, Theoretical; Quantitative Biology - Quantitative Methods; Article; Phase Transition; 3. Good health; 03 medical and health sciences; Nonlinear Dynamics; Biological Physics (physics.bio-ph); FOS: Biological sciences; Thermodynamics; Computer Simulation; Gene Regulatory Networks; Physics - Biological Physics; Monte Carlo Method; Condensed Matter - Statistical Mechanics; Quantitative Methods (q-bio.QM)

The central question of systems biology is to understand how individual components a biological system such as genes or proteins cooperate in emerging phenotypes resulting the evolution diseases. As living cells are open quasi-steady state type equilibrium continuous exchange with their environment, computational techniques that have been successfully applied statistical thermodynamics describe phase transitions may provide new insights behavior systems. Here we will systematically evaluate translation from solid-state physics network models closely resemble networks and develop specific translational rules tackle problems unique Hence focus on logic exhibiting only two states each node. Motivated by apparent asymmetry between where an entity exhibits boolean i.e. active inactive, present adaptation symmetric Ising model towards asymmetric one fitting here referred modified gene-type spins. We analyze Monte Carlo simulations propose mean-field solution resembles real-world network, Barab\'{a}si-Albert scale-free networks. show similarities external field undergoes discontinuous transition first-order hysteresis. simulation setup presented can be directly used for any connectivity dataset also applicable other exhibit similar activity. This general method deal non-linear large scale arising context scalable size.