Journal of Mathematical Biology ( IF 1.9 ) Pub Date : 2020-09-08 , DOI: 10.1007/s00285-020-01518-6 Jeyashree Krishnan 1, 2 , Reza Torabi 3 , Andreas Schuppert 1, 2 , Edoardo Di Napoli 1, 4
The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.
中文翻译:
具有基因型自旋的 Barabási-Albert 网络的改进 Ising 模型。
系统生物学的核心问题是了解生物系统的各个组成部分(如基因或蛋白质)如何在新出现的表型中协同作用,从而导致疾病的演变。由于活细胞是与环境持续交换的处于准稳态类型平衡的开放系统,因此已成功应用于统计热力学以描述相变的计算技术可能为生物系统的新兴行为提供新的见解。在这里,我们系统地评估了计算技术从固态物理学到与生物网络非常相似的网络模型的转换,并开发了特定的转换规则来解决生命系统特有的问题。我们专注于在每个网络节点中仅显示两种状态的逻辑模型。受实体表现出布尔状态(即活跃或不活跃)的生物状态之间明显不对称的启发,我们提出了一种对称 Ising 模型的改编,以适应生命系统的不对称模型,此处称为具有基因型自旋的修改 Ising 模型。我们通过 Monte Carlo 模拟分析相变,并提出一种改进的 Ising 模型的平均场解决方案,该模型的网络类型与现实世界的网络非常相似,即无标度网络的 Barabási-Albert 模型。我们表明,非对称 Ising 模型显示出与具有外部场的对称 Ising 模型的相似性,并且经历了一阶的不连续相变并表现出滞后。本文提出的模拟设置可直接用于任何生物网络连接数据集,也适用于表现出类似活动状态的其他网络。这里提出的方法是一种通用的统计方法,用于处理在生物系统环境中出现的非线性大规模模型,并且可以扩展到任何网络规模。