Proulx-Giraldeau Félix, Rademaker Thomas J, François Paul
Ernest Rutherford Physics Building, McGill University, Montreal, Québec, Canada.
Ernest Rutherford Physics Building, McGill University, Montreal, Québec, Canada; Département de Physique Théorique, Université de Genève, Genève, Switzerland.
Biophys J. 2017 Oct 17;113(8):1893-1906. doi: 10.1016/j.bpj.2017.08.036.
Complex mathematical models of interaction networks are routinely used for prediction in systems biology. However, it is difficult to reconcile network complexities with a formal understanding of their behavior. Here, we propose a simple procedure (called ϕ¯) to reduce biological models to functional submodules, using statistical mechanics of complex systems combined with a fitness-based approach inspired by in silico evolution. The ϕ¯ algorithm works by putting parameters or combination of parameters to some asymptotic limit, while keeping (or slightly improving) the model performance, and requires parameter symmetry breaking for more complex models. We illustrate ϕ¯ on biochemical adaptation and on different models of immune recognition by T cells. An intractable model of immune recognition with close to a hundred individual transition rates is reduced to a simple two-parameter model. The ϕ¯ algorithm extracts three different mechanisms for early immune recognition, and automatically discovers similar functional modules in different models of the same process, allowing for model classification and comparison. Our procedure can be applied to biological networks based on rate equations using a fitness function that quantifies phenotypic performance.
相互作用网络的复杂数学模型在系统生物学中经常用于预测。然而，要将网络复杂性与对其行为的形式化理解协调起来是困难的。在此，我们提出一种简单的程序（称为ϕ¯），利用复杂系统的统计力学并结合受计算机模拟进化启发的基于适应度的方法，将生物学模型简化为功能子模块。ϕ¯算法通过将参数或参数组合置于某些渐近极限来起作用，同时保持（或略微提高）模型性能，并且对于更复杂的模型需要参数对称性破缺。我们通过生化适应以及T细胞免疫识别的不同模型来说明ϕ¯。一个具有近百个个体转换率的难以处理的免疫识别模型被简化为一个简单的双参数模型。ϕ¯算法提取出早期免疫识别的三种不同机制，并自动在同一过程的不同模型中发现相似的功能模块，从而实现模型分类和比较。我们的程序可以应用于基于速率方程的生物网络，使用量化表型性能的适应度函数。
