Boolean constraint satisfaction problems for reaction networks

Piecewise linear and Boolean models of chemical reaction networks

Models of biochemical networks are frequently high-dimensional and complex. Reduction methods that preserve important dynamical properties are therefore essential in their study. Interactions between the nodes in such networks are frequently modeled using a Hill function, $x^n/(J^n+x^n)$. Reduced ODEs and Boolean networks have been studied extensively when the exponent $n$ is large. However, the case of small constant $J$ appears in practice, but is not well understood. In this paper we provide a mathematical analysis of this limit, and show that a reduction to a set of piecewise linear ODEs a…

Counting attractors in synchronously updated random Boolean networks

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in the special case of one input per node. Approximating some other non-chaotic networks to be of this class, we apply the analytic results to them. For this approximation, we observe a strikingly good agreement on the numbers of attractors of various lengths. Furthermore, we find that for long cycle lengths, there are some properties that seem strange in comp…

Lethality and synthetic lethality in the genome-wide metabolic network of Escherichia coli

Recent genomic analyses on the cellular metabolic network show that reaction flux across enzymes are diverse and exhibit power-law behavior in its distribution. While one may guess that the reactions with larger fluxes are more likely to be lethal under the blockade of its catalyzing gene products or gene knockouts, we find, by in silico flux analysis, that the lethality rarely has correlations with the flux level owing to the widespread backup pathways innate in the genome-wide metabolism of \textit{Escherichia coli}. Lethal reactions, of which the deletion generates cascading failure of foll…

布尔网络作为涌现生物行为的预测模型

Boolean Networks as Predictive Models of Emergent Biological Behaviors

本文提供了生物系统布尔网络模型的方法论概述，介绍了模型构建、分析、验证及其在预测系统扰动响应和行为控制中的应用，并通过三个案例研究展示了结构与动力学特性的相互作用。

On the Complexity of Reconstructing Chemical Reaction Networks

The analysis of the structure of chemical reaction networks is crucial for a better understanding of chemical processes. Such networks are well described as hypergraphs. However, due to the available methods, analyses regarding network properties are typically made on standard graphs derived from the full hypergraph description, e.g.\ on the so-called species and reaction graphs. However, a reconstruction of the underlying hypergraph from these graphs is not necessarily unique. In this paper, we address the problem of reconstructing a hypergraph from its species and reaction graph and show NP-…

调制-反应网络

Modulation-Reaction Networks

本文提出调制-反应网络（MR-networks）框架，统一处理生物化学系统中的物质流和信息流，并开发调制-反应逻辑（MRL）以推理其同步布尔语义，通过模型检验和互模拟关系验证生物相关性质。

Using rxncon to develop rule based models

We present a protocol for building, validating and simulating models of signal transduction networks. These networks are challenging modelling targets due to the combinatorial complexity and sparse data, which have made it a major challenge even to formalise the current knowledge. To address this, the community has developed methods to model biomolecular reaction networks based on site dynamics. The strength of this approach is that reactions and states can be defined at variable resolution, which makes it possible to adapt the model resolution to the empirical data. This improves both scalabi…

变分动力学：通过圆锥优化的基元反应动力学

Variational kinetics: elementary reaction kinetics via conic optimisation

针对基因组规模建模与实验技术在反应动力学研究上的矛盾，提出变分动力学方法，通过数学重新表述和指数圆锥优化，满足稳态反应动力学，放宽非线性约束，经计算验证该方法可处理多种相关情况。

用于基因组尺度代谢网络模型中基因功能主动学习的布尔矩阵逻辑编程

Boolean matrix logic programming for active learning of gene functions in genome-scale metabolic network models

本文提出布尔矩阵逻辑编程方法BMLP及主动学习系统$BMLP_{active}$，通过可解释逻辑程序编码GEM并指导低成本实验，以更少样本学习基因相互作用、优化代谢模型。