An Introduction to Systems Biology

CH1 。 CH12 Every time the goal changes, these modules need only be rewired in order to satisfy the new goal. If the goal stops changing for a sufficient length of time, the networks in the simulation begin to lose modularity and evolve toward a nonmodular design, a design that is typically more optimal(e.g. uses fewer components). 这与软件开发和软件优化的思想如出一辄！ 。 Thus, the ability to reconfigure and adapt to new confitions may be one force that helps to maintain modular structure in biological systems. 这有点到哲学层面的味道 。 simplicity level 1: the structural simplicity associated with modularity and the small number of network motifs that make up the networks. 。 simplicity level 2: be able to treat regulatory circuits with simplified mathematical models(the dynamics of transcription circuits) that capture the essence of the behavior and have a certain degree of universality. 也就是说： 把the dynamics of transcription circuits)表示为：ODE/PDE 把molecular details(proteins data)表示为：ODE/PDE的系数(或者说是参数) 。 Integral feedback can be shown in many cases to be a unique solution to the problem of robust adaptation in the context of engineering control theory. 。 modularity,即模块和模块之间相互独立，这类似于数学上的正交分解。 modularity的目的是为了模块可以重复使用：用已有的若干模块的组合去解决新的问题。（模块之间尽可能相互独立） 正交分解的目的是为了找出线性无关的基向量（或基函数），用这些基向量（或基函数）的线性组合去表示问题空间。 modularity和正交分解都可以看作是把复杂问题转化为稍微简单一些的问题。

Evolution can be fast. Mutations can occur at a comparatively high rate. A single bacterium in 10ml culture grows and divides to reach saturation of 10^10 cells in less than a day. Since mutation rate is 10^(-9) per base-pair per generation, up to saturation, the bacterial population reach 10 mutation per base-pair. If we treat mutation as randomized force, which abolishes edges in gene regulatory graph, evolutionarily conserved edges preserve fitness to the organism. Autoregulation, including positive and negative autoregulations, are over-represented in E.coli transcription network. Parameters of such autoregulation are under natural selection. Negative repression efficiently and robustly lock the gene into steady-state expression. Presence of such repression reduces cell-cell variation. Positive autoregulation is slower than unregulated gene. Such slow dynamics can be useful in relatively long developmental processes.

While activation/repression graph reveals a qualitative dynamics of simple circuits, further consideration has to be done on separation of time scale of different cellular processes. For stable proteins, especially protein assuming static structural roles, which do not belong to response module to external signals, have a response time similar to that of a cell generation time.

Appendix C - Graph Properties of Transcription Networks sparse connectivity: Transcription networks are sparse, since ratio of existing edges and theoretical upper limit of edges << 1. Typically, less than 0.1% of possible edges are found in the network. degree distribution: Typically mean degree is 2 to 10 edges/node. Out-degree distribution can be approximately described as a power law, i.e. P(k) ~ k^(-r), with r ~ 1 to 2. Transcription network often have many transcription factors regulate a few genes, fewer nodes that regulate tens of genes, and even fewer global regulators that regulate hundreds of genes. Global regulators usually respond to key environmental signal to control large ensembles of genes, e.g. bacteria CRP to glucose starvation, RpoS respond to general stress. In-degree distribution instead resembles compact distribution such as Poisson distribution. This may correspond in part to physical limitation that promoters are short in simple organisms. In more complex organisms, DNA looping action can increase the number of input transcription factors to a given gene. Higher organisms often display larger in-degrees than microorganisms, accommodating the complex computational needed during development. motifs: Clustering coefficient C is the average number of triangles that a node participates in. Feed-forward loop (a type of triangle) is generally overrepresented in motifs of sensory transcription networks. The major contribution to the clustering coefficient therefore stems from feed-forward loops. This pattern appears to be selected due to its function, such as filtering and response acceleration. Generally, it appears that global statistical properties of biological network such as degree sequences and cluster sequences are the result of selection working on the detailed circuit patterns in each individual system. Different networks have different selection constraints, which must be understood in order to understand their graphical properties. modularity: Network modularity is the degree to which it can be separated into nearly independent sub-networks. A measure of modularity is proposed by Newman and Girvan, 2004 and 2005. The rationale of this modularity measure is that: a good partition of a network into modules must comprise many within-modular edges and as few as possible between-module edges. This is achieved by maximizing a modularity measure Q.