On the architecture of cell regulation networks

BMC Systems Biology On the architecture of cell regulation networks Yueheng Lan 2 Igor Mezi 0 1 0 The Center for Control, Dynamical Systems and Computation, University of California , Santa Barbara, CA 93106 , USA 1 Department of Mechanical Engineering, University of California , Santa Barbara, CA 93106 , USA 2 Department of Physics, Tsinghua University , Beijing 100084 , China Results: Our approach allows us to identify two structurally important components: the minimal production unit"(MPU) which responds quickly and robustly to external signals, and the feedback controllers which adjust the output of the MPU to desired values usually at a larger time scale. The successful application of our technique to several of the most common cell regulation networks indicates that such architectural feature could be universal. Detailed illustration and discussion are made to explain the network structures and how they are tied to biological functions. Conclusions: The proposed scheme may be potentially applied to various large-scale cell regulation networks to identify functional modules that play essential roles and thus provide handles for analyzing and understanding cell activity from basic biochemical processes. - Background Cellular behavior, including motility, metabolism and reproduction is controlled by complex biochemical reaction networks, many of which have been identified and studied in detail [1]. These networks realize their regulatory roles through complex molecular interactions. Contemporary high throughput experiments produce unprecedented amount of data that serve to pinpoint the players and their interactions, resulting in complex chemical reaction graphs. How to analyze these intricate graphs and gain insight into the regulation mechanism employed by cell has become a central problem of molecular biology. Much progress has been made in the analysis of functions of complex networks, no matter if they are modeled deterministically [2,3] or stochastically [4-9]. These studies concentrate on the investigation of dynamics of given networks by checking their stability, parameter dependence, robustness and input-output relation. However, for large-scale networks such as those commonly found in important biological processes [10,11], the incurred computational load often severely limits our ability for performing detailed analysis. More critically, with continued experimental efforts that are revealing more details of networks global wiring, their growing complexity has made it harder and harder to identify the underlying local functional structures and thus probe the network function. Normal cell life involves physical or chemical activities at vast range of spatial and temporal scales and it is vital to identify characteristic structures at all scales and study their roles in relation to a particular cell function [12-17]. These key structures are called modules, the existence of which contributes almost to every aspect of the cell regulation: robustness, sensitivity, adaptivity, evolvability. Their detection and study much simplifies the analysis of complex networks since a small set of modules could come from and be a lot simpler than a collection of many entangled individual agents [18]. The simplification may be carried on by constructing modules of modules. Recently, useful concepts distilled from statistical physics such as the small-world and the scale-free networks [19,20], began to see their application in gene regulation networks and lead to considerable success in unraveling the statistical nature of these networks. However, this type of statistical analysis mainly aims at gross features of networks [21] and thus ignores local structural properties and heterogeneities, which often determine the operation of a network in an essential way, since disparate network modules generally imply distinct dynamics and fit for different functional requirements [22,23]. Nevertheless, the determination of modular structure in a large network is not straightforward since one molecular species may be involved in many different pathways with very distinct external connections. Such inter-correlation is easily under-appreciated and yet has profound consequences on the organism. In this paper we propose a new theory of architecture of biochemical networks based on control and graph theoretic analysis. In this theory, a network consists of two major modules: one is the pipeline of linear information production unit which serves to generate the required output (e.g. protein concentrations); the other is the set of feedback loops which act as controllers of the production. These two modules are identified based on the information flow in a network. Specifically, input and output nodes define a polarity of the network. Information is received at the input, processed and then sent to the output. The agents that carry on the information along the forward direction belong to the production unit. The remaining agents direct part of the information in the opposite direction and thus are elements of the feedback controller [22]. In the paper, detailed algorithm are presented for the construction of the production unit and the feedback controller. The concept of modules has been used in modeling of biological networks for decades. The existence of this special structure is universally agreed upon but its exact definition is done on case-by-case basis. Recently, modules and community structures are defined in the graph theoretic studies of many real-world networks [20,24], based on the connectivity between nodes. Useful as it is, this type of definitions ignore the importance of controller loops. The community structure in the synchronization study involves more dynamics information but it works for a special class of networks and for particular types of equations of motion. Closely related concepts, such as network motif are also proposed [13,25]. Motifs consist of a small number of nodes and appear repeatedly (more than expected from pure statistical consideration) in a network. The modules determined by our algorithm are different from all these in that we emphasize the information processing and controlling units but not simple fixed graph structures given a priori. In contrast, the decomposition procedure based on the function of the network and the associated polarity supplies the detailed structures of our modules. Different polarities may result in different decompositions and different initial conditions may define different MPUs. So our concept of modules depends on the information flow through or the function of the network. In the following, we will use the NF B regulation network [26] as an example to explain our graph theoretic analysis procedure and display the generic producercontroller structure. We also analyze the chemotaxis network of E. coli, TNF-a initiated apoptosis network [27], the circadian clock network in Drosophila [28] as interesting example (...truncated)