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1,The topological property of regulation entropy measures the robustness in regulatory networks (PLoS Comp. Biol. 5 (2009) e1000442)

Living organisms exert very complicated control on the functionality of their components. Such control systems can often operate in a surprisingly robust manner, in spite of constant perturbations from fluctuating internal conditions and a volatile external environment. What feature makes such control mechanisms robust? Is there a general way to achieve robustness? Here, we address these questions by investigating the wiring of interaction networks, which contains the most condensed information about the control mechanisms of biological systems. We suggest that one of the most important factors in therealization of biological robustness rests in the global coherency of the control strategy, i.e., the consistency of commands flowing through different routes in the network to the same destination. To implement this idea, we propose an order parameter termed ‘regulation entropy’ to quantitatively describe this control consistency of networks.

 

 

An illustrative example of the calculation of the regulation entropy. The network is shown in A, and the sets P(i->j) are listed in B. Note that the node ‘D’ is trivially connected, and thus is ignored in the calculation from the very beginning. Green arrows and red blunt-end ones are activating and inhibiting interactions, respectively. For self-pointed arrows in A, orange blunt-end indicates self-degradation, whereas cyan indicates self-activation.

 

The simplified cell-cycle networks. The cell-cycle control networks of the budding yeast and the fission yeast are shown in A and B, respectively. Green arrows and red blunt-end ones are activating and inhibiting interactions, respectively. For self-pointed arrows, orange blunt-end indicates self-degradation, whereas cyan indicates self-activation.

 

2,Synthesizing a push-on push-off switch (Mol. Sys. Biol. 6,(2010) 350; doi:10.1038/msb.2010.2)

Design and synthesis of basic functional circuits are the fundamental tasks of synthetic biologists. Before it is possible to engineer higher-order genetic networks that can perform complex functions, a toolkit of basic devices must be developed. Among those devices, sequential logic circuits are expected to be the foundation of the genetic information-processing systems. We designed and constructed a genetic sequential logic circuit in Escherichia coli. It can generate different outputs in response to the same input signal on the basis of its internal state, and ‘memorize’ the output. The circuit is composed of two parts, a bistable switch memory module and a double-repressed promoter NOR gate module. The modules were individually rationally designed, and were coupled together by fine-tuning the interconnecting parts through directed evolution. After fine-tuning, the circuit could be repeatedly, alternatively triggered by the same input signal.

 

 

Construction of the bistable memory module. (A) The memory module incorporates three mechanisms: positive feedback, double-negative feedback, and the repressor binding cooperativity. (B) The arrangement of the genes and promoter region in the memory module. (C) Images of cells carrying the memory module. 

Construction of the NOR gate module.(A) The circuit for quantitative measurement of NOR gate. The promoter PNOR is suppressed by both LacI and LexA, which can be eliminated by IPTG and UV irradiation, respectively. (B) The truth table of the NOR gate. (C) Experimental measurement of the NOR gate by flow cytometry. 

3, The yeast cell-cycle network is robustly designed(PNAS, 101, (2004) 4781-4786.)

The interactions between proteins, DNA, and RNA in living cells constitute molecular networks that govern various cellular functions. To investigate the global dynamical properties and stabilities of such networks, we studied the cell-cycle regulatory network of the budding yeast. With the use of a simple dynamical model, it was demonstrated that the cell-cycle network is extremely stable and robust for its function. The biological stationary state, the G1 state, is a global attractor of the dynamics. The biological pathway, the cell-cycle sequence of protein states, is a globally attracting trajectory of the dynamics. These properties are largely preserved with respect to small perturbations to the network. These results suggest that cellular regulatory networks are robustly designed for their functions.

 

The cell-cycle network of the budding yeast.

Dynamical trajectories of the 1,764 protein states (green nodes) flowing to the G1 fixed point (blue node). Arrows between states indicate the direction of dynamic flow from one state to another. The cell-cycle sequence is colored blue. The size of a node and the thickness of an arrow are proportional to the logarithm of the traffic flow passing through them.