Discussion What It May All Mean

The large-scale organization of molecular networks deduced from correlation profiles of protein interaction and transcription regulatory networks in yeast is consistent with compart-mentalization and modularity characteristic of many cellular processes.22 Indeed, the suppression of connections between highly-connected proteins (hubs) suggests the picture of semi-independent modules centered around or regulated by individual hubs. On the other hand, the very fact that these molecular networks do not separate into many isolated components but are dominated by one "giant component" suggests that this tendency towards modularity is not taken to its logical end. The observed patterns can in fact be characterized as "soft modularity", where interactions between individual modules are suppressed but not completely eliminated. Thus on sufficiently large scale molecular networks exhibit system-wide properties making their behavior different from that of a set of mutually independent modules.

A further implication of the deficit of connections between highly connected proteins (Figs. 6, 7) is in the suppression of propagation of deleterious perturbations over the network. It is reasonable to assume that certain perturbations such as e.g., a significant change in the concentration of a given protein (including it vanishing altogether in a null-mutant cell) with a ceratin probability can affect its first, second, and sometimes even more distant neighbors in the corresponding network. While the number of immediate neighbors of a node is by definition equal to its own degree Kq, the average number of its second neighbors is bound from above by Kq ((K\ - 1))a"0 and thus depends on the correlation profile of the network. Since highly connected nodes serve as powerful amplifiers for the propagation of deleterious perturbations it is especially important to suppress this propagation beyond their immediate neighbors. It was argued that scale-free networks in general are very vulnerable to cascading failures started at individual hubs.23'24 The deficit of edges directly connecting hubs to each other reduces the branching ratio around these nodes and thus provides a certain degree of protection against such accidents.

Finally, we would like to mention that the tendency of highly connected proteins to be positioned at the periphery of signaling and regulatory networks teaches us something about the overall computational architecture of such networks and origins of their broad degree distributions. Indeed, the peripheral position of hubs indicates that they presumably execute collective orders of other more "computationally-involved" regulators, rather than performing computations and making decision on their own. This principle is nicely illustrated in the lambda-phage regulatory network (see Fig. 10), where the decision making/computation is done by CI , CII, and Cro proteins, which (with the exception of CI) are characterized by low-to-intermediate out-degrees and high in-degrees. Their orders on the other hand are executed through the N and LexA hub-proteins which have high out-degree and low in-degree.

Broad degree distributions observed in molecular networks presumably reflect the widely different needs associated with different functions that a living cell needs to cope with changes in its environment. Thus highly connected regulatory proteins usually correspond to rather complicated tasks such as e.g., the heat shock response, where about 40 chaperones are controlled by a single sigma factor, or the chemotaxis where a few regulatory proteins switch on a large number of proteins associated with flagella, flagellar motor, and sensing of the environment.

To summarize the above discussion, it is feasible that molecular networks operating in living cells have organized themselves in a particular computational architecture that makes their dynamical behavior both robust and specific. Topologically the specificity of different functional modules is enhanced by limiting interactions between hubs and suppressing the average degree of their neighbors. On a larger scale there is evidence for interconnections

Figure 10. Lambda-phage regulatory network. The actual computation is done by centrally positioned Cro and CII that have low-to-intermediate out-degree and relatively large in-degree. Their decision is transmitted to peripherally positioned, highly connected hub-proteins such as N and LexA, which in their turn broadcast it to the whole battery of response genes. As a curiosity, note that the HflB protease from E. colts heat-shock response network interacts with the lambda-phage regulatory network. Another curiosity: the HflB direcdy regulates DnaK, which at least indirecdy has substantial influence on the overall transcription of ribosomal RNAs of the E coli. Thus the lambda network integrates as a small subnetwork in the overall bacterial regulatory network of R coli. The notation used in this figure: T indicates positive regulation, _L indicates passive negative regulation; ± indicates active degradation through the protease activity.

Figure 10. Lambda-phage regulatory network. The actual computation is done by centrally positioned Cro and CII that have low-to-intermediate out-degree and relatively large in-degree. Their decision is transmitted to peripherally positioned, highly connected hub-proteins such as N and LexA, which in their turn broadcast it to the whole battery of response genes. As a curiosity, note that the HflB protease from E. colts heat-shock response network interacts with the lambda-phage regulatory network. Another curiosity: the HflB direcdy regulates DnaK, which at least indirecdy has substantial influence on the overall transcription of ribosomal RNAs of the E coli. Thus the lambda network integrates as a small subnetwork in the overall bacterial regulatory network of R coli. The notation used in this figure: T indicates positive regulation, _L indicates passive negative regulation; ± indicates active degradation through the protease activity.

between these modules, although the principles of such global organization of living cells remain unclear from the present day data and analysis tools.

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