As you probably may (or may not!) know, molecular biology often study biological functions from interaction network between molecules rather than studying each component one-by-one. It's the opposite of the universal divide-and-conquer strategy, I would call it the all-inclusive strategy.
Those interactions networks involves myriads (10.000) of molecules that interacts by various chemical ways, which is generally represented as an oriented graph between each molecular compound. The transcriptional networks describe the relationship between genes and proteins, the protein-protein networks defines the cascades of interactions between some, ingenuously lumped, proteins, the metabolic networks attempt to mimic the flush of metabolic reactions inside living organisms. So the idea is to understand how the main 'thing' works from all those interactions linked together.
Of course, other kind of networks are used in many different domain to study more-or-less linked items such as social networks (linking people that met 10 years ago in high-school and who don't have anything in common except the same social network), web pages, etc, etc.
In 2002, the team of professor Uri Alon from the Weizmann Institute of Science realized that those networks generally contain smaller repetitive networks, called patterns appearing in biological networks with much more probability than in random networks, so they should be there for a reason. The general idea is that some biological sub-functions are recurrently defined by similar chains of triggering events.
Therefore, mathematicians have been looking for a method to capture the effect of those smaller sub-networks. For instance, the model of Erdös-Rényi, obtained by linking two nodes with a constant probability p in [0,1] have some features of those natural networks (smaller world with shorter closed paths), but not all.
Recently, E. Ravasz and A. L. Barabási developed the concept of hierarchical networks: network is formed by aggregating with the same pattern in a hierarchical manner. First nodes are aggregated with the base pattern giving a handfull of the same pattern, which are themselve connected with the same pattern etc, etc.
In hierarchical networks, the clustering rate ( average of links between neighbors of a node and the potential number of links between them, ie a clique) is close to 0.606 for the above graph is a constant independent of the number of nodes in the graph. But the c(k) function, measuring the clustering rate per node degree k, is a power-law c(k) = 1/k. Those researcher proved [2] that the metabolic network of Eschiria coli, after reduction, is very similar to a hierarchical network.
Source: Images des mathématiques Fernando Alcade (in french)
[2]Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, A. L. Barabási, Hierarchical organization of modularity in Metabolic networks. Science, 297 (2002), 1551-1555.
Those interactions networks involves myriads (10.000) of molecules that interacts by various chemical ways, which is generally represented as an oriented graph between each molecular compound. The transcriptional networks describe the relationship between genes and proteins, the protein-protein networks defines the cascades of interactions between some, ingenuously lumped, proteins, the metabolic networks attempt to mimic the flush of metabolic reactions inside living organisms. So the idea is to understand how the main 'thing' works from all those interactions linked together.
Of course, other kind of networks are used in many different domain to study more-or-less linked items such as social networks (linking people that met 10 years ago in high-school and who don't have anything in common except the same social network), web pages, etc, etc.
In 2002, the team of professor Uri Alon from the Weizmann Institute of Science realized that those networks generally contain smaller repetitive networks, called patterns appearing in biological networks with much more probability than in random networks, so they should be there for a reason. The general idea is that some biological sub-functions are recurrently defined by similar chains of triggering events.
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| Some pattern occuring in biological networks |
Therefore, mathematicians have been looking for a method to capture the effect of those smaller sub-networks. For instance, the model of Erdös-Rényi, obtained by linking two nodes with a constant probability p in [0,1] have some features of those natural networks (smaller world with shorter closed paths), but not all.
Recently, E. Ravasz and A. L. Barabási developed the concept of hierarchical networks: network is formed by aggregating with the same pattern in a hierarchical manner. First nodes are aggregated with the base pattern giving a handfull of the same pattern, which are themselve connected with the same pattern etc, etc.
Source: Images des mathématiques Fernando Alcade (in french)
[2]Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, A. L. Barabási, Hierarchical organization of modularity in Metabolic networks. Science, 297 (2002), 1551-1555.
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