New theory tests limits to complexity

By Graeme O'Neill
Monday, 14 February, 2005

Functionally, the genomes of humans and other higher life forms have more in common with the intricate circuitry of a computer processor chip than with the simple genomes of bacteria, according to a new theory advanced by Australian researchers.

In a paper in the current issue of Science, Prof John Mattick and Dr Michael Gagen, of the Institute of Molecular Bioscience at the University of Queensland, argue that all regulatory networks, whether in biology, engineering or society, belong to a class of complex systems called accelerating networks.

Accelerating networks are highly interconnected, and operate in a globally responsive way that requires complex regulatory systems to coordinate the operation of their functional components -- proteins, in the case of plant and animal genomes Mattick and Gagen say.

The requirement for rapid, global responsiveness imposes an upper limit on the complexity of accelerating networks -- Mattick has previously suggested that the human genome, which has about 30,000 genes coding for as many as 250,000 different proteins, may approach the limit of complexity.

The limit is imposed by the costs incurred by the need for increasing numbers of connections between the individual functional components or 'nodes' in the network, and the number of regulatory layers required to coordinate their activity.

The Science paper expands on Mattick's hypothesis, developed over the past two decades, that the proteins encoded by the 30,000-odd genes of the mammalian genome are the components of an analogue machine, that is operated by a digital control system coded in RNA, that he calls the 'R-nome'.

Evidence for Mattick's hypothesis has emerged with the discovery that the long tracts of non-protein-coding DNA within and between genes, once dismissed as 'junk' DNA, in fact codes for myriad RNA molecules that regulate and integrate the activity of proteins.

These non-protein-coding tracts of DNA are a basic difference between eukaryotic and prokaryotic genes, which do not have introns, and are arranged end-to-end without intervening tracts of non-coding DNA.

Mattick and Gagen suggest that the transition from the prokaryotic system, which is analogue and protein-based, to a digital, RNA-based control architecture was the critical step that enabled the evolution and development of complex, multicellular organisms, leading ultimately to the so-called 'Cambrian explosion' around half a billion years ago.

They say most studies of networks to date have focused on simple, usually large connectionist systems like telephone networks and the internet, which are generally scale-free -- they look structurally similar at any scale, in terms of the average number and distribution of the connections for each node.

"These networks can become large precisely because they have no need to rapidly integrate information from, or respond globally to, the current state of their nodes," Mattick and Gagen say.

"For example, it does not matter to the overall function of the internet whether any individual is connected or not, and the state of one node is quite irrelevant to most of the others, although the system as a whole is vulnerable to damage to very highly connected nodes."

With functionally organised systems that rely on the integrated activity of any or all of their component nodes, like a stock exchange, an office, or a computer processor, the number of informative connections must increase with the size of the network.

As a result, the number of connections between nodes scales more rapidly than the number of nodes -- in an accelerating network, the number of interconnections scales quadratically, not linearly, imposing an upper size limit on the network's functional complexity.

"We contend that accelerating networks are far more common in the natural world than has hitherto been appreciated," Mattick and Gagen write.

The interconnectivity eventually reaches saturation, or the accelerating proportional cost the connections becomes prohibitive. At this point, an accelerating network can only continue increasing in size If the number of interconnections is reduced, resulting in a loss of coordinated function and fragmentation - as seen in the social transition from small communities to large cities.

But an accelerating network can continue to grow if some technical breakthrough allows an increase in connectivity -- such as evolution's 'invention' of the eukaryotic genome's RNA-based digital control system.

Mattick and Gagen say computer systems are the pre-eminent example of accelerating networks -- the millions of components on an integrated chip must be interconnected by shared bus lines that require hundreds of metres of metal wires to be arranged in multiple layers across a thumbnail-sized chip.

In biology, Mattick and Gagen say their theory may explain the observation that, in bacteria, the number of regulatory proteins controlling gene expression in bacteria increases quadratically with gene number and genome size.

"in any competitive system, whether biological of industrial -- the speed and efficiency of organisation, and the sophistication of responses to changing circumstances, are critical determinants of the system's survival and success.

"We suggest that this is the imperative that results on biological regulatory networks scaling quadratically with system size to maintain optimal integration."

The researchers say there are few, if any, fully scalable technologies: "Biological organisms are a collection of technologies optimal in some respects, but sub-optimal in others, which limits life's potential.

"Understanding where the points of regulatory saturation and technological limitation occur will be necessary to break through present and future complexity barriers."

Ref: John S Mattick and Michael J Gagen, 'Accelerating Networks', Science February 11, 2005

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