When high-throughput methods uncovered that the protein-protein interaction network of yeast is scale-free, it was also found that highly connected proteins are negatively correlated with evolutionary rate 1. This means that the sequence of the highly connected proteins in the yeast interactions network is more fixed compared to less connected proteins. This makes sense since highly connected proteins commonly participate in many cellular functions and pathways that must be maintained, and as such, these proteins are under stricter evolutionary constrains. A similar observation was also reported in a more recent comparative genomics study that looked at changes in genes between the human genome and the genome of chimpanzee. The authors of this study identified that the genes mostly prone to evolve are less connected and most likely to be membrane proteins; two aspects of evolution at the network periphery 2. These observations suggest that central hub genes in complex intracellular biological systems are less flexible for evolutionary changes, whereas membrane proteins and less connected proteins are more flexible for acquiring mutations, which means that these genes are more likely to take on new roles. This concept of growth and flexibility at the network periphery is true for many complex systems in general. It is observed in social and economic networks where innovation and growth are more probable at the network periphery. An intuitive non-biological example of growth at the periphery can be given by looking at the rate of construction in and around major cities. Construction at suburbs can be achieved more rapidly than construction in the downtown of a major city where the streets, piping, electricity and buildings reached a level of maximal complexity and if not completely destroyed and rebuilt the streets and building are relatively fixed. Anther example is the core design of cars, planes or personal computers. These systems are evolving but their core looks and functions similarly today and many years ago. The concept of growth at the periphery means that if you look at a complex system, its overall core design is almost completely fixed and was achieved very early.
The concept of growth at the periphery seems to contradict the rich-get-richer network growth paradigm because hubs are usually found at the center of the network, and based on rich-get-richer, hubs grow fastest. Growth at the periphery might be acting as a check to ensure that the rich does not become too rich, and provides opportunities for the poor and less connected to also compete more fairly with the rich. This does not mean that rich-get-richer is not a driving force. Rich-get-richer works up to a point where the hubs can no longer grow. As complexity increases the complex system’s internals become more fixed and more rigid to changes and growth. As the system continues to evolve, it is mostly changing functions and mechanisms related to interactions with the environment, cosmetic changes and not core basic functions. Changing the internal structure is often too costly, risky, or impossible.
Growth at the periphery is linked to the concept of life-at-the-edge-of-chaos. Stuart Kauffman Boolean dynamic simulations in the early 70s’ helped him realize that life has to exist at a fine toned zone between complete freeze and chaos. Simulations of Boolean networks and cellular automata showed that interesting patterns, similar patterns observed in natural life, can be reproduced by simple dynamical models when the dynamics are set to be just right at that edge between order and chaos. Here, with growth at the periphery, the edge-of-chaos is at a circular periphery of the complex system’s network giving the edge-of-chaos concept a circular geometry.