From Genes to the Edge of Chaos

SARIYER, Turkey - July 20, 2022 - PRLog -- Genes that are always active or always non-functional are not too sensitive. However, the main thing to notice is that the sensitivity values ​​always stay above a certain curve. So, is this a biological requirement for gene networks to operate, or is it an imperative of the mathematical definition of sensitivity?

At this point, biology continues to provide more clues. The "canalizing" effect that genes have on other genes has long been a subject of debate among researchers. This characteristic expresses the determining effect of a specific gene on the activity of another gene. For example, if gene B is turned off in all cases where gene A is active, this means that gene A canalizes gene B to become non-functional. In a more restrictive version of this phenomenon, called "nested canalization," all genes that affect a certain gene have a say in that gene's activity in a hierarchical order. Our observations show that an intense nested canalizing effect is found in gene networks. When we compare the activity and sensitivity of only the genes with this special condition, the stones begin to fall into place. The genes with the least sensitivity regarding their activity levels should have this nested characteristic.

When we examine this phenomenon mathematically, it is not possible to go under the curve created by those with nested structures.

This curve, which determines the minimum sensitivity, has a fractal structure. In the complexity of biology, it is not unusual to see such a degree of order and pattern structure.

After these observations, even though Kauffman's "edge of chaos" argument and the minimum sensitivity of genes in gene networks seem to contradict at first, they actually fit together quite well. According to Kauffman, gene networks should be neither too stable nor too chaotic, but our observations show that individual genes have the possible most stable structure with respect to their average activity levels. The characteristics of individual genes may cause different observations in networks formed by genes.

In summary, we have discovered a fractal pattern hidden inside the complex interaction networks of cellular biology. This fractal boundary acts as an invisible wall, pushing the organisms towards the borderline of order and chaos, most suitable for living systems. Our findings were recently published in Physical Review Letters (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett...).

While we are inspired by nature in the world of design and engineering, biological observations also drive pure scientific progress. Our study provides deeper insight into the interplay between mathematics and biology and nurtures further studies on both fronts. We currently continue our investigations on the theoretical front by examining the cases where the above-nested structure is occasionally broken.