Nature likes it simple!

The bacterium E.Coli knows how to deal with heat. When exposed to high temperatures, it switches on genes that help it adapt to a warmer environment. This is just one tiny example of the way myriads of biological functions occur within a living system.

The variety of functions is made possible because cells differ in terms of which genes are flicked on and which are flicked off in them. Cells integrate cues from their local environment and decide this. This ability of cells to switch on and off genes is what makes it possible for living organisms to perform multiple functions at the same time.

Researchers have for long tried to probe the regulatory mechanisms behind this process. One way to understand this, especially when dealing with a large group of genes, is to model them using the Boolean framework. Boolean modelling is a widely used mathematical framework used to study the dynamics of gene regulatory networks, where you consider the genes as switches that can turn other genes on or off in the network. It allows researchers to computationally assess the state of a gene network — not just of one gene but a set of several genes at one go.

In a new study in the journal PNAS Nexus by researchers from The Institute of Mathematical Sciences, Chennai, PhD candidate Ajay Subbaroyan and his mentor Areejit Samal explain how they used the Boolean framework to study the regulatory mechanisms in 88 gene networks. When dealing with small gene networks one may not feel the need to create a Boolean model to capture the different ways in which genes interact. But in large gene networks, it helps capture the entire range of interactions among genes and underlines how one part of the network affects the rest.

The researchers compiled Boolean models of the 88 gene networks from humans, plants and even lower organisms. When using this framework, they assigned to every entity in the network two possible states: one or zero (that is, true or false). The state of each network entity is determined by a Boolean function, which is a mathematical function that maps binary inputs to a binary output with the value 1/0 or true/false.

The scientists then ran simulations to see how the presence or absence of different entities was dependent on each other.

The more the number of regulators of a gene in a network, the greater is the number of possible Boolean functions. The numbers are mind-boggling. If a gene is controlled by three other genes, the number of Boolean functions that are possible with three inputs is 256. If you have four genes controlling one gene, the possible number of Boolean functions becomes two to the power of two to the power 4 — that is, 65,536. And if you have one gene controlled by five other genes, then the number of possible Boolean functions is more than a billion.So, as you increase the number of regulators, the possible number of regulatory logic explodes.

How does nature then choose from such a wide range? Are functions assigned to genes in real organisms randomly picked? Or does nature favour some types of functions?

Through their analyses, Subbaroyan and Samal found that a category in the Boolean framework — called nested canalyzing functions — is particularly enriched in nature. They discovered that these functions have minimal complexity. It led the researchers to conclude that nature has a preference for functions with minimum complexity.

They quantified the complexity of Boolean functions using two notions in computer science: Boolean complexity and Average Sensitivity.

"To the best of our knowledge, a systematic exploration of the complexity of Boolean functions associated with gene regulation, like in our work, has not been performed previously," Samal says. "Going ahead, our work will have implications for Boolean model construction at the genome-scale and can help automate this model reconstruction process," he adds.