In the quest for a general theory of the critical behaviour of biological systems

Is it possible to describe the functioning of the brain and the cell with the same mathematical laws that regulate a simple sandpile? Grain by grain, sand accumulates. Over time, the growth of the pile reaches a critical point where it is so unstable that the next grain could cause it to collapse. It is through this series of avalanches of various sizes that the sandpile - a complex system comprising millions of items - can restore its general stability. Theoretical and empirical studies suggest that biological networks when they operate on the threshold of this criticality improve their functionality in terms of information processing, robustness and evolvability.

Although some studies have attempted to explain criticality according to specific features of the system, a general theory of critical behaviour is still lacking in biological systems.

In a study recently published in the journal Frontiers in Physiology, involving Sergi Valverde, visiting professor to the Department of Experimental and Health Sciences and a member of the Complex Systems Lab of the Institute of Evolutionary Biology (UPF-CSIC), and Jordi García-Ojalvo, a researcher of the Department of Experimental and Health Sciences (CEXS) at UPF, among other authors, this problem is dealt with from the perspective of complex systems, since many biological systems share the common trait that their internal organization can be described as a complex network.

In this article the authors review and discuss the recent breakthroughs published on the criticality of brain and gene networks and reflect as to the implications of the network theory in the evolutionary features of criticality.

The criticality of biological networks

The brain is an incredibly complex machine that contains in the order of 10 ⁹ neurons, each connected to thousands of others. All interactions give rise to the emerging process known as conscience. As Valverde and García Ojalvo comment, "the electrical activity of neuronal networks varies between periods of calm and avalanches - in the same way as the grains in a sandpile - because the brain is in the precarious balance of this critical point", adding that "when we move away from the state of criticality, the system loses flexibility and adaptability as it cannot operate on different time scales and it becomes more rigid. A better understanding of what is the relationship between structural properties and critical dynamics can help us understand what happens when the brain is not working properly (for example, due to anatomical injuries and alterations). A similar situation occurs in the networks of proteins that regulate the behaviour of any type of cell.

Biological networks differ from physical systems

The authors conclude that biological networks show significant differences from physical systems. To begin with, the elements of biological networks (neurons in the brain or proteins in a cell) are very different from each other. Likewise, biological systems usually operate far from thermodynamic equilibrium, and in many very different time scales. All of these distinguishing features suggest that the notion of criticality, as defined in statistical physics, may be insufficient in the context of really complex systems such as the brain or even a "simple" cell.

Reference work:

Sergi Valverde, Sebastian Ohse, Malgorzata Turalska, Bruce J. West and Jordi García-Ojalvo (2015), " Structural Determinants of Criticality in Biological Networks", Frontiers in Physiology, doi: 10.3389/fphys.2015.00127.