It might be baffling to think that tissues, comprising of motile cells, behave like glass. But, did you know that many living systems, like armies of ants, flocks of birds, and cancerous cells are also glass-like? One thing that is common to all these systems is that the others in the system severely restrict the movement of one of the constituent units. In a recent study, researchers from Bengaluru’s Indian Institute of Science (IISc), National Centre for Biological Sciences (NCBS), International Centre for Theoretical Sciences (ICTS) and Israel’s Weizmann Institute of Science, have successfully developed a model to explain the dynamics of collective systems that are motile at high density.
What makes such collective systems glassy? Imagine some motile cells confined to a small region. When there are far too many ants, there would be multiple head-on collisions between them, leading to a significant rise in the ‘cellular traffic’. On a larger scale, the increase in traffic could bring some regions to a standstill, without any movement. Some parts that do not have many encounters, on the other hand, continue to have a fluid-like motion. The solid-like and fluid-like regions may interchange their positions over time. This behaviour is akin to glass—a state of matter that behaves like a solid for short periods of time but relaxes to a liquid state over an infinitely long time.
The other property common to both collective living systems and glass is jamming. When a liquid changes to a solid in a slow process at low temperatures, the atoms have enough time to rearrange themselves in an orderly fashion. However, in the case of glass, this change from liquid to solid is rapid, resulting in a disordered solid through a process called jamming.
Studying the properties of such active systems has many implications. “Developing a proper theoretical framework for such a system should help to understand them within a coherent framework. Beyond biology, activity provides an interesting control parameter for a glassy system. We hope, our work will lead to deeper insights into the glassy systems in general”, says Dr. Saroj Nandi, a Postdoctoral Fellow at the Weizmann Institute of Science, Rehovot, Israel.
The researchers of the current study, published in the Proceedings of the National Academy of Sciences, have used random first-order theory—a fundamental mathematical concept—to understand the behaviour of complex systems. The total energy of the system depends on the surface density and evolves depending on the movement within the collective system. It also influences a thermodynamic property called configurational entropy—the different ways in which constituent particles rearrange within a system. In systems devoid of activity, configurational entropy is determined only by the temperature, the number of constituent particles, and the internal energy.
Since the random first-order approximation applies for systems in equilibrium, the researchers modified it to suit active collective systems that are out of equilibrium. They constructed a new model to incorporate the effects of activity in a collective system. The researchers then validated their model through simulations and showed that the behaviour of active glassy systems depends on the nature of the activity.
“We have a well-established theory for an equilibrium system. We now extend it for active systems so we can understand the assumptions of the theory. It will also be easier to test and establish the predictions by others. This approach is in contrast to modelling a particular biological system”, says Dr Nandi.
The study is an essential milestone in the exploration of activity-driven glass-like systems. It is funded by the Koshland Foundation, Council of Scientific and Industrial Research (India), and the Harold Perlman Family Foundation, and has broad applications not just in studying the nature of the collective behaviour of biological systems but also in areas such as non-equilibrium thermodynamics and disordered magnetism.