Biological processes depend on the pieces of the puzzle coming together and interacting. Under specific conditions, these interactions can create something new without external input. This is called self-organization, as seen in a school of fish or a flock of birds. Interestingly, the mammalian embryo develops in a similar way. In PNASDavid Brückner and Gašper Tkačik from the Austrian Institute of Science and Technology (ISTA) present a mathematical framework that analyzes self-organization from a single cell to a multicellular organism.
When an embryo develops, it is necessary to generate many types of cells with different functions. For example, some cells will become part of the eye and register visual stimuli, while others will become part of the intestine and help digest food. To determine their functions, cells constantly communicate with each other using chemical signals.
Thanks to this communication, during development everything is well synchronized and coordinated, and yet there is no central control responsible for it. The cellular collective is self-organized and orchestrated by the interactions between individuals. Each cell reacts to signals from its neighbors. On the basis of such self-organization, the mammalian embryo develops from a single fertilized egg into a multicellular organism.
David Brückner and Gašper Tkačik from the Austrian Institute of Science and Technology (ISTA) have established a mathematical framework that helps analyze this process and predict its optimal parameters. Published in PNAS, this approach represents a unifying mathematical language for describing biological self-organization in embryonic development and beyond.
The self-assembling embryo
In nature, self-organization is all around us: we can observe it in schools of fish, flocks of birds or collectives of insects, and even in microscopic processes regulated by cells. David Brückner, a NOMIS fellow and ISTA postdoc, is interested in better understanding these processes from a theoretical point of view. His focus is on embryonic development, a complex process governed by genetics and cells that communicate with each other.
During embryonic development, a single fertilized cell becomes a multicellular embryo containing organs with many different characteristics. “During many steps of this developmental process, the system does not have any extrinsic signals telling it what to do. There is an intrinsic property of the system that allows it to establish patterns and structures,” says Brückner. “The intrinsic property is what is known as self-organization.” Even with unpredictable factors, which physicists call “noise,” embryonic patterns form reliably and consistently. In recent years, scientists have gained a deeper understanding of the molecular details that drive this complex process. However, a mathematical framework to analyze and quantify their performance was missing. The language of information theory provides answers.
Bridge experience
“Information theory is a universal language for quantifying structure and regularity in statistical sets, which are a collection of replicas of the same process. Embryonic development can be viewed as a process that reproducibly generates functional organisms that are very similar but not identical.” says Gašper Tkačik, professor at ISTA and expert in this field. Tkačik has long studied how information is processed in biological systems, for example in the embryo of a fly. “In the early fly embryo, the patterns are not self-organized,” he continues. “The mother fly puts chemicals in the egg that instruct the cells what actions to take.” As the Tkačik group had already developed a framework for this system, Brückner set out to develop one for the mammalian embryo as well. “Thanks to Gašper’s knowledge of information theory, we were able to achieve this,” Brückner enthuses.
Beyond embryonic development?
During embryonic development, cells exchange signals and are constantly subject to random and unpredictable fluctuations (noise). Therefore, cellular interactions must be robust. The new framework measures how these interactions are possibly optimized to resist noise. Using computer simulations of interacting cells, the scientists explored the conditions under which a system can still have a stable end result despite introducing fluctuations.
Although the framework has proven successful in three different developmental models that rely on chemical and mechanical cues, additional work will be required to apply it to experimental recordings of developmental systems. “In the future we want to study more complex models with more parameters and dimensions,” says Tkačik. “By quantifying more complex models, we could also apply our framework to experimentally measured chemical signal patterns in developing embryos,” adds Brückner. To do this, the two theoretical scientists will collaborate with experimenters.