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Is there a single optimal arrangement that an organism can achieve through evolution? Is there a universal equation that outlines the path to this optimum? Can we develop it purely through theoretical means? A research team has provided insights into these questions. Their mathematical model predicts the ideal body design of a fruit fly’s early embryo, indicating that evolution may have had numerous viable options to choose from.
Is there a single optimal arrangement that an organism can achieve through evolution? Is there a universal equation that outlines the path to this optimum? Can we develop it purely through theoretical means? A research team, including members from the Institute of Science and Technology Austria (ISTA), has addressed these questions. Their mathematical model predicts the ideal body structure of a fruit fly’s early embryo, implying that evolution might have had several optimal options available.
The concept of optimization is thought to be fundamental to many stunning features of nature, suggesting that the universe tends toward states of minimal energy, optimal output, or heightened fitness. From pods of whales to clusters of tiny cells, the elements of life seem to have been selected to self-organize near peak efficiency.
The evolution of an animal embryo, transitioning from a small cluster of cells to a complex organism, may have also been optimized to be nearly flawless. However, a clear mathematical formula that can predict this optimal structure has remained elusive until now.
Physicists from the Institute of Science and Technology Austria (ISTA), the Frankfurt Institute for Advanced Studies, and Princeton University present just that: a theoretical model of the early embryonic development of the fruit fly, developed over almost twenty years. Their comprehensive model successfully predicts the optimal configuration of the gene-regulation network that governs the initial stages of development. The findings were published in PNAS.
Evolution = Optimization
Evolution serves as the central force behind every organism. In response to its environment, an organism adapts, survives, and endures selective pressures. “Adaptation can be viewed as an optimization process, or at least a process that necessitates the optimization of certain attributes and functions,” says Thomas Sokolowski, the study’s lead author.
In contrast to physical systems, where optimization typically leads to a stable state with minimal energy, biological systems appear to present multiple optimal solutions to similar challenges. For instance, eyes formed independently in various species, yet maintain a remarkably similar structure across different organisms.
“Eyes have been optimized for the same well-defined objective function, which focuses on maximizing light intake and converting it into neural spikes. Hence, they are strongly influenced by fundamental physical principles. The subtle differences between species can often be attributed to the varying contexts in which they evolved,” Sokolowski adds.
Similarly, various strategies have developed for embryonic formation, all producing the same result: a highly accurate and reproducible body structure. While these methods have likely been refined by evolution for specific purposes, determining which objective dominated the optimization process can be quite challenging.
“We increasingly understand how an embryo develops, but identifying the exact mathematical function guiding this process is still unclear,” Sokolowski remarks. “It’s akin to searching for a mathematical needle in a biological haystack.”
The fruit fly
Drosophila, as biologists refer to it, is extensively studied, notably due to the 1995 Nobel Prize-winning contributions of Eric Wieschaus, Christiane Nüsslein-Volhard, and Edward B. Lewis. They uncovered essential genes that govern the accurate development of the fly, especially “gap genes” and the gradients of signaling molecules (morphogens) that regulate them.
The gap gene network is crucial in forming the head-to-tail axis of the embryo. This “genetic positioning system” allows individual cells to adopt the correct fate in the proper location, ultimately constructing the segmented body of a fruit fly. The varying levels of activation among the gap genes create an incredibly precise “positional code” along this axis, supplying each cell with the exact information regarding its location within the embryo.
Time flies
Two decades ago, research by William Bialek, Gašper Tka?ik, Curtis Callan, Aleksandra Walczak, Thomas Gregor, and others indicated that the gap gene network in fruit flies has been refined through evolution to deliver high positional information while using limited signaling molecules — much like providing a precise GPS signal with minimal satellites. This insight prompted scientists to search for a mathematical function explaining this phenomenon.
Initially, Tka?ik and his colleagues investigated simplified theoretical models that captured only aspects of the gap gene network’s regulatory mechanisms. They progressively increased the complexity of their models to enhance realism. While these initial “toy” models did not account for all characteristics of the gap gene system, they laid the groundwork for a comprehensive optimization effort.
“Our early work demonstrated that it was feasible to derive nontrivial and unexpectedly accurate predictions regarding gene regulatory interactions by optimizing them for maximum information throughput within practical biophysical and molecular resource constraints,” Tka?ik states.
Subsequently, Thomas Sokolowski and his team examined detailed stochastic models — which incorporate randomness — of spatially interacting genes similar to the gap genes. In 2014, Sokolowski joined the Tka?ik group at ISTA, creating a unique chance to blend the original optimization approach with in-depth spatial-stochastic modeling. Together, they quickly developed a model that was realistic with respect to actual fruit fly behavior while remaining computationally efficient.
The model began as a simplified version encompassing only two genes, but later expanded to include the complete set of four interacting gap genes and three morphogen gradients, ideal for executing comprehensive optimizations of the gap gene system. “Interestingly, the optimal networks we derived closely aligned with the defining traits of the spatial gene expression patterns observed in real fruit flies,” Tka?ik adds.
Many “optimal” ways
Additionally, the researchers discovered that there isn’t merely one optimal approach to encoding positional information within the gap network. Various biophysical parameters can produce the necessary optimal characteristics of the system. While these optimal solutions are just a tiny fraction of all physically feasible solutions, they exhibit remarkable diversity.
“We believe this is not a disadvantage but rather a benefit for evolution, as the same level of fitness can be potentially attained through numerous imaginable evolutionary pathways,” Sokolowski posits. “While the evolution that led to the Drosophila we study today followed one specific path, the existence of many alternative routes may have made it easier for this organism to achieve high fitness.” The greater the number of options, the better the chances of selecting a functional one.
In order to comprehend the processes leading to effective body plans in greater depth and to create a more accurate reflection of the actual evolutionary dynamics, the researchers need to conduct additional modeling that goes beyond mere numerical optimization of parameters. This will entail considering influences such as environmental factors or the mechanisms of natural selection — an exciting and challenging venture for future theoretical biology research.
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