Biology subjects

Piskovsky, V.

Publications and source records attributed to Piskovsky, V..

3 recordsLinked to original sources

bioRxiv2024

Will a large complex system form Turing patterns?

From atomic spins in magnets to galaxies, and from embryonic development to patchy vegetation in arid environments, the physical world is filled with complex systems that spontaneously form spatial patterns. While simple mathematical models, such as reaction-diffusion systems, can explain the formation of such patterns, the complexity of the physical systems these models aim to describe necessitates the analysis of model robustness. Our work utilizes random matrix theory to provide arguably the first definition of robustness that is analytically tractable, providing an easy guide for identifying spatial interactions that robustly generate spatial patterns. We illustrate our theory on examples from mathematical biology, showing that diffusion alone cannot robustly generate spatial Turing patterns in large and unstructured systems, while advection, chemotaxis and non-local interactions can robustly promote pattern formation. Furthermore, we use our theory to prove that the spinodal decompositon of soft condensed matter is dynamically robust and predict the dynamics beyond regimes permitted by the standard Landau-Ginzburg theory. By classifying different spatial interactions based on the robustness of pattern formation, this work provides insights into which mechanisms are fundamental for pattern formation in large and unstructured physical systems.

biophysics↗

bioRxiv2024

Evolution of predators and prey kills Turing patterns

The spatiotemporal patterns of predators and their prey play a pivotal role in ecology and ecological interactions can drive their formation at fine scales (1). While motility can explain the emergence of such predator-prey patterns (2-14) via the Turing mechanism (15), the predicted Turing patterns do not exhibit temporal changes that are common in experiments (16-24) and nature (25-31). Moreover, the Turing mechanism treats motility as fixed, even though predators and prey adjust their motility in response to each other (32-37) and their interactions influence their evolution (38-47). Using adaptive dynamics (48), I prove that the evolution of motility prevents the formation of Turing patterns and promotes the formation of dynamic patterns, such as predator-prey waves (28, 49-54). The resulting predator-prey cycles are shown to be induced by heterogeneous motility, which extends the emergence of predator-prey cycles beyond regimes predicted by Lotka-Volterra (55) or Rosenzweig-MacArthur (56) models. This work unites models for predator-prey spatiotemporal patterns (2-14) and evolution of motility (57-64) to explain how dynamic spatiotemporal patterns of co-evolving predators and prey emerge and persist. The novel mathematical theory is general and extends to other ecological situations, such as ecological public goods games (65). Significance StatementThe spatio-temporal patterns of predators and their prey play a key role in ecology and are crucial for their conservation. Yet, even at fine scales, such patterns are often complex and exhibit spatial and temporal heterogeneity. While simple mathematical models often predict static spatial patterns (Turing patterns), I show that such patterns of predators and prey are unstable if their motility can evolve. In particular, I suggest that the evolution of motility can give rise to complex spatio-temporal patterns of predators and prey, such as predator-prey waves. Moreover, the mathematical results can be generalised to other contexts, providing novel insights into the evolution of cooperation.

ecology↗

bioRxiv2022

Bacterial motility governs the evolution of antibiotic resistance in spatially heterogeneous environments

Bacteria evolving in natural and clinical settings experience spatial fluctuations of multiple factors and this heterogeneity is expected to affect bacterial adaptation. Notably, spatial heterogeneity in antibiotic concentrations is believed to accelerate the evolution of antibiotic resistance. However, current literature overlooks the role of cell motility, which is key for bacterial survival and reproduction. Here, we consider a quantitative model for bacterial evolution in antibiotic gradients, where bacteria evolve under the stochastic processes of proliferation, death, mutation and migration. Numerical and analytical results show that cell motility has major effects on bacterial adaptation. If migration is relatively rare, it accelerates adaptation because resistant mutants can colonize neighbouring patches of increasing antibiotic concentration avoiding competition with wild-type cells; but if migration is common throughout the lifespan of bacteria, it decelerates adaptation by promoting genotypic mixing and ecological competition. If migration is sufficiently high, it can limit bacterial survival, and we derive conditions for such a regime. Similar patterns are observed in more complex scenarios, namely where bacteria can bias their motion or switch between motility phenotypes either stochastically or in a density-dependent manner. Overall, our work reveals limits to bacterial adaptation in antibiotic landscapes that are set by cell motility.

microbiology↗