Spatial Wave Patterns

Self-organization in space is a striking process that can be observed in many areas of the natural world. It is especially relevant in the development of an organism.

The emergence of spatial order results when the underlying interactions extend in space affecting the surroundings. Commonly spatial coupling is mediated by diffusion of the constituents. However, long-range interactions are often found to play an important role in spatial self-organization, such as mechanical forces between microtubules or actin filaments. Multiple dynamical behaviors have been found depending on the local dynamics, such as traveling waves and spatially extended patterns, which can have a big impact for the biological function.

Oscillatory dynamics may lead to traveling waves, which can serve to spatially coordinate different events in an organism. Different waves can emerge, such as target patterns, which radially emerge from inhomogeneities, or spiral waves, which are driven by the presence of topological defects. A different type of waves, also named fronts, emerge as a result of bistability. When multiple stable states coexist, an interface separating those different states may propagate in different directions depending on the relative stability between both.

Spatial coupling can lead to different extended patterns, such as stripes or hexagonal arrangements, which create impressive patterns of spatial organization. Turing patterns emerge in reaction-diffusion systems and represent the most prominent example in the literature. In general, these patterns appear when the fastest diffusing reactants inhibit the other. Moreover, not only reaction-diffusion systems can create patterns, but other non-local interactions can lead to self-organization, such as those produced by mechanical forces.

Often waves and extended patterns can occur simultaneously. This scenario leads to highly complex spatio-temporal dynamics involving oscillatory patterns, waves in patterns, isolated pulses or even turbulence.

In the lab, we especially investigate spatially-extended behavior using a combination of theory and experiments with frog egg extracts. With our work, we try to identify the leading mechanisms driving different types of spatio-temporal dynamics.

Selected publications

Ruiz-Reynés, D.; Mayol, E.; Sintes, T.; Hendriks, I. E; Hernández-García, E.; Duarte, C. M; Marbà, N.; Gomila, D.

Self-organized sulfide-driven traveling pulses shape seagrass meadows

In: Proceedings of the National Academy of Sciences, vol. 120, iss. 3, pp. e2216024120, 2023.

Abstract | Links | BibTeX

@article{nokey,

title = {Self-organized sulfide-driven traveling pulses shape seagrass meadows},

author = {D. Ruiz-Reynés and E. Mayol and T. Sintes and I. E Hendriks and E. Hernández-García and C. M Duarte and N. Marbà and D. Gomila},

doi = {https://doi.org/10.1073/pnas.2216024120},

year  = {2023},

date = {2023-01-17},

urldate = {2023-01-17},

journal = {Proceedings of the National Academy of Sciences},

volume = {120},

issue = {3},

pages = {e2216024120},

abstract = {Seagrasses provide multiple ecosystem services and act as intense carbon sinks in coastal regions around the globe but are threatened by multiple anthropogenic pressures, leading to enhanced seagrass mortality that reflects in the spatial self-organization of the meadows. Spontaneous spatial vegetation patterns appear in such different ecosystems as drylands, peatlands, salt marshes, or seagrass meadows, and the mechanisms behind this phenomenon are still an open question in many cases. Here, we report on the formation of vegetation traveling pulses creating complex spatiotemporal patterns and rings in Mediterranean seagrass meadows. We show that these structures emerge due to an excitable behavior resulting from the coupled dynamics of vegetation and porewater hydrogen sulfide, toxic to seagrass, in the sediment. The resulting spatiotemporal patterns resemble those formed in other physical, chemical, and biological excitable media, but on a much larger scale. Based on theory, we derive a model that reproduces the observed seascapes and predicts the annihilation of these circular structures as they collide, a distinctive feature of excitable pulses. We show also that the patterns in field images and the empirically resolved radial profiles of vegetation density and sediment sulfide concentration across the structures are consistent with predictions from the theoretical model, which shows these structures to have diagnostic value, acting as a harbinger of the terminal state of the seagrass meadows prior to their collapse.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}