arXiv subjects

Daniel Ruiz-Reynés

Publications and source records attributed to Daniel Ruiz-Reynés.

6 recordsLinked to original sources

arXiv2025

Six decades of the FitzHugh-Nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines

The FitzHugh-Nagumo equation, originally conceived in neuroscience during the 1960s, became a key model providing a simplified view of excitable neuron cell behavior. Its applicability, however, extends beyond neuroscience into fields like cardiac physiology, cell division, population dynamics, electronics, and other natural phenomena. In this review spanning six decades of research, we discuss the diverse spatio-temporal dynamical behaviors described by the FitzHugh-Nagumo equation. These include dynamics like bistability, oscillations, and excitability, but it also addresses more complex phenomena such as traveling waves and extended patterns in coupled systems. The review serves as a guide for modelers aiming to utilize the strengths of the FitzHugh-Nagumo model to capture generic dynamical behavior. It not only catalogs known dynamical states and bifurcations, but also extends previous studies by providing stability and bifurcation analyses for coupled spatial systems.

nlin.PS↗

arXiv2024

Spiral waves speed up cell cycle oscillations in the frog cytoplasm

Spiral waves are a well-known phenomenon in excitable media, playing critical roles in biological systems such as cardiac tissues, where they are involved in arrhythmias, and in slime molds, where they guide collective cell migration. However, their presence in the cytoplasm of cells has not been reported to date. In this study, we present the observation of spiral waves in a Xenopus laevis frog egg extract reconstituting periodic cell cycle transitions. We find that the emergence of these spiral waves accelerates the cell division cycle nearly twofold. Using two distinct computational models, we demonstrate that this behavior arises from generic principles and is driven primarily by time-scale separation in the cell cycle oscillator. Additionally, we investigate the interplay between these spiral waves and the more commonly observed target pattern waves in the frog cytoplasm, providing new insights into their dynamic interactions.

nlin.PS↗

arXiv2024

Dynein-driven self-organization of microtubules: An entropy- and network-based analysis

Microtubules self-organize to form part of the cellular cytoskeleton. They give cells their shape and play a crucial role in cell division and intracellular transport. Strikingly, microtubules driven by motor proteins reorganize into stable mitotic/meiotic spindles with high spatial and temporal precision during successive cell division cycles. Although the topic has been extensively studied, the question remains: What defines such microtubule networks' spatial order and robustness? Here, we aim to approach this problem by analyzing a simplified computational model of radial microtubule self-organization driven by a single type of motor protein -- dyneins. We establish that the spatial order of the steady-state pattern is likely associated with the dynein-driven microtubule motility. At the same time, the structure of the microtubule network is likely linked to its connectivity at the beginning of self-organization. Using the continuous variation of dynein concentration, we reveal hysteresis in microtubule self-organization, ensuring the stability of radial filament structures.

nlin.AO↗

arXiv2022

Bifurcation structure of traveling pulses in Type-I excitable media

We have studied the existence of traveling pulses in a general Type-I excitable 1-dimensional medium. We have obtained the stability region and characterized the different bifurcations behind either the destruction or loss of stability of the pulses. In particular, some of the bifurcations delimiting the stability region have been connected, using singular limits, with the two different scenarios that mediated the Type-I local excitability, i.e. homoclinic (saddle-loop) and Saddle-Node on the Invariant Circle bifurcations. The existence of the traveling pulses has been linked, outside the stability region, to a drift pitchfork instability of localized steady structures.

nlin.PS↗

arXiv2020

A general model for vegetation patterns including rhizome growth

Vegetation patterns, a natural phenomenon observed worldwide, are typically driven by spatially distributed feedback. However, the spatial colonization mechanisms of clonal plants, driven by the growth of a rhizome, are usually not considered in prototypical models. Here we propose a general equation for the vegetation density that includes all main clonal-growth features as well as the essential ingredients leading to spatial self-organization. This generic model reproduces the phase diagram of a fully detailed model of clonal growth. The relation of each term of the model with the mechanisms of clonal growth is discussed.

q-bio.PE↗

arXiv2017

Fairy circle landscapes under the sea

Short-scale interactions yield large-scale vegetation patterns that, in turn, shape ecosystem function across landscapes. Fairy circles, which are circular patches bare of vegetation within otherwise continuous landscapes, are characteristic features of semiarid grasslands. We report the occurrence of submarine fairy circle seascapes in seagrass meadows and propose a simple model that reproduces the diversity of seascapes observed in these ecosystems as emerging from plant interactions within the meadow. These seascapes include two extreme cases, a continuous meadow and a bare landscape, along with intermediate states that range from the occurrence of persistent but isolated fairy circles, or solitons, to seascapes with multiple fairy circles, banded vegetation, and "leopard skin" patterns consisting of bare seascapes patterns consisting of bare seascapes dotted with plant patches. The model predicts that these intermediate seascapes extending across kilometers emerge as a consequence of local demographic imbalances along with facilitative and competitive interactions among the plants with a characteristic spatial scale of 20 to 30 m, consistent with known drivers of seagrass performance. The model, which can be extended to clonal growth plants in other landscapes showing fairy rings, reveals that the different seascapes observed hold diagnostic power as to the proximity of seagrass meadows to extinction points that can be used to identify ecosystems at risks.

q-bio.PE↗