arXiv subjects

Lendert Gelens

Publications and source records attributed to Lendert Gelens.

At least 19 recordsLinked to original sources

arXiv2026

The Belousov-Zhabotinsky reaction reveals two regimes of non-Arrhenius temperature scaling in relaxation oscillators

The period of biological and chemical oscillators scales with temperature in a characteristic way. Some oscillators are very well described by an Arrhenius law, while others show systematic deviations. Several frameworks have been proposed to explain such deviations, but they are either phenomenological, focus on activation energy imbalances in specific circuits, or restrict themselves to sequential processes. Here we develop a mechanistic account of the temperature scaling of relaxation oscillators, using the Belousov-Zhabotinsky (BZ) reaction as a model system. We distinguish two typical scenarios by their temperature-scaling signatures. In the first, an Arrhenius-dependent timescale separation parameter produces a biphasic Arrhenius scaling of the period as the oscillator approaches a Hopf bifurcation. In the second, Arrhenius-dependent nullclines hide the same bifurcation behind a canard explosion, yielding apparent single-line Arrhenius scaling. Measuring the electrode potential of a classical and an uncatalyzed BZ reaction, over a very wide temperature range ({\approx} 100 {\deg}C), and comparing to dynamical models, we find that the two reactions represent these two distinct scenarios. Furthermore, we show that a single parameter characterizing the waveform asymmetry between fast and slow phases quantitatively predicts the temperature scaling of three other observables close to the Hopf bifurcation: the period, amplitude, and phase noise. This analysis also recovers elementary activation energies of the BZ mechanism, including a new estimate for the autocatalytic step. We discuss how this framework and its waveform-based diagnostics apply to the analysis of general biochemical relaxation oscillators

nlin.CD↗

arXiv2026

Simulating is not always understanding: When model complexity obscures biology

In cell biology, computational models of biological systems range from minimal representations with a handful of parameters to whole-cell simulations tracking thousands of molecular species across a complete cell cycle. While these models span a continuum of detail, increasing complexity changes what they capture and are able to explain, what they can predict, and how they can fall short. A model contributes to understanding only when it makes novel predictions, reveals an unexpected coupling between processes, or fails in a way that identifies missing parameters. We contend that what is important for understanding is not the number of components or spatial dimensions a model contains, but the ratio of free parameters to the experimental constraints available to pin them down, and whether we can see why it produces the behaviors it does. Large-scale agent-based models of cytoskeletal dynamics or tissue mechanics that are built on a small number of physically grounded rules can reveal rich self-organization behavior precisely because their parameter spaces are small enough to explore systematically. By contrast, when free parameters grow faster than the data available to constrain them, models become progressively harder to interpret -- and even disprove --regardless of their biological scope. We argue that the field needs to reconsider the goal of complex models. We should move away from trying to include as many parameters as possible and instead aim for systematic comparisons with simpler representations, dynamical analysis, and explicit model hierarchies that trace how cellular behavior emerges from its parts.

q-bio.MN↗

arXiv2026

Isolas of limit cycles and birhythmicity induced by cooperative feedback in a glycolysis model

We investigate how cooperative feedback shapes global oscillatory dynamics in a glycolysis model with product recycling and allosteric phosphofructokinase regulation. Using bifurcation theory and numerical continuation, we analyze the stability of equilibria and characterize Hopf and generalized Hopf bifurcations, using the Hill exponent as an effective measure of cooperativity. We show that a codimension-2 cusp-of-cycles point governs the creation and annihilation of detached branches of limit cycles (isolas) and, together with saddle-node bifurcations of limit cycles, organizes a regime map of six qualitatively distinct dynamical regions. In the birhythmic regime two stable oscillatory states coexist on connected branches; in the isola regime a stable oscillation exists on a fully disconnected branch, producing threshold-dependent onset of rhythmic activity. Time-domain simulations confirm coexistence of distinct rhythms and illustrate how the choice of initial condition determines which attractor is reached. Together, these results show how variations in cooperative feedback strength can generate isolated oscillatory modes and multistability in metabolic networks, highlighting isola dynamics as a general mechanism for rhythm selection and switching in nonlinear biological oscillators.

nlin.CD↗

arXiv2026

Understanding the temperature response of biological systems: Part II -- Network-level mechanisms and emergent dynamics

Building on the phenomenological and microscopic models reviewed in Part I, this second part focuses on network-level mechanisms that generate emergent temperature response curves. We review deterministic models in which temperature modulates the kinetics of coupled biochemical reactions, as well as stochastic frameworks, such as Markov chains, that capture more complex multi-step processes. These approaches show how Arrhenius-like temperature dependence at the level of individual reactions is transformed into non-Arrhenius scaling, thermal limits, and temperature compensation at the system level. Together, network-level models provide a mechanistic bridge between empirical temperature response curves and the molecular organization of biological systems, giving us predictive insights into robustness, perturbations, and evolutionary constraints.

q-bio.MN↗

arXiv2025

Understanding the temperature response of biological systems: Part I -- Phenomenological descriptions and microscopic models

Virtually every biological rate depends on temperature, yet the resulting rate-temperature relationships often deviate strongly from simple Arrhenius behavior. In this first part of a two-part review, we survey phenomenological models used to describe biological temperature responses across scales, from enzymatic reactions to organismal performance. We discuss common functional forms, including symmetric and asymmetric thermal performance curves and extensions of the Arrhenius law, and we highlight how these models define operational quantities such as optimal temperatures, thermal breadths, and thermal limits. We also discuss microscopic models for the effect of temperature, which however do not capture cooperative effects. In Part II of this review, we will discuss how system-level temperature response curves emerge from the interaction of many underlying reactions.

q-bio.QM↗

arXiv2025

Data-driven discovery of dynamical models in biology

Dynamical systems theory provides a mathematical framework for describing how interacting biological components evolve over time and space, from molecular oscillators to large-scale biological patterns. Such systems often involve nonlinear feedbacks, delays, and multiscale interactions, making mechanistic model construction increasingly challenging as experimental measurements become richer and higher-dimensional. This has motivated the development of data-driven approaches that infer model structure directly from data, offering alternative routes to constructing dynamical models. In this review, we discuss and compare data-driven approaches for model discovery in biological dynamical systems, focusing on three major methodological families: regression-based methods, network-based architectures, and decomposition techniques. We compare how these approaches address three core objectives: forecasting future behavior, identifying interactions between system components, and characterizing qualitative dynamical solutions such as steady states, oscillations, and transitions between them. To enable a direct comparison, representative methods are applied to a common benchmark - the Oregonator model - a minimal nonlinear oscillator that captures shared design principles of chemical and biological systems. By highlighting practical strengths, limitations, and degrees of interpretability, this review aims to guide researchers in selecting appropriate tools for analyzing complex, nonlinear, and high-dimensional biological dynamics.

q-bio.QM↗

arXiv2025

Machine learning identifies nullclines in oscillatory dynamical systems

We introduce CLINE (Computational Learning and Identification of Nullclines), a neural network-based method that uncovers the hidden structure of nullclines from oscillatory time series data. Unlike traditional approaches aiming at direct prediction of system dynamics, CLINE identifies static geometric features of the phase space that encode the (non)linear relationships between state variables. It overcomes challenges such as multiple time scales and strong nonlinearities while producing interpretable results convertible into symbolic differential equations. We validate CLINE on various oscillatory systems, showcasing its effectiveness.

cs.LG↗

arXiv2025

Spatial localization in the FitzHugh-Nagumo model

The FitzHugh-Nagumo model, originally introduced to study neural dynamics, has since found applications across diverse fields, including cardiology and biology. However, the formation and bifurcation structure of spatially localized states in this model remain underexplored. In this work, we present a detailed bifurcation analysis of such localized structures in one spatial dimension in the FitzHugh-Nagumo model. We demonstrate that these localized states undergo a smooth transition between standard and collapsed homoclinic snaking as the system shifts from pattern-uniform to uniform-uniform bistability. Additionally, we explore the oscillatory dynamics exhibited by these states when varying the time-scale separation and diffusion coefficient. Our study leverages a combination of analytical and numerical techniques to uncover the stability and dynamic regimes of spatially localized structures, offering new insights into the mechanisms governing spatial localization in this widely used model system.

nlin.PS↗

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↗

arXiv2025

Wave-driven phase wave patterns in a ring of FitzHugh-Nagumo oscillators

We explore a biomimetic model that simulates a cell, with the internal cytoplasm represented by a two-dimensional circular domain and the external cortex by a surrounding ring, both modeled using FitzHugh-Nagumo systems. The external ring is dynamically influenced by a pacemaker-driven wave originating from the internal domain, leading to the emergence of three distinct dynamical states based on the varying strengths of coupling. The range of dynamics observed includes phase patterning, the propagation of phase waves, and interactions between traveling and phase waves. A simplified linear model effectively explains the mechanisms behind the variety of phase patterns observed, providing insights into the complex interplay between a cell's internal and external environments.

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

Enhancing model identification with SINDy via nullcline reconstruction

Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse Identification of Nonlinear Dynamics (SINDy). This paper illustrates the importance of accurately determining the system's limit cycle position in phase space for identifying sparse and effective models. We introduce a method for identifying the limit cycle position and the system's nullclines by applying SINDy to datasets adjusted with various offsets. This approach is evaluated using three criteria: model complexity, coefficient of determination, and generalization error. We applied this method to several models: the oscillatory FitzHugh-Nagumo model, a more complex model consisting of two coupled cubic differential equations with a single stable state, and a multistable model of glycolytic oscillations. Our results confirm that incorporating detailed information about the limit cycle in phase space enhances the accuracy of model identification in oscillatory systems.e space can improve the success of model identification efforts in oscillatory systems.

nlin.AO↗

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↗

arXiv2023

Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data

The rapid increase of population and settlement structures in the Global South during recent decades motivates the development of suitable models to describe their formation and evolution. Such settlement formation has been previously suggested to be dynamically driven by simple pattern-forming mechanisms. Here, we explore the use of a data-driven white-box approach, called SINDy, to discover differential equation models directly from available spatiotemporal demographic data for three representative regions of the Global South. We show that the current resolution and observation time of the available data is insufficient to uncover relevant pattern-forming mechanisms in settlement development. Using synthetic data generated with a generic pattern-forming model, the Allen-Cahn equation, we characterize what the requirements are on spatial and temporal resolution, as well as observation time, to successfully identify possible model system equations. Overall, the study provides a theoretical framework for the analysis of large-scale geographical/ecological systems, and it motivates further improvements in optimization approaches and data collection.

physics.soc-ph↗

arXiv2021

Mitotic waves in an import-diffusion model with multiple nuclei in a shared cytoplasm

Nuclei import and export proteins, including cell cycle regulators. These import-export processes are modulated periodically by the cell cycle, for example due to the periodic assembly and breakdown of the nuclear envelope. As such, replicated DNA can be segregated between the two daughter cells and the proteins that were localized in the nucleus are free to diffuse throughout the cytoplasm. Here, we study a mathematical import-diffusion model to show how proteins, i.e. cell cycle regulators, could be redistributed in the cytoplasm by nuclei that periodically toggle between interphase and mitosis. We show that when the cell cycle period depends on the local concentration of regulators, the model exhibits mitotic waves. We discuss how the velocity and spatial origin of these mitotic waves depend on the different model parameters. This work is motivated by recent in vitro experiments reporting on mitotic waves in cycling cell-free extracts made with Xenopus laevis frog eggs, where multiple nuclei share the same cytoplasm. Such experiments have shown that nuclei act as pacemakers for the cell cycle and thus play an important role in collectively defining the spatial origin of mitotic waves.

physics.bio-ph↗

arXiv2021

Analytical approximations for the speed of pacemaker-generated waves

In an oscillatory medium, a region which oscillates faster than its surroundings can act as a source of outgoing waves. Such pacemaker-generated waves can synchronize the whole medium and are present in many chemical and biological systems, where they are a means of transmitting information at a fixed speed over large distances. In this paper, we apply analytical tools to investigate the factors that determine the speed of these waves. More precisely, we apply singular perturbation and phase reduction methods to two types of negative-feedback oscillators, one built on underlying bistability and one including a time delay in the negative feedback. In both systems, we investigate the influence of timescale separation on the resulting wave speed, as well as the effect of size and frequency of the pacemaker region. We compare our analytical estimates to numerical simulations which we described previously [1].

nlin.PS↗

arXiv2016

Dark solitons in the Lugiato-Lefever equation with normal dispersion

The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organized in a bifurcation structure known as collapsed snaking implying the presence of a region in parameter space with a finite multiplicity of dark solitons. For some parameter values dynamical instabilities are responsible for the appearance of oscillations and temporal chaos. The importance of the results for understanding frequency comb generation in microresonators is emphasized.

nlin.PS↗

arXiv2016

Origin and stability of dark pulse Kerr combs in normal dispersion resonators

We analyze dark pulse Kerr frequency combs in optical resonators with normal group-velocity dispersion using the Lugiato-Lefever model. We show that in the time domain these correspond to interlocked switching waves between the upper and lower homogeneous states, and explain how this fact accounts for many of their experimentally observed properties. Modulational instability does not play any role in their existence. Furthermore, we provide a detailed map indicating where stable dark pulse Kerr combs can be found in parameter space, and how they are destabilized for increasing values of frequency detuning.

nlin.PS↗