arXiv subjects

Nikita Frolov

Publications and source records attributed to Nikita Frolov.

10 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 °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

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↗

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

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↗

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↗

arXiv2024

Self-organized bistability on globally coupled higher-order networks

Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to undergo enduring shifts between the coexisting states, achieved through the self-regulation of a controlling parameter. Recently, SOB has been established in a scale-free network as a recurrent transition to a short-living state of global synchronization. Here, we embark on a theoretical exploration that extends the boundaries of the SOB concept on a higher-order network (implicitly embedded microscopically within a simplicial complex) while considering the limitations imposed by coupling constraints. By applying Ott-Antonsen dimensionality reduction in the thermodynamic limit to the higher-order network, we derive SOB requirements under coupling limits that are in good agreement with numerical simulations on systems of finite size. We use continuous synchronization diagrams and statistical data from spontaneous synchronized events to demonstrate the crucial role SOB plays in initiating and terminating temporary synchronized events. We show that under weak coupling consumption, these spontaneous occurrences closely resemble the statistical traits of the epileptic brain functioning.

nlin.AO↗

arXiv2022

Self-organized bistability on scale-free networks

A dynamical system approaching the first-order transition can exhibit a specific type of critical behavior known as self-organized bistability (SOB). It lies in the fact that the system can permanently switch between the coexisting states under the self-tuning of a control parameter. Many of these systems have a network organization that should be taken into account to understand the underlying processes in detail. In the present paper, we theoretically explore an extension of the SOB concept on the scale-free network under coupling constraints. As provided by the numerical simulations and mean-field approximation in the thermodynamic limit, SOB on scale-free networks originates from facilitated criticality reflected on both macro- and mesoscopic network scales. We establish that the appearance of switches is rooted in spatial self-organization and temporal self-similarity of the network's critical dynamics and replicates extreme properties of epileptic seizure recurrences. Our results, thus, indicate that the proposed conceptual model is suitable to deepen the understanding of emergent collective behavior behind neurological diseases.

nlin.AO↗

arXiv2020

Chimera-like behavior in a heterogeneous Kuramoto model: the interplay between the attractive and repulsive coupling

Interaction within an ensemble of coupled nonlinear oscillators induces a variety of collective behaviors. One of the most fascinating is a chimera state which manifests the coexistence of spatially distinct populations of coherent and incoherent elements. Understanding of the emergent chimera behavior in controlled experiments or real systems requires a focus on the consideration of heterogeneous network models. In this study, we explore the transitions in a heterogeneous Kuramoto model under the monotonical increase of the coupling strength and specifically find that this system exhibits a frequency-modulated chimera-like pattern during the explosive transition to synchronization. We demonstrate that this specific dynamical regime originates from the interplay between (the evolved) attractively and repulsively coupled subpopulations. We also show that the above mentioned chimera-like state is induced under weakly non-local, small-world and sparse scale-free coupling and suppressed in globally coupled, strongly rewired and dense scale-free networks due to the emergence of the large-scale connections.

nlin.AO↗