Slow Time Scale Research Articles

Precise control of neural activity using dynamically optimized electrical stimulation.

Neural implants have the potential to restore lost sensory function by electrically evoking the complex naturalistic activity patterns of neural populations. However, it can be difficult to predict and control evoked neural responses to simultaneous multi-electrode stimulation due to nonlinearity of the responses. We present a solution to this problem and demonstrate its utility in the context of a bidirectional retinal implant for restoring vision. A dynamically optimized stimulation approach encodes incoming visual stimuli into a rapid, greedily chosen, temporally dithered and spatially multiplexed sequence of simple stimulation patterns. Stimuli are selected to optimize the reconstruction of the visual stimulus from the evoked responses. Temporal dithering exploits the slow time scales of downstream neural processing, and spatial multiplexing exploits the independence of responses generated by distant electrodes. The approach was evaluated using an experimental laboratory prototype of a retinal implant: large-scale, high-resolution multi-electrode stimulation and recording of macaque and rat retinal ganglion cells ex vivo. The dynamically optimized stimulation approach substantially enhanced performance compared to existing approaches based on static mapping between visual stimulus intensity and current amplitude. The modular framework enabled parallel extensions to naturalistic viewing conditions, incorporation of perceptual similarity measures, and efficient implementation for an implantable device. A direct closed-loop test of the approach supported its potential use in vision restoration.

Characterising Cancer Cell Responses to Cyclic Hypoxia Using Mathematical Modelling

In vivo observations show that oxygen levels in tumours can fluctuate on fast and slow timescales. As a result, cancer cells can be periodically exposed to pathologically low oxygen levels; a phenomenon known as cyclic hypoxia. Yet, little is known about the response and adaptation of cancer cells to cyclic, rather than, constant hypoxia. Further, existing in vitro models of cyclic hypoxia fail to capture the complex and heterogeneous oxygen dynamics of tumours growing in vivo. Mathematical models can help to overcome current experimental limitations and, in so doing, offer new insights into the biology of tumour cyclic hypoxia by predicting cell responses to a wide range of cyclic dynamics. We develop an individual-based model to investigate how cell cycle progression and cell fate determination of cancer cells are altered following exposure to cyclic hypoxia. Our model can simulate standard in vitro experiments, such as clonogenic assays and cell cycle experiments, allowing for efficient screening of cell responses under a wide range of cyclic hypoxia conditions. Simulation results show that the same cell line can exhibit markedly different responses to cyclic hypoxia depending on the dynamics of the oxygen fluctuations. We also use our model to investigate the impact of changes to cell cycle checkpoint activation and damage repair on cell responses to cyclic hypoxia. Our simulations suggest that cyclic hypoxia can promote heterogeneity in cellular damage repair activity within vascular tumours.

Emergence of cyclic hypoxia and the impact of PARP inhibitors on tumor progression.

Tumor hypoxia is a dynamic phenomenon marked by fluctuations in oxygen levels across both rapid (seconds to minutes) and slow (hours to days) time scales. While short hypoxia cycles are relatively well understood, the mechanisms behind longer cycles remain largely unclear. In this paper, we present a novel mechanistic mathematical model that explains slow hypoxia cycles through feedback loops involving vascular expansion and regression, oxygen-regulated tumor growth, and toxic cytokine production. Our study reveals that, for the emergence of slow hypoxia cycles, endothelial cells must adapt by decreasing receptor activation as ligand concentration increases. Additionally, the interaction between tumor cells and toxic cytokines influences frequency and intensity of these cycles. By examining the effects of pharmacological interventions, specifically poly (ADP-ribose) polymerase inhibitors, we also demonstrate how targeting cell proliferation can help regulate oxygen levels. Our findings enhance the understanding of hypoxia regulation and suggest PARP proteins as promising therapeutic targets.

Model-predictive kinetic control with data-driven models on EAST

Abstract In this work, model-predictive control (MPC) was combined for the first time with singular perturbation theory, and an original plasma kinetic control method based on extremely simple data-driven models and a two-time-scale MPC algorithm has been developed. A comprehensive review is presented in this paper. Slow and fast semi-empirical models are identified from data, by considering the fast kinetic plasma dynamics as a singular perturbation of a quasi-static equilibrium, which itself is governed, on the slow time scale, by the flux diffusion equation. This control technique takes advantage of the large ratio between the time scales involved in magnetic and kinetic plasma transport. It is applied here to the simultaneous control of the safety factor profile, q(x), and of several kinetic variables, such as the poloidal beta parameter, βp, and the internal inductance parameter, li, on the EAST tokamak. In the experiments, the available control actuators were lower hybrid current drive (LHCD) and co-current neutral beam injection (NBI) from different sources. Ion cyclotron resonant heating (ICRH) and electron cyclotron resonant heating (ECRH) are used as additional actuators in control simulations. In the controller design, an observer provides, in real time, an estimate of the system states and of the mismatch between measured and predicted outputs, which ensures robustness to model errors and offset-free control. A number of control applications are described in the paper, either in nonlinear simulations with EAST-like parameters or in real experiments on EAST. Various controller configurations were tested, with up to three controlled variables chosen among q0 = q(x=0), q1 = q(x=0.5), βp and li. Both the extensive nonlinear simulations and the experiments described in this paper have demonstrated the relevance of combining model-predictive control, data-driven models and singular perturbation methods for plasma kinetic control.

Canard explosions in turbulent thermo-fluid systems.

A sudden transition to a state of high-amplitude periodic oscillations is catastrophic in a thermo-fluid system. Conventionally, upon varying the control parameter, a sudden transition is observed as an abrupt jump in the amplitude of the fluctuations in these systems. In contrast, we present an experimental discovery of a canard explosion in a turbulent reactive flow system where we observe a continuous bifurcation with a rapid rise in the amplitude of the fluctuations within a narrow range of control parameters. The observed transition is facilitated via a state of bursting, consisting of the epochs of large amplitude periodic oscillations amidst the epochs of low-amplitude periodic oscillations. The amplitude of the bursts is higher than the amplitude of the bursts of an intermittency state in a conventional gradual transition, as reported in turbulent reactive flow systems. During the bursting state, we observe that temperature fluctuations of the exhaust gas vary at a slower time scale in correlation with the amplitude envelope of the bursts. We also present a phenomenological model for thermoacoustic systems to describe the observed canard explosion. Using the model, we explain that the large amplitude bursts occur due to the slow-fast dynamics at the bifurcation regime of the canard explosion.

An integrative characterization of proline cis and trans conformers in a disordered peptide

Intrinsically disordered proteins (IDPs) often contain proline residues that undergo cis/trans isomerization. While molecular dynamics (MD) simulations have the potential to fully characterize the proline cis and trans subensembles, they are limited by the slow timescales of isomerization and force field inaccuracies. NMR spectroscopy can report on ensemble-averaged observables for both the cis-proline and trans-proline states, but a full atomistic characterization of these conformers is challenging. Given the importance of proline cis/trans isomerization for influencing the conformational sampling of disordered proteins, we employed a combination of all-atom MD simulations with enhanced sampling (metadynamics), NMR, and small-angle x-ray scattering (SAXS) to characterize the two subensembles of the ORF6 C-terminal region (ORF6CTR) from SARS-CoV-2 corresponding to the proline-57 (P57) cis and trans states. We performed MD simulations in three distinct force fields: AMBER03ws, AMBER99SB-disp, and CHARMM36m, which are all optimized for disordered proteins. Each simulation was run for an accumulated time of 180–220 μs until convergence was reached, as assessed by blocking analysis. A good agreement between the cis-P57 populations predicted from metadynamic simulations in AMBER03ws was observed with populations obtained from experimental NMR data. Moreover, we observed good agreement between the radius of gyration predicted from the metadynamic simulations in AMBER03ws and that measured using SAXS. Our findings suggest that both the cis-P57 and trans-P57 conformations of ORF6CTR are extremely dynamic and that interdisciplinary approaches combining both multiscale computations and experiments offer avenues to explore highly dynamic states that cannot be reliably characterized by either approach in isolation.

Tracking the Distance to Criticality in Systems with Unknown Noise

Many real-world systems undergo abrupt changes in dynamics as they move across critical points, often with dramatic and irreversible consequences. Much existing theory on identifying the time-series signatures of nearby critical points, such as increased signal variance and slower timescales, is derived from analytically tractable systems, typically considering the case of fixed, low-amplitude noise. However, real-world systems are often corrupted by unknown levels of noise that can distort these temporal signatures. Here we aim to develop noise-robust indicators of the distance to criticality (DTC) for systems affected by dynamical noise in two cases: when the noise amplitude is either fixed or is unknown and variable across recordings. We present a highly comparative approach to this problem that compares the ability of over 7000 candidate time-series features to track the DTC in the vicinity of a supercritical Hopf bifurcation. Our method recapitulates existing theory in the fixed-noise case, highlighting conventional time-series features that accurately track the DTC. But in the variable-noise setting, where these conventional indicators perform poorly, we highlight new types of high-performing time-series features and show that their success is accomplished by capturing the shape of the invariant density (which depends on both the DTC and the noise amplitude) relative to the spread of fast fluctuations (which depends on the noise amplitude). We introduce a new high-performing time-series statistic, the rescaled autodensity (RAD), that combines these two algorithmic components. We then use RAD to provide new evidence that brain regions higher in the visual hierarchy are positioned closer to criticality, supporting existing hypotheses about patterns of brain organization that are not detected using conventional metrics of the DTC. Our results demonstrate how large-scale algorithmic comparison can yield theoretical insights that can motivate new theory and interpretable algorithms for solving important real-world problems. Published by the American Physical Society 2024

Navigating Central Oxytocin Transport: Known Realms and Uncharted Territories.

Complex mechanisms govern the transport and action of oxytocin (Oxt), a neuropeptide and hormone that mediates diverse physiologic processes. While Oxt exerts site-specific and rapid effects in the brain via axonal and somatodendritic release, volume transmission via CSF and the neurovascular interface can act as an additional mechanism to distribute Oxt signals across distant brain regions on a slower timescale. This review focuses on modes of Oxt transport and action in the CNS, with particular emphasis on the roles of perivascular spaces, the blood-brain barrier (BBB), and circumventricular organs in coordinating the triadic interaction among circulating blood, CSF, and parenchyma. Perivascular spaces, critical conduits for CSF flow, play a pivotal role in Oxt diffusion and distribution within the CNS and reciprocally undergo Oxt-mediated structural and functional reconstruction. While the BBB modulates the movement of Oxt between systemic and cerebral circulation in a majority of brain regions, circumventricular organs without a functional BBB can allow for diffusion, monitoring, and feedback regulation of bloodborne peripheral signals such as Oxt. Recognition of these additional transport mechanisms provides enhanced insight into the systemic propagation and regulation of Oxt activity.

Insertion and Anchoring of HIV-1 Fusion Peptide into Complex Membrane Mimicking Human T-cell.

A fundamental understanding of how HIV-1 envelope (Env) protein facilitates fusion is still lacking. The HIV-1 fusion peptide, consisting of 15 to 22 residues, is the N-terminus of the gp41 subunit of the Env protein. Further, this peptide, a promising vaccine candidate, initiates viral entry into target cells by inserting and anchoring into human immune cells. The influence of membrane lipid reorganization and the conformational changes of the fusion peptide during the membrane insertion and anchoring processes, which can significantly affect HIV-1 cell entry, remains largely unexplored due to the limitations of experimental measurements. In this work, we investigate the insertion of the fusion peptide into an immune cell membrane mimic through multiscale molecular dynamics simulations. We mimic the native T-cell by constructing a 9-lipid asymmetric membrane, along with geometrical restraints accounting for insertion in the context of gp41. To account for the slow timescale of lipid mixing while enabling conformational changes, we implement a protocol to go back and forth between atomistic and coarse-grained simulations. Our study provides a molecular understanding of the interactions between the HIV-1 fusion peptide and the T-cell membrane, highlighting the importance of conformational flexibility of fusion peptides and local lipid reorganization in stabilizing the anchoring of gp41 into the targeted host membrane during the early events of HIV-1 cell entry. Importantly, we identify a motif within the fusion peptide critical for fusion that can be further manipulated in future immunological studies.

Mapping the dynamics of epigenetic adaptation in S. pombe during heterochromatin misregulation

Epigenetic mechanisms enable cells to develop novel adaptive phenotypes without altering their genetic blueprint. Recent studies show histone modifications, such as heterochromatin-defining H3K9 methylation (H3K9me), can be redistributed to establish adaptive phenotypes. We developed a precision-engineered genetic approach to trigger heterochromatin misregulation on-demand in fission yeast. This enabled us to trace genome-scale RNA and H3K9me changes over time in long-term, continuous cultures. Adaptive H3K9me establishes over remarkably slow timescales relative to the initiating stress. We captured dynamic H3K9me redistribution events which depend on an RNA binding complex MTREC, ultimately leading to cells converging on an optimal adaptive solution. Upon stress removal, cells relax to new transcriptional and chromatin states, establishing memory that is tunable and primed for future adaptive epigenetic responses. Collectively, we identify the slow kinetics of epigenetic adaptation that allow cells to discover and heritably encode novel adaptive solutions, with implications for drug resistance and response to infection.

Synchronization under saturable nonlinearity.

In this theoretical work, we introduce a nonlinear gain saturation law representative of the experimentally observed properties manifested by phenomena ranging from aeroacoustic shear layers in self-sustained cavity oscillations to flame heat release rate in thermoacoustic instabilities. Furthermore, this type of saturable gain may be relevant for a wider class of physical systems, such as active laser media in photonics. The nonlinearity discussed herein governs the fullscale behavior of a self-oscillator exhibiting linear loss under large amplitude perturbations, in contrast to the cubic damping and linear gain of the Van der Pol model. A distinctive characteristic of the proposed equation is the simple, well behaved gain term in the slow timescale dynamics.

A new class of efficient high order semi-Lagrangian IMEX discontinuous Galerkin methods on staggered unstructured meshes

In this paper we present a new high order semi-implicit discontinuous-Galerkin (DG) scheme on two-dimensional staggered triangular meshes applied to different nonlinear systems of hyperbolic conservation laws such as advection-diffusion models, incompressible Navier-Stokes equations and natural convection problems. While the temperature and pressure field are defined on a triangular main grid, the velocity field is defined on a quadrilateral edge-based staggered mesh. A semi-implicit time discretization is proposed, which separates slow and fast time scales by treating them explicitly and implicitly, respectively. The nonlinear convection terms are evolved explicitly using a semi-Lagrangian approach, whereas we consider an implicit discretization for the diffusion terms and the pressure contribution. High-order of accuracy in time is achieved using a new flexible and general framework of IMplicit-EXplicit (IMEX) Runge-Kutta schemes specifically designed to operate with semi-Lagrangian methods. To improve the efficiency in the computation of the DG divergence operator and the mass matrix, we propose to approximate the numerical solution with a less regular polynomial space on the edge-based mesh, which is defined on two sub-triangles that split the staggered quadrilateral elements. This allows for a fast computation of the DG operators and matrices without any need to store them for each mesh element. Due to the implicit treatment of the fast scale terms, the resulting numerical scheme is unconditionally stable for the considered governing equations because the semi-Lagrangian approach is the only explicit discretization for convection terms that does not need any stability restriction on the maximum admissible time step. Contrarily to a genuinely space-time discontinuous-Galerkin scheme, the IMEX discretization permits to preserve the symmetry and the positive semi-definiteness of the arising linear system for the pressure that can be solved at the aid of an efficient matrix-free implementation of the conjugate gradient method. We present several convergence results, including nonlinear transport and density currents, up to third order of accuracy in both space and time.

Anomaly detection in hydrological network time series via multiresolution analysis

The territorial extension of Brazil imposes logistic challenges on hydrologic monitoring and increases the chances of systematic observational errors, gauge displacements, downsampling during observation, and low density of streamflow samples on high water stage. Consequently, time series would exhibit artifacts such as gaps, high-frequency anomalies, inhomogeneity, and trends. An innovative anomaly detection system based on multiresolution analysis (MADE) was developed and used to detect synthetic anomalies in raw water stage time series. MADE uses both time and frequency as contextual attributes to identify anomalies. The balance between temporal and frequency resolution allows for capturing low-frequency coarse information and high-frequency details. On MADE, Generalized Extreme Studentized Deviate (GESD) detected short time anomalies on water stage wavelet faster modes (2-, 4-, and 8-days periods). For periods greater than 16 days, Wavelet Coherence and Multiple Wavelet Coherence detected similar water stage time series anomalies. MADE outperformed a Long Short-Term Memory model, a time regression neural network k-Nearest Neighbor model and an Empirical Data Analytics model coupled with clustering techniques on detecting both fast and slow time-scales synthetic anomalies introduced in a São Francisco River water stage time series, using time and frequency domain to pursuit point, collective and contextual anomalies.

Dynamic UAV Deployment Scheme Based on Edge Computing for Forest Fire Scenarios.

This study investigates the dynamic deployment of unmanned aerial vehicles (UAVs) using edge computing in a forest fire scenario. We consider the dynamically changing characteristics of forest fires and the corresponding varying resource requirements. Based on this, this paper models a two-timescale UAV dynamic deployment scheme by considering the dynamic changes in the number and position of UAVs. In the slow timescale, we use a gate recurrent unit (GRU) to predict the number of future users and determine the number of UAVs based on the resource requirements. UAVs with low energy are replaced accordingly. In the fast timescale, a deep-reinforcement-learning-based UAV position deployment algorithm is designed to enable the low-latency processing of computational tasks by adjusting the UAV positions in real time to meet the ground devices' computational demands. The simulation results demonstrate that the proposed scheme achieves better prediction accuracy. The number and position of UAVs can be adapted to resource demand changes and reduce task execution delays.

Probing conformational dynamics of DNA binding by CO-sensing transcription factor, CooA

The transcription factor CooA is a CRP/FNR (cAMP receptor protein/ fumarate and nitrate reductase) superfamily protein that uses heme to sense carbon monoxide (CO). Allosteric activation of CooA in response to CO binding is currently described as a series of discrete structural changes, without much consideration for the potential role of protein dynamics in the process of DNA binding. This work uses site-directed spin-label electron paramagnetic resonance spectroscopy (SDSL-EPR) to probe slow timescale (μs-ms) conformational dynamics of CooA with a redox-stable nitroxide spin label, and IR spectroscopy to probe the environment at the CO-bound heme. A series of cysteine substitution variants were created to selectively label CooA in key functional regions, the heme-binding domain, the 4/5-loop, the hinge region, and the DNA binding domain. The EPR spectra of labeled CooA variants are compared across three functional states: Fe(III) “locked off”, Fe(II)-CO “on”, and Fe(II)-CO bound to DNA. We observe changes in the multicomponent EPR spectra at each location; most notably in the hinge region and DNA binding domain, broadening the description of the CooA allosteric mechanism to include the role of protein dynamics in DNA binding. DNA-dependent changes in IR vibrational frequency and band broadening further suggest that there is conformational heterogeneity in the active WT protein and that DNA binding alters the environment of the heme-bound CO.

Explanation of flicker noise with the Bak-Tang-Wiesenfeld model of self-organized criticality.

With the original Bak-Tang-Wisenefeld (BTW) sandpile we uncover the 1/φ noise in the mechanism maintaining self-organized criticality (SOC)-the question raised together with the concept of SOC. The BTW sandpile and the phenomenon of SOC in general are built on the slow time scale at which the system is loaded and the fast time scale at which the stress is transported outward from overloaded locations. Exploring the dynamics of stress in the slow time in the BTW sandpile, we posit that it follows cycles of gradual stress accumulation that end up with an abrupt stress release and the drop of the system to subcritical state. As the system size grows, the intracycle dynamics exhibits the 1/φ-like spectrum that extends boundlessly and corresponds to the stress release within the critical state.

Color-switching in an optical parametric oscillator using a phase-conjugate mirror.

We construct a phase-conjugate resonator which passively produces stable pulses that alternate between the probe and the conjugate colors. The requisite phase-conjugate mirror inside the resonator is constructed using non-degenerate four-wave mixing (4WM) in rubidium vapor. The glancing-angle phase-conjugate mirror is a 100% output coupler, and therefore this resonator is unusual in that no light circulates the cavity more than once. Without the gain of the phase-conjugate mirror, the cavity boundary conditions, and thus resonant modes, are not defined and therefore can be tuned by the pump. The output of the optical parametric oscillator that is formed above threshold can passively mode-lock. The phase-conjugate mirror removes thermal or acoustic instabilities that are on a MHz or slower timescale. This work provides a new method for stable pulsing using phase-conjugate optics, and suggests a platform for producing mode-locked pulses with squeezed light, as the 4WM process has already demonstrated quantum correlations.

Reversible kink instability drives ultrafast jumping in nematodes and soft robots.

Entomopathogenic nematodes (EPNs) exhibit a bending-elastic instability, or kink, before becoming airborne, a feature hypothesized but not proven to enhance jumping performance. Here, we provide the evidence that this kink is crucial for improving launch performance. We demonstrate that EPNs actively modulate their aspect ratio, forming a liquid-latched closed loop over a slow timescale O (1 s), then rapidly open it O (10 µs), achieving heights of 20 body lengths (BL) and generating ∼ 10 4 W/Kg of power. Using jumping nematodes, a bio-inspired Soft Jumping Model (SoftJM), and computational simulations, we explore the mechanisms and implications of this kink. EPNs control their takeoff direction by adjusting their head position and center of mass, a mechanism verified through phase maps of jump directions in simulations and SoftJM experiments. Our findings reveal that the reversible kink instability at the point of highest curvature on the ventral side enhances energy storage using the nematode's limited muscular force. We investigated the impact of aspect ratio on kink instability and jumping performance using SoftJM, and quantified EPN cuticle stiffness with AFM, comparing it with C. elegans . This led to a stiffness-modified SoftJM design with a carbon fiber backbone, achieving jumps of ∼25 BL. Our study reveals how harnessing kink instabilities, a typical failure mode, enables bidirectional jumps in soft robots on complex substrates like sand, offering a novel approach for designing limbless robots for controlled jumping, locomotion, and even planetary exploration.

Recurrent chaotic clustering and slow chaos in adaptive networks.

Adaptive dynamical networks are network systems in which the structure co-evolves and interacts with the dynamical state of the nodes. We study an adaptive dynamical network in which the structure changes on a slower time scale relative to the fast dynamics of the nodes. We identify a phenomenon we refer to as recurrent adaptive chaotic clustering (RACC), in which chaos is observed on a slow time scale, while the fast time scale exhibits regular dynamics. Such slow chaos is further characterized by long (relative to the fast time scale) regimes of frequency clusters or frequency-synchronized dynamics, interrupted by fast jumps between these regimes. We also determine parameter values where the time intervals between jumps are chaotic and show that such a state is robust to changes in parameters and initial conditions.

Phase synchronization between culture and climate forcing.

Over the history of humankind, cultural innovations have helped improve survival and adaptation to environmental stress. This has led to an overall increase in human population size, which in turn further contributed to cumulative cultural learning. During the Anthropocene, or arguably even earlier, this positive sociodemographic feedback has caused a strong decline in important resources that, coupled with projected future transgression of planetary boundaries, may potentially reverse the long-term trend in population growth. Here, we present a simple consumer/resource model that captures the coupled dynamics of stochastic cultural learning and transmission, population growth and resource depletion in a changing environment. The idealized stochastic mathematical model simulates boom/bust cycles between low-population subsistence, high-density resource exploitation and subsequent population decline. For slow resource recovery time scales and in the absence of climate forcing, the model predicts a long-term global population collapse. Including a simplified periodic climate forcing, we find that cultural innovation and population growth can couple with climatic forcing via nonlinear phase synchronization. We discuss the relevance of this finding in the context of cultural innovation, the anthropological record and long-term future resilience of our own predatory species.