Subthreshold Activities Research Articles

Pixel-wise programmability enables dynamic high-SNR cameras for high-speed microscopy.

High-speed wide-field fluorescence microscopy has the potential to capture biological processes with exceptional spatiotemporal resolution. However, conventional cameras suffer from low signal-to-noise ratio at high frame rates, limiting their ability to detect faint fluorescent events. Here, we introduce an image sensor where each pixel has individually programmable sampling speed and phase, so that pixels can be arranged to simultaneously sample at high speed with a high signal-to-noise ratio. In high-speed voltage imaging experiments, our image sensor significantly increases the output signal-to-noise ratio compared to a low-noise scientific CMOS camera (~2-3 folds). This signal-to-noise ratio gain enables the detection of weak neuronal action potentials and subthreshold activities missed by the standard scientific CMOS cameras. Our camera with flexible pixel exposure configurations offers versatile sampling strategies to improve signal quality in various experimental conditions.

Designing around NATO’s deterrence: Russia’s Nordic information confrontation strategy

ABSTRACT This article examines Russia’s evolving information confrontation strategy in the Nordic region between 2022–2023. It assesses Russia’s approaches toward NATO members Norway, new member Finland, and prospective member Sweden. Despite decreased regional influence, the article finds that Russia persists with sub-threshold information confrontation tactics to bypass NATO deterrence. The strategy aims to shape NATO’s presence, undermine Western cohesion, and reduce support for Ukraine. These sub-threshold activities underscore the coercive utility of Russia’s information confrontation strategy in Russian strategic thinking. As tensions escalate due to the Ukraine conflict, Moscow will continue seeking to influence domestic debates in Nordic and European countries.

Bright and sensitive red voltage indicators for imaging action potentials in brain slices and pancreatic islets.

Genetically encoded voltage indicators (GEVIs) allow the direct visualization of cellular membrane potential at the millisecond time scale. Among these, red-emitting GEVIs have been reported to support multichannel recordings and manipulation of cellular activities with reduced autofluorescence background. However, the limited sensitivity and dimness of existing red GEVIs have restricted their applications in neuroscience. Here, we report a pair of red-shifted opsin-based GEVIs, Cepheid1b and Cepheid1s, with improved dynamic range, brightness, and photostability. The improved dynamic range is achieved by a rational design to raise the electrochromic Förster resonance energy transfer efficiency, and the higher brightness and photostability are approached with separately engineered red fluorescent proteins. With Cepheid1 indicators, we recorded complex firings and subthreshold activities of neurons on acute brain slices and observed heterogeneity in the voltage‑calcium coupling on pancreatic islets. Overall, Cepheid1 indicators provide a strong tool to investigate excitable cells in various sophisticated biological systems.

Effects of logic glitch and (area-power dissipation) leakage on cryptosystems using clock gating technique to enhance web etiquette

The last century has seen an evolution in technology that has improved communication systems and, in general, made life easier for people. Our communication systems have become faster and more dependable as a result of the explosion of gadgets and services. But, these upgrades come at a price. The power consumption is one of the most worrying costs. In recent years, the solution involved installing larger, more powerful batteries—so long as doing so did not limit mobility. Today's economic and environmental problems compel us to consider alternative solutions, like methods for lowering the power consumption of digital devices. This study focuses on using digital circuits, which promise to deliver good energy efficiency and desirable performance at very low voltage savings. Certain digital switches are allegedly redundant and not required for the circuit to function properly, yet they continue to use energy. So, one of the primary issues for low power design is reducing such redundant switches. Subthreshold conduction in digital circuits is typically seen as a “parasitic” leakage in a condition where there should ideally be no conduction. Sub-threshold activities thereby reduce the problem of lowering power consumption, but do so at the expense of system throughput deterioration, fluctuations in system stability and functionality, temperature variations, and most critically, design space utilization. In order to minimize some of these redundant switches and to make circuits more energy-efficient while maintaining functionality, this study suggests two novel techniques. It uses an optimization method based on threshold voltage change to reduce glitch power. A glitch-free circuit netlist is created using an algorithm, while still maintaining the requisite delay performance. Using this approach results in a 6.14% overall reduction in energy consumption.

Studying Moscow’s Coercive Campaign Against Norway

Norway’s geopolitical position as both a neighbour of Russia and a member of NATO places it at the forefront of Moscow’s self-assertive and aggressive foreign and security policy. However, Norway’s NATO membership reduces Russia’s room for manoeuvre to actions below the threshold of armed conflict. In this article, Runar Spansvoll examines how Russia has made use of such aggressive and coercive sub-threshold activities in the political, information and military domains between 2014–23 in a campaign to compel Oslo to comply with its foreign and security policy objectives.◼

Uncovering the organization of neural circuits with Generalized Phase Locking Analysis.

Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings.

Discrete scaling and criticality in a chain of adaptive excitable integrators

We describe a chain of unidirectionally coupled adaptive excitable elements slowly driven by a stochastic process from one end and open at the other end, as a minimal toy model of unresolved irreducible uncertainty in a system performing inference through a hierarchical model. Threshold potentials adapt slowly to ensure sensitivity without being wasteful. Activity and energy are released as intermittent avalanches of pulses with a discrete scaling distribution largely independent of the exogenous input form. Subthreshold activities and threshold potentials exhibit Lorentzian temporal spectra, with a power-law range determined by position in the chain. Subthreshold bistability closely resembles empirical measurements of intracellular membrane potential. We suggest that critical cortical cascades emerge from a trade-off between metabolic power consumption and performance requirements in a critical world, and that the temporal scaling patterns of brain electrophysiological recordings ensue from weighted linear combinations of subthreshold activities and pulses from different hierarchy levels.

Nonlinear computational models of dynamical coding patterns in depression and normal rats: from electrophysiology to energy consumption

Major depressive disorder (MDD) is one of the most serious neuropsychiatric disorders. Exploring the pathogenesis and dynamical coding patterns of MDD can provide new targets for clinical drug treatment and new ideas for the research of other neuropsychiatric and neurodegenerative diseases. We selected the medium spiny neuron (MSN) of nucleus accumbens (NAc) as the research objective. NAc is located in the dopaminergic pathway, regulating rewards, emotions and other behaviors. Abnormalities in these behaviors are considered as the main clinical symptoms of MDD. We simulated the different spike patterns of MSNs in MDD group and control group by dynamical Hodgkin–Huxley model. The simulated results can match the electrophysiological experiments, which occurred due to following reasons: (1) The external stimulus current of MDD group was amplified by the local neural microcircuit; (2) the selective permeability to sodium was abnormally decreased; and (3) the dopamine D2 receptor signaling pathway was abnormal in the MDD group. Furthermore, we proposed a dynamical energy model, and the energy results demonstrated that the energy cost in MDD group was lower, which led to persistent depression in patients with MDD. Simultaneously, the negative-to-total energy ratio of MSN in MDD group was higher than that in control group, and the delay time of the power peak and the potential peak in MDD group was shorter than that in the control group. The results showed that the abnormal firing patterns were the direct cause of abnormal behaviors of MDD and indicated that subthreshold activities of MDD group were more intense.

The Design of a CMOS Nanoelectrode Array with 4096 Current-Clamp/Voltage-Clamp Amplifiers for Intracellular Recording/Stimulation of Mammalian Neurons.

CMOS microelectrode arrays (MEAs) can record electrophysiological activities of a large number of neurons in parallel but only extracellularly with low signal-to-noise ratio. Patch clamp electrodes can perform intracellular recording with high signal-to-noise ratio but only from a few neurons in parallel. Recently we have developed and reported a neuroelectronic interface that combines the parallelism of the CMOS MEA and the intracellular sensitivity of the patch clamp. Here, we report the design and characterization of the CMOS integrated circuit (IC), a critical component of the neuroelectronic interface. Fabricated in 0.18-μm technology, the IC features an array of 4,096 platinum black (PtB) nanoelectrodes spaced at a 20 μm pitch on its surface and contains 4,096 active pixel circuits. Each active pixel circuit, consisting of a new switched-capacitor current injector--capable of injecting from ±15 pA to ±0.7 μA with a 5 pA resolution--and an operational amplifier, is highly configurable. When configured into current-clamp mode, the pixel intracellularly records membrane potentials including subthreshold activities with ∼23 μVrms input referred noise while injecting a current for simultaneous stimulation. When configured into voltage-clamp mode, the pixel becomes a switched-capacitor transimpedance amplifier with ∼1 pArms input referred noise, and intracellularly records ion channel currents while applying a voltage for simultaneous stimulation. Such voltage/current-clamp intracellular recording/stimulation is a feat only previously possible with the patch clamp method. At the same time, as an array, the IC overcomes the lack of parallelism of the patch clamp method, measuring thousands of mammalian neurons in parallel, with full-frame intracellular recording/stimulation at 9.4 kHz.

Near-Infrared Voltage Nanosensors Enable Real-Time Imaging of Neuronal Activities in Mice and Zebrafish.

Optical voltage sensors with the ability to monitor neuronal activities are invaluable tools for studying information processing of the brain. However, the current genetically encoded voltage indicators usually require high-power visible light for excitation and are limited to genetically addressable model animals. Here, we report a near-infrared (NIR)-excited nongenetic voltage nanosensor that achieves stable recording of neuronal membrane potential in intact animals. The nanosensor is composed of a Förster resonance energy transfer (FRET) pair, the outer membrane-anchored upconversion nanoparticle (UCNP), and the membrane-embedded dipicrylamine (DPA). The negative charge of DPA allows membrane potential fluctuation to affect the distance between the DPA and UCNP, therefore changing the FRET efficiency. Consequently, the emission intensity of the nanosensor can report the membrane potential. Using the nanosensor, we monitor not only electrically evoked changes in the membrane potential of cultured cells but also sensory responses of neurons in intact zebrafish and brain state-modulated subthreshold activities of cortical neurons in intact mice.

Imaging Neuronal Activity with Fast and Sensitive Red-Shifted Electrochromic FRET Indicators.

Genetically encoded voltage indicators (GEVIs) allow optical recording of neuronal activities with high spatial resolution. While most existing GEVIs emit in the green range, red-shifted GEVIs are highly sought after because they would enable simultaneous stimulation and recording of neuronal activities when paired with optogenetic actuators, or two-color imaging of signaling and neuronal activities when used along with GFP-based indicators. In this study, we present several improved red-shifted GEVIs based on the electrochromic Förster resonance energy transfer (eFRET) between orange/red fluorescent proteins/dyes and rhodopsin mutants. Through structure-guided mutagenesis and cell-based sensitivity screening, we identified a mutant rhodopsin with a single mutation that exhibited more than 2-fold improvement in voltage sensitivity. Notably, this mutation has been independently discovered by Pieribone et al. ( Pieribone, V. A. et al. Nat Methods 2018 , 15 ( 12 ), 1108 - 1116 ). In cultured rat hippocampal neurons, our sensors faithfully reported action potential waveforms and subthreshold activities. We also demonstrated that this mutation could enhance the sensitivity of hybrid indicators, thus providing insights for future development.

Excitation wavelength optimization improves photostability of ASAP-family GEVIs

Recent interest in high-throughput recording of neuronal activity has motivated rapid improvements in genetically encoded calcium or voltage indicators (GECIs or GEVIs) for all-optical electrophysiology. Among these probes, the ASAPs, a series of voltage indicators based on a variant of circularly permuted green fluorescent protein (cpGFP) and a conjugated voltage sensitive domain (VSD), are capable of detecting both action potentials and subthreshold neuronal activities. Here we show that the ASAPs, when excited by blue light, undergo reversible photobleaching. We find that this fluorescence loss induced by excitation with 470-nm light can be substantially reversed by low-intensity 405-nm light. We demonstrate that 405-nm and 470-nm co-illumination significantly improved brightness and thereby signal-to-noise ratios during voltage imaging compared to 470-nm illumination alone. Illumination with a single wavelength of 440-nm light also produced similar improvements. We hypothesize that reversible photobleaching is related to cis-trans isomerization and protonation of the GFP chromophore of ASAP proteins. Amino acids that influence chromophore isomerization are potential targets of point mutations for future improvements.

Mixed-mode oscillations in pyramidal neurons under antiepileptic drug conditions.

Subthreshold oscillations in combination with large-amplitude oscillations generate mixed-mode oscillations (MMOs), which mediate various spatial and temporal cognition and memory processes and behavioral motor tasks. Although many studies have shown that canard theory is a reliable method to investigate the properties underlying the MMOs phenomena, the relationship between the results obtained by applying canard theory and conductance-based models of neurons and their electrophysiological mechanisms are still not well understood. The goal of this study was to apply canard theory to the conductance-based model of pyramidal neurons in layer V of the Entorhinal Cortex to investigate the properties of MMOs under antiepileptic drug conditions (i.e., when persistent sodium current is inhibited). We investigated not only the mathematical properties of MMOs in these neurons, but also the electrophysiological mechanisms that shape spike clustering. Our results show that pyramidal neurons can display two types of MMOs and the magnitude of the slow potassium current determines whether MMOs of type I or type II would emerge. Our results also indicate that slow potassium currents with large time constant have significant impact on generating the MMOs, as opposed to fast inward currents. Our results provide complete characterization of the subthreshold activities in MMOs in pyramidal neurons and provide explanation to experimental studies that showed MMOs of type I or type II in pyramidal neurons under antiepileptic drug conditions.

Neural Energy Supply-Consumption Properties Based on Hodgkin-Huxley Model.

Electrical activity is the foundation of the neural system. Coding theories that describe neural electrical activity by the roles of action potential timing or frequency have been thoroughly studied. However, an alternative method to study coding questions is the energy method, which is more global and economical. In this study, we clearly defined and calculated neural energy supply and consumption based on the Hodgkin-Huxley model, during firing action potentials and subthreshold activities using ion-counting and power-integral model. Furthermore, we analyzed energy properties of each ion channel and found that, under the two circumstances, power synchronization of ion channels and energy utilization ratio have significant differences. This is particularly true of the energy utilization ratio, which can rise to above 100% during subthreshold activity, revealing an overdraft property of energy use. These findings demonstrate the distinct status of the energy properties during neuronal firings and subthreshold activities. Meanwhile, after introducing a synapse energy model, this research can be generalized to energy calculation of a neural network. This is potentially important for understanding the relationship between dynamical network activities and cognitive behaviors.

Modeling interneuron-specific (IS) interneurons in hippocampus

The hippocampus and cortex have a large diversity in inhibitory interneuron types. These local interneurons exert inhibitory control over neuronal populations in the hippocampus [1]. Although much is known about how hippocampal inhibitory interneurons exert control over pyramidal cells and synchronize local network activity, less is known about how the activity of these interneurons are controlled themselves. Moreover, the existence of interneuron-specific (IS) interneurons is known and information about how these IS interneurons exert their influence is accumulating [2]. In particular, interneuron-specific 3 (IS3) cells are being characterized and they have been shown to primarily synapse onto other interneuron dendrites with the ability to control their firing patterns. Morphological and synaptic aspects are being examined, but what type, how much and where voltage-gated channels are present on IS3 has not been determined. As other hippocampal interneuron types are known to have high densities of voltage-gated channels on their dendrites [3,4], it seems likely that this could be the case for IS3 cells also. Determining and understanding particular characteristics of particular cell types is a highly challenging endeavour using purely experimental means. Thus, we have begun development of IS3 computational cell models to help address this challenge. Using the NEURON software environment [5], we have reconstructed IS3 cell morphologies and built multi-compartment models from them in which appropriate passive properties were obtained. Further, we were able to match several characteristics of representative IS3 cell firings (spike amplitude, spike threshold, rheobase) using four somatically located voltage-gated channel types (sodium current (INa), slow delayed rectifier potassium current (IKdrs), fast delayed rectifier potassium current (IKdrf) and A-type potassium current (IKa). Preliminary data from IS3 cells indicate that they express intrinsic, subthreshold activities similar to other hippocampal interneuron types [6], and previous models captured this aspect with the incorporation of additive white noise to represent stochastic gating characteristics [7]. Similarly here, to capture these aspects, we somatically injected white noise current into our models and found that output similar to experimental data was observed. Given the present correspondence with data, our models already make predictions about channel types and balances found in IS3 cells. Thus our present multi-compartment IS3 models represent a solid basis for determining and understanding the biophysical contributions for IS3 cell firings and their ability to control inhibitory cells and functionally contribute to the generation of hippocampal oscillations.

Fluorescent Protein Voltage Probes Derived from ArcLight that Respond to Membrane Voltage Changes with Fast Kinetics

We previously reported the discovery of a fluorescent protein voltage probe, ArcLight, and its derivatives that exhibit large changes in fluorescence intensity in response to changes of plasma membrane voltage. ArcLight allows the reliable detection of single action potentials and sub-threshold activities in individual neurons and dendrites. The response kinetics of ArcLight (τ1-on ~10 ms, τ2-on ~ 50 ms) are comparable with most published genetically-encoded voltage probes. However, probes using voltage-sensing domains other than that from the Ciona intestinalis voltage sensitive phosphatase exhibit faster kinetics. Here we report new versions of ArcLight, in which the Ciona voltage-sensing domain was replaced with those from chicken, zebrafish, frog, mouse or human. We found that the chicken and zebrafish-based ArcLight exhibit faster kinetics, with a time constant (τ) less than 6ms for a 100 mV depolarization. Although the response amplitude of these two probes (8-9%) is not as large as the Ciona-based ArcLight (~35%), they are better at reporting action potentials from cultured neurons at higher frequency. In contrast, probes based on frog, mouse and human voltage sensing domains were either slower than the Ciona-based ArcLight or had very small signals.

Fluctuating Inhibitory Inputs Promote Reliable Spiking at Theta Frequencies in Hippocampal Interneurons

Theta-frequency (4–12 Hz) rhythms in the hippocampus play important roles in learning and memory. CA1 interneurons located at the stratum lacunosum-moleculare and radiatum junction (LM/RAD) are thought to contribute to hippocampal theta population activities by rhythmically pacing pyramidal cells with inhibitory postsynaptic potentials. This implies that LM/RAD cells need to fire reliably at theta frequencies in vivo. To determine whether this could occur, we use biophysically based LM/RAD model cells and apply different cholinergic and synaptic inputs to simulate in vivo-like network environments. We assess spike reliabilities and spiking frequencies, identifying biophysical properties and network conditions that best promote reliable theta spiking. We find that synaptic background activities that feature large inhibitory, but not excitatory, fluctuations are essential. This suggests that strong inhibitory input to these cells is vital for them to be able to contribute to population theta activities. Furthermore, we find that Type I-like oscillator models produced by augmented persistent sodium currents (INaP) or diminished A-type potassium currents (IA) enhance reliable spiking at lower theta frequencies. These Type I-like models are also the most responsive to large inhibitory fluctuations and can fire more reliably under such conditions. In previous work, we showed that INaP and IA are largely responsible for establishing LM/RAD cells’ subthreshold activities. Taken together with this study, we see that while both these currents are important for subthreshold theta fluctuations and reliable theta spiking, they contribute in different ways – INaP to reliable theta spiking and subthreshold activity generation, and IA to subthreshold activities at theta frequencies. This suggests that linking subthreshold and suprathreshold activities should be done with consideration of both in vivo contexts and biophysical specifics.

Loss of olfactory cell adhesion molecule reduces the synchrony of mitral cell activity in olfactory glomeruli

Odours generate activity in olfactory receptor neurons, whose axons contact the dendritic tufts of mitral cells within olfactory bulb glomeruli. These axodendritic synapses are anatomically separated from dendrodendritic synapses within each glomerulus. Mitral cells within a glomerulus show highly synchronized activity as assessed with whole-cell recording from pairs of mitral cells. We examined glomerular activity in mice lacking the olfactory cell adhesion molecule (OCAM). Glomeruli in mice lacking OCAM show a redistribution of synaptic subcompartments, but the total area occupied by axonal inputs was similar to wild-type mice. Stimulation of olfactory nerve bundles showed that excitatory synaptic input to mitral cells as well as dendrodendritic inhibition was unaffected in the knockout. However, correlated spiking in mitral cells was significantly reduced, as was electrical coupling between apical dendrites. To analyse slow network dynamics we induced slow oscillations with a glutamate uptake blocker. Evoked and spontaneous slow oscillations in mitral cells and external tufted cells were broader and had multiple peaks in OCAM knockout mice, indicating that synchrony of slow glomerular activity was also reduced. To assess the degree of shared activity between mitral cells under physiological conditions, we analysed spontaneous sub-threshold voltage oscillations using coherence analysis. Coherent activity was markedly reduced in cells from OCAM knockout mice across a broad range of frequencies consistent with a decrease in tightly time-locked activity. We suggest that synchronous activity within each glomerulus is dependent on segregation of synaptic subcompartments.

Nonlinear Dynamic Modeling of Synaptically Driven Single Hippocampal Neuron Intracellular Activity

A high-order nonlinear dynamic model of the input-output properties of single hippocampal CA1 pyramidal neurons was developed based on synaptically driven intracellular activity. The purpose of this study is to construct a model that: 1) can capture the nonlinear dynamics of both subthreshold activities [postsynaptic potentials (PSPs)] and suprathreshold activities (action potentials) in a single formalism; 2) is sufficiently general to be applied to any spike-input and spike-output neurons (point process input and point process output neural systems); and 3) is computationally efficient. The model consisted of three major components: 1) feedforward kernels (up to third order) that transform presynaptic action potentials into PSPs; 2) a constant threshold, above which action potentials are generated; and 3) a feedback kernel (first order) that describes spike-triggered after-potentials. The model was applied to CA1 pyramidal cells, as they were electrically stimulated with broadband Poisson random impulse trains through the Schaffer collaterals. The random impulse trains used here have physiological properties similar to spiking patterns observed in CA3 hippocampal neurons. PSPs and action potentials were recorded from the soma of CA1 pyramidal neurons using whole-cell patch-clamp recording. We evaluated the model performance separately with respect to PSP waveforms and the occurrence of spikes. The average normalized mean square error of PSP prediction is 14.4%. The average spike prediction error rate is 18.8%. In summary, although prediction errors still could be reduced, the model successfully captures the majority of high-order nonlinear dynamics of the single-neuron intracellular activity. The model captures the general biophysical processes with a small set of open parameters that are directly constrained by the intracellular recording, and thus, can be easily applied to any spike-input and spike-output neuron.

In vivo mouse inferior olive neurons exhibit heterogeneous subthreshold oscillations and spiking patterns

In vitro whole-cell recordings of the inferior olive have demonstrated that its neurons are electrotonically coupled and have a tendency to oscillate. However, it remains to be shown to what extent subthreshold oscillations do indeed occur in the inferior olive in vivo and whether its spatiotemporal firing pattern may be dynamically generated by including or excluding different types of oscillatory neurons. Here, we did whole-cell recordings of olivary neurons in vivo to investigate the relation between their subthreshold activities and their spiking behavior in an intact brain. The vast majority of neurons (85%) showed subthreshold oscillatory activities. The frequencies of these subthreshold oscillations were used to distinguish four main olivary subtypes by statistical means. Type I showed both sinusoidal subthreshold oscillations (SSTOs) and low-threshold Ca(2+) oscillations (LTOs) (16%); type II showed only sinusoidal subthreshold oscillations (13%); type III showed only low-threshold Ca(2+) oscillations (56%); and type IV did not reveal any subthreshold oscillations (15%). These subthreshold oscillation frequencies were strongly correlated with the frequencies of preferred spiking. The frequency characteristics of the subthreshold oscillations and spiking behavior of virtually all olivary neurons were stable throughout the recordings. However, the occurrence of spontaneous or evoked action potentials modified the subthreshold oscillation by resetting the phase of its peak toward 90 degrees . Together, these findings indicate that the inferior olive in intact mammals offers a rich repertoire of different neurons with relatively stable frequency settings, which can be used to generate and reset temporal firing patterns in a dynamically coupled ensemble.