Source-linked AI summary
Dynamic effective connectivity of inter-areal brain circuits
Demian Battaglia, Annette Witt, Fred Wolf, Theo Geisel
TL;DR
The paper asks how effective connectivity can rapidly reconfigure when anatomical connections remain fixed. Using model cortical circuits and causal and information-theoretic analyses, it shows that dynamical states generate distinct effective networks and reconfigurable information-routing pathways.
Problem
It remains unclear how effective connectivity can rapidly reconfigure among brain areas when their underlying structural connectivity is fixed.
Method
The study models interacting cortical areas and analyzes simulated neural-activity time series using transfer entropy and mutual information.
Results
Different dynamical states and phase-locking patterns produce distinct effective connectivity motifs and alternative information-routing modalities within the same structural network.
Takeaways & Limitations
Self-organized interactions between brain rhythms can support reconfigurable, on-demand routing of spike-pattern information across fixed anatomical connections.
Takeaways & Limitations
The theory does not yet address control of effective connectivity across multiple frequency bands.
Abstract
from arXiv · showhide
Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity, related to the more elusive question "Which areas cause the present activity of which others?". Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that a dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal [...] Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer [...] Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this "communication-through-coherence", making thus possible a fast "on-demand" reconfiguration of global information routing modalities.
Author Summary
The study examines how brain states can be flexibly controlled despite fixed anatomic inter-areal connections. It shows that effective connectivity and information flow vary with the dynamical state of a shared structural network.
- Motivation: The study distinguishes structural connectivity, which describes actual synaptic connections, from effective connectivity, which quantifies directed causal influences beyond correlation.This distinction motivates examining how fixed anatomic connections can support flexible brain states.
- Approach: Effective connectivity is measured from time-series of neural activity generated by model inter-areal circuits.The analysis uses modeled neural activity to infer directed causal interactions.
- Findings: Different effective networks correspond to different dynamical states of the same structural network, particularly different phase-locking patterns between local neuronal oscillations.The central conclusion is summarized as “causality follows dynamics.”
- Findings: Information flow follows effective causality and therefore also follows the underlying dynamics.The study summarizes this relationship as “information follows causality.”
Introduction
The paper argues that effective connectivity can rapidly reconfigure despite fixed structural connections, emerging from multistable, phase-locked brain rhythms. It further proposes that rhythm dynamics enable self-organized, reconfigurable routing of spiking information between areas.
- Effective connectivity must flexibly change on timescales faster than synaptic changes, even when underlying structural connectivity remains fixed.
- Dynamic effective connectivity emerges from self-organized brain rhythmic activity, enabling reconfigurable routing of information through interacting rhythms.
- Different dynamical states of one structural motif produce distinct effective connectivity motifs through different phase-locking patterns of coherent gamma oscillations.The study’s transfer-entropy analysis captures the simulated multistable dynamics and associated causal motifs.
- Brief perturbations timed to ongoing rhythms can reliably induce effective-connectivity transitions through nonlinear phase-response properties.This mechanism is described as faster than neuromodulation and more metabolically efficient than coordinated synaptic plasticity.
- Mutual-information analysis evaluates how much information encoded in local spiking activity is transferred to distant interconnected areas.The framework treats oscillations as carriers of data packets associated with spike patterns of synchronously active cell assemblies.
Results
Across spiking-network and rate-model analyses, symmetric structural motifs generated distinct effective-connectivity regimes as inter-areal coupling changed. Spontaneous symmetry breaking enabled directional, switchable information routing, whereas stronger coupling restored dynamical symmetry and eliminated effective anisotropy.
- Effective motif families: Weak coupling produced periodic, out-of-phase rhythms with a statistically identifiable leader area driving laggard areas.The leader’s oscillations led in phase over those of laggard areas.
- Effective motif families: Intermediate coupling disrupted periodicity through correlated fluctuations, leaving approximate out-of-phase locking and more irregular laggard rhythms.Cycle amplitudes and durations fluctuated strongly, while the leader remained comparatively more regular.
- Effective motif families: Stronger coupling made all rhythms similarly irregular, causing leadership to exchange continually rather than stabilizing into a persistent direction.Leader areas could still appear during brief transients, but these did not produce stable dynamic behavior.
- Symmetry breaking and switching: Spontaneous symmetry breaking converted symmetric structural connectivity into asymmetric causal influence, and phase perturbations could switch the system within a few oscillation cycles to another effective motif.Successful switching depended on the perturbation phase interval; noise-induced transitions in the network model typically occurred on time-scales of the order of seconds.
- Symmetry breaking and switching: When inter-areal coupling became sufficiently strong, dynamical symmetry was restored, eliminating effective driving and the emergent anisotropy needed for dynamic connectivity control.This transition corresponded to the mutual-driving family of effective motifs.
- Information transmission: Spiking patterns were treated as a higher-information communication substrate than stereotyped rate fluctuations, with a single neuron conveying H ≃0.7 bits per oscillation cycle on average.Transmission efficiency was assessed using Mutual Information between digitized spike trains and normalized by source entropy H.
Discussion
The discussion shows that one structural motif can support multiple, dynamically switchable effective-connectivity motifs, while rhythmic self-organization regulates causal directionality and information routing. It also establishes robustness and methodological limits of TE-based analyses, alongside possible control mechanisms and extensions.
- A single structural motif can generate multiple effective motifs, with dynamic multistability enabling switching within a family without structural change.Transitions between different motif families require changing inter-areal coupling delays, although the structural topology can remain unchanged.
- Effective connectivity may be controlled by phased perturbations, with oscillation cycles providing distinct functional windows for identical interventions.Noise-driven switching may also occur spontaneously, while exogenous sensory-driven and endogenous cognitive-driven signals can trigger on-demand transitions.
- Although absolute TE depends on signal quantization and time-lag, the resulting effective-motif topology remains stable across the broad parameter range tested.TE peaks at time-lags associated with inter-area oscillation latencies, and directional asymmetries persist under the significance analyses described.
- Spontaneous symmetry breaking can create dominant causal directionality between reciprocally coupled areas, while coherence reorganization adjusts inter-areal interaction modes.The authors note that other mechanisms may generate dynamic effective connectivity in activity regimes differing from the model’s symmetry-breaking regime.
- TE-based effective connectivity and spike-based mutual information jointly link control of causal interactions to communication-through-coherence.Suitable inter-areal phase relations can transmit detailed spiking correlations rather than only population firing-rate fluctuations.
Methods
The study combines spiking-neuron and rate-unit models of reciprocally connected cortical areas with phase-based analysis and symbolic transfer entropy to characterize dynamics and causal influences. Methods include perturbation-based phase-response measurements, phase-locking predictions, and information-theoretic estimation with parameter-sensitivity and bias limitations.
- Model construction: Each cortical area is modeled either as a random network of 4,000 excitatory and 4,000 inhibitory Wang–Buzsáki neurons or as a single rate unit.The spiking model includes conductance-based AMPA and GABAA synapses, noisy external drive, and recurrent interactions.
- Connectivity motifs: Structural motifs use random local connections and excitatory long-range projections, while the rate model focuses on fully symmetric motifs of N mutually connected areas.For information-transfer simulations, stronger long-range synapses form directed transmission lines between randomly selected source and target sub-populations.
- Phase and perturbation analysis: Oscillation phase is linearly interpolated between successive maxima, allowing phase estimates to adapt elastically to fluctuations in cycle duration.Phase shifts are measured using analytically evaluated rate-model PRCs or directly simulated perturbations in the network model.
- Phase and perturbation analysis: For network models, perturbation responses are sampled at 100 phases and averaged over 100 different cycles to estimate phase-shift curves and confidence intervals.The qualitative perturbation-phase location of the maximum is relatively insensitive to perturbation strength, although its amplitude changes.
- Phase locking and causal analysis: Stable phase-locked states are predicted from top-down zero-crossings of phase-interaction functionals, including approximations that identify in-phase, anti-phase, or out-of-phase locking.Causal influences are estimated from symbolic transition-probability matrices and transfer entropy, whose relative strengths remain qualitatively stable across broad parameter ranges despite lag, binning, and finite-sampling effects.
Figure Legends
The figure illustrates dynamics in two interacting areas using LFPs, representative spike trains, and matching rate traces, with associated effective connectivity reported alongside. Other parameters match those used in Figures 3–5.
- Figure illustration: N = 2 interacting areas are illustrated with green and orange signals in the network model.The figure shows LFPs and representative spike trains from the network model.
- Figure illustration: Matching rate traces from the rate model accompany the network-model LFPs and spike trains.The rate traces use arbitrary time units.
- Figure illustration: The figure reports the associated effective connectivity, while other parameters match analyses of Figures 3, 4 and 5.The network-model scale bars are 20 ms horizontally and 20 mV vertically.
Supporting Information Legends
The supporting information documents phase reduction, perturbation-based switching, transmission-line tests, mutual-information scaling, and complete model descriptions. These analyses clarify how effective connectivity is measured, controlled, and compared across model variants.
- Phase reduction and phase response: Oscillating neural time series are represented by an interpolated instantaneous phase, and pulse currents produce shifts in the ongoing oscillation phase.Supporting Figure S1 illustrates phase interpolation for generally unequal oscillation cycles and the phase shift induced by δI.
- Dynamic control of effective connectivity: Successful switching is evaluated across pulse phases, with predicted intervals shown for unidirectional and leaky effective-driving motifs in rate and network models.The perturbations use h = 0.2I for the rate model and h = 500 pA for the network model.
- Transmission lines: Embedding unidirectional transmission lines in a fully symmetric two-area structural motif does not alter the overall effective connectivity.The transmission-line synapses are strengthened by multiplying ordinary excitatory peak conductance by KTL.
- Mutual-information scaling: Mutual information normalized by entropy is assessed against inverse data fraction, with reduced-length spike trains averaged and asymptotic values extrapolated quadratically.The source spike trains span 3 min at q = 1, and error bars represent standard error.
- Model documentation: The supporting text provides full model parameters and complete analytic expressions covering neurons, synapses, background noise, rate-model phase response, and phase-locking.These topics are organized into five sections in Supporting Text S1.
Supporting Text S1 · Model neurons
The model represents each excitatory and inhibitory neuron with a single-compartment Wang–Buzsáki conductance-based formulation. Membrane dynamics include sodium, potassium, leakage, external-driving, and recurrent-interaction currents, with voltage-dependent gating and specified parameter values.
- Model neurons: Each excitatory and inhibitory neuron is modeled using the Wang–Buzsáki conductance-based model in a single compartment.The compartment includes sodium and potassium currents.
- Model neurons: The membrane-potential dynamics include capacitance, leakage current, external driving current, and recurrent interaction current.Leakage is defined as I_L = g_L(V − V_L).
- Model neurons: Sodium and potassium currents are voltage-dependent and defined as I_Na = g_Na m^3∞h(V − V_Na) and I_K = g_Kn^4(V − V_K).These currents provide the model’s voltage-dependent conductances.
- Model neurons: Sodium-current activation is instantaneous and follows m∞(V) = α_m(V) / [α_m(V) + β_m(V)].The activation variable is therefore determined directly by membrane potential.
- Model neurons: Sodium-current inactivation and potassium-current activation evolve dynamically according to gating equations for x = h, n.The rate functions α_x and β_x(V) are nonlinear functions of membrane potential.
Model synapses
The model represents synaptic currents as voltage-dependent conductance responses to presynaptic spikes, with excitatory and inhibitory reversal potentials. Recurrent input sums contributions from all presynaptic spikes using fast synaptic kinetics fixed across simulations.
- Synaptic current: A presynaptic action potential induces a postsynaptic current proportional to synaptic conductance and the voltage difference from the synapse’s reversal potential.The reversal potentials are VE = 0 mV for excitation and VI = −80 mV for inhibition.
- Conductance dynamics: The postsynaptic conductance response is defined by presynaptic spike time, latency, rise-time, and decay-time, with zero conductance before the response begins.The spike-response normalization sets its peak value to 1.
- Recurrent input: The recurrent current is the sum of time-dependent synaptic contributions from all presynaptic spikes fired up to the current time.All simulations use τ1 = 1 ms, τ2 = 3 ms, and d = 0.5 ms, producing relatively fast postsynaptic-current decay.
Parameters of the background noise
The model includes independent Poisson-driven excitatory background input for every neuron, with fixed firing rate and peak conductance parameters.
- Parameters of the background noise: Each neuron receives statistically independent Poisson noise modeled as an excitatory recurrent-like synaptic current.The external input represents background spiking activity.
- Parameters of the background noise: The simulations use fext = 5 kHz and gext = gE = 5 µS/cm2 for the background input.fext is the Poisson spike-train firing rate, while gext is the peak conductance.
Phase response of the rate model
The rate model’s oscillation and phase response are characterized analytically under conditions involving inhibitory coupling, delay, and sub-threshold dynamics. Its phase response curve is null across a broad phase interval, indicating refractoriness to perturbations.
- Oscillation conditions: The single-area oscillation analysis assumes sufficiently strong local inhibitory coupling, with negative total input lasting longer than the delay and satisfying D < T − Tst < 2D.These conditions involve the sub-threshold duration Tst, delay D, and oscillation period T.
- Oscillation conditions: The oscillation period T and sub-threshold time Tst are obtained numerically by solving a system of non-linear equations.The equations describe the delayed inhibitory dynamics of the rate model.
- Oscillation conditions: The peak amplitude Rpeak depends linearly on the background current I.Rpeak denotes the peak amplitude of the periodic rate oscillation.
- Phase response: Phase is defined as φ(t) = mod (t−t0, T), normalized between 0 and 1 with oscillation peaks assigned phase 0, then translated to 0°–360° for main-text results.The time shift t0 is chosen so that oscillation peaks have phase 0.
- Phase response: The resulting phase response curve is null over a broad phase interval, producing refractoriness to perturbations across that range.The study reports the corresponding Z(φ) curve for its model parameters in Figure 4D.
Phase-locking in the rate model
In the weak-coupling rate model, the phase difference between coupled areas evolves through a phase interaction function Γ(∆φ). Stable phase-lockings are identified by zero crossings of Γ with negative slope, using a piecewise analytic expression for C(∆φ).
- Phase evolution: The instantaneous phase shift ∆φ(t) between two coupled areas is described by a weak-coupling phase-evolution equation.The supplied passage introduces this equation as the basis for analyzing phase-locking.
- Interaction function: Γ(∆φ) is defined as C(∆φ) − C(−∆φ), combining the phase response and limit-cycle waveform of the uncoupled oscillating areas.The construction uses analytic expressions for the phase response Z(φ) and rate-oscillation limit cycle R(φ) with KE = 0.
- Phase-locking criterion: Stable phase-lockings occur at zeroes of Γ with negative slope crossing.The analytic integral C(∆φ) is evaluated piecewise across six different ∆φ intervals.
- Piecewise analytic solution: C(∆φ) is specified by interval-dependent combinations of Cij terms, including distinct expressions for ∆φ ∈ [φst −1 + 3φD, 2φD] and ∆φ > 2φD.The final intervals add C12 contributions, and the ∆φ > 2φD expression includes e^T C10(1 + φD −∆φ, 1 −φD).
- Numerical illustration: A plot of Γ(∆φ) for the study’s parameters is reported in Figure 4B.The passage also defines a = f(b) −f(a) in the accompanying analytic presentation.
Figures
The figures show how reciprocal structural motifs generate distinct effective-connectivity patterns as inter-areal coupling changes, including directional driving, leaky or mutual driving, and asymmetric dynamics from symmetry breaking. They also illustrate how effective connectivity influences information propagation and how transfer-entropy estimates depend on time lag and quantization.
- Models of interacting areas: The models represent cortical areas as large, sparse networks of excitatory and inhibitory spiking neurons whose collective activity exhibits fast oscillations.Each area uses nE = nI = 4000 neurons, with irregular individual spiking and collective network rhythms.
- Effective motifs: Weak coupling produces unidirectional-driving effective motifs from out-of-phase locking of local periodic oscillations, despite fully symmetric structural motifs.The figure compares symmetric two-area and three-area motifs with their corresponding effective connectivities.
- Effective motifs: Intermediate and large coupling produce leaky-driving and mutual-driving effective motifs, respectively, with mutual driving characterized by symmetrically irregular oscillations without stable phase relations.These motif families are shown for fully symmetric structural motifs with N = 2 or N = 3 areas.
- Dynamic control of effective connectivity: Symmetric structural motifs can generate asymmetric dynamics in which one area leads another through spontaneous symmetry breaking.Distinct phase-locking configurations are represented by basins of attraction, with stable out-of-phase lockings corresponding to unidirectional-driving motifs.
- Information propagation: Effective connectivity affects information propagation by shaping how information is encoded in irregular neuronal spike patterns during collective oscillations.Figure 8 contrasts irregular individual firing with regular local-area rhythms and illustrates codeword-like activity across oscillation cycles.
- Information propagation: Transfer entropy varies with both the number B of discretization bins and the adopted time lag τlag used to analyze neural-activity time series.The figure evaluates both interaction directions, TEXY and TEYX, in a fully symmetric two-area network motif.