Fig 1.
Collective burst firing drives synaptic weights towards attractor in the weight space.
A. The network model consists of one inhibitory neuron () projecting to all the excitatory neurons, connected in a feedforward configuration with
presynaptic neurons (
) to
postsynaptic neurons (
). An external current applied to the inhibitory neuron controls the network state (
). Each excitatory neuron is subjected to an individual external current mimicking an external input. B. Hyperpolarizing the current applied to the inhibitory neuron (
) switches the network state from input-driving tonic firing to collective burst firing. Raster plot activity of the excitatory neurons and local field potential (LFP) traces are displayed. C. Evolution of the synaptic weights during switches from input-driven tonic firing to collective burst firing. The network comprises 50 presynaptic neurons connected to 50 postsynaptic neurons for 100 traces among 2500 (gray lines) with 5 randomly highlighted lines (colored lines).
and
indicate the end of the
-th tonic and burst firing state, respectively. D-E. Comparison of the synaptic weights at the end of the third and fourth tonic firing states (dark blue) or the third and fourth burst firing states (light blue), normalized between the minimal and maximal values shown on a scatter plot. The histograms highlight the weight distribution. The weights converge to a fixed point in the weight space, we call burst-induced attractor (
,
).
Fig 2.
Burst firing constrains synaptic weights toward an attractor via shared calcium dynamics.
A. Calcium trace decomposition into potentiation, depression, and neutral zones, based on pre- and postsynaptic spike timing. Red and orange shading indicate time spent above the potentiation threshold or below the depression threshold, respectively. Right: effective time in each region, weighted by corresponding time constants (,
). B-C. Example spike trains and calcium traces for two synapses during tonic and burst firing. Tonic activity produces diverse calcium dynamics, while burst firing induces synchronized fluctuations across synapses. D-E. Distribution of effective time allocated in different plasticity regions during tonic and burst firing. Tonic firing shows broad distributions, while burst firing produces narrower, more consistent distributions across synapses. F-H. Evolution of synaptic weights over time during tonic (F) and burst (H) firing, starting from the same initial conditions. Weights diverge toward distinct values under tonic input, whereas they converge to a narrow range under burst firing, indicating the emergence of a burst-induced attractor. G-I. Predicted steady-state weight using analytical equations Eq (1) compared with actual simulated weights at different time steps. The linear regression between the predicted values and the actual final values at the end of the stimulation is closer in burst firing compared to tonic firing (
in burst and
in tonic).
Fig 3.
Modulation of burst-induced attractor in synaptic weights.
A. Evolution of the network activity and synaptic weights when the network is driven from tonic to burst firing epochs with three variations of the collective burst firing (achieved by modulating the external current applied to the inhibitory neuron). indicates the end of the tonic firing state, and
indicates the end of the
-th burst firing state. 100 traces are randomly displayed among 2500 synaptic connections. The steady-state values associated can be modulated by the collective burst firing, moving the attractor in the weight space as a function of burst structure (e.g., spike content and duration). B. Summary of synaptic weights at the end of each burst epoch as a function of
. Vertical segments denote the standard deviation across all synapses, while horizontal bars indicate the mean weight. Tonic firing yields a broad spread of synaptic weights, whereas collective bursting compresses weights toward a narrow attractor whose location shifts smoothly with
.
Fig 4.
Neuromodulated and tag-dependent synaptic plasticity rules exploit the burst-induced attractor for memory consolidation.
A. Calcium-based (left) and spike-based (right) plasticity rules, in which potentiation and depression parameters (,
,
) are modified by neuromodulation. B. Evolution of synaptic weights in six circuits subjected to two tonic–burst epochs. In the last burst epoch, the plasticity rule is down-neuromodulated (yellow bar), leading to a different lower burst-induced attractor. Half of the circuits display correlated excitatory activity (gray) and half uncorrelated activity (black). C. Calcium-based (left) and spike-based (right) plasticity rules with tag-dependent neuromodulation. Tagged synapses (orange) receive up-neuromodulation, while untagged synapses (yellow) receive down-neuromodulation. D. Same protocol as in B, but with tag-dependent neuromodulation during the last burst epoch (yellow–purple hatched bar). Synapses tagged during the tonic state (weights above threshold) converge to a higher burst-induced attractor, while untagged synapses converge to a lower one, resulting in bimodal weight consolidation.
Fig 5.
Conceptual illustration of the burst-induced attractor and its modulation.
A. Example trajectories in synaptic weight space during transitions between tonic (light blue) and burst firing (dark blue). Tonic firing leads to more dispersed convergence points , whereas burst firing drives weights toward a narrower attractor region
. B. Neuromodulation shifts the location of the burst-induced attractor; either by modulating the collective burst firing (pink, referring to Fig 3), or by modulating the plasticity parameters in a weight-dependent manner mimicking synaptic tag (referring to Fig 4). Up-neuromodulation moves the attractor toward higher weights (orange), while down-neuromodulation shifts it toward lower weights (yellow).