Overview of Hebbian and homeostatic plasticity.

(Ai) Neural network activity is driven by external inputs in a static network. (Aii) Hebbian plasticity amplifies network responses to external inputs through a positive feedback mechanism. (Aiii) Homeostatic plasticity restores activity to a set-point via a negative feedback mechanism, essential for maintaining firing rate homeostasis. (Bi) Hebbian functional plasticity is synapse-specific, strengthening recurrent connectivity by potentiating the weights of specific synapses involved in neural activation. In contrast to synapse-specific Hebbian potentiation, synaptic depression can be induced in the same activated synapse (homosynaptic depression) or neighbor-ing synapses (heterosynaptic depression) using specific protocols. (Bii) Homeostatic synaptic scaling is cell-autonomous, involving proportional upscaling or downscaling of all input synaptic weights in response to chronic changes in neural activity. (B) Homeostatic structural plasticity is also cell-autonomous char-acterized by compensatory spine loss during chronic excitation of the postsynaptic neuron. Conversely, chronic inhibition induces divergent, often non-homeostatic, changes in spine density.

Non-monotonical modification of spine numbers following three-day synaptic inhibi-tion via NBQX informs a biphasic structural plasticity rule.

(A) The integral feedback control framework for homeostatic synaptic scaling and structural plasticity. Both rules use intracellular calcium concentration ([Ca2+]i, C(t)) to track neural activity (AP, action potential, S(t)). Calcium concentra-tion is updated each time via calcium influx (βCa) upon the emission of a post-synaptic action potential and decays with a time constant τCa. Synaptic scaling follows a weight-dependent rule, multiplicatively adjusting the synaptic weight w(t) with a scaling factor ρ, based on the discrepancy from the setpoint ɛ of calcium concentration. Structural plasticity uses the same guidance signal (i.e., calcium concentration) to regulate the growth and retraction of axonal boutons and dendritic spines, aiming to reach the same setpoint value. Two versions of the structural plasticity rule are shown: one with a linear dependency and the other with a non-linear dependency on intracellular calcium concentration. (B) Example CA1 pyramidal neuron recorded from entorhinal-hippocampal tissue culture to assess the effects of different NBQX concentrations. Scale bar: 500 µm. (Ci-Cii) Group data of spontaneous excitatory postsynaptic currents (sEPSC) in three groups (N = 18 for the control group, N = 18 for the 200 nM NBQX-treated group, N = 12 for the 50 µM NBQX-treated group). (D) Example Thy1-eGPF culture and dendritic segments from the stratum radiatum (rad.) before and after three-day treatment. Scale bars: 200 µm and 5 µm. (E) Spine density at baseline and after the three-day treatment. All values are normalized to the corresponding baseline values. Light-shaded lines show raw data (solid lines represent increased spine density; dashed lines represent decreased density). Dark-shaded lines with error bars represent the means and standard error of the means (s.e.m.s) for each group. (N = 19 for the control group, N = 24 for the 200 nM-treated group, N = 33 for the 50 µM-treated group.)

Growing a neural network with three distinct structural plasticity rules.

(A) A network of point neurons was used to study structural plasticity, with simplified dendritic morphology. Dendritic spines are depicted as pink sticks on the soma, and axonal boutons are represented by empty or solid half-circles. An empty half-circle with a dashed line indicates an axon during retraction. In this model, intracellular calcium concentration is linearly correlated with neural firing rate, so neural activity is used to reflect “firing rate homeostasis” throughout the manuscript, as it has a meaningful physical unit compared to the arbitrary unit (a.u.) for calcium concentration. (Bi-Biii) Three structural plasticity growth rules regulate changes in synaptic element numbers. (Bi) Linear rule with a single setpoint (ɛ = 7.9, orange line). (Bii) Gaussian rule with two setpoints, one at zero (η = 0, grey line; ɛ = 7.9, orange line). (Biii) Gaussian rule with two non-zero setpoints (η = 0.7, grey line; ɛ = 7.9, orange line). Three shades represent 100%, 50%, or 10% of the original growth rate (ν), with positive and negative values indicating the rate of synaptic element growth or loss. (C) Neural network architecture based on the Brunel network model, consisting of 10 000 excitatory (blue, E) and 2 500 inhibitory neurons (red, I) stimulated by external Poissonian inputs (P). All I-I, I-E, and E-I synapses are hard-wired with 10% probability, while E-E synapses are subject to structural plasticity rules. (Di-Diii) Temporal dynamics of neural activity and network connectivity (Γ) during network growth, guided by the three distinct rules. Unless otherwise stated, the curve and shaded areas in activity plots represent the mean and standard deviation of the neural activity for the I and E populations. The network reached an equilibrium state (Γ = 10%) in Di and Dii but not in Diii. The firing rates distribution and network connectivity matrices of the indicated time points (solid triangles) are provided in Supplementary Fig. 3 for Di-Dii, and in Fig. 4 for Diii.

Silent neurons remain isolated in the network regulated by the biphasic Gaussian rule.

(A) Histogram of firing rates for excitatory and inhibitory neurons sampled at the time point indicated in Fig. 3Diii. Nearly half of the excitatory neurons were silent. The blue vertical line repre-sents the mean firing rate of non-silent neurons, while the orange dashed line marks the target firing rate (ɛ = 7.9 Hz). (Bi-Bii) Network connectivity matrix and distribution of synapse numbers for individ-ual excitatory neurons. (C) Correlation heatmap showing the relationship between neural activity and synapse number of individual excitatory neurons. Silent neurons did not form synapses, whereas active neurons firing around the target rate formed approximately 1 000 synapses with other active excitatory neurons. (D) Network architecture when a damping facilitating current (Ifacilitating) was injected to en-hance network development. (E) Temporal dynamics of neural activity and network connectivity when a facilitating current was injected. The inset shows the firing rate distributions of both excitatory and inhibitory neurons at a selected time point (solid triangle). The facilitating current started at 750 pA and decayed linearly to zero during a 4 000 s period. (F) Different initial values of facilitating currents resulted in varying network connectivities. An initial value of 750 pA was used throughout the manuscript.

Divergent regulation of network connectivity under stimulation and deprivation via three structural plasticity rules.

(A) A subpopulation (S) consisting of 10% excitatory neurons (E) was subject to activity perturbation. All E-E, S-S, and E-S synapses were governed by the biphasic Gaussian rule. (Bi) Activity perturbation protocol. Three different folds of the original intensity (FOI) from the Poisson generator were used as examples to represent stimulation (110% FOI), mild deprivation (95% FOI), and silencing (0% FOI). (Bii) Temporal dynamics of neural activity of S, E, and inhibitory neurons (I) under each protocol. (Biii) Temporal evolution of the overall network connectivity (Γoverall) and subgroup connectivity (Γsubs) under each protocol. The synaptic connection probability from E to S is identical to that from S to E, as the same rules were applied to spines and boutons. Therefore, only S-E traces are shown unless otherwise stated. (C) Network connectivity matrices at the end of the three protocols. (D) Average incoming synapse numbers of S neurons under different FOIs. The empty green circles represent data from networks subjected to extreme stimulation or inhibition, where both neural activity and network connectivity were unstable. (E) Examples of two neurons receiving the same external inputs but with different calcium decay time constants (τCa). The upper panel shows membrane potential; the middle panel displays spike trains; the lower panel depicts the integrated calcium concentration over time. (F) Connectivity traces of the subnetwork under silencing across three different conditions. The dashed circle area is shown at higher magnification.

Activity perturbation and recurrent connectivity shape the evolution of network connectivity.

(A) In the default network, the same growth rule was applied to both axonal boutons (A, light brown curve) and dendritic spines (D, pink curve), with ηA = ηD, as shown in the upper inset. Different η values could be used for axonal and dendritic elements, such as ηA > ηD or ηA < ηD. A silencing protocol was applied (fold of original intensity, FOI). (B) Neural activity of the stimulated subpopulation (S), excitatory neurons (E), and inhibitory neurons (I) under two conditions. (C) Network connectivity matrices at the conclusion of the silencing protocol under the two conditions. (D) Protocols used to investigate the effects of recurrent connectivity and external stimulation. The same growth rule was applied to both axonal and dendritic elements (ηA = ηD) here. (E, F) Time courses of neural activity and connectivity following silencing and external stimulation. In Protocol 1, the growth rate for the left panel (Prtcl. 1; left panel) was ten times faster than in the left panel (Prtcl. 1; right panel). In Protocol 2 (Prtcl. 2), the intensity of external stimulation was doubled as compared to the one used in Prtcl. 1.

Homeostatic synaptic scaling (HSS) shapes effective connectivity and interacts with homeostatic structural plasticity (HSP).

(A) Protocol of silencing – 0% FOI, applied to a subpopu-lation of excitatory neurons (S) – and synaptic scaling activation. Three different scaling strengths were applied: ρ = 0 represents no scaling, ρ = 0.01 represents weak scaling, and ρ = 0.02 represents strong scaling. (B-C) Time courses of network activity and connectivity. Γstruc. refers to synapse-number-based structural connectivity, while Γeffec. represents effective connectivity, which is the product of synapse numbers and synaptic weights. (Di-Dii) Structural and effective connectivity matrices of the entire net-work at t2. (Ei-Eii) Structural and effective connectivity matrices of the entire network at t3. (F) Raster plots for 100 selected neurons, including inhibitory (red, I), excitatory (blue, E), and silenced excitatory neurons (grey; S), from the network at the time points t1, t2, and t3.

Spine size analysis suggests interactions between functional and structural plasticity.

(A) Activity trajectories and average weights of incoming excitatory synapses to two sample excitatory neurons, N1 (deprived) and N2 (non-deprived). The grey dashed line in the upper panel indicates the setpoint activity level. Incoming synapses were grouped into two categories: those from the deprived subpopulation (S, grey) and those from non-deprived excitatory neurons (E, blue). The triangles in the middle panel mark the time points at which synaptic weight distributions were analyzed in panel B. (B) Synaptic weight distributions of neuron N1 at two time points, labeled as before and after. The numbers indicate the total synapse count for each type at the corresponding time point. (C) Normalized synapse number of the neuron N1 (solid line) and the averaged value across all deprived neurons (dashed line). (Di-Diii) Baseline spine size distributions for three groups. (N = 489 for the control group, N = 736 for the 200 nM-NBQX group, N = 675 for 50 µM-NBQX group) (E) Cumulative distribution function (cdf) of spine sizes before and after the three-day treatment. The inset shows the corresponding averages of normalized spine sizes. (F) Normalized changes in spine sizes, grouped by their initial spine sizes. The values on the x-axis represent the upper limits of each binning group. Data points above the dashed line indicate spine enlargement, while those below indicate spine shrinkage.

Systematic study of the interaction between synaptic scaling and structural plasticity in response to activity silencing.

(A) Correlation between each dendritic segment’s average change in spine size and its initial spine density. Marker size represents the net change in spine density over a three-day period. (B) Correlation between each dendritic segment’s average changes in spine size and its change in spine density. (C) Hypothesis: Different combinations of homeostatic synaptic scaling (HSS) and homeostatic structural plasticity (HSP) may form a spectrum, allowing different neuron types or dendritic segments within the same neuron to be governed by unique subsets of these rules. This spectrum could explain the high diversity observed in empirical studies of structural plasticity. (Sample neurons were reconstructed based on a CA1 pyramidal neuron (left two) and a dentate gyrus granule cell (right two), previously recorded in our lab.) (D) Simulation protocol. We systematically varied the growth rate of the HSP rule (ν) and the scaling strength of the HSS rule (ρ). (Ei-Eii) Example traces of structural connection probability and neural activity of the deprived subpopulation (S) under different parameter combinations. (Fi-Fii) Discrepancies in connectivity and firing rates when different growth rates and scaling strengths were combined. Discrepancies were calculated by estimating the area between the actual time course and the equilibrium connection probability (10%) or the target rate (ɛ) from the time of silencing until the end of the simulation. Results are averaged from 11 random trials and displayed in panels E and F.