Synaptic plasticity of the cortico-striatal synapse, the tasks for learning, and the dopamine signals for the two types of patterns in the tasks.

(A) Scheme describing the requirements for synaptic plasticity at the cortico-striatal synapse (adapted from Shen et al. (2008) by adding the calcium thresholds, which are the focus of this study). (B) The FBP and the NFBP, illustrated using features common to the visual system. SPNs might instead receive, e.g. sensory- and motor-related features. (C) Dopamine signals from the midbrain are assumed to arrive in the striatum after every pattern. Dopamine peaks are emitted after the relevant patterns, and dopamine pauses after the irrelevant patterns. (The midbrain and its projections are not explicitly modeled in this study, dopamine is programatically provided to the SPN a certain time after pattern arrival.) This figure is adapted from Figure 1 from Khodadadi et al. (2025).

Linear versus supralinear integration of synaptic inputs by SPNs.

(A) Illustrations of the two scenarios of linear integration of distributed synaptic inputs by the soma, and supralinear integration of clustered synaptic inputs in a dendrite. In both scenarios, each synapse is activated with 3 incoming spikes within a window of 35 milliseconds. (B1-B4) Somatic voltage, spine voltage, spine [Ca]NMDA and spine [Ca]L-type evoked in the linear integration scenario (randomly distributed across the dendrites). Line color indicates the number of distributed synapses. (C1-C4) Somatic voltage, spine voltage, spine [Ca]NMDA and spine [Ca]L-type evoked in the supralinear integration scenario (synaptic cluster placed on one dendrite, in a 20-micrometer region approximately 120 micrometers away from the soma). Similarly, line color represents the size of the synaptic cluster, which is varied from 1 to 30 synapses. (D1-D4) The amplitude of the somatic voltage, spine voltage, spine [Ca]NMDA and [Ca]L-type compared between the cases of linear and supralinear integration. Results are averages over 20 trials, and in the case of synaptic clusters, over 8 different dendrites (clusters located in a 20-micrometer in a dendritic region starting at approximately between 120 micrometers from the soma).

Learning outcome on the FBP and NFBP.

(A) The stimulation protocol used. Patterns are presented in random order. A pattern is represented with synaptic inputs arriving within a window of 35 ms, 3 spikes per synapse. The dopamine signal, during which synapses are updated, is given 400 ms after the start of a pattern, and lasts for 20 ms. The next pattern arrives 600 ms after the start of the current pattern. (B1) Illustration of the setup for the FBP with linear integration. Each feature is represented by 15 synapses distributed across the dendrites. (B2) Illustration of the setup for the FBP with supralinear integration. Each feature is represented by 10 synapses clustered in one dendrite. (B3) Illustration of the setup for the NFBP (only supralinear integration). Each feature is represented by 10 clustered synapses, and clusters are located on two different dendrites. (C1-C3) The somatic and dendritic voltages in the FBP with linear (C1) and supralinear (C2) integration, and the NFBP (C3), before and after learning (gray and black traces, respectively), elicited by the relevant and irrelevant pattern(s). (D1-D3) The performance on the FBP with linear (D1) and supralinear (D2) integration, and on the NFBP (D3). In (D1) and (D2) the performance is averaged over 50 trials, and in (D2) the cluster was placed at random in one of 8 dendrites in each trial. In (D3) the performance is averaged over 12 trials per input configuration, which are divided into two groups (with 18 and 13 input configurations, shown in Figure 3–figure supplement 1). (This totals to 216 and 156 trials in the two groups, respectively.) Each point in the plots is the average score over the 20 previous patterns, and the shaded area shows the standard deviation. The dashed lines are the threshold scores for solving the FBP and NFBP, which are 75% and 87.5%, respectively. (See the Methods section for what these threshold scores represent). Figure 3—figure supplement 1. All input configurations used in the NFBP.

The synaptic weights and calcium thresholds during learning of the FBP and NFBP.

(A) Illustrations of the setups for the FBP with linear (A1) and supralinear (A2) integration, and the NFBP (A3) (same as in Fig. 3). (B-D) The evolution of synaptic weights (B), LTP thresholds (C) and LTD thresholds (D) in the FBP with linear (B1-D1) and supralinear (B2-D2) integration, and the NFBP (B3-D3 and B4-D4). In (B) all synaptic weights for the features are shown, while in (C) and (D) only one synapse per feature is chosen to show its calcium threshold (solid lines). Dots in (C) and (D) represent the amplitudes of [Ca]NMDA and [Ca]L-type, respectively, during pattern presentation. For clarity, the calcium amplitudes for some patterns are omitted. (C) and (D) are shown in larger scale in Figure 4–figure supplement 1, with much more detail in the calcium amplitudes. Arrows show the moment in time when the weakened synapses become low enough for their calcium levels to mostly stay below the calcium thresholds. Figure 4—figure supplement 1. Calcium thresholds and calcium amplitudes from Fig. 4 in greater detail. Figure 4—figure supplement 2. The effect of having no upper LTP threshold on supralinear integration. Figure 4—figure supplement 3. The effect of the learning rate on learning. Figure 4—figure supplement 4. The effect of the metaplasticity rate on learning.

Learning outcome on the NFBP without metaplasticity in the LTD threshold.

(A) An illustration of the setup for the NFBP (same as in Fig. 3B3). (B) The dendritic and somatic voltage before (gray traces) and after learning (black traces) for all four patterns. (C-E) The evolution of synaptic weights (C), LTP thresholds (D) and LTD thresholds (E) for the synapses in each dendrite. (E) shows the fixed LTD thresholds. In (C) all synapses are shown, and in (D, E) only one synapse per feature is used to show its calcium threshold. Dots represent the amplitudes of [Ca]NMDA (D) and [Ca]L-type (E) during pattern presentation, omitting some patterns for clarity. (F) The performance on the NFBP without metaplasticity in the LTD threshold. Figure 5—figure supplement 1. The effect of a fixed LTD threshold on solving the FBP.

Learning outcome on the NFBP without metaplasticity in the LTP threshold.

(A) An illustration of the setup for the NFBP (same as in Fig. 3B3). (B) The dendritic and somatic voltage before (gray traces) and after learning (black traces) for all four patterns. (C-E) The evolution of synaptic weights (C), LTP thresholds (D) and LTD thresholds (E) for the synapses in each dendrite. (D) shows the fixed LTP thresholds, and the dashed lines show the upper LTP threshold, ΘLTP. In (C) all synapses are shown, and in (D, E) only one synapse per feature is used to show its calcium threshold. Dots represent the amplitudes of [Ca]NMDA (D) and [Ca]L-type (E) during pattern presentation, omitting some patterns for clarity. (F) The performance on the NFBP without metaplasticity in the LTP threshold. Figure 6—figure supplement 1. The effect of a fixed LTP threshold on solving the FBP.

Learning outcome on the NFBP with partial metaplasticity, where the LTP threshold is updated only during LTP, and the LTD threshold is updated only during LTD.

(A) An illustration of the setup for the NFBP (same as in Fig. 3B3). (B) The dendritic and somatic voltage before (gray traces) and after learning (black traces) for all four patterns. (C-E) The evolution of synaptic weights (C), LTP thresholds (D) and LTD thresholds (E) for the synapses in each dendrite. In (C) all synapses are shown, and in (D, E) only one synapse per feature is used to show its calcium threshold. Dots represent the amplitudes of [Ca]NMDA (D) and [Ca]L-type (E) during pattern presentation, omitting some patterns for clarity. (F) The performance on the NFBP with partial metaplasticity. Figure 7—figure supplement 1. The effect of partial metaplasticity on solving the FBP.

Learning outcome on the NFBP without metaplasticity (the LTP and the LTD thresholds are fixed).

(A) An illustration of the setup for the NFBP (same as in Fig. 3B3). (B) The dendritic and somatic voltage before (gray traces) and after learning (black traces) for all four patterns. (C) The evolution of synaptic weights in both dendrites. (D, E) The fixed LTP thresholds (D) and LTD thresholds (E) in each dendrite, with calcium amplitudes during pattern presentation shown with dots (omitting some patterns for clarity). (F) The performance on the NFBP without metaplasticity. Figure 8—figure supplement 1. The effect of having no metaplasticity on solving the FBP.

The parameters in the plasticity rule.

Alternative models of calcium accumulation.

(A) Spine [Ca]NMDA without axial diffusion. [Ca]NMDA is described with a pool model similar to that in Eq. 4 (except that instead of [Ca]L-type, this pool accumulates [Ca]NMDA arising from the NMDA current in Eq. 6). (B) Spine [Ca]NMDA + [Ca]VGCC without axial diffusion. Calcium from the NMDA current and all voltage-gated calcium channels (except L-type) accumulates in a pool model. (C) Spine [Ca]NMDA with axial diffusion. Compared to Fig. 2C3, in this plot only calcium from NMDARs diffuses in the neuron, without calcium from other voltage-gated calcium channels. Figure 9—figure supplement 1. Axial diffusion of calcium from NMDARs only.

The parameters for the axial calcium diffusion model.

Compared to Dorman et al. (2018), we have reduced the concentration of the immobile calcium buffer from 2.5 mM to 0.15 mM and changed the catalytic rate of the PMCA. The diffusion coefficient of Ca2+ is 200 (same as in Dorman et al. (2018)).

The parameters for the pool model for [Ca]L-type.

The parameters in the dual exponential synaptic model.

The parameters in the saturating synapse model.

All possible input configurations of four features on two dendrites that allow the NFBP to be learned.

They are divided in two groups: those with up to 3 features per dendrite (group 1), and those with 4 features in at least 1 dendrite (group 2). We have made this division because when a dendrite is innervated with all four features (group 2), learning to solve the NFBP depends on the order in which the patterns arrive. In this case, often only one of the relevant patterns is stored by the neuron (the same pattern in both dendrites), and solving the NFBP requires additional mechanisms, such as branch plasticity (Legenstein and Maass, 2011).

The calcium thresholds and calcium amplitudes from Fig. 4 shown in larger panels with greater detail.

(A) LTP thresholds for the FBP with distributed (A1) and clustered (A2) synapses, and for the NFBP (A3, A4). (B) LTD thresholds for the FBP with distributed (B1) and clustered (B2) synapses, and for the NFBP (B3, B4). In (B3), regions with calcium amplitudes of interest are highlighted. (The same regions exist in all panels, although they are not highlighted.)

The effect of no upper threshold ΘLTP on supralinear integration.

(A) The somatic and dendritic voltages before and after learning in the FBP (A1) and NFBP (A2). Not having an upper threshold causes somatic spiking for the irrelevant patterns after learning in the NFBP, but not the FBP. (B-D) The evolution of synaptic weights (B), LTP thresholds (C) and LTD thresholds (D) in the FBP (B1-D1) and the NFBP (B2-D2 and B3-D3). Strengthened synapses saturate at their maximal levels, also driving more weakening in the weakened synapses. Having no upper threshold does not affect the thresholds of the strengthened synapses, but causes the thresholds of the weakened synapses to stabilize at higher levels. (E) Performance on the FBP (E1) and NFBP (E2).

The effect of the learning rate η on learning.

(A) The average score on the FBP and NFBP for three values of the learning rate, η ∈ {0.4, 0.85, 1.7}. Increasing the learning rate causes faster learning of the tasks (less pattern presentations are needed). (B) The score at the end of learning varies little with η, except in group 2 for the NFBP, where a higher learning rate increases performance, so that one of the relevant patterns is remembered. (C) The standard deviation at the end of learning also varies little with η (there is a 5% decrease for the NFBP, group 1 only). (D) The speed of learning measured by the number of patterns, Ns, needed to reach the score threshold for solving each task (the dashed line in (A)). The speed of learning to solve the tasks is affected by the learning rate η, as is also seen in (A). Increasing the learning rate speeds up learning.

The effect of the metaplasticity rate ηθ on learning.

(A) The average score on the FBP and NFBP for four values of the metaplasticity rate, ηθ ∈ {1, 2, 3, 4} (the standard deviation is ommited for figure clarity). There is little effect of the metaplasticity rate on the final score (B), the final tandard deviation of the score (C) and the speed of learning (D). (B) The score at the end of learning varies little with ηθ (only slightly for the NFBP). (C) The standard deviation at the end of learning also varies little with ηθ (up to 5% increase for the NFBP only). (D) The speed of learning measured by the number of patterns, Ns, needed to reach the score threshold for solving each task (the dashed line in (A)). The speed of learning to solve the FBP varies very little with ηθ, while that for solving the NFBP only shows a large increase between ηθ = 1 and ηθ = 2.

Learning outcome on the FBP with linear (A1–E1) and supralinear integration (A2–E2) without metaplasticity in the LTD threshold.

(A) The somatic and dendritic voltage evoked by both patterns before and after learning. (B, C) The evolution of synaptic weights (B) and LTP thresholds (C) during learning. (D) The LTD thresholds are fixed. In (B) all synapses are shown, and in (C, D) only one synapse per feature is used to show its calcium threshold. (E) The performance on the FBP.

Learning outcome on the FBP with linear (A1-E1) and supralinear integration (A2-E2) without metaplasticity in the LTP threshold.

(A) The somatic and dendritic voltage evoked by both patterns before and after learning. (B) The evolution of synaptic weights during learning. (C) The LTP thresholds are fixed. (D) The evolution of the LTD thresholds during learning. (E) The performance on the FBP.

Learning outcome on the FBP with linear (A1-E1) and supralinear integration (A2-E2) with partial metaplasticity.

(A) The somatic and dendritic voltage evoked by both patterns before and after learning. (B-D) The evolution of synaptic weights (B), LTP thresholds (C) and LTD thresholds (D) during learning. In (B) all synaptic weights are shown, and in (C, D) the thresholds for only one synapse per feature are shown. (E) The performance on the FBP.

Learning outcome on the FBP with linear (A1-E1) and supralinear integration (A2-E2) without metaplasticity.

(A) The somatic and dendritic voltage evoked by both patterns before and after learning. (B) The evolution of synaptic weights during learning. (C, D) The LTP (C) and LTD thresholds (D) are fixed. In (B) all synaptic weights are shown, and in (C, D) the thresholds for only one synapse per feature are shown. (E) The performance on the FBP.

Voltage and calcium elevations when only [Ca]NMDA diffuses axially through the SPN.

(A1-C4) Somatic voltage, spine voltage, spine [Ca]NMDA and spine [Ca]L-type evoked in the supralinear integration scenario, to be compared with Fig. 2C (synaptic cluster placed on one dendrite, in a 20-micrometer region approximately 120 micrometers away from the soma). Line color represents the size of the synaptic cluster, which is varied from 1 to 30 synapses. (B1-B4) The amplitude of the somatic voltage, spine voltage, spine [Ca]NMDA and [Ca]L-type compared between the cases of only [Ca]NMDA diffusing and [Ca]NMDA + [Ca]VGCC diffusing (the latter is replfrom Fig. 2D). Results are averages over 20 trials, and in the case of synaptic clusters, over 8 different dendrites (clusters located in a 20-micrometer in a dendritic region starting at approximately between 120 micrometers from the soma).