In our plasticity model, we introduced four pathways that contributed to changes in both pre- and postsynaptic weight factors. Although implemented as a phenomenological rule, its mechanisms were inspired by well-established biophysical pathways described in a multitude of experimental studies on long-term synaptic plasticity.

Briefly, presynaptically expressed LTD (pre-LTD; Figure 1A, left) occurs when metabotropic glutamate receptors (mGluRs) and postsynaptic voltage-gated Ca²⁺ channels (VGCCs) are activated simultaneously (Heifets and Castillo, 2009). Phospholipase C (PLC) then integrates these two signals in the process of synthesizing endocannabinoids (eCBs) (Hashimotodani et al., 2005), which retrogradely act on presynaptic type 1 cannabinoid receptors (CB1Rs) to reduce transmitter release probability (Heifets and Castillo, 2009), causing pre-LTD. Presynaptically expressed LTP (pre-LTP) is thought to occur when postsynaptic L-type VGCCs (L-VGCCs) are activated, presumably triggering synthesis of nitric oxide (NO) (Padamsey et al., 2017, Pigott and Garthwaite, 2016), possibly by calmodulin (CaM) at nitric oxide synthases (NOSs) (Abu-Soud et al., 1994). NO retrogradely acts on presynaptic guanylyl cyclase (GC) (Koesling et al., 2004), triggering a signaling chain that is combined with a presynaptic signal by a presynaptic coincidence detector that has yet to be discovered (Padamsey et al., 2017). Postsynaptically expressed LTD and LTP (post-LTD/-LTP; Figure 1A, right) are described as both being driven by coincident binding of glutamate and depolarization of postsynaptic NMDA receptors (NMDARs) (Lüscher and Malenka, 2012). Strong NMDAR-gated Ca²⁺ influx activates protein kinases, such as Ca²⁺/CaM-dependent protein kinase II (CaMKII), whereas weak Ca²⁺ influx activates their counterpart molecules, protein phosphatases such as protein phosphatase 1 and calcineurin (Lisman, 1989). Kinases increase and phosphatases decrease synaptic efficacy determined by α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs), essentially forming complementary mechanisms of postsynaptic LTD and LTP induction (Lüscher and Malenka, 2012). Studies indicate that CaMKII is able to phosphorylate itself (autophosphorylation) due to its specific subunit structure and that this process is more likely to take effect if pulses of Ca²⁺ bound to CaM are applied rapidly (De Koninck and Schulman, 1998), suggesting that this mechanism could play a role in the frequency dependence of plasticity.Figure 1

A Plasticity Rule Based on Separate Pathways for Pre- and Postsynaptic Plasticity

(A) Simplified illustration of the biophysical pathways that inspired our model. Pre-LTD (left) is induced if postsynaptic Ca²⁺ influx through VGCCs coincides with an mGluR-mediated signaling cascade, causing eCB release by PLC and subsequent downregulation of transmitter release probability (minus sign) by CB1Rs. Pre-LTP (left) reportedly requires Ca²⁺ influx through VGCCs, triggering NO synthesis, which is then detected by GC and integrated with a presynaptic signal by an unknown presynaptic coincidence detector to increase release probability (plus sign). Post-LTD and post-LTP (right) are driven by coincident depolarization and activation of NMDARs. Lower amounts of NMDAR-gated Ca²⁺ (thin arrow) activate phosphatases (P), causing a reduction of AMPAR efficacy (minus sign). Higher amounts of NMDAR-gated Ca²⁺ (bold arrow) activate kinases (K), causing an increase in AMPAR efficacy (plus sign). Coincidence detectors of pre- and postsynaptic activity are indicated with orange color.

(B) Model interpretation and abstraction of the biophysical pathways in (A). Pre-LTD (left) is dependent on the coincidence between the presynaptic signal D and a postsynaptic signal based on membrane voltage, reflected in the variable T. The resulting trace E indicates the amount of pre-LTD (minus sign). Pre-LTP (left) requires coincidence of a presynaptic signal Z and a postsynaptic trace N (based on membrane voltage by Nα and Nβ). The amount of pre-LTP (plus sign) is indicated by X. Post-LTD and post-LTP (right) depend on coincidence between the presynaptic signal G and a portion of membrane voltage u. If the resulting trace C reaches lower levels, P is activated, indicating post-LTD (minus sign), whereas higher levels activate K, indicating post-LTP (plus sign).

(C) Traces computed by the plasticity rule for two sample stimulation patterns (see top): post-pre-post pairing (left column) and pre-post-post pairing (right column). The various rows include all fundamental variables of the plasticity rule with color code from (B). Overall synaptic weight W is shown in the bottom row in red. Loose analogies of the model’s variables to biophysical processes are given in italic type to the right.

(D) Transfer function for post-LTD and post-LTP. Activation of either −P or Kα is shown as a function of C.

(E) Voltage clamp simulation while a single presynaptic event is evoked. As a function of clamped voltage, absolute contribution of each of the four pathways is plotted (black lines), as well as the overall relative weight change (red line).

See also Figure S1.

In our model, pre-LTD (indicated by the variable E; Figure 1B, left; see also Figure S1) was induced when the low-pass-filtered postsynaptic voltage trace T coincided with the brief presynaptic signal D. Due to the transient nature of D, pre-LTD was only induced if the postsynaptic cell experienced depolarization shortly before the presynaptic signal, e.g., if the stimulation included a post-pre pair (Figure 1C, medium green color in left versus right column). Consequently, this mechanism only detected post-pre timings and was insensitive to pre-post timings, consistent with pre-LTD in experimental studies (Nevian and Sakmann, 2006, Sjöström et al., 2003). Pre-LTP (indicated by the variable X; Figure 1B, left) in our model required that two consecutively filtered traces based on postsynaptic voltage Nα and Nβ coincided to result in a trace N. Owing to Nβ being filtered from Nα, N was sensitive to the frequency of postsynaptic events during postsynaptic activity due to summation (Figure 1C, light violet color). Only if N was sufficiently elevated during the occurrence of the slow presynaptic signal Z, pre-LTP was switched on. Post-LTD (indicated by the variable P; Figure 1B, right) was modeled by calculating the coincidence of the slow presynaptic signal G and a portion of membrane voltage u. The resulting variable C was subjected to an activation function with two thresholds, namely, θC− and θC+ (Figure 1D). This formalism was consistent with Ca²⁺-level-based rules (Artola and Singer, 1993, Lisman, 1989, Shouval et al., 2002) that have previously been used for modeling synaptic plasticity (see Discussion). No synaptic weight changes were induced below θC−. Whenever C resided between θC− and θC+, post-LTD was activated (Figure 1C, orange color). To model post-LTP (indicated by the variable K; Figure 1B, right), the portion of C above θC+, named Kα, was used to compute the two slower traces Kβ and Kγ, which were filtered versions of Kα. The variable ρ limited the sum of Kα and Kβ. Post-LTP was only switched on when Kα, Kβ, and Kγ were nonzero. Thus, similarly to pre-LTP, this mechanism was frequency dependent. A pre-post-post protocol, therefore, evoked considerably more post-LTP than a post–pre-post protocol (Figure 1C, turquoise color in right versus left column).

The rule’s voltage dependence is demonstrated in Figure 1E. One single presynaptic event was evoked while the postsynaptic cell was clamped to values between −75 mV and −15 mV. Voltages below −60 mV led to no change in weight, whereas voltages between −60 mV and about −28 mV caused LTD and voltages above that caused net LTP. Consistent with experiments on voltage dependence of LTD pathways (Oliet et al., 1997), post-LTD more strongly depended on depolarization than pre-LTD. To consider all the effects of realistic firing behavior, active dendrites, and synapse location, we incorporated our plasticity model into a highly detailed cortical layer 5b (L5b) pyramidal cell model (Hay et al., 2011).

In the first stimulation protocol we used, regular bursts of five pre- and five postsynaptic APs were evoked at either pre-post (Δt=+10ms) or post-pre (Δt=−10ms) timings (Figure 2A inset; see STAR Methods). The frequency within the bursts (intra-burst frequency) varied between 0.1 Hz and 50 Hz. Even at 50 Hz, distal dendrites in the neuron model experienced only weak depolarization due to bAP attenuation (Figure 2A). We optimized the plasticity rule’s parameters (Table S1, set 1) to match the experimental data (Sjöström and Häusser, 2006, Sjöström et al., 2001). At proximal locations (90 μm from the soma; Figure 2B, left panel), a pre-post timing at a frequency of 0.1 Hz led to no change in weight, whereas at and above 10 Hz, in accordance with experiments (Sjöström et al., 2001), LTP was induced. In the model, 0.1-Hz bursts were unable to cause any relevant summation of postsynaptic traces in either LTP pathway. In contrast, at 10 Hz and above, such summation was achieved, leading to LTP. A post-pre timing caused LTD below a frequency of about 30 Hz and LTP beyond 30 Hz both in experiments (Sjöström et al., 2001) and in the model. Here, mainly pre-LTD was initiated in the model at lower frequencies. However, at higher frequencies, summation in both LTP pathways caused the overall switch. When pre-LTD was blocked in the model, this caused even stronger LTP, whereas blockade of pre-LTP substantially reduced the amount of LTP (Figure S2), which is in line with experimental studies (Sjöström et al., 2007). At distal locations (669 μm from the soma; Figure 2B, right panel), LTP was absent for both timings and across all frequencies, whereas frequencies above 20 Hz resulted in slight LTD. Except for pre-post at 50 Hz (Sjöström and Häusser, 2006), no further experimental data were available so all other conditions can be regarded as predictions by the model. Due to the strong attenuation of bAPs (Figure 2A), the local voltage signal at this distance was not strong enough to drive LTP pathways and rather caused LTD.Figure 2

Effects of Synapse Location on Rate- and Timing-Dependent Plasticity

(A) Stimulation protocol (Sjöström et al., 2001) (inset) and postsynaptic voltage profile of the neuron model with five somatic spikes (50 Hz) starting at time 10 ms. Voltage profile is shown as a function of time and location along one specific path from the soma into the apical dendrite.

(B) Model results as relative weight changes (lines) when fit to experimental data (filled circles, mean ± SEM) at a proximal location (90 μm in the model; left) and at a distal location (669 μm in the model; right) for different intra-burst frequencies. Pre- and postsynaptic bursts were shifted by either +10 ms (blue) or −10 ms (red). Experimental data was recreated from Sjöström et al. (2001) Figure 1D and Figure 7B and from Sjöström and Häusser (2006) Figure 3 (by using the exponential fit of inset data).

(C) Spatiotemporal plasticity windows showing relative weight changes (color coded) as a function of burst timing (x axis) and distance from the soma (y axis; see cell morphology on the left). Synaptic weight changes were calculated at 41 different locations and 101 different timings.

See also Figure S2.

To illustrate the overall interactions between spike timing, frequency, and location, we created spatiotemporal plasticity windows for this protocol (Figure 2C). At 10 Hz, the plasticity curve at the shortest distance (about 30 μm from the soma) resembled the typical relationship described by classical STDP paradigms (Bi and Poo, 1998). There were local maxima of LTD and LTP close to 0-ms timing, and with increasing delays, the amount of plasticity exponentially decayed to zero in both directions. With increasing distance to the soma, the LTD window (post-pre) became wider, whereas the LTP window (pre-post) rapidly became smaller, as reported in experiments on layer 2/3 (L2/3) pyramidal cells (Froemke et al., 2005) and ultimately vanished at far distal locations. Post–pre timings led to LTD across a wide range of distances from the soma, whereas pre-post timings led to LTP only below 200 μm, which is in accordance with experimental results (Sjöström and Häusser, 2006). At higher frequencies, local peaks were visible in addition to the one at 0 ms. These peaks repeated at multiples of the period (the inverse of the intra-burst frequency). For example, the 20-Hz condition exhibited peaks at −50 ms, 0 ms, and +50 ms. Furthermore, at 40 Hz and 50 Hz, pre-post timings showed a tendency toward overlapping LTP phases, overwriting proximal LTD entirely. This result was partly due to the fact that the presynaptic signals Z and G (which could loosely represent an unknown presynaptic signal and glutamate activation of NMDARs, respectively) decayed slowly and summated at higher frequencies (see Figure 1C). These windows clearly demonstrate that no configuration in this stimulation protocol could evoke distal LTP based solely on the backpropagation of axo-somatic APs, as seen in experiments (Sjöström and Häusser, 2006).

In a second experimental study, the dynamics of burst-timing-dependent plasticity were studied in basal dendrites of L2/3 pyramidal cells (Nevian and Sakmann, 2006). In this case, one presynaptic spike was paired with a burst consisting of one to three postsynaptic spikes at different frequencies. We implemented the corresponding protocols in a proximal basal dendrite (55 μm from the soma) of the L5 pyramidal neuron model, assuming that the electrophysiological properties of basal dendrites in L2/3 and L5 cells did not differ fundamentally with respect to this stimulation protocol. Using our plasticity rule with adjusted parameters (Table S1, set 2), we showed that all experimental outcomes were reproduced (Figure 3). Plasticity was not induced when there was only pre- or postsynaptic activity or when the delays were too long (Figure 3A). Pure post-pre and pre-post burst pairings at 50 Hz led to similar amounts of LTD and LTP, respectively, whereas intermediate timings caused intermediate effects (Figure 3B). In our model, this was explained by fast saturation of T (which could be loosely linked to postsynaptic VGCC-Ca²⁺; see Figure 1C). Pairings with single postsynaptic events at 50 Hz led to either LTD (−10 ms) or weak LTP (+10 ms), and pairings with two postsynaptic events caused similar results as with three events (Figure 3C). At 20 Hz, pairing one presynaptic spike with three postsynaptic spikes resulted in similar outcomes compared to evoking only one postsynaptic spike at 50 Hz (Figure 3D) because most time constants in the model were too small to cause substantial summation effects. When three postsynaptic spikes were generated at a frequency of 100 Hz, a pre-post timing led to very strong LTP, whereas a post-pre timing led to LTD (Figure 3D). Our plasticity model, thus, faithfully captured all of the outcomes observed in the experimental study. The plasticity changes induced through this set of stimulation protocols were mainly due to pre-LTD and post-LTP in our plasticity rule. Considering the loose biophysical analogies of the pathways, this matched experimental results after pharmacological manipulation, which indicated that LTD depended on activation of mGluRs and Ca²⁺ influx through VGCCs, whereas LTP depended on Ca²⁺ influx through postsynaptic NMDARs (Nevian and Sakmann, 2006).Figure 3

Burst-Timing-Dependent Plasticity

(A) STDP induction protocols pairing single presynaptic events with postsynaptic bursts. Comparison between experimental data (blue, mean ± SEM; from Nevian and Sakmann, 2006) and our simulations (orange) for only pre- or postsynaptic activity and for long delays at 50 Hz. Spike timing is defined as the interval between the onset of the presynaptic event and the first step current injection of the postsynaptic burst.

(B) As in (A) but with shorter delays between pre- and postsynaptic activity at 50 Hz.

(C) As in (A) but with either one or two instead of three postsynaptic events at 50 Hz.

(D) As in (A) but with three postsynaptic events at either 20 Hz or 100 Hz.

Next, we tested whether active properties of dendrites combined with our plasticity rule could reproduce plastic changes measured at distal synapses where a pre-post-post-post pairing led to LTD and a post-post-post-pre pairing induced LTP (Letzkus et al., 2006). Here, single presynaptic spikes were paired with a rapid (200 Hz) burst of three postsynaptic spikes (Figure 4A, inset). Such rapid bursts were found to sum up distally and evoke dendritic Ca²⁺ spikes, which was reproduced by the L5 pyramidal cell model (Hay et al., 2011) (Figure 4A). We then found a set of parameters (Table S1, set 3) for the plasticity model where simulation results matched the experimental outcomes of all four combinations of timings (+10/−10 ms) and locations (proximal at 90 μm from the soma and distal at 669 μm from the soma). At proximal locations, results of both the experiments and our simulations matched classical STDP, as pre-post led to LTP and post-pre led to LTD (Figure 4B, left). Without any distance-dependent changes to the plasticity rule, our simulations then also captured the experimentally observed plasticity switch at distal locations, where pre-post timings caused LTD and post-pre timings caused LTP (Figure 4B, right). We found the crucial property of these results to be the dendritic spike. It was delayed by about 20 ms compared to the first somatic AP and provided a long-lasting depolarization (Figure 4A). In the model, with pre-post stimulation, the presynaptic signal G at the distal synapse had already decayed substantially when the dendritic spike occurred and, thus, caused only intermediate elevation of C (which could be an abstraction of NMDAR-gated Ca²⁺) over most of the duration (Figure S3, left). Consequently, P was activated more strongly than K (loosely describing phosphatase-kinase competition), which caused post-LTD to surpass post-LTP. Conversely, with post-pre stimulation, the presynaptic event, although 10 ms late, strongly coincided with the delayed dendritic spike, elevating C beyond the threshold θC+ for a long duration and, thus, causing post-LTP to surpass post-LTD (Figure S3, right). To investigate this in detail, we also visualized the spatiotemporal plasticity window for this induction protocol (Figure 4C, left panel). There was a switch at around 200 μm from the soma where the classical proximal timing requirements changed to more complex distal ones that were shaped by the characteristic voltage curve of the dendritic Ca²⁺ spike. Interestingly, we found that between 200 μm and 400 μm, even the combined depolarization of bAPs and the forward-propagating dendritic spike were below LTP requirements so that only LTD was induced. The four conditions of the experiment (Figures 4C and 4D, triangles) matched the distinct areas in the spatiotemporal plot. We removed post-LTD to illustrate its contribution to these effects, which loosely corresponded to pharmacological inhibition of phosphatases or any other crucial component within this pathway (Figure 4C, right panel). The simulations predict that LTD is then entirely abolished at positive timings, leading to larger LTP areas, whereas pre-LTD remains present at negative timings. We conclude that our plasticity rule, when implemented at synapses on biophysically realistic dendrites with local dendritic Ca²⁺ electrogenesis, is able to reproduce the counterintuitive STDP data for distal synapses (Letzkus et al., 2006).Figure 4

Rapid Bursts and Dendritic Ca²⁺ Spikes

(A) Stimulation protocol (Letzkus et al., 2006) (inset) and postsynaptic voltage profile of the neuron model with a dendritic spike induced by high-frequency somatic stimulation (200 Hz) starting at time 10 ms.

(B) Relative weight changes in the model (orange) and experimental data (blue, mean ± SEM; from Letzkus et al., 2006, their Figure 5) are plotted as a function of burst timing for proximal (left, 90 μm) and distal (right, 669 μm) locations along the apical dendrite.

(C) Spatiotemporal plasticity windows showing relative weight change (color coded) as a function of burst timing (x axis) and distance from the soma (y axis; see cell morphology on the left). In the control condition (left), all pathways were functional. Downward triangles indicate proximal locations, and upward triangles indicate distal locations used for the model simulations in (B). In the blockade condition (right), post-LTD was deactivated.

See also Figure S3.

A recent study found that subthreshold activation of a small cluster of four synapses led to plasticity at thin dendritic branches that depended on the relative location of the cluster on the respective branch (Weber et al., 2016). Due to massive increases in input resistance, such thin, distal dendrites are expected to experience considerably more powerful voltage transients caused by synaptic inputs than proximal dendrites (Williams and Stuart, 2002), which could explain these results. We tested this idea by implementing a stimulation protocol in which four synapses located on the same branch segment were strongly activated in rapid succession and repeated simulations for every single segment of the neuron model. Such activation of a small cluster of synapses did indeed result in plasticity, revealing a gradient in relation to the dendritic location (Figure 5A, boxes and center). At proximal, thick dendritic segments, LTD was predominant, which switched to LTP at more distal locations close to the dendritic tips. This gradient was due to dramatic differences in local synaptic potentials that occurred even within single branches (Figure 5B, top left panel). The experimental study focused mainly on oblique dendrites of hippocampal CA1 pyramidal cells (Weber et al., 2016). In our configuration, we found weaker relative weight changes in oblique dendrites of the L5 pyramidal cell model, although our results in distal tuft dendrites agree with the experimental data (Figure 5B, bottom left panel). Generally, at branch points (light orange and green example locations in Figure 5), no plasticity or LTD was common, whereas LTP was typically induced close to the tips (dark orange and green example locations in Figure 5). Due to the absence of a clear post-pre timing in this protocol, pre-LTD was ineffective and the majority of changes were caused by post-LTD and both LTP pathways. We noticed that synaptic potentials in the cell model were boosted by dendritic voltage-dependent Na⁺ and Ca²⁺ channels. Blocking both of these channel types resulted in overall less LTP and more LTD close to the dendritic tips in our specific case (Figures 5A and 5B, right). However, the experimental study showed no significant change in plasticity at oblique dendrites after blocking voltage-dependent Na⁺ channels alone (Weber et al., 2016). We conclude that based on strong input resistance increases, it is possible in thin dendrites to induce bidirectional location-dependent plasticity with subthreshold synaptic inputs alone, as recently observed in some experiments (Sandler et al., 2016, Weber et al., 2016).Figure 5

Subthreshold Activation of Small Synaptic Clusters

(A) Color-coded dendritic maps of plasticity during subthreshold activation of a cluster of four synapses. Simulations were repeated for all possible locations in the neuron model (boxes on the left show zoomed-in view of example cluster locations). Dendritic maps show average cluster weight changes for control conditions (center) and during block of dendritic Na⁺ and Ca²⁺ channels (right).

(B) Voltage traces and average relative weight changes for the example locations shown in the boxes in (A) for both control (left) and channel block (right) conditions. Plasticity data recreated from Weber et al., 2016 Figure 7f, shown as mean ± SEM).

After confirming the functionality of our plasticity model by reproducing experimental data of several different stimulation protocols, we predicted how synapses in different locations change in response to more naturally occurring input patterns to pyramidal cells, for which no experimental data exist as of now. As L5 pyramidal cells possess the exclusive property of spanning all six cortical layers, they could potentially act as integrating units for different streams of information (Larkum, 2013). A possible integration mechanism, called backpropagation-activated Ca²⁺ (BAC) firing, involves coincidence of strong proximal and distal inputs that may lead to dendritic spikes and bursts of axo-somatic APs, thereby changing the output mode of the neuron (Larkum et al., 1999), which we expected to have an effect on synaptic plasticity. We implemented a scenario where synapses were placed randomly across basal and tuft regions of the L5b neuron model in a similar way as done in a recent study (Shai et al., 2015) (Figure 6A, shaded areas). In addition to these “background” input synapses, we placed a subset of 10 synapses close to each of the two main spiking zones (Figure 6A, pipette symbols) and equipped them with our plasticity rule. The stimulation protocol consisted of a 100-ms phase of random synaptic activity. In one example, basal activity alone (Figure 6B, left) evoked a few irregularly occurring axo-somatic APs with weak impact on tuft dendrites. Apical synapses did not show plasticity under these circumstances, whereas basal synapses showed a tendency toward LTD. Apical activity alone (Figure 6B, center) did not cause any plasticity in either group of synapses. Coincident activation of both basal and apical synapses (Figure 6B, right) caused BAC firing in the neuron model, evoking both dendritic spikes as well as bursts of APs. There was no absolute switch toward either LTP or LTD in any of the two groups of synapses. Instead, synaptic weights diverged from baseline in both directions. What determines whether a synapse potentiates or depresses during BAC firing? We monitored the time course of synaptic weight during the example simulation for both the most potentiated and most depressed synapse of each group (Figure 6C). This revealed that synapses underwent LTP if they were active during BAC firing but experienced LTD if they were active slightly before or after BAC firing. To assess the underlying weight distributions, we ran 100 simulations with different random seeds, resulting in a total of 1,000 plastic apical and basal synapses in each condition (Figure 6D). We noticed that dendritic spikes were much more common when both groups were concurrently active (probability of about 10% in apical only, 15% in basal only, and 95% in apical and basal conditions). The plasticity results showed that basal activity alone shifted basal synaptic weights toward the LTD regime (Figure 6D, left), whereas apical activity alone did not cause much plasticity (Figure 6D, center). Coincident basal and apical activity led to almost the same distribution of basal weights but opened up LTP for apical synapses (Figure 6D, right). Thus, our simulations predict that BAC firing potentially gates profound bidirectional changes in synaptic weights, especially at apical locations.Figure 6

Coincident Activation of Basal and Apical Tuft Inputs

(A) Morphology of the neuron model highlighting locations of random background inputs at basal (light purple) and tuft (light green) dendrites, as well as locations of synapses equipped with the plasticity rule at basal (purple pipette) and tuft (green pipette) dendrites.

(B) Example voltage traces and weight changes experienced by plastic synapses at basal (purple) and tuft (green) dendrites. Shaded areas indicate intervals of active background inputs, which were either basal alone (left), tuft alone (center), or both (right).

(C) Example comparison of most potentiated (red) and most depressed (blue) synapses during coincident basal and tuft inputs, including voltage traces (from B; top right), presynaptic activation G and weight changes over time.

(D) Weight distribution histograms of 100 randomly initialized simulations for all three conditions.

Finally, we wanted to know what our model’s predictions would be regarding heterosynaptic plasticity effects based on local voltage differences. In principle, strong depolarization at one point in the dendrite, e.g., by high-frequency synaptic input, should have the potential to lead to depression in neighboring synapses with low-frequency activity (Jedlicka et al., 2015, Jungenitz et al., 2018) if these synapses experienced depolarization below LTP requirements due to attenuation. We tested this by placing two clusters of 8 synapses each to a thin apical tuft dendrite in the neuron model (location a: 1,077 μm from the soma, location b: 950 μm from the soma; Figure 7A, left). Synapses in each cluster were then randomly activated in two modes, either uniform (mimicking 8-Hz spontaneous Poisson activity) or synchronized (mimicking 8-Hz stochastic oscillatory activity; Figure 7A, right). Using this protocol, we found that when both clusters were uniformly activated for 350 ms, levels of depolarization were moderate (below −40 mV), NMDA conductances were relatively small, and weights barely changed (Figure 7B, left column). However, when distal synapses at location a were switched to synchronized activation, NMDA spikes were elicited, causing strong local depolarization (up to about −12 mV) by substantial increases in NMDA conductance and leading to LTP on average (Figure 7B, right column). In contrast, proximal synapses at location b then experienced moderate prolonged depolarization (up to about −35 mV) without major increases in NMDA conductance, resulting mainly in LTD (Figure 7B, right column). Here, the distance of synapses at location b from the origin of NMDA spikes was far enough so that depolarization had already been attenuated considerably, preventing LTP and, thus, leading to LTD. These simulations show that local voltage-based heterosynaptic effects can be modeled using our plasticity rule. The results suggest that NMDA spikes could serve as powerful triggers for LTP, but due to their spatially restricted profile might cause opposing effects in weakly active neighboring synapses.

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Software and Algorithms
Cortical L5b pyramidal cell model	Hay et al., 2011	ModelDB: 139653
Four-pathway phenomenological synaptic plasticity model	This paper	ModelDB: 251493
NEURON	Carnevale and Hines, 2006	RRID: SCR_005393
ModelDB	McDougal et al., 2017	RRID: SCR_007271

Further information and requests for resources should be directed to and will be fulfilled by the Lead Contact, Christian Ebner (ebner@fias.uni-frankfurt.de). This study did not generate new unique reagents.

For experimental results reproduced by our model, original data is always given as mean ± SEM (see Figures 2B, 3, 4B, and 5B). Simulation data presented in the histograms of Figure 6D was acquired using 100 different random seeds for generating Poisson-distributed event sequences in 10 plastic synapses each, leading to n = 1,000 plastic synapses per location and condition. Identical seeds were used between conditions.

The accession number for the stimulation procedures and the plasticity model reported in this paper is ModelDB: 251493.