Synaptic plasticity is thought to induce memory traces in the brain that are the foundation of learning. To ensure the stability of these traces in the presence of further learning, however, a regulation of plasticity appears beneficial. Here, we take up the recent suggestion that dendritic inhibition can switch plasticity of excitatory synapses on and off by gating backpropagating action potentials (bAPs) and calcium spikes, i. e. , by gating the coincidence signals required for Hebbian forms of plasticity. We analyze temporal and spatial constraints of such a gating and investigate whether it is possible to suppress bAPs without a simultaneous annihilation of the forward-directed information flow via excitatory postsynaptic potentials (EPSPs). In a computational analysis of conductance-based multi-compartmental models, we demonstrate that a robust control of bAPs and calcium spikes is possible in an all-or-none manner, enabling a binary switch of coincidence signals and plasticity. The position of inhibitory synapses on the dendritic tree determines the spatial extent of the effect and allows a pathway-specific regulation of plasticity. With appropriate timing, EPSPs can still trigger somatic action potentials, although backpropagating signals are abolished. An annihilation of bAPs requires precisely timed inhibition, while the timing constraints are less stringent for distal calcium spikes. We further show that a wide-spread motif of local circuits—feedforward inhibition—is well suited to provide the temporal precision needed for the control of bAPs. Altogether, our model provides experimentally testable predictions and demonstrates that the inhibitory switch of plasticity can be a robust and attractive mechanism, hence assigning an additional function to the inhibitory elements of neuronal microcircuits beyond modulation of excitability.
To successfully interact with our environment, we need to adjust to new or changing conditions. It is widely accepted that this ability involves alterations of synaptic connections in the brain, so-called synaptic plasticity [1]. While synaptic plasticity fulfills key requirements for the incorporation of new knowledge and memories into neural circuits, it also introduces the risk of changing connections that are essential for previously stored information, a problem termed plasticity-stability dilemma [2,3]. Hence, a mechanism to selectively switch plasticity on or off would be useful. In this context, inhibition has been proposed as a means to regulate plasticity [4–6]. GABAergic interneurons that target the dendrites of pyramidal cells may control backpropagation of action potentials to excitatory synapses and hence the coincidence signal required for Hebbian forms of synaptic plasticity. Alternatively, such inhibition could affect the NMDA-receptor-mediated component of excitatory postsynaptic potentials (EPSPs) [5,7]. Indeed, recent experimental work has shown that inhibitory dendritic synapses can weaken the backpropagating action potential (bAP) in the dendrite of pyramidal cells so that calcium signals required for the plasticity of excitatory synapses are reduced [8]. These findings provide strong support for a crucial role of inhibition as a regulator of plasticity, in particular as direct stimulation of inhibitory neurons leads to a cancellation of bAPs in pyramidal cells. For an effective switch in plasticity, however, it needs to be ensured that while the dendritic inhibition cancels the bAP, the forward-directed EPSP (that is meant to cause the bAP in the first place) still reaches the soma and orthodromic information flow is preserved. Whether a separation of the effect of inhibition on EPSP and bAP is possible on physiological timescales is currently unclear and needs to be explored in view of the well-known efficiency of ‘on-path’ inhibition in impairing passive EPSPs in the dendrite [9]. We here address this question as well as identify the temporal and spatial constraints that are required to reliably modulate plasticity of excitatory synapses in pyramidal cells. To this end, mathematical modeling suggests itself, because it allows to systematically vary both the strength and dendritic location of inhibition and to monitor bAPs and calcium spikes in the whole dendrite with high temporal and spatial resolution. We hence adapted a multi-compartmental model of pyramidal cells to reproduce a number of key electrophysiological characteristics. These included a realistic decrease of the amplitude of bAPs along the dendritic tree [10], characteristics of bAP-activated calcium spike (BAC) firing [11], and the generation of distal calcium spikes at a critical frequency of somatic stimulation [12]. Using this model, we identify conditions under which a modulation of bAPs and calcium spikes is possible and does not impair the forward-directed information flow to the soma. We demonstrate that shunting inhibition gates bAPs and calcium spikes in an all-or-none manner, laying the foundation for a binary switch of plasticity of excitatory synapses. Further, we identify the timing constraints for an efficient inhibitory gating of bAPs and calcium spikes. Implementing an additive spike-timing-dependent plasticity (STDP) rule [13], we find that plasticity of excitatory synapses is indeed switched as a consequence of the effects of inhibition on the coincidence signal. Depending on the site of inhibition, this effect can be more global or constrained to smaller dendritic compartments and hence also distinct pathways converging onto pyramidal neurons. We observe that timing constraints for the gating of bAPs are relatively strict in that inhibition has to arrive with a precision of ∼1 ms. Local gating of distal calcium spikes, however, can be achieved within a wider time window of several milliseconds. Additionally, calcium spikes are more sensitive to inhibition in that smaller conductances suffice to abolish them. Importantly, with appropriate timing of inhibition, forward-directed EPSPs can still drive somatic firing while Hebbian coincidence signals are canceled. Finally, we suggest that a common circuit motif of feedforward inhibition can ensure the appropriate timing required for the plasticity switch by inhibition. Our model study provides testable experimental predictions and strengthens the view that the functional role of interneurons includes a pathway-specific regulation of plasticity, in addition to the widely studied regulation of excitability and information flow in local networks [14].
First, we sought to understand the effect of local dendritic inhibition on bAPs. To this end, we placed a shunting inhibitory input on the proximal apical dendrite, systematically varied its strength, and monitored the amplitude of a somatically-induced bAP along the apical dendrite. For weak inhibition, the bAP amplitude was reduced around the dendritic location of the inhibitory input, but recovered to its full amplitude as the bAP propagated down the dendrite. In contrast, strong inhibition barred the bAP from invading the dendrite (Fig 2A). The transition from a fully intact bAP to a complete bAP failure occurred abruptly at a critical inhibitory conductance (Fig 2B). This all-or-none behavior was observed for inhibition at different locations along the shaft of the apical dendrite, albeit with different critical amounts of inhibition (Fig 2B). From the perspective of a synapse further up in the dendrite, the bAP was either fully intact or completely canceled. Fig 2 shows the case for a synapse on the oblique dendrite, which is taken as a representative for one excitatory pathway subject to bAP-dependent STDP throughout the paper. The same effect could, however, also be observed for propagation into the apical tuft. The amount of inhibition required to cancel a bAP appeared to be in a realistic range. For example, when inhibition was placed at 90 μm from the soma (Fig 2A and 2B), the critical inhibitory conductance was slightly above 25 nS, corresponding to about 25 co-activated inhibitory synapses of 1 nS [24]. Such inhibition could be provided by about 2–3 co-activated interneurons, given that interneurons form up to a dozen contacts onto a single pyramidal cell [25]. We checked that the core observations of the effects of inhibition onto bAPs were not altered when shunting synaptic inputs were distributed along the dendrite (S1 Fig). A moderate temporal jitter (on the order of 1 ms) in the activation of inhibitory synapses also did not abolish the all-or-none behavior, but when a critical amount of inhibition was reached too early, the neuron was prevented from spiking. Overall, however, timing of inhibition needed to be relatively precise, as we will outline in the following section, where we first present data on the compartment-specificity of the effects. Due to its relatively local effect, shunting inhibition can control dendritic signals in a manner that is distinct between compartments, such as basal and apical dendrites. We hence investigated the effect of inhibition in different compartments (i. e. the basal, oblique and distal apical dendrites, as well as the soma/axon), on the bAPs and calcium spikes, in the same and other compartments. While many neurons exhibit bAPs, some neuron types (such as cortical layer 5 and CA1 pyramidal neurons) can additionally generate distal calcium spikes that trigger BAC firing. Because calcium spikes can also serve as plasticity signals [26], we analyzed the effects of inhibition on bAPs and calcium spikes during this firing mode. To trigger calcium spikes in the distal dendrite, we here combined somatic current injection in our model with coincident depolarization in the distal dendrite. In the control situation without inhibition (Fig 4A–a), a calcium spike was triggered in the distal dendrite and the resulting BAC-firing-induced bursts of APs could be observed in the other compartments. Calcium spikes (and the accompanying burst of APs) proved highly sensitive to inhibitory inputs in the distal part of the apical dendrite (Fig 4A–bI). In contrast, the bAP was relatively robust to distal inhibition and readily invaded both the apical oblique and basal dendrites despite the presence of distal inhibition (Fig 4A–bII/III). In the basal dendrite, inhibition was not sufficient to cancel all BAC firing related bAPs, because the single GABAA conductance decayed too fast, and hence could not exert an influence on later bAPs (Fig 4A–dIII). bAPs in the basal dendrite could, however, be controlled by inhibition that outlasted the burst. Such inhibition could be mediated by inhibitory synapses of the same dynamics but an activation that is distributed in time (as it could be provided by bursting interneurons). Along these lines, four temporally spread out inhibitory inputs were able to cancel the bAPs in the basal dendrite (Fig 4A–eIII). The quantitative dependence of this effect on frequency and number of such repetitive inhibitory inputs is shown in S2 Fig. Altogether, we have seen that, in principle, inhibition can cancel coincidence signals in a manner that is selective between compartments. To demonstrate the robustness of our results with respect to morphological and physiological detail, we replicated the main findings in an anatomically reconstructed L5 neuron model with different physiology [23] (Fig 5). To demonstrate that cancelation of the coincidence signals indeed results in the anticipated changes to synaptic plasticity, we next subjected the model cell to a classical plasticity paradigm. Contemporary biophysical and phenomenological models of STDP [13,27–29] depend on postsynaptic variables such as depolarization or calcium concentration, which are in turn shaped by bAPs and calcium spikes. Because the latter can be abolished by properly timed and placed inhibition, we suggest that cancellation of these signals via inhibition will lead to a noticeable change in the predicted learning rule (or abolish plasticity altogether). To demonstrate this, we simulated a typical STDP pairing protocol (see, for example, [30,31]). Somatic current injection was paired with excitatory synaptic activation on either basal, oblique or distal dendrites with a time delay Δt. Excitatory synaptic plasticity was Hebbian with a positive weight change for positive timings between the activation of the synapse and the arrival of a depolarizing postsynaptic potential and a negative weight change for negative timings (for details see Methods). We implemented the simple additive rule by [13], leading to the classical asymmetric STDP window (Fig 6). While the learning windows for oblique and basal synapses resembled the classical one (Fig 6II/III), we found the distal learning window to be more symmetric (Fig 6I). The latter results from the assumption that at distal synapses a calcium spike serves as the signal for plasticity. Because a calcium spike required the coincidence of bAP and EPSP, a calcium spike could only occur (see Methods) after presynaptic activation, such that the synaptic change was positive unless the relative timing of bAP and EPSP did not lead to a calcium spike (in which case it was zero). As expected, inhibitory cancellation of bAPs and calcium spikes in the dendrite resulted in flat learning windows, corresponding to zero synaptic change (compare Figs 3A, 4A and 6). Because of the all-or-none effect of inhibition on dendritic signals, we predict a switch-like effect on learning for any plasticity rule relying on the coincidence of pre- and postsynaptic spiking. Above, we have shown that the modulation of the bAP requires inhibition to fall into a small time window closely tied to the initiation of the somatic action potential in the pyramidal neuron. The question arises whether such timing is realistic and how it can be achieved. As a proof of principle, we here show that the common local circuit motif of feedforward inhibition [32] is a good candidate to provide the appropriate timing. In feedforward inhibition an excitatory signal is passed on to a pyramidal neuron along two parallel pathways: one direct excitatory pathway to the pyramidal cell and one indirect pathway, where the signal first excites an inhibitory neuron that sends its output on to the pyramidal cell (see Fig 7A, black parts of the schematic representation). From the perspective of the pyramidal neuron, excitation in this circuit arrives first to be followed by a delayed inhibition [33]. Embedding our pyramidal cell model into this circuit we found that inhibition arriving 2 ms after the EPSP was suited to control the bAP signal (Fig 7B, Δt = 2 ms). This delay matched experimentally measured inhibition delays well [33,34] and was suited to control backpropagation without affecting forward-directed signal flow responsible for the initiation of postsynaptic somatic spikes. Interestingly, interneuron dynamics play a role for the timing requirements. Dependent on interneuron type, spike latencies and firing frequencies can vary. The size of the temporal window where inhibition can cancel bAPs (without canceling EPSPs) tends to be smaller for proximal inhibitory synapses than more distal synapses, as outlined above. One may hence speculate that the dynamics of interneurons innervating proximal parts of the dendritic tree should be sufficiently fast. To highlight the role of interneuron dynamics, we probed the circuit with two interneurons differing in their spiking dynamics. We used the interneuron model from the previous paragraph and compared its performance in the circuit to that of a second interneuron with slower dynamics. The latter was implemented by artificially slowing down the opening and closing rates of the interneuron’s sodium channels. In this example, only the interneuron with a short spike latency met the tight timing requirements for bAP modulation at a more proximal synaptic location (S6A Fig). The timing provided by the slower interneuron did not suffice to cancel the bAP proximally. In contrast, both (faster and slower) interneurons were able to cancel the bAP (and accompanying calcium spike) when their synapses were located at more distal parts of the dendritic tree (S6B Fig).
The central hypothesis that inhibition can control synaptic plasticity has been discussed in the experimental and theoretical literature [5–7,35–37]. Its feasibility and functional relevance relate to three observations. First, different compartments within a neuron often receive excitatory input from distinct synaptic pathways [15], such that a compartment-specific regulation of plasticity could be functionally advantageous. Second, different compartments are targeted by different inhibitory interneuron classes [25,38], so that Hebbian coincidence signals could be regulated locally. Third, dendrites support different plasticity-related coincidence signals, namely bAPs [39,40] and calcium spikes [11,18,26], which are sensitive to inhibitory control [4,11,41–43]. Besides a switch in plasticity, inhibition has been shown to contribute to the shape of temporal requirements for plasticity in different parts of the dendrite [44–46]. Moreover, the induction and coincidence requirements of plasticity have been described to change with development, potentially through an increase in inhibition [47–49]. Strong experimental evidence in support of the ability of inhibition to modulate plasticity via gating of bAPs was recently provided by Müllner et al. (2015) [8]. They showed that one important step in this mechanism—the suppression of somatically elicited bAPs by dendritic inhibitory synapses with high temporal precision—is indeed possible. For a robust switch of plasticity, however, several points remain to be shown: (1) gating of coincidence signals can be exerted in a controlled and systematic manner, (2) forward information flow via EPSPs can be maintained, and (3) plasticity itself is altered. Our analysis on the basis of mathematical models with physiologically constrained properties demonstrates that all three points can be fulfilled. In particular, we find that shunting inhibition is sufficient to cancel bAPs and calcium spikes while preserving the ability of EPSPs to elicit somatic APs. Timing of inhibition needs to be precise, but is not unrealistic (∼1 ms for bAPs and >5 ms for calcium spikes). Our study makes several testable predictions. In particular, the all-or-none nature of bAP modulation enabling the binary switch as well as the compartment specificity could be tested in experiments. To investigate the latter, classical paired recording paradigms for synaptic plasticity could be extended by optogenetic stimulation of different interneuron classes. Particularly promising candidates are the above mentioned SOM or PV interneurons that target perisomatic and distal dendritic regions of pyramidal cells, respectively [25,38]. Moreover, perisomatic versus distal modulation of dendritic coincidence signals poses different timing requirements on inhibition. The proximity of inhibition to the soma constrains the modulation window, because the times of passage of the forward-directed EPSP and the backward-directed bAP (at the location of the inhibitory synapse) are very close. Therefore, inhibitory synapses ought to have a certain distance to the soma to be well suited to control the bAP and plasticity without canceling somatic spiking. Our results suggest that at a distance of ∼100 μm, which is relatively proximal for apical dendrites, the timing window becomes wide enough to enable inhibitory control (S4 Fig). We predict that the regulation of bAPs caused by more proximal excitation in the pyramidal neuron may be better achieved by interneurons with short latencies, such as fast-spiking interneurons. We found that distal inhibition of the calcium spike did not require very precise timing and tolerated longer delays to the onset of shunting inhibition. In the context of the here discussed mechanism of plasticity regulation, it would be functionally useful if proximal and distal inhibition were accomplished by interneurons of different dynamics. This proposition is in line with the fact that the many interneuron types connected to pyramidal cells differ in their spiking dynamics as well as their dendritic target location in pyramidal cells. Regulation of calcium spikes in the distal dendrite, on the other hand, need not be provided by local circuits, but could be mediated by longer-range connections including multiple synaptic transmissions. One may speculate that this time scale is beneficial when incorporating top-down information that tends to arrive in superficial layers [50]. From the perspective of the pyramidal neuron, we find that, a short rise time of synaptic inhibition (like that typical for GABAA-mediated inhibition (∼0. 5 ms) ) is crucial for the mechanism to operate effectively. In contrast, the temporal extent of inhibition (determined by the temporal extent of inhibitory input as well as the decay time constant of inhibition) is less important. These variables are likely to be more relevant in setting a lower frequency limit to excitatory signals because they could interfere with a following EPSP if inhibition lasted for too long. For GABAA-typical decay time constants on the order of 5 ms (as used here), such limits to the frequency of EPSPs are sufficiently large (>100 Hz). We note that GABAA-mediated inhibitory postsynaptic potentials (IPSPs) have been described to differ between proximal and distal sites [20]. The difference is mainly in half-width and decay time constant, less in rise time. We hence used the same time constants for proximal and distal GABAA-mediated currents. Our results suggest that, in contrast to the other compartments, in basal dendrites several volleys of interneuron input may be needed to suppress all bAPs. In this scenario, a burst of bAPs invades the dendrite in the BAC firing mode. For this compartment, an innervation by bursting interneurons may hence be advantageous and several bursting interneuron types, including double bouquet cells [51] and bistratified cells [52–54], have been described. Our prediction on the timing dependence of the modulation of bAPs quantitatively agrees with the experimental study by [8]. They found that calcium transients, evoked by a train of bAPs, are maximally inhibited with a spike timing (between interneuron and pyramidal cell) on the order of < 5 ms. This time scale is compatible with our predictions for the required timing of bAP modulation (see Fig 3B/C). Also space constants of inhibition, observed to be on the order of 23–28 μm by Müllner and colleagues, are comparable to our results (see Fig 2). As our study showed, inhibition has to fall into a narrow time window to gate APs without simultaneously canceling EPSPs that are meant to drive the postsynaptic cell, potentially casting some doubt on the robustness of the mechanism of an inhibition-mediated plasticity switch. Feedforward inhibition, however, seems a good candidate to guarantee the appropriate timing, in particular, as in such a circuit inhibition follows excitation within a relatively fixed time interval. Feedforward inhibition is a common circuit motif [55,56] that has, for example, been implicated in keeping a balance of excitation and inhibition and to open time windows for precise firing events [33,34,57]. While we do not suggest that it is the only mechanism that can provide suitable timing for the plasticity switch discussed here, it can satisfy both temporal requirements for the cancellation of bAPs: the delay between forward-directed excitation and the shunting inhibition, as well as the temporal precision on the order of a millisecond. In the circuit model (Fig 7A, black part of the schematic), a delay on the order of 2–3 ms between onset of the excitatory EPSP and the onset of the inhibitory IPSP in the pyramidal neuron was required to cancel the bAP triggered by the EPSP. This delay has to be accounted for by the processing in the inhibitory neuron itself and comprises the time the EPSP in the interneuron needed to reach this neuron’s soma, spike generation in this cell, propagation of the action potential along the axon, and the inhibitory synaptic transmission between interneuron and pyramidal cell. The timescale of 2–3 ms is plausible for these processes and agrees with the range reported in experiments [33,34]. Characteristics of the interneuron allow for some flexibility of this delay [58]. For example, a fast spike generation (as in fast-spiking interneurons, due to lower firing threshold and/or stronger excitation on interneurons [59,60]) plays an important role in keeping the delay short. Additionally, dendritic propagation is slower than axonal propagation, so that the relative length of these cables influences the required delay (which may potentially be correlated to the somatic location of the interneuron, assuming a regular, bipolar morphology where the soma lies in between dendrites and axon). For example, a more proximal excitation in the pyramidal neuron requires a shorter delay of inhibition. The integration time in the pyramidal neuron depends on the location, and distribution of synaptic excitatory inputs, next to being negatively proportional to the number, strength and rise time of the synaptic conductances. In a feedforward inhibitory circuit, inhibition, by default, comes along with excitation. This means that an additional source is required to switch off the inhibitory influence (see Fig 7A, gray part of the schematic). Per se, when the interneuron is active, plasticity of excitatory pyramidal synapses is switched off. In turn, silencing the interneuron up-regulates pyramidal cell plasticity. This design indicates a disinhibitory regulation of Hebbian plasticity, which is in line with recent findings for behavioral learning [61,62]. Interestingly, advances in unraveling the connectivity profile of different interneuron classes suggest that the cortical mircocircuitry seems to be well suited for a disinhibitory and compartment-specific regulation [24,36,63–65]. In particular, vaso-intestinal peptide (VIP) expressing interneurons and other supragranular interneuron classes have been proposed to modulate the activity of somatostatin (SOM) - and parvalbumin (PV) - positive cells—inhibitory interneurons with distinct postsynaptic targets within the pyramidal dendrite—in a way that is consistent with a rapid redistribution of inhibition between perisomatic and distal apical dendrites of pyramidal cells [24,66]. We note that distal disinhibition in pyramidal cells is special because it can significantly and reversibly increase the occurrence of calcium spikes and somatic bursts [67]. Calcium-induced bursting has been proposed as a mechanism for the association of inputs arriving through different pathways [11]. Because synaptic plasticity is often more efficiently induced by pairing presynaptic inputs with postsynaptic bursts, it is tempting to speculate that calcium spikes can induce a form of global synaptic plasticity within a neuron. Consequently, plasticity in the entire dendritic tree could be regulated at a single spot through local disinhibition. Note that such a form of plasticity regulation does not exclude, but complements our main hypothesis, because proximal inhibition could contribute to impair the arrival of bursts of backpropagating APs at basal and oblique synapses (see Results on basal signaling). However, our prediction that basal plasticity regulation requires more complex inhibitory innervation in the presence of a calcium spike, possibly indicates that calcium-dependent burst firing is in place to overcome the effects of inhibition by increasing the likelihood of backpropagating action potentials passing the barrage. STDP is an important and commonly observed mechanism underlying many forms of learning [68]. Regulation of STDP (a potential mechanism is considered in this study) is hence highly relevant. However, there are other, non-Hebbian forms of synaptic plasticity which are independent of postsynaptic spiking. For example, plasticity can be directly triggered by spikes of dendritic origin that arise locally from cooperative or strong synaptic activation [26]. The proposed pathway-specific switch does not apply to these types of plasticity. Still, theoretical and experimental studies have shown that dendritic spikes can be affected by inhibition on a local (spine- or branch-specific) or global level [69–71], possibly providing a mechanism to control timing-independent plasticity. Especially NMDA spikes cannot be excluded as a target for inhibitory modulation. Because they present a more local phenomenon that carries limited information about somatic spiking, an investigation thereof is beyond the scope of the present study. One kind of synaptic plasticity which is unlikely to be regulated by inhibition of dendritic events at all is presynaptically induced and expressed LTD [72]. In this study, we provide computational evidence that the known physiological characteristics of pyramidal cells are sufficient to exert a binary control of plasticity while preserving excitatory, forward-directed information flow. Despite the fact that the identified timing requirements for this mechanism may at first seem tight, the proposed local circuit motif of feedforward inhibition seems well suited to provide inhibition at appropriate times. Our modeling work substantiates the point of view that inhibition is likely to play a crucial role for Hebbian plasticity of excitatory synapses in a manner that can be specific to individual pathways of the local network [5]. Recent advances of optogenetic methods allow to shed further light on the computational relevance of interneuron diversity [50,63,64,73] and could—by targeting specific interneuron types—help to reveal whether (and if so which) neurons can regulate plasticity in local circuits.
To study the impact of inhibition on dendritic spikes, we recorded the membrane voltage in the basal dendrite (75 μm), the oblique dendrite (370 μm) and the apical tuft (650 μm). Additionally, we monitored the calcium current in the apical tuft at the same spot. Spike amplitudes were measured as the maximum voltage deviation from rest (a membrane voltage reaching 10 mV would be a spike of amplitude 10 mV- (-73 mV) = 83 mV). bAPs were normalized to the non-inhibited amplitude of the first bAP. Calcium spikes were quantified by the integral of the calcium current (to clearly disambiguate between calcium and sodium components of the voltage trace at the same spot), normalized to the non-inhibited calcium current. A somatic spike was detected when its amplitude reached a threshold of 80 mV. Synaptic plasticity was implemented with an additive spike-timing dependent plasticity rule as in [13]: Δ w = { - A - exp (Δ t τ -) if Δ t ≤ 0 A + exp (- Δ t τ +) if Δ t > 0 where Δt is the difference between pre- and postsynaptic spike time: tpost-tpre. A postsynaptic spike was counted when the membrane voltage at the synapse reached a threshold of -20 mV. For apical tuft plasticity, a postsynaptic spike was counted when the calcium concentration reached a threshold of 0. 5 mM. We used a different model for distal plasticity, assuming that the calcium spike governs calcium dynamics and thus plasticity in the distal dendrite (for an illustration of our argument, see S5 Fig). Parameters were: potentiation factor A+ = 0. 001, depression factor A− = 0. 00106, potentiation time constant τ+ and depression time constant τ− were both 20 ms. Hard bounds set to 0 and 0. 0001 μS were imposed on synaptic weights. Somatic current injection was paired with dendritic synapse activation 100 times with a frequency of 1 Hz with varying Δt. The feedforward inhibitory circuit contained the introduced multi-compartment pyramidal neuron model and a model of a fast-spiking interneuron (IN). The latter, a single-compartment model with Hodgkin-Huxley-type sodium and potassium conductances, was taken from [85] (ModelDB accession: 3817). The interneuron with slower spike initiation was adapted from the fast-spiking interneurons by changing the sodium dynamics. The opening rate α was changed by a factor of 0. 1, the closing rate β by a factor of 0. 2. Both, the interneuron and the pyramidal neuron received EPSPs (NEURON Exp2Syn with rise and decay time constants of 0. 5 ms and 2 ms, respectively, and a reversal potential of 0 mV) from an excitatory source (EX) at time t0. The excitatory synapse onto the interneuron had a maximum conductance of 300 nS. To mimic inputs from oblique dendrites, eight synapses were distributed onto the apical trunk of the pyramidal neuron between 140 and 420 μm [86] with a total maximum conductance of 20 nS. The inhibitory synapse from the fast-spiking interneuron had the same properties as all shunting synapses modeled in this study (τrise = 0. 5 ms; τdecay = 5 ms; reversal potential -73 mV). From [23], we took the neocortical L5 pyramidal cell model constrained by both BAC firing and perisomatic step current firing with an anatomically reconstructed morphology (ModelDB accession: 139653). We did not change any parameters. To investigate the all-or-none effect, the model was stimulated with somatic current injection as in [23]. We added inhibitory synapses (NEURON Exp2Syn synapses; rise and decay time constants 0. 5 and 5 ms, respectively) to the model and placed them ∼ 100 μm (proximal) and ∼617 μm (distal) from the soma. The onset of inhibition was 2. 5 ms after the onset of the somatic pulse if not varied. Voltage traces were measured in the soma, the oblique branch and an apical tuft branch. In Fig 5E and 5F, inhibition had maximum conductances of 100 nS (proximal) and 200 nS (distal).
We must constantly learn in order to meet the demands of a dynamically changing environment. The basis of learning is believed to be synaptic plasticity, i. e. the potential of neuronal connections to change. Depending on context, however, it may be either useful to learn and modify connections or, alternatively, to keep an established network structure stable to maintain what has been already learned (also referred to as the plasticity-stability dilemma). The ability to switch synaptic plasticity on and off in a flexible way hence constitutes an attractive feature of neuronal processing. Here, we analyze a cellular mechanism based on the inhibition-mediated gating of coincidence signals required for Hebbian forms of excitatory synaptic plasticity. While experimental evidence in support of individual steps involved in this mechanism is accumulating, it is as of now unclear whether this mechanism can indeed operate robustly under physiologically realistic parameters of pyramidal cells, in particular, without impairing information flow in these cells altogether. Computational modeling allows us to demonstrate that this is indeed possible if inhibition is well timed (on the order of 1 ms). Moreover, we show that a specific design of the local circuit can ensure the necessary timing.
action potentials
medicine and health sciences
nervous system
membrane potential
electrophysiology
neuroscience
signal inhibition
synaptic plasticity
interneurons
calcium signaling
neuronal dendrites
developmental neuroscience
animal cells
signal transduction
cellular neuroscience
cell biology
anatomy
synapses
physiology
neurons
biology and life sciences
cellular types
cell signaling
neurophysiology
Inhibition as a Binary Switch for Excitatory Plasticity in Pyramidal Neurons