Abstract
Excitation in neural circuits must be carefully controlled by inhibition to regulate information processing and network excitability. During development, inhibitory and excitatory inputs in the cerebral cortex are initially mismatched but become co-tuned or ‘balanced’ with experience. However, little is known about the set-points for excitatory-inhibitory balance or the mechanisms for establishing or maintaining this balance. Here we show how coordinated long-term synaptic modifications calibrate populations of excitatory and inhibitory inputs onto mouse auditory cortical pyramidal neurons. Pairing pre- and postsynaptic activity induced plasticity at paired inputs and different forms of heterosynaptic plasticity at the strongest unpaired synapses, which required minutes of activity and dendritic Ca2+ signaling to be computed. Theoretical analyses demonstrated how the relative amount of heterosynaptic plasticity could normalize and stabilize synaptic strengths to achieve any possible excitatory-inhibitory correlation. Thus excitatory-inhibitory balance is dynamic and cell-specific, determined by distinct plasticity rules across multiple excitatory and inhibitory synapses.
One-Sentence Abstract Heterosynaptic plasticity can rapidly and specifically balance inhibition with excitation across multiple inputs onto cortical pyramidal neurons.
In mature cortical networks and elsewhere throughout the adult nervous system, excitation is regulated by a complex set of inhibitory circuits. GABAergic inhibition is important in many features of nervous system function, including spike generation, dendritic integration, synaptic plasticity, sleep, learning and memory, and prevention of pathological activity such as epilepsy (15). Consequentially, inhibitory synapses must be calibrated to the relative strengths of excitatory synapses to ensure that neurons and networks are neither hypo-nor hyper-excitable for prolonged periods. In sensory cortex, this balance between excitation and inhibition seems to be established during early postnatal development (6-11). In particular, frequency tuning curves in the primary auditory cortex (AI) tend to be initially broad or erratic; excitatory inputs mature within the first 1-2 weeks of postnatal life in rodents, but inhibitory tuning requires auditory experience over weeks 2-4 to balance excitation (7,12,13). This balance is usually quantified in terms of the correlation between excitation and inhibition across a stimulus dimension such as visual orientation or sound frequencies, or the temporal correlation between the patterns of excitation and inhibition measured over time. Experimental studies have found that in most neurons even in mature circuits, these correlation values are not perfect (i.e., linear correlation coefficient r: 1.0) but instead are often distributed across a range centered around lower positive levels (r: 0.4-0.7). It is unclear if these observations indicate that it is difficult to maintain higher levels of balance in biological neural networks, or if instead the set-point at which excitation and inhibition are in equilibrium is actively maintained at this lower level.
Excitatory-inhibitory balance must also be dynamically maintained throughout life, as experience-dependent modification of excitatory synapses (e.g., occurring during and after development, learning, or conditioning) requires corresponding changes to inhibitory inputs (7,8,14). Network simulation studies supported by experimental data in vitro and in vivo indicate that disruptions of excitatory-inhibitory balance can rapidly produce epileptiform activity and seizures within minutes (1,15-18), meaning that compensatory mechanisms must act quickly to re-stabilize neural circuits before pathological activity emerges. At least some of these compensatory or homeostatic adjustments take place over hours to days to retain overall cell excitability, as demonstrated in a variety of neural systems (19-22). It remains unclear if these processes would be able to correct for changes in excitability on the shorter time-scale of activity-dependent plasticity (seconds to minutes) in the input-specific manner required to preserve or promote differential neural computations. This may depend on different set-points for excitatory-inhibitory balance, based on the function of the neuron or neural circuit (e.g., single spike firing vs bursting, or narrowly vs broadly tuned for stimulus features).
An alternative for regulating overall excitability is heterosynaptic plasticity, defined as modifications to inputs not activated during induction of long-term potentiation (LTP) or other forms of long-term plasticity triggered at specific inputs (14,23-25). Heterosynaptic long-term modifications at specific subsets of monitored inputs have been observed after excitatory LTP at paired ‘homosynaptic’ sites (7,26-32). It is unknown whether inhibitory synapses also undergo heterosynaptic modifications or how these changes across multiple inputs might be coordinated to alter excitatory-inhibitory balance. Recently, we showed that spike-timing-dependent plasticity (STDP) could be induced at co-activated excitatory and inhibitory synapses (33). Spike pairing induced excitatory and inhibitory LTP, with the degree of inhibitory potentiation depending on the initial amplitude of co-evoked excitatory events. This naturally led to a normalization of the excitation-inhibition ratio at the paired inputs. Here we ask whether spike pairing also leads to heterosynaptic excitatory and inhibitory modifications, and if these changes might collectively reorganize or enhance the relationship between excitation and inhibition across inputs.
To examine how homosynaptic and heterosynaptic modifications might synergistically affect cortical excitatory-inhibitory balance, we made 129 whole-cell recordings from layer 5 pyramidal neurons in slices of mouse auditory cortex. An array of stimulation electrodes (interelectrode spacing: 120 μm) was placed in layer 4 and used to sequentially evoke 4-8 sets of excitatory and inhibitory postsynaptic currents (EPSCs and IPSCs), each at a low presentation rate (0.033-0.2 Hz) recorded in voltage-clamp (Fig. 1A). This form of stimulation recruited separate populations of excitatory and inhibitory presynaptic inputs with a low degree of overlap across channels (Fig. 1B, fig. S1), in a manner that mimics the recruitment of thalamocortical inputs onto cortical neurons in vivo by sensory stimulation (34-37). After measuring baseline synaptic strength for 5-20 minutes, recordings were switched to current-clamp to pair synaptic inputs evoked by one channel of stimulation with postsynaptic spiking induced by brief depolarization through the whole-cell electrode (33,38,39). The other stimulation channels were not activated during pairing. Following pairing, we resumed sequential stimulation of all channels and monitored paired and unpaired EPSCs and IPSCs for at least 16-25 minutes after pairing.
We found that pairing presynaptic and postsynaptic activity could lead to long-term synaptic modifications at multiple inputs, including inputs that were not activated during the pairing procedure. While some of these changes could be variable from cell to cell, we consistently found that the strongest unpaired excitatory and inhibitory inputs (the ‘original best’ inputs) were specifically modified minutes after pairing. For example, in the recording shown in Figure 1C, repetitively pairing presynaptic activation of channel S4 with postsynaptic spiking (pre→post pairing) induced excitatory and inhibitory LTP at the paired channel (Fig. 1C, red symbols; EPSC amplitude indicated by filled circles increased by 39%, IPSC amplitude indicated by open circles increased by 51%). These forms of excitatory and inhibitory STDP are consistent with our previous study (33). In contrast, the original best unpaired inputs (excitation evoked by channel S3 and inhibition evoked by S2) were both depressed (Fig. 1C, blue symbols; EPSCs decreased by −27%, IPSCs decreased by −72%). The other unpaired inputs were not substantially affected on average (Fig. 1C, black symbols). Thus spike pairing induces rapid and specific heterosynaptic modifications in addition to more conventional STDP at paired (homosynaptic) inputs.
These selective modifications to the paired and original best inputs acted together to reorganize the overall profile of excitation and inhibition (i.e., excitatory-inhibitory balance). As a metric of excitatory-inhibitory balance, we used the linear correlation coefficient rei of EPSCs and IPSCs evoked across stimulation channels. Linear correlation has previously been used to quantify excitatory-inhibitory balance in vivo (7,40-43) and in vitro (44,45). For this cell, the initial IPSC amplitudes evoked by each of the six channels were mostly unrelated to the strengths of excitation across the stimulation channels (Fig. 1D, left, rei-before: 0.25). This was unsurprising as, a priori, excitatory and inhibitory synapses activated by extracellular stimulation need not be functionally related despite spatial proximity near each electrode (in this recording, the original best EPSCs and IPSCs were evoked by different channels). After pairing, however, this correlation increased, and the amplitudes of EPSCs and IPSCs evoked by each stimulation site were more similar across all channels (Fig. 1D, right, rei-after: 0.48); i.e., when EPSCs were smaller, IPSCs tended to be smaller; conversely, when EPSCs were larger, IPSCs also tended to be larger. This was a consequence of coordinated homosynaptic and heterosynaptic modifications to the paired input (Fig. 1D, red arrow) and original best unpaired inputs (Fig. 1D, blue arrowheads). Such activity-dependent changes over multiple paired and unpaired synapses-which collectively act to improve excitatory-inhibitory balance- are similar to experience-dependent changes to excitatory and inhibitory synaptic tuning curves in young rodent auditory cortex in vivo (7).
The relative timing of pre/postsynaptic spiking during pairing determined the sign of heterosynaptic plasticity at the original best inputs. In 25 recordings, we found that pre→post pairing reliably induced LTP at paired excitatory and inhibitory inputs with concomitant heterosynaptic LTD, which was reliably induced at the original best excitatory and inhibitory inputs (Fig. 2A, fig. S2A, fig. S3A). Across the other non-best unpaired inputs, we did not observe any systematic changes after pairing (Fig. 2A, bottom). In contrast, in 11 other recordings we observed that post→pre pairing induced excitatory LTD and inhibitory LTP at the paired inputs, as previously reported (33,39), together with heterosynaptic LTP at the original best excitatory and inhibitory inputs (Fig. 2B, fig. S2B, fig. S3B). As pre→post pairing potentiates paired inhibitory inputs, heterosynaptic inhibitory LTD provides a mechanism for bi-directional regulation of inhibitory synaptic strength. In contrast, heterosynaptic excitatory LTP might be useful for compensating for reductions in excitability after homosynaptic LTD at the paired excitatory input.
These coordinated synaptic modifications, induced by either pre→post or post→pre pairing, could affect overall excitatory-inhibitory correlation rei in similar ways. In general, when the correlation coefficient was initially low (rei-before <0.4), the correlation increased after pairing (Fig. 2C, fig. S2). This occurred for both pre→post and post→pre pairing (Fig. 2C, top; cells to left of red line at r=0.4 are almost all above the unity line), indicating that although the specific valence of synaptic modifications might be different, these changes act together to reorganize populations of synaptic inputs and enhance excitatory-inhibitory balance. However, when the excitatory-inhibitory correlation was initially high (rei-before >0.4), the correlation instead decreased after pairing (Fig. 2C, fig. S3). In the absence of postsynaptic spiking, no STDP was induced, and excitatory-inhibitory correlation was unchanged (Fig. 2C, bottom, gray ‘No STDP’).
Changes in excitatory-inhibitory correlation were due mainly to heterosynaptic modifications of unpaired inputs rather than homosynaptic plasticity of paired inputs, especially when the initial correlation was low. Considered independently, computing rei-after assuming only changes to paired inputs led to smaller correlation changes than only changes to unpaired inputs (Fig. 2D).
Thus pre/post spike pairing rapidly induces heterosynaptic plasticity to effectively normalize excitatory-inhibitory balance, adjusting the relation of inhibition to excitation to promote a moderate level of correlation of ~0.4. This value is close to that observed in rodent auditory cortex in vivo towards the end of the critical period for tonal frequency tuning (7), suggesting this value is a set-point that is actively maintained during this developmental stage of cortical organization. Intuitively, when the excitatory-inhibitory correlation was initially low, this was at least in part because the original best excitatory and inhibitory inputs were activated by different channels (in 12/14 pre→post and 5/5 post→pre pairing recordings). Heterosynaptic plasticity at the best excitatory and inhibitory inputs would naturally make those inputs more similar, since they were both depressed after pre→post pairing and potentiated after post→pre pairing. Note that when excitatory-inhibitory correlation was initially high, changes to the paired channel also served to normalize (in this case reducing) the correlation levels. This is expected for post→pre pairing, given that excitation and inhibition were modified in opposite directions. These findings indicate that single neurons have mechanisms for sensing and selectively modifying relative input strengths. In principle, these mechanisms could achieve nearly any degree of excitatory-inhibitory co-tuning. It may be computationally advantageous to not perfectly match excitation and inhibition, especially during postnatal developmental critical periods when cortical plasticity may be important for initializing sensory processing circuits.
To quantitatively assess this capacity in a theoretical framework, we simulated the effects of homosynaptic and heterosynaptic plasticity onto a model postsynaptic neuron driven by 12 excitatory and inhibitory inputs. We first considered a probabilistic model, where 50,000 excitatory and inhibitory tuning curves were generated randomly by sampling from a uniform distribution across channels (Fig. 3A, rei-before). This resulted in initial correlation rei-before values ranging from −0.9 to 0.9. One channel was chosen as the ‘paired’ channel, where excitation and inhibition were increased, and the original best excitatory and inhibitory channels were decreased by a fixed amount (Fig. 3A, rei-after). Following weight modification, we recomputed excitatory-inhibitory correlation rei across channels. As expected, the probability of rei correlation increasing or decreasing strongly depended on the initial correlation rei-before. Without heterosynaptic plasticity, the probability of rei increasing was higher than the probability of decreasing due to homosynaptic plasticity. However, with sufficiently strong heterosynaptic plasticity, a crossover occurred between the probability of rei increasing vs decreasing at an equilibrium point where excitatory-inhibitory correlation settled as increases and decreases of rei were themselves balanced (Fig. 3B). Correlation values initially higher than this set-point were likely to decrease, while correlation values initially lower were more likely to increase, as in the slice experiments (Fig. 2C,D). The most prominent influence on the updated correlation value (rei-after) to which the system converged was determined by the strength of heterosynaptic plasticity relative to homosynaptic plasticity, independent of the number of stimulus channels (Fig. 3C). The excitatory-inhibitory correlation equilibrium point (average rei-after) decreased as heterosynaptic plasticity strength was increased relative to homosynaptic plasticity strength. Thus, by titrating the relative strengths of heterosynaptic and homosynaptic plasticity, the system can in principle achieve any correlation value, i.e., an arbitrary set-point for stable excitatory-inhibitory balance.
To determine whether this relationship between the excitatory-inhibitory correlation and the relative strengths of heterosynaptic vs. homosynaptic plasticity holds under more realistic conditions, we simulated a single postsynaptic integrate-and-fire neuron driven by 12 excitatory and inhibitory input channels. Each channel consisted of 10 excitatory and 10 inhibitory presynaptic conductance-based inputs, with weights modified by homosynaptic vs. heterosynaptic activity-dependent plasticity (Fig. 3D, fig. S4A). During the simulation, we made paired and unpaired channels fire at different rates to elicit postsynaptic spiking only during paired channel activation. Homosynaptic and heterosynaptic plasticity were implemented with biophysical traces that tracked pre- and postsynaptic activation online. As a consequence, rei fluctuated around a constant mean (Fig. 3E, top), which was consistent across different initial conditions (Fig. 3E, bottom). Similar to the probabilistic model (Fig. 3A-C), the excitatory-inhibitory correlation converged to a value that depended on the relative learning rates of heterosynaptic vs. homosynaptic plasticity (Fig. 3F). In particular, when homosynaptic plasticity was dominant, rei was high and the excitatory and inhibitory weights gradually increased over the simulation. In contrast, when heterosynaptic plasticity was dominant, rei was low and the excitatory and inhibitory weights during training gradually decreased. When the strengths of homosynaptic and heterosynaptic plasticity were approximately balanced, the excitatory and inhibitory weights were relatively stable during an extended period of training (fig. S4B) and rei-after converged to the value of 0.45-0.5, close to the values observed experimentally. These simulations demonstrate that heterosynaptic plasticity can powerfully control the positive feedback of homosynaptic plasticity, compensating for this process to achieve nearly any relation between excitatory and inhibitory tuning curves simply by adjusting the strength relative to homosynaptic plasticity.
We next examined the biological mechanisms that might enable heterosynaptic plasticity to occur selectively at the original best unpaired inputs. We first used two-photon Ca2+ imaging to examine dendritic Ca2+ events in layer 5 pyramidal cells during spike pairing (fig. S5A). We found that both pre→post and post→pre pairing led to a broadening of backpropagating action potential-evoked Ca2+ transients (fig. S5B,C; ‘Normal solution’). We wondered if this enhanced Ca2+ signaling triggered by spike pairing was related to the phenomenon of Ca2+-induced Ca2+ release from internal stores (46,47). This mechanism could potentially provide a means for intracellular communication across multiple synapses and has been implicated in heterosynaptic modifications in other temporal lobe structures, including amygdala (30) and hippocampus (48). We found that intracellular perfusion with thapsigargin (to deplete internal calcium stores, 10 μΜ) prevented this broadening of the Ca2+ event, such that transients evoked during pre→post and post→pre pairing were no different than Ca2+ transients triggered by postsynaptic spikes alone (fig. S5B,C; ‘Thapsigargin’).
Ca2+-induced Ca2+ release was also the major mechanism for heterosynaptic plasticity (fig. S6). Either intracellular thapsigargin (10 μΜ, fig. S6A,E) or ruthenium red (which blocks Ca2+ release from internal stores, 20 μΜ; fig. S6D, fig. S7) prevented heterosynaptic modifications but spared changes to paired excitatory and inhibitory inputs after pre→post or post→pre pairing, which were comparable to the magnitudes of those forms of plasticity under normal recording conditions (fig. S6B). In contrast, bath application of APV (50 μΜ) to block NMDA receptors (fig. S6C) prevented all changes to paired and unpaired excitatory and inhibitory inputs. Therefore, the intracellular calcium signaling initiated by activation of NMDA receptors at paired excitatory synapses subsequently triggered a set of other modifications, mainly to paired inhibitory synapses and the original best unpaired excitatory and inhibitory synapses.
These results show that heterosynaptic plasticity can be selectively induced at a specific subset of excitatory and inhibitory inputs onto individual postsynaptic neurons. The original best inputs are necessarily locally but not globally maximal, as only a fraction of the total inputs received by these neurons were activated by the stimulation electrode array. As heterosynaptic changes were expressed ~10-20 minutes after pairing, we hypothesized that these locally-maximal inputs were computed by postsynaptic cells within this brief post-pairing period. To test this prediction, we performed a final set of experiments in which multiple inputs were monitored before and after pre→post or post→pre pairing, as before; however, for ten minutes immediately following pairing, the original best excitatory and inhibitory inputs (selected to be on the same input channel) were not stimulated.
We found that during this ten-minute period, the second-largest inputs (‘relative best’ inputs) were selectively affected by heterosynaptic modifications rather than the original best inputs. In the recording shown in Figure 4A, channel 8 evoked the originally-largest EPSCs and IPSCs, channel 6 evoked the second-largest EPSCs and IPSCs, and channel 4 was the paired channel. After pre→post pairing, channel 8 was turned off for ten minutes. During that period, the paired EPSCs and IPSCs increased, while heterosynaptic LTD was induced at the ‘relative best’ EPSCs and IPSCs evoked by channel 6. When channel 8 was reactivated, the EPSCs and IPSCs at that channel remained at their initial amplitudes and were stable until the end of the recording. Over all recordings, the relative best input during the ten-minute post-pairing period was selectively affected by heterosynaptic modifications rather than the original best inputs (Fig. 4B). Similarly, when the original best input was not presented after post→pre pairing, the relative best input instead experienced heterosynaptic plasticity; in this case, heterosynaptic LTP of both excitation and inhibition (fig. S8).
This experiment demonstrates that heterosynaptic plasticity can be specifically manipulated, such that these changes selectively occur at whichever inputs were most strongly activated in a restricted post-pairing period. Furthermore, these results show that cortical neurons have a Ca2+-dependent mechanism for determining and adjusting overall excitation and excitatory-inhibitory balance in a rapid and stimulus-specific manner.
Here we have described how organized forms of long-term homosynaptic and heterosynaptic plasticity selectively adjust populations of synaptic inputs onto mouse cortical pyramidal neurons to achieve a particular set-point for excitatory-inhibitory balance. Although inputs evoked by each stimulation channel may not initially be functionally related, these inputs become bound together via repetitive co-activation together with postsynaptic spiking. This might emulate how novel sensory stimuli recruit initially-unrelated inputs, which become functionally coupled via mechanisms of experience-dependent plasticity. Part of this mechanism involves computing local maxima of incoming inputs for selective modifications of specific synapses. Combined with slower forms of homeostatic plasticity (22), individual cortical neurons have the capability to integrate or accumulate recent activity over minutes to hours, enabling flexible representations of external stimuli and control over excitability on multiple short and long time-scales.
Although excitatory-inhibitory balance is a fundamental feature of neural networks (10,14,40,45), it has remained unclear how this organization is set up and calibrated on-line, especially in response to changes of excitatory synapses believed to be important for learning and memory storage. Instead of a slower global optimization process-which might be difficult to implement biologically-our results demonstrate that a restricted set of activity-dependent changes is sufficient to normalize excitatory-inhibitory balance within minutes, enhancing the relation between inhibition and excitation when mismatched, or reducing this value if inhibition is too restrictive. Our theoretical analysis indicates that the definition of excitatory-inhibitory balance can be dynamic, and this set-point is determined by the relative degree to which heterosynaptic modifications are engaged. Consequentially, heterosynaptic plasticity and inhibitory plasticity work together to automatically restructure cortical circuits after induction of long-term excitatory modifications, to update information storage and enable flexible computation without disrupting overall network function.
Author Contributions
All authors designed the studies and wrote the paper. R.E. Field, J.A. D’amour, and R. Tremblay performed the experiments and analyzed the data. C. Miehl and J. Gjorgjieva performed the modeling.
Acknowledgements
We thank K. Kuchibhotla, M. Jin, E. Morina, D. Talos, and N. Zaika for comments, discussions, and technical assistance. This work was funded by grants from the Max Planck Society and a Career Award at the Scientific Interface from the Burroughs Wellcome Fund (to J.G.); and NIDCD (DC009635 and DC012557), NICHD (HD088411), a Sloan Research Fellowship, a Klingenstein Fellowship, and a Howard Hughes Medical Institute Faculty Scholarship (to R.C.F.).
Footnotes
↵† Co-first authorship