A-type K+ channels impede supralinear summation of clustered glutamatergic inputs in layer 3 neocortical pyramidal neurons

A-type K+ channels restrain the spread of incoming signals in tufted and apical dendrites of pyramidal neurons resulting in strong compartmentalization. However, the exact subunit composition and functional significance of K+ channels expressed in small diameter proximal dendrites remain poorly understood. We focus on A-type K+ channels expressed in basal and oblique dendrites of cortical layer 3 pyramidal neurons, in ex vivo brain slices from young adult mice. Blocking putative Kv4 subunits with phrixotoxin-2 enhances depolarizing potentials elicited by uncaging RuBi-glutamate at single dendritic spines. A concentration of 4-aminopyridine reported to block Kv1 has no effect on such responses. 4-aminopyridine and phrixotoxin-2 increase supralinear summation of glutamatergic potentials evoked by synchronous activation of clustered spines. The effect of 4-aminopyridine on glutamate responses is simulated in a computational model where the dendritic A-type conductance is distributed homogeneously or in a linear density gradient. Thus, putative Kv4-containing channels depress excitatory inputs at single synapses. The additional recruitment of Kv1 subunits might require the synchronous activation of multiple inputs to regulate the gain of signal integration.


Introduction
Dendritic integration of synaptic potentials is regulated by several biophysical and molecular factors linked to synaptic transmission and changes in intrinsic excitability (Araya, 2014;Major et al., 2013;Spruston, 2008;Stuart and Spruston, 2015;Williams and Stuart, 2002). These factors include the number, location, timing, and sequence of operation of synaptic inputs (Katz et al., 2009;Magee, 2000). Signal integration is also dependent on the electrotonic structure of the dendritic tree (Korogod and Tyc-Dumont, 2009), as well as the nature, density, and gradient of voltage-gated ion channels present in somatodendritic membranes (Hille, 2001).
Dendritic patch-clamp recordings from CA1 pyramidal neurons have revealed a functional six-fold increase in I A current density along the proximal to distal path of the main apical dendrite (Hoffman et al., 1997). This distribution in positive gradient restrains dendritic plateau potentials and reduces the amplitude of back-propagating axo-somatic action potentials (Andrasfalvy et al., 2008;Cai et al., 2004) enabling synaptic plasticity and branch-specific storage (Chen et al., 2006(Chen et al., , 2011Frick et al., 2003;Golding et al., 1999;Losonczy and Magee, 2006;Losonczy et al., 2008). Similarly, an increasing density of dendritic Kv4 channels along the apical dendrite is maintained by the auxiliary subunit DPP6, restricting action potential back-propagation and calcium spike generation (Sun et al., 2011). In contrast, a small decrease in the density of dendritic K þ channels has been reported in the large dendrite of layer 5 (L5) pyramidal neurons in young rats (Korngreen and Sakmann, 2000).
Despite this wealth of evidence, much less is known about Atype K þ channels in small diameter neocortical dendrites. I A regulates input summation throughout the apical dendritic tuft of L5 pyramidal neurons resulting in strong electrical compartmentalization at distal synapses (Harnett et al., 2013). However, it remains unclear whether such I A -dependent regulation of signal integration occurs in basal and oblique dendrites of layer 3 (L3) pyramidal neurons. In addition, novel computational approaches are needed to comprehend the functional significance of I A in small diameter dendrites, the vast majority of which is unamenable to patch-clamp recordings.
To understand how K þ channels regulate signal integration in L3 pyramidal neurons, we examine the effect of K þ channel blockers on electrical membrane properties and summation of excitatory synaptic potentials. We use two-photon laser scanning microscopy and photolysis of RuBi-glutamate to mimic the activation of excitatory synapses in basal and oblique dendrites. We show that blocking putative Kv4 channels enhances the response evoked by glutamate uncaging at a single dendritic spine. The block of putative Kv1 channels has no effect on such unitary responses. Both Kv1 and Kv4 channels impede supralinear summation of glutamatergic signals elicited by synchronous activation of clustered spines. Using computational modeling we show that a linear gradient in A-type conductance density distribution along the dendrite is not required to explain the effect of K þ blockers on dendritic integration. Remarkably in these neurons the interplay between A-type K þ channels and NMDA receptors results in a highly dynamic modulation of the gain of dendritic integration of glutamatergic signals.

Physiological and pharmacological properties of EPSPs evoked by glutamate uncaging at single spines in basal and apical oblique dendrites
We recorded from the soma of L3 pyramidal neurons in currentclamp mode at 32 C with pipettes containing Alexa Fluor 594 (150 mM), and imaged portions of basal and apical oblique dendrites using two-photon laser scanning microscopy (distance from soma: 27e183 mm). We selected dendritic segments that showed no overlap with neighboring dendrites from the same neuron above or below the focal plane. Glutamate receptors on individual spines were stimulated using 0.2 ms single-photon uncaging of bathapplied RuBi-glutamate (500 mM). The resulting glutamateevoked EPSPs (gluEPSPs) were detected at somatic level. The lateral resolution of glutamate uncaging was near 3 mm for~0.9 mV responses whilst uncaging at positions located 10 mm away from the focal plane of the spine head halved gluEPSPs (Fig. 1A). Gradually increasing laser intensity enhanced the peak and half width of gluEPSPs, and repeatedly uncaging at the same spine head every 15 s yielded stable and reproducible responses indicating little phototoxicity (Fig. 1B). In normal artificial cerebro spinal fluid (nACSF) the mean peak amplitude of gluEPSPs elicited by uncaging at single spines in basal dendrites was similar to that of gluEPSPs evoked in apical obliques (medians; oblique: 0.88 mV, n ¼ 168 spines in 13 dendrites; basals: 0.87, n ¼ 96 spines in 7 dendrites; P ¼ 0.48, Kruskal-Wallis test). The distribution of peak amplitude of gluEPSPs recorded in the presence of tetrodotoxin (TTX 1 mM; mean ± S.D., 0.7 ± 0.38 mV; n ¼ 152 spines in 19 dendrites) was unimodal and not different from that of gluEPSPs recorded in nACSF (0.69 ± 0.40 mV, 352 spines from 44 dendrites; P ¼ 0.77, unpaired ttest). Glu-EPSP amplitude remained constant with increasing distance from the soma although the increased rise time indicated cable filtering in both basal and apical oblique dendrites (Fig. 1C). Such ranges of amplitude and rise time were comparable to those reported for gluEPSPs elicited by 2-photon uncaging at single spines in brain slices, in L3 neurons (Branco and Hausser, 2011), hippocampal pyramidal cells (Losonczy and Magee, 2006;Makara et al., 2009) or dentate granule cells (Krueppel et al., 2011).

A-type K þ channels depress gluEPSPs generated by single spine activation
To get insight into the nature of K þ conductances present in basal and oblique dendrites, we focused on pharmacological compounds that have been reported to inhibit A-type K þ channels in cortical slice preparations (Kang et al., 2000;Kim et al., 2007;Korngreen and Sakmann, 2000;Makara et al., 2009;Pathak et al., 2016;Wang et al., 2014;Zhou and Hablitz, 1996). TTX (1 mM) was added to the control perfusion solution to prevent epileptiform activity. We started by examining the effect of low millimolar 4aminopyridine (4-AP, 1 mM) on gluEPSPs evoked by uncaging at single dendritic spines. Although this concentration of 4-AP has been shown to preferentially block native K þ channels containing Kv1 subunits, it will also affect some Kv4s (Coetzee et al., 1999;Gutman et al., 2003;Tseng, 1999). Superfusion of 4-AP (1 mM; in 64 spines, 8 dendrites in 8 cells) had no effect on the amplitude and duration of gluEPSPs ( Fig. 2A). However, a higher concentration of 4-AP (5 mM; in 48 spines, 6 dendrites in 5 cells) prolonged the duration of gluEPSPs but had no effect on their amplitude (Fig. 2B). In a separate set of control experiments in which TTX was omitted from the perfusion solution we verified that 4-AP (1 and 5 mM) broadened action potentials elicited by supra-threshold depolarizing current steps (data not shown). To test the hypothesis that Kv4-containing K þ channels regulate gluEPSPs elicited by single spine activation we examined the effect of phrixotoxin-2, a peptide derived from the venom of the Chilean copper tarantula. Phrixotoxin-2 has been shown to block Kv4.2 and Kv4.3 channels but no other Kv subtypes expressed in heterologous systems (Diochot et al., 1999). In intact tissue, the application of phrixotoxin-2 (5 mM) decreased by 30% the peak of the A-type current recorded from sympathetic preganglionic neurons (Whyment et al., 2011), whereas in arcuate kisspeptin neurons this effect reached 50% (Mendonca et al., 2018). We used a similar concentration of phrixotoxin-2 in our experiments. Superfusion of phrixotoxin-2 (5 mM) increased the amplitude of gluEPSPs but the half width remained unchanged (Fig. 2C). Altogether, these data suggested that putative Kv4-containing K þ channels strongly depressed gluEPSPs generated by single spine stimulation.
Because changes in electrical membrane properties could in part explain the enhancing effect of K þ channel blockers on gluEPSPs, we analyzed how 4-AP and phrixotoxin-2 affected the membrane potential (V m ), input resistance (R in ) and membrane time-constant (t m ) of the recorded neurons. As shown in Fig. 2D, superfusion of phrixotoxin-2 (5 mM) had no effect on V m , R in and t m . Analyzing the changes over the entire data pool and for each pharmacological manipulation revealed that 4-AP (1 and 5 mM) depolarized L3 neurons, and that 4-AP (5 mM) significantly increased R in and t m (Fig. 2D). We also tested the effect of the inorganic cation Ba 2þ (Gasparini et al., 2007;Losonczy et al., 2008). When Ba 2þ (150 mM) was added to the perfusion solution it substantially increased the Fig. 1. Glutamate uncaging at single and multiple dendritic spines imaged with 2-photon laser scanning microscopy in L3 pyramidal neurons. A, 3-D resolution of singlephoton uncaging at single dendritic spines and corresponding somatic gluEPSPs. Left, maximum intensity projection of 2-photon images of two Alexa Fluor 594 (150 mM) filled L3 pyramidal neurons. Single spines were chosen randomly along the basal dendrites (at 50 mm, top; and 100 mm from the soma, bottom cell). Top, moving the uncaging beam in random order (numbered spots, 1e8) along a longitudinal axis within the focal plane of the spine head, elicits EPSPs of graded amplitudes, the largest of which is obtained when the beam is positioned closest to the spine head (red spot; corresponding voltage trace is red). Bottom, positioning the uncaging beam along the Z-axis at different distances from the spine head (red spot, in focus) yields graded EPSPs. The amplitude of gluEPSPs decays almost linearly with distance from the spine head in the focal plane (top right; double Boltzmann fitting). Uncaging at different focal planes yields a bell-shaped relation (bottom right; Gauss fitting). B, Properties of gluEPSPs elicited by uncaging at single spines and summation when uncaging at several spines. Maximum intensity projection of a 2-photon Z-stack from an Alexa Fluor 594-filled neuron with uncaging region of interest magnified showing 8 individual uncaging sites. (i) Superimposed gluEPSPs evoked by uncaging at single spines (3 different spines, the 3 crossed-over yellow spots; 8e9 successive trials for each spine). No run-down is observed. (ii) Co-stimulation of an increasing number of spines evokes gluEPSPs of graded amplitudes. Color traces (single traces or averages of 2 traces) amplitude, rise time, and half width of gluEPSPs (medians; peak amplitude: 0.87 versus 0.97 mV, P ¼ 2E À5 ; half width: 14.56 versus 25.18 mV, P ¼ 2E À8 ; Wilcoxon signed rank tests; data are from 56 spines, 9 dendrites in 9 cells, not shown). This effect was accompanied by membrane depolarization (DV m : 9.81 ± 3.34 mV) and a large increase in neuronal R in (DR in : 121.45 ± 47.43%). Such dramatic changes in electrical membrane properties of L3 pyramidal neurons prevented a robust interpretation of the enhancing effect of Ba 2þ on gluEPSPs. However, that phrixotoxin-2 enhanced gluEPSP amplitude with no other effect on V m , R in , and t m , strengthened the finding that putative Kv4 channels exert a powerful brake on glutamatergic signals initiated at single spines.
Supralinear integration in layer 2/3 pyramidal cell dendrites depends on NMDA receptors, the recruitment of which is facilitated by activation of voltage-gated sodium channels and calcium channels (Branco and Hausser, 2011). Consistent with this finding, we found that the block of K þ currents led to a multiplicity of summed response shapes. Some cells (5 out of 8) showed a delayed and enhanced gluEPSP peak in 4-AP ( Fig. 5A), whereas others exhibited dendritic spikes (4 out of 6) or gluEPSP broadening (2 out of 6) in the presence of phrixotoxin-2 ( Fig. 5B). To test whether Atype K þ channels interact with NMDA receptors and voltage-gated conductances at clustered synaptic inputs we used again pharmacology (Fig. 5C). Switching from nACSF to a perfusion solution containing the NMDA receptor antagonist D(À)-2-amino-5phosphonopentanoic acid (D-AP5, 100 mM) was accompanied by a reduction in the degree of supralinearity of summed gluEPSPs (10e90% rise time, nACSF: 13.13 ± 7.4 ms versus D-AP5: 0.35 ± 0.88 ms; n ¼ 4 dendrites in 4 cells; P ¼ 0.048, paired t-test; Fig. 5C, left). The block of Na þ channels by TTX (1 mM) had no effect (10e90% rise time, P ¼ 0.079; peak amplitude, P ¼ 0.067; half width, P ¼ 0.06; n ¼ 3 dendrites in 3 cells; paired t-tests). In contrast, superfusion of 4-AP (1 mM) in the background of TTX enhanced supralinear integration of gluEPSPs (peak amplitude, TTX: 3.95 ± 3.37 mV versus þ4-AP 1 mM: 5.54 ± 5.12 mV; P ¼ 0.037, n ¼ 8 dendrites in 8 cells; Fig. 5C, middle). A higher concentration of 4-AP (5 mM), however, did not cause significant changes (n ¼ 6 dendrites in 6 cells). Lastly, phrixotoxin-induced facilitation in supralinearity was mainly manifested by changes in gluEPSP half width (ACSF/BSA: 13.77 ± 20.25 ms versus phrixotoxin-2: 19.21 ± 22.48 ms; P ¼ 0.034, n ¼ 7 dendrites in 6 cells; Fig. 5C, right). We also performed experiments where we first blocked K þ channels, and subsequently the NMDA receptors (n ¼ 3 dendrites in 3 cells). As shown in the integration plots in Fig. 5D, the application of 4-AP (5 mM) enhanced gluEPSPs and increased the slope of the relation between gluEPSP amplitude and arithmetic sum of individual components. In contrast, the application of D-AP5 (100 mM) in the background of 4-AP reduced the steepness of this relationship. Altogether, these results highlighted the concerted role of Atype K þ channels and NMDA receptors in controlling the gain of signal integration in oblique and basal dendrites. I A acted as a brake on supralinear input summation mediated by NMDA receptors during the synchronous activation of highly localized synapses. correspond to gluEPSPs elicited at 1e8 spines, as indicated on the imaged dendrite. Grey is for single sites, same colors indicate same number (2, 3 or 4) but different combination of co-stimulated spines. C, The amplitude of gluEPSPs evoked by uncaging at single spines does not relate to distance from the soma (<60 mm: 0.73 ± 0.40 mV, n ¼ 136 spines; 60e90 mm: 0.67 ± 0.39 mV, n ¼ 208 spines; > 90 mm: 0.70 ± 0.40 mV, n ¼ 160, Kruskal-Wallis test, P ¼ 0.320), nor does the half width (right). The rise time is increased with distance both for oblique and basal dendrites (<60 mm: 2.68 ± 0.86 ms, n ¼ 135 spines; 60e90 mm: 3.64 ± 1.03 ms, n ¼ 202 spines; > 90 mm: 4.16 ± 1.02 ms, n ¼ 154 spines; Kruskal-Wallis test, P ¼ 2.69E À34 ). Linear fit: obliques (dashed) and basals (solid). Grey and black symbols, recordings in nACSF; blue symbols, in TTX (1 mM). Closed symbols, spines on basal branches; open symbols, spines on obliques. Average uncaging distance from the soma was 83.1 ± 27.5 mm; average span of 8 spines, 23.4 ± 6.7 mm, n ¼ 63 dendrites; yielding an average distance between stimulated spines of 3.3 ± 1.0 mm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

A mechanistic description of I A in a passive compartmental model supports close-to-homogenous distribution of A-type K þ conductance
The pattern of distribution of A-type K þ channels along the fine dendrites of L3 pyramidal neurons is unknown. We took a modeling approach and asked whether I A gradients were required to explain the set of changes in gluEPSP properties observed experimentally when bath-applying I A blockers. To replicate the set of changes seen in 4-AP (1 mM) we created a computational model of a reconstructed L3 pyramidal neuron embedded with a transient A-type conductance (g[A], Fig. 6A). In one condition, we ran simulations where the g[A] density was set to a positive linear gradient along the dendritic path, caped at 250 mm from the soma (Fig. 6B). In an other condition, the g[A] density was distributed homogenously (Fig. 6C). We found that the largest value of match between model and experimental data was 0.88 for the gradient distribution and 0.87 for the homogenous distribution, defining regions of best match illustrated on heat maps ( Fig. 6B and C). These regions extended over a range of g[A] densities set in pre-drug condition (1.30e5.41 mS/cm 2 for gradient distribution; 1.29e5.93 mS/cm 2 for homogenous distribution). An increase in amplitude and duration of summed gluEPSPs was replicated in the model as illustrated by simulated traces (Fig. 6B and C). Altogether, these finding suggest that a positive density gradient in g[A] along these dendrites is not required for explaining the set of experimental changes in gluEPSP properties in the presence of 4-AP.

Discussion
Our pharmacological analysis indicated that putative Kv4 channels depress glutamatergic signals elicited at single spines in basal and apical oblique dendrites of L3 pyramidal neurons. Putative Kv1 and Kv4 channels counteracted NMDA receptor contribution to summed gluEPSPs, hence reducing the gain of dendritic integration. In a computational model, we found that a linear density gradient of A-type conductance was not required for explaining the observed experimental changes in gluEPSP properties caused by K þ channel blockade.
Our results showing that phrixotoxin-2 enhanced the amplitude of gluEPSPs elicited by single spine excitation indicate that Kv4 channels impede small membrane depolarization and subsequent signal integration in L3 pyramidal neurons, confirming observations made in CA1 (Chen et al., 2006;Frick et al., 2003), in L5 pyramidal neurons (Carrasquillo et al., 2012), and in medial intercalated cells of the amygdala (Strobel et al., 2017). In hippocampal and cortical pyramidal neurons, Kv1 channels are blocked by a sub-millimolar concentration of 4-AP (Grissmer et al., 1994;Rasmusson et al., 1995), whereas Kv4 channels are blocked by 4-AP in the millimolar range (Norris and Nerbonne, 2010;Serodio et al., 1996). Because 4-AP (100 mM and 1 mM) had no effect on gluEPSPs evoked by uncaging at single spines, our data suggest that Kv1 channels might not be recruited by the depolarization resulting from the activation of a single synaptic input. The longer half width seen with a higher concentration of 4-AP (5 mM) could be explained by the 38% increase in t m although the amplitude of gluEPSPs did not change despite an overall similar increase in R in (see Fig. 2D). Nevertheless, the 4-AP and phrixotoxin-2 data suggest that photostimulation at a single spine head generates a dendritic depolarization that is sufficiently large to activate Kv4 channels. Local EPSPs then propagate and attenuate along the dendritic path and are recorded as smaller somatic waveforms. In contrast, Kv1 channel activation might require a larger transmembrane voltage drop, such as seen during the synchronous activity of converging excitatory synaptic inputs (Rall, 1964). Besides the greater depolarization with multiple spine activation, a prolonged time course may also be important for activating the slower Kv1 channels to in turn, modulate the inputs. We found that 4-AP (100 mM and 1 mM) did not increase the amplitude and duration of summed gluEPSPs. The lack of statistical significance in the effect could have resulted from Kv channel inactivation in some of the studied dendrites, local saturation of dendritic potentials, or a combination of both. Further complication stems from the uncertainty about V m in stimulated dendrites, and the fact that gluEPSPs attenuated from distinct branch divisions when propagating towards the soma. These confounding factors may have contributed to low statistical power in our analysis despite the reasonable number of repeats when studying summed responses ( Fig. 4A and B; 16 dendrites). Notwithstanding this, our finding showing an increase in supralinearity in 4-AP (1 mM) indicates that putative Kv1 subunits (and some Kv4s) restrain the amplification of voltage components mediated by NMDA receptors. Because millimolar concentrations of 4-AP also blocked the persistent component of the K þ current expressed in neocortical pyramidal neurons, other Kv subunits might have contributed to the effect on supralinearity, notably Kv2 and Kv7 channels (Bishop et al., 2015;Guan et al., 2011;Pathak et al., 2016). Taken together, our phrixotoxin and 4-AP data support a role for Kv4 and Kv1 channels in reducing the amount of supralinearity of input summation at clustered synapses.
With regard to the pharmacological signature of the K þ channel blockers used here, we found that phrixotoxin-2 enhanced the peak amplitude of gluEPSPs whereas 4-AP (5 mM) prolonged the timecourse. We interpret these effects as follows: Phrixotoxin-2 binds with high affinity at both closed and inactivated states of Kv4 channels where it disrupts the transmembrane movement of the voltage-sensing domain. Inhibition occurs as a result of a shift of the conductance-voltage relation and steady-state inactivation curve to more depolarized potentials (Chagot et al., 2004;Diochot et al., 1999). Thus, a maximum number of Kv4 channels will be bound to the toxin in baseline condition, mainly affecting the peak of gluEPSPs. In contrast, the 4-AP block is use-dependent and occurs preferentially at open Kv channels, via the intracellular side, with binding site accessibility and affinity controlled by channel gating (Choquet and Korn, 1992;Stephens et al., 1994). It is a slow process, which requires membrane depolarization, and most likely to prolong the rate of decay of gluEPSPs. Furthermore, 4-AP is a relatively less specific I A blocker than is phrixotoxin-2, and at millimolar concentration it blocks a slow-activating and persistent K þ current, as well as other conductances that set the resting membrane potential and input resistance of L3 pyramidal neurons. Blockade of A-type K þ channels is also known to drastically increase synaptic release of neurotransmitters. The depolarization of neighboring pyramidal neurons by 4-AP could in principle promote presynaptic changes, and contribute to the observed enhancement of gluEPSPs. We believe this was not the case. First, 4-AP (1 mM) did not affect gluEPSPs elicited by the activation of single spines despite significant depolarization and spike broadening. As for the high concentration of 4-AP (5 mM) we would expect the amplitude of gluPSPs to increase both as a result of enhanced neurotransmitter release and decreased input impedance, but there was no change. Secondly, the 4-AP experiments were conducted in the presence of TTX, which blocked action potential dependent neurotransmitter release, and reduced epileptiform activity secondary to K þ channel blockade. Thirdly, asynchronous glutamate release caused by K þ channel blockade in neighboring pyramidal neurons might as well increase the baseline occupancy of glutamate receptors in the recorded cell, and cause a minor reduction in the amplitude of gluEPSPs.
The functional diversity of Kv channels in L3 pyramidal cells could be further expanded by the patterned distribution of the A-  type K þ conductance density as shown with dendritic patch-clamp in CA1 pyramidal cells and L5 neocortical neurons (Andrasfalvy et al., 2008;Gasparini et al., 2007;Harnett et al., 2013;Korngreen and Sakmann, 2000;Sun et al., 2011). We found that the effects of 4-AP and phrixotoxin-2 on supralinearity of synaptic integration did not depend on distance from the soma. Furthermore, our modeling could replicate the set of experimental changes in gluEPSP waveforms whether a positive linear gradient or a homogenous distribution of A-type conductance density was defined along the dendritic path. These results suggest that a steep gradient of A-type K þ channels might not be present in basal and oblique dendrites of L3 pyramidal cells. We also showed in the model that the region of best match to experimental 4-AP data extended over a range of reduction in g[A] density with mid-values greater than 60%. This level of block was in good agreement with the previously reported inhibition of I A currents by 4-AP (1 mM) in L5 pyramidal neurons (Korngreen and Sakmann, 2000). In terms of channel numbers, and for the linear density distribution gradient of g[A], the region of best match to experimental data extended over a range of g[A] densities of 1.30e5.41 mS/cm 2 . Considering a mean single-channel conductance of 9 pS (Bekkers, 2000a)  These numbers were slightly smaller than the number of gold particles per mm 2 counted in SDS-digested freeze-fracture replicaimmunolabeling of Kv4.2 in radial oblique dendrites of CA1 pyramidal neurons (Kerti et al., 2012). However, they remained consistent with the number of Kv4.3 immunogold particles localized in spines and dendritic shaft in Purkinje cells (Otsu et al., 2014). Our findings reveal that presumptive Kv1 and Kv4 channels restrain the window for summation of clustered glutamatergic inputs made onto basal and oblique dendrites of L3 pyramidal neurons. Kv4 channels regulate single synaptic inputs whereas Kv1mediated modulation requires the activation of multiple inputs. Our results also lend support to the notion that Kv1 and Kv4 channels form separate functional entities (Carrasquillo et al., 2012;Foehring, 2012). Beyond, decreased expression and aberrant localization of Kv1.4, Kv4.2 and Kv4.3 have been reported in rodent models of epilepsy Lugo et al., 2008;Monaghan et al., 2008) and in a patient with temporal lobe epilepsy (Singh et al., 2006). Impaired closed-state inactivation of Kv4.2 channels caused by a de novo mutation in the KCND2 gene was recently discovered in identical twins affected by autism and intractable epilepsy (Lee et al., 2014). Finally, newly developed gene therapy where the K þ channel Kv1.1 was over-expressed in the Kv4 channels with phrixotoxin-2 (red trace) reveals additional gluEPSP components forming a delayed enhanced peak. B, Summary graphs show increased gluEPSP amplitude in phrixotoxin-2, and no effect on the rise time and half width (medians; 10e90% rise time: 5.66 versus 10 ms, P ¼ 0.089; peak amplitude: 4.66 versus 8.30 mV, P ¼ 0.024; half width: 20.74 versus 23.77 ms, P ¼ 0.264; paired t-tests, 7 dendrites in 6 cells). The peak ratio of evoked (Ev) to linear sum of individual components (Ar) does not change (supralinearity index; 1.64 versus 1.60; P ¼ 0.705). *P < 0.05; n.s. non-significant. C, Deviation of gluEPSP properties from the linear sum of individual components, plotted against distance from the soma. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) epileptogenic focus successfully prevented the occurrence of electroencephalographic seizures (Wykes et al., 2012). A similar approach targeting both Kv1 and Kv4 channels could thus enhance the silencing of neocortical regions affected in paroxysmal excitability disorders.

Animals
4-to-8 week-old C57BL/6J mice (Harlan Laboratories and Charles River or bred in-house) of both sexes were used. All the procedures were in accordance with the Home Office and UCL School of Pharmacy regulations regarding animal handling and experimental procedures (https://ethics.grad.ucl.ac.uk/).

Electrophysiological recordings
Whole-cell recordings were obtained from pyramidal neurons in L3 in putative cortical area V1. This cell type was chosen because of the relatively large number of oblique dendrites emerging from the main apical trunk. L3 pyramidal neurons were identified by Dodt-contrast imaging. Their morphological characteristics were revealed during live imaging followed by post-hoc analysis in fixed tissue. Patch pipettes were pulled from borosilicate glass capillaries (ID 0.86 mm, OD 1.50 mm with filament) with a Sutter P-2000 puller (Sutter Instruments). Pipettes of 3e5 MU resistance were filled with an internal solution containing (in mM): K gluconate (120), KCl (20), HEPES (10), NaCl (4), EGTA (0.05), MgATP (4), Na 2 GTP (0.45), phosphocreatinine-Na 2 (14). Biocytin (0.2%w/v) and Alexa Fluor 594 (150 mM) were added to the internal solution (pH 7.25, osmolality 290e300 mOsm.kg À1 ). V m was recorded using a Multiclamp 700B (Molecular Devices) amplifier, the NI USB-6259 board (National Instruments; data digitized at 20 kHz), and the NeuroMatic 2.6 software (http://www.neuromatic.thinkrandom. com; J. Rothman, UCL) running under Igor 6.2 (Wavemetrics). Following "break-in", the access resistance was monitored in voltage-clamp mode and did not exceed 35 MU (typically below 20 MU). The bridge was then adjusted for all current-clamp recordings. A set of IeV relations and current injection protocols inspired by Toledo-Rodriguez et al. (2004) was applied to characterize the electrical membrane properties of the recorded neurons. R in was measured as the steady-state voltage deflection in response to a hyperpolarizing current pulse (À30 pA, 300 ms) monitored throughout the experiment, and if it changed by more than 30% in control condition, the recording was discarded. Τ m was determined by fitting a mono-exponential to the rising phase of the voltage traces used for determining R in . Supra-threshold depolarizing current steps (1 s) were also applied to characterize the firing pattern of the recorded cell. The pyramidal morphology of the recorded cell was then confirmed using two-photon imaging. During electrophysiological protocols, cells were held at À70 or À80 mV by DC current injection, except when monitoring V m change during drug application. During uncaging protocols, current injection was performed by Multiclamp 700B function (dynamic, slow current injection, t ¼ 1 s). The effect of drugs on V m , t m and R in was assessed for each cell by comparing averages of 10 trials of 300 ms current injections at 0.1 Hz, in each condition.

Two-photon imaging and one-photon glutamate uncaging
Two-photon laser-scanning microscopy was performed using a two-photon imaging system (Bruker Nano Surfaces, Middleton, USA), a titanium:sapphire MaiTai DeepSee ultrafast pulsed laser (Newport SpectraPhysics, UK), and a water-immersion objective (LUMPlanFL N 60Â W, N.A. 1; Olympus UK). Alexa Fluor 594 included in intracellular solutions was excited at 870 nm. Glutamate was uncaged at 473 nm using a laser (Bruker Nano Surfaces, Middleton, USA) whose beam was directed into the microscope through optical fibers. A second set of galvanometers was used to control the targeting of the uncaging beam. In a typical experiment, a whole-cell recording was obtained from a putative L3 pyramidal neuron and the electrophysiological properties characterized. RuBiglutamate (0.5 mM) was then bath-applied in nACSF (10 ml) and recirculated via a peristaltic pump, at a perfusion rate of 2e3 ml/min, in dark or red light, for at least 15 min before the start of the uncaging. Alexa Fluor 594 was then visualized and dendritic segments that looked intact imaged. We selected dendritic regions that ran parallel to the slice surface for at least 20e50 mm at a depth of 40e60 mm. For each of these regions of interest, eight dendritic spines from the same branch were identified over a span of 20e30 mm. A locus near the head of each spine was then marked as uncaging site. The position, timing and intensity of laser pulses were controlled with TriggerSync (Bruker Nano Surfaces, Middleton, USA). Uncaging was performed using 0.2 ms duration laser pulses, and the evoked EPSPs (gluEPSP) were recorded at the soma. We designed two protocols to activate both single and multiple inputs within the same uncaging session: A short protocol, where 1 trial of group activation of 8 selected spines (with a 0.15 ms interval between stimulation of each spine) was followed 15 s later by 7 trials of uncaging at each of the spine (every 15 s, with a 700 ms interval between spines), yielding individual components of the EPSP. This was repeated 3 times in control condition, and 3 times in the presence of a blocker. A long protocol, made of 1 trial of group stimulation of an increasing number of spines (2, 3, 4, until 8) interleaved 15 s later with separate stimulation of each spine represented within the groups (with a 700 ms interval between spines). This was repeated 3 times in control and in the presence of a blocker to obtain integration curves for each condition.
To control for perturbing movements during long imaging experiments, a harp-shaped platinum wire was positioned at the surface of the slice. X-Y stage adjustments and objective refocusing to the location of dendritic spines were made in between stimulation protocols, in particular after a solution containing a pharmacological agent had been circulated. Successive responses elicited by uncaging at a particular spine (or group of spines) were very reproducible (see Fig. 1Bi) indicating that movements of the specimen did not contribute to pharmacological effects.

Drugs
4-aminopyridine (4-AP) was purchased from Sigma-Aldrich (St Louis, MO, USA). D-(À)-2-Amino-5-phosphonopentanoic acid (D-AP5) and TTX were obtained from Abcam Plc. (Cambridge, UK). Phrixotoxin-2 was purchased from Alomone Labs (Jerusalem, Israel) and diluted in 0.1% bovine serum albumin (BSA) solution. The dissolved phrixotoxin-2 was added to a perfusion solution containing 0.1% BSA. RuBi-glutamate was obtained from Tocris Cookson (Bristol, UK). To prevent dilution or contamination of recirculated solutions, the perfusion tubing was drained when switching between drugs. Drugs were dissolved and kept as stock solutions at À20 C, then diluted freshly before each experiment and applied for at least 10 min.

Data analysis
Electrophysiological data were analyzed using Igor Pro (Wavemetrics, Lake Oswego, USA), NeuroMatic (http://www.neuromatic. thinkrandom.com), Matlab 7.10 (MathWorks, Natick, USA) and Microsoft Excel 2010. Averaged waveforms were built from single sweeps aligned in time on the onset of the laser pulse and baselinesubtracted by the averaged voltage within 5 ms preceding the pulse. The 10e90% rise time, peak amplitude and half width of gluEPSPs were measured on such traces. To quantify the degree of supralinearity of input summation we excluded sweeps showing dendritic spikes. The peak amplitude, 10e90% rise time, and half width were measured on gluEPSP waveforms elicited by group stimulation of 8 spines (short protocol) or stimulation of 2 to all spines (long protocol). Similar measurements were performed on interleaved sweeps containing gluEPSPs evoked by activation of each spine involved in the summed response (individual components). GluEPSP supralinearity index was defined as the recorded EPSP peak over the peak of the linear sum of individual components. We also calculated the difference in peak amplitude, rise time and half width between the recorded gluEPSP and the linear sum of individual components D(Ev-Ar). Plotting the index of supralinearity against the age of the animals yielded no change postnatal days 22e48 (n ¼ 20 mice; Pearson's coefficient R ¼ 0.12, P ¼ 0.6, ANOVA). For each selected dendrite where uncaging was performed, the peak of evoked gluEPSPs was plotted against the linear sum of individual components (integration curves, Fig. 5D) depicting changes in the gain of dendritic integration. Morphological measurements were performed using Neurolucida (Micro-BrightField), NeuronStudio (Wearne et al., 2005), ImageJ (U. S. National Institutes of Health, Bethesda, Maryland) and Inkscape (www.inkscape.org). The path distance from the soma to the uncaging location was defined as the cumulative length of straight segments drawn onto the Z-projection of two-photon stacks. The branch order was determined from Neurolucida reconstructions or two-photon Z-stacks. Data from basal and oblique dendrites were pooled together and reported as mean ± S.D. unless otherwise indicated.

Statistical analysis
The Lilliefors test was used to inform data normality assumptions. One-way ANOVA test was used when comparing more than two samples. The Kruskal-Wallis test was used instead when the normality assumption could not be met for all groups. Similarly, paired comparisons were performed using either Student's t-test or Wilcoxon signed rank test, and unpaired comparisons were performed using either Student's t-test or Wilcoxon rank sum test. Statistical significance was considered when P < 0.05.

Histology and anatomical reconstructions
Following the experiment, slices were fixed overnight in 4% paraformaldehyde solution with 0.2% saturated picric acid solution and 0.1% gluteraldehyde in 0.1 M phosphate buffer (PB) at 4 C. Slices were then washed and the fixative was exchanged with PB and slices subsequently processed with avidin-Texas Red (Vector Laboratories, CA, USA) to visualize biocytin (Sigma-Aldrich, St Louis, MO, USA). Briefly, slices were cryoprotected with sucrose and permeabilised by freeze-thawing over liquid nitrogen. Any endogenous peroxidase was blocked using 1% aqueous hydrogen peroxide and 1% sodium borohydride in PB to block free aldehyde groups. A goat serum block was performed with 10% normal goat serum prior to overnight incubation at 4 C with ABC and Avidin Texas-Red (both Vector Laboratories, CA, USA). Slices were then mounted with Vectashield (Vector Laboratories, CA, USA) on a microscope slide. High-resolution Z-stacks of whole cells were acquired at 561 nm excitation with a Zeiss LSM 710 confocal microscope equipped with a 40Â oil immersion objective (N.A. 1.3) to produce a 3-D tile-scan of the recovered cells. Slices were then sectioned to 60 mm and treated for HRP -DAB staining (Vectastain ABC kit) to produce a permanent record of neuronal morphology. Sections were osmocated then dehydrated with increasing concentration of ethanol, cleared with propylene and impregnated with resin (Durcupan) prior to mounting and curing. Neurolucida (MicroBrightField, Colchester, VT) was used to reconstruct the cells in 3-D both from confocal Z-stacks and HRP stained sections.

Computational modeling
The NEURON simulation environment (Hines and Carnevale, 1997) was used to perform simulations. The model was based on the detailed 3-D reconstruction (Neurolucida; Microbrightfield, Williston, VT) of a biocytin-filled L3 pyramidal neuron from one experiment. The spatial resolution of the digital morphological reconstruction was verified to comply with the 'd_lambda rule' (Carnevale and Hines, 2006). Passive parameters were R a ¼ 150 U cm, C m ¼ 1 mF/cm<sup>2</sup> in the soma, 2 mF/ cm<sup>2</sup> in the dendrites accounting for spines, R m ¼ 6200 U cm 2 , resulting in a somatic R in of 120 MU and a membrane time-constant of 10 ms. Simulations were performed at a resting V m of À70 mV and a temperature of 32 C. The responses from 8 identical synaptic sites separated by 2.4 mm were simulated on a dendritic section in random sequential combination with 0.35 ms inter-stimulus interval. AMPA receptor-mediated conductances were modeled as the difference between two exponential functions using the built-in class Exp2Syn, with time-constant and maximum conductance values that generated somatically recorded single-site responses comparable to those measured in experiments in control condition (1 mV peak amplitude, 16 ms width at half-amplitude e.g. t 1 ¼ 0.33 ms, t 2 ¼ 3.3 ms, g max ¼ 0.65 nS).
NMDA receptor-mediated conductances were modeled using the implementation of a 10 state kinetic model from Kampa et al. (2004) by . The maximal NMDA conductance was adjusted together with the maximal AMPA conductance to preserve the properties of somatically recorded gluEPSPs evoked by uncaging at single spines, while providing levels of supralinearity comparable to that seen in experiments when uncaging at 8 sites (effective maximal NMDA conductance of 1.33 nS for AMPA to NMDA ratio of 1:3). The mechanism used for the A-type conductance is available from ModelDB at http://senselab.med.yale.edu/ modeldb with accession number 3660, implemented by M. Migliore for superficial neocortical pyramidal neurons based on a study by Zhou and Hablitz (1996). Activation and inactivation kinetics were left unchanged, whereas steady-state voltage at half activation and inactivation, and corresponding slopes were modified to match the average values in Zhou and Hablitz (1996): V 1/2 activ ¼ 0.5 mV, slope activ ¼ À12.2 mV; V 1/2 inact ¼ À47.4 mV, slope inact ¼ 7.2 mV, for Boltzmann functions in the form: where G max is the maximal conductance, and G the conductance at a particular steady-state potential V. Somatic V m was stabilized at À70 mV with increasing densities of A-type conductance by current injection. Match between model and experimental data was calculated using the following formula: where k is an index of the five gluEPSP parameters considered for the simulations (peak amplitude and half width of gluEPSPs evoked by uncaging at single spines and eight spines, and index of supralinearity calculated as the ratio of amplitude of evoked to summed gluEPSPs), Xe is the average relative change between drug and control condition detected experimentally, and Xm is the same change measured on simulated traces, in the model.

Funding
This work was supported by the Medical Research Council UK (Project grant number G1000629) and partly by the Human Brain Project (HBP-604102 grant) awarded to Alex M Thomson.

Conflicts of interest
The authors declare no financial and non-financial competing interests.

Authors contribution
ABi, ABr, and AR designed the study. ABi and AR performed the imaging, uncaging, and electrophysiology. ABr performed the computational modeling. JF did the histological analysis and anatomical reconstructions. ABi, ABr and AR analyzed the electrophysiological and imaging data. AR wrote the manuscript, which was then revised by all the authors.