BK channel inactivation gates daytime excitability in the circadian clock

Inactivation is an intrinsic property of several voltage-dependent ion channels, closing the conduction pathway during membrane depolarization and dynamically regulating neuronal activity. BK K+ channels undergo N-type inactivation via their β2 subunit, but the physiological significance is not clear. Here, we report that inactivating BK currents predominate during the day in the suprachiasmatic nucleus, the brain's intrinsic clock circuit, reducing steady-state current levels. At night inactivation is diminished, resulting in larger BK currents. Loss of β2 eliminates inactivation, abolishing the diurnal variation in both BK current magnitude and SCN firing, and disrupting behavioural rhythmicity. Selective restoration of inactivation via the β2 N-terminal ‘ball-and-chain' domain rescues BK current levels and firing rate, unexpectedly contributing to the subthreshold membrane properties that shift SCN neurons into the daytime ‘upstate'. Our study reveals the clock employs inactivation gating as a biophysical switch to set the diurnal variation in suprachiasmatic nucleus excitability that underlies circadian rhythm.

I nactivation gating of ion channels is essential to electrical signalling in most neurons. First characterized in Hodgkin and Huxley's classic studies of the action potential 1 , since then, several distinct inactivation mechanisms have been identified in Na þ , Ca 2 þ and K þ channels [2][3][4][5] . Among voltage-gated K þ channels, inactivation can occur via the classic 'ball-and-chain' mechanism involving pore occlusion by an intrinsic N-terminal 'ball' located on the cytosolic side of the a pore-forming subunit 6 . In contrast, large conductance Ca 2 þ -and voltage-activated BK K þ channels (K Ca 1.1, KCNMA1) are not intrinsically inactivating 7,8 . However, inactivating BK currents have been observed in some central neurons, sensory neurons and neuroendocrine cells [9][10][11][12][13][14][15][16][17] . In adrenal chromaffin cells, BK inactivation is mediated by the b2 subunit 18 and shares several common features with Shaker N-type inactivation, including a rapid time course and contribution of intracellular domains sensitive to proteolytic cleavage 19 . Chromaffin cells express both inactivating and non-inactivating BK channels, associated with distinct action potential behaviour 20 . Yet despite the welldescribed mechanistic basis, understanding the physiological relevance for BK inactivation has been complicated by other properties conferred by the b2 subunit, including a shift in the voltage dependence of activation and slowing of activation and deactivation kinetics 18,21 .
To understand the role of BK channel inactivation in neuronal excitability, we identified a circuit where b2 is expressed 22 and where dynamic regulation of the BK current is critical for neural coding, the suprachiasmatic nucleus (SCN) of the hypothalamus [23][24][25] . The SCN circuit undergoes synchronized daily oscillations in action potential firing frequency 26 , and circadian behavioural and physiological characteristics are established by the parameters of the SCN circuit rhythm 27,28 . BK channel expression varies over the circadian cycle in both mouse SCN and fly clock neurons 24,[29][30][31] . The daily rhythm in BK protein abundance is linked to Per2 (ref. 24), a component of the canonical transcription-translation feedback loop that encodes circadian time 32 . Correlated with expression levels, SCN neurons exhibit a diurnal difference in steady-state BK current magnitude, with smaller currents recorded during the day and larger currents at night 23,24,31 . Both loss of BK current at night and aberrant increase in BK current during the day result in disrupted circuit rhythmicity, establishing the diurnal variation in BK current as essential for expressing behavioural rhythms [23][24][25]29,33 . Loss of this diurnal rhythm in BK current has been recently linked to degradation of circadian rhythm in aged animals 33 , underscoring the significance of understanding the mechanisms that drive rhythms in BK channel activity in SCN.
Here we report that the b2 subunit produces inactivation of SCN BK channels. Using patch-clamp, long-term action potential, and behavioural recordings, we show that loss of b2 (b2 KO) abolishes the diurnal variation in both BK current magnitude and SCN firing, and disrupts circadian circuit and locomotor rhythmicity. We link these changes in excitability specifically to BK channel inactivation by taking advantage of the modular nature of b2, which allows selective rescue of inactivation via delivery of the isolated b2 N-terminal 'ball-and-chain' domain. We further reveal that neurons with inactivating BK currents fire faster, have depolarized membrane potentials and increased input resistance, demonstrating that inactivation unexpectedly contributes to the daytime 'upstate' in SCN neurons by controlling the amount of subthreshold BK current during the inter-spike interval. Thus, inactivation underlies the shift in BK's influence on excitability between day and night, and regulation of this biophysical mechanism is a central node for the circadian regulation of firing in the SCN clock circuit.

Results
b2 regulates SCN circuit rhythmicity and circadian behaviour. The SCN expresses two subunits with the potential to modify BK channel properties, b2 and b4 (ref. 22), but of these, only b2 can cause inactivation of BK currents 7,8 . Since b subunits are proposed to tailor BK channel properties and contribute to distinct patterns of excitability across tissues 34 , to establish the importance of the b2 subunit in the SCN circuit, we made longterm recordings of spontaneous action potential activity from wild-type (WT) and b2 KO SCNs. Individual SCN neurons function as coupled, autonomous oscillators, generating a robust synchronized rhythm in firing in ex vivo cultures (Fig. 1a) 28,35 . b2 KO SCNs had significantly reduced rhythmicity overall (Fig. 1b). This was due to both a decrease in the number of rhythmic recordings, as well as a reduction in the circadian amplitude of the rhythmic recordings (Fig. 1c,d) 36 . The circadian period of the rhythmic activity was not different (WT, 24.2 ± 1.3 h and b2 KO, 23.4±1.2 h, P ¼ 0.8), instead, the reduced circadian amplitude stemmed from decreased action potential activity at the peak (Fig. 1e).
Alterations in the SCN circuit were correlated with disrupted circadian behaviour ( Fig. 1f-g). Like SCN circuit activity, circadian behavioural amplitudes were reduced in b2 KO mice ( Fig. 1h; Supplementary Table 1). Decreased circadian behavioural amplitudes are associated with a more labile pacemaker 23,37,38 , and consistent with this, b2 KO mice re-entrained about a day faster to a 6-h phase advance of the light:dark cycle and had augmented responses to a phase-shifting light pulse (  Table 1). Taken together, these results suggest that b2 is important for the circadian patterning of action potential activity in the SCN circuit, and that this mechanism is required for proper circadian rhythmicity in the animal as a whole. Furthermore, the circadian alterations were specific to loss of b2, as deletion of the b4 subunit, which is also expressed in SCN 22 , did not result in significant changes in neuronal firing or behavioural activity ( Fig. 1c- b2 mediates BK current inactivation in SCN neurons. To determine the functional relevance of b2 regulation of SCN circuit rhythmicity, we recorded BK currents from SCN neurons using whole-cell voltage clamp. We observed two types of macroscopic BK currents which varied by the amount of current decay observed during the voltage step (Fig. 2a). Currents that exhibited a pronounced decay within 30 ms were termed BK i and had a fractional current ratio (I BK /I BKpeak )o0.7 at þ 90 mV ( Fig. 1b; Supplementary Fig. 2a,b). These BK i currents decayed with time constants of 44±4 ms (at þ 90 mV, n ¼ 13) (Fig. 2c; Supplementary Fig. 2c,d), similar to inactivating BK currents described in other neuronal types 18,20 . Other currents were relatively sustained with little decay, termed BK s (I BK /I BKpeak 40.7). The much slower time course of decay for BK s currents (172 ± 13 ms, n ¼ 17; Fig. 2c; Supplementary Fig. 2c) is consistent with non-inactivating BK currents that show a limited attenuation of current due to Ca 2 þ clearance 18 . Overall, during the day, most currents were BK i , while at night, most currents were BK s (Fig. 2d). This suggested that the number of neurons exhibiting BK i and BK s currents between day and night SCNs was responsible for the diurnal difference observed in the steady-state BK current magnitude within SCN (Fig. 2e).
Supporting this idea, we did not find that daytime BK i currents decayed more rapidly, and thus to a lower fractional current value, compared with night time BK i currents. Instead, the average BK i current density (Fig. 2f) and fractional current values ( Supplementary Fig. 2b) were similar between day and night.
These observations support a model where the simple summation of BK i to BK s currents is a central factor in the day versus night BK current levels observed across the SCN.
Since the b2 subunit produces inactivation of BK channels expressed in heterologous cells and native tissues 7,8,18,34,39 , we examined b2 levels to determine whether expression of the b2 subunit was correlated with the increased number of BK i currents observed in daytime SCNs. BK complexes were immunoprecipitated from SCNs harvested across the circadian cycle. Although the expression of b2 did not differ across time points (Fig. 3a,b), the relative ratio of b2 associated with the BK a subunit was higher during the day (Fig. 3c), correlated with the higher proportion of BK i currents (Fig. 2d). At night as a expression increased, the ratio of b2:a was lower and consistent with the increased number of BK s currents.
To determine whether b2 was required for the macroscopic BK i current decay in SCN, we recorded BK currents from b2 KO neurons. Only BK s currents were observed in b2 KO neurons (Fig. 4a,b; Supplementary Fig. 2a SCNs (Fig. 4c). Although the small number of BK i currents observed in WT neurons at night were also eliminated, the overall night time b2 KO BK current levels remained unchanged. This was expected since the vast majority of currents were already identified as BK s in WT neurons at night. Further consistent with loss of inactivation, the fractional current values and macroscopic current decay time constants were increased in b2 KO during the day, with no change at night (Fig. 4d,e; Supplementary Fig. 2a-c). These results demonstrate that b2 underlies the reduction in steady-state BK current levels during the day and is thereby the central regulator of the diurnal difference in SCN BK current. As a control, we also assayed the expression level and diurnal pattern of the BK channel a subunit in b2 KO SCNs and found no difference ( Supplementary Fig. 4a-c), corroborating the alterations in BK current magnitude stemmed from a loss of b2 function and not alteration of BK channel trafficking.
b Subunits produce complex effects on BK channel gating, including slowing activation and deactivation, and shifting the voltage dependence of activation to more hyperpolarized potentials 7,8,34,39 . However, b2-mediated inactivation is separably mediated by the intracellular N terminus, and transplantation or exogenous application of this domain confers inactivation gating to the BK a subunit in the absence of the b2 subunit 7,11,40,41 . Conversely, mutation of the three residues comprising the hydrophobic 'ball' (DFIW) removes inactivation while leaving other gating properties of b2 intact 42 . If inactivation is the major determinant of the day versus night difference in steady-state current levels, then selective restoration of inactivation during the day with the isolated N terminus should restore this difference to b2 KO neurons. Alternatively, failure to restore the decreased daytime BK current levels via inactivation with the b2N terminus would suggest that other properties conferred by the b2 subunit are necessary for the daytime decrease in steady-state BK current levels.
To test this, we first delivered the b2N terminus (b2N) as a soluble peptide to BK channels expressed in heterologous HEK293 cells (Fig. 5). b2N produced a dose-dependent inactivation, while a peptide harbouring the FIW mutation produced no effect (b2N DFIW ; Fig. 5a-d). The voltage dependence of inactivation with b2N was similar to the intact b2 subunit (Fig. 5e), and t inact values at b2N concentrations above 50 mM were similar to WT BK i currents recorded during the day from SCN neurons (Fig. 5d). We next applied the b2N peptide to SCN neurons via the patch pipette.
In b2 KO SCN neurons, application of b2N, but not b2N DFIW , restored the macroscopic decay and reduced the fractional current ( Fig. 6a; Supplementary Fig. 2a). The voltage dependence of inactivation and t inact values with b2N in b2 KO were similar to WT BK i currents recorded during the day (b2 KO þ b2N at þ 90 mV: 40±4 ms, n ¼ 20, Fig. 6a; Supplementary Fig. 2c,d). Furthermore, b2N decreased b2 KO BK current levels back to levels comparable to WT neurons (Fig. 6b), without affecting the voltage dependence of BK current activation ( Supplementary  Fig. 5) or other voltage-activated outward currents ( Supplementary Fig. 6). The restoration of daytime BK current levels by b2N support the conclusion that inactivation is the critical function of the b2 subunit that underlies its role in driving the diurnal variation in BK current properties in SCN.
Inactivation controls daytime membrane properties and firing. If inactivation is required for the diurnal difference in BK currents, then loss of the b2 subunit or selective rescue of inactivation with b2N should alter neuronal activity. To test this, we recorded spontaneous action potentials from WT and b2 KO SCN neurons. WT neurons fire at higher frequencies during the day and decrease firing at night (Fig. 7a,b). Neurons with BK i currents fired faster than those with BK s currents regardless of time of day, suggesting that inactivation may play a role in setting firing rate. Furthermore, the relative difference in firing between BK i and BK s neurons during the day was as large as the net diurnal difference in firing across the SCN (Fig. 7b), suggesting BK inactivation may be fundamental to the diurnal regulation of firing rate. Consistent with this, b2 KO neurons did not exhibit a day-night difference in firing rate, stemming from a marked reduction in daytime firing (Fig. 7b,c). To verify that the reduced firing, which was correlated with larger BK currents in b2 KO neurons (Fig. 6b), was due to BK, the BK channel blocker paxilline was applied. The reduced firing in b2 KO neurons was reversed by paxilline ( Fig. 7b), demonstrating that BK channels were responsible for the altered excitability in b2 KO neurons.
These results corroborate the reduced peak firing observed in SCN circuit recordings (Fig. 1e). In addition, these data may also explain why loss of BK currents during the day has apparently little effect on WT firing rates 24,43 . A detectable change in firing after BK block in WT neurons may be precluded under standard daytime conditions when two-thirds of SCN neurons undergo BK inactivation. Following this idea, application of b2N, but not b2N DFIW , increased daytime b2 KO firing rates back to WT levels ( Fig. 7b,d). b2N had no further consequences on firing beyond that of blocking the BK current with paxilline ( Fig. 7b), demonstrating that the restoration of firing with b2N acts selectively through BK channels. These results suggest that inactivation normally removes BK currents from influencing action potential firing rate during the day. Illustrating this in another way, b2N could also aberrantly suppress BK current ( Fig. 8a-c) and elevate firing if applied to WT neurons at night (Fig. 8d), underscoring the basis for the normal reduction in the number of BK i currents found in the SCN at night.
What membrane properties does BK inactivation regulate to facilitate daytime firing? A central node for circadian regulation of action potential frequency is the balance of subthreshold excitatory and inhibitory currents that bring the resting membrane potential closer to the firing threshold during the day, or further from threshold at night 26,44 . K þ currents are proposed to be central regulators of the day-night difference in firing by regulating the daily transition between the daytime   [44][45][46][47] . These states are designated by differences in the subthreshold membrane properties, with the most attention focused on the increase in night time K þ current associated with hyperpolarization of the membrane and lower input resistance 44,45,47,48 . BK channels comprise a component of this upregulated K þ current, and loss or block of BK currents causes depolarization of the baseline membrane potential and hyperactive firing at night [23][24][25] . However, block of BK currents also depolarizes the membrane potential during the day 43,47,49 , suggesting a role for BK channels in daytime excitability not previously explored. Thus to determine whether BK inactivation makes a converse contribution to the daytime reduction in K þ current that defines the 'upstate' that is required for higher frequency firing, we compared membrane parameters from neurons during the day and night, and with loss of b2 or restoration of inactivation. First, we found that BK i neurons had inter-spike membrane potentials ranging from À 36 to À 51 mV, while BK s neurons ranged from À 47 to À 54 mV during the day. Loss of inactivation in b2 KO neurons resulted in hyperpolarization of the inter-spike membrane potential compared with WT BK i neurons ( À 57 ± 1.4 mV versus À 50 ± 1.1 mV, respectively; Po0.001, t-test). This shift could be rescued by b2N ( À 52 ± 0.8 mV), but not b2N DFIW ( À 56 ± 1.5 mV; one-way ANOVA, P ¼ 0.04; Bonferroni post hoc, Po0.05 for BK i versus b2 KO or b2N DFIW ), suggesting that BK channel inactivation affects membrane potential during the inter-spike interval. To further address this, resting membrane potential (V m ) and input  resistance (R i ) recordings were made in the presence of tetrodotoxin to block action potential activity. Daytime neurons had more positive V m and higher R i , while night time neurons had more hyperpolarized V m and lower R i (Fig. 9a,b), consistent with previous studies 45 Fig. 9a,b). This suggests less current would be required to elicit an action potential in BK i compared with BK s neurons. If inactivation of BK currents is involved in the changes in V m and R i between BK i and BK s neurons, then loss of b2 should also alter these parameters. We found that the V m and R i of daytime b2 KO neurons was more similar to WT neurons at night (Fig. 9a,b), suggesting b2 is required for the daytime 'upstate'. Furthermore, b2N restored the V m and R i values in b2 KO neurons back to values comparable to WT, establishing the sufficiency for inactivation of the BK current to convert the daytime membranes to pro-excitable. Although b2 can also affect excitability by shifting the voltage dependence of activation and slowing activation and deactivation gating 18,21 (Supplementary Discussion), the data presented here affirm that these functions are not directly involved in the diurnal regulation of membrane properties that control firing frequency in SCN.
The effect of inactivation on resting membrane potential and input resistance predicts that inactivation of BK currents would occur during the inter-spike interval. To demonstrate this, we recorded BK currents from traditional voltage step commands across the subthreshold range of membrane potentials, as well as BK currents evoked by SCN action potential commands ( Fig. 10; Supplementary Fig. 7). BK s current-voltage relationships showed that daytime BK current activated at voltages more positive than À 60 mV (Fig. 10a,b). There was 5-12 pA of current evoked in the subthreshold range, between the average resting and threshold potentials of SCN neurons ( À 55 to À 40 mV). Night time subthreshold BK currents (BK s ) were also larger than the net daytime BK current (Supplementary Fig. 7a). In contrast, daytime BK i neurons had significantly reduced current in the subthreshold voltage range (Fig. 10a,b). Consistent with data obtained from voltage steps, using daytime SCN action potential commands delivered at the normal daytime firing frequency, the amount of BK current activated during the inter-spike interval was negligible in BK i neurons compared with BK s neurons (Fig. 10c,d) or at night ( Supplementary Fig. 7b,c). BK currents evoked at the peak of the action potential command were also reduced in BK i neurons compared with BK s neurons during the day (Fig. 10e) or at night ( Supplementary Fig. 7d). In parallel experiments using daytime action potential commands applied to channel complexes expressed in HEK293 cells ( Supplementary Fig. 8a-j), the subthreshold current was reduced in patches containing BK/b2 or BK/b2N compared with a-only channels ( Supplementary Fig. 8f-i).
To further demonstrate that inactivation could affect BK current levels at these subthreshold voltages in SCNs, b2 KO neurons were held at a conditioning voltage for 100 ms, corresponding to the shortest inter-spike intervals encountered in spontaneously firing SCN neurons, followed by a step to þ 90 mV to elicit a maximal BK current response (Fig. 10f). Inactivation delivered via b2N reduced the maximal BK current elicited following conditioning voltages in the subthreshold range, compared with b2 KO cells treated with b2N DFIW (Fig. 10f,g). Further depolarization of the conditioning potential resulted in progressive current reduction that was dependent on the presence of inactivation (Fig. 10f,g). Similar results were obtained with BK channels expressed in heterologous cells with the intact b2 subunit or with b2N ( Supplementary Fig. 8a,b). These results suggest that inactivation can reduce BK current under conditions similar to the native inter-spike interval and provide a basis for understanding the effect of BK inactivation on the resting membrane potential and input resistance.
The data further propose that because some BK current would be inactivated before an action potential, the current evoked by an action potential would be reduced. This would be expected to occur during the day in BK i neurons. To test this, we quantified the peak BK current evoked by daytime action potentials applied to SCN neurons (Fig. 10c,e) and to BK/b2 or BK/b2N channels expressed in heterologous cells ( Supplementary Fig. 8e-h,j). The action potential-evoked BK current was reduced in BK i versus BK s neurons (Fig. 10e) and in BK/b2 or BK/b2N conditions in HEK293 cells compared with a-only channels ( Supplementary  Fig. 8j). Taken together, these data support a model where BK current inactivation is necessary during the day to regulate the membrane parameters that initiate firing (membrane potential and input resistance), while concurrently reducing the BK current activated during an action potential. This idea further predicts there would be little difference in the action potential waveforms of BK i versus BK s neurons, an observation confirmed by analysis of daytime action potential parameters (Supplementary Fig. 9). b2-mediated inactivation thus comprises an essential switch that shifts membrane properties between day and night states by inhibiting or permitting subthreshold BK current activation.

Discussion
The circadian patterning of neuronal excitability is an evolutionarily conserved feature of time-encoding circuits 26,50 .
In SCN neurons, which fire relatively slow, spontaneous action potentials characteristic of pacemaker neurons 49 , the balance of currents during the inter-spike interval is proposed to be the predominant regulator of firing rate and a major node for circadian regulation 26,44,45,48 . Correlated with the increased number of BK i currents in SCN during the day, most neurons have a more depolarized resting membrane potential that is closer to threshold (DV B7 mV, from our data), increasing the likelihood of firing an action potential. At night, and correlated with the shift to BK s currents, the hyperpolarizing shift places the membrane potential further from threshold (DV B12 mV), reducing excitability. The amount of current required to produce this shift is small (B5 pA), owing to the high input resistance of SCN neurons, and the balance can be tipped either by altering the . BK currents were identified as BK i or BK s from a maximally activating step to þ 90 mV (as in Fig. 2). (b) Current-voltage relationship showing significantly more activation of BK s current above À 60 mV compared to BK i . (c) Pre-recorded action potential commands (top) were used to elicit BK currents from BK i or BK s neurons. From a holding potential of À 150 mV to remove inactivation completely, cells were stepped to the inter-spike potential ( À 48 mV) with a sequence of three action potential commands as depicted (Peak, 8 mV; t 1/2 , 5.5 ms; and AHP/antipeak, À 54 mV). Arrow, the subthreshold current level in d was taken just before the second action potential command. (d,e) Average subthreshold BK current density from the inter-spike interval (d) or at the peak of the action potential (e). n values for (a-d): WT: day/BK i (9), day/BK s (5). (f) BK current as a function of conditioning potential in SCN neurons. Representative macroscopic BK current traces from b2 KO neurons during the day with 50 mM b2N DFIW or b2N. Neurons were held at À 90 mV for 150 ms to remove inactivation, and then stepped to a conditioning potential for 100 ms to allow channels to transition into the inactivated state, followed by a maximally activating step to þ 90 mV. (g) The peak BK current elicited from the þ 90 mV step was plotted as a function of the conditioning potential. b2N causes a reduction in current, but no reduction is observed in the absence of inactivation with b2N DFIW . n ¼ 5 for each condition. All values are mean ± s.e.m. *Po0.05, Bonferroni post hoc.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10837 ARTICLE excitatory currents that bring the membrane potential closer threshold, or the inhibitory currents that take the membrane away from threshold. Recently, the identity of the channel underlying the persistent Na þ current that provides the depolarizing drive on excitability was identified as the leak Na þ channel NALCN 51 . However, the identity of the K þ channels counterbalancing the excitatory current has been uncertain, particularly during the day when SCN neurons undergo a dramatic reduction in K þ current 44,45,49 . Although abrogation of one type of K þ current during the day, the fast delayed rectifier, has also been shown to decrease firing frequency, the reduced firing stems from slower action potential repolarization and not from depolarization of the resting membrane potential 52 . Consequently, a direct test of whether the daily shift in submembrane K þ currents is required to drive the day-night difference in action potential firing has been elusive.
In this study we provide surprising evidence linking alterations in BK current with the daytime increase in input resistance, depolarization of the membrane and higher frequency firing. BK currents were previously thought to mainly play a night time-restricted role as part of the surge of K þ current that results in the firing nadir 24,44,45 . The less significant role for BK channels in setting daytime frequency was attributed to a decrease in expression of the pore-forming a subunit. However, in the b2 KO, the intact circadian pattern of a expression was insufficient to support normal diurnal variation in BK current or SCN firing, suggesting there must be other mechanisms that limit BK channels from influencing daytime membrane properties. We demonstrate that inactivation, achieved through b2-dependent regulation of BK channel biophysical properties between day and night, is the central mechanism that changes the influence of BK channels on membrane properties between day and night. Inactivation facilitates the daytime membrane 'upstate' by reducing the BK current between spikes that would normally inhibit action potential initiation. Inactivation also reduces action potential-evoked current, and the sum of these two mechanisms effectively removes BK channels from influencing daytime excitability. In b2 KO SCN neurons, the absence of BK inactivation during the day results in passive membrane properties that look much like night time membranes. Correspondingly, with b2N, restoration of inactivation is both necessary and sufficient to recapitulate the V m and R i properties that define the daytime membrane state. Importantly, the identification of this biophysical mechanism to functionally reduce a K þ current suggests that the balance of excitatory and inhibitory currents is more actively regulated during the day than previously thought 45 . Moreover, the disruption of circadian behaviour in the absence of the b2 subunit underscores the importance of both BK inactivation, and the diurnal variation in SCN submembrane properties, in the regulation of circadian rhythmicity. As such, BK i currents comprise an electrophysiological signature for a previously undetected class of essential oscillator in SCN that makes a vital contribution to circadian behaviour. Even so, the residual rhythmicity in b2 KOs hints that neuronal heterogeneity contributes redundant mechanisms to circadian behavioural rhythmicity (Supplementary Discussion), and it remains to be determined how SCN neurons without inactivating BK channels balance their daytime currents to control firing, and what separable contribution these cells make to circadian behaviour.
Given that the BK current must be functionally reduced by inactivation, what is the relevance of the daytime clock-linked decrease in BK a subunit expression 24,30 ? Such differences in ion channel expression across the circadian cycle are broadly proposed to be central to rhythmicity 26 , but an explicit mechanism that translates channel expression differences into action potential activity has not been established. In this study, we showed b2 KO SCNs retained the normal day-night difference in BK a expression, yet still displayed disrupted BK steady-state current levels and action potential firing, demonstrating that circadian differences in the BK a subunit alone are insufficient to drive rhythmicity. Our data instead suggest a model in which the clock-linked changes in a expression control the ratio of b2:a. Since expression of b2 does not vary appreciably between day and night, the higher daytime b2:a ratio facilitates inactivation in the majority of SCN neurons, permitting transition to the 'upstate'. At night, inactivation is overcome by increased a subunit expression, reducing the b2:a ratio and facilitating the 'downstate'. In support of this hypothesis, aberrantly increasing daytime BK expression reduces inactivation in the SCN (Supplementary Discussion).
The data in SCN also provide a framework for understanding the physiological relevance of BK channel inactivation, which is too slow to produce substantial BK current decay during a typical central nervous system action potential 53 . In other neurons where higher frequency firing prevails, BK inactivation is thought to contribute to spike frequency adaptation, which also integrates over timeframes longer than a single action potential 10,15,17 . In SCN neurons, which exhibit depolarized membrane potentials and slow spontaneous firing, the results here suggest that enough channels undergo inactivation, or remain cumulatively inactivated, during the inter-spike interval (100-500 ms) to impact the input resistance and resting membrane potential. Given t inact values of 35-100 ms in BK i neurons, steady-state inactivation may be most relevant for setting the subthreshold BK current level during the inter-spike interval. SCN neurons have been shown to undergo subthreshold Ca 2 þ oscillations 49,54 , raising the possibility that Ca 2 þ influx independent of the action potential could contribute to BK channel activation, and consequently BK inactivation, during the inter-spike interval. In addition, the restoration of firing rate with b2N reveals that inactivation mediated by the N terminus is sufficient for this role. N-type inactivation typically occurs from the open state 7,8 , but BK channels may also inactivate from closed states, affecting the amount of steady-state current 55 . Thus, the data in this study reveal a surprising twist to how cells use BK channels to regulate excitability. While BK channels perform diverse roles spanning excitable and non-excitable cells, in the CNS they are mostly known for regulating firing frequency by underlying the fast AHP [56][57][58] . Here we show in SCN, BK current activated outside of the action potential is potentially the major contributor to frequency regulation, making dynamic regulation of subthreshold BK current via inactivation a novel role for BK channels.
In summary, although the combination of BK i and BK s expressing cells has been observed within other tissues 18 , the significance for how these currents work together to set the ensemble properties underpinning physiological function is not yet apparent 53 . In SCN, the cycling between predominantly BK i currents during the day and predominantly BK s currents at night suggests that partnering with the b2 subunit generates a hardwired mechanism linked to the intrinsic clock to dynamically disengage BK channels from regulating action potentials during one phase of the circadian cycle.

Methods
Mice. WT, b2 KO (KCNMB2 À / À , gift from C. Lingle), b4 KO (KCNMB4 À / À , gift from R. Brenner), and Kcnma1 À / À mice were maintained on inbred C57BL/6 background and genotyped as previously described 18,24,59 . KCNMB2 floxed mice are available at The Jackson Laboratory (Stock no. 028416). Male and female mice were used (3 weeks to 5 months old) and were group housed separated by sex until experimental procedures as indicated. Day time points were collected from mice housed on a standard 12 h light, 12 h dark cycle (12:12 LD), and night time points were collected from mice housed on a reverse 12:12 LD cycle. All procedures involving mice were conducted in accordance with the University of Maryland School of Medicine Animal Care and Use Guidelines and approved by the IACUC Committee.
Organotypic slice culture. Brains were harvested from postnatal day 4 mice, and the hypothalamus was blocked and sectioned into 300 mm coronal slices using a manual chopper (Stoelting, Wood Dale, IL, USA). Slices containing SCN nuclei were transferred onto Millicell filters (Millipore, Billerica, MA, USA) and cultured as interface explants in a CO 2 incubator as described 23 . After 2 days, 20 mM cytosine b-D-arabinofuranoside (ara-C, no. C6645; Sigma) was added to inhibit glial proliferation, and the media was changed every 3 days thereafter.
Multielectrode array recordings. After 7 days in culture, organotypic slices were cut from the surrounding membrane, inverted over the 64-electrode grid, and adhered to 0.1% polyethylenimine and collagen-treated P210A probes (Alpha MED Scientific, Osaka, Japan). Probes were placed on a MED CO2P connector headstage, sealed with a vacuum-greased coverslip, and maintained in a humidified 5% CO 2 incubator at 37°C for the duration of the recordings. Media changes were maintained every 3 days.
Signals from all electrodes on the probe were collected simultaneously with the 64-channel integrated amplifier (Alpha MED Scientific) and analysed as described previously 23 . Five-second data samples were collected every 5 min at 20 kHz in Conductor v3.1f (Alpha MED Scientific) and filtered at 100 Hz. Spontaneous extracellular action potentials from visually identified electrodes within the SCN were discriminated offline using threshold-based event counting. Circuit analysis was performed on each slice from three cycles of activity at all electrodes within the SCN. The multiunit spontaneous action potential activity from each electrode located within the SCN was classified as rhythmic or arrhythmic. For rhythmic recordings, a 2 h moving window average was applied to the raw data to calculate the daily firing rate peak, and the 'day' firing rate value was the average of activity for 2 h centred around the peak for each recording. Firing rate at the trough was calculated from 2 h of activity at the nadir between two peaks. Arrhythmic firing was calculated as the average firing across the whole cycle. Circadian amplitude was reported as the w 2 periodogram peak value (Clocklab; Actimetrics, Wilmette, IL, USA). t, the length of the circadian period of the neural activity rhythm, was determined as the highest peak above the 99% confidence interval of a w 2 periodogram.
Circadian behavioural rhythms. For locomotor rhythms, mice (3-5 months old) were housed individually in cages containing a running wheel for 10 days in LD and 16 days in constant darkness (DD). Activity was sampled every 10 min in ClockLab software (Actimetrics). Actograms were constructed by double-plotting consecutive days of activity over the recording period. Circadian period and amplitude were determined from 10 days of wheel running activity in DD in Clocklab software as described previously 23,24 . For re-entrainment experiments, after 7 days of stable entrainment, the LD cycle was phase advanced by 6 h. The response was calculated as the number of days to stable re-entrainment. After keeping mice in DD for 8 days, phase shifts in response to light pulses were calculated as the number of hours between the activity onset regression fits before and after a 30-min light pulse delivered in early subjective night (CT16). Alpha was determined as the length of time an animal had consolidated activity using default settings with manual adjustment, with rho defined as the portion of the cycle outside of alpha. Bouts were calculated using default settings. Data was excluded from mice that failed to run on wheels for two consecutive days.
Western blots. A single block of hypothalamus containing the SCN (B2 mm) was harvested at the indicated time points from mice (2-to 3-months old). Four micrograms solubilized protein from individual SCNs were loaded per lane. Densitometry of BK doublet band (1 mg ml À 1 L6/60 mouse monoclonal a-BK antibody, Neuromab; University of California, Davis, CA, USA) to DM1a anti-tubulin (1:75,000; Sigma T-9026) was performed as described previously 23 and presented as a proportion of ZT20. Three independent circadian cycle tissue harvests were performed for each condition.
For immunoprecipitation, individual SCNs (B50 mg of protein) were precleared by incubation with 20 ml TrueBlot anti-rabbit Ig IP beads (Rockland Immunochemicals; Limerick, PA, USA) for 2 h at 4°C (ref. 18). Protein samples were centrifuged at 13,200 r.p.m. for 30 min to precipitate the beads. Supernatant was collected and mixed with 1 mg of anti-BK a subunit antibody (anti-KCa1.1, #1184-1200, Alamone Labs; Jerusalem, Israel) and rotated for 2 h at 4°C. 50 ml TrueBlot anti-rabbit Ig IP beads were added, and the mixture was rotated overnight at 4°C, centrifuged at 13,200 r.p.m. for 30 min to precipitate beads, and the supernatant was discarded. Beads were washed three times and resuspended in 20 ml lysis buffer. Protein was run on a western blot as detailed previously and probed with 1 mg ml À 1 anti-BK (L6/60; Antibodies Incorporated; Davis, CA, USA); 1:75,000 anti-a-Tubulin (DM1a; Sigma; St Louis, MO, USA); or 1 mg ml À 1 anti-b2 (N53/32; Antibodies Incorporated; Davis, CA, USA). Full size images for western blots are presented in Supplementary Figs 3 and 4.
Acute SCN slice preparation. Mice were sacrificed in the light, at zeitgeber time (ZT) ZT0-2 (day time points) or ZT11-12 (night) from 3-to 6-week-old mice. Brains were rapidly removed and placed into ice-cold sucrose-substituted saline containing the following (in mM): 1. Slices containing SCN were transferred to the recording chamber (RC26GLP/PM-1; Warner Instruments, Hamden, CT, USA) with gravity flow bath perfusion of 1-2 ml min À 1 oxygenated artificial cerebrospinal fluid at 25°C. Neurons were visualized with a Luca-R DL-604 EMCCD camera (Andor, Belfast, UK) under IR-DIC illumination on an FN1 upright microscope (Nikon, Melville, NY, USA). Recordings were made from cells in the centre of the SCN. Current-and voltage-clamp recordings were made with a Multiclamp 200B or 700B amplifier and pCLAMP v10 software (Molecular Devices, Sunnyvale, CA, USA). Data were acquired at a 20 or 100 kHz sampling rate. Drugs were delivered to the bath by a computer-controlled pressurized perfusion system (ValveLink 8.2; Automate Scientific, Berkeley, CA, USA) at the concentrations indicated from 1,000 Â stocks. Recording windows were at the peak (ZT4-8) and nadir (ZT17-21) of the circadian rhythm in spontaneous action potential firing, corresponding to the 'day' and 'night' time points, respectively. Although the action potential frequencies in this study were lower than our previous studies performed at 35°(refs 22,23), the day-night difference in firing frequency in this study is preserved (Fig. 4a,c). All recordings were made with synaptic transmission intact, unless indicated (Tetrodotoxin was applied for all V m and R i measurements, as well as the subthreshold BK currents in Fig. 5). Reported N's are the number of neurons, and data for each condition was derived from 5 to 15 slices (1-6 neuronal recordings per slice).
SCN electrophysiology. SCN neurons were recorded in whole-cell configuration, first in current-clamp mode to collect action potential data, then switched into voltage clamp mode to obtain macroscopic voltage-activated outward K þ currents. Electrodes (4-7 MO) were filled with internal solution, in mM: 123 K-methanesulfonate, 9 NaCl, 0.9 EGTA, 9 HEPES, 14 Tris-phosphocreatine, 2 Mg-ATP, 0.3 Tris-GTP, and 2 Na 2 -ATP, pH adjusted to 7.3 with KOH. The electrode solution was adjusted to 305 mosM with glucose, and bath osmolarity was 300 mosM. This internal solution supports BK current activation and spontaneous firing 23,49 . After GO seal and whole-cell break-in, membrane properties were elicited from a þ 20 mV voltage step from a holding potential (V h ) of À 90 mV. Access resistance was verified to beo25 MO witho ± 5% change at the end of the recording (on average B15 MO). Series resistance was compensated at 80%.
For action potentials, data were acquired in 10 s sweeps and filtered at 10 kHz. Frequency was calculated as the average of each sweep. Baseline potential was determined as the average inter-spike potential in the presence of spontaneous activity. Template-based action potential analysis was performed in Clampfit 10 (Molecular Devices) to obtain action potential peak and half-width (t 1/2 ) values. Afterhyperpolarization (AHP) peak was determined as the peak negative value of the action potential, and AHP amplitude was the baseline membrane potential minus the AHP peak value. Threshold analysis was performed by taking the derivative of each action potential event in the 10 s segment to determine the inflection in the voltage trajectory (Clampfit). This method gives a set of values per neuron with lower standard deviation than automated analysis using dV/dt of 4-5 V s À 1 (ref. 49). Action potential analysis was performed blind with respect to genotype or time point.
In voltage-clamp mode, total voltage-activated K þ currents were elicited from a holding potential of À 90 mV, stepping from À 110 to þ 90 mV for either 30 or 150 ms in 20 mV increments. BK currents were isolated by focal application of the BK antagonist paxilline (10 mM), and subtracting currents after paxilline from the initial current. The effective concentration of paxilline in the recoding chamber was 3.75 mM. Currents were averaged from three to five voltage families. Current-voltage (I-V) relationships were constructed from the current level at 30 ms from each potential, unless noted otherwise (peak or steady-state values). Current density values were obtained by normalizing to cell capacitance, which did not differ between day and night (7.0 ± 0.5 and 6.8 ± 0.4 pF, respectively) or between WT and b2 KO (7.7±0.7 and 7.1±0.4 pF, n ¼ 27, 20, respectively). Voltage values were adjusted for the liquid junction potential of 10 mV. t inact values were calculated from single exponential fits of the macroscopic current decay from the þ 90 mV step for 150 ms (Clampfit, Molecular Devices). BK i and BK s currents were categorized as described using the current ratio at 30 ms from þ 90 mV step (BK i o0.07, BK s 40.07), corresponding to t inact valueso110 ms.
For passive membrane properties, whole-cell recordings were performed as above using the same internal solution as for current-and voltage-clamp recording, with tetrodotoxin (1 mM) in the bath. After break in, the membrane potential was recorded, followed by current injection steps (0 to À 25 pA, in 5 pA increments). Input resistance was calculated as the linear slope of the voltage. For experiments where currents were categorized as BK s or BK i , cells were switched to voltageclamp mode after recording V m and R i , and BK currents were isolated and t inact values were obtained as described in the previous section. For BK i and BK s recordings of V m , R i , subthreshold SCN BK currents, and BK currents evoked by action potential commands, recordings were performed in 1 mM tetrodotoxin. After recording V m and R i as described above, cells were switched to voltage-clamp mode and stepped from a holding potential of À 90 to þ 90 mV for 150 ms to determine BK i and BK s by t inact as described previously. After holding at À 150 mV for 100 ms, cells were stepped from À 60 to À 30 mV (in 5 mV increments), and then stepped back to À 150 mV for 100 ms followed by action potential commands. Previously acquired native action potential waveform was obtained from daytime or night time SCN recordings. For day (Fig. 10c) and night ( Supplementary Fig. 7), the action potential parameters are indicated in the figure legends. Three sequenced action potentials were applied at the average BK i daytime firing rate (2.25 Hz) or night time BK s firing rate (1 Hz) as depicted in the figures. Current-voltage relationships were plotted, and the action potential-evoked peak and subthreshold currents were normalized to the cell capacitance.
Drugs and b2N peptides. Paxilline and tetrodotoxin (Tocris, Bristol, UK) were prepared as 1,000 Â stocks in DMSO and water, respectively. b2N, was synthesized as the first 45 amino acids of the b2 subunit (MFIWTSGRTSSSYRQDEKR-NIYQKIRDHDLLDKRKTVTALKAGED) (GenScript, Piscatawa, NJ, USA) 41 . b2N DFIW was a 42 amino acid peptide with the underlined FIW deletion. Lyophilized peptides were reconstituted in intracellular solution as 100 Â stocks and added at the final indicated concentrations.
HEK cell patch-clamp electrophysiology. HEK293T cells (ATCC, Manassas, VA, USA) were transfected with the BK SRKR a subunit cDNA (Genbank accession #JX46275), with or without b2 (ref. 34), both in pcDNA3.1. DNA was transfected at 1 mg (a only) or 1 mg a and 1.7 mg b2 per 35 mm dish using TransIT (Mirus Bio, Madison, WI, USA). Cells were plated on glass coverslips 3-5 h later and recorded from 20 to 30 h after transfection. Patch-clamp recording was performed using the voltage-clamp mode in the inside-out patch configuration using thin-walled borosilicate pipettes with resistances of 2-5 MO as described previously 60 . Recordings were made at room temperature, and the data were acquired at 50 kHz and filtered at 10 kHz. The bath (intracellular) solution was composed of (mM): 140 KMeSO 3 , 2 KCl, 20 HEPES and 5 HEDTA. Free [Ca 2 þ ] i was calculated using Webmax C Standard software 61 , to a final concentration of 50 mM (from 1 M CaCl 2 stock). The pipette (extracellular) solution consisted of (mM): 145 NaCl, 5 KCl, 2 CaCl 2 , 1 MgCl2 and 10 HEPES, with pH adjusted to 7.2 with NaOH. Cells were held at À 150 mV, followed by a maximally activating test step to þ 150 mV for 150 ms. Data were collected only from patches with o0.7 fractional current (I peak /I ss ). BK currents were elicited from patches using the voltage protocols indicated in the figures. Single-exponential functions were fit to the macroscopic current decay at þ 90 mV.
For activation of BK currents by action potential commands ( Supplementary  Fig. 8e), the daytime action potential waveform (as in Fig. 10c) was applied after the standard voltage protocol in whole-cell voltage-clamp mode. The pipette (intracellular) and bath (extracellular) solution were the same as used in the SCN whole recordings above. The action potential-evoked peak current, or the subthreshold current, was normalized to the maximal current elicited from each patch.
Statistics. The number of neurons (BK current and action potential recordings), the number of mice (circadian behaviour) or the number of SCN slice cultures (multielectrode array recordings) are represented as n. Group sample sizes were determined based on power calculations using effect sizes estimated from previous experiments. Behavioural comparisons were performed as comparisons between WT and b2 KO, or WT and b4 KO, using an unpaired Student's t-test. One-way ANOVAs were used for comparisons with more than two conditions, and the P values reported in the text are the Bonferroni post hoc tests only for comparisons where the main effect was Po0.05. Factorial ANOVA was used for comparing multiple conditions across voltages, with Bonferroni post hoc P values for specific comparisons reported in the text. Categorical data (number of rhythmic versus arrhythmic recordings, or BK i versus BK s ) were compared with Fisher's exact test, with the Fisher's P value reported in the text. Statistical tests were run in Origin (Originlabs, Northampton, MA, USA). All values are presented as mean ± s.e.m.