Prolonged Intracellular Na+ Dynamics Govern Electrical Activity in Accessory Olfactory Bulb Mitral Cells

Persistent activity has been reported in many brain areas and is hypothesized to mediate working memory and emotional brain states and to rely upon network or biophysical feedback. Here, we demonstrate a novel mechanism by which persistent neuronal activity can be generated without feedback, relying instead on the slow removal of Na+ from neurons following bursts of activity. We show that mitral cells in the accessory olfactory bulb (AOB), which plays a major role in mammalian social behavior, may respond to a brief sensory stimulation with persistent firing. By combining electrical recordings, Ca2+ and Na+ imaging, and realistic computational modeling, we explored the mechanisms underlying the persistent activity in AOB mitral cells. We found that the exceptionally slow inward current that underlies this activity is governed by prolonged dynamics of intracellular Na+ ([Na+]i), which affects neuronal electrical activity via several pathways. Specifically, elevated dendritic [Na+]i reverses the Na+-Ca2+ exchanger activity, thus modifying the [Ca2+]i set-point. This process, which relies on ubiquitous membrane mechanisms, is likely to play a role in other neuronal types in various brain regions.

The accessory olfactory system is essential for chemical communication in animals during social interactions. During this process, the principle cells of the accessory olfactory bulb (AOB) may respond to transient stimulation with prolonged activity, sometimes lasting for minutes-a property known as persistent activity. This property, which has been observed in other brain areas, is usually attributed to positive feedback mechanisms either at the cellular or the network level. Here, we show how persistent activity can emerge without feedback, relying on slow changes in internal ionic concentrations, which keep a record of past neuronal activity for long periods of time. We used a combined computational and experimental approach to show that the complex interaction between various ions, their extrusion mechanisms, and the membrane potential leads to stimulus-Introduction The accessory olfactory system, also known as the vomeronasal system, mediates chemical communication between conspecifics of most mammalian and reptilian species during social interactions [1]. Inputs to this chemosensory system originate from the sensory neurons of the vomeronasal organ (VNO) that synapse on the mitral cells of the accessory olfactory bulb (AOB), which provide the output of the bulb [2]. Previously, we have shown that AOB mitral cells in vitro respond to brief afferent nerve stimulation with persistent firing activity lasting several minutes [3].
Persistent activity, defined as the ability of neurons to remain active in the absence of external inputs, was documented in many brain areas. Such activity enables the brain to maintain an internal state without continuous external input. It has been suggested that persistent activity is a neuronal correlate of working memory [4], and that it can mediate neuronal integration over long time scales [5].
The time scale of persistent activity (>1 min) is much longer than that of most biophysical mechanisms (typically 0.5-100 ms). Most attempts to explain how the extremely prolonged time scales of persistent activity emerge from such rapid biophysical processes have involved feedback mechanisms [6]. Such feedback can be implemented with recurrent excitation at the network level [7][8][9], or alternatively, by biochemical pathways at the cellular level. An example of the latter is the mechanism proposed to underlie persistent activity in the entorhinal cortex [10,11] and hippocampal CA1 pyramidal neurons [12,13]. The mechanism involves an interaction between Ca 2+ influx during spiking and a calcium-activated non-selective (CAN) cation conductance that depolarizes the cell. However, theoretical models of prolonged spiking based on feedback mechanisms are hard to construct in a way that is robust to small parameter changes, immune to noise and continuously graded [10,[14][15][16].
Persistent activity in AOB mitral cells was shown to depend upon Ca 2+ influx and CAN conductance. However, this intrinsic cellular mechanism does not depend on a feedback cycle involving ongoing neural activity, as persistent firing readily resumes after a temporal firing cessation [3].
In the present study we combined electrophysiological, imaging, and computational approaches to explore the mechanisms underlying persistent firing in AOB mitral cells. We describe a novel mechanism involving interplay between homeostatic processes controlling intracellular Na + and Ca 2+ concentrations. This novel mechanism, which does not rely upon feedback, is both resistant to noise and allows multiple stable firing states.
While response dynamics often matched those attributed to the vomeronasal pump [18,19], in other cases, elevated firing rates remained high well beyond this time scale, sometimes even after the stimulus was flushed from the nasal cavity and the VNO. Under a highly strict statistical criterion (see Data Analysis in Materials and Methods), reliable cases of persistent activity were found in about one percent (n = 7) of the recorded units, and were associated with a  Fig  1A and 1B). This stimulus selectivity is consistent with a requirement for a high level of activation to trigger the prolonged firing (see below).
Similarly, prolonged single unit AOB spiking activity could be readily elicited in anesthetized mice by direct stimulation of the vomeronasal nerve with a metal electrode (Fig 1C), further confirming that the sustained responses are independent of VNO dynamics. Finally, In agreement with our previous study [3], persistent firing could be elicited in AOB mitral cells in brain slices. An example is shown in Fig 1D (top), where a 4 s train of action potentials is followed by a prolonged period of persistent spiking at a rate of 1-3 Hz lasting for over a minute. The reproducibility of this firing epoch is demonstrated by the mean rate response for the three recorded cells (Fig 1D, bottom). Altogether, these results and the results of our previous studies [3,20] prove that AOB mitral cells are capable of persistent firing responses, both in vitro and in vivo to either electrical or chemical sensory stimulation.

Persistent Firing Activity in AOB Mitral Cells Involves a Prolonged Depolarizing Current with Complex Dynamics
Conducting the in vitro protocol described above while shifting the membrane potential to −60 mV (Fig 2A) blocked the persistent firing and unmasked a prolonged depolarization with a similar time course as the firing activity (compare to Fig 1D). To analyze the currents underlying the prolonged depolarization, the hybrid-clamp methodology was used (see Materials and Methods). Cells were voltage-clamped to −80 mV and trains of action potentials at various frequencies were delivered during a 4 s long current-clamp period. The evoked inward current ( Fig 2B) comprised an initial, rapidly decaying phase (transient phase, enlarged in Fig 2C), followed by a second, prolonged phase (persistent phase), that peaked after >10 s (Fig 2B, arrows) and slowly decayed with a more prolonged time course (>30 s). Notably, the charge transfer during each of the phases monotonically increased with the stimulus frequency ( Fig 2D). Thus, the prolonged inward current underlying persistent firing in AOB mitral cells seems to involve transient and persistent components that are proportional to the firing frequency during the stimulation.
The Prolonged Inward Current Is the Sum of a Na + -K + Pump-Mediated Outward Current and a Ca 2+ -Dependent Inward Current (I CAN ) The complex dynamics of the prolonged inward current suggest that multiple biophysical mechanisms are involved. To isolate the participating processes, we abolished the inward current, previously shown to be mediated by Ca 2+ -dependent, CAN conductance [3]. Removal of Ca 2+ from the extracellular solution, as well as blocking the increase in [Ca 2+ ] i by adding 5 mM BAPTA to the pipette solution (S2 Fig), abolished the prolonged inward current. Under these conditions, the stimulating train was followed by an outward current of 18±3 pA that monotonically decayed with a single time constant (τ = 5±1 s, n = 11 cells, Fig 2E, green trace). Subtracting the outward current from the control condition current (Fig 2E, blue trace) yields a net inward current (Fig 2E, black trace), which is likely due to the CAN conductance. Similar results were previously obtained by blocking N/R type voltage-sensitive Ca 2+ channels [3].
As shown in Fig 2F, the outward current measured in the absence of Ca 2+ ions was independent of membrane potential, suggesting that it is not mediated by ionic conductance. The most likely candidate for a voltage-insensitive outward current is an ionic pump current, such as the one produced by the plasma membrane Na + -K + pump (Na + -K + ATPase) [21]. As shown in Fig  2G (green), blocking the Na + -K + pump using ouabain unmasks a strong net inward current peaking immediately after the spike train. The difference between the currents before and after The mean current (n = 11 cells) following an evoked 4 s long spike train at 30 Hz before (blue) and after removal of Ca 2+ from the bath solution (green). The difference between the two traces is shown in black, presumably reflecting the prolonged Ca 2+ -dependent current per se. Shaded areas denote SEM. (F) The outward current recorded after Ca 2+ removal at a holding voltage of −80 mV (dark green) and −50 mV (light green). (G) The mean inward current (n = 5 cells) following an evoked 4 s long spike train at 30 Hz before (blue) and after application of the Na + -K + pump blocker ouabain (green). The difference between the two traces is shown in black. Low opacity traces show the average responses of individual cells. ouabain application is a net outward current resembling the one measured in the absence of Ca 2+ ions (Fig 2G, black). Thus, the outward current is most likely mediated by the Na + -K + pump.
Overall, these data suggest that the complex dynamics of the prolonged inward current reflect the sum of two opposing currents-a voltage-independent outward current (Na + -K + pump) decaying over a few seconds and a prolonged Ca 2+ -dependent inward current (I CAN ) that remains active for minutes.

The Magnitude of the Inward Current Is Correlated with [Ca 2+ ] i at the Dendritic Tuft
To study the spatio-temporal relationship between [Ca 2+ ] i and I CAN , we correlated [Ca 2+ ] i indicator fluorescence in various cellular compartments with the simultaneously recorded somatic inward current. To that end, AOB mitral cells were filled with a Ca 2+ indicator using the patch pipette (inset in Fig 3). Then, tuft fluorescence ( Fig 3A) and the corresponding inward currents ( Fig 3B) were simultaneously monitored as trains of action potentials at various frequencies were delivered via the patch pipette to activate the neurons. The transient increase in [Ca 2+ ] i in the dendritic tuft was followed by an extremely prolonged decay lasting longer than the interval between stimuli, resulting in summation of [Ca 2+ ] i levels over consecutive trains (Fig 3A). Similarly, the prolonged inward current also persisted longer than the interval between stimuli, resulting in progressive increase in inward current as well (Fig 3B).
To analyze the relationship between dendritic [Ca 2+ ] i and the inward current, the current amplitude at each time point was plotted against the simultaneously measured fluorescence level. Fig 3C shows Fig 3E) revealed that the decay of [Ca 2+ ] i in the tuft followed two distinct time scales: fast initial decay (τ = 1.9 s, mean of three cells) followed by very slow decay (τ = 47.0 s). This slow process suggests that [Ca 2+ ] i is in a quasi-stable state, the level of which is determined by the stimulus frequency. Consistent with this, increasing the stimulation frequency from 15 Hz to 30 Hz almost doubled the quasi-stable state level (Fig 3E, blue and green traces).
Overall, these results suggest that the inward current underlying persistent firing of AOB mitral cells is mediated by dendritic Ca 2+ -dependent ionic conductance (CAN) and that its slow dynamics likely reflect a complex interaction between several ionic extrusion mechanisms.
A Hypothetical Mechanism Involving the Na + -K + Pump, the Plasma Membrane Ca 2+ Pump, and the Na + -Ca 2+ Exchanger Can Explain the Observed Slow Current Dynamics The result described above, in which the tuft [Ca 2+ ] i decays to a quasi-stable state determined by the stimulation frequency, suggests that the quasi-stable state is generated by slowly changing, activity-dependent quantity. One such quantity may be the tuft [Na + ] i , which affects the Ca 2+ dynamics by interacting with ionic transport mechanisms such as the Na + -Ca 2+ exchanger. This exchanger, which is the major mechanism for control of large excess Ca 2+ [22], uses the Na + electrochemical gradient to extrude Ca 2+ . Thus, increase in [Na + ] i which leads to a decreased Na + gradient, reduce or even reverse the Ca 2+ flux through the exchanger [23]. We examined this possibility in a simple abstract dynamical model, with a minimal number of parameters ( Fig 4A; see S1 Text for a description of the model equations). In this model, [Ca 2+ ] i and [Na + ] i increase at a rate proportional to an abstract "voltage" quantity, given that the "voltage" is above a certain threshold. [Na + ] i decays exponentially to zero over time, while [Ca 2+ ] i decays to a level linearly determined by [Na + ] i (the quasi-stable state). The "voltage" is a sum of three components: externally applied current, inward Ca 2+ -dependent current, and outward (negative) Na + -dependent "pump" current. Fig 4B and 4D shows the results of running this model with a pulse of externally applied current (black bar). As apparent, the "voltage" (Fig 4B) (Fig 4C) and the corresponding currents ( Fig 4D). Thus, the feasibility of the mechanism suggested above is confirmed by this simple abstract model. In order  channels, pumps, and exchangers overlaid on the reconstruction of the mitral cell used for the model. g leak : leak conductance, composed from separate passive Na + and K + conductances; g nat : transient voltage-gated Na + conductance; g k-fast /g k-slow : fast and slow voltage-gated K + channels; g Ca : voltage-gated Ca 2+ conductance; g CAN : Ca 2+ -dependent non-specific cation conductance. to further test this hypothetical mechanism and produce quantitative predictions, we incorporated the principles of this mechanism into a realistic conductance-based model.

A Conductance-Based Model Reproduces the Dynamics of the Ca 2+ -Dependent Fluorescence and the Membrane Currents
A realistic conductance-based model (see Materials and Methods), was constructed using the detailed morphology of a single typical mitral cell ( Fig 4E and S4 Fig) for which the electrophysiological properties were characterized. The model assumes that active conductances reside in the apical dendrites and dendritic tufts, as well as in the soma and axon initial segment [24], so that [Na + ] i increase in these compartments following firing. A novel feature of our model is the incorporation of compartmental [Na + ] i as state variables along with longitudinal ionic diffusion. Accordingly, [Na + ] i not only sets the local Na + reversal potential but also affects localized ionic extrusion mechanisms (Na + -K + pumps, Na + -Ca 2+ exchangers). The Ca 2+ influx, buffering and extrusion mechanisms (including a simulated Ca 2+ indicator), as well as a Ca 2+ dependent conductance, were introduced in the dendritic tufts. The spatial distribution of membranal mechanisms in the model is shown in Fig 4E (See Materials and Methods for a link to the model source code and S1 Text for a full description of the model equations and parameters). Using such a model, one can calculate the temporal dynamics of [Na + ] i and [Ca 2+ ] I in various cellular compartments.
An evolutionary multi-objective algorithm [25,26] was used to find the biophysical parameters that best fit our electrophysiological observations. An initial evolutionary process was employed to find the best fit to the following measured parameters: the response to a hyperpolarizing current pulse (Fig 5A), the shape of the action potential (Fig 5B), the modulation of the spike amplitude during a strong (350 pA) current injection (Fig 5G), and the I-f curve ( Fig  5H). As shown, the model accurately reproduces the behavior of the real cell with respect to these objectives. Notably, the spike amplitude modulation during depolarizing current injection simulated by the model precisely fitted the experimental observations, despite the fact that only a 350 pA current injection was used as an objective (Fig 5E-5G). Importantly, the spike amplitude modulation in the model was the result of [Na + ] i accumulation during the spike train and would not be reproduced when [Na + ] i accumulation was prevented (S5 Fig).
The goal of the next evolutionary process was to find the parameters that reproduce the tuft Ca 2+ indicator fluorescence and the prolonged somatic inward current (see Materials and Methods). Trains of action potentials with frequencies of 1, 15, and 30 Hz were used to activate the model neuron. The simulated dendritic tuft fluorescence and the accompanying prolonged inward current were then compared to the experimental observations. At a frequency of 1 Hz (Fig 6A), the simulation (red line) perfectly reproduced the observed fluorescence signal (blue line). At higher frequencies (15 Hz and 30 Hz, Fig 6B), both measured (blue and green lines) and simulated (orange and red lines) fluorescence levels, rapidly increased to saturation levels during the stimulation (Fig 6B, top green bar). The rapid increase was followed by an equally rapid decline to a low quasi-stable level that strongly depended on the stimulation frequency ( Fig 6B). Moreover, the simulated prolonged inward current also closely fit the experimentally measured current (Fig 6C).
In order to assess the sensitivity of the model to changes in its parameters, we created a population of 1,200 model neurons. In each model, each parameter (except the channels' half-activation voltage parameters) was randomly selected from a uniform distribution that spanned between -10% and +10% relative to the original value. We then examined, in each of the models, the predicted prolonged inward currents evoked by 30Hz spike train. The properties of the resulting currents distribute normally (see example histograms for the maximum current in A critical validation of the model is its ability to reproduce the persistent firing recorded in AOB mitral cells. Indeed, a train of simulated spikes evoked long lasting persistent activity ( Fig  6D) which resembled the experimental observations ( Fig 1D). Adding Gaussian current noise introduced variability to the responses that upon averaging reproduced the PSTH observed in vitro (compare Figs 6E to 1D).
Another critical validation is the ability of the model to predict the time course of dendritic [Na + ] i , and particularly its rise during stimulation and very slow subsequent decay that maintains a quasi-stable state for the tuft [Ca 2+ ] i . To that end, we used two fluorescent Na + indicators, sodium-binding benzofuran isophthalate (SBFI) and Sodium Green, to image the dendritic Na + dynamics following a stimulus train [27]. As shown in Fig 6F, the averaged observed dynamics (thick green line) indeed match the predicted dynamics (red line) (For dF/ F signal not normalized by standard deviation and similar results using the Sodium Green indicator, see S7 Fig) As shown in the presence of tetrodotoxin (TTX,blue lines), the signal does relate to opening of voltage-gated Na + channels. Notably, similar dynamics were previously observed experimentally in cortical pyramidal neurons [27].
Thus, we conclude that our mitral cell model adequately reproduces the experimental observations.   Hz stimulation, respectively), followed by a relatively rapid decline (τ = 3.85 s) to baseline levels. The large increase in AIS [Na + ] i is due to the high density of voltage-gated Na + channels and the limited volume of the compartment. The relatively fast recovery results from the activity of the Na + -K + pump and the fast diffusion to the compartments adjacent to the AIS (axon and soma) that serve as diffusion sinks.
In contrast to the AIS, tuft [Na + ] i increased only to a moderate level (15 and 17 mM for 15 and 30 Hz stimulation-solid orange and red traces in Fig 7A, respectively), followed by extremely slow exponential recovery over a time course of minutes (τ = 130 s and 115 s for 15 and 30 Hz stimulation, respectively). This slow time course, also observed in real mitral cells using Na + fluorescent indicators (Fig 6F), stems from the slow diffusion in the thin dendritic process and the low density of Na + -K + pumps in this compartment.
The prolonged elevated [Na + ] i in the dendritic tuft is bound to affect the Na + -Ca 2+ exchanger, hence to determine the quasi-stable state of [Ca 2+ ] i . We examined this prediction using the model by calculating the stable-state [Ca 2+ ] i for various fixed [Na + ] i. values. As shown in Fig 7B ( Fig 7C and 7D, where the Ca 2+ currents of the exchanger (dashed green line) and the Ca 2+ pump (dashed orange line) are shown along with schematic diagrams depicting each state. Immediately following the stimulus train, both currents are positive (outward, Fig 7D, middle), but then the exchanger current becomes negative (inward) while the pump current remains positive. As a result, the net current of the Ca 2+ regulatory mechanisms reaches a near-zero value (Fig 7C, blue line; Fig 7D, right). The inward current mediated by the exchanger reflects the condition of high [Na + ] i level, that causes the exchanger to operate in a "reverse mode" (Ca 2+ influx). In this state [Ca 2+ ] i is determined by the slow change of the quasi-stable state, which is due to the slow return of tuft [Na + ] i back to baseline levels ( Fig 7A).
Blocking the Exchanger by Substituting Na + with Li + Shortens the Duration of Tuft Ca 2+ Elevation and the Inward Current As described above, the prolonged quasi-stable state of [Ca 2+ ] i is the result of the opposing actions of the pump Ca 2+ efflux and Ca 2+ influx due to the reverse-mode of the Na + -Ca 2+ exchanger (Fig 7C and 7D). Therefore, blockade of the exchanger should result in acceleration of the recovery of [Ca 2+ ] i . We examined this prediction using the model by calculating the decay of the tuft fluorescence under control conditions (Fig 8A, orange line) and after blocking the exchanger (Fig 8A, red line). Indeed, a much faster return to baseline levels was obtained in the absence of exchanger activity. Experimentally, such blockade can be realized by substituting Na + ions in the extracellular solution with Li + , which cannot be transported by the exchanger [28][29][30]. This manipulation was simulated by modeling the effect of Li + on the exchanger and the Na + -K + pump [31,32]. Fig 8B shows that following substitution of Na + by Li + in the model, the slow inward current (orange line) is replaced by a fast, transient inward current (red line) that rapidly declines to baseline.
Similar results were obtained experimentally (Fig 8C and 8D) by substituting Na + with Li + in the bath solution. In the presence of Li + (green) the decay of the fluorescence signal in the tuft ( Fig 8C) followed a single time constant (τ = 11 s, dashed line, compare to inset in Fig 8A). Thus, in the absence of exchanger activity the elevated quasi-stable state was blocked. In accordance with the fluorescence measurements, the inward current ( Fig 8D) decayed faster in the presence of Li + (compare green to blue lines) and the initial "bump" (arrow in Fig 8D) created by the Na + -K + pump outward current was absent (compare to the effect of ouabain application, Fig 2G). These experimental observations strongly support the proposed model in which a quasi-stable state of [Ca 2+ ] i is generated by the reversed action of the Na + -Ca 2+ exchanger.

Simulated Synaptic Input Reproduces a Transition from Transient to Prolonged Firing Response
We examined the response of our detailed model to VNO inputs using a simple feed-forward network simulation (see Materials and Methods). The input stage of the network represents the responses of vomeronasal sensory neurons (VSNs) to natural stimuli, which follow a simple ligand-receptor interaction [33,34]. A simple model of VSN firing was established by first calculating the predicted time course (Fig 9A, red line) of a response to a brief stimulus application (red bar), and then using it to generate a random spike train (vertical lines). For the purpose of the model, we assumed that each tuft is innervated by 13 VSNs (Fig 9B; within the lower range of reported convergence [35]).
The unitary synaptic response of an AOB mitral cell to sensory fiber stimulation (Fig 9C, blue line) was measured by stimulating the dendritic tuft of a mitral cell (see Materials and Methods, micrograph in Fig 9C). A model of synaptic conductance was fitted to the averaged response ( Fig 9C, orange line) and assigned to the dendritic tufts of the aforementioned mitral cell model. The simulated response was then tested for two ligands presented simultaneously to two groups of 13 VSNs, converging on two different dendritic tufts of the model mitral cell (Fig 9B). This simulation was run using a range of stimulus durations for both ligands, and a range of concentrations for one of them (the concentration of the second ligand was kept constant). Random white noise was also injected to the model mitral cell. Using these parameters, we encountered two possible outcomes: one was a transient firing response (Fig 9D) while in the other firing persisted for~200 s (Fig 9E). Fig 9F summarizes the average firing durations for different combinations of stimulus duration and concentration. As shown, longer stimulus durations and higher concentrations led to persistent firing responses. The bimodal distribution of the response duration is shown in Fig  9G. As apparent, the response was either transient, following the stimulus application, or persistent peaking at 200 s, as previously demonstrated for AOB mitral cells [3]. Thus, our model cell embedded in a realistic small network simulation reproduces the transition of the

Discussion
Here, we combined in vivo and in vitro electrophysiological recordings, Ca 2+ and Na + imaging, and computational modeling to investigate how persistent firing responses are generated in AOB mitral cells. We first demonstrated that these cells are capable of responding in vivo with persistent firing to natural stimuli applied to the VNO, in a stimulus-specific manner. We then used AOB slices to explore the ohmic and non-ohmic currents that underlie the persistent firing responses. The dynamics and inter-relationships of these current sources were analyzed by pharmacological and ionic manipulations. By combining patch-clamp recordings with Ca 2+ and Na + imaging we showed that the dynamics of the currents underlying persistent firing rely on slow changes in internal ionic concentrations within specific cellular compartments. Using first abstract and then realistic computational models of AOB mitral cell we demonstrated that these changes are governed by passive diffusion, as well as by local active processes involving ionic pumps and exchangers. The model results accurately predict the persistent firing responses, the dynamics of Na + in the dendrites and the results of substituting Na + by Li + . Finally, we employed our model in a local network simulation and established that the model cell indeed shifts between transient and persistent firing responses to stimuli detected by VNO neurons, as a function of the duration and strength of stimulation.

Functional Significance of Persistent Activity in AOB Mitral Cells
We have previously hypothesized [3] that the accessory olfactory system reports the social context to an animal by inducing specific brain states based on the persistent activity of its mitral cells. These states can then change the processing of sensory information in other brain areas [36][37][38]. This hypothesis is supported by the current study where we showed, both in vivo and in vitro that AOB mitral cells shift from transient to persistent firing responses to stimuli arriving from the VNO. In agreement with our previous reports [3,20], this transition is relatively sharp and depends on sufficient stimulus strength and duration. This may correspond, for example, to the presence of a rich source of social chemosensory cues, e.g., a conspecific animal, which would elicit persistent firing in AOB mitral cells, thereby conveying to higher brain centers the presence of a social partner.

A Novel Mechanism for Persistent Activity
Persistent activity has been reported in several brain areas, including mitral cells of the main olfactory bulb in vivo [39], and was suggested to mediate working memory or prolonged brain states [4]. To date, most of the mechanisms purposed for persistent activity include either network or biophysical feedback loops [5,10,16,39,40]. We propose a novel mechanism for persistent neuronal activity in AOB mitral cells, in which a train of action potentials that backpropagate to the dendritic tuft [24] elevates the tuft [Na + ] i . This increase in the tuft [Na + ] i shifts the [Ca 2+ ] i stable state upwards [29], thus creating an elevated quasi-stable state for [Ca 2+ ] i . The slow decay of [Ca 2+ ] i is dictated by the slow removal of Na + ions from the tuft (Fig 7). The novelty of our model is in the absence of biochemical, biophysical, or network feedback mechanisms or hysteresis.

Exploring Alternative Mitral Cell Models
Two alternative models were examined in an attempt to reproduce the observed experimental results. One model incorporated two distinct CAN conductances-a fast one and a slow one (compare with [41]), without activity-dependent outward current. Each of these currents produces a different phase of the observed inward current (Fig 2B and 2C). While this model reproduces the results used as objectives in the model training phase (Figs 5 and 6A-6C), it failed to produce the persistent activity (Fig 6D and 6E), emphasizing the importance of this validation. The long time constant kept the slow Ca 2+ -dependent current away from its stablestate value in the hybrid clamp simulations, but this current would greatly intensify and cause a runaway effect in a current clamp simulation (S8A Fig). In another model, a single Ca 2+ -dependent non-specific cation conductance was used, along with a Ca 2+ -dependent K + conductance (SK/BK) that account for the outward current observed immediately after the stimulating train of action potentials. Although this model reproduces the results used as objectives in the model training phase (Figs 5 and 6A-6C), it failed to explain the outward current recorded in the absence of [Ca 2+ ] o (Fig 2E).
The ultimate rejection of these models demonstrates the importance of the model validation step.

The Role of Na + As an Integrator of Spiking Activity
According to our results, [Na + ] i plays a key role in both transient and prolonged biophysical processes. First, increase in AIS [Na + ] i alters the Na + Nernst potential, thus lowering the spike amplitude (Fig 5E-5I and S5 Fig). Second, elevation in [Na + ] i increases the Na + -K + pumpmediated outward current that terminates bursts of activity by hyperpolarizing the cell ( Fig  2E). Third, increase in [Na + ] i decreases Ca 2+ efflux by modulating the Na + -Ca 2+ exchanger (Fig 8). The latter endows [Na + ] I with the ability to dictate [Ca 2+ ] i and thus the inward I CAN .
In thin and slightly active processes like the dendritic tuft, [Na + ] i is only moderately increased by neuronal activity and its extrusion is exceptionally slow (Fig 6F,[27]). Thus, [Na + ] i can attain a range of quasi-stable states-a property that renders it an ideal candidate to integrate epochs of high neural activity. This is in contrast to [Ca 2+ ] i , which is highly dynamic as a function of neuronal activity on one hand, and rapid extrusion on the other.
Notably, changes in [Na + ] i are rarely tracked in conductance-based models (important exceptions in [42][43][44][45]), although in thin active processes, such as axons and dendrites, they may substantially affect neuronal activity. Indeed, the effects of [Na + ] i on a variety of Ca 2+dependent processes were previously demonstrated: reducing Na + extrusion or inhibiting the Na + -Ca 2+ exchanger were shown to extend [Ca 2+ ] i transients, and thus to facilitate Ca 2+dependent mechanisms, such as synaptic plasticity and learning [29,46,47].
The activity-dependent Na + -K + pump-mediated outward current is an important factor protecting neurons from a runaway positive feedback loop (S8B and S8C Fig). Without this current, the high [Ca 2+ ] i during and immediately after stimulation would result in a strong inward current (as demonstrated using ouabain- Fig 2G, red line) that would in turn evoke high frequency spiking, and thus a further increase in [Ca 2+ ] i .

Relevance to Other Brain Areas
Since the mechanism described here contains mostly elements which are ubiquitous in neurons, we argue that it is relevant (wholly or partially) to other brain areas. The essential nontrivial building blocks required to produce persistent activity by this mechanism are: a) changes in [Na + ] i and [Ca 2+ ] i in thin processes (axon or dendrites), attained by (back)-propagation of action potentials and/or excitatory synaptic activity; b) Co-localization of an excitatory Ca 2+dependent conductance at the site of [Na + ] i changes; c) Low density of [Na + ] i active extrusion mechanisms at the site of [Na + ] i changes.
Thus, the proposed mechanism is very likely to explain persistent activity in other brain areas, most likely with some variation of the time scale and of the factors necessary to evoke it. For example, [Na + ] i dynamics may take alternative forms in other neuronal types, as a function of the spatial distribution of Na + channels and Na + -K + pumps as well as cell morphology. Moreover, the persistent activity may be either superthreshold, i.e. persistent firing, or long term integrative changes in membrane potential and excitability. It may be assumed that very slow changes in resting potential or firing rate, such as those produced by the mechanism presented here, may be under-reported because they are frequently filtered out and require prolonged recording sessions.
Furthermore, the importance of the mechanism proposed by us is beyond the scope of persistent activity. We show that the long-term behavior of intracellular Ca 2+ depends upon past activity-an idea previously presented in [29], though in a much shorter time scale. Given that Ca 2+ is an important cellular signaling molecule, long-term changes in its concentration may broaden the time scale of processes such as synaptic plasticity [47], activity-dependent gene expression, and more. Similarly to membrane potential changes, reports about [Ca 2+ ] i changes may also suffer from "time-scale bias," wherein long-term changes in [Ca 2+ ] i seems to be regularly filtered out or not recorded due to photo damage and dye-bleaching concerns.
An even broader consequence is the ability of Na + to integrate activity (discussed above), which at the very least causes changes to Na + reversal potential. Thus, persistent activity is only one of several end results of the mechanism we describe. Our results at least demonstrate that changes in [Na + ] i should not be regarded as negligible in conceptual and computational models of neuronal activity.

Natural Secretion Collection
Secretions for in vivo recordings were collected from C57BL/6J and BalbC females (housed in the animal facility of the Hebrew University). Samples were pooled and immediately frozen in liquid nitrogen and stored at −80°C until use. For urine collection, mice were gently held over a plastic sheet until they urinated. Vaginal secretions were collected by flushing the vagina with 30μl of ringer's solution repeatedly. 20 μl were stored. For saliva collection, isoproterenol hydrochloride (0.2 mg/100 g) and pilocarpine (0.05 mg/100 g) were injected i.p. to increase salivation [48]. Following a delay of 5 min, saliva was collected from the mouth using a micropipette. Stimuli were diluted in Ringer's solution.

In Vivo Electrophysiology
In vivo multi-unit activity followed by electrical stimuli was recorded in anesthetized mice (ketamine, 10 mg/kg, medatomidine, Pfizer, 1 mg/kg). A recording electrode (glass micropipette filled with 1 M potassium acetate) was placed in the AOB external plexiform layer using a micromanipulator (Luigs and Neumann). A stimulating coaxial bipolar electrode was inserted through the medial frontal lobe, to the point where contact was made with the vomeronasal nerve and field potentials appeared in the AOB in response to brief stimuli. A train of brief shocks (0.1 ms, 1-100 V), given at 2 Hz for 2.5 s was applied to the vomeronasal nerve at intervals of 60 s via an isolated stimulator.
Electrophysiological recordings of AOB neurons followed by natural stimuli were performed as previously described in detail [18]. Briefly, BalbC mice were anesthetized with 100 mg/kg ketamine and 10 mg/kg xylazine. A tracheotomy was made using a polyethylene tube to allow breathing during flushing; a cuff electrode was placed on the sympathetic nerve trunk with the carotid serving as a scaffold. Incisions were closed and the mouse was placed in a custom-built stereotaxic apparatus where anesthesia was maintained throughout the entire experiment with 0.5-1% isoflurane in O 2 . A craniotomy was opened immediately rostral to the rhinal sinus, the dura was removed around the penetration site, and electrophysiological probes were advanced into the AOB using an electronic micromanipulator (MP-285; Sutter instruments). All recordings were made with 32 channel probes (NeuroNexus Technologies). During each trial, 2 μl of stimulus solution was placed directly in the nostril ("stimulus application") and after 20 s, a square-wave stimulation train (duration: 1.6 s, current: ±120 μA, frequency: 30 Hz) was applied through the sympathetic nerve cuff electrode to induce VNO pumping and, accordingly, stimulus entry to the VNO lumen ("sympathetic stimulation"). A pump was turned on 40 s after each stimulus presentation, followed (after 10 s) by application of Ringer's solution (1-2 ml) to the nostril that was flushed through the nasopalatine duct to cleanse the nasal cavity. 20 s after Ringer's application sympathetic stimulation was performed to ensure the VNO lumen cleansing (the second stimulation).
Using an RZ2 processor, PZ2 preamplifier, and two RA16CH head-stage amplifiers (Tucker-Davis Technologies), neuronal activity was sampled at 25 kHz and band-pass filtered at 0.3-5 kHz. Custom MATLAB (Mathworks) programs were used to extract spike waveforms. Spikes were sorted automatically according to their projections on two principle components using KlustaKwik [49] and then manually verified and adjusted using the Klusters program [50].
For electrophysiological recordings, slices were submerged in oxygenated physiological solution (identical to above) at room temperature in a recording chamber and perfused at a constant rate of 5-7 ml/min. To test the effect of substituting Na + by Li + , equimolar amount of LiCl was used instead of NaCl. To test the effect of Ca 2+ removal, equimolar amount of MgCl 2 was used instead of CaCl 2 . Where indicated, picrotoxin (100 μM) was added to the bath solution to block GABA A receptors, or ouabain (Tocris Bioscience) was added to the bath solution in excess (10-100 μM) to block the Na + -K + pump.
Mitral cells were visualized using infrared differential interference contrast (DIC) video microscopy via a 40x or a 60x water-immersion objective. Mitral neurons were identified by the location of the cell body on the ventral side of the external plexiform layer of the AOB. Whole-cell recordings were performed using borosilicate pipettes filled with standard intracellular recording solution containing the following (mM): 130 K-gluconate, 10 Na-gluconate, 10 HEPES, 10 phosphocreatine, 4 MgATP, 0.3 NaGTP, and 4 NaCl (pH = 7.25 with KOH, 5-12 MO). When BAPTA was used, BAPTA-tetrapotassium (Sigma) was dissolved in this solution to a final concentration of 5 mM. Seal resistance was at least 2 GO and typically 5-10 GO.
In most experiments, a 4-s-long spike train was evoked by injecting a series of depolarizing pulses (rate, 1-30 Hz; amplitude, 1-2 nA; pulse duration, 10 ms). In the hybrid-clamp procedure, membrane potential was clamped to −80 or −70mV throughout the experiment, excluding 4 s periods during which the amplifier was switched to current-clamp mode to deliver the train of current pulses. It should be noted that the hybrid-clamp methodology has been proven useful for investigating the firing activity of neurons, since by preventing most of the feedback and interference that ongoing firing activity may elicit upon itself, it enables a relatively clean examination of the underlying currents.
All amplified signals were digitized at 2-20 kHz using a National Instruments board and homemade software written in LabVIEW (National Instruments).
A unitary measurement of EPSC was done by filling a cell with Alexa 488 (Life Technologies) and visually positioning a bipolar theta electrode filled with physiological solution and Alexa 488 close to one of the dendritic tufts (Fig 8C).

Calcium Imaging
For calcium imaging experiments, Oregon Green BAPTA-1 (OGB-1, Life Technologies, 50 μM) was added to the pipette solution. Fluorescence signals were recorded during the hybrid clamp protocol using a high speed camera (MiCAM Ultima, Brainvisions) and converted to (F −F min )/F min ratio after subtracting the ongoing background signal. In order to perform imaging of the dendritic tuft, a 60x water-immersion objective was used, and the dye was allowed to fill the cell for >20 min before recording was started. Evoked spikes were used to increase fluorescence and facilitate the visual search for a dendritic tuft.

Sodium Imaging
For sodium imaging experiments, SBFI salt (TEFLabs, 2mM) and Sodium Green salt (Life Technologies, 500uM) was added to a modified pipette solution containing (mM): 130 K-gluconate, 10 HEPES, 5 phosphocreatine, 4 MgATP, 0.3 NaGTP, 20 KCl, and 0.2 EGTA (pH = 7.2 with KOH, 5-12 MO). Fluorescence signals were recorded from the apical dendrite as in the case of calcium imaging. A standard Fura-2 filter set (Ex. 380 nm; Em. 510 nm, Chroma Technology) was used for SBFI imaging. In order to cancel the substantial dye bleaching, trials without stimulus were subtracted from stimulus trials.

Data Analysis
Unless otherwise noted, recorded current or voltage traces were averaged for each recorded cell, and the presented result is the mean of the cell population.
Value error range reported is SEM unless otherwise noted. For stimulus-induced in vivo AOB recordings, units from various sets of experiments were considered. Six hundred and sixty-three single units for which at least one stimulus was presented at least five times were considered. The procedure for identifying persistent responses was as follows: For each single trace (one unit, one presentation of one stimulus), the responses in consecutive 2 s bins were defined as significant if the rate within it was larger than the mean baseline rate by at least five times the SEM of the baseline rate. The bins spanned a period of 160 s, which includes the baseline period, stimulus delivery, and the VNO flushing period, extending 20 s after the sympathetic stimulation during flushing (second stimulation, see above). The response duration was defined as a period beginning and ending with a significant bin, and in which at least 85% of the bins were significant. If this response lasted more than 10 s following the second sympathetic stimulation, it was designated as a persistent response. Finally, units for which at least half of the responses were persistent for a given stimulus were defined as persistent.
The seven persistent firing units came from three sets of experiments differing in stimulus sets used. For three units the stimuli were undiluted saliva, urine, and vaginal secretions. In three other units the stimuli were saliva, 100F diluted urine, and vaginal secretions. For the remaining units, the stimuli were urine at 1F, 10F, and 30F dilutions.

Computational Models
The abstract dynamical model was constructed in MATLAB/SIMULINK (Mathworks). See S1 Text for details and equations.
We constructed the conductance-based model using the NEURON simulation environment with Python [52,53]. The model was based on experimental measurements and morphological reconstruction of an AOB mitral cell [54], and included influx, diffusion, and extrusion of Na + and Ca 2+ . It assumed a presence of active Na + channels in the apical dendrites and tufts [24], as well as non-uniform channel properties across different compartments (Fig 4E, [55]). Evolutionary multi objective optimization algorithm [25,26] was used to find the model parameters, based on recorded electrophysiological and imaging data. Some membranal mechanisms were based upon published models hosted by ModelDB [56][57][58][59][60]. See S1 Text for additional information. The model code is available online at: https://senselab.med.yale.edu/ModelDB/ShowModel.cshtml?model=185332

Network Model
In order to test the response of the model mitral cell to natural stimuli, a simple two-layer network model was constructed. The firing response of the VNO sensory neurons was modeled using a simple ligand-receptor interaction [33] that triggers a semi-random spike train ( Fig  8A). Thirteen of such sensory neurons converged on each of the mitral cell's dendritic tufts (Fig 8B) [35], where the synaptic current was modeled using a double exponential fit to the unitary response measured experimentally using a theta electrode (a bipolar micropipette pulled from a tubing with a θ-like cross-section) positioned next to a dye-filled mitral cell's dendritic tuft (Fig 8C).
Supporting Information S1 Text. Describing the computational models construction steps and equations.