Introduction

Learned temporal sequences are expressed in many brain regions and play a critical role in temporal information encoding, such as navigation (Skaggs et al., 1996), the timing of motor actions (Wang et al., 2018), time generation (MacDonald et al., 2011; Pastalkova et al., 2008), decision making (Harvey et al., 2012; Schmitt et al., 2017) and skilled movement (Peters et al., 2014). Zebra finches sing remarkably stereotyped songs rendering them as an excellent model for studying the mechanisms underlying neural sequences (Hahnloser et al., 2002). The anatomical basis for song production and learning is a highly developed neural network known as the song system (Fig. 1A), with nucleus HVC exhibiting a rhythmic pattern-generating role encoding for the syllable order and the overall temporal structure of the birdsong (Fee & Goldberg, 2011; Fee et al., 2004; Fee & Scharff, 2010; Mooney, 2009; Yu & Margoliash, 1996).

Figure 1.

There are three main neuronal populations in the HVC exhibiting different functional, cellular and pharmacological properties (Daou et al., 2013; Kubota & Taniguchi, 1998; Mooney, 2000; Mooney & Prather, 2005): neurons that project to the robust nucleus of arcopallium (RA; HVC_RA), neurons that project to Area X (HVC_X), and interneurons (HVCINT, Fig. 1B). HVCAv neurons (projecting to nucleus Avalanche) exists and play a role in song learning, yet their intrinsic and synaptic properties remains unknown (Roberts et al., 2017). Intracellular recordings showed that HVCRA, HVCX, and HVCINT neurons have distinctive in vivo and in vitro electrophysiological properties (Daou et al., 2013; Dutar et al., 1998; Kubota & Taniguchi, 1998; Mooney et al., 2001; Shea et al., 2010), which are orchestrated via a family of ion channels (Daou et al., 2013).

During singing, HVCRA neurons produce a single burst of spikes (∼10 ms) that are tightly locked to the song (Fig. 1C, (Hahnloser et al., 2002; Kozhevnikov & Fee, 2007). HVCX neurons in their turn elicit 1-4 bursts that are also time-locked to vocalizations (Fig. 1D, (Kozhevnikov & Fee, 2007), while HVCINT neurons exhibit tonic activation (Fig. 1C), with bursting and suppression at different locations throughout the song (Amador et al., 2013; Cannon et al., 2015; Hahnloser et al., 2002; Kosche et al., 2015; Kozhevnikov & Fee, 2007; Long et al., 2010; Markowitz et al., 2015).

Several models of how sequence is generated within HVC have been proposed (Cannon et al., 2015; Drew & Abbott, 2003; Egger et al., 2020; Elmaleh et al., 2021; Galvis et al., 2018; Gibb et al., 2009a, 2009b; Hamaguchi et al., 2016; Jin, 2009; Long & Fee, 2008; Markowitz et al., 2015). These models either rely on intrinsic HVC circuitry to propagate sequential activity, rely on extrinsic feedback to advance the sequence or rely on both. The proposed models do not capture the complex details of spike morphology, do not include the right ionic currents, do not incorporate all classes of HVC neurons, or do not generate realistic firing patterns as seen in vivo.

Here, we developed a physiologically realistic network model incorporating the three classes of HVC neurons based on the ion channels and the synaptic currents that had been pharmacologically identified (Daou et al., 2013; Kosche et al., 2015; Mooney & Prather, 2005). Our model is based on a feedforward chain of microcircuits that encode for the different sub-syllabic segments (SSSs) and that interact with each other through structured feedback inhibition. The network developed unveiled key intrinsic and synaptic mechanisms that govern the sequential propagation of neural activity by highlighting important roles for the T-type Ca²⁺ current, Ca²⁺-dependent K⁺ current, A-type K⁺ current, hyperpolarization activated inward current, as well as excitatory and inhibitory synaptic currents. Our model provides a new way of thinking about sequence generation during birdsong vocalizations and in network architectures more generally.

Methods

Single-compartment conductance-based Hodgkin-Huxley-type (HH) biophysical models of cells from the HVC were developed and connected together via biologically realistic synaptic currents. Simulations of these model neurons and of the model network composed of synaptically coupled HVC_RA, HVC_X, and HVC_INT neurons were performed using the ode45 numerical integrator in MATLAB (MathWorks). Source codes for each network will be made available online at our lab’s website as well as on ModelDB. HVC model cells that are used to connect the networks exhibited ionic and synaptic currents that had been shown to be expressed pharmacologically (Daou et al., 2013; Kosche et al., 2015; Long et al., 2010; Mooney & Prather, 2005). The functional forms of activation/inactivation functions and time constants were based on previous published mathematical neural models (Daou et al., 2013; Destexhe & Babloyantz, 1993; Dunmyre et al., 2011; Hodgkin & Huxley, 1952; Terman et al., 2002; Wang et al., 2003), and the parameters that were varied were merely the maximal conductances of some ionic currents that vary among the various neuronal subtypes (Daou et al., 2013), as well as the synaptic conductances. Every model neuron is represented by ordinary differential equations for the different state variables as illustrated below.

Ion channels of model HVC neurons

We added a hyperpolarization-activated inward current conductance (I_H) to HVC_X and HVC_INT because it is responsible for the sag seen in these neurons (Daou et al., 2013; Dutar et al., 1998; Kubota & Saito, 1991; Kubota & Taniguchi, 1998), and we added a low-threshold T-type Ca²⁺ current (I_CaT)conductance responsible for the post-inhibitory rebound firing seen in HVC_X and HVC_INT neurons (Daou et al., 2013). A small-conductance Ca²⁺-activated K⁺ current (I_SK) was added for HVC_RA and HVC_X neurons as it is responsible for the spike frequency adaptation feature that these two classes exhibit (Daou et al., 2013). For interneurons, we integrated a large magnitude of the delayed rectifier K⁺ current conductance allowing these neurons to undershoot the resting membrane potential as seen experimentally (Daou et al., 2013; Dutar et al., 1998; Kubota & Saito, 1991; Kubota & Taniguchi, 1998). For HVC_RA neurons, we added an A-type K+ current that supports the delay to spiking seen in response to depolarizing current pulses (Daou et al., 2013; Kubota & Taniguchi, 1998; Mooney & Prather, 2005). High-threshold Ca²⁺ conductance was added to all classes of HVC neurons (Daou et al., 2013; Kubota & Saito, 1991; Long et al., 2010). In total, the model was designed to include spike-producing currents (I_K and I_Na), a high-threshold L-type Ca²⁺ current (I_CaL), a low-threshold T-type Ca²⁺ current (I_CaT), a small-conductance Ca²⁺ – activated K⁺ current (I_SK), an A-type K⁺ current (I_A), a hyperpolarization-activated current (I_H), and a leak current (I_L). The membrane potential of each HVC neuron obeys the following equations:

where C_m is the membrane capacitance. The associated equations and parameters for each of the activation/inactivation gating variables for each ionic current are given in (Daou et al., 2013) and shown below. In total, every single model HVC_RA, HVC_X, and HVC_INT neuron had a total of 6, 8 and 7 ODEs, respectively, that govern their intrinsic dynamics. Every synaptic current that was integrated to any model neuron added a new ODE to the set of ODEs governing the membrane potential of the corresponding model neuron.

Voltage-gated ionic currents

The constant-conductance leak current is I_L = g_L(V−V_L). The remaining voltage-gated ionic currents have non-constant dependent currents with activation/inactivation kinetics:

where x_∞(V) for n and e is given by (8) and for ℎ_∞ as follows

Low-voltage activated T-type calcium current

The low-voltage activated T-type Ca2+ current is described by the Goldman-Hodgkin-Katz formula:

Calcium-dependent Potassium current

The small conductance potassium current (I_SK) is modeled as

Hyperpolarization-activated inward current

The hyperpolarization activated inward current’s activation is modeled as in Destexhe and Babloyantz (1993) using a fast component (r_f) and a slow component (r_s) as follows:

The fast activation component is given by:

with its time constant τ

The slow activation component obeys:

Synaptic currents

In addition to the ionic currents above that orchestrate the internal dynamics of each HVC neuron, we integrated synaptic currents in order to reproduce the biological features of the voltage traces observed in vivo. Excitatory (AMPA) and inhibitory (GABA_A) synaptic currents were used to connect neurons inside each architecture based on the pharmacological dual synaptic connections as described by Mooney and Prather (2005). Each synaptic current represents the synaptic input(s) from the presynaptic cell(s) to the particular HVC model neuron, and is modeled as I_syn = ∑_X I_X→Y where I_X→Y = g_X→Ys_X→Y(V − V_X→Y). Here the summation is taken over the presynaptic HVC neurons where X represents a presynaptic cell, Y represents a postsynaptic cell, V_X→Y is the reversal potential for the synapse in the postsynaptic cell with V_X→Y = V_AMPA for excitatory input and V_X→Y = V_GABA−A for inhibitory input.

The model equations for the synaptic currents are the following, taken after (Destexhe et al., 1994; Varela et al., 1997).

where s_AMPA and s_GABAA are given by

with T_max = 1, K_p = 5, V_T = 2. For GABA_A, a_r = 5 and a_d = 0.18, while for AMPA, a_r = 1.1 and a_d = 0.19.

We limited our synaptic currents’ choices in all networks to AMPA (excitatory) and GABA_A (inhibitory) without integrating NMDA and GABA_B for the following reasons: 1) both AMPA and GABA_A currents are voltage-dependent with simple activation kinetics that do not depend on further parameters that are very hard to tune or calibrate (for example, NMDA current relies on Mg²⁺ concentration and GABA_B on G-proteins dynamics, both which require additional ODEs and series of parameters that we don’t know about in the HVC), 2) adding the additional synaptic currents do not have a significant contribution to the network dynamics we’re building because the emphasis is on excitation and inhibition and we could convey the mechanisms we envision that orchestrate each network with these two currents solely. Therefore, model HVC_RA neurons send their excitatory afferents to other HVC_RA neurons as well as to HVC_INT neurons via AMPA currents. Model HVC_INT neurons send their inhibitory afferents to both HVC_RA and HVC_X neurons via GABA_A currents. And lastly, model HVC_X neurons excite HVC_INT neurons via AMPA currents.

Desired network activity

Our aim here is to generate the optimal and desired network activity that’s generated by the three classes of HVC neurons during singing. Therefore, we focused on model parameters and their underlying mechanisms that play key roles in 1) reproducing the patterns without breaking the sequence of activity propagation and 2) generate biologically realistic traces for each class as shown using intracellular recordings in vivo in a way to maintain spike shapes, burst patterns, rebound firing/bursting, subthreshold oscillations, etc … In a nutshell, the behavior of the network was considered desired and “good” if the model voltage traces for the total populations in each of the three classes of HVC neurons in the network matched the following: 1) the time-locked and characteristic bursting of HVC_RA neurons (3-6 spikes for a ∼10 ms duration), with spikes riding on a plateau, 2) HVC_X neurons eliciting 1-4 bursts (4-9 spikes per burst) that are also time-locked and that are mostly rebound bursts from inhibition (Lewicki, 1996; Mooney, 2000), 3) HVC_INT neurons exhibiting tonic activation with spiking and bursting throughout the song, and 4) spike frequency, spike amplitude, sags and/or rebound upon inhibition, resting membrane potential and other known features of the intrinsic properties of the three classes of HVC neurons exhibited for each of the classes that exhibit them (Daou et al., 2013).

Maximal and synaptic conductances variations

Automated adjustment of model parameters was performed to qualitatively reproduce desired membrane potential trajectories, as described next. Fixed parameter values for HVC neurons used in the simulations are given in Table 1. Parameters that vary between the different model neurons are shown in Figure 2-A.

Figure 2.

Table 1.

Some maximal conductances were fixed while others were allowed to vary. We fixed g_Na and g_K for each class of the HVC neurons to values that had been shown earlier to accurately fit the spike morphologies (upstrokes and downstrokes of action potentials, plateaus, etc…) in response to applied current given in vitro (Daou et al., 2013). For example, HVC_INT neurons’ spikes exhibit a relatively large undershoot of the resting membrane potential, while HVC_X and HVC_RA spikes ride on a plateau with characteristic properties (Daou et al., 2013). We also fixed the value of g_CaL because we could achieve the same accuracy of fitting by varying g_SK, and so could not distinguish between the two.

The four key conductances in our model that played crucial roles in controlling not only the intrinsic properties of the HVC neurons they’re expressed in but also in shaping overall network activity and sequence propagation are g_SK, g_h, g_A and g_CaT. As a recap, g_SK is expressed in HVC_X and HVC_RA, g_H and g_CaT in HVC_X and HVC_INT, and g_A in HVC_RA only (Daou et al., 2013). Random variations in these four parameters were performed to qualitatively reproduce membrane potential trajectories of the three classes of HVC neurons as seen firing when the bird is singing.

In a previous study, Daou and Margoliash (2020) showed that intracellular recordings from X-projecting neurons in adult zebra finch brain slices share similar spike waveform morphologies, with modeling indicating similar magnitudes of their principal ion currents. To that end, we fixed in our network the intrinsic properties of the population of HVC_X neurons to the same values. Therefore, the automated variations in the conductances held for HVC_X neurons were done at the population level by varying a corresponding ionic conductance value (say, g_SK) and setting its value to all of the HVC_X population. We also checked the effects of removing this constraint in Figure 13, that is, allowing the intrinsic properties of HVC_X neurons to vary like other parameters.

We first manually selected the four key conductances to default values that generate the desired behavior of the network as described in the previous section. Network robustness to varied maximal conductances as well as the legitimate ranges for each maximal conductance was determined by simulating the network many times, each time with a random variation in the maximal conductance about its default value. The network response was considered accurate if the network generated sequential bursting and all of the desired features described earlier. The range of variation of the randomly-varying parameter was increased or decreased randomly up until the point that the network ceased to be accurate.

The variation in parameters was done at the population level (setting the maximal conductance for all neurons of the same class to a single value and randomly changing that value for all), well as on the individual neuronal level (varying the maximal conductance for one neuron at a time of the same class while fixing the others to their default values). This is different for the HVC_X parameters, where the corresponding conductances at the population and the neuronal levels are considered the same since we assumed same intrinsic properties as described earlier. If any of the simulations generated networks where any of the HVC_RA neurons elicit bursts exhibiting spikes outside the 3-6 number of spikes range or duration of any burst longer than 10 ms, then we ignore that parameter value. Similarly, if any of the simulations generate networks where any of the HVC_X neurons eliciting more than 4 bursts, individual bursts exhibiting spikes outside the 4-9 spikes/burst range, then the corresponding parameters are ignored. Moreover, we also ignore parameters that generate unrealistic intrinsic properties of individual HVC neurons; for instance, if the resting membrane potentials of individual HVC neurons were outside the reported ranges (Daou et al., 2013), if HVC_X and HVC_INT neurons failed to generate sags and rebounds (depolarization or bursting) in response to inhibition, or if spikes’ amplitudes were not realistic (HVC_X and HVC_RA spikes not riding on plateaus or HVC_INT spikes not undershooting the RMP). We realize this might be inducing tough constraints on the selection of the parameters limiting the space for which the conductances are allowed to vary, but we opted for this method in order to generate the optimal ranges in which intrinsic and synaptic conductances are able to reproduce the biophysically realistic firing patterns seen during singing. We therefore ended up with lists of ranges for each conductance that was varied and in each class of HVC neuron, such that the desired network activity is maintained. Figure 2-A shows the ranges for each maximal conductance that had been allowed to vary for the three classes of HVC neurons, while maintaining robust network propagation and biologically realistic in vivo behavior.

Similar to what was done with the maximal ionic conductances, we conducted automated and random variations for all synaptic conductances in the model (no synaptic conductance was fixed). Figure 2-B reports the ranges of the synaptic conductances that were able to maintain the robustness of network propagation and the general in vivo-like desired behavior of all neuronal classes. All synaptic conductances showed considerable ranges during which sequential activity is propagated and the overall desired network activity is maintained, with the exception of the GABA conductance from HVC_INT to HVC_RA (g_GABAINT→RA). Increasing g_GABAINT→RA to larger magnitudes would induce an inhibition in the HVC_RA pushing its voltage below its resting membrane potential (due to the dense bursting and firing in HVC_INT), and this is not realistic because it’s been shown that during singing HVC_RA neurons ride on a depolarizing plateau throughout the song (Long et al., 2010). Moreover, while the intrinsic properties of HVC_X neurons were set to the same values, the synaptic parameters associated with each HVC_X neuron (afferent and efferent) were allowed to vary from one neuron to another.

Results

Adult zebra finches generate intricate songs composed of sequences of distinct song elements, each characterized by a stereotypical acoustic pattern across every rendition of song. The neural circuitry that governs this behavior consists of HVCRA neuronal population where each emits a single and stereotyped 6-10 ms burst during each rendition of song, HVCX neurons eliciting 1-4 bursts that are similarly time locked to vocalizations, and HVCINT neurons that tend to burst densely throughout song. Intrinsic and synaptic mechanisms that orchestrate these neurons’ behaviors are well known (Daou et al., 2013; Kornfeld et al., 2017; Mooney & Prather, 2005). We next describe the steps of building our biophysical network model to describe this ongoing behavior in the following order: 1) tuning the synaptic parameters to fit the dual-intracellular recording traces collected experimentally by Mooney and Prather (2005) as well as Kosche et al (2015), and then 2) describing the network components that are essential for the patterned output of the system, as well as the internal dynamics of the network that govern the strength and duration of individual bursts, the duration of silent gaps between bursts, sparseness versus tonicity, the interplay between excitation and inhibition, role of intrinsic properties and so on that explain how the firing activity of the three classes of HVC neurons propagate through the network in sequential manner.

Tuning synaptic parameters

We initiated our HVC network modeling study calibrating the synaptic parameters (excitatory and inhibitory currents’ activation/inactivation constants, etc..) by reproducing the voltage traces elicited by the dual intracellular recordings from identified pairs of HVC neurons in brain slices conducted by Mooney and Prather (2005). While we are using off-the-shelf synaptic currents from the literature (Destexhe et al., 1994; Varela et al., 1997), we needed to make sure that the synaptic parameters used can replicate the dual synaptic connectivity patterns (strengths of excitation/inhibition, magnitudes of voltage deflections and other trace morphologies). Mooney and Prather’s findings revealed robust disynaptic feedforward inhibition from HVCRA to HVCX neurons (mediated by HVCINT neurons), potent monosynaptic excitation from HVCRA and HVCX to HVCINT neurons (via NMDA and AMPA currents), and substantial monosynaptic inhibition from HVCINT neurons to HVCRA and HVCX (via GABA currents).

Figure 3 displays the dual intracellular recordings conducted by Mooney and Prather (left column) as well as the mathematical model replications (right column) after the synaptic parameters’ calibration. DC-evoked action potentials in HVCRA neurons trigger inhibitory postsynaptic potentials (iPSPs) in HVCX neurons (Fig. 3-A1), as well as fast depolarizing postsynaptic potentials (dPSP) in HVCINT neurons (Fig. 3-B1). To replicate the effects of stimulating HVCRA neurons onto the other two classes of HVC neurons, we connected one HVCRA neuron to excite one HVCINT neuron via an AMPA current. The HVCINT neuron in its turn was connected with one HVCX neuron via a GABA current, thereby making a di-synaptic pathway from HVCRA to HVCX. DC-evoked action potentials in the model HVCRA neuron (brief ∼10 ms depolarizing current pulses (0.5 nA, similar to what Mooney and Prather applied to HVCRA neurons) evoked a fast-depolarizing postsynaptic potential (dPSP) in the corresponding model HVCINT neuron (Fig. 3-B2) as well as inhibitory postsynaptic potential (iPSP) in the corresponding model HVCX neuron (Fig. 3-A2) mediated via HVCINT. Similarly, DC-evoked action potentials in HVCINT neurons generate fast iPSPs in HVCX neurons (Figures 3-C1, D1). The unequal magnitude of the four sags elicited in the HVCX neuron (due to the four brief stimuli) and the large sag after the stimuli ends (Fig. 3-C1), as well as the jagged long sag in response to the repetitive action potentials elicited by the HVCINT neuron (Fig. 3-D1) is probably due to the fact that the corresponding HVCX neurons are receiving multiple synaptic inputs from neurons other than the neurons being stimulated by Mooney and Prather, which adds to the underlying nonlinearities of the responses being recorded. Model HVCINT and HVCX neurons were connected and synaptic parameters were calibrated to generate similar waveforms by giving brief ∼10 ms depolarizing current pulses of 0.5 nA to HVCINT (Fig. 3-C2), or giving a DC-pulse of 0.5 nA for 500 ms (Fig. 3-D2). In the model, the sag seen in the HVCX neuron response is due to the build-up of the H-current as the model HVCINT neurons continues firing, exerting its inhibition onto the HVCX neuron. Finally, model HVCX-HVCINT monosynaptic connectivity (Fig. 3-E2) was calibrated to match the experimental findings (Fig. 3-E1).

Figure 3.

Network Architecture: Non-sequential random sampling in HVC

We next describe the activity patterns generated by our network model, and explain how the firing activity of the three classes of HVC neurons propagate through the network in sequential bursts of activity. The network developed is composed of chains of HVC subnetworks or microcircuits, each with its own intrinsic dynamics. The microcircuit represents a basic architectural unit that encodes for a syllable or a sub-syllabic segment (SSS) in the motif (Fig. 4). Each neuron in a microcircuit is representative of a neural population. In other words, a model neuron (belonging to any class) firing is representative of a population of that neuronal class firing, which could be many neurons of the same class exhibiting very similar intrinsic and synaptic properties leading to their firing at the same time. We refer here to “microcircuits” in a more functional sense, rather than rigid, isolated spatial divisions (Cannon et al. 2015). A microcircuit in our model reflects the local rules that govern the interaction between all HVC neuron classes within the broader network, and that are essential for proper activity propagation.

Figure 4.

The number of microcircuits in the chain determines the number of SSSs in the motif. We envision the HVC to be composed of many copies of such microcircuit chains that are associated with SSSs with roughly synchronized activity. The duration of the sub-syllabic segments need not be the same; therefore, the number of neurons that each microcircuit encompasses need not be equal as we will see next. The network is comprised of a total pool of HVCRA neurons (120 neurons, red circles), a pool of interneurons (50 neurons, black circles) and a pool of HVCX neurons (50 neurons, blue circles), thereby maintaining a 2:1:1 proportionality factor across the populations of HVCRA: HVCINT: HVCX as reported earlier (Kornfeld et al., 2017; Wild et al., 2005). The total number of neurons in the pool is arbitrary and can be made larger, but we limited it to these values given the huge number of ODEs that are being simulated (∼2000 ODEs). Figure 4-A shows the network diagram illustrating three sample microcircuits encoding for three sub-syllabic segments (SSSi-1, SSSi, and SSSi+1) in sequence. Each microcircuit (enclosed by a gray oval) is made up of a number of HVCRA neurons (red circles) and a number of HVCINT neurons (black circles), all selected randomly from their corresponding pools, as we will describe next. In our model, we limited the number of microcircuits to twenty (i.e., the motif is encoded by twenty sub-syllabic segments), but this number is also arbitrary and can be made larger or smaller.

Network organization: The total pool of HVCRA neurons is comprised of smaller groups of HVCRA neurons, the number in each group of which is chosen randomly from the pool (red background circles in each gray oval). Each group of HVCRA neurons belongs to a unique microcircuit and no HVCRA neuron is allowed to be part of more than one microcircuit for reasons described next. Since we set the motif to be represented by twenty microcircuits in our illustration, HVCRA neurons were recruited to their corresponding microcircuits randomly, with each microcircuit allowing a random number (3 – 10) neurons of the RA-projectors to belong to it. In addition to that, the numbers of HVCINT neurons (black background circles) that a microcircuit exhibit is a random number between 1 and 4, as well as the number of HVCX neurons (blue background circles) in each microcircuit is random between 1 and 4, where the individual neurons are selected arbitrarily one neuron at a time from their corresponding pools. Each HVCINT neuron can belong to a single microcircuit and similarly each HVCX neuron can belong to a single microcircuit for reasons described next.

Synaptic Connectivity: Within each microcircuit, HVCRA neurons are selected randomly, one after the other, to send AMPA excitatory synapses to each other in a chain-like mode. Specifically, if there are m HVCRA neurons recruited to belong to microcircuit i (where m is the random number generated between 3 and 10 in this case), a neuron from the m is first selected randomly and designated as the first neuron in the chain (). After that, a second neuron () from the remaining m − 1 is selected randomly and an AMPA synapse is connected from to . Similarly, a third neuron () is selected randomly from the remaining m − 2 neurons and an AMPA synapse is connected from to , and so on, until the HVCRA neurons in every microcircuit are connected together (Fig. 4A, small red circles in each microcircuit).

Each HVCINT in a microcircuit was assigned a random number (between 3 and 8) of excitatory AMPA connections from the HVCRA neurons in the same microcircuit it belongs to, as well as from HVCRA neurons in the other microcircuits (Fig. 4B). In their turn, each HVCINT neuron sends a random number (between 2 and 4) of GABAergic inputs to HVCRA neurons, chosen arbitrarily from any microcircuit in the chain except the microcircuit that the HVCINT neuron belongs to, due to the following reason: if HVCINT inhibits HVCRA in the same microcircuit, some of the HVCRA bursts in the microcircuit might be silenced by the dense and strong HVCINT inhibition breaking the chain of activity. However, if HVCINT inhibits HVCRA in any other microcircuit, activity is ensured to propagate because the HVCINT inhibition of the corresponding HVCRA would arrive at times that are not the “assigned” times of the HVCRA to elicit their ultra-sparse code (Hahnloser et al., 2002).

Unlike HVCRA, HVCINT neurons belonging to a particular microcircuit can burst at times other than the moments when the corresponding encoded SSS is being “sung”; however, we chose to house interneurons within microcircuits for the mere fact that any given interneuron cannot inhibit any given HVCRA neuron, rather there are some “rules of engagement” where we ensure that no inhibition arrives to any HVCRA neuron while it’s eliciting its burst of activity (Fig. 4B). In other words, what makes a particular interneuron belong to this microcircuit or the other is merely the fact that it cannot inhibit HVCRA neurons that are housed in the microcircuit it belongs to for the reasons described. In this regard, this arrangement is similar to the Cannon et al (2015) model in the context of structured inhibition amid the ongoing feedforward excitation.

At the HVCX side, each X-projecting neuron excites via AMPA currents a random selection (1 – 3) of HVCINT neurons that belong to the same microcircuit, and in their turn, each HVCINT neuron inhibits via GABA synapses a random selection (1-2) of HVCX neurons in the same microcircuit (Fig. 4B). These numbers are again arbitrary, but we limited the number of connections from HVCINT to HVCX due to that fact that X-projecting neurons in our model fire upon rebound from inhibition, and the more inhibitory inputs they receive, the more rebound bursts they elicit, which is not realistic since HVCX neurons are known to elicit 1 – 4 bursts during singing (Fujimoto et al., 2011; Kozhevnikov & Fee, 2007), which is what we achieved with this number of synapses. HVCX neurons were selected to be housed within microcircuits and their synapses connecting to interneurons within the same microcircuit due to the following reason: if an HVCX neuron belonging to microcircuit i sends excitatory input to an HVCINT neuron in microcircuit j, and that interneuron happens to select an HVCRA neuron from microcircuit i as its afferent inhibitory connection (via random sampling), then the propagation of sequential activity will halt, and we’ll be in a scenario similar to what was described earlier for HVCINT neurons inhibiting HVCRA neurons in the same microcircuit. Similarly, if an HVCINT neuron in microcircuit i inhibits an HVCX neuron in another microcircuit j, and that HVCX neuron excites an interneuron that synapses onto an HVCRA from microcircuit i, then sequential activity might be disrupted.

While HVCRA neurons are connected to each other in each microcircuit in a chain-like mode as described earlier, the microcircuits interact with each other via the projections from the last HVCRA in a microcircuit i to the first HVCRA in a following microcircuit i + 1. The network is kick-started by a stochastic DC input to HVC¹, that is, only HVC¹ receives input from outside HVC. The propagation of sequential activity along with the realistic firing of the three classes of HVC neurons is maintained and orchestrated by HVC’s intrinsic and synaptic processes without relying on extrinsic inputs as shown next (Figures. 5-11).

Figure 5.

Sequential propagation of HVCRA activity

The activity patterns that RA-projecting neurons of this network display are illustrated in Figure 5. HVCRA neurons burst extremely sparsely generating at most a single burst per simulation (song motif) and with different HVCRA neurons bursting at different times in the song. HVCRA bursts had a duration of 8.12 ± 0.89 ms, and comprised of 4.76 ± 0.48 spikes. The inset of Fig. 5 shows the delay from the onset of the first spike in an HVCRA neuron to the onset of the first spike in the next HVCRA it synapses to. This duration is controlled by two factors: 1) the magnitude of the AMPA conductance, with larger magnitudes corresponding to shorter delays and vice versa (Fig. 6A). In short, the faster the AMPA current is (modeled as larger magnitude in the gAMPA parameter that connects two HVCRA neurons), the shorter the delay between the successive HVCRA bursts. 2) the magnitude of the A-type K⁺ current conductance (g_A) with larger magnitudes corresponding to longer delays (Fig. 6B). This conductance increases rapidly on depolarization due to I_A’s fast activation. The rapid increase in g_A halts after a few milliseconds and switches to a slow decrease that is due to the slow inactivation that this current exhibit. The slow decrease is reflected in the voltage trace as a slow depolarization in the membrane potential (encoding for the delay to spiking), and this allows the model HVCRA neuron to eventually escape the inhibition produced by I_A and fire its delayed burst.

Figure 6.

The number of spikes in HVCRA neurons and the strength of the burst is controlled by three factors: 1) the strength of the AMPA conductance itself where stronger excitatory coupling corresponds to larger number of spikes (Fig. 6A), 2) the A-type K⁺ conductance where larger magnitudes of the conductance reduce the general excitability of the HVCRA neuron and limit its number of spikes (Fig. 6B), and 3) the interplay between the L-type Ca²⁺ (g_CaL) and the Ca²⁺-dependent K⁺ (g_SK) conductances that control the strong adaptation which these neurons exhibit (Daou et al., 2013). In short, intracellular Ca²⁺ (due to ICaL) accumulates during the HVCRA burst. This result in a buildup of Ca²⁺-activated K⁺ current (I_SK) that terminates the HVCRA burst, which in turn terminates any burst in a post-synaptic neuron since HVCRA can no longer provide excitation.

The propagation of sequential bursting in HVCRA neurons halts and the chain of HVCRA activity is broken if any of the following is satisfied: 1) if an AMPA conductance for any of the HVCRA’s that connects it to the next HVCRA in its chain is small enough such that it’s not able to elicit sufficient excitability on the postsynaptic side, 2) if a g_A conductance (Fig. 7A) or a g_SK conductance (Fig. 7B) in any of the HVCRA’s is large enough (mimicking an up-regulation in the corresponding channel) to eliminate the corresponding HVCRA’s burst. Therefore, in order to generate accurate HVCRA bursting patterns that maintain the sequential propagation of neural activity, accurate number of spikes and delays between spikes across the population of HVCRA’s in all microcircuits, as well as the general intrinsic properties of the HVCRA neurons’ spike morphologies (see Methods), both intrinsic and synaptic constraints are needed with key roles in this process for the A-type K⁺ and the Ca²⁺-dependent K⁺ currents that HVCRA model neurons exhibit, as well as the AMPA currents connecting the HVCRA population together within and across microcircuits. Recall that we envision each HVC neuron of any class in our model as a representative of a neural population of the same class that exhibits the same intrinsic as well as afferent and efferent synaptic connectivity. Therefore, in Fig. 7 and the subsequent figures (10,12 and 13) where we show disruption of sequential activity due to changes in synaptic or intrinsic properties of HVC neurons, the modeled synaptic/intrinsic changes to the selected neurons shown are envisioned to be changes applied to the whole neural population encoded by our model neuron. In other words, disrupting the properties of a single neuron within that neural population will not cause harm to the propagation of activity due to what could be thought of as homeostatic mechanisms of the network (Golowasch et al., 1999; Marder & Goaillard, 2006; Williams et al., 2013). This redundancy within the population allows the propagation of activity to be maintained. It is an important feature of our model and is consistent with biological observations where neural populations exhibit robust collective behavior and the loss of a single neuron does not result in a major disruption of network activity.

Figure 7.

Bursting patterns of HVCINT and HVCX neurons

The activity patterns that HVCINT neurons exhibit in our network architecture are illustrated in Figure 8A (shown here for 10 HVCINT neurons). In contrast to the sparse activity in RA-projecting neurons, HVC interneurons generate multiple bursts and spike densely as reported during the song (Hahnloser et al., 2002). The number of bursts each HVCINT neuron exhibits as well as the strength of each burst is controlled by network and synaptic mechanisms as described next (Figures. 9, 10). HVCX neurons in their turn generate 1 – 4 bursts per song motif (Fig. 8B, shown here for 10 HVCX neurons) similar to experimental results (Fujimoto et al., 2011; Hahnloser et al., 2002). Similarly, the number of bursts and strength of each HVCX burst depends on a set of synaptic and intrinsic mechanisms, illustrated in Figures 11 and 12. HVCX neurons differed in the number of bursts and the number of spikes per burst rendering the results more realistic.

Figure 8.

Figure 9.

Dense bursting in HVCINT

The random connections from HVCRA and HVCX neurons to HVCINT as well as the multiple bursts HVCINT and HVCX exhibit in this network are illustrated in Figure 9 by highlighting a sample interneuron (). Here the firing patterns of in addition to all HVCRA and HVCX neurons that connect to it are shown. received random synaptic inputs from neurons, as well as from X-projecting neurons in the same microcircuit it belongs to. Notice that each HVCRA neuron (which happen to belong to separate microcircuits in this case), bursts only once as reported experimentally (Hahnloser et al., 2002). generates multiple bursts as well as spike sparsely. Each of the bursts are aligned with one of the bursts in HVCRA and/or HVCX neurons due to excitatory coupling.

The number of bursts an HVCINT neuron exhibits is largely determined by the number of bursts that each HVCRA and each HVCX neuron that synapses onto that interneuron exhibits. In other words, the larger the number of bursts that a population of HVCRA and HVCX that connects to an interneuron exhibit, the larger the number of bursts elicited in the interneuron. The strength of the bursts in HVCINT neurons is determined by two factors: 1) the strength of the excitatory synaptic conductance from HVCRA and/or HVCX to HVCINT, with stronger bursts in HVCINT corresponding to larger magnitudes of gAMPA from HVCRA and/or HVCX onto the interneuron, 2) the number of spikes/bursts in HVCRA and HVCX that are aligned and occur simultaneously at the HVCINT synapses. For example, the asterisk shown in Figure 9 under the spike train highlights a stronger burst (compared to the rest of the spiking pattern) because neurons tended to fire/burst at the same moment (or within a close interval of each other), thereby generating a stronger response in . Therefore, the characteristic tonic activity that HVC interneurons exhibit with bursting and suppression at different locations during singing is explained in our model by the excitatory and inhibitory coupling between the interneurons and both classes of projecting neurons.

The inhibitory effect of HVCINT neurons, their interplay with the excitatory projection neurons, and their intrinsic properties plays a key role in the modulation of sequence propagation and overall desired network behavior. In particular, if the excitation from the projection neurons onto the interneurons was very large (>> gAMPA), then HVCINT neurons enter regimes of very dense and continuous bursting/spiking (above their natural and basic, yet already enhanced potentiation), thereby leading to the inhibition of the HVCRA’s, halting the sequence. Similarly, if the GABAergic conductances from HVCINT to HVCRA was relatively strong, outside their ideal ranges (Figure 2-B), then HVCRA neurons won’t be able to elicit their bursts.

Besides the synaptic modulations of HVCINT neurons on network activity, intrinsic mechanisms orchestrated primarily by the T-type Ca²⁺ current and the hyperpolarization-activated inward current need to be tightly regulated to ensure desired network activity. The T-type calcium channel opens near resting membrane potential and markedly influence neuronal excitability (Huguenard, 1996; Jagodic et al., 2008). In our model, if the T-type Ca²⁺ current in an HVCINT neuron is up-regulated (due to a depolarizing shift in its voltage-dependent inactivation or simply setting g_CaT to a relatively large value), then the interneuron will fire with much larger firing frequency, silencing the corresponding HVCRA and HVCX neurons that it connects to and breaking the sequence (Fig. 10A). Similarly, the H-channels regulate the resting membrane potentials of the neurons they’re expressed in and play a key role in regulating the spontaneous firing activity (Datunashvili et al., 2018; Funahashi et al., 2003; Yao et al., 2003). In our model, if the H conductance of an HVCINT was upregulated (by increasing the magnitude of gh), then the neuron switches to continuous firing, silencing the HVCRA’s that is connects to (Fig. 10B). Therefore, both the interplay between excitation and inhibition between HVCINT and HVC projection neurons as well as the intrinsic properties of HVCINT neurons (ICaT and IH) are necessary elements to ensure an accurate propagation of sequential activity.

Figure 10.

Rebound bursting in HVCX

The activity patterns that HVCX neurons exhibit in the network are illustrated in Figure 8B (shown here for 10 HVCX neurons). The X-projecting neuronal firing is characterized by regions of inhibition throughout singing, interrupted by occasional rebound bursting. The strength of each burst and the number of total bursts in an HVCX depend on synaptic and intrinsic mechanisms summarized briefly as such: 1) the degree of inhibition from HVCINT neurons, 2) the number and timing of bursts of HVCINT neurons and 3) the intrinsic properties and magnitudes of the T – type Ca²⁺ and H – currents that the HVCX neurons exhibit. In short, the stronger the GABAergic maximal conductance(s) from the HVCINT neurons that inhibit a given HVCX neuron, the stronger the HVCX neuron’s rebound burst (Figures 8-11). Similarly, if multiple HVCINT neurons’ bursts that inhibit an HVCX neuron aligned simultaneously, then the rebound in HVCX is potentiated due to the stronger inhibition. This is primarily due to the T-type Ca²⁺ current and the H-current that HVCX neurons exhibit, facilitating rapid calcium influx into the neurons when they rebound from hyperpolarization. The calcium influx is correlated to the degree and the duration of inhibition that the neuron receives, and can trigger a potentiated burst of action potentials leading to more robust rebound responses. In other words, the stronger the inhibition of HVCX, the stronger the activation of ICaT and Ih, leading to stronger rebounds. Moreover, the number of spikes in each HVCX burst is controlled by several factors including 1) the degree of inhibition from HVCINT and its effect on ICaT and Ih as described earlier, and 2) the strength of the Ca²⁺-dependent K⁺ conductance (g_SK) with stronger magnitudes of this conductance dampening the excitability of these neurons and reducing the number of spikes.

Figure 11.

The interplay between HVCINT and HVCX in shaping the characteristic HVCX responses is illustrated in Figure 11 from exemplar neurons in the network. Two interneurons, (black) and (green) were selected randomly to inhibit (blue trace, Fig. 11A). There are several regions in the membrane potential trajectory where the neuron is inhibited (sags/sinks in the voltage trace). These regions correspond to the moments in time when either or neurons, or both simultaneously, are bursting, thereby silencing . Eventually, is able to escape inhibition at a few instances in time and generate multiple post inhibitory rebound bursts mediated by I_CaT and I_h. Figure 11B shows a zoomed version of panel A illustrating the three rebound bursts in as a result of escape from inhibition. and neurons generated multiple successive bursts of firing, during which cannot escape the inhibition. There are only a few intervals where is able to elicit rebound bursts; the first opportunity was at the beginning of the trace (Fig. 11A) where the sag generated in as a result of inhibition from is clear, but the inhibition from was not strong enough to elicit a rebound burst in , rather eliciting only a rebound depolarization. The subsequent three opportunities where is able to escape the inhibition all elicited rebound bursts due to the strong inhibitory input arriving from both interneurons.

All rebound bursts in HVCX are orchestrated by the hyperpolarization-activated inward current (I_H) and the T-type Ca²⁺ current (I_CaT). The longer the duration of the inhibition prior to a rebound, the longer the time I_H and I_CaT take to fully activate and generate the rebound burst. The shorter the inhibitory silent interval (that is, the interval in which HVCX is receiving no inhibition), the shorter the rebound and the fewer the number of spikes in the rebound burst (Fig. 11A, first rebound burst). Moreover, HVC interneurons inhibit multiple HVCX neurons in our network. Figure 11C shows an exemplar interneuron (, black) that happens to inhibit two X-projecting neurons (, blue and , orange). Each burst in elicits an iPSP in and , and can contribute to subsequent rebound bursts in them unless silenced by other interneurons that connect to or (Fig. 11D). All HVCX neurons differed in their corresponding number of rebound bursts as well as in the number of spikes per burst rendering the results biologically accurate.

As mentioned earlier, the T-type Ca²⁺ and the H-conductances play a significant role in modulating the rebound bursting in HVCX neurons. As a matter of fact, these two conductances, along with the Ca²⁺ – dependent K⁺ conductance can halt the sequential propagation of activity and mess up the overall desired network behavior as described next. Ramping up gH in HVCX neurons to values outside the allowed ranges (Figure 2-A) will break the sequence of propagation and generate nonrealistic firing patterns. The g_H parameter was increased in Figure 12A in an exemplar HVCX neuron () to large values, driving into regimes of runaway excitation due to the up-regulation of I_H and generating a non-realistic firing pattern for a typical X-projecting neuron during singing. The reason the sequential propagation of HVCRA is halted is because happens to have an excitatory coupling with (along with other interneurons, but we illustrate it here for ), and as a result of ’s increased firing, generates a mostly-continuous firing trace of bursting and spiking, which silences the HVCRA neuron that it happens to inhibit (in this case, , Fig. 12A).

Figure 12.

Similarly, altering gCaT in HVCX neurons can have similar effects on network activity. Figure 12B shows an exemplar HVCX neuron () where gCaT was ramped up to large values and as a result, stronger rebound bursts in were elicited as well as larger number of rebound spikes in each burst. This is primarily due to the up-regulation of the T-type Ca²⁺ current that was induced, markedly influencing the neuronal excitability. The stronger rebounding in generated stronger excitation in their postsynaptic interneurons’ counterparts that they excite (for example, ), which in their turn silenced the HVCRA neurons that they inhibit (for example, is the first neuron in the chain that inhibits, breaking the sequence at ). And finally, the Ca²⁺ – dependent K⁺ conductance, which plays a key role in governing HVCX neurons’ excitability and their characteristic spike frequency adaptation (Daou et al., 2013) can have similar effects if the channel was down-regulated (rather than up-regulated as in I_CaT and I). Figure 12C shows the effects of blocking the g_SK conductance in an exemplar HVCX neuron () leading to its increased firing, which in turn leads to stronger bursting and spiking in the HVCINT neurons it excites (for example, ). in its turn generates stronger and wider-range inhibition onto the HVCRA neurons it sends its axons to (for example, is the first neuron in the chain inhibits, silencing it and breaking the sequence at ).

Finally, we checked the consequences of altering the intrinsic properties of HVC_X neurons on the network’s desired behavior. To do so, we varied the maximal conductances of the three principal ionic currents of the X-projecting neurons (I_CaT, I_SK, I_H) across all neurons of the population, while keeping this variation within the reported ranges shown in Figure 2A (because certainly going outside these ranges will disrupt network activity for other reasons as reported in Figures 10 and 12). Varying those three key paramters across the HVCx population had different results. In 100 different simulations that generated random maximal conductances for I_CaT,I_SK and I_H, 41% of the simulations did not have any considerable effect on the desired network activity, whereas 59% resulted in disrupted network activity, and sometimes detrimental. For example, Figure 13 shows an example where the sequential propagation of activity was halted and the firing patterns of some interneurons and X-projecting neurons were rendered non-biophysically realistic. Particularly, some interneurons switched to continuous spiking or phasic bursting with little episodic bursting modes, while some HVC_X neurons generated longer rebounds, fewer number of bursts or fewer number of spikes per burst (Fig. 13 B-C). Hence, changes in the intrinsic properties of X-projecting neurons can disrupt activity propagation necessary for song production, and produce biologically unrealistic bursting patterns in HVC neurons. This can wreak havoc on our network model hinting to the finding that biophysical parameters are distinct and consistent for an individual bird and this unique combination is needed for song (Daou & Margoliash, 2020). The homogeneity in the intrinsic properties of X-projectors might be a strategy allowing it to adapt or respond to changes in the network.

Figure 13.

In conclusion, we developed a detailed and biophysically realistic neural network model for sequence propagation in the HVC of the zebra finch. Our model consisted of chains of microcircuits, each comprised of a selection of HVCRA, HVCINT and HVCX model neurons selected randomly from a total pool of neurons. The maximal conductances of the four key and principle ionic currents for each model neuron, the number of neurons of each class in any microcircuit, and the excitatory and inhibitory connections between the different classes within a microcircuit and across microcircuits are all selected randomly. This activity propagates throughout the chain of microcircuits causing a sequence of HVCRA bursts while leaving behind realistic bursting patterns for all classes of HVC neurons as seen during singing. The model incorporates all known ionic and synaptic currents for each HVC neuron. The network architecture we developed was able to replicate the in vivo biologically realistic firing behavior for each class by including sparse timely-locked bursting in the RA-projecting neurons (with accurate intrinsic properties for each burst in terms of number of spikes, duration and spike morphology), multiple bursting in the X-projecting neurons that are also sparse and time-locked, and dense bursting/spiking in the interneurons with few intermittent quiescence. The ability of our network to reproduce the sequential propagation of activity in the presence of excitatory and inhibitory connections involving all neuronal subclasses as well as over a range of values for each synaptic and ionic maximal conductances is an indication of its robustness. Our network unveiled key intrinsic and synaptic mechanisms that modulate the sequential propagation of neural activity by highlighting important roles for the T-type Ca²⁺ current and hyperpolarization activated (H) inward current in HVCX and HVCINT neurons, Ca²⁺-dependent K⁺ current in HVCX and HVCRA, A-type K⁺ current in HVCRA, as well as GABAergic and glutamatergic synaptic currents that connects all neuronal subclasses together. The result is an improved characterization of the HVC network responsible for song production in the zebra finch.

Discussion

In this study, we have designed a neural network model that describe zebra finch song production in the HVC. The biophysically realistic network architecture that we designed combine both classes of HVC projection neurons with local inhibitory interneurons. A fundamental goal that we have achieved in our design is a successful replication of the in vivo firing behaviors of all the HVC neuronal classes: single sparse timely-precise bursting (3-6 spikes for ∼10 ms) in the RA-projecting neurons, multiple bursting (1-4 bursts with 4-9 spikes/burst) in the X-projecting neurons, dense and frequent bursting in the interneurons, as well as the general intrinsic properties that each class of HVC neurons exhibit (Daou et al., 2013; Lewicki, 1996; Long et al., 2010). The patterning activity in HVC is largely shaped in our model by the intrinsic properties of the individual neurons as well as the synaptic properties where excitation and inhibition play a major role in enabling neurons to generate their characteristic bursts during singing.

The three classes of model neurons incorporated to our network as well as the synaptic currents that connect them are based on Hodgkin-Huxley formalisms that contain ion channels and synaptic currents which had been pharmacologically identified (Daou et al., 2013; Kosche et al., 2015; Mooney & Prather, 2005). Our network showed that sequence propagation can be broken if several intrinsic mechanisms are perturbed. In particular, if ICaT or IH are upregulated in HVCX or HVCINT, if ISK is downregulated in HVCX or if ISK is upregulated in HVCRA, then the corresponding chain of activity stops and the rhythmic activity of the network is disrupted (Figures 7, 10 and 12). Synaptically, perhaps the most critical role in our network design is played by interneurons which orchestrate the activity of the two projection neurons in a structured manner. Interneurons adjust the timing of HVC projection neurons’ bursts (Amador et al., 2013; Kosche et al., 2015), and developmental learning regulates inhibition onto HVCRA (Vallentin et al., 2016). HVCRA neurons interact with HVCX through local interneurons, a disynaptic inhibitory pathway that conveys information to HVCX neurons (Prather et al., 2008). Focal application of the GABAA receptor antagonist, gabazine, restricted inhibitory impact in HVC leading to stronger and faster responses relative to call onset (Benichov & Vallentin, 2020), showing that local HVC interneurons form an inhibitory mask that can greatly constrain the spiking activity of projecting neurons (Kornfeld et al., 2017; Kosche et al., 2015; Mooney & Prather, 2005) suggesting that HVC model networks that lack inhibitory neurons are inadequate for explaining sequential propagation of neural activity.

Various models of how the song is encoded within HVC have been proposed. Some groups suggested that bursting activity propagates through a chain of synaptically connected HVCRA neurons either as single neurons (Fee et al., 2004; Hahnloser et al., 2002; Long et al., 2010) or as pools of HVCRA neurons, each group driving a distinct ensemble of RA neurons (Jin et al., 2007; Leonardo & Fee, 2005; Li & Greenside, 2006). These models assume that HVCRA neurons generate a continuous, feed-forward sequence of activity over time, with little or no role played by X-projecting HVC neurons and interneurons. Other models have incorporated alternative temporal encoding mechanisms by necessitating synaptic integration at the levels of HVCRA and HVCINT populations (Drew & Abbott, 2003; Gibb et al., 2009a; Jin, 2009; Weber & Hahnloser, 2007) while yet other approaches gave emphasis to brainstem feedback processes by incorporating inter-hemispheric coordination to activate sequences of syllable-specific HVCRA and HVCINT neurons (Galvis et al., 2018; Gibb et al., 2009b). A prominent model used spatially recurrent excitatory chains and local feedback inhibition to show how the HVC network stabilize synchrony while propagating sequential activity (Cannon et al., 2015; Markowitz et al., 2015).

All existing models that describe premotor sequence generation in the HVC either assume a distributed model (Elmaleh et al., 2021) that dictates that local HVC circuitry is not sufficient to advance the sequence but rather depends upon moment-to-moment feedback through Uva (Hamaguchi et al., 2016), or assume models that rely on intrinsic connections within HVC to propagate sequential activity. In the latter case, some models assume that HVC is composed of multiple discrete subnetworks that encode individual song elements (Glaze & Troyer, 2013; Long & Fee, 2008; Wang et al., 2008), but lacks the local connectivity to link the subnetworks, while other models assume that HVC may have sufficient information in its intrinsic connections to form a single continuous network sequence (Long et al., 2010).

The network architecture we developed here exhibits overlap with the various models presented. First, in agreement with the continuous model, our network architecture displays a feed-forward mechanism regulating the circuit dynamics e.g., (Gibb et al., 2009a; Jin, 2009; Jin et al., 2007; Li & Greenside, 2006; Long et al., 2010). Nonetheless, diverging from a linear progression of HVC neurons directing the song, the network’s structure comprises sequences of microcircuits incorporating all classes of HVC neurons, where sequential activity transmits from one microcircuit to the next, as opposed to transitioning directly between individual neurons. Second, in agreement with the subnetwork models, our model envisions HVC as comprised of multiple discrete subcircuits (SSSs) where each microcircuit incorporates its own pool of neurons; however, in our model HVC’s connectivity is sufficient to link the microcircuits together and extrinsic influences are not needed. Moreover, our network is in agreement with the (Cannon et al., 2015) model where structured inhibition is needed to propagate sequential activity, synchronize the firing of pools of neurons and stabilize spike timing along the chain. The pivotal element in advancing sequential activity through time is the inhibition exerted by HVCINT onto HVCX and HVCRA neurons, facilitated in the case of HVCX through rebound firing, and all orchestrated by intrinsic mechanisms.

A potential drawback of our model is that it does not incorporate brainstem feedback processes or address inter-hemispheric coordination as proposed by others (Galvis et al., 2018; Gibb et al., 2009b). Another drawback is its sole focus on local excitatory connectivity within the HVC (Kornfeld et al., 2017; Long et al., 2010). Moreover, HVC neurons receive afferent excitatory connections (Akutagawa & Konishi, 2010; Nottebohm et al., 1982) that plays significant roles in their local dynamics. For example, the excitatory inputs that HVC neurons receive from Uvaeformis may be crucial in initiating (Andalman et al., 2011; Danish et al., 2017; Galvis et al., 2018) or sustaining (Hamaguchi et al., 2016) the sequential activity.

The role of ion channels in controlling network activity

Our model highlights the role of principal ion channels (IH, ICaT, ISK and IA) in controlling HVC’s network dynamics and progressing its neural sequence. Hyperpolarization-activated ionic conductances had been widely observed across various electrically excitable cells (Pape, 1996) and play significant roles in rhythmogenesis (Budde et al., 1997; Golowasch et al., 1992; Golowasch & Marder, 1992). In our network, model HVCX neurons are not able to elicit their rebound bursting without I_H and sequence is halted if this conductance is upregulated in either of HVCX or HVCINT (Figures 8-10, 11 and 12). Similarly, the T-type Ca²+ current is recognized as crucial in various systems as an ionic contributor to burst generation (Deschenes et al., 1982; Fraser & MacVicar, 1991; Huguenard, 1996; Llinás & Yarom, 1981). Lewicki (1996) observed a significant hyperpolarization in some HVC neurons in vivo before they emit their corresponding bursts, and the intensity of the burst correlates with the degree of hyperpolarization. In this study, we have illustrated its pivotal role in rebound spiking where up-regulating this conductance in HVCX or HVCINT halts sequence propagation (Figures 8-10, 11 and 12). Moreover, the A-type K⁺ current is involved in several rhythmogenic activities controlling membrane excitability (Coetzee et al., 1999; Ellis et al., 2007; Gross et al., 2016) and in our network, upregulating IA suppress bursting in model HVCRA and breaks sequence propagation (Fig. 7). Finally, the small conductance Ca²⁺-activated potassium current (I_SK) plays important roles in the regulation of excitable cells controlling network rhythmic activity (Benítez et al., 2011; Chen et al., 2014; Pedarzani et al., 2005) and in our network I_SK plays a significant role since its upregulation in HVCRA or its downregulation in HVCX eliminates sequence propagation (Fig.7 and Fig. 12 respectively).

In conclusion, the network model developed provide a large step forward in describing the biophysics of HVC circuitry, and may throw a new light on certain dynamics in the mammalian brain, particularly the motor cortex (Shmiel et al., 2006) and the hippocampus regions (Lee & Wilson, 2002) where precisely-timed sequential activity is crucial. We suggest that temporally-precise sequential activity may be a manifestation of neural networks comprised of chain of microcircuits, each containing pools of excitatory and inhibitory neurons, with local interplay among neurons of the same microcircuit and global interplays across the various microcircuits, and with structured inhibition and intrinsic properties synchronizing the neuronal pools and stabilizing timing within the ongoing sequence.