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In recent years, the field of neuroscience has gone through rapid experimental advances and extensive use of quantitative and computational methods. This accelerating growth has created a need for methodological analysis of the role of theory and the modeling approaches currently used in this field. Toward that end, we start from the general view that the primary role of science is to solve empirical problems, and that it does so by developing theories that can account for phenomena within their domain of application. We propose a commonly-used set of terms - descriptive, mechanistic, and normative - as methodological designations that refer to the kind of problem a theory is intended to solve. Further, we find that models of each kind play distinct roles in defining and bridging the multiple levels of abstraction necessary to account for any neuroscientific phenomenon. We then discuss how models play an important role to connect theory and experiment, and note the importance of well-defined translation functions between them. Furthermore, we describe how models themselves can be used as a form of experiment to test and develop theories. This report is the summary of a discussion initiated at the conference Present and Future Theoretical Frameworks in Neuroscience, which we hope will contribute to a much-needed discussion in the neuroscientific community., deposited on: https://arxiv.org/abs/2003.13825

Neurons in oscillatory networks often exhibit membrane potential resonance, a peak impedance at a non-zero input frequency. In electrically coupled oscillatory networks, the coupling coefficient (the ratio of post- and prejunctional voltage responses) could also show resonance. Such coupling resonance may emerge from the interaction between the coupling current and resonance properties of the coupled neurons, but this relationship has not been clearly described. Additionally, it is unknown if the gap-junction mediated electrical coupling conductance may have frequency dependence. We examined these questions by recording a pair of electrically coupled neurons in the oscillatory pyloric network of the crabCancer borealis. We performed dual current- and voltage-clamp recordings and quantified the frequency preference of the coupled neurons, the coupling coefficient, the electrical conductance, and the postjunctional neuronal response. We found that all components exhibit frequency selectivity, but with distinct preferred frequencies. Mathematical and computational analysis showed that membrane potential resonance of the postjunctional neuron was sufficient to give rise to resonance properties of the coupling coefficient, but not the coupling conductance. A distinct coupling conductance resonance frequency therefore emerges either from other circuit components or from the gating properties of the gap junctions. Finally, to explore the functional effect of the resonance of the coupling conductance, we examined its role in synchronizing neuronal the activities of electrically coupled bursting model neurons. Together, our findings elucidate factors that produce electrical coupling resonance and the function of this resonance in oscillatory networks.

Both the cerebellum and the basal ganglia are known for their roles in motor control and motivated behavior. These two systems have been classically considered as independent structures that coordinate their contributions to behavior via separate cortico-thalamic loops. However, recent evidence demonstrates the presence of a rich set of direct connections between these two regions. Although there is strong evidence for connections in both directions, for brevity we limit our discussion to the better-characterized connections from the cerebellum to the basal ganglia. We review two sets of such connections: disynaptic projections through the thalamus and direct monosynaptic projections to the midbrain dopaminergic nuclei, the VTA and the SNc. In each case, we review the evidence for these pathways from anatomic tracing and physiological recordings, and discuss their potential functional roles. We present evidence that the disynaptic pathway through the thalamus is involved in motor coordination, and that its dysfunction contributes to motor deficits, such as dystonia. We then discuss how cerebellar projections to the VTA and SNc influence dopamine release in the respective targets of these nuclei: the NAc and the dorsal striatum. We argue that the cerebellar projections to the VTA may play a role in reward-based learning and therefore contribute to addictive behavior, whereas the projection to the SNc may contribute to movement vigor. Finally, we speculate how these projections may explain many of the observations that indicate a role for the cerebellum in mental disorders, such as schizophrenia.

Evidence of direct reciprocal connections between the cerebellum and basal ganglia has challenged the long-held notion that these structures function independently. While anatomical studies have suggested the presence of cerebellar projections to the substantia nigra pars compacta (SNc), the nature and function of these connections (Cb-SNc) is unknown. Here we show that the Cb-SNc form monosynaptic glutamatergic synapses with both dopaminergic and non-dopaminergic neurons in the SNc. Optogenetic activation Cb-SNc axons in the SNc rapidly increases SNc activity, elevates striatal dopamine levels, and increases the probability of locomotion. During ongoing behavior, Cb-SNc axons are bilaterally activated prior to ambulation and unilateral lever manipulation. The Cb-SNc axons show prominent activation to water reward, and higher activation for sweet water, suggesting that the pathway also encodes reward value. Thus, the cerebellum directly, rapidly, and effectively modulates basal ganglia dopamine levels and conveys information related to movement initiation, vigor, and possibly reward processing.

Neural circuits can generate many spike patterns, but only some are functional. The study of how circuits generate and maintain functional dynamics is hindered by a poverty of description of circuit dynamics across functional and dysfunctional states. For example, although the regular oscillation of a central pattern generator is well characterized by its frequency and the phase relationships between its neurons, these metrics are ineffective descriptors of the irregular and aperiodic dynamics that circuits can generate under perturbation or in disease states. By recording the circuit dynamics of the well-studied pyloric circuit in C. borealis, we used statistical features of spike times from neurons in the circuit to visualize the spike patterns generated by this circuit under a variety of conditions. This unsupervised approach captures both the variability of functional rhythms and the diversity of atypical dynamics in a single map. Clusters in the map identify qualitatively different spike patterns hinting at different dynamical states in the circuit. State probability and the statistics of the transitions between states varied with environmental perturbations, removal of descending neuromodulation, and the addition of exogenous neuromodulators. This analysis reveals strong mechanistically interpretable links between complex changes in the collective behavior of a neural circuit and specific experimental manipulations, and can constrain hypotheses of how circuits generate functional dynamics despite variability in circuit architecture and environmental perturbations.

Visual Abstract, Postsynaptic responses depend on input patterns as well as short-term synaptic plasticity, summation, and postsynaptic membrane properties, but the interactions of those dynamics with realistic input patterns are not well understood. We recorded the responses of the two pyloric dilator (PD) muscles, cpv2a and cpv2b, that are innervated by and receive identical periodic bursting input from the same two motor neurons in the lobster Homarus americanus. Cpv2a and cpv2b showed quantitative differences in membrane nonlinearities and synaptic summation. At a short timescale, responses in both muscles were dominated by facilitation, albeit with different frequency and time dependence. Realistic burst stimulations revealed more substantial differences. Across bursts, cpv2a showed transient depression, whereas cpv2b showed transient facilitation. Steady-state responses to bursting input also differed substantially. Neither muscle had a monotonic dependence on frequency, but cpv2b showed particularly pronounced bandpass filtering. Cpv2a was sensitive to changes in both burst frequency and intra-burst spike frequency, whereas, despite its much slower responses, cpv2b was largely insensitive to changes in burst frequency. Cpv2a was sensitive to both burst duration and number of spikes per burst, whereas cpv2b was sensitive only to the former parameter. Neither muscle showed consistent sensitivity to changes in the overall spike interval structure, but cpv2b was surprisingly sensitive to changes in the first intervals in each burst, a parameter known to be regulated by dopamine (DA) modulation of spike propagation of the presynaptic axon. These findings highlight how seemingly minor circuit output changes mediated by neuromodulation could be read out differentially at the two synapses.

Visual Abstract, In oscillatory circuits, some actions of neuromodulators depend on the oscillation frequency. However, the mechanisms are poorly understood. We explored this problem by characterizing neuromodulation of the lateral pyloric (LP) neuron of the crab stomatogastric ganglion (STG). Many peptide modulators, including proctolin, activate the same ionic current (IMI) in STG neurons. Because IMI is fast and non-inactivating, its peak level does not depend on the temporal properties of neuronal activity. We found, however, that the amplitude and peak time of the proctolin-activated current in LP is frequency dependent. Because frequency affects the rate of voltage change, we measured these currents with voltage ramps of different slopes and found that proctolin activated two kinetically distinct ionic currents: the known IMI, whose amplitude is independent of ramp slope or direction, and an inactivating current (IMI-T), which was only activated by positive ramps and whose amplitude increased with increasing ramp slope. Using a conductance-based model we found that IMI and IMI-T make distinct contributions to the bursting activity, with IMI increasing the excitability, and IMI-T regulating the burst onset by modifying the postinhibitory rebound in a frequency-dependent manner. The voltage dependence and partial calcium permeability of IMI-T is similar to other characterized neuromodulator-activated currents in this system, suggesting that these are isoforms of the same channel. Our computational model suggests that calcium permeability may allow this current to also activate the large calcium-dependent potassium current in LP, providing an additional mechanism to regulate burst termination. These results demonstrate a mechanism for frequency-dependent actions of neuromodulators.

In similar states, neural circuits produce similar outputs across individuals despite substantial interindividual variability in neuronal ionic conductances and synapses. Circuit states are largely shaped by neuromodulators that tune ionic conductances. It is therefore possible that, in addition to producing flexible circuit output, neuromodulators also contribute to output similarity despite varying ion channel expression. We studied whether neuromodulation at saturating concentrations can increase the output similarity of a single identified neuron across individual animals. Using the lateral pyloric (LP) neuron of the crab stomatogastric ganglion, we compared the variability off–I(frequency–current) curves and rebound properties in the presence of neuropeptides. The two neuropeptides we used converge to activate the same target current, which increases neuronal excitability. Output variability was lower in the presence of the neuropeptides, regardless of whether the neuropeptides significantly changed the mean of the corresponding parameter or not. However, the addition of the second neuropeptide did not add further to the reduction of variability. With a family of computational LP-like models, we explored how increased excitability and target variability contribute to output similarity and found two mechanisms: saturation of the responses and a differential increase in baseline activity. Saturation alone can reduce the interindividual variability only if the population shares a similar ceiling for the responses. In contrast, the reduction of variability due to the increase in baseline activity is independent of ceiling effects.

The levels of voltage-gated and synaptic currents in the same neuron type can vary substantially across individuals. Yet, the phase relationships between neurons in oscillatory circuits are often maintained, even in the face of varying oscillation frequencies. We examined whether synaptic and intrinsic currents are matched to maintain constant activity phases across preparations, using the lateral pyloric (LP) neuron of the stomatogastric ganglion of the crab, Cancer borealis. LP produces stable oscillatory bursts upon release from inhibition, with an onset phase that is independent of oscillation frequency. We quantified the parameters that define the shape of the synaptic current inputs across preparations and found no linear correlations with voltage-gated currents. However, several synaptic parameters were correlated with oscillation period and burst onset phase, suggesting they may play a role in phase maintenance. We used the dynamic clamp to apply artificial synaptic inputs and found that those synaptic parameters correlated with phase and period were ineffective in influencing burst onset. Instead, parameters that showed the least variability across preparations had the greatest influence. Thus, parameters that influence circuit phasing are constrained across individuals, while those that have little effect simply co-vary with phase and frequency.

Multiple neuromodulators act in concert to shape the properties of neural circuits. Different neuromodulators usually activate distinct receptors but can have overlapping targets. Therefore, circuit output depends on neuromodulator interactions at shared targets, a poorly understood process. We explored quantitative rules of co-modulation of two principal targets of neuromodulation: synapses and voltage-gated ionic currents. In the stomatogastric ganglion of the male crabCancer borealis, the neuropeptides proctolin (Proc) and the crustacean cardioactive peptide (CCAP) modulate synapses of the pyloric circuit and activate a voltage-gated current (IMI) in multiple neurons. We examined the validity of a simple dose-dependent quantitative rule, that co-modulation by Proc and CCAP is predicted by the linear sum of the individual effects of each modulator up to saturation. We found that this rule is valid for co-modulation of synapses, but not for the activation ofIMI, in which co-modulation was sublinear. The predictions for the co-modulation ofIMIactivation were greatly improved if we assumed that the intracellular pathways activated by two peptide receptors inhibit one another. These findings suggest that the pathways activated by two neuromodulators could have distinct interactions, leading to distinct co-modulation rules for different targets even in the same neuron. Given the evolutionary conservation of neuromodulator receptors and signaling pathways, such distinct rules for co-modulation of different targets are likely to be common across neuronal circuits.SIGNIFICANCE STATEMENTWe examine the quantitative rules of co-modulation at multiple shared targets, the first such characterization to our knowledge. Our results show that dose-dependent co-modulation of distinct targets in the same cells by the same two neuromodulators follows different rules: co-modulation of synaptic currents is linearly additive up to saturation, whereas co-modulation of the voltage-gated ionic current targeted in a single neuron is nonlinear, a mechanism that is likely generalizable. Given that all neural systems are multiply modulated and neuromodulators often act on shared targets, these findings and the methodology could guide studies to examine dynamic actions of neuromodulators at the biophysical and systems level in sensory and motor functions, sleep/wake regulation, and cognition.

Regenerative inward currents help produce slow oscillations through a negative-slope conductance region of their current-voltage relationship that is well approximated by a linear negative conductance. We used dynamic-clamp injections of a linear current with such conductance, INL, to explore why some neurons can generate intrinsic slow oscillations whereas others cannot. We addressed this question in synaptically isolated neurons of the crab Cancer borealis after blocking action potentials. The pyloric network consists of a distinct pacemaker and follower neurons, all of which express the same complement of ionic currents. When the pyloric dilator (PD) neuron, a member of the pacemaker group, was injected with INL with dynamic clamp, it consistently produced slow oscillations. In contrast, all follower neurons failed to oscillate with INL To understand these distinct behaviors, we compared outward current levels of PD with those of follower lateral pyloric (LP) and ventral pyloric (VD) neurons. We found that LP and VD neurons had significantly larger high-threshold potassium currents (IHTK) than PD and LP had lower-transient potassium current (IA). Reducing IHTK pharmacologically enabled both LP and VD neurons to produce INL-induced oscillations, whereas modifying IA levels did not affect INL-induced oscillations. Using phase-plane and bifurcation analysis of a simplified model cell, we demonstrate that large levels of IHTK can block INL-induced oscillatory activity whereas generation of oscillations is almost independent of IA levels. These results demonstrate the general importance of a balance between inward pacemaking currents and high-threshold K+ current levels in determining slow oscillatory activity.NEW & NOTEWORTHY Pacemaker neuron-generated rhythmic activity requires the activation of at least one inward and one outward current. We have previously shown that the inward current can be a linear current (with negative conductance). Using this simple mechanism, here we demonstrate that the inward current conductance must be in relative balance with the outward current conductances to generate oscillatory activity. Surprisingly, an excess of outward conductances completely precludes the possibility of achieving such a balance.

Many neurons receive synchronous input from heterogeneous presynaptic neurons with distinct properties. An instructive example is the crustacean stomatogastric pyloric circuit pacemaker group, consisting of the anterior burster (AB) and pyloric dilator (PD) neurons, which are active synchronously and exert a combined synaptic action on most pyloric follower neurons. Previous studies in lobster have indicated that AB is glutamatergic, whereas PD is cholinergic. However, although the stomatogastric system of the crab Cancer borealis has become a preferred system for exploration of cellular and synaptic basis of circuit dynamics, the pacemaker synaptic output has not been carefully analyzed in this species. We examined the synaptic properties of these neurons using a combination of single-cell mRNA analysis, electrophysiology, and pharmacology. The crab PD neuron expresses high levels of choline acetyltransferase and the vesicular acetylcholine transporter mRNAs, hallmarks of cholinergic neurons. In contrast, the AB neuron expresses neither cholinergic marker but expresses high levels of vesicular glutamate transporter mRNA, consistent with a glutamatergic phenotype. Notably, in the combined synapses to follower neurons, 70–75% of the total current was blocked by putative glutamatergic blockers, but short-term synaptic plasticity remained unchanged, and although the total pacemaker current in two follower neuron types was different, this difference did not contribute to the phasing of the follower neurons. These findings provide a guide for similar explorations of heterogeneous synaptic connections in other systems and a baseline in this system for the exploration of the differential influence of neuromodulators. NEW & NOTEWORTHY The pacemaker-driven pyloric circuit of the Jonah crab stomatogastric nervous system is a well-studied model system for exploring circuit dynamics and neuromodulation, yet the understanding of the synaptic properties of the two pacemaker neuron types is based on older analyses in other species. We use single-cell PCR and electrophysiology to explore the neurotransmitters used by the pacemaker neurons and their distinct contribution to the combined synaptic potentials.

In oscillatory systems, neuronal activity phase is often independent of network frequency. Such phase maintenance requires adjustment of synaptic input with network frequency, a relationship that we explored using the crab,Cancer borealis, pyloric network. The burst phase of pyloric neurons is relatively constant despite a >2-fold variation in network frequency. We used noise input to characterize how input shape influences burst delay of a pyloric neuron, and then used dynamic clamp to examine how burst phase depends on the period, amplitude, duration, and shape of rhythmic synaptic input. Phase constancy across a range of periods required a proportional increase of synaptic duration with period. However, phase maintenance was also promoted by an increase of amplitude and peak phase of synaptic input with period. Mathematical analysis shows how short-term synaptic plasticity can coordinately change amplitude and peak phase to maximize the range of periods over which phase constancy is achieved.

Many neurons receive synchronous input from heterogeneous presynaptic neurons with distinct properties. An instructive example is the crustacean stomatogastric pyloric circuit pacemaker group, consisting of the anterior burster (AB) and pyloric dilator (PD) neurons, which are active synchronously and exert a combined synaptic action on most pyloric follower neurons. Previous studies in lobster have indicated that AB is glutamatergic, whereas PD is cholinergic. However, although the stomatogastric system of the crab Cancer borealis has become a preferred system for exploration of cellular and synaptic basis of circuit dynamics, the pacemaker synaptic output has not been carefully analyzed in this species. We examined the synaptic properties of these neurons using a combination of single-cell mRNA analysis, electrophysiology, and pharmacology. The crab PD neuron expresses high levels of choline acetyltransferase and the vesicular acetylcholine transporter mRNAs, hallmarks of cholinergic neurons. In contrast, the AB neuron expresses neither cholinergic marker but expresses high levels of vesicular glutamate transporter mRNA, consistent with a glutamatergic phenotype. Notably, in the combined synapses to follower neurons, 70–75% of the total current was blocked by putative glutamatergic blockers, but short-term synaptic plasticity remained unchanged, and although the total pacemaker current in two follower neuron types was different, this difference did not contribute to the phasing of the follower neurons. These findings provide a guide for similar explorations of heterogeneous synaptic connections in other systems and a baseline in this system for the exploration of the differential influence of neuromodulators. NEW & NOTEWORTHY The pacemaker-driven pyloric circuit of the Jonah crab stomatogastric nervous system is a well-studied model system for exploring circuit dynamics and neuromodulation, yet the understanding of the synaptic properties of the two pacemaker neuron types is based on older analyses in other species. We use single-cell PCR and electrophysiology to explore the neurotransmitters used by the pacemaker neurons and their distinct contribution to the combined synaptic potentials.