Research paper
Modeling dopaminergic modulation of clustered gamma rhythms

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Highlights

  • Model of dopamine modulation of pyramidal-interneuron weak gamma is constructed with multiple synchronous clusters.

  • Dopamine modulates cluster formation in the network decreasing cluster number and increasing/decreasing global coherence depending on the external stimulus (reward for example).

  • Spike frequency adaptation of pyramidal neurons is key to cluster formation of the weak gamma and its modulation.

  • Hysteresis in number of clusters is identified under dopaminergic modulation.

Abstract

Gamma rhythm (20–100 Hz) plays a key role in numerous cognitive tasks: working memory, sensory processing and in routing of information across neural circuits. In comparison with lower frequency oscillations in the brain, gamma-rhythm associated firing of the individual neurons is sparse and the activity is locally distributed in the cortex. Such “weak” gamma rhythm results from synchronous firing of pyramidal neurons in an interplay with the local inhibitory interneurons in a "pyramidal-interneuron gamma" or PING. Experimental evidence shows that individual pyramidal neurons during such oscillations tend to fire at rates below gamma, with the population showing clear gamma oscillations and synchrony. One possible way to describe such features is that this gamma oscillation is generated within local synchronous neuronal clusters. The number of such synchronous clusters defines the overall coherence of the rhythm and its spatial structure. The number of clusters in turn depends on the properties of the synaptic coupling and the intrinsic properties of the constituent neurons. We previously showed that a slow spike frequency adaptation current in the pyramidal neurons can effectively control cluster numbers. These slow adaptation currents are modulated by endogenous brain neuromodulators such as dopamine, whose level is in turn related to cognitive task requirements. Hence we postulate that dopaminergic modulation can effectively control the clustering of weak gamma and its coherence. In this paper we study how dopaminergic modulation of the network and cell properties impacts the cluster formation process in a PING network model.

Introduction

Gamma rhythm (20–100 Hz) is ubiquitous in the cortex and plays a key role in numerous cognitive tasks [1]: short-term memory formation, sensory processing and routing of information across neural circuits [2]. Gamma oscillations have also been implicated in navigational coding and attentional modulation of cognitive constructs [3]. Several lines of evidence indicate that gamma oscillations in the cortex are locally generated [4], yet may have a non-trivial structure with emergent coherence of local oscillatory populations across multiple cortical areas [5] and with non-trivial phase relationships [6]. One way we may conceptualize this structure is as the emergence of multiple internally synchronized clusters of gamma oscillations. How such a spatially clustered structure may emerge from the interactions of the intrinsic cellular properties and the synaptic connectivity is one of the key computational questions is cortical neuroscience. How the structure of gamma oscillations may be affected by the endogenous neuromodulators of the central nervous system is also a question of significant interest.

In general, one can split gamma oscillations into two types: “strong” gamma, where both interneuron and pyramidal neurons fire on every cycle of the global oscillation, and “weak” gamma, where the interneurons fire coherently on each cycle, but the excitatory pyramidal cells skip across cycles. In this work we consider the weak gamma regime such that the frequency of the pyramidal cells is much below than the interneurons frequency and the frequency of the population gamma rhythm. Spatial organization of the weak gamma is also a question of interest that has not been completely resolved. Gamma rhythm that is observed in the cortex is generated by local interacting populations of excitatory pyramidal (PY) cells and inhibitory interneurons (IN) [7]. This is the so-called Pyramidal Interneuron Gamma (PING) mechanism [8]. Typically, it is not a global gamma rhythm – in comparison with other (lower frequency) oscillations the PING rhythm is sparse and locally distributed in the cortex [9]. One of the possibilities to describe gamma organization is to suggest that PING is generated within local synchronous neuronal clusters [10,11]. Such patterns of clusters are dependent on the intrinsic properties of the constituent neurons (e.g., spike frequency adaptation) as well as the synaptic coupling parameters and this may be returned by processes in the cortex that affect these properties.

PING oscillations have previously received significant attention as a mathematical object. For example, classical work of Kopell and Borgers analyzed the stability of synchronized gamma and, using the method of rivers, showed that inhibition effectively synchronizes the sparse pyramidal activity [12]. They showed that for the homogeneous network parameters and all-to-all connectivity, a perfect synchronization takes place. Moreover, an imperfect synchronization is possible even for the case of sparse and random connectivity. The crucial quantity to ensure this synchronization was the number of inputs per cell. Kilpatrick and Ermentrout [11] constructed a biophysical model of the weak gamma where excitatory neurons form several clusters that fire every few cycles of the fast oscillations of inhibitory neurons. Using singular perturbation theory, they studied scaling of cluster number with respect to the adaptation time constant. They found that essential properties for the formation of clusters are a sufficiently slow spike frequency adaptation and sufficiently strong feedback inhibition. In particular, the number of clusters increases with the time constant of adaptation. Time-dependent neuromodulatory influences on the process of cluster formation have not been studied yet.

We hypothesize that action of endogenous brain neuromodulators such as dopamine, acetylcholine and adrenaline maybe key to tuning the number of clusters in a weak gamma network and hence, to the global coherence of the gamma rhythm as well as its spatial organization. It has been previously shown semi-analytically [10] that spike frequency adaptation of the pyramidal neurons is a key determinant of cluster formation. This adaptation is the result of slow hyperpolarizing potassium currents. It is known that dopamine (DA) modulates adaptation of the PY cells by partially inactivating the slow K-currents and hence reducing the adaptation [13]. From a mathematical point of view, such modulation changes the shape of the phase-response curves for the PY cells, e.g., decreasing the skew induced by the adaptation and in some cases even changing the type of the PRC form class II to class I (from biphasic PRCs to monophasic). Dynamically speaking, this change is a result of a transition in the spike generating dynamics fromm those associated with a Hopf bifurcation to those associated, for example, with a saddle-node on an invariant cycle bifurcation (SNIC). Previously such mechanisms have been linked with the modulation of stable synchrony in networks of spiking neurons (e.g., see [14]).

Furthermore, data show that dopamine modulates synaptic connections between the neurons [15,16]. Dopamine can both increase the recurrent excitation in the network and increase the recurrent inhibition. Thereby dopaminergic modulation alters both the intrinsic properties of the constituent cells in the network as well as the coupling between them. A clear question is then, what are the network consequences of such modulation, and more specifically for this work, how changing levels of dopamine impact the formation of clusters in a weak PING rhythm? We should also add that dopamine levels in the cortex can change rapidly in response to behaviorally relevant events. For example, cognitive effort is known to modulate the overall tonic levels of dopamine in the cortex [17], while delivery of unexpected rewards and/or appearance of sensory stimuli predictive of rewards evoke fast phasic dopamine transients.

In [10] it was shown that shunting inhibition and adaptation determine the maximal number of synchronous clusters in PING networks. Interestingly, for the weak gamma, where the rhythm is formed by the alternately firing PY-cell clusters, changes in their number also entrains changes of the frequency, power and synchronization level of the gamma rhythm as a whole. In this paper we set out to understand how dynamic variation in dopamine levels controls the formation of multiple clusters in an oscillatory network and, in turn, controls the power of the gamma and its coherence. In the first part of the paper we consider the network model reproducing the PING mechanism of the gamma rhythm generation which was suggested in [10] and clarify modifications we have made. We introduce a minimal model of the positive and negative DA modulations of the two control parameters of the PING network model: the spike frequency adaptation of the PY cells and the strength of the inhibitory synapses located on them. Then we describe the results of such modulation and show how the cluster structure depends on these parameters and amplitude of the modulation. Finally, we discuss the obtained results.

Section snippets

The model

As a basis for the model of clustered gamma we took the weak PING network previously analyzed by Krupa et al. in [10].

Results

As we indicated above, DA levels modulate the AHP current strength as well as the synaptic coupling strengths, notably the inhibitory synapses impinging on the excitatory cells. Here we will profile the effects of these modulations in turn. Let us consider a PING network with a basal level of DA that exhibits 3 clusters in the population of pyramidal cells (as in [10]). We see in Fig. 1 that the PY cells from different clusters firing alternately in accordance with the spike-times of the

Discussion

In this paper we extend the analysis of clustered gamma with adapation from [10] to include dynamic modulation of the spike-frequency adaptation and of the GABAergic inhibition. We examine numerically the sensitivity of the cluster number to the AHP and inhibition modulation and find that clusters are most sensitive to the former. Our results thus imply that changes in the network structure of gamma (via cluster formation) is most sensitive to the changes in the intrinsic properties of the

Acknowledgements

This work was prepared within the framework of the HSE University Basic Research Program and funded by the Russian Academic Excellence Project '5-100′.

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