Elsevier

Neural Networks

Volume 19, Issue 8, October 2006, Pages 1137-1152
Neural Networks

2006 Special Issue
The role of short-term depression in sustained neural activity in the prefrontal cortex: A simulation study

https://doi.org/10.1016/j.neunet.2006.05.041Get rights and content

Abstract

Recent experimental researches have suggested that sustained neural activity in the prefrontal cortex is a process of memory retention in decision making. Previous theoretical studies indicate that a balance between recurrent excitation and feedback inhibition is important for sustaining the activity. To investigate a plausible balancing mechanism, we simulated a biophysically realistic network model. Our model shows that short-term depression (STD) enables the network to sustain its activity despite the presence of long-term inhibition by GABAB receptors and that the sustained firing rates have a bell-shaped dependence on the degree of STD. By analyzing the neural network dynamics, we show that the bell-shaped dependence on STD is formed by destabilizing the balance with either excessive or insufficient STD. We also show that the optimal degree of STD has a linear relationship with the neural network size. These results suggest that STD provides a balancing mechanism and controls levels of sustained activities of various size networks.

Introduction

Fundamental functions of decision making are retention and selection of memory. The neural mechanisms underlying memory retention have been investigated experimentally by using delayed response tasks that require memory-guided motor responses (Funahashi et al., 1989, Funahashi et al., 1993, Fuster and Alexander, 1971, Kubota and Niki, 1971, Sawaguchi and Yamane, 1999). During a delayed response task, the neurons in the prefrontal cortex (PFC) of a monkey showed mnemonic and sustained activity throughout a delay period that followed a cue period. Drug-induced modulations of the sustained activity could partially control the memory-guided movements (Arnsten et al., 1994, Iba and Sawaguchi, 2003, Sawaguchi, 2000, Sawaguchi and Goldman-Rakic, 1991, Sawaguchi et al., 1989, Wang et al., 2004, Williams and Goldman-Rakic, 1995). Thus, this sustained activity has been thought to be the process by which information is retained. Therefore, to reveal the neural basis of memory retention, considerable theoretical and experimental effort has been directed at the mechanisms that realize the sustained activity (Durstewitz and Seamans, 2002, Goldman-Rakic, 1995, Sawaguchi, 1996, Wang, 2001).

Theoretical studies have suggested that bistable responses of a neural assembly to a transient stimulation in the cue period are essential for the sustained activity in the delay period (Amit and Brunel, 1997, Durstewitz et al., 2000, Wang, 1999). This bistability is achieved by “recurrent excitation” among excitatory neurons. The recurrent excitatory connections were detected experimentally in layer 3 of the PFC by staining and electrophysiological techniques (Gonzalez-Burgos et al., 2000, Kritzer and Goldman-Rakic, 1995, Levitt et al., 1993). It is clear that inhibitory connections to excitatory neurons exist and inhibitory neurons are activated by excitatory ones. This indicates that the inhibitory connections generate feedback stimuli for excitatory neurons because the activity of excitatory neurons is transformed into inhibitory stimuli. Such a “feedback inhibition” may interrupt the sustained activity of the excitatory neurons. Therefore, it is necessary to investigate a balancing mechanism between recurrent excitation and feedback inhibition. From the viewpoint of synaptic properties, Wang suggested that NMDA receptors are important for sustaining the activity because NMDA receptors have a longer decay time constant (80 ms) than GABAA receptors (10 ms) (Wang, 1999, Wang, 2001). NMDA receptors, however, may not be sufficient to sustain the neural activity in the presence of GABAB receptors, which are the major metabotropic receptors in the PFC and have a longer decay time constant (more than 100 ms) than NMDA receptors (Destexhe et al., 1998, Karlsson and Olpe, 1989, Otis et al., 1993, Seamans, Gorelova et al., 2001). Inhibitory currents, whose decay time constant is longer than that of excitatory ones, are known to terminate the sustained activity (Tegner, Compte, & Wang, 2002). Although it has been suggested that Hebbian learning such as spike-timing-dependent plasticity can self-organize the network connectivity to produce the sustained activity (Abbott and Nelson, 2000, Amit and Brunel, 1997, Kitano et al., 2002, Mongillo et al., 2003), these models lacked GABAB receptors, whose long decay time constant cannot be ignored when considering the mechanisms of the sustained activity.

As the balancing mechanism, we focus on short-term depression (STD), which is a common feature of PFC neurons to reduce synaptic transmission efficacy when presynaptic neurons are generating repetitive spikes (Gao et al., 2001, Seamans, Durstewitz et al., 2001). Although STD strongly influences neural activity (Abbott et al., 1997, Tsodyks and Markram, 1997, Tsodyks et al., 2000), there is little information on its roles in sustained activity. Wang suggested that STD of excitatory neurons in the PFC could regulate the strength of recurrent excitation, but the model did not include inhibitory feedback connections (Wang, 1999).

In this study, we constructed a neural network model that employed STD dynamics and neurons containing Hodgkin–Huxley-type ion channels, as well as AMPA, NMDA, GABAA, and GABAB receptors. Through simulations using this model, we examined the effects of STD of excitatory neurons on the mutual interactions between excitatory and inhibitory neurons. First, our model produced sustained neural activity with firing rates that had a bell-shaped dependence on the degree (vesicle recovery time constant) of STD, suggesting that moderate STD supports sustainability of the activity. Moreover, we show that as the network size increases, a stronger STD is required to produce the sustained activity. Second, we use rate-clamp analysis to clarify the dynamic characteristics of the activated network. The rate-clamp analysis shows that STD regulates sustained firing rates by preserving the balance between recurrent excitation and feedback inhibition. Third, we quantify how STD changes the stability of the sustained activity in relation to a variable that is introduced from an eigenvalue analysis. The results from this analysis suggest that STD plays an essential role in stabilizing the sustained activity. Our results suggest that the role of STD is not only to allow the sustained activity to be achieved despite the long-term inhibition by GABAB receptors, but also to promote the stability of the sustained activity.

Finally, to include the discussion of decision making, we examined the contribution of STD and network size to a competition among multiple neural clusters, via the sustained activity by means of STD. We found that the strength of STD regulates the effects of the network size, with which the network sustains its activity, so that one of the competing clusters maintains activity and suppresses the other clusters. This suggests that STD may play a role in providing memory hierarchy in the memory selection process during decision making.

Section snippets

Network model

The model neural network (Fig. 1A) consists of excitatory (EPFC) and inhibitory (IPFC) neural assemblies in the PFC, and an excitatory (EPPC) neural assembly in the posterior parietal cortex (PPC). It was assumed that a pair of EPFC and IPFC assemblies corresponds to a cluster of neurons in layer 3, which is suggested to be the functional unit of sustained neural activity (Constantinidis et al., 2001, Constantinidis and Goldman-Rakic, 2002, Goldman-Rakic, 1995, Sawaguchi, 1994, Sawaguchi, 1996,

Discussion

We demonstrated that STD affected the sustained activity of PFC neurons after spike stimulations from PPC neurons were given (Fig. 3). To clarify how STD controls the sustained activity, we employed a rate-clamp analysis that derived the nullclines of the network dynamics (Fig. 6), and then quantified the attracting level of the attractors based on the eigenvalue analysis (Fig. 7A). The quantification of the attractor strength in the PFC network is a novel attempt to examine the dynamics of the

Acknowledgements

We would like to thank Dr. Masato Okada for valuable suggestions on STD dynamics. We also thank Tomokazu Doi, Yuki Tsukada, and Honda Naoki for their helpful comments on the manuscript. This work was supported by the 21st Century COE Program and Special Coordination Funds Promoting Science and Technology (both from the Japanese Ministry of Education, Culture, Sports, Science, and Technology).

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