A prefrontal network model operating near steady and oscillatory states links spike desynchronization and synaptic deficits in schizophrenia

  1. David A Crowe
  2. Andrew Willow
  3. Rachael K Blackman
  4. Adele L DeNicola
  5. Matthew V Chafee
  6. Bagrat Amirikian

  • Curated by eLife

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    This manuscript reports important new results, but it provides incomplete support for its claims. Recent data has shown that schizophrenia-related synaptic alterations induce changes in neural network synchrony, and this manuscript provides the first theoretical understanding of the underlying network mechanisms. Proper support for this result, however, requires a tighter link between the computational model and the experimental data and a more in-depth understanding of the model mechanisms.

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Abstract

Schizophrenia results in part from a failure of prefrontal networks but we lack full understanding of how disruptions at a synaptic level cause failures at the network level. This is a crucial gap in our understanding because it prevents us from discovering how genetic mutations and environmental risks that alter synaptic function cause prefrontal network to fail in schizophrenia. To address that question, we developed a recurrent spiking network model of prefrontal local circuits that can explain the link between NMDAR synaptic and 0-lag spike synchrony deficits we recently observed in a pharmacological monkey model of prefrontal network failure in schizophrenia. We analyze how the balance between AMPA and NMDA components of recurrent excitation and GABA inhibition in the network influence oscillatory spike synchrony to inform the biological data. We show that reducing recurrent NMDAR synaptic currents prevents the network from shifting from a steady to oscillatory state in response to extrinsic inputs such as might occur during behavior. These findings strongly parallel dynamic modulation of 0-lag spike synchrony we observed between neurons in monkey prefrontal cortex during behavior, as well as the suppression of this 0-lag spiking by administration of NMDAR antagonists. As such, our cortical network model provides a plausible mechanism explaining the link between NMDAR synaptic and 0-lag spike synchrony deficits observed in a pharmacological monkey model of prefrontal network failure in schizophrenia.

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  1. Version published to 10.7554/elife.79352 on eLife
  2. eLife

    Author Response

    Reviewer #1 (Public Review):

    In this manuscript, the authors investigated plausible circuit mechanisms for their recently reported effect of NMDAR antagonists on the synchrony of prefrontal neurons in a cognitive task. On the basis of previously proposed computational network models of spiking excitatory and inhibitory neurons and their mean-field and linear stability analysis descriptions, they show that a specific network configuration set close to the onset of instability of the asynchronous state can replicate qualitatively key empirical observations. For such a network, a small increase in external drive causes a large increase in neuronal synchrony, and this is not happening if NMDAR-dependent transmission is reduced. This shows parallelism with the empirical data thus representing its first neural network explanation.

    The paper provides valuable insights into possible mechanisms related to cortical dysfunction under NMDAR hypofunction, a topic of importance for several neuropsychiatric disorders. However, the fact that the manuscript remains at a rather abstract level and does not attempt a closer match to the experimental data is a limitation of the study.

    1. The manuscript is strongly based on state diagrams and parametric descriptions of neural dynamics in a computational model that has been extensively studied before (Brunel, Wang 2003). Many of the parametric dependencies of this model shown here were already reported before, although not specifically altering concurrently external inputs and NMDAR-dependent transmission as done now. The main novelty of the study is the application of this framework to a specific empirical dataset of great scientific relevance. However, the manuscript emphasizes the model exploration in relation to a limited set of effects in the data (changes in synchrony immediately before motor response) and not so much the comparison to the neural recordings more generally (for instance, firing rates, other time periods in the task, etc.)

    We are grateful to the Reviewer for thoroughly reviewing the manuscript and the constructive critique. Our work is built on the computational framework that has been developed earlier in several seminal computational and theoretical studies, including Compte et al. (2000) and Brunel and Wang (2003), that we acknowledge throughout our paper. However, we would like to emphasize, without diminishing the importance of these earlier studies, that our work provides new theoretical and computational insights on the impact of NMDAR synaptic transmission modulation on spiking dynamics by further developing the theoretical framework of Brunel and Wang (2003). For example, in Brunel and Wang (2003) it is stated that “NMDA conductances could be removed from all simulations without affecting any of the results” (p. 416). In fact, equations provided in Brunel and Wang (2003) are only for the special case of the oscillatory instability growth rate λ=0 and they do not include the NMDAR synaptic conductances. Thus, the consideration presented in Brunel and Wang (2003) cannot explain the NMDAR-dependent modulation of synchrony effect observed in Zick et al. (2018). In our study, we extended the theoretical framework of Brunel and Wang (2003) and provided equations that explicitly include both λ and NMDAR conductance. It is this extension of the framework that allowed us to provide an NMDAR dependent mechanism to explain the Zick et al. (2018) effect.

    In the revised manuscript, by suggestion of Reviewer 2, we have further extended theoretical consideration and obtained an analytic approximation in closed form for the oscillatory instability growth rate λ describing the dependence on the AMAPR, NMDAR, GABAR synaptic conductances and external rate. We believe that this is the first paper in which such approximation for the instability growth rate λ accounting for the effects of more realistic synaptic currents is obtained. Based on this consideration, we have now provided in a new Results section “Dependence of oscillatory instability growth rate on synaptic parameters” a substantially more detailed theoretical account of the precise mechanism implemented in our model for the transition between the steady and oscillatory states and the lack thereof when the NMDAR conductance is blocked.

    We agree with the reviewer that it would be beneficial for the paper to extend the model exploration in relation to other measurable variables provided by neural data such us firing rates. At the reviewers’ suggestions we have now carried out new series of simulations with transient external inputs and compared the simulation results with the dynamics of both synchrony and firing rates that were estimated from neural data. We address these questions in more detail in the corresponding points in the Recommendations for the authors section below.

    1. As discussed in the introduction, empirical data available suggests that 0-lag synchrony in prefrontal networks is affected by manipulations that reduce NMDAR function (Zick et al. 2018) and by manipulations that enhance NMDAR function (Zick et al. 2021). The computational model presented in this manuscript does not show this U-shaped behavior and the discussion does not mention this. It should be discussed whether the model can accommodate this or not.

    This is a very good point which we now explicitly address in a new section in the revised Discussion (‘Potential U-shaped relation between NMDAR function and spike synchrony’, see new text in blue starting at line 953). The reviewer provides an excellent insight by noting that that our prior neural recording data (specifically convergent reduction in 0-lag synchrony in monkey drug and mouse genetic models) could be explained by an inverted U-shaped relationship between NMDAR function and 0-lag synchrony. In the new section we also note the precedent for such a relationship by drawing a parallel to the work of Vijayraghavan, Arnsten and colleagues (2007) showing an inverted U-shaped relationship between D1R synaptic actions and the strength of persistent activity in monkey prefrontal neurons during working memory tasks.

    However, in the new section we note also that we cannot yet conclude that the relationship between 0-lag spike synchrony and NMDAR activation is indeed an inverted U-shaped function based on our neural data. Reaching this conclusion would require completing a dose-response function between the concentration of NMDAR agonist (or antagonist) administered and the strength of 0-lag synchrony (which we have not done). In addition, we note in the new section that we can’t conclude the reduction of 0-lag synchrony in mouse prefrontal cortex is indeed due to increased expression of NMDAR, since deletion of Dgcr8, given its role in miRNA synthesis, would be expected to upregulate the expression of many different mRNA corresponding to many different genes. However, the possibility of a U-shaped relation is an important and interesting one, which we now fully discuss.

    Reviewer #2 (Public Review):

    In this paper, the authors carry out neural circuit modeling to theoretically elucidate the mechanism underlying the empirically observed (in a previous study by some of the current authors) reduction in neural synchrony in the monkey prefrontal cortex (PFC), as a result of NMDAR blockade. Empirically it was previously found that in monkeys performing a cognitive control task, PFC neurons exhibit precisely timed synchronous firing, especially in the short period before the monkey's response, leading to "0-lag" (zero in the 1-2 millisecond timescale) spiking correlations. This signature of synchrony was then found to be extinguished or diminished with the systemic administration of an NMDAR antagonist.

    In the current study, the authors simulate and analyze a network of excitatory and inhibitory spiking neurons as a model of a local PFC circuit, to elucidate the mechanism underlying this effect. The model network is composed of leaky integrate-and-fire neurons with conductance-based synaptic inputs and is sparsely and randomly connected as in the classic studies of balanced networks in which neurons fire irregularly as observed in the cortex. Using mean-field theory, the authors start by mapping out the phase boundary between the asynchronous irregular and synchronous irregular states in the network as a function of network parameters controlling synaptic connectivity and external background inputs (which they parametrize as ratios of recurrent or external currents mediated by AMPAR, NMDAR or GABAA). The transition between the two phases corresponds to a Hopf-like bifurcation above which synchronous oscillations with frequency in the gamma-band (or above) emerge. It is found that with an increase in external inputs, a network in the asynchronous state (but close to criticality) can switch to the synchronous state. Based on this, the authors hypothesize that an increase in the external drive is the mechanism underlying the empirically observed increase in synchrony before the behavioral response. It is then shown that a reduction in NMDAR conductance (keeping AMPAR or GABAR conductances fixed) has the opposite effect, and pushes the network towards the asynchronous state, and can counteract or weaken the effect of increased external input. In both cases increase or decrease in synchrony is quantified by an increase or decrease in 0-lag pairwise correlations; transition to synchrony is shown to also lead to the development of nonzero-lag peaks in the average spiking correlation reflecting gamma-band oscillations. The authors then show that (with the appropriate choice of primary network parameters) their proposed mechanisms for the (natural) increase in synchrony via an increase in external inputs and the weakening of this effect with the weakening of NMDA conductances do semi-quantitatively match the observed changes in 0-lag synchrony and nonzero lag peaks in spiking correlations. Finally, they discuss the effect of the balance between average NMDA and GABA currents in the primary (baseline) network on the above effects.

    Strengths:

    • The modeling and analysis are solid and overall this work succeeds in providing a convincing mechanistic explanation for the specific empirically observed effects in monkey PFC: the natural task-dependent modulation of 0-lag synchrony and its extinction with NMDA blockage.
    • The manuscript is very readable and the figures and plots are clearly described.
    • The mathematical mean-field analysis in the Methods section is also sound and well written and does/can (see below) provide a sufficient mathematical explanation of the simulation results.

    We appreciate the positive comments.

    Weaknesses:

    1. I found the intuitive explanation of the effects of external input or NMDAR conductance on synchrony incomplete. While simulations and mean-field analysis both predict this effect, the mean-field theory and the linearization analysis and stability analysis can be used to further shed light on the precise mechanism by which external input and NMDAR conductance promote synchrony (or destabilization of the asynchronous state).
    1. An important natural question (which is relevant to the connection with schizophrenia) is what are the distinct roles of AMPAR-based and NMDAR-based excitation on the transition to synchrony, and this is not addressed in this study. It would be important to clarify what is special/distinct about NMDAR in the current findings.
    1. In the Introduction and Discussion, the authors speculate on the possible connection between their empirical and theoretical findings (on the effect of NMDAR hypofunction on synchronous spiking) and the pathogenesis of schizophrenia. While this is not central to the findings of the paper, because it is relevant to the broader significance and impact of this work I will note the following. Their proposed specific link to pathogenesis is as follows: the reduction in precisely timed synchrony resulting from NMDAR hypofunction can disrupt spike-timing dependent plasticity (STDP) and lead to "disconnection" of cortical circuits as observed in schizophrenia. Letting aside the fact that observations in schizophrenia relate to functional connectivity and not synaptic connectivity, previous theoretical studies of STDP in spiking networks do not support the claim that lack of synchronous activity would lead to disconnection of the circuit.

    Thank you for the thorough review and critique, bringing up these important issues. We address them in detail in the corresponding points in the Recommendations for the authors section below.

    Reviewer #3 (Public Review):

    The starting point of the paper is the observation by the group of Matthew Chafee that zero-lag correlations in pairs of prefrontal cortex neurons transiently increase close to the motor response in a dot-pattern expectancy task', and that this increase in synchrony is abolished by NMDA blockers. The goal of this paper is to understand the mechanisms of this NMDA-dependent increase in synchrony using computational modeling. They simulate and analyze a network of sparsely connected spiking neurons in which synaptic interactions are mediated by AMPA, NMDA, and GABA conductances with realistic time constants. In this network, it had been shown previously that when parameters are such that the network is close to a bifurcation separating asynchronous from synchronous oscillatory states, an increase in external inputs can push the network towards synchrony. They show that when the NMDA component of synaptic inputs is removed, the network moves away from the bifurcation, and thus the same increase in external inputs no longer leads to a significant increase in synchronization.

    Thus, this study provides a potential explanation for the NMDA-dependent increase of synchrony observed in their data. The authors further argue that this effect might be responsible for symptoms observed in schizophrenia, through spike-timing-dependent mechanisms. Overall, this is an interesting study, but there are several weaknesses that dampened my initial enthusiasm: In particular, the model predicts a tight link between synchrony and mean firing rate that should hold during the whole task, not only at the time of the motor response but this is not explored by the authors.

    Thank you for critically reviewing the manuscript and valuable comments. We address them in the corresponding points in the Recommendations for the authors section below.

    Also, the relationship between changes in synchrony due to NMDAR dysfunction and schizophrenia is not very convincing. Many forms of synaptic plasticity, including STDP are dependent on NMDA receptors, and thus synaptic plasticity in schizophrenic patients is likely to be impacted independently of any synchrony. Thus, the link between the results of this paper and schizophrenia seems tenuous.

    These are good points. To address them we have limited the link between the current study and schizophrenia in the Introduction to the motivation for the original neurophysiological experiments (as this link dictated the pharmacological and genetic manipulations we employed in the animal models). We have also added a new section to the Discussion with the heading ‘Spike timing disruptions and rewiring of prefrontal local circuits via STDP’ where we discuss the complexity of the interaction between STDP, synchrony, and connectivity in prior modeling studies. Namely, it is difficult to predict whether loss of synchronous spiking would cause disconnection via STDP without additional data. We acknowledge this constraint on our original hypothesis that asynchrony would cause disconnection considering these prior theoretical studies in this new section. In this section, we also note that altered NMDAR function that has been implicated in schizophrenia could impact STDP directly independently of any change in spike synchrony (see new blue text, starting at line 950) as suggested.

  3. eLife

    eLife assessment

    This manuscript reports important new results, but it provides incomplete support for its claims. Recent data has shown that schizophrenia-related synaptic alterations induce changes in neural network synchrony, and this manuscript provides the first theoretical understanding of the underlying network mechanisms. Proper support for this result, however, requires a tighter link between the computational model and the experimental data and a more in-depth understanding of the model mechanisms.

  4. eLife

    Reviewer #1 (Public Review):

    In this manuscript, the authors investigated plausible circuit mechanisms for their recently reported effect of NMDAR antagonists on the synchrony of prefrontal neurons in a cognitive task. On the basis of previously proposed computational network models of spiking excitatory and inhibitory neurons and their mean-field and linear stability analysis descriptions, they show that a specific network configuration set close to the onset of instability of the asynchronous state can replicate qualitatively key empirical observations. For such a network, a small increase in external drive causes a large increase in neuronal synchrony, and this is not happening if NMDAR-dependent transmission is reduced. This shows parallelism with the empirical data thus representing its first neural network explanation.

    The paper provides valuable insights into possible mechanisms related to cortical dysfunction under NMDAR hypofunction, a topic of importance for several neuropsychiatric disorders. However, the fact that the manuscript remains at a rather abstract level and does not attempt a closer match to the experimental data is a limitation of the study.

    1. The manuscript is strongly based on state diagrams and parametric descriptions of neural dynamics in a computational model that has been extensively studied before (Brunel, Wang 2003). Many of the parametric dependencies of this model shown here were already reported before, although not specifically altering concurrently external inputs and NMDAR-dependent transmission as done now. The main novelty of the study is the application of this framework to a specific empirical dataset of great scientific relevance. However, the manuscript emphasizes the model exploration in relation to a limited set of effects in the data (changes in synchrony immediately before motor response) and not so much the comparison to the neural recordings more generally (for instance, firing rates, other time periods in the task, etc.)

    2. As discussed in the introduction, empirical data available suggests that 0-lag synchrony in prefrontal networks is affected by manipulations that reduce NMDAR function (Zick et al. 2018) and by manipulations that enhance NMDAR function (Zick et al. 2021). The computational model presented in this manuscript does not show this U-shaped behavior and the discussion does not mention this. It should be discussed whether the model can accommodate this or not.

  5. eLife

    Reviewer #2 (Public Review):

    In this paper, the authors carry out neural circuit modeling to theoretically elucidate the mechanism underlying the empirically observed (in a previous study by some of the current authors) reduction in neural synchrony in the monkey prefrontal cortex (PFC), as a result of NMDAR blockade. Empirically it was previously found that in monkeys performing a cognitive control task, PFC neurons exhibit precisely timed synchronous firing, especially in the short period before the monkey's response, leading to "0-lag" (zero in the 1-2 millisecond timescale) spiking correlations. This signature of synchrony was then found to be extinguished or diminished with the systemic administration of an NMDAR antagonist.

    In the current study, the authors simulate and analyze a network of excitatory and inhibitory spiking neurons as a model of a local PFC circuit, to elucidate the mechanism underlying this effect. The model network is composed of leaky integrate-and-fire neurons with conductance-based synaptic inputs and is sparsely and randomly connected as in the classic studies of balanced networks in which neurons fire irregularly as observed in the cortex. Using mean-field theory, the authors start by mapping out the phase boundary between the asynchronous irregular and synchronous irregular states in the network as a function of network parameters controlling synaptic connectivity and external background inputs (which they parametrize as ratios of recurrent or external currents mediated by AMPAR, NMDAR or GABAA). The transition between the two phases corresponds to a Hopf-like bifurcation above which synchronous oscillations with frequency in the gamma-band (or above) emerge. It is found that with an increase in external inputs, a network in the asynchronous state (but close to criticality) can switch to the synchronous state. Based on this, the authors hypothesize that an increase in the external drive is the mechanism underlying the empirically observed increase in synchrony before the behavioral response. It is then shown that a reduction in NMDAR conductance (keeping AMPAR or GABAR conductances fixed) has the opposite effect, and pushes the network towards the asynchronous state, and can counteract or weaken the effect of increased external input. In both cases increase or decrease in synchrony is quantified by an increase or decrease in 0-lag pairwise correlations; transition to synchrony is shown to also lead to the development of nonzero-lag peaks in the average spiking correlation reflecting gamma-band oscillations. The authors then show that (with the appropriate choice of primary network parameters) their proposed mechanisms for the (natural) increase in synchrony via an increase in external inputs and the weakening of this effect with the weakening of NMDA conductances do semi-quantitatively match the observed changes in 0-lag synchrony and nonzero lag peaks in spiking correlations. Finally, they discuss the effect of the balance between average NMDA and GABA currents in the primary (baseline) network on the above effects.

    Strengths:
    - The modeling and analysis are solid and overall this work succeeds in providing a convincing mechanistic explanation for the specific empirically observed effects in monkey PFC: the natural task-dependent modulation of 0-lag synchrony and its extinction with NMDA blockage.

    - The manuscript is very readable and the figures and plots are clearly described.

    - The mathematical mean-field analysis in the Methods section is also sound and well written and does/can (see below) provide a sufficient mathematical explanation of the simulation results.

    Weaknesses:

    1. I found the intuitive explanation of the effects of external input or NMDAR conductance on synchrony incomplete. While simulations and mean-field analysis both predict this effect, the mean-field theory and the linearization analysis and stability analysis can be used to further shed light on the precise mechanism by which external input and NMDAR conductance promote synchrony (or destabilization of the asynchronous state).

    2. An important natural question (which is relevant to the connection with schizophrenia) is what are the distinct roles of AMPAR-based and NMDAR-based excitation on the transition to synchrony, and this is not addressed in this study. It would be important to clarify what is special/distinct about NMDAR in the current findings.

    3. In the Introduction and Discussion, the authors speculate on the possible connection between their empirical and theoretical findings (on the effect of NMDAR hypofunction on synchronous spiking) and the pathogenesis of schizophrenia. While this is not central to the findings of the paper, because it is relevant to the broader significance and impact of this work I will note the following. Their proposed specific link to pathogenesis is as follows: the reduction in precisely timed synchrony resulting from NMDAR hypofunction can disrupt spike-timing dependent plasticity (STDP) and lead to "disconnection" of cortical circuits as observed in schizophrenia. Letting aside the fact that observations in schizophrenia relate to functional connectivity and not synaptic connectivity, previous theoretical studies of STDP in spiking networks do not support the claim that lack of synchronous activity would lead to disconnection of the circuit.

  6. eLife

    Reviewer #3 (Public Review):

    The starting point of the paper is the observation by the group of Matthew Chafee that zero-lag correlations in pairs of prefrontal cortex neurons transiently increase close to the motor response in a dot-pattern expectancy task', and that this increase in synchrony is abolished by NMDA blockers. The goal of this paper is to understand the mechanisms of this NMDA-dependent increase in synchrony using computational modeling. They simulate and analyze a network of sparsely connected spiking neurons in which synaptic interactions are mediated by AMPA, NMDA, and GABA conductances with realistic time constants. In this network, it had been shown previously that when parameters are such that the network is close to a bifurcation separating asynchronous from synchronous oscillatory states, an
    increase in external inputs can push the network towards synchrony. They show that when the NMDA component of synaptic inputs is removed, the network moves away from the bifurcation, and thus the same increase in external inputs no longer leads to a significant increase in synchronization.

    Thus, this study provides a potential explanation for the NMDA-dependent increase of synchrony observed in their data. The authors further argue that this effect might be responsible for symptoms observed in schizophrenia, through spike-timing-dependent mechanisms. Overall, this is an interesting study, but there are
    several weaknesses that dampened my initial enthusiasm: In particular, the model predicts a tight link between synchrony and mean firing rate that should hold during the whole task, not only at the time of the motor response but this is not explored by the authors.

    Also, the relationship between changes in synchrony due to NMDAR dysfunction and schizophrenia is not very convincing. Many forms of synaptic plasticity, including STDP are dependent on NMDA receptors, and thus synaptic plasticity in schizophrenic patients is likely to be impacted independently of any synchrony. Thus, the link between the results of this paper and schizophrenia seems tenuous.

  7. Version published to 10.1101/2022.06.10.495666v1 on bioRxiv