Differential Excitatory-Inhibitory Balance within Dorsolateral Prefrontal Cortex Shapes Inter-network Interactions in Working Memory

doi:10.21203/rs.3.rs-5319088/v1

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Differential Excitatory-Inhibitory Balance within Dorsolateral Prefrontal Cortex Shapes Inter-network Interactions in Working Memory

https://doi.org/10.21203/rs.3.rs-5319088/v1

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Working memory involves complex activation of and interactions among multiple brain areas. However, little is known about how these large-scale activity and interaction patterns relate to resting state activity and originate from excitatory and inhibitory interactions. Here, we combine the analysis of fMRI activation, functional and structural connectivity with large-scale neural network modelling and molecular-enriched PET analysis to show how the excitatory and inhibitory neuronal activities within dorsolateral prefrontal cortex (DLPFC) relate to the inter-network interactions and activation patterns aroused by working memory tasks. Our results indicate that the activation and interaction of the frontoparietal and default-mode networks, which differ between resting state and working memory, depend on the level of DLPFC activity and on its functional and structural interactions with these networks. By perturbing a large-scale neural network model developed using resting-state fMRI and performing molecular-enriched analysis on both fMRI and PET images, we find evidence that a differential activation of excitatory and inhibitory vs neuron populations within DLPFC may ignite the transition from the resting state to working memory. Our study provides a mechanistic understanding of how regional DLPFC excitatory and inhibitory neural activity combines with functional and structural inter-area connections to support the large-scale network dynamics supporting working memory.

Biological sciences/Neuroscience/Computational neuroscience

Biological sciences/Neuroscience/Cognitive neuroscience

Working memory plays a fundamental role in information storage, manipulation, and processing. It involves the mnemonic delayed activity of multiple brain regions in the absence of external sensory stimuli (Funahashi et al., 1989; Fuster 1973; Hidehiko et al., 2019), and is believed to rely on interactions across large-scale brain networks (Guo et al., 2017; Sreenivasan et al., 2019; Wasmuht et al., 2017; Miller et al., 2018). Extensive evidence supports the involvement of the frontoparietal (FP) and default-mode (DM) networks in working memory (Wang et al., 2019; Anticevic et al., 2019; Murphy et al., 2020). These networks exhibit dynamic engagement and disengagement compared to the resting state, with greater engagement observed under higher cognitive load (Cornblath et al., 2020; Kelly et al., 2008; Anticevic et al., 2008). The FP network is crucial for processing external stimuli and executive function (Radek, 2012), while the DM network facilitates the integration of internal and external stimuli (Andrews-Hanna, 2012). Their anti-correlated activities and time-varying functional connectivity (FC) during working memory tasks suggest a potential competition (Kelly et al., 2008), and a dynamic inter-network interaction across the cortex. Individual performance in working memory tasks correlates with the level of sustained activation in these brain regions (Schicktanz et al., 2015; Rahmati et al., 2020) and the strength of functional interactions between areas within these brain networks (Bertolero et al., 2018; Keller et al., 2014).

Previous studies have suggested that the dynamics of the entire brain and the sustained activity observed in multiple brain regions during working memory have a structural basis and may be initiated by specific localized source areas (Cai et al., 2021). The FP network contributes to the functional connectivity patterns observed during working memory tasks, particularly under high cognitive load (Murphy et al., 2020). Network analysis methods applied to fMRI data have identified the anterior insula node and DLPFC node as potential source areas that drive different brain dynamics depending on the cognitive load (Cai et al., 2021). Recent studies (Cai et al., 2021; Mejías & Wang, 2022; Murray et al., 2020) have increasingly focused on the casual role of local areas in the large-scale interactions of brain networks. However, the mechanism underlying the differences in large-scale interactions between resting state and working memory is still not fully understood. Simulation studies using the structural connectivity of macaque brains have suggested that the areas within prefrontal cortex may serve as key driver of the whole-brain dynamics during working memory (Mejías & Wang, 2022). Despite this and other progress in understanding regional activity variations and large-scale interactions involved in working memory (Zou et al., 2013; Cornblath et al., 2020; Kelly et al., 2008; Anticevic et al., 2008), little is known about whether the multi-regional brain activation and large-scale interactions of working memory emerge simultaneously or are initiated by specific localized source areas, and about the possible mechanisms of working memory initiation.

Importantly, previous simulation studies (Robert& Terrence, 2021; Kyle et al., 2010; Lu et al., 2023) and experimental data (Murray et al., 2015; Xu et al., 2019; Giorgi et al., 2021; Woodcock et al., 2018; Yang et al., 2013; Rodermund et al., 2020) have suggested a differential activation of excitatory and inhibitory neuron populations involved in working memory. Other studies have additionally indicated the performance or the dynamics of working memory tasks may be modulated by spatially heterogeneous expressions of glutamatergic and GABAergic neurotransmitters (Parasuraman et al., 2005; Yoon et al., 2016; Woodcock et al., 2018; Tsubomoto et al., 2019, Ma et al., 2018). Although these results suggest that excitatory-inhibitory interactions are important for working memory, we still do not know whether excitatory-inhibitory interactions within a localized source area may be a mechanism for igniting the large-scale working memory brain dynamics.

In this study, we investigate whether the competition observed during working memory tasks is influenced by differentially activated excitatory and inhibitory neural populations within specific localized source areas. Specifically, we hypothesize that differences in activation between excitatory and inhibitory activity in the right and left dorsolateral prefrontal cortex (rDLPFC and lDLPFC) ignites the engagement and disengagement of FP and DM networks through structural linkages.

Our hypothesis is grounded in a substantial body of evidence from electrophysiological, neuroimaging, and simulation studies. Electrophysiological observations have shown sustained neuronal activity within the DLPFC during the maintenance context-specific information (Curtis & D'Esposito, 2003). Human neuroimaging studies consistently demonstrate the engagement of DLPFC during working memory tasks (Barch et al., 2013), and stimulation studies further emphasize its importance in working memory performance (Webler et al., 2022). Computational modelling constrained by anatomy data from macaque has suggested the DLPFC has the structural capacity to drive large-scale brain dynamics, providing testable prediction regarding its causal role in working memory (Mejías & Wang, 2022). Furthermore, deficits or damage to the DLPFC have been associated with reduced performance in working memory tasks (Barbey et al., 2013; Smucny et al., 2022). Therefore, it is reasonable to assume that DLPFC may be one of drivers of the internetwork dynamics underlying working memory.

To investigate our hypothesis, we leverage the fMRI and diffusion tensor imaging (DTI) data from 737 subjects obtained from Human Connectome Project and the PET images that reflect the receptor distributions of GABA-A and NMDA (Hansen et al., 2022). We first investigate the regional activity, interregional connectivity, and structural connectivity (SC) in both resting state and working memory tasks. By employing causal perturbation of a large-scale parametric mean-field model, we then elucidate the directed interactions between the DLPFC and the two brain networks that give rise to the observed activation pattern during working memory tasks, particularly focusing on the distinct roles played by the excitatory or inhibitory neural populations within each DLPFC area. Finally, we perform molecular-enriched analysis on both fMRI and PET images to further complement the results of the differentially activated excitatory or inhibitory neuron populations.

Overview. We focus on the mechanistic framework where neuron populations within DLPFC may shape the competition between frontoparietal and default-mode networks aroused by working memory (Fig. 1A). We first investigate the correlational relationships of the activation, function connectivity and structural connectivity of the four brain regions, i.e., DLPFC areas and the two networks. We investigate whether functional differences exist between resting state (RS) and working memory (WM), how the functional differences within DLPFC relate to functional differences between the two networks and whether these differences can be understood from structural connections (Fig. 1B). Then, we build a mean-field model based on resting state fMRI to investigate how changes in local balance between excitation and inhibition may ignite larger network dynamics. Namely, we perturb in simulations excitatory and inhibitory activity within the DLPFC (Fig. 1C), we test whether this local unbalance can trigger changes in activation and FC similar to the observed changes in activity and FC between resting state and WM observed in fMRI data. Finally, we perform molecular-enriched network analysis enabled by the density maps of GABA-A and NMDA receptors on DLPFC areas to test the intuition of the role of excitatory and inhibitory interactions gained with model perturbations.

The DLPFC plays a significant role in the activation and interactions observed within the frontoparietal and default-mode networks. We propose that the dynamics of DLPFC can explain the difference in the activation and function connectivity of the FP and DM networks between resting state and working memory tasks. We first used fMRI data to study how the activation and function connectivity of DLPFC correlate to those of the two networks. We employed the Desikan-Killiany anatomical parcellation (Desikan et al., 2006) with 68 cortical regions of interest (ROIs) and the Schaefer 100 parcellation (Schaefer et al., 2018) with 100 cortical ROIs. Analyses under different parcellations yield similar conclusions (see Supplemental Information).

We first examined how the activation of DLPFC, FP and DM differ between resting state and working memory. For each subject and region of interest, we computed the activation levels and the strengths of the function connectivity between all pairs of regions affiliated to DLPFC, FP or DM networks. To assess the statistical significance of the differences in these measures between working memory and resting state conditions, we employed a nonparametric permutation test (see “Methods”). To estimate the activation of each ROI, we employed two metrics: the fractional amplitude of low-frequency fluctuations (fALFF) and the amplitude of low-frequency fluctuations (ALFF) (see “Methods”). Consistent with previous studies (Rowe et al., 2000; Manoach et al., 1997), we found a significant increase in activation within both right and left DLPFC regions, a significant engagement of FP and disengagement of DM networks during working memory tasks compared with resting state (Fig. 2A). To examine the correlations between the activation of DLPFC and the two brain networks (FP and DM), we employed robust linear regression methods that are insensitive to outliers. Initially, we tested the correlation between the activity of left and right DLPFC and the activity of FP and DM. We averaged the fALFF and ALFF of the voxels within a ROI, calculated the difference of activation between resting state and working memory, concatenated across subjects and calculate the correlations by the robust linear regression. Variations in activation within both the left and right DLPFC areas were significantly correlated with the variations observed in the FP and DM networks (Fig. 2B). Moreover, when considering both the variations in the left and right DLPFC as predictors, we identify significant correlations with the variations in the FP and DM networks (Z scored, FP: r = 0.4656, p = 0.0004 for lDLPFC, r = 0.5346, p = 0.0001 for rDLPFC; DM: r = 0.6700, p < 0.00001 for lDLPFC, r = 0.3300, p = 0.0013 for rDLPFC). We next performed multivariable linear regression analyses. In these analyses, we treated the activation of both DLPFC areas as regressors and the activation of FP or DM as the dependent variable. Separate regressions were performed for both resting state and working memory conditions, respectively. We found that the activation of both DLPFC areas is significantly correlated with the activation of FP or DM, irrespective of whether it is during resting state or working memory (Z scored, RS,DM: r = 0.1831 p = 0.0343 for lDLPFC, r = 0.0246, p = 0.7806 for rDLPFC; RS, FP: r = -0.0278, p = 0.7702 for lDLPFC, r = 0.1216, p = 0.2181 for rDLPFC; WM, DM: r = 0.6607, p < 0.001 for lDLPFC, r = 0.3393, p < 0.001 for rDLPFC; WM, FP: r = 0.5212, p < 0.001 for lDLPFC, r = 0.4788, p < 0.001 for rDLPFC). The results on Schaefer 100 parcellation were similar (Supplementary Fig. 1). Consistent with our hypothesis, these findings indicate the activation pattern of DLPFC can account for the activation pattern of FP and DM networks, as well as their variations observed during working memory tasks. This supports the notion of a potential functional role of DLPFC in orchestrating the interactions and dynamics between these networks.

To assess how the functional activation of DLPFC may relate to FP and DM, we next conducted analyses on their function connectivity. The strength of the function connectivity (measured as Pearson correlation between the time series of two brain regions) between FP and DM decreased significantly when involved in working memory compared with resting state (Fig. 2C). Moreover, the strength of the function connectivity between the DLPFC and FP, as well as between the DLPFC and DM, significantly decreased during working memory compared with resting state condition (Fig. 2C). Given the right DLPFC is part of the frontoparietal network, we further examined whether the functional connectivity pattern differ between the rDLPFC and other FP areas. We excluded rDLPFC from FP network. We then calculated the strengths of function connectivity between rDLPFC and the brain regions within each network. Next, we averaged the strengths of the function connectivity across each network to obtain one value for each subject, representing the function connectivity between the rDLPFC and each network. Finally, we concatenated the averaged function connectivity across subjects for further analysis. The function connectivity between right DLPFC and either brain network presented asymmetrical correlations with the connection strengths of the two brain networks (r = 0.0041, p = 0.9403 for rDLPFC-FP & FP-DM, r = 0.3873, p < 0.001 for rDLPFC-DM & FP-DM). Multivariable linear regression using the connection strengths between the right DLPFC and the two networks as predictors showed a significant correlation is observed (Z scored, r = 0.8672, p < 0.0001 for rDLPFC-DM & FP-DM, r = 0.0345, p = 0.0643 for rDLPFC-FP & FP-DM). Similar observations were made for left DLPFC (Fig. 2C). Furthermore, the multivariable linear regression using both lDLPFC-FP and lDLPFC-DM as predictors reported a significant correlation (Z scored, r = 0.4711, p < 0.001 for lDLPFC-FP, r = 0.5066, p < 0.001 for lDLPFC-DM). These findings support the notion that the interactions between the DLPFC and the two networks can modulate the dynamic interactions between the networks, which exhibit different patterns during resting state and working memory.

We turned to assess the relationship between these patterns and task performance. We used the fMRI data during the 2-back working memory task of the HCP dataset (see “Methods”). We compared the strengths of function connectivity during error and success trials of the 2-back task. To assess the possible behavioral impact on the differences in function connectivity between the two networks, we then performed a regression of the difference of the strength of function connectivity between DLPFC regions and the two networks against the difference of the strength of function connectivity between the two networks between success and error trials. Remarkably, we find that the differences in the function connectivity between FP and DM is modulated by the difference of the function connectivity between DLPFC and either network (Fig. 2E), again suggesting a link between the pattern of function connectivity and the performance of the cognitive task. Similar results were observed in the Schaefer 100 (see Supplementary Fig. 1). To explore the potential impact of different calculation methods of functional activation, we performed the same analysis using the amplitude of low frequency fluctuation (ALFF) as the functional activation metric for both parcellations (Supplementary Figs. 2 and 3), finding results fully consistent with the above analyses. These findings support the idea that the DLPFC interacts with the FP and DM networks in a manner that influences cognitive task performance.

The structural role of the DLPFC areas. We next investigated the potential structural basis underlying the observed functional variations and associations. First, we tested whether the working memory-aroused competition between FP and DM has a structural basis. We estimated the structural connections between the brain regions within FP and those within DM using the structure connectivity matrix obtained from the DTI images of the same subjects we used for fMRI analysis (one matrix for each subject, see “Methods”). Then, we averaged these structural connections across the FP and DM networks to obtain a single value for each subject, denoting the structural connection between FP and DM. Using the structural connections as the predictors, we performed a regression analysis to assess their relationship with the difference in function connectivity between FP and DM (WM minus RS, one value for each subject). The results of the robust regression analysis present that the WM-aroused changes of function connectivity between FP and DM have a significant correlation with the strength of the structural connections between FP and DM areas (Fig. 3, r = 0.1287, p < 0.001). The result suggests the direct connections of the white matter tracts between FP and DM can, at least partially account for the WM-aroused changes of the function connectivity between the two regions.

To further explore the structural origin of the functional role of DLPFC in the competition between FP and DM, we turned to examine whether there is a structural association of the WM-aroused changes in the function connectivity between DLPFC areas and the two brain networks. Using the same method applied above, we calculated the differences of the function connectivity of the DLPFC and the two networks between RS and WM and regressed the structural connections of such regions against the difference. We found a significantly positive correlation in the left DLPFC and DM and a significantly negative correlation in the left DLPFC and FP (Fig. 3). These results indicate that the structure connection between the left DLPFC and the two brain networks may have opposite effects on the WM-involved functional variations. Additionally, we observed a significantly positive correlation in the right DLPFC and FP (Fig. 3). However, the correlation between the right DLPFC and DM was not significant, suggesting an asymmetric structural influence of the right DLPFC. Experiments repeated on the Schaefer 100 template present similar results (Supplementary Fig. 4).

In order to exclude the spurious correlation, we further evaluate the reliability of the results by retaining the structural connections with the strengths over 50%, 60%, 70%, 80% of the original connections. We reassessed the correlations presented in Fig. 3. We find there is no significant change in the correlations presented in Fig. 3, indicating that the structure-function coupled arrangement is not driven by spurious connections.

Fitting the excitation and inhibition-balanced mean-field model (EI-MFM) to resting-state functional measures. The results of the tests above revealed the associations between the function and structure of the DLPFC and the brain networks FP and DM, observed in both resting state and working memory conditions, as well as the variations aroused by the working memory tasks. To investigate the causal relationship underlying these associations, we constructed a biologically plausible network model. Specifically, we built the model using structural connections and fit its biophysical parameters using to the functional measures observed in the resting state. We then perturbed the simulated neuronal activities of DLPFC areas to assess whether specific variations in DLPFC activity may trigger the functional changes observed during working memory in real fMRI data. To achieve this, we employed a neural network model which incorporates realistic local excitation-inhibition balance within regions and inter-regional excitatory inputs (Deco et al., 2014; Zhang et al., 2023), and a realistic model of neurovascular coupling, hemodynamics and blood oxygen level-dependent (BOLD) generation (Fig. 4A). This model allows us to perturb independently excitatory and inhibitory activities within region, and to test the effects of mechanisms of generation of network dynamics that include inter-regional feedforward inhibition.

The parameters estimated by fitting the model are ROI-specific to account for the local heterogeneity across cortex. The free parameters fitted to the fMRI data for each ROI were the local recurrent connection strength \(\:{w}_{EE}\) for excitatory neurons and \(\:{w}_{EI}\) for inhibitory neurons, a global scaling factor \(\:G\) that scales the inter-regional structural connections and thus the inter-regional excitatory inputs, external input \(\:{I}_{0}\) and the standard deviation of neuronal noise \(\:{\sigma\:}\) (see “Methods”). We set the ROI-specific parameters \(\:{w}_{EE}\), \(\:{w}_{EI}\), \(\:{I}_{0}\) and \(\:{\sigma\:}\) as the linear combination of the principal resting-state FC gradient (Margulies et al, 2016) and T1w/T2w myelin estimate (Glasser & David, 2011). This results in 13 unknown parameters to be estimated by fitting the model.

We used the group-averaged SC, FC and functional connectivity dynamics (FCD) obtained from both Desikan-Killiany anatomical parcellation and Schaefer 100 parcellation to fit the model. We adopted the data of 1052 participants in the HCP S1200 release and randomly divide their data into training (N = 351), validation (N = 350) and test (N = 351) sets. By fitting the model on the training set, we obtained 5000 parameter candidates. Then, we selected the top 10 of them on the validation set and test the performance on the test set. The comparison of considering long-range/inter-regional feedforward inhibition or not follows the same training-validation-test paradigm, consistent with previous studies (Kong et al., 2021; Zhang et al., 2023).

To evaluate the effectiveness of including the inter-regional feedforward inhibition, we compared the disagreements between simulations and empirical measures with and without such inhibitions (\(\:{\lambda\:}\:=\:1\:\)versus 0, see “Methods” and Eq. (2)). Consistent with the previous study (Deco et al., 2014), we observed greater disagreements between empirical and simulated FC and FCD for the model with inter-regional feedforward inhibitions (\(\:{\lambda\:}\:=\:1\), Fig. 4B). Given the better performance of the model without inter-regional feedforward inhibitions, we set \(\:{J}_{NMDA}\) = 0.15nA and \(\:{J}_{i}\) = 1 and retained the model configuration for subsequent experiments. Furthermore, the estimated parameters revealed gradients among brain networks, indicating localized heterogeneity across cortex (Fig. 4C). We also conducted the same model fitting using the Schaefer 100 parcellation, which yielded similar results favoring the model without inter-regional feedforward inhibitions (Supplementary Fig. 5A and B).

Perturbing the activation of neuronal activities of right and left DLPFC areas may push the interaction between FP and DM towards the dynamics of working memory. In the previous sections, we have gathered evidence supporting (but not proving) the notion of the causal role of DLPFC areas in transitioning brain activity from resting state toward working memory. It is difficult to evaluate such causal relationships in healthy human subjects. Given that the EI-MFM considers the structural connections among brain regions and can capture the local heterogeneity, FC and FCD patterns during the resting state, we propose to test the notion in silico. Specifically, we performed perturbations on the activity of the excitatory or the inhibitory neuron populations of the DLPFC areas and tested whether solely manipulating the activities of DLPFC can push the brain functional dynamics towards the pattern of working memory. As working memory involves persistent activation of brain regions, we manually increased the neuronal activity of each DLPFC area with a constant as the perturbation. In order to evaluate the potentially predominant contributions of different neuron population and areas, we perturbed the simulated activities of either excitatory or inhibitory neuron populations of each DLPFC area accordingly. The amplitude of the perturbation also varied to simulate the possible scenarios where different neuron populations activate at different levels.. In this way, we can selectively influenced a specific neuron population with an area or the combinations of different neuron populations in different areas. Then, we tested whether the perturbed FC patterns across the whole brain and between the frontoparietal and the default-mode networks are closer to those of working memory. We evaluated this similarity using different brain parcellations. Although we applied a constant perturbation to the activity of each neuron population, the increase in perturbed neuronal activity varies over time due to the coupling between excitatory and inhibitory neurons and the time-evolved dynamics of the neuronal activity (Fig. 5A and Eqs. (5) and (6)).

We performed the perturbations step by step. Among the perturbation experiments involving the perturbation amplitude of 0.1 on one DLPFC area (Fig. 5B), we found L-E + 0.1 significantly improves the similarities in both the whole brain FC and the FC between FP and DM for the Desikan-Killiany Atlas. However, no perturbation manner consistently demonstrates robust improvements across different parcellations (Supplementary Fig. 5C). Then, we tested the perturbations on both DLPFC areas with the same amplitude. Initially, we found perturbing the excitatory neuron population of the left DLPFC and the inhibitory neuron population of the right DLPFC leads to a relatively robust improvement in the similarities of the whole brain FC and the FC between FP and DM across brain parcellations. Specifically, among the perturbation approaches tested (L-E + 0.1, L-I + 0.1, R-E + 0.1, R-I + 0.1, L-E + 0.1&R-E + 0.1, L-I + 0.1&R-I + 0.1 and L-I + 0.1&R-E + 0.1), L-E + 0.1&R-I + 0.1 presents robust improvements across parcellations compared with the RS condition (Fig. 5B and Supplementary Fig. 5C). These findings indicate that activating both DLPFC areas under the condition of L-E + 0.1&R-I + 0.1 pushes the brain dynamics toward the pattern of working memory. The robust improvement of L-E + 0.1&R-I + 0.1 aligns with the existing evidence of and the vital functions of the NMDAergic and GABAergic modulation (Yang et al., 2013; Rodermund et al., 2020) and the neurotransmitters levels varying across working memory and resting state (Woodcock et al., 2018) within DLPFC.

Based on the same perturbation amplitudes applied to each DLPFC area, we further tested whether activating the two DLPFC areas to different degrees can further push the brain pattern toward working memory. Using L-E + 0.1 & R-I + 0.1 as the baseline, we evaluated the performance of activating the two neuron populations with differentiated amplitudes, i.e., L-E + 0.05&R-I + 0.1 and L-E + 0.1&R-I + 0.05. It is important to note that the hypothesis-driven study focuses on the potentially causal role of DLPFC areas without excluding the possibility that other brain regions may have the similar role in shaping the inter-network dynamics.

To ensure the robustness of the perturbation, we performed control analyses. Generally, we performed the similar step-by-step perturbations on other brain areas and compared the similarity improvements with those of the DLPFC areas. Considering the similarities after perturbing the neuronal activities of one area (Fig. 5B and Supplementary Fig. 5C) do not present a robust improvement over resting state across the two parcellations, we directly performed the first control analysis on the symmetrical areas on left and right hemispheres (e.g. left and right Anterior Insula) and perturbed their excitatory or inhibitory neuronal activities, respectively (i.e. L-E/I + 0.1&R-E/I + 0.1 for the symmetrical areas). We remained the perturbations with significantly improved similarities of whole-brain FC and inter-network FC across both parcellations (p < 0.05) and compare their improvements with that of L-E + 0.1&R-I + 0.1 of DLPFC areas. We find that 19 areas for the Desikan-Killiany Atlas and 31 areas for the Schaefer 100 Atlas present a significantly improved similarities over the similarities between the FC of the unperturbed simulations (i.e. RS) and the empirical FC of working memory. None of them presents a larger improvement over L-E + 0.1&R-I + 0.1 of DLPFC areas. Then, we performed the second control analysis on perturbing the neuronal activities with different amplitudes. That is, after we find the areas that present the significantly improved similarities under the same-amplitude perturbations (i.e. the 19 areas for the Desikan-Killiany Atlas and 31 areas for the Schaefer 100 Atlas), we remained the perturbation manner, used different perturbation amplitudes and tested the similarities, which is similar to the perturbation manner of Fig. 5B and Supplementary Fig. 5C. From the the 19 areas for the Desikan-Killiany Atlas and 31 areas for the Schaefer 100 Atlas, we found that only L-I + 0.05&R-E + 0.1 of the anterior insula presents a significant improvement over Rest and over the same perturbation manner with the same amplitudes (i.e. L-I + 0.1&R-E + 0.1 of the Anterior Insula) (p < 0.05, after the Bonferroni correction). The improvement is robust across both parcellations and across the whole-brain FC and the inter-network FC. We presented the results of perturbing the neuronal activities of the Anterior Insula in Supplementary Fig. 6. It can be seen that its improvements (no matter L-I + 0.1&R-E + 0.1, L-I + 0.05&R-E + 0.1 or L-I + 0.1&R-E + 0.05) are smaller than those of L-E + 0.1&R-I + 0.05 of DLPFC. These control analyses reveal that the perturbation of DLPFC (i.e. L-E + 0.1&R-I + 0.05 of DLPFC) presents the largest improvements of the similarity between perturbed FC and the empirical FC corresponding to the working memory tasks, suggesting that DLPFC may be one of the main drivers for arousing the brain dynamics of working memory. The prediction of the computational model-based analysis is that the increase of the activity of excitatory neurons within lDLPFC and the increase of the activity of inhibitory neurons within rDLPFC can push the function connectivity pattern of resting state toward that of working memory.

GABA and NMDA receptor-enriched network analysis on working memory and resting states. The above results used the model perturbation to predict that the excitatory and inhibitory neuronal activities within DLPFC may be one of the main drivers of larger-scale network changes during working memory. In the following, we turned to test whether the prediction made above corresponds to the excitatory and inhibitory neurotransmitter systems, using the PET images of GABA and NMDA receptors. We first tested the function connectivity difference between RS and WM correlates with the distribution of neurotransmitter receptors. Previous research has shown that the density distribution of neurotransmitter receptors reflects the structural and functional organization of the brain and may shape the neuronal oscillations (Hansen et al., 2022). We used the PET images that reflects the receptor density distributions across cortex of 19 neurotransmitters (Hansen et al., 2022) and calculated the receptor similarity matrix from the cortical distribution of the 19 receptors and transporters across 9 neurotransmitter networks by the Pearson’s coefficient between each pair of brain area. Then, we correlated the matrix with the difference in function connectivity of FP and DM between WM and RS, and tested its significance through the spatial permutation (see “Methods”). The results indicate that the receptor similarity between the frontoparietal and default-mode networks exhibits a correlation with the working memory-aroused variation in the strength of the function connectivity between the frontoparietal and default-mode networks (Schaefer100: r = -0.0272, p = 0.0168, p < 0.0001 when compared against the null model constructed by spatial permutations; Desikan-Killiany: r = 0.0339, p = 0.2351 when compared against the null model constructed by spatial permutations), as presented by Fig. 6A. Figure 6A presents different trends, but only the trend in Schaefer 100 reaches statistical significance. This discrepancy may attribute to the relatively sparse brain regions of the Desikan-Killary atlas. These findings suggest that the neurotransmitter receptors, may shape the competition between FP and DM emerging from the resting state to working memory, highlighting their potential role in modulating these processes.

We examined how the receptor densities of GABA and NMDA modulate the functional maps of resting state and working memory. We utilized the REACT toolbox (Dipasquale et al., 2019) and performed a two-step multivariate regression analysis separately for GABA or NMDA during resting state or working memory (see “Methods”), using the PET images of the receptor density distribution of GABA-A (Nørgaard et al., 2021) and NMDA (Galovic et al., 2021a; Galovic et al., 2021b). The molecular-enriched network analysis was used to identify the neurotransmitters’ role in functional changes between brain states (Dipasquale et al., 2020; Pfeffer et al., 2021; Wong et al., 2022). Compared with spatial correlation between receptors and FC, the analysis method provides more detailed information on the receptor specificity and the underlying neuromodulator mechanism driving functional variations (Lawn et al., 2023).

The voxel-wise maps enriched by the GABA and NMDA receptor densities were averaged within ROIs for each template, resulting in molecular-enriched activation values (again, one value for each subject and each ROI). Then, we compared the distributions of the molecular-enriched activation across conditions. We found a significantly improved NMDA-enriched activation of the left DLPFC (Fig. 6B, p < 0.001, Supplementary Fig. 8A, p < 0.001) and GABA-enriched activation of the right DLPFC (Fig. 6B, p < 0.001, Supplementary Fig. 7A, p < 0.001) during working memory compared with resting state. There is no significant difference for GABA-enriched activation of the left DLPFC and NMDA-enriched activation of the right DLPFC between working memory and resting state (Fig. 6B). This finding suggests the significantly increased activation of excitatory neuron population in lDLPFC and inhibitory neuron population in rDLPFC during working memory compared to resting state, supporting the notion indicated by the in silico perturbation experiments described above. Furthermore, after averaging the voxel-wise maps within ROIs, we calculated the difference in the NMDA-enriched activation of lDLPFC across conditions (WM minus RS), as well as the difference in the GABA-enriched activation of rDLPFC (WM minus RS). We found that the molecular-enriched activation of lDLPFC and rDLPFC is larger for the inhibitory neurons of rDLPFC (Fig. 6C p = 0.1648, Supplementary Fig. 7B, p < 0.001). Despite the discrepancy on the activation levels of the excitatory neurons within lDLPFC and the inhibitory neurons within rDLPFC on the two parcellations, the results further support that the excitatory neurons within lDLPFC activate with a larger amplitude than the inhibitory neurons within lDLPFC, the inhibitory neurons within rDLPFC activate with a larger amplitude than the excitatory neurons within rDLPFC. This suggests that the ratios between the activation of excitatory neurons and inhibitory neurons within both DLPFC areas are different between resting state and working memory.

Previous studies have reported the key role of DLPFC in working memory at multiple levels (Arnsten& Lu, 2014; Yoon et al., 2016; Smucny et al., 2022; Barch et al., 2013; Webler et al., 2022; Schicktanz et al., 2015; Rahmati et al., 2020; Cai et al., 2021; Tomasi&Nora, 2011). Our results provide a cross-scale understanding by proposing the evidence that the local imbalance of excitation and inhibition within the DLPFC areas may ignite and shape the multi-regional activation patterns that are key for working memory. Also, our study supports the hypothesis that the brain dynamics of working memory arises from local sources by integrating fMRI, DTI, PET images and biophysical models.

Many empirical studies have emphasized the vital role of the DLPFC areas on working memory and the effect of local imbalance of excitation and inhibition during the working memory tasks on separate levels. Studies on the neuron circuit level showed that the perturbing the local balance between excitatory and inhibitory activities can change the behavioral aspects of working memory (Murray et al., 2015; Xu et al., 2019; Giorgi et al., 2021; Yang et al., 2013; Rodermund et al., 2020; Ma et al., 2018), revealing that the differential activation of the excitatory and inhibitory neurons may contribute to the performance of working memory. But given that working memory relates to the multiregional changes of functional activation and interactions, how the local imbalance of excitation and inhibition influences the functional patterns of whole brain is still underexplored. Neuroimage-level studies revealed the involvement of brain networks (Wang et al., 2019; Anticevic et al., 2019; Murphy et al., 2020) and the association between behavioral performance and the strengths of the function functional activation and interactions (Schicktanz et al., 2015; Rahmati et al., 2020; Bertolero et al., 2018; Keller et al., 2014). Some studies indicated the GABA concentration within DLPFC correlates with the performance and load of the working memory tasks (Woodcock et al., 2018; Yoon et al., 2016). However, causal mechanism on how the brain dynamics translates from resting state to working memory is largely unknown, albeit some localized sources have been found to account for the activation changes during different cognitive loads (Cai et al., 2021). Brain stimulation-based studies and behavioral studies on patients with brain deficits suggested the causal association between DLPFC and the performance during the working memory tasks (Barbey et al., 2013; Smucny et al., 2022; Zanto et al., 2011; Feredoes et al., 2011; Soto et al., 2012), but the mechanism behind the phenomena is still largely unanswered. Biophysical work proposed that the interactions of excitatory and inhibitory activities within prefrontal cortex may shape the persistent activity and the multi-regional activation pattern specific to working memory (Robert& Terrence, 2021; Kyle et al., 2010; Lu et al., 2023; Mejías & Wang., 2022). Empirical support for this is still limited. Thus, from the previous work it may be challenging to have the cross-scale understanding of how the multiregional activation and interaction patterns of working memory are ignited from resting state and how they relate to the excitatory and inhibitory activities within local areas.

Here we develop a framework that integrates the analysis of fMRI, DWI and PET images of neurotransmitter receptors and the biophysical model, to answer whether the emergence of the multiregional functional patterns of working memory is aroused by localized sources or aroused simultaneously across multiple regions. It has been hypothesized that the dynamics of brain networks during working memory has some localized sources (Mejías & Wang., 2022) and DLPFC mat be one of the origins (Webler et al., 2022). Furthermore, previous studies indicated that working memory involves the differential activation of excitatory and inhibitory neurons across cortex (Rodermund et al., 2020; Barbas et al., 2018). Our work unites and connects these hypotheses by demonstrating that the local imbalance of the excitatory and inhibitory activity within DLPFC may ignite and shape the inter-network dynamics of working memory, which cannot be answered by either biophysical modelling or correlational analysis of neuroimages.

We also add the knowledge of how local imbalance of excitation and inhibition shapes the network interactions and contributes to the switching of the network-level changes from resting state to working memory. Excitation-inhibition ratio has long been thought as a vital mechanism for various cognitive conditions and psychiatric diseases (Berstelsen et al., 2023; Koren et al. 2024; Lee et al., 2017; Deco et al., 2014; Yizhar et al., 2011). A recent study has shown that the local imbalance of excitation and inhibition can shape the activity within circuits and thus influence the behaviour (Kuan et al., 2024). Our study shows in a larger scale that the local imbalance can shape the inter-network dynamics, thus enlarges the scope of the influence of excitation-inhibition imbalance in the current literature.

Our results can be further supported by future studies as follows. First, future studies on biophysical modelling that can link the dynamics of multiple neurotransmitters with the inter-network interactions can be applied in our workflow to further reveal how the local interaction among multiple neurotransmitters within DLPFC shapes the inter-network interaction of working memory. The mean-field model used in this study considers only the dynamics of GABA-A and NMDA because their dynamics have a similar timescale with the sampling time of fMRI (Deco et al., 2014; Zhang et al., 2024). Second, although we analyze the correlation between the functional interaction patterns and the behavioral performance of working memory, how the local imbalance within DLPFC causally shapes the behavioural performance during the working memory tasks needs further animal study, which induces the excitation-inhibition imbalance within DLPFC by optogenetically manipulating or pharmacologically silencing the excitatory or inhibitory neurons. Finally, our study considers the persistent activity during the working memory tasks without considering the detailed synapse basis of the persistent activity (Kozachkov et al., 2022; Mongillo et al., 2006). Previous studies have suggested the persistent activity corresponded to working memory may be caused by the short-term plasticity of synapses (Mongillo et al., 2006)., and the synaptic plasticity is shaped by the local excitation-inhibition ratio (Tatti et al., 2017; Froemke et al., 2015). Future studies that can infer the coupling between excitation-inhibition ratio and the synaptic plasticity from neuroimages would extend our results on synaptic plasticity level.

HCP data selection and acquisition. We utilize the resting-state (RS) fMRI scans, the fMRI scans during the n-back tasks, the performance of the n-back tasks and the diffusion tensor imaging (DTI) scans from the Human Connectome Project (HCP) S1200 release (Van Essen et al., 2013). For analyzing the activation, function connectivity and structural connections, we select 737 right-handed subjects (age: 22–36 years old, 413 female/324 male) from the data release based on the selection criteria (Cai et al., 2021). For fitting the EI-MFM model, we consider the resting-state (RS) data of 1052 participants from the HCP S1200 release. The participants underwent scanning using a multi-band sequence. Each individual completed four fMRI runs in two sessions, either during resting state or working memory (WM) tasks. Scans were acquired on a customized Siemens 3T Skyra scanner using multiband, gradient-echo planar imaging. Each RS-fMRI run comprised 1200 frames, while each WM-fMRI run consists of 405 frames. Diffusion imaging consisted of 6 runs, each lasting approximately 9 min and 50s. Details of the data collection can be found in the overview (Van Essen et al., 2013).

Data acquisition for the HCP was approved by the Institutional Review Board of The Washington University in St. Louis (IRB # 201204036), informed consent was obtained from each participant, and all data were de-identified.

HCP n-back working-memory task. During the HCP working-memory task, subjects were presented with a stream of pictures presenting faces, places, tools and body parts (Barch et al., 2013). Within each session, blocks of trials of the four stimulus types were presented. The n-back task contained two levels of difficulty: 0-back and 2-back. Each session contained half of the blocks of the 2-back task and the other half of the blocks of the 0-back task. During the 2-back task blocks, the subjects were asked to respond whether the currently presented picture matched the one shown two pictures earlier in the same session. In the 0-back task blocks, the subjects were asked to respond whether the currently presented picture matched the cue presented in the beginning of each block. The cognitive load of the 0-back task was minimal. Each session contained 8 tasks blocks and 4 fixation blocks (“rest”). Each task block began with a 2.5s cue indicating whether it was a 0-back or 2-back task, followed by 10 trials in which the stimulus was presented for 2s with a 0.5s inter-trial interval (ITI). Each fixation block lasted 15s.

Data preprocessing. According to the HCP S1200 manual, we utilized the fMRI data that had already been preprocessed under standard preprocessing steps, including realignment, slice-time correction, normalization, and spatial smoothing (2mm FWHM).

For the fMRI data of working memory, a conventional generalized linear model (GLM) was constructed to determine the contrast of load-dependent and performance-dependent activation or deactivation peaks. The onset and offset of each vector correspond to the onset and offset of each block (including 0-back-error, 0-back-success, 2-back-error, 2-back success). The contrast of interest includes 0-back & 2-back versus resting state and 2-back-error versus 2-back-success.

Function connectivity. For each run of each subject, the Desikan-Killiary and Schaefer 100 templates were used to extract the time series for each region of interest (ROI), resulting in a 68*T matrix for the Desikan-Killiary template and a 100*T matrix for the Schaefer100 template (T = 1200 for each run of RS, T = 405 for each run of WM). Functional connectivity (FC) was calculated as the Pearson's correlation between ROIs. To ensure an unbiased analysis, we excluded DLPFC areas from the FP and DM networks during the regression analysis on FC.

In order to fit the EI-MFM model, the RS-FCs within the training set, validation set, and test set were separately averaged across subjects. For the RS-fMRI data of each subject, functional connectivity dynamics (FCD) were computed using sliding windows. Each sliding windows had a length of 83 frames, resulting in a total of 1118 sliding windows (Allen et al., 2014; Liegeois et al., 2017). The FC of each sliding window was vectorized and Pearson's correlations were calculated among the sliding windows, generating a 1118×1118 FCD matrix for each subject. It is worth noting that the results obtained from fitting the model remained robust across different window lengths, as previously demonstrated (Zhang et al. 2023; Kong et al., 2021).

Determination of DLPFC, frontoparietal and default-mode networks. We determined the right and left DLPFC regions by the overlap between the brain regions of the two templates and the DLPFC regions of the Brodmann template. We first calculated to what extent each brain region of the two templates overlapped the right and left DLPFC of the Brodmann template. The overlapping extent of a brain region in the Desikan-Killiary and Schaefer 100 templates was calculated by was calculated as the ratio of the number of overlapped voxels to the total number of voxels within that specific brain region. Then, we set the threshold as 50%, and used the threshold to determine which brain regions corresponded to the DLPFC regions. For the Desikan-Killiary template, we determined the frontoparietal and default-mode networks through majority voting procedure. We calculated the overlapping extent of each brain region of the Desikan-Killiary template by calculating the ratio of the overlapped voxels to the total number of voxels within that specific region. We then determined which brain regions corresponded to the two brain networks by majority voting based on these overlapping extents.

Activation calculation. To generate activation map of each subject, we employed the following procedures. For working memory, we used the parameter estimate images obtained by GLM. Then, we calculated the fractional amplitude of low-frequency fluctuations (fALFF) and amplitude of low-frequency fluctuations (ALFF) for each voxel to construct the activation maps of each subject (Zou et al., 2008; Zang et al., 2007). When comparing the activation between pairs of ROI, the fALFF and ALFF values were averaged across voxels within each ROI.

Structural connectivity. To calculate the structural connectivity (SC), we used the minimally preprocessed diffusion-weighted MRI in the HCP S1200 release (Van Essen et al., 2013). The process involved performing whole-brain tractography by estimating multiple fiber orientations for each white matter voxel using constrained spherical deconvolution (CSD) and then track then track fibers to propagate streamlines throughout the white matter volume. The tractography is performed using the MRtrix software package (www.mrtrix.org). SC was calculated by determining the number of streamlines between ROIs. A 68 × 68 SC matrix and a 100 ×100 SC matrix were generated for the Desikan-Killiary template and the Schaefer100 templatevper subject, respectively. Group-level SC matrices were generated by thresholding the individual matrices. If any entry was zero in more than half of the individual SC matrices, the corresponding entry in the group-level SC matrix was set to zero. Otherwise, the entries were averaged across subjects. The group-level SC matrices was generated separately for the training set, validation set, and test set.

The excitation and inhibition-balanced dynamic mean-field model (EI-MFM). The mean-field model derives from the mean-field simplification of a network composed of spiking neuronal models, including excitatory (NMDA and AMPA) and inhibitory neurons (Deco et al., 2014). For each ROI, the populational neuron activity can be described by the following nonlinear stochastic differential equations:

\(\:{I}_{i}^{\left(E\right)}\:=\:{W}_{E}{I}_{0}+{w}_{EE}{J}_{NMDA}{S}_{i}^{\left(E\right)}+G{J}_{NMDA}\sum\:_{j}{C}_{ij}{S}_{j}^{\left(E\right)}-{J}_{i}{S}_{i}^{\left(I\right)}\)	(1)
\(\:{I}_{i}^{\left(I\right)}\:=\:{W}_{I}{I}_{0}+{w}_{EI}{J}_{NMDA}{S}_{i}^{\left(E\right)}-{{w}_{II}S}_{i}^{\left(I\right)}+\lambda\:G{J}_{NMDA}\sum\:_{j}{C}_{ij}{S}_{j}^{\left(E\right)}\)	(2)
\(\:{r}_{i}^{\left(E\right)}\:=\:\frac{{a}_{E}{I}_{i}^{\left(E\right)}-{b}_{E}}{1-exp(-{d}_{E}({a}_{E}{I}_{i}^{\left(E\right)}-{b}_{E}\left)\right)}\)	(3)
\(\:{r}_{i}^{\left(I\right)}\:=\:\frac{{a}_{I}{I}_{i}^{\left(I\right)}-{b}_{I}}{1-exp(-{d}_{I}({a}_{I}{I}_{i}^{\left(I\right)}-{b}_{I}\left)\right)}\)	(4)
\(\:\frac{d{S}_{i}^{\left(E\right)}}{dt}\:=\:-\frac{{S}_{i}^{\left(E\right)}}{{\tau\:}_{E}}+(1-{S}_{i}^{\left(E\right)})\gamma\:{r}_{i}^{\left(E\right)}+{\sigma\:}_{i}{v}_{i}\left(t\right)\)	(5)
\(\:\frac{d{S}_{i}^{\left(I\right)}}{dt}\:=\:-\frac{{S}_{i}^{\left(I\right)}}{{\tau\:}_{I}}+{r}_{i}^{\left(I\right)}+{\sigma\:}_{i}{v}_{i}\left(t\right)\)	(6)

where \(\:{\text{I}}_{\text{i}},\:{\text{r}}_{\text{i}}\) and \(\:{\text{S}}_{\text{i}}\) denote the input current, population firing rate and the average synaptic gait variable in the \(\:\text{i}\)th local cortical ROI, the superscripts \(\:\text{E}\:\text{a}\text{n}\text{d}\:\text{I}\:\)denote the excitatory and inhibitory neuron population.

Eq. (1) contains four inputs for the input current of the excitatory neuron population. \(\:{W}_{E}{I}_{0}\) denotes the external input, including sub-cortical input. \(\:{w}_{EE}{J}_{NMDA}{S}_{i}^{\left(E\right)}\) denotes the within-regional excitation-excitation current, where \(\:{w}_{EE}\) denotes the excitation-to-excitation recurrent connection strength, \(\:{J}_{NMDA}\) denotes the synaptic coupling constant. \(\:G{J}_{NMDA}\sum\:_{j}{C}_{ij}{S}_{j}^{\left(E\right)}\) denotes the inter-regional excitation-to-excitation current, where \(\:G\) denotes the global scaling factor, \(\:{C}_{ij}\) denotes the inter-regional structural connection between the \(\:i\)th and the \(\:j\)th ROI controlled by the SC matrix. \(\:{J}_{i}{S}_{i}^{\left(I\right)}\) denotes the within-regional inhibition-to-excitation current, where \(\:{J}_{i}\) denotes the local feedback inhibitory input which can either be tuned separately for each ROI or set as 1, according to the original study (Deco et al., 2014). In this study, we set it as 1.

Eq. (2) also contains four inputs for the current input of the inhibitory neuron population. \(\:{W}_{I}{I}_{0}\) denotes the external input, weighted by the inhibition weighting factor \(\:{W}_{I}\). \(\:{w}_{EI}{J}_{NMDA}{S}_{i}^{\left(E\right)}\) denotes the excitation-to-inhibition current input, where \(\:{w}_{EI}\)denotes the excitation-to-inhibition recurrent connection strength. \(\:{{w}_{II}S}_{i}^{\left(I\right)}\) denotes the inhibition-to-inhibition current input, where \(\:{w}_{II}\) denotes inhibition-to-inhibition recurrent connection strength. \(\:\lambda\:G{J}_{NMDA}\sum\:_{j}{C}_{ij}{S}_{j}^{\left(E\right)}\) denotes the inter-regional excitation-to-inhibition current, where \(\:\lambda\:\) denotes the long-range feedforward inhibition and can be set as either 1 or 0. As evaluated by our result, the performance of \(\:\lambda\:\:=\:0\) outperforms that of \(\:\lambda\:\:=\:1\). \(\:{W}_{E}\),\(\:{W}_{I}\), \(\:{w}_{II}\) and \(\:{J}_{NMDA}\) are set as 1, 0.7, 1, \(\:0.15\:\text{n}\text{A}\) and \(\:0.382\:\text{n}\text{A}\), respectively, according to the parameter setting (Deco et al., 2014).

Eqs. (3) and (4) denote the population firing rate of excitatory and inhibitory neurons. According to the parameter setting of the original study (Deco et al., 2014), we set the parameters as \(\:{a}_{E}\:=\:310n/C\), \(\:{a}_{I}\:=\:615n/C\), \(\:{b}_{E}\:=\:125Hz\), \(\:\:{b}_{I}\:=\:177Hz\), \(\:\:{d}_{E}\:=\:0.16s\), \(\:,\:{d}_{I}\:=\:0.087s\).

Eqs. (5) and (6) denote the dynamics of the synaptic gating variables of both excitatory and inhibitory neurons. The parameters \(\:{\tau\:}_{E}\), \(\:{\tau\:}_{I}\) and \(\:\gamma\:\) are set as 100ms, 10ms and 0.641, respectively. \(\:{v}_{i}\left(t\right)\) is uncorrelated standard Gaussian noise.

The ROI-specific parameters \(\:{w}_{EE},\:{w}_{EI},\:{I}_{0}\) and \(\:{\sigma\:}_{i}\) and the global parameter \(\:G\) are unknown and can be obtained by fitting the EI-MFM model.

Parameterizing the unknown parameters of EI-MFM. We follow the experience of the study (Kong et al., 2021) and parameterize the unknown parameters as follows:

\(\:{w}_{EE,i}\:=\:a\bullet\:{Meylin}_{i}+b\bullet\:{FCgradient}_{i}+c\)	(7)
\(\:{w}_{EI,i}\:=\:e\bullet\:{Meylin}_{i}+f\bullet\:{FCgradient}_{i}+g\)	(8)
\(\:{I}_{0}\:=\:ℎ\bullet\:{Meylin}_{i}+k\bullet\:{FCgradient}_{i}+l\)	(9)
\(\:{\sigma\:}_{i}\:=\:m\bullet\:{Meylin}_{i}+n\bullet\:{FCgradient}_{i}+p\)	(10)

where \(\:{Meylin}_{i}\) and \(\:{FCgradient}_{i}\) denote the T1w/T2w ratio map and the first principal FC gradient of the \(\:i\)th ROI. In this way, the EI-MFM can be parameterized by \(\:3\times\:4+1\:=\:13\) parameters. According to the ablation experiments performed by the study (Zhang et al., 2023), such a parameterizing manner can achieve a considerable fitting performance.

Optimization of EI-MFM. We employed the optimization procedure from the previous study (Zhang et al., 2023) to obtain ten parameter candidates via minimizing the disagreement of the empirical FC and FCD. These candidates were obtained by minimizing the disagreement between the empirical FC and FCD.

The 1052 subjects were randomly divided into training (N = 351), validation (N = 350) and test (N = 351) sets. To minimize the overall cost function during training, we utilized the covariance matrix adaptation evolution strategy (CMA-ES) (Hansen, 2006). We repeated the parameter selection procedure procedure was repeated until a total of 10 parameter sets were selected (Kong et al., 2021, Zhang et al., 2023).

The selected top 10 candidate parameter sets were then applied on the test set. For each candidate, 1000 simulations were performed, resulting in 10000 simulated FC and FCD matrices in total. The disagreement of the test set can be calculated as the Pearson’s correlation for FC and the KS distance for FCD and averaged.

Causal perturbation of EI-MFM. To investigate the directed role of DLPFC areas in eliciting competition between the frontoparietal and default-mode networks, we conducted perturbations on either the excitatory or the inhibitory neuron populations within each DLPFC area. Consistent with the sustained firing associated with working memory, we increased the neuronal activity, i.e., the synaptic gating variables \(\:{S}_{j}^{\left(E\right)}\) or \(\:{S}_{j}^{\left(I\right)}\) with a constant for each DLPFC area. Two different amplitudes were used: 0.1 or 0.05, representing different levels of activation. For each perturbation condition, 1000 random simulations were performed. Then, how the perturbed simulations are pushed toward the pattern of working memory was determined by the Pearson’s correlation between the FC of the empirical measurement during working memory and the FC of the simulations. Specifically, the FC of the empirical measurement was calculated individually for each subject and then averaged across subjects. The Pearson’s correlation was then calculated between the averaged empirical FC and the 1000 simulations for each perturbation condition.

Statistical analysis. To assess the significance of differences in regional activation or function connectivity, we conducted a permutation test. By permuting the data points in groups A and B for 10,000 times, we constructed a null model for the difference. The difference between group A and B was then compared with the null model to determine the significance. When performing the spatial permutation, we employed the spin test. Particularly, we spun the Desikan-Killiary and Schaefer 100 temples with randomly placed parcels of the same size, shape, and relative position to each other. The permutation was also repeated 10,000 times. For the correlation test, we employed robust linear regression methods that are insensitive to outliers. These tests were used to assess the correlation as well as its statistical significance. We further confirmed the significance of the correlation by permuting across the subjects. Bonferroni correction was performed for multiple comparisons.

Correlative analysis between FC difference and receptor distribution. We first calculated the differences in the strength of the function connectivity between FP and DM networks. Specifically, we subtracted the function connectivity during resting state from those observed during working memory and averaged these differences across subjects. Next, we parcellated the receptor density maps of the 19 neurotransmitter systems (Hansen et al., 2022) using the Desikan-Killiary atlas and Schaefer100 atlas. For each ROI, we calculated the averaged receptor densities for each neurotransmitter system. This results in a 19-dimentional vector representing the receptor density distribution for each ROI. Then, we calculated the cosine distance between ROIs and created a receptor similarity matrix. We selected cortical areas predominantly corresponding to FP and DM, ensuring that at least 50% of the area was covered by FP or DM. This process yielded two matrices of the same dimension: one for the differences in function connectivity differences and the other for the receptor similarity between FP and DM. We vectorized the two matrices and performed the robust regression analysis on them. Finally, we performed the spatial permutation on the function connectivity differences for 10,000 times and then analyzed their correlations with the receptor similarity vector to construct the null model.

Molecular-enriched network analysis. We employed receptor density maps from the glutamatergic and GABAergic networks. The NMDA template was derived from 29 healthy subjects using ¹⁸F-GE-179 PET images (McGinnity et al., 2014) as described in the study (Galovic et al., 2021a; Galovic et al., 2021b). The GABA-A template was derived from 16 healthy subjects using [¹¹C] lumazenil PET images (Myers et al., 2012) as described in the study (Nørgaard et al., 2021). To estimate the functional networks enriched by the GABA-A and NMDA, receptor density maps in each subject and condition (resting state and working memory), we employed the REACT toolbox (Dipasquale and Frigo, 2021). This involved a two-step multivariate regression analysis (Dipasquale et al., 2019). The resulting maps represent the neuromodulator network-related activation (Dipasquale et al., 2020; Pfeffer et al., 2021; Wong et al., 2022). These maps were averaged within ROIs and across subjects, allowing for comparisons across different conditions.

Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 62306083), the Postdoctoral Science Foundation of Heilongjiang Province of China (LBH-Z22175) and the China Scholarship Council. We appreciate the suggestions on writing the manuscript from Prof. Dr. Stefano Panzeri and Prof. Dr. Thomas Yeo.

Author Contributions

C.Y. and B.W. conceived the project and designed the experiments. All authors contributed to the development of the concepts presented in the paper. C.Y. and B.W. performed the experiments. All authors designed the data analysis approaches. C.Y., B.W. and H.Z. conceived the application of the EI-MFM. S.Z. conceived statistical analysis. C.Y. performed the data analysis. C.Y. and H.Z. wrote the manuscript with contributions from all the rest authors. All authors contributed to the content and writing of the Supplementary Information.

Competing Interests

The authors declare no competing interests.

Data Availability

The HCP data is publicly available (https://www.humanconnectome.org/). The PET images used to perform the analyses are also public available ( https://github.com/netneurolab/hansen_receptors).

Code Availability

The code for this study is available at: https://github.com/ChunzhiYi/Excitation-Inhibition-Balance-Model.

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Differential Excitatory-Inhibitory Balance within Dorsolateral Prefrontal Cortex Shapes Inter-network Interactions in Working Memory

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