Mapping Brain Synergy Dysfunction in Schizophrenia: Understanding Individual Differences and Underlying Molecular Mechanisms

Abstract To elucidate the brain‐wide information interactions that vary and contribute to individual differences in schizophrenia (SCZ), an information‐resolved method is employed to construct individual synergistic and redundant interaction matrices based on regional pairwise BOLD time‐series from 538 SCZ and 540 normal controls (NC). This analysis reveals a stable pattern of regionally‐specific synergy dysfunction in SCZ. Furthermore, a hierarchical Bayesian model is applied to deconstruct the patterns of whole‐brain synergy dysfunction into three latent factors that explain symptom heterogeneity in SCZ. Factor 1 exhibits a significant positive correlation with Positive and Negative Syndrome Scale (PANSS) positive scores, while factor 3 demonstrates significant negative correlations with PANSS negative and general scores. By integrating the neuroimaging data with normative gene expression information, this study identifies that each of these three factors corresponded to a subset of the SCZ risk gene set. Finally, by combining data from NeuroSynth and open molecular imaging sources, along with a spatially heterogeneous mean‐field model, this study delineates three SCZ synergy factors corresponding to distinct symptom profiles and implicating unique cognitive, neurodynamic, and neurobiological mechanisms.


Table of Contents
. Comparison of synergy between SCZ and NC at the levels of connection matrices, brain regions, and functional networks.a) Group-average synergy matrices display the synergistic interactions between each pair of brain regions (left: SCZ, right: NC).The SCZ synergy showed a similar (Pearson's correlation: r = 0.958) but overall decreased connectivity pattern compared to the NC group.b) Brain plots show regional mean synergy maps calculated by averaging the synergy matrices across brain regions for SCZ and NC groups.The SCZ synergy showed a similar (Pearson's correlation: r = 0.88) but overall decreased regional pattern compared to the NC group.c) Violin plot shows the distribution of brain regions assigned to the functional subnetwork [3] indicated on the x axis.White circles represent median values; box limits represent upper and lower quartiles and whiskers represent 1.5× the interquartile range.Significance levels are denoted by asterisks (* indicating p < 0.05, ** indicating p < 0.01, *** indicating p < 0.01), determined by one-sample non-parametric permutation t-test (two-sided) compared to the mean value of whole brain (gray line), without correction for multiple comparisons.In the NC group (right), the synergistic connectivity of the SOM network (primary motor cortex; modular dissociative network) was significantly lower than the overall brain average, while the FPN and DMN (higher-order association networks; modular integrated networks) exhibited significantly higher synergy levels, consistent with the definition of synergy where two brain regions depend on each other to generate new information.However, in the SCZ group (left), this network-specific differentiation lost significance, particularly in the SOM and DMN networks, underscoring the importance of examining synergistic factors from a whole-brain perspective.values display between-group differences in synergistic interactions within the DK-83 parcellation, [4] derived from Desikan-Killiany anatomical atlas encompassing 68 cortical regions and 15 subcortical regions.b) Robustness of synergy t-statistic map to DK-83 parcellation.Significant correlation between augmented Scheafer-115 parcellation and DK-83 parcellation (r = 0.65, p SA < 0.001) underscores the resilience of synergy dysfunction to various parcellation schemes.c) Scatter-box chart of the mean synergy of schizophrenia groups (SCZ, red) and normal controls (NC, blue) across different sites using DK-83 parcellation.Synergy networks dysfunction in the schizophrenia group was evident at all independent sites, despite variations in scanning equipment.d) Matrix of t-statistic values display between-group differences of the synergistic interactions in the BN-246 parcellation, [5] obtained by brainnetome anatomical atlas with 210 cortical regions and 36 subcortical regions.e) Robustness of synergy t-statistic map to BN-246 parcellation.Significant correlation between augmented Scheafer-115 parcellation and BN-246 parcellation (r = 0.65, p SA < 0.001) confirms the robustness of synergy dysfunction to different parcellation schemes.f) Scatter-box chart of the mean synergy of schizophrenia groups (SZ, red) and normal controls (NC, blue) across different sites using DK83 parcellation.Synergy networks dysfunction in the schizophrenia group was evident at all independent sites, despite acquisition using different scanners.Items marked in factor-specific colors indicate p < 0.05, FDR adjusted.Among them, 14 items (significantly more than the random value) showed a significant correlation with one of the factors.For positive subscale, blue line encloses the largest area, suggesting that factor 1 was positively correlated with most of these symptom items.For negative and general subscales, purple line encloses the smallest area, suggesting that factor 3 was negatively correlated with most of these symptom items.b) Spider plot for Pearson correlations of the 30 PANSS item scores with the three latent factors without regressing out control variables.Schematic of transcriptomics analysis to test whether gene expression explains three latent factors.First, we calculated Pearson correlations between gene expression at each brain region (ROI) and synergistic interaction dysfunction summed over ROIs for each factor.Second, we ranked gene by correlation coefficient, and selected top and bottom 10% for each factor as the factorspecific gene sets.Third, we calculated the gene expression similarity using the selected gene set and tested whether the constructed co-expression matrix correlates to the latent factors.Forth, we derived gene contribution indicator (GCI) gene sets using the virtual gene knock-out (KO) method. [6]Finally, we conducted GO enrichment analysis for GCI + and GCI − gene sets of each factor.b) Chord plot shows gene co-expression matrix in a.3 averaged over the networks.The color intensity of chords is the same as the color bar in a.    [8] The factor maps were transformed into the native space of the target maps.Points represent Pearson's correlations between source and target maps (with significance defined as PSA<0.05).All correlations underwent correction for multiple comparisons. .

Figure S4 .
Figure S4.Synergistic interactions showed significantly higher inter-individual variance among SCZ compared to NC. ..

Figure S1 .
Figure S1.Subject mean redundancy and FC showed no significant between-group differences at each site.a) Scatter-box chart of the mean redundancy of schizophrenia groups (SCZ, red) and normal controls (NC, blue) across different sites.b) Scatter-box chart of the mean redundancy of schizophrenia groups (SCZ, red) and normal controls (NC, blue) across different sites.Each colored circle represents one subject.In the box plots, horizontal lines indicate the median and the hinges of the box denote the first and third quartiles above and below.The lower and upper whiskers represent 1.5 times the interquartile range (IQR).

rFigure S3 .
Figure S3.Synergy networks dysfunction in schizophrenia are robust to the use of brain parcellations.a) Matrix of t-statistic values display between-group differences in synergistic interactions within the DK-83 parcellation,[4] derived from Desikan-Killiany anatomical atlas encompassing 68 cortical regions and 15 subcortical regions.b) Robustness of synergy t-statistic map to DK-83 parcellation.Significant correlation between augmented Scheafer-115 parcellation and DK-83 parcellation (r = 0.65, p SA < 0.001) underscores the resilience of synergy dysfunction to various parcellation schemes.c) Scatter-box chart of the mean synergy of schizophrenia groups (SCZ, red) and normal controls (NC, blue) across different sites using DK-83 parcellation.Synergy networks dysfunction in the schizophrenia group was evident at all independent sites, despite variations in scanning equipment.d) Matrix of t-statistic values display between-group differences of the synergistic interactions in the BN-246 parcellation,[5] obtained by brainnetome anatomical atlas with 210 cortical regions and 36 subcortical regions.e) Robustness of synergy t-statistic map to BN-246 parcellation.Significant correlation between augmented Scheafer-115 parcellation and BN-246 parcellation (r = 0.65, p SA < 0.001) confirms the robustness of synergy dysfunction to different parcellation schemes.f) Scatter-box chart of the mean synergy of schizophrenia groups (SZ, red) and normal controls (NC, blue) across different sites using DK83 parcellation.Synergy networks dysfunction in the schizophrenia group was evident at all independent sites, despite acquisition using different scanners.

Figure S4 .
Figure S4.Synergistic interactions showed significantly higher inter-individual variance among SCZ compared to NC. a) Boxplot shows the variance in the distribution of synergistic interactions for SCZ and NC groups.Each point represents variance of a synergistic interaction.As indicated by the asterisks (p < 0.001; t-test), the variance of the synergistic interactions was significantly higher in SCZ group, compared to NC group.b) Higher variance of the synergistic interactions among SCZ compared to NC was significant at six of the seven sites.Items marked by asterisks indicate p < 0.05, FDR adjusted.At WUHAN site, the synergy variance of SCZ group (0.269±0.055) was slightly higher than that of SCZ group (0.268±0.054), although not reaching significance (p = 0.57).c) Higher variance of the synergistic interactions within cortical regions among SCZ compared to NC was significant at six of the seven sites, consistent with the results of considering the whole-brain synergy in b.Items marked by asterisks indicate p < 0.05, FDR adjusted.At WUHAN site, the synergy variance of SCZ group (0.274±0.058) was higher than that of SCZ group (0.272±0.056), although not reaching significance (p = 0.11).d) Higher variance of the synergistic interactions among SCZ compared to NC was significant for six of the eight networks.Items marked by asterisks indicate p < 0.05, FDR adjusted.

Figure S5 .Figure S6 .
Figure S5.Correlations between the final estimate and solutions from the 100 random initializations in two-, three-, and fourfactor estimates.a) We ran 100 times with random initializations for two-, three-, and four-factor estimates and we choosed the final estimate as solution having the highest average correlation with other solutions for each number of latent factors K. Factor estimation K = 3 achieved both the highest correlation with final estimate (r = 0.89, left) the highest average correlation with other estimates (r = 0.84, right), indicating that three-factor estimate was the most robust and stable answer.b) Scatter chart shows the distribution of correlations with final estimate (left) and the average correlation with other estimates (right) for K = 3.

Figure S7 .
Figure S7.Associations between synergy factors and symptoms.a) Spider plot for Pearson correlations between the three latent factors and the 30 PANSS item scores, with control variables (site, gender, age) regressed out.Items marked in factor-specific colors indicate p < 0.05, FDR adjusted.Among them, 14 items (significantly more than the random value) showed a significant correlation with one of the factors.For positive subscale, blue line encloses the largest area, suggesting that factor 1 was positively correlated with most of these symptom items.For negative and general subscales, purple line encloses the smallest area, suggesting that factor 3 was negatively correlated with most of these symptom items.b) Spider plot for Pearson correlations of the 30 PANSS item scores with the three latent factors without regressing out control variables.

Figure S13 .
Figure S13.Transcriptomic correlates of synergistic interaction dysfunction patterns in three schizophrenia latent factors.a) Schematic of transcriptomics analysis to test whether gene expression explains three latent factors.First, we calculated Pearson correlations between gene expression at each brain region (ROI) and synergistic interaction dysfunction summed over ROIs for each factor.Second, we ranked gene by correlation coefficient, and selected top and bottom 10% for each factor as the factorspecific gene sets.Third, we calculated the gene expression similarity using the selected gene set and tested whether the constructed co-expression matrix correlates to the latent factors.Forth, we derived gene contribution indicator (GCI) gene sets using the virtual gene knock-out (KO) method.[6]Finally, we conducted GO enrichment analysis for GCI + and GCI − gene sets of each factor.b) Chord plot shows gene co-expression matrix in a.3 averaged over the networks.The color intensity of chords is the same as the color bar in a.3.c) Gene co-expression correlates with the latent factors.The significance was estimated by a spatial autocorrelation (SA) permutation (spin of the gene expression) test.d) Bar plots showing the result of disease enrichment analysis for both of the top and bottom 10% factor-specific gene sets.The bar length indicates the p values (Bonferroni corrected).The result showed that the both of the top and bottom gene sets were most significantly enriched in the schizophrenia, which further confirmed three factors inferred by LDA as schizophrenia-specific factors.
Figure S13.Transcriptomic correlates of synergistic interaction dysfunction patterns in three schizophrenia latent factors.a) Schematic of transcriptomics analysis to test whether gene expression explains three latent factors.First, we calculated Pearson correlations between gene expression at each brain region (ROI) and synergistic interaction dysfunction summed over ROIs for each factor.Second, we ranked gene by correlation coefficient, and selected top and bottom 10% for each factor as the factorspecific gene sets.Third, we calculated the gene expression similarity using the selected gene set and tested whether the constructed co-expression matrix correlates to the latent factors.Forth, we derived gene contribution indicator (GCI) gene sets using the virtual gene knock-out (KO) method.[6]Finally, we conducted GO enrichment analysis for GCI + and GCI − gene sets of each factor.b) Chord plot shows gene co-expression matrix in a.3 averaged over the networks.The color intensity of chords is the same as the color bar in a.3.c) Gene co-expression correlates with the latent factors.The significance was estimated by a spatial autocorrelation (SA) permutation (spin of the gene expression) test.d) Bar plots showing the result of disease enrichment analysis for both of the top and bottom 10% factor-specific gene sets.The bar length indicates the p values (Bonferroni corrected).The result showed that the both of the top and bottom gene sets were most significantly enriched in the schizophrenia, which further confirmed three factors inferred by LDA as schizophrenia-specific factors.

Figure S14 .
Figure S14.Validation analysis for three schizophrenia-specific factors from gene perspective.a) The gene ontology (GO) enrichment analysis for GCI + and GCI − gene sets of each factor.A Bubble plots showing the GO enrichment top 15 terms for GCI + (up) and GCI − (down).The biological process (BP), cellular component (CC), and molecular function (MF) are displayed separately.The dot size (count) represents the number of genes that are within the interest GCI + or GCI − gene panels as well as a specific GO term (y-axis).The different color intensities indicate the p values (Bonferroni corrected).b) Differences and similarities in GO enrichment results of factors.Factors 1 and 3 were the result of the most distinct pathological mechanisms.While factor 2 shared some similarities with both factors 1 and 3. c) 6 groups of GCI + and GCI − gene sets for each factor were all significantly enriched in the schizophrenia (Bonferroni corrected).

Figure S15 .Figure S16 .
Figure S15.Microcircuit parameters and biophysical simulations.a) The scatter plot for linear correlations between empirical FC and SC, and empirical FC and simulated FC.Left: NC; right: SZ.Upper: train; lower: test.The optimal model predicted functional connectivity nominally higher than the corresponding baseline correlations between structural (SC) and functional connectivity (FC).b) Recurrent connection of NC (left) and SCZ (right) inferred from pMFM.c) Subcortical input of NC (left)and SCZ (right) inferred from pMFM.[7]

Figure S17 .
Figure S17.Use of Neuromaps to contextualize brain maps of the three factors.The analysis incorporated the classic 17 maps, which provide comprehensive insights into various aspects of neuroanatomy and function, offering in-depth details for the study of the spatial associations with the three factors.The findings revealed that these three factors corresponded to a diverse and distinct set of maps compared to the initial map of synergy dysfunction.This discovery sheds further light on the heterogeneity of schizophrenia and offers insights into potential mechanisms underlying its development.

Table S1 . Demographic and clinical characteristics of schizophrenia participants, stratified according to site.
3Supplementary Table

Table S3 . Correlations across factors in split-half control analysis. a
) Correlations between latent factors in the two half-split samples and factors inferred from the whole sample.b) Correlations between factors in the two half-split samples.

Original factors Factor 1 Factor 2 Factor 3 COBRE factors
.001; t-test), the variance of the synergistic interactions was significantly higher in SCZ group, compared to NC group.b) Higher variance of the synergistic interactions among SCZ compared to NC was significant at six of the seven sites.Items marked by asterisks indicate p < 0.05, FDR adjusted.At WUHAN site, the synergy variance of SCZ group (0.269±0.055) was slightly higher than that of SCZ group (0.268±0.054), although not reaching significance (p = 0.57).c) Higher variance of the synergistic interactions within cortical regions among SCZ compared to NC was significant at six of the seven sites, consistent with the results of considering the whole-brain synergy in b.