Introduction

Schizophrenia is a complex and severe psychotic disorder featuring impaired functions across multiple dimensions, including cognition, language, movement, emotion, and social behavior1. This disorder affects approximately 1% of the global population and results in considerable burdens on patients, families, and society2,3. In the clinic, schizophrenia is ordinarily diagnosed through the observation of positive symptoms (delusions, hallucinations, disordered speech, and behavior disturbances) and negative symptoms (avolition, alogia, and anhedonia)4,5. However, schizophrenia has considerable overlap with other neurological disorders (e.g., bipolar disorder, autistic spectrum disorder, and Huntington’s disease) at both the clinical and genetic levels6,7,8, which makes accurate diagnosis quite challenging. Identifying the neural mechanisms of schizophrenia and linking neural signatures to multidimensional clinical symptoms are promising approaches for develo** more effective and individual-specific diagnoses.

Noninvasive neuroimaging technology advances the investigation of cognition and brain disorders on the whole-brain scale. The brain has been modeled as a complex network wherein regions of interest (ROIs) are set as nodes, while the functional connections measured by correlation or synchronization between regional signals are edges. Schizophrenia has been widely regarded as a dysconnectivity disorder9. In general, schizophrenia is characterized by overall reductions in functional connectivity (FC) compared to that of healthy controls9,10,11, as well as alterations in network topologies, including a decline in global efficiency, decreased functional integration, reduced modular structure, and increased global network robustness12,13,14,15. Abnormal connectivity can predict the total score of schizophrenia and explain part of its neural mechanism, but opposite results have been widely reported56. Both systems are typically task-positive, and their abnormalities are related to the brain imbalance between top-down and bottom-up controls57 that may underlie the impaired hallucinations58 in terms of functional organization and structural anatomy1,53,58,59. Our results further reinforce the importance of the salient attention system in schizophrenia27. Meanwhile, many studies have proposed that hallucinations may arise with dysconnectivity of the salient attention system with other systems27, especially with the DMN27,58,60. Here, we did not find a close relationship between the DMN and hallucinations, as observed in previous studies58,60, e.g., strong FC within the DMN and spontaneous DMN withdrawal for the hallucination state58,60, but we found that a less variable segregation process in the DMN and control systems is related to more severe avolition, which is the core negative symptom in schizophrenia61 and reflects a reduction in the motivation to initiate or persist in goal-directed behavior. The DMN and control networks are associated with goal-directed behavior62, and their abnormalities are closely related to avolition63,64,65, as confirmed in our study. Meanwhile, the salience-monitoring theory proposes that abnormal coupling between the salient attention system and DMN begets positive and negative symptoms of schizophrenia66. Our relationships between the DMN and avolition and between the salient attention system and hallucinations provide further support for this hypothesis.

We did not find a significant relationship between SANS/SAPS scores and brain features, including both NSP and graph theory measures, at the whole-brain level or the system level, but we adopted the machine-learning method to successfully predict the scores. Compared to classical graph theory, the NSP-based method had superior performance in predicting SANS/SAPS scores and detecting network alterations, reflecting the advantages of our method based on hierarchical modules in brain FC networks. This result is highly consistent with a series of our works wherein the NSP-based method is more powerful in linking the brain to diverse cognitive abilities32, task performance31, stress conditions67, ADHD symptoms33, and bipolar disorder symptoms68. All these findings demonstrated that the NSP-based features detected across multiple levels are promising biomarkers for schizophrenia and other brain disorders.

In the prediction models, the features in the DMN have opposite contributions to SAPS and SANS, and using a multivariate regression model, we further confirmed that SANS and SAPS have opposite effects on brain networks. Previous studies found that primary motor and cerebellar connectivity have opposite predictions on positive and negative symptoms22,23, and self-similarity and multifractality of resting-state brain signals with opposite distribution patterns have the same associations with negative and positive symptoms24. Here, we provided the first direct evidence that positive and negative symptoms of schizophrenia have opposite effects on the functional organization of resting-state brains while excluding their interaction, especially that the DMN has opposite contributions to the predictions of SANS and SAPS scores. The DMN is negatively correlated with other systems69, and its abnormality may underlie the positive symptoms58,60,70 and negative symptoms63,64,65 of schizophrenia. Hare SM et al. reported that FC with a 4 s lag between the anterior DMN and posterior DMN was negatively associated with the severity of disordered thought and attentional deficits, and FC with a 2 s lag between the anterior DMN and salience network was positively related to the severity of flat affect and bizarre behavior66, which is highly consistent with our observations of opposite functions of the DMN on positive and negative symptoms. In particular, negative symptoms often persist after treatment with antipsychotic medication71. Even though negative symptoms (e.g., anhedonia/asociality) were found to be related to the posterior cingulate and precuneus, part of the DMN, in a two-tone auditory oddball task, identifying reliable targets of regions for treatment remains a challenge in the clinic72. Our results greatly extend the understanding of schizophrenia and provide that distinct DMN regions may be targets for positive and negative symptoms.

Using GO enrichment, we demonstrated that the SANS × SAPS interaction is related to the pathology of intracellular transport and cellular localization, such as in mitochondria35,52. These biological processes may impact neuronal development, synaptic function, and plasticity36,37. The corresponding phenotypes are related to ataxia and abnormal motor function, which have been widely observed in schizophrenia38,51. In particular, visual control influenced the age-associated increase in ataxic gait51, and we found that the visual system contributed to both positive and negative symptoms in the machine-learning prediction models. These results may suggest baseline pathological changes in motor function in schizophrenia. Meanwhile, we confirmed that 12/32 schizophrenia-related genes had damaging ultrarare mutations34, and 9/12 genes were related to the SANS × SAPS interaction, indicating that ultrarare mutation genes may mainly contribute to the baseline symptoms of abnormal motor function in schizophrenia. Thus, beginning with motor abnormalities, further development of the disorder in different directions may generate positive and negative symptoms. More specifically, negative symptoms may be inherent to the alternated biological process in synapses that transfer neural information between neurons, as also suggested by the genetics and protein-interaction evidence for the role of postsynaptic signaling processes in schizophrenia36,73. In human phenotypes, negative symptoms are related to autistic and aggressive behaviors that extensively overlap between schizophrenia38 and autism74. As language disturbances are a key feature of schizophrenia75, our results suggest that patients are unable to flexibly communicate with others and effectively express themselves, resulting in impulsive and violent behaviors in the clinic, as also seen in autism76. Finally, we found that positive symptoms are related to the abnormal biological process of metabolism and the phenotypes of hyperammonemia, increased serum lactate, and acidosis. A recent meta-analysis on lactate or pH in schizophrenia revealed a significant increase in lactate in schizophrenia and a nonsignificant decrease in pH77. Our GO enrichment results provide further evidence that abnormal metabolic processes in schizophrenia brains result in the accumulation of ammonia, inducing hyperammonemia, acidosis, and increased serum lactate39. All these abnormalities are closely related to schizophrenia39,78, especially acidosis altering dopamine and glutamate neurotransmission, causing symptoms of schizophrenia39.

Methods

Participants

The dataset was extracted from the UCLA Consortium for Neuropsychiatric Phenomics LA5c Study79. Fifty schizophrenia patients (female: 12; age: 36.46 ± 8.88 years old) and 50 healthy controls (female; 12, age: 34.84 ± 9.03 years old) were included. There was no significant difference in age (two-sample t-test, t(98) = 0.905, p = 0.354). The clinical symptoms of schizophrenia patients were evaluated with the Scale for the Assessment of Positive Symptoms (SAPS) and the Scale for the Assessment of Negative Symptoms (SANS)80. The SANS includes five symptom dimensions, namely, avolition, alogia, anhedonia, attention, and affective flattening; the SAPS includes hallucinations, delusions, bizarre behavior, thought disorder, and blunted affect. The clinical scores of these symptoms are provided in the Supplementary Data. 3 (SANS) and Supplementary Data. 4 (SAPS). All studies were conducted in accordance with principles for human experimentation as defined in the Declaration of Helsinki and the International Conference on Harmonization Good Clinical Practice guidelines. All participants gave written informed consent according to the procedures approved by the University of California Los Angeles Institutional Review Board.

MRI data processing

Each participant completed one resting-state fMRI scanning session (time of repetition [TR] = 2 s), lasting for 304 s (152 frames); see ref. 81 for more detailed scanning parameters. Resting-state fMRI data were processed using FSL (http://www.fmrib.ox.ac.uk/fsl/) and AFNI (http://afni.nimh.nih.gov/afni/) software in the Ubuntu 14.04 system29. The procedure included (1) slice-timing correction to the median slice; (2) motion correction; (3) segmenting the anatomical image; (4) Montreal Neurological Institute (MNI) normalization; (5) spatial smoothing using a Gaussian kernel with a 6-mm full width at half maximum (FWHM); (6) bandpass filtering (0.01–0.1 Hz); and (7) elimination of 6 rigid body motion correction parameters and the signal from the white matter and a ventricular region of interest using linear regression. The mean framewise displacement (FD) was 0.160 ± 0.159 mm for the healthy control group and 0.267 ± 0.215 mm for the schizophrenia group. The difference in FD between the two groups was significant (two-sample t-test, t(98) = 2.779, p = 0.004). Thus, an analysis of covariance (ANCOVA) was carried out for the group comparison. Since the global whole-brain signal was related to brain network integration and segregation (Supplementary Table. 3) and may contain the clinical information of schizophrenia symptoms82,83,84, it was not removed from our analysis.

Brain functional connectivity

The brain was parcellated into N = 200 regions of interest (ROIs) using the Schaefer atlas85, and the results were similar for the brain parcellation of 500 regions (see Supplementary Figs. 3, 6, 8, 10, 11). The blood oxygen level-dependent (BOLD) signals of voxels within each region were averaged to obtain the regional fMRI time series, and the Pearson correlation coefficient was used to estimate the FC between regions. The BOLD signals were divided into pieces using the sliding window method, and temporal-dynamic FC was calculated in each window. As suggested by ref. 86, we chose a window width of 60 s (30 points) and a sliding step of 2 s (1 point), and there were 132 windows. Meanwhile, group-stable, individual static FC networks were also constructed, which were used to address the limitation of shorter fMRI series lengths resulting in stronger network segregation32 (see fMRI length calibration). For the group-stable FC, the fMRI time series for all participants in each group were concentrated, and the FC was computed on a sufficiently long time scale. Individual static FC networks were constructed using the whole fMRI time series in each participant. In all FC networks, negative connectivity was set to zero, and the diagonal elements were kept at one32,87,88.

Nested-spectral partition (NSP) method

The NSP method was introduced to detect hierarchical modules in FC networks based on eigenmodes. The FC matrix C can be decomposed into functional modes with eigenvectors U and eigenvalues Λ, and the modes were sorted according to the descending order of eigenvalues Λ. The NSP method has the following procedures32:

  1. 1.

    In the first functional mode, all regions had the same negative or positive eigenvector value; this mode was regarded as the first level, with one module (i.e., whole-brain network).

  2. 2.

    In the second functional mode, the regions with positive eigenvector signs were assigned to a module, and the regions with negative signs formed the second module. This mode was regarded as the second level, with two modules.

  3. 3.

    Based on the positive or negative sign of regions in the third mode, each module in the second level was further partitioned into two submodules, forming the third level. Subsequently, the FC network could be modularly partitioned into multiple levels with the order of functional modes increasing (see Supplementary Fig. 12 for a more detailed description of the process). Regions within a module in a level may have the same sign of eigenvector values in the next level, and then the module is indivisible, which has no effect on the subsequent partitioning process. When each module contained only a single region at a given level, the partitioning process was stopped.

After the partitioning process, the NSP method outputs the module number \({M}_{i}(i=1,\cdots ,N)\) and the modular size \({m}_{j}(j=1,\cdots ,{M}_{i})\), e.g., the number of regions within a module, at each level.

Hierarchical segregation and integration components

Functional segregation and integration in brain FC networks were defined across hierarchical modules that were detected by the NSP method31,32. Consistent with the graph-based modularity30, modules at a given level support the segregation between them and integration within them. The increased module number Mi with the increasing order of functional mode reflects higher segregation. At each level, segregation and integration can be defined as32:

$${H}_{i}=\frac{{\varLambda }_{i}^{2}{M}_{i}(1-{p}_{i})}{N}$$
(1)

with

$${p}_{i}=\frac{{\sum }_{j}|{m}_{j}-N/{M}_{i}|}{N}$$
(2)

Here, N is the number of regions; Λi is the eigenvalue for the i-th functional mode; pi is a correction factor for heterogeneous modular size and reflects the deviation from the optimized modular size \({m}_{j}=N/{M}_{i}\) at the i-th level. Since the first level contains only a single module for all regions, this level was taken to reflect the global integration component:

$${H}_{In}=\frac{{H}_{1}}{N}=\frac{{\varLambda }_{1}^{2}{M}_{1}(1-{p}_{1})}{{N}^{2}}$$
(3)

With the increasing order of functional modes, the levels contain more modules with smaller sizes and support higher segregation. Thus, the segregation component was summed from the second to Nth levels:

$${H}_{Se}=\mathop{\sum }\limits_{i=2}^{N}\frac{{H}_{i}}{N}=\mathop{\sum }\limits_{i=2}^{N}\frac{{\varLambda }_{i}^{2}{M}_{i}(1-{p}_{i})}{{N}^{2}}$$
(4)

Consequently, for a single FC network, we obtained the separated integration component HIn and segregation component HSe. A larger HSe and smaller HIn reflect stronger network segregation and weaker global integration.

The contribution of each region to the integration and segregation components can be further defined as:

$${H}_{In}^{j}={H}_{1}{U}_{1j}^{2}\,{{{{{\rm{and}}}}}}\,{H}_{Se}^{j}=\mathop{\sum }\limits_{2}^{N}{H}_{i}{U}_{ij}^{2}$$
(5)

where \({\sum }_{j=1}^{N}{U}_{ij}^{2}=1\) for the i-th functional mode. The integration and segregation of the functional system were obtained by averaging the corresponding components of regions within this system.

For the dynamic FC networks, the time-resolved segregation component \({H}_{Se}(t)\) and integration component \({H}_{In}(t)\) at each time window for each individual were obtained. The values of integration and segregation strength were defined as the average values of \({H}_{In}(t)\) and \({H}_{Se}(t)\) over time, respectively. The values of integration and segregation variability were calculated as follows:

$${F}_{In}^{j}={\sigma }_{{H}_{In}^{j}}\,{{{{{\rm{and}}}}}}\,{F}_{Se}^{j}={\sigma }_{{H}_{Se}^{j}}$$
(6)

where \({\sigma }_{{H}_{In}^{j}}\) and \({\sigma }_{{H}_{Se}^{j}}\) represent the standard deviations of the \({H}_{In}^{j}(t)\) and \({H}_{Se}^{j}(t)\) time series.

Notably, finer parcellation of the brain (i.e., 500 regions) would generate more modules with smaller sizes in higher-order levels of brain functional networks, accompanied by a larger segregation component and lower integration component (see Supplementary Fig. 13). However, the results for schizophrenia are robust for different brain parcellations (see Supplementary Figs. 3, 6, 8, 10, 11).

fMRI length calibration

Since shorter fMRI series lengths result in stronger apparent network segregation32, we adopted a proportional calibration scheme to address this limitation32. Assume that the integration component of the stable FC network in each group is \({H}_{In}^{S}\) and that the integration components of individual static FC networks for all participants are \({H}_{In}=[{H}_{In}(1),{H}_{In}(2),\cdots ,{H}_{In}(50)]\). The group-averaged integration component is calibrated to the stable component:

$${H}_{In}^{{\prime} }(n)={H}_{In}(n)\times {H}_{In}^{S}/\langle {H}_{In}\rangle$$
(7)

Here, \(\langle \rangle\) represents the group average across all participants, and n represents the individual. Then, calibration was also performed for the regional integration component \({H}_{In}^{j}\). For region j of the n-th participant, the calibrated regional integration component is \({H}_{In}^{j{{\hbox{'}}}}={H}_{In}^{j}/{H}_{In}(n)\times {H}_{In}^{{{\hbox{'}}}}(n)\), where the relative contribution of each region to network integration remains consistent.

For dynamic FC networks, the temporal integration component \({H}_{In}(t)\) for each individual was calibrated to its static integration component \({H}_{In}^{{{\hbox{'}}}}\) to maintain the individual rankings. The vector of the dynamic integration component for an individual across all windows was \({h}_{In}=[{h}_{In}^{1},{h}_{In}^{2},\cdots ,{h}_{In}^{132}]\), and the calibrated result was calculated as \({h}_{In}^{t{\prime} }={h}_{In}^{t}{H}_{In}^{i{\prime} }/\langle {h}_{In}\rangle\). Here, \(\langle \rangle\) represents the average across time windows.

The same calibration processes were performed for the segregation component on the global and local scales and in static and dynamic networks, and the calibration was performed separately in each group.

Machine-learning prediction model

The scikit-learn toolbox was used to construct a machine-learning prediction model89. First, we used the function linear_model. Linear regression to build linear predictive models. The independent variables were regional measures (i.e., \({H}_{{{{{{\mathrm{In}}}}}}}^{j}\), \({H}_{Se}^{j}\), \({F}_{In}^{j}\), \({F}_{Se}^{j}\)), and the dependent variables were the SANS or SAPS scores. Second, leave-one-out cross-validation (LOO-CV) was applied with the function cross_val_predict. In each iteration of LOO-CV, one participant was selected as the test set, and the remaining participants were selected as the training set. This process was repeated until every participant had been selected as a test set once. Then, we used the correlation between the real clinical score and the predicted score to evaluate the prediction accuracy, and the statistical comparison was performed by permuting the ranks of clinical scores (10,000 times). In the prediction model, the functions f_regression and SelectKBest were used to select features. The f_regression function calculated the correlations between regional measures and clinical scores and sorted the regions according to their F values. Then, the first K features were selected and fed into the prediction model. Here, we varied K from 1 to N and chose the best K, defined as the value at which the model had the best predictive performance. The input features were normalized such that the weights of regions were comparable.

Effects of SANS and SAPS on the brain

To extract the effects of positive and negative symptoms, as well as their interaction effect on brain FC networks, we built a multiple regression model:

$$H \sim {{{{{\mathrm{SANS}}}}}}+{{{{{\mathrm{SAPS}}}}}}+{{{{{\mathrm{SANS}}}}}}\times {{{{{\mathrm{SAPS}}}}}}+{{{{{\mathrm{sex}}}}}}+{{{{{\mathrm{age}}}}}}+{{{{{\mathrm{FD}}}}}}$$
(8)

Here, H is the brain measure for each region, i.e., \({H}_{{{{{{\mathrm{In}}}}}}}^{j}\), \({H}_{{{{{{\mathrm{Se}}}}}}}^{j}\), \({F}_{{{{{{\mathrm{In}}}}}}}^{j}\) and \({F}_{{{{{{\mathrm{Se}}}}}}}^{j}\). The regression coefficients of SANS and SAPS reflect the effects of negative and positive symptoms on the brain, and the coefficient of SANS × SAPS indicates the interaction effect. FD is the mean framewise displacement.

Gene Ontology (GO) enrichment analysis

The gene expression data used in this study were extracted from the Allen Human Brain Atlas (AHBA)90. This open-source project contains ~3700 tissue samples from six donors and provides the Montreal Neurological Institute (MNI) coordinates of the tissues. The tissue samples from four donors are limited to the left hemisphere, and the samples from the remaining two donors span the whole brain. The abagen toolbox was used to map the microarray gene expression data to 200 regions in the Schaefer atlas91. This toolbox provides a standardized processing procedure of accepting an atlas and returning a parcellated regional gene expression matrix. Here, we used the default settings, as suggested by ref. 91. Although only two donors had gene expression data available from the right hemisphere, we chose to use whole-brain gene expression due to the asymmetry between the left and right hemispheres. We calculated the Pearson correlations between gene expression and network components affected by SANS/SAPS scores to identify the significant genes (p < 0.05, FDR corrected), which were further processed with ToppGene Suite to perform GO annotation analysis (FDR correction method, significance cutoff level of 0.01).

Statistics and reproducibility

Statistical analysis was performed with MATLAB R2016b and R (v4.0.4). A two-sample t-test was used to compare the age and FD between the two groups. ANCOVA (analysis of covariance) tested the between-group differences in brain network measures with FD as the confounding variable. FDR method of Benjamini–Hochberg was used for multiple comparisons. A permutation test (1000 times) was conducted to test the differences in relative changes between different systems. Pearson correlation was used to evaluate the relationships between brain network measures and symptom scores. P value < 0.05 was considered statistically significant.

To test the reproducibility of results, we used the Schaefer atlas to parcellate the brain into N = 200 regions (main analysis) and N = 500 regions (reproducibility analysis), and reported consistent results for these two parcellations. We also performed the graph theory analysis for N = 200 regions, and the results are also similar.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.