Biomarker Identification Through Integrating fMRI and Epigenetics

Abstract

Objective:

Integration of multiple datasets is a hot topic in many fields. When studying complex mental disorders, great effort has been dedicated to fusing genetic and brain imaging data. However, an increasing number of studies have pointed out the importance of epigenetic factors in the cause of psychiatric diseases. In this study, we endeavor to fill the gap by combining epigenetics (e.g., DNA methylation) with imaging data (e.g., fMRI) to identify biomarkers for schizophrenia (SZ).

Methods:

We propose to combine linear regression with canonical correlation analysis (CCA) in a relaxed yet coupled manner to extract discriminative features for SZ that are co-expressed in the fMRI and DNA methylation data.

Result:

After validation through simulations, we applied our method to real imaging epigenetics data of 184 subjects from the Mental Illness and Neuroscience Discovery Clinical Imaging Consortium. After significance test, we identified 14 brain regions and 44 cytosine-phosphate-guanine(CpG) sites. Average classification accuracy is 88.89%. By linking the CpG sites to genes, we identified pathways Guanosine ribonucleotides de novo biosynthesis and Guanosine nucleotides de novo biosynthesis, and a GO term Perikaryon.

Conclusion:

This imaging epigenetics study has identified both brain regions and genes that are associated with neuron development and memory processing. These biomarkers contribute to a good understanding of the mechanism underlying SZ but are overlooked by previous imaging genetics studies.

Significance:

Our study sheds light on the understanding and diagnosis of SZ with a imaging epigenetics approach, which is demonstrated to be effective in extracting novel biomarkers associated with SZ.

I. Introduction

SINCE the discovery of genetics by Gregor Mendel in the late 19th century, researchers have dedicated considerable efforts to understanding the language of genes. In abundant studies, various linkages have been established between genetic factors and disease. Building upon the field of genetics, the term epigenetics was first introduced in the early 1940’s by Conrad Waddington[1]. Now, epigenetics can be viewed as the branch of genetics which studies heritable phenotype changes that occur without alternations in the underlying DNA sequence[2].

Epigenetic changes are natural and regular, and they can be influenced by environmental factors including age and lifestyle. These processes increase the complexity of genomic responses by allowing short-term, fine-tuning of the genome, and provide a mechanism for preserving information on environmental exposures[3]. DNA methylation, for example, has drawn a lot of attention from the scientific community. It is the process by which methyl groups are added to the DNA molecule. The dynamic interaction between DNA methylation and environment continues throughout one’s life, thereby promoting genome plasticity and short-term adaptation to the environment. DNA methylation can be heritable and has been proven to strongly associate with gene silencing in a variety of biological contexts[4–6]. Especially in CpG dense contexts, DNA methylation is regarded as a powerful transcriptional repressor. Researchers have also identified linkages between DNA methylation and brain functions. The work by Griffith and Mahler suggests that DNA methylation could provide a basis for long-term memory in the brain[7]. Multiple studies have also found a connection between DNA methylation and psychiatric diseases including schizophrenia (SZ)[8–10]. In this study, we further investigate SZ with the help of both DNA methylation and brain imaging fMRI data.

Multi-view learning has many advantages over single-view learning with regards to disease classification and biomarker identification[11, 12]. A number of studies have evaluated the integration of fMRI and genetic data in SZ[13, 14]. However, there has been little work on the fusion of epigenetics and fMRI data for the study of SZ. In this study, we intend to fill the gap by jointly analysing DNA methylation and fMRI data. More specifically, we will combine fMRI and DNA methylation data to identify significant co-expressed biomarkers for SZ, which will then be input into a classifier for the classification of SZ. Both brain imaging and epigenetics markers have been shown to have a strong connection with SZ, and their combination can help identify latent information shared by them. This approach will also enable us to identify genes (based on where CpG sites reside) that are overlooked by other approaches. A preliminary version of this work has been reported [15].

The rest of the paper is organized as follows. In Section II, we review sparse regression models and CCA, and describe the collaborative model we have proposed. Then, we present experimental results on both hybrid simulation and real SZ datasets in Section III. We conclude the paper in Section IV by summarizing the major contributions of the work.

II. Method

A. Sparse regression models

Let’s denote a set of observations $\mathit{y}\in {ℝ}^{n\times 1}$ and the corresponding measurements $\mathit{X}\in {ℝ}^{n\times p}$, where n is the number of observations, and p is the dimension of the measurement. Assuming that an observation y_i is conditionally independent given its measurement x_i, $i=1,2,\dots ,n$, linear regression estimates the prediction coefficients $\mathit{\beta }={\left[{\beta }_1,{\beta }_2,\dots {\beta }_p\right]}^T$ through the minimization of the following objective function:

$$\beta =\arg \underset{\mathit{\beta }}{\min }\sum _{i=1}^n{\left(y_i-{\mathit{x}}_i\mathit{\beta }\right)}^2$$ (1)

However, when the dimension of measurement p far exceeds the number of observation n, Eq. (1) is underdetermined. LASSO (least absolute shrinkage and selection operator) regression is useful in this context [16], and takes the following form:

$$\begin{gathered} \beta =\arg \underset{\mathit{\beta }}{\min }\sum _{i=1}^n{\left(y_i-{\mathit{x}}_i\mathit{\beta }\right)}^2 \\ \text{subject to}\sum _{i=1}^p\left|{\beta }_i\right|\le t \end{gathered}$$ (2)

where t is a hyper-parameter that determines the level of sparsity.

For the purpose of optimization, this objective function can be re-written as:

$$\beta =\arg \underset{\mathit{\beta }}{\min }\parallel \mathit{y}-\mathit{X}\mathit{\beta }{\parallel }_2^2+\lambda \parallel \mathit{\beta }{\parallel }_1$$ (3)

The last term is the LASSO penalty term, taking the form of l₁ norm. For large values of the hyper-parameter λ, many entries of β are set to 0. The use of sparsity constraints helps select only a few informative features from the measurement X. In this study, this property is very useful because of the basic assumption that only a limited number of features are associated with the phenotypes.

Besides l₁ norm based penalty, there are other penalty functions that can be used. For example, ridge regression, which adopts l₂ norm $P_{ridge}(\mathit{\beta })=\parallel \mathit{\beta }{\parallel }_2^2$, can give a smooth estimator. Fused LASSO uses another popular penalty, $P_{fused}(\mathit{\beta })={\lambda }_1\parallel \beta {\parallel }_1+{\lambda }_2{\sum }_{i=2}^p\left|{\beta }_i-{\beta }_{i-1}\right|$. The fused LASSO combines both sparsity and smoothness constraints so that consecutive variables are encouraged to be similar.However, there is a limitation of the LASSO regression model.

Many real-world problems involve more than one type of measurements on the same group of subjects, and the formulation of LASSO fails to deal with this situation. A straightforward way to accommodate this problem is to conduct multiple independent LASSO to extract features from different views. However, this will overlook the intrinsic relationship between each measurement.

To study the relationship between different views, we consider learning through canonical correlation analysis in the next section.

B. Canonical correlation analysis

In bioinformatics, a variety of problems amount to joint analysis of measurements from different sources describing the same observations. In statistics, there are several techniques to address this problem: sparse partial least square (sPLS), cross-modal factor analysis (CFA), and canonical correlation analysis (CCA). In this section, we focus on using CCA to study the relationship between different measurements on the same observations.

Unlike LASSO regression described in the last section, CCA is an unsupervised learning algorithm that is widely used in statistics to find the linear combinations of variables from two types of measurements with maximal correlation. Specifically, given two datasets X₁ and X₂, CCA seeks the projection vectors θ₁ and θ₂ that minimize the following objective function:

$$\begin{gathered} \left({\mathit{\theta }}_1,{\mathit{\theta }}_2\right)=\arg \underset{{\mathit{\theta }}_1,{\mathit{\theta }}_2}{\min }{\Vert {\mathit{X}}_1{\mathit{\theta }}_1-{\mathit{X}}_2{\mathit{\theta }}_2\Vert }_2^2 \\ \text{subject to}{\mathit{\theta }}_1^T{\mathit{X}}_1^T{\mathit{X}}_1{\mathit{\theta }}_1=1, \\ {\mathit{\theta }}_2^T{\mathit{X}}_2^T{\mathit{X}}_2{\mathit{\theta }}_2=1 \end{gathered}$$ (4)

where the constraints are applied to avoid null solutions.

To solve the overfitting problem, sparse CCA (sCCA) is proposed. In particular, sCCA uses sparsity constraint so that dimension reduction or feature selection can be performed. It also facilitates the interpretation of selected features. A formulation of sCCA is as follows:

$$\begin{gathered} \left({\mathit{\theta }}_1,{\mathit{\theta }}_2\right)=\arg \underset{{\mathit{\theta }}_1,{\mathit{\theta }}_2}{\min }{\Vert {\mathit{X}}_1{\mathit{\theta }}_1-{\mathit{X}}_2{\mathit{\theta }}_2\Vert }_2^2 \\ \text{subject to}{{\mathit{\theta }}_1}^T{\mathit{\theta }}_1=1,{{\mathit{\theta }}_2}^T{\mathit{\theta }}_2=1 \\ P\left({\mathit{\theta }}_1\right)\le t_1,P\left({\mathit{\theta }}_2\right)\le t_2 \end{gathered}$$ (5)

where $P(\ast )$ is a chosen sparse penalty, such as l₁ norm. In recent years, sCCA has been widely applied to genomic data analysis[17]. In the following section, we rely on sCCA to enforce the co-expression between features extracted from different data views.

C. Collaborative regression

Collaborative regression (CoRe) was first proposed in [18], which is a form of sparse supervised CCA. Given two measurements X₁ and X₂ and one set of observation y, CoRe aims at finding the estimator β₁ and β₂ that minimize the following objective function:

$$\begin{gathered} {\lambda }_1{\Vert \mathit{y}-{\mathit{X}}_1{\mathit{\beta }}_1\Vert }_2^2+{\lambda }_2{\Vert \mathit{y}-{\mathit{X}}_2{\mathit{\beta }}_2\Vert }_2^2 \\ +{\lambda }_3{\Vert {\mathit{X}}_1{\mathit{\beta }}_1-{\mathit{X}}_2{\mathit{\beta }}_2\Vert }_2^2 \end{gathered}$$ (6)

where λs are hyper-parameters that control the relative importance of each term in the objective function. The first two terms are linear regression terms. The third is a CCA, which is designed to minimize the disagreement between the extracted features from X₁ and X₂. The formulation aims at uncovering discriminative features from each dataset, while ensuring that the features have maximal correlation. Since Eq. (6) is convex, and in classical cases where $\left(p_1,p_2\right)<n$, ${\mathit{X}}_1^T{\mathit{X}}_1$ and ${\mathit{X}}_2^T{\mathit{X}}_2$ are generally nonsingular, closed-form solutions for β₁ and β₂ can be found [18].

To cope with the high dimensionality of multi-view data (which is always the case for brain imaging and epigenetics), we can adopt l₁ norm to enforce sparsity:

$$\begin{gathered} \sum _{i=1}^2{\lambda }_i{\Vert \mathit{y}-{\mathit{X}}_i{\mathit{\beta }}_i\Vert }_2^2+{\lambda }_3{\Vert {\mathit{X}}_1{\mathit{\beta }}_1-{\mathit{X}}_2{\mathit{\beta }}_2\Vert }_2^2 \\ +{\lambda }_4{\Vert {\mathit{\beta }}_1\Vert }_1+{\lambda }_5{\Vert {\mathit{\beta }}_2\Vert }_1 \end{gathered}$$ (7)

where λ₄ and λ₅ are the weight parameters of l₁ penalty norm. To simplify the model, we set ${\lambda }_1={\lambda }_2=1-\gamma$, ${\lambda }_3=\gamma$, and ${\lambda }_4={\lambda }_5=\lambda$, where $\gamma \subset [0,1]$. Then we get a simplified version of the formulation:

$$\begin{gathered} (1-\gamma )\sum _{i=1}^2{\Vert \mathit{y}-{\mathit{X}}_i{\mathit{\beta }}_i\Vert }_2^2 \\ +\gamma {\Vert {\mathit{X}}_1{\mathit{\beta }}_1-{\mathit{X}}_2{\mathit{\beta }}_2\Vert }_2^2+\lambda \parallel \mathit{\beta }{\parallel }_1 \end{gathered}$$ (8)

where $\beta =\left[{\beta }_1;{\beta }_2\right]$, is a vector of $\left(p_1+p_2\right)$ length. In this formulation, each entry of the estimator β is forced to fit to both the linear regression and the CCA term simultaneosly; however, this might be too restricting. Thus, we propose an alternative formulation to combine linear regression and CCA in a more relaxed manner as recently proposed by us in [19]. First, we use α to fit the linear regression term, and use θ to fit the CCA term. Second, we re-define ${\mathit{\beta }}_k=\left[{\mathit{\alpha }}_k,{\mathit{\theta }}_k\right]$ for the k-th view. Then, we use ${\mathit{\beta }}_k^i$ to denote the i-th row of k-th view, which is $\left[{\mathit{\alpha }}_k(i),{\mathit{\theta }}_k(i)\right]$. Third, we can form a relaxed yet coupled model to combine both CCA and linear regression as follows:

$$\begin{gathered} \arg \underset{{\mathit{\beta }}_1,{\mathit{\beta }}_2}{\min }(1-\gamma )\sum _{k=1}^2{\Vert \mathit{y}-{\mathit{X}}_k{\mathit{\alpha }}_k\Vert }_2^2+ \\ \gamma {\Vert {\mathit{X}}_1{\mathit{\theta }}_1-{\mathit{X}}_2{\mathit{\theta }}_2\Vert }_2^2+\lambda \sum _{k=1}^2\sum _{i=1}^{p_k}{\Vert {\mathit{\beta }}_{\mathit{k}}^i\Vert }_2 \end{gathered}$$ (9)

We refer this model as multi-task, collaborative regression(MT-CoReg). The third term in Eq. (9) is actually a $l_1/l_2$ norm, which encourages α and θ to be coupled but not necessarily with the same value.

To our understanding, this model does not only combine CCA with linear regression, but also allows for flexibility. Because of the sparsity term, many entries of α and θ will be zeros, and the non-zero entries are the features selected by this model. Then for each view, $\left|{\mathit{\alpha }}_k(i)\right|+\left|{\mathit{\theta }}_k(i)\right|$ is used to represent the importance of i-th feature of the k-th view. By ranking this value, we can estimate the importance of selected features. In this way, by minimizing Eq. (9), we can successfully extract discriminative features that are co-expressed among different views. Thus, we can call this model as multi-task collaborative regression.

To solve this optimization problem, we optimize β_k alternatively. Given ${\mathit{\beta }}_1^{\ast }$ the optimization problem degenerates to the following optimization:

$$\begin{gathered} \arg \underset{{\mathit{\beta }}_2\mid {\mathit{\beta }}_1^{*}}{\min }(1-\gamma ){\Vert \mathit{y}-{\mathit{X}}_2{\mathit{\alpha }}_2\Vert }_2^2+ \\ \gamma {\Vert {\mathit{X}}_1{\mathit{\theta }}_1^{\ast }-{\mathit{X}}_2{\mathit{\theta }}_2\Vert }_2^2+\lambda \sum _{i=1}^{p_2}{\Vert {\mathit{\beta }}_2^i\Vert }_2 \end{gathered}$$ (10)

Let us define the following quantities:

$$\begin{gathered} {\widehat{\mathit{y}}}_2=\left[\sqrt{1-\gamma }\mathit{y},\sqrt{\gamma }{\mathit{X}}_1{\mathit{\theta }}_1\right] \\ {\widehat{\mathit{X}}}_2=\left[\sqrt{1-\gamma }{\mathit{X}}_2,\sqrt{\gamma }{\mathit{X}}_2\right] \end{gathered}$$ (11)

then the optimization problem (10) can be rewritten as the following form:

$$\arg \underset{{\mathit{\beta }}_2\mid {\mathit{\beta }}_{\text{i}}^{*}}{\min }{\Vert {\widehat{\mathit{y}}}_2-{\widehat{\mathit{X}}}_2{\mathit{\beta }}_2\Vert }_2^2+\lambda \sum _{i=1}^{p_2}{\Vert {\mathit{\beta }}_2^i\Vert }_2$$ (12)

which becomes a classical group-lasso regression problem. Similarly, given a ${\mathit{\beta }}_2^{\ast }$, we can solve β₁ in the same way. Thus, we can solve problem (10) by finding both βs iteratively until their convergence. In this study, we adopt software SPAMS[20] to solve the group-lasso problem.

D. Model performance

To illustrate the performance of our proposed method, we conducted simulation experiment. We generated a two-view toy dataset ${\mathit{X}}_1\in {ℝ}^{100\times 200}$, ${\mathit{X}}_2\in {ℝ}^{100\times 200}$ with binary phenotype $\mathit{y}\in {ℝ}^{100}$. For each feature in X₁ and X₂, it follows a normal distribution. We generated a latent variable u to simulate cross-correlated components so that columns 101 ∼ 125 of X₁ and columns 101 ∼ 130 of X₂ are mutually co-expressed. Then we generated a binary phenotype vector y and added discriminative signals to columns 116 ∼ 130 of X₁ and columns 116 ∼ 135 of X₂. This simulation setting is visualized in Fig. 1 as blue and orange lines respectively. True features to extract are the overlap of blue and orange lines. To mimic the real scenario, we added salt-and-pepper noise when generating the cross-correlated components, and white noise when generating the discriminative components. The signal-to-noise ratio (SNR) is set as −3dB.

Figure 1:

Results on synthetic toy dataset with our MT-CoReg model. Each graph represents one view where blue and orange lines correspond to the simulation settings, and green bars correspond to the selected features ($|\alpha |+|\theta |$ value).

Results from our MT-CoReg are visualized and presented in Fig. 1. The green bar represents the $|\alpha |+|\theta |$ value, by which we rank the importance of each feature. During the experiment, for simplicity, we set $\gamma =0.5$ and tuned the λ through cross-validation. As shown in the figure, the result of feature selection is satisfactory and we succeeded in exempting the irrelevant features.

For comparison, we applied both LASSO and sparse CCA(sCCA) to this toy dataset, and the results are presented in Fig. S3 and Fig. S4, respectively. Hyper-parameters of LASSO and sCCA were tuned to select a comparable number of features to that of the proposed model. Having high specificity of selected features is one goal of the proposed model. In the simulation setting, both the number of features and that of ‘true features’ are relatively small. If cross-validation is adopted to tune the parameter, more features will be selected. This could lead to a higher classification accuracy in the subsequent test but at the cost of having worse specificity in feature selection.

It is clear that features selected by LASSO are more dense and evenly spread throughout the orange lines; sCCA makes no use of phenotype information so it favours the blue lines. Note that, feature selection by MT-CoReg slightly favors the discriminative features. This is expected because we tune the hyper-parameters based on classification accuracy and the discriminative features are also correlated through the link with phenotypic data. This result is desirable because not all co-expressed features are directly relevant to the phenotype, and the biomarkers to be identified should be phenotype-specific.

To better compare the performance, we calculated both the sensitivity and the specificity of three methods in terms of feature selection and the results are presented in Table I. A good feature selection should lead to better classification. To evaluate this, we input the selected features by MT-CoReg, LASSO, and sCCA to SVM respectively, and calculated the average classification accuracy, which are presented in Table I. For comparison, we also tested the classification performance on the raw data, which is referred to as ‘baseline’, and the true features (i.e., the overlap between the discriminative components and correlated components), which is referred to as ”True features”. The result is reported in Table I. It is clear that MT-CoReg has both higher sensitivity and specificity than LASSO. Sparse CCA has slightly better sensitivity and specificity in the first view, but worse in the second view, and it has the worst classification accuracy among the three methods. Note that, compared to baseline, feature sets selected by these methods all lead to higher accuracy in subsequent classification.

Table I:

Sensitivity and specificity of feature selection and averaged classification accuracy

Method	View	Feature Selection		Classification Accuracy
		Sensitivity	Specificity
baseline	X 1	0.0750	0	69.75%
	X 2	0.0750	0	72.39%
MT-CoReg	X 1	0.7273	0.9843	89.75%
	X 2	0.8333	0.9892	90.25%
LASSO	X 1	0.3950	0.9358	87.13%
	X 2	0.7031	0.9422	86.75%
sCCA	X 1	0.8000	0.9895	80.75%
	X 2	0.6667	0.9784	78.93%
True features	X 1	1	1	96.67%
	X 2	1	1	93.89%

Feature selection and classification are two closely related but separate steps; from the results, even ‘true features’ cannot predict the observation with 100% accuracy. The reason is that the ‘true features’ here are defined as the overlap between correlation components and regression components. Because of the simulation setting with added noise, we cannot get perfect classification even with these ‘true features’.

III. Experiments and results

A. Hybrid simulation test

To evaluate the potential of the proposed method for more realistic scenes, we tested on hybrid data by manipulating real data with some simulations. We carefully selected a subset of 50 fMRI images and a subset of 50 methylation data from the Mental Illness and Neuroscience Discovery (MIND) Clinical Imaging Consortium (MCIC) (more details about this data are described in Section III-B1) [21]. There was no overlap between the two subsets to avoid dependency. For fMRI images, we selected 18 ROIs with voxel size between 250 and 350, resulting in 5299 voxels in total. For methylation data, we randomly selected 5000 CpG sites to match with the dimension of the fMRI data. We selected the first 100 voxels and first 100 CpG sites to add a linear correlation. Then we added exploratory signals to 70 ∼ 140 voxels and 70 ∼ 120 CpG sites, and generated a binary phenotype vector. In this setting, the 70 ∼ 100 features of both views are considered as true features.

We follow the same process described in Section II-D for performance evaluation and present the results in Table II. Based on the high sensitivity and specificity, we can draw a conclusion that our algorithm is suitable for real fMRI and DNA methylation data analysis. We present the classification accuracy of using the selected features with SVM and compare with that of ”true features”. Note that, ‘true features’ in this hybrid simulation cannot reach 100% accuracy either. The reason is the same as in the toy data experiment. Based on this comparison, we can draw a conclusion that the features selected by MT-CoReg can lead to satisfactory classification accuracy.

Table II:

Performance of MT-CoReg on feature selection with synthetic data and subsequent classification accuracy with SVM

View	Feature Selection		Classification Accuracy/True features
	Sensitivity	Specificity
fMRI	0.8710	0.9421	88.57%/93.75%
Methylation	0.9677	0.9825	89.71%/98.85%

B. Real data analysis

1). Data acquisition and pre-processing:

In the real data analysis, we used fMRI imaging and epigenetic data collected by the MCIC to extract biomarkers for schizophrenia. We used DNA methylation and fMRI data of 184 participants, including 80 SZ patients (33.75 ± 10.55 years old, 60 males and 20 females) and 104 healthy controls (32.37 ± 11.06 years old, 66 males and 38 females). SZ patients were diagnosed based on the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV) diagnostic criteria. A concerted effort was made to recruit patients at the early stage of their illness and especially those who were antipsychotic drug naive. Healthy controls were restricted to not having any current or past history of psychiatric illness including substance abuse.

To verify if we can exclude gender as a measurement in our analysis, we have conducted a one-way analysis of variance (ANOVA). The null hypothesis is that the probability of a male participant being diagnosed as SZ patient is equal to the probability of a female participant. The p value calculated is 0.0959, which is higher than 0.05. Thus, we don’t reject the null hypothesis. Gender is not considered as a factor in terms of SZ. Similarly, we tested on the age influence, and the p value is calculated as 0.2972, which is higher than 0.05. As a result, we don’t consider age to be an influential factor on SZ either. The same conclusion can be drawn if we conduct a Student’s t-test.

The fMRI data used in this study were collected when participants were performing the auditory oddball (AOD) task. It is one of the most popular fMRI paradigms, which can successfully capture the abnormalities in brain activations presented in SZ patients in comparison to healthy subjects[22–26]. The AOD task required participants to detect and respond to the infrequent target sound stimuli which randomly appears by pressing a button. Prior to fMRI scanning, participants went through a “mock scanner” session to acclimate themselves to the scanner environment and the AOD task. No data were collected until participants were comfortable with the scanning environment and the task. Detailed experiment setting for the fMRI AOD paradigm can be found in [27, 28]. The preprocessing of fMRI data was achieved by the SPM¹ software. After a successive processing of realignment, spatial normalization and smoothing, data were analysed by multiple regression considering factors including the audio stimulus. As a result, a 53 × 63 × 46 stimuluson versus stimulus-off contrast image was then extracted for each participant. After excluding voxels with missing measurements, each image consists of 116 ROIs based on the Automated Anatomical Labeling (AAL) template, with 41236 voxels in total. The average number of voxels contained in each ROI is 355, and the median is 306.

For all the participants involved, ETDA blood samples were available for 234 participants. DNA extraction was performed at the Harvard Partners Center for Genetics and Genomics. Bisulphite modification and hybridization on the blinded DNA were conducted at the Mind Research Network Neurogenetics Core Lab. After excluding participants that failed the quality control procedures, we ended up with DNA methylation data for the mentioned 184 participants, covering 27508 CpG sites.

Since there are two types of data to be jointly analysed, we standardized each measurement before combining them. We started with converting them to standard scores (z-score). By doing so, two measurements are adjusted to the similar scales and outliers can be avoided. This avoids dominance by either view and allows for direct comparison between the calculated features in the follow-up analysis.

During each test, we conducted a preliminary feature reduction based on the training data. We partitioned the training data into 10 sub-training groups. Each time, we excluded one sub-training group, and used the remaining training data and their phenotype to conduct a Student’s t-test, in order to select a number of significant features. After repeating this process 10 times, the intersection of selected features were selected as the input measurement. This procedure shares a similar idea as stability selection[29], and thus, we call it a ”stable t-test.” This process is illustrated in Fig. S1.

We visualize the result of the stable t-test on fMRI data in Fig. 2 using the toolbox BrainNet Viewer[30]. Each node in the figure represents a brain region defined in AAL template. We calculate the frequency of each voxel being selected throughout the cross-validation. The size of each node represents the sum of the frequency of all voxels in the corresponding ROI. Then we calculate the averaged frequency of voxels in each ROI. These values are then adjusted to fall between 0 and 1. The color of each node represents the adjusted value.

Figure 2:

Visualization of feature selection results after stable t-test on fMRI. From left to right: (a) sagittal view, (b) axial view, (c) coronal view. Each node corresponds a brain region defined in AAL template. The size of the node represents the sum of frequency of the corresponding voxels. The color of the node represents the adjusted average frequency of corresponding voxels. The visualization is by BrainNet Viewer.

For different permutations, the results of stable t-test differ and the subsequent results of MT-CoReg will further differ. To eliminate the bias introduced by data permutation, we took advantage of cross-validation and conducted a significance analysis: during each run, the data was partitioned into training and testing set in a different way. MT-CoReg was applied to training data for feature selection. The performance of selected features was evaluated based on the testing data. This process was repeated and the frequency of each feature being selected during all permutations was calculated and used to identify biomarkers. This cross-validation process is illustrated in Fig. 3.

Figure 3:

Flow chart of one run of experiment. During each run of experiment, the feature selection result will differ because of the data permutation. To reduce this type of bias, we repeat the process by resampling the raw data. After multiple runs of experiments, a significance test on βs is conducted to detect the biomarkers.

2). Result analysis:

There are two hyper-parameters in the model: $\gamma$ and λ. Conventionally, hyper-parameters are determined through either cross validation or stability selection[29]. Experiments suggested that, based on classification accuracy, $\gamma$ values determined by stability selection were not effective for selecting discriminative features. As a result, we generated a set of candidate values for $\gamma$ from 0 to 1. Note that, when $\gamma$ equals 0, our model degenerates to a sparse CCA model; when $\gamma$ equals 1, our model is equivalent to a linear regression model. We trained the model based on each $\gamma$ value, and then conducted a significance analysis on the resulting features. As for λ, which controls the sparsity level, it is determined through cross validation. Specifically, the selected features were input into a support vector machine (SVM) and the classification accuracy was calculated.

During the experiment, we divided 184 participants into training and testing groups. We trained the model on the training data, and based on the β values, we selected a set of features from two data views. Theses features were then concatenated and imported into a SVM to test the classification performance on the testing data. The training and testing were repeated for 50 times by resampling to evaluate the significance and stability. Fig. S2 demonstrates the averaged ${\left|{\beta }_1(i)\right|}_1$ and ${\left|{\beta }_2(j)\right|}_1$ values for i-th voxel and j-th CpG site at different $\gamma$ values (i.e., for different ratios between regression and CCA) over all the cross-validations.

Overall, on average, the classification accuracy is 85.12%, false positive rate is 6.73%, and false negative rate is 21.25%. We present in Fig. S5 the correlation (mean value and standard derivation) between (a) ${\mathit{X}}_1{\theta }_1$ and ${\mathit{X}}_2{\theta }_2$, (b) ${\mathit{X}}_1{\alpha }_1$ and ${\mathit{X}}_2{\alpha }_2$, (c) ${\mathit{X}}_1{\widehat{\beta }}_1$ and ${\mathit{X}}_2{\widehat{\beta }}_2$, where $\widehat{\beta }=|\alpha |+|\theta |$. Note that, θ, α, and β correspond to the extracted CCA, regression, and MT-CoReg factors, respectively. It is obvious that the features extracted by MT-CoReg have strong correlation across different views, nearly as strong as features extracted by CCA.

To better demonstrate the brain regions from which the voxels are most frequently selected, we first conducted a significance test on individual feature (voxel) level: we calculated the indicator $F(v)=\frac{1}{450}{\sum }_{i=1}^{50}{\sum }_{j=1}^9\mathit{I}\left({\left|{\mathit{\beta }}_1^{ij}(v)\right|}_1\ne 0\right)$ for feature v, where $\mathit{I}(\cdot )$ is the indicator function. $F(v)$ is the frequency of the v-th feature (voxel/CpG site) being selected during all the cross-validations. Another screening was performed to exclude the voxels with $F(v)$ lower than 0.10. Then, we were left with 41 voxels. In Table III, we presented the 14 regions that have at least 2 selected voxels. We also include in the table the relevant works with the same findings. We visualize the identified ROIs in Fig 4.We discuss how these ROIs are related to SZ biologically in following paragraphs.

Table III:

A list of selected ROIs and relevant research works

ROI ID	ROI Name	Related Research
33,34	bilateral midcingulate area	[31, 32]
35,36	bilateral posterior cingulate gyrus	[33, 34]
38	right hippocampus	[35–38]
40	right parahippocampal gyrus	[39–41]
51	left middle occipital gyrus	[42]
55	left fusiform gyrus	[39, 42–44]
57	left postcentral gyrus	[45]
68	right precuneus	[34, 46, 47]
78	right thalamus	[45, 48, 49]
79	left transverse temporal gyrus	[50]
81,82	bilateral superior temporal gyrus	[42, 51, 52]

Figure 4:

Visualization of the 14 ROIs that have no less than 2 selected voxels. The visualization is by the BrainNet Viewer toolbox. From left to right: (a) sagittal view, (b) axial view, (c) coronal view.

Among these ROIs, the cingulate cortex, as an integral part of the limbic system, receives inputs from the thalamus and the neocortex, and is associated with memory formation and processing [53], emotional and social behavioral disturbances [54]. More specifically, researchers have found that the bilateral midcingulate area (MCC)[31, 32] and the right thalamus [48] are less metabolically active in SZ patients; the posterior cingulate cortex (PCC) has higher CB1(cannabinoid receptor type one) receptor density in SZ patients[33]. Furthermore, the precuneus/PCC interaction has also been found to play a pivotal role in Default Mode Network (DMN) [34], which is relevant to the origin and experience of mood and psychotic symptoms [55]. Hippocampus is also part of the limbic system, and plays a central role in the consolidation of new memories. Hippocampal volume reduction is one of the most consistent structure abnormalities found in SZ patients, and along with the hippocampal hyperactivity, these two abnormalities are correlated with memory deficit and the degree of psychotic disorganization (i.e., delusions and hallucinations) of SZ patients [38].

The parahippocampal and fusiform gyri (FG) are adjacent to each other. As for healthy people, a left-greater-than-right volume asymmetry is found in both structures. However, this asymmetry is reversed for SZ patients [39, 43]. As part of the paralimbic cortex, the parahippocampus has been assumed to play a central role in memory recollection, sending information from the hippocampus to association areas [40]. The presence of FG gray matter volume reduction has been found in the course of first-episode SZ and has been proven to be specific to SZ instead of being a product of long-term treatment [43]. While the exact functionality of FG is still disputed, its involvement in the following pathways has been identified: face and body recognition [56] and word recognition [57]. The left middle occipital gyrus and superior temporal gyrus, similar to the FG, have also been found to be related to the perception of human figures [42]. Similar to thalamus, the presence of grey matter density (GMD) reduction has also been verified in the postcentral gyrus of SZ patients[45]. It is the prominent gyrus in the lateral parietal lobe of human brain, which integrates sensory information among various modalities. Thus, dysfunction of this area could possibly account for the hallucinations that SZ patients suffer. The volume decrease of left transverse temporal gyrus has been found to be significantly correlated with the severity of auditory hallucinations [50].

Similarly, we calculated $F(v)$ for features selected from methylation data. At a cut-off of 0.15, we are left with CpG sites that reside in 44 genes. Table IV shows this list of genes. It is both encouraging and convincing that some of the listed genes have been identified as being relevant to SZ by other studies[58–61].

Table IV:

A list of selected genes

Gene Names
CLCN6	GBP6	CHD1L	C1orf109	OBFC2A	FLJ42986	IGFBP2	KPNA1
SMN2	NEUROG1	TRIM41	MRPL18	HRBL	IMPDH1	FLJ20097	TMEM67
BARHL1	TBC1D13	ECHS1	ACBD5	LRRTM3	HBG2	ATM	ITGA7
CAPS2	KBTBD7	PIG38	C14orf133	ANKS3	NME3	DLX3	NPB
SPATA22	KIAA0753	COG1	CDH20	F2RL3	RANBP3	KLK7	TOP1
SALL4	GSS	MID1	WDR40B

After extracting the 41 voxels and 44 CpG sites, we concatenated these data and entered them into a SVM to classify SZ patients and HCs. We conducted 10-fold cross validation. The average classification accuracy is 88.89%. To further asses the classification performance, we calculated the true positive rate (TPR) and false positive rate (FPR). Then we plotted the receiver operating characteristic (ROC) curve in Fig. 5, where the x axis corresponds to the FPR values and y axis corresponds to the TPR values. The area under the ROC curve (AUC) is 0.8951, which is satisfactory. To compare the performance, we input whole DNA methylation data, the whole fMRI data, and their concatenation to SVM separately. The corresponding classification accuracy is 72.12% for DNA methylation, 62.15% for fMRI, and 79.25% for the concatenated data. We also calculated and presented the ROCs in Fig. 5. The corresponding AUC is 0.7875 for DNA methylation, 0.6497 for fMRI, and 0.8125 for their concatenation.

Figure 5:

The ROC curve of classification using SVM to classify SZ and HC with extracted features, concatenation of DNA methylation and fMRI data, and each individual data. The x axis corresponds to FPR value, and the y axis is the TPR value. The closer the curve to the top left, the better. The AUC is 0.8951 for using extracted features, 0.7875 for using methylation, 0.6497 for using fMRI data, and 0.8125 for using the concatenation of raw data.

By comparing the classification accuracy of using extracted features with raw data (after pre-processing), we can draw a conclusion that our method has successfully identified significant features.

To examine the correlation among the extracted features, we calculated the pairwise Pearson correlation between voxels and methylations. The result is presented as a heatmap in Fig. 6. For comparisons, we applied Lasso to the data and extracted two different sets of features. For a fair comparison, we required that the number of features selected by Lasso is close to the number of MT-CoReg. As a result, without compromising the classification accuracy, we selected 40 CpG sites and 41 voxels. The pairwise voxel-methylation correlation is also presented in Fig. 6. On both x and y axis, we display the brain region that each voxel belongs to, and the gene that the CpG sites reside respectively.

Figure 6:

The correlation heatmaps between the selected voxels (rows) and CpG sites(columns). Left: correlation of features selected by MT-CoReg; right: correlation of features selected by Lasso. Y axis displays the corresponding brain regions defined by AAL template; and x axis displays the corresponding gene names. It is clear that the heatmap calculated from MT-CoReg has much higher absolute values compared to the one calculated from Lasso. Furthermore, the left heatmap is more structured than the right one and the blocks of same color (blue or red) tend to form clusters.

Based on the color pattern, we can observe that the heatmap calculated based on features selected by MT-CoReg has a larger number of high absolute values. Furthermore, the blocks in the heatmap from MT-CoReg have a higher tendency to form columns (clusters). This indicates that the blocks of positive or negative correlation values seem to follow a similar pattern as in the AAL template: the voxels in the same brain region defined by AAL template are likely to have the similar correlation with the same CpG sites. For example, the selected voxels in the cingulate gyrus (denoted as “Cingulum”) have negative correlation with CpG sites in gene GBP6, CHD1L, C1orf109, FLJ42986, SMN2, TRM41, MRPL18, COG1, and CDH20, but positive correlation with CpG sites in BARHL1, TBC1D13 and NPB; the selected voxels in superior temporal gyrus (denoted as “Temporal-Sup”) have positive correlation with CpG sites in gene CLCN6, CHD1L, OBFC2A, KPNA1, IMPDH1, pIG38, F2RL3, RANBP3, TOP1, GSS and WDR40B, but negative correlation with CpG sites in NEUROG1, ANKS3, KLK7 and SALL4. The strength of correlation might differ, but the sign of these correlations matches. Note that, for clearer demonstration, the y axis of the heatmaps in Fig. 6 is not exactly the same as the ROIs defined in AAL template. Brain regions that are symmetric (e.g., left and right superior temporal gyrus) or belong to same larger region (e.g., left and right midcingulate area; left and right posterior cingulate gyrus) are grouped in the heatmaps. This does not hurt the observation we just made; on the contrary, it further strengthen our conclusion. Such structures cannot be found in the correlation heatmap generated by features selected by Lasso.

In order to uncover the biological functions of the identified CpG sites, we linked the CpG sites to genes and conducted a gene enrichment analysis on these genes using the ConsensusPathDB interaction database [62]. With a screening of q-value < 0.05 (q-value refers to the multiple testing corrected p-value), two pathways and one gene ontology (GO) term were identified, as shown in Table V. Pathways “Guanosine ribonucleotides de novo biosynthesis” and “Guanosine nucleotides de novo biosynthesis” are involved with the synthesis of guanosine, which is related to the synthesis of DNA. It has been reported that guanosine is related to neuroprotection and can protect cells from glutamate induced death in hippocampal gyrus[63]. Hippocampal gyrus is a brain region related to processing information of short-term and long-term memories, and right hippocampus was also identified by our study from fMRI data, as shown in Table III. Moreover, cyclic guanosine monophosphate (cGMP) is an intracellular seccond messenger related to neurotransmission [64]. Fig. 7 visualizes the biological interactions of genes, proteins, and compounds in the two enriched pathways, respectively.

Table V:

Enriched pathways and Gene Ontology (GO) terms

Pathway name or GO term	Set size	Number of candidates contained	p-value	q-value	sources
Guanosine ribonucleotides de novo biosynthesis	13	2(15.4%)	0.000376	0.011	HumanCyc Pathway
Guanosine nucleotides de novo biosynthesis	16	2(12.5%)	0.000577	0.011	HumanCyc Pathway
Perikaryon	118	3(2.5%)	0.00139	0.0376	GO term

Figure 7:

Visualization of biological interactions in the Pathways ”Guanosine nucleotides de novo biosynthesis” (subfigure a) and ”Guanosine ribonucleotides de novo biosynthesis” (subfigure b).

Besides playing a role in the two discovered pathways, the genes IMPDH1 and NME3 are also annotated as GO term perikaryon, which is a portion of the neuronal cell body. IMPDH1, the abbreviation for Inosine Monophosphate Dehydrogenase 1, is a Protein Coding gene that acts as a homotetramer to regulate cell growth. While no direct causal relationship between IMPDH1 and SZ has been reported to date, it is reported that IMPDH1 mutation can cause retinitis pigmentosa (RP) [65, 66], which is a set of hereditary retinal diseases that feature degeneration of rod and cone photoreceptors [67]. Several research works have found that there is a link between RP associated brain abnormalities and SZ-like symptoms as a consequence of relevant brain damage [68–71]. NME3, abbreviated from Nucleoside Diphosphate Kinase 3, is also a Protein Coding gene. Both IMPDH1 and NME3 are also included in the purine nucleotides de novo biosynthesis pathway (which consists of 40 genes), and it is in the same superpathway with the two identified pathways. Thus, these genes are also associated with SZ through regulating the synthesis of purine [72–74].

We can observe in Fig. 6 that, the CpG sites linked to IMPDH1 have strong positive correlation with voxels in superior temporal gyrus, and strong negative correlation with most selected voxels in right precuneus; the CpG site linked to NME3 has strong negative correlation with selected voxels in right crus 1 of cerebellar hemisphere and in bilateral posterior cingulate gyrus and also positive correlation with selected voxels in superior temporal gyrus.

The results of enrichment analysis indicate that the identified CpG sites may be involved in the regulation of guanosine synthesis during neuron formation. Misregulation of guanosine synthesis in neuron can affect the brain development and lead to dysfunction of the brain, especially the processing of long-short-term memory by affecting the hippocampal gyrus, which can further result in SZ or other psychiatric disorders.

IV. Conclusion

In this paper, we proposed a novel integration approach that can extract co-expressed discriminative features from two types of data. We combined Lasso with CCA in a relaxed yet coupled manner to obtain a good data fitting while incorporating their correlations. We also presented an efficient algorithm to solve the optimization problem and discussed how we determined the hyper-parameters.

By integrating DNA methylation with fMRI data, we successfully identified 14 brain regions (as listed in Table III and visualized in Fig. 4) that are linked to the epigenetic markers (e.g., DNA methylation). A subset of identified genes are involved in two important pathways “Guanosine ribonucleotides de novo biosynthesis” and “Guanosine nucleotides de novo biosynthesis”. These pathways are related to the synthesis of guanosine, which plays a crucial role in long-short-term memory processing. Guanosine can protect cells from glutamate-induced death in hippocampal gyrus, which is also detected by our study. Three other identified genes are included in the GO term “Perikaryon”, which refers to the cell body of a neuron. These results helped to justify that the features we extracted from DNA methylation and fMRI are truly correlated. Based on the classification accuracy from SVM using these features, the discriminative power of the extracted features are demonstrated.

Building upon our previous study using both fMRI and single nucleotide polymorphism (SNP) data [19], we identified a new set of genes and brain regions, with some overlap from our previous work (Fig. 8). Incorporating the epigenetic markers can potentially identify genes that are left out by an imaging genomics approach. This also points to a promising future research direction: combining fMRI, SNP and DNA methylation altogether to uncover discriminative features that are co-expressed in all these three types of data. The approaches for multiple data combination, such as multiple CCA[17] or joint nonnegative matrix factorization[75], that we proposed recently can be applied for this purpose.

Figure 8:

The Venn diagram to demonstrate the brain regions identified using CoReg on fMRI-SNP study (red) and on fMRI-Methylation study (green). There are two regions identified in both studies: left middle occipital gyrus and right parahippocampal gyrus. Brain regions are defined by AAL template.