 Research
 Open access
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Differential coexpression analysis reveals early stage transcriptomic decoupling in alzheimer’s disease
BMC Medical Genomics volume 13, Article number: 53 (2020)
Abstract
Background
Alzheimer’s disease (AD) is one of the leading causes of death in the US and there is no validated drugs to stop, slow or prevent AD. Despite tremendous effort on biomarker discovery, existing findings are mostly individual biomarkers and provide limited insights into the transcriptomic decoupling underlying AD. We propose to explore the gene coexpression patterns in multiple AD stages, including cognitively normal (CN), early mild cognitive impairment (EMCI), late MCI and AD.
Methods
We modified traiditonal joint graphical lasso to model our asusmption that the coexpression networks in consecutive disease stages are largely similar with critical differences. In addition, we performed subsequent network comparison analysis for identification of stage specific transcriptomic decoupling. We focused our analysis on top ADenriched pathways.
Results
We observed that 419 edges in CN, 420 edges in EMCI, 381 edges in LMCI and 250 edges in AD were frequently estimated with non zero weights. With modified JGL, the weight of all estimated edges in CN, EMCI and LMCI are zero. In AD group, 299 edges were occasionally estimated to be nonzero and the average correlation between genes was 0.0023. For coexpression change during AD progression, there are 66 pairs of genes that demonstrated a continuously decreasing or increasing coexpression from CN to EMCI, LMCI and AD.The network level clustering coefficient remains stable from CN to LMCI and then decreases significantly when progressing to AD. When evaluating edge level differences, we identified eight gene modules with continuously decreasing or increasing coexpression patterns during AD progression. Five of them shows significant changes from CN to EMCI and thus have the potential to serve system biomarkers for early screening of AD.
Conclusion
We employed a modified joint graphical lasso for estimation of coexpression networks for multiple stages of AD. Comparing with graphical lasso, our modified joint graphical lasso model accounts for the similarity in consecutive disease stages. Our results on real data set revealed five gene clusters with obvious coexpression pattern change from CN to EMCI, which could be used as potential systemlevel biomarkers for early screening of AD.
Background
Alzheimer’s disease (AD) is a major neurodegenerative disorder that has been characterized by gradual memory loss and brain behavior impairment. According to the latest report [1], an estimated number of 5.7 million aging Americans are living with Alzheimer’s and this number is expected to escalate in coming years given the rapid increase of aging population. To prevent this public health crisis, tremendous effort has been dedicated to discovery of effective AD biomarkers. In addition to APOE e4 alleles known as major genetic determinants [2], largescale genomewide association studies (GWAS) have led to identification of many novel genetic risk locus [3]. However, extant work largely investigated genetic variations or individual genes associated with AD. Very few studies paid attention to the interactions and associations among the gene products and how they are gradually disrupted during AD progression [4, 5].
Gene coexpression networks describes the correlation patterns among genes. Differential coexpression analysis examines the altered patterns between coexpression networks of two states, e.g., healthy controls vs. patients. It has great potential to identify the gene clusters affected by stage transition and therefore provide valuable information on how the biological system alters during disease progression. According to the Alzheimer’s Disease Neuroimaging Initiative (ADNI) project, subjects usually progress from cognitive normal (CN) status (i.e., those without any signs of depression, dementia or cognitive impairment), to early mild cognitive impairment (EMCI), late mild cognitive impairment (LMCI) (i.e., those with deteriorating memory concerns, but not decline in performing daily activities and no signs of dementia), and finally AD. In this project, we propose to perform a differential coexpression analysis across all the stages of AD, including CN, EMCI, LMCI and AD.
One common method to generate coexpression network is through pairwise Pearson’s correlation and WGCNA is the widely used package for coexpression analysis [6], which is based on marginal correlation. Although frequently used, these methods do not distinguish direct relationships from indirect relationships, e.g., two genes that show similar coexpression patterns due to a common intermediate gene. Unlike these methods, graphical lasso models the joint distribution of genes and can infer the direct relationships by capturing the conditional independence between genes [7]. A graph generated from graphical lasso, where genes are represented as nodes and their coexpression are represented as edges, provides valuable insights into the transcriptomic coupling under specific condition and therefore can help with generating new biological hypothesis. However, it can only estimate one network at a time. When applied to differential coexpression analysis, they estimate the network for each group separately by treating them as independent. This assumption clearly does not hold in disease research since disease formation is a progressive procedure. Coexpression networks in consecutive disease stages should be largely similar with critical differences. For example, coexpression networks in CN group and EMCI group are expected to be largely similar with critical differences. Toward this, we propose to employ joint graphical Lasso [8] for simultaneous estimation of coexpression networks in multiple disease stages. A joint analysis borrows the strength of the relatedness across disease stages and can potentially reveal the differential coexpression patterns with increased statistical power, which is useful especially when the sample size is very limited.
Given the increasing interest in and evidence of bloodbased AD biomarkers [9–12], we focused our analysis on the plasma expression data of genes in top ADenriched pathways highlighted in [13]. We first estimated the coexpression networks of all diagnosis groups using our modified JGL to better model our assumption of network similarity between consecutive disease stages. Subsequently, we performed a comprehensive network comparison analysis of coexpression networks using edgelevel, nodelevel and networklevel metrics. We used global clustering coefficient to identify structural property of each network. Node and edge centrality values were calculated to allow comparison of basic network components present in the network [14] and identification of critical network entities [15]. Finally, we were able to identify eight gene clusters showing gradual changes during the progression of AD. Five of them shows significant changes from CN to EMCI and therefore have the potential to serve as system level biomarkers for early screening of AD.
Methods
Dataset
All the plasma microarray data used in this study were directly obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) project (http://adni.loni.usc.edu). Raw expression values obtained directly from CEL files were preprocessed using the Robust Multichip Average (RMA) normalization method. The RMA normalized expression array data further went through several quality control (QC) steps [16]. First, we checked the sex of samples using sexspecific gene expression data, including XIST and USP9Y. Second, sample identity was verified on the basis of expression profiling to Omni2.5M genotype match using a Bayesian method to predict individual SNP genotypes from gene expression data. Detailed data description and the preprocessing steps can be found in ADNI LONI website (http://adni.loni.usc.edu). We focused our analysis on five ADenriched pathways highlighted in [13]. For each pathway, we extracted all the involved genes from Metacore. In total, there are 75 genes included in this study (Table 1). In the microarray data, if there are multiple probes corresponding to the same gene, we choose the probe with the maximum mean expression to represent the gene. Gene expression values were adjusted for RNA integrity Number (RIN), baseline age and sex to remove potential bias. Finally, 662 ADNI 1 subjects without missing gene expression values were included. Shown in Table 2 is the detailed demographic information of all subjects. We will jointly learn the gene coexpression networks for four consecutive disease stages.
Joint graphical lasso
We first briefly introduce the graphical lasso method [7]. Suppose we have the expression data of p genes for n subjects in K diagnostic groups. Denote the gene expression profile for kth group as \(\mathbf {X}^{(k)} \subseteq \Re ^{n_{k}\times p}\), where n_{k} is the number of subjects in kth group and \(k=1,\dots,K\). Assuming that the gene expression levels within each group \(\mathbf {x}_{1}^{(k)},x_{2}^{(k)},\cdots, x_{n}^{(k)}\) are independent and identically distributed with the positive definite p×p covariance matrix Σ_{k}. The values in the covariance matrix reveal how the expression of two genes vary together; the inverse covariance matrix \(\mathbf {\Sigma }_{k}^{1}\) indicates the conditional independence between pairs of genes. Zero values in the inverse covariance matrix \(\mathbf {\Sigma }_{k}^{1}\) indicates conditionally independence of corresponding gene pairs. That is, two genes are independent of each other after removing the effect of all other genes in the data set.
Traditional graphical lasso estimates individual coexpression networks separately by solving Eq. 1:
Where S^{(k)}=(X^{(k)})^{T}X^{(k)} is the empirical covariance matrix. Θ^{(k)}_{1} is the L_{1} norm. Θ^{(k)} is the inverse covariance matrix (i.e., coexpression network) to be estimated for kth group. λ_{1} is the nonnegative tuning parameter to enforce the sparsity of estimated coexpression network.
However, multiple groups may be related and ignoring the common structures shared across groups will inevitably yield suboptimal results. To address this problem, joint graphical lasso (Eq. 2) was later proposed to enable the estimation of multiple related inverse covariance matrices together through maximizing penalized log likelihood [8]. It borrows the strength of the relatedness across groups and can potentially reveal the differential coexpression patterns with increased statistical power, which is especially useful when the sample size is very limited.
The sparsity within each covariance matrix and the similarity across covariance matrices in K groups are encouraged by penalty P({Θ}). λ_{1} and λ_{2} are two nonnegative parameters to control the enforcement of sparsity and similarity. In [8], it assumed that the coexpression networks across all pair of groups are similar. However, this assumption does not always hold, especially for discovery of disease stagespecific networks. AD is a slowly progressive brain disorder that networks are expected to gradually dissolve or rewire during the progression. Gene coexpression network in the AD patients may have become very different compared to that of cognitive normals after years of progression. Therefore, we modified the penalty term P({Θ}) to Eq. 3 such that the similarity among networks is only enforced for consecutive stages. For example, networks between CN and EMCI and networks between EMCI and LMCI groups are encouraged to be similar.
To solve the modified JGL model, we followed the steps in [8] using alternating directions method of multipliers (ADMM) algorithm. With the constraints Θ^{(k)}=Z^{(k)}, the dual variables U^{(k)} are introduced to form scaled augmented Lagrangian [17].
The exact solution steps can be referred to the JGL paper [8]. We modified the step to update {Z} (Eq. 5).
We found that this minimization problem is completely separable for each element (i,j) in the matrices,
The last penalty term is known as 1d fused lasso and penalizes the absolute differences in adjacent values of β = \([ \boldsymbol {Z}_{ij}^{(1)},\dots,\boldsymbol {Z}_{ij}^{(K)}]\). It can be easily reformulated as ∥Dβ∥_{1}, where D⊆ℜ^{(K−1)×K}.
If we first consider λ_{1} as zero and set y=\(\left [\mathbf {A}_{ij}^{(1)},\dots,\mathbf {A}_{ij}^{(K)}\right ]\). The convex optimization problem becomes a simple 1d fused lasso problem (Eq. 8). Note that rank(D)= K−1. With a vector s⊆ℜ^{K} that is orthogonal to all the rows in D, we can construct \(\hat {\mathbf {D}}=\left [\begin {array}{c}\mathbf {D}\\ \mathbf {s}\end {array}\right ]\) with rank(\(\hat {\mathbf {D}}\))=K. Let \(\theta = (\theta _{1},\theta _{2})^{T} = \hat {\mathbf {D}}\beta \) and θ_{1}⊆ℜ^{K−1}, then Eq. 8 will be transformed into a regular lasso problem (Eq. 9).
Note that the L1 penalty is only partially applied to θ_{1}. In order to solve this, we rewrite Eq. 9 to a standard form with transformation \(\hat {\mathbf {D}}^{1}\theta = \left [ {\begin {array}{*{20}{c}} {{}^{K\backslash K1}\boldsymbol {X}_{1}}&{\left  {} \right.{}^{K\backslash 1}\boldsymbol {X}_{2}} \end {array}} \right ]{\left [ {\begin {array}{*{20}{c}} {\boldsymbol {\theta }_{1} {} }&{\left  {} \right.\boldsymbol {\theta }_{2}} \end {array}} \right ]^{T}}\),
While \(\boldsymbol {\hat {\theta }_{2}}\) can be solved as \(\boldsymbol {\hat {\theta }_{2}} = {\left ({\boldsymbol {X}_{2}^{T}{\boldsymbol {X}_{2}}} \right)^{ 1}} \boldsymbol {X}_{2}^{T}\left ({\mathbf {y}  {\boldsymbol {X}_{1}}{\boldsymbol {\hat \theta }_{1}}} \right)\), the above equation can be rewritten as
Where \(\boldsymbol {P}= \boldsymbol {X}_{2} {\left ({ \boldsymbol {X}_{2}^{T}\boldsymbol {X}_{2}} \right)^{ 1}} \boldsymbol {X}_{2}^{T}\). The above equation can be easily solved using the LARS algorithm [18], from which we can backtransform to get the solution for Eq. 8: \(\beta = \hat {\mathbf {D}}^{1}\theta \). By applying softthresholding to β, we can get the solution for Eq. 6.
Tuning parameter selection
The tuning parameters λ_{1} and λ_{2} in the modified JGL model were selected using the Akaike information criterion (AIC) (Eq. 12).
Here, \(\hat {\mathbf {\Theta }}_{\lambda _{1},\lambda _{2}}^{(k)}\) is the estimated inverse covariance matrix for group k under the tuning parameters λ_{1} and λ_{2}. E_{k} is the number of nonzero elements in \(\hat {\mathbf {\Theta }}_{\lambda _{1},\lambda _{2}}^{(k)}\). We performed a grid search and λ_{1} and λ_{2} with minimal AIC score were selected.
Performance evaluation
In the subsequent gene coexpression analysis, we refer our modified JGL model as JGL. To evaluate the performance of JGL, we compared the performance of joint graphical lasso and traditional graphical lasso, where the coexpression network of each group is estimated separately. Using 1000 permuted datasets, we generated 1000 coexpression networks using JGL and derived a frequency network for each group, where each link has a value between 0 and 1000 indicating how many times it is observed to be nonzero. Similarly, we generate another frequency network for each group using the results from graphical lasso. Since all the gene expression has been permuted and they should be independent from each other, the ground truth value for all edges should be zero. Any nonzero values will be considered as false positives. That is, the value of each edge in the frequency network indicates its chance to be a false positive. We compared the performance of JGL and graphical lasso in terms of how frequently we will observe the false positives using the permuted data set.
Construction of coexpression network
We applied the modified JGL model to estimate the coexpression networks of four diagnostic groups simultaneously. To evaluate the significance of the estimated networks, we generated a random data set by running 1000 times of permutation for each gene and each group. Random data sets were then fed into the modified JGL model to estimate 1000×4 coexpression networks. For each group, we compared our results against these randomly generated networks and estimated an empirical p value for each edge in each group. Edges with empirical P >0.05 were considered insignificant. There were no insignificant edges identified for CN, EMCI and LMCI groups. Five edges in AD were found to be insignificant and were removed from subsequent network comparison analysis.
Centrality of the network nodes
For every node in the network, four weighted centrality values were calculated: weighted degree, weighted betweeness, weighted closeness and weighted clustering coefficient. Weighted degree is the sum of number of connections in terms of the weight of each edge in the network [19]. R package tnet provides the platform to calculate weighted centrality of a network. The weighted degree method proposed method by [20] uses the tuning parameter alpha to tune the connections and connection weights. The alpha value of 1 was used to calculate weighted degree. When an alpha value is 1, it equals to the definition of weighted degree by [19]. That is, degree is based on the connection weights of the network [19, 21]. Similarly, betweenness and closeness centrality are based on the theory of shortest paths in a network. closeness implies to how close a node is to other nodes in a network. Betweenness is the measure of how often an edge lies in the path of the other edge. We used alpha value as 1 for both calculation. Finally, clustering coefficient explains how connected neighbours of a node are in an overall network. Arithmetic mean measure was used to calculate the global clustering coefficient of the network as well as nodal clustering coefficients [20].
Network comparison
We examined and compared all four coexpression networks using edge level, node level and network level metrics. For each edge, its weight indicates the correlation between two connecting genes. We compared four networks by each edge and looked for edges with continuously increasing or decreasing weights from CN to EMCI, LMCI and AD. Edges with absolute differences >0.01 in consecutive groups (i.e, (CN EMCI), (EMCI LMCI) or (LMCI  AD)) were considered as potential biomarkers. We further clustered these edges based on their patterns of change across four disease stages. Similarly, we also compared the centrality values of each node and edge to identify nodes with gradual changes from CN to EMCI, LMCI and AD.
Results
Comparison of jGL and graphical lasso
We examined the difference of our modified JGL and graphical lasso in terms of their performance in estimation of coexpression networks based on permuted data sets. While the permuted data sets are completely random, it is expected that none of the genes are correlated. So all the edges in the estimated networks should have zero weight. However, with networks estimated using graphical lasso, we observed that 419 edges in CN, 420 edges in EMCI, 381 edges in LMCI and 250 edges in AD were frequently (i.e., more than 100 out of 1000 times) estimated with non zero weights (i.e., false positives) (Fig. 1). With modified JGL, the weight of all estimated edges in CN, EMCI and LMCI are zero. In AD group, 299 edges were occasionally (i.e., less than 100 out of 1000 times) estimated to be nonzero and the average correlation between genes was 0.0023 (Additional file 1: Fig. S1).
Nodal centrality change during aD progression
There are totally 19 genes showing significant nodal centrality changes from CN to AD. For clustering coefficient, we found C3, MAPK1, PAK1, PRKCH and SLA with continuously increasing values from CN to EMCI, LMCI and AD. In contrast, CALM3, MAPK8 and RASA1 showed a decreasing pattern. For degree centrality, MAPK8 and RHOA were found to increase and GRB2, PAK1, PRKCD, PRKCH, PRKCI, SORT1 were found to decrease when subjects progress to a more severe stage. For betweenness, CR1, GRB2 and RPS6KB1 demonstrated a decreasing pattern. For closeness, DLG4 and SRC were observed to increase while PRKCD, RAP1A and RPS6KA1 showed a decreasing pattern. Among these, early centrality changes are captured by RPS6KB1, MAPK8, PRKCD, PRKCH and CR1 from CN to EMCI. A complete list of genes with continuous centrality changes is shown in Table 3. The detail centrality values of identified genes are in (Additional file 1: Tables S2–S5.) In Fig. 2 is the coexpression network module in the CN group that includes only genes showing gradual nodal changes. RPS6KB1 is observed to be the top hub.
Coexpression change during aD progression
There are 66 pairs of genes that demonstrated a continuously decreasing or increasing coexpression from CN to EMCI, LMCI and AD. Based on their change patterns, we further divided these genes into eight clusters (Fig. 3). For clusters 1 and 2, correlation between those gene pairs shows continuous increase or decrease from CN to AD. For clusters 3 and 4, correlation between those gene pairs remains relatively stable until LMCI. On the contrary, gene pairs in clusters 5 and 7 show significant correlation change from CN to EMCI, but then remain stable until AD. After merging all of these modules, we observed several hub genes including RPS6KB1 (Ribosomal Protein S6 Kinase B1), SORT1, MAPK3, textitPRKCD, MAPK8 and GRINA. We further performed an pathway enrichment analysis for these clusters using hypergeometric test (Additional file 1: Table S1). Five candidate pathways are significantly enriched for all clusters except cluster 7 and 8. Among eight gene clusters, early correlation changes occurred in five of them, either decreasing or increasing. We combined these five gene clusters and formed a gene module as shown in Fig. 4. RPS6KB1 (Ribosomal Protein S6 Kinase B1) was found to be the hub gene, followed by GRINA, MAPK3, PRKCD, MAPK8 and SORT1.
Global network change during aD progression
Shown in Fig. 5 is the global clustering coefficient change of coexpression networks from CN to AD. It shows that the overall weighted clustering coefficient of the coexpression network remains relatively stable from CN to EMCI.
Discussion
The superior performance of modified JGL over traditional graphical lasso, when using the randomly permuted data, suggests that the similarity constraints on the coexpression networks of consecutive disease stages can help effectively control the probability to generate false positives. Therefore, the differential coexpression patterns identified through JGL results will provide more accurate information of the altered biological system during disease formation. On the other hand, while the high false positive rate of traditional graphical lasso could be controlled by the multiple test correction, it will be subject to the selection of correction method and significance threshold. In contrast, the similarity constraint used in JGL played a key role in controlling the false positive rate even without multiple correction. Therefore, JGL does not require as large number of permutations as traditional JGL and is more computationally costeffective.
The global clustering coefficient change of coexpression networks from CN to AD suggests strong structural resilience of the coexpression network in the early development of AD. However, the global clustering coefficient drops significantly when patients progress from LMCI to AD, which indicates the overall decoupling of genes in ADenriched pathways starts dissolve at the late stage of AD. There is less probability to hold modular structures within coexpression network when the disease progresses from less severe to more severe stages.
Among all the genes showing significant changes in node or edge level metrics, RPS6KB1 has consistently been observed as the top hub. Given that its centrality and coexpression changes occur in the early stage of AD, it holds great potential to serve as the biomarker for early diagnosis of AD. RPS6KB1 encodes for a Ser/Thr (S/T)directed kinase, 70kDa S6 kinase (p70S6K), that plays a crucial role in cell growth, cell differentiation, and cell cycle control. The p70S6K can phosphorylate tau at S262, S214, and T212 sites [22]. It is found to be highly expressed in cerebral cortex and hippocampus, a brain region affected by AD, according to the Human Protein Atlas (HPA) [23]. In a largescale genome wide association study (GWAS), it was reported to be a genetic risk loci for multiple sclerosis [24]. Findings from earlier studies suggest that the additive effect of alleles in RPS6KB1 and several other genes in tau kinase pathway are associated with lateonset of AD in APOE none4 carriers [22, 25].
MAPK8, also known as JNK1, is one of the three proteins in cJun Nterminal Kinase family. It is identified to be involved in the regulation and maintenance of physiological responses in central nervous system [26]. Studies have also found positive correlation between JNK phosphorylation and expression of amyloid beta (A β) peptide, which is a wellknown AD hallmark[27].
Other top hub genes that also show early changes in nodal centrality or coexpression patterns are MAPK8,MAPK3, GRINA, PRKCD, SORT1, RASA1 and PAK1. A few studies have reported the association of these genes with AD. For example, [28] suggests a potential causative role of P21 activated kinases defects on the cognitive deficits of AD patients. However, their coordination has not been previously studied yet. This work is the first study to reveal how their coexpression pattern changes during AD progression. Given that the coexpression and nodal centrality of these genes start to change in the CN stage, they have great potential to serve as systems biomarker to capture the biological alterations in the very early stage of AD and further help with the development of AD therapeutic intervention.
Conclusion
We employed a modified joint graphical lasso for estimation of coexpression networks for multiple stages of AD. Comparing with graphical lasso, JGL accounts for the similarity in consecutive disease stages. Our results on random data sets shows that it is less likely to generate false positives. In the subsequent differential coexpression analysis, we found that the clustering coefficient of the coexpression network shows significant changes only when subjects progress from LMCI to AD. Node wise and edge wise comparison have led to eight gene clusters that demonstrate continuous changes from CN, EMCI to LMCI and AD. Particularly, five of them shows differential coexpression patterns from CN to EMCI. Genes in these modules could be used as systems biomarkers for early screening in AD. However, more efforts are warranted to validate their downstream function.
Availability of data and materials
Demographic information, gene expression data, and diagnostic information are available from the ADNI data repository at http://adni.loni.usc.edu/datasamples/accessdata/.
Abbreviations
 A β :

Amyloid βprotein
 AD:

Alzheimer’s disease
 ADNI:

Alzheimer’s disease neuroimaging initiative
 AIC:

Akaike information criterion
 CN:

Cognitive normal
 EMCI:

Early mild cognitive impairment
 GWAS:

Genomewide association studies
 JGL:

Joint graphic Lasso
 Lasso:

Least absolute shrinkage and selection operator
 LMCI:

Late mild cognitive impairment
 LONI:

Laboratory of neuro imaging
 QC:

Quality control
 RMA:

Robust multichip average
 SNP:

Single Nucleotide Polymorphism
 WGCNA:

Weighted correlation network analysis
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Funding
This research was supported by NIH grants R21 AG066135, R01 EB022574, R01 AG019771, P30 AG010133, NSF CRII 1755836 and Indiana University Collaborative Research Grant (IUCRG). This project was also funded, in part, with support from the Indiana Clinical and Translational Sciences Institute funded, in part by Grant Number UL1TR001108 from the National Institutes of Health, National Center for Advancing Translational Sciences, Clinical and Translational Sciences Award. The results published here are in whole or in part based on data obtained from the AMPAD Knowledge Portal (doi:10.7303/syn2580853). Study data were provided by the Rush Alzheimer’s Disease Center, Rush University Medical Center, Chicago. Data collection was supported through funding by NIA grants P30AG10161, R01AG15819, R01AG17917, R01AG30146, R01AG36836, U01AG32984, U01AG46152, the Illinois Department of Public Health, and the Translational Genomics Research Institute.
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Contributions
JY conceived this study. YU and LX designed and performed the experiment. LX and PS modified the algorithm. KN contributed to the genetic data preparation. AS helped with the result interpretation. YU wrote the manuscript with the input from all of the authors. All authors have participated in study discussion and manuscript preparation. All of the authors have read and approved the final manuscript.
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This work does not involve any new data collection. It focuses on the analysis of existing data sets in the ADNI. More information about the ethics approval for the ADNI data can be found in https://adni.loni.usc.edu/wpcontent/uploads/2017/09/ADNID_Approved_Protocol_11.19.14.pdf.
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Additional file 1
Differential coexpression analysis reveals early stage transcriptomic decoupling in Alzheimer’s disease.
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Upadhyaya, Y., Xie, L., Salama, P. et al. Differential coexpression analysis reveals early stage transcriptomic decoupling in alzheimer’s disease. BMC Med Genomics 13 (Suppl 5), 53 (2020). https://doi.org/10.1186/s129200200689y
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DOI: https://doi.org/10.1186/s129200200689y