Integrating molecular interactions and gene expression to identify biomarkers to predict response to tumor necrosis factor inhibitor therapies in rheumatoid arthritis patients 1

1. Introduction

Rheumatoid arthritis (RA) is a complex autoimmune disease for which there is no cure. However, to relieve symptoms and prevent the disease from progressing, a variety of powerful treatments are available. TIn order to prevent permanent loss of function associated with structural damage to the joint, early therapeutic intervention is recommended [1]. For 90% of biologically untreated patients with RA, anti-TNF therapy provides the first effective treatment option if conventional synthetic disease-modifying antirheumatic drugs such as methotrexate do not work [2]. However, of these RA patients, *70% do not gain meaningful clinical change with anti-TNF treatment [3]. To predict which patients will not benefit from anti-TNF therapy, clinical tests should be performed prior to treatment beginning.

As genomic technologies have advanced, we have better understood inflammatory diseases and developed new treatments. Through the transcriptome, we can view specific genes over-expressed or under-expressed in diseases as a way to gain insight into a cellular response. Although various efforts have been made for identifying biomarkers and pathways [3], the specific response to anti-TNF therapy still remains unraveled. The statistical framework in most of these studies is based on a single set of data and does not take into account the knowledge in protein-protein interactions, biological regulatory networks and signaling pathways. In such a framework, the lack of biological information leads to the stability of prediction factors and reduces the predictive ability of the model [4]. In order to introduce modern precision medicine to autoimmune diseases, an advanced computational method combining genetic data with biological processes is needed.

There are many types of biological network information, such as functional interaction networks [5], protein-protein interactions (PPI) [6], correlations between genes [7, 8], KEGG pathways [9]. There are several studies that use biological knowledge, including those by Li and Li [10], Huang et al. [11], Wang et al. [12] and Chen et al. [13]. They described genomic knowledge as a graph that encoded genetic relationships (edges) among genes (nodes). Following that, they implemented linear and classification models with penalties based on Laplace matrices. Models that exploit biological information a priori are known as network-based approaches.

The hypothesis that complex diseases such as RA arise and develop due to interactions between several interrelated pathogenic genes, is supported by a growing body of evidence, indicating that the evaluation of the influence of any single variant is complicated [14]. This study hypothesizes that combining biological interaction information with gene expression data would help identify more robust biomarkers to predict the clinical response to anti-TNF treatment. Therefore, we tried to select the predictive biomarkers by using a network-based computational method to guide the therapy of RA patients. Our results have provided new candidate genes and pathways that may be predicting the response the anti-TNF therapy.

2. Method

In order to integrate the analysis of gene expression data with biological networks, we propose using the Laplace constraint method [10]. Let a network G = ( V , E ) , where V represents the genes with p dimensional, E represents the connections between genes. w u ⁢ v denotes the weight of edge e u ∼ v . The typical Laplacian form L for G is:

where d u , d v denote the degrees (including in and out) of features u and v , respectively. Then, the network-based model can be expressed as:

L ⁢ ( λ , β ) = l ⁢ ( β ) + λ ⁢ β T ⁢ L ⁢ β .(1)

The first term in Eq. (1) represents the loss function, secondly, network-based penalty provides a chance to capture interactive biological knowledge. Parameter λ is used to control the strength of the penalty.

Equation (1) struggles in high-dimensional applications where the number of genes, is larger than the sample size [15, 16, 17, 18]. To solve the problem of large p and small n , the regularization approach is widely applied. When the regularization term is added to Eq. (1), the sparse network constraint regression is expressed as Eq. (2).

L ⁢ ( λ 1 , λ 2 , β ) = l ⁢ ( β ) + λ 1 ⁢ P ⁢ ( β ) + λ 2 ⁢ β T ⁢ L ⁢ β(2)

where λ 1 and λ 2 are parameters, which play a role in balancing the trade-off between complexity and fitness. The most widely used regularization method is Lasso ( L 1 ), which has the form P ⁢ ( β ) = ∑ j = 1 p | β j | . However, in the lasso method, λ 1 needs to be adjusted very carefully, because if λ 1 is too large, the model β may be heavily biased, and if λ 1 is too small, the model β may not be sparse enough. To avoid this issue, Fan el al. [19] proposed SCAD method, which is shown as follows:

(3)

Its higher estimation accuracy and Oracle property make it more advantageous than the lasso method. Therefore, we use the SCAD method to penalize the network-based methods as proposed in Eq. (5). Finally, the model we adopted in this article is defined as:

L ⁢ ( λ 1 , λ 2 , β ) = l ⁢ ( β ) + P λ 1 , λ 2 , SCAD-Net ⁢ ( β )(4)

Where

(5)

and l ⁢ ( β ) is defined as a logistics regression model.

To solve Eq. (4), we use the following coordinate descent method. More detailed information can be found in Eq. (5).

Algorithm:

Input: Training dataset { X n × p , y n } , λ 1 , λ 2 and L .

Output: Model parameter β

Step 1: Update β ⁢ ( i ) t , i = 1 , … , p .

Step 2: Let t ← t + 1 , if , then repeat Step 1.

4. Discussion

A systemic inflammatory disease, RA is manifested by destructive distal polyarthritis. It can cause progressive joint damage, affect other organs, and even lead to cardiovascular disease unless diagnosed and treated. Targeted therapy using anti-TNF is the first option for patients with RA. Anti-TNF therapy, however, does not lead to meaningful clinical improvement in many RA patients. To predict which patients will not benefit from anti-TNF therapy, clinical tests should be performed prior to treatment beginning. Although various efforts have been made to identify biomarkers and pathways that may be helpful to predict the response to anti-TNF treatment, gaps remain in clinical use due to the low predictive power of the selected biomarkers. In this paper, we used a network-based computational method to identify the select the predictive biomarkers to guide the treatment of RA patients. We select 69 genes from peripheral blood expression data from 46 subjects using a sparse network-based method. The result shows that the selected 69 genes might influence biological processes and molecular functions related to the treatment.

5. Conclusion

Our approach advances the predictive power of anti-TNF therapy response and provides new genetic markers and pathways that may influence the treatment. One limitation of this paper is the lack of deep verification of the selected genes and network module.