Discovering driver nodes in chronic kidney disease-related networks using Trader as a newly developed algorithm

Highlights

• A novel optimization algorithm named Trader was used to spot driver nodes in the chronic kidney disease-related PPI networks.

• The Trader algorithm outperformed four other well-known algorithms with producing further disjoint sets in the networks.

• The Trader was able to successfully identify a list of potential therapeutic targets in the kidney disease-related networks.

Abstract

Thanks to the advances in the field of computational-based biology, a huge volume of disease-related data has been generated so far. From the existing data, the disease-related protein-protein interaction (PPI) networks seem to yield effective treatment plans due to the informative/systematic representation of diseases. Yet, a large number of previous studies have failed due to the complex nature of such disease-related networks. For addressing this limitation, in the present study, we combined Trader and the DFS algorithms to identify a minimal subset of nodes (driver nodes) whose removal produces a maximum number of disjoint sub-networks. We then screened the nodes in the disease-associated PPI networks and to evaluate the efficiency of the suggested method, it was applied to six PPI networks of differentially expressed genes in chronic kidney diseases. The performance of Trader was superior to other well-known algorithms in terms of identifying driver nodes. Besides, the proportion of proteins that were targeted by at least one FDA-approved drug was significantly higher among the identified driver nodes when compared with the rest of the proteins in the networks. The proposed algorithm could be applied for predicting future therapeutic targets in complex disorder networks. In conclusion, unlike the common methods, computationally efficient algorithms can generate more practical outcomes which are compatible with real-world biological facts.

Introduction

Identifying novel and efficient therapeutic targets is a pressing need for clinical pharmaceutics. In this regard, predicting the key molecules in disease conditions is not only crucial for life science research, but it may also help develop the novel medicines [[1], [2], [3]]. Medical investigations like a gene knockout technique and the RNA interference (RNAi) mechanism have conventionally been used to identify such molecules [4]. However, thanks to the high-resolution analytical 'omics' platforms, researchers can access the big biological data associated with various disease conditions and identify the key molecules [5,6]. Big biological data can be presented as networks, as a complicated series of binary interactions or relationships between different biological elements [7,8]. When the availability of high-throughput data as networks accompanies systems biology, machine learning, and different bio-computing tools, the initial search space for the prediction of key molecules can be narrowed considerably. As a result, the identified molecules can be considered therapeutic targets since they are believed to play a central role in regulating other nodes and governing the pathological pathways [[9], [10], [11], [12], [13]]. According to a rule called “the centrality-lethality rule” there are only a limited number of highly-linked nodes (known as the hubs) in protein-protein interaction (PPI) networks whose deletion are more likely to be lethal for the system [1,[14], [15], [16], [17], [18]]. However, apart from the centrality measures, such hub molecules could be identified via other strategies. Generally, the main biological concept behind identifying the hub molecules in the disease-related networks would be to knock out them in experimental research or target them using small chemical/non-chemical molecules in therapeutic strategies.

So far, various computational-based studies have been conducted to identify the key molecules in biological networks. The prior investigations can be divided into four main categories, including:

• Network topology-based studies; These approaches which focus on the features of a given disease-associated network (e.g., degree, closeness, and betweenness of nodes), introduce the kind of key molecules that can control all the other nodes in the network [[19], [20], [21]]. However, erroneous networks may affect the performance of these techniques. To deal with this limitation, in a study, an algorithm, named WDNFinder, has been proposed, combining the structural properties of a network with the nodes' strength. To evaluate the method, the researchers applied it to the human cancer signaling and P53-mediated DNA damage response networks. Based on the results, the identified key molecules were consistent with real-world biological facts [22].

• Biological information-based studies; Since the topology-based methods overlook the biological information and focus just on the network parameters, they may suffer from high false-positive prediction rates. Therefore, the integration of the information on a network topology with the information on the biological world can yield the most practical outcomes [23]. In this regard, Li et al. proposed a two-step algorithm for identifying the key molecules and examined its performance on the PPI networks. To this end, first, the authors specified the critical nodes of a PPI network using the information on the network topology. Second, they analyzed the discovered key molecules with the gene expression data and filtered them based on the biological facts. The findings showed that the approach derived from the combination of the topological data and the biological information outperformed the other methods in terms of prediction precision/accuracy [24].

• Controllability-based studies; such studies aim to discover a minimum number of nodes that can transfer the signal/information of a node of interest to the other nodes in the network [[25], [26], [27], [28]]. The controllability concept was shown to be capable of addressing the restriction resulted from the failure of some of the previous studies to notice the fact that a key molecule can control just a node from among the ones placed at the same distance [25]. Considering this important role of the controllability concept, Ebrahimi et al. introduced a novel mathematical-based theoretical method for selecting the key molecules from a network of interest by minimizing the total number of both the key molecules and mediators at the same time [7,8,29,30]. The researchers designed their method according to the Kalman's controllability rank condition based on which a network is controllable only if its related matrix is full rank.

• Machine learning-based studies; in the last category of the literary works, researchers employed the machine learning approaches, especially deep learning techniques, to further improve the process of identifying key molecules [31,32]. For instance, from the theoretical perspective, Muzio et al. depicted the ways by which different machine learning-based approaches can be employed for analyzing the biological networks. To identify the key molecules, a candidate solution was established based on a k-layer graph convolutional network (GCN) in which every node aggregates the input signals (received from the previous layer) and sends the calculated value to an active function. Then, all the nodes of a graph of interest were classified, and the biological functions of every node were specified. Next, the nodes which could control the remaining nodes of a network, were introduced as possible druggable targets through additional analysis of the classes and their related data. The mentioned technique can also be applied for dividing a given graph into smaller parts (a graph classification) and identifying the key molecules using the depicted method [33].

CKDs are defined as kidney function impairments existing for more than three months resulting in different health pathological states [34,35]. Based on reports, the global estimated prevalence of CKD is around 10%, and it is the 12th leading cause of mortality in patients, responsible for 1.1 million deaths across the world [36]. Despite a large number of changeable risk factors, preventing the progression of CKD is still challenging. Patient compliance, racial inequality in treatment, and the lack of effective drug therapies are just a few of the challenges [37]. Therefore, prompt actions are needed to develop novel treatments with the capacity to prevent or delay the progression of CKDs and their undesirable complications in an efficient manner. In this regard, identifying the key molecules in the CKD-related biological networks could be valuable.

In the present study, we applied our previously introduced optimization algorithm, Trader, to identify the key molecules as driver nodes (DNs) in the CKD-related networks and then, merged it with the depth-first search (DFS) algorithm to score the generated candidate solutions [[38], [39], [40], [41]]. Here, the DNs are defined as a minimal subset of the nodes whose removal from the network could produce a maximum number of the disjoint sub-networks. In terms of performance, we also compared the Trader with four popular optimization algorithms [[42], [43], [44], [45], [46], [47]]. Then, for the first time, we proposed a novel concept for selecting the DNs whose removal generated further disjoint sets. Furthermore, we assessed the differentially expressed genes-based PPI networks associated with different CKDs using the Trader algorithm to identify the potential DNs in each network. Next, we checked the druggability of the discovered DNs and introduced the currently known potential targets.