Prediction of influential proteins and enzymes of certain diseases using a directed unimodular hypergraph

1.   Introduction

The protein-protein interaction (PPI) network represents the biological interactions between proteins ^[1], in which the nodes represent proteins and the edges represent interactions between proteins ^[2]. PPI is a vital tool in the identification of influential proteins and the cellular and molecular functions of proteins ^[3,4]. Identifying essential proteins may give a new perception in drug discovery for diseases and have control in signaling pathways, gene expressions and others. The proteins have different types of interactions between themselves. Direct or binary interactions and indirect (n-ary) or pathway interactions are a few of them ^[5]. There are various perspectives, such as experimental and computational, that can be utilized to analyze PPI and thereby to predict the influential proteins. However, PPI networks are intricate and hence computational analysis is more expensive ^[6].

Traditional experiments are efficient in analyzing biological networks. However, these methods reasonably consume a long running time and more cost. Thus, the researchers employ computational models to analyze biological networks ^{[7,8,9,10,11,12]}.

The graph is an effective tool for analysing biological networks, identifying patterns, significant components and many more. However, analyzing multi-way interactions of biological networks using graphs is difficult since graphs represent binary relations. Hypergraphs are the generalization of graphs that represent the n-ary relations and effectively analyze the multi-way interactions of biological networks. Additionally, compared to graph methods, hypergraphs have a lower computational complexity. For instance, using hypergraphs, Klimm et al. ^[13] predicted essential genes from a multi-protein network and established that the hypergraphs are more efficient for analzing multi-protein networks (complex networks) than pairwise graphs. Feng et al. ^[14] identified critical genes for pathogenic viral responses using hypergraph and infers that hypergraph potentially predicts the essential genes for complex biological networks.

In complex biological network analysis, exploring pathways or indirect interactions is challenging. Investigating the indirect or pathway interactions helps determine the nature of biological networks. Traversal algorithms efficiently identify pathway interactions. Depth-first search (DFS), a robust algorithm, is one of the traversal algorithms that significantly identifies the pathway interactions. Here, the directed hypergraph DFS has been constructed to obtain the pathway interaction between proteins. A minor hypergraph, an induced hypergraph, reduces the complexity of the analysis of pathway interactions by reducing dimension.

Some induced hypergraphs (obtained by dimensionality reduction using minor hypergraphs) are unimodular. The unimodular property of a hypergraph provides better classifications and clusters for data. For instance, Swaminathan et al. ^[15,16] used unimodular hypergraphs for DNA sequencing, and Madhu et al. ^[17] applied them to the multi-objective optimization problem for disease classification.

In this work, PPI networks for three diseases, Parkinson's, COVID-19 and diabetes mellitus, are constructed as directed hypergraphs, and the pathway interactions between the host proteins are obtained using directed hypergraph DFS. Then, the recursive application of the minor hypergraph algorithm reduces the dimension further and results in a unimodular matrix.

Section 2 reviews some related work, Section 3 presents the proposed method, Section 4 presents the results and discussion and the final section delivers concluding remarks.

2.   Related works

This section discusses previous works on three diseases: Parkinson's disease, COVID-19 and diabetes mellitus and their associated enzymes.

2.1.   Parkinson's and its enzymes

Typically, Parkinson's disease is an age-related disorder of brain functioning, a kind of neurological disorder. It progressively affects the nervous system and the nerve's controlled body parts. The tremors, slowed movement, rigid muscles, imbalanced posture and balance, loss of automatic movement and speech and writing changes are some symptoms of Parkinson's. It causes various brain disorder problems and leads to death if the nervous system does not work properly.

Kim et al. ^[18] reviewed the literature on treating neurological disease (ND), specifically Alzheimer's and Parkinson's, and they inferred that asparagine endopeptidase, neprilysin, amyloid-degrading and insulin-degrading enzymes efficiently treat ND. They notably concluded that the amyloid-degrading enzymes potentially have a vital role in treating ND. Goldstein et al. ^[19] investigated the role of regulatory enzyme tyrosine hydroxylase (TH) in stimulating L-DOPA collection and hypothesized that modulating TH levels could reduce the dopamine deficit and increase striatal L-DOPA levels. It provides a new strategy to treat Parkinson's disease. Rasch et al. ^[20] reviewed articles related to the role of TH and infers from clinical research that L-DOPA offered the best prospects for treating Parkinson's disease that concurred with Goldstein's ^[19] opinion.

Nakano et al. ^[21] analyzed Parkinson's disease using mouse models and performed two types of adenosine triphosphate (ATP) enzyme regulation. They suggested that maintaining the ATP level would be an efficient treatment for Parkinson's disease. Angelopoulou et al. ^[22] analyzed COVID-19 and Parkinson's disease and found that ACE2 was a crucial enzyme for both diseases. They also identified essential features of Parkinson's that are related to ACE2.

2.2.   COVID-19 and its enzymes

COVID-19 is a virus from the family of Severe Acute Respiratory Syndrome (SARS). COVID-19 causes cold, cough, fever and tiredness at the beginning stage. Later, it becomes complicated, affect the weaker body parts and organs and lead to diseases, organ failure and death. Also, COVID-19 predominantly affects the lungs.

Estrada et al. ^[23] analyzed a PPI of COVID-19 and concluded that some COVID-19 patients might be affected by Parkinson's disease. Jia et al. ^[24] inspected the human viral-host PPI of COVID-19 using two tensor-decomposition models (CP-N3 and ComplEx-N3) and a knowledge graph (constructed from biomedical information). They predicted the links between viruses and antiviral drug attributes. Guo et al. ^[25] analyzed the PPI of COVID-19 using the concept of core decomposition and dense graphs. They initially took the PPI of an affected person and developed it using a bio mine database ^[26] for analysis and obtained some of the gene hypotheses of humans for predicting further clarification for detecting the drug for COVID-19.

Hasan et al. ^[27] analyzed blood cells of COVID-19 affected people to obtain hub proteins. Also, they discovered hub proteins to develop therapeutic drugs for COVID-19 using gene ontology. Li et al. ^[28] found that ACE2, a cytokine-related enzyme, could be a receptor for SARS-COV-2, potentially the first receptor that helps the SARS-COV-2 viral protein to enter the human body. They also constructed a PPI of COVID-19 and identified hub genes involved in viral cytokine activity; these were beneficial for drug discovery in a biological laboratory. Messina et al. ^[29] analyzed a PPI of viral and human proteins involved in COVID-19 and presented a pathogenic mechanism for COVID-19 host protein interactions.

2.3.   Diabetes and its enzymes

Diabetes mellitus is the metabolism of heterogeneous disturbances in which chronic hyperglycaemia is the key. The impaired insulin action or secretion or both is the cause of diabetes mellitus. Some of the symptoms are unexpected weight loss, frequent urination, blurry vision, feeling tired all the time and many infections. Various types of diseases like coronary, neurological and organ damage are the causes of diabetes. Types 1 and 2 are the most common types of diabetes.

Noroozi et al. ^[30] analyzed a sample of 9991 adults and inferred that the liver enzymes alanine aminotransferase (ALT), aspartate aminotransferase (AST), alkaline phosphatase (ALP) and $\gamma$-glutamyl-transferase (GGT) were related to higher odds of diabetes. Chen et al. ^[31] sampled 132,377 adults and found that the enzymes GGT, ALT, ALP and AST were associated with high-risk factors for type Ⅱ diabetes. Ross et al. ^[32] characterized serological biomarkers related to the exocrine pancreas, analyzed their role and found three pancreas enzymes, amylase, lipase and trypsinogen, which are potential risk factors for type Ⅰ diabetes in serological biomarkers of pancreas volume. Al-Kouh et al. ^[33] studied eight male Wistar rats with high glucose levels and induced diabetes to evaluate the potential of angiotensin-converting enzyme (ACE) and angiotensin-Ⅱ receptor in the renin-angiotensin system (RAS) for the prevention of heart ischaemia/reperfusion injury. They found that the RAS protected the heart from diabetes and that glucose transporter type 4 pathways protected against cytokine-related diseases.

3.   Proposed method

In this work, we analyze PPI networks of diseases using our proposed method, which consists of the following steps:

● Construction of a directed hypergraph for PPI.

● Finding the pathway interaction of proteins using directed hypergraph DFS.

● Construction of a path-directed hypergraph and its corresponding matrix using the pathway interactions.

● Dimensionality reduction of the matrix of the path-directed hypergraph using the properties of minor hypergraphs.

● Clustering of proteins using the unimodular matrix.

The algorithm of the proposed method is given in the Algorithm 1.

3.1.   Directed hypergraph construction

If there is a PPI between the viral or host proteins $v_i$, $i = \{1, 2, \cdots ,s; \; s \in \mathbb{N}\}$ and human proteins

then the hyperedge of a directed hypergraph ($DH_{G}$)

is constructed, where

and

The PPI network of the host (viral) and the corresponding host-human proteins of diseases are constructed as a directed hypergraph using the Algorithm 2.

Definition 3.1. [Minimal hypergraph] ^[34] The directed hypergraph $DH_{M_{G}}$ (hyperedges are either in B-arc or F-arc) with $|E(DH_{M_{G}})| = n_m$, and there is no $DH_{M'_{G}}$ with $|E(DH_{M'_{G}})| = n'_m < n_m$, is said to be minimal hypergraph.

Theorem 1. ^[34] If $DH_{G} = (V_{DH_{G}}, E_{DH_{G}})$ is a directed hypergraph with $|V_{DH_{G}}| = n$, then there exists a minimal hypergraph $DH_{BM_G} = (V_{DH_{G}}, E_{{HBM}_{G}})$ such that every directed hyperedge $E_{HBM_G}$ of $H_{BM_G}$ is B-hyperarc or $H_{BM_G}$ is a B-hypergraph. Also, there exist a minimal hypergraph $H_{FM_G} = (V_{DH_{G}}, E_{HFM_G})$ such that every hyperedge $E_{HFM_G}$ of $H_{FM_G}$ is F-hyperarc or $H_{FM_G}$ is an F-hypergraph.

From the Theorem 1, the maximum possible number of hyperedges equals the number of nodes ($n$) of the directed hypergraph. So, the maximum number of iterations required for every node is $n$, a parameter.

3.2.   Paths

DFS is a widely used traversal algorithm to obtain the longest paths for the nodes in a network, which performs an exhaustive node search until reaching the required source. It uses the stack for appending the visited nodes and terminates its process when no new elements exist as non-visited nodes or when the stack is empty.

In this paper, the $DH_{G}\_DFS$ algorithm is designed to obtain the paths. Each viral or host protein is the origin of a path in which the disease's viral (or host) and human proteins represent the source and destination, respectively. The directed hypergraph obtained using Algorithm 2 is an input for the $DH_{G}\_DFS$ Algorithm 3 to get the pathway interactions for viral or host proteins.

The directed hypergraph DFS procedure works as follows and the parameter used in $DH_{G}\_DFS$ is the length of the path. Here, the length of the path is 1,000,000:

${\rm{a}})$ Take a viral or host protein as a root node.

${\rm{b}})$ Perform deep searching for the relevant human proteins using a directed hypergraph from the viral or host protein.

${\rm{c}})$ Mark all human proteins as "seen" when they have been visited.

${\rm{d}})$ Terminate the search process when there is no new human protein to visit.

3.3.   Pathway matrix

The pathway matrix is constructed with the following steps:

${\rm{i}})$ Row elements are viral or host proteins;

${\rm{ii}})$ Column elements are human proteins that are involved in pathway interactions.

Assume an interaction exists between the viral or host protein and human proteins based on pathway interactions obtained using Algorithm 2. The enzymes that correspond to the human protein's diseases are then taken. Thus, the procedure for assigning matrix entries to viral or host and human proteins is defined based on the following and the procedure for obtaining matrix, and its corresponding hypergraph is given in Algorithm 5:

3.4.   Dimensionality reduction

The dimensionality of the path-directed hypergraph or pathway interaction matrix is reduced using minor hypergraphs. Here are some preliminary definitions and properties of minor hypergraphs.

The hyperedge $e \in E(DH_{G})$ is said to be a subhyperedge if there exists a hyperedge $e' \in E(DH_{G})$ such that $e \subseteq e'$. If $e \subset e'$, then $e$ is a proper subhyperedge ^[35].

For a hypergraph $DH_{G}$, the hypergraph obtained from $DH_{G}$ by contracting an hyperedge $\{v_{x}, v_{y}, v_{z}, \ldots\} \in E(DH_{G})$ is the hypergraph $DH_{G}/e$ or $DH'_{G}$ with $V(DH_{G}/e) = V(DH_{G}) \setminus \{v_{x}, v_{y}, v_{z}, \ldots\} \cup \{v_{xyz\ldots}\}$ and

In other words, $v_{xy}$ is the new contracted vertex, and every hyperedge containing either $x$ or $y$ is set to contain $v_{xy}$.

Let $DH_{G}$ be a hypergraph. Then, the minor of $DH_{G}$, denoted $DH'_{G}$ ($DH'_{G} \preceq DH_{G}$), can be obtained using the following set of operations ^[35]:

${\rm{i}})$ Removal of a vertex.

${\rm{ii}})$ Contraction of the vertices that share a common hyperedge.

${\rm{iii}})$ Addition of a hyperedge with contracted vertices.

${\rm{iv}})$ Removal of proper subhyperedges.

There are different types of directed hyperedges based on pathway matrix, as follows:

${\rm{i}}.$ Take a viral or host protein ($v_{i}$) as the 'head' of the hyperedge, and human proteins ($h_{j}$s) as the 'tail', with $P_{DH_{G}}[v_{i}h_{j}] = 1$.

${\rm{ii}}.$ Take the 'head' to be viral or host proteins ($v_{i}$s) and the 'tail' to be human protein $h_{j}$, with $P_{DH_{G}}[v_{i}h_{j}] = 1$.

The standard elementary operations of matrices are

● Interchange any two rows (columns).

● Subtracting or adding any row (column) from another.

● Multiply the scalar -1 with any row (column).

Consider a unimodular matrix $C = (c_{ij})$ with $m$ rows and $n$ columns, then define the following operations to obtain the dimensionality reduced unimodular matrices:

● Interchange any column with zero in an ascending manner.

● Delete the columns with zeros from the matrix.

● If there is a column $c_{i1}$, with the leading element as non-zero, then make all $c_{j1} = 0$ using elementary operations.

● Delete the column $c_{i1}$ and reduce the dimensionality of the matrix with dimension $m \times (n-1)$.

● Make all the columns $c_{k1} > 0, k = 1, 2, \ldots, m$, separately as a reduced matrices.

Raghavachari ^[36] proved Theorem 2 concerning the above operations.

Theorem 2. The given matrix $C = (c_{ij})$ with $m$ rows and $n$ columns is totally unimodular if and only if each of the above defined reduced matrices are totally unimodular.

Suppose that the viral or host proteins $v_i, v_j$ have interactions with the human proteins $\{h_a, h_b, h_c\}$ and $\{h_d, h_e, h_f\}$ respectively. Then, the elementary row (column) operations between the rows (columns) of the proteins $v_i, v_j$ in the interaction matrix may lead to an erroneous interaction between proteins. Thus, the following set of operations are defined to overcome this:

● Apply the logical operator OR between any two rows ($r_{i}$) (columns ($c_{i}$)) and ($r_{j}$) ($c_{j}$), if $r_{i} \lor r_{j} = r_{i}$ or $r_{i} \lor r_{j} = r_{j}$ (for columns $c_{i} \lor c_{j} = c_{i}$ or $c_{i} \lor c_{j} = c_{j}$).

● Make the identical rows ($r_{i}$) (columns ($c_{i}$)) and ($r_{j}$) (($c_{j}$)) as zero rows ($r_{0}$) (columns ($c_{0}$)) by using the logical operator XOR between rows (columns) (i.e., ) $r_{i} \bigoplus r_{j} = r_{0}$ (for columns $c_{i} \bigoplus c_{j} = c_{0}$).

● Delete the zero rows ($r_{0}$) (columns ($c_{0}$)).

● Suppose there are no new rows (columns) that satisfy $r_{i} \lor r_{j} = r_{i}$ or $r_{i} \lor r_{j} = r_{j}$ (for columns $c_{i} \lor c_{j} = c_{i}$ or $c_{i} \lor c_{j} = c_{j}$). Then make all distinct rows ($r_{k}$) (columns ($c_{k}$)) as a reduced matrices with dimension $s \times t$, where $s < m$ and $t < n$.

Theorem 3. Let $A = (a_{ij})$ be a matrix with $m$ rows and $n$ columns. If $(a_{ij}) = 0$ or $+1,$ for $i \in \{1, 2, \ldots, m\}$ and $j \in \{1, 2, \ldots, n\}$. Then, the dimensionality reduced matrix $A_R = (r_{ij})$ with dimension $s < m$ rows and $t < n$ columns, obtained using the above operations is totally unimodular.

Example for reduction of hyperedges

The following example shows the reduction of directed hyperedges using minor hypergraph operations where the distinct hyperedges are highlighted using different colors in the Figures 2–5.

3.4.1.   Dimensionality reduction based on hyperedges

The following minor hypergraph properties are developed to reduce the length of the directed hyperedges.

The dimensionality reduction of hyperedge has two subcategories: Removing the hyperedges which have the same head/tail, and the other is the removal of subhyperedge.

3.4.1.1.   Blending hyperedges with same head/tail

If there are any two hyperedges $e_{i}, e_{j}$ that have the same head/tail, then blend the hyperedges $e_{i}, e_{j}$ as $e_{ij}$ (i.e., blend their head/tail).

3.4.1.2.   Blending subhyperedge

For any two hyperedges $e_{i}, e_{j}$ wìth $e_{i}$ is the subhyperedge of the hyperedge $e_{j}$, blend the hyperedges $e_{i}, e_{j}$ in the following way:

${\rm{i}})$ Combine the head/tail of the hyperedges.

${\rm{ii}})$ Combine the remaining nodes of the hyperedges using the minor hypergraph operations.

The resultant hypergraph with reduced hyperedges in the form of matrix is a unimodular that does not require any optimization.

The procedure to obtain the hypergraph in the reduced dimension is presented in Algorithm 6.

3.5.   Unimodular matrix

The matrix that results from the dimensionality reduction procedure is unimodular. We use the properties of this unimodular matrix to cluster disease-related proteins. Some definitions and properties of unimodular hypergraphs are given below.

For any square sub-matrix of a given matrix, if the determinant value is $-1, 0,$ or $+1$, the matrix is said to be a totally unimodular matrix.

If the incidence matrix of a hypergraph is totally unimodular, then the hypergraph is said to be a unimodular hypergraph.

Algorithm 7 presents clustering with the unimodular property.

4.   Results and discussion

The proposed methodology is implemented to the PPI of the following disease networks ^[37] using a Google Colab TPU processor:

● Pakinson's,

● COVID-19,

● Diabetes.

The PPI interactions of diseases are implemented using the following steps:

● The viral or host and the corresponding human protein interactions involved in diseases are constructed as a directed hypergraph using $CDH_{G}$ Algorithm 2.

● The $DH_{G}\_DFS$ Algorithm 3 is applied to the directed hypergraph to obtain the pathway interaction for every viral or host protein involved in the disorder.

● The pathway matrix of proteins is constructed using the CPM Algorithm 5.

● The dimensionality of the pathway matrix is reduced using the DM Algorithm 6.

● The resultant matrix of DM Algorithm 6 is unimodular. Thus, the proteins and their related enzymes of diseases are clustered using the Cluster Algorithm 7.

Table 5 presents the number of nodes ($N(DH_{G}$)), the number hyperedges ($M(DH_{G})$) & edges ($M(G)$), the path length for hypergraph ($P_{L}(DH_{G})$) & graph ($P_{L}(G)$) used in the proposed method for implementation. The Tables 2–4 presents the number of influential proteins of the diseases obtained by proposed method and graph algorithm. Also, the number of influential proteins of the diseases equals to the number of proteins in the data-set from Uniprotkb database ^[37].

Using the proposed method, we obtained unimodular matrices for the diseases taken for this study. The unimodular matrices and their possible clusterings are as follows:

For Parkinson's disease, the unimodular matrix is

and the possible clusters are

For COVID-19, the unimodular matrix is

Finally, for diabetes, the unimodular matrix is

and the possible clusters are

In the case of Parkinson's disease, the proteins identified belong to the enzyme tyrosine hydroxylase (TH). The regulation of TH enzyme may provide a new strategy in the treatment of Parkinson's ^[19,20], and controlling the activity of the amyloid-degrading enzymes (ADE) (neprilysin, insulin-degrading enzymes, asparagine endopeptidase) could be a crucial role in the treatment of Parkinson's ^[18]. Also, the algorithm yields the proteins that are components of the enzyme ATP, the maintenance level of ATC, would give the therapeutic strategy for Parkinson's ^[21]. From the Table 2 some influential proteins were obtained in the Neprilysin enzyme for Parkinson's disease. Moreover, Neprilysin is one of the enzymes involved in the aggregation control of amyloidogenic proteins to cure Parkinson's ^[18]. However, the graph algorithm does not yields these proteins.

For COVID-19, we obtained the proteins that are the components of enzymes Tmprss2, Ace2, liver-related enzymes (IL6, cytoplasmic enzymes, cytokines), the diabetes-mellitus-related enzymes (alanine transaminase, alkaline, At Ⅱ, serum, glucose oxidase), digestive-system-related enzymes (pancreatic lipase, pepsin, lactase, maltase, trypsin), and blood-pressure-related enzymes (matrix metalloproteinases). The enzymes Tmprss2 and Ace2 are the hosts for COVID-19 ^[38]. The liver-related enzymes may lead to liver injury, diabetes and digestive-related enzymes may increase the risk level of COVID-19, and the blood-pressure-related enzymes may aggregate COVID-19 infection ^[39].

Also, the proteins involved in DNA replication (DNA helicase, DNA ligase, DNA polymerase, DNA primase, topoisomerase), stroke-related enzymes (proteolytic enzymes) and tuberculosis-related enzymes (mura, Murc, Mure, Murf) are obtained using the proposed method. Sathyanarayanan et al. ^[34] analyzed the PPI of COVID-19 and identified influential proteins and corresponding enzymes. The present algorithm identifies the same set of enzymes, with more proteins and other enzymes related to common diseases. Therefore, based on the enzymes, a person affected by COVID-19 may be overwhelmed by the new disease. Thus, clustering hub proteins for COVID-19 is not possible because many intersecting hub proteins are obtained in the enzymes (or clusters). From Table 3, some significant proteins of enzymes Alanine Transaminase, AT-Ⅱ, MurA and MurC are obtained, but these influential proteins and hence the enzymes are not obtained from the graph algorithm.

For diabetes, we obtain proteins that belong to the enzymes alanine transaminase (ALT), ALP, aspartate transaminase (AST), GGT, sirtuins and the pancreas enzymes (amylase, lipase), as well as the receptor angiotensin-Ⅱ. These enzymes are risk factors for type Ⅰ and type Ⅱ diabetes. The enzymes ALT, ALP, AST and GGT are the factors of diabetes with increased odds. The normal level of these enzymes has a good response in drugs ^[30,31]. The pancreas enzymes serve as biomarkers for type Ⅰ diabetes. These enzymes may prevent diabetes in the initial stage ^[32]. The enzyme sirtuins are used in pathogenesis and treating diabetes mellitus ^[40,41]. These enzymes are risk factors for type Ⅰ and type Ⅱ diabetes ^[33]. Therefore, these enzymes have a crucial role in treating diabetes. From Table 4, there are no significant proteins in the enzyme ALT by the graph algorithm, but some influential proteins are obtained using the proposed methodology. The proteins in this enzyme are related to the increased odds of diabetes and are used in the drug for diabetes ^[30].

5.   Conclusions

In this work, directed hypergraphs and their unimodular properties are being exploited to analyze the PPI of Parkinson's disease, COVID-19 and diabetes mellitus. Here, the pathway network of PPI was obtained using the novel-directed hypergraph depth-first search. The pathway network consists of the most extended possible pathway interactions of PPI. Thus, the complexity of pathway network analysis is a challenge. The minor hypergraph reduces the pathway network dimension and complexity. Hence, the logical operations on the matrices approach to implement the properties of the minor hypergraph for dimensionality reduction are introduced. These logical operations have a significant advantage over elementary operations on matrices. Finally, the properties of unimodular hypergraph identifies the influential enzymes based on the clusters of proteins related to the diseases. It leads to a new prospect to treat the diseases or to identify the pattern and characteristics of diseases in the analysis. Also, the results obtained were verified by comparing the literature on the diseases as presented in Section 4. Furthermore, the proposed methodology outperforms the graph algorithms that are limited in the path length. The future scope is to predict more interaction features of pathway network analysis using biological experimental and / or mathematical modeling, and extending path lengths that could handle MB's and GB's of data.

Use of AI tools declaration

The authors declare that have not used Artificial Intelligence (AI) tools in the creation of this article.

Acknowledgments

The authors would like to acknowledge SASTRA Deemed University for supporting this research work.

Conflict of interest

The authors declare that there are no conflicts of interest.