PRWHMDA: Human Microbe-Disease Association Prediction by Random Walk on the Heterogeneous Network with PSO.

Microorganisms resided in human body play a vital role in metabolism, immune defense, nutrition absorption, cancer control and protection against pathogen colonization. The changes of microbial communities can cause human diseases. Based on the known microbe-disease association, we presented a novel computational model employing Random Walking with Restart optimized by Particle Swarm Optimization (PSO) on the heterogeneous interlinked network of Human Microbe-Disease Associations (PRWHMDA) (see Figure 1). Based on the known human microbe-disease associations, we constructed the heterogeneous interlinked network with Cosine similarity. The extended random walk with restart (RWR) method was derived to get the potential microbe-disease associations. PSO was utilized to get the optimal parameters of RWR. To evaluate the prediction effectiveness, we performed leave one out cross validation (LOOCV) and 5-fold cross validation (CV), which got the AUC (The area under ROC curve) of 0.915 (LOOCV) and the average AUCs of 0.8875 ± 0.0046 (5-fold CV). Moreover, we carried out three case studies of asthma, inflammatory bowel disease (IBD) and type 1 diabetes (T1D) for the further evaluation. The result showed that 10, 10 and 9 of top-10 predicted microbes were verified by previously published experimental results, respectively. It is anticipated that PRWHMDA can be effective to identify the disease-related microbes and maybe helpful to disclose the relationship between microorganisms and their human host.

Introduction

Microorganisms include bacteria, archaea, protists, fungi and viruses 1. In human body, there are numerous microorganisms colonizing the gut, skin, uterus, lung, saliva, and so on 2. They play an important role in human health, metabolism, immune defense, nutrition absorption, cancer control and protection against pathogen colonization 3, 4.

Numerous lab experiments have revealed that many diseases are associated with the changes of microorganisms. For example, evidences from both rodent models and human researches suggested that the composition of the gut microorganisms had a significant influence on the immune system and might influence T1D risks 5. Fusobacterium was much more abundant in asthmatic patients comparing with healthy group 6. Some evidences revealed that lecithinase-negative Clostridium and Lactobacillus were detected to be more abundant in colorectal carcinoma patients 7, 8. More and more clinic studies revealed new associations between microbes and human diseases.

Computational biology can help identify essential gene 9, 10 and secretory protein 11 in disease, identify immunoglobulin 12, reveal the relationship between diseases and environmental factors, predict drug reactions, identify the early diagnostic markers of diseases, and carry out computer-aided drug design and production 13. Recently, a lot of computational biologic methods provide novel and effective tools for identifying the key associations between microbes and diseases. Ma et al. constructed a human microbe-disease associations database, which facilitated the study of the relationships between microbes and diseases 8. Based on the Gaussian kernel similarity, some prediction methods were studied as follows. Chen et al. presented a computational model (KATZHMDA) based on KATZ method, the number of walks, and their lengths for calculating the potential association probability between microbes and diseases 14. For high prediction accuracy, Huang et al. proposed the prediction model (PBHMDA) with a depth-first search algorithm to get all possible paths between microbes and diseases 15. Wang et al. adopted Laplacian regularized least squares classifier (LRLSHMDA) to construct a prediction model 16. Shen et al. developed a model utilizing Collaborative Matrix Factorization for Human Microbe-Disease Association prediction (CMFHMDA) 17. Various Random Walk Methods were utilized to rank the probabilities of predicted microbe-disease association. Based on traditional random walk with three parameters on the heterogeneous network constructed by Spearman correlation, Shen et al. derived a method (RWRHMDA) for prioritization of candidate microbes to predict disease-microbe association 18. Zou et al. developed a computational model (BiRWHMDA) to predict potential microbe-disease associations by bi-random walk on the heterogeneous network 19. It is anticipated that various computational prediction models could improve the identification of novel microbe-disease association.

Researching the interaction of the microorganism with disease will provide critical insight into the pathogenesis of disease and the development of strategies to prevent and treat disease. However, the knowledge in this field is far from satisfied. The aim of this article is to present a computational model to predict potential microbe-disease associations based on the known ones. In this study, we put forward a novel computational model of extended Random Walking with Restart optimized by PSO on the heterogeneous interlinked network of Human Microbe-Disease Associations (PRWHMDA) (see Figure 1). Firstly, under the hypothesis that microbes involved in similar disease tend to be functionally similar, we computed the similarities of diseases and microbes with Cosine measurement, respectively. With the disease-disease similarity matrix, the network of diseases was constructed. The microbe network was dealt with the same method. Combing the above-mentioned networks with the known microbe-disease network, we got the heterogeneous interlinked network. Then, the extended RWR method was presented to get the potential associations. In RWR method, we set a disease and the known associated microbes as seed nodes, after several steps, the probabilities of reaching each node (microbe) could be calculated. The higher the probability of reaching the node was, the more believable the association was. PSO was utilized to get the four optimal parameters of RWR. With PSO, PRWHMDA model performed well with 325 of 450 associations ranked in top 10. To evaluate the prediction performance, we performed the LOOCV and 5-fold CV, made the comparison with some state-of-the-art methods and analyzed the three case studies on the proposed model. The CV verified the effectiveness of the proposed model with the AUC of 0.915 (LOOCV) and average AUCs of 0.8875 ± 0.0046 (5-fold CV), which are higher than some other existing methods. In our case studies, 10, 10 and 9 of top-10 inferred microbes have been confirmed to have associations with asthma, IBD and T1D according to the literature evidences. The results indicate that PRWHMDA is effective to identify the disease-related microbes and could be helpful in future to disclose the relationship between microorganisms and their human host.

Figure 1

Flowchart of PRWHMDA.

The paper is organized as follows. In Materials and Methods section, we describe the similarity calculation using Cosine measurement. The construction of networks of microbes, diseases and microbe-disease associations are also presented. Furthermore, the random walk with restart method is outlined in this section. In Results and Discussion section, we show the optimized parameters by PSO of RWR. In addition, the results of CV, comparison results with state-of-the-art methods and the top 10 most potential microbes for asthma, IBD and T1D are presented, respectively. In Conclusion part, we discuss the results succinctly and conclude the paper.

Materials and Methods

Materials

We adopted the microbe-disease association data set called HMDAD which was constructed by Ma et al. 8. HMDAD contains manually curated 483 microbe-disease associations, which involves 39 diseases and 292 microbes. As some associations have more than one evidences, we extracted 450 distinct disease-microbe associations. Based on these known microbe-disease associations, we constructed the network of diseases, the network of microbes, and the network of microbe-disease associations, respectively. In this paper, N = 39 denotes the number of diseases, and N = 292 denotes the number of microbes.

Construction of the disease network

In the disease-disease similarity network, there are 39 nodes representing the diseases. The value of the edge between two nodes represents the similarity of the two diseases. We utilized the Cosine similarity measurement to calculate disease similarity with the known microbe-disease associations.

The disease-disease similarity matrix was

where sd(d,d) calculated by (2) denoted the similarity of the two diseases d and d.

The similarity of two diseases d and d was calculated by Cosine similarity as

where

MS(d) denoted the associations of disease i with all the microbes,

M(d) denoted whether microbe m was associated with disease i.

Therefore, the disease-disease similarity network could be constructed by nodes representing the diseases and edges representing the similarities defined by (1).

Construction of microbe network

Similarly, in the microbe-microbe similarity network, there are 292 nodes representing the microbes. The value of the edge between two nodes is the similarity of the two microbes.

The microbe-microbe similarity matrix was

where sm(m calculated by (6) denoted the similarity of the two microbes m and m

The similarity of two microbes m and m was defined by Cosine similarity as

where

DS(m) denoted the associations of microbe i with all the diseases,

which denoted whether disease j was associated with microbe i.

Therefore, the microbe-microbe similarity network could be constructed according to adjacency matrix defined by (5).

Construction of heterogeneous interlinked network

Based on the two networks, i.e., microbe-microbe network and disease-disease network, we used the known microbe-disease associations to construct the heterogeneous interlinked network. In the heterogeneous interlinked network, there are two types of node sets defined as D = [d, d, …, d] and M = [m, m, …, m] corresponding to diseases and microbes, respectively.

The associations between microbes and diseases was

where

md(d) denoted the association or non-association pattern between microbe m and disease d

The adjacency matrix of the network was

where SM denoted the similarity of microbes inferred by (5), SD denoted the similarity of diseases inferred by (1), MD defined by (8) denoted the associations of microbes and diseases, DM denoted the transpose of the matrix MD. In this way, the heterogeneous interlinked network was constructed.

Random walk with restart on heterogeneous interlinked network

RW was first put forward by Karl Pearson in 1905 20. In Bioinformatics, it has been applied to disease-gene prediction 21 and inferring gene-phenotype relationship 22. To emphasize the different weights of jumping between different networks, we extended the traditional RW method to predict microbe-disease association.

The walker can walk in disease network and microbe network, respectively and jump to the other network by disease-microbe network. Thus, at each step, the probabilities of reaching the nodes could be calculated. For the (s+1)-th step, the probability was

where denoted the s-th iteration probability of reaching microbe m, denoted the initial probability of microbe m, γ∈(0, 1) denoted the restart probability, η denoted the weights of the two networks. M defined by (11) denoted the transition matrix as

SM′ that represented the transition probability from a microbe to a microbe was defined by

where

sm′(i,j) denoted the transition probability from microbe m to m∈(0, 1) denoted that the walker stayed in the microbe network with the weight (1-λ).

MD′ that represented the transition probability from microbe network to disease network was defined by

where

md′(i,j) denoted the transition probability from microbe m to disease d, λ∈(0, 1) denoted that the walker jumped from the microbe network to disease network with the weight λ.

DM′ that represented the transition probability from disease network to microbe network was defined by

where

dm′(i,j) denoted the transition probability from disease d to microbe m, ξ∈(0, 1) denoted the weight of jumping from disease to microbe network.

SD′ represented the transition probability from a disease to a disease, defined by

where

sd′(i,j) denoted the transition probability from disease d to disease d (1-ξ) denoted the weight of staying in disease network.

In (12)-(15), the value was set to be 0 if the denominator was 0. After several iterations, the difference between the vectors pand p become negligible such as 1e-10. Thus, we got a stationary probability distribution which represented a proximity measure from the seed node(s) to each node.

Determination of parameters based on PSO with mutation

In the RW algorithm, the parameters λ, γ, η, and ξ are important to the prediction performance. For example, in Figure 2, if with parameters 1 (λ = 0.99, γ = 0.078, η = 0.44, ξ = 0.10), the ROC of LOOCV is shown as the pink curve with AUC = 0.49. While with parameters 2 (λ = 0.35, γ = 0.2, η = 0.25, ξ = 0.6), the ROC of LOOCV is shown as the blue curve with 0.8996. In order to get the optimal parameters i.e. λ, γ, η, and ξ, we utilized the PSO method.

Figure 2

Prediction performance of PRWHMDA with different parameters.

PSO is a population-based stochastic optimization technique, proposed by Kennedy and Eberhart (1995) 23. In PSO, the solution was thought of as a bird, called a particle. In this study, all particles were searched in a four dimensional space with values between 0 and 1. All particles (parameters values) were evaluated by a fitness-function (16) to judge whether the current solution was good. Considering the accuracy and high AUC, the fitness function F(x) was defined as

where NActual = 450 denoted the number of actual disease-microbe associations, NPredicted(x) denoted the number of tested associations ranked top 10 with parameter x, x [λ, γ, η, ξ]. The target was to get a suitable parameters vector to get the minimum value of F(x).

In the canonical PSO, each particle had position and velocity. For example, the position x and velocity v particle i was updated at each iteration according to

where v denoted the velocity of the i-th particle, w denoted the weight of current velocity, c1 and c2 denoted two positive constants representing learning parameters, r1, r2 denoted a random number between 0 and 1, pb denoted the optimal parameters value of the i-th particle had searched for, gb denoted global best particle, xi denoted the current value of the i-th particle. In order to avoid the locally optimal solution, we allowed particles to mutate with a certain probability, i.e. they could reset their positions sometimes. Thus, each particle's velocity was updated according to (17) and (18) until the convergence criterion was satisfied. After the convergence criterion was satisfied, we got global best particle to be the optimal parameters.

Results and Discussion

We set c1 = 1.49445, c2 = 1.49445, and set iteration times to be 27, the size of population to be 2, respectively. The iteration result is shown in Figure 3. The x-axis represented the iteration times, while the y-axis represented the fitness or called predicted error number of associations. Figure 3 showed that at the first iteration, there were 447 wrongly predicted associations, after 26 generations the number reduced to 125. Finally, the parameters calculated by PSO were λ = 0.6, γ = 0.5, η = 0.76, ξ = 0.79.

Figure 3

The optimal fitness of each iteration.

Cross validation

To effectively evaluate the prediction performance of PRWHMDA, LOOCV was implemented on the known disease-microbe associations from HMDAD database. Each known microbe-disease association was taken out in turns as a test association and the others were used for training to reconstruct the prediction model. Each test association was ranked in all unverified microbe-disease associations with their final probabilities. Receiver-operating characteristics (ROC) curve is widely used in binary classification problems. By changing the thresholds, the true positive rate (TPR, sensitivity) versus false positive rate (FPR, 1-specificity) can be calculated to plot the ROC curves. In the proposed method, TPR refers to the percentage of the positive test samples with higher ranks than the specific threshold, and FPR refers to the percentage of negative test samples with higher ranks than the specific threshold. AUC was calculated to further evaluate the prediction performance. As a result, our model obtained the AUC of 0.915 (see Figure 4 in red line).

Figure 4

The ROC curves and AUC values of different methods.

Furthermore, 5-fold CV was carried out. All the known microbe-disease associations were randomly divided into five disjoint groups, in which one group was for testing in turn and the other four groups were for training model. To reduce the bias brought by sample divisions, we executed the 5-fold CV 100 times to evaluate the robustness of PRWHMDA. As a result, the average AUC value was 0.8875 with the standard deviation of 0.0046.

Comparison with other methods

KATZHMD 14, RW3RHMDA 18 and BiRWHMDA 19 are state-of-the-art methods for predicting microbe-disease associations. All these methods are based on a heterogeneous network which was constructed by connecting the microbe similarity network and the disease similarity network via the known microbe-disease associations. To further validate the performance of the proposed method, we implemented these three methods using the same data sets and calculated the LOOCVs (see Figure 4). Comparing to other methods, the proposed method got a better ROC and higher AUC, while RWR3HMDA, KATZHMDA and BiRWHMDA had AUC values of 0.8112, 0.8332, and 0.8964, respectively.

Case studies

To further evaluate the prediction performance of PRWHMDA, we also implemented case studies of asthma, IBD, and T1D to predict novel associated microbes. The association strength score calculated by the proposed method and the benchmark was also presented, respectively. We used the RWR with three parameters as the benchmark.

Asthma

Asthma is a common chronic lung disease. To evaluate the prediction performance on asthma, we implemented a case study of asthma with our approach. In the prediction list, 10 of top-10 predicted microbes have been verified to have an impact on the asthmatic patients (see Table 1).

Table 1

Candidate microbes of Asthma

Rank	Microbe	Evidence	Score of PRW- HMDA (%)	Score of RWR3- HMDA (%)
1	Actinobacteria	PMID: 23265859	0.23	0.08
2	Firmicutes	PMID: 23265859	0.22	0.09
3	Clostridium coccoides	PMID: 21477358	0.15	0.05
4	Streptococcus	PMID: 17950502	0.13	0.05
5	Lactobacillus	PMID: 20592920	0.12	0.05
6	Lachnospiraceae	Validated by 24	0.12	0.04
7	Veillonella	PMID: 25329665	0.10	0.03
8	Propionibacterium	PMID: 27433177	0.10	0.04
9	Propionibacterium acnes	PMID: 27433177	0.10	0.04
10	Fusobacterium	Validated by 25	0.09	0.03

For example, Actinobacteria, Firmicutes, Lachnospiraceae, and Veillonella (1st, 2nd, 6th and 7th in the prediction list) were found to have a lower proportion in asthmatic patients when compared to non-asthmatic people 24, 26, 27. Clostridium coccoides (3rd in the prediction list) was found significantly associated with a positive Asthma Predictive Index (API) 28. Based on the effect of Streptococcus pneumonia (4th in the prediction list) on the development of asthma, effective immune-modulatory therapies were hoped to be presented 29. Lactobacillus (5th in the prediction list) could inhibit airway inflammation in an ovalbumin (OVA)-induced murine model of asthma 30. Propionibacterium acnes (9th in the prediction list) was more prevalent in asthma patients; therefore, Propionibacterium (8th in the prediction list) was also considered to be associated with asthma 31. Fusobacterium (10th in the prediction list) was much more abundant in asthmatic patients relative to healthy people 25. These predictions may give an insight into the potential prevention action of asthma.

Inflammatory bowel disease (IBD)

In the prediction list of IBD, 10 of top-10 predicted microbes have been validated by experimental literatures (see Table 2).

Table 2

Candidate microbes of IBD

Rank	Microbe	Evidence	Score of PRW- HMDA (%)	Score of RWR3- HMDA (%)
1	Clostridium coccoides	PMID: 19235886	0.33	0.15
2	Firmicutes	PMID: 25307765, 28842640	0.27	0.12
3	Bacteroidetes	PMID: 25307765, 28842640, 24013298	0.27	0.11
4	Prevotella	PMID: 25307765, 24013298	0.20	0.08
5	Staphylococcus	PMID: 28174737	0.19	0.08
6	Streptococcus	PMID: 23679203, 28842640	0.15	0.06
7	Haemophilus	PMID: 24013298	0.14	0.05
8	Lactobacillus	PMID: 26340825, 17897884	0.14	0.05
9	Veillonella	PMID: 28842640, 24013298	0.13	0.05
10	Bacteroidaceae	PMID: 17897884	0.13	0.05

Clostridium coccoides (1st in the prediction list) were less represented in A-IBD patients, compared to healthy subjects 32. In the IBD group, Firmicutes (2nd in the prediction list) was significantly increased, whereas Bacteroidetes (3rd in the prediction list) was decreased. At genus level Streptococcus (6th in the prediction list) and Veillonella (9th in prediction list) were increased 33. The results showed that Bacteroidetes (3rd in the prediction list) was significantly increased in Proteobacteria in the salivary microbiota of IBD patients. The dominant genera Prevotella (4th in the prediction list), Haemophilus (7th in the prediction list) and Veillonella (9th in prediction list) were found to largely contribute to dysbiosis (dysbacteriosis) observed in the salivary microbiota of IBD patients 34. Conventional culture showed that the counts of total obligate anaerobes and of obligate anaerobes such as Bacteroidaceae (10th in the prediction list) was decreased in the faeces of IBD patients. On the other hand, the counts of total facultative anaerobes such as Lactobacillus (8th in the prediction list) were increased 35. Research showed that dysbiosis within deeper layers of the ileum of CD patients, there were specifically enrichment of enterotoxigenic Staphylococcus aureus. Staphylococcus(5th in the prediction list) was thus validated 36.

Type 1 diabetes

In the prediction list of T1D, 9 of predicted microbes in the top 10 have been validated by experimental literatures (see Table 3).

Table 3

Candidate microbes of T1D

Rank	Microbe	Evidence	Score of PRW- HMDA (%)	Score of RWR3- HMDA (%)
1	Clostridium coccoides	PMID: 23433344	0.09	0.02
2	Enterobacteriaceae	PMID: 24475780	0.05	0.01
3	Staphylococcus	PMID: 26068542	0.04	0.01
4	Faecalibacterium prausnitzii	PMID: 20613793	0.03	0.01
5	Clostridium	PMID: 23433344	0.03	0.01
6	Clostridium leptum	PMID: 22046124	0.03	0.01
7	Enterococcus	PMID: 26176548	0.03	0.01
8	Desulfovibrio	Confirmed by 37	0.03	0.01
9	Tannerella	PMID: 24236037	0.03	0.01
10	Bacilli	Not confirmed	0.03	0.01

At the genus level, a significant increase in the number of Clostridium (Genus of 1st in the prediction list) was found in the children with diabetes 38. It was found that Enterobacteriaceae (2nd in the prediction list) was increased in patients with type 1 diabetes compared to the control group. A concomitant increase in Enterobacteriaceae may lead to a disturbance in the ecological balance of intestinal flora, which could be a triggering factor in type 1 diabetes etiology 39. Furthermore, subjects with autoantibodies, seronegative FDRs, and new-onset patients had different levels of the genera Firmicutes, Lactobacillus, and Staphylococcus (3rd in the prediction list) compared with healthy control subjects with no family history of autoimmunity 40. An increase of Faecalibacterium prausnitzii (4th in the prediction list) might result in a disturbance in the ecological balance, which could cause type 1 diabetes 41. At genus level, Mora Murri et al. 38 found a significant increase in the number of Clostridium (5th in the prediction list) in the children with diabetes. A study was performed on in non-obese prediabetic (NOD) mice. Metabolic changes of NOD mice were accompanied by diminished gut microbial diversity of the Clostridium leptum group (6h in the prediction list) 42. Two species in the genus Staphylococcus were abundantly presented in the conjunctiva of healthy rats, and were replaced by Enterococcus species (7th in the prediction list) and other bacterial species in diabetic rats 43. Members of the genus Desulfovibrio (8th in the prediction list) were identified in the colon samples of the control rats, with <0.5% abundance. It was noted that the insulin treatment was accompanied by fundamental changes within the phylum Proteobacteria: their overall abundance decreased spectacularly, and the genus Klebsiella was basically eradicated, being replaced by the genera Desulfovibrio (8th in the prediction list) and Bifidobacterium, with a combined abundance of 4% 37. GCC-fed NOD mice had the expected high incidence of hyperglycemia whereas NOD mice fed with a GFC had significantly reduced incidence of hyperglycemia. When the fecal microbes were compared, Tannerella species (9th in the prediction list) were increased in the microbes of GCC mice44.

Moreover, as shown in Tables 1-3, the association strength score of the proposed method is higher than that of the benchmark. In summary, these case studies further demonstrate that the proposed approach is effective to predict novel microbe-disease associations. The top-10 potential associated microbes for all the 39 diseases are listed in Table s1 of Supplementary File.

Conclusion

In this paper, we proposed a novel computational model based on the known microbe-disease associations. Cosine similarity was adopted to construct the microbe similarity network and disease similarity network. Using the experimental validated associations, we connected the two networks. The extended RWR method was utilized to walk on the network to get the association probability, which represented candidate microbe-disease associations. PSO was incorporated to get the optimal parameters for optimizing the prediction performance. As a result, the proposed model achieved a reliable prediction performance of LOOCV with AUC of 0.915 and 5-fold CV with average AUCs of 0.8875 ± 0.0046. In our case studies, 10, 10, and 9 of top-10 inferred microbes have been confirmed to have associations with asthma, IBD, and T1D according to the literature evidences. Given the promising prediction performance, it is believed that PRWHMDA could be an effective tool accelerating the progress of biomedical identification of potential disease-related microbes.

The good performance of the new method benefits from several major factors as the following. (1) We used Cosine similarity to extract the potential similarity for microbes and diseases by making use of known microbe-disease associations. (2) The proposed model is based on semi-supervised learning method, i.e., the training data is regarded as labeled samples while other test data as unlabeled samples. (3) Based on the training data set, PSO with mutation was adopted to get the optimal parameters. (4) We used the extended RW method that has adjustable parameters to emphasize the probabilities of transitions of different networks.

There are some limitations in the performance of PRWHMDA. Because the experimentally verified microbe-disease associations used in our approach are relatively insufficient, the sparse association network could affect the predictive capability. It is anticipated that this problem will be solved when collecting more microbe-disease associations in the future. Furthermore, PRWHMDA cannot be applied to diseases and microbes which are not in HMDAD. It is believed that the network would be powerful with the introducing of other types of disease/microbe similarity based on different kinds of data, such as symptom-based disease similarity, etc. We think that this method can guide medical experiments to get the potential associations.

Table S1.

Click here for additional data file.