Recently, high-throughput experimental techniques have generated a large amount of protein-protein interaction (PPI) data which can construct large complex PPI networks for numerous organisms. System biology attempts to understand cellular organization and function by analyzing these PPI networks. However, most studies still focus on static PPI networks which neglect the dynamic information of PPI.The gene expression data under different time points and conditions can reveal the dynamic information of proteins. In this study, we used an active probability-based method to distinguish the active level of proteins at different active time points. We constructed dynamic probabilistic protein networks (DPPN) to integrate dynamic information of protein into static PPI networks. Based on DPPN, we subsequently proposed a novel method to identify protein complexes, which could effectively exploit topological structure as well as dynamic information of DPPN. We used three different yeast PPI datasets and gene expression data to construct three DPPNs. When applied to three DPPNs, many well-characterized protein complexes were accurately identified by this method.The shift from static PPI networks to dynamic PPI networks is essential to accurately identify protein complex. This method not only can be applied to identify protein complex, but also establish a framework to integrate dynamic information into static networks for other applications, such as pathway analysis. Saccharomyces cerevisiae. PPIs are of central importance for most biological processes, and thus PPI networks can provides a global picture of cellular mechanisms. A key task of system biology is to reveal cellular organization and function by analyzing the PPI networks. Protein complexes are molecular aggregations of two or more proteins assembled by multiple PPIs, which play critical roles in many biological processes. Most proteins are only functional after assembly into protein complexes. Accurate determination of protein complexes in large PPI networks is crucial for understanding principles of cellular organization and function from the networks level [Recent advances in high-throughput experimental techniques such as yeast two-hybrid and mass spectrometry have generated a large amount of protein-protein interaction (PPI) data , 2. Thesks level .. [. [. proposed a clustering tool (GIBA) to detect protein complexes [. [. [. proposed ProRank method which uses a protein ranking algorithm to identify essential proteins in a PPI network and predicts complexes based on the essential proteins [. proposed a hub-attachment based method called HUNTER to detect functional modules and protein complexes from confidence-scored protein interactions [. [. [Over the past decade, great effort has been made to identify protein complexes in PPI networks. As protein complexes are groups of proteins that interact with each other, they are generally dense subgraph in PPI networks. Some computational methods based on graph theory or dense regions finding have been proposed to identify protein complexes from PPI networks. The molecular complex detection (MCODE ) algorit.  proposed. [.  develope. [.  to detecomplexes , which ilexes [.  proposedlexes [. , Wu et aes [. [.  developeproteins . Chin etractions . Since ptions [.  proposedtions [. . Since tns [. [.  proposedSo far most studies on protein complex identification only focused on static PPI networks. However, cellular systems are highly dynamic and responsive to cues from the environment , 18. PPI. [. [. [. proposed a framework termed DyCluster to detect complexes based on PPI networks and gene expression data [To address this problem, the shift from static PPI networks to dynamic PPI networks is essential for protein complex identification and other similar applications. The gene expression data under different time points and conditions can reveal the dynamic information of protein. Some studies have integrated gene expression data to reveal the dynamics of PPI. For example, Lin et al.  revealed. [.  analyzed. [. [.  used theion data . Firstlyion data  and CMC ion data , to deteIn general, the inevitable background noise exists in the gene expression data. How to identify the active time point of each protein based on gene expression data is crucial for constructing dynamic PPI networks. In this study, we proposed a novel method to calculate the active probability of proteins at different time points. Furthermore, we constructed dynamic probabilistic PPI networks (DPPN) to integrate gene expression data and PPI data based on attributed graph theory, and proposed a clustering method to identify protein complex from DPPN. There are two key differences between our method and DyCluster. Firstly, the DPPN constructed by our method can effectively distinguish the active level of a protein at a time point which is of benefit to the complex identification. Secondly, our method doesn’t directly apply other complex-detection algorithms, but proposes a new clustering method for the characteristics of DPPN. We demonstrated the utility of the method by applying it to three different yeast PPI datasets and gene expression data. Three DPPNs were constructed and many well-characterized protein complexes were accurately identified. In addition, the method was compared with current protein complexes identification methods. The advantages of the method, potential applications and improvements were discussed.Since a protein has its active periods in the cell , 18, the. [X be a real random variable of normal distribution N, which describes for each individual gene its distribution of gene expression values across time. For any k > 0, P{|X − α| < kσ} = 2Φ(k) − 1, where Φ(.) is the distribution function of the standard normal law. In particular, for k = 1, 2, 3 it follows that P{|X ‐ α| < σ} = P{α − σ < X < α + σ} ≈ 0.6827, P{|X ‐ α| < 2σ} ≈ 0.9545 and P{|X ‐ α| < 3σ} ≈ 0.9973. Based on the above empirical rules, Wang et al. [A simple idea is to use a single global threshold for identifying the active time point of each protein. If the gene expression value of a gene is higher than the global threshold at a time point, the gene is considered as expressed at that time point. However, the expression level of genes in activity period is different. Wang et al.  proposedg et al.  designedg et al. . Compareg et al. , our metn time points. Let Gi(p) be the gene expression value of gene p at the time point i. Let α(p) and σ(p) be the algorithmic mean and SD of gene expression data G(p), respectively.In fact, gene expression data always includes inevitable noise. The active proteins with low expression values are likely to be filtered out even though using an active threshold for each gene. To deal with this problem, we calculate the active probability of each protein at different time points based on three-sigma method. Gene expression data often contain expression profiles of k-sigma  threshold can be calculated based three-sigma method [Since different genes correspond to different expression curves, we calculate the active probability of a protein based on the algorithmic mean and SD of the corresponding gene. Firstly, the a method  as folloGe_thresk is the active threshold of gene p which is determined by the values of α(p),σ2(p) and k (the times of sigma). If σ2(p) is very low, it indicates that the fluctuation of the expression curve of gene p is also very small and the value of Gi(p) tends to be very close to α(p). In this case, the value of Ge_threshk is close to α(p). If σ2(p) is very high, it indicates that the value of Gi(p) is spread out over a large range of values. A large σ2(p) generally indicates much noise in the gene expression data of gene p. In this case, the value of Ge_threshk is close to α(p) + k · σ(p). Note that the range of k (the times of sigma) is in , while 3 is the maximum times of sigma. The larger k is, the higher Ge_threshk gets. If we choose a larger k, the active proteins filtered by Ge_threshk will be with higher confidence. For instance, based on three-sigma rules, when Gi(p)> α(p) + 3 · σ(p), the probability that the protein p (product of gene p) is active at the i time point is 99.7 %, but when Gi(p) > α(p) + σ(p), the probability that the protein p (product of gene p) is active at the i time point is only 68.3 %. Based on the Ge_threshk, we calculate the active probability of a protein in the i time point as follows.X ‐ α| < σ} ≈ 0.6827, P{|X ‐ α| < 2σ} ≈ 0.9545 and P{|X ‐ α| < 3σ} ≈ 0.9973). In particular, if the value of Gi(p) is lower than Ge_thres1(p), the active probability is 0. This indicates that the protein p is not active in the i time point. In general, the active probability value of a protein can represent its active level at a time point. Thus, we can distinguish the active level of a protein at a time point based on its active probability. Neither global threshold method nor active threshold method can effectively distinguish the active level of a protein at a time point based on gene expression data. Based on the active probability of a protein, we can not only effectively identify the active time point of the protein, but also distinguish the active level of the protein.In the equation (4), the active probability of a protein contains four levels based on the sigma rules  where V is the set of protein vertices, E is the set of PPIs, A = {T1, T2, … Tn} is the set of active time points for protein vertices, and P = {P1, P2, P3} is the set of active probability for protein vertices at each active time point. Fv is a function that returns the set of active time attributes of a protein vertex. Each protein vertex vi in V has a set of active time attributes Fv(vi) = {Ti1, Ti2, …, Tim}, where m = |Fv(vi)| and Fv(vi) ⊆ A. Likewise, Fp = Pk is a function that returns active probability Pk for the protein vertex vi at Tij time point. In this study, the active probability set P includes three values P1 = 0.99, P2 = 0.95, and P3 = 0.68, respectively. Each PPI e in E also has a set of active time attributes Fe) = Fv(vi) ∩ Fv(vj) and Fe) ≠ ∅.We define a DPPN as a 7-tuple v1. From Fig. T1 and T5 protein v1 are significantly higher than at T2, T3 and T4. According to the equation (4), Ge_thresh2 > GT1(v1) > Ge_thresh1 at the time point T1, and GT5(v1) > Ge_thresh3 at the time point T5. Therefore, the active probability of protein v1 are P3 (0.68) and P1 (0.99) at the time point T1 and T5, respectively. Figure v1 has two active time attributes (T1 and T5), and v2 has three active time attributes . In particular, each protein vertex has an active probability at an active time attribute. In Fig. v1 is P3 (0.68) and P1 (0.99) at the T1 and T5 time points, respectively. Figure e1 represents the PPI between v1 and v2. The active time attributes sets of v1 and v2 are {T1,T5} and {T1, T2, T4} based on Fig. e1 is {T1} which is calculate by {T1, T5}∩{T1, T2, T4}. If the active time attribute set of an edge is empty, the edge will not appear in DPPN.Figure G, the topology score of edge e is defined as follows:Compared to static PPI networks, DPPN can effectively represent not only the topological structure but also the dynamic information of PPI networks. Since protein complexes are groups of proteins that interact with each other in the same time , 3, theyNi and Nj denote the neighbors of vi and vj respectively. |Ni ∩Nj | denotes the common neighbors of vi and vj, and Avg.(G) calculates the average degree of the DPPN G. If vi and vj share more common neighbors, the topology score will be larger. Max{Avg.(G), |Ni|}can penalize protein vi with very few neighbors effectively [e at the k active time point is given as:where ectively . Based ok(vi) and Pk(vj) are the active probability of vi and vj at the k time point, respectively. The equation (7) can consider not only the topological structure but also the dynamic information of DPPN. Since the active probability of vi and vj is likely different at different active time point, the weight of edge e dynamically changes during all active time points.where PC and an edge set Ec in DPPN G, an active correlated clique is a pair , Ac), such that for each protein vertex vi in C, the degree of vi is |C|-1. Ac is the common active time attribute set of each protein vertex vi in C and Ac ≠ ∅.Definition 1 - Active correlated clique. Given a protein vertex set In general, we can mine many Active correlated cliques in a DPPN. Figure Ec), Ac), the Active clique score of , Ac) at the k (k∈Ac) active time point, is given as:Definition 2 – Active clique score. Given an active correlated clique  is the active probability of vi at the k time point. ∏vi ∈ CPk(vi) calculates the active probability of clique, Ac) at the k time point. Clique_Pr. , Ac) choose the maximum ∏vi ∈ CPk(vi) as the active probability for the clique from all the common active time points. Therefore, active probability of an active correlated clique is associated with an unique active time point. We can use , Tc) to denote an active correlated clique which gets the clique probability at Tc active time point. Clique score provides a reasonable combination of topology connectivity and the dynamic active attributes of DPPN. If an active correlated clique is associated with a large clique score, this indicates that the proteins of the clique are all in dense subgraph structure of DPPN as well as highly active at a same time point. Therefore, the clique score can effectively evaluate how possible an active correlated clique is the core structure of a protein complex.where P. [Gavin et al.  revealedCandidate_CORE was comprised of all active correlated cliques, which generally overlapped. We used equation (8) to calculate the active clique score for all active correlated cliques in Candidate_CORE, and ranked them in descending order of active clique score, denoted as {, Tc1), , Tc2),…,, Tcn)}. The top ranked clique, Tc1) was then deleted from Candidate_CORE and inserted into the core set CORE. To ensure that the active correlated cliques in CORE were non-overlapping, we used the same method [Candidate_CORE was empty. In this way, we could generate core structures for most protein complexes. However, some protein complexes are with low density or only contain two proteins [CORE. We used the equation (7) to calculate the weight for the edges which were not contained in all active correlated cliques. If the weight of an edge was larger than the predefined threshhold core_thresh, we directly added the edge to core set CORE. Therefore, we chose not only active correlated cliques but also the edges associated with high weight score as core structures of protein complexes.In the first phase, we used the cliques mining algorithm  to enumee method  to removproteins , 29. To vk with active time attribute Ak was connected to a core structure , Tc), where vk ∉ C and Tc ∈ Ak. The attached score of vk with respect to , Tc) is given as:In the second phase, we augmented the core structure by adding each close neighbor protein one by one. We used attached score to measure how closely a protein extend_thresh, then vk was added to the core structure , Tc). Therefore the final identified protein complexes were generated by adding the close neighbor proteins to the core structure. Here, extend_thresh was a predefined threshold. The optimal value of extend_thresh and core_thresh can usually be determined in preliminary experiments.If the Attach_score was larger than core_thresh and extend_thresh parameters are assessed. Finally, our method is compared with current state-of-the-art protein complex identification methods.In this section, the datasets and evaluation metrics used in the experiments are described. The impact of the The three high-throughput PPI datasets used in our experiment were the Krogan dataset , DIP datT1,T2,…,T12) for each gene in a cycle. We constructed three DPPN networks to integrate high-throughput PPI data and gene expression data as described in the Section “Construction of DPPN”. DPPN I, DPPN II and DPPN III were constructed by integrating gene expression data GSE3431 with the Krogan dataset, DIP dataset and MIPS dataset, respectively. Compared to the static PPI networks, DPPNs could effectively distinguish the active period of a protein by active time attribute of the protein. In this study, if the active probability of a protein higher than or equal to P3 (0.68) at a time point, the protein is considered as active at that time point. The distributions of the number of active proteins with different active time attributes on DPPN I, DPPN II and DPPN III were given in Fig. T9 in Fig. T9 on DPPN I, DPPN II and DPPN III, respectively.The gene expression data used in our experiment was GSE3431 [P be an identified complex and B be a known complex. We defined the neighborhood affinity score NA between P and B as follows:Let NA is 1, it means that the identified complex P has the same proteins as a known complex B. On the contrary, if NA is 0, it indicates no shared protein between P and B. We considered P and B to match each other if NA was larger than 0.2, which is the same as most methods for protein complex identification [If fication .F-score have been used to evaluate the performance of protein complex identification methods by most previous studies. The definitions of precision, recall and F-score are given as follows:Precision, recall and Ncp is the number of identified complexes which match at least one known complex and Ncb is the number of known complexes that match at least one identified complex. Identified_Set denotes the set of complexes identified by a method and Benchmark_Set denotes the reference benchmark set. Precision measures the fidelity of the identified protein complex set. Recall quantifies the extent to which a identified complex set captures the known complexes in the benchmark set. F-score provides a reasonable combination of both precision and recall, and can be used to evaluate the overall performance.where n benchmark complexes and m identified complexes, let Tij denote the number of proteins in common between ith benchmark complex and jth identified complex. Sn and PPV are then defined as follows:Recently, sensitivity (Sn), positive predictive value (PPV) and accuracy (Acc) have also been used to evaluate protein complex identification tools. Given Ni is the number of proteins in the ith benchmark complex. Generally, high Sn value indicates that the prediction has a good coverage of the proteins in the benchmark complexes, while high PPV value indicates that the predicted complexes are likely to be true positives. Accuracy is the geometrical mean of the Sn and PPV, which is defined as follows:Here F-score as the major evaluate measures in this study, and also reported Sn, PPV and Accuracy.Accuracy represents a tradeoff between Sn and PPV value. The advantage of taking the geometric mean is that it yields a low score when either the Sn or PPV metric is low. High accuracy values thus require a high performance for both criteria. To keep in line with most previous studies, we chose precision, recall and extend_thresh and core_thresh, range from 0 to 1. We can choose the optimal value of extend_thresh and core_thresh by the experimental approach. Firstly, we kept extend_thresh =0.05 and evaluated the effect of core_thresh. The detailed experimental results on the DPPN I with different core_thresh were shown in Table In this experiment, we evaluated the effect of the threshold parameters of our method on the DPPN I. The parameters, core_thresh was too small, many edges with low weight score would be added to core set. This would lead to identify many false protein complexes and degrade the F-score of our method. On the contrary, when core_thresh was too large, little edges would be added to core set even though some edges with high weight score. Overall, our method achieved the highest F-score, when core_thresh =0.09.As shown in Table core_thresh =0.09 and evaluated the effect of extend_thresh. The detailed experimental results on DPPN I with different extend_thresh were shown in Table extend_thresh between 0 and 0.1. F-score performance ranged from 0.433 to 0.471. When extend_thresh = 0, precision, recall and F-score were 0.428, 0.439 and 0.433, respectively. As extend_thresh was increased, the number of proteins added decreased sharply. When extend_thresh = 0.05, precision, recall and F-score achieved 0.468, 0.475 and 0.471, respectively. When extend_thresh was increased from 0.05 to 0.1, precision, recall and F-score all decreased.Secondly, we kept extend_thresh on DPPN I in Table extend_thresh was changed from 0 to 0.1, PPV increased whereas Sn decreased. When extend_thresh ranged between 0.1 and 1.0, Sn, PPV and Acc did not change appreciably. Acc was defined as the geometric mean of Sn and PPV, which was maximized (0.523) when extend_thres = 0.02. Compared with Acc, F-score is more effectively and reasonably to evaluate the performance of a method. From Table3, it can be seen that our method can achieve highest F-score, when extend_thresh =0.05.Then we evaluated Sn, PPV and Acc metrics for core_thresh and extend_thresh is set to 0.09 and 0.05, respectively. For ClusterONE, the “Overlap” parameter is set to 0.8. For COAN, the “Threshold” parameter is set to 0.6. For COACH, the “Omega” parameter is set to 0.2. For CMC, the “overlap_thres” and “merge_thres” parameters are set to 0.5 and 0.25, respectively. For MCL, the “inflation” parameter is set to 2.5. The highest value in each row was shown in bold.We compared our method on three DPPNs with the following state-of-the-art protein complex identification methods Tables , 8 and 9F-score of 0.471, the highest recall of 0.475 and the highest PPV of 0.729, which was significantly superior to the other methods. Secondly, we compared our method using DPPN II with the other methods using the DIP PPI network. From Table F-score of 0.477 and the highest Acc of 0.509. HUNTER and MCL also achieved the highest precision (0.685) and the highest Sn (0.555) in Table F-score of 0.382 and the highest Acc of 0.403 in Table Tables cision 0.85 and thF-score of 0.398 and the highest Acc of 0.495, respectively. From Table F-score of 0.378. COAN also achieved the highest F-score of 0.409 and the highest Acc of 0.505, respectively. Form Table F-score of 0.372, respectively. ClusterONE achieved the highest Acc of 0.426 in the Table F-score of 0.285 in the Table F-score of 0.471 in the Table Table . DyCluster uses biclustering techniques to construct dynamic PPI networks by incorporating gene expression data, and then applies the existing complex-detection algorithms, such as ClusterONE and CMC, to detect the complexes from the dynamic PPI networks. Based on DyCluster framework, we can compare our method with existing methods that integrate gene expression data with PPI data. In the Tables F-score in Tables F-score and Acc in Tables Next, we compared our method with DyCluster  in the TFinally, we shuffled the gene expression data and tested whether or not the temporal information in the gene expression data can help identify protein complexes. There are expression levels at 12 time points for each gene in the GSE3431 gene expression data. In this experiment, we took these expression levels for each gene, and shuffled them between the different time points. Each gene retained the same set of gene expression levels, but the order in which these expression level changes happen was now shuffled. We compared the performance of our method on GSE3431 gene expression data with the gene expression data shuffled randomly in the Tables In summary, our approach achieved the state-of-the-art performance on three DPPNs, which was competitive or superior to the existing protein complexes identification methods. Compared with the prior works, DPPN can not only effectively identify the active time point of the protein, but also distinguish the active level of the protein. The experimental results indicated that DPPN could effectively integrate dynamic information of protein into static PPI networks, and improve the performance of protein complex identification.Figure T10. This indicates that all these proteins will be active on the DPPN I at the active time point T10. Eventually, our method not only considered the topology information of high-throughput PPI dataset but also the dynamic information of gene expression data to identify the Golgi Transport Complex exactly from DPPN I. Furthermore, this result suggested that the life period of the Golgi Transport Complex is mostly at T10 time point. Compared with other methods, our method can integrate the dynamic information of gene expression data to improve the performance of protein complex identification, and distinguish the active time point of the identified protein complexes during the cell cycle.From Fig. A challenging task in post-genomic era is to construct dynamic PPI networks and identify protein complex from dynamic PPI networks. In this paper, we first proposed active probability-based method to distinguish the active level of proteins. Based on this, we constructed DPPN to integrate the dynamic information of gene expression data into static PPI networks. Compared with static PPI networks, DPPN could effectively represent the dynamic information as well as topological structure of proteins. Furthermore, we developed a novel method to identify protein complex on DPPN. Experimental comparisons on three DPPNs showed that this approach outperformed established leading protein complex identification tools. The model and the construction method of DPPN could not only be applied to identify protein complex, but also provide a framework to integrate dynamic information into static networks for other applications, such as pathway analysis.Using gene expression data to construction dynamic PPI networks is based on the assumption that gene expression and protein expression are well correlated. Some studies have suggested that protein levels are not proportional to mRNA levels , which c


Uncovering the hidden organizational characteristics and regularities among biological sequences is the key issue for detailed understanding of an underlying biological phenomenon. Thus pattern recognition from nucleic acid sequences is an important affair for protein function prediction. As proteins from the same family exhibit similar characteristics, homology based approaches predict protein functions via protein classification. But conventional classification approaches mostly rely on the global features by considering only strong protein similarity matches. This leads to significant loss of prediction accuracy.Here we construct the Protein-Protein Similarity (PPS) network, which captures the subtle properties of protein families. The proposed method considers the local as well as the global features, by examining the interactions among 'weakly interacting proteins' in the PPS network and by using hierarchical graph analysis via the graph pyramid. Different underlying properties of the protein families are uncovered by operating the proposed graph based features at various pyramid levels.Experimental results on benchmark data sets show that the proposed hierarchical voting algorithm using graph pyramid helps to improve computational efficiency as well the protein classification accuracy. Quantitatively, among 14,086 test sequences, on an average the proposed method misclassified only 21.1 sequences whereas baseline BLAST score based global feature matching method misclassified 362.9 sequences. With each correctly classified test sequence, the fast incremental learning ability of the proposed method further enhances the training model. Thus it has achieved more than 96% protein classification accuracy using only 20% per class training data. The life of an organism is encrypted in the sequence of a genome, but decryption of the genetic information depends upon functions of the proteins that it encodes. The assignment of biological or biochemical roles to proteins has many challenges. Knowing just amino-acid sequence and structure of a protein does not guarantee that we can predict everything about that protein. However these measures are a good starting point for quickly predicting protein functions with the help of known homology. There are plenty of proteins which have totally unknown functions and the whole genome sequencing projects are major sources of these. So an approach based on protein homology is a fast, approximate and a primary way used to tackle such a daunting task of protein function prediction. The rationale behind this is that two proteins with similar sequence or structure could evolve from a common ancestor and thus have similar functions.The homology of protein sequence is usually found by assessing similarity between pairs of sequences. An optimal algorithm based on dynamic programming like Needleman-Wunsch  is compuGlobal features try to succinctly summarize the raw data, so they are rich in semantics. They have been found to be useful in the domains where semantic analysis of the raw data is important for pattern recognition, like audio event recognition  and videIn attempts to overcome the above limitations, various matching methods have been developed that use the features extracted from multiple sequence alignment (MSA) of the protein family sequences. These methods use sequence templates  and profPattern recognition based only on local features could be useful for analyzing the large amount of data in real time like abnormal event detection from video . Use of MSA of a protein family reveals selective pressures for conservation of specific residues with evolutionary functional importance. Some MSA regions seem to tolerate insertions and deletions while others tend to remain conserved. So position-specific features from MSA are desirable when searching databases for homologies. Profile HMM, a generative model used widely for protein sequence classification, uses these position-specific features . It usesMethods based on similarity clustering, k-nearest neighbors, phylogenetic clustering , gene fuIntermediate sequence search (ISS) has also been successfully used for detecting remote homology . For theProtein-Protein Interaction (PPI)  plays a Relationships among biological sequences can be effectively represented by building a PPS network. However, in protein families, modularity, local clustering and scale-free topology coexist . Thus usAn edge connecting a pair of nodes with the largest weight in the PPS network represents the strongest match and it accounts for the global feature in similarity space. Only considering the nodes connected through the edges having lower weights, constitutes weak local features and with also considering interactions among weakly interacting nodes boost up the local features. In addition, PPS networks are analyzed hierarchically in the form of the Graph Pyramid (GP). It helps to extract more vital information about proteins from the network topology and looks for stronger global and local features. Unlike most of the existing methods, the proposed approach also shows that 'how the query sequence interacts with each protein in the family'. PPS interaction topology shows 'small world network'  propertiThis paper is organized as follows. In the section 'Methods', we present the PPS network construction approach and its modeling via graph pyramid. The same section also discusses the important graph topological or graph structured features and the hierarchical protein classification algorithm. Experimental evaluation results of the proposed method, their comparison with existing prediction methods and the techniques of searching for the optimal algorithm parameters are presented in section 'Results'. We conclude our work with discussions about related issues and the direction of our future work.s1 and s2 is defined as follows,Similarity between sequences can be assessed by local or global alignment score. A score is a numerical value that describes the overall quality of an alignment. The protein sequence classification algorithm which relies solely on an optimal alignment score is not practical for a large protein database. Protein sequence similarity can be readily found by suboptimal alignment using protein-protein BLAST . BitscorH(·) is the Heaviside-step function,where The performance comparison given in the section 'Results', shows importance of the EB-score over the Bitscore.M classes. Let the set of class labels be given as th itraining sequence in that class. Similarly q cis what we have to find.The proposed algorithm uses the graphical modeling of protein sequences from each protein family/class. Consider the large protein database having c has N training sequences . This is a weighted and an undirected graph. An edge weight is nothing but the strength of protein sequence similarity.These edges form a set To construct the graph of each protein class, we just need to consider interaction (EB-score) among all protein sequences within that class. Number of proteins in a class is far smaller than that of the entire database. So graphs of all protein classes can be easily and independently constructed by using protein-protein BLAST within the corresponding classes.In protein similarity graphs, modularity, local clustering and scale-free topology  coexist.i as an indicator variable, and let ∅ be the null (empty) set, ∅ = {} then 'set element' is formed asFor any set c, at certain hierarchy (i.e. at threshold t), the edge set is given as,Cardinality of a set , instead of G = G.The corresponding graph is given as For any sets qc. Now G, we will get the new graph and note that G, in the similarity space.Most of the real world and biological  networks communicate via a few highly connected nodes known as Hubs. These hubs determine the properties of networks . In realFigure n, the clustering coefficient nC, measures the extent to which neighbors of n are also the neighbors of each other , whose th entry is given as, In a graph, the smallest clique with three nodes is a triangle. The number of triangles gives an important information about structure of the PPS network. Let the graph q interacts with the nodes a, b, c and d. So they constitute an 'interacting neighborhood' to the query. TR has capability to simultaneously assess the interactions within interacting neighborhood. After the query interaction, one extra triangle is formed since only the nodes b and c were previously interacting. Whereas at node a SM power has increased from 3 to 4. Formation of new triangles in a graph indicates the fact that 'query interacts simultaneously to the already interacting nodes'. Newly formed number of triangles due to query interaction ΔTR, are found similarly as equation (8).Either the graph is dense or sparse, TR can be computed readily within the same time as the computation is only associated with the matrix of the same size. TR inherently captures different network properties than SM. Figure q1 interacts with a graph then its spread remains almost unaffected but in case of q2 interaction, the spread of a graph alters drastically. GE is defined as the sum of the absolute values of the eigenvalues of the adjacency matrix [The original graph structure changes when the query interacts with it. Figure y matrix , and givGE depends only on the adjacency matrix, the density of the graph does not affect its computation time. The effect of query interaction on the original graph structure is captured by change in GE ), given similarly like equation (8). We are dealing with graphs whose edge strength is the similarity between connecting nodes, which is inverse of the usual edge length definition. So we need to look for the maximum ΔGE.Since Graphs are analyzed hierarchically  and threshold plays an important role in making hierarchical graph structure. If the query can interact at the higher layer of GP  where we look for class AC AC > Tand collect them in q1 we can not find any such classes c at t3, so we descend the GP to t2 and discover ∗ t= t2. The secondary threshold (ACT) is necessary, otherwise there will be many spurious classes i.e. false positives (FP), having nonzero change in average clustering coefficient Let ∗ tis the maximum threshold  at which the query starts interacting with the graph of some class. Let us represent the subroutine by abusing the notation for simplicity and readability as,In the subroutine given in an algorithm 1, H(·) is 1, so all the arguments (classes c) are assigned to SM and TR slightly changes . Here we look for k maximally influenced classes from SM and TR. Subroutine for GE finds the class from GE(·) is maximum. Thus this produces a hierarchical class voting scheme which helps to improve the classification accuracy and to reduce the computational load.Maximum value of ∗t. To avoid these problems, the GP based hierarchical voting scheme is necessary. And the rational behind placing different GSF at different GP levels, is explained in the next 'Results' section.Each GSF has an ability to extract different information from different levels of the protein family GP. However, applying each GSF to entire GP, is computationally inefficient when dealing with large numbers of protein families. In addition, it may add up the FP, when a decision is being made in the much lower GP level than the level defined by Algorithm 1 Graph pyramid search subroutineACT; primary threshold i t>j tfor i >jinput: output: 1: for t ∈ AC tfrom n tto t1 do2: if then3:   for all classes do4:      AC I= H −(ACT))5:         6:         t* = t7:         end for8:      end if9:   end for10: cd), wrong decision (wd) or no decision  are constructed training: all G for them at the particular threshold. In the implementation, ∗p= 2 for all GP levels, while ∗r is set 3 for lower and 5 for higher GP levels. Other thresholds are set using the validation set by analyzing the maximum values for each GSF. And each set in theFigure Figure qc, like replacing G with GP based modeling of protein families provides an extra advantage of fast incremental learning. In this procedure, mean bit score' classification method, bit score is used as an edge weight for constructing the graph. The class, qc. The performance of this type of bit score based methods, is poorer than EB-score based methods. Top part of the Table Improvement in the classification performance can be achieved by combining the GSF in GP and using majority voting. This is shown more elaborately with ROC curves in Figure As discussed initially in the background section, here we took an approach based on protein homology for protein function prediction. According to this approach an entire task boils down to protein classification, because two proteins with similar sequence or structure could evolve from a common ancestor and thus have similar functions. So once we classify a protein to its true family, we can easily ascertain its probable functions from the characteristics of its family. We took this approach because it is fast, an approximate and primary way to tackle a daunting task of function prediction of a large number of proteins.This paper proposes a novel protein classification method based on PPS network modeling using the proposed EB-scores. It tries to blend important characteristics from PPI network and ISS methods for protein classification. Importance of the method is that it exploits the topological structural information of the PPS network, using hierarchical network analysis guided by the graph pyramid. This helps to analyze the different protein interactions at different pyramid levels. Thus the necessary information for protein classification from weak interactions in the PPS network is not suppressed by the other strong interactions. And proposed features extract the different network properties at various pyramid levels. This makes it possible to more objectively and reasonably predict the protein class.The hierarchical voting algorithm helps to improve the computational efficiency with maintaining high classification accuracy. Some of the salient features of the proposed method are; protein sequences as the only input requirement; fast and easy incremental learning; can show topologically, how the query sequence interacts with the protein family; quick training and the high performance. The proposed graph based modeling, has an extra advantage that the relationship between protein families can also be found by finding the corresponding inter-graph similarities. The experimental evaluation on COG database demonstrated the effectiveness of the proposed method.This graph pyramid approach is also promising to use in the PPI network and various other graph based bioinformatics methods. Protein characteristics like 3D structure and presence of various domains, along with sequence similarity measure can be used for more efficient protein network construction. Our future work will try to address these issues.The authors declare that they have no competing interests.All authors read and approved the final manuscript. TS proposed the algorithm and drafted the paper. YJ helped for dataset analysis. KS proposed, supervised the project, gave suggestions and revised the manuscript. JYC gave suggestions and revised the manuscript.


For this task, an effective fitness function should allow identification of correct sequences that would fold into the desired structure. In this study, we showed that nonlinear fitness function for protein design can be constructed using a rectangular kernel with a basis set of proteins and decoys chosen a priori. The full landscape for a large number of protein folds can be captured using only 480 native proteins and 3,200 non-protein decoys via a finite Newton method. A blind test of a simplified version of fitness function for sequence design was carried out to discriminate simultaneously 428 native sequences not homologous to any training proteins from 11 million challenging protein-like decoys. This simplified function correctly classified 408 native sequences , which outperforms several other statistical linear scoring function and optimized linear function. Our results further suggested that for the task of global sequence design of 428 selected proteins, the search space of protein shape and sequence can be effectively parametrized with just about 3,680 carefully chosen basis set of proteins and decoys, and we showed in addition that the overall landscape is not overly sensitive to the specific choice of this set. Our results can be generalized to construct other types of fitness landscape.The construction of fitness landscape has broad implication in understanding molecular evolution, cellular epigenetic state, and protein structures. We studied the problem of constructing fitness landscape of inverse protein folding or protein design, with the aim to generate amino acid sequences that would fold into an  Protein design has been the focus of many experimental, theoretical, and computational studies a priori specified three-dimensional template protein fold. This problem was first formulated 30 years ago Here we studied the problem of designing a protein sequence that is compatible with an A key component for designing a protein sequence is a fitness function: it can detect if a solution has been found, and can also guide the search of viable sequences. An ideal fitness function can characterize the properties of fitness landscape of many proteins simultaneously. Such a fitness function would be useful for designing novel proteins and novel functions, as well as for studying the global evolution of protein structure and protein functions.The development of a fitness function for protein design is closely related to the development of a scoring function for protein structure predictions, protein folding, and protein-protein/ligand docking A promising alternative approach is to use nonlinear function to capture the complex design of fitness landscape. In the study of a priori, we obtained a nonlinear kernel function via a finite Newton method. The total number of native proteins and decoy conformations included in the function was reduced to about 3,680. In the blind test of sequence design to discriminate 428 native sequences from 11 million challenging protein-like decoy sequences, this fitness function misclassified only 20 native sequences (correct rate 95%), which far outperform statistical function In this study, we demonstrated how to significantly improve nonlinear function for characterizing fitness landscape of protein design. Using a rectangular kernel with proteins and decoys chosen This paper is organized as follows. We first describe our theory and methods for sequence design. We then discuss computational details. Results of a blind test are then presented. We conclude with discussion and remarks.We use a In protein design, the native amino acid sequence A commonly used form for fitness function We can further require that the difference in fitness must be greater than a constant There is a natural geometric view of the inequality requirement. Each of the inequalities divides the space of For each native protein There is another geometric view of the inequality requirements. The relationship There may exist multiple Note that a solution of the above problem satisfies the system of inequalities (3), since subtracting the second inequality from the first inequality in the constraint conditions of (5) will give us i.e., the interior of the final convex polyhedron i.e., i.e., no weight vector can be found that can make all native proteins simultaneously the fittest against decoys.However, it is possible that no weight vector A fundamental reason for this failure is that the functional form of linear sum of pairwise interaction is too simplistic. To resolve this issue, we obtain nonlinear fitness function for sequence design using an alternative functional form Intuitively, the fitness landscape has smooth Gaussian hills of height To obtain such a nonlinear function, our goal is to find a set of parameters The use of nonlinear kernels on large datasets typically demands a prohibiting size of the computer memory in solving the potentially enormous unconstrained optimization problem. Moreover, the representation of the landscape surface using a large data set requires costly storage and computing time for the evaluation of a new unseen contact vector In order to solve i.e., Here, The main step of the Newton method is to solve iteratively the system of linear equations We present below the algorithm, whose convergence was proved in Start with any Stop if Since protein molecules are formed by thousands of atoms, their shapes are complex. In this study, we use the count vector We found that there is a relationship between the number of total contacts of a protein and the length of the protein. A linear regression on the relationship between the number of total contacts and the length of the protein gives the following equation, We followed Maiorov and Crippen protein  . BecauseWe used the list of 1,515 protein chains compiled from the PISCES server We used only a subset of the 36 million decoys and native structures so they could fit into the computer memory during training. These structures formed the data matrix Initially, we randomly selected 10 decoys from the set of decoys Strategy 1] In the  In the [To construct In the subsequent studies, we evaluated our method with different choices of challenging native proteins. The selection ranges from the top 10% to 60% most challenging native proteins. The choice of the challenging decoys was also varied, where we experimented with choosing the top one to the top four most challenging decoys for each native protein, while the number randomly selected decoys varies from three to zero.There are two important parameters: the constant apackThe algorithm was implemented in the C language. It called LWe used the set of 428 natives proteins and 11,144,381 decoys for testing the designed fitness function. We took the sequence Sequence decoys obtained by gapless threading were quite challenging, since all native contacts of the protein structures were maintained, and decoy sequences were from real proteins. In a previous study, we showed that no linear fitness function can be found that would succeed in the challenging task of identifying all 440 native sequences in the training set We also use the Here we succeeded in obtaining a simplified nonlinear fitness function for protein design that are capable of discriminating 796 of the 800 native sequences . It alsoThe matrix We examined the effects of different sizes of The results of classifying both the training set of 800 native proteins with 36 million decoys and the test set of 428 native proteins with 11 million decoys are shown in We examined the effects of different choices in constructing matrix We found that using Strategy 2  leads toFurthermore, our method is robust. The overall performance using either Strategy 1 or Strategy 2 is stable when decoy selection rate changes from 5% to 90%. Using the To further assess our fitness function, we examine how well decoys generated by a different approach can be discriminated using our nonlinear fitness function. We selected 799 training proteins and 428 test proteins for this test. Our results show that as expected, the number of misclassified decoys decreases rapidly as the number of swaps increases. When  length  . Only 62ength  , finer resolution cutoff (1.6 Å), and lower R-factor cutoff (0.25). This native dataset is better than previous study As protein length is linearly correlated with the total number of contacts, we found that length corrections is important for improving fitness function. For example, the rate of misclassification is 7.2% in an earlier study without length correction (14 out 494 natives) We developed two strategies to search for improving fitness landscape. Strategy 1 mostly uses misclassified decoys in the next iteration of construction of matrix Our final fitness landscape can correctly classify most of the native proteins, except 4 proteins  in the training set and 20 proteins in the test set . Among mIn protein folding studies, it is well known that contact maps of decoys formed by gapless threading have considerable higher energy than the native contact map, and these protein folding decoys are not as challenging as decoys generated by other methods such as Monte Carlo simulation. Results showed in e.g., adding solvation terms, including higher-order interactions.The representation of protein structures will likely have important effects on the success of protein design. The approach of the reduced nonlinear function is general and applicable when alternative representations of protein structures are used, a priori.We showed that a simplified nonlinear fitness function for protein design can be can be obtained using a simplified nonlinear kernel function via a finite Newton method. We used a rectangular kernel with a basis set of native proteins and decoys chosen We succeeded in predicting 408 out of the 428 (95%) native proteins and misclassified only 218 out of 11 million decoys in a large blind test set. Although the test sets used is different, as other method were based on relatively small (201 native proteins and 3 million decoys) blind test set. Our result outperforms statical linear scoring function  and optimized linear function . The performance is also comparable with results obtained from a far more complex nonlinear fitness function with The rectangle kernel matrix with a finite Newton method works well in constructing fitness landscape. In addition, we showed that the overall landscape is not overly sensitive to the specific choice of the dataset.Overall, our strategy of reduced kernel can be generalized to constructing other types of fitness function.


Proteins fold using a two-state or multi-state kinetic mechanisms, but up to now there is not a first-principle model to explain this different behavior. We exploit the network properties of protein structures by introducing novel observables to address the problem of classifying the different types of folding kinetics. These observables display a plain physical meaning, in terms of vibrational modes, possible configurations compatible with the native protein structure, and folding cooperativity. The relevance of these observables is supported by a classification performance up to 90%, even with simple classifiers such as discriminant analysis. Protein folding is one of the most studied biophysical problems4567910129In this paper we focus on the problem of the discrimination of protein folding state, and not on the real-valued prediction of the folding rates. Our aim is to find physics-based, and easy interpretable observables, that can be related to the folding state classification. We propose novel observables based on the network properties of the native structure only, and we show that, together with a clear physical interpretation, they also predict with high performance if a protein behaves as Two-State or Multi-State by using simple discriminant methods. As done before by other authors161719As previously mentioned, we introduced three main groups of observables (see Methods), i.e.SR, a measure related to the possible configurations consistent with the native protein structure PCN combined with the contact potential matrix P (see Methods).Network Entropy-based ratio λN, λN−1, λN−2, related to the highest-frequency vibrational modes of a modified PCN, in which the backbone is removed.Laplacian-based observables R0, measuring the fraction of sequence separation  that do not contain residue contact pairs.Inter-residue link density All the defined observables were considered as features for classification of TS and MS proteins by Fisher discriminant analysis (see Methods).MCC = 0.76 (see Methods). Previous results, with a more complex classifier , with 88.33% ± 1.10% correctly classified proteins, and a highly homogeneous performance on both classes . Considering the full PCN matrix, the classification performance of the Laplacian eigenvalue was reduced (see Methods). The entropy ratio SR is the best single classifier , and it also has a very high performance in combination with R0 . Classifying without cross-validation, i.e. using the entire set of  features, we obtain a performance of 90.48%, with 92.00% for MS proteins and 89.47% for TS proteins. In λN−1, R0) and . It appears that MS and TS proteins are almost linearly separated in this parameter space, and this may allow a simple interpretation in terms of the observables, as stated in the Discussion section.Classification with combinations of the novel observables is very high and balanced between the two classes, with performances up to 88% and Matthews Correlation Coefficient NC is a good classifier of folding classes, we rescaled our observables in order to keep them as much independent as possible from protein length. Moreover, as a comparison for classification performance, we used NC as a variable for discrimination. In our dataset, the NC parameter correctly classifies 78.23% ± 1.52 proteins, with a large unbalance between correctly classified proteins from the two classes: 57.61% ± 3.04 for MS proteins and 91.80% ± 1.29 for TS proteins (MCC = 0.54 ± 0.03). We also evaluated the classification power of some measures typically used in literature, i.e. the average hydrophobicity value 〈h〉12NC, 〈h〉) correctly classifies 73.71% ± 2.15 proteins, with MCC = 0.44 ± 0.05. Both the structural topology measures perform poorly: CO correctly classifies 68.42% ± 0.65 proteins with MCC = 0.36 ± 0.01 while LRCO guesses right 54.38% ± 2.41 proteins with MCC = 0.14 ± 0.05. The best performing couple of observables (NC and LRCO) reaches a performance of 80% ± 1, with a high heterogeneity of performance for TS and MS proteins (MCC = 0.57 ± 0.02). A complete summary of the performances of classical measures (both singularly and in couples) can be found in SR: 81.4% ± 1.8, MCC = 0.61 ± 0.04).Since in previous studieshttp://kineticdb.protres.ru/db/index.pl), containing 85 proteins for which the PDB structure is available. In this dataset we found the same top-performing variables: the combination of R0 with SR had a 80.9% ± 1.3% ratio of correctly classified protein with MCC = 0.58 ± 0.03, while R0 for λN−2 we found 79.7% ± 1.1% and MCC = 0.59 ± 0.02.We also performed the same analysis on a different and more recent datasetTrying to deduce properties of the proteins from their structure is still an open challenge: in this paper we propose novel observables, based on the network properties of PCN, that allow the discrimination between proteins with a different folding dynamics (TS proteins that present only two configurations (folded/unfolded) and MS proteins with a richer landscape of stable and metastable states) by looking only at information on their native state structure. Since previous work used the number of protein residues as a discriminating variable, but this may have some bias as we will discuss later, we only considered size-independent observables, by rescaling their value with an appropriate function of protein size. Thanks to this processing our analysis resulted more performing and robust, in particular in the “grey region” of short MS and long TS proteins. The performance of these observables is achieved by simple Fisher Discriminant Analysis, that allows a plain physical interpretation, in terms of vibrational modes, possible configurations compatible with the native protein structure, and folding cooperativity.R0 simply counts the density of inter-residue distances in which there are no contacts, but nonetheless it results to be very powerful for this classification purposes though being independent on protein size. This means that the information contained in the PCN bands  is very relevant, and possibly more complex measures could be developed based on this information. Another class of observables that we have introduced is based on the eigenvalues of the Laplacian operator applied to PCNs. In analogy with the physical Laplacian operator (acting on Euclidean space) the eigenvalues and eigenvectors can be put in relation with the main vibrational modes of the network and their respective frequencies. We remark that for Laplacian observables it was important to emphasize the role of long-range residue contacts, that effectively characterize the protein 3D structure, by removing the protein backbone with a procedure that preserves the network connectivity as a unique component: based on PCN properties, this filtering of non-relevant links is protein-specific, differently from the more general definition of long-range interaction commonly used, with a unique threshold for all proteins. Our Discriminant Analysis showed that in general TS and MS proteins are better classified by larger Laplacian eigenvalues, corresponding to high-frequency vibrating modes, at difference with small eigenvalues such as the Fiedler number. From the best performing couple of observables, λN−1 and R0 see SR, that can be interpreted as a smaller number of topological configurations available to the related networks. A high number of available PCN states, given a fixed degree and strength sequence, is thus very likely associated with MS proteins, with more intermediate states during the folding process.The observable NC, are “extensive” variables that depend on protein size, thus their performances might be biased from the fact that many MS proteins are “long” and many TS proteins are “short” (e.g. considering protein size of the used database), and might not reflect real physical properties of the studied proteins. Since our analysis has a better performance of at least 10% with respect to these observables, this means that protein size is very relevant but not crucial to characterize MS and TS classes.We remark that some known parameters used for TS-MS classification, such as the residue number In conclusion, the high classification performance achieved, together with a direct physical interpretation, indicate that the newly introduced network-based observables can be relevant for a better comprehension of protein folding processes.www.rcsb.org). We model the protein structure with its alpha carbon (Cα) trace. We collapse the entire protein structures into related contact matrices between the Cαs of the residues. Contact matrices represent a common way of modeling proteins, that guarantees a good representation of the complex relationship between structure and function of proteins, while cutting out the redundant information embedded in the whole 3D structure. Contact matrices are essentially networks in which the role of nodes is played by residues and edges or “contacts” depend upon a notion of “distance” between each couple of residues. The position of an entire amino acid is usually collapsed into the corresponding Cα and the ordering of nodes is physically justified by the primary structure of the protein, i.e. the protein backbone. The backbone is composed by residues that are in sequence and whose distance ranges 3–4 Å, the so-called “peptide bond”. Once obtained the Cα spatial distribution, the contact matrix D is considered, where each element dij is the 3D Euclidean distance between the ith and jth residues. The protein contact network PCN is then obtained by choosing an upper threshold of 8 Å252627The proteins to be classified as TS or MS are obtained from the manually-annotated dataset curated by Ivankov and FinkelsteinM, as described in ref. 32P in whichIn order to build our Entropy-based observables, we retrieved also data regarding amino acidic interactions, such as hydropathy indexes293132ri is the amino acid residue corresponding to the ithCα, and the matrix P has the same size of the related PCN. Since Pij can assume negative values, in order to have only positive weights  we shifted their values in each PCN to have the smallest weight equal to one. For the Entropy calculations only, we use the Hadamard (element-wise) product of PCN and P.where Pij} as weights for the existing PCN links , while in the second ensemble (Sks) we fix both strength sequence {si} and degree sequence {ki}. The degree sequence {ki} and the strength sequence {si} are respectively defined as the number of contacts and the weighted sum of contacts of the nodes in the network.For each protein, we calculated the Network Entropy Network Entropy can be generally defined asw are positive and πij(w) is the probability to observe weight w between residue i and j. The constraints previously defined for the calculation of maximum network entropy are written aswhere weights SR is defined as the ratio between the two entropies with a different number of constraintswhere the average values of strength sequence and degree sequence over the network ensemble are enforced to match the real features of the selected protein, i.e. Ss ≥ Sks given the fewer number of constraints. The closer is the value of SR to 1, the less relevant is the role of the degree sequence constraint {ki}, and thus most of the information on possible PCN configurations is enclosed in the strength sequence {si} only. On the contrary, a large value of SR implies that the given strength sequence is compatible with a larger number of degree sequences (corresponding to more possible PCNs). Thus, MS proteins could in principle have larger SR values than TS proteins: having more stable (or metastable) configurations available could be reflected in a larger number of available configurations as measured by SR.with L on networks is a positive semi-definite operator that plays a major role in the study of diffusion processes on networks, in node clustering and network visualization37A without self loops, we define the Laplacian operator asThe Laplacian operator Remarkably, in case of a N-lattice network, the eigenvalue problem for the Laplacian operator can be put in analogy with the discretization of an N-dimensional elastic membraneb, the number of d–diagonals  with respect to the protein backbone. The observable R0 is defined as the ratio between the number of d-diagonals without links and the number of residues NC of the protein, i.e.contain all the links between residues with a sequence separation equal to δ is the Kronecker delta. For a given protein, a low value of R0 implies that the residues interact at many different levels of sequence separation . On the contrary, a high value of R0 indicates that, in such protein structure, the residue interactions are more localized and show less cooperativity.where Fisher Discriminant Analysis, a robust classifier that allows plain interpretations of the classifying parameters due to the simple boundaries separating the classes, was applied to single observables and to their combinations . A 10-fold cross-validation with 10000 re-samplings was used to assess the performance of our classifiers, that will be described by the average value over the re-samplings and by the standard deviation as confidence interval. Given the presence of homologous proteins, in each partition of the 10-fold cross-validation all the homologous proteins were kept together, to reduce the risk of overestimating the classifier performance. In order to characterize the homogeneity of the classification performance over both TS and MS classes, we consider the Matthews Correlation Coefficient MCC, defined asTP is the number of true positives, TN the number of true negatives, FP the number of false positives and FN the number of false negatives. A coefficient of +1 defines a perfect prediction, 0 is nothing more than a random prediction, while −1 reflects total disagreement between prediction and observation.where We investigated the classification power of some classical observables, with the main purpose to have a comparison with the introduced measures. The statistical analysis and the estimation of the classification performances were the same as for the novel observables (see previous Subsection).NC, the average hydrophobicity value 〈h〉, the contact order CO and the long range contact order LRCO.We analyzed the performance of the chain length h is chosen since hydrophobic force has always been indicated as one of the major drivers for protein foldinghi, a number representing the hydrophobic or hydrophilic properties of its side-chain, thus each protein can be associated with an average hydrophobicity value 〈h〉:The parameter i when the Kyte-Doolittle (KD) scaleh〉 has been often coupled with NC to classify the protein folding kinetics.where We also considered the classification power of structural topology measures such as contact order1213LC is the total number of contacts for the given PCN, and long range contact order14where which were used before for TS/MS classification purposes.How to cite this article: Menichetti, G. et al. Network measures for protein folding state discrimination. Sci. Rep.6, 30367; doi: 10.1038/srep30367 (2016).


Spirulina (Arthrospira) platensis is the only cyanobacterium that in addition to being studied at the molecular level and subjected to gene manipulation, can also be mass cultivated in outdoor ponds for commercial use as a food supplement. Thus, encountering environmental changes, including temperature stresses, is common during the mass production of Spirulina. The use of cyanobacteria as an experimental platform, especially for photosynthetic gene manipulation in plants and bacteria, is becoming increasingly important. Understanding the mechanisms and protein-protein interaction networks that underlie low- and high-temperature responses is relevant to Spirulina mass production. To accomplish this goal, high-throughput techniques such as OMICs analyses are used. Thus, large datasets must be collected, managed and subjected to information extraction. Therefore, databases including (i) proteomic analysis and protein-protein interaction (PPI) data and (ii) domain/motif visualization tools are required for potential use in temperature response models for plant chloroplasts and photosynthetic bacteria.in silico analyses of protein-protein interactions affected at the metabolic level and, particularly, analyses of interactions between and within the affected metabolic pathways under temperature stresses for comparative proteomic analysis. The developed tool, which is coded in HTML with CSS/JavaScript and depicted in Scalable Vector Graphics (SVG), is designed for interactive analysis and exploration of the constructed network. SpirPro is publicly available on the web at http://spirpro.sbi.kmutt.ac.th.A web-based repository was developed including an embedded database, SpirPro, and tools for network visualization. Proteome data were analyzed integrated with protein-protein interactions and/or metabolic pathways from KEGG. The repository provides various information, ranging from raw data (2D-gel images) to associated results, such as data from interaction and/or pathway analyses. This integration allows SpirPro is an analysis platform containing an integrated proteome and PPI database that provides the most comprehensive data on this cyanobacterium at the systematic level. As an integrated database, SpirPro can be applied in various analyses, such as temperature stress response networking analysis in cyanobacterial models and interacting domain-domain analysis between proteins of interest. Synechocystis sp., Synechococcus sp., and Spirulina (Arthrospira) platensis, have been studied at the genomic and proteomic levels.Cyanobacteria have been experimentally used as a model for plants and bacteria, especially for the study of photosynthesis , due to Spirulina is the only cyanobacterium that can be mass cultivated in outdoor ponds, where fluctuating environmental temperatures can cause unwanted effects on biomass yields and cell contents. Thus, investigation of the high- and low-temperature response mechanisms of Spirulina was performed through proteomic analyses.In addition to its wide recognition due to its use in food supplements, Spirulina (Arthrospira) obtained using high-throughput techniques at the genomic and proteomic levels have been previously collected [Spirulina genome sequence became available [Spirulina under optimal and temperature stress conditions were conducted by our research group [Large datasets for ollected –8. Thus,vailable , proteomch group –8.Furthermore, a recent study by our group focused on comparative proteomic analyses of low- and high-temperature stresses and potential protein-protein interaction networks, constructed using a bioinformatics approach, in response to both types of stress conditions . The datSpirulina, was developed. This database provides possible mechanisms, in term of PPI networks and proteome-wide expression levels, underlying the temperature stress response of this cyanobacterium for use as model mechanisms for other photosynthetic organisms, such as plants, algae and other cyanobacteria. Moreover, proteome-wide domain identification is available in the database, which might be useful for further studies on protein-protein interaction domain analyses.Extreme environmental temperature change is currently one of the problems being caused by global warming and is leading to more negative effects on the mass cultivation of cells in outdoor systems. Thus, understanding the temperature stress response at the systematic level is relevant. In this work, SpirPro, an integrated database for Spirulina (Arthrospira) platensis strain C1, which currently consist of the genome, quantitative proteome data and phosphoproteome and interactome data. The Spirulina genome and proteome were obtained from our previous work [SpirPro was constructed as a useful resource for examining proteomic effects on protein-protein interaction networks and metabolic pathway studies. At the front-end, web-based tools were developed, with a user-friendly web interface for information queries and retrieval from the back-end database. In the present work, we collected all available multi-level data on ous work , 6–8, whous work .Synechocystis sp. PCC 6803. Moreover, pathway information associated with the Spirulina prototype PPI network was incorporated into the database obtained from KEGG pathways. All of the data in SpirPro were organized into 17 relational tables and maintained with MySQL, as depicted in Fig. Based on our quantitative proteomic data, interactome data were computationally generated through inference from orthologous proteins involved in PPIs in another cyanobacterium, (A)Genome-scale data, protein orthologs and domain visualizationMoreover, SpirPro provides various visualization tools in the menu that were designed for interactive analysis and network exploration of the integrated data across multi-level data, including genome, proteome, interactome and metabolic pathways. The details regarding the contents of the integrated database and how we constructed it are provided in this section, organized into 4 subsections (A-D), as follows.Synechocystis sp. PCC6803 was chosen as reference, or template genome for our analyses due to the complete genome-scale information available for this species. The complete genomes of Synechocystis and Spirulina were retrieved from the NCBI website and our previous work, respectively. Groups of protein orthologs were identified through reciprocal Blast analysis with the default parameters and E-values under the threshold of 1e-10. Proteins in the same orthologous group were identified and assigned an identifier, which we referred to as the ortholog-id, using the OrthoMCL algorithm and tool [The cyanobacterial model organism and tool . For fur(B)Interactions and network constructionUnder the hypothesis that proteins with similar sequences (orthologous) and domains may share the same function, we reconfirmed all of the protein orthologs through protein domain analysis using our in-house web-based tool CyanoCOG. Taking ortholog-ids, ORF names, gene symbols, function descriptions, or even words in COG function categories as input keywords, the tool performs searches against the constructed database and returns a list of all keyword-matched genes or information on proteins. It also provides a feature in which the protein domains of designated proteins can be visualized on the output page. This feature facilitates comparisons of protein domains and analyses of protein orthologous groups, which allows functions to be assigned to groups of protein orthologs.Spirulina were constructed using Synechocystis interaction data from Cyanobase [Spirulina PPI network. In the present study, orthologous proteins and their Synechocystis-inferable interactions were used for the construction of a Spirulina prototype PPI network, which was represented as graph nodes and edges, respectively(C)Proteome-scale data and integrationPPI networks for yanobase , 13, whiyanobase . The intSpirulina prototype PPI network was enriched with our previous proteomic data obtained under temperature-stress conditions. Under conditions of a growth temperature up-shift (35 °C to 40 °C) or down-shift (35 °C to 22 °C), two proteomic techniques  [(D)Metabolism-level data and integrationThe 2D-DIGE) , 7 and l2D-DIGE) ) were apSpirulina proteins in proteome-enriched PPI network were integrated and highlighted in all possible KEGG metabolic pathways by using the KEGG Mapper tool [To obtain biological meaning in metabolic scale, per tool , 16 and Spirulina proteins based on 2199 experimental interactions across 1167 Synechocystis proteins screened using the yeast two-hybrid system. Moreover, 4804 proteins (covering 79 % of the Spirulina genome) identified under two different temperature-stress conditions and optimal temperature conditions are shown in 12 images obtained through 2D-gel analyses. A set of 144 differentially expressed proteins were mapped onto the PPI template and onto 97 KEGG pathways. Thus far, we have developed six tools to facilitate interactive analyses of proteomic data.2D-gel Images; The tool provides proteomic results, in the form of intensity images of protein spots  as a model in comparison with data obtained from Cyanobase. We developed a data repository integrated with an analysis support tool and provided following data: 1) raw image results and proteins identified through proteomic analyses conducted under temperature stress conditions and optimal growth conditions; 2) protein-protein interactions around proteins in interest; 3) data from in silico analyses of interactions between and within affected metabolic pathways; 4) interactions and overall metabolism; and 5) certain interactions that have been experimentally verified using the yeast two-hybrid technique. A visualization tool with embedded data facilitates biological demonstration of the stress effects on the cells via networking interactions, which will be useful for further in-depth analyses of the mechanisms and regulation of cellular stress responses.A platform for integrative genome and proteomic data analysis was developed using the available genome- and proteome-scale data for http://spirpro.sbi.kmutt.ac.th.SpirPro was developed as a web database tool running on Apache HTTP Server with MySQL database server (version: 5.0). All data entries are stored and maintained as a MySQL database. Each tool in the menu was coded in HTML using the jQuery JavaScript Library (version: 1.5.1) and Cascading Style Sheets (CSS) for web design for interactive use. The Scalable Vector Graphics (SVG) format was preferred to visualize the networks and allow dynamic functions of picture panning and zooming. The web server and database are available at