Proteins interact through specific binding interfaces that contain many residues in domains. Protein interactions thus occur on three different levels of a concept hierarchy: whole-proteins, domains, and residues. Each level offers a distinct and complementary set of features for computationally predicting interactions, including functional genomic features of whole proteins, evolutionary features of domain families and physical-chemical features of individual residues. The predictions at each level could benefit from using the features at all three levels. However, it is not trivial as the features are provided at different granularity.To link up the predictions at the three levels, we propose a multi-level machine-learning framework that allows for explicit information flow between the levels. We demonstrate, using representative yeast interaction networks, that our algorithm is able to utilize complementary feature sets to make more accurate predictions at the three levels than when the three problems are approached independently. To facilitate application of our multi-level learning framework, we discuss three key aspects of multi-level learning and the corresponding design choices that we have made in the implementation of a concrete learning algorithm. 1) Architecture of information flow: we show the greater flexibility of bidirectional flow over independent levels and unidirectional flow; 2) Coupling mechanism of the different levels: We show how this can be accomplished via augmenting the training sets at each level, and discuss the prevention of error propagation between different levels by means of soft coupling; 3) Sparseness of data: We show that the multi-level framework compounds data sparsity issues, and discuss how this can be dealt with by building local models in information-rich parts of the data. Our proof-of-concept learning algorithm demonstrates the advantage of combining levels, and opens up opportunities for further research.. The programs are written in Java, and can be run on any platform with Java 1.4 or higher and Apache Ant 1.7.0 or higher installed. The software can be used without a license.The software and a readme file can be downloaded at  The functions of many proteins depend highly on their interactions with other proteins. Complete protein-protein interaction (PPI) networks provide insights into the working mechanisms of proteins at a global level. While high-throughput experiments such as yeast two-hybrid (Y2H) -4 and taThe construction of more reliable PPI networks has been assisted by computational techniques. These techniques usually employ a supervised -12 or unSince binding interfaces of proteins are enriched in conserved domains in permanent interactions , it is pAs will be described in the next section, some recent studies have started to perform interaction predictions at the domain and residue levels. The data features used by each level are quite distinct. While protein level features are mostly from functional genomic and proteomic data such as gene expression and sub-cellular localization of whole genes and proteins, domain level features are mainly evolutionary information such as phylogenetic-occurrence statistics of the domain families, and residue level features are largely structural or physical-chemical information derived from the primary sequences.In the literature of domain-level prediction, the term "domain" is usually used to mean a domain family, which could have multiple occurrences in different proteins. In this study we use the terms "domain family" and "domain instance" to refer to these two concepts respectively, in order to make a clear distinction between them. For example, PF07974 is a domain family from Pfam, where ADP1_YEAST.PF07974 is a domain instance in the protein ADP1_YEAST.Since the data features of the three levels describe very different aspects of the biological objects, potentially they could contribute to the prediction of different portions of the interaction networks. For example, some protein interactions could be difficult to detect using whole-protein level features since they lack fine-grained physical-chemical information. These can be supplemented by the residue level features such as charge complementarity.Likewise, for the protein interactions that occur within protein complexes, there could be a high correlation between the expressions of the corresponding genes. With proper gene expression datasets included in the protein features, there is a good chance of correctly predicting such protein interactions. Then if one such interaction involves a pair of proteins each with only one conserved domain, it is very likely that the domain instances actually interact.One may worry that if the predictions at a particular level are inaccurate, the errors would be propagated to the other levels and worsen their predictions. As we will discuss, this issue can be handled algorithmically by carefully deciding what information to propagate and how it is propagated. With a properly designed algorithm, combining the predictions and utilizing the data features of all three levels can improve the predictions at each level.In this work we propose a new multi-level machine-learning framework that combines the predictions at different levels. Since the framework is also potentially useful for other problems in computational biology that involve a hierarchy, such as biomedical text mining , we start with a high-level description of multi-level learning and discuss three key aspects of it. Then we suggest a practical algorithm for the problem of predicting interactions at the protein, domain and residue levels, which integrates the information of all three levels to improve the overall accuracy. We demonstrate the power of this algorithm by showing the improvements it brings to the prediction of yeast interactions relative to the predictions from independent levels  predicting which residues are in any interaction interfaces of a protein , and 2) From a theoretical perspective, our multi-level learning framework is loosely related to co-training  and the We now formally describe the learning problem we tackle in this study. The inputs of the problem consist of the following:• Objects: a set of proteins, each containing the instances of one or more conserved domains, each of which contains some residues. Each protein, domain instance and residue is described by a vector of feature values. Some additional features are available for pairs of objects, such as the likelihood for a pair of proteins to interact according to a high-throughput experiment.• Gold standard positive sets of known protein-protein, domain instance-domain instance and residue-residue interactions. As in other studies on protein interaction networks, we use the term "gold standard set" to mean a set of sufficiently reliable data useful for the prediction purpose, instead of a ground-truth set that is absolutely correct. The positive sets could be 1) contaminated with false positives, and 2) incomplete, with false negatives, and a pair of upper-level objects in the positive set may not have any corresponding lower-level object pairs known to be in the positive sets.• Gold standard negative sets of non-interactions at the three levels.We assume no crystal structures are available except for the proteins in the gold-standard positive sets, so that the input features cannot be derived from known structures. This is a reasonable assumption given the small number of known structures as compared to the availability of other data features.The objective is to use the gold standard sets and the data features to predict whether the object pairs outside the gold standard sets interact or not. Prediction accuracies are estimated by cross-validation using holdout testing examples in the gold standard sets not involved in the training process.In this study we focus on kernel methods  for learIn order to develop a method for predicting interactions at all three levels in a cohesive manner, we need to define the relationships between the levels, which is the topic of Section. We first describe two information flow architectures already considered in previous studies, and then propose a new architecture that maximally utilizes the available data. In Section we discuss various possible approaches to coupling the levels, i.e., ways to pass information between levels. In Section we discuss the data sparsity issue. In particular, we describe the idea of local modeling, which is also useful for network predictions in general. Finally, in Section we outline the actual concrete algorithm that we have developed and used in our experiments.A traditional machine-learning algorithm learns patterns from one single set of training examples and predicts the class labels of one single set of testing instances. When there are three sets of examples and instances instead, the most straightforward way to learn from all three levels is to handle them separately and make independent predictions Figure . We use A second architecture is to allow downward (from protein to domain to residue) or upward (from residue to domain to protein) flow of information, but not both Figure . This arA third architecture is to allow the learning algorithm of each level to access the information of any other levels, upper or lower Figure . By alloTo design a concrete learning algorithm, we need to specify what information is to be passed between different levels and how it is passed. Here we suggest several possibilities, and briefly discuss the pros and cons of each of them.One simple idea is to pass training data to other levels Figure , arrow 1The major limitation of passing only training data is that the usually much larger set of data instances not in the training sets (the "unlabeled data") would not benefit from multi-level learning. In contrast, if the predictions made at a level are also passed to the other levels, much more data instances could benefit  , which iTaking a closer look at the prediction problem at each individual level, one would realize that applying a traditional learning method is actually non-trivial since we are dealing with network data. In a traditional setting, each training instance has a class label and the job of a learning algorithm is to identify patterns in the feature values for predicting the class label of each unlabeled object. In our current situation, each data instance is a pair of biological objects (proteins/domain instances/residues), with two possible class labels: interacting and non-interacting. In order to construct a learner, one would need features for pairs of objects. A model can then be learned using a traditional machine learning method for all object pairs. We call this 'global modeling' since a single regression model is built for all the data instances. Global modeling has a number of major drawbacks:1. Features for object pairs: it is not easy to construct features for pairs of objects, since most available data features are for single objects. This is particularly a problem for kernel methods, which require a kernel matrix to encapsulate the similarity between each pair of data instances. For network data, this means a similarity value for each pair of object pairs. While methods have been proposed to construct such kernel matrices , the res2. Time complexity: working with pairs of objects squares the time requirement with respect to the number of objects in the dataset. While state-of-the-art implementations of kernel methods could easily handle thousands of proteins, it would still be challenging to deal with millions of protein pairs, let alone the even more daunting numbers of domain instance pairs and residue pairs.n objects at a level, there are O(n2) pairs and thus the kernel matrix contains O(n4) entries.3. Space complexity: the kernel matrix has a size quadratic in the number of data instances. With 4. Sub-clusters: the two classes of data instances may contain many sub-clusters that cannot be handled by one single global model. For instance, proteins involved in permanent complexes may use a very different interaction mechanism from transient interactions in signaling pathways.n proteins, then n models are built, one for each protein, for predicting whether this protein interacts with each of the n proteins. The advantages of local modeling are obvious: 1) data features are needed for individual objects only, 2) the time complexity is smaller than global modeling whenever the learning method has a super-linear time complexity, 3) much less memory space is needed for the kernel matrix, and 4) each object can have its very specific local model. For all these benefits, in our experiments we only considered local modeling.To avoid these problems, one alternative is local modeling . InsteadLocal modeling is most useful when the training data are abundant and evenly distributed across different objects, such that each object receives a reasonable amount of positive and negative examples to train its local model. However, when the training data are sparse and uneven, some objects may have insufficient  training examples. For instance, among the millions of yeast protein pairs, there are only a few thousand known interactions, so many proteins have very few of them.Our proposed solution uses concepts related to semi-supervised learning: use high confidence predictions to augment training sets. Suppose protein A has sufficient known positive and negative examples in the original training sets, and the local model learned from these examples predicts with high confidence protein B to be an interaction partner with A. Then when building the local model for B, A can be used as a positive training example. Predicted non-interactions can be added as negative examples in a similar way. This idea is consistent with the training set expansion method proposed above for inter-level communication. As a result, the information flow both between levels and within a level can be handled in a unified framework. The expanded training set of a level thus involves the input training data, highly confident predictions of the local models of the level, and highly confident predictions from other levels. Practically, training set expansion within the same level requires an ordered construction of the local models. Objects with many (input or derived) training examples should have their local models constructed first, as more accurate models are likely to be obtained from larger training sets. As these objects are added as training examples of their predicted interaction partners and non-partners, they would progressively accumulate training examples for their own local models.We now explain how we used the ideas described in the previous sections, namely bidirectional information flow, coupling by predictions passing, and local modeling with training set expansion, to develop out concrete learning algorithm for prediction of protein, domain instance and residue interactions. We first give a high-level overview of the algorithm, then explain the components in more detail.The main steps of the algorithm are:1. Setup a learning sequence of the levels.2. Use the model learned for the first level in the sequence to predict interactions at the level.3. Propagate the most confident predictions to the next level in the sequence as auxiliary training examples.4. Repeat the previous two steps for the second and third levels, and so on.We use training set expansion with support vector regression (SVR) to perform learning at each level. Each pair of objects in the positive and negative training sets is given a class label of 1 and 0, respectively. An SVR model is learned for the object (e.g. protein) with the largest number of training examples (denoted as A). The model predicts a real value for each object, indicating the likelihood that it interacts with A. The ones with the largest and smallest predicted values are treated as the most confident positive and negative predictions, and are used to expand the training set. For example, if B is an object with the largest predicted value, then A and B are predicted to interact, and A is added as an auxiliary positive training example of B. After training set expansion, the next object with the largest number of training examples is re-determined, its SVR is learned, and the most confident predictions are used to expand the training set in the same manner. The whole process then repeats until all models have been learned. Finally, each pair of objects A and B received two predicted values, one from the model learned for A and one from the model learned for B. The two values are weighted according to the training accuracies of the local models for A and B to produce the predicted value for the pair. Sorting the predicted values in descending order gives a list of predictions from the pair most likely to interact to the one least likely. The list is then used to evaluate the accuracy by the area under the receiver operator characteristic curve (AUC) . We haveOne way to setup the learning sequence is to use the above procedure to deduce the training accuracy of the three levels when treated independently, then order the three levels into a learning sequence according to their accuracies. For example, if the protein level gives the highest accuracy, followed by the domain level, and then the residue level, the sequence would be "PDRPDR...", where P, D and R stand for the protein, domain and residue levels, respectively. Having the level with the highest training accuracy earlier in the sequence ensures the reliability of the initial predictions of the whole multi-level learning process, which is important since all latter levels depend on them. Notice that after learning at the last level, we feedback the predictions to the first level to start a new iteration of learning.In our computational experiments we also tested the accuracy when only two levels are involved. In such situations, we simply bypassed the left-out level. For example, to test how much the domain and residue levels could help each other without the protein level, the learning sequence would be "DRDR...".The mechanism of propagating predictions from a level to another depends on the direction of information flow.X and Y be the two sets of lower-level objects, and p denotes the probability of interaction between two objects x ∈ X and y ∈ Y, then the chance that the two parent objects interact is 1 - ∏x∈X, y∈Y), i.e., the parent objects interact if and only if at least one pair of its children objects interact. In the second method, we simply take the maximum of the values. In the ideal case where all predicted values are either 0 or 1, both methods are exactly the same as taking the OR of the values. When the values are noisy, the former is more robust as it does not depend on a single value. Yet its value is dominantly affected by a large number of fuzzy predicted values with intermediate confidence, and is thus less sensitive. Since in our tests it does not provide superior performance, in the following we report results for the second method.For an upward propagation , each object pair in the next level receives a predicted likelihood of interaction from each pair of their child objects. For example, if predictions are propagated from the domain level to the protein level, each pair of domain instances provides a predicted value to their pair of parent proteins. We tried two methods to integrate these values. In the first method, we normalize the predicted values to the  range as a proxy of the probability of interaction, then use the noisy-OR function  to inferFor a downward propagation , we inherit the predicted value of the parent pair as the prior belief that the object pairs from the two parents will interact. For example, if we are propagating information from the protein level to the domain level, each pair of domain instances has a prior belief of interaction equal to the predicted likelihood that their parent proteins interact.In both cases, after computing the probability of interaction for each pair of objects in the next level based on the predicted values at the current level, we again add the most confident positive and negative predictions as auxiliary training examples for the next level, with the probabilities used as the confidence values of these examples. for some matrix manipulations.In the actual implementation, we used the Java package libsvm  for SVR,We tested the effectiveness of multi-level learning by predicting protein, domain instance and residue interactions of the yeast Saccharomyces cerevisiae.Data features were gathered from multiple sources Table , includiA gold standard positive set was constructed from the union of experimentally verified or structurally determined protein interactions from MIPS , DIP 6565 and iPWe included two types of features at the domain level: co-evolution and statistics related to parent proteins Table . These aThe gold standard positive set was taken from iPfam, where two domain instances are defined as interacting if they are close enough in 3D structure and some of their residues are predicted to form bonding according to their distances and chemistry. After intersecting with the proteins considered at the protein level, a total of 422 domain instance interactions were included, which involves 272 protein interactions and 317 domain instances from 223 proteins and 252 domain families. A negative set with the same number of domain instance pairs was then formed from random pairs of domain instances in the positive set. All known yeast Pfam domain instances of the proteins were involved in the learning, many of which do not have any known interactions in the gold standard positive set. Altogether 2389 domain instances from 1681 proteins and 1184 domain families were included.We used three data features derived from sequences Table . Charge In a previous study , the feaThe gold standard positive set was taken from iPfam, where the interacting residues are determined based on their proximity in known crystal structures of interacting proteins. Since there is a large number of residue pairs, we only sampled 2000 interactions, which involve 228 protein pairs, 327 domain instance pairs and 3053 residues from 195 proteins, 279 domain instances and 224 domain families. Only these 3053 residues were included in the data set. A negative set was created by randomly sampling from these residues 2000 residue pairs that do not have known interactions in iPfam.We used ten-fold cross validation to evaluate the performance of our algorithm. Since the objects in the three levels are correlated, an obvious performance gain would be obtained if in a certain fold the training set of a level contains some direct information about the testing set instances of another level. For example, if a residue interaction in the positive training set comes from a protein pair in the testing set, then the corresponding protein interaction can be directly inferred and thus the residue interaction would create a fake improvement for the predictions at the protein level. This problem was avoided by partitioning the object pairs in the three levels consistently. First, the known protein interactions in iPfam were divided into ten folds. Then, each domain instance interaction and each residue interaction was put into the fold in which the parent protein interaction was assigned. Finally, the remaining protein interactions and all the negative sets were randomly divided into ten folds.Each time, one of the folds was held out as the testing set and the other nine folds were used for training. We used the area under the ROC (Receiver Operator Characteristics) curve (AUC)  to evaluWe compared the prediction accuracies in three cases: independent levels, unidirectional flow of training information only, and bidirectional flow of both training information and predictions. For the latter two cases, we compared the performance when different combinations of the three levels were involved in training.For independent levels, we trained each level independently using its own training set, and then used the predictions as initial estimates to retrain for ten feedback iterations. This iterative procedure was to make sure that any accuracy improvements observed in the other architectures were at least in part due to the communications between the different levels, instead of merely the effect of semi-supervised learning at a single level. For unidirectional flow, we focused on downward flow of information. The levels were always arranged with upper levels coming before lower levels.Table We first notice that the results for independent levels are consistent with our expectations. Having many diverse data features, the protein level has a satisfactory accuracy. On the other hand, the accuracies of the domain and residue levels were relatively low due to their weak and noisy features. Note that we are predicting whether two arbitrary domain instances or two arbitrary residues interact, rather than only those in known interacting protein pairs. This setting is more realistic for organisms with no known protein interaction network, and the problem is significantly harder than when the protein interaction network is available.Downward flow of training information did help the prediction of domain instance interactions. However, the results of the residue level are quite unsatisfactory, with accuracies even lower than those with independent levels no matter assisted by the training examples of the protein level or domain level. In contrast, the results for bidirectional flow are encouraging. In all cases, the accuracies are higher than the other two architectures. For example, while using the domain level to help the residue level decreased the accuracy of the latter from 0.5675 to 0.5128 with unidirectional flow, the accuracy was increased to 0.6182 with bidirectional flow. As an illustration of the difference in performance of the three architectures, the various ROC curves of protein, domain and residue interaction predictions are shown in Figures The improvements for both the domain and residue levels are quite dramatic, with maximum AUC gains of more than 0.15. This clearly shows the benefits of passing not only training information, but also highly confident predictions. Consider a domain instance pair in the testing set of a certain fold. Since the corresponding parent protein pair must not be in the training set at the protein level of the fold, the passing of training information does not directly help predict the interaction status of the domain instance pair. On the other hand, if the interaction status of the protein pair is predicted correctly with high confidence, passing this information to the domain level can make a direct influence on the prediction of the domain instance interaction. For instance, if the protein pair is correctly predicted as not interacting, the domain instance pair would probably be correctly predicted as not interacting, too.In general, it is observed that levels with a higher raw accuracy with independent levels could offer a bigger improvement to the other levels. For example, the protein level increased the accuracy of the residue interaction predictions from 0.5675 to 0.6581, while the domain level could only increased it to 0.6182. However, it is also crucial to note that although the domain level has a low accuracy with independent levels, it could still make good improvements to the prediction of residue interactions. This observation supports our design of passing only highly confident predictions in avoiding the propagation of errors. The combination of all three levels has the potential to further improve accuracy. For both the protein and residue levels, the best results were obtained when all three levels were involved in training. In particular, while each of the protein and domain levels improved the residue level by a certain amount, the combination of them provided yet another significant amount of improvement.As a concrete example of information flow between the three levels, several of the interacting residue pairs between the hexokinase 1 (PF00349) and hexokinase 2 (PF03727) domains of the hexokinase isoenzyme 2 (HXK2) protein are correctly identified with high likelihood of interaction. For example, residue 46 in the hexokinase 1 domain and residue 278 in the hexokinase 2 domain are predicted to interact with a score of 0.89 out of 1.0. This might be partially due to the charge complementarity of the two residues in their PSI-BLAST profiles, with the most conserved residues being the positively-charged arginine and the negatively-charged aspartic acid at the two positions, respectively. The detecting of such residue interaction helps raise the likelihood of the corresponding domain interaction from a score of 0.27 to 0.72. In turn, this helps detect the self-interaction of the glucokinase (GLK1) protein, which also has the two domains. The interaction was verified in a two-hybrid assay [The experimental results have demonstrated the great potential of linking up the prediction problems at the different levels. This initial success encourages deeper investigations of the idea along various directions. Algorithmically, other approaches to combining the different levels, including combined optimization and predictions as extra features, need to be studied. Currently the features at the domain and residue levels are weak, as reflected by their low accuracy when learned independently, and the small improvement they could cause to the protein level. It is interesting to study ways to improve the predictions at these two levels, and more directly extract the complementary information hidden in these levels that are useful for the protein level.The current study is limited by a highly disproportionate dataset, with much more training examples at the protein level than the domain level. Together with a much weaker feature set, the raw accuracy at the domain level is much lower than the protein level, and the former could only slightly improve the predictions of the latter in the multi-level learning framework. It is hoped that as more structures of protein complexes are solved, the disproportionality would be alleviated. In the meantime, it is interesting to study ways to derive other features that could better predict the domain interactions, and the mechanism by which the domain-level information improved the protein-level predictions.In this article we have pointed out some important issues of both multi-level learning and network prediction, including data sparseness and the existence of sub-clusters. While we have proposed methods to tackle them, a detailed analysis of how these issues affect prediction performance and what other algorithmic strategies for tackling them are yet to be studied.To predict the whole interaction network, it is needed to reduce the time and space requirements. One possible way is to intelligently select what data to exclude, such as residues that are predicted to be buried deep inside the core of a protein. Another idea is to group objects into interaction groups so that each cluster can be handled independently.More insights could be gained by studying some theoretical aspects of multi-level learning, such as the hierarchical structure of the prediction problems, and the issue of noisy and incomplete training sets. With multiple levels, performance evaluation is very tricky. As we discussed, careless definitions of training and testing sets could produce biases to the resulting performance. It is instrumental to study the optimal way of evaluation.Biologically, there are many interesting follow-up questions to be studied. The intricate interactions between the different levels are not yet clear, and could form a larger study of how the predictions change after receiving information from the other levels. One could compare different kinds of data features at the three levels and identify the ones with the greatest complementary effects. Another direction is to choose different kinds of residue samples  and inspect the relative improvements they provide to the protein and domain levels, to determine the residues that are more significant in a protein interaction.In this article we have introduced the approach of integrating protein interaction prediction at the protein, domain and residue levels. We have described the potential benefits of this multi-level learning framework due to the availability of distinct and complementary data features at each level. We have defined three information flow architectures for learning from the different levels, and proposed various ways to couple the levels in terms of what and how information is passed between them. We have focused on the training set expansion method, which is a meta-algorithm that passes predictions of a level as augmented training examples of other levels. To avoid the propagation of errors, we have discussed soft coupling, which associates confidence values to predictions and passes only highly confident predictions other levels. The confidence values are used as the inputs of support vector regression. For learning the interaction network at each level, we have compared global and local modeling, which has also highlighted the issue of data sparsity. We have performed computational experiments using yeast data, and shown that the bidirectional flow of supervised and semi-supervised information between the different levels improved the predictions over independent levels and mere downward flow of training information. The evaluation procedure involved special experimental procedures including training-set balancing and consistent cross validation. Finally, we have suggested a number of follow-up research topics.All authors conceived the project and design. KY and PK prepared the data. KY implemented the algorithms, performed the computational experiments, and analyzed the results. KY and MG wrote the paper. All authors read and approved the document.The multi-level learning program. Compiled Java code of the multi-level learning program.Click here for file


Many studies showed inconsistent cancer biomarkers due to bioinformatics artifacts. In this paper we use multiple data sets from microarrays, mass spectrometry, protein sequences, and other biological knowledge in order to improve the reliability of cancer biomarkers. We present a novel Bayesian network (BN) model which integrates and cross-annotates multiple data sets related to prostate cancer. The main contribution of this study is that we provide a method that is designed to find cancer biomarkers whose presence is supported by multiple data sources and biological knowledge. Relevant biological knowledge is explicitly encoded into the model parameters, and the biomarker finding problem is formulated as a Bayesian inference problem. Besides diagnostic accuracy, we introduce reliability as another quality measurement of the biological relevance of biomarkers. Based on the proposed BN model, we develop an empirical scoring scheme and a simulation algorithm for inferring biomarkers. Fourteen genes/proteins including prostate specific antigen (PSA) are identified as reliable serum biomarkers which are insensitive to the model assumptions. The computational results show that our method is able to find biologically relevant biomarkers with highest reliability while maintaining competitive predictive power. In addition, by combining biological knowledge and data from multiple platforms, the number of putative biomarkers is greatly reduced to allow more-focused clinical studies. Biomarkers, in the context of cancer diagnosis, usually refer to specific genes and their products which are indicators of disease states and can be detected in clinical settings. Microarrays and mass spectrometry, a pair of complementary tools for studying genome activity and proteome activity respectively, have emerged to bring hopes for discovering biomarkers and building diagnosis models. The idea is to screen genome or proteome activity with microarray or mass spectrometry to find a panel of biomarkers  and use them to build a diagnosis model that could outperform established single-protein biomarkers, such as PSA (Prostate Specific Antigen) for prostate cancer and CA-125 (Cancer Antigen) for ovarian cancer .m/z) in mass spectrometry. 3. Classification model building: standard classification tools, such as SVM (Support Vector Machine), DT (Decision Trees), DL (Decision List), kNN (k-Nearest Neighbors), etc., are routinely used to build predictive models based on selected biomarkers. Note that in some studies, steps 1 and 2 or steps 2 and 3 are combined.The large-scale screening of genes and their products made the technologies extremely appealing not only for diagnosis but also for finding treatment for the diseases. Numerous studies have been performed on data sets using either microarray  or mass Our study focuses on the biomarker extraction step because the quality of the extracted biomarkers holds the potential for reliable diagnosis and treatment of the diseases. The extraction of consistent and biologically relevant biomarkers can also significantly improve our understanding of the disease and its mechanisms. However, many issues exist in this area due to either technology limitations or computational artifacts which have been extensively discussed in the literature . For exaFrom the data mining point of view, biomarkers extraction from both mass spectrometry and microarray suffers from “curse of dimensionality” ; that isreliability, which is defined as the probability of a gene being a true biomarker given the experimental data. Biomarker extraction strategies include filters, which select biomarkers independent of the choice of classifiers, and wrappers, which search biomarkers by optimizing given classifiers. We take the filter approach because wrappers are classifier-dependent and tend to capitalize on chance especially for large-scale microarray and mass spectrometry data (data having dimension curse). Therefore, our goal is not to invent another search algorithm which picks up one set of biomarkers from possibly many biomarker sets. Instead, our approach is designed to narrow down the number of candidate biomarkers so that their presence is supported by multiple experimental platforms. While previous studies focus on extracting biomarkers from either microarray or mass spectrometry data sets independently, our approach is to associate microarray and mass spectrometry biomarkers to cross-validate their existence by the evidence from each. We use multiple data sets including mass spectrometry and microarray profiles to introduce more constraints to the biomarker extraction system. In addition, we apply available biological knowledge in the biomarker extraction process to further limit the search space and obtain a very small list of biomarkers.The quality of selected biomarkers is usually determined by their predictive power—that is, accuracy in predicting new samples. Due to the foregoing reasons, we introduce another quality measurement of biomarkers, reliability, which is the posterior probability of a protein being a biomarker after seeing the experimental mass spectrometry and microarray data. This Bayesian concept is mathematically defined in section 3 and calculated using our proposed Bayesian network (BN) model. Intuitively, if a gene biomarker shows evidence in microarray data and its associated peaks also appear in the mass spectrometry markers, this biomarker shows high reliability and we have greater belief that the gene and its products could be a reliable biomarker. In addition to the computational prediction accuracy, reliability is another performance measurement of putative biomarkers and it is very important in multi- or cross-platform biomarker analysis.We introduce the concept of We find that the BN model and its algorithms are especially effective in integrating multiple heterogeneous data and performing biomarker extraction and analysis. Relevant biological knowledge can be built into the model by the use of proper prior parameters and appropriately designed network structure. The biomarker extraction problem can be nicely formulated as a probability inference problem and efficiently solved using an existing inference algorithm. To connect specific proteins and mass spectrometry data, an algorithm is developed by simulating post-translational modifications (PTMs) of proteins. The computational results show that our method can find biomarkers with the highest reliability while maintaining competitive predictive power. In addition, by combining biological knowledge and data from multiple platforms, the number of candidate biomarkers is greatly reduced, allowing more-focused on clinical studies.pre-biomarkers. Basically the pre-biomarkers are genes or peaks that are expressed differentially in cancer and healthy samples. The pre-biomarkers are used for inferring biomarkers in our BN model. The details of each component in the flowchart are explained in the following sections.The flowchart of this study is displayed in http://home.ccr.cancer.gov/ncifdaproteomics/ppatterns.asp. It is important to note that the mass spectrometry samples are from serum while the microarray samples are from prostate tissues. The spectra were exported with the baseline subtracted. The m/z values range from 0 to 20,000. The sample proteins were not processed by external proteases such as trypsin. However, serum proteins are frequently found to be cleaved by chymotrypsin, trypsin and elastase  pairs, where x axis records m/z values with corresponding intensity on y axis. Therefore, we have 15,154 features for only 132 samples. Obviously the number of features is too large to build a reliable diagnosis model. The peak detection is the first step in reducing the number of features. Peaks are basically the features which have local maximum intensities. Current peak detections are usually made by the software bundled with a spectrometer and hence the algorithms are hidden from users. The algorithm we use here is very simple and straightforward: we register all the m/z values if the corresponding peaks  exceed user-specified thresholds. We use both absolute threshold (intensity from baseline) and relative threshold (intensity from both the left and the right hill feet of the peak). Both thresholds are empirically set by a human annotator at 0.3.The raw spectrum for each sample is composed of 15,154 ) associated with each node X. A BN can be viewed as a probabilistic expert system which encodes a set of knowledge and makes inference based on observations.A BN  is a graOver-expressed: With a few exceptions, the most promising cancer biomarkers are over-expressed in cancer patients  that directs the post-translational transport of a protein. The existence of signal peptides is an important factor in determining whether a protein is secretory or not.Ionized peptides: Ionized peptides generated in SELDI (Surface-Enhanced Laser Desorption and Ionization) mass spectrometry are predominantly singly charged  in human serum  to the BN model. The output would be the final cancer biomarkers of interest. The design and implementation of the BN model are guided by the biological knowledge extracted from literatures and from experts in cancer and blood biology. The rules are as follows:The first three rules are general and used to guide our overall BN model design. We are most interested in the genes with elevated mRNA levels detected by microarrays and those whose protein products are secreted into the circulatory system and detected by mass spectrometry as over-expressed peaks. To accommodate rule 1, we focus only on over-expressed genes and peaks in patients in this study. For rules 2 and 3, we explicitly model the influence of secretory proteins because they are a key factor in connecting the microarray and mass spectrometry data. We use the outputs from the SignalP 3.0 server  to deterFor rule 4, we simply assign a small probability to the peptides having double or higher charges. Rules 5–8 are mainly concerned about PTMs which significantly affect the mass spectrometry patterns. Many proteins are synthesized as inactive precursors that are activated under proper physiological conditions by limited proteolysis. A protein may undergo numerous PTMs so that it could be present in many forms at one time in the sample. Proteins and the mass spectrometry data are connected by theoretical mass spectra which are stochastically simulated using rules 4–8. The simulation is designed based on probabilistically modeling the biological knowledge about the modification of nascent proteins and the SELDI system. There is also some quantitative knowledge about PTMs. Specifically, about 30% of all mammalian proteins are phosphorylated , and morProtein” is to model the probability distribution of all proteins to be biomarkers. The prior distribution for Protein is uniform, indicating every protein has the same probability to be a biomarker. Since the choice of Protein determines its microarray pattern and its probability to contain a signal peptide, we have edges from the node Protein to nodes MA (microarray) and SP  respectively. The Protein node together with the PTM nodes determines the pattern of the theoretical mass spectra (denoted as MST) of specific proteins. The variable MSE represents the experimental mass spectra which contain a mixture of a large number of proteins and peptides from serum. MST is introduced to connect Protein with MSE and to help annotate the mass markers at the protein level. Single-circled nodes are hidden variables in the sense that their values are not observed by the experiments, while double-circled nodes indicate observed variables which are used to model the outputs from MA, SP, and MS (mass spectra) respectively. Node MST is shaded to indicate it is a non-founder hidden variable. Nodes without parents are founder variables whose prior distributions need to be specified.The data entities and knowledge are modeled as a BN shown in 1, α2) where α1, α2 are parameters to specify the belief distribution. In order to use a BN for inference, we also need to specify the conditional probability distribution P(X|parents(X)) for every non-founder node X. We will discuss these conditional probability distributions in the next section.Beta distributions are used to model our prior belief of the occurrence of each PTM. (See supplementary information for Beta distribution and its simulation.) The prior distributions for the founder nodes are set up according to rules 4–8, and their effects on amino acids (AA) are displayed in MST is a hidden node. Its conditional distribution, given a protein sequence and all the PTM probabilities, is determined by simulation. MST for a single protein is represented in the following format:mzj is the m/z ratio, fj is the frequency of the jth peak, and r is the number of peaks generated by simulation of the protein.The variable MA, SP and MSE are observed and they are used to model the outputs from the preprocessed experimental data sets. MSE, MA and SP are represented in the following format:n is the number of pre-biomarkers of mass spectra after preprocessing; tprotein is the t-score for the protein in the microarray experiments; and pprotein is the probability of the protein containing a signal peptide generated by the SignalP 3.0 server.We use PRO to denote the set of all proteins in the universe of discourse. Other variables MSE, MA, and SP. The objective is to find a set of biomarkers with the highest posterior probabilities.Using our BN model, the biomarker extraction problem can be regarded as a classic Bayesian posterior probability inference problem. The posterior probability of interest is the probability of a protein given the observation of MST patterns by applying rules 4–8 as random events. For each amino acid in the protein sequence, we tested every PTM to see whether a PTM is possible at that position. If it is possible, we draw a sample θ from Beta  as the prior distribution for that PTM. Then we performed a Bernoulli trial with a probability of success θ. If the trial is successful, we perform the PTM on the protein sequence; otherwise we skip the PTM. We repeated the simulation 1,000 times and recorded the peak distribution as MST for that protein.Simulation AlgorithmInput: a protein sequence and the prior distribution of all PTMs where residue position is indexed by i, PTM is indexed by j.OutPut: MST for the proteinfor (each position i in the protein sequence)for (each PTM j)  if (position i meets the constraint of PTM j)    1, α2);      1. Draw X ~ Beta ;      3. if Y < X, perform modification; otherwise, no modification;endif    else try next PTM j + 1;    endfor  i + 1;  go to next position endforThe goal of the simulation algorithm is to generate m/z of simulated peptides in MST;When the end of the protein sequence is reached, record MST;Repeat the above procedure 1,000 times and output MST simulation of a protein with GI 9955963. Note that the y axis shows the frequency of each peak in 1,000 simulations (not the intensity of standard mass spectra outputs). A red peak (bold line) means the peak matched a peak in the MSE pre-biomarker, while a blue one (thin line) means unmatched. By simulating and matching MST against MSE, we built the connection between a protein and experimental mass spectra.MST is a deterministic variable given the protein sequence so that P(MST|protein) =1; and MSE is independent of the protein given MST.The BN allows us not only to conveniently represent the biological knowledge but also to analyze and formalize the problem of biomarker extraction. The posterior probability of a protein, which is of our interest, is computed as followsSP), we further generalize this equation into a form that can be determined empirically,S(protein) is called the reliability of biomarkers which is a generalization of the posterior probability in The above analysis indicates that the score of a protein can be decomposed into three parts: its likelihood containing a signal peptide, its microarray profile, and its mass spectra pattern. Since the likelihood terms are difficult to define and estimate , we first define S'(MSE|Protein), which is the raw score of observing the experimental spectra given a protein,length is the number of amino acids contained in the protein; MSE ∩ MST denotes the set of peaks shared (within a certain threshold) by the two spectra. WSPC (Weighted Shared Peaks Count) is the sum of all frequencies of the shared peaks greater than a certain threshold δ. WSPC is then divided by the length of the protein to eliminate the dependency between the raw score and length  is further normalized by dividing its raw score by the supremum of the scores for all proteins.The score S higher than 0.1. We will discuss why 0.1 was used as a score standard to select candidate biomarkers in the following paragraphs. This group of 32 proteins is notated as candidate biomarkers and most of them are clustered into a sphere as indicated in S(MS|protein). We see that the scores for the population  are distributed in a shape similar to exponential distribution . The scores for 32 candidate biomarkers have a higher mean but the two distributions are not sufficiently separated . S(protein) distributions of the candidate biomarkers and all human proteins. The candidate biomarker distribution is clearly separated from the population distribution and the number of candidate biomarkers is considerably reduced as a result of introducing multiple data sets in our BN model.The BN method is also applied to all human protein sequences, including 12,484 sequences obtained from SWISS-PROT release 47.2 . The his0) states that a protein with a reliability score is randomly picked from the population, while the alternative hypothesis (H1) states that the protein is NOT randomly selected from the population. If we use the reliability as the test statistic, we observed from p-value less than 0.01. This is the reason we use 0.1 as a score standard to select candidate biomarkers. Caution should be taken when interpreting p-values. The statistical test determines whether a protein with a specific reliability is likely due to chance (H0) or significantly unlikely due to chance (H1). This indirect test is intended to simulate a direct test that determines whether the protein is a biomarker or not, but the two tests are not equivalent and the latter one can only be justified by experimental study. The distributions in Although we specified the prior distributions according to biological rules, the BN model should be robust regardless of the choice of subjective parameters. Robustness is a characteristic of the model and its assumptions, while reliability is a characteristic of a protein given the model.The robustness was studied by sensitivity analysis of how the prior parameters’ changes influence the inference of biomarkers. We assigned six sets of values  to the parameters . For each setting of parameters, we performed BN inference and selected 20 candidate biomarkers with the highest scores. The values of the six sets of parameters are displayed in p-values < 0.01) and relatively high mass spectrometry scores, indicating that their MST  match MSE  to a relatively large extent. An immediate finding is that PSA (APS)  in , probabl(APS) in  search f(APS) in . CDH12 alignt , microarrays, and biological rules can facilitate the analysis and annotation of mass biomarkers. The greatest difficulty in using mass spectrometry data in our model is to associate individual proteins with the experimental mass spectrometry profile. We know that individual mass spectrometry peaks from mixture samples such as serum proteins cannot be accurately annotated to the sequence level without using tandem mass spectrometry. Our solution is to associate each individual protein NOT with individual peaks, but with the entire MS pattern so that the association of mass spectrometry data with each protein is not easily affected by individual peaks. This is done by simulating MST, which reflects the existence of proteases and other PTM factors in serum, and comparing MST with MSE. This strategy of linking proteins to mass spectra is supported by the fact that the protein biomarker PSA yields a large score (0.34) for its MST compared with MSE. Admittedly, the existence and the use of biomarkers are not valid until they are clinically validated. However, with the resolution and sensitivity improvement of mass spectrometry technology, and with more cross-platforms, cross-labs becoming available, our computational model could shed more light into clinical studies.Unlike the samples for peptide mass fingerprinting which are enzymatically digested proteins after being purified, our mass spectrometry samples are one-level-more complex because they consist of multiple unknown proteins which are then post-translationally modified Currently, there are no reliable computational methods to discriminate secreted proteins from membrane proteins. Some membrane proteins such as CANX  are inevitably selected by our method, although our goal is to find serum biomarkers. This example shows the importance of incorporating further biological knowledge into bioinformatics tools.Distinguished with the methods focusing on applying search algorithms to a single data set, our method emphasizes the use of multiple data sets and biological knowledge to reduce the effect of bioinformatics artifacts and to enhance the reliability and relevance of biomarker searching. The merit of the BN model lies in its power to explicitly represent and compute biological knowledge and multiple entities.One limitation of our current study is that we used only one data set from each type of experiments. It is possible that one error in the assay could change the conclusion on one biomarker. The power of our BN model lies in its ability to make inference on multiple observations—the more data it sees, the more accurate the results will be. To fully utilize the convenience of Bayesian models in biomarker analysis, we will include replicate data sets from multiple labs in future study.The biomarker finding and its clinical use is a very complex issue, and a completed discussion is beyond the scope of this article. Refer to In this study, we focused on integrating microarray and mass spectrometry data and made inference of biomarkers using a BN model. However, our approach is not limited to such usages. With the fact that biomarkers are now generated from different types of instruments, multiple labs, various sets of samples and controls, the data analysis of biomarkers will be becoming increasingly complex and the integration and meta-analysis of multiple results will be attracting more attention in the near future. Our proposal of Bayesian strategy and the concept of reliability are important in evaluating biomarkers generated from heterogeneous platforms.In the proposed model, unknown patient samples are scored according to a scoring system that is derived from gene-expression patterns of all training samples. Biomarkers based on a subset of samples or individual samples could allow the detection of subtle difference between subsets of samples and increase the overall prediction accuracy . The croWe must also point out that the current biological knowledge base in the BN model is a limited version; we included a few general biological rules and three numerical data sets. We are currently working on expanding and improving the current BN model to incorporate gene-specific information such as PubMed, OMIM, and GO. It has been shown that BN models are flexible and expandable to deal with complicated biological data types and data structures . Our lonFigure S1.Figure S2.Beta Distribution and its SimulationBeta distribution is denoted by Beta  where α1, α2 are parameters to specify the belief distribution. Beta  has the mean


In recent years, the biomolecular sciences have been driven forward by overwhelmingadvances in new biotechnological high-throughput experimental methods and bioinformaticgenome-wide computational methods. Such breakthroughs are producinghuge amounts of new data that need to be carefully analysed to obtain correct anduseful scientific knowledge. One of the fields where this advance has become moreintense is the study of the network of ‘protein–protein interactions’, i.e. the ‘interactome’.In this short review we comment on the main data and databases producedin this field in last 5 years. We also present a rationalized scheme of biological definitionsthat will be useful for a better understanding and interpretation of ‘what aprotein–protein interaction is’ and ‘which types of protein–protein interactions arefound in a living cell’. Finally, we comment on some assignments of interactome datato defined types of protein interaction and we present a new bioinformatic tool calledAPIN (Agile Protein Interaction Network browser), which is in development and willbe applied to browsing protein interaction databases.


Recent advances in proteomic technologies have enabled us to create detailed protein-protein interaction maps in multiple species and in both normal and diseased cells. As the size of the interaction dataset increases, powerful computational methods are required in order to effectively distil network models from large-scale interactome data.Module Inference by Parametric Local Modularity), to infer protein complexes in a protein-protein interaction network. The algorithm uses a novel graph theoretic measure, parametric local modularity, to identify highly connected sub-networks as candidate protein complexes. Using gold standard sets of protein complexes and protein function and localization annotations, we show our algorithm achieved an overall improvement over previous algorithms in terms of precision, recall, and biological relevance of the predicted complexes. We applied our algorithm to predict and characterize a set of 138 novel protein complexes in S. cerevisiae.We present an algorithm, miPALM (http://www.medicine.uiowa.edu/Labs/tan/software.html.miPALM is a novel algorithm for detecting protein complexes from large protein-protein interaction networks with improved accuracy than previous methods. The software is implemented in Matlab and is freely available at  Protein complexes carry out the majority of biological processes within a cell. Correctly identifying protein complexes in an organism is useful for deciphering the molecular mechanisms underlying many cellular functions. Recent advances in proteomics technologies such as two-hybrid system and mass spectrometry has allowed enormous amount of data on protein-protein interactions (PPI) to be released into the public domain . As the de novo protein complex detection in PPI networks. These methods can be roughly divided into three categories. Methods in the first group define explicit complex criterion such as dense connectivity within a complex. A heuristic search strategy is then employed to identify complexes  ← GrowSeedLQ)8      [return S' and s'N9      end10   Algorithm 3: GrowSeed )input: triangle seed S, adjacency matrix A, a set of neighbor nodes of sS N, coarseness parameter α, change in local modularity Δα LQ for all v in sN1   output: Expanded sub-network ' Sand its neighbor nodes s'N2   begin3   4      v* ← Nall neighbor nodes of v*5      S' ← {S, v*}6      7      8      9      if max ) < 0 then10      return S' and s'N11         12      end13   Unpromising seeds are those that cannot be expanded into larger sub-networks. In other words, they are triangles that have no neighbors that can cause positive change in local modularity if merged. We filtered out those triangles after seed expansion step to speed up the algorithm and reduce the number of false positives .Proteins in a PPI network could belong to one or more protein complexes simultaneously. This multiple membership of proteins should be uncovered by the clustering algorithm. Complexes found by our method can be overlapped if they are within the same densely connected region in the PPI network. While revealing overlapped complexes is important for understanding their dynamics, allowing algorithm to make overlapped predictions often produce an excessive number of complexes. For example, the algorithm DME  predictes δthat is defined as the product of the connectivity and size of complex After merging complexes produced by the seed expansion step, we rank the candidate complexes by their density score Gn, m={V, E} with n nodes and m edges and outputs a set of predicted protein complexes, M. The pseudo code of the algorithm is shown in Algorithm 4.Our algorithm takes as input an unweighted PPI network Algorithm 4: miPALM Input: Unweighted graph Gn, m ={V, E}, n=/V/, m=/E|, coarseness parameter α, and density score threshold δ1   Output: a set of sub-networks, M3   begin4   T ← TriangleEnumeration (G)5      t ← choose the top ranked triad-seed in T6      T ← delete t from list T7      while T is not empty do8      S ← RecursiveGreedySearch 9         t ← choose the top triad-seed uncovered by the previous search10         T ← delete t from list T11         if the size of S is three then12         13         continueS ← refine S by looking around S14         M ← {M, S}, output S15         S ← merge sub-networks in S16      for S ∈ M do17      s ← 18         δget density score f Sif s δ<δ then19         S from M20            delete end21   We used the F-measure to evaluate the performance of complex prediction algorithms. F-measure is the harmonic mean of the two quantities, precision (Pre) and recall (Rec), 2 Pre Rec/(Pre + Rec). Precision is defined as the ratio of the number of matched sub-networks to the number of predicted sub-networks by each algorithm. Recall is the ratio of the number of matched sub-networks to the number of known complexes.2/a·bω = c, where a, b are the size of the sub-network and the known complex, respectively, and c is the number of protein members overlapped between the prediction and the known complex. We also examine the precision and recall rates at different overlap scores  slim terms were used to evaluate the biological relevance of predicted complexes. P-value for GO term enrichment was calculated using the hypergeometric distribution. A Bonferroni-corrected p-value of 0.05 is considered to be significant.et al. [http://yeastgfp.yeastgenome.org. To compute a log-odds score of complex sub-cellular localization, we compared the observed number of protein pairs within a sub-network S that are co-localized to sub-cellular compartment k (skm) to the expected number of such pairs in a random network Based on fluorescence imaging, Huh et al.  classifiandsk nis the number of proteins localized in compartment k in sub-network S and s pis the connectivity for the sub-network. We consider a complex to be localized to a compartment k if the log-odds score where JK and KT conceived and designed the study. JK performed the experiments. JK and KT analyzed the data. All authors have read and approved the final manuscript.Supplemental Methods and Materials.Click here for fileSupplemental Table S1.Click here for fileSupplemental Table S2.Click here for fileSupplemental Table S3.Click here for file


In the current climate of high-throughput computational biology, the inference of a protein's function from related measurements, such as protein-protein interaction relations, has become a canonical task. Most existing technologies pursue this task as a classification problem, on a term-by-term basis, for each term in a database, such as the Gene Ontology (GO) database, a popular rigorous vocabulary for biological functions. However, ontology structures are essentially hierarchies, with certain top to bottom annotation rules which protein function predictions should in principle follow. Currently, the most common approach to imposing these hierarchical constraints on network-based classifiers is through the use of transitive closure to predictions.We propose a probabilistic framework to integrate information in relational data, in the form of a protein-protein interaction network, and a hierarchically structured database of terms, in the form of the GO database, for the purpose of protein function prediction. At the heart of our framework is a factorization of local neighborhood information in the protein-protein interaction network across successive ancestral terms in the GO hierarchy. We introduce a classifier within this framework, with computationally efficient implementation, that produces GO-term predictions that naturally obey a hierarchical 'true-path' consistency from root to leaves, without the need for further post-processing.Saccharomyces cerevisiae, shows our method offers substantial improvements over both standard 'guilt-by-association'  and more refined Markov random field methods, whether in their original form or when post-processed to artificially impose 'true-path' consistency. Further analysis of the results indicates that these improvements are associated with increased predictive capabilities , and that this increase is consistent uniformly with GO-term depth. Additional in silico validation on a collection of new annotations recently added to GO confirms the advantages suggested by the cross-validation study. Taken as a whole, our results show that a hierarchical approach to network-based protein function prediction, that exploits the ontological structure of protein annotation databases in a principled manner, can offer substantial advantages over the successive application of 'flat' network-based methods.A cross-validation study, using data from the yeast  Proteins are fundamental to the complex molecular and biochemical processes taking place within organisms. An understanding of their role is therefore critical in biology and bio-related areas, for purposes ranging from general knowledge to the development of targeted medicine and diagnostics. High-throughput sequencing technology has identified a tremendous number of genes with no known functional annotation. On average, as many as 70% of the genes in a genome have poorly known or unknown functions . Not surProtein function prediction can take many forms. The traditional and most popular methodologies use homology modeling and sequence similarity to infer biochemical function ,3. In siFor example, microarrays are often used to cluster proteins into groups of genes that respond concordantly to a given environmental stimuli. When these groups are strongly enriched in proteins in a given biological process such as insulin signaling and also contain proteins without annotation we often take the leap of faith and predict the unknown proteins to be associated with this process as well. Similarly, when two proteins are found to interact in a high throughput assay we also tend to use this as evidence of functional linkage.However, enrichment and guilt by association are often highly misleading and can lead to a very high false positive rate if not used with caution. The work in  and sevea priori. For example, while many scientists use GO in their daily research, it can be (and has been) claimed that overlap among categories, as well as the inherent ambiguity and semantic complexity of naming biological functions and processes, can frequently lead to misleading interpretations and wild goose chases. Classic statistical approaches are based on flat disjoint categories, and quantitative measures of annotation similarity such as through semantic similarity remain somewhat ad hoc.More broadly, the work in this paper is important in demonstrating that an important role can be played in this context by the knowledge captured in biological ontologies, when properly harnessed. That this should be the case is not obvious Nevertheless, despite such concerns, our work here shows that in the present context of automated protein function prediction, the leverage of hierarchies grounded in biological ontologies can yield real, quantifiable advantages over 'flat' network-based approaches.i and the label G of a potential function for that protein, the goal is to predict whether or not i has label G, using a classifier built from a set of training cases and additional related data. Such related data can be of many types  but often can be summarized in the form of a functional linkage graph . The labels G typically derive from a database of terms.Computational protein function prediction is typically treated as a classification problem. From this perspective, given a protein Protein-protein interaction (PPI) data are common, and have been used widely in the protein function prediction problem. A functional linkage graph is used to represent the information in the PPI, where nodes represent proteins and edges indicate pairwise interactions, as in Fig. G are commonly structured in a hierarchical form ). The Gene Ontology (GO) database is one such example . Viewed as a DAG, nodes represent labels and a link represents the is_a and part_of relations between labels. Function assignments to proteins must obey the true-path rule: if a child term  describes the gene product, then all its parent terms  must also apply to that gene product. Fig. A, it may or may not have term D, the child of A; on the other hand, if it does not have term A, it surely does not have D.Databases of labels D for the central protein in Fig. A and the neighbors labeled with D. The exploitation of GO hierarchy is not novel, and indeed is natural. It has been used in functional annotation of genes, as mentioned in the Related Work section, as well as for other purposes, such as identifying over- and under-representation of GO terms in a gene dataset, and clustering functionally related genes , using the annotations in the other four folds as training data.We apply our Hierarchical Binomial-Neighborhood (HBN) method, as well as the "Nearest-Neighbor" (NN) algorithm and the Binomial-Neighborhood (BN) method of , to the We use three metrics by which to evaluate the performance characteristics of each classification method. The first is the standard Receiver Operating Characteristic (ROC) curve, which evaluates a classifier's performance in a manner that aggregates across all terms. We examine ROC curves both for the overall GO hierarchy and within each of the 47 sub-hierarchies.βhF, proposed in [i that is annotated with the hierarchy root, first take the transitive closure of all of the most specific +1 predictions and change -1's into +1's, if there is any. Note that this step is only necessary here for "Nearest-Neighbor" and the "Binomial-Neighborhood" method.Since the ROC curve, as a metric, is 'flat', in that it ignores any hierarchical structure among terms, we use as a second metric a hierarchical performance measure, called posed in ,26 and di, calculate the true positive (TP), false positive (FP), and false negative (FN) counts, based on the true labels of all terms in the hierarchy and the corrected predictions, denoted as TPi,Next, for each protein FPi and FNi, respectively. Define hierarchical precision (hP) and hierarchical recall (hR) asβ hFis then defined as a weighted combination of hP and hR, in the formThe value β ∈ [0, ∞) is a tuning parameter. In this paper, we use hF1 with equal weights on precision and recall, simply denoted as hF. Note that hF, hP and hR are all scaled between 0 and 1, with higher hF indicating better performance over the hierarchy.where Lastly, because accurate positive predictions are of most biological interest in this area, and because predictions of terms increasingly deeper in the GO hierarchy are of increasingly greater use, we examine the positive predictive value (PPV) of each of the methods, as a function of depth in the hierarchy. However, as the prevalence of known terms tends to decrease substantially with depth, and PPV decreases similarly with decreasing prevalence, we normalize PPV by prevalence to allow meaningful comparison across depths. Specifically, we compute a log-odds version of PPV in the formf is the prevalence of a given term. This quantity therefore indicates relative performance of a given classifier, in comparison with a method that simply predicts proteins to have a given term with a priori probability f.where Gpa = GO:0045449, or regulation of transcription, we want to predict whether YGL017W is labeled with the child term Gch = GO:0045941, or positive regulation of transcription. All six neighbors are in the training set, and used together with other training nodes to estimate parameters. Three out of six neighbors are labeled with Gpa, and two with Gch. The prediction from HBN results from applying a threshold to Equation. The analogous probability for BN is given byTo better appreciate the performance gains from HBN that we describe momentarily below, we first present an illustrative example. Consider protein YGL017W (AFT1) and its neighborhood, as depicted in Fig. whereG is the target GO term, GO:0045941;• k is the number of training neighbors labeled with G;• N is the training neighborhood size;• G, given protein YGL017W is labeled with G;• G, given protein YGL017W is NOT labeled with G;• f* is the relative frequency of G in the training set, and f*.• t = 0.5, only HBN provides a correct positive prediction. The improvement here comes from the additional information provided by including parent-term information.Table hF measure, is shown in Fig. hF are calculated by combining, within each of the 5 folds, the true positive (TP), false positive (FP), true negative (TN) and false negative (FN) counts, over all proteins and all terms for varying thresholds, and averaging across folds. Precision and recall are defined as t < 0.1) in the hF plot. Comparison of the area under the curve (AUC) for each method, in the ROC and hF plots, through a simple paired t-test on four degrees of freedom, confirms this observation, i.e., p < 10-5 for comparison of HBN with BN and with NN. The gains of HBN over BN directly reflects the benefit of effectively integrating the GO hierarchical information into the construction of our classifier.A comparison of the overall performance of the three methods, by ROC curves and the biological process hierarchy actually breaks into 47 sub-hierarchies. Examination of performance on these sub-hierarchies provides some sense of the extent to which the HBN performance improvements are uniform across the GO hierarchy. We compute a ROC curve and hF plot for each of the sub-hierarchies . Numerical comparison of the corresponding AUCs finds, at a 5% significance level that HBN improves on BN in 38 of the 47 sub-hierarchies, according to the ROC curves, 19 of the sub-hierarchies, according to the hF plots, and 18 commonly between them. Conversely, BN outperforms HBN in only 1 of the 47 sub-hierarchies, according to the ROC curves, and 9 of the sub-hierarchies, according to the hF plots. (NN was uniformly the worse performer.)Recall that, as a result of our predicting only for GO terms annotated with less than 300 proteins in the database, the full hF plots, which incorporate transitive closure for BN (and NN) directly into their definition, and are designed to provide a more accurate summary of classification accuracy with hierarchically related class labels, support this conclusion. The gains of HBN over BN, although reduced, are still substantial, with HBN outperforming BN in just over 40% of the 47 hierarchies, and BN outperforming HBN, in less than 20%.These ROC plots are constructed using the original BN (and NN) predictions, without any correction for "true-path" consistency. However, the overwhelming improvement of HBN over BN indicated by the ROC curves is actually similar when the initial predictions of BN are post-processed by applying transitive closure. Specifically, HBN improves on BN in 28 of the sub-hierarchies, while BN outperforms HBN in only 4 sub-hierarchies. These results strongly suggest the validity of our premise as to the importance of incorporating hierarchical information in the GO database in the initial construction of a classifier. The response to stimulus, with 72 more specific terms below it, 40 out of which are predicted for 536 proteins annotated with root. The shapes and locations of the curves in these plots are similar to those in Fig. hF plot. For instance, using a threshold of t = 0.5 for prediction, HBN produces an hF measure nearly 254% and 60% higher than NN and BN, respectively .As an illustration, consider the performance on the sub-hierarchy corresponding to Fig. protein metabolism. Examination of the predictions seems to suggest that the comparatively poorer relative performance of HBN in this sub-hierarchy is due to its over-optimistic positive predictions, i.e., HBN produces a higher rate of false positives (FP) that lowers the hierarchical precision (hP) and hence the hF measure.In contrast, Fig. Lastly, Fig. t-test at each depth confirmed the differences to be highly significant  at depths 3, 4, and 5, but not at depths 1, 2, 6, 7, or 8. We note, however, that the lack of significance at the latter depths is likely partly driven by sample size, since at each of these depths there were less than 30 cases of positive protein-term predictions by all three methods used in calculating LO-PPV, while at the other three depths there were well in excess of 100.Shown in Fig. in silico proxy to in vitro validation, beyond that of the cross-validation study, we examined the performance of HBN, in comparison to NN and BN, when applied to new gene-GO term annotations found in the updated May 2007 database. Here our goal is to evaluate the robustness of our cross-validation results for predicting naturally occurring unknowns .Recall that the above results are based on gene-GO term annotations in the January 2007 GO database. As an hF function. We present the hF plots for only those sub-hierarchies (17) with sufficiently many annotations to yield meaningful results ; the hF measures for the others are trivial, due to too few new annotations. Over 40%  of these hF plots find HBN to work best in correctly detecting more specific associations, over a reasonably broad range of threshold values; in the majority of the remaining plots, HBN yields results similar to the at least one of the two other methods.We applied HBN, BN, and NN in each of the 47 sub-hierarchies to genes that (i) were annotated with only the root term in the June 2006 database, and (ii) were assigned more specific functions in that sub-hierarchy in the May 2007 database. There were a total of 508 genes that had received at least one new annotation in one of the sub-hierarchies, with as few as 1 gene and as many as 74 genes per hierarchy. There were 33 sub-hierarchies having such genes. The methods were compared for their accuracy through the in silico validation than in the cross-validation study. For example, for the sub-hierarchy with root term response to stimulus, the new hF curve for HBN exceeds that for BN by as much as 300%, dominating those for the other two methods for most of the thresholds. See Fig. hF curve is significantly improved in the in silico study, and in fact outperforms the other two methods. The sub-hierarchy with root term protein metabolism is of this sort. The hF curve for HBN in Fig. Overall, most of the plots are consistent with the cross-validation results. Interestingly, however, there are a number of cases where HBN clearly outperforms NN and BN by a larger margin in the Overall, these results suggest that the performance advantages of HBN indicated by the cross-validation study are, if anything, potentially understated.S. cerevisiae, one can make certain inferences about genes for which there is no annotated function. First, it is likely that the gene has low sequence similarity to any gene of known function, thus preventing the most straightforward computational methods of predicting gene function. Secondly, it is likely that no altered phenotype is observed upon protein overexpression, knockdown, or knockout, foiling first-pass experimental attempts to discover gene function. In these cases, the next step would involve more elaborate experimental methods, which would typically be guided by a co-expression analysis of publicly available microarray data. The experiments selected will, in general, be time-consuming, costly, different for each gene being investigated, and offer modest chances for success. Thus, the development of more sophisticated and accurate methods of computational prediction of function which could precisely guide experimental activity remains a top priority.For a well-studied organism, such as Biological and biomedical ontologies have become a prominent, and perhaps indispensable, tool in bioinformatics and biological research. GO in particular has been used in numerous papers to detect biological process enrichment of co-expressed genes, identify biological processes associated with disease, etc. However in the vast majority of applications the hierarchical nature of GO is actually not being used directly. For example, in enrichment testing such as GSEA or GNEA we typically test for every biological process if the differentially expressed genes in some condition are associated with this process more than expected by chance.Thus while GO and other ontologies obviously organize biological knowledge in an intuitive fashion, the structure is not typically exploited for actual inference by predictive analysis tools. This is rather different from evolutionary analysis tools and genetics frameworks where probabilistic ancestor/descendant relationships in phylogenies (hierarchies) are exploited very directly with substantial practical and theoretical benefits.Our work here suggests that similar developments of probabilistic frameworks are not only feasible, but promising, for improved protein function inference with gene ontologies. In addition, it suggests the need for further research to be done to clarify the utility of different representations for such purposes. Finally, it also raises the prospect of re-engineering ontologies or other similar representations, from the perspective of seeking to provide maximal value for probabilistic inference programs.in silico study, on the genome of yeast, for terms from the biological process category in the Gene Ontology. Results showed that our proposed method, by utilizing the ontological structure, significantly improved the prediction accuracy and the capability of detecting positive annotations over the hierarchies. Furthermore, our analysis suggests that such improvement persists across the ontology depths.We have developed a probabilistic framework for automated prediction of protein function using relational information  which exploits the hierarchical structure of ontologies, and guarantees the predictions obey a 'true-path' annotation rule. We have evaluated the performance of our method and compared it with two other network-based methods by both cross-validation and an XJ carried out the statistical study, implemented and performed the computation, drafted the manuscript. NN prepared the datasets and helped the computation. MS interpreted the results and took part in the analysis. SK participated in the design of the study and the analysis. EDK conceived of the study, participated in its design, supervised the analysis and finalized the manuscript. All authors read and approved the final manuscript.hF plots for 47 sub-hierarchies in cross-validation studyROC curves and . This file contains the ROC curves and plots of hF score versus predicting threshold of the three methods for 47 individual sub-hierarchies in the 5-fold cross-validation study. The root term ID's and names of the root terms, the sizes of sub-hierarchies, numbers of terms and genes predicted within sub-hierarchy are also shown. Colors: HBN (red); BN (light blue); NN (blue).Click here for filehF plots for 17 sub-hierarchies in in silico study. This file contains the plots of hF score versus threshold of the three methods for individual sub-hierarchies in the in silico validation study. The root term ID's and names of the root terms, the sizes of sub-hierarchies, numbers of terms and genes predicted within sub-hierarchy are also shown. Colors: HBN (red); BN (light blue); NN (blue).Click here for file


Cancer is caused by genetic abnormalities, such as mutations of oncogenes or tumor suppressor genes, which alter downstream signal transduction pathways and protein-protein interactions. Comparisons of the interactions of proteins in cancerous and normal cells can shed light on the mechanisms of carcinogenesis.We constructed initial networks of protein-protein interactions involved in the apoptosis of cancerous and normal cells by use of two human yeast two-hybrid data sets and four online databases. Next, we applied a nonlinear stochastic model, maximum likelihood parameter estimation, and Akaike Information Criteria (AIC) to eliminate false-positive protein-protein interactions in our initial protein interaction networks by use of microarray data. Comparisons of the networks of apoptosis in HeLa  cells and in normal primary lung fibroblasts provided insight into the mechanism of apoptosis and allowed identification of potential drug targets. The potential targets include BCL2, caspase-3 and TP53. Our comparison of cancerous and normal cells also allowed derivation of several party hubs and date hubs in the human protein-protein interaction networks involved in caspase activation.Our method allows identification of cancer-perturbed protein-protein interactions involved in apoptosis and identification of potential molecular targets for development of anti-cancer drugs. Study of interactome, the entire set of molecular interactions within cells, has provided many insights into the etiology and regulation of cancer ,2. TumorApoptosis is necessary for normal human development and survival, in that cells must die in order to prevent uncontrolled growth . ApoptosMost gene products mediate their functions within complex networks of interconnected macromolecules, forming a dynamic topological interactome ,12. HighHowever, experimental and database approaches often yield "false-positives" . For exaIn this study, we built an initial protein-protein interaction network based on two human yeast two-hybrid data sets ,14 and fc, somatic), and DIABLO . Networks, such as ours, that are developed from initially selected genes or proteins as the core nodes are referred to as "BRAC-centered networks"  represents stochastic molecular events, such as molecular fluctuations of the target protein.We used a nonlinear stochastic model to mimic the dynamic interactions among proteins to remove false-positives and refine the network. In recent years, some systems and computational biologists employ a dynamic perspective to describe biological functions, because of their dynamic nature -55. We cx [t] denotes the expression profile of target protein x at time point t; a denotes the influence of a target protein at one time point to the target protein at the next time point; bi denotes individual or binary interaction of protein i with target protein x [t]; and cij denotes the cooperative interaction ability of protein i and protein j on the target protein x. Thus, Fig. x [t]  and one cooperative interaction between protein x1 [t] and x2 [t] to the target protein x [t]. By consideration of basal interactions k and stochastic events ε[t], we can express the dynamic model of the target protein time profile x [t] as: x [t + 1] = ax [t] +b1x1 [t] +b2x2 [t] + b3x3 [t] + c12x12 [t] + k + ε [t]. This equation is based on a previously developed model . By unit sampling and with x[t + 1] - x[t], we get the following discrete model [where te model :ora denotes the influence of x [t] on x [t +1] and is dependent of the decay rate, λ.where x [t] represents the expression profile of the target protein at time point t, which is estimated from mRNA expression profiles via a translational sigmoid function . xij [t] denotes nonlinear cooperative interaction between protein xi and protein xj on the target protein, that is, xij [t] = f (yi [t]) · f (yj [t]), and cij denotes the cooperative interaction ability of protein i and protein j on the target protein  represents unknown protein-protein interactions that result from other possible interacting proteins or other influences . ε[t] represents random noise arising from model uncertainty and molecular fluctuations of protein interactions with the target protein  denotes the regression vector composed of many elements that represent expression levels of protein candidates in the initial network at time point t.where x [t] xi [tl] xj [tl]} for l ∈ {1 2 ... M} and i ∈ {1 2 ... N}, j ∈ {1 2 ... S}, where M denotes the number of microarray data points, N denotes the number of possible protein interactions for the target protein, and S denotes the number of protein complexes in the network. These data points are used as the basis in our regression vector φ[t]. Computation of equation (3) at different time points allows us to construct the following vector-form equation:Employing the cubic spline method ,58 to inFor simplicity, we represent this as:ε[tk] is regarded as a white Gaussian noise with zero mean and unknown variance σ2, that is, E{ν} = 0, and Σν = E{ννT} = σ2I. Next, we employed a maximum likelihood estimation method  and φ[tk] are the kth elements of X and Φ respectively.In equation (8), θ = σ2 = Here, we expect the log-likelihood function to have the maxima at nsist of :After some computational arrangements from equation (9), the estimated parameters After obtaining estimate We quantified the interactions of all candidate proteins by the process described above.i and the target protein, and i and protein j, i.e. protein complex ij, to the target protein. A positive value implies positive interaction, a negative value implies negative interaction, and the interactions are more likely as the parameters get larger.In equation (12), the estimated parameter Although our maximum likelihood estimation method allows quantification of all possible interactions of a target protein, we still do not know the significance of the interaction and whether it can be regarded as a true interaction. Thus, we used a statistical approach that involves model validation to evaluate significance levels and refine the network. In this procedure, we employed the Akaike Information Criterion (AIC) to validate the model order or the number of model parameters of the network .p increases. As the expected residual variance decreases with increasing P for inadequate model complexities, there should be a minimum near the correct number of interaction parameters P. For a protein interaction model with P interaction parameters to fit with data from N samples, the Akaike Information Criterion (AIC) can be written as follows [The Akaike Information Criterion (AIC) considers estimated residual variance and model complexity as one statistic and provides a measure of the information lost when a model is used. In other words, the AIC is an operational way of trading off the complexity of an estimated model against how well the model fits the data. AIC decreases as residual variance  follows φ · P parameters by minimizing the AIC, we can determine whether the protein interaction is significant or a false positive.where i interacting with protein j if the interaction is within P significant interactions, and '0' represents protein i not interacting with protein j if the interaction has less than P significant interactions. It must be considered that protein-protein interaction networks represent mutual binding relationships; if protein i binds to protein j, then protein j also binds to protein i. To determine mutual relationships in the high false positive yeast-two-hybrid experiments, we use the Boolean logical 'AND' to determine the interaction maps. Two proteins were considered to interact only if each protein binds to the other protein (see Supplementary Table 1). If an interaction is detected only in HeLa cells but not in normal cells, we call this a 'gain-of-function'; if the interaction is detected in normal cells but not HeLa cells, we call it a 'loss-of-function'. Table In our results, '1' represents protein We provide all Matlab programs and codes of these figures drawn by Osprey 1.2.0  in 'AddiLHC performed simulations, evaluated the results and wrote the paper. BSC provided the topic, direction and some suggestions.Supplementary Table 1. Global protein-protein interactions of apoptosis in HeLa cells and normal primary human lung fibroblasts.Click here for fileSupplementary Table 2. Gain-of-function proteins in Figure Click here for fileSupplementary Table 3. Loss-of-function proteins in Figure Click here for fileSupplementary Table 4. Eighty-six BCL2-interacting proteins identified from our results, the HPRD (Human Protein Reference Database), and literature review.Click here for fileSupplementary Table 5. Dynamic caspase protein-protein interactions in HeLa cells.Click here for fileSupplementary Table 6. Dynamic caspase protein-protein interactions in normal human primary lung fibroblasts.Click here for fileSupplementary Table 7. Microarray data [ray data  containiClick here for fileSupplementary Table 8. Microarray data [ray data  containiClick here for fileMatlab Programs. Five Matlab programs were used in this study. These include the AIC method, protein-protein interaction networks of apoptosis under ER stress in HeLa cells and normal primary human lung fibroblasts, and dynamic protein-protein interaction networks of caspase activation under ER stress in HeLa and normal cells.Click here for fileCodes of Figures. Eight Osprey codes used to drawing the Figures showing protein-protein interactions in this study (Figs. dy Figs. , and 4.Click here for file