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A fundamental problem when trying to define the functional relationships between proteins is the difficulty in quantifying functional similarities, even when well-structured ontologies exist regarding the activity of proteins (i.e. 'gene ontology' -GO-). However, functional metrics can overcome the problems in the comparing and evaluating functional assignments and predictions. As a reference of proximity, previous approaches to compare GO terms considered linkage in terms of ontology weighted by a probability distribution that balances the non-uniform 'richness' of different parts of the Direct Acyclic Graph. Here, we have followed a different approach to quantify functional similarities between GO terms.
We propose a new method to derive 'functional distances' between GO terms that is based on the simultaneous occurrence of terms in the same set of Interpro entries, instead of relying on the structure of the GO. The coincidence of GO terms reveals natural biological links between the GO functions and defines a distance model Df which fulfils the properties of a Metric Space. The distances obtained in this way can be represented as a hierarchical 'Functional Tree'.
The method proposed provides a new definition of distance that enables the similarity between GO terms to be quantified. Additionally, the 'Functional Tree' defines groups with biological meaning enhancing its utility for protein function comparison and prediction. Finally, this approach could be for function-based protein searches in databases, and for analysing the gene clusters produced by DNA array experiments.
Current genome sequencing projects are producing a wealth of data in the form of sequences of biological polymers. For this data to be useful, it has to be interpreted in functional terms. Thus, efficient systems to describe and classify protein function are needed, as well as tools to predict the function of the huge number of new sequences.
There is much evidence for the need of well-defined and structured functional descriptions [1-4]. However, the main difficulty encountered is that 'function' is not a well defined concept and it is not as un-equivocal as 'sequence' or 'structure'. Indeed, protein function is a very complex and multidimensional phenomenon.
In many cases, functional descriptors are based on the available experimental techniques or are due to historical reasons. However, they do not necessarily have any meaning in biological terms (evolution, molecular mechanism). The methods we use to study biological systems require conceptualization and categorization, which are sometimes taken beyond their role as mere tools of the scientific method and are 'imposed' on the cell. One example is the artificial distinction between processes such as 'transmission of information' (for example DNA/RNA processing), 'metabolism' (of small compounds) and 'transport' (communication with the environment). Such disjointed classifications, as used in the first schemes to describe protein function, clearly do not extend to the molecular or evolutionary level. These schemes have been used in the past for classifying proteins into functional classes and for developing systems to assign newly sequenced proteins to them [5,6].
The current tendency is to use vocabularies and ontologies that allow complex functional descriptions beyond disjointed classes. Among these, the important effort of the Open Biomedical Ontologies (OBO) [7] in developing controlled vocabularies for a wide scope of applications in a biological and medical context must be recognised. The OBO ontologies are designed as graphic architectures formed by univocal concepts (terms) that are linked together by relationships that satisfy some prefixed and formal rules [8]. The Gene Ontology (GO) project [9] has become the 'de-facto' standard in biomedical ontologies. Formally, GO is designed as a Direct Acyclic Graph (DAG) based on two unconstrained relationships ('is-a' and 'part-of') that link a vocabulary of functional terms [2]. This graph structure, together with the simple conceptualization, permits comparisons between any two GO terms to assess their functional similarity. However, certain problems, such as the function-based search for potential genes/proteins of interest across multiple annotated databases and the analysis of high throughput microarray data, have led to the in depth exploration of ontology in order to propose models and criteria to measure the functional relationships between the terms.
In recent years, many studies have addressed this matter [10-14], although Lord was the first to establish a semantic distance for any two terms in GO [10], adjusting the ideas of Resnik [15] for general taxonomies. In the model proposed by Lord, the similarity of any two GO terms is determined as a function of the information content of common ancestors that are calculated from corpus statistics. Recently, further efforts to identify functionally related gene products in annotated databases based on the distances calculated by Lord [11] have been shown to produce a good agreement with homology searches [12]. Nevertheless, using the more informative common ancestors as a proximity reference presents some restrictions. First, the depth of the shared parent nodes is not a suitable criteria for some limited cases in which the terms to be compared are close to the root. Furthermore, the information content (i.e. probability) of a node is highly dependent on the annotated database selected and its release version.
Models have been developed to overcome these limitations that take into account other aspects of the ontology structure. For example, the distance between two terms may also integrate the density of the terms and the path that links them [13]. Alternatively, a new definition has been used that considers the local relationships in the subgraph generated by the terms, rather than their global positions in the DAG [14].
A common feature of these different approaches is that they rely mainly on the semantic links of the DAG. Unfortunately, there are inherent problems in this approach due to the non-homogeneity and the uneven distribution of the biological knowledge. As a result some regions of the DAG are more densely populated than others, so that the connections between terms are not comparable. In addition, the depth of a node (which is related to its specificity) can not be assigned in an unequivocal way. This type of problem is especially relevant for nodes that are profusely connected to the root by various paths of different lengths.
In this work, we propose a novel method that associates the Molecular Function GO (MF-GO) terms based on their co-occurrences in a 'curated' set of proteins and enriched by the semantic relationships from the ontology. Interpro is used as a curated database as it integrates protein information from other databases that describe protein families, domains and functional sites, such as PROSITE, PRINTS, Pfam, ProDom, SMART and TIGRFAMs [16].
Conceptually, the method is, to some extend, similar to the way in which similarities between aminoacids are 'learnt' from examples (structural curated alignments) rather than obtained from the raw chemical properties of the aminoacids. Methodologically, it shares aspects of the algorithm used in the DAVID tool [17] for clustering heterogeneous annotation contents from different resources into annotation groups based on the co-association of the annotated genes in the databases.
The method analyses the mutual occurrences of the MF-GO terms across the Interpro entries. The occurrences are used as the basis of the comparison of the terms on the assumption that the persistent coincidence of two terms describes its 'relation' in the general functional space. The analysis of the occurrences provides a useful mathematical tool to quantify the functional similarity between terms. A hierarchical tree linking the MF-GO terms is built from the similarity matrix. We termed this tree the 'Functional Tree' and it formally constitutes a Distance Model since it satisfies the ultrametric triangle inequality. In this context, the Functional Distance for a pair of terms, Df, is defined as the height of their least common ancestor in the 'Functional Tree'. In addition, the tree allows the GO terms to be clustered into compact and homogeneous groups with biological meaning.
We describe here how the Functional Tree was built, how the tree is clustered and the groups generated are analyzed in terms of the functions they describe. The Functional Distance Df derived from the Functional Tree was used to calculate the distances between pairs of yeast proteins to assess the reliability of the tree. We also compare this new metric with another based on semantic similarities.
The steps followed to obtain the Metric Model are schematically represented in Figure 1.
Figure 1. Scheme of the method used for obtaining the Metric Model based on Gene Ontology annotations. (1) Profile vectors are built by retrieving the Molecular Function Gene Ontology annotations (MF-GO terms) of Interpro domains from the file interpro2go. (2) From the profiles, a co-occurrence matrix is calculated by counting how many times two MF-GO terms occur in the same set of Interpro domains. (3) The co-occurrence vectors are feature vectors that describe the functional links of each MF-GO term. The similarity between the MF-GO terms is calculated by the cosine distance between the vectors. (4) The similarity values are arranged in a matrix S. The similarity matrix was considered as the Adjacency Matrix of a weighted graph G. The terms can be clustered by means of the partition of the graph. To obtain the best partition of G, a Spectral Clustering algorithm is applied. The Spectral Clustering algorithm projects the terms in a K dimensional space which can be clustered with standard clustering techniques. (5) The GO terms are grouped in a Hierarchical Tree representing the Functional Distance Df that satisfy the mathematical properties of a Metric Space.
First, for each Molecular Function term we create a profile vector that represents its presence/absence in different Intepro entries (Figure 1, box 1). These vectors resemble the 'phylogenetic profiles' used to encode the proteins present in different organisms and to detect protein relationships [18,19].
Initially, we started with 1532 MF-GO terms present in 5535 Intepro entries. Additionally, we included the semantic relationships represented by the Gene Ontology DAG by assigning the same Interpro domain to the parent(s) of a given GO term. The profiles were checked to detect the terms that were associated exclusively to one Interpro entry and to ensure that this entry was not annotated with any other term. Any such profiles were removed because they do not help to extract relationships between the terms. After filtering, we obtained a matrix of 1778 Interpro entries with 1392 MF-GO terms. In a second step (Figure 1, box 2), we built a matrix of co-occurrences of GO terms in Interpro entries. The occurrences were accumulated through all the profiles and we obtained the total mutual occurrences in the universe of the 1392 terms. Each co-occurrence vector describes a MF-GO term in relation to the rest of the MF-GO terms, which enables it to be used as a feature vector in the application of statistical learning techniques.
Third, the similarity between the terms was calculated using the cosine distance between their corresponding co-occurrence vectors (Figure 1, box 3). The similarity matrix S was obtained by crossing the vectors all-against-all (as graphically represented in Figure 2A) and the functional groups were obtained by the clustering of S. Full details of the Similarity matrix calculus are available in the Methods section. Finally we applied a Spectral Clustering algorithm [20,21] as it performs a dimensional reduction of the data (Figure 1, box 4). The general ideas behind Spectral Clustering methods are introduced in the 'Spectral Clustering' subsection from the appendix. This approach improved the search for functional groups in the MF-GO terms space.
Figure 2. (A) Initial Similarity matrix of 1329 × 1329 dimensions. The similarity colour scale is shown at the right of the matrix. S is obtained from the set of co-occurrence vectors. Note that S is symmetric, positive, and its values are ranked between 0 and 1. (B) Distribution of the similarity values. The distribution shows that S is sparse and depicts a general view of the structure of the search space for the clustering of S.
Spectral Clustering considers S as the Adjacency Matrix of a normalized weighted graph G, where the nodes stand for the MF-GO terms linked by the similarity values. Thus, the clustering problem is transformed into a partitioning graph problem. We only considered the graph comprised of terms that were connected with significant relationships, that is those connected by a pairwise similarity greater than a manually selected threshold value (see Methods, 'Similarity Matrix' subsection). After imposing this constraint, we obtained 995 MF-GO terms from the total of approximately 7500 terms integrated in the released version of this work.
We have also considered the NJW adaptation of Spectral Clustering (NJM-SC) by Ng, Jordan and Weiss [21], which is summarized in the general scheme in Figure 3 (see the 'NJW Spectral Clustering Algorithm' subsection from the appendix). The algorithm calculates a Transition Probability Matrix, P, from a N × N Similarity matrix, S, that represents the probability of transit from one node to another in the graph. P is diagonalized and its K first eigenvectors are stacked and normalized in a new K × K matrix, Y. The rows of Y can be treated as N vectors K dimensional. Therefore, NJM-SC projects the MF-GO terms (nodes of G) onto points in a K dimensional space. Subsequently, the terms can be grouped with any standard clustering technique. K was thus selected as the number of clusters in the optimum partition of G. The optimization procedure is presented in detail in the Methods section. The resulting number of optimal groups was 93.
Figure 3. Scheme of the spectral clustering methodology. Spectral clustering techniques aim to find the best partition of a weighted graph. A graph is constructed where the nodes are MF-GO terms linked by similarity values sij derived by calculating the cosine distance between the vectors of the co-occurrence matrix. The similarity matrix S = [sij] is treated as a real-value adjacency matrix of the graph. Let P be a normalized matrix named the Transition Probability matrix that represents the probability of transit from one node to another in this weighted graph. P is calculated from S. The first K eigenvalues of P are used to map the nodes of the graph to a K-dimensional space and the points in this reduced space can be grouped by any clustering algorithm. In this work, we have applied a hierarchical clustering algorithm.
Finally, from the vector projections of the MF-GO terms, we built a dendrogram with an Agglomerative Hierarchical Clustering algorithm [22] (Figure 1, box 5). The tree obtained ('Functional Tree') defines a distance Df between any two MF-GO terms from the set of 995 (see Additional file 1). The distance for two terms was the minimum height of their common nodes. From a mathematical point of view, Df satisfies the topological properties that induces a metric space (see 'Properties of a Metric Space' from the appendix). So, the metric generated by the Functional Tree establishes a 'distance scheme' that provides a measure of the closeness of any two MF-GO terms within the tree.
Additional file 1. Functional Tree. The data provided represent the 'Functional Tree' joining the Molecular Function Gene Ontology terms.
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Functional Groups
The nodes of the Functional Tree are divided into groups imposing the number of clusters obtained in the optimization step. The 93 groups of Molecular Function terms are inspected and 20 groups with highly homogeneous biological function are detected. In the Functional Tree (Figure 4, see Additional file 1), the functionally homogeneous groups are coloured and ranked, and the labels assigned are shown with their rank number.
Figure 4. Functional Tree representation. The tree is divided into 93 groups. The groups for which a functional 'homogeneity' was qualitatively assessed are labelled and coloured over the tree. The functional labels are specified. The tree was generated with iTol [30].
Some of these groups were very specific, like the group containing the 21 amino acyl-tRNA ligase activities. This group includes all the tRNA ligases and no other GO term, and hence the automatic clustering algorithm achieved a perfect segregation of this functional group (group 2).
Another big group mostly composed by activities related to hydrolysis (hydrolases, peptidases, nucleases, lipases) was labelled as group 1. Although this group was homogeneous for this activity, the coverage was not perfect since other hydrolases lay outside of this group. For example, group 7, which was far from group 2 in the tree, was mainly comprised of peptidase activities.
Interestingly, many different activities associated with DNA processing tended to cluster together despite the fact that they were apparently unrelated (i.e.: transcription factors and enzymes involved in DNA metabolism, DNA ligases, topoisomerases, etc... – group 3). As for the hydrolases case commented above, although this group contained only DNA-related activities and other DNA-related functional terms were not included in this group.
Most of the kinases of small metabolic compounds were clustered in a large group (group 15), while protein kinases were more widespread even though some of them clustered together in group 6. Many membrane transporters of apparently different nature (transporters for inorganic ions, drugs, proteins, etc...) were also clustered together in homogeneous groups.
All the 'protein inhibitor' activities within the dataset were clustered together in a homogeneous group (group 20), which is interesting given that the proteins they inhibit are of a very different nature (phos-phatases, ribonucleases, proteases, etc...).
Functional clustering was also evident for many other GO terms: methyl-transferases, phosphorybo-syltransferases, peptidases, some peptidic hormones, neurotransmitter receptors, phosphate-hydrolases, hy-dratases/dehydrateses, adenylyltransferases, etc....
For other clusters, this functional 'homogeneity' was not so evident. For example, oxidoreductases were spread across many groups even though some groups contained oxidoreductase activities only (group 19). This dispersion could be explained by the fact that this function is present in proteins with a very different evolutionary origin. Similarly, activities related to RNA metabolism were spread among the different clusters, except the tRNA-ligases discussed above.
In general, the clustering represented by the tree makes sense, meaning that GO molecular functions that are intuitively 'similar' were close in the tree and vice versa. This emphasise that the metric represented by the tree can be used to quantify functional similarities.
The Functional Tree as Metric Model
The functional distance Df defined from the Functional Tree allows a new quantitative analysis of the functional relationship between gene products. To assess Df as a functional similarity measure we correlated sequence and annotated function similarity over a set of aligned pairs of yeast proteins. The benchmark set has been selected by applying a very restrictive criterion to obtain a high reliable set of annotated proteins. The selection process (see Methods section) takes as quality assay the evidence codes in GOA. In this work, we picked only those sequences that had been functionally characterized either by experimental assay (IDA evidence code) or by traceable published works (TAS evidence code) and whose GO terms were included in our functional tree.
The functional distance between proteins (through their sets of annotated terms) is calculated using the hausdorff definition. The details are exposed in the 'Functional Comparison between Gene Products' subsection from Methods. The distance values are represented against the sequence similarity (Figure 5A). Lord semantic similarity Ds was also implemented and represented in Figure 5B. Note that the Lord distance values are normalised in order to analize the metric derived in this work with respect to Lord's model.
Figure 5. Comparison between functional distance and sequence similarity for pairs of Yeast proteins annotated with TAS and IDA evidence codes. The alignments covers most of the range of sequence similarities, whose distribution is shown in panel D. (A) Hausdorff distance (calculated using our functional metric) vs. sequence identity. The mean and the deviation values for each interval are also shown. (B) Hausdorff distance calculated using Lord's Semantic Similarity vs. sequence identity. (C) Mean values for both distance metrics. (D) Distribution of the percentage of Yeast protein pairs in each sequence similarity category.
To compare the models the mean distance values for each bin of sequence identity are superposed in figure 5C. In average, both approaches correlate well with sequence similarity and exhibit a similar trend for homologous pairs. This is partly due to the homology-based mechanism of annotation that transfers directly a source set of MF-GO terms to many homologous sequences.
In consequence, more than 84% of the alignments with sequence similarity values greater than 80% share the same annotations. This lack of richness in the annotations limits further analysis of the methods. However, we can observe that Df and Ds show a different behavior. The distance space is discretized into three well-defined groups (Figure 5A) whereas the semantic similarity values produced a great spread.
These natural 'cut-offs' allow classifying the pairs into three categories with biological meaning that can be roughly labelled as 'closely functionally related' (distances less than 0.1), 'not related at all' (more than 0.9) and 'divergence in functionality' (in the intermediate interval with distances between 0.5 and 0.7). This partition results from the structure of the clusters (Figure 6B) showing small intra-group and large intergroup distances. This is in part due to 'biological' reasons but is also affected by the function transfer by sequence homology.
The repetitive and persistent presence of the same MF-GO terms in the Intepro domains indicates clear functional associations of the terms but it is also originated by the usage of a reduced set of annotations producing redundancy in the functional information of the sequences and low coverage with respect to the total number of terms in the ontology (1532 from a total of 7417 MF-GO terms).
Figure 6. (A) Similarity Matrix in spectral space. The rows of the matrix represent the MF-GO terms in the reduced space of dimension 93. The terms are stacked in the same order that the Functional Tree (B) Ordered Similarity Matrix. The matrix was packed according to the optimal clustering. Each diagonal block correspond to a group in the Functional Tree. This matrix is close to an ideal block diagonal matrix (correlation coefficient of 0.86) that reveals a compact structure of functional groups.
In addition, the Functional Distance Model Df becomes very useful from the perspective of recovering proteins functionally similar to a query, as it provides new associations between the terms inferred from the homology information in the database entries. These new links enrich the ontology relationships among the terms. This is the case of group 3 (analized in the 'Functional Groups' from Testing section) whose MF-GO terms are spread across different lineages of the ontology involving DNA-related activities. These associations are very visible in many Pfam domains (Hormone receptor, Sigma-70 factor, Ets-domain, HSF-DNA binding, GATA-type transcription activator etc ...) but are not detected with a criteria based on the semantic proximity of the terms. Group 3 is partially represented in Figure 7 showing the relations of some terms in the ontology. Some terms of the group, such as 'DNA binding' and 'specific transcriptional repressor activity', are very distant in the DAG and share the root as common ancestor. This produces a semantic distance of 1. Other terms like 'transcription factor activity' and 'DNA replication origin binding' share the node 'DNA binding' that is three levels apart from to the root.
Figure 7. Graph representation of the ontology relations of a subset of MF-GO terms belonging to 'group 3' of the Functional Tree (orange nodes). The nodes in blue (GO:0016566 and GO:0003700) correspond to members of the 'group 3' that are also annotations of the pair [Uniprot:P20134]/[Uniprot:P10961]. The paths that links them are highlighted in black. Note there are two paths that connect them, and the least common ancestor is the node GO:0030528 ('transcription regulator activity') one level down from the root node. The Semantic Distance of the protein pair [Uniprot:P20134]/[Uniprot:P10961] is 0.76 whereas the Functional Distance is close to 0.
The benchmark set includes some example pairs in which Df assigns close distances to functionally related pairs while Ds does not. One is the pair formed by [Uniprot:P20134] and [Uniprot:P10961] that shares 50% sequence identity. The first is a transcriptional repressor and activator annotated with the term GO:0016566 ('specific transcriptional repressor activity'). The second is a trimeric heat shock transcription factor annotated with GO:0003700 ('transcription factor activity'). Both are characterized by HSF-type DNA-binding Pfam domain. The relative posititions of their annotated terms in the DAG can be checked in Figure 7. Ds is 0.76 indicating a weak relation between the proteins. However, Df situates the pair into the 'closely functionally related' region because the terms belong to the cluster 3 described before.
Other similar example is the pair formed by the protein kinases [Uniprot:P32801] and [Uniprot:P41808]. The proteins are characterized by protein kinase pfam domain and are annotated respectively with GO:0004674 ('protein serine/threonine kinase activity') and GO:0004707 ('MAP kinase activity'). Both terms belong to group 6 (Functional Groups subsection). So, as in the example before, the distance Df is 0 whereas Ds is 0.6. Although these terms are close in the ontology ('protein serine/threonine kinase activity' is ancestor of 'MAP kinase activity' and separated only by two depth levels), the Lord model assigns such a value distance because the shared parent ('protein serine/threonine kinase activity') is referred many times in the gene association.goa human file. According to Lord definition, high probable terms carry low information content producing high distance values in the comparison of terms. In the case of the kinases pair, the probability introduces a bias that shifts the semantic distance value to a region that indicates, as the example before, a weak relation between the proteins.
Finally, the Functional Distance model is sensitive enough to detect subtle differences in the pairs [Uniprot:P15700]/[Uniprot:P07170] and [Uniprot:P15700]/[Uniprot:P26364] that are explained by sequence analyses. In both cases, the members of the pair were annotated with GO:0004849 ('uridine kinase activity') and GO:0004017 ('adenylate kinase activity') respectively. Lord's Semantic Model produced a distance of 0.37 between these proteins, indicating semantical relation. In fact, the aforementioned terms are close in the GO hierarchy, and the deepest common parent shared by both GO terms, two levels above, is 'nucleobase, nucleoside, nucleotide kinase activity' (GO:0019205). However, our Functional Distance located that pair of GO terms within the intermediate interval at a distance of 0.65. A thorough analysis of the sequences revealed that [Uniprot:P15700] has the 'ADK' Pfam domain. Adenylate kinases are phosphotransferases with well conserved ADK domains that include an important arginine which inactivates the enzyme if mutated, and an aspartate that is located in the catalytic cleft and that forms a crucial salt bridge. However, in the particular case of [Uniprot:P07170] and [Uniprot:P26364], the putative ADK domain is interrupted by another PFAM domain, the ADK lid. Looking at the sequence of this particular region, the ADK domain boundaries were not clearly delineated due to a high degree of divergence in the active site. So, in this example our metric is able to capture the 'functional difference' between these two proteins due to the inserted domain.
The Spectral Clustering algorithm is implemented in Matlab 7.4.0 using the clustering functions available in the Statistics Toolbox. Lord's model is implemented in Python 2.5, and Python was also used to calculate the functional and semantic distances.
Discussion and Conclusion
Here, we propose a new method to derive 'functional distances' between GO terms based on the co-occurrence of them in the same set of proteins. The simultaneous occurrence of terms in Interpro entries provides a natural biological link between the GO functions. The relationship between terms in the GO structure provides additional semantic information that helps to refine the metric model.
In this method, an initial profile is constructed for each GO term representing its association with a set of Interpro domains (after expanding the Interpro annotations with the parenthood relationships of the GO terms). These profiles are used to generate a matrix of co-occurrence between GO terms. A graph is constructed where the nodes are the GO terms and the edges are weighted according to the distances extracted from this co-occurrence matrix. Spectral clustering is applied to this graph in order to obtain an optimal number of groups of functionally similar GO terms. The distances derived in this way provide a hierarchical clustering of GO terms (functional tree) where the groups of terms with similar biological meaning tend to be close. Additionally, this 'Functional Tree' represents a metric model Df whereby the distances between the terms fulfil the mathematical properties of a metric space.
The main difference of this method from previous approaches [10-14] is that Df is learned from examples. Hence, in contrast to other proposed methods that derive the distances from the semantic relationships within the GO ontology, our method provides new associations between the terms that enables a different way to compare proteins in functional terms. We have selected some cases to illustrate this point, for which the functional similarity between related proteins is better estimated with this metric model than with currently available algorithms, such as Lord's 'Semantic Similarity Model' [10]. Moreover, we also tried to qualitatively assess some of the groups automatically extracted from the distances by a clustering algorithm. Over and above the comparison with these examples and the qualitative assessment of the functional tree, it is actually difficult to assess the general quality of any functional metric.
The overall representation of the functional distances in the Functional Tree originates very compact groups of terms separated by well defined intervals as it is shown in Figure 6B. This structure of the clusters produces a not uniform distribution of distances because the values tend to concentrate in three regions (low, intermediate and high), which is obviously a problem since it makes the metric to some extent 'qualitative'. On the other hand, this categorisation produces natural 'cut-offs' and functional similarities that are naturally classified by the method in three categories with biological meaning in a totally unsupervised way as been discussed in Results section.
This discretization is in part due to 'biological' reasons but is also affected by the homology-based transfer that causes that only a reduced set of terms is used for annotation purposes. In consequence, the coverage with respect to the total number of terms in the Molecular Function ontology is low (around 20%). In addition, only clear relations are selected resulting a set of 995 MF-GO terms that are considered in the Functional Distance Model.
It is important to note that the relationships between the GO terms obtained and the relationships in the GO ontology represent different elements. The GO DAG represents qualitative semantic relationships ('is-a' and 'part-of') while our relationships represent quantitative 'functional distances'.
Thus, the metric proposed here provides a way of quantifying how similar two functional annotations are. This can be very useful for training systems for function prediction, for function-based protein searches in databases, or to assess the accuracy of a functional prediction (comparing the predicted set of annotations with the real one). This metric could also be useful for analysing the gene clusters produced by DNA array experiments. We think it may also provide insights into how functions evolved and the relationships between sequence, structure and functional spaces.
Similarity Matrix
The GO annotations for a given Interpro entry are retrieved from the mapping of Interpro to Gene Ontology [23] (interpro2go file, release May 2006). Only the GO terms belonging to the MF-GO are considered.
For each MF-GO term a profile vector is created that describes the presence/absence of the terms throughout the database. The profiles are constructed to analyze the simultaneous occurrence of pair MF-GO terms in the Interpro entries and filter the cases that do not contribute to the extraction of the relationship between the terms. The similarity between two terms is calculated by the cosine distance between their co-occurrence vectors:
Note that the cosine distance generates values ranking between 0 and 1. The similarity value can be considered as a description of the functional relationship between these terms, whereby similarities equal to 0 stand for unrelated terms and 1 stands for strongly related. The similarity matrix S is plotted in Figure 2A together with its histogram (Figure 2B).
The distribution of the similarity values shows that almost 90 per cent of the pairs of terms are only weakly related. This structure of the relationships reflects the presence of well-defined groups of terms. However, the search space has been limited as the cosine distance assigns a non-zero value even to pairs of terms that rarely share the same Interpro entry. Thus, based on the inspection of the histogram, we set a threshold of 0.8 to select strong functional links. In total there are 995 MF-GO terms that are significantly connected.
Additionally, we reduced the dimension of S by applying a NJW Spectral Clustering (NJW-SC) algorithm [21]. The similarity matrix in spectral space is shown in 6A, while the details of the algorithm are outlined in the 'Spectral Clustering Algorithm' subsection from the appendix.
Optimization Approach
As the number of clusters K is not initially known, an optimization approach is used, such as the multiway normalized cut value MNCut, (see 'Multiway Cuts' subsection from the appendix). The MNCut was calculated from the normalized matrix P (Transition Probability matrix). P represents the total probability of transit between any two clusters Ci and Cj for a given partition C = {C1 ... CK} of the graph and MNCut and represents the total sum of the transition probabilities between the clusters. The goal of optimization is to find the eigenvalue cut-off that generates a partition C* (K) that minimizes the MNCut value. In particular, we addressed optimization by exploiting the minimization of the gap value over the spectra of S.
The optimization curve is shown in Figure 8A. Note that a wide range of eigenvalues minimizes the gap (from 4 to 93). Thus, we applied an additional criteria to select the optimal cut-off, the correlation coefficient between the S matrix packed according to C* (K) and the ideal block diagonal matrix for this partition. The correlation calculation is used as a measure of the 'compactness' of the each partition. The correlation coefficient values are shown in 8B where the partition for the 93rd eigenvalue maximizes the procedure (correlation of 0.86). In Figure 6B the S matrix packed for the optimal clustering is represented.
Figure 8. The whole spectra of the P matrix [λi(P)]i∈U is analyzed selecting the first K eigenvalues and for each selection obtaining a partition of the MF-GO terms CK. In panel A, the values of the gap measure calculated for CK are represented and according to the Spectral Clustering theory, the best partition C* minimizes the gap value. The red circle encloses the eigenvalues of the spectra that generate 'good' clusterings (interval [4, 93]). Panel B shows the result of applying a second criterion to select the best number of groups from the interval. The correlation coefficient of the ordered similarity matrix with an ideal block diagonal matrix is calculated for each partition. The best clustering is obtained by selecting the first 93 eigenvalues.
Benchmark Dataset of aligned proteins
To compare our metric with others developed previously and to evaluate its relationship with sequence similarity, we took a set of proteins with reliable annotations taken from the Saccharomyces Genome Database (SGD). As an annotation source we used the file gene association.sgd (release October 2006).
The confidence of the Gene Ontology Annotations (GOA) is represented by the Evidence Code (EVC). Although there is no consensus rule that establishes a standard order of annotations based on the EVCs, the Gene Ontology Consortium has outlined a rank of EVCs as a guide [24]. The hierarchy of confidence establishes that the TAS (Traceable Author Statement) and IDA (Inferred from Direct Assay) tagged annotations offer the highest confidence.
Despite the efforts of the GOA project to improve the general reliability of its databases, the bulk of GO assignments are still made by automatic techniques with no expert curation. This homology-based transfer generates highly redundant sets of GO annotations. Moreover, as our method to derive the similarity between GO terms is to some extent affected by sequence similarity (given that it uses Interpro domains), we decided to exclude GO annotations derived from sequence relationships.
In gene association.sgd, there were 1264 yeast proteins annotated with GO terms with EVCs unrelated by homology (TAS and IDA) that also appeared in our functional tree. After filtering this set for sequence redundancy with CD-hit [25] at 95%, we obtained a final set of 1193 yeast proteins. We then perform fast alignments of all-against-all using BLAST, having chosen a permissive e-value (0.1) to permit alignments between distant sequences. Nevertheless, alignments covering less than 50 residues and/or with less than 10% similarity were excluded. The final set comprised 1426 protein pairs and the distribution of sequence similarity for these pairs is shown in Figure 5D.
Functional Comparison between Gene Products
To calculate the functional similarity between two proteins from their set of GO terms and the metric relating these terms, we applied the Hausdorff Distance. The Hausdorff Distance is defined as the maximum value between any point within one set and the nearest point in the other set. Formally, from set A to B is:
As the Hausdorff Distance is not symmetrical, a symmetrical measure was formulated as:
Usually the Hausdorff distance is evaluated over the Euclidean space, although in this work we applied equation 3 using two distances: (A) the distance Df obtained from our Functional Tree and (B) the distance proposed by Lord et al. [10]
We implemented Lord's semantic similarity using as a reference the annotated database gene associa-tion.goa human [26] (released version 45.0), and we normalised the values between 0 and 1 to compare it with the metric derived in this work.
Authors' contributions
All authors contributed to the development of the methodology. AP implemented the algorithm and evaluated the method for the alignment set. FP analyzed and interpreted the functional groups. AP and FP contributed to writing the manuscript, and all the authors read and approved the final manuscript.
Spectral Clustering
Spectral clustering has its origin in spectral graph partitioning [27] and is intended to efficiently identify good discrete partitions of a graph based on the eigenvalues and eigenvectors of the Laplacian matrix of the graph.
Spectral clustering belongs to a collection of techniques that are designed to overcome the problems of previous approaches by using new ideas such as the eigenvectors of the generalised/normalized Laplacian or the multi-way spectral cut. A systematic comparison between the existing published algorithms can be found in the work of Verma and Meila [20]. Therein, the authors present a clear description of the basic steps of the algorithms and their general classification based on three different strategies: (I) recursive spectral; (II) multi-way spectral; and (III) non-spectral.
In this section we will introduce the notation and the basic steps for the NJW spectral clustering algorithm [21] and the ideas behind multi-way spectral cuts as a criterion of optimisation to find the best partition of the data. Here we implemented a modified version of NJW algorithm suggested in [20].
NJW Spectral Clustering Algorithm
Consider a dataset U formed by N points to be clustered. For each pair of points within U, a similarity value can be defined as sij = sji ≥ 0 by any similarity measure. U can be represented by a weighted directed graph G = (V, E) where the S = [sij] matrix plays the role of the adjacency matrix of the graph. A clustering C = C1, C2,..., CK is a partitioning of U into non-empty disjointed subsets C1, C2,..., CK.
The out-degree of a node j is defined as . We represent D for a diagonal matrix of out-degrees as: D = diag(d1,..., dN).
The nodes can be grouped by following the steps:
1. Compute the transition probability matrix P = D-1 S.
where P defines the probability to navigate from node i to node j in a random walk over G. By construction, the eigenvalues of P are delimited as [-1, 1], 1 = λ1 ≥ λ2 ≥ ⋯ λ N ≥ -1. The corresponding eigenvectors are v1,..., vN.
2. Select the first K eigenvalues of P and form the X matrix by stacking the eigenvectors in columns:
3. Normalize each row of X to unit length to form the Y matrix:
4. Treat each row of Y as a point in K dimensions. The points can be grouped by any standard clustering technique. In this work, the points are organized in a hierarchical tree.
Multiway Cuts
The majority of approaches in spectral clustering deal with partitioning the graph in two optimal parts by using one eigenvector at a time and applying this approach reiteratively until K clusters are found.
A way to use the K first eigenvectors simultaneously to find the optimum partition of the graph has been proposed, minimizing the cut of two partitions over all possible partitions in U [28]. Most of the approaches assume that the number of clusters K is known in advance, but in many problems related to clustering there is not indirect evidence that reveals the optimal number of groups.
Here we expose the basics of the multi-way normalized cut (MNCut) concept that has been applied to find the optimum number K:
The volume of node i is defined as the out-degree of the node:
D denotes the diagonal matrix formed by Di. The volume of a subset A ⊆ U is , (we assume that no node has volume 0).
Given two disjoint subsets (A, B) ⊂ U, the set of edges between the subsets is the cut between A and B:
and the probability of transit from set A to set B is:
Given the partition C = {C1,...CK}, over U the multi-way normalized cut clustering criteria introduced in [28] is defined as:
The multi-way normalized cut represents the total sum of the transition probabilities between the clusters of C. If MNCut(C) is small then the probability of evading Ck in a random walk is also small.
It has been shown that for any clustering, the MNCut(C) is low-bounded by a function of the number of clusters K and the eigenvalues of P [29]:
The non-negative difference between the MNCut(C) and its lower bound is the gap(C):
It has been also shown that gap(C) is 0 if P has piecewise constant eigenvectors, that is if P is an ideal block stochastic matrix [29].
Therefore, from a set of M different partition solutions of the data [Ci]i∈M, the optimal C* is that which minimizes the gap measure.
Properties of a Metric Space
By construction, the hierarchical clustering procedure over the Gene Ontology terms defines a generalized distance D between any two terms goa and gob that satisfies the mathematical properties of a metric space [22]. That is, any set of elements (terms) of the space x1, x2 and x3 fulfil:
• Nonnegativity: D(x1, x2) ≥ 0
• Reflexivity: D(x1, x2) = 0 if and only if x1 = x2
• Symmetry: D(x1, x2) = D(x2, x1)
• Triangle Inequality: D(x1, x2) + D(x2, x3) ≥ D(x1, x3)
The authors want to acknowledge the members of the Structural Bioinformatics Group (CNIO), especially Dr. Ana Rojas for her help analysing the biological examples and Dr. Michael Tress for critical reading of the manuscript. This work has been partially funded by the GeneFun EU project (LSG-CT-2004-503567).
Friedberg I: Automated protein function prediction-the genomic challenge.
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Harris MA, Clark J, Ireland A, Lomax J, Ashburner M, Foulger R, Eilbeck K, Lewis S, Marshall B, Mungall C, Richter J, Rubin GM, Blake JA, Bult C, Dolan M, Drabkin H, Eppig JT, Hill DP, Ni L, Ringwald M, Balakrishnan R, Cherry JM, Christie KR, Costanzo MC, Dwight SS, Engel S, Fisk DG, Hirschman JE, Hong EL, Nash RS, Sethuraman A, Theesfeld CL, Botstein D, Dolinski K, Feierbach B, Berardini T, Mundodi S, Rhee SY, Apweiler R, Barrell D, Camon E, Dimmer E, Lee V, Chisholm R, Gaudet P, Kibbe W, Kishore R, Schwarz EM, Sternberg P, Gwinn M, Hannick L, Wortman J, Berriman M, Wood V, de la Cruz N, Tonellato P, Jaiswal P, Seigfried T, White R: The Gene Ontology (GO) database and informatics resource.
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Lord P, Stevens R, Brass A, Goble C: Investigating semantic similarity measures across the Gene Ontology: the relationship between sequence and annotation.
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Zhang P, Zhang J, Sheng H, Russo J, Osborne B, Buetow K: Gene functional similarity search tool (GF-SST).
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Schlicker A, Domingues F, Rahnenfuhrer J, Lengauer T: A new measure for functional similarity of gene products based on Gene Ontology.
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Couto F, Silva M, Coutinho P: Semantic similarity over the gene ontology: family correlation and selecting disjunctive ancestors. In In CIKM '05: Proceedings of the 14th ACM international conference on Information and knowledge management. New York, NY, USA: ACM Press; 2005:343-344.
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Mulder NJ, Apweiler R, Attwood TK, Bairoch A, Bateman A, Binns D, Bradley P, Bork P, Bucher P, Cerutti L, Copley R, Courcelle E, Das U, Durbin R, Fleischmann W, Gough J, Haft D, Harte N, Hulo N, Kahn D, Kanapin A, Krestyaninova M, Lonsdale D, Lopez R, Letunic I, Madera M, Maslen J, McDowall J, Mitchell A, Nikolskaya AN, Orchard S, Pagni M, Ponting CP, Quevillon E, Selengut J, Sigrist CJ, Silventoinen V, Studholme DJ, Vaughan R, Wu CH: InterPro, progress and status in 2005.
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Huang D, Sherman B, Tan Q, Kir J, Liu D, Bryant D, Guo Y, Stephens R, Baseler M, Lane H, Lempicki R: DAVID Bioinformatics Resources: expanded annotation database and novel algorithms to better extract biology from large gene lists.
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Bioinformatics 2007, 23:127-128. PubMed Abstract | Publisher Full Text


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- 9 Places That Are Surprisingly Cheap This Year Call it the year of the bucket list. A strong dollar in destinations around the world is making this an amazing time to go farther and do more for much, much less in 2015.
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Margaret Thatcher and members of John Major's cabinet
1 portrait
Margaret Thatcher and members of John Major's cabinet
by Ian Waldie, for Reuters
digital colour print, 12 October 1994
15 1/8 in. x 24 in. (385 mm x 609 mm)
Given by Reuters, 2003
Photographs Collection
NPG x126072
Click on the links below to find out more:
Sitterback to top
- Margaret Hilda Thatcher (née Roberts), Baroness Thatcher of Kesteven (1925-2013), Prime Minister. Sitter in 38 portraits.
Artistsback to top
- Reuters. Artist associated with 6 portraits.
- Ian Waldie. Artist associated with 1 portrait.
Linked displays and exhibitionsback to top
- Iconic Women in the Press (6 February 2003 - 26 May 2003)


text:
The Stanislaus County Sheriff's Department is investigating a suspicious death at a Turlock rest stop.
A search warrant served Tuesday morning on E. Linwood Avenue led to the discovery of a large scale marijuana growing operation and the recovery of an assault weapon by the Turlock Narcotics Enforcement Team.
One man's purchase at a Turlock estate sale almost ended with a real bang, when his recently acquired military relic was thought to be a live bomb.
A coordinated effort between multiple law enforcement agencies Friday night resulted in the dismantling of an unsanctioned quasi car show setting up in a parking lot of a Turlock grocer, and saw dozens cited for multiple infractions.
Local law enforcement is warning that the ringing telephone may be a harbinger of some crooked cons trying to weasel into people's wallets.
The Stanislaus County Sheriff's Department is investigating the gunshot deaths of two local men in the county.
Merced County Sheriff's deputies raided two Delhi homes after receiving tips they were being used as sites to grow marijuana.
A man who spotted a woman riding his stolen bicycle Thursday afternoon also ended up in trouble with law enforcement after brandishing a knife at the suspected thief.
The friendship between two Turlock men likely took a hit Wednesday when one man, while trying to avoid arrest, inadvertently led police officers to his friend's garage, where hundreds of marijuana plants were being grown.
When the Turlock American Little League opens its season March 1, it could be standing room only.
Turlock Police detectives are looking for a third suspect in the fatal shooting of Amripal Sandhu in Turlock on Nov. 6, 2013.
Two masked men, one of whom was armed with a gun, broke into a Turlock home Friday night, but fled empty-handed when the resident fought them off.
Turlock Police officers arrested a 19-year-old man on a vandalism charge after he was seen spray-painting near a bus stop.
Motorists traveling along W. Monte Vista Avenue Wednesday afternoon were greeted with the site of a naked man.
Residents of Joett Drive had their quiet evening interrupted when a strange man started pounding on their door and demanded to be let in.
Page 32 of 113
The Turlock Police Department is investigating the death of a 22-year-old man who was fatally shot outside a marijuana grow house.
A Turlock man who tried to avoid a search based on his probation status by running from officers, ended up in custody for drug, weapon and resisting charges.
A man wanted in connection with the killing of a 38-year-old Turlock man was apprehended in Modesto during a traffic stop.
The Merced County Sheriff's Department has arrested three Turlock men in connection with armed robberies at two pharmacies.
A federal grand jury returned a 15-count indictment on Thursday against seven individuals, charging them with conspiracy to commit mail fraud and bank fraud, mail fraud and aiding and abetting, and making false statements to a bank in a mortgage fraud scheme, United States Attorney Benjamin B. Wagner announced.
The Oklahoma police officer accused of taking a 15-year-old girl from the Turlock home of her grandparents has been fired from his job and is facing a kidnapping charge in Stanislaus County.
The rate of vehicle thefts in Stanislaus County saw a decline for a second year, according to the latest report from the National Insurance Crime Bureau.
A federal grand jury returned a three-count indictment today against four Central Valley men, including two from Turlock, on drug trafficking charges, according to the U.S. Attorney's office.
The 15-year-old girl reported missing by her grandparents in Turlock was found Thursday morning in a Las Vegas hotel room and the Oklahoma police officer she was with has been taken into custody on an arrest warrant for kidnapping.
A Turlock teen taken by an Oklahoma police officer in his 30s was found safe in Las Vegas.
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Dark Void - Jetpack Fight gameplay
Dark Void - Jetpack Fight gameplay....
- published: 15 Jan 2010
- author: funkyoulol2
The old-fashioned jetpack doesn't make much sense as a way to get around. Physics, gravity and the limitations of the human physique - not to mention the potential threat of flaming buttocks - have all conspired against the technology,...The State 2010-01-20
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The 1920s was the decade that started on January 1, 1920, and ended on December 31, 1929. It was the third decade of the 20th century. It is sometimes referred to as the Roaring Twenties or the Jazz Age, when speaking about the United States, Canada or the United Kingdom. In Europe the decade is sometimes referred to as the "Golden Twenties" because of the economic boom following World War I.
Since the end of the 20th century, the economic strength during the 1920s has drawn close comparison with the 1950s and 1990s, especially in the United States of America. These three decades are regarded as periods of economic prosperity, which lasted throughout nearly each entire decade. Each of the three decades followed a tremendous event that occurred in the previous decade (World War I and Spanish flu in the 1910s, World War II in the 1940s, and the end of the Cold War in the late 1980s).
However, not all countries enjoyed this prosperity. The Weimar Republic, like many other European countries, had to face a severe economic downturn in the opening years of the decade, because of the enormous debt caused by the war as well as the Treaty of Versailles. Such a crisis would culminate with a devaluation of the Mark in 1923, eventually leading to severe economic problems and, in the long term, favour the rise of the Nazi Party.


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I was working on a better contacts app that would bring a simpler display of the informations. So I was thinking that instead of having the contact photo as a little avatar, we could set it as the background of the contact page. Then you'd be able to scroll down to see more infos.
I wanted the design to be as unobtrusive as possible.
The rounded avatar at the top left is the group of the current contact.
PS: Sorry Zooey.
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New beginnings to capture. A new life to celebrate.
Styled sessions inspired by the iconic historical American Girls.
New families. New little people in your lives. In your home, where you are most comfortable, we will create your everyday extraordinary.
Together. Your family photos will last for a lifetime. The experience will be one you will treasure. One that you will cherish.
A collection of still life portraits, featuring both commercial and editorial work.
Senior portraits with an ethereal feel.
In black and white, an image is simplified to it's basic premise: light and dark.
Styled Children's Portraits that capture the whimsy and playfulness of childhood.
Styled sessions planned and executed by Mud Goddess Photography.
The Vintage Twilight Carnival shoot, featured in the May issue of Gothesque Magazine.
The possibility of forever. The optimism of a new day and a new life together. There is simply nothing more beautiful.


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Originally written on WhoDeyFans | Last updated 10/11/11
EAST RUTHERFORD, NJ - OCTOBER 5: Linebacker Dhani Jones #55 of the New York Giants watches from the sidelines during the game against the Miami Dolphins at Giants Stadium on October 5, 2003 in East Rutherford, New Jersey. The Dolphins defeated the Giants 23-10. (Photo by Al Bello/Getty Images)
Dhani Jones quickly moved up the list as one of my favorite Bengals. I liked him on his tv shows, I liked the leadership on the field and I liked how cool he was in person. Several times I crossed paths with Dhani and made a point to say hello and introduce myself. After the [...]
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Create Desk Accessories From Cans
Aluminum cans headed for the recycling bin are pretty desk accessories in the making.
Full Metal Jackets
Andy Warhol elevated the soup can to a work of art, and so can you. Replace the chipped mugs that have been holding your No. 2's with aluminum cans wrapped in leftover strips of wallpaper. This pencil-cup idea is M'm! M'm! Good!


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Why did you choose this product?
This princess-cut diamond anniversary ring is a stunning reminder of how much you care that is sure to take her breath away. with five 1/2 carat diamonds set into a white gold band, this ring is both timeless and beautiful,. Gift box included.
ITEM#: 13358205This enchanting anniversary band is crafted of 10-karat white gold with five sparkling princess-cut diamonds. The beautifully-set diamond band glimmers with a highly polished finish.
Center stones
- Center cut: Princess
- Diamonds: Five
- Weight: 1/2 carat
- Color: G-H
- Clarity: I2-I3
- Setting: Prong
- Metal:10k white gold
- Finish: High polish
- Style: Diamond band
- Weight: 2.25 grams
- Ring setting: 14 mm wide x 3.75 mm long x 3 mm high
- Band: 1.5 mm wide
Diamond total weight: 1/2* carat TW
All weights and measurements are approximate and may vary slightly from the listed information. *T.W. (total weight) is approximate. 1/2 carat T.W. may be 0.45 to 0.57 carat. Treatment code N (white diamond). See Treatment Guide for further information.
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This item is part of the Miadora Wedding Collection
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I am not a fan of flashy or big rings. My original wedding band was very thin and I loved the look, but it was very uncomfortable. I wasn't happy about getting a "bigger" ring, but I am IN LOVE with this ring. I wasn't 100% sure on my ring size, so I guessed (wrong lol), and I am going to have to end up getting it re-sized soon, but I don't want to take it off of my finger!!!Read More
This ring is gorgeous! Do not hesitate!
This ring is absolutely beautiful, diamonds are shiny bright and the band is a nice weight not thin or flimsy as others I have seen are! Diamonds have some inclusions but not obvious, bright clear and dazzling! I highly recommend! I hope to see this around long enough to be able to purchase a second in a couple of months to wear on either side of my engagement ring!Read More
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After: Fresh Contemporary White Kitchen
Add an edge to basic cabinets with angular stainless steel hardware.
A wall of classic white subway tile is a fresh alternative to paint and also doubles as the backsplash. Its light grey grout helps camouflage dirt. Post-renovation, the dishwasher was positioned next to the sink to help cleanup go faster. It's concealed behind panelling and fitted with a handle that matches the cabinets.
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Benefits of Apple Cider Vinegar
I want to thank Diane from Still Point Massage for showing me this very interesting article on Apple Cider Vinegar. I did not realize all the health benefits.
APPLE CIDER VINEGAR health benefits!
1. Apple Cider Vinegar helps get rid of hiccups!
2. Apple Cider Vinegar helps sooth sore throats.
To read the other benefits of Apple Cider Vinegar click here.
Holiday Treats
Does your gluten-free or dairy free diet and lifestyle make you miss out on your favorite holiday treats? In my Eastern European decedent family holiday get togethers, Povatica or Croatian Nut Roll Bread is always present. I set out to make a gluten & diary free recipe this year and it turned out pretty good. Try this gluten-free and dairy free recipe!!
Nut filling:
- 3 ounces ground walnuts w/ 1 once lightly chopped
- 1/8 cup and 2 tablespoons full fat coconut milk
- 1/3 cup sugar
- 1 egg
- 2 tablespoons butter/substitute or coconut oil
- Cinnamon and Nutmeg to taste
Wet Dough Ingredients
- 2 eggs
- 1/4 cup dairy-free yogurt or Greek if not sensitive
- 1 tablespoons butter/substitute or coconut oil
- 1/8 cup suger
- 1/2 packet yeast from Bobs Red Mill Pizza Dough Mix
Dry Dough
- Half packet of Bob's Red Mill Pizza Dough Mix
Preparing Filling
- Grind 3 oz of nuts into saw dust
- Place all nuts, milk, sugar, egg, butter and spices in sauce pan
- Cook over medium heat until it begins to bubble, stir constantly to not burn
- Lower heat and stir for 2-3 minutes
- Cool for at least 30 minutes
Preparing Dough
- Separate egg whites and yolks. Place one yolk in a sauce pan and the other aside for egg wash
- Add milk, yogurt, butter, and sugar to 1 egg yolk in sauce pan
- Cook over medium heat and stir until it begins to boil
- Remove from heat until lukewarm and add yeast.
- Still and let sit for 5 minutes.
- Beat egg whites until frothy not stiff
- Add Bob's Red Mill Pizza Dough dry mix
- Add wet mixture and mix for 3-4 minutes until sticky ball is formable
- Spray/grease surface to roll dough on
- Wet hands and roller and roll dough into square/rectangle sheet about 1/4 inch thick
- Spread nut mixture over dough leaving 1/2 inch on all sides.
- Slowly and gently roll up the dough starting at long end
- When finished rolling pinch/seal the seam
- Let rise for 60-90 minutes covered with plastic wrap in a warm location
- Preheat oven to 350 degrees
- Transfer roll to silicone baking mat or non-stick sheet
- Add 1 tablespoon warm water to left over egg yolk, whisk and brush over roll
- Bake for 15 minutes and re-egg wash
- Bake for 15-20 more minutes until golden brown
- Cut into 1/2 inch to inch strips
Do you have Bunions?
Bunions have become a normal appearance in many chiropractic and manual therapy offices. This has occurred due to shoe and footwear choices and improper ankle mobility. Surgery is the only option to decrease the size of the bunion, but to stop growth and decrease pain soft tissue work and rehabilitation is your best bet. Strengthening the peroneal muscles can help stabilize the big toe joint and ankle mobility exercises can help decrease the rate growth. Here is an easy way to start stabilizing the toe.
- Stand facing a wall using your hands to balance yourself.
- Spread your feet apart wider than shoulder width.
- Flatten your inner foot and raise your heels off the ground.
- Only raise the heels, do not come up on the toes.
- Repeat 3 sets of 25.
- This is not a calf exercise, do not perform calf raises.
Meat Additives
One reason I recommend and buy grass fed and grass finished local hormone free beef.
Digestion and Core Stability
Great link on how digestion and stability are linked!
Hope you enjoy
Dr. Justin Hildebrand
Knee Pain
Do you have knee pain and do not like to squat? Your problem may not be the knee themselves but who you squat and how you move through the hips. Proper hip posterior/backwards translation can take pressure off the knees and allow you to squat and train your hip and gluts without pain. Try these ball squats and see if your pain while squatting goes away.
- Begin by standing feet shoulder width apart just far enough from the wall that the ball is sandwiched between your low back and the wall.
- Start your squat by sitting BACK and down.
- Go down until your knees reach a 90°, angle being sure that your knees do not extend past your toes.
- Return to the standing.
- Perform 3 sets of 10 repetitions 2-3 times every day.
- Begin with a band around your knees, standing feet shoulder width apart just far enough from the wall that the ball is sandwiched between your low back and the wall.
- Repeat setup above.
- You should be able to do 3 sets of 10 of the regular ball squats with little to no fatigue before beginning the advanced ball squats.
- Make sure you are squatting back and down.
VMO Exercises
I have only found one VMO exercise that consistently activates the VMO. Oh, and it does a number of the gluteus as well.
Diagonal Sit Backs
- Start with the patient on one knee and heel directly under opposite buttocks. (right knee on the ground with right heel in line with left buttocks)
- Now the leg should be at a 45 degree angle, slight hip external rotation.
- Instruct the patient to perform a brace & breathe and slow start to sit back onto their heel. Do not have them go into lumbar flexion.
- They may not be able to touch their heel.
- Return to the starting position and repeat.
- No flexion or posterior pelvic tilting should be noted.
- The arms can be raised for balance.
- This should be felt in the VMO and gluts.


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20 Cute Tea Infusers That Will Make Coffee Lovers Jealous
Some of us like coffee, others are crazy about tea. We are fans of both, and more so of the wacky... Continue reading
Everyone knows how hard it is shopping for the perfect gift for someone, which is why if you need perfect gift ideas for all sorts of occasions (hint: you might need help for Valentine's and anniversaries) or type of receiver, you are going to love this section.
Whether your friend or loved one has a preference for pocket-sized items or they love to embrace their geeky side, or you are on a string budget, we won't let you down.
Some of us like coffee, others are crazy about tea. We are fans of both, and more so of the wacky... Continue reading
For most of us stuck in long commutes or in overwhelming workloads at work, we need our daily cup(s) of coffee.... Continue reading
Valentine's Day is approaching and nothing says "I love you" better than a gift made with your own hands. This Valentine's... Continue reading
Valentine's day is fast approaching and it's the perfect time to think about what you're going to give to your significant... Continue reading
You probably have checked out most of the gift ideas available out there, but if you're not into bulky gifts that... Continue reading
These days, many people think of fancy, high-end and expensive smart gadgets when it comes to the perfect Christmas gift. It's... Continue reading
Christmas and 2015 are just around the corner and the holiday season is almost here! It's the time to detach ourselves... Continue reading
Christmas is almost here and as much as it is a time for giving, it is also a time to treat... Continue reading
With the release of the first Android Wear watches, many developers have started releasing apps that work with the wearable. Along... Continue reading
There's a wide variety of factors involved in maintaining a healthy lifestyle. Sometimes, this makes it quite hard to identify whether... Continue reading
They say that "home is where the heart is", still, it doesn't hurt to have your home decorated the way you... Continue reading
One of the things that the MacBook has going for it is its pretty solid battery life except if you have... Continue reading
The whole do-it-yourself (DIY), open source maker electronics scene that's really gained in popularity over the past few years has led... Continue reading
Let's face it, we all love our gadgets. We love how they make things easier for us and how we use... Continue reading


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You can now invite anyone to meet at your favorite Starbucks.
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38 year old woman | Dieppe, NB, CAN | Seeking men 28-43 within 50 miles
Want to writte our own romantic story?
Well, i'm a pretty big girl, and not only on the waist line, i have a huge personality. I love to hang out with that special someone and do nothing but chill, or go out with friends, play cards. I'm looking for a guy who knows what he wants, and is not afraid to go after it. I've missed out on a lot these last years, and I want to be someones queen, cause i'm sure missing a king. My name is JOSELINE, spelled with and S, and not a C, and for the record, i do find it difficult being a big girl, while trying to find a good man, its great that some guys like big girls, but i don't plan on always being this size, so that makes it kind of useless now doesn't it. I want a guy to like me for me, cuz i'm pretty great no matter what size i am. I would love to look like JLO, and have her looks and body, lol, yeah, that will never happen, but hey i got her last name! lol, and my nick name is jlo, so thats kinda cool, i know this is like a super cheezzzzy paragraph, but some of you will catch on, and some of you won't. So im looking for a guy who is a romantic at heart, i love roses, and candle lit dinners, but i also love a cold beer and moose meet on the Q. I like to chat on FACEBOOK once in a while, keep up with my family that is spread around north america.I've travelled all over Canada, and lived in a lot of major cities, but i've never been across the border, don't even own a passport yet, that will change someday soon i hope lol. i dont know what else to tell you, if you think you could be interested in me, talk to me, lets get to know each other, but plz if you are the jealous type, don't bother, most of my firends are guys, including my x husband, he is my very best friend, just not husband material.
Camping , Coffee and conversation , Cooking , Dining out , Fishing/Hunting , Gardening/Landscaping , Movies/Videos , Museums and art , Music and concerts , Nightclubs/Dancing , Playing cards , Shopping/Antiques , Travel/Sightseeing , Watching sports , Wine tasting
Aerobics, Bowling, Dancing, Swimming
I don't exercise regularly.
I have Cats, Fish
I like Dogs, Exotic Pets, Horses
Middle of the Road
fun, hmmm, i like going to the casino and play machines, but try to keep that to a minimal, besides that, my fun is pretty tame, i work all week, and love to relax. once in a while like to kick back and have a few drinks with friends
Z{{Cta}} {{#if HasMoreInfo}} ?{{CtaSecondary}} {{/if}}
|What she is looking for
|5'8" (172cms)
|6'0" (182cms) to 6'11" (210cms)
|Body type:
|Big and beautiful
|About average, Athletic and toned, Heavyset, A few extra pounds, Stocky
|No preference
|No preference
|Yes, but trying to quit
|Yes, but trying to quit
|Social Drinker
|Social Drinker, Moderately
|Administrative / Secretarial
|Administrative / Secretarial, Artistic / Creative / Performance, Executive / Management, Financial / Accounting / Real Estate, Labor / Construction, Legal, Medical / Dental / Veterinary / Fitness, Political / Govt / Civil Service / Military, Retail / Food services, Sales / Marketing, Self-Employed / Entrepreneur, Student, Education / Teacher / Professor, Technical / Science / Computers / Engineering, Travel / Hospitality / Transportation, Other profession, Nonprofit / Volunteer / Activist, Law enforcement / Security / Military, Fashion / Model / Beauty, Architecture / Interior design
|Less Than $25,000
|Less Than $25,000, $25,001 to $35,000
|No preference
|Have kids:
|Yes, and they live at home (1)
|Yes, and they live at home
|Wants kids:
|Not sure
|White / Caucasian
|Black / African descent, Latino / Hispanic, Middle Eastern, Native American, White / Caucasian
i love cultural diversity, my background is mainly whilte and aboriginal, even tho my last name is spanish, i'm not, was married to a man from trini
|Spiritual but not religious
|Spiritual but not religious
i am catholic, but i do not attend church, but i do have a very strong beleif in God
|English, French
|Some college
|High school, Some college, Associates degree, Bachelors degree, Graduate degree


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While I've enjoyed my time with Amalur I'm sure I will be done with the game by the time ME3 comes out which leads me to the question trading the game in?? The game was fine but as always, with trading stuff in soon is always better. Started on hard to begin with so I can't go back and turn up difficultly. There also haven't been too many choices that really seem to swing the story one way or another. So the only good reason to keep it will be the promised great big huge DLC. So keep amalur or get $40-$30 towards ME3???
will you keep amalur or trade it for ME3
- Forum Posts: 318
- Wiki Points: 515
- Followed by: 4
- Reviews: 0 Lists: 8
I'm waiting on ME3 to drop to $20-$30, I don't like the combat in that series and there is too much of it.
I generally only trade in stuff long after I know I won't play it anymore.
- Forum Posts: 3076
- Wiki Points: 19
- Followed by: 51
- Reviews: 0 Lists: 1
Trading it for SSX.
- Forum Posts: 16426
- Wiki Points: 5553
- Followed by: 163
- Reviews: 8 Lists: 10
Keeping it because I'm not buying Mass Effect 3. And I still have a ton to do in Amalur.
- Forum Posts: 2792
- Wiki Points: 203
- Followed by: 46
- Reviews: 0 Lists: 1
Eh, if I had bought Amalur and traded in games then I probably would, didn't really like the demo and from what I have seen and heard from most people I wouldn't like it too much anyway...
- Forum Posts: 4172
- Wiki Points: 0
- Followed by: 72
- Reviews: 0 Lists: 2
You can't trade Steam versions.
And even then I don't trade games.
- Forum Posts: 4814
- Wiki Points: 947
- Followed by: 75
- Reviews: 0 Lists: 2
I would personally take the trade in value and put it toward ME3. Nothing about it really impressed me, and it makes me sad to say that since I thought it looked cool.
- Forum Posts: 1091
- Wiki Points: 0
- Followed by: 10
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@BoFooQ: I put a lot of hours into it and had fun with it but I am starting to get pretty burned out from it now. I will probably end up trading it in if I beat it this weekend or selling it to one of my buddies.
- Forum Posts: 992
- Wiki Points: 0
- Followed by: 12
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PC, can't trade in. I also don't trade in games. But I think I will be finished with Reckoning by the time ME3 comes out, or at least I hope I will be. 110 quest finished and just got the the second land mass.... might not make it by ME3 time.
Hmm brand new fantastical IP or Aliens invade earth. Tough Decision.
- Forum Posts: 747
- Wiki Points: 4129
- Followed by: 66
- Reviews: 1 Lists: 12
Even if I lived somewhere I could trade it in, I wouldn't. Really enjoying it. I understand the criticisms and if falls short on some fronts, but overall I really am enjoying it about 35ish hours in. I will definitely be getting ME3 though, had the CE preordered since it was announced last year. Good thing too, as Amazon seems to be sold out of it.
@Fredchuckdave said:
Hmm brand new fantastical IP or Aliens invade earth. Tough Decision.
Hmmm generic fantasy IP that I have seen dozens of times before or the conclusion to the only sci-fi rpg/shooter trilogy on the market. Tough Decisions.
@Tennmuerti: Why did you play it then? Also what's a good house of ballads equivalent anywhere? The 3rd game in sequel frenzy has almost universally been worse than the 2nd. But at any rate this is kind of a moot point: http://rampantgames.com/blog/wp-content/uploads/2010/12/bwcliches.png
Note: I realize this forum is extremely fanboy heavy and thus incredibly easy to troll, but if you want to make a legitimate argument I'm eager to hear it. I don't think Amalur is fantastic by any means other than Cam Clarke voicing half the characters, but what is so appealing about a game bound to be worse than the 2nd, with a worse premise than the 2nd, with a deteriorating company that was pretty damn overrated to begin with?
@Tennmuerti said:
@Fredchuckdave said:
Hmm brand new fantastical IP or Aliens invade earth. Tough Decision.
Hmmm generic fantasy IP that I have seen dozens of times before or the conclusion to the only sci-fi rpg/shooter trilogy on the market. Tough Decisions.
To explain "what I did there": You boiled down the 2 games to extremely narrow one sided views, I did the exact same thing but from the other direction.
I did this out of sheer principle regardless of how much I actually agree/disagree with your opinion on them (mostly due to the snarky "tough decisions" remark at the end)
@Tennmuerti: Why did you play it then?
Because I like playing games, seems self explanatory. Sometimes you play a game and dislike things about it. How can I dislike aspects of a game without having played it?
Also what's a good house of ballads equivalent anywhere?
House of balads is a cool new interesting thing I will give it that. If only the game did not beat you over the head with it in every conversation, it got old fast, eternal cycle blah blah
Note: I realize this forum is extremely fanboy heavy and thus incredibly easy to troll, but if you want to make a legitimate argument I'm eager to hear it.
My argument is I found Amalur "new IP" to offer nothing really new over it's 100+ hour, just repetition of the same shit over and over. House of balads is a drop in the ocean of cliches, tropes and repetition which made me want to bash my head on the keyboard at seeing. And even HoB manages to grate after a couple of missions. If you want my full arguments you can lookup my other posts in the Amalur board (they are many) I'm not going to repost all of it here.
Where as at least ME3 will offer something I don't really get from other games (regardless of it's assumed overall quality, which i said nothing of btw). Amusingly I am actually one of the biggest ME2 critics on these boards.
Note: I realize this forum is extremely fanboy heavy and thus incredibly easy to troll
I highly advise not to pre judge people, makes you biased before even starting an argument/disgussion.
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The Tech Pocket is a heavy-duty dry suit pocket made from durable CODURA fabric designed for the Technical/Cave Diver looking for a high volume pocket. The pocket provides 219.38 cubic inches (3,594 cubic cm) of pocket volume and provides ample storage for a variety of dive gear. Pocket includes 2 sets of elastic draw cords (main compartment & zippered pocket) for securing equipment. External zippered pocket placed on oversized Velcro closure flap to secure smaller items and for convenience. Pocket flap made of durable KEPROTEC an extremely abrasion and tear resistant fabric with Kevlar. Grommets on both sides and a drainage valve for main compartment provide quick drainage and reduce pocket drag. There are also internal pocket compartment for separating items within the pocket. Pocket is black in color and is covered by a 12 month limited warranty.
This product has a limited warranty of 24 months.
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