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Popular items for guilt gold edge 4 Results. Enter minimum price. Enter maximum price. Only 1 available and it's in 1 person's cart. Previous page Next page. In systems biology, there is enormous interest in using high-throughput approaches to systematically glean information from these networks e. Information from such networks is now embedded in numerous studies and tools used by molecular biologists e.
If one agrees that the function of a gene is partially a property determined by its context or relationships in the network, assessing the functional role of any given gene is challenging, as in principle one must consider all the interactions of the gene, in the context of the network. GBA states that genes with related function tend to be protein interaction partners or share features such as expression patterns .
While not always referred to by name, GBA is a concept used extremely commonly in biology and which underlies a key way in which gene function is analyzed and discovered, whether on a gene-by-gene basis or using high-throughput methods. For example, an experimentalist who identifies a protein interaction infers a functional relationship between the proteins. Similarly two genes which interact genetically can be inferred to play roles in a common process leading to the phenotype .
This basic biological principle has been exploited by computational biologists as a method for assigning function in general, using machine learning approaches  , . This is made possible by the development of large interaction networks, often created by aggregating numerous isolated reports of associations as well as from high-throughput data sets. It has been repeatedly shown that in such networks there is a very statistically significant relationship between, for example, shared Gene Ontology annotations and network edges.
Tremendous effort has gone into improving computational GBA approaches for the purpose of predicting function  — . However, the number of biologically proven predictions based on such high-throughput approaches is still small and the promise of GBA as a general unbiased method for filling in unknown gene function has not come to fruition. In addition to their use in interpreting or inferring gene function, GBA approaches are also commonly used to assess the quality of networks, under the assumption that a high-quality network should map well onto known gene function information see, for example,  , .
A common metric is the precision with which genes sharing a function preferentially connect to one another  ,  ; readers unfamiliar with prediction assessment methods are also referred to  and Text S1 section 1. Built into this approach is the key assumption that GBA performance allows one to make statements about the network as a whole. Gene function is not the only way in which networks are assessed.
Another popular approach is to examine structural properties of the network, such as the distribution of node degrees in the network number of associations per gene. Similar to the situation for gene function, it is thought that a sign of high network quality is a power-law distribution of node degrees and some authors have even used this as a criterion for refining networks, on the assumption that data which conflicts with a power-law distribution is low-quality  , .
The relationship between such properties and GBA has not been well-explored. We observed that a trivial ranking of genes by their node degrees results in surprisingly good GBA performance; about one-half of performance could be attributed entirely to node degree effects . Node degree is predictive because genes that have high node degree tend to have many functions e.
Thus for any given prediction task, algorithms that assign any given function to high node-degree genes are rewarded by good performance without using information on which genes are associated with which.
vobybuwobo.tk More concretely, when studying any biological process, simply assuming P53 for example is implicated will go a surprisingly long way, and networks encode this completely generic information in their node degree. In this paper, we show that multifunctionality has a second effect on the interpretation of gene networks, and one that has especially serious implications for the interpretation and utility of GBA, and more generally for current assumptions about the how networks encode function.
We show that networks of millions of edges can be reduced in size by four orders of magnitude while still retaining much of the functional information. We go on to show that this effect guarantees that cross-validation performance of GBA as currently conceived is a useless measure of generalizability with respect to the ability to extract novel information. We determine that as currently formulated, gene function information is not distributed in the network as is commonly assumed. Instead, almost all existing functional information is encoded either in a tiny number of edges involving only a handful of genes, or not at all.
We conclude that computational attempts to scale up and automate GBA have failed to capture the essential elements that made it effective on a case-by-case basis. A key concept for our work is cross-validation, which is the means by which it is inferred that gene function can be predicted. While there are some nuances as to how this is arranged, in general the investigator observes whether the algorithm can correctly assign function to the held-out set, using the remaining genes as a training set and likewise that the function is not inappropriately assigned to genes considered negative examples.
Importantly, cross-validation only evaluates whether a function can be correctly predicted; it does not provide new predictions. This is essential if one wants to predict gene function, as opposed to merely test algorithms. We will explore the problem of generalization by dissecting what part of the network structure provides performance in cross-validation and determining whether it has a large impact on future predictions.
More specifically, we ask which connections in the networks are necessary and which connections are sufficient to generate function prediction performance. AP is closely related to the area under the precision-recall curve and is defined as:. Methods performing well will rank genes having the function highly, yielding high average precisions. AP values can then be averaged across groups e. The AP values can also be calibrated by comparing them to the distribution of APs obtained for randomly-generated rankings.
In order to characterize the functionality of edges in a network, we use some specific terminology. Such edges encode functional information by the GBA principle, but which edges are truly functionally relevant in the network can only be evaluated using known information or independent verification.
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Ideally, the network would only contain functionally relevant edges, but this is far from reality; the relevance of an edge may be function-dependent that is, relevant to some functions and not others and the networks likely contain edges that are in some sense artifactual. Criticality can be used as a proxy for functional relevance, but it must be borne in mind that the relationship is not necessarily straightforward. We use these definitions and quantification approaches throughout this paper.
We concern ourselves with questions such as the number and distribution of critical edges and exceptional edges, and finally with the relationship these have to functionally relevant edges. At the far left, the input network is shown with the genes having the function F we wish to predict shaded black and edges which turn out to be critical are bolded. In the second column, an edge is removed for simplicity this is only shown for the critical edges. The third column shows three cases of treating a gene as having unknown function crossed-out grey nodes.
At right, the predictions made using neighbor voting are shown with grey meaning a split decision. In Case 1, a correct prediction depends on one edge; removal of this edge will result in a false negative circled. In Case 2, there is no single edge that can be removed to cause an error, and the held out gene is correctly predicted. In Case 3, the critical edge of interest is between two genes that lack function F.
If this edge is removed, the circled gene is strongly predicted to have function F. In a cross-validation setting, this is considered a false positive. Our experiments show that such effects account for most of the apparent performance of GBA in practice. While we focus on GO terms as the definition of gene function, our findings are not specific to GO see Text S1 , section 2.
Indeed this is expected because function based on GO is highly correlated with other gene organization schemes . Our results are also not dependent on the choice of learning algorithm or evaluation metric see Text S1 , section 2. A key phenomenon is what happens when two highly multifunctional genes are connected in the network. Such edges will tend to be both critical and exceptional.
An edge between two genes that share a GO term is useful for prediction of that GO term during cross-validation, thus such edges have an increased probability of being critical compared to randomly selected edges. Intuitively, the more GO terms two connected genes share, the more GO terms for which that edge is likely to be critical. In principle this can have dramatic effects. That is, the average rank of genes predicted to possess a given function based on their neighbours in the network is substantially elevated across many functions, even using data for only a few genes.
This level of performance, with interactions present for only genes, is higher than that obtained with a real network; for a carefully characterized mouse gene network of 4. These connections are therefore sufficient to generate the results obtained with the real network. We assessed 10 mouse gene networks of different types for their degree of overlap with the exceptional edges. The amount of overlapping is strongly predictive of the MAP performance of the real networks correlation 0.
Because these networks incorporate data of diverse types see Table 1 , this suggests the effects of exceptionality are not an artifact of a particular type of network data. In the aggregated mouse network mentioned earlier, removing the 26 edges 0.
This suggests that a tiny number of edges may account for a large fraction of performance across most GO groups while using no information about most genes and that not only are these connections sufficient to obtain function prediction performance, but they may also be necessary. These results strongly suggest that in the mouse network, information on gene function is concentrated on too few genes to be of much practical use, at least with regards to how gene function is typically defined e.
A Average precision as exceptional edges are added, B Network performance is predicted by overlap with a network of the edges predicted to be most exceptional. The 10 constituent networks of the combined kernel are assessed individually for their precisions and overlap with the edge network.
We propose that these networks and their aggregate are representative of the highest-quality data available for gene function analysis. Using an aggregate of five of the networks, we identified critical edges by removing single edges and testing the average precision of each of GO terms see Methods , for each edge in the network. This yielded a dataset consisting of gene function prediction performance for each GO term in each of networks, each differing from the complete network by just one edge. This data set allows us to determine which individual connections are necessary to generate meaningful predictions for any given function; it can be visualized as a matrix of connections by average precisions of gene function prediction for that GO group using that network missing one connection.
A critical edge, then, is one in which edge removal changes precision substantially for a given GO group, while exceptionality can be determined by aggregating the criticality of a connection across all GO groups. Removing any single edge usually has little effect on performance for any given GO term, but when it does have an effect, it is drastic.
In Figure 3A , a sub-network for a representative GO term is shown; the distribution of the average precision values for this GO term with edges removed contains an extreme outlier Figure 3B.
These genes have 27 unique interactions with one another and over connections to other genes.