Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Motivation: Finding a good network null model for protein–protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay beten network structure and biological function as ll as into evolution. Also, network (graph) models are used to guide biological experiments and discover new biological features. It has been proposed that geometric random graphs are a good model for PPI networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space and edges (links) exist beten pairs of nodes for which the corresponding points in the metric space are close enough according to some distance norm. Computational experiments have revealed close matches beten key topological properties of PPI networks and geometric random graph models. In this work,  push the comparison further by exploiting the fact that the geometric property can be tested for directly. To this end,  develop an algorithm that takes PPI interaction data and embeds proteins into a low-dimensional Euclidean space, under the premise that connectivity information corresponds to Euclidean proximity, as in geometric-random graphs.  judge the sensitivity and specificity of the fit by computing the area under the Receiver Operator Characteristic (ROC) curve. The network embedding algorithm is based on multi-dimensional scaling, with the square root of the path length in a network playing the role of the Euclidean distance in the Euclidean space. The algorithm exploits sparsity for computational efficiency, and requires only a few sparse matrix multiplications, giving a complexity of O(N2) where N is the number of proteins.#R##N##R##N#Results: The algorithm has been verified in the sense that it successfully rediscovers the geometric structure in artificially constructed geometric networks, even when noise is added by re-wiring some links. Applying the algorithm to 19 publicly available PPI networks of various organisms indicated that: (a) geometric effects are present and (b) two-dimensional Euclidean space is generally as effective as higher dimensional Euclidean space for explaining the connectivity. Testing on a high-confidence yeast data set produced a very strong indication of geometric structure (area under the ROC curve of 0.89), with this network being essentially indistinguishable from a noisy geometric network. Overall, the results add support to the hypothesis that PPI networks have a geometric structure.#R##N##R##N#Availability: MATLAB code implementing the algorithm is available upon request.#R##N##R##N#Contact: natasha@ics.uci.edu
['Desmond J. Higham', 'Marija Rasajski', 'Nataša Pržulj']
I am writing a research paper on a idea Fitting a geometric graph to a protein–protein interaction network
[{"from": "human", "value": "I am writing a research paper on a idea Fitting a geometric graph to a protein\u2013protein interaction network"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Motivation: Finding a good network null model for protein\u2013protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay beten network structure and biological function as ll as into evolution. Also, network (graph) models are used to guide biological experiments and discover new biological features. It has been proposed that geometric random graphs are a good model for PPI networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space and edges (links) exist beten pairs of nodes for which the corresponding points in the metric space are close enough according to some distance norm. Computational experiments have revealed close matches beten key topological properties of PPI networks and geometric random graph models. In this work,  push the comparison further by exploiting the fact that the geometric property can be tested for directly. To this end,  develop an algorithm that takes PPI interaction data and embeds proteins into a low-dimensional Euclidean space, under the premise that connectivity information corresponds to Euclidean proximity, as in geometric-random graphs.  judge the sensitivity and specificity of the fit by computing the area under the Receiver Operator Characteristic (ROC) curve. The network embedding algorithm is based on multi-dimensional scaling, with the square root of the path length in a network playing the role of the Euclidean distance in the Euclidean space. The algorithm exploits sparsity for computational efficiency, and requires only a few sparse matrix multiplications, giving a complexity of O(N2) where N is the number of proteins.#R##N##R##N#Results: The algorithm has been verified in the sense that it successfully rediscovers the geometric structure in artificially constructed geometric networks, even when noise is added by re-wiring some links. Applying the algorithm to 19 publicly available PPI networks of various organisms indicated that: (a) geometric effects are present and (b) two-dimensional Euclidean space is generally as effective as higher dimensional Euclidean space for explaining the connectivity. Testing on a high-confidence yeast data set produced a very strong indication of geometric structure (area under the ROC curve of 0.89), with this network being essentially indistinguishable from a noisy geometric network. Overall, the results add support to the hypothesis that PPI networks have a geometric structure.#R##N##R##N#Availability: MATLAB code implementing the algorithm is available upon request.#R##N##R##N#Contact: natasha@ics.uci.edu"}]