The elastic net algorithm and protein structure prediction

A diagnostic model for sepsis-induced acute lung injury using a consensus machine learning approach and its therapeutic implications

BACKGROUND

A significant proportion of septic patients with acute lung injury (ALI) are recognized late due to the absence of an efficient diagnostic test, leading to the postponed treatments and consequently higher mortality. Identifying diagnostic biomarkers may improve screening to identify septic patients at high risk of ALI earlier and provide the potential effective therapeutic drugs. Machine learning represents a powerful approach for making sense of complex gene expression data to find robust ALI diagnostic biomarkers.

METHODS

The datasets were obtained from GEO and ArrayExpress databases. Following quality control and normalization, the datasets (GSE66890, GSE10474 and GSE32707) were merged as the training set, and four machine learning feature selection methods (Elastic net, SVM, random forest and XGBoost) were applied to construct the diagnostic model. The other datasets were considered as the validation sets. To further evaluate the performance and predictive value of diagnostic model, nomogram, Decision Curve Analysis (DCA) and Clinical Impact Curve (CIC) were constructed. Finally, the potential small molecular compounds interacting with selected features were explored from the CTD database.

RESULTS

The results of GSEA showed that immune response and metabolism might play an important role in the pathogenesis of sepsis-induced ALI. Then, 52 genes were identified as putative biomarkers by consensus feature selection from all four methods. Among them, 5 genes (ARHGDIB, ALDH1A1, TACR3, TREM1 and PI3) were selected by all methods and used to predict ALI diagnosis with high accuracy. The external datasets (E-MTAB-5273 and E-MTAB-5274) demonstrated that the diagnostic model had great accuracy with AUC value of 0.725 and 0.833, respectively. In addition, the nomogram, DCA and CIC showed that the diagnostic model had great performance and predictive value. Finally, the small molecular compounds (Curcumin, Tretinoin, Acetaminophen, Estradiol and Dexamethasone) were screened as the potential therapeutic agents for sepsis-induced ALI.

CONCLUSION

This consensus of multiple machine learning algorithms identified 5 genes that were able to distinguish ALI from septic patients. The diagnostic model could identify septic patients at high risk of ALI, and provide potential therapeutic targets for sepsis-induced ALI.

The Noncompacted Folding of Proteins by Modified Elastic Net Algorithm

In this article, a protein sequence of length n is embedded in a two-dimensional lattice with m (>n) points. Thus the obtained minimal energy configurations are expected to have flexible shapes in contrast to the compact rectangular conformations. To fulfill this extension, the elastic net algorithm is modified to deal with the difficulty brought by the unsymmetrical relationship between amino acids and lattice points. New set partition strategy in the embedding phase is introduced, and two local search methods are applied to overcome the multimapping phenomena. Several HP benchmark examples with up to 48 amino acids are tested to verify the effectiveness of the proposed approach.

New aspects of the elastic net algorithm for cluster analysis

The elastic net algorithm formulated by Durbin–Willshaw as a heuristic method and initially applied to solve the traveling salesman problem can be used as a tool for data clustering in n-dimensional space. With the help of statistical mechanics, it is formulated as a deterministic annealing method, where a chain with a fixed number of nodes interacts at different temperatures with the data cloud. From a given temperature on the nodes are found to be the optimal centroids of fuzzy clusters, if the number of nodes is much smaller than the number of data points. We show in this contribution that for this temperature, the centroids of hard clusters, defined by the nearest neighbor clusters of every node, are in the same position as the optimal centroids of the fuzzy clusters. The same is true for the standard deviations. This result can be used as a stopping criterion for the annealing process. The stopping temperature and the number and sizes of the hard clusters depend on the number of nodes in the chain. Test was made with homogeneous and nonhomogeneous artificial clusters in two dimensions. A medical application is given to localize tumors and their size in images of a combined measurement of X-ray computed tomography and positron emission tomography.

Mining gold dust under the genome wide significance level: a two-stage approach to analysis of GWAS

We propose a two-stage approach to analyze genome-wide association data in order to identify a set of promising single-nucleotide polymorphisms (SNPs). In stage one, we select a list of top signals from single SNP analyses by controlling false discovery rate. In stage two, we use the least absolute shrinkage and selection operator (LASSO) regression to reduce false positives. The proposed approach was evaluated using simulated quantitative traits based on genome-wide SNP data on 8,861 Caucasian individuals from the Atherosclerosis Risk in Communities (ARIC) Study. Our first stage, targeted at controlling false negatives, yields better power than using Bonferroni-corrected significance level. The LASSO regression reduces the number of significant SNPs in stage two: it reduces false-positive SNPs and it reduces true-positive SNPs also at simulated causal loci due to linkage disequilibrium. Interestingly, the LASSO regression preserves the power from stage one, i.e., the number of causal loci detected from the LASSO regression in stage two is almost the same as in stage one, while reducing false positives further. Real data on systolic blood pressure in the ARIC study was analyzed using our two-stage approach which identified two significant SNPs, one of which was reported to be genome-significant in a meta-analysis containing a much larger sample size. On the other hand, a single SNP association scan did not yield any significant results.

A novel approach for large-scale polypeptide folding based on elastic networks using continuous optimization

We present a new computationally efficient method for large-scale polypeptide folding using coarse-grained elastic networks and gradient-based continuous optimization techniques. The folding is governed by minimization of energy based on Miyazawa-Jernigan contact potentials. Using this method we are able to substantially reduce the computation time on ordinary desktop computers for simulation of polypeptide folding starting from a fully unfolded state. We compare our results with available native state structures from Protein Data Bank (PDB) for a few de-novo proteins and two natural proteins, Ubiquitin and Lysozyme. Based on our simulations we are able to draw the energy landscape for a small de-novo protein, Chignolin. We also use two well known protein structure prediction software, MODELLER and GROMACS to compare our results. In the end, we show how a modification of normal elastic network model can lead to higher accuracy and lower time required for simulation.

Optimal HP configurations of proteins by combining local search with elastic net algorithm

The prediction of protein conformation from its amino-acid sequence is one of the most prominent problems in computational biology. But it is NP-hard. Here, we focus on an abstraction widely studied of this problem, the two-dimensional hydrophobic-polar protein folding problem (2D HP PFP). Mathematical optimal model of free energy of protein is established. Native conformations are often sought using stochastic sampling methods, but which are slow. The elastic net (EN) algorithm is one of fast deterministic methods as travelling salesman problem (TSP) strategies. However, it cannot be applied directly to protein folding problem, because of fundamental differences in the two types of problems. In this paper, how the 2D HP protein folding problem can be framed in terms of TSP is shown. Combination of the modified elastic net algorithm and novel local search method is adopted to solve this problem. To our knowledge, this is the first application of EN algorithm to 2D HP model. The results indicate that our approach can find more optimal conformations and is simple to implement, computationally efficient and fast.

Exploration of two-dimensional hydrophobic-polar lattice model by combining local search with elastic net algorithm

Determining the functional conformation of a protein from its amino acid sequence remains a central problem in computational biology. In this paper, we establish the mathematical optimal model of protein folding problem (PFP) on two-dimensional space based on the minimal energy principle. A novel hybrid of elastic net algorithm and local search method (ENLS) is applied successfully to simulations of protein folding on two-dimensional hydrophobic-polar (HP) lattice model. Eight HP benchmark instances with up to 64 amino acids are tested to verify the effectiveness of proposed approach and model. In several cases, the ENLS method finds new lower energy states. The numerical results show that it is drastically superior to other methods in finding the ground state of a protein.

Exploring protein's optimal HP configurations by self-organizing mapping

Self-organizing map (SOM) has been used in protein folding prediction when the HP model is employed. The existing work uses a square-like shape lattice with l = m x n points to represent the optimal compact structure of a sequence of l amino acids. In this paper, a general l'-size sequence of amino acids is self-organized in a two dimensional lattice with l (> l') points. The obtained minimum configuration then has a flexible shape, in contrast to the compact structure limited in the lattice. To fulfil this extension, a new self-organizing map (SOM) technique is proposed to deal with the difficulty of the unsymmetric input and output spaces. New competition rules in the training phase are introduced and a local search method is applied to overcome the multi-mapping phenomena. Several HP benchmark examples with up to 36 amino acids are tested to verify the effectiveness of the proposed approach in this paper.

Minimum energy configurations of the 2-dimensional HP-model of proteins by self-organizing networks

We use self-organizing maps (SOM) as an efficient tool to find the minimum energy configurations of the 2-dimensional HP-models of proteins. The usage of the SOM for the protein folding problem is similar to that for the Traveling Salesman Problem. The lattice nodes represent the cities whereas the neurons in the network represent the amino acids moving towards the closest cities, subject to the HH interactions. The valid path that maximizes the HH contacts corresponds to the minimum energy configuration of the protein. We report promising results for the cases when the protein completely fills a lattice and discuss the current problems and possible extensions. In all the test sequences up to 36 amino acids, the algorithm was able to find the global minimum and its degeneracies.