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With the rapid development of communication networks and the establishment of 5G networks, there is a growing demand for the transmission of images and videos with different sizes and formats. Since these can contain sensitive and personal information, security is of great importance when transferring the contents of such files. Therefore, the use of powerful encryption mechanisms is an absolute requirement to protect the confidentiality of the exchanged data. In this study, we propose an image encryption algorithm with a high level of security. Thus, a chaotic system is proposed, and its state variables have been used to create a new substitution matrix. The importance of this matrix lies both in its use to generate encryption keys and in the encryption algorithm itself. In formulating the proposed encryption algorithm, we adopted the Feistel network in addition to some steps of the Advanced Encryption Standard (AES). The results of the various tests prove that the proposed algorithm guarantees high resistance to statistical and differential attacks and can therefore be used safely in image encryption. The incorporation of various algorithms suggested in this article in the form of IPcore for FPGA platforms amply promotes the use of our cryptosystem in various embedded systems or IoT environments.

Simple Summary: The relative rates of amino acid substitution over evolutionary time reflect the chemical properties of amino acids. Substitutions that result in an amino acid similar to an ancestral residue accumulate more rapidly than those resulting in a dissimilar amino acid. The substitution rates for each amino acid pair are the parameters in models of evolutionary change for proteins. Although the best-fitting model of protein evolution is known to differ among taxa, a comprehensive picture of model changes across the tree of life is not available. In principle, models of protein change might reflect evolutionary history (i.e., closely related taxa have similar models) or the environment (i.e., taxa living in similar environments have similar models). We estimated models of amino acid evolution for organisms across the tree of life, finding evidence that history and the environment have both contributed to model differences. Bacterial models differed from archaeal and eukaryotic models. Models for Halobacteriaceae (archaea that live in highly saline environments) and Thermoprotei (a group of thermophilic archaea) were found to be very distinctive. The rates of substitution for pairs of aromatic amino acids were especially variable. Overall, these results paint a picture of the "evolutionary model space" for proteins across the tree of life. The factors that determine the relative rates of amino acid substitution during protein evolution are complex and known to vary among taxa. We estimated relative exchangeabilities for pairs of amino acids from clades spread across the tree of life and assessed the historical signal in the distances among these clade-specific models. We separately trained these models on collections of arbitrarily selected protein alignments and on ribosomal protein alignments. In both cases, we found a clear separation between the models trained using multiple sequence alignments from bacterial clades and the models trained on archaeal and eukaryotic data. We assessed the predictive power of our novel clade-specific models of sequence evolution by asking whether fit to the models could be used to identify the source of multiple sequence alignments. Model fit was generally able to correctly classify protein alignments at the level of domain (bacterial versus archaeal), but the accuracy of classification at finer scales was much lower. The only exceptions to this were the relatively high classification accuracy for two archaeal lineages: Halobacteriaceae and Thermoprotei. Genomic GC content had a modest impact on relative exchangeabilities despite having a large impact on amino acid frequencies. Relative exchangeabilities involving aromatic residues exhibited the largest differences among models. There were a small number of exchangeabilities that exhibited large differences in comparisons among major clades and between generalized models and ribosomal protein models. Taken as a whole, these results reveal that a small number of relative exchangeabilities are responsible for much of the structure of the "model space" for protein sequence evolution. The clade-specific models we generated may be useful tools for protein phylogenetics, and the structure of evolutionary model space that they revealed has implications for phylogenomic inference across the tree of life. [ABSTRACT FROM AUTHOR]

With the rapid development of communication networks and the establishment of 5G networks, there is a growing demand for the transmission of images and videos with different sizes and formats. Since these can contain sensitive and personal information, security is of great importance when transferring the contents of such files. Therefore, the use of powerful encryption mechanisms is an absolute requirement to protect the confidentiality of the exchanged data. In this study, we propose an image encryption algorithm with a high level of security. Thus, a chaotic system is proposed, and its state variables have been used to create a new substitution matrix. The importance of this matrix lies both in its use to generate encryption keys and in the encryption algorithm itself. In formulating the proposed encryption algorithm, we adopted the Feistel network in addition to some steps of the Advanced Encryption Standard (AES). The results of the various tests prove that the proposed algorithm guarantees high resistance to statistical and differential attacks and can therefore be used safely in image encryption. The incorporation of various algorithms suggested in this article in the form of IPcore for FPGA platforms amply promotes the use of our cryptosystem in various embedded systems or IoT environments. [ABSTRACT FROM AUTHOR]

Abstract Background The alignment of character sequences is important in bioinformatics. The quality of this procedure is determined by the substitution matrix and parameters of the insertion-deletion penalty function. These matrices are derived from sequence alignment and thus reflect the evolutionary process. Currently, in addition to evolutionary matrices, a large number of different background matrices have been obtained. To make an optimal choice of the substitution matrix and the penalty parameters, we conducted a numerical experiment using a representative sample of existing matrices of various types and origins. Results We tested both the classical evolutionary matrix series (PAM, Blosum, VTML, Pfasum); structural alignment based matrices, contact energy matrix, and matrix based on the properties of the genetic code. This study presents results for two test set types: first, we simulated sequences that reflect the divergent evolution; second, we performed tests on Balibase sequences. In both cases, we obtained the dependences of the alignment quality (Accuracy, Confidence) on the evolutionary distance between sequences and the evolutionary distance to which the substitution matrices correspond. Optimization of a combination of matrices and the penalty parameters was carried out for local and global alignment on the values of penalty function parameters. Consequently, we found that the best alignment quality is achieved with matrices corresponding to the largest evolutionary distance. These matrices prove to be universal, i.e. suitable for aligning sequences separated by both large and small evolutionary distances. We analysed the correspondence of the correlation coefficients of matrices to the alignment quality. It was found that matrices showing high quality alignment have an above average correlation value, but the converse is not true. Conclusions This study showed that the best alignment quality is achieved with evolutionary matrices designed for long distances: Gonnet, VTML250, PAM250, MIQS, and Pfasum050. The same property is inherent in matrices not only of evolutionary origin, but also of another background corresponding to a large evolutionary distance. Therefore, matrices based on structural data show alignment quality close enough to its value for evolutionary matrices. This agrees with the idea that the spatial structure is more conservative than the protein sequence.

The factors that determine the relative rates of amino acid substitution during protein evolution are complex and known to vary among taxa. We estimated relative exchangeabilities for pairs of amino acids from clades spread across the tree of life and assessed the historical signal in the distances among these clade-specific models. We separately trained these models on collections of arbitrarily selected protein alignments and on ribosomal protein alignments. In both cases, we found a clear separation between the models trained using multiple sequence alignments from bacterial clades and the models trained on archaeal and eukaryotic data. We assessed the predictive power of our novel clade-specific models of sequence evolution by asking whether fit to the models could be used to identify the source of multiple sequence alignments. Model fit was generally able to correctly classify protein alignments at the level of domain (bacterial versus archaeal), but the accuracy of classification at finer scales was much lower. The only exceptions to this were the relatively high classification accuracy for two archaeal lineages: Halobacteriaceae and Thermoprotei. Genomic GC content had a modest impact on relative exchangeabilities despite having a large impact on amino acid frequencies. Relative exchangeabilities involving aromatic residues exhibited the largest differences among models. There were a small number of exchangeabilities that exhibited large differences in comparisons among major clades and between generalized models and ribosomal protein models. Taken as a whole, these results reveal that a small number of relative exchangeabilities are responsible for much of the structure of the “model space” for protein sequence evolution. The clade-specific models we generated may be useful tools for protein phylogenetics, and the structure of evolutionary model space that they revealed has implications for phylogenomic inference across the tree of life.

Abstract Objective BLOSUM matrices serve as standard matrices for many protein sequence alignment programs. BLOSUM matrices have been constructed using BLOCKS version5.0 with 27,102 BLOCKS, whereas the latest updated version14.3 has 6,739,916 BLOCKS. We read with interest the research article by Hess et al. (BMC Bioinform 17:189, 2016) on CorBLOSUM, wherein it is argued that an inaccuracy in the BLOSUM code affects the cluster memberships of sequences. They show that replacing the integer based clustering threshold to floating point arguably improves the performances of CorBLOSUM over BLOSUM and RBLOSUM matrices. They compare BLOSUM6214.3 against RBLOSUM69, with relative entropies of 0.2685 and 0.2662 respectively. The present work attempts to repeat the computation to verify the respective analog matrices. Results In our attempt to repeat the computation, we observed that the relative entropy of BLOSUM6214.3 is 0.2360 and BLOSUM5014.3 is 0.1198. As only matrices of similar entropies can be compared, BLOSUM62 can be compared only with RBLOSUM66 and BLOSUM50 can be compared only with RBLOSUM56. We conducted experiments with Astral data sets, and demonstrated the improved accuracy in the coverage. Our results imply that RBLOSUM performs statistically better than CorBLOSUM and BLOSUM matrices.

Phylogenomic analyses have revolutionized the study of biodiversity, but they have revealed that estimated tree topologies can depend, at least in part, on the subset of the genome that is analyzed. For example, estimates of trees for avian orders differ if protein-coding or non-coding data are analyzed. The bird tree is a good study system because the historical signal for relationships among orders is very weak, which should permit subtle non-historical signals to be identified, while monophyly of orders is strongly corroborated, allowing identification of strong non-historical signals. Hydrophobic amino acids in mitochondrially-encoded proteins, which are expected to be found in transmembrane helices, have been hypothesized to be associated with non-historical signals. We tested this hypothesis by comparing the evolution of transmembrane helices and extramembrane segments of mitochondrial proteins from 420 bird species, sampled from most avian orders. We estimated amino acid exchangeabilities for both structural environments and assessed the performance of phylogenetic analysis using each data type. We compared those relative exchangeabilities with values calculated using a substitution matrix for transmembrane helices estimated using a variety of nuclear- and mitochondrially-encoded proteins, allowing us to compare the bird-specific mitochondrial models with a general model of transmembrane protein evolution. To complement our amino acid analyses, we examined the impact of protein structure on patterns of nucleotide evolution. Models of transmembrane and extramembrane sequence evolution for amino acids and nucleotides exhibited striking differences, but there was no evidence for strong topological data type effects. However, incorporating protein structure into analyses of mitochondrially-encoded proteins improved model fit. Thus, we believe that considering protein structure will improve analyses of mitogenomic data, both in birds and in other taxa.

Abstract Background Detecting homologous protein sequences and computing multiple sequence alignments (MSA) are fundamental tasks in molecular bioinformatics. These tasks usually require a substitution matrix for modeling evolutionary substitution events derived from a set of aligned sequences. Over the last years, the known sequence space increased drastically and several publications demonstrated that this can lead to significantly better performing matrices. Interestingly, matrices based on dated sequence datasets are still the de facto standard for both tasks even though their data basis may limit their capabilities. We address these aspects by presenting a new substitution matrix series called PFASUM. These matrices are derived from Pfam seed MSAs using a novel algorithm and thus build upon expert ground truth data covering a large and diverse sequence space. Results We show results for two use cases: First, we tested the homology search performance of PFASUM matrices on up-to-date ASTRAL databases with varying sequence similarity. Our study shows that the usage of PFASUM matrices can lead to significantly better homology search results when compared to conventional matrices. PFASUM matrices with comparable relative entropies to the commonly used substitution matrices BLOSUM50, BLOSUM62, PAM250, VTML160 and VTML200 outperformed their corresponding counterparts in 93% of all test cases. A general assessment also comparing matrices with different relative entropies showed that PFASUM matrices delivered the best homology search performance in the test set. Second, our results demonstrate that the usage of PFASUM matrices for MSA construction improves their quality when compared to conventional matrices. On up-to-date MSA benchmarks, at least 60% of all MSAs were reconstructed in an equal or higher quality when using MUSCLE with PFASUM31, PFASUM43 and PFASUM60 matrices instead of conventional matrices. This rate even increases to at least 76% for MSAs containing similar sequences. Conclusions We present the novel PFASUM substitution matrices derived from manually curated MSA ground truth data covering the currently known sequence space. Our results imply that PFASUM matrices improve homology search performance as well as MSA quality in many cases when compared to conventional substitution matrices. Hence, we encourage the usage of PFASUM matrices and especially PFASUM60 for these specific tasks.

Pairwise alignment of amino acid sequences is the basic tool of bioinformatics, which is widely used both independently and within numerous more complex methods. The effectiveness of this tool critically depends on the scoring function used, which consists of a substitution matrix and gap penalties. In this work, amino acid substitution matrices for the superfamily of microbial rhodopsins (RHOD) were constructed and analyzed and then compared with a set of general-purpose matrices (BLOSUM, VTML, PFASUM). It was shown that all matrices allow constructing alignments of microbial rhodopsin sequences of almost the same quality, but only BLOSUM and VTML matrices and their linear combinations with RHOD matrices allow revealing homology between microbial rhodopsins and heliorhodopsin. [ABSTRACT FROM AUTHOR]

Phylogenetic systematics seeks to describe and reconstruct the evolutionary relationships among and between organisms making use of molecular data. This field has become immensely popular in recent years, with the associated computational demands growing in leaps and bounds. Here, we review the progress made in statistical phylogenetics, compare the various methods and highlight the recent trends and pitfalls. Furthermore, we delve into the mathematical models associated with these methods to understand the underlying assumptions, while tracking the improvements made. Lastly, we look at the impact and use of phylogenetics in ecology.

Understanding how proteins mutate is critical to solving a host of biological problems. Mutations occur when an amino acid is substituted for another in a protein sequence. The set of likelihoods for amino acid substitutions is stored in a matrix and input to alignment algorithms. The quality of the resulting alignment is used to assess the similarity of two or more sequences and can vary according to assumptions modeled by the substitution matrix. Substitution strategies with minor parameter variations are often grouped together in families. For example, the BLOSUM and PAM matrix families are commonly used because they provide a standard, predefined way of modeling substitutions. However, researchers often do not know if a given matrix family or any individual matrix within a family is the most suitable. Furthermore, predefined matrix families may inaccurately reflect a particular hypothesis that a researcher wishes to model or otherwise result in unsatisfactory alignments. In these cases, the ability to compare the effects of one or more custom matrices may be needed. This laborious process is often performed manually because the ability to simultaneously load multiple matrices and then compare their effects on alignments is not readily available in current software tools. This paper presents SubVis, an interactive R package for loading and applying multiple substitution matrices to pairwise alignments. Users can simultaneously explore alignments resulting from multiple predefined and custom substitution matrices. SubVis utilizes several of the alignment functions found in R, a common language among protein scientists. Functions are tied together with the Shiny platform which allows the modification of input parameters. Information regarding alignment quality and individual amino acid substitutions is displayed with the JavaScript language which provides interactive visualizations for revealing both high-level and low-level alignment information.

The 20 naturally occurring amino acids have different environmental preferences of where they are likely to occur in protein structures. Environments in a protein can be classified by their proximity to solvent by the residue depth measure. Since the frequencies of amino acids are different at various depth levels, the substitution frequencies should vary according to depth. To quantify these substitution frequencies, we built depth dependent substitution matrices. The dataset used for creation of the matrices consisted of 3696 high quality, non redundant pairwise protein structural alignments. One of the applications of these matrices is to predict the tolerance of mutations in different protein environments. Using these substitution scores the prediction of deleterious mutations was done on 3500 mutations in T4 lysozyme and CcdB. The accuracy of the technique in terms of the Matthews Correlation Coefficient (MCC) is 0.48 on the CcdB testing set, while the best of the other tested methods has an MCC of 0.40. Further developments in these substitution matrices could help in improving structure-sequence alignment for protein 3D structure modeling. [ABSTRACT FROM AUTHOR]

Background: Detecting homologous protein sequences and computing multiple sequence alignments (MSA) are fundamental tasks in molecular bioinformatics. These tasks usually require a substitution matrix for modeling evolutionary substitution events derived from a set of aligned sequences. Over the last years, the known sequence space increased drastically and several publications demonstrated that this can lead to significantly better performing matrices. Interestingly, matrices based on dated sequence datasets are still the de facto standard for both tasks even though their data basis may limit their capabilities. We address these aspects by presenting a new substitution matrix series called PFASUM. These matrices are derived from Pfam seed MSAs using a novel algorithm and thus build upon expert ground truth data covering a large and diverse sequence space. Results: We show results for two use cases: First, we tested the homology search performance of PFASUM matrices on up-to-date ASTRAL databases with varying sequence similarity. Our study shows that the usage of PFASUM matrices can lead to significantly better homology search results when compared to conventional matrices. PFASUM matrices with comparable relative entropies to the commonly used substitution matrices BLOSUM50, BLOSUM62, PAM250, VTML160 and VTML200 outperformed their corresponding counterparts in 93% of all test cases. A general assessment also comparing matrices with different relative entropies showed that PFASUM matrices delivered the best homology search performance in the test set. Second, our results demonstrate that the usage of PFASUM matrices for MSA construction improves their quality when compared to conventional matrices. On up-to-date MSA benchmarks, at least 60% of all MSAs were reconstructed in an equal or higher quality when using MUSCLE with PFASUM31, PFASUM43 and PFASUM60 matrices instead of conventional matrices. This rate even increases to at least 76% for MSAs containing similar sequences. Conclusions: We present the novel PFASUM substitution matrices derived from manually curated MSA ground truth data covering the currently known sequence space. Our results imply that PFASUM matrices improve homology search performance as well as MSA quality in many cases when compared to conventional substitution matrices. Hence, we encourage the usage of PFASUM matrices and especially PFASUM60 for these specific tasks. [ABSTRACT FROM AUTHOR]

Protein-protein Interactions (PPIs) play important roles in a wide variety of cellular processes, including metabolic cycles, DNA transcription and replication, and signaling cascades. High-throughput biological experiments for identifying PPIs are beginning to provide valuable information about the complexity of PPI networks, but are expensive, cumbersome, and extremely time-consuming. Hence, there is a need for accurate and robust computational methods for predicting PPIs. In this article, a sequence-based approach is proposed by combining a novel amino acid substitution matrix feature representation and Rotation Forest (RF) classifier. Given the protein sequences as input, the proposed method predicts whether or not the pair of proteins interacts. When performed on the PPI data of Saccharomyces cerevisiae , the proposed method achieved 93.74% prediction accuracy with 90.05% sensitivity at the precision of 97.08%. Extensive experiments are performed to compare our method with the existing sequence-based method. Experimental results demonstrate that PPIs can be reliably predicted using only sequence-derived information. Achieved results show that the proposed approach offers an inexpensive method for computational construction of PPI networks, so it can be a useful supplementary tool for future proteomics studies. [ABSTRACT FROM AUTHOR]

The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the 2n-th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers of CASTs are discussed as well as practical use cases to identify specimen with individual dihedral symmetry Dn or D2n, i.e., the tiling contains an infinite number of patches of any size with dihedral symmetry Dn or D2n only by iteration of substitution rules on a single tile. [ABSTRACT FROM AUTHOR]

The number of substitutions (of nucleotides, amino acids, etc.) that take place during the evolution of a sequence is a stochastic variable of fundamental importance in the field of molecular evolution. Although the mean number of substitutions during molecular evolution of a sequence can be estimated for a given substitution model, no simple solution exists for the variance of this random variable. We show in this article that the computation of the variance is as simple as that of the mean number of substitutions for both short and long times. Apart from its fundamental importance, this result can be used to investigate the dispersion index R, that is, the ratio of the variance to the mean substitution number, which is of prime importance in the neutral theory of molecular evolution. By investigating large classes of substitution models, we demonstrate that although R ≥ 1, to obtain R significantly larger than unity necessitates in general additional hypotheses on the structure of the substitution model. [ABSTRACT FROM AUTHOR]

Background: Multiple sequence alignment (MSA) is one of the most important research contents in bioinformatics. A number of MSA programs have emerged. The accuracy of MSA programs highly depends on the parameters setting, mainly including gap open penalties (GOP), gap extension penalties (GEP) and substitution matrix (SM). This research tries to obtain the optimal GOP, GEP and SM rather than MAFFT default parameters. Results: The paper discusses the MAFFT program benchmarked on BAliBASE3.0 database, and the optimal parameters of MAFFT program are obtained, which are better than the default parameters of CLUSTALW and MAFFT program. Conclusions: The optimal parameters can improve the results of multiple sequence alignment, which is feasible and efficient. [ABSTRACT FROM AUTHOR]

Background: BLOSUM matrices belong to the most commonly used substitution matrix series for protein homology search and sequence alignments since their publication in 1992. In 2008, Styczynski et al. discovered miscalculations in the clustering step of the matrix computation. Still, the RBLOSUM64 matrix based on the corrected BLOSUM code was reported to perform worse at a statistically significant level than the BLOSUM62. Here, we present a further correction of the (R)BLOSUM code and provide a thorough performance analysis of BLOSUM-, RBLOSUM- and the newly derived CorBLOSUM-type matrices. Thereby, we assess homology search performance of these matrix-types derived from three different BLOCKS databases on all versions of the ASTRAL20, ASTRAL40 and ASTRAL70 subsets resulting in 51 different benchmarks in total. Our analysis is focused on two of the most popular BLOSUM matrices—BLOSUM50 and BLOSUM62. Results: Our study shows that fixing small errors in the BLOSUM code results in substantially different substitution matrices with a beneficial influence on homology search performance when compared to the original matrices. The CorBLOSUM matrices introduced here performed at least as good as their BLOSUM counterparts in ∼ 75 % of all test cases. On up-to-date ASTRAL databases BLOSUM matrices were even outperformed by CorBLOSUM matrices in more than 86 % of the times. In contrast to the study by Styczynski et al., the tested RBLOSUM matrices also outperformed the corresponding BLOSUM matrices in most of the cases. Comparing the CorBLOSUM with the RBLOSUM matrices revealed no general performance advantages for either on older ASTRAL releases. On up-to-date ASTRAL databases however CorBLOSUM matrices performed better than their RBLOSUM counterparts in ∼ 74 % of the test cases. Conclusions: Our results imply that CorBLOSUM type matrices outperform the BLOSUM matrices on a statistically significant level in most of the cases, especially on up-to-date databases such as ASTRAL ⩾ 2.01. Additionally, CorBLOSUM matrices are closer to those originally intended by Henikoff and Henikoff on a conceptual level. Hence, we encourage the usage of CorBLOSUM over (R)BLOSUM matrices for the task of homology search. [ABSTRACT FROM AUTHOR]