TEMPROT: protein function annotation using transformers embeddings and homology search.

BACKGROUND: Although the development of sequencing technologies has provided a large number of protein sequences, the analysis of functions that each one plays is still difficult due to the efforts of laboratorial methods, making necessary the usage of computational methods to decrease this gap. As the main source of information available about proteins is their sequences, approaches that can use this information, such as classification based on the patterns of the amino acids and the inference based on sequence similarity using alignment tools, are able to predict a large collection of proteins. The methods available in the literature that use this type of feature can achieve good results, however, they present restrictions of protein length as input to their models. In this work, we present a new method, called TEMPROT, based on the fine-tuning and extraction of embeddings from an available architecture pre-trained on protein sequences. We also describe TEMPROT+, an ensemble between TEMPROT and BLASTp, a local alignment tool that analyzes sequence similarity, which improves the results of our former approach. RESULTS: The evaluation of our proposed classifiers with the literature approaches has been conducted on our dataset, which was derived from CAFA3 challenge database. Both TEMPROT and TEMPROT+ achieved competitive results on [Formula: see text], [Formula: see text], AuPRC and IAuPRC metrics on Biological Process (BP), Cellular Component (CC) and Molecular Function (MF) ontologies compared to state-of-the-art models, with the main results equal to 0.581, 0.692 and 0.662 of [Formula: see text] on BP, CC and MF, respectively. CONCLUSIONS: The comparison with the literature showed that our model presented competitive results compared the state-of-the-art approaches considering the amino acid sequence pattern recognition and homology analysis. Our model also presented improvements related to the input size that the model can use to train compared to the literature methods.

Reversal and Transposition Distance on Unbalanced Genomes Using Intergenic Information.

The most common way to calculate the rearrangement distance between two genomes is to use the size of a minimum length sequence of rearrangements that transforms one of the two given genomes into the other, where the genomes are represented as permutations using only their gene order, based on the assumption that genomes have the same gene content. With the advance of research in genome rearrangements, new works extended the classical models by either considering genomes with different gene content (unbalanced genomes) or including more genomic characteristics to the mathematical representation of the genomes, such as the distribution of intergenic regions sizes. In this study, we study the Reversal, Transposition, and Indel (Insertion and Deletion) Distance using intergenic information, which allows comparing unbalanced genomes, because indels are included in the rearrangement model (i.e., the set of possible rearrangements allowed when we compute the distance). For the particular case of transpositions and indels on unbalanced genomes, we present a 4-approximation algorithm, improving a previous 4.5 approximation. This algorithm is extended so as to deal with gene orientation and to maintain the 4-approximation factor for the Reversal, Transposition, and Indel Distance on unbalanced genomes. Furthermore, we evaluate the proposed algorithms using experiments on simulated data.

Rearrangement distance with reversals, indels, and moves in intergenic regions on signed and unsigned permutations.

Genome rearrangement events are widely used to estimate a minimum-size sequence of mutations capable of transforming a genome into another. The length of this sequence is called distance, and determining it is the main goal in genome rearrangement distance problems. Problems in the genome rearrangement field differ regarding the set of rearrangement events allowed and the genome representation. In this work, we consider the scenario where the genomes share the same set of genes, gene orientation is known or unknown, and intergenic regions (structures between a pair of genes and at the extremities of the genome) are taken into account. We use two models, the first model allows only conservative events (reversals and moves), and the second model includes non-conservative events (insertions and deletions) in the intergenic regions. We show that both models result in NP-hard problems no matter if gene orientation is known or unknown. When the information regarding the orientation of genes is available, we present for both models an approximation algorithm with a factor of 2. For the scenario where this information is unavailable, we propose a 4-approximation algorithm for both models.

Genome Rearrangement Distance With a Flexible Intergenic Regions Aspect.

Most mathematical models for genome rearrangement problems have considered only gene order. In this way, the rearrangement distance considering some set of events, such as reversal and transposition events, is commonly defined as the minimum number of rearrangement events that transform the gene order from a genome G1 into the gene order from a genome G2. Recent works initiate incorporating more information such as the sizes of the intergenic regions (i.e., number of nucleotides between pairs of consecutive genes), which yields good results for estimated distances on real data. In these models, besides transforming the gene order, the sequence of rearrangement events must transform the list of intergenic regions sizes from G1 into the list of intergenic regions sizes from G2 (target list). We study a new variation where the target list is flexible, in the sense that each target intergenic region size is in a range of acceptable values. This allows us to model scenarios where the main objective is still to transform the order of genes from the source genome into the target genome, allowing flexibility in the sizes of the intergenic regions, since the nucleotides in these regions tend to undergo more changes when compared to genes. We investigate the rearrangement distance considering three sets of events, two with the exclusive use of reversals or transpositions, and the other allowing both rearrangement events. We present approximation algorithms for the problems and an NP-hardness proof. Our results rely on the Flexible Weighted Cycle Graph, adapted from the breakpoint graph to deal with flexible intergenic regions sizes.

Reversal and Indel Distance With Intergenic Region Information.

Recent works on genome rearrangements have shown that incorporating intergenic region information along with gene order in models provides better estimations for the rearrangement distance than using gene order alone. The reversal distance is one of the main problems in genome rearrangements. It has a polynomial time algorithm when only gene order is used to model genomes, assuming that repeated genes do not exist and that gene orientation is known, even when the genomes have distinct gene sets. The reversal distance is NP-hard and has a 2-approximation algorithm when incorporating intergenic regions. However, the problem has only been studied assuming genomes with the same set of genes. In this work, we consider the variation that incorporates intergenic regions and that allows genomes to have distinct sets of genes, a scenario that leads us to include indels operations (insertions and deletions). We present a 2.5-approximation algorithm using the labeled intergenic breakpoint graph, which is based on the well-known breakpoint graph structure. We also present an experimental analysis of the proposed algorithm using simulated data, which showed that the practical approximation factor is considerably less than 2.5. Furthermore, we used the algorithm in real genomes to construct a phylogenetic tree.

Labeled Cycle Graph for Transposition and Indel Distance.

In the comparative genomics field, one way to infer the evolutionary distance between two organisms of related species is by finding the minimum number of large-scale mutations, called genome rearrangements, that transform one genome into the other. This number is referred to as the rearrangement distance. Since problems in this area emerged in the mid-1990s, several genome rearrangements have been proposed. Rearrangements that do not alter the genome content are called conservative, and in this group we have the following: the reversal, which inverts a segment of the genome; the transposition, which exchanges two consecutive segments; and the double cut and join, which cuts two different pairs of adjacent blocks and joins them differently. Seminal works compared genomes sharing the same set of conserved blocks, but nowadays, researchers started looking at genomes with unequal gene content, by allowing the use of nonconservative rearrangements such as insertion and deletion (jointly called indel). The transposition distance and the transposition and indel distance are both NP-hard. We investigate the transposition and indel distance and present a structure called labeled cycle graph, representing an instance of rearrangement distance problems for genomes with unequal gene content. This structure is used to devise a lower bound and a 2-approximation algorithm for the transposition and indel distance.

An improved approximation algorithm for the reversal and transposition distance considering gene order and intergenic sizes.

BACKGROUND: In the comparative genomics field, one of the goals is to estimate a sequence of genetic changes capable of transforming a genome into another. Genome rearrangement events are mutations that can alter the genetic content or the arrangement of elements from the genome. Reversal and transposition are two of the most studied genome rearrangement events. A reversal inverts a segment of a genome while a transposition swaps two consecutive segments. Initial studies in the area considered only the order of the genes. Recent works have incorporated other genetic information in the model. In particular, the information regarding the size of intergenic regions, which are structures between each pair of genes and in the extremities of a linear genome. RESULTS AND CONCLUSIONS: In this work, we investigate the SORTING BY INTERGENIC REVERSALS AND TRANSPOSITIONS problem on genomes sharing the same set of genes, considering the cases where the orientation of genes is known and unknown. Besides, we explored a variant of the problem, which generalizes the transposition event. As a result, we present an approximation algorithm that guarantees an approximation factor of 4 for both cases considering the reversal and transposition (classic definition) events, an improvement from the 4.5-approximation previously known for the scenario where the orientation of the genes is unknown. We also present a 3-approximation algorithm by incorporating the generalized transposition event, and we propose a greedy strategy to improve the performance of the algorithms. We performed practical tests adopting simulated data which indicated that the algorithms, in both cases, tend to perform better when compared with the best-known algorithms for the problem. Lastly, we conducted experiments using real genomes to demonstrate the applicability of the algorithms.

Ensemble of Template-Free and Template-Based Classifiers for Protein Secondary Structure Prediction.

Protein secondary structures are important in many biological processes and applications. Due to advances in sequencing methods, there are many proteins sequenced, but fewer proteins with secondary structures defined by laboratory methods. With the development of computer technology, computational methods have (started to) become the most important methodologies for predicting secondary structures. We evaluated two different approaches to this problem-driven by the recent results obtained by computational methods in this task-(i) template-free classifiers, based on machine learning techniques; and (ii) template-based classifiers, based on searching tools. Both approaches are formed by different sub-classifiers-six for template-free and two for template-based, each with a specific view of the protein. Our results show that these ensembles improve the results of each approach individually.

Incorporating intergenic regions into reversal and transposition distances with indels.

Problems in the genome rearrangement field are often formulated in terms of pairwise genome comparison: given two genomes [Formula: see text] and [Formula: see text], find the minimum number of genome rearrangements that may have occurred during the evolutionary process. This broad definition lacks at least two important considerations: the first being which features are extracted from genomes to create a useful mathematical model, and the second being which types of genome rearrangement events should be represented. Regarding the first consideration, seminal works in the genome rearrangement field solely used gene order to represent genomes as permutations of integer numbers, neglecting many important aspects like gene duplication, intergenic regions, and complex interactions between genes. Regarding the second consideration, some rearrangement events are widely studied such as reversals and transpositions. In this paper, we shed light on the first consideration and created a model that takes into account gene order and the number of nucleotides in intergenic regions. In addition, we consider events of reversals, transpositions, and indels (insertions and deletions) of genomic material. We present a 4-approximation algorithm for reversals and indels, a [Formula: see text]-approximation algorithm for transpositions and indels, and a 6-approximation for reversals, transpositions, and indels.

Approximation algorithm for rearrangement distances considering repeated genes and intergenic regions.

The rearrangement distance is a method to compare genomes of different species. Such distance is the number of rearrangement events necessary to transform one genome into another. Two commonly studied events are the transposition, which exchanges two consecutive blocks of the genome, and the reversal, which reverts a block of the genome. When dealing with such problems, seminal works represented genomes as sequences of genes without repetition. More realistic models started to consider gene repetition or the presence of intergenic regions, sequences of nucleotides between genes and in the extremities of the genome. This work explores the transposition and reversal events applied in a genome representation considering both gene repetition and intergenic regions. We define two problems called Minimum Common Intergenic String Partition and Reverse Minimum Common Intergenic String Partition. Using a relation with these two problems, we show a [Formula: see text]-approximation for the Intergenic Transposition Distance, the Intergenic Reversal Distance, and the Intergenic Reversal and Transposition Distance problems, where k is the maximum number of copies of a gene in the genomes. Our practical experiments on simulated genomes show that the use of partitions improves the estimates for the distances.

Heuristics for Genome Rearrangement Distance With Replicated Genes.

In comparative genomics, one goal is to find similarities between genomes of different organisms. Comparisons using genome features like genes, gene order, and regulatory sequences are carried out with this purpose in mind. Genome rearrangements are mutational events that affect large extensions of the genome. They are responsible for creating extant species with conserved genes in different positions across genomes. Close species - from an evolutionary point of view - tend to have the same set of genes or share most of them. When we consider gene order to compare two genomes, it is possible to use a parsimony criterion to estimate how close the species are. We are interested in the shortest sequence of genome rearrangements capable of transforming one genome into the other, which is named rearrangement distance. Reversal is one of the most studied genome rearrangements events. This event acts in a segment of the genome, inverting the position and the orientation of genes in it. Transposition is another widely studied event. This event swaps the position of two consecutive segments of the genome. When the genome has no gene repetition, a common approach is to map it as a permutation such that each element represents a conserved block. When genomes have replicated genes, this mapping is usually performed using strings. The number of replicas depends on the organisms being compared, but in many scenarios, it tends to be small. In this work, we study the rearrangement distance between genomes with replicated genes considering that the orientation of genes is unknown. We present four heuristics for the problem of genome rearrangement distance with replicated genes. We carry out experiments considering the exclusive use of the reversals or transpositions events, as well as the version in which both events are allowed. We developed a database of simulated genomes and compared our results with other algorithms from the literature. The experiments showed that our heuristics with more sophisticated rules presented a better performance than the known algorithms to estimate the evolutionary distance between genomes with replicated genes. In order to validate the application of our algorithms in real data, we construct a phylogenetic tree based on the distance provided by our algorithm and compare it with a know tree from the literature.

Reversals and transpositions distance with proportion restriction.

In the field of comparative genomics, one way of comparing two genomes is through the analysis of how they distinguish themselves based on a set of mutations called rearrangement events. When considering that genomes undergo different types of rearrangements, it can be assumed that some events are more common than others. To model this assumption, one can assign different weights to different events, where common events tend to cost less than others. However, this approach, called weighted, does not guarantee that the rearrangement assumed to be the most frequent will be also the most frequently returned by proposed algorithms. To overcome this issue, we investigate a new problem where we seek the shortest sequence of rearrangement events able to transform one genome into the other, with a restriction regarding the proportion between the events returned. Here, we consider two rearrangement events: reversal, that inverts the order and the orientation of the genes inside a segment of the genome, and transposition, that moves a segment of the genome to another position. We show the complexity of this problem for any desired proportion considering scenarios where the orientation of the genes is known or unknown. We also develop an approximation algorithm with a constant approximation factor for each scenario and, in particular, we describe an improved (asymptotic) approximation algorithm for the case where the gene orientation is known. At last, we present the experimental tests comparing the proposed algorithms with others from the literature for the version of the problem without the proportion restriction.

Sorting Permutations by Intergenic Operations.

Genome Rearrangements are events that affect large stretches of genomes during evolution. Many mathematical models have been used to estimate the evolutionary distance between two genomes based on genome rearrangements. However, most of them focused on the (order of the) genes of a genome, disregarding other important elements in it. Recently, researchers have shown that considering regions between each pair of genes, called intergenic regions, can enhance distance estimation in realistic data. Two of the most studied genome rearrangements are the reversal, which inverts a sequence of genes, and the transposition, which occurs when two adjacent gene sequences swap their positions inside the genome. In this work, we study the transposition distance between two genomes, but we also consider intergenic regions, a problem we name Sorting by Intergenic Transpositions. We show that this problem is NP-hard and propose two approximation algorithms, with factors 3.5 and 2.5, considering two distinct definitions for the problem. We also investigate the signed reversal and transposition distance between two genomes considering their intergenic regions. This second problem is called Sorting by Signed Intergenic Reversals and Intergenic Transpositions. We show that this problem is NP-hard and develop two approximation algorithms, with factors 3 and 2.5. We check how these algorithms behave when assigning weights for genome rearrangements. Finally, we implemented all these algorithms and tested them on real and simulated data.

Sorting Signed Permutations by Intergenic Reversals.

Genome rearrangements are mutations affecting large portions of a genome, and a reversal is one of the most studied genome rearrangements in the literature through the Sorting by Reversals (SbR) problem. SbR is solvable in polynomial time on signed permutations (i.e., the gene orientation is known), and it is NP-hard on unsigned permutations. This problem (and many others considering genome rearrangements) models genome as a list of its genes in the order they appear, ignoring all other information present in the genome. Recent works claimed that the incorporation of the size of intergenic regions, i.e., sequences of nucleotides between genes, may result in better estimators for the real distance between genomes. Here we introduce the Sorting Signed Permutations by Intergenic Reversals problem, that sorts a signed permutation using reversals both on gene order and intergenic sizes. We show that this problem is NP-hard by a reduction from the 3-partition problem. Then, we propose a 2-approximation algorithm for it. Finally, we also incorporate intergenic indels (i.e., insertions or deletions of intergenic regions) to overcome a limitation of sorting by conservative events (such as reversals) and propose two approximation algorithms.

Genome Rearrangement Distance with Reversals, Transpositions, and Indels.

The rearrangement distance is a well-known problem in the field of comparative genomics. Given two genomes, the rearrangement distance is the minimum number of rearrangements in a set of allowed rearrangements (rearrangement model), which transforms one genome into the other. In rearrangement distance problems, a genome is modeled as a string, where each element represents a conserved region within the two genomes. When the orientation of the genes is known, it is represented by (plus or minus) signs assigned to the elements of the string. Two of the most studied rearrangements are reversals, which invert a segment of the genome, and transpositions, which exchange the relative positions of two adjacent segments of the genome. The first works in genome rearrangements considered that the genomes being compared had the same genetic material and that rearrangement events were restricted to reversals, transpositions, or both. El-Mabrouk extended the reversal model on signed strings to include the operations of insertion and deletion of segments in the genome, which allowed the comparison of genomes with different genetic material. Other studies also addressed this problem and, recently, this problem was proved to be solvable in polynomial time by Willing et al. For unsigned strings, we still observe a lack of results. That said, in this study we prove that computing the rearrangement distance for the following models is NP-Hard: reversals and indels on unsigned strings; transpositions and indels on unsigned strings; and reversals, transpositions, and indels on signed and unsigned strings. Along with the NP-hardness proofs, we present a 2-approximation algorithm for reversals on unsigned strings and 3-approximation algorithms for the other models.

Sorting permutations by fragmentation-weighted operations.

One of the main problems in Computational Biology is to find the evolutionary distance among species. In most approaches, such distance only involves rearrangements, which are mutations that alter large pieces of the species' genome. When we represent genomes as permutations, the problem of transforming one genome into another is equivalent to the problem of Sorting Permutations by Rearrangement Operations. The traditional approach is to consider that any rearrangement has the same probability to happen, and so, the goal is to find a minimum sequence of operations which sorts the permutation. However, studies have shown that some rearrangements are more likely to happen than others, and so a weighted approach is more realistic. In a weighted approach, the goal is to find a sequence which sorts the permutations, such that the cost of that sequence is minimum. This work introduces a new type of cost function, which is related to the amount of fragmentation caused by a rearrangement. We present some results about the lower and upper bounds for the fragmentation-weighted problems and the relation between the unweighted and the fragmentation-weighted approach. Our main results are 2-approximation algorithms for five versions of this problem involving reversals and transpositions. We also give bounds for the diameters concerning these problems and provide an improved approximation factor for simple permutations considering transpositions.

Sorting by Genome Rearrangements on Both Gene Order and Intergenic Sizes.

During the evolutionary process, genomes are affected by various genome rearrangements, that is, events that modify large stretches of the genetic material. In the literature, a large number of models have been proposed to estimate the number of events that occurred during evolution; most of them represent a genome as an ordered sequence of genes, and, in particular, disregard the genetic material between consecutive genes. However, recent studies showed that taking into account the genetic material between consecutive genes can enhance evolutionary distance estimations. Reversal and transposition are genome rearrangements that have been widely studied in the literature. A reversal inverts a (contiguous) segment of the genome, while a transposition swaps the positions of two consecutive segments. Genomes also undergo nonconservative events (events that alter the amount of genetic material) such as insertions and deletions, in which genetic material from intergenic regions of the genome is inserted or deleted, respectively. In this article, we study a genome rearrangement model that considers both gene order and sizes of intergenic regions. We investigate the reversal distance, and also the reversal and transposition distance between two genomes in two scenarios: with and without nonconservative events. We show that these problems are NP-hard and we present constant ratio approximation algorithms for all of them. More precisely, we provide a 4-approximation algorithm for the reversal distance, both in the conservative and nonconservative versions. For the reversal and transposition distance, we provide a 4.5-approximation algorithm, both in the conservative and nonconservative versions. We also perform experimental tests to verify the behavior of our algorithms, as well as to compare the practical and theoretical results. We finally extend our study to scenarios in which events have different costs, and we present constant ratio approximation algorithms for each scenario.

Heuristics for the Reversal and Transposition Distance Problem.

We present three heuristics-Sliding Window, Look Ahead, and Iterative Sliding Window-to improve solutions for the Sorting Signed Permutations by Reversals and Transpositions Problem. We investigate the classical version of the problem as well as versions restricted to prefix and prefix or suffix operations. To assess the heuristics based on its improvement, we implemented algorithms described in the literature to provide initial solutions. Although we have a limited number of problems, these heuristics can be applied to many others within the area of genome rearrangement. When time is a crucial factor, Sliding Window is a better choice because it runs in linear time. If the quality of the solution is a priority, Look Ahead should be preferred. Iterative Sliding Window is the most flexible heuristic and allows us to find a trade-off for specific scenarios where running time and solution quality are relevant.

Super short operations on both gene order and intergenic sizes.

BACKGROUND: The evolutionary distance between two genomes can be estimated by computing a minimum length sequence of operations, called genome rearrangements, that transform one genome into another. Usually, a genome is modeled as an ordered sequence of genes, and most of the studies in the genome rearrangement literature consist in shaping biological scenarios into mathematical models. For instance, allowing different genome rearrangements operations at the same time, adding constraints to these rearrangements (e.g., each rearrangement can affect at most a given number of genes), considering that a rearrangement implies a cost depending on its length rather than a unit cost, etc. Most of the works, however, have overlooked some important features inside genomes, such as the presence of sequences of nucleotides between genes, called intergenic regions. RESULTS AND CONCLUSIONS: In this work, we investigate the problem of computing the distance between two genomes, taking into account both gene order and intergenic sizes. The genome rearrangement operations we consider here are constrained types of reversals and transpositions, called super short reversals (SSRs) and super short transpositions (SSTs), which affect up to two (consecutive) genes. We denote by super short operations (SSOs) any SSR or SST. We show 3-approximation algorithms when the orientation of the genes is not considered when we allow SSRs, SSTs, or SSOs, and 5-approximation algorithms when considering the orientation for either SSRs or SSOs. We also show that these algorithms improve their approximation factors when the input permutation has a higher number of inversions, where the approximation factor decreases from 3 to either 2 or 1.5, and from 5 to either 3 or 2.

On the Complexity of Sorting by Reversals and Transpositions Problems.

In comparative genomics, rearrangements are mutations that affect a stretch of DNA sequences. Reversals and transpositions are well-known rearrangements, and each has a vast literature. The reversal and transposition distance, that is, the minimum number of reversals and transpositions needed to transform one genome into another is a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations was proposed >20 years ago and received the name of sorting by reversals and transpositions problem. It has been the focus of a number of studies, but the computational complexity has remained open until now. We hereby solve this question and prove that it is NP-hard no matter whether genomes are represented by signed or unsigned permutations. In addition, we prove that a usual generalization of this problem, which assigns weights wρ for reversals and wτ for transpositions, is also NP-hard as long as wτ/wρ ≤ 1.5 for both signed and unsigned permutations.