Using Genetic Algorithm to solve Median Problem and Phylogenetic Inference

Genome rearrangement analysis has attracted a lot of attentions in phylogenetic com- putation and comparative genomics. Solving the median problems based on various distance definitions has been a focus as it provides the building blocks for maximum parsimony analysis of phylogeny and ancestral genomes. The Median Problem (MP) has been proved to be NP-hard and although there are several exact or heuristic al- gorithms available, these methods all are difficulty to compute distant three genomes containing high evolution events. Such as current approaches, MGR[1] and GRAPPA [2], are restricted on small collections of genomes and low-resolution gene order data of a few hundred rearrangement events. In my work, we focus on heuristic algorithms which will combine genomic sorting algorithm with genetic algorithm (GA) to pro- duce new methods and directions for whole-genome median solver, ancestor inference and phylogeny reconstruction. In equal median problem, we propose a DCJ sorting operation based genetic algorithms measurements, called GA-DCJ. Following classic genetic algorithm frame, we develop our algorithms for every procedure and substitute for each traditional genetic algorithm procedure. The final results of our GA-based algorithm are optimal median genome(s) and its median score. In limited time and space, especially in large scale and distant datasets, our algorithm get better results compared with GRAPPA and AsMedian. Extending the ideas of equal genome median solver, we develop another genetic algorithm based solver, GaDCJ-Indel, which can solve unequal genomes median prob- lem (without duplication). In DCJ-Indel model, one of the key steps is still sorting operation[3]. The difference with equal genomes median is there are two sorting di- rections: minimal DCJ operation path or minimal indel operation path. Following different sorting path, in each step scenario, we can get various genome structures to fulfill our population pool. Besides that, we adopt adaptive surcharge-triangle inequality instead of classic triangle inequality in our fitness function in order to fit unequal genome restrictions and get more efficient results. Our experiments results show that GaDCJ-Indel method not only can converge to accurate median score, but also can infer ancestors that are very close to the true ancestors. An important application of genome rearrangement analysis is to infer ancestral genomes, which is valuable for identifying patterns of evolution and for modeling the evolutionary processes. However, computing ancestral genomes is very difficult and we have to rely on heuristic methods that have various limitations. We propose a GA-Tree algorithm which adapts meta-population [4], co-evolution and repopulation pool methods In this paper, we describe and illuminate the first genetic algorithm for ancestor inference step by step, which uses fitness scores designed to consider co- evolution and uses sorting-based methods to initialize and evolve populations. Our extensive experiments show that compared with other existing tools, our method is accurate and can infer ancestors that are much closer to true ancestors

Phylogenetic reconstruction from transpositions

Background Because of the advent of high-throughput sequencing and the consequent reduction in the cost of sequencing, many organisms have been completely sequenced and most of their genes identified. It thus has become possible to represent whole genomes as ordered lists of gene identifiers and to study the rearrangement of these entities through computational means. As a result, genome rearrangement data has attracted increasing attentions from both biologists and computer scientists as a new type of data for phylogenetic analysis. The main events of genome rearrangements include inversions, transpositions and transversions. To date, GRAPPA and MGR are the most accurate methods for rearrangement phylogeny, both assuming inversion as the only event. However, due to the complexity of computing transposition distance, it is very difficult to analyze datasets when transpositions are dominant. Results We extend GRAPPA to handle transpositions. The new method is named GRAPPA-TP, with two major extensions: a heuristic method to estimate transposition distance, and a new transposition median solver for three genomes. Although GRAPPA-TP uses a greedy approach to compute the transposition distance, it is very accurate when genomes are relatively close. The new GRAPPA-TP is available from http://phylo.cse.sc.edu/ Conclusion Our extensive testing using simulated datasets shows that GRAPPA-TP is very accurate in terms of ancestor genome inference and phylogenetic reconstruction. Simulation results also suggest that model match is critical in genome rearrangement analysis: it is not accurate to simulate transpositions with other events including inversions

Heuristics for the inversion median problem

Background: The study of genome rearrangements has become a mainstay of phylogenetics and comparative genomics. Fundamental in such a study is the median problem: given three gene arrangements, find a fourth that minimizes the sum of the evolutionary distances between itself and the given three. Many exact algorithms and heuristics have been developped for the inversion median problem, of which the best known is MGR. Results: We present a unifying framework for median heuristics, which enables us to clarify existing strategies and to place them in a partial ordering. Analysis of this framework leads to a new insight: the best strategies continue to refer to the input data rather than just to updated estimates. Using this insight, we develop a new heuristic for inversion medians that uses input data to the end of its computation and leverages our previous work with DCJ medians. Finally, we present the results of extensive experimentation showing that our new heuristic outperforms all others in accuracy and, especially, in running time: the heuristic typically returns solutions within 1 % of optimal and runs in seconds to minutes even on genomes with 25’000 genes—in contrast, MGR can take days on instances of 200 genes and cannot be used beyond 1’000 genes. Conclusions: Finding good rearrangement medians, in particular inversion medians, had long been regarded as the computational bottleneck in whole-genome studies. Our new heuristic for inversion medians, ASM, which dominates all others in our framework, puts that issue to rest by providing near-optimal solutions within seconds to minutes on even the largest genomes

Phylogenetic Reconstruction Analysis on Gene Order and Copy Number Variation

Genome rearrangement is known as one of the main evolutionary mechanisms on the genomic level. Phylogenetic analysis based on rearrangement played a crucial role in biological research in the past decades, especially with the increasing avail- ability of fully sequenced genomes. In general, phylogenetic analysis aims to solve two problems: Small Parsimony Problem (SPP) and Big Parsimony Problem (BPP). Maximum parsimony is a popular approach for SPP and BPP which relies on itera- tively solving a NP-hard problem, the median problem. As a result, current median solvers and phylogenetic inference methods based on the median problem all face se- rious problems on scalability and cannot be applied to datasets with large and distant genomes. In this thesis, we propose a new median solver for gene order data that combines double-cut-join (DCJ) sorting with the Simulated Annealing algorithm (SA- Median). Based on this median solver, we built a new phylogenetic inference method to solve both SPP and BPP problems. Our experimental results show that the new median solver achieves an excellent performance on simulated datasets and the phylo- genetic inference tool built based on the new median solver has a better performance than other existing methods. Cancer is known for its heterogeneity and is regarded as an evolutionary process driven by somatic mutations and clonal expansions. This evolutionary process can be modeled by a phylogenetic tree and phylogenetic analysis of multiple subclones of cancer cells can facilitate the study of the tumor variants progression. Copy-number aberration occurs frequently in many types of tumors in terms of segmental ampli- fications and deletions. In this thesis, we developed a distance-based method for reconstructing phylogenies from copy-number profiles of cancer cells. We demon- strate the importance of distance correction from the edit (minimum) distance to the estimated actual number of events. Experimental results show that our approaches provide accurate and scalable results in estimating the actual number of evolutionary events between copy number profiles and in reconstructing phylogenies. High-throughput sequencing of tumor samples has reported various degrees of ge- netic heterogeneity between primary tumors and their distant subpopulations. The clonal theory of cancer evolution shows that tumor cells are descended from a common origin cell. This origin cell includes an advantageous mutation that cause a clonal expansion with a large amount of population of cells descended from the origin cell. To further investigate cancer progression, phylogenetic analysis on the tumor cells is imperative. In this thesis, we developed a novel approach to infer the phylogeny to analyze both Next-Generation Sequencing and Long-Read Sequencing data. Experi- mental results show that our new proposed method can infer the entire phylogenetic progression very accurately on both Next-Generation Sequencing and Long-Read Se- quencing data. In this thesis, we focused on phylogenetic analysis on both gene order sequence and copy number variations. Our thesis work can be categorized into three parts. First, we developed a new median solver to solve the median problem and phylogeny inference with DCJ model and apply our method to both simulated data and real yeast data. Second, we explored a new approach to infer the phylogeny of copy number profiles for a wide range of parameters (e.g., different number of leaf genomes, different number of positions in the genome, and different tree diameters). Third, we concentrated our work on the phylogeny inference on the high-throughput sequencing data and proposed a novel approach to further investigate and phylogenetic analyze the entire expansion process of cancer cells on both Next-Generation Sequencing and Long-Read Sequencing data

Phylogeny and Ancestral Genome Reconstruction from Gene Order Using Maximum Likelihood and Binary Encoding

Over the long history of genome evolution, genes get rearranged under events such as rearrangements, losses, insertions and duplications, which in all change the ordering and content along the genome. Recent progress in genome-scale sequencing renews the challenges in the reconstructions of phylogeny and ancestral genomes with gene-order data. Such problems have been proved so interesting that a large number of algorithms have been developed rigorously over the past few years in attempts to tackle these problems following various principles. However, difficulties and limitations in performance and scalability largely prevent us from analyzing emerging modern whole-genome data, our study presented in this dissertation focuses on developing appropriate evolutionary models and robust algorithms for solving the phylogenetic and ancestral inference problems using gene-order data under the whole-genome evolution, along with their applications. To reconstruct phylogenies from gene-order data, we developed a collection of closely-related methods following the principle of likelihood maximization. To the best of our knowledge, it was the first successful attempt to apply maximum likelihood optimization technique into the analysis of gene-order phylogenetic problem. Later we proposed MLWD (in collaboration with Lin and Moret) in which we described an effective transition model to account for the transitions between presence and absence states of an gene adjacency. Besides genome rearrangements, other evolutionary events modify gene contents such as gene duplications and gene insertion/deletion (indels) can be naturally processed as well. We present our results from extensive testing on simulated data showing that our approach returns very accurate results very quickly. With a known phylogeny, a subsequent problem is to reconstruct the gene-order of ancestral genomes from their living descendants. To solve this problem, we adopted an adjacency-based probabilistic framework, and developed a method called PMAG. PMAG decomposes gene orderings into a set of gene adjacencies and then infers the probability of observing each adjacency in the ancestral genome. We conducted extensive simulation experiments and compared PMAG with InferCarsPro, GASTS, GapAdj and SCJ. According to the results, PMAG demonstrated great performance in terms of the true positive rate of gene adjacency. PMAG also achieved comparable running time to the other methods, even when the traveling sales man problem (TSP) were exactly solved. Although PMAG can give good performance, it is strongly restricted from analyzing datasets underwent only rearrangements. To infer ancestral genomes under a more general model of evolution with an arbitrary rate of indels , we proposed an enhanced method PMAG+ based on PMAG. PMAG+ includes a novel approach to infer ancestral gene contents and a detail description to reduce the adjacency assembly problem to an instance of TSP. We designed a series of experiments to validate PMAG+ and compared the results with the most recent and comparable method GapAdj. According to the results, ancestral gene contents predicted by PMAG+ coincided highly with the actual contents with error rates less than 1%. Under various degrees of indels, PMAG+ consistently achieved more accurate prediction of ancestral gene orders and at the same time, produced contigs very close to the actual chromosomes

Streaming Breakpoint Graph Analytics for Accelerating and Parallelizing the Computation of DCJ Median of Three Genomes

AbstractThe problem of finding the median of three genomes is the key process in building the most parsimonious phylogenetic trees from genome rearrangement data. The median problem using Double-Cut-and-Join (DCJ) distance is NP-hard and the best exact algorithm is based on a branch-and-bound best-first search strategy to explore sub-graph patterns in Multiple BreakPoint Graph (MBG). In this paper, by taking advantage of the “streaming” property of MBG, we introduce the “footprint-based” data structure to reduce the space requirement of a single search nodes from O(v2) to O(v); minimize the redundant computation in counting cycles/paths to update bounds, which leads to dramatically decrease of workload of a single search node. Additional heuristic of branching strategy is introduced to help reducing the searching space. Last but not least, the introduction of a multi-thread shared memory parallel algorithm with two load balancing strategies bring in additional benefit by distributing search work efficiently among different processors. We conduct extensive experiments on simulated datasets and our results show significant improvement on all datasets. And we test our DCJ median algorithm with GASTS, a state of the art software phylogenetic tree construction package. On the real high resolution Drosophila data set, our exact algorithm run as fast as the heuristic algorithm and help construct a better phylogenetic tree

Robustness Evaluation for Phylogenetic Reconstruction Methods and Evolutionary Models Reconstruction of Tumor Progression

During evolutionary history, genomes evolve by DNA mutation, genome rearrangement, duplication and gene loss events. There has been endless effort to the phylogenetic and ancestral genome inference study. Due to the great development of various technology, the information about genomes is exponentially increasing, which make it possible figure the problem out. The problem has been shown so interesting that a great number of algorithms have been developed rigorously over the past decades in attempts to tackle these problems following different kind of principles. However, difficulties and limits in performance and capacity, and also low consistency largely prevent us from confidently statement that the problem is solved. To know the detailed evolutionary history, we need to infer the phylogeny of the evolutionary history (Big Phylogeny Problem) and also infer the internal nodes information (Small Phylogeny Problem). The work presented in this thesis focuses on assessing methods designed for attacking Small Phylogeny Problem and algorithms and models design for genome evolution history inference from FISH data for cancer data. During the recent decades, a number of evolutionary models and related algorithms have been designed to infer ancestral genome sequences or gene orders. Due to the difficulty of knowing the true scenario of the ancestral genomes, there must be some tools used to test the robustness of the adjacencies found by various methods. When it comes to methods for Big Phylogeny Problem, to test the confidence rate of the inferred branches, previous work has tested bootstrapping, jackknifing, and isolating and found them good resampling tools to corresponding phylogenetic inference methods. However, till now there is still no system work done to try and tackle this problem for small phylogeny. We tested the earlier resampling schemes and a new method inversion on different ancestral genome reconstruction methods and showed different resampling methods are appropriate for their corresponding methods. Cancer is famous for its heterogeneity, which is developed by an evolutionary process driven by mutations in tumor cells. Rapid, simultaneous linear and branching evolution has been observed and analyzed by earlier research. Such process can be modeled by a phylogenetic tree using different methods. Previous phylogenetic research used various kinds of dataset, such as FISH data, genome sequence, and gene order. FISH data is quite clean for the reason that it comes form single cells and shown to be enough to infer evolutionary process for cancer development. RSMT was shown to be a good model for phylogenetic analysis by using FISH cell count pattern data, but it need efficient heuristics because it is a NP-hard problem. To attack this problem, we proposed an iterative approach to approximate solutions to the steiner tree in the small phylogeny tree. It is shown to give better results comparing to earlier method on both real and simulation data. In this thesis, we continued the investigation on designing new method to better approximate evolutionary process of tumor and applying our method to other kinds of data such as information using high-throughput technology. Our thesis work can be divided into two parts. First, we designed new algorithms which can give the same parsimony tree as exact method in most situation and modified it to be a general phylogeny building tool. Second, we applied our methods to different kinds data such as copy number variation information inferred form next generation sequencing technology and predict key changes during evolution