Sequence Length Requirements Research Articles

A Versatile in Vivo DNA Assembly Toolbox for Fungal Strain Engineering.

Efficient homologous recombination in baker’s yeast allows accurate fusion of DNA fragments via short identical sequence tags in vivo. Eliminating the need for an Escherichia coli cloning step speeds up genetic engineering of this yeast and sets the stage for large high-throughput projects depending on DNA construction. With the aim of developing similar tools for filamentous fungi, we first set out to determine the genetic- and sequence-length requirements needed for efficient fusion reactions, and demonstrated that in nonhomologous end-joining deficient strains of Aspergillus nidulans, efficient fusions can be achieved by 25 bp sequence overlaps. Based on these results, we developed a novel fungal in vivo DNA assembly toolbox for simple and flexible genetic engineering of filamentous fungi. Specifically, we have used this method for construction of AMA1-based vectors, complex gene-targeting substrates for gene deletion and gene insertion, and for marker-free CRISPR based gene editing. All reactions were done via single-step transformations involving fusions of up to six different DNA fragments. Moreover, we show that it can be applied in four different species of Aspergilli. We therefore envision that in vivo DNA assembly can be advantageously used for many more purposes and will develop into a popular tool for fungal genetic engineering.

Phase transition in the sample complexity of likelihood-based phylogeny inference

Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical physics and that connection has led to important insights on the theoretical properties of phylogenetic reconstruction algorithms as well as the development of new inference methods. Here, we study maximum likelihood, a classical statistical technique which is perhaps the most widely used in phylogenetic practice because of its superior empirical accuracy. At the theoretical level, except for its consistency, that is, the guarantee of eventual correct reconstruction as the size of the input data grows, much remains to be understood about the statistical properties of maximum likelihood in this context. In particular, the best bounds on the sample complexity or sequence-length requirement of maximum likelihood, that is, the amount of data required for correct reconstruction, are exponential in the number, n, of tips—far from known lower bounds based on information-theoretic arguments. Here we close the gap by proving a new upper bound on the sequence-length requirement of maximum likelihood that matches up to constants the known lower bound for some standard models of evolution. More specifically, for the r-state symmetric model of sequence evolution on a binary phylogeny with bounded edge lengths, we show that the sequence-length requirement behaves logarithmically in n when the expected amount of mutation per edge is below what is known as the Kesten-Stigum threshold. In general, the sequence-length requirement is polynomial in n. Our results imply moreover that the maximum likelihood estimator can be computed efficiently on randomly generated data provided sequences are as above. Our main technical contribution, which may be of independent interest, relates the total variation distance between the leaf state distributions of two trees with a notion of combinatorial distance between the trees. In words we show in a precise quantitative manner that the more different two evolutionary trees are, the easier it is to distinguish their output.

Alignment-free phylogenetic reconstruction: Sample complexity via a branching process analysis

We present an efficient phylogenetic reconstruction algorithm allowing insertions and deletions which provably achieves a sequence-length requirement (or sample complexity) growing polynomially in the number of taxa. Our algorithm is distance-based, that is, it relies on pairwise sequence comparisons. More importantly, our approach largely bypasses the difficult problem of multiple sequence alignment.

Phylogenetic mixtures: Concentration of measure in the large-tree limit

The reconstruction of phylogenies from DNA or protein sequences is a major task of computational evolutionary biology. Common phenomena, notably variations in mutation rates across genomes and incongruences between gene lineage histories, often make it necessary to model molecular data as originating from a mixture of phylogenies. Such mixed models play an increasingly important role in practice. Using concentration of measure techniques, we show that mixtures of large trees are typically identifiable. We also derive sequence-length requirements for high-probability reconstruction.

The impact and interplay of long and short branches on phylogenetic information content

In molecular systematics, evolutionary trees are reconstructed from sequences at the tips under simple models of site substitution. A central question is how much sequence data is required to reconstruct a tree accurately? The answer depends on the lengths of the branches (edges) of the tree, with very short and very long edges requiring long sequences for accurate tree inference, particularly when these branch lengths are arranged in certain ways. For four-taxon trees, the sequence length question has been investigated for the case of a rapid speciation event in the distant past. Here, we generalize results from this earlier study, and show that the same sequence length requirement holds even when the speciation event is recent, provided that at least one of the four taxa is distantly related to the others. However, this equivalence disappears if a molecular clock applies, since the length of the long outgroup edge becomes largely irrelevant in the estimation of the tree topology for a recent divergence. We also discuss briefly some extensions of these results to models in which substitution rates vary across sites and to settings where more than four taxa are involved.

Identifiability and inference of non-parametric rates-across-sites models on large-scale phylogenies

Mutation rate variation across loci is well known to cause difficulties, notably identifiability issues, in the reconstruction of evolutionary trees from molecular sequences. Here we introduce a new approach for estimating general rates-across-sites models. Our results imply, in particular, that large phylogenies are typically identifiable under rate variation. We also derive sequence-length requirements for high-probability reconstruction. Our main contribution is a novel algorithm that clusters sites according to their mutation rate. Following this site clustering step, standard reconstruction techniques can be used to recover the phylogeny. Our results rely on a basic insight: that, for large trees, certain site statistics experience concentration-of-measure phenomena.

Fast Phylogeny Reconstruction Through Learning of Ancestral Sequences

Given natural limitations on the length DNA sequences, designing phylogenetic reconstruction methods which are reliable under limited information is a crucial endeavor. There have been two approaches to this problem: reconstructing partial but reliable information about the tree (Mossel in IEEE Comput. Biol. Bioinform. 4:108–116, 2007; Daskalakis et al. in SIAM J. Discrete Math. 25:872–893, 2011; Daskalakis et al. in Proc. of RECOMB 2006, pp. 281–295, 2006; Gronau et al. in Proc. of the 19th Annual SODA 2008, pp. 379–388, 2008), and reaching “deeper” in the tree through reconstruction of ancestral sequences. In the latter category, Daskalakis et al. (Proc. of the 38th Annual STOC, pp. 159–168, 2006) settled an important conjecture of M. Steel (My favourite conjecture. Preprint, 2001), showing that, under the CFN model of evolution, all trees on n leaves with edge lengths bounded by the Ising model phase transition can be recovered with high probability from genomes of length O(logn) with a polynomial time algorithm. Their methods had a running time of O(n 10). Here we enhance our methods from Daskalakis et al. (Proc. of RECOMB 2006, pp. 281–295, 2006) with the learning of ancestral sequences and provide an algorithm for reconstructing a sub-forest of the tree which is reliable given available data, without requiring a-priori known bounds on the edge lengths of the tree. Our methods are based on an intuitive minimum spanning tree approach and run in O(n 3) time. For the case of full reconstruction of trees with edges under the phase transition, we maintain the same asymptotic sequence length requirements as in Daskalakis et al. (Proc. of the 38th Annual STOC, pp. 159–168, 2006), despite the considerably faster running time.

On the Inference of Large Phylogenies with Long Branches: How Long Is Too Long?

The accurate reconstruction of phylogenies from short molecular sequences is an important problem in computational biology. Recent work has highlighted deep connections between sequence-length requirements for high-probability phylogeny reconstruction and the related problem of the estimation of ancestral sequences. In Daskalakis et al. (in Probab. Theory Relat. Fields 2010), building on the work of Mossel (Trans. Am. Math. Soc. 356(6):2379-2404, 2004), a tight sequence-length requirement was obtained for the simple CFN model of substitution, that is, the case of a two-state symmetric rate matrix Q. In particular the required sequence length for high-probability reconstruction was shown to undergo a sharp transition (from O(log n) to poly(n), where n is the number of leaves) at the "critical" branch length g (ML)(Q) (if it exists) of the ancestral reconstruction problem defined roughly as follows: below g (ML)(Q) the sequence at the root can be accurately estimated from sequences at the leaves on deep trees, whereas above g (ML)(Q) information decays exponentially quickly down the tree.Here, we consider a more general evolutionary model, the GTR model, where the q×q rate matrix Q is reversible with q≥2. For this model, recent results of Roch (Preprint, 2009) show that the tree can be accurately reconstructed with sequences of length O(log (n)) when the branch lengths are below g (Lin)(Q), known as the Kesten-Stigum (KS) bound, up to which ancestral sequences can be accurately estimated using simple linear estimators. Although for the CFN model g (ML)(Q)=g (Lin)(Q) (in other words, linear ancestral estimators are in some sense best possible), it is known that for the more general GTR models one has g (ML)(Q)≥g (Lin)(Q) with a strict inequality in many cases. Here, we show that this phenomenon also holds for phylogenetic reconstruction by exhibiting a family of symmetric models Q and a phylogenetic reconstruction algorithm which recovers the tree from O(log n)-length sequences for some branch lengths in the range (g (Lin)(Q),g (ML)(Q)). Second, we prove that phylogenetic reconstruction under GTR models requires a polynomial sequence-length for branch lengths above g (ML)(Q).

Sequence length bounds for resolving a deep phylogenetic divergence

In evolutionary biology, genetic sequences carry with them a trace of the underlying tree that describes their evolution from a common ancestral sequence. The question of how many sequence sites are required to recover this evolutionary relationship accurately depends on the model of sequence evolution, the substitution rate, divergence times and the method used to infer phylogenetic history. A particularly challenging problem for phylogenetic methods arises when a rapid divergence event occurred in the distant past. We analyse an idealised form of this problem in which the terminal edges of a symmetric four-taxon tree are some factor ( λ ) times the length of the interior edge. We determine an order λ 2 lower bound on the growth rate for the sequence length required to resolve the tree (independent of any particular branch length). We also show that this rate of sequence length growth can be achieved by existing methods (including the simple ‘maximum parsimony’ method), and compare these order λ 2 bounds with an order λ growth rate for a model that describes low-homoplasy evolution. In the final section, we provide a generic bound on the sequence length requirement for a more general class of Markov processes.

Nucleotide synthetase ribozymes may have emerged first in the RNA world

Though the "RNA world" hypothesis has gained a central role in ideas concerning the origin of life, the scenario concerning its emergence remains uncertain. It has been speculated that the first scene may have been the emergence of a template-dependent RNA synthetase ribozyme, which catalyzed its own replication: thus, "RNA replicase." However, the speculation remains uncertain, primarily because of the large sequence length requirement of such a replicase and the lack of a convincing mechanism to ensure its self-favoring features. Instead, we propose a nucleotide synthetase ribozyme as an alternative candidate, especially considering recent experimental evidence suggesting the possibility of effective nonenzymatic template-directed synthesis of RNA. A computer simulation was conducted to support our proposal. The conditions for the emergence of the nucleotide synthetase ribozyme are discussed, based on dynamic analysis on a computer. We suggest the template-dependent RNA synthetase ribozyme emerged later, perhaps after the emergence of protocells.