Ruriko Yoshida

Plant-symbiotic fungi as chemical engineers: multi-genome analysis of the clavicipitaceae reveals dynamics of alkaloid loci

The fungal family Clavicipitaceae includes plant symbionts and parasites that produce several psychoactive and bioprotective alkaloids. The family includes grass symbionts in the epichloae clade (Epichloë and Neotyphodium species), which are extraordinarily diverse both in their host interactions and in their alkaloid profiles. Epichloae produce alkaloids of four distinct classes, all of which deter insects, and some—including the infamous ergot alkaloids—have potent effects on mammals. The exceptional chemotypic diversity of the epichloae may relate to their broad range of host interactions, whereby some are pathogenic and contagious, others are mutualistic and vertically transmitted (seed-borne), and still others vary in pathogenic or mutualistic behavior. We profiled the alkaloids and sequenced the genomes of 10 epichloae, three ergot fungi (Claviceps species), a morning-glory symbiont (Periglandula ipomoeae), and a bamboo pathogen (Aciculosporium take), and compared the gene clusters for four classes of alkaloids. Results indicated a strong tendency for alkaloid loci to have conserved cores that specify the skeleton structures and peripheral genes that determine chemical variations that are known to affect their pharmacological specificities. Generally, gene locations in cluster peripheries positioned them near to transposon-derived, AT-rich repeat blocks, which were probably involved in gene losses, duplications, and neofunctionalizations. The alkaloid loci in the epichloae had unusual structures riddled with large, complex, and dynamic repeat blocks. This feature was not reflective of overall differences in repeat contents in the genomes, nor was it characteristic of most other specialized metabolism loci. The organization and dynamics of alkaloid loci and abundant repeat blocks in the epichloae suggested that these fungi are under selection for alkaloid diversification. We suggest that such selection is related to the variable life histories of the epichloae, their protective roles as symbionts, and their associations with the highly speciose and ecologically diverse cool-season grasses.

Effective lattice point counting in rational convex polytopes

Abstract This paper discusses algorithms and software for the enumeration of all lattice points inside a rational convex polytope: we describe LattE , a computer package for lattice point enumeration which contains the first implementation of A. Barvinok’s algorithm (Math. Oper. Res. 19 (1994) 769). We report on computational experiments with multiway contingency tables, knapsack type problems, rational polygons, and flow polytopes. We prove that these kinds of symbolic–algebraic ideas surpass the traditional branch-and-bound enumeration and in some instances LattE is the only software capable of counting. Using LattE , we have also computed new formulas of Ehrhart (quasi-)polynomials for interesting families of polytopes (hypersimplices, truncated cubes, etc). We end with a survey of other “algebraic–analytic” algorithms, including a “homogeneous” variation of Barvinok’s algorithm which is very fast when the number of facet-defining inequalities is much smaller compared to the number of vertices.

A Novel Test for Host-Symbiont Codivergence Indicates Ancient Origin of Fungal Endophytes in Grasses

Significant phylogenetic codivergence between plant or animal hosts (H) and their symbionts or parasites (P) indicates the importance of their interactions on evolutionary time scales. However, valid and realistic methods to test for codivergence are not fully developed. One of the systems where possible codivergence has been of interest involves the large subfamily of temperate grasses (Pooideae) and their endophytic fungi (epichloae). These widespread symbioses often help protect host plants from herbivory and stresses and affect species diversity and food web structures. Here we introduce the MRCALink (most-recent-common-ancestor link) method and use it to investigate the possibility of grass-epichloë codivergence. MRCALink applied to ultrametric H and P trees identifies all corresponding nodes for pairwise comparisons of MRCA ages. The result is compared to the space of random H and P tree pairs estimated by a Monte Carlo method. Compared to tree reconciliation, the method is less dependent on tree topologies (which often can be misleading), and it crucially improves on phylogeny-independent methods such as ParaFit or the Mantel test by eliminating an extreme (but previously unrecognized) distortion of node-pair sampling. Analysis of 26 grass species-epichloë species symbioses did not reject random association of H and P MRCA ages. However, when five obvious host jumps were removed, the analysis significantly rejected random association and supported grass-endophyte codivergence. Interestingly, early cladogenesis events in the Pooideae corresponded to early cladogenesis events in epichloae, suggesting concomitant origins of this grass subfamily and its remarkable group of symbionts. We also applied our method to the well-known gopher-louse data set.

Short rational functions for toric algebra and applications

Abstract We encode the binomials belonging to the toric ideal I A associated with an integral d × n matrix A using a short sum of rational functions as introduced by Barvinok (Math. Operations Research 19 (1994) 769) and Barvinok and Woods (J. Amer. Math. Soc. 16 (2003) 957). Under the assumption that d and n are fixed, this representation allows us to compute a universal Grobner basis and the reduced Grobner basis of the ideal I A , with respect to any term order, in time polynomial in the size of the input. We also derive a polynomial time algorithm for normal form computations which replaces in this new encoding the usual reductions typical of the division algorithm. We describe other applications, such as the computation of Hilbert series of normal semigroup rings, and we indicate applications to enumerative combinatorics, integer programming, and statistics.

On connectivity of fibers with positive marginals in multiple logistic regression

In this paper we consider exact tests of a multiple logistic regression with categorical covariates via Markov bases. In many applications of multiple logistic regression, the sample size is positive for each combination of levels of the covariates. In this case we do not need a whole Markov basis, which guarantees connectivity of all fibers. We first give an explicit Markov basis for multiple Poisson regression. By the Lawrence lifting of this basis, in the case of bivariate logistic regression, we show a simple subset of the Markov basis which connects all fibers with a positive sample size for each combination of levels of covariates.

Indispensable monomials of toric ideals and Markov bases

Extending the notion of indispensable binomials of a toric ideal [Takemura, Akimichi, Aoki, Satoshi, 2004. Some characterizations of minimal Markov basis for sampling from discrete conditional distributions. Ann. Inst. Statist. Math. 56 (1), 1-17; Ohsugi, Hidefumi, Hibi, Takayuki, 2005. Indispensable binomials of finite graphs. J. Algebra Appl. 4 (4), 421-434], we define indispensable monomials of a toric ideal and establish some of their properties. They are useful for searching indispensable binomials of a toric ideal and for proving the existence or non-existence of a unique minimal system of binomial generators of a toric ideal. Some examples of indispensable monomials from statistical models for contingency tables are given.

Approximate Techniques in Solving Optimal Camera Placement Problems

While the theoretical foundation of the optimal camera placement problem has been studied for decades, its practical implementation has recently attracted significant research interest due to the increasing popularity of visual sensor networks. The most flexible formulation of finding the optimal camera placement is based on a binary integer programming (BIP) problem. Despite the flexibility, most of the resulting BIP problems are NP-hard and any such formulations of reasonable size are not amenable to exact solutions. There exists a myriad of approximate algorithms for BIP problems, but their applications, efficiency, and scalability in solving camera placement are poorly understood. Thus, we develop a comprehensive framework in comparing the merits of a wide variety of approximate algorithms in solving the optimal camera placement problems. We first present a general approach of adapting these problems into BIP formulations. Then, we demonstrate how they can be solved using different approximate algorithms including greedy heuristics, Markov-chain Monte Carlo, simulated annealing, and linear and semidefinite programming relaxations. The accuracy, efficiency, and scalability of each technique are analyzed and compared in depth. Extensive experimental results are provided to illustrate the strength and weakness of each method.

A generating function for all semi-magic squares and the volume of the Birkhoff polytope

We present a multivariate generating function for all n×n nonnegative integral matrices with all row and column sums equal to a positive integer t, the so called semi-magic squares. As a consequence we obtain formulas for all coefficients of the Ehrhart polynomial of the polytope Bn of n×n doubly-stochastic matrices, also known as the Birkhoff polytope. In particular we derive formulas for the volumes of Bn and any of its faces.

Markov bases for two-way subtable sum problems

Abstract It is well known that for two-way contingency tables with fixed row sums and column sums the set of square-free moves of degree two forms a Markov basis. However when we impose an additional constraint that the sum of cell counts in a subtable is also fixed, then these moves do not necessarily form a Markov basis. Thus, in this paper, we show a necessary and sufficient condition on a subtable so that the set of square-free moves of degree two forms a Markov basis.

Optimality of the Neighbor Joining Algorithm and Faces of the Balanced Minimum Evolution Polytope

Balanced minimum evolution (BME) is a statistically consistent distance-based method to reconstruct a phylogenetic tree from an alignment of molecular data. In 2000, Pauplin showed that the BME method is equivalent to optimizing a linear functional over the BME polytope, the convex hull of the BME vectors obtained from Pauplin’s formula applied to all binary trees. The BME method is related to the Neighbor Joining (NJ) Algorithm, now known to be a greedy optimization of the BME principle. Further, the NJ and BME algorithms have been studied previously to understand when the NJ Algorithm returns a BME tree for small numbers of taxa. In this paper we aim to elucidate the structure of the BME polytope and strengthen knowledge of the connection between the BME method and NJ Algorithm. We first prove that any subtree-prune-regraft move from a binary tree to another binary tree corresponds to an edge of the BME polytope. Moreover, we describe an entire family of faces parameterized by disjoint clades. We show that these clade-faces are smaller dimensional BME polytopes themselves. Finally, we show that for any order of joining nodes to form a tree, there exists an associated distance matrix (i.e., dissimilarity map) for which the NJ Algorithm returns the BME tree. More strongly, we show that the BME cone and every NJ cone associated to a tree T have an intersection of positive measure.