The discretizable molecular distance geometry problem is easier on proteins
نویسندگان
چکیده
Distance geometry methods are used to turn a set of interatomic distances given by NMR experiments into a consistent molecular conformation. In a set of papers (see the survey [8]) we proposed a Branch-and-Prune (BP) algorithm for computing the set X of all incongruent embeddings of a given protein backbone. Although BP has a worst-case exponential running time in general, we always noticed a linear-like behaviour in computational experiments. In this paper we provide a theoretical explanation to our observations. We show that the BP is fixed-parameter tractable on protein-like graphs, and empirically show that the parameter is constant on a set of proteins from the Protein Data Bank.
منابع مشابه
A Clifford Algebra approach to the Discretizable Molecular Distance Geometry Problem
The Discretizable Molecular Distance Geometry Problem (DMDGP) consists in a subclass of the Molecular Distance Geometry Problem for which an embedding in R can be found using a Branch & Prune (BP) algorithm in a discrete search space. We propose a Clifford Algebra model of the DMDGP with an accompanying version of the BP algorithm.
متن کاملOn the Number of Solutions of the Discretizable Molecular Distance Geometry Problem
The Generalized Discretizable Molecular Distance Geometry Problem is a distance geometry problems that can be solved by a combinatorial algorithm called “Branch-and-Prune”. It was observed empirically that the number of solutions of YES instances is always a power of two. We give a proof that this event happens with probability one.
متن کاملThe discretizable distance geometry problem
We introduce the Discretizable Distance Geometry Problem in R (DDGP3), which consists in a subclass of instances of the Distance Geometry Problem for which an embedding in R can be found by means of a discrete search. We show that the DDGP3 is a generalization of the Discretizable Molecular Distance Geometry Problem (DMDGP), and we discuss the main differences between the two problems. We prove...
متن کاملRecent advances on the Discretizable Molecular Distance Geometry Problem
The Molecular Distance Geometry Problem (MDGP) consists in finding an embedding in R of a nonnegatively weighted simple undirected graph with the property that the Euclidean distances between embedded adjacent vertices must be the same as the corresponding edge weights. The Discretizable Molecular Distance Geometry Problem (DMDGP) is a particular subset of the MDGP which can be solved using a d...
متن کاملAn exponential algorithm for the Discretizable Molecular Distance Geometry Problem is polynomial on proteins
An important application of distance geometry to biochemistry studies the embeddings of the vertices of a weighted graph in the three-dimensional Euclidean space such that the edge weights are equal to the Euclidean distances between corresponding point pairs. When the graph represents the backbone of a protein, one can exploit the natural vertex order to show that the search space for feasible...
متن کامل