17 research outputs found
New error measures and methods for realizing protein graphs from distance data
The interval Distance Geometry Problem (iDGP) consists in finding a
realization in of a simple undirected graph with
nonnegative intervals assigned to the edges in such a way that, for each edge,
the Euclidean distance between the realization of the adjacent vertices is
within the edge interval bounds. In this paper, we focus on the application to
the conformation of proteins in space, which is a basic step in determining
protein function: given interval estimations of some of the inter-atomic
distances, find their shape. Among different families of methods for
accomplishing this task, we look at mathematical programming based methods,
which are well suited for dealing with intervals. The basic question we want to
answer is: what is the best such method for the problem? The most meaningful
error measure for evaluating solution quality is the coordinate root mean
square deviation. We first introduce a new error measure which addresses a
particular feature of protein backbones, i.e. many partial reflections also
yield acceptable backbones. We then present a set of new and existing quadratic
and semidefinite programming formulations of this problem, and a set of new and
existing methods for solving these formulations. Finally, we perform a
computational evaluation of all the feasible solverformulation combinations
according to new and existing error measures, finding that the best methodology
is a new heuristic method based on multiplicative weights updates
A study on the impact of the distance types involved in protein structure determination by NMR
International audienceThe Distance Geometry Problem (DGP) consists of finding the coordinates of a given set of points where the distances between some pairs of points are known. The DGP has several applications and one of the most relevant ones arises in the context of structural biology, where NMR experiments are performed to estimate distances between some atom pairs in a given molecule, and the possible conformations for the molecule are calculated through the formulation and the solution of a DGP. We focus our attention on DGP instances for which some special assumptions allow us to discretize the DGP search space and to potentially perform the complete enumeration of the solution set. We refer to the subclass of DGP instances satisfying such discretizability assumptions as the Discretizable DGP (DDGP). In this context, we propose a new procedure for the generation of DDGP instances where real data and simulated data (from known molecular models) can coexist. Our procedure can give rise to peculiar DDGP instances that we use for studying the impact of every distance type, involved in NMR protein structure determination, on the quality of the found solutions. Surprisingly, our experiments suggest that the distance types implying a larger effect on the solution quality are not the ones related to NMR data, but rather the more abundant, but much less informative, van der Waals distance type
Euclidean distance geometry and applications
Euclidean distance geometry is the study of Euclidean geometry based on the
concept of distance. This is useful in several applications where the input
data consists of an incomplete set of distances, and the output is a set of
points in Euclidean space that realizes the given distances. We survey some of
the theory of Euclidean distance geometry and some of the most important
applications: molecular conformation, localization of sensor networks and
statics.Comment: 64 pages, 21 figure
An algorithm to enumerate all possible protein conformations verifying a set of distance constraints
Discretization orders for distance geometry problems
Fundação de Amparo Ă Pesquisa do Estado de SĂŁo Paulo (FAPESP)Conselho Nacional de Desenvolvimento CientĂfico e TecnolĂłgico (CNPq)Given a weighted, undirected simple graph G = (V, E, d) (where d : E -> R+), the distance geometry problem (DGP) is to determine an embedding x : V -> R-K such that for all{i, j} is an element of E parallel to x(i) - x(j)parallel to = d(ij). Although, in general, the DGP is solved using continuous methods, under certain conditions the search is reduced to a discrete set of points. We give one such condition as a particular order on V. We formalize the decision problem of determining whether such an order exists for a given graph and show that this problem is NP-complete in general and polynomial for fixed dimension K. We present results of computational experiments on a set of protein backbones whose natural atomic order does not satisfy the order requirements and compare our approach with some available continuous space searches.64783796Fundação de Amparo Ă Pesquisa do Estado de SĂŁo Paulo (FAPESP)Conselho Nacional de Desenvolvimento CientĂfico e TecnolĂłgico (CNPq)Fundação de Amparo Ă Pesquisa do Estado de SĂŁo Paulo (FAPESP)Conselho Nacional de Desenvolvimento CientĂfico e TecnolĂłgico (CNPq
Discretization Orders for Distance Geometry Problems
International audienceGiven a weighted, undirected simple graph G = (V,E,d) the Distance Geometry Problem (DGP) consists in determining an embedding x such that for each (i,j) in E ||xi - xj|| = d(i,j) . Although in general the DGP is solved using continuous methods, under certain conditions the search is reduced to a discrete set of points. We give one such condition as a particular order on V. We formalize the decision problem of determining whether such an order exists for a given graph and show that this problem is NP-complete in general and polynomial for fixed K. We exhibit computational experiments on a set of proteins whose natural atomic order does not satisfy the order requirements, and compare our approach with some available continuous space searches