54 research outputs found
Dynamics based alignment of proteins: an alternative approach to quantify dynamic similarity
<p>Abstract</p> <p>Background</p> <p>The dynamic motions of many proteins are central to their function. It therefore follows that the dynamic requirements of a protein are evolutionary constrained. In order to assess and quantify this, one needs to compare the dynamic motions of different proteins. Comparing the dynamics of distinct proteins may also provide insight into how protein motions are modified by variations in sequence and, consequently, by structure. The optimal way of comparing complex molecular motions is, however, far from trivial. The majority of comparative molecular dynamics studies performed to date relied upon prior sequence or structural alignment to define which residues were equivalent in 3-dimensional space.</p> <p>Results</p> <p>Here we discuss an alternative methodology for comparative molecular dynamics that does not require any prior alignment information. We show it is possible to align proteins based solely on their dynamics and that we can use these dynamics-based alignments to quantify the dynamic similarity of proteins. Our method was tested on 10 representative members of the PDZ domain family.</p> <p>Conclusions</p> <p>As a result of creating pair-wise dynamics-based alignments of PDZ domains, we have found evolutionarily conserved patterns in their backbone dynamics. The dynamic similarity of PDZ domains is highly correlated with their structural similarity as calculated with Dali. However, significant differences in their dynamics can be detected indicating that sequence has a more refined role to play in protein dynamics than just dictating the overall fold. We suggest that the method should be generally applicable.</p
Absolute Convergence of Rational Series is Semi-decidable
International audienceWe study \emph{real-valued absolutely convergent rational series}, i.e. functions , defined over a free monoid , that can be computed by a multiplicity automaton and such that . We prove that any absolutely convergent rational series can be computed by a multiplicity automaton which has the property that is simply convergent, where is the series computed by the automaton derived from by taking the absolute values of all its parameters. Then, we prove that the set composed of all absolutely convergent rational series is semi-decidable and we show that the sum can be estimated to any accuracy rate for any . We also introduce a spectral radius-like parameter which satisfies the following property: is absolutely convergent iff
Impact Of The Energy Model On The Complexity Of RNA Folding With Pseudoknots
International audiencePredicting the folding of an RNA sequence, while allowing general pseudoknots (PK), consists in finding a minimal free-energy matching of its positions. Assuming independently contributing base-pairs, the problem can be solved in -time using a variant of the maximal weighted matching. By contrast, the problem was previously proven NP-Hard in the more realistic nearest-neighbor energy model. In this work, we consider an intermediate model, called the stacking-pairs energy model. We extend a result by Lyngs\o, showing that RNA folding with PK is NP-Hard within a large class of parametrization for the model. We also show the approximability of the problem, by giving a practical algorithm that achieves at least a -approximation for any parametrization of the stacking model. This contrasts nicely with the nearest-neighbor version of the problem, which we prove cannot be approximated within any positive ratio, unless .La prédiction du repliement, avec pseudonoeuds généraux, d'une séquence d'ARN de taille est équivalent à la recherche d'un couplage d'énergie libre minimale. Dans un modèle d'énergie simple, où chaque paire de base contribue indépendamment à l'énergie, ce problème peut être résolu en temps grâce à une variante d'un algorithme de couplage pondéré maximal. Cependant, le même problème a été démontré NP-difficile dans le modèle d'énergie dit des plus proches voisins. Dans ce travail, nous étudions les propriétés du problème sous un modèle d'empilements, constituant un modèle intermédiaire entre ceux d'appariement et des plus proches voisins. Nous démontrons tout d'abord que le repliement avec pseudo-noeuds de l'ARN reste NP-difficile dans de nombreuses valuations du modèle d'énergie. . Par ailleurs, nous montrons que ce problème est approximable, en proposant un algorithme polynomial garantissant une -approximation. Ce résultat illustre une différence essentielle entre ce modèle et celui des plus proches voisins, pour lequel nous montrons qu'il ne peut être approché à aucun ratio positif par un algorithme en temps polynomial sauf si
Inapproximability of maximal strip recovery
In comparative genomic, the first step of sequence analysis is usually to
decompose two or more genomes into syntenic blocks that are segments of
homologous chromosomes. For the reliable recovery of syntenic blocks, noise and
ambiguities in the genomic maps need to be removed first. Maximal Strip
Recovery (MSR) is an optimization problem proposed by Zheng, Zhu, and Sankoff
for reliably recovering syntenic blocks from genomic maps in the midst of noise
and ambiguities. Given genomic maps as sequences of gene markers, the
objective of \msr{d} is to find subsequences, one subsequence of each
genomic map, such that the total length of syntenic blocks in these
subsequences is maximized. For any constant , a polynomial-time
2d-approximation for \msr{d} was previously known. In this paper, we show that
for any , \msr{d} is APX-hard, even for the most basic version of the
problem in which all gene markers are distinct and appear in positive
orientation in each genomic map. Moreover, we provide the first explicit lower
bounds on approximating \msr{d} for all . In particular, we show that
\msr{d} is NP-hard to approximate within . From the other
direction, we show that the previous 2d-approximation for \msr{d} can be
optimized into a polynomial-time algorithm even if is not a constant but is
part of the input. We then extend our inapproximability results to several
related problems including \cmsr{d}, \gapmsr{\delta}{d}, and
\gapcmsr{\delta}{d}.Comment: A preliminary version of this paper appeared in two parts in the
Proceedings of the 20th International Symposium on Algorithms and Computation
(ISAAC 2009) and the Proceedings of the 4th International Frontiers of
Algorithmics Workshop (FAW 2010
Combinatorial RNA Design: Designability and Structure-Approximating Algorithm
In this work, we consider the Combinatorial RNA Design problem, a minimal
instance of the RNA design problem which aims at finding a sequence that admits
a given target as its unique base pair maximizing structure. We provide
complete characterizations for the structures that can be designed using
restricted alphabets. Under a classic four-letter alphabet, we provide a
complete characterization of designable structures without unpaired bases. When
unpaired bases are allowed, we provide partial characterizations for classes of
designable/undesignable structures, and show that the class of designable
structures is closed under the stutter operation. Membership of a given
structure to any of the classes can be tested in linear time and, for positive
instances, a solution can be found in linear time. Finally, we consider a
structure-approximating version of the problem that allows to extend bands
(helices) and, assuming that the input structure avoids two motifs, we provide
a linear-time algorithm that produces a designable structure with at most twice
more base pairs than the input structure.Comment: CPM - 26th Annual Symposium on Combinatorial Pattern Matching, Jun
2015, Ischia Island, Italy. LNCS, 201
Codesigning a Measure of Person-Centred Coordinated Care to Capture the Experience of the Patient: The Development of the P3CEQ
Background: Person-centred coordinated care (P3C) is a priority for stakeholders (ie, patients, carers, professionals, policy makers). As a part of the development of an evaluation framework for P3C, we set out to identify patient-reported experience measures (PREMs) suitable for routine measurement and feedback during the development of services. Methods: A rapid review of the literature was undertaken to identity existing PREMs suitable for the probing person-centred and/or coordinated care. Of 74 measures identified, 7 met our inclusion criteria. We critically examined these against core domains and subdomains of P3C. Measures were then presented to stakeholders in codesign workshops to explore acceptability, utility, and their strengths/weaknesses. Results: The Long-Term Condition 6 questionnaire was preferred for its short length, utility, and tone. However, it lacked key questions in each core domain, and in response to requests from our codesign group, new questions were added to cover consideration as a whole person, coordination, care plans, carer involvement, and a single coordinator. Cognitive interviews, on-going codesign, and mapping to core P3C domains resulted in the refinement of the questionnaire to 11 items with 1 trigger question. The 11-item modified version was renamed the P3C Experiences Questionnaire. Conclusions: Due to a dearth of brief measures available to capture people’s experience of P3C for routine practice, an existing measure was modified using an iterative process of adaption and validation through codesign workshops. Next steps include psychometric validation and modification for people with dementia and learning difficulties.</p
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