A Mathematical Framework for Protein Structure Comparison

Comparison of protein structures is important for revealing the evolutionary relationship among proteins, predicting protein functions and predicting protein structures. Many methods have been developed in the past to align two or multiple protein structures. Despite the importance of this problem, rigorous mathematical or statistical frameworks have seldom been pursued for general protein structure comparison. One notable issue in this field is that with many different distances used to measure the similarity between protein structures, none of them are proper distances when protein structures of different sequences are compared. Statistical approaches based on those non-proper distances or similarity scores as random variables are thus not mathematically rigorous. In this work, we develop a mathematical framework for protein structure comparison by treating protein structures as three-dimensional curves. Using an elastic Riemannian metric on spaces of curves, geodesic distance, a proper distance on spaces of curves, can be computed for any two protein structures. In this framework, protein structures can be treated as random variables on the shape manifold, and means and covariance can be computed for populations of protein structures. Furthermore, these moments can be used to build Gaussian-type probability distributions of protein structures for use in hypothesis testing. The covariance of a population of protein structures can reveal the population-specific variations and be helpful in improving structure classification. With curves representing protein structures, the matching is performed using elastic shape analysis of curves, which can effectively model conformational changes and insertions/deletions. We show that our method performs comparably with commonly used methods in protein structure classification on a large manually annotated data set

Intrinsically disordered domains: Sequence ➔ disorder ➔ function relationships

Disordered domains are long regions of intrinsic disorder that ideally have conserved sequences, conserved disorder, and conserved functions. These domains were first noticed in protein–protein interactions that are distinct from the interactions between two structured domains and the interactions between structured domains and linear motifs or molecular recognition features (MoRFs). So far, disordered domains have not been systematically characterized. Here, we present a bioinformatics investigation of the sequence–disorder–function relationships for a set of probable disordered domains (PDDs) identified from the Pfam database. All the Pfam seed proteins from those domains with at least one PDD sequence were collected. Most often, if a set contains one PDD sequence, then all members of the set are PDDs or nearly so. However, many seed sets have sequence collections that exhibit diverse proportions of predicted disorder and structure, thus giving the completely unexpected result that conserved sequences can vary substantially in predicted disorder and structure. In addition to the induction of structure by binding to protein partners, disordered domains are also induced to form structure by disulfide bond formation, by ion binding, and by complex formation with RNA or DNA. The two new findings, (a) that conserved sequences can vary substantially in their predicted disorder content and (b) that homologues from a single domain can evolve from structure to disorder (or vice versa), enrich our understanding of the sequence ➔ disorder ensemble ➔ function paradigm

Long Lamai community ICT4D E‐commerce system modelling: an agent oriented role‐based approach

This paper presents the post‐mortem report upon completion of the Long Lamai e‐commerce development project. Some weaknesses with regards to the current software modelling approach are identified and an alternative role‐based approach is proposed. We argue that the existing software modelling technique is not suitable for modelling, making it difficult to establish a good contract between stakeholders causing delays in the project delivery. The role‐based approach is able to explicitly highlight the responsibilities among stakeholders, while also forming the contract agreement among them leading towards sustainable ICT4D