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A computer system to perform structure comparison using TOPS representations of protein structure
We describe the design and implementation of a fast topology–based method
for protein structure comparison. The approach uses the TOPS topological representation
of protein structure, aligning two structures using a common discovered
pattern and generating measure of distance derived from an insert score. Heavy
use is made of a constraint-based pattern matching algorithm for TOPS diagrams
that we have designed and described elsewhere Gilbert et al. (1999). The comparison
system is maintained at the European Bioinformatics Institute and is available
over the Web via the at tops.ebi.ac.uk/tops. Users submit a structure description in
Protein Data Bank (PDB) format and can compare it with structures in the entire
PDB or a representative subset of protein domains, receiving the results by email
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Complex macrocycle exploration: parallel, heuristic, and constraint-based conformer generation using ForceGen.
ForceGen is a template-free, non-stochastic approach for 2D to 3D structure generation and conformational elaboration for small molecules, including both non-macrocycles and macrocycles. For conformational search of non-macrocycles, ForceGen is both faster and more accurate than the best of all tested methods on a very large, independently curated benchmark of 2859 PDB ligands. In this study, the primary results are on macrocycles, including results for 431 unique examples from four separate benchmarks. These include complex peptide and peptide-like cases that can form networks of internal hydrogen bonds. By making use of new physical movements ("flips" of near-linear sub-cycles and explicit formation of hydrogen bonds), ForceGen exhibited statistically significantly better performance for overall RMS deviation from experimental coordinates than all other approaches. The algorithmic approach offers natural parallelization across multiple computing-cores. On a modest multi-core workstation, for all but the most complex macrocycles, median wall-clock times were generally under a minute in fast search mode and under 2 min using thorough search. On the most complex cases (roughly cyclic decapeptides and larger) explicit exploration of likely hydrogen bonding networks yielded marked improvements, but with calculation times increasing to several minutes and in some cases to roughly an hour for fast search. In complex cases, utilization of NMR data to constrain conformational search produces accurate conformational ensembles representative of solution state macrocycle behavior. On macrocycles of typical complexity (up to 21 rotatable macrocyclic and exocyclic bonds), design-focused macrocycle optimization can be practically supported by computational chemistry at interactive time-scales, with conformational ensemble accuracy equaling what is seen with non-macrocyclic ligands. For more complex macrocycles, inclusion of sparse biophysical data is a helpful adjunct to computation
How round is a protein? Exploring protein structures for globularity using conformal mapping.
We present a new algorithm that automatically computes a measure of the geometric difference between the surface of a protein and a round sphere. The algorithm takes as input two triangulated genus zero surfaces representing the protein and the round sphere, respectively, and constructs a discrete conformal map f between these surfaces. The conformal map is chosen to minimize a symmetric elastic energy E S (f) that measures the distance of f from an isometry. We illustrate our approach on a set of basic sample problems and then on a dataset of diverse protein structures. We show first that E S (f) is able to quantify the roundness of the Platonic solids and that for these surfaces it replicates well traditional measures of roundness such as the sphericity. We then demonstrate that the symmetric elastic energy E S (f) captures both global and local differences between two surfaces, showing that our method identifies the presence of protruding regions in protein structures and quantifies how these regions make the shape of a protein deviate from globularity. Based on these results, we show that E S (f) serves as a probe of the limits of the application of conformal mapping to parametrize protein shapes. We identify limitations of the method and discuss its extension to achieving automatic registration of protein structures based on their surface geometry
Entropy-scaling search of massive biological data
Many datasets exhibit a well-defined structure that can be exploited to
design faster search tools, but it is not always clear when such acceleration
is possible. Here, we introduce a framework for similarity search based on
characterizing a dataset's entropy and fractal dimension. We prove that
searching scales in time with metric entropy (number of covering hyperspheres),
if the fractal dimension of the dataset is low, and scales in space with the
sum of metric entropy and information-theoretic entropy (randomness of the
data). Using these ideas, we present accelerated versions of standard tools,
with no loss in specificity and little loss in sensitivity, for use in three
domains---high-throughput drug screening (Ammolite, 150x speedup), metagenomics
(MICA, 3.5x speedup of DIAMOND [3,700x BLASTX]), and protein structure search
(esFragBag, 10x speedup of FragBag). Our framework can be used to achieve
"compressive omics," and the general theory can be readily applied to data
science problems outside of biology.Comment: Including supplement: 41 pages, 6 figures, 4 tables, 1 bo
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
The study of probability model for compound similarity searching
Information Retrieval or IR system main task is to retrieve relevant documents according to the users query. One of IR most popular retrieval model is the Vector Space Model. This model assumes relevance based on similarity, which is defined as the distance between query and document in the concept space. All currently existing chemical compound database systems have adapt the vector space model to calculate the similarity of a database entry to a query compound. However, it assumes that fragments represented by the bits are independent of one another, which is not necessarily true. Hence, the possibility of applying another IR model is explored, which is the Probabilistic Model, for chemical compound searching. This model estimates the probabilities of a chemical structure to have the same bioactivity as a target compound. It is envisioned that by ranking chemical structures in decreasing order of their probability of relevance to the query structure, the effectiveness of a molecular similarity searching system can be increased. Both fragment dependencies and independencies assumption are taken into consideration in achieving improvement towards compound similarity searching system. After conducting a series of simulated similarity searching, it is concluded that PM approaches really did perform better than the existing similarity searching. It gave better result in all evaluation criteria to confirm this statement. In terms of which probability model performs better, the BD model shown improvement over the BIR model
Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways
Diverse classes of proteins function through large-scale conformational
changes; sophisticated enhanced sampling methods have been proposed to generate
these macromolecular transition paths. As such paths are curves in a
high-dimensional space, they have been difficult to compare quantitatively, a
prerequisite to, for instance, assess the quality of different sampling
algorithms. The Path Similarity Analysis (PSA) approach alleviates these
difficulties by utilizing the full information in 3N-dimensional trajectories
in configuration space. PSA employs the Hausdorff or Fr\'echet path
metrics---adopted from computational geometry---enabling us to quantify path
(dis)similarity, while the new concept of a Hausdorff-pair map permits the
extraction of atomic-scale determinants responsible for path differences.
Combined with clustering techniques, PSA facilitates the comparison of many
paths, including collections of transition ensembles. We use the closed-to-open
transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for
the assessment enhanced sampling algorithms---to examine multiple microsecond
equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free
form alongside transition ensembles from the MD-based dynamic importance
sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting
algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for
instance, that differences in DIMS-MD and FRODA paths were mediated by a set of
conserved salt bridges whose charge-charge interactions are fully modeled in
DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis
methods relying on pre-defined collective variables, such as native contacts or
geometric quantities, can be used synergistically with PSA, as well as the
application of PSA to more complex systems such as membrane transporter
proteins.Comment: 9 figures, 3 tables in the main manuscript; supplementary information
includes 7 texts (S1 Text - S7 Text) and 11 figures (S1 Fig - S11 Fig) (also
available from journal site
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