Quantitative reasoning and techniques are increasingly ubiquitous across the life sciences. However, new graduate researchers with a biology background are often not equipped with the skills that are required to utilize such techniques correctly and efficiently. In parallel, there are increasing numbers of engineers, mathematicians, and physical scientists interested in studying problems in biology with only basic knowledge of this field. Students from such varied backgrounds can struggle to engage proactively together to tackle problems in biology. There is therefore a need to establish bridges between those disciplines. It is our proposal that the beginning of graduate school is the appropriate time to initiate those bridges through an interdisciplinary short course. We have instigated an intensive 10-day course that brought together new graduate students in the life sciences from across departments within the National University of Singapore. The course aimed at introducing biological problems as well as some of the quantitative approaches commonly used when tackling those problems. We have run the course for three years with over 100 students attending. Building on this experience, we share 11 quick tips on how to run such an effective, interdisciplinary short course for new graduate students in the biosciences.

BACKGROUND: The amino acid sequence of a protein is the blueprint from which its structure and ultimately function can be derived. Therefore, sequence comparison methods remain essential for the determination of similarity between proteins. Traditional approaches for comparing two protein sequences begin with strings of letters (amino acids) that represent the sequences, before generating textual alignments between these strings and providing scores for each alignment. When the similitude between the two protein sequences to be compared is low however, the quality of the corresponding sequence alignment is usually poor, leading to poor performance for the recognition of similarity. RESULTS: In this study, we develop an alignment free alternative to these methods that is based on the concept of string kernels. Starting from recently proposed kernels on the discrete space of protein sequences (Shen et al, Found. Comput. Math., 2013,14:951-984), we introduce our own version, SeqKernel. Its implementation depends on two parameters, a coefficient that tunes the substitution matrix and the maximum length of k-mers that it includes. We provide an exhaustive analysis of the impacts of these two parameters on the performance of SeqKernel for fold recognition. We show that with the right choice of parameters, use of the SeqKernel similarity measure improves fold recognition compared to the use of traditional alignment-based methods. We illustrate the application of SeqKernel to inferring phylogeny on RNA polymerases and show that it performs as well as methods based on multiple sequence alignments. CONCLUSION: We have presented and characterized a new alignment free method based on a mathematical kernel for scoring the similarity of protein sequences. We discuss possible improvements of this method, as well as an extension of its applications to other modeling methods that rely on sequence comparison.

BACKGROUND: Alignment-free methods for comparing protein sequences have proved to be viable alternatives to approaches that first rely on an alignment of the sequences to be compared. Much work however need to be done before those methods provide reliable fold recognition for proteins whose sequences share little similarity. We have recently proposed an alignment-free method based on the concept of string kernels, SeqKernel (Nojoomi and Koehl, BMC Bioinformatics, 2017, 18:137). In this previous study, we have shown that while Seqkernel performs better than standard alignment-based methods, its applications are potentially limited, because of biases due mostly to sequence length effects. METHODS: In this study, we propose improvements to SeqKernel that follows two directions. First, we developed a weighted version of the kernel, WSeqKernel. Second, we expand the concept of string kernels into a novel framework for deriving information on amino acids from protein sequences. RESULTS: Using a dataset that only contains remote homologs, we have shown that WSeqKernel performs remarkably well in fold recognition experiments. We have shown that with the appropriate weighting scheme, we can remove the length effects on the kernel values. WSeqKernel, just like any alignment-based sequence comparison method, depends on a substitution matrix. We have shown that this matrix can be optimized so that sequence similarity scores correlate well with structure similarity scores. Starting from no information on amino acid similarity, we have shown that we can derive a scoring matrix that echoes the physico-chemical properties of amino acids. CONCLUSION: We have made progress in characterizing and parametrizing string kernels as alignment-based methods for comparing protein sequences, and we have shown that they provide a framework for extracting sequence information from structure.

A new algorithm is presented that provides a constructive way to conformally warp a triangular mesh of genus zero to a destination surface with minimal metric deformation, as well as a means to compute automatically a measure of the geometric difference between two surfaces of genus zero. The algorithm takes as input a pair of surfaces that are topological 2-spheres, each surface given by a distinct triangulation. The algorithm then constructs a map $(f)$ between the two surfaces. First, each of the two triangular meshes is mapped to the unit sphere using a discrete conformal mapping algorithm. The two mappings are then composed with a Möbius transformation to generate the function $(f)$. The Möbius transformation is chosen by minimizing an energy that measures the distance of $(f)$ from an isometry. We illustrate our approach using several "real life" data sets. We show first that the algorithm allows for accurate, automatic, and landmark-free nonrigid registration of brain surfaces. We then validate our approach by comparing shapes of proteins. We provide numerical experiments to demonstrate that the distances computed with our algorithm between low-resolution, surface-based representations of proteins are highly correlated with the corresponding distances computed between high-resolution, atomistic models for the same proteins.

A new exact algorithm is proposed to compute the 3D geometric moments of a homogeneous shape defined by an unstructured triangulation of its surface. This algorithm relies on the analytical integration of the moments on tetrahedra defined by the surface triangles and a central point and on a set of recurrent relationships between the corresponding integrals, and achieves linear running time complexities with respect to the number of triangles in the surface mesh and with respect to the number of moments that are computed. This effectively reduces the complexity for computing moments up to order N from N^6 to N^3 with respect to the fastest previously proposed exact algorithm.

BACKGROUND: The analysis of protein structures provides fundamental insight into most biochemical functions and consequently into the cause and possible treatment of diseases. As the structures of most known proteins cannot be solved experimentally for technical or sometimes simply for time constraints, in silico protein structure prediction is expected to step in and generate a more complete picture of the protein structure universe. Molecular modeling of protein structures is a fast growing field and tremendous works have been done since the publication of the very first model. The growth of modeling techniques and more specifically of those that rely on the existing experimental knowledge of protein structures is intimately linked to the developments of high resolution, experimental techniques such as NMR, X-ray crystallography and electron microscopy. This strong connection between experimental and in silico methods is however not devoid of criticisms and concerns among modelers as well as among experimentalists. RESULTS: In this paper, we focus on homology-modeling and more specifically, we review how it is perceived by the structural biology community and what can be done to impress on the experimentalists that it can be a valuable resource to them. We review the common practices and provide a set of guidelines for building better models. For that purpose, we introduce the H-factor, a new indicator for assessing the quality of homology models, mimicking the R-factor in X-ray crystallography. The methods for computing the H-factor is fully described and validated on a series of test cases. CONCLUSIONS: We have developed a web service for computing the H-factor for models of a protein structure. This service is freely accessible at http://koehllab.genomecenter.ucdavis.edu/toolkit/h-factor.

BACKGROUND: The problem of determining the physical conformation of a protein dimer, given the structures of the two interacting proteins in their unbound state, is a difficult one. The location of the docking interface is determined largely by geometric complementarity, but finding complementary geometry is complicated by the flexibility of the backbone and side-chains of both proteins. We seek to generate candidates for docking that approximate the bound state well, even in cases where there is backbone and/or side-chain difference from unbound to bound states. RESULTS: We divide the surfaces of each protein into local patches and describe the effect of side-chain flexibility on each patch by sampling the space of conformations of its side-chains. Likely positions of individual side-chains are given by a rotamer library; this library is used to derive a sample of possible mutual conformations within the patch. We enforce broad coverage of torsion space. We control the size of the sample by using energy criteria to eliminate unlikely configurations, and by clustering similar configurations, resulting in 50 candidates for a patch, a manageable number for docking. CONCLUSIONS: Using a database of protein dimers for which the bound and unbound structures of the monomers are known, we show that from the unbound patch we are able to generate candidates for docking that approximate the bound structure. In patches where backbone change is small (within 1 Å RMSD of bound), we are able to account for flexibility and generate candidates that are good approximations of the bound state (82% are within 1 Å and 98% are within 1.4 Å RMSD of the bound conformation). We also find that even in cases of moderate backbone flexibility our candidates are able to capture some of the overall shape change. Overall, in 650 of 700 test patches we produce a candidate that is either within 1 Å RMSD of the bound conformation or is closer to the bound state than the unbound is.

In this paper, we present a novel surface meshes coarsening algorithm for generating hierarchical skin surface meshes with decreasing size and guaranteed quality. Each coarse surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface as well.

The amino acid sequence of a protein is the key to understanding its structure and ultimately its function in the cell. This paper addresses the fundamental issue of encoding amino acids in ways that the visualization of protein sequences facilitates the decoding of its information content. We show that a feature-based representation in a three-dimensional (3D) space derived from substitution matrices provides an adequate representation from which the domain content of a protein can be predicted. In addition, we show that each dimension of the feature space can be related to a physical property of the amino acids.