Representation of protein 3D structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications

Words of advice: teaching macromolecular crystallography

The ability to view structures of proteins at atomic resolution, facilitated by the rise of macromolecular crystallography, has had a tremendous impact in many areas of sciences, including molecular pharmacology, drug discovery and biotechnology. However, the teaching of macromolecular crystallography in universities across the globe has been less than optimal. This could be attributed to the interdisciplinary nature of this subject, making it appear esoteric and incomprehensible, at least at first glance, for students who have exclusive training in only one specific discipline. For the instructor, this problem is compounded further by the plethora of complex concepts and specialized terminologies that the science of macromolecular crystallography has accumulated over the course of its evolution. Moreover, the advent of robotics and several sophisticated software algorithms have reduced the incentive to understand the beautiful conceptual bedrock on which this subject is based. As a way of addressing some of the challenges delineated above, this Words of Advice article attempts to formulate the broad framework within which the teaching and learning of macromolecular crystallography should be approached. It advocates the acknowledgement that this is an interdisciplinary field, with substantial contributions from chemical, physical, biological and mathematical sciences, requiring the evolution of teaching approaches that acknowledge this reality. Moreover, it suggests the use of visual tools, use of computational resources and history to make the subject more relatable to students.

Multifarious aspects of the chaos game representation and its applications in biological sequence analysis

Chaos game representation (CGR) has been successfully applied in bioinformatics for over 30 years. Since then, many further extensions were announced. Numerical encoding of biological sequences is especially convenient in the visualisation process, free-alignment methods and input preparation for machine learning techniques. The development and applications of CGR have embraced mainly linear nucleotide sequences. However, there were also some attempts to create a representation of proteins. The latter need to be more sophisticated, as arbitrary coordinates for amino acids do not reflect their properties which is crucial during the encoding process. In this paper, the authors summarised various variations of CGRs and their limitations. We began by studying the PROSITE motifs and showed the immense number of amino acid properties employed by different proteins. To this aim, we harnessed the Principal Component Analysis (PCA) and studied the relation between explained variance and the number of features that describe them. It appeared that even after many reductions, about 50 features are non-redundant. This was the reason we introduced an embedding concept from natural language processing which enables adjusting features for a given list of sequences. We presented a simple neural network architecture with one hidden layer and one neuron within it and showed it provides satisfactory results in phylogenetic tree construction in ND5 and SPARC protein cases. To this aim, we transformed CGR representations for all considered sequences using Discrete Fourier Transform (DFT) and applied Unweighted Pair Group Method with Arithmetic Mean (UPGMA) algorithm. Moreover, we indicated some similarities between CGR and Recurrent Neural Networks (RNN). In the end, we attempted to include information about the RNA secondary structure and defined some measures to validate biological significance. We studied their properties and showed on ALMV-3 example its usefulness.