Exploration of Reaction Pathways and Chemical Transformation Networks

For the investigation of chemical reaction networks, the identification of all relevant intermediates and elementary reactions is mandatory. Many algorithmic approaches exist that perform explorations efficiently and automatedly. These approaches differ in their application range, the level of completeness of the exploration, as well as the amount of heuristics and human intervention required. Here, we describe and compare the different approaches based on these criteria. Future directions leveraging the strengths of chemical heuristics, human interaction, and physical rigor are discussed.Comment: 48 pages, 4 figure

Thermochromic liquid crystals as a temperature indicators

Byl proveden stručný přehled termochromních kapalných krystalů pro měření povrchové teploty. Praktický aspekt se zaměřil na získání a kalibraci křivky barevného odstínu a teploty pro různé úhly osvětlení a vertikální vzdálenosti osvětlení.A concise review of the application of thermochromic liquid crystals for surface temperature measurement was conducted. The practical aspect focused on obtaining a hue-temperature calibration curve for different angles of illumination and vertical distances of illumination, in order to evaluate of illumination source on accuracy of measurement

Modelling protein localisation and positional information in subcellular systems

Cells and their component structures are highly organised. The correct function of many biological systems relies upon not only temporal control of protein levels but also spatial control of protein localisation within cells. Mathematical modelling allows us to quantitatively test potential mechanisms for protein localisation and spatial organisation. Here we present models of three examples of spatial organisation within individual cells. In the bacterium E. coli, the site of cell division is partly determined by the Min proteins. The Min proteins oscillate between the cell poles and suppress formation of the division ring here, thereby restricting division to midcell. We present a stochastic model of the Min protein dynamics, and use this model to investigate partitioning of the Min proteins between the daughter cells during cell division. The Min proteins determine the correct position for cell division by forming a timeaveraged concentration gradient which is minimal at midcell. Concentration gradients are involved in a range of subcellular processes, and are particularly important for obtaining positional information. By analysing the low copy number spatiotemporal uctuations in protein concentrations for a single polar gradient and two oppositelydirected gradients, we estimate the positional precision that can be achieved in vivo. We nd that time-averaging is vital for high precision. The embryo of the nematode C. elegans has become a model system for the study of cell polarity. At the one-cell stage, the PAR proteins form anterior and posterior domains in a dynamic process driven by contraction of cortical actomyosin. We present a continuum model for this system, including a highly simpli ed model of the actomyosin dynamics. Our model suggests that the known PAR protein interactions 5 are insu cient to explain the experimentally observed cytoplasmic polarity. We discuss a number of modi cations to the model which reproduce the correct cytoplasmic distributions

Spherical Message Passing for 3D Graph Networks

We consider representation learning from 3D graphs in which each node is associated with a spatial position in 3D. This is an under explored area of research, and a principled framework is currently lacking. In this work, we propose a generic framework, known as the 3D graph network (3DGN), to provide a unified interface at different levels of granularity for 3D graphs. Built on 3DGN, we propose the spherical message passing (SMP) as a novel and specific scheme for realizing the 3DGN framework in the spherical coordinate system (SCS). We conduct formal analyses and show that the relative location of each node in 3D graphs is uniquely defined in the SMP scheme. Thus, our SMP represents a complete and accurate architecture for learning from 3D graphs in the SCS. We derive physically-based representations of geometric information and propose the SphereNet for learning representations of 3D graphs. We show that existing 3D deep models can be viewed as special cases of the SphereNet. Experimental results demonstrate that the use of complete and accurate 3D information in 3DGN and SphereNet leads to significant performance improvements in prediction tasks.Comment: 16 pages, 8 figures, 8 table

Accurate Structural Correlations from Maximum Likelihood Superpositions

The cores of globular proteins are densely packed, resulting in complicated networks of structural interactions. These interactions in turn give rise to dynamic structural correlations over a wide range of time scales. Accurate analysis of these complex correlations is crucial for understanding biomolecular mechanisms and for relating structure to function. Here we report a highly accurate technique for inferring the major modes of structural correlation in macromolecules using likelihood-based statistical analysis of sets of structures. This method is generally applicable to any ensemble of related molecules, including families of nuclear magnetic resonance (NMR) models, different crystal forms of a protein, and structural alignments of homologous proteins, as well as molecular dynamics trajectories. Dominant modes of structural correlation are determined using principal components analysis (PCA) of the maximum likelihood estimate of the correlation matrix. The correlations we identify are inherently independent of the statistical uncertainty and dynamic heterogeneity associated with the structural coordinates. We additionally present an easily interpretable method (“PCA plots”) for displaying these positional correlations by color-coding them onto a macromolecular structure. Maximum likelihood PCA of structural superpositions, and the structural PCA plots that illustrate the results, will facilitate the accurate determination of dynamic structural correlations analyzed in diverse fields of structural biology