A power law distribution of metabolite abundance levels in mice regardless of the time and spatial scale of analysis

Dense random packing with a power-law size distribution: The structure factor, mass-radius relation, and pair distribution function

We consider a dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation, and pair distribution function of the disk centers. A toy model of dense segments in one dimension (1D) is solved exactly. It is shown theoretically in 1D and numerically in 1D and 2D that such a packing exhibits fractal properties. It is found that the exponent of the power-law distribution and the fractal dimension coincide. An approximate relation for the structure factor in arbitrary dimensions is derived, which can be used as a fitting formula in small-angle scattering. These findings can be useful for understanding the microstructural properties of various systems such as ultra-high performance concrete, high-internal-phase-ratio emulsions, or biological systems.

Unsupervised machine learning using an imaging mass spectrometry dataset automatically reassembles grey and white matter

Current histological and anatomical analysis techniques, including fluorescence in situ hybridisation, immunohistochemistry, immunofluorescence, immunoelectron microscopy and fluorescent fusion protein, have revealed great distribution diversity of mRNA and proteins in the brain. However, the distributional pattern of small biomolecules, such as lipids, remains unclear. To this end, we have developed and optimised imaging mass spectrometry (IMS), a combined technique incorporating mass spectrometry and microscopy, which is capable of comprehensively visualising biomolecule distribution. We demonstrated the differential distribution of phospholipids throughout the cell body and axon of neuronal cells using IMS analysis. In this study, we used solarix XR, a high mass resolution and highly sensitive MALDI-FT-ICR-MS capable of detecting higher number of molecules than conventional MALDI-TOF-MS instruments, to create a molecular distribution dataset. We examined the diversity of biomolecule distribution in rat brains using IMS and hypothesised that unsupervised machine learning reconstructs brain structures such as the grey and white matters. We have demonstrated that principal component analysis (PCA) can reassemble the grey and white matters without assigning brain anatomical regions. Hierarchical clustering allowed us to classify the 10 groups of observed molecules according to their distributions. Furthermore, the group of molecules specifically localised in the cerebellar cortex was estimated to be composed of phospholipids.