Deformable Protein Shape Classification Based on Deep Learning, and the Fractional Fokker-Planck and Kähler-Dirac Equations.

The classification of deformable protein shapes, based solely on their macromolecular surfaces, is a challenging problem in protein-protein interaction prediction and protein design. Shape classification is made difficult by the fact that proteins are dynamic, flexible entities with high geometrical complexity. In this paper, we introduce a novel description for such deformable shapes. This description is based on the bifractional Fokker-Planck and Dirac-Kähler equations. These equations analyse and probe protein shapes in terms of a scalar, vectorial and non-commuting quaternionic field, allowing for a more comprehensive description of the protein shapes. An underlying non-Markovian Lévy random walk establishes geometrical relationships between distant regions while recalling previous analyses. Classification is performed with a multiobjective deep hierarchical pyramidal neural network, thus performing a multilevel analysis of the description. Our approach is applied to the SHREC'19 dataset for deformable protein shapes classification and to the SHREC'16 dataset for deformable partial shapes classification, demonstrating the effectiveness and generality of our approach.

Characterisation of Growth Plate Dynamics in Murine Models of Osteoarthritis.

The purpose of this study was to investigate growth plate dynamics in surgical and loading murine models of osteoarthritis, to understand whether abnormalities in these dynamics are associated with osteoarthritis development. 8-week-old C57BL/6 male mice underwent destabilisation of medial meniscus (DMM) (n = 8) surgery in right knee joints. Contralateral left knee joints had no intervention (controls). In 16-week-old C57BL/6 male mice (n = 6), osteoarthritis was induced using non-invasive mechanical loading of right knee joints with peak force of 11N. Non-loaded left knee joints were internal controls. Chondrocyte transiency in tibial articular cartilage and growth plate was confirmed by histology and immunohistochemistry. Tibial subchondral bone parameters were measured using microCT and correlated to 3-dimensional (3D) growth plate bridging analysis. Higher expression of chondrocyte hypertrophy markers; Col10a1 and MMP13 were observed in tibial articular cartilage chondrocytes of DMM and loaded mice. In tibial growth plate, Col10a1 and MMP13 expressions were widely expressed in a significantly enlarged zone of proliferative and hypertrophic chondrocytes in DMM (p=0.002 and p<0.0001, respectively) and loaded (both p<0.0001) tibiae of mice compared to their controls. 3D quantification revealed enriched growth plate bridging and higher bridge densities in medial compared to lateral tibiae of DMM and loaded knee joints of the mice. Growth plate dynamics were associated with increased subchondral bone volume fraction (BV/TV; %) in medial tibiae of DMM and loaded knee joints and epiphyseal trabecular bone volume fraction in medial tibiae of loaded knee joints. The results confirm articular cartilage chondrocyte transiency in a surgical and loaded murine models of osteoarthritis. Herein, we reveal spatial variation of growth plate bridging in surgical and loaded osteoarthritis models and how these may contribute to anatomical variation in vulnerability of osteoarthritis development.

In situ characterization of nanoscale strains in loaded whole joints via synchrotron X-ray tomography.

Imaging techniques for quantifying changes in the hierarchical structure of deforming joints are constrained by destructive sample treatments, sample-size restrictions and lengthy scan times. Here, we report the use of fast low-dose pink-beam synchrotron X-ray tomography in combination with mechanical loading at nanometric precision for in situ imaging, at resolutions below 100 nm, of the mechanical strain in intact untreated joints under physiologically realistic conditions. We show that in young, older and osteoarthritic mice, hierarchical changes in tissue structure and mechanical behaviour can be simultaneously visualized, and that the tissue structure at the cellular level correlates with the mechanical performance of the whole joint. We also use the tomographic approach to study the colocalization of tissue strains to specific chondrocyte lacunar organizations within intact loaded joints and to explore the role of calcified-cartilage stiffness on the biomechanics of healthy and pathological joints.

The development of a high throughput drug-responsive model of white adipose tissue comprising adipogenic 3T3-L1 cells in a 3D matrix.

Adipose models have been applied to mechanistic studies of metabolic diseases (such as diabetes) and the subsequent discovery of new therapeutics. However, typical models are either insufficiently complex (2D cell cultures) or expensive and labor intensive (mice/in vivo). To bridge the gap between these models and in order to better inform pre-clinical studies we have developed a drug-responsive 3D model of white adipose tissue (WAT). Here, spheroids (680 ± 60 µm) comprising adipogenic 3T3-L1 cells encapsulated in 3D matrix were fabricated manually on a 96 well scale. Spheroids were highly characterised for lipid morphology, selected metabolite and adipokine secretion, and gene expression; displaying significant upregulation of certain adipogenic-specific genes compared with a 2D model. Furthermore, induction of lipolysis and promotion of lipogenesis in spheroids could be triggered by exposure to 8-br-cAMP and oleic-acid respectively. Metabolic and high content imaging data of spheroids exposed to an adipose-targeting drug, rosiglitazone, resulted in dose-responsive behavior. Thus, our 3D WAT model has potential as a powerful scalable tool for compound screening and for investigating adipose biology.

A Computed Microtomography Method for Understanding Epiphyseal Growth Plate Fusion.

The epiphyseal growth plate is a developmental region responsible for linear bone growth, in which chondrocytes undertake a tightly regulated series of biological processes. Concomitant with the cessation of growth and sexual maturation, the human growth plate undergoes progressive narrowing, and ultimately disappears. Despite the crucial role of this growth plate fusion "bridging" event, the precise mechanisms by which it is governed are complex and yet to be established. Progress is hindered by the current methods for growth plate visualization; these are invasive and largely rely on histological procedures. Here, we describe our non-invasive method utilizing synchrotron X-ray computed microtomography for the examination of growth plate bridging, which ultimately leads to its closure coincident with termination of further longitudinal bone growth. We then apply this method to a dataset obtained from a benchtop micro computed tomography scanner to highlight its potential for wide usage. Furthermore, we conduct finite element modeling at the micron-scale to reveal the effects of growth plate bridging on local tissue mechanics. Employment of these 3D analyses of growth plate bone bridging is likely to advance our understanding of the physiological mechanisms that control growth plate fusion.

A correlative imaging based methodology for accurate quantitative assessment of bone formation in additive manufactured implants.

A correlative imaging methodology was developed to accurately quantify bone formation in the complex lattice structure of additive manufactured implants. Micro computed tomography (µCT) and histomorphometry were combined, integrating the best features from both, while demonstrating the limitations of each imaging modality. This semi-automatic methodology registered each modality using a coarse graining technique to speed the registration of 2D histology sections to high resolution 3D µCT datasets. Once registered, histomorphometric qualitative and quantitative bone descriptors were directly correlated to 3D quantitative bone descriptors, such as bone ingrowth and bone contact. The correlative imaging allowed the significant volumetric shrinkage of histology sections to be quantified for the first time (~15 %). This technique demonstrated the importance of location of the histological section, demonstrating that up to a 30 % offset can be introduced. The results were used to quantitatively demonstrate the effectiveness of 3D printed titanium lattice implants.