Cross-modality mapping using image varifolds to align tissue-scale atlases to molecular-scale measures with application to 2D brain sections.

This paper explicates a solution to building correspondences between molecular-scale transcriptomics and tissue-scale atlases. This problem arises in atlas construction and cross-specimen/technology alignment where specimens per emerging technology remain sparse and conventional image representations cannot efficiently model the high dimensions from subcellular detection of thousands of genes. We address these challenges by representing spatial transcriptomics data as generalized functions encoding position and high-dimensional feature (gene, cell type) identity. We map onto low-dimensional atlas ontologies by modeling regions as homogeneous random fields with unknown transcriptomic feature distribution. We solve simultaneously for the minimizing geodesic diffeomorphism of coordinates through LDDMM and for these latent feature densities. We map tissue-scale mouse brain atlases to gene-based and cell-based transcriptomics data from MERFISH and BARseq technologies and to histopathology and cross-species atlases to illustrate integration of diverse molecular and cellular datasets into a single coordinate system as a means of comparison and further atlas construction.

Space-feature measures on meshes for mapping spatial transcriptomics.

Advances in the development of largely automated microscopy methods such as MERFISH for imaging cellular structures in mouse brains are providing spatial detection of micron resolution gene expression. While there has been tremendous progress made in the field of Computational Anatomy (CA) to perform diffeomorphic mapping technologies at the tissue scales for advanced neuroinformatic studies in common coordinates, integration of molecular- and cellular-scale populations through statistical averaging via common coordinates remains yet unattained. This paper describes the first set of algorithms for calculating geodesics in the space of diffeomorphisms, what we term space-feature-measure LDDMM, extending the family of large deformation diffeomorphic metric mapping (LDDMM) algorithms to accommodate a space-feature action on marked particles which extends consistently to the tissue scales. It leads to the derivation of a cross-modality alignment algorithm of transcriptomic data to common coordinate systems attached to standard atlases. We represent the brain data as geometric measures, termed as space-feature measures supported by a large number of unstructured points, each point representing a small volume in space and carrying a list of densities of features elements of a high-dimensional feature space. The shape of space-feature measure brain spaces is measured by transforming them by diffeomorphisms. The metric between these measures is obtained after embedding these objects in a linear space equipped with the norm, yielding a so-called "chordal metric".

Human Vitamin K Epoxide Reductase as a Target of Its Redox Protein.

Human vitamin K epoxide reductase (hVKORC1) enzymatic activity requires an initial activation by a specific redox protein, a less studied step in the hVKORC1 vital cycle. Significant steric conditions must be met by enzymes, being that to adapt their configurations is mandatory for hVKORC1 activation. We studied, by molecular dynamics (MD) simulations, the folding and conformational plasticity of hVKORC1 in its inactive (fully oxidised) state using available structures, crystallographic and from de novo modelling. According to the obtained results, hVKORC1 is a modular protein composed of the stable transmembrane domain (TMD) and intrinsically disordered luminal (L) loop, possessing the great plasticity/adaptability required to perform various steps of the activation process. The docking (HADDOCK) of Protein Disulfide Isomerase (PDI) onto different hVKORC1 conformations clearly indicated that the most interpretable solutions were found on the target closed L-loop form, a prevalent conformation of hVKORC1's oxidised state. We also suggest that the cleaved L-loop is an appropriate entity to study hVKORC1 recognition/activation by its redox protein. Additionally, the application of hVKORC1 (membrane protein) in aqueous solution is likely to prove to be very useful in practice in either in silico studies or in vitro experiments.

The Inherent Coupling of Intrinsically Disordered Regions in the Multidomain Receptor Tyrosine Kinase KIT.

RTK KIT regulates a variety of crucial cellular processes via its cytoplasmic domain (CD), which is composed of the tyrosine kinase domain, crowned by the highly flexible domains-the juxtamembrane region, kinase insertion domain, and C-tail, which are key recruitment regions for downstream signalling proteins. To prepare a structural basis for the characterization of the interactions of KIT with its signalling proteins (KIT INTERACTOME), we generated the 3D model of the full-length CD attached to the transmembrane helix. This generic model of KIT in inactive state was studied by molecular dynamics simulation under conditions mimicking the natural environment of KIT. With the accurate atomistic description of the multidomain KIT dynamics, we explained its intrinsic (intra-domain) and extrinsic (inter-domain) disorder and represented the conformational assemble of KIT through free energy landscapes. Strongly coupled movements within each domain and between distant domains of KIT prove the functional interdependence of these regions, described as allosteric regulation, a phenomenon widely observed in many proteins. We suggested that KIT, in its inactive state, encodes all properties of the active protein and its post-transduction events.

Molecular Computational Anatomy: Unifying the Particle to Tissue Continuum via Measure Representations of the Brain.

Objective: The objective of this research is to unify the molecular representations of spatial transcriptomics and cellular scale histology with the tissue scales of computational anatomy for brain mapping. Impact Statement: We present a unified representation theory for brain mapping based on geometric varifold measures of the microscale deterministic structure and function with the statistical ensembles of the spatially aggregated tissue scales. Introduction: Mapping across coordinate systems in computational anatomy allows us to understand structural and functional properties of the brain at the millimeter scale. New measurement technologies in digital pathology and spatial transcriptomics allow us to measure the brain molecule by molecule and cell by cell based on protein and transcriptomic functional identity. We currently have no mathematical representations for integrating consistently the tissue limits with the molecular particle descriptions. The formalism derived here demonstrates the methodology for transitioning consistently from the molecular scale of quantized particles-using mathematical structures as first introduced by Dirac as the class of generalized functions-to the tissue scales with methods originally introduced by Euler for fluids. Methods: We introduce two mathematical methods based on notions of generalized functions and statistical mechanics. We use geometric varifolds, a product measure on space and function, to represent functional states at the micro-scales-electrophysiology, molecular histology-integrated with a Boltzmann-like program to pass from deterministic particle descriptions to empirical probabilities on the functional states at the tissue scales. Results: Our space-function varifold representation provides a recipe for traversing from molecular to tissue scales in terms of a cascade of linear space scaling composed with nonlinear functional feature mapping. Following the cascade implies every scale is a geometric measure so that a universal family of measure norms can be introduced which quantifies the geodesic connection between brains in the orbit independent of the probing technology, whether it be RNA identities, Tau or amyloid histology, spike trains, or dense MR imagery. Conclusions: We demonstrate a unified brain mapping theory for molecular and tissue scales based on geometric measure representations. We call the consistent aggregation of tissue scales from particle and cellular scales, molecular computational anatomy.

Folding and Intrinsic Disorder of the Receptor Tyrosine Kinase KIT Insert Domain Seen by Conventional Molecular Dynamics Simulations.

The kinase insert domain (KID) of RTK KIT is the key recruitment region for downstream signalling proteins. KID, studied by molecular dynamics simulations as a cleaved polypeptide and as a native domain fused to KIT, showed intrinsic disorder represented by a set of heterogeneous conformations. The accurate atomistic models showed that the helical fold of KID is mainly sequence dependent. However, the reduced fold of the native KID suggests that its folding is allosterically controlled by the kinase domain. The tertiary structure of KID represents a compact array of highly variable α- and 310-helices linked by flexible loops playing a principal role in the conformational diversity. The helically folded KID retains a collapsed globule-like shape due to non-covalent interactions associated in a ternary hydrophobic core. The free energy landscapes constructed from first principles-the size, the measure of the average distance between the conformations, the amount of helices and the solvent-accessible surface area-describe the KID disorder through a collection of minima (wells), providing a direct evaluation of conformational ensembles. We found that the cleaved KID simulated with restricted N- and C-ends better reproduces the native KID than the isolated polypeptide. We suggest that a cyclic, generic KID would be best suited for future studies of KID f post-transduction effects.

A Langevin-Based Model With Moving Posturographic Target to Quantify Postural Control.

Falls are a major concern of public health, particularly for older adults, as the consequences of falls include serious injuries and death. Therefore, the understanding and evaluation of postural control is considered key, as its deterioration is an important risk factor predisposing to falls. In this work we introduce a new Langevin-based model, local recall, that integrates the information from both the center of pressure (CoP) and the center of mass (CoM) trajectories, and compare its accuracy to a previously proposed model that only uses the CoP. Nine healthy young participants were studied under quiet bipedal standing conditions with eyes either open or closed, while standing on either a rigid surface or a foam. We show that the local recall model produces significantly more accurate prediction than its counterpart, regardless of the eyes and surface conditions, and we replicate these results using another publicly available human dataset. Additionally, we show that parameters estimated using the local recall model are correlated with the quality of postural control, providing a promising method to evaluate static balance. These results suggest that this approach might be interesting to further extend our understanding of the underlying mechanisms of postural control in quiet stance.

Identification of the Primary Factors Determining theSpecificity of Human VKORC1 Recognition by Thioredoxin-Fold Proteins.

Redox (reduction-oxidation) reactions control many important biological processes in all organisms, both prokaryotes and eukaryotes. This reaction is usually accomplished by canonical disulphide-based pathways involving a donor enzyme that reduces the oxidised cysteine residues of a target protein, resulting in the cleavage of its disulphide bonds. Focusing on human vitamin K epoxide reductase (hVKORC1) as a target and on four redoxins (protein disulphide isomerase (PDI), endoplasmic reticulum oxidoreductase (ERp18), thioredoxin-related transmembrane protein 1 (Tmx1) and thioredoxin-related transmembrane protein 4 (Tmx4)) as the most probable reducers of VKORC1, a comparative in-silico analysis that concentrates on the similarity and divergence of redoxins in their sequence, secondary and tertiary structure, dynamics, intraprotein interactions and composition of the surface exposed to the target is provided. Similarly, hVKORC1 is analysed in its native state, where two pairs of cysteine residues are covalently linked, forming two disulphide bridges, as a target for Trx-fold proteins. Such analysis is used to derive the putative recognition/binding sites on each isolated protein, and PDI is suggested as the most probable hVKORC1 partner. By probing the alternative orientation of PDI with respect to hVKORC1, the functionally related noncovalent complex formed by hVKORC1 and PDI was found, which is proposed to be a first precursor to probe thiol-disulphide exchange reactions between PDI and hVKORC1.

A Diffeomorphic Vector Field Approach to Analyze the Thickness of the Hippocampus From 7 T MRI.

OBJECTIVE: 7-Tesla MRI of the hippocampus enhances the visualization of its internal substructures. Among these substructures, the cornu Ammonis and subiculum form a contiguous folded ribbon of gray matter. Here, we propose a method to analyze local thickness measurements of this ribbon. METHODS: We introduce an original approach based upon the estimation of a diffeomorphic vector field that traverses the ribbon. The method is designed to handle specificities of the hippocampus and corresponding 7-Tesla acquisitions: highly convoluted surface, non-closed ribbon, incompletely defined inner/outer boundaries, anisotropic acquisitions. We furthermore propose to conduct group comparisons using a population template built from the central surfaces of individual subjects. RESULTS: We first assessed the robustness of our approach to anisotropy, as well as to inter-rater variability, on a post-mortem scan and on in vivo acquisitions respectively. We then conducted a group study on a dataset of in vivo MRI from temporal lobe epilepsy (TLE) patients and healthy controls. The method detected local thinning patterns in patients, predominantly ipsilaterally to the seizure focus, which is consistent with medical knowledge. CONCLUSION: This new technique allows measuring the thickness of the hippocampus from 7-Tesla MRI. It shows good robustness with respect to anisotropy and inter-rater variability and has the potential to detect local atrophy in patients. SIGNIFICANCE: As 7-Tesla MRI is increasingly available, this new method may become a useful tool to study local alterations of the hippocampus in brain disorders. It is made freely available to the community (code: https://github.com/aramis-lab/hiplay7-thickness, postmortem segmentation: https://doi.org/10.5281/zenodo.3533264).

Age and Glaucoma-Related Characteristics in Retinal Nerve Fiber Layer and Choroid: Localized Morphometrics and Visualization Using Functional Shapes Registration.

Optical coherence tomography provides high-resolution 3D imaging of the posterior segment of the eye. However, quantitative morphological analysis, particularly relevant in retinal degenerative diseases such as glaucoma, has been confined to simple sectorization and averaging with limited spatial sensitivity for detection of clinical markers. In this paper, we present point-wise analysis and visualization of the retinal nerve fiber layer and choroid from cross-sectional data using functional shapes (fshape) registration. The fshape framework matches two retinas, or generates a mean of multiple retinas, by jointly optimizing the surface geometry and functional signals mapped on the surface. We generated group-wise mean retinal nerve fiber layer and choroidal surfaces with the respective layer thickness mapping and showed the difference by age (normal, younger vs. older) and by disease (age-matched older, normal vs. glaucomatous) in the two layers, along with a more conventional sector-based analysis for comparison. The fshape results visualized the detailed spatial patterns of the differences between the age-matched normal and glaucomatous retinal nerve fiber layers, with the glaucomatous layers most significantly thinner in the inferior region close to Bruch's membrane opening. Between the young and older normal cases, choroid was shown to be significantly thinner in the older subjects across all regions, but particularly in the nasal and inferior regions. The results demonstrate a comprehensive and detailed analysis with visualization of morphometric patterns by multiple factors.

Amotl1 mediates sequestration of the Hippo effector Yap1 downstream of Fat4 to restrict heart growth.

Although in flies the atypical cadherin Fat is an upstream regulator of Hippo signalling, the closest mammalian homologue, Fat4, has been shown to regulate tissue polarity rather than growth. Here we show in the mouse heart that Fat4 modulates Hippo signalling to restrict growth. Fat4 mutant myocardium is thicker, with increased cardiomyocyte size and proliferation, and this is mediated by an upregulation of the transcriptional activity of Yap1, an effector of the Hippo pathway. Fat4 is not required for the canonical activation of Hippo kinases but it sequesters a partner of Yap1, Amotl1, out of the nucleus. The nuclear translocation of Amotl1 is accompanied by Yap1 to promote cardiomyocyte proliferation. We, therefore, identify Amotl1, which is not present in flies, as a mammalian intermediate for non-canonical Hippo signalling, downstream of Fat4. This work uncovers a mechanism for the restriction of heart growth at birth, a process which impedes the regenerative potential of the mammalian heart.

Parametric Surface Diffeomorphometry for Low Dimensional Embeddings of Dense Segmentations and Imagery.

In the field of Computational Anatomy, biological form (including our focus, neuroanatomy) is studied quantitatively through the action of the diffeomorphism group on example anatomies - a technique called diffeomorphometry. Here we design an algorithm within this framework to pass from dense objects common in neuromaging studies (binary segmentations, structural images) to a sparse representation defined on the surface boundaries of anatomical structures, and embedded into the low dimensional coordinates of a parametric model. Our main new contribution is to introduce an expanded group action to simultaneously deform surfaces through direct mapping of points, as well as images through functional composition with the inverse. This allows us to index the diffeomorphisms with respect to two-dimensional surface geometries like subcortical gray matter structures, but explicitly map onto cost functions determined by noisy 3-dimensional measurements. We consider models generated from empirical covariance of training data, as well as bandlimited (Laplace-Beltrami eigenfunction) models when no such data is available. We show applications to noisy or anomalous segmentations, and other typical problems in neuroimaging studies. We reproduce statistical results detecting changes in Alzheimer's disease, despite dimensionality reduction. Lastly we apply our algorithm to the common problem of segmenting subcortical structures from T1 MR images.

Atlas-based shape analysis and classification of retinal optical coherence tomography images using the functional shape (fshape) framework.

We propose a novel approach for quantitative shape variability analysis in retinal optical coherence tomography images using the functional shape (fshape) framework. The fshape framework uses surface geometry together with functional measures, such as retinal layer thickness defined on the layer surface, for registration across anatomical shapes. This is used to generate a population mean template of the geometry-function measures from each individual. Shape variability across multiple retinas can be measured by the geometrical deformation and functional residual between the template and each of the observations. To demonstrate the clinical relevance and application of the framework, we generated atlases of the inner layer surface and layer thickness of the Retinal Nerve Fiber Layer (RNFL) of glaucomatous and normal subjects, visualizing detailed spatial pattern of RNFL loss in glaucoma. Additionally, a regularized linear discriminant analysis classifier was used to automatically classify glaucoma, glaucoma-suspect, and control cases based on RNFL fshape metrics.

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson.

The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

How Intrinsic Molecular Dynamics Control Intramolecular Communication in Signal Transducers and Activators of Transcription Factor STAT5.

Signal Transducer and Activator of Transcription STAT5 is a key mediator of cell proliferation, differentiation and survival. While STAT5 activity is tightly regulated in normal cells, its constitutive activation directly contributes to oncogenesis and is associated with a broad range of hematological and solid tumor cancers. Therefore the development of compounds able to modulate pathogenic activation of this protein is a very challenging endeavor. A crucial step of drug design is the understanding of the protein conformational features and the definition of putative binding site(s) for such modulators. Currently, there is no structural data available for human STAT5 and our study is the first footprint towards the description of structure and dynamics of this protein. We investigated structural and dynamical features of the two STAT5 isoforms, STAT5a and STAT5b, taken into account their phosphorylation status. The study was based on the exploration of molecular dynamics simulations by different analytical methods. Despite the overall folding similarity of STAT5 proteins, the MD conformations display specific structural and dynamical features for each protein, indicating first, sequence-encoded structural properties and second, phosphorylation-induced effects which contribute to local and long-distance structural rearrangements interpreted as allosteric event. Further examination of the dynamical coupling between distant sites provides evidence for alternative profiles of the communication pathways inside and between the STAT5 domains. These results add a new insight to the understanding of the crucial role of intrinsic molecular dynamics in mediating intramolecular signaling in STAT5. Two pockets, localized in close proximity to the phosphotyrosine-binding site and adjacent to the channel for communication pathways across STAT5, may constitute valid targets to develop inhibitors able to modulate the function-related communication properties of this signaling protein.

Hotspot mutations in KIT receptor differentially modulate its allosterically coupled conformational dynamics: impact on activation and drug sensitivity.

Receptor tyrosine kinase KIT controls many signal transduction pathways and represents a typical allosterically regulated protein. The mutation-induced deregulation of KIT activity impairs cellular physiological functions and causes serious human diseases. The impact of hotspots mutations (D816H/Y/N/V and V560G/D) localized in crucial regulatory segments, the juxtamembrane region (JMR) and the activation (A-) loop, on KIT internal dynamics was systematically studied by molecular dynamics simulations. The mutational outcomes predicted in silico were correlated with in vitro and in vivo activation rates and drug sensitivities of KIT mutants. The allosteric regulation of KIT in the native and mutated forms is described in terms of communication between the two remote segments, JMR and A-loop. A strong correlation between the communication profile and the structural and dynamical features of KIT in the native and mutated forms was established. Our results provide new insight on the determinants of receptor KIT constitutive activation by mutations and resistance of KIT mutants to inhibitors. Depiction of an intra-molecular component of the communication network constitutes a first step towards an integrated description of vast communication pathways established by KIT in physiopathological contexts.

Diffeomorphometry and geodesic positioning systems for human anatomy.

The Computational Anatomy project has largely been a study of large deformations within a Riemannian framework as an efficient point of view for generating metrics between anatomical configurations. This approach turns D'Arcy Thompson's comparative morphology of human biological shape and form into a metrizable space. Since the metric is constructed based on the geodesic length of the flows of diffeomorphisms connecting the forms, we call it diffeomorphometry. Just as importantly, since the flows describe algebraic group action on anatomical submanifolds and associated functional measurements, they become the basis for positioning information, which we term geodesic positioning. As well the geodesic connections provide Riemannian coordinates for locating forms in the anatomical orbit, which we call geodesic coordinates. These three components taken together - the metric, geodesic positioning of information, and geodesic coordinates - we term the geodesic positioning system. We illustrate via several examples in human and biological coordinate systems and machine learning of the statistical representation of shape and form.

Morphometry of anatomical shape complexes with dense deformations and sparse parameters.

We propose a generic method for the statistical analysis of collections of anatomical shape complexes, namely sets of surfaces that were previously segmented and labeled in a group of subjects. The method estimates an anatomical model, the template complex, that is representative of the population under study. Its shape reflects anatomical invariants within the dataset. In addition, the method automatically places control points near the most variable parts of the template complex. Vectors attached to these points are parameters of deformations of the ambient 3D space. These deformations warp the template to each subject's complex in a way that preserves the organization of the anatomical structures. Multivariate statistical analysis is applied to these deformation parameters to test for group differences. Results of the statistical analysis are then expressed in terms of deformation patterns of the template complex, and can be visualized and interpreted. The user needs only to specify the topology of the template complex and the number of control points. The method then automatically estimates the shape of the template complex, the optimal position of control points and deformation parameters. The proposed approach is completely generic with respect to any type of application and well adapted to efficient use in clinical studies, in that it does not require point correspondence across surfaces and is robust to mesh imperfections such as holes, spikes, inconsistent orientation or irregular meshing. The approach is illustrated with a neuroimaging study of Down syndrome (DS). The results demonstrate that the complex of deep brain structures shows a statistically significant shape difference between control and DS subjects. The deformation-based modelingis able to classify subjects with very high specificity and sensitivity, thus showing important generalization capability even given a low sample size. We show that the results remain significant even if the number of control points, and hence the dimension of variables in the statistical model, are drastically reduced. The analysis may even suggest that parsimonious models have an increased statistical performance. The method has been implemented in the software Deformetrica, which is publicly available at www.deformetrica.org.

Comparison of the endocranial ontogenies between chimpanzees and bonobos via temporal regression and spatiotemporal registration.

This paper aims at quantifying ontogenetic differences between bonobo (Pan paniscus) and chimpanzee (Pan troglodytes) endocrania, using dental development as a timeline. We utilize a methodology based on smooth and invertible deformations combined with a metric of "currents" that defines a distance between endocranial surfaces and does not rely on correspondence between landmarks. This allows us to perform a temporal surface regression that estimates typical endocranial ontogenetic trajectories separately for bonobos and chimpanzees. We highlight non-linear patterns of endocranial ontogenetic change and significant differences between species at local anatomical levels rather than considering the endocranium as a uniform entity. A spatiotemporal registration permits the quantification of inter-species differences decomposed into a morphological deformation (accounting for size and shape differences independently of age) and a time warp (accounting for changes in the dynamics of development). Our statistical simulations suggest that patterns of endocranial volume (EV) increase may differ significantly between bonobos and chimpanzees, with an earlier phase of a relatively rapid increase (preferentially at some endocranial subdivisions) in the former and a much later phase of relatively rapid increase in the latter. As a consequence, the chimpanzee endocranium appears to reach its adult size later. Moreover, the time warp indicates that juvenile bonobos develop much slower than juvenile chimpanzees, suggesting that inter-specific ontogenetic shifts do not only concern EV increase, but also the rate of shape changes over time. Our method provides, for the first time, a quantitative estimation of inter-specific ontogenetic shifts that appear to differentiate non-linearly.

Topology preserving atlas construction from shape data without correspondence using sparse parameters.

Statistical analysis of shapes, performed by constructing an atlas composed of an average model of shapes within a population and associated deformation maps, is a fundamental aspect of medical imaging studies. Usual methods for constructing a shape atlas require point correspondences across subjects, which are difficult in practice. By contrast, methods based on currents do not require correspondence. However, existing atlas construction methods using currents suffer from two limitations. First, the template current is not in the form of a topologically correct mesh, which makes direct analysis on shapes difficult. Second, the deformations are parametrized by vectors at the same location as the normals of the template current which often provides a parametrization that is more dense than required. In this paper, we propose a novel method for constructing shape atlases using currents where topology of the template is preserved and deformation parameters are optimized independently of the shape parameters. We use an L1-type prior that enables us to adaptively compute sparse and low dimensional parameterization of deformations. We show an application of our method for comparing anatomical shapes of patients with Down's syndrome and healthy controls, where the sparse parametrization of diffeomorphisms decreases the parameter dimension by one order of magnitude.