In the current study, the three-dimensional (3D) topologies of dyadic clefts and associated membrane organelles were mapped in mouse ventricular myocardium using electron tomography. The morphological details and the distribution of membrane systems, including transverse tubules (T-tubules), junctional sarcoplasmic reticulum (SR) and vicinal mitochondria, were determined and presumed to be crucial for controlling cardiac Ca2+ dynamics. The geometric complexity of T-tubules that varied in diameter with frequent branching was clarified. Dyadic clefts were intricately shaped and remarkably small (average 4.39×105 nm3, median 2.81×105 nm3). Although a dyadic cleft of average size could hold maximum 43 ryanodine receptor (RyR) tetramers, more than one-third of clefts were smaller than the size that is able to package as many as 15 RyR tetramers. The dyadic clefts were also adjacent to one another (average end-to-end distance to the nearest dyadic cleft, 19.9 nm) and were distributed irregularly along T-tubule branches. Electron-dense structures that linked membrane organelles were frequently observed between mitochondrial outer membranes and SR or T-tubules. We, thus, propose that the topology of dyadic clefts and the neighboring cellular micro-architecture are the major determinants of the local control of Ca2+ in the heart, including the establishment of the quantal nature of SR Ca2+ releases (e.g. Ca2+ sparks).

We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a number of molecules are demonstrated, showing that our methods possess several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). We also demonstrate an example of molecular simulation using the finite element method and the meshes generated by our method. The approaches presented and their implementations are also applicable to other types of inputs such as 3D scalar volumes and triangular surface meshes with low quality, and hence can be used for generation/improvment of meshes in a broad range of applications.

Key points• We have developed a detailed computational model of a cardiac Ca 2+ spark based on a three dimensional reconstruction of electron tomograms.• Our model predicts near total junctional Ca 2+ depletion after the spark, while regional Ca 2+ reserve is preserved. The local Ca 2+ gradient inferred by these findings reconciles previous model predictions with experimental measurements.• Differences in local distribution of calsequestrin have a profound impact on spark termination time, as reported by Fluo5, solely based on its Ca 2+ buffering capacity.• The SERCA pump can prolong spark release time by pumping Ca 2+ back into the junctional SR during the spark. Abstract Triggered release of Ca2+ from an individual sarcoplasmic reticulum (SR) Ca 2+ release unit (CRU) is the fundamental event of cardiac excitation-contraction coupling, and spontaneous release events (sparks) are the major contributor to diastolic Ca 2+ leak in cardiomyocytes. Previous model studies have predicted that the duration and magnitude of the spark is determined by the local CRU geometry, as well as the localization and density of Ca 2+ handling proteins. We have created a detailed computational model of a CRU, and developed novel tools to generate the computational geometry from electron tomographic images. Ca 2+ diffusion was modelled within the SR and the cytosol to examine the effects of localization and density of the Na + /Ca 2+ exchanger, sarco/endoplasmic reticulum Ca 2+ -ATPase 2 (SERCA), and calsequestrin on spark dynamics. We reconcile previous model predictions of approximately 90% local Ca 2+ depletion in junctional SR, with experimental reports of about 40%. This analysis supports the hypothesis that dye kinetics and optical averaging effects can have a significant impact on measures of spark dynamics. Our model also predicts that distributing calsequestrin within non-junctional Z-disc SR compartments, in addition to the junctional compartment, prolongs spark release time as reported by Fluo5. By pumping Ca 2+ back into the SR during a release, SERCA is able to prolong a Ca 2+ spark, and this may contribute to SERCA-dependent changes in Ca 2+ wave speed. Finally, we show that including the Na + /Ca 2+ exchanger inside the dyadic cleft does not alter local [Ca 2+ ] during a spark.

We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the PoissonBoltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this twoterm regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L ∞ estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem. The convergence and accuracy of the overall AFEM algorithm is also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein.

SummaryChilo iridescent virus (CIV) is a large (~1850 Å diameter) insect virus with an icosahedral, T=147 capsid, a dsDNA genome, and an internal lipid membrane. The structure of CIV was determined to 13 Å resolution by means of cryo-electron microscopy (cryoEM) and three-dimensional image reconstruction. A homology model of P50, the CIV major capsid protein (MCP), was built based on its amino acid sequence and the structure of the homologous Paramecium bursaria chlorella virus 1 (PBCV-1) Vp54 MCP. This model was fitted into the cryoEM density for each of the 25 trimeric CIV capsomers per icosahedral asymmetric unit. A difference map, in which the fitted CIV MCP capsomers were subtracted from the CIV cryoEM reconstruction, showed that there are at least three different types of minor capsid proteins associated with the capsomers outside the lipid membrane. "Finger" proteins are situated at many, but not all, of the spaces between three adjacent capsomers within each trisymmetron, and "zip" proteins are situated between sets of three adjacent capsomers at the boundary between neighboring trisymmetrons and pentasymmetrons. Based on the results of segmentation and density correlations, there are at least eight finger proteins, and three dimeric and two monomeric zip proteins in one asymmetric unit of the CIV capsid. These minor proteins appear to stabilize the virus by acting as intercapsomer cross-links. One transmembrane "anchor" protein per icosahedral asymmetric unit, which extends from beneath one of the capsomers in the pentasymmetron to the internal leaflet of the lipid membrane, may provide additional stabilization for the capsid. These results are consistent with the observations for other large, icosahedral dsDNA viruses that also utilize minor capsid proteins for stabilization and determining their assembly.

Acute and chronic wounds have varying etiologies and are an economic burden to healthcare systems around the world. The advanced wound care market is expected to exceed $22 billion by 2024. Wound care professionals rely heavily on images and image documentation for proper diagnosis and treatment. Unfortunately lack of expertise can lead to improper diagnosis of wound etiology and inaccurate wound management and documentation. Fully automatic segmentation of wound areas in natural images is an important part of the diagnosis and care protocol since it is crucial to measure the area of the wound and provide quantitative parameters in the treatment. Various deep learning models have gained success in image analysis including semantic segmentation. This manuscript proposes a novel convolutional framework based on MobileNetV2 and connected component labelling to segment wound regions from natural images. The advantage of this model is its lightweight and less compute-intensive architecture. The performance is not compromised and is comparable to deeper neural networks. We build an annotated wound image dataset consisting of 1109 foot ulcer images from 889 patients to train and test the deep learning models. We demonstrate the effectiveness and mobility of our method by conducting comprehensive experiments and analyses on various segmentation neural networks. The full implementation is available at https://github.com/uwm-bigdata/wound-segmentation.

No abstract

The t-tubules of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca2+). To investigate how the t-tubule microanatomy and the distribution of membrane Ca2+ flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca2+ signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca2+ signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca2+ flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca2+ buffers, including the Ca2+ indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca2+ transients was found when the Ca2+ flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca2+ signals are predicted. Even at modest elevation of Ca2+, reached during Ca2+ influx, large and steep Ca2+ gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca2+ flux density along the cell membrane support initiation and propagation of Ca2+ waves in rat myocytes.