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The presence of a 22q11.2 microdeletion (22q11.2 deletion syndrome [22q11DS]) ranks among the greatest known genetic risk factors for the development of psychotic disorders. There is emerging evidence that the cerebellum is important in the pathophysiology of psychosis. However, there is currently limited information on cerebellar neuroanatomy in 22q11DS specifically.High-resolution 3T magnetic resonance imaging was acquired in 79 individuals with 22q11DS and 70 typically developing control subjects (N = 149). Lobar and lobule-level cerebellar volumes were estimated using validated automated segmentation algorithms, and subsequently group differences were compared. Hierarchical clustering, principal component analysis, and graph theoretical models were used to explore intercerebellar relationships. Cerebrocerebellar structural connectivity with cortical thickness was examined via linear regression models.Individuals with 22q11DS had, on average, 17.3% smaller total cerebellar volumes relative to typically developing subjects (p.0001). The lobules of the superior posterior cerebellum (e.g., VII and VIII) were particularly affected in 22q11DS. However, all cerebellar lobules were significantly smaller, even after adjusting for total brain volumes (all cerebellar lobules p.0002). The superior posterior lobule was disproportionately associated with cortical thickness in the frontal lobes and cingulate cortex, brain regions known be affected in 22q11DS. Exploratory analyses suggested that the superior posterior lobule, particularly Crus I, may be associated with psychotic symptoms in 22q11DS.The cerebellum is a critical but understudied component of the 22q11DS neuroendophenotype.

NUP98 fusion oncoproteins (FO) are drivers in pediatric leukemias and many transform hematopoietic cells. Most NUP98 FOs harbor an intrinsically disordered region from NUP98 that is prone to liquid–liquid phase separation (LLPS) in vitro. A predominant class of NUP98 FOs, including NUP98–HOXA9 (NHA9), retains a DNA-binding homeodomain, whereas others harbor other types of DNA- or chromatin-binding domains. NUP98 FOs have long been known to form puncta, but long-standing questions are how nuclear puncta form and how they drive leukemogenesis. Here we studied NHA9 condensates and show that homotypic interactions and different types of heterotypic interactions are required to form nuclear puncta, which are associated with aberrant transcriptional activity and transformation of hematopoietic stem and progenitor cells. We also show that three additional leukemia-associated NUP98 FOs (NUP98–PRRX1, NUP98–KDM5A, and NUP98–LNP1) form nuclear puncta and transform hematopoietic cells. These findings indicate that LLPS is critical for leukemogenesis by NUP98 FOs.Significance:We show that homotypic and heterotypic mechanisms of LLPS control NUP98–HOXA9 puncta formation, modulating transcriptional activity and transforming hematopoietic cells. Importantly, these mechanisms are generalizable to other NUP98 FOs that share similar domain structures. These findings address long-standing questions on how nuclear puncta form and their link to leukemogenesis.This article is highlighted in the In This Issue feature, p. 873

Supplementary Table from Phase Separation Mediates NUP98 Fusion Oncoprotein Leukemic Transformation

Supplementary Data from Phase Separation Mediates NUP98 Fusion Oncoprotein Leukemic Transformation

Serial-section electron microscopy (ssEM) is the method of choice for studying macroscopic biological samples at extremely high resolution in three dimensions. In the nervous system, nanometer-scale images are necessary to reconstruct dense neural wiring diagrams in the brain, so calledconnectomes. In order to use this data, consisting of up to 108individual EM images, it must be assembled into a volume, requiring seamless 2D stitching from each physical section followed by 3D alignment of the stitched sections. The high throughput of ssEM necessitates 2D stitching to be done at the pace of imaging, which currently produces tens of terabytes per day. To achieve this, we present a modular volume assembly software pipelineASAP(Assembly Stitching and Alignment Pipeline) that is scalable to datasets containing petabytes of data and parallelized to work in a distributed computational environment. The pipeline is built on top of theRender[18] services used in the volume assembly of the brain of adultDrosophila melanogaster[2]. It achieves high throughput by operating on the meta-data and transformations of each image stored in a database, thus eliminating the need to render intermediate output. ASAP is modular, allowing for easy incorporation of new algorithms without significant changes in the workflow. The entire software pipeline includes a complete set of tools for stitching, automated quality control, 3D section alignment, and final rendering of the assembled volume to disk. ASAP has been deployed for continuous processing of several large-scale datasets of the mouse visual cortex and human brain samples including one cubic millimeter of mouse visual cortex [1, 25] at speeds that exceed imaging. The pipeline also has multi-channel processing capabilities and can be applied to fluorescence and multi-modal datasets like array tomography.

NUP98 fusion oncoproteins (FO) are drivers in pediatric leukemias and many transform hematopoietic cells. Most NUP98 FOs harbor an intrinsically disordered region from NUP98 that is prone to liquid–liquid phase separation (LLPS) in vitro. A predominant class of NUP98 FOs, including NUP98–HOXA9 (NHA9), retains a DNA-binding homeodomain, whereas others harbor other types of DNA- or chromatin-binding domains. NUP98 FOs have long been known to form puncta, but long-standing questions are how nuclear puncta form and how they drive leukemogenesis. Here we studied NHA9 condensates and show that homotypic interactions and different types of heterotypic interactions are required to form nuclear puncta, which are associated with aberrant transcriptional activity and transformation of hematopoietic stem and progenitor cells. We also show that three additional leukemia-associated NUP98 FOs (NUP98–PRRX1, NUP98–KDM5A, and NUP98–LNP1) form nuclear puncta and transform hematopoietic cells. These findings indicate that LLPS is critical for leukemogenesis by NUP98 FOs. Significance: We show that homotypic and heterotypic mechanisms of LLPS control NUP98–HOXA9 puncta formation, modulating transcriptional activity and transforming hematopoietic cells. Importantly, these mechanisms are generalizable to other NUP98 FOs that share similar domain structures. These findings address long-standing questions on how nuclear puncta form and their link to leukemogenesis. This article is highlighted in the In This Issue feature, p. 873

The neural circuits responsible for animal behavior remain largely unknown. We summarize new methods and present the circuitry of a large fraction of the brain of the fruit fly Drosophila melanogaster. Improved methods include new procedures to prepare, image, align, segment, find synapses in, and proofread such large data sets. We define cell types, refine computational compartments, and provide an exhaustive atlas of cell examples and types, many of them novel. We provide detailed circuits consisting of neurons and their chemical synapses for most of the central brain. We make the data public and simplify access, reducing the effort needed to answer circuit questions, and provide procedures linking the neurons defined by our analysis with genetic reagents. Biologically, we examine distributions of connection strengths, neural motifs on different scales, electrical consequences of compartmentalization, and evidence that maximizing packing density is an important criterion in the evolution of the fly’s brain., eLife digest Animal brains of all sizes, from the smallest to the largest, work in broadly similar ways. Studying the brain of any one animal in depth can thus reveal the general principles behind the workings of all brains. The fruit fly Drosophila is a popular choice for such research. With about 100,000 neurons – compared to some 86 billion in humans – the fly brain is small enough to study at the level of individual cells. But it nevertheless supports a range of complex behaviors, including navigation, courtship and learning. Thanks to decades of research, scientists now have a good understanding of which parts of the fruit fly brain support particular behaviors. But exactly how they do this is often unclear. This is because previous studies showing the connections between cells only covered small areas of the brain. This is like trying to understand a novel when all you can see is a few isolated paragraphs. To solve this problem, Scheffer, Xu, Januszewski, Lu, Takemura, Hayworth, Huang, Shinomiya et al. prepared the first complete map of the entire central region of the fruit fly brain. The central brain consists of approximately 25,000 neurons and around 20 million connections. To prepare the map – or connectome – the brain was cut into very thin 8nm slices and photographed with an electron microscope. A three-dimensional map of the neurons and connections in the brain was then reconstructed from these images using machine learning algorithms. Finally, Scheffer et al. used the new connectome to obtain further insights into the circuits that support specific fruit fly behaviors. The central brain connectome is freely available online for anyone to access. When used in combination with existing methods, the map will make it easier to understand how the fly brain works, and how and why it can fail to work correctly. Many of these findings will likely apply to larger brains, including our own. In the long run, studying the fly connectome may therefore lead to a better understanding of the human brain and its disorders. Performing a similar analysis on the brain of a small mammal, by scaling up the methods here, will be a likely next step along this path.

The neural circuits responsible for animal behavior remain largely unknown. We summarize new methods and present the circuitry of a large fraction of the brain of the fruit fly Drosophila melanogaster. Improved methods include new procedures to prepare, image, align, segment, find synapses in, and proofread such large data sets. We define cell types, refine computational compartments, and provide an exhaustive atlas of cell examples and types, many of them novel. We provide detailed circuits consisting of neurons and their chemical synapses for most of the central brain. We make the data public and simplify access, reducing the effort needed to answer circuit questions, and provide procedures linking the neurons defined by our analysis with genetic reagents. Biologically, we examine distributions of connection strengths, neural motifs on different scales, electrical consequences of compartmentalization, and evidence that maximizing packing density is an important criterion in the evolution of the fly’s brain.

The neural circuits responsible for behavior remain largely unknown. Previous efforts have reconstructed the complete circuits of small animals, with hundreds of neurons, and selected circuits for larger animals. Here we (the FlyEM project at Janelia and collaborators at Google) summarize new methods and present the complete circuitry of a large fraction of the brain of a much more complex animal, the fruit fly Drosophila melanogaster. Improved methods include new procedures to prepare, image, align, segment, find synapses, and proofread such large data sets; new methods that define cell types based on connectivity in addition to morphology; and new methods to simplify access to a large and evolving data set. From the resulting data we derive a better definition of computational compartments and their connections; an exhaustive atlas of cell examples and types, many of them novel; detailed circuits for most of the central brain; and exploration of the statistics and structure of different brain compartments, and the brain as a whole. We make the data public, with a web site and resources specifically designed to make it easy to explore, for all levels of expertise from the expert to the merely curious. The public availability of these data, and the simplified means to access it, dramatically reduces the effort needed to answer typical circuit questions, such as the identity of upstream and downstream neural partners, the circuitry of brain regions, and to link the neurons defined by our analysis with genetic reagents that can be used to study their functions.Note: In the next few weeks, we will release a series of papers with more involved discussions. One paper will detail the hemibrain reconstruction with more extensive analysis and interpretation made possible by this dense connectome. Another paper will explore the central complex, a brain region involved in navigation, motor control, and sleep. A final paper will present insights from the mushroom body, a center of multimodal associative learning in the fly brain.

Recent advancements in microscopy, protein engineering, and genetics have rendered the larval zerbrafish a powerful model system for which whole brain, real time, functional neuroimaging at cellular resolution is accessible. Supplementing functional data with additional modalities in the same fish such as structural connectivity and transcriptomics will enable interpretation of structure-function relationships across the entire brains of individual animals. However, proper identification of corresponding cells in the large image volumes produced depends on accurate and efficient deformable registration. To address this challenge, we implemented the Fourier-approximated Lie Algebras for Shooting (FLASH) algorithm within the well-known Advanced Normalization Tools (ANTs) package. This combines the speed of FLASH with the extensive set of image matching functionals and multi-staging multi-resolution capabilities of ANTs. We registered longitudinal data from nine fish, using a line that uniquely identifies subsets of neurons in an independent channel. We validate our approach by demonstrating accurate cell-to-cell correspondence while requiring significantly less time and memory than the Symmetric Normalization (SyN) implementation in ANTs, and without compromising the theoretical foundations of the Large Deformation Diffeomorphic Metric Mapping (LDDMM) model.

Summary Drosophila melanogaster has a rich repertoire of innate and learned behaviors. Its 100,000-neuron brain is a large but tractable target for comprehensive neural circuit mapping. Only electron microscopy (EM) enables complete, unbiased mapping of synaptic connectivity; however, the fly brain is too large for conventional EM. We developed a custom high-throughput EM platform and imaged the entire brain of an adult female fly at synaptic resolution. To validate the dataset, we traced brain-spanning circuitry involving the mushroom body (MB), which has been extensively studied for its role in learning. All inputs to Kenyon cells (KCs), the intrinsic neurons of the MB, were mapped, revealing a previously unknown cell type, postsynaptic partners of KC dendrites, and unexpected clustering of olfactory projection neurons. These reconstructions show that this freely available EM volume supports mapping of brain-spanning circuits, which will significantly accelerate Drosophila neuroscience. Video Abstract, Graphical Abstract, Highlights • A complete adult Drosophila brain was imaged with EM and has been made publicly available • The imaged volume enables brain-spanning mapping of circuits at synaptic resolution • All mushroom body (MB) calyx inputs were mapped, revealing a new cell type, MB-CP2 • Previously unidentified synaptic partners form recurrent microcircuits in MB calyx, Electron microscopy imaging of the entire adult fruit fly brain at synapse resolution reveals circuitry spanning multiple regions and connectivity between known and previously unknown cell types.

Mechanics plays a key role in the development of higher organisms. However, understanding this relationship is complicated by the difficulty of modeling the link between local forces generated at the subcellular level and deformations observed at the tissue and whole-embryo levels. Here we propose an approach first developed for lipid bilayers and cell membranes, in which force-generation by cytoskeletal elements enters a continuum mechanics formulation for the full system in the form of local changes in preferred curvature. This allows us to express and solve the system using only tissue strains. Locations of preferred curvature are simply related to products of gene expression. A solution, in that context, means relaxing the system's mechanical energy to yield global morphogenetic predictions that accommodate a tendency toward the local preferred curvature, without a need to explicitly model force-generation mechanisms at the molecular level. Our computational framework, which we call SPHARM-MECH, extends a 3D spherical harmonics parameterization known as SPHARM to combine this level of abstraction with a sparse shape representation. The integration of these two principles allows computer simulations to be performed in three dimensions on highly complex shapes, gene expression patterns, and mechanical constraints. We demonstrate our approach by modeling mesoderm invagination in the fruit-fly embryo, where local forces generated by the acto-myosin meshwork in the region of the future mesoderm lead to formation of a ventral tissue fold. The process is accompanied by substantial changes in cell shape and long-range cell movements. Applying SPHARM-MECH to whole-embryo live imaging data acquired with light-sheet microscopy reveals significant correlation between calculated and observed tissue movements. Our analysis predicts the observed cell shape anisotropy on the ventral side of the embryo and suggests an active mechanical role of mesoderm invagination in supporting the onset of germ-band extension.

Simultaneous multiview light-sheet microscopy using two illumination and two detection arms with one- or two-photon illumination is coupled to a fast data acquisition framework and analysis pipeline for quantitative imaging and tracking of individual cells and the developing nervous system throughout a living fly embryo. A related paper by Krzic et al. is also in this issue.

Mechanics plays a key role in the development of higher organisms. However, working towards an understanding of this relationship is complicated by the fact that it has proven difficult to model the link between local forces generated at the subcellular level, and tissue deformation at the whole-embryo level. Here we propose an approach first developed for lipid bilayers and cell membranes, in which force-generation at the cytoskeletal level only enters the shape mechanics calculation in the form of local changes in preferred tissue curvature. This allows us to formulate the continuum mechanics problem purely in terms of tissue strains. Relaxing the system by lowering its mechanical energy yields global morphogenetic predictions that accommodate the tendency towards this local preferred curvature, without explicitly modeling force-generating mechanisms at the molecular level. Our computational framework, which we call SPHARMMECH, extends a three-dimensional spherical harmonics parameterization known as SPHARM to combine this level of abstraction with a sparse shape representation. The integration of these two principles allows computer simulations to be performed in three dimensions, on highly complex shapes, gene expression patterns, and mechanical constraints.We demonstrate our approach by modeling mesoderm invagination in the fruit-fly embryo, where local forces generated by the acto-myosin meshwork in the region of the future mesoderm lead to formation of a ventral tissue fold. The process is accompanied by substantial changes in cell shape and long-range cell movements. Applying SPHARM-MECH to whole-embryo live imaging data acquired with light-sheet microscopy reveals significant correlation between calculated and observed tissue movements. Our analysis predicts the observed cell shape anisotropy on the ventral side of the embryo and suggests an active mechanical role of mesoderm invagination in supporting the onset of germ-band extension.

Light sheet-based fluorescence microscopy (LSFM) is emerging as a powerful imaging technique for the life sciences. LSFM provides an exceptionally high imaging speed, high signal-to-noise ratio, low level of photo-bleaching and good optical penetration depth. This unique combination of capabilities makes light sheet-based microscopes highly suitable for live imaging applications. There is an outstanding potential in applying this technology to the quantitative study of embryonic development. Here, we provide an overview of the different basic implementations of LSFM, review recent technical advances in the field and highlight applications in the context of embryonic development. We conclude with a discussion of promising future directions.

A comparison between the full Newton-type optimization NL2SNO, the Levenberg–Marquardt method with the model-trust region modification, and the simplex algorithm is made in the context of the iterative fitting of EPR spectra. EPR lineshape simulations are based on the stochastic Liouville equation (SLE), with an anisotropic diffusion tensor and an anisotropic restraining potential describing the motional amplitude of the spin label. The simplex algorithm was found to be the most reliable, and an approach—incorporating both NL2SNO as well as the downhill simplex methods—is proposed as a strategy-of-choice.

Collagen fibres within the extracellular matrix lend tensile strength to tissues and form a functional scaffold for cells. Cells can move directionally along the axis of fibrous structures, in a process important in wound healing and cell migration. The precise nature of the structural cues within the collagen fibrils that can direct cell movement are not known. We have investigated the structural features of collagen that are required for directional motility of mouse dermal fibroblasts, by analysing cell movement on two-dimensional collagen surfaces. The surfaces were prepared with aligned fibrils of collagen type I, oriented in a predefined direction. These collagen-coated surfaces were generated with or without the characteristic 67 nm D-periodic banding. Quantitative analysis of cell morphodynamics showed a strong correlation of cell elongation and motional directionality with the orientation of D-periodic collagen microfibrils. Neither directed motility, nor cell body alignment, was observed on aligned collagen lacking D-periodicity, or on D-periodic collagen in the presence of peptide containing an RGD motif. The directional motility of fibroblast cells on aligned collagen type I fibrils cannot be attributed to contact guidance, but requires additional structural information. This allows us to postulate a physiological function for the 67 nm periodicity.

The atomic force microscope (AFM) is introduced as a biomolecular manipulation machine capable of assembling biological molecules into well-defined molecular structures. Native collagen molecules were mechanically directed into well-defined, two-dimensional templates exhibiting patterns with feature sizes ranging from a few nanometers to several hundreds of micrometers. The resulting nanostructured collagen matrices were only approximately 3-nm thick, exhibited an extreme mechanical stability, and maintained their properties over the time range of several months. Our results directly demonstrate the plasticity of biological assemblies and provide insight into the physical mechanisms by which biological structures may be organized by cells in vivo. These nanoscopic templates may serve as platforms on non-biological surfaces to direct molecular and cellular processes.

The fruit fly is an excellent model system for investigating the sequence of epithelial tissue invaginations constituting the process of gastrulation. By combining recent advancements in light sheet fluorescence microscopy (LSFM) and image processing, the three-dimensional fly embryo morphology and relevant gene expression patterns can be accurately recorded throughout the entire process of embryogenesis. LSFM provides exceptionally high imaging speed, high signal-to-noise ratio, low level of photoinduced damage, and good optical penetration depth. This powerful combination of capabilities makes LSFM particularly suitable for live imaging of the fly embryo.The resulting high-information-content image data are subsequently processed to obtain the outlines of cells and cell nuclei, as well as the geometry of the whole embryo tissue by image segmentation. Furthermore, morphodynamics information is extracted by computationally tracking objects in the image. Towards that goal we describe the successful implementation of a fast fitting strategy of Gaussian mixture models.The data obtained by image processing is well-suited for hypothesis testing of the detailed biomechanics of the gastrulating embryo. Typically this involves constructing computational mechanics models that consist of an objective function providing an estimate of strain energy for a given morphological configuration of the tissue, and a numerical minimization mechanism of this energy, achieved by varying morphological parameters.In this chapter, we provide an overview of in vivo imaging of fruit fly embryos using LSFM, computational tools suitable for processing the resulting images, and examples of computational biomechanical simulations of fly embryo gastrulation.

The fruit fly is an excellent model system for investigating the sequence of epithelial tissue invaginations constituting the process of gastrulation. By combining recent advancements in light sheet fluorescence microscopy (LSFM) and image processing, the three-dimensional fly embryo morphology and relevant gene expression patterns can be accurately recorded throughout the entire process of embryogenesis. LSFM provides exceptionally high imaging speed, high signal-to-noise ratio, low level of photoinduced damage, and good optical penetration depth. This powerful combination of capabilities makes LSFM particularly suitable for live imaging of the fly embryo.The resulting high-information-content image data are subsequently processed to obtain the outlines of cells and cell nuclei, as well as the geometry of the whole embryo tissue by image segmentation. Furthermore, morphodynamics information is extracted by computationally tracking objects in the image. Towards that goal we describe the successful implementation of a fast fitting strategy of Gaussian mixture models.The data obtained by image processing is well-suited for hypothesis testing of the detailed biomechanics of the gastrulating embryo. Typically this involves constructing computational mechanics models that consist of an objective function providing an estimate of strain energy for a given morphological configuration of the tissue, and a numerical minimization mechanism of this energy, achieved by varying morphological parameters.In this chapter, we provide an overview of in vivo imaging of fruit fly embryos using LSFM, computational tools suitable for processing the resulting images, and examples of computational biomechanical simulations of fly embryo gastrulation.

Light sheet-based fluorescence microscopy (LSFM) is emerging as a powerful imaging technique for the life sciences. LSFM provides an exceptionally high imaging speed, high signal-to-noise ratio, low level of photo-bleaching, and good optical penetration depth. This unique combination of capabilities makes light sheet-based microscopes highly suitable for live imaging applications. Here, we provide an overview of light sheet-based microscopy assays for in vitro and in vivo imaging of biological samples, including cell extracts, soft gels, and large multicellular organisms. We furthermore describe computational tools for basic image processing and data inspection.

Light sheet-based fluorescence microscopy (LSFM) is emerging as a powerful imaging technique for the life sciences. LSFM provides an exceptionally high imaging speed, high signal-to-noise ratio, low level of photo-bleaching, and good optical penetration depth. This unique combination of capabilities makes light sheet-based microscopes highly suitable for live imaging applications. Here, we provide an overview of light sheet-based microscopy assays for in vitro and in vivo imaging of biological samples, including cell extracts, soft gels, and large multicellular organisms. We furthermore describe computational tools for basic image processing and data inspection.

Novel approaches to bio-imaging and automated computational image processing allow the design of truly quantitative studies in developmental biology. Cell behavior, cell fate decisions, cell interactions during tissue morphogenesis, and gene expression dynamics can be analyzed in vivo for entire complex organisms and throughout embryonic development. We review state-of-the-art technology for live imaging, focusing on fluorescence light microscopy techniques for system-level investigations of animal development, and discuss computational approaches to image segmentation, cell tracking, automated data annotation, and biophysical modeling. We argue that the substantial increase in data complexity and size requires sophisticated new strategies to data analysis to exploit the enormous potential of these new resources.

We address the problem of segmenting 3D microscopic volumetric intensity images of a collection of spatially correlated objects (such as fluorescently labeled nuclei in a tissue). This problem arises in the study of tissue morphogenesis where cells and cellular components are organized in accord with biological role and fate. We formulate the image model as stochastically generated based on biological priors and physics of image formation. We express the segmentation problem in terms of Bayesian inference and use data-driven Markov Chain Monte Carlo to fit the image model to data. We perform an initial step in which the intensity volume is approximated as an expansion in 4D spherical harmonics, the coefficients of which capture the general organization of objects. Since cell nuclei are membrane-bound their shapes are subject to membrane lipid bilayer bending energy, which we use to constrain individual contours. Moreover, we parameterize the nuclear contours using spherical harmonic functions, which provide a shape description with no restriction to particular symmetries. We demonstrate the utility of our approach using synthetic and real fluorescence microscopy data.

We address the problem of segmenting 3D microscopic volumetric intensity images of a collection of spatially correlated objects (such as fluorescently labeled nuclei in a tissue). This problem arises in the study of tissue morphogenesis where cells and cellular components are organized in accord with biological role and fate. We formulate the image model as stochastically generated based on biological priors and physics of image formation. We express the segmentation problem in terms of Bayesian inference and use data-driven Markov Chain Monte Carlo to fit the image model to data. We perform an initial step in which the intensity volume is approximated as an expansion in 4D spherical harmonics, the coefficients of which capture the general organization of objects. Since cell nuclei are membrane-bound their shapes are subject to membrane lipid bilayer bending energy, which we use to constrain individual contours. Moreover, we parameterize the nuclear contours using spherical harmonic functions, which provide a shape description with no restriction to particular symmetries. We demonstrate the utility of our approach using synthetic and real fluorescence microscopy data.

Numerical deconvolution of 3D fluorescence microscopy data yields sharper images by reversing the known optical aberrations introduced during the acquisition process. When additional prior information such as the topology and smoothness of the imaged object surface is available, the deconvolution can be performed by fitting a parametric surface directly to the image data. In this work, we incorporate such additional information into the deconvolution process and focus on a parametric shape description suitable for the study of organelles, cells and tissues. Such membrane-bound closed biological surfaces are often topologically equivalent to the sphere and can be parameterized as series expansions in spherical harmonic functions (SH). Because image data are noisy and the SH-parameterization is prone to the formation of high curvatures even at low expansion orders, the parametric deconvolution problem is ill-posed and must be regularized. We use the shape bending energy as a regularizing (smoothing) function, and determine the regularization parameter graphically with the help of the L-curve method. We demonstrate the complete deconvolution scheme, including the initial image segmentation, the calculation of a good starting surface and the construction of the L-curve, using real and synthetic image data.

A number of groups have utilized molecular dynamics (MD) to calculate slow-motional electron paramagnetic resonance (EPR) spectra of spin labels attached to biomolecules. Nearly all such calculations have been based on some variant of the trajectory method introduced by Robinson, Slutsky and Auteri (J. Chem. Phys. 1992, 96, 2609-2616). Here we present an alternative approach that is specifically adapted to the diffusion operator-based stochastic Liouville equation (SLE) formalism that is also widely used to calculate slow-motional EPR line shapes. Specifically, the method utilizes MD trajectories to derive diffusion parameters such as the rotational diffusion tensor, diffusion tilt angles, and expansion coefficients of the orienting potential, which are then used as direct inputs to the SLE line shape program. This approach leads to a considerable improvement in computational efficiency over trajectory-based methods, particularly for high frequency, high field EPR. It also provides a basis for deconvoluting the effects of local spin label motion and overall motion of the labeled molecule or domain: once the local motion has been characterized by this approach, the label diffusion parameters may be used in conjunction with line shape analysis at lower EPR frequencies to characterize global motions. The method is validated by comparison of the MD predicted line shapes to experimental high frequency (250 GHz) EPR spectra.

We define four complex numbers representing the parameters needed to specify an elephantine shape. The real and imaginary parts of these complex numbers are the coefficients of a Fourier coordinate expansion, a powerful tool for reducing the data required to define shapes.

An important open question in biophysics is to understand how mechanical forces shape membrane-bounded cells and their organelles. A general solution to this problem is to calculate the bending energy of an arbitrarily shaped membrane surface, which can include both lipids and cytoskeletal proteins, and minimize the energy subject to all mechanical constraints. However, the calculations are difficult to perform, especially for shapes that do not possess axial symmetry. We show that the spherical harmonics parameterization (SHP) provides an analytic description of shape that can be used to quickly and reliably calculate minimum energy shapes of both symmetric and asymmetric surfaces. Using this method, we probe the entire set of shapes predicted by the bilayer couple model, unifying work based on different computational approaches, and providing additional details of the transitions between different shape classes. In addition, we present new minimum-energy morphologies based on non-linear models of membrane skeletal elasticity that closely mimic extreme shapes of red blood cells. The SHP thus provides a versatile shape description that can be used to investigate forces that shape cells.

Electron paramagnetic resonance (EPR) spectra are simulated by solving the stochastic Liouville equation (SLE) of motion with the incorporation of a hindering potential that restricts the Brownian rotational diffusion of the spin-label. Such a potential has been expanded in spherical harmonic functions in the past, under the assumptions of cylindrical and inversion symmetries appropriate for the description of liquid crystals and other ordered systems. In this work, the theory is formulated to allow for a general potential with no symmetry restrictions. This extends the utility of EPR as a structural tool, by facilitating its connection with molecular dynamics (MD),since the spectral simulation incorporates a more realistic representation of the complicated topology around the spin-label that is found in labeled biomolecules.