Imaging and characterizing cells using tomography

Loss of ZNF148 enhances insulin secretion in human pancreatic β cells

Insulin secretion from pancreatic β cells is essential to the maintenance of glucose homeostasis. Defects in this process result in diabetes. Identifying genetic regulators that impair insulin secretion is crucial for the identification of novel therapeutic targets. Here, we show that reduction of ZNF148 in human islets, and its deletion in stem cell-derived β cells (SC-β cells), enhances insulin secretion. Transcriptomics of ZNF148-deficient SC-β cells identifies increased expression of annexin and S100 genes whose proteins form tetrameric complexes involved in regulation of insulin vesicle trafficking and exocytosis. ZNF148 in SC-β cells prevents translocation of annexin A2 from the nucleus to its functional place at the cell membrane via direct repression of S100A16 expression. These findings point to ZNF148 as a regulator of annexin-S100 complexes in human β cells and suggest that suppression of ZNF148 may provide a novel therapeutic strategy to enhance insulin secretion.

Soft X-ray tomograms provide a structural basis for whole-cell modeling

Developing in silico models that accurately reflect a whole, functional cell is an ongoing challenge in biology. Current efforts bring together mathematical models, probabilistic models, visual representations, and data to create a multi-scale description of cellular processes. A realistic whole-cell model requires imaging data since it provides spatial constraints and other critical cellular characteristics that are still impossible to obtain by calculation alone. This review introduces Soft X-ray Tomography (SXT) as a powerful imaging technique to visualize and quantify the mesoscopic (~25 nm spatial scale) organelle landscape in whole cells. SXT generates three-dimensional reconstructions of cellular ultrastructure and provides a measured structural framework for whole-cell modeling. Combining SXT with data from disparate technologies at varying spatial resolutions provides further biochemical details and constraints for modeling cellular mechanisms. We conclude, based on the results discussed here, that SXT provides a foundational dataset for a broad spectrum of whole-cell modeling experiments.

ClusterAlign: A fiducial tracking and tilt series alignment tool for thick sample tomography

Thick specimens, as encountered in cryo-scanning transmission electron tomography, offer special challenges to conventional reconstruction workflows. The visibility of features, including gold nanoparticles introduced as fiducial markers, varies strongly through the tilt series. As a result, tedious manual refinement may be required in order to produce a successful alignment. Information from highly tilted views must often be excluded to the detriment of axial resolution in the reconstruction. We introduce here an approach to tilt series alignment based on identification of fiducial particle clusters that transform coherently in rotation, essentially those that lie at similar depth. Clusters are identified by comparison of tilted views with a single untilted reference, rather than with adjacent tilts. The software, called ClusterAlign, proves robust to poor signal to noise ratio and varying visibility of the individual fiducials and is successful in carrying the alignment to the ends of the tilt series where other methods tend to fail. ClusterAlign may be used to generate a list of tracked fiducials, to align a tilt series, or to perform a complete 3D reconstruction. Tools to evaluate alignment error by projection matching are included. Execution involves no manual intervention, and adherence to standard file formats facilitates an interface with other software, particularly IMOD/etomo, tomo3d, and tomoalign.

Evaluation of imaging setups for quantitative phase contrast nanoCT of mineralized biomaterials

X-ray nano-tomography with phase contrast (nanoCT) using synchrotron radiation is a powerful tool to non-destructively investigate 3D material properties at the nanoscale. In large bone lesions, such as severe bone fractures, bone cancer or other diseases, bone grafts substituting the lost bone might be necessary. Such grafts can be of biological origin or be composed of a synthetic bone substitute. The long-term functioning of artificial bone substitutes depends on many factors. Synchrotron nanoCT imaging has great potential to contribute to further the understanding of integration of implants into bone tissue by imaging the spatial interaction between bone tissue and implant, and by accessing the interface between implant material and bone tissue. With this aim, a methodology for evaluating the image quality is presented for in-line phase contrast nanoCT images of bone scaffold samples. A PMMA-embedded tricalcium phosphate scaffold was used with both a closed and an open porosity structure and bone ingrowths as a representative system of three known materials. Parameters such as spatial resolution and signal-to-noise ratio were extracted and used to explore and quantitatively compare the effects of implementation choices in the imaging setup, such as camera technology and imaging energy, on the resulting image quality. Increasing the X-ray energy from 17.5 keV to 29.6 keV leads to a notable improvement in image quality regardless of the camera technology used, with the two tested camera setups performing at a comparable level when the recorded intensity was kept constant.

Soft X-ray tomography to map and quantify organelle interactions at the mesoscale

Inter-organelle interactions are a vital part of normal cellular function; however, these have proven difficult to quantify due to the range of scales encountered in cell biology and the throughput limitations of traditional imaging approaches. Here, we demonstrate that soft X-ray tomography (SXT) can be used to rapidly map ultrastructural reorganization and inter-organelle interactions in intact cells. SXT takes advantage of the naturally occurring, differential X-ray absorption of the carbon-rich compounds in each organelle. Specifically, we use SXT to map the spatiotemporal evolution of insulin vesicles and their co-localization and interaction with mitochondria in pancreatic β cells during insulin secretion and in response to different stimuli. We quantify changes in the morphology, biochemical composition, and relative position of mitochondria and insulin vesicles. These findings highlight the importance of a comprehensive and unbiased mapping at the mesoscale to characterize cell reorganization that would be difficult to detect with other existing methodologies.

Single-Cell Chemistry of Photoactivatable Platinum Anticancer Complexes

The Pt(IV) prodrug trans, trans, trans-[Pt(pyridine)2(N3)2(OH)2] (Pt1) and its coumarin derivative trans, trans, trans-[Pt(pyridine)2(N3)2(OH)(coumarin-3-carboxylate)] (Pt2) are promising agents for photoactivated chemotherapy. These complexes are inert in the dark but release Pt(II) species and radicals upon visible light irradiation, resulting in photocytotoxicity toward cancer cells. Here, we have used synchrotron techniques to investigate the in-cell behavior of these prodrugs and visualize, for the first time, changes in cellular morphology and Pt localization upon treatment with and without light irradiation. We show that photoactivation of Pt2 induces remarkable cellular damage with extreme alterations to multiple cellular components, including formation of vacuoles, while also significantly increasing the cellular accumulation of Pt species compared to dark conditions. X-ray absorption near-edge structure (XANES) measurements in cells treated with Pt2 indicate only partial reduction of the prodrug upon irradiation, highlighting that phototoxicity in cancer cells may involve not only Pt(II) photoproducts but also photoexcited Pt(IV) species.

Toward Compositional Contrast by Cryo-STEM

Electron microscopy (EM) is the most versatile tool for the study of matter at scales ranging from subatomic to visible. The high vacuum environment and the charged irradiation require careful stabilization of many specimens of interest. Biological samples are particularly sensitive due to their composition of light elements suspended in an aqueous medium. Early investigators developed techniques of embedding and staining with heavy metal salts for contrast enhancement. Indeed, the Nobel Prize in 1974 recognized Claude, de Duve, and Palade for establishment of the field of cell biology, largely due to their developments in separation and preservation of cellular components for electron microscopy. A decade later, cryogenic fixation was introduced. Vitrification of the water avoids the need for dehydration and provides an ideal matrix in which the organic macromolecules are suspended; the specimen represents a native state, suddenly frozen in time at temperatures below -150 °C. The low temperature maintains a low vapor pressure for the electron microscope, and the amorphous nature of the medium avoids diffraction contrast from crystalline ice. Such samples are extremely delicate, however, and cryo-EM imaging is a race for information in the face of ongoing damage by electron irradiation. Through this journey, cryo-EM enhanced the resolution scale from membranes to molecules and most recently to atoms. Cryo-EM pioneers, Dubochet, Frank, and Henderson, were awarded the Nobel Prize in 2017 for high resolution structure determination of biological macromolecules.A relatively untapped feature of cryo-EM is its preservation of composition. Nothing is added and nothing removed. Analytical spectroscopies based on electron energy loss or X-ray emission can be applied, but the very small interaction cross sections conflict with the weak exposures required to preserve sample integrity. To what extent can we interpret quantitatively the pixel intensities in images themselves? Conventional cryo-transmission electron microscopy (TEM) is limited in this respect, due to the strong dependence of the contrast transfer on defocus and the absence of contrast at low spatial frequencies.Inspiration comes largely from a different modality for cryo-tomography, using soft X-rays. Contrast depends on the difference in atomic absorption between carbon and oxygen in a region of the spectrum between their core level ionization energies, the so-called water window. Three dimensional (3D) reconstruction provides a map of the local X-ray absorption coefficient. The quantitative contrast enables the visualization of organic materials without stain and measurement of their concentration quantitatively. We asked, what aspects of the quantitative contrast might be transferred to cryo-electron microscopy?Compositional contrast is accessible in scanning transmission EM (STEM) via incoherent elastic scattering, which is sensitive to the atomic number Z. STEM can be regarded as a high energy, low angle diffraction measurement performed pixel by pixel with a weakly convergent beam. When coherent diffraction effects are absent, that is, in amorphous materials, a dark field signal measures quantitatively the flux scattered from the specimen integrated over the detector area. Learning to interpret these signals will open a new dimension in cryo-EM. This Account describes our efforts so far to introduce STEM for cryo-EM and tomography of biological specimens. We conclude with some thoughts on further developments.

X-ray-Based Techniques to Study the Nano-Bio Interface

X-ray-based analytics are routinely applied in many fields, including physics, chemistry, materials science, and engineering. The full potential of such techniques in the life sciences and medicine, however, has not yet been fully exploited. We highlight current and upcoming advances in this direction. We describe different X-ray-based methodologies (including those performed at synchrotron light sources and X-ray free-electron lasers) and their potentials for application to investigate the nano-bio interface. The discussion is predominantly guided by asking how such methods could better help to understand and to improve nanoparticle-based drug delivery, though the concepts also apply to nano-bio interactions in general. We discuss current limitations and how they might be overcome, particularly for future use in vivo.

Strong intracellular signal inactivation produces sharper and more robust signaling from cell membrane to nucleus

For a chemical signal to propagate across a cell, it must navigate a tortuous environment involving a variety of organelle barriers. In this work we study mathematical models for a basic chemical signal, the arrival times at the nuclear membrane of proteins that are activated at the cell membrane and diffuse throughout the cytosol. Organelle surfaces within human B cells are reconstructed from soft X-ray tomographic images, and modeled as reflecting barriers to the molecules’ diffusion. We show that signal inactivation sharpens signals, reducing variability in the arrival time at the nuclear membrane. Inactivation can also compensate for an observed slowdown in signal propagation induced by the presence of organelle barriers, leading to arrival times at the nuclear membrane that are comparable to models in which the cytosol is treated as an open, empty region. In the limit of strong signal inactivation this is achieved by filtering out molecules that traverse non-geodesic paths.

The inside of cells is a complex spatial environment, filled with organelles, filaments and proteins. It is an open question how cell signaling pathways function robustly in the presence of such spatial heterogeneity. In this work we study how organelle barriers influence the most basic of chemical signals; the diffusive propagation of an activated protein from the cell membrane to nucleus. Three-dimensional B cell organelle and membrane geometries reconstructed from soft X-ray tomographic images are used in building mathematical models of the signal propagation process. Our models demonstrate that organelle barriers significantly increase the time required for a diffusing protein to traverse from the cell membrane to nucleus when compared to a cell with an empty cytosolic space. We also show that signal inactivation, a fundamental component of all signaling pathways, can provide robustness in the signal arrival time in two ways. Increasing rates of signal inactivation reduce variability in the arrival time, while also dramatically reducing the degree to which organelle barriers increase the arrival time (in comparison to a cell with an empty cytosol).

Assaying three-dimensional cellular architecture using X-ray tomographic and correlated imaging approaches

Much of our understanding of the spatial organization of and interactions between cellular organelles and macromolecular complexes has been the result of imaging studies utilizing either light- or electron-based microscopic analyses. These classical approaches, while insightful, are nonetheless limited either by restrictions in resolution or by the sheer complexity of generating multidimensional data. Recent advances in the use and application of X-rays to acquire micro- and nanotomographic data sets offer an alternative methodology to visualize cellular architecture at the nanoscale. These new approaches allow for the subcellular analyses of unstained vitrified cells and three-dimensional localization of specific protein targets and have served as an essential tool in bridging light and electron correlative microscopy experiments. Here, we review the theory, instrumentation details, acquisition principles, and applications of both soft X-ray tomography and X-ray microscopy and how the use of these techniques offers a succinct means of analyzing three-dimensional cellular architecture. We discuss some of the recent work that has taken advantage of these approaches and detail how they have become integral in correlative microscopy workflows.

Precise correlative method of Cryo-SXT and Cryo-FM for organelle identification

Cryogenic soft X-ray tomography (Cryo-SXT) is ideally suitable to image the 3D sub-cellular architecture and organization of cells with high resolution in the near-native preservation state. Cryogenic fluorescence microscopy (Cryo-FM) can determine the location of a molecule of interest that has been labeled with a fluorescent tag, thus revealing the function of the cells. To understand the relations between the sub-cellular architecture and the function of cells, correlative Cryo-SXT and Cryo-FM was applied. This method required the matching of images of different modalities, and the accuracy of the matching is important. Here, a precise correlative method of Cryo-SXT and Cryo-FM is introduced. The capability of matching images of different modalities with high resolution was verified by simulations and practical experiments, and the method was used to identify vacuoles and mitochondria.

Soft X-ray tomography: virtual sculptures from cell cultures

Cellular complexity is represented best in high-spatial resolution, three-dimensional (3D) reconstructions. Soft X-ray tomography (SXT) generates detailed volumetric reconstructions of cells preserved in a near-to-native, frozen-hydrated state. SXT is broadly applicable and can image specimens ranging from bacteria to large mammalian cells. As a reference, we summarize light and electron microscopic methods. We then present an overview of SXT and discuss its role in cellular imaging. We detail the methods used to image biological specimens and present recent highlights that illustrate the capabilities of the technique. We conclude by discussing correlative imaging, specifically the combination of SXT and fluorescence microscopy performed on the same specimen. This correlated approach combines the structural morphology of a cell with its physiological characteristics to build a deeply informative composite view.

Imaging cell morphology and physiology using X-rays

Morphometric measurements, such as quantifying cell shape, characterizing sub-cellular organization, and probing cell-cell interactions, are fundamental in cell biology and clinical medicine. Until quite recently, the main source of morphometric data on cells has been light- and electron-based microscope images. However, many technological advances have propelled X-ray microscopy into becoming another source of high-quality morphometric information. Here, we review the status of X-ray microscopy as a quantitative biological imaging modality. We also describe the combination of X-ray microscopy data with information from other modalities to generate polychromatic views of biological systems. For example, the amalgamation of molecular localization data, from fluorescence microscopy or spectromicroscopy, with structural information from X-ray tomography. This combination of data from the same specimen generates a more complete picture of the system than that can be obtained by a single microscopy method. Such multimodal combinations greatly enhance our understanding of biology by combining physiological and morphological data to create models that more accurately reflect the complexities of life.

Studying the Spatial Organization of ESCRTs in Cytokinetic Abscission Using the High-Resolution Imaging Techniques SIM and Cryo-SXT

The ESCRT machinery mediates scission of the intercellular bridge that connects two daughter cells at the end of cytokinesis. Structured illumination microscopy (SIM) and cryo-soft-X-ray tomography (cryo-SXT) have been used in recent years to study the topology of ESCRT-driven cytokinetic abscission. These studies revealed that the intercellular bridge is occupied by cortical rings and spiral-like filaments and that ESCRTs form ring-like structures in this region during abscission. In this chapter, we provide two protocols: a protocol for determining the spatial organization of specific ESCRT components at the intercellular bridge using SIM and a protocol for resolving the ultrastructural organization of cortical filaments at the intercellular bridge using cryo-SXT.

A comparison of absorption and phase contrast for X-ray imaging of biological cells

X-ray imaging allows biological cells to be examined at a higher resolution than possible with visible light and without some of the preparation difficulties associated with electron microscopy of thick samples. The most used and developed technique is absorption contrast imaging in the water window which exploits the contrast between carbon and oxygen at an energy of around 500 eV. A variety of phase contrast techniques are also being developed. In general these operate at a higher energy, enabling thicker cells to be examined and, in some cases, can be combined with X-ray fluorescence imaging to locate specific metals. The various methods are based on the differences between the complex refractive indices of the cellular components and the surrounding cytosol or nucleosol, the fluids present in the cellular cytoplasm and nucleus. The refractive indices can be calculated from the atomic composition and density of the components. These in turn can be obtained from published measurements using techniques such as chemical analysis, scanning electron microscopy and X-ray imaging at selected energies. As examples, the refractive indices of heterochromatin, inner mitochondrial membranes, the neutral core of lipid droplets, starch granules, cytosol and nucleosol are calculated. The refractive index calculations enable the required doses and fluences to be obtained to provide images with sufficient statistical significance, for X-ray energies between 200 and 4000 eV. The statistical significance (e.g. the Rose criterion) for various requirements is discussed. The calculations reveal why some cellular components are more visible by absorption contrast and why much greater exposure times are required to see some cellular components. A comparison of phase contrast as a function of photon energy with absorption contrast in the water window is provided and it is shown that much higher doses are generally required for the phase contrast measurements. This particularly applies to those components with a high carbon content but with a mass density similar to the surrounding cytosol or nucleosol. The results provide guidance for the most appropriate conditions for X-ray imaging of individual cellular components within cells of various thicknesses.

Comparison of 3D cellular imaging techniques based on scanned electron probes: Serial block face SEM vs. Axial bright-field STEM tomography

Microscopies based on focused electron probes allow the cell biologist to image the 3D ultrastructure of eukaryotic cells and tissues extending over large volumes, thus providing new insight into the relationship between cellular architecture and function of organelles. Here we compare two such techniques: electron tomography in conjunction with axial bright-field scanning transmission electron microscopy (BF-STEM), and serial block face scanning electron microscopy (SBF-SEM). The advantages and limitations of each technique are illustrated by their application to determining the 3D ultrastructure of human blood platelets, by considering specimen geometry, specimen preparation, beam damage and image processing methods. Many features of the complex membranes composing the platelet organelles can be determined from both approaches, although STEM tomography offers a higher ∼3 nm isotropic pixel size, compared with ∼5 nm for SBF-SEM in the plane of the block face and ∼30 nm in the perpendicular direction. In this regard, we demonstrate that STEM tomography is advantageous for visualizing the platelet canalicular system, which consists of an interconnected network of narrow (∼50-100 nm) membranous cisternae. In contrast, SBF-SEM enables visualization of complete platelets, each of which extends ∼2 µm in minimum dimension, whereas BF-STEM tomography can typically only visualize approximately half of the platelet volume due to a rapid non-linear loss of signal in specimens of thickness greater than ∼1.5 µm. We also show that the limitations of each approach can be ameliorated by combining 3D and 2D measurements using a stereological approach.

Quantitative imaging of Candida utilis and its organelles by soft X-ray Nano-CT

Soft X-ray microscopy has excellent characteristics for imaging cells and subcellular structures. In this paper, the yeast strain, Candida utilis, was imaged by soft X-ray microscopy and three-dimensional volumes were reconstructed with the SART-TV method. We performed segmentation on the reconstruction in three dimensions and identified several types of subcellular architecture within the specimen cells based on their linear absorption coefficient (LAC) values. Organelles can be identified by the correlation between the soft X-ray LAC values and the subcellular architectures. Quantitative analyses of the volume ratio of organelles to whole cell in different phases were also carried out according to the three-dimensional datasets. With such excellent features, soft X-ray imaging has a great influence in the field of biological cellular and subcellular research.

Chromatin organization regulates viral egress dynamics

Various types of DNA viruses are known to elicit the formation of a large nuclear viral replication compartment and marginalization of the cell chromatin. We used three-dimensional soft x-ray tomography, confocal and electron microscopy, combined with numerical modelling of capsid diffusion to analyse the molecular organization of chromatin in herpes simplex virus 1 infection and its effect on the transport of progeny viral capsids to the nuclear envelope. Our data showed that the formation of the viral replication compartment at late infection resulted in the enrichment of heterochromatin in the nuclear periphery accompanied by the compaction of chromatin. Random walk modelling of herpes simplex virus 1-sized particles in a three-dimensional soft x-ray tomography reconstruction of an infected cell nucleus demonstrated that the peripheral, compacted chromatin restricts viral capsid diffusion, but due to interchromatin channels capsids are able to reach the nuclear envelope, the site of their nuclear egress.

Mesoscale imaging with cryo-light and X-rays: Larger than molecular machines, smaller than a cell

In the context of cell biology, the term mesoscale describes length scales ranging from that of an individual cell, down to the size of the molecular machines. In this spatial regime, small building blocks self-organise to form large, functional structures. A comprehensive set of rules governing mesoscale self-organisation has not been established, making the prediction of many cell behaviours difficult, if not impossible. Our knowledge of mesoscale biology comes from experimental data, in particular, imaging. Here, we explore the application of soft X-ray tomography (SXT) to imaging the mesoscale, and describe the structural insights this technology can generate. We also discuss how SXT imaging is complemented by the addition of correlative fluorescence data measured from the same cell. This combination of two discrete imaging modalities produces a 3D view of the cell that blends high-resolution structural information with precise molecular localisation data.

Towards correlative super-resolution fluorescence and electron cryo-microscopy

Correlative light and electron microscopy (CLEM) has become a powerful tool in life sciences. Particularly cryo-CLEM, the combination of fluorescence cryo-microscopy (cryo-FM) permitting for non-invasive specific multi-colour labelling, with electron cryo-microscopy (cryo-EM) providing the undisturbed structural context at a resolution down to the Ångstrom range, has enabled a broad range of new biological applications. Imaging rare structures or events in crowded environments, such as inside a cell, requires specific fluorescence-based information for guiding cryo-EM data acquisition and/or to verify the identity of the structure of interest. Furthermore, cryo-CLEM can provide information about the arrangement of specific proteins in the wider structural context of their native nano-environment. However, a major obstacle of cryo-CLEM currently hindering many biological applications is the large resolution gap between cryo-FM (typically in the range of ∼400 nm) and cryo-EM (single nanometre to the Ångstrom range). Very recently, first proof of concept experiments demonstrated the feasibility of super-resolution cryo-FM imaging and the correlation with cryo-EM. This opened the door towards super-resolution cryo-CLEM, and thus towards direct correlation of structural details from both imaging modalities.

"Reduced" Coumarin Dyes with an O-Phosphorylated 2,2-Dimethyl-4-(hydroxymethyl)-1,2,3,4-tetrahydroquinoline Fragment: Synthesis, Spectra, and STED Microscopy

Large Stokes-shift coumarin dyes with an O-phosphorylated 4-(hydroxymethyl)-2,2-dimethyl-1,2,3,4-tetrahydroquinoline fragment emitting in the blue, green, and red regions of the visible spectrum were synthesized. For this purpose, N-substituted and O-protected 1,2-dihydro-7-hydroxy-2,2,4-trimethylquinoline was oxidized with SeO2 to the corresponding α,β-unsaturated aldehyde and then reduced with NaBH4 in a "one-pot" fashion to yield N-substituted and 7-O-protected 4-(hydroxymethyl)-7-hydroxy-2,2-dimethyl-1,2,3,4-tetrahydroquinoline as a common precursor to all the coumarin dyes reported here. The photophysical properties of the new dyes ("reduced coumarins") and 1,2-dihydroquinoline analogues (formal precursors) with a trisubstituted C=C bond were compared. The "reduced coumarins" were found to be more photoresistant and brighter than their 1,2-dihydroquinoline counterparts. Free carboxylate analogues, as well as their antibody conjugates (obtained from N-hydroxysuccinimidyl esters) were also prepared. All studied conjugates with secondary antibodies afforded high specificity and were suitable for fluorescence microscopy. The red-emitting coumarin dye bearing a betaine fragment at the C-3-position showed excellent performance in stimulation emission depletion (STED) microscopy.

Resolving new ultrastructural features of cytokinetic abscission with soft-X-ray cryo-tomography

Mammalian cytokinetic abscission is mediated by the ESCRT membrane fission machinery. While much has been clarified on the topology and kinetics of abscission through high-resolution microscopy, key questions regarding the mechanism of abscission remain open. Here we apply cryogenic soft-X-ray tomography to elucidate new ultrastructural details in the intercellular membrane bridge connecting cells undergoing abscission. In particular, we resolve defined ring-like structures inside the midbody dark zone that have been inaccessible to EM, and identify membrane extrusions at the abscission sites. In cells at late stages of abscission we resolve a complex array of helical spirals, extending the structural information obtained by EM. Our results highlight the advantages of soft-X-ray tomography and emphasize the importance of using complementary approaches for characterizing cellular structures. Notably, by providing new structural data from intact cells we present a realistic view on the topology of abscission and suggest new mechanistic models for ESCRT mediated abscission.

Cox process representation and inference for stochastic reaction-diffusion processes

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction–diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction–diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction–diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.

Stochastic reaction-diffusion systems are used for modelling spatial dynamics in many disciplines, but parameter inference and model selection remain challenging. Here the authors offer a solution enabled by a connection between reaction-diffusion and the well-studied spatio-temporal Cox processes.

Interface Detection Using a Quenched-Noise Version of the Edwards-Wilkinson Equation

We report here a multipurpose dynamic-interface-based segmentation tool, suitable for segmenting planar, cylindrical, and spherical surfaces in 3D. The method is fast enough to be used conveniently even for large images. Its implementation is straightforward and can be easily realized in many environments. Its memory consumption is low, and the set of parameters is small and easy to understand. The method is based on the Edwards-Wilkinson equation, which is traditionally used to model the equilibrium fluctuations of a propagating interface under the influence of temporally and spatially varying noise. We report here an adaptation of this equation into multidimensional image segmentation, and its efficient discretization.