Spatial organization and correlations of cell nuclei in brain tumors

Non-invasive scoring of cellular atypia in keratinocyte cancers in 3D LC-OCT images using Deep Learning

Diagnosis based on histopathology for skin cancer detection is today's gold standard and relies on the presence or absence of biomarkers and cellular atypia. However it suffers drawbacks: it requires a strong expertise and is time-consuming. Moreover the notion of atypia or dysplasia of the visible cells used for diagnosis is very subjective, with poor inter-rater agreement reported in the literature. Lastly, histology requires a biopsy which is an invasive procedure and only captures a small sample of the lesion, which is insufficient in the context of large fields of cancerization. Here we demonstrate that the notion of cellular atypia can be objectively defined and quantified with a non-invasive in-vivo approach in three dimensions (3D). A Deep Learning (DL) algorithm is trained to segment keratinocyte (KC) nuclei from Line-field Confocal Optical Coherence Tomography (LC-OCT) 3D images. Based on these segmentations, a series of quantitative, reproducible and biologically relevant metrics is derived to describe KC nuclei individually. We show that, using those metrics, simple and more complex definitions of atypia can be derived to discriminate between healthy and pathological skins, achieving Area Under the ROC Curve (AUC) scores superior than 0.965, largely outperforming medical experts on the same task with an AUC of 0.766. All together, our approach and findings open the door to a precise quantitative monitoring of skin lesions and treatments, offering a promising non-invasive tool for clinical studies to demonstrate the effects of a treatment and for clinicians to assess the severity of a lesion and follow the evolution of pre-cancerous lesions over time.

Remodelling of the fibre-aggregate structure of collagen gels by cancer-associated fibroblasts: A time-resolved grey-tone image analysis based on stochastic modelling

Introduction

Solid tumors consist of tumor cells associated with stromal and immune cells, secreted factors and extracellular matrix (ECM), which together constitute the tumor microenvironment. Among stromal cells, activated fibroblasts, known as cancer-associated fibroblasts (CAFs) are of particular interest. CAFs secrete a plethora of ECM components including collagen and modulate the architecture of the ECM, thereby influencing cancer cell migration. The characterization of the collagen fibre network and its space and time-dependent microstructural modifications is key to investigating the interactions between cells and the ECM. Developing image analysis tools for that purpose is still a challenge because the structural complexity of the collagen network calls for specific statistical descriptors. Moreover, the low signal-to-noise ratio of imaging techniques available for time-resolved studies rules out standard methods based on image segmentation.

Methods

In this work, we develop a novel approach based on the stochastic modelling of the gel structure and on grey-tone image analysis. The method is then used to study the remodelling of a collagen matrix by migrating breast cancer-derived CAFs in a three-dimensional spheroid model of cellular invasion imaged by time-lapse confocal microscopy.

Results

The structure of the collagen at the scale of a few microns consists in regions with high fibre density separated by depleted regions, which can be thought of as aggregates and pores. The approach developped captures this two-scale structure with a clipped Gaussian field model to describe the aggregates-and-pores large-scale structure, and a homogeneous Boolean model to describe the small-scale fibre network within the aggregates. The model parameters are identified by fitting the grey-tone histograms and correlation functions of the images. The method applies to unprocessed grey-tone images, and it can therefore be used with low magnification, noisy time-lapse reflectance images. When applied to the CAF spheroid time-resolved images, the method reveals different matrix densification mechanisms for the matrix in direct contact or far from the cells.

Conclusion

We developed a novel and multidisciplinary image analysis approach to investigate the remodelling of fibrillar collagen in a 3D spheroid model of cellular invasion. The specificity of the method is that it applies to the unprocessed grey-tone images, and it can therefore be used with noisy time-lapse reflectance images of non-fluorescent collagen. When applied to the CAF spheroid time-resolved images, the method reveals different matrix densification mechanisms for the matrix in direct contact or far from the cells.

Is the Fixed Periodic Treatment Effective for the Tumor System without Complete Information?

Objective

The treatment plans designed with the guidance of the mathematical model and adaptive strategy can trap tumor subpopulations in a periodic and controllable loop. But this process requires detailed information about the tumor system, which is difficult to obtain. Therefore, we wondered whether the fixed periodic treatment plans designed with the typical values of population parameters could be applied to a similar tumor system without complete information.

Methods

A binary tumor system constructed by an EGFR-mutant and a KRAS-mutant cell line was used to explore the applicability of the fixed periodic treatment plans. The dynamics of this system were described by combining the Lotka-Volterra model with the framework of the nonlinear mixed-effects model. The typical values of population parameters were used to design the plans, and the robust plans were screened through parameter variation. These screened plans were examined their applicability in animal experiments and simulations.

Results

In animal experiments where system parameters vary from -30% to 30%, the "osimertinib administration, withdrawal, FK866 administration and withdrawal" plan can trap subpopulations of the system in periodic cycles. In simulation, when there was an unknown resistant subpopulation, the screened fixed periodic treatment plans can still delay the evolution of resistance. The median outcomes of screened plans were better than conventional sequential treatment in most cases. There was no significant difference between the outcomes of the screened plan with median stability and the optimal therapy. The evolutionary trajectories of these two plans were similar.

Conclusion

According to the results, these fixed periodic plans should be tried in treatment even the information of the tumor system was incomplete.

Probing information content of hierarchical n-point polytope functions for quantifying and reconstructing disordered systems

Disordered systems are ubiquitous in physical, biological, and material sciences. Examples include liquid and glassy states of condensed matter, colloids, granular materials, porous media, composites, alloys, packings of cells in avian retina, and tumor spheroids, to name but a few. A comprehensive understanding of such disordered systems requires, as the first step, systematic quantification, modeling, and representation of the underlying complex configurations and microstructure, which is generally very challenging to achieve. Recently, we introduced a set of hierarchical statistical microstructural descriptors, i.e., the "n-point polytope functions" P_{n}, which are derived from the standard n-point correlation functions S_{n}, and successively included higher-order n-point statistics of the morphological features of interest in a concise, explainable, and expressive manner. Here we investigate the information content of the P_{n} functions via optimization-based realization rendering. This is achieved by successively incorporating higher-order P_{n} functions up to n=8 and quantitatively assessing the accuracy of the reconstructed systems via unconstrained statistical morphological descriptors (e.g., the lineal-path function). We examine a wide spectrum of representative random systems with distinct geometrical and topological features. We find that, generally, successively incorporating higher-order P_{n} functions and, thus, the higher-order morphological information encoded in these descriptors leads to superior accuracy of the reconstructions. However, incorporating more P_{n} functions into the reconstruction also significantly increases the complexity and roughness of the associated energy landscape for the underlying stochastic optimization, making it difficult to convergence numerically.

Curcumin Effects on Memory Impairment and Restoration of Irregular Neuronal Distribution in the Hippocampal CA1 Region After Global Cerebral Ischemia in Male Rats

Introduction:

Global Cerebral Ischemia (GCI) causes neuronal damage with subsequent neurological and cognitive impairments. Curcumin has anti-inflammatory, antioxidant, and neuroprotective properties, which makes it a potential candidate for improving GCI-induced impairments. This study aimed to investigate the effects of curcumin on the neurological and memory deficits, as well as spatial neuronal distribution in the Cornu Ammonis 1 region after GCI in rats.

Methods:

56 Sprague-Dawley male rats were randomly assigned into 4 groups of sham (n=14), control (n=14), curcumin 50 mg/kg (n=14), and curcumin 100 mg/kg (n=14). Each group was divided into the two subgroups of short-term (7 days) and long-term (28 days) treatment periods. The Neurological Severity Score (NSS), passive avoidance task, and the traction test were performed at postoperative days of 0, 1, 2, 3, 7, 14, 21, and 28. The novel object recognition test and Voronoi tessellation were carried out on days 7 and 28 after GCI.

Results:

Curcumin 100 mg/kg significantly decreased neurological severity score on postoperative days of 7 and 28 compared with the control (P<0.001) and curcumin 50 mg/kg groups (P<0.05–P<0.001), respectively. Also, curcumin 100 mg/kg significantly increased step-through latency times on postoperative days of 3–28 and 14–28 compared with the control (P<0.05–P<0.001) and curcumin 50 mg/kg groups (P<0.01–P<0.001). Moreover, it increased the novelty preference index during the novel object recognition test in the 28-day treatment subgroup after GCI. Curcumin (100 mg/kg) could maintain the neuronal aggregation in the CA1 region after GCI at a level near to what is generally observed in normal rats.

Conclusion:

Curcumin could improve memory and neurological deficits and restore irregular neuronal distribution in the CA1 region after GCI in a time-dependent manner, and its higher dose was more effective than its lower dose. Curcumin may have beneficial effects on reducing brain complications after ischemia.

Hidden Hyperuniformity in Soft Polymeric Materials

We investigate the nature of long-range density fluctuations in melts of model "soft" polymers, specifically stars and bottlebrushes, over a wide temperature range by molecular dynamics simulation. The cores of the stars and the backbones of bottlebrush polymers are found to have a hyperuniform distribution; i.e., they exhibit anomalously small density fluctuations over a wide temperature range above the glass transition temperature. The hyperuniformity of these substituent polymer subregions is hidden since the fluid as a whole does not exhibit this property. These findings offer a strategy for the practical design of hyperuniform polymeric materials.

Mechanical characterization of disordered and anisotropic cellular monolayers

We consider a cellular monolayer, described using a vertex-based model, for which cells form a spatially disordered array of convex polygons that tile the plane. Equilibrium cell configurations are assumed to minimize a global energy defined in terms of cell areas and perimeters; energy is dissipated via dynamic area and length changes, as well as cell neighbor exchanges. The model captures our observations of an epithelium from a Xenopus embryo showing that uniaxial stretching induces spatial ordering, with cells under net tension (compression) tending to align with (against) the direction of stretch, but with the stress remaining heterogeneous at the single-cell level. We use the vertex model to derive the linearized relation between tissue-level stress, strain, and strain rate about a deformed base state, which can be used to characterize the tissue’s anisotropic mechanical properties; expressions for viscoelastic tissue moduli are given as direct sums over cells. When the base state is isotropic, the model predicts that tissue properties can be tuned to a regime with high elastic shear resistance but low resistance to area changes, or vice versa.

The biology and mathematical modelling of glioma invasion: a review

Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion.

Three-dimensional virtual histology of human cerebellum by X-ray phase-contrast tomography

The complex cytoarchitecture of human brain tissue is traditionally studied by histology, providing structural information in 2D planes. This can be partly extended to 3D by inspecting many parallel slices, however, at nonisotropic resolution. This work shows that propagation-based X-ray phase-contrast tomography, both at the synchrotron and even at a compact laboratory source, can be used to perform noninvasive 3D virtual histology on unstained paraffin-embedded human cerebellum at isotropic subcellular resolution. The resulting data quality is high enough to visualize and automatically locate ∼10⁶ neurons within the different layers of the cerebellum, providing unprecedented data on its 3D cytoarchitecture and spatial organization.

To quantitatively evaluate brain tissue and its corresponding function, knowledge of the 3D cellular distribution is essential. The gold standard to obtain this information is histology, a destructive and labor-intensive technique where the specimen is sliced and examined under a light microscope, providing 3D information at nonisotropic resolution. To overcome the limitations of conventional histology, we use phase-contrast X-ray tomography with optimized optics, reconstruction, and image analysis, both at a dedicated synchrotron radiation endstation, which we have equipped with X-ray waveguide optics for coherence and wavefront filtering, and at a compact laboratory source. As a proof-of-concept demonstration we probe the 3D cytoarchitecture in millimeter-sized punches of unstained human cerebellum embedded in paraffin and show that isotropic subcellular resolution can be reached at both setups throughout the specimen. To enable a quantitative analysis of the reconstructed data, we demonstrate automatic cell segmentation and localization of over 1 million neurons within the cerebellar cortex. This allows for the analysis of the spatial organization and correlation of cells in all dimensions by borrowing concepts from condensed-matter physics, indicating a strong short-range order and local clustering of the cells in the granular layer. By quantification of 3D neuronal “packing,” we can hence shed light on how the human cerebellum accommodates 80% of the total neurons in the brain in only 10% of its volume. In addition, we show that the distribution of neighboring neurons in the granular layer is anisotropic with respect to the Purkinje cell dendrites.

Structural Characterization and Statistical-Mechanical Model of Epidermal Patterns

In proliferating epithelia of mammalian skin, cells of irregular polygon-like shapes pack into complex, nearly flat two-dimensional structures that are pliable to deformations. In this work, we employ various sensitive correlation functions to quantitatively characterize structural features of evolving packings of epithelial cells across length scales in mouse skin. We find that the pair statistics in direct space (correlation function) and Fourier space (structure factor) of the cell centroids in the early stages of embryonic development show structural directional dependence (statistical anisotropy), which is a reflection of the fact that cells are stretched, which promotes uniaxial growth along the epithelial plane. In the late stages, the patterns tend toward statistically isotropic states, as cells attain global polarization and epidermal growth shifts to produce the skin's outer stratified layers. We construct a minimalist four-component statistical-mechanical model involving effective isotropic pair interactions consisting of hard-core repulsion and extra short-range soft-core repulsion beyond the hard core, whose length scale is roughly the same as the hard core. The model parameters are optimized to match the sample pair statistics in both direct and Fourier spaces. By doing this, the parameters are biologically constrained. In contrast with many vertex-based models, our statistical-mechanical model does not explicitly incorporate information about the cell shapes and interfacial energy between cells; nonetheless, our model predicts essentially the same polygonal shape distribution and size disparity of cells found in experiments, as measured by Voronoi statistics. Moreover, our simulated equilibrium liquid-like configurations are able to match other nontrivial unconstrained statistics, which is a testament to the power and novelty of the model. The array of structural descriptors that we deploy enable us to distinguish between normal, mechanically deformed, and pathological skin tissues. Our statistical-mechanical model enables one to generate tissue microstructure at will for further analysis. We also discuss ways in which our model might be extended to better understand morphogenesis (in particular the emergence of planar cell polarity), wound healing, and disease-progression processes in skin, and how it could be applied to the design of synthetic tissues.

Spatial and Structural Metrics for Living Cells Inspired by Statistical Mechanics

Experimental observations in cell biology have advanced to a stage where theory could play a larger role, much as it has done in the physical sciences. Possibly the lack of a common framework within which experimentalists, computational scientists and theorists could equally contribute has hindered this development, for the worse of both disciplines. Here we demonstrate the usage of tools and concepts from statistical mechanics to describe processes inside living cells based on experimental data, suggesting that future theoretical/computational models may be based on such concepts. To illustrate the ideas, we describe the organisation of subcellular structures within the cell in terms of (density) pair correlation functions, and subsequently use the same concepts to follow nano-sized objects being transported inside the cell. Finally, we quantify an interesting subcellular re-organisation, not previously discerned by molecular biology methods.

Hyperuniformity and its generalizations

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystal and liquid: They are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These exotic states of matter play a vital role in a number of problems across the physical, mathematical as well as biological sciences and, because they are endowed with novel physical properties, have technological importance. Given the fundamental as well as practical importance of disordered hyperuniform systems elucidated thus far, it is natural to explore the generalizations of the hyperuniformity notion and its consequences. In this paper, we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area (one of the Minkowski functionals) in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, and statistically anisotropic many-particle systems and two-phase media. In all cases, the relevant mathematical underpinnings are formulated and illustrative calculations are provided. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems (e.g., fluid-saturated porous media), physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space is approached (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. Among other results, we show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical, and acoustic characteristics) to these states of matter. Such tunability could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity. The generalizations of hyperuniformity introduced here provide theoreticians and experimentalists new avenues to understand a very broad range of phenomena across a variety of fields through the hyperuniformity "lens."

Spatial Habitat Features Derived from Multiparametric Magnetic Resonance Imaging Data Are Associated with Molecular Subtype and 12-Month Survival Status in Glioblastoma Multiforme

One of the most common and aggressive malignant brain tumors is Glioblastoma multiforme. Despite the multimodality treatment such as radiation therapy and chemotherapy (temozolomide: TMZ), the median survival rate of glioblastoma patient is less than 15 months. In this study, we investigated the association between measures of spatial diversity derived from spatial point pattern analysis of multiparametric magnetic resonance imaging (MRI) data with molecular status as well as 12-month survival in glioblastoma. We obtained 27 measures of spatial proximity (diversity) via spatial point pattern analysis of multiparametric T1 post-contrast and T2 fluid-attenuated inversion recovery MRI data. These measures were used to predict 12-month survival status (≤12 or >12 months) in 74 glioblastoma patients. Kaplan-Meier with receiver operating characteristic analyses was used to assess the relationship between derived spatial features and 12-month survival status as well as molecular subtype status in patients with glioblastoma. Kaplan-Meier survival analysis revealed that 14 spatial features were capable of stratifying overall survival in a statistically significant manner. For prediction of 12-month survival status based on these diversity indices, sensitivity and specificity were 0.86 and 0.64, respectively. The area under the receiver operating characteristic curve and the accuracy were 0.76 and 0.75, respectively. For prediction of molecular subtype status, proneural subtype shows highest accuracy of 0.93 among all molecular subtypes based on receiver operating characteristic analysis. We find that measures of spatial diversity from point pattern analysis of intensity habitats from T1 post-contrast and T2 fluid-attenuated inversion recovery images are associated with both tumor subtype status and 12-month survival status and may therefore be useful indicators of patient prognosis, in addition to providing potential guidance for molecularly-targeted therapies in Glioblastoma multiforme.

Electrical coupling in ensembles of nonexcitable cells: modeling the spatial map of single cell potentials

We analyze the coupling of model nonexcitable (non-neural) cells assuming that the cell membrane potential is the basic individual property. We obtain this potential on the basis of the inward and outward rectifying voltage-gated channels characteristic of cell membranes. We concentrate on the electrical coupling of a cell ensemble rather than on the biochemical and mechanical characteristics of the individual cells, obtain the map of single cell potentials using simple assumptions, and suggest procedures to collectively modify this spatial map. The response of the cell ensemble to an external perturbation and the consequences of cell isolation, heterogeneity, and ensemble size are also analyzed. The results suggest that simple coupling mechanisms can be significant for the biophysical chemistry of model biomolecular ensembles. In particular, the spatiotemporal map of single cell potentials should be relevant for the uptake and distribution of charged nanoparticles over model cell ensembles and the collective properties of droplet networks incorporating protein ion channels inserted in lipid bilayers.

Quantitative image analysis of cell colocalization in murine bone marrow

Long-term antibody production is a key property of humoral immunity and is accomplished by long-lived plasma cells. They mainly reside in the bone marrow, whose importance as an organ hosting immunological memory is becoming increasingly evident. Signals provided by stromal cells and eosinophils may play an important role for plasma cell maintenance, constituting a survival microenvironment. In this joint study of experiment and theory, we investigated the spatial colocalization of plasma cells, eosinophils and B cells by applying an image-based systems biology approach. To this end, we generated confocal fluorescence microscopy images of histological sections from murine bone marrow that were subsequently analyzed in an automated fashion. This quantitative analysis was combined with computer simulations of the experimental system for hypothesis testing. In particular, we tested the observed spatial colocalization of cells in the bone marrow against the hypothesis that cells are found within available areas at positions that were drawn from a uniform random number distribution. We find that B cells and plasma cells highly colocalize with stromal cells, to an extent larger than in the simulated random situation. While B cells are preferentially in contact with each other, i.e., form clusters among themselves, plasma cells seem to be solitary or organized in aggregates, i.e., loosely defined groups of cells that are not necessarily in direct contact. Our data suggest that the plasma cell bone marrow survival niche facilitates colocalization of plasma cells with stromal cells and eosinophils, respectively, promoting plasma cell longevity.

Propagating waves of directionality and coordination orchestrate collective cell migration

The ability of cells to coordinately migrate in groups is crucial to enable them to travel long distances during embryonic development, wound healing and tumorigenesis, but the fundamental mechanisms underlying intercellular coordination during collective cell migration remain elusive despite considerable research efforts. A novel analytical framework is introduced here to explicitly detect and quantify cell clusters that move coordinately in a monolayer. The analysis combines and associates vast amount of spatiotemporal data across multiple experiments into transparent quantitative measures to report the emergence of new modes of organized behavior during collective migration of tumor and epithelial cells in wound healing assays. First, we discovered the emergence of a wave of coordinated migration propagating backward from the wound front, which reflects formation of clusters of coordinately migrating cells that are generated further away from the wound edge and disintegrate close to the advancing front. This wave emerges in both normal and tumor cells, and is amplified by Met activation with hepatocyte growth factor/scatter factor. Second, Met activation was found to induce coinciding waves of cellular acceleration and stretching, which in turn trigger the emergence of a backward propagating wave of directional migration with about an hour phase lag. Assessments of the relations between the waves revealed that amplified coordinated migration is associated with the emergence of directional migration. Taken together, our data and simplified modeling-based assessments suggest that increased velocity leads to enhanced coordination: higher motility arises due to acceleration and stretching that seems to increase directionality by temporarily diminishing the velocity components orthogonal to the direction defined by the monolayer geometry. Spatial and temporal accumulation of directionality thus defines coordination. The findings offer new insight and suggest a basic cellular mechanism for long-term cell guidance and intercellular communication during collective cell migration.

The fundamental mechanisms underlying intercellular coordination during collective cell migration remain elusive despite considerable research efforts. We present a novel analytical framework that considers spatiotemporal dynamics across several traits. Our approach was applied to discover new modes of organized collective dynamics of cancer and normal cells. Following disruption of a cell monolayer, a propagating wave of coordinated migration emerges as clusters of coordinately moving cells are formed away from the wound and disintegrate near the advancing front. Activation of Met signal transduction by hepatocyte growth factor/scatter factor, master regulators of cell motility in malignant and normal processes, generates coinciding waves of cellular acceleration and stretching that propagate backward from the wound front and trigger a delayed wave of directional migration. Amplified coordination is intrinsically associated with enhanced directionality suggesting that even a weak directional cue is sufficient to promote a coordinated response that is transmitted to cells within the cell sheet. Our findings provide important novel insights on the basic cellular organization during collective cell migration and establish a mechanism of long-range cell guidance, intercellular coordination and pattern formation during monolayer wound healing.

Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem

Optimal spatial sampling of light rigorously requires that identical photoreceptors be arranged in perfectly regular arrays in two dimensions. Examples of such perfect arrays in nature include the compound eyes of insects and the nearly crystalline photoreceptor patterns of some fish and reptiles. Birds are highly visual animals with five different cone photoreceptor subtypes, yet their photoreceptor patterns are not perfectly regular. By analyzing the chicken cone photoreceptor system consisting of five different cell types using a variety of sensitive microstructural descriptors, we find that the disordered photoreceptor patterns are "hyperuniform" (exhibiting vanishing infinite-wavelength density fluctuations), a property that had heretofore been identified in a unique subset of physical systems, but had never been observed in any living organism. Remarkably, the patterns of both the total population and the individual cell types are simultaneously hyperuniform. We term such patterns "multihyperuniform" because multiple distinct subsets of the overall point pattern are themselves hyperuniform. We have devised a unique multiscale cell packing model in two dimensions that suggests that photoreceptor types interact with both short- and long-ranged repulsive forces and that the resultant competition between the types gives rise to the aforementioned singular spatial features characterizing the system, including multihyperuniformity. These findings suggest that a disordered hyperuniform pattern may represent the most uniform sampling arrangement attainable in the avian system, given intrinsic packing constraints within the photoreceptor epithelium. In addition, they show how fundamental physical constraints can change the course of a biological optimization process. Our results suggest that multihyperuniform disordered structures have implications for the design of materials with novel physical properties and therefore may represent a fruitful area for future research.

Distribution of decidual natural killer cells and macrophages in the neighbourhood of the trophoblast invasion front: a quantitative evaluation

STUDY QUESTION

Do decidual natural killer (dNK) cells and decidual macrophages (dMph) become enriched in the vicinity of the trophoblast invasion front?

SUMMARY ANSWER

Morphometric image analysis and areal cell density calculations, which excluded observer bias, showed an enrichment of decidual leukocytes in the neighbourhood of the trophoblast invasion front.

WHAT IS KNOWN ALREADY

In previous studies, the number of decidual leukocytes was visually counted in medium- or high power fields. These methods, however, cannot reveal the exact spatial relationship between leukocytes and invasive trophoblast cells, and are therefore prone to subjective errors. Thus, a more objective approach is required.

STUDY DESIGN, SIZE, DURATION

Applying a new method of morphometric image analysis, leukocyte populations were studied in human tissue fragments derived from first trimester placentation sites (n = 7) as well as in co-cultures of first trimester decidual tissue with placental villi of the same pregnancy representing an appropriate in vitro model of trophoblast invasion (n = 15).

PARTICIPANTS/MATERIALS, SETTINGS, METHODS

First trimester decidual tissue was obtained from women undergoing elective terminations of pregnancy at 7-10 weeks of gestational age. Tissue sections were double-stained immunohistochemically for markers of dNK cells or dMph on one hand, and for invasive extravillous trophoblast cells on the other. To analyse the distribution of leukocytes, distinct cell compartments as well as cell neighbourhood areas were defined. Finally, relative areal cell densities were calculated and these data were compared with those of an in vitro model of trophoblast invasion as well as with tissue fragments derived from decidua parietalis without trophoblast cells.

MAIN RESULTS AND THE ROLE OF CHANCE

At first trimester placentation sites, a higher density of dNK cells as well as of dMph was found in close proximity to the invasive trophoblast (P ≤ 0.01), compared with the average areal cell density of decidual leukocytes in the tissue with exclusion of the trophoblast. The highest areal cell density of leukocytes was determined up to a distance of 20 μm from the trophoblast cells, whereas in more distant regions it was even lower than average, indicating a migration of these leukocytes towards the trophoblast invasion front. In the three-dimensional co-culture model, however, we found an enrichment of dMph (P ≤ 0.01) but not of dNK cells (P > 0,05) in the neighbourhood of the invasive trophoblast.

LIMITATIONS, REASONS FOR CAUTION

The morphometric image analysis depends on intense immunohistochemical staining that is free of background and cross-reactivity.

WIDER IMPLICATIONS OF THE FINDINGS

The presented method will be useful not only for the investigation of recurrent miscarriage but also in the fields of tumour immunology and inflammation.

STUDY FUNDING/COMPETING INTEREST(S)

The study was supported by the European Commission (Network of Excellence 'The Control of Embryo Implantation (EMBIC)', FP6-512040, lead researcher: P.S.), and by the Franz Lanyar Foundation of the Medical University of Graz, Austria (Grant #347). None of the authors declared a conflict of interests.

Simplified method for including spatial correlations in mean-field approximations

Biological systems involving proliferation, migration, and death are observed across all scales. For example, they govern cellular processes such as wound healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration, and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behavior. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pairwise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplification in the form of a partial differential equation description for the evolution of pairwise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behavior in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before and find our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.

Evolution and morphology of microenvironment-enhanced malignancy of three-dimensional invasive solid tumors

The emergence of invasive and metastatic behavior in malignant tumors can often lead to fatal outcomes for patients. The collective malignant tumor behavior resulting from the complex tumor-host interactions and the interactions between the tumor cells is currently poorly understood. In this paper, we employ a cellular automaton (CA) model to investigate microenvironment-enhanced malignant behaviors and morphologies of in vitro avascular invasive solid tumors in three dimensions. Our CA model incorporates a variety of microscopic-scale tumor-host interactions, including the degradation of the extracellular matrix by the malignant cells, nutrient-driven cell migration, pressure buildup due to the deformation of the microenvironment by the growing tumor, and its effect on the local tumor-host interface stability. Moreover, the effects of cell-cell adhesion on tumor growth are explicitly taken into account. Specifically, we find that while strong cell-cell adhesion can suppress the invasive behavior of the tumors growing in soft microenvironments, cancer malignancy can be significantly enhanced by harsh microenvironmental conditions, such as exposure to high pressure levels. We infer from the simulation results a qualitative phase diagram that characterizes the expected malignant behavior of invasive solid tumors in terms of two competing malignancy effects: the rigidity of the microenvironment and cell-cell adhesion. This diagram exhibits phase transitions between noninvasive and invasive behaviors. We also discuss the implications of our results for the diagnosis, prognosis, and treatment of malignant tumors.

Quantitative characterization of the microstructure and transport properties of biopolymer networks

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient D(e) and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient D(e) for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation and the Torquato approximation. The Hashin-Strikman upper bound on the effective diffusion coefficient D(e) and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient D(e) as well as the mean survival time τ, which is related to nuclear magnetic resonance relaxation times. Our numerical results for D(e) are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of D(e) for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Torquato and Yeong (1997 J. Chem. Phys. 106 8814). We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed.

Diversity of dynamics and morphologies of invasive solid tumors

Complex tumor-host interactions can significantly affect the growth dynamics and morphologies of progressing neoplasms. The growth of a confined solid tumor induces mechanical pressure and deformation of the surrounding microenvironment, which in turn influences tumor growth. In this paper, we generalize a recently developed cellular automaton model for invasive tumor growth in heterogeneous microenvironments [Y. Jiao and S. Torquato, PLoS Comput. Biol.7, e1002314 (2011)] by incorporating the effects of pressure. Specifically, we explicitly model the pressure exerted on the growing tumor due to the deformation of the microenvironment and its effect on the local tumor-host interface instability. Both noninvasive-proliferative growth and invasive growth with individual cells that detach themselves from the primary tumor and migrate into the surrounding microenvironment are investigated. We find that while noninvasive tumors growing in "soft" homogeneous microenvironments develop almost isotropic shapes, both high pressure and host heterogeneity can strongly enhance malignant behavior, leading to finger-like protrusions of the tumor surface. Moreover, we show that individual invasive cells of an invasive tumor degrade the local extracellular matrix at the tumor-host interface, which diminishes the fingering growth of the primary tumor. The implications of our results for cancer diagnosis, prognosis and therapy are discussed.