Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics

Two conjectures on 3D Voronoi structures: a toolkit with biomedical case studies

3D Voronoi scaffolds are widely applied in the field of additive manufacturing as they are known for their light weight structural resilience and share many topological similarities to various natural (bone, tumours, lymph node) and synthetic environments (foam, functionally gradient porous materials). Unfortunately, the structural design features that promote these topological similarities (such as the number of vertices) are often unpredictable and require the trial and error of varying design features to achieve the desired 3D Voronoi structure. This article provides a toolkit, consisting of equations, based on over 12 000 3D Voronoi structures. These equations allow design features, such as the number of generating points (G), to be efficiently and accurately predicted based on the desired structural parameters (within ±3G). Based on these equations we are proposing, to the best of our knowledge, two new mathematical conjectures that relate the number of vertices or edges, and the average edge length to G in Voronoi structures. These equations have been validated for a wide range of parameter values and Voronoi network sizes. A design code is provided allowing any of over 12 000 structures to be selected, easily adjusted based on user requirements, and 3D printed. Biomedical case studies relevant to T-cell culturing, bone scaffolds and kidney tumours are presented to illustrate the design code.

Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.

Modelling contractile ring formation and division to daughter cells for simulating proliferative multicellular dynamics

Cell proliferation is a fundamental process underlying embryogenesis, homeostasis, wound healing, and cancer. The process involves multiple events during each cell cycle, such as cell growth, contractile ring formation, and division to daughter cells, which affect the surrounding cell population geometrically and mechanically. However, existing methods do not comprehensively describe the dynamics of multicellular structures involving cell proliferation at a subcellular resolution. In this study, we present a novel model for proliferative multicellular dynamics at the subcellular level by building upon the nonconservative fluid membrane (NCF) model that we developed in earlier research. The NCF model utilizes a dynamically-rearranging closed triangular mesh to depict the shape of each cell, enabling us to analyze cell dynamics over extended periods beyond each cell cycle, during which cell surface components undergo dynamic turnover. The proposed model represents the process of cell proliferation by incorporating cell volume growth and contractile ring formation through an energy function and topologically dividing each cell at the cleavage furrow formed by the ring. Numerical simulations demonstrated that the model recapitulated the process of cell proliferation at subcellular resolution, including cell volume growth, cleavage furrow formation, and division to daughter cells. Further analyses suggested that the orientation of actomyosin stress in the contractile ring plays a crucial role in the cleavage furrow formation, i.e., circumferential orientation can form a cleavage furrow but isotropic orientation cannot. Furthermore, the model replicated tissue-scale multicellular dynamics, where the successive proliferation of adhesive cells led to the formation of a cell sheet and stratification on the substrate. Overall, the proposed model provides a basis for analyzing proliferative multicellular dynamics at subcellular resolution.

MorphoSim: an efficient and scalable phase-field framework for accurately simulating multicellular morphologies

The phase field model can accurately simulate the evolution of microstructures with complex morphologies, and it has been widely used for cell modeling in the last two decades. However, compared to other cellular models such as the coarse-grained model and the vertex model, its high computational cost caused by three-dimensional spatial discretization hampered its application and scalability, especially for multicellular organisms. Recently, we built a phase field model coupled with in vivo imaging data to accurately reconstruct the embryonic morphogenesis of Caenorhabditis elegans from 1- to 8-cell stages. In this work, we propose an improved phase field model by using the stabilized numerical scheme and modified volume constriction. Then we present a scalable phase-field framework, MorphoSim, which is 100 times more efficient than the previous one and can simulate over 100 mechanically interacting cells. Finally, we demonstrate how MorphoSim can be successfully applied to reproduce the assembly, self-repairing, and dissociation of a synthetic artificial multicellular system - the synNotch system.

Examining the efficacy of localised gemcitabine therapy for the treatment of pancreatic cancer using a hybrid agent-based model

The prognosis for pancreatic ductal adenocarcinoma (PDAC) patients has not significantly improved in the past 3 decades, highlighting the need for more effective treatment approaches. Poor patient outcomes and lack of response to therapy can be attributed, in part, to a lack of uptake of perfusion of systemically administered chemotherapeutic drugs into the tumour. Wet-spun alginate fibres loaded with the chemotherapeutic agent gemcitabine have been developed as a potential tool for overcoming the barriers in delivery of systemically administrated drugs to the PDAC tumour microenvironment by delivering high concentrations of drug to the tumour directly over an extended period. While exciting, the practicality, safety, and effectiveness of these devices in a clinical setting requires further investigation. Furthermore, an in-depth assessment of the drug-release rate from these devices needs to be undertaken to determine whether an optimal release profile exists. Using a hybrid computational model (agent-based model and partial differential equation system), we developed a simulation of pancreatic tumour growth and response to treatment with gemcitabine loaded alginate fibres. The model was calibrated using in vitro and in vivo data and simulated using a finite volume method discretisation. We then used the model to compare different intratumoural implantation protocols and gemcitabine-release rates. In our model, the primary driver of pancreatic tumour growth was the rate of tumour cell division. We were able to demonstrate that intratumoural placement of gemcitabine loaded fibres was more effective than peritumoural placement. Additionally, we quantified the efficacy of different release profiles from the implanted fibres that have not yet been tested experimentally. Altogether, the model developed here is a tool that can be used to investigate other drug delivery devices to improve the arsenal of treatments available for PDAC and other difficult-to-treat cancers in the future.

Spotting Local Environments in Self-Assembled Monolayer-Protected Gold Nanoparticles

Organic-inorganic (O-I) nanomaterials are versatile platforms for an incredible high number of applications, ranging from heterogeneous catalysis to molecular sensing, cell targeting, imaging, and cancer diagnosis and therapy, just to name a few. Much of their potential stems from the unique control of organic environments around inorganic sites within a single O-I nanomaterial, which allows for new properties that were inaccessible using purely organic or inorganic materials. Structural and mechanistic characterization plays a key role in understanding and rationally designing such hybrid nanoconstructs. Here, we introduce a general methodology to identify and classify local (supra)molecular environments in an archetypal class of O-I nanomaterials, i.e., self-assembled monolayer-protected gold nanoparticles (SAM-AuNPs). By using an atomistic machine-learning guided workflow based on the Smooth Overlap of Atomic Positions (SOAP) descriptor, we analyze a collection of chemically different SAM-AuNPs and detect and compare local environments in a way that is agnostic and automated, i.e., with no need of a priori information and minimal user intervention. In addition, the computational results coupled with experimental electron spin resonance measurements prove that is possible to have more than one local environment inside SAMs, being the thickness of the organic shell and solvation primary factors in the determining number and nature of multiple coexisting environments. These indications are extended to complex mixed hydrophilic-hydrophobic SAMs. This work demonstrates that it is possible to spot and compare local molecular environments in SAM-AuNPs exploiting atomistic machine-learning approaches, establishes ground rules to control them, and holds the potential for the rational design of O-I nanomaterials instructed from data.

Identification of spatially variable genes with graph cuts

Single-cell gene expression data with positional information is critical to dissect mechanisms and architectures of multicellular organisms, but the potential is limited by the scalability of current data analysis strategies. Here, we present scGCO, a method based on fast optimization of hidden Markov Random Fields with graph cuts to identify spatially variable genes. Comparing to existing methods, scGCO delivers a superior performance with lower false positive rate and improved specificity, while demonstrates a more robust performance in the presence of noises. Critically, scGCO scales near linearly with inputs and demonstrates orders of magnitude better running time and memory requirement than existing methods, and could represent a valuable solution when spatial transcriptomics data grows into millions of data points and beyond.

Aperiodic crystals in biology

Biological systems display a broad palette of hierarchically ordered designs spanning over many orders of magnitude in size. Remarkably enough, periodic order, which profusely shows up in non-living ordered compounds, plays a quite subsidiary role in most biological structures, which can be appropriately described in terms of the more general aperiodic crystal notion instead. In this topical review I shall illustrate this issue by considering several representative examples, including botanical phyllotaxis, the geometry of cell patterns in tissues, the morphology of sea urchins, or the symmetry principles underlying virus architectures. In doing so, we will realize that albeit the currently adopted quasicrystal notion is not general enough to properly account for the rich structural features one usually finds in biological arrangements of matter, several mathematical tools and fundamental notions belonging to the aperiodic crystals science toolkit can provide a useful modeling framework to this end.

3D fluorescence microscopy data synthesis for segmentation and benchmarking

Automated image processing approaches are indispensable for many biomedical experiments and help to cope with the increasing amount of microscopy image data in a fast and reproducible way. Especially state-of-the-art deep learning-based approaches most often require large amounts of annotated training data to produce accurate and generalist outputs, but they are often compromised by the general lack of those annotated data sets. In this work, we propose how conditional generative adversarial networks can be utilized to generate realistic image data for 3D fluorescence microscopy from annotation masks of 3D cellular structures. In combination with mask simulation approaches, we demonstrate the generation of fully-annotated 3D microscopy data sets that we make publicly available for training or benchmarking. An additional positional conditioning of the cellular structures enables the reconstruction of position-dependent intensity characteristics and allows to generate image data of different quality levels. A patch-wise working principle and a subsequent full-size reassemble strategy is used to generate image data of arbitrary size and different organisms. We present this as a proof-of-concept for the automated generation of fully-annotated training data sets requiring only a minimum of manual interaction to alleviate the need of manual annotations.

Effect of nicorandil on the spatial arrangement of primary motor cortical neurons in the sub-acute phase of stroke in a rat model

INTRODUCTION

Ischemic stroke remains a major cause of disability and death worldwide. The density and the spatial distribution of the primary motor (M1) cortical neurons are important in signal transmission and control the movement-related functions. Recently, the neuroprotective effect of nicorandil in cerebral ischemia was described through its anti-apoptosis, antioxidant and anti-inflammatory properties. This study aimed to determine the effects of nicorandil on the neurobehavioral outcome, infarct size, and density, and spatial distribution of M1 cortical neurons after cerebral ischemia.

METHODS

Thirty Sprague-Dawley rats were randomly divided into three groups. Sham underwent surgery without middle cerebral artery occlusion (MCAO) and drug. The MCAO and treatment groups after MCAO received saline or nicorandil 2, 24, 48, and 72 h after the induction of brain ischemia. Neurobehavioral tests were performed, brains removed, sectioned, and stained by 2,3,5-triphenyltetrazolium chloride (TTC) to estimate the size of the infarction and Nissl staining to evaluate the numerical density, mean area, and the distribution pattern of M1 cortical neurons, using Voronoi spatial tessellation.

RESULTS

Although nicorandil treatment significantly decreased the neurological deficits and density of neuronal neighbors, it could not preserve the normal regular spatial distributions of M1 cortical neurons after MCAO. It also could not significantly improve motor function or reduce ischemic lesion size.

CONCLUSIONS

Treatment using the present dose of nicorandil during sub-acute ischemic stroke could not increase neuronal density or preserve the normal regular spatial distributions after MCAO. However, it had beneficial effects on neurobehavioral and motor function and somewhat reduced ischemic lesion size.

Theory and simulation for equilibrium glassy dynamics in cellular Potts model of confluent biological tissue

Glassy dynamics in a confluent monolayer is indispensable in morphogenesis, wound healing, bronchial asthma, and many others; a detailed theoretical framework for such a system is, therefore, important. Vertex-model (VM) simulations have provided crucial insights into the dynamics of such systems, but their nonequilibrium nature makes theoretical development difficult. The cellular Potts model (CPM) of confluent monolayers provides an alternative model for such systems with a well-defined equilibrium limit. We combine numerical simulations of the CPM and an analytical study based on one of the most successful theories of equilibrium glass, the random first-order transition theory, and develop a comprehensive theoretical framework for a confluent glassy system. We find that the glassy dynamics within the CPM is qualitatively similar to that in the VM. Our study elucidates the crucial role of geometric constraints in bringing about two distinct regimes in the dynamics, as the target perimeter P_{0} is varied. The unusual sub-Arrhenius relaxation results from the distinctive interaction potential arising from the perimeter constraint in such systems. The fragility of the system decreases with increasing P_{0} in the low-P_{0} regime, whereas the dynamics is independent of P_{0} in the other regime. The rigidity transition, found in the VM, is absent within the CPM; this difference seems to come from the nonequilibrium nature of the former. We show that the CPM captures the basic phenomenology of glassy dynamics in a confluent biological system via comparison of our numerical results with existing experiments on different systems.

The Voronoi theory of the normal liver lobular architecture and its applicability in hepatic zonation

The precise characterization of the lobular architecture of the liver has been subject of investigation since the earliest historical publications, but an accurate model to describe the hepatic lobular microanatomy is yet to be proposed. Our aim was to evaluate whether Voronoi diagrams can be used to describe the classic liver lobular architecture. We examined the histology of normal porcine and human livers and analyzed the geometric relationships of various microanatomic structures utilizing digital tools. The Voronoi diagram model described the organization of the hepatic classic lobules with overall accuracy nearly 90% based on known histologic landmarks. We have also designed a Voronoi-based algorithm of hepatic zonation, which also showed an overall zonal accuracy of nearly 90%. Therefore, we have presented evidence that Voronoi diagrams represent the basis of the two-dimensional organization of the normal liver and that this concept may have wide applicability in liver pathology and research.

Fluctuation-Induced Phase Separation in Metric and Topological Models of Collective Motion

We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a density-dependent shift of the onset of order, which in turn changes the nature of the transition into a phase-separation scenario. Our results apply to a range of systems, including models in which particles interact with their "topological" neighbors that have been believed so far to exhibit a continuous onset of order. Our analytical predictions are confirmed by numerical simulations of fluctuating hydrodynamics and microscopic models.

Effect of Dimethyl Fumarate on the Motor Function and Spatial Arrangement of Primary Motor Cortical Neurons in the Sub-Acute Phase of Stroke in a Rat Model

BACKGROUND

The therapeutic effects of dimethyl fumarate (DMF) in patients with multiple sclerosis and animal models of neurologic disease were reported. The density and the distribution pattern of motor neurons are important in transmitting the signal and controlling the movement-related functions. The present study evaluated the effects of DMF treatment on the neurological functions, infarct volume, and spatial distribution of the neurons in the primary motor cortex after cerebral ischemia.

METHODS

Thirty-three Sprague-Dawley rats were randomly divided into three groups: The sham group underwent surgery without middle cerebral artery occlusion (MCAO) and drug. The vehicle and treatment groups after MCAO received a vehicle or DMF for three consecutive days. Post-stroke neurological and motor functions were assessed. At the end of the third day, the brains were removed, and the cerebral infarct volume was evaluated. We used cresyl violet staining to analyze the density and the spatial arrangement of motor cortical neurons using Voronoi tessellation.

RESULTS

Treatment of the brain ischemia for three days with DMF could not significantly reduce the neurological and motor function deficits and infarct volume. However, it reduced the neuronal area and death and preserved their spatial distribution in the normal regular pattern.

CONCLUSION

Cerebral ischemia decreased the neuronal density of the primary motor cortex and changed their distributions to a random pattern. DMF treatment during sub-acute ischemic stroke did not significantly improve the neurological deficit scores. However, it could prevent neuronal swelling and death and preserved the spatial distribution of the cortical neurons in their normal pattern.

Unmasking the immune microecology of ductal carcinoma in situ with deep learning

Despite increasing evidence supporting the clinical relevance of tumour infiltrating lymphocytes (TILs) in invasive breast cancer, TIL spatial variability within ductal carcinoma in situ (DCIS) samples and its association with progression are not well understood. To characterise tissue spatial architecture and the microenvironment of DCIS, we designed and validated a new deep learning pipeline, UNMaSk. Following automated detection of individual DCIS ducts using a new method IM-Net, we applied spatial tessellation to create virtual boundaries for each duct. To study local TIL infiltration for each duct, DRDIN was developed for mapping the distribution of TILs. In a dataset comprising grade 2-3 pure DCIS and DCIS adjacent to invasive cancer (adjacent DCIS), we found that pure DCIS cases had more TILs compared to adjacent DCIS. However, the colocalisation of TILs with DCIS ducts was significantly lower in pure DCIS compared to adjacent DCIS, which may suggest a more inflamed tissue ecology local to DCIS ducts in adjacent DCIS cases. Our study demonstrates that technological developments in deep convolutional neural networks and digital pathology can enable an automated morphological and microenvironmental analysis of DCIS, providing a new way to study differential immune ecology for individual ducts and identify new markers of progression.

A hybrid model of intercellular tension and cell-matrix mechanical interactions in a multicellular geometry

Epithelial cells form continuous sheets of cells that exist in tensional homeostasis. Homeostasis is maintained through cell-to-cell junctions that distribute tension and balance forces between cells and their underlying matrix. Disruption of tensional homeostasis can lead to epithelial-mesenchymal transition (EMT), a transdifferentiation process in which epithelial cells adopt a mesenchymal phenotype, losing cell-cell adhesion and enhancing cellular motility. This process is critical during embryogenesis and wound healing, but is also dysregulated in many disease states. To further understand the role of intercellular tension in spatial patterning of epithelial cell monolayers, we developed a multicellular computational model of cell-cell and cell-substrate forces. This work builds on a hybrid cellular Potts model (CPM)-finite element model to evaluate cell-matrix mechanical feedback of an adherent multicellular cluster. Cellular movement is governed by thermodynamic constraints from cell volume, cell-cell and cell-matrix contacts, and durotaxis, which arises from cell-generated traction forces on a finite element substrate. Junction forces at cell-cell contacts balance these traction forces, thereby producing a mechanically stable epithelial monolayer. Simulations were compared to in vitro experiments using fluorescence-based junction force sensors in clusters of cells undergoing EMT. Results indicate that the multicellular CPM model can reproduce many aspects of EMT, including epithelial monolayer formation dynamics, changes in cell geometry, and spatial patterning of cell-cell forces in an epithelial tissue.

High-efficiency procedure to characterize, segment, and quantify complex multicellularity in raw micrographs in plants

BACKGROUND

The increasing number of novel approaches for large-scale, multi-dimensional imaging of cells has created an unprecedented opportunity to analyze plant morphogenesis. However, complex image processing, including identifying specific cells and quantitating parameters, and high running cost of some image analysis softwares remains challenging. Therefore, it is essential to develop an efficient method for identifying plant complex multicellularity in raw micrographs in plants.

RESULTS

Here, we developed a high-efficiency procedure to characterize, segment, and quantify plant multicellularity in various raw images using the open-source software packages ImageJ and SR-Tesseler. This procedure allows for the rapid, accurate, automatic quantification of cell patterns and organization at different scales, from large tissues down to the cellular level. We validated our method using different images captured from Arabidopsis thaliana roots and seeds and Populus tremula stems, including fluorescently labeled images, Micro-CT scans, and dyed sections. Finally, we determined the area, centroid coordinate, perimeter, and Feret's diameter of the cells and harvested the cell distribution patterns from Voronoï diagrams by setting the threshold at localization density, mean distance, or area.

CONCLUSIONS

This procedure can be used to determine the character and organization of multicellular plant tissues at high efficiency, including precise parameter identification and polygon-based segmentation of plant cells.

Hybrid Automata Library: A flexible platform for hybrid modeling with real-time visualization

The Hybrid Automata Library (HAL) is a Java Library developed for use in mathematical oncology modeling. It is made of simple, efficient, generic components that can be used to model complex spatial systems. HAL's components can broadly be classified into: on- and off-lattice agent containers, finite difference diffusion fields, a GUI building system, and additional tools and utilities for computation and data collection. These components are designed to operate independently and are standardized to make them easy to interface with one another. As a demonstration of how modeling can be simplified using our approach, we have included a complete example of a hybrid model (a spatial model with interacting agent-based and PDE components). HAL is a useful asset for researchers who wish to build performant 1D, 2D and 3D hybrid models in Java, while not starting entirely from scratch. It is available on GitHub at https://github.com/MathOnco/HAL under the MIT License. HAL requires the Java JDK version 1.8 or later to compile and run the source code.

Interkinetic nuclear movements promote apical expansion in pseudostratified epithelia at the expense of apicobasal elongation

Pseudostratified epithelia (PSE) are a common type of columnar epithelia found in a wealth of embryonic and adult tissues such as ectodermal placodes, the trachea, the ureter, the gut and the neuroepithelium. PSE are characterized by the choreographed displacement of cells’ nuclei along the apicobasal axis according to phases of their cell cycle. Such movements, called interkinetic movements (INM), have been proposed to influence tissue expansion and shape and suggested as culprit in several congenital diseases such as CAKUT (Congenital anomalies of kidney and urinary tract) and esophageal atresia. INM rely on cytoskeleton dynamics just as adhesion, contractility and mitosis do. Therefore, long term impairment of INM without affecting proliferation and adhesion is currently technically unachievable. Here we bypassed this hurdle by generating a 2D agent-based model of a proliferating PSE and compared its output to the growth of the chick neuroepithelium to assess the interplay between INM and these other important cell processes during growth of a PSE. We found that INM directly generates apical expansion and apical nuclear crowding. In addition, our data strongly suggest that apicobasal elongation of cells is not an emerging property of a proliferative PSE but rather requires a specific elongation program. We then discuss how such program might functionally link INM, tissue growth and differentiation.

Pseudostratified epithelia (PSE) are a common type of epithelia characterized by the choreographed displacement of cells’ nuclei along the apicobasal axis during proliferation. These so-called interkinetic movements (INM) were proposed to influence tissue expansion and suggested as culprit in several congenital diseases. INM rely on cytoskeleton dynamics. Therefore, longer term impairment of INM without affecting proliferation and adhesion is currently technically unachievable. We bypassed this hurdle by generating a mathematical model of PSE and compared it to the growth of an epithelium of reference. Our data show that INM drive expansion of the apical domain of the epithelium and suggest that apicobasal elongation of cells is not an emerging property of a proliferative PSE but might rather requires a specific elongation program.

A quantitative high-resolution computational mechanics cell model for growing and regenerating tissues

Mathematical models are increasingly designed to guide experiments in biology, biotechnology, as well as to assist in medical decision making. They are in particular important to understand emergent collective cell behavior. For this purpose, the models, despite still abstractions of reality, need to be quantitative in all aspects relevant for the question of interest. This paper considers as showcase example the regeneration of liver after drug-induced depletion of hepatocytes, in which the surviving and dividing hepatocytes must squeeze in between the blood vessels of a network to refill the emerged lesions. Here, the cells' response to mechanical stress might significantly impact the regeneration process. We present a 3D high-resolution cell-based model integrating information from measurements in order to obtain a refined and quantitative understanding of the impact of cell-biomechanical effects on the closure of drug-induced lesions in liver. Our model represents each cell individually and is constructed by a discrete, physically scalable network of viscoelastic elements, capable of mimicking realistic cell deformation and supplying information at subcellular scales. The cells have the capability to migrate, grow, and divide, and the nature and parameters of their mechanical elements can be inferred from comparisons with optical stretcher experiments. Due to triangulation of the cell surface, interactions of cells with arbitrarily shaped (triangulated) structures such as blood vessels can be captured naturally. Comparing our simulations with those of so-called center-based models, in which cells have a largely rigid shape and forces are exerted between cell centers, we find that the migration forces a cell needs to exert on its environment to close a tissue lesion, is much smaller than predicted by center-based models. To stress generality of the approach, the liver simulations were complemented by monolayer and multicellular spheroid growth simulations. In summary, our model can give quantitative insight in many tissue organization processes, permits hypothesis testing in silico, and guide experiments in situations in which cell mechanics is considered important.

Modeling and analysis of melanoblast motion

Melanoblast migration is important for embryogenesis and is a key feature of melanoma metastasis. Many studies have characterized melanoblast movement, focusing on statistical properties and have highlighted basic mechanisms of melanoblast motility. We took a slightly different and complementary approach: we previously developed a mathematical model of melanoblast motion that enables the testing of biological assumptions about the displacement of melanoblasts and we created tests to analyze the geometric features of cell trajectories and the specific issue of trajectory interactions. Within this model, we performed simulations and compared the results with experimental data using geometric tests. In this paper, we developed the associated mathematical model and the main focus is to study the crossings between trajectories with new theoretical results about the variation of number of intersection points with respect to the crossing times. Using these results it is possible to study the random nature of displacements and the interactions between trajectories. This analysis has raised new questions, leading to the generation of strong arguments in favor of a trail left behind each moving melanoblast.

Mechanics of epithelial tissue formation

A key process in the life of any multicellular organism is its development from a single egg into a full grown adult. The first step in this process often consists of forming a tissue layer out of randomly placed cells on the surface of the egg. We present a model for generating such a tissue, based on mechanical interactions between the cells, and find that the resulting cellular pattern corresponds to the Voronoi tessellation of the nuclei of the cells. Experimentally, we obtain the same result in both fruit flies and flour beetles, with a distribution of cell shapes that matches that of the model, without any adjustable parameters. Finally, we show that this pattern is broken when the cells grow at different rates.

A simple developmental model recapitulates complex insect wing venation patterns

Insect wings are typically supported by thickened struts called veins. These veins form diverse geometric patterns across insects. For many insect species, even the left and right wings from the same individual have veins with unique topological arrangements, and little is known about how these patterns form. We present a large-scale quantitative study of the fingerprint-like "secondary veins." We compile a dataset of wings from 232 species and 17 families from the order Odonata (dragonflies and damselflies), a group with particularly elaborate vein patterns. We characterize the geometric arrangements of veins and develop a simple model of secondary vein patterning. We show that our model is capable of recapitulating the vein geometries of species from other, distantly related winged insect clades.

3D multicellular model of shock wave-cell interaction

Understanding the interaction between shock waves and tissue is critical for advancing the use of shock waves for medical applications, such as cancer therapy. This work aims to study shock wave-cell interaction in a more realistic environment, relevant to in vitro and in vivo studies, by using 3D computational models of healthy and cancerous cells. The results indicate that for a single cell embedded in an extracellular environment, the cellular geometry does not influence significantly the membrane strain but does influence the von Mises stress. On the contrary, the presence of neighbouring cells has a strong effect on the cell response, by increasing fourfold both quantities. The membrane strain response of a cell converges with more than three neighbouring cell layers, indicating that a cluster of four layers of cells is sufficient to model the membrane strain in a large domain of tissue. However, a full 3D tissue model is needed if the stress evaluation is of main interest. A tumour mimicking multicellular spheroid model is also proposed to study mutual interaction between healthy and cancer cells and shows that cancer cells can be specifically targeted in an early stage tumour-mimicking environment.

STATEMENT OF SIGNIFICANCE

This work presents 3D computational models of shock-wave/cell interaction in a biophysically realistic environment using real cell morphology in tissue-mimicking phantoms and multicellular spheroids. Results show that cell morphology does not strongly influence the membrane strain but influences the von Mises stress. While the presence of neighbouring cells significantly increases the cell response, four cell layers are enough to capture the membrane strain change in tissue. However, a full tissue model is necessary if accurate stress analysis is needed. The work also shows that cancer cells can be specifically targeted in early stage tumour mimicking environment. This work is a step towards realistic modelling of shock-wave/cell interactions in tissues and provides insight on the use of 3D models for different scenarios.

Investigation of Voronoi diagram based direction choices using uni- and bi-directional trajectory data

In a crowd, individuals make different motion choices such as "moving to destination," "following another pedestrian," and "making a detour." For the sake of convenience, the three direction choices are respectively called destination direction, following direction, and detour direction in this paper. Here, it is found that the featured direction choices could be inspired by the shape characteristics of the Voronoi diagram. To be specific, in the Voronoi cell of a pedestrian, the direction to a Voronoi node is regarded as a potential "detour" direction and the direction perpendicular to a Voronoi link is regarded as a potential "following" direction. A pedestrian generally owns several alternative Voronoi nodes and Voronoi links in a Voronoi cell, and the optimal detour and following direction are determined by considering related factors such as deviation. Plus the destination direction which is directly pointing to the destination, the three basic direction choices are defined in a Voronoi cell. In order to evaluate the Voronoi diagram based basic directions, the empirical trajectory data in both uni- and bi-directional flow experiments are extracted. A time series method considering the step frequency is used to reduce the original trajectories' swaying phenomena which might disturb the recognition of actual forward direction. The deviations between the empirical velocity direction and the basic directions are investigated, and each velocity direction is classified into a basic direction or regarded as an inexplicable direction according to the deviations. The analysis results show that each basic direction could be a potential direction choice for a pedestrian. The combination of the three basic directions could cover most empirical velocity direction choices in both uni- and bi-directional flow experiments.

Simulation of melanoblast displacements reveals new features of developmental migration

To distribute and establish the melanocyte lineage throughout the skin and other developing organs, melanoblasts undergo several rounds of proliferation, accompanied by migration through complex environments and differentiation. Melanoblast migration requires interaction with extracellular matrix of the epidermal basement membrane and with surrounding keratinocytes in the developing skin. Migration has been characterized by measuring speed, trajectory and directionality of movement, but there are many unanswered questions about what motivates and defines melanoblast migration. Here, we have established a general mathematical model to simulate the movement of melanoblasts in the epidermis based on biological data, assumptions and hypotheses. Comparisons between experimental data and computer simulations reinforce some biological assumptions, and suggest new ideas for how melanoblasts and keratinocytes might influence each other during development. For example, it appears that melanoblasts instruct each other to allow a homogeneous distribution in the tissue and that keratinocytes may attract melanoblasts until one is stably attached to them. Our model reveals new features of how melanoblasts move and, in particular, suggest that melanoblasts leave a repulsive trail behind them as they move through the skin.

Riding the cell jamming boundary: Geometry, topology, and phase of human corneal endothelium

It is important to assess the viability of eye-banked corneas prior to transplantation due to inherent senescence and known loss of endothelial cells during surgical manipulation. Corneal endothelial cells have a complex basal and paracellular shape making them challenging to accurately measure, particularly in oedematous ex vivo tissue. This study used calibrated centroidal Voronoi Diagrams to segment cells in images of these human corneas, in order to characterize endothelial geometry, topology, and phase. Hexagonal cells dominated the endothelia, with most comprised of five different pleomorphs exhibiting self-similar topological coarsening through most of the endothelial cell density range. There was a linear relationship between cell size and shape, though cells with greater than six sides were present in larger proportions than cells with less. Hexagonal cell regularity was stable and largely independent of density. Cell and tissue phase was also examined, using the cell shape index relative to the recently discovered 'cell jamming' phase transition boundary. Images showed fluid endothelia with a range of shape indices spanning the boundary, independent of density but dependent on hexagonal regularity. The cells showed a bimodal distribution centred at the boundary, with the largest proportion of cells on the fluid side. A shoulder at the boundary suggested phase switching via shape transformation across the energy barrier, with cells either side having distinctly different size and shape characteristics. Regular hexagonal cells were closest to the boundary. This study showed the corneal endothelium acts as a glassy viscous foam characterized by well-established physical laws. Endothelial cell death transiently and locally increases cell fluidity, which is subsequently arrested by jamming of the pleomorphically diverse cell collective, via rearrangement and shape change of a small proportion of cells, which become locked in place by their neighbours thereby maintaining structural equilibrium with little energy expenditure.

Single seed precise sowing of maize using computer simulation

In order to test the feasibility of computer simulation in field maize planting, the selection of the method of single seed precise sowing in maize is studied based on the quadratic function model Y = A×(D-Dm)²+Ym, which depicts the relationship between maize yield and planting density. And the advantages and disadvantages of the two planting methods under the condition of single seed sowing are also compared: Method 1 is optimum density planting, while Method 2 is the ideal seedling emergence number planting. It is found that the yield reduction rate and yield fluctuation of Method 2 are all lower than those of Method 1. The yield of Method 2 increased by at least 0.043 t/hm², and showed more advantages over Method 1 with higher yield level. Further study made on the influence of seedling emergence rate on the yield of maize finds that the yields of the two methods are both highly positively correlated with the seedling emergence rate and the standard deviations of their yields are both highly negatively correlated with the seedling emergence rate. For the study of the break-up problem of sparse caused by the method of single seed precise sowing, the definition of seedling missing spots is put forward. The study found that the relationship between number of hundred-dot spot and field seedling emergence rate is as the parabola function y = -189.32x²+ 309.55x - 118.95 and the relationship between number of spot missing seedling and field seedling emergence rate is as the negative exponent function y = 395.69e^-6.144x. The results may help to guide the maize seeds production and single seed precise sowing to some extent.

Quasi-Random Single-Point Imaging Using Low-Discrepancy $k$ -Space Sampling

Magnetic resonance imaging of short relaxation time spin systems has been a widely discussed topic with serious clinical applications and led to the emergence of fast imaging ultra-short echo-time sequences. Nevertheless, these sequences suffer from image blurring, due to the related sampling point spread function and are highly prone to imaging artefacts arising from, e.g., chemical shifts or magnetic susceptibilities. In this paper, we present a concept of spherical quasi-random single-point imaging. The approach is highly accelerateable, due to intrinsic undersampling properties and capable of strong metal artefact suppression. Imaging acceleration is achieved by sampling of quasi-random points in -space, based on a low-discrepancy sequence, and a combination with non-linear optimization reconstruction techniques [compressed sensing (CS)]. The presented low-discrepancy trajectory shows ideal noise like undersampling properties for the combination with CS, leading to denoised images with excellent metal artefact reduction. Using eightfold undersampling, acquisition time of a few minutes can be achieved for volume acquisitions.

Active Vertex Model for cell-resolution description of epithelial tissue mechanics

We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cell-specific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies.

Simulating Heterogeneous Tumor Cell Populations

Certain tumor phenomena, like metabolic heterogeneity and local stable regions of chronic hypoxia, signify a tumor's resistance to therapy. Although recent research has shed light on the intracellular mechanisms of cancer metabolic reprogramming, little is known about how tumors become metabolically heterogeneous or chronically hypoxic, namely the initial conditions and spatiotemporal dynamics that drive these cell population conditions. To study these aspects, we developed a minimal, spatially-resolved simulation framework for modeling tissue-scale mixed populations of cells based on diffusible particles the cells consume and release, the concentrations of which determine their behavior in arbitrarily complex ways, and on stochastic reproduction. We simulate cell populations that self-sort to facilitate metabolic symbiosis, that grow according to tumor-stroma signaling patterns, and that give rise to stable local regions of chronic hypoxia near blood vessels. We raise two novel questions in the context of these results: (1) How will two metabolically symbiotic cell subpopulations self-sort in the presence of glucose, oxygen, and lactate gradients? We observe a robust pattern of alternating striations. (2) What is the proper time scale to observe stable local regions of chronic hypoxia? We observe the stability is a function of the balance of three factors related to O2-diffusion rate, local vessel release rate, and viable and hypoxic tumor cell consumption rate. We anticipate our simulation framework will help researchers design better experiments and generate novel hypotheses to better understand dynamic, emergent whole-tumor behavior.

A versatile pipeline for the multi-scale digital reconstruction and quantitative analysis of 3D tissue architecture

A prerequisite for the systems biology analysis of tissues is an accurate digital three-dimensional reconstruction of tissue structure based on images of markers covering multiple scales. Here, we designed a flexible pipeline for the multi-scale reconstruction and quantitative morphological analysis of tissue architecture from microscopy images. Our pipeline includes newly developed algorithms that address specific challenges of thick dense tissue reconstruction. Our implementation allows for a flexible workflow, scalable to high-throughput analysis and applicable to various mammalian tissues. We applied it to the analysis of liver tissue and extracted quantitative parameters of sinusoids, bile canaliculi and cell shapes, recognizing different liver cell types with high accuracy. Using our platform, we uncovered an unexpected zonation pattern of hepatocytes with different size, nuclei and DNA content, thus revealing new features of liver tissue organization. The pipeline also proved effective to analyse lung and kidney tissue, demonstrating its generality and robustness.

Geometrical Formation of Compound Starch Grains in Rice Implements Voronoi Diagram

Starch forms transparent grains, called starch grains (SGs), in amyloplasts. One of the major morphological SG forms in Poaceae, called a compound SG, is formed by assemblies of small starch granules in an amyloplast. Starch granules assemble as a well-ordered structure; however, the mechanism that regulates this organization has not been identified. In this study, we examined how starch granules grow and converge into the final SG morphology. First, we found that the number of starch granules in an amyloplast is almost constant from the early developmental stage until endosperm maturity. Next, we quantitatively evaluated the geometrical similarities between starch granules and a Voronoi diagram, which is a mathematical tessellation of space based on the distance to a specific set of points in the space. The in silico growth simulation showed that the geometrical patterns of compound SGs resembling a Voronoi diagram is determined by physical interactions among the free-growing starch granules and the amyloplast envelope membrane. The geometrical similarity between compound SGs and a Voronoi diagram is likely a result of maximum loading and storage of starch in the amyloplast. The simulation described in this study provides a greater understanding of how compound SGs are formed and also has the potential to explain morphological variations of SGs.

PROLIFERATION AND COLLECTIVE MIGRATION OF SMALL CELL GROUPS RELEASED FROM CIRCULAR PATCHES

Collective cell migration is a key element in morphogenesis, cancer formation and wound healing. The multicellular dynamics of epithelial cell layers were studied in experiment and theory over the last years. Yet little is known about cell patches of finite size that should lead over from single cell behavior to collective motion. Here we study the migration and proliferation of small assemblies of epithelial cells (5-23 cells initially). Cells are released at defined time using removable poly(ethylene glycol)-dimethlacrylate (PEG-DMA) stencils with circular apertures, wherein cells were seeded. Using time-lapse microscopy we determine cell number, cell patch area and shape of multiple patches in parallel. We confirm exponential growth in cell number but find the area of the patches expanding faster than exponential in the early phase. The area is, however, well-described if cell proliferation is superimposed by elastic area dilation assuming that the cell groups were initially compressed. The elastic relaxation time is of the same order as the measured doubling time. Furthermore, analysis of the center-of-mass movement of the patches reveals bursts of directed motion, which coincide with asymmetric cell growth. In these cases the contours of the patches seem to result from a tug-of-war like scenario of opposing leader cells.

Ka-me: a Voronoi image analyzer

Summary: Ka-me is a Voronoi image analyzer that allows users to analyze any image with a convex polygonal tessellation or any spatial point distribution by fitting Voronoi polygons and their dual, Delaunay triangulations, to the pattern. The analytical tools include a variety of graph theoretic and geometric tools that summarize the distribution of the numbers of edges per face, areas, perimeters, angles of Delaunay triangle edges (anglograms), Gabriel graphs, nearest neighbor graphs, minimal spanning trees, Ulam trees, Pitteway tests, circumcircles and convexhulls, as well as spatial statistics (Clark–Evans Nearest Neighborhood and Variance to Mean Ratio) and export functions for standard relationships (Lewis's Law, Desch's Law and Aboav–Weaire Law).

Availability: Ka-me: a Voronoi image analyzer is available as an executable with documentation and sample applications from the BioQUEST Library (http://bioquest.org/downloads/kame_1.0.rar).

Contact:noppadon.khiripet@nectec.or.th

A steering model of endothelial sheet migration recapitulates monolayer integrity and directed collective migration

Cells in endothelial cell monolayers maintain a tight barrier between blood and tissue, but it is not well understood how endothelial cells move within monolayers, pass each other, migrate when stimulated with growth factor, and also retain monolayer integrity. Here, we develop a quantitative steering model based on functional classes of genes identified previously in a small interfering RNA (siRNA) screen to explain how cells locally coordinate their movement to maintain monolayer integrity and collectively migrate in response to growth factor. In the model, cells autonomously migrate within the monolayer and turn in response to mechanical cues resulting from adhesive, drag, repulsive, and directed steering interactions with neighboring cells. We show that lateral-drag steering explains the local coordination of cell movement and the maintenance of monolayer integrity by allowing closure of small lesions. We further demonstrate that directional steering of cells at monolayer boundaries, combined with adhesive steering of cells behind, can explain growth factor-triggered collective migration into open space. Together, this model provides a mechanistic explanation for the observed genetic modularity and a conceptual framework for how cells can dynamically maintain sheet integrity and undergo collective directed migration.