Discrete Element Framework for Modelling Extracellular Matrix, Deformable Cells and Subcellular Components

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

An in silico study on the influence of extracellular matrix mechanics on vasculogenesis

BACKGROUND AND OBJECTIVES

Blood vessels form a network of capillaries throughout the body that perform essential functions for life. Vasculogenesis, i.e. the formation of new blood vessels, is regulated by many factors, biochemical ones being among the most important. However, others such as the biomechanical influence on shape, organization and structure of vessel networks require further investigation. In this paper, we develop a 3D agent-based mechanobiological model of vasculogenesis with the aim of analyzing how the mechanics of the extracellular matrix (ECM) affects vasculogenesis.

METHODS

For this purpose, we consider a growing domain composed of different cells: tip cells, which are the driving cells located at the end of the vessels and stalk cells, which are found in the interior of the vascular network. ECM is considered as particles (agents) that surround the growth of the vascular network. Depending on the cell type, different sets of forces are considered, such as chemotactic, mechanical, random and viscoelastic forces among others.

RESULTS

The growth of the network is iteratively analyzed and updated at each time step based on a mechanically-driven proliferation rule. The influence of different biomechanical factors, such as ECM stiffness or viscoelasticity are explored through in silico simulations. A number of indicators are defined along the algorithm, like number of cells, branches, tortuosity and anisotropy, in order to compare topological differences of the vascular network during vasculogenesis under different ECM conditions. The obtained results are qualitatively compared with other related works in the literature.

CONCLUSIONS

The present study sheds some light and partially explain, from an in silico perspective, the role of ECM mechanics on vasculogenesis. The main conclusions of this work are: (i) increased stiffness increases proliferation, (ii) the network tends to migrate towards stiffer areas, and (iii) increased viscoelasticity decreases proliferation.

Transcription factor NFE2L3 promotes the proliferation of esophageal squamous cell carcinoma cells and causes radiotherapy resistance by regulating IL-6

OBJECTIVE

To scrutinize the impact of overexpression and interference of NFE2L3 on radiosensitivity of esophageal squamous cell carcinoma cells (ESCC) and its downstream mechanism and to assess whether NFE2L3 expression alters in vivo radiosensitivity of ESCC by developing a subcutaneous tumor model in mice.

METHODS

Through RNA-Seq, we compared the differentially expressed genes between the ECA-109R cell line and its parent ECA-109 cell line. The differentially expressed genes were selected and verified by qRT-PCR. Transfection of ESCC cell lines with NFE2L3 inhibitor or mimic lentivirus constructs was done to study the activity of NFE2L3. To assess the effect of NFE2L3 on cellular growth and proliferation, clonogenic survival assay, EdU incorporation assay, and CCK-8 assay were done after irradiation. To probe how many irradiated DNA double-strand breaks were produced, the corresponding intensity of γ-H2AX foci were detected by immunofluorescence. Apoptotic cells were assayed by flow cytometry assay after irradiation; To investigate the downstream genes of NFE2L3, we knocked NFE2L3, and RNA-Seq was used to find out the downstream genes. qRT-PCR and western blot ensued to score associated protein profiles. The in vivo ESCC cell radiosensitivity was scrutinized by nude mouse xenograft models.

RESULTS

The differential genes between ECA-109R cells and its parent ECA-109 cells were compared by qRT-PCR to unveil a significant increase in NFE2L3 expression. Functional analysis indicated that NFE2L3 increased radioresistance in ESCC cells. Then, through high-throughput sequencing and bioinformatics analysis, IL-6 was found to be a hub gene that played a role downstream of NFE2L3 and was verified by qRT-PCR, western blot, and double luciferase reporter gene experiment. NFE2L3 could regulate ESCC cell radiosensitivity via the IL-6-STAT3 signaling pathway, and downregulation of IL-6 expression could reverse the effects of highly expressed NFE2L3. In vivo tumor xenograft experiments confirmed that NFE2L3 affects the sensitivity to radiation therapy.

CONCLUSION

NFE2L3 can affect the radiosensitivity of ESCC cells through IL-6 transcription and IL-6/STAT3 signaling pathway. This makes NFE2L3 a putative target to regulate ESCC cell radiosensitivity.

High-resolution medical image reconstruction based on residual neural network for diagnosis of cerebral aneurysm

Objective

Cerebral aneurysms are classified as severe cerebrovascular diseases due to hidden and critical onset, which seriously threaten life and health. An effective strategy to control intracranial aneurysms is the regular diagnosis and timely treatment by CT angiography (CTA) imaging technology. However, unpredictable patient movements make it challenging to capture sub-millimeter-level ultra-high resolution images in a CTA scan. In order to improve the doctor's judgment, it is necessary to improve the clarity of the cerebral aneurysm medical image algorithm.

Methods

This paper mainly focuses on researching a three-dimensional medical image super-resolution algorithm applied to cerebral aneurysms. Although some scholars have proposed super-resolution reconstruction methods, there are problems such as poor effect and too much reconstruction time. Therefore, this paper designs a lightweight super-resolution network based on a residual neural network. The residual block structure removes the B.N. layer, which can effectively solve the gradient problem. Considering the high-resolution reconstruction needs to take the complete image as the research object and the fidelity of information, this paper selects the channel domain attention mechanism to improve the performance of the residual neural network.

Results

The new data set of cerebral aneurysms in this paper was obtained by CTA imaging technology of patients in the Department of neurosurgery, the second affiliated of Guizhou Medical University Hospital. The proposed model was evaluated from objective evaluation, model effect, model performance, and detection comparison. On the brain aneurysm data set, we tested the PSNR and SSIM values of 2 and 4 magnification factors, and the scores of our method were 33.01, 28.39, 33.06, and 28.41, respectively, which were better than those of the traditional SRCNN, ESPCN and FSRCNN. Subsequently, the model is applied to practice in this paper, and the effect, performance index and diagnosis of auxiliary doctors are obtained. The experimental results show that the high-resolution image reconstruction model based on the residual neural network designed in this paper plays a more influential role than other image classification methods. This method has higher robustness, accuracy and intuition.

Conclusion

With the wide application of CTA images in the clinical diagnosis of cerebral aneurysms and the increasing number of application samples, this method is expected to become an additional diagnostic tool that can effectively improve the diagnostic accuracy of cerebral aneurysms.

Renal oxygenation: From data to insight

Computational models have made a major contribution to the field of physiology. As the complexity of our understanding of biological systems expands, the need for computational methods only increases. But collaboration between experimental physiologists and computational modellers (ie theoretical physiologists) is not easy. One of the major challenges is to break down the barriers created by differences in vocabulary and approach between the two disciplines. In this review, we have two major aims. Firstly, we wish to contribute to the effort to break down these barriers and so encourage more interdisciplinary collaboration. So, we begin with a "primer" on the ways in which computational models can help us understand physiology and pathophysiology. Second, we aim to provide an update of recent efforts in one specific area of physiology, renal oxygenation. This work is shedding new light on the causes and consequences of renal hypoxia. But as importantly, computational modelling is providing direction for experimental physiologists working in the field of renal oxygenation by: (a) generating new hypotheses that can be tested in experimental studies, (b) allowing experiments that are technically unfeasible to be simulated in silico, or variables that cannot be measured experimentally to be estimated, and (c) providing a means by which the quality of experimental data can be assessed. Critically, based on our experience, we strongly believe that experimental and theoretical physiology should not be seen as separate exercises. Rather, they should be integrated to permit an iterative process between modelling and experimentation.

Formal description of plant morphogenesis

Plant morphogenesis may be characterized by complex feedback mechanisms between signals specifying growth and by the growth of the plant body itself. Comprehension of such feedback mechanisms is an ongoing research task and can be aided with formal descriptions of morphogenesis. In this review, we present a number of established mathematical paradigms that are useful to the formal representation of plant shape, and of biomechanical and biochemical signaling. Specifically, we discuss work from a range of research areas including plant biology, material sciences, fluid dynamics, and computer graphics. Treating plants as organized systems of information processing allows us to compare these different mathematical methods in terms of their expressive power of biological hypotheses. This is an attempt to bring together a large number of computational modeling concepts and make them accessible to the analytical as well as empirical student of plant morphogenesis.

Integrated lung tissue mechanics one piece at a time: Computational modeling across the scales of biology

The lung is a delicately balanced and highly integrated mechanical system. Lung tissue is continuously exposed to the environment via the air we breathe, making it susceptible to damage. As a consequence, respiratory diseases present a huge burden on society and their prevalence continues to rise. Emergent function is produced not only by the sum of the function of its individual components but also by the complex feedback and interactions occurring across the biological scales - from genes to proteins, cells, tissue and whole organ - and back again. Computational modeling provides the necessary framework for pulling apart and putting back together the pieces of the body and organ systems so that we can fully understand how they function in both health and disease. In this review, we discuss models of lung tissue mechanics spanning from the protein level (the extracellular matrix) through to the level of cells, tissue and whole organ, many of which have been developed in isolation. This is a vital step in the process but to understand the emergent behavior of the lung, we must work towards integrating these component parts and accounting for feedback across the scales, such as mechanotransduction. These interactions will be key to unlocking the mechanisms occurring in disease and in seeking new pharmacological targets and improving personalized healthcare.

Essential steps in bioprinting: From pre- to post-bioprinting

An increasing demand for directed assembly of biomaterials has inspired the development of bioprinting, which facilitates the assembling of both cellular and acellular inks into well-arranged three-dimensional (3D) structures for tissue fabrication. Although great advances have been achieved in the recent decade, there still exist issues to be addressed. Herein, a review has been systematically performed to discuss the considerations in the entire procedure of bioprinting. Though bioprinting is advancing at a rapid pace, it is seen that the whole process of obtaining tissue constructs from this technique involves multiple-stages, cutting across various technology domains. These stages can be divided into three broad categories: pre-bioprinting, bioprinting and post-bioprinting. Each stage can influence others and has a bearing on the performance of fabricated constructs. For example, in pre-bioprinting, tissue biopsy and cell expansion techniques are essential to ensure a large number of cells are available for mass organ production. Similarly, medical imaging is needed to provide high resolution designs, which can be faithfully bioprinted. In the bioprinting stage, compatibility of biomaterials is needed to be matched with solidification kinetics to ensure constructs with high cell viability and fidelity are obtained. On the other hand, there is a need to develop bioprinters, which have high degrees of freedom of movement, perform without failure concerns for several hours and are compact, and affordable. Finally, maturation of bioprinted cells are governed by conditions provided during the post-bioprinting process. This review, for the first time, puts all the bioprinting stages in perspective of the whole process of bioprinting, and analyzes their current state-of-the art. It is concluded that bioprinting community will recognize the relative importance and optimize the parameter of each stage to obtain the desired outcomes.

Simulation enabled search for explanatory mechanisms of the fracture healing process

A significant portion of bone fractures fail to heal properly, increasing healthcare costs. Advances in fracture management have slowed because translation barriers have limited generation of mechanism-based explanations for the healing process. When uncertainties are numerous, analogical modeling can be an effective strategy for developing plausible explanations of complex phenomena. We demonstrate the feasibility of engineering analogical models in software to facilitate discovery of biomimetic explanations for how fracture healing may progress. Concrete analogical models—Callus Analogs—were created using the MASON simulation toolkit. We designated a Target Region initial state within a characteristic tissue section of mouse tibia fracture at day-7 and posited a corresponding day-10 Target Region final state. The goal was to discover a coarse-grain analog mechanism that would enable the discretized initial state to transform itself into the corresponding Target Region final state, thereby providing an alternative way to study the healing process. One of nine quasi-autonomous Tissue Unit types is assigned to each grid space, which maps to an 80×80 μm region of the tissue section. All Tissue Units have an opportunity each time step to act based on individualized logic, probabilities, and information about adjacent neighbors. Action causes transition from one Tissue Unit type to another, and simulation through several thousand time steps generates a coarse-grain analog—a theory—of the healing process. We prespecified a minimum measure of success: simulated and actual Target Region states achieve ≥ 70% Similarity. We used an iterative refinement protocol to explore many combinations of Tissue Unit logic and action constraints. Workflows progressed through four stages of analog mechanisms. Similarities of 73–90% were achieved for Mechanisms 2–4. The range of Upper-Level similarities increased to 83–94% when we allowed for uncertainty about two Tissue Unit designations. We have demonstrated how Callus Analog experiments provide domain experts with a fresh medium and tools for thinking about and understanding the fracture healing process.

Translation barriers have limited the generation of mechanism-based explanations of fracture healing processes. Those barriers help explain why, to date, biological therapeutics have had only a minor impact on fracture management. Alternative approaches are needed, and we present one that is intended to help develop incrementally better mechanism-based explanations of fracture healing phenomena. We created virtual Callus Analogs to simulate how the histologic appearance of a mouse fracture callus may transition from day-7 to day-10. Callus Analogs use software-based model mechanisms, and simulation experiments enable challenging and improving those model mechanisms. During execution, model mechanism operation provides a coarse-grain explanation (a theory) of a four-day portion of the healing process. Simulated day-10 callus histologic images achieved 73–94% Similarity to a corresponding day-10 fracture callus image, thus demonstrating feasibility. Simulated healing provides an alternative perspective on the actual healing process and an alternative way of thinking about plausible fracture healing mechanisms. Our working hypothesis is that the approach can be extended to cover more of the healing process while making features of simulated and actual fracture healing increasingly analogous. The methods presented are intended to be extensible to other research areas that use histologic analysis to investigate and explain tissue level phenomena.

Colonoscopy procedure simulation: virtual reality training based on a real time computational approach

BACKGROUND

Colonoscopy plays an important role in the clinical screening and management of colorectal cancer. The traditional 'see one, do one, teach one' training style for such invasive procedure is resource intensive and ineffective. Given that colonoscopy is difficult, and time-consuming to master, the use of virtual reality simulators to train gastroenterologists in colonoscopy operations offers a promising alternative.

METHODS

In this paper, a realistic and real-time interactive simulator for training colonoscopy procedure is presented, which can even include polypectomy simulation. Our approach models the colonoscopy as thick flexible elastic rods with different resolutions which are dynamically adaptive to the curvature of the colon. More material characteristics of this deformable material are integrated into our discrete model to realistically simulate the behavior of the colonoscope.

CONCLUSION

We present a simulator for training colonoscopy procedure. In addition, we propose a set of key aspects of our simulator that give fast, high fidelity feedback to trainees. We also conducted an initial validation of this colonoscopic simulator to determine its clinical utility and efficacy.

A hybrid computational model to explore the topological characteristics of epithelial tissues

Epithelial tissues show a particular topology where cells resemble a polygon-like shape, but some biological processes can alter this tissue topology. During cell proliferation, mitotic cell dilation deforms the tissue and modifies the tissue topology. Additionally, cells are reorganized in the epithelial layer and these rearrangements also alter the polygon distribution. We present here a computer-based hybrid framework focused on the simulation of epithelial layer dynamics that combines discrete and continuum numerical models. In this framework, we consider topological and mechanical aspects of the epithelial tissue. Individual cells in the tissue are simulated by an off-lattice agent-based model, which keeps the information of each cell. In addition, we model the cell-cell interaction forces and the cell cycle. Otherwise, we simulate the passive mechanical behaviour of the cell monolayer using a material that approximates the mechanical properties of the cell. This continuum approach is solved by the finite element method, which uses a dynamic mesh generated by the triangulation of cell polygons. Forces generated by cell-cell interaction in the agent-based model are also applied on the finite element mesh. Cell movement in the agent-based model is driven by the displacements obtained from the deformed finite element mesh of the continuum mechanical approach. We successfully compare the results of our simulations with some experiments about the topology of proliferating epithelial tissues in Drosophila. Our framework is able to model the emergent behaviour of the cell monolayer that is due to local cell-cell interactions, which have a direct influence on the dynamics of the epithelial tissue.

Multi-scale computational study of the mechanical regulation of cell mitotic rounding in epithelia

Mitotic rounding during cell division is critical for preventing daughter cells from inheriting an abnormal number of chromosomes, a condition that occurs frequently in cancer cells. Cells must significantly expand their apical area and transition from a polygonal to circular apical shape to achieve robust mitotic rounding in epithelial tissues, which is where most cancers initiate. However, how cells mechanically regulate robust mitotic rounding within packed tissues is unknown. Here, we analyze mitotic rounding using a newly developed multi-scale subcellular element computational model that is calibrated using experimental data. Novel biologically relevant features of the model include separate representations of the sub-cellular components including the apical membrane and cytoplasm of the cell at the tissue scale level as well as detailed description of cell properties during mitotic rounding. Regression analysis of predictive model simulation results reveals the relative contributions of osmotic pressure, cell-cell adhesion and cortical stiffness to mitotic rounding. Mitotic area expansion is largely driven by regulation of cytoplasmic pressure. Surprisingly, mitotic shape roundness within physiological ranges is most sensitive to variation in cell-cell adhesivity and stiffness. An understanding of how perturbed mechanical properties impact mitotic rounding has important potential implications on, amongst others, how tumors progressively become more genetically unstable due to increased chromosomal aneuploidy and more aggressive.

Physical models of collective cell motility: from cell to tissue

In this article, we review physics-based models of collective cell motility. We discuss a range of techniques at different scales, ranging from models that represent cells as simple self-propelled particles to phase field models that can represent a cell's shape and dynamics in great detail. We also extensively review the ways in which cells within a tissue choose their direction, the statistics of cell motion, and some simple examples of how cell-cell signaling can interact with collective cell motility. This review also covers in more detail selected recent works on collective cell motion of small numbers of cells on micropatterns, in wound healing, and the chemotaxis of clusters of cells.

Controlling seepage in discrete particle simulations of biological systems

It is now commonplace to represent materials in a simulation using assemblies of discrete particles. Sometimes, one wishes to maintain the integrity of boundaries between particle types, for example, when modelling multiple tissue layers. However, as the particle assembly evolves during a simulation, particles may pass across interfaces. This behaviour is referred to as 'seepage'. The aims of this study were (i) to examine the conditions for seepage through a confining particle membrane and (ii) to define some simple rules that can be employed to control seepage. Based on the force-deformation response of spheres with various sizes and stiffness, we develop analytic expressions for the force required to move a 'probe particle' between confining 'membrane particles'. We analyse the influence that particle's size and stiffness have on the maximum force that can act on the probe particle before the onset of seepage. The theoretical results are applied in the simulation of a biological cell under unconfined compression.