COMPUCELL, a multi-model framework for simulation of morphogenesis

Mathematical and In Silico Analysis of Synthetic Inhibitory Circuits That Program Self-Organizing Multicellular Structures

Bottom-up approaches are becoming increasingly popular for studying multicellular self-organization and development. In contrast to the classic top-down approach, where parts of the organization/developmental process are broken to understand the process, the goal is to build the process to understand it. For example, synthetic circuits have been built to understand how cell-cell communication and differential adhesion can drive multicellular development. The majority of current bottom-up efforts focus on using activatory circuits to engineer and understand development, but efforts with inhibitory circuits have been minimal. Yet, inhibitory circuits are ubiquitous and vital to native developmental processes. Thus, inhibitory circuits are a crucial yet poorly studied facet of bottom-up multicellular development. To demonstrate the potential of inhibitory circuits for building and developing multicellular structures, several synthetic inhibitory circuits that combine engineered cell-cell communication and differential adhesion were designed, and then examined for synthetic development capability using a previously validated in silico framework. These designed inhibitory circuits can build a variety of patterned, self-organized structures and even morphological oscillations. These results support that inhibitory circuits can be powerful tools for building, studying, and understanding developmental processes.

Balancing competing effects of tissue growth and cytoskeletal regulation during Drosophila wing disc development

How a developing organ robustly coordinates the cellular mechanics and growth to reach a final size and shape remains poorly understood. Through iterations between experiments and model simulations that include a mechanistic description of interkinetic nuclear migration, we show that the local curvature, height, and nuclear positioning of cells in the Drosophila wing imaginal disc are defined by the concurrent patterning of actomyosin contractility, cell-ECM adhesion, ECM stiffness, and interfacial membrane tension. We show that increasing cell proliferation via different growth-promoting pathways results in two distinct phenotypes. Triggering proliferation through insulin signaling increases basal curvature, but an increase in growth through Dpp signaling and Myc causes tissue flattening. These distinct phenotypic outcomes arise from differences in how each growth pathway regulates the cellular cytoskeleton, including contractility and cell-ECM adhesion. The coupled regulation of proliferation and cytoskeletal regulators is a general strategy to meet the multiple context-dependent criteria defining tissue morphogenesis.

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 individual-based model to explore the impact of psychological stress on immune infiltration into tumour spheroids

In recentin vitroexperiments on co-culture between breast tumour spheroids and activated immune cells, it was observed that the introduction of the stress hormone cortisol resulted in a decreased immune cell infiltration into the spheroids. Moreover, the presence of cortisol deregulated the normal levels of the pro- and anti-inflammatory cytokines IFN-γand IL-10. We present an individual-based model to explore the interaction dynamics between tumour and immune cells under psychological stress conditions. With our model, we explore the processes underlying the emergence of different levels of immune infiltration, with particular focus on the biological mechanisms regulated by IFN-γand IL-10. The set-up of numerical simulations is defined to mimic the scenarios considered in the experimental study. Similarly to the experimental quantitative analysis, we compute a score that quantifies the level of immune cell infiltration into the tumour. The results of numerical simulations indicate that the motility of immune cells, their capability to infiltrate through tumour cells, their growth rate and the interplay between these cell parameters can affect the level of immune cell infiltration in different ways. Ultimately, numerical simulations of this model support a deeper understanding of the impact of biological stress-induced mechanisms on immune infiltration.

An in silico modeling approach to understanding the dynamics of the post-burn immune response

Introduction

Burns are characterized by a massive and prolonged acute inflammation, which persists for up to months after the initial trauma. Due to the complexity of the inflammatory process, Predicting the dynamics of wound healing process can be challenging for burn injuries. The aim of this study was to develop simulation models for the post-burn immune response based on (pre)clinical data.

Methods

The simulation domain was separated into blood and tissue compartments. Each of these compartments contained solutes and cell agents. Solutes comprise pro-inflammatory cytokines, anti-inflammatory cytokines and inflammation triggering factors. The solutes diffuse around the domain based on their concentration profiles. The cells include mast cells, neutrophils, and macrophages, and were modeled as independent agents. The cells are motile and exhibit chemotaxis based on concentrations gradients of the solutes. In addition, the cells secrete various solutes that in turn alter the dynamics and responses of the burn wound system.

Results

We developed an Glazier-Graner-Hogeweg method-based model (GGH) to capture the complexities associated with the dynamics of inflammation after burn injuries, including changes in cell counts and cytokine levels. Through simulations from day 0 - 4 post-burn, we successfully identified key factors influencing the acute inflammatory response, i.e., the initial number of endothelial cells, the chemotaxis threshold, and the level of chemoattractants.

Conclusion

Our findings highlight the pivotal role of the initial endothelial cell count as a key parameter for intensity of inflammation and progression of acute inflammation, 0 - 4 days post-burn.

A computational modeling approach for predicting multicell spheroid patterns based on signaling-induced differential adhesion

Physiological and pathological processes including embryogenesis and tumorigenesis rely on the ability of individual cells to work collectively to form multicell patterns. In these heterogeneous multicell systems, cell-cell signaling induces differential adhesion between cells that leads to tissue-level patterning. However, the sensitivity of pattern formation to changes in the strengths of signaling or cell adhesion processes is not well understood. Prior work has explored these issues using synthetically engineered heterogeneous multicell spheroid systems, in which cell subpopulations engage in bidirectional intercellular signaling to regulate the expression of different cadherins. While engineered cell systems provide excellent experimental tools to observe pattern formation in cell populations, computational models of these systems may be leveraged to explore more systematically how specific combinations of signaling and adhesion parameters can drive the emergence of unique patterns. We developed and validated two- and three-dimensional agent-based models (ABMs) of spheroid patterning for previously described cells engineered with a bidirectional signaling circuit that regulates N- and P-cadherin expression. Systematic exploration of model predictions, some of which were experimentally validated, revealed how cell seeding parameters, the order of signaling events, probabilities of induced cadherin expression, and homotypic adhesion strengths affect pattern formation. Unsupervised clustering was also used to map combinations of signaling and adhesion parameters to these unique spheroid patterns predicted by the ABM. Finally, we demonstrated how the model may be deployed to design new synthetic cell signaling circuits based on a desired final multicell pattern.

The Role of in silico Research in Developing Nanoparticle-Based Therapeutics

Nanoparticles (NPs) hold great potential as therapeutics, particularly in the realm of drug delivery. They are effective at functional cargo delivery and offer a great degree of amenability that can be used to offset toxic side effects or to target drugs to specific regions in the body. However, there are many challenges associated with the development of NP-based drug formulations that hamper their successful clinical translation. Arguably, the most significant barrier in the way of efficacious NP-based drug delivery systems is the tedious and time-consuming nature of NP formulation—a process that needs to account for downstream effects, such as the onset of potential toxicity or immunogenicity, in vivo biodistribution and overall pharmacokinetic profiles, all while maintaining desirable therapeutic outcomes. Computational and AI-based approaches have shown promise in alleviating some of these restrictions. Via predictive modeling and deep learning, in silico approaches have shown the ability to accurately model NP-membrane interactions and cellular uptake based on minimal data, such as the physicochemical characteristics of a given NP. More importantly, machine learning allows computational models to predict how specific changes could be made to the physicochemical characteristics of a NP to improve functional aspects, such as drug retention or endocytosis. On a larger scale, they are also able to predict the in vivo pharmacokinetics of NP-encapsulated drugs, predicting aspects such as circulatory half-life, toxicity, and biodistribution. However, the convergence of nanomedicine and computational approaches is still in its infancy and limited in its applicability. The interactions between NPs, the encapsulated drug and the body form an intricate network of interactions that cannot be modeled with absolute certainty. Despite this, rapid advancements in the area promise to deliver increasingly powerful tools capable of accelerating the development of advanced nanoscale therapeutics. Here, we describe computational approaches that have been utilized in the field of nanomedicine, focusing on approaches for NP design and engineering.

Finite Element Models of Osteocytes and Their Load-Induced Activation

PURPOSE OF REVIEW

Osteocytes are the conductors of bone adaptation and remodelling. Buried inside the calcified matrix, they sense mechanical cues and signal osteoclasts in case of low activity, and osteoblasts when stresses are high. How do osteocytes detect mechanical stress? What physical signal do they perceive? Finite element analysis is a useful tool to address these questions as it allows calculating stresses, strains and fluid flow where they cannot be measured. The purpose of this review is to evaluate the capabilities and challenges of finite element models of bone, in particular the osteocytes and load-induced activation mechanisms.

RECENT FINDINGS

High-resolution imaging and increased computational power allow ever more detailed modelling of osteocytes, either in isolation or embedded within the mineralised matrix. Over the years, homogeneous models of bone and osteocytes got replaced by heterogeneous and microstructural models, including, e.g. the lacuno-canalicular network and the cytoskeleton. The lacuno-canalicular network induces strain amplifications and the osteocyte protrusions seem to be stimulated much more than the cell body, both by strain and fluid flow. More realistic cell geometries, like minute constrictions of the canaliculi, increase this effect. Microstructural osteocyte models describe the transduction of external stimuli to the nucleus. Supracellular multiscale models (e.g. of a tunnelling osteon) allow to study differential loading of osteocytes and to distinguish between strain and fluid flow as the pivotal stimulatory cue. In the future, the finite element models may be enhanced by including chemical transport and intercellular communication between osteocytes, osteoclasts and osteoblasts.

THREE-DIMENSIONAL COMPUTATIONAL MODEL OF EARLY UPPER LIMB DEVELOPMENT

Limb development begins during embryogenesis when a series of biochemical interactions are triggered between a particular region of the mesoderm and the ectoderm. These processes affect the morphogenesis and growth of bones, joints, and all the other constituent elements of limbs; nevertheless, how the biochemical regulation affects mesenchymal condensation is not entirely clear. In this study, a three-dimensional computational model is designed to predict the appearance and location of the mesenchymal condensation in the stylopod and zeugopod; the biochemical events were described with reaction–diffusion equations that were solved using the finite elements method. The result of the gene expression in our model was consistent with the one reported in literature; the obtained patterns of Fgf8, Fgf10, and Wnt3a can predict the shape of the mesenchymal condensation of early upper limb development; the simple diffusive patterns of molecules were suitable to explain the areas where sox9 is expressed. Furthermore, our results suggest that the expression of Tgf-[Formula: see text] in the upper limb could be due to the inhibition of retinoic acid. These results suggest the importance of building computational scenarios where pathologies may be comprehensively examined.

Navigating Multi-Scale Cancer Systems Biology Towards Model-Driven Clinical Oncology and Its Applications in Personalized Therapeutics

Rapid advancements in high-throughput omics technologies and experimental protocols have led to the generation of vast amounts of scale-specific biomolecular data on cancer that now populates several online databases and resources. Cancer systems biology models built using this data have the potential to provide specific insights into complex multifactorial aberrations underpinning tumor initiation, development, and metastasis. Furthermore, the annotation of these single- and multi-scale models with patient data can additionally assist in designing personalized therapeutic interventions as well as aid in clinical decision-making. Here, we have systematically reviewed the emergence and evolution of (i) repositories with scale-specific and multi-scale biomolecular cancer data, (ii) systems biology models developed using this data, (iii) associated simulation software for the development of personalized cancer therapeutics, and (iv) translational attempts to pipeline multi-scale panomics data for data-driven in silico clinical oncology. The review concludes that the absence of a generic, zero-code, panomics-based multi-scale modeling pipeline and associated software framework, impedes the development and seamless deployment of personalized in silico multi-scale models in clinical settings.

Manipulating Extracellular Matrix Organizations and Parameters to Control Local Cancer Invasion

Metastasis contributes to over 90 percent of cancer mortalities and may be influenced by the extracellular matrix (ECM). ECM microenvironments differ in matrix organization, cell-matrix adhesions, and fiber rigidity, which may affect cancer migration and, thus, should be investigated. To understand the interactions between cancer cells and the ECM, we simulate local invasion through ECM organizations of varying determinants. Randomly curved organizations of normal ovarian stroma exhibit minimal local invasion. In contrast, wave-like and parallel linear structures in reorganized ECM organizations provide contact guidance, which increases cancer invasiveness. ECM organizations with strong cell-matrix attachments generate cell pseudopodia, which aid in increasing invasion rate, while weaker attachments prevent the cells from attaching to the fibers and forming pseudopodia, limiting local invasion. ECM organizations with rigid fibers elongate the cell body, allowing them to form cell protrusions and spread rapidly. Conversely, soft fibers stimulate cell rounding and limit migration. Optimizing cell-matrix adhesions and fiber rigidity results in below 10 percent local invasion and reinforces the importance of using computational modeling to discover novel approaches to restricting cancer movement.

Matrix adhesion and remodeling diversifies modes of cancer invasion across spatial scales

The metastasis of malignant epithelial tumors begins with the egress of transformed cells from the confines of their basement membrane (BM) to their surrounding collagen-rich stroma. Invasion can be morphologically diverse: when breast cancer cells are separately cultured within BM-like matrix, collagen I (Coll I), or a combination of both, they exhibit collective-, dispersed mesenchymal-, and a mixed collective-dispersed (multimodal)- invasion, respectively. In this paper, we asked how distinct these invasive modes are with respect to the cellular and microenvironmental cues that drive them. A rigorous computational exploration of invasion was performed within an experimentally motivated Cellular Potts-based modeling environment. The model comprised of adhesive interactions between cancer cells, BM- and Coll I-like extracellular matrix (ECM), and reaction-diffusion-based remodeling of ECM. The model outputs were parameters cognate to dispersed- and collective- invasion. A clustering analysis of the output distribution curated through a careful examination of subsumed phenotypes suggested at least four distinct invasive states: dispersed, papillary-collective, bulk-collective, and multimodal, in addition to an indolent/non-invasive state. Mapping input values to specific output clusters suggested that each of these invasive states are specified by distinct input signatures of proliferation, adhesion and ECM remodeling. In addition, specific input perturbations allowed transitions between the clusters and revealed the variation in the robustness between the invasive states. Our systems-level approach proffers quantitative insights into how the diversity in ECM microenvironments may steer invasion into diverse phenotypic modes during early dissemination of breast cancer and contributes to tumor heterogeneity.

Biofabrication of spheroids fusion-based tumor models: computational simulation of glucose effects

In vitro tumor models consisting of cell spheroids are increasingly used for mechanistic studies and pharmacological testing. However, unless vascularized, the availability of nutrients such as glucose to deeper layers of multicellular aggregates is limited. In addition, recent developments in cells-only biofabrication (e.g. 'scaffold-free bioprinting'), allow the creation of more complex spheroid-based structures, further exposing the cells to nutrient deprivation within these constructs. To explore the impact of glucose availability on such tumor-like structures, we used the CompuCell3D (CC3D) platform for modeling of tumor spheroids. By monitoring the types of cells, fusing pairs geometry and the distance between spheroids centers of mass, we made novel heuristic observations on how binary- and multi-spheroid fusions are impacted by glucose availability. At limiting glucose concentrations mimicking hypoglycemia we noted an abrupt collapse of the tumor spheroids, unexpectedly amplified by the contact with normal cell spheroids. At higher glucose concentrations, we found an increased intermixing of cancerous cells, strong anti-phase oscillations between proliferating and quiescent tumor cells and a structural instability of fusing tumor spheroids, leading to their re-fragmentation. In a model of tumor microenvironment composed of normal cell spheroids fusing around a tumoral one, the competition for glucose lead to either the tumor's disappearance, or to its steady expansion. Moreover, the invasion of this microenvironment by individual tumor cells was also strongly depended on the available glucose. In conclusion, we demonstrate the value of computational simulations for anticipating the properties of biofabricated tumor models, and in generating testable hypotheses regarding the relationship between cancer, nutrition and diabetes.

Software for Bioprinting

The bioprinting of heterogeneous organs is a crucial issue. To reach the complexity of such organs, there is a need for highly specialized software that will meet all requirements such as accuracy, complexity, and others. The primary objective of this review is to consider various software tools that are used in bioprinting and to reveal their capabilities. The sub-objective was to consider different approaches for the model creation using these software tools. Related articles on this topic were analyzed. Software tools are classified based on control tools, general computer-aided design (CAD) tools, tools to convert medical data to CAD formats, and a few highly specialized research-project tools. Different geometry representations are considered, and their advantages and disadvantages are considered applicable to heterogeneous volume modeling and bioprinting. The primary factor for the analysis is suitability of the software for heterogeneous volume modeling and bioprinting or multimaterial three-dimensional printing due to the commonality of these technologies. A shortage of specialized suitable software tools is revealed. There is a need to develop a new application area such as computer science for bioprinting which can contribute significantly in future research work.

Mechanosensitive Junction Remodeling Promotes Robust Epithelial Morphogenesis

Morphogenesis of epithelial tissues requires tight spatiotemporal coordination of cell shape changes. In vivo, many tissue-scale shape changes are driven by pulsatile contractions of intercellular junctions, which are rectified to produce irreversible deformations. The functional role of this pulsatory ratchet and its mechanistic basis remain unknown. Here we combine theory and biophysical experiments to show that mechanosensitive tension remodeling of epithelial cell junctions promotes robust epithelial shape changes via ratcheting. Using optogenetic control of actomyosin contractility, we find that epithelial junctions show elastic behavior under low contractile stress, returning to their original lengths after contraction, but undergo irreversible deformation under higher magnitudes of contractile stress. Existing vertex-based models for the epithelium are unable to capture these results, with cell junctions displaying purely elastic or fluid-like behaviors, depending on the choice of model parameters. To describe the experimental results, we propose a modified vertex model with two essential ingredients for junction mechanics: thresholded tension remodeling and continuous strain relaxation. First, junctions must overcome a critical strain threshold to trigger tension remodeling, resulting in irreversible junction length changes. Second, there is a continuous relaxation of junctional strain that removes mechanical memory from the system. This enables pulsatile contractions to further remodel cell shape via mechanical ratcheting. Taken together, the combination of mechanosensitive tension remodeling and junctional strain relaxation provides a robust mechanism for large-scale morphogenesis.

Synthetic development: building mammalian multicellular structures with artificial genetic programs

Synthetic biology efforts began in simple single-cell systems, which were relatively easy to manipulate genetically (Cameron et al., 2014). The field grew exponentially in the last two decades, and one of the latest frontiers are synthetic developmental programs for multicellular mammalian systems (Black et al., 2017; Wieland and Fussenegger, 2012) to genetically control features such as patterning or morphogenesis. These programs rely on engineered cell-cell communications, multicellular gene regulatory networks and effector genes. Here, we contextualize the first of these synthetic developmental programs, examine molecular and computational tools that can be used to generate next generation versions, and present the general logic that underpins these approaches. These advances are exciting as they represent a novel way to address both control and understanding in the field of developmental biology and tissue development (Elowitz and Lim, 2010; Velazquez et al., 2018; White et al., 2018; Morsut, 2017). This field is just at the beginning, and it promises to be of major interest in the upcoming years of biomedical research.

Addressing Interdisciplinary Difficulties in Developmental Biology/Mathematical Collaborations: A Neural Crest Example

Mathematical modeling can allow insight into the biological processes that can be difficult to access by conventional biological means alone. Such projects are becoming increasingly attractive with the appearance of faster and more powerful quantitative techniques in both biological data acquisition and data storage, manipulation, and presentation. However, as is frequent in interdisciplinary research, the main hurdles are not within the mindset and techniques of each discipline but are usually encountered in attempting to meld the different disciplines together. Based upon our experience in applying mathematical methods to investigate how neural crest cells interact to form the enteric nervous system, we present our views on how to pursue biomathematical modeling projects, what difficulties to expect, and how to overcome, or at least survive, these hurdles. The main advice being: persevere.

Agent-based modeling of morphogenetic systems: Advantages and challenges

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

Optimal Coarse-Grained Site Selection in Elastic Network Models of Biomolecules

Elastic network models, simple structure-based representations of biomolecules where atoms interact via short-range harmonic potentials, provide great insight into a molecule's internal dynamics and mechanical properties at extremely low computational cost. Their efficiency and effectiveness have made them a pivotal instrument in the computer-aided study of proteins and, since a few years, also of nucleic acids. In general, the coarse-grained sites, i.e. those effective force centers onto which the all-atom structure is mapped, are constructed based on intuitive rules: a typical choice for proteins is to retain only the C _α atoms of each amino acid. However, a mapping strategy relying only on the atom type and not the local properties of its embedding can be suboptimal compared to a more careful selection. Here, we present a strategy in which the subset of atoms, each of which is mapped onto a unique coarse-grained site of the model, is selected in a stochastic search aimed at optimizing a cost function. The latter is taken to be a simple measure of the consistency between the harmonic approximation of an elastic network model and the harmonic model obtained through exact integration of the discarded degrees of freedom. The method is applied to two representatives of structurally very different types of biomolecules: the protein adenylate kinase and the RNA molecule adenine riboswitch. Our analysis quantifies the substantial impact that an algorithm-driven selection of coarse-grained sites can have on a model's properties.

Emergence of form in embryogenesis

The development of form in an embryo is the result of a series of topological and informational symmetry breakings. We introduce the vector-reaction-diffusion-drift (VRDD) system where the limit cycle of spatial dynamics is morphogen concentrations with Dirac delta-type distributions. This is fundamentally different from the Turing reaction-diffusion system, as VRDD generates system-wide broken symmetry. We developed 'fundamental forms' from spherical blastula with a single organizing axis (rotational symmetry), double axis (mirror symmetry) and triple axis (no symmetry operator in three dimensions). We then introduced dynamics for cell differentiation, where genetic regulatory states are modelled as a finite-state machine (FSM). The state switching of an FSM is based on local morphogen concentrations as epigenetic information that changes dynamically. We grow complicated forms hierarchically in spatial subdomains using the FSM model coupled with the VRDD system. Using our integrated simulation model with four layers (topological, physical, chemical and regulatory), we generated life-like forms such as hydra. Genotype-phenotype mapping was investigated with continuous and jump mutations. Our study can have applications in morphogenetic engineering, soft robotics and biomimetic design.

OpenWorm: overview and recent advances in integrative biological simulation of Caenorhabditis elegans

The adoption of powerful software tools and computational methods from the software industry by the scientific research community has resulted in a renewed interest in integrative, large-scale biological simulations. These typically involve the development of computational platforms to combine diverse, process-specific models into a coherent whole. The OpenWorm Foundation is an independent research organization working towards an integrative simulation of the nematode Caenorhabditis elegans, with the aim of providing a powerful new tool to understand how the organism's behaviour arises from its fundamental biology. In this perspective, we give an overview of the history and philosophy of OpenWorm, descriptions of the constituent sub-projects and corresponding open-science management practices, and discuss current achievements of the project and future directions.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Heuristic Modeling and 3D Stereoscopic Visualization of a Chlamydomonas reinhardtii Cell

The structural modeling and representation of cells is a complex task as different microscopic, spectroscopic and other information resources have to be combined to achieve a three-dimensional representation with high accuracy. Moreover, to provide an appropriate spatial representation of the cell, a stereoscopic 3D (S3D) visualization is favorable. In this work, a structural cell model is created by combining information from various light microscopic and electron microscopic images as well as from publication-related data. At the mesoscopic level each cell component is presented with special structural and visual properties; at the molecular level a cell membrane composition and the underlying modeling method are discussed; and structural information is correlated with those at the functional level (represented by simplified energy-producing metabolic pathways). The organism used as an example is the unicellular Chlamydomonas reinhardtii, which might be important in future alternative energy production processes. Based on the 3D model, an educative S3D animation was created which was shown at conferences. The complete workflow was accomplished by using the open source 3D modeling software Blender. The discussed project including the animation is available from: http://Cm5.CELLmicrocosmos.org.

Cell studio: A platform for interactive, 3D graphical simulation of immunological processes

The field of computer modeling and simulation of biological systems is rapidly advancing, backed by significant progress in the fields of experimentation techniques, computer hardware, and programming software. The result of a simulation may be delivered in several ways, from numerical results, through graphs of the simulated run, to a visualization of the simulation. The vision of an in-silico experiment mimicking an in-vitro or in-vivo experiment as it is viewed under a microscope is appealing but technically demanding and computationally intensive. Here, we report “Cell Studio,” a generic, hybrid platform to simulate an immune microenvironment with biological and biophysical rules. We use game engines—generic programs for game creation which offer ready-made assets and tools—to create a visualized, interactive 3D simulation. We also utilize a scalable architecture that delegates the computational load to a server. The user may view the simulation, move the “camera” around, stop, fast-forward, and rewind it and inject soluble molecules into the extracellular medium at any point in time. During simulation, graphs are created in real time for a broad view of system-wide processes. The model is parametrized using a user-friendly Graphical User Interface (GUI). We show a simple validation simulation and compare its results with those from a “classical” simulation, validated against a “wet” experiment. We believe that interactive, real-time 3D visualization may aid in generating insights from the model and encourage intuition about the immunological scenario.

ParaCells: A GPU Architecture for Cell-Centered Models in Computational Biology

In computational biology, the hierarchy of biological systems requires the development of flexible and powerful computational tools. Graphics processing unit (GPU) architecture has been a suitable device for parallel computing in simulating multi-cellular systems. However, in modeling complex biological systems, scientists often face two tasks, mathematical formulation and skillful programming. In particular, specific programming skills are needed for GPU programming. Therefore, the development of an easy-to-use computational architecture, which utilizes GPU for parallel computing and provides intuitive interfaces for simple implementation, is needed so that general scientists can perform GPU simulations without knowing much about the GPU architecture. Here, we introduce ParaCells, a cell-centered GPU simulation architecture for NVIDIA compute unified device architecture (CUDA). ParaCells was designed as a versatile architecture that connects the user logic (in C++) with NVIDIA CUDA runtime and is specific to the modeling of multi-cellular systems. An advantage of ParaCells is its object-oriented model declaration, which allows it to be widely applied to many biological systems through the combination of basic biological concepts. We test ParaCells with two applications. Both applications are significantly faster when compared with sequential as well as parallel OpenMP and OpenACC implementations. Moreover, the simulation programs based on ParaCells are cleaner and more readable than other versions.

The vertebrate limb: An evolving complex of self-organizing systems

The paired appendages (fins or limbs) of jawed vertebrates contain an endoskeleton consisting of nodules, bars and, in some groups, plates of cartilage, or bone arising from replacement of cartilaginous templates. The generation of the endoskeletal elements occurs by processes involving production and diffusion of morphogens, with, variously, positive and negative feedback circuits, adhesion, and receptor dynamics with similarities to the mechanism for chemical pattern formation proposed by Alan Turing. This review presents a unified interpretation of the evolution and functioning of these mechanisms. Studies are described indicating that protocondensations, compacted mesenchymal cell aggregates that prefigure the appendicular skeleton, arise through the adhesive activity of galectin-1, a matricellular protein with skeletogenic homologs in all jawed vertebrates. In the cartilaginous and lobe-finned fishes (and to a variable extent in ray-finned fishes) it additionally cooperates with an isoform of galectin-8 to constitute a self-organizing network capable of generating arrays of preskeletal nodules, bars and plates. Further, in the tetrapods, a putative galectin-8 control module was acquired that may have enabled proximodistal increase in the number of protocondensations. In parallel to this, other self-organizing networks emerged that acted, via Bmp, Wnt, Sox9 and Runx2, as well as transforming factor-β and fibronectin, to convert protocondensations into skeletal tissues. The progressive appearance and integration of these skeletogenic networks over evolution occurred in the context of an independently evolved system of Hox protein and Shh gradients that interfaced with them to tune the spatial wavelengths and refine the identities of the resulting arrays of elements.

Sequence entropy of folding and the absolute rate of amino acid substitutions

Adequate representations of protein evolution should consider how the acceptance of mutations depends on the sequence context in which they arise. However, epistatic interactions among sites in a protein result in time and spatial substitution rate heterogeneity beyond the capabilities of current models. Here, we exploit parallels between amino acid substitutions and chemical reaction kinetics to develop an improved theory of protein evolution. We constructed a mechanistic framework for modelling amino acid substitution rates that employs the formalisms of statistical mechanics, with population genetics principles underlying the analysis. Theoretical analyses and computer simulations of proteins under purifying selection for thermodynamic stability show that substitution rates and the stabilisation of resident amino acids (the ‘evolutionary Stokes shift’) can be predicted from biophysics and the effect of sequence entropy alone. Furthermore, we demonstrate that substitutions predominantly occur when epistatic interactions result in near neutrality; substitution rates are determined by how often epistasis results in such nearly neutral conditions. This theory provides a general framework for modelling protein sequence change under purifying selection, potentially explains patterns of convergence and mutation rates in real proteins that are incompatible with previous models, and provides a better null model for the detection of adaptive changes.

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.

Comparing individual-based approaches to modelling the self-organization of multicellular tissues

The coordinated behaviour of populations of cells plays a central role in tissue growth and renewal. Cells react to their microenvironment by modulating processes such as movement, growth and proliferation, and signalling. Alongside experimental studies, computational models offer a useful means by which to investigate these processes. To this end a variety of cell-based modelling approaches have been developed, ranging from lattice-based cellular automata to lattice-free models that treat cells as point-like particles or extended shapes. However, it remains unclear how these approaches compare when applied to the same biological problem, and what differences in behaviour are due to different model assumptions and abstractions. Here, we exploit the availability of an implementation of five popular cell-based modelling approaches within a consistent computational framework, Chaste (http://www.cs.ox.ac.uk/chaste). This framework allows one to easily change constitutive assumptions within these models. In each case we provide full details of all technical aspects of our model implementations. We compare model implementations using four case studies, chosen to reflect the key cellular processes of proliferation, adhesion, and short- and long-range signalling. These case studies demonstrate the applicability of each model and provide a guide for model usage.

A Liver-Centric Multiscale Modeling Framework for Xenobiotics

We describe a multi-scale, liver-centric in silico modeling framework for acetaminophen pharmacology and metabolism. We focus on a computational model to characterize whole body uptake and clearance, liver transport and phase I and phase II metabolism. We do this by incorporating sub-models that span three scales; Physiologically Based Pharmacokinetic (PBPK) modeling of acetaminophen uptake and distribution at the whole body level, cell and blood flow modeling at the tissue/organ level and metabolism at the sub-cellular level. We have used standard modeling modalities at each of the three scales. In particular, we have used the Systems Biology Markup Language (SBML) to create both the whole-body and sub-cellular scales. Our modeling approach allows us to run the individual sub-models separately and allows us to easily exchange models at a particular scale without the need to extensively rework the sub-models at other scales. In addition, the use of SBML greatly facilitates the inclusion of biological annotations directly in the model code. The model was calibrated using human in vivo data for acetaminophen and its sulfate and glucuronate metabolites. We then carried out extensive parameter sensitivity studies including the pairwise interaction of parameters. We also simulated population variation of exposure and sensitivity to acetaminophen. Our modeling framework can be extended to the prediction of liver toxicity following acetaminophen overdose, or used as a general purpose pharmacokinetic model for xenobiotics.

Spatio-temporal morphology changes in and quenching effects on the 2D spreading dynamics of cell colonies in both plain and methylcellulose-containing culture media

To deal with complex systems, microscopic and global approaches become of particular interest. Our previous results from the dynamics of large cell colonies indicated that their 2D front roughness dynamics is compatible with the standard Kardar-Parisi-Zhang (KPZ) or the quenched KPZ equations either in plain or methylcellulose (MC)-containing gel culture media, respectively. In both cases, the influence of a non-uniform distribution of the colony constituents was significant. These results encouraged us to investigate the overall dynamics of those systems considering the morphology and size, the duplication rate, and the motility of single cells. For this purpose, colonies with different cell populations (N) exhibiting quasi-circular and quasi-linear growth fronts in plain and MC-containing culture media are investigated. For small N, the average radial front velocity and its change with time depend on MC concentration. MC in the medium interferes with cell mitosis, contributes to the local enlargement of cells, and increases the distribution of spatio-temporal cell density heterogeneities. Colony spreading in MC-containing media proceeds under two main quenching effects, I and II; the former mainly depending on the culture medium composition and structure and the latter caused by the distribution of enlarged local cell domains. For large N, colony spreading occurs at constant velocity. The characteristics of cell motility, assessed by measuring their trajectories and the corresponding velocity field, reflect the effect of enlarged, slow-moving cells and the structure of the medium. Local average cell size distribution and individual cell motility data from plain and MC-containing media are qualitatively consistent with the predictions of both the extended cellular Potts models and the observed transition of the front roughness dynamics from a standard KPZ to a quenched KPZ. In this case, quenching effects I and II cooperate and give rise to the quenched-KPZ equation. Seemingly, these results show a possible way of linking the cellular Potts models and the 2D colony front roughness dynamics.

A cell-centered, agent-based framework that enables flexible environment granularities

BACKGROUND

Mechanistic explanations of cell-level phenomena typically adopt an observer perspective. Explanations developed from a cell's perspective may offer new insights. Agent-based models lend themselves to model from an individual perspective, and existing agent-based models generally utilize a regular lattice-based environment. A framework which utilizes a cell's perspective in an off-lattice environment could improve the overall understanding of biological phenomena.

RESULTS

We present an agent-based, discrete event framework, with a demonstrative focus on biomimetic agents. The framework was first developed in 2-dimensions and then extended, with a subset of behaviors, to 3-dimensions. The framework is expected to facilitate studies of more complex biological phenomena through exploitation of a dynamic Delaunay and Voronoi off-lattice environment. We used the framework to model biological cells and to specifically demonstrate basic biological cell behaviors in two- and three-dimensional space. Potential use cases are highlighted, suggesting the utility of the framework in various scenarios.

CONCLUSIONS

The framework presented in this manuscript expands on existing cell- and agent-centered methods by offering a new perspective in an off-lattice environment. As the demand for biomimetic models grows, the demand for new methods, such as the presented Delaunay and Voronoi framework, is expected to increase.

Adult Stem Cell Therapies for Wound Healing: Biomaterials and Computational Models

The increased incidence of diabetes and tumors, associated with global demographic issues (aging and life styles), has pointed out the importance to develop new strategies for the effective management of skin wounds. Individuals affected by these diseases are in fact highly exposed to the risk of delayed healing of the injured tissue that typically leads to a pathological inflammatory state and consequently to chronic wounds. Therapies based on stem cells (SCs) have been proposed for the treatment of these wounds, thanks to the ability of SCs to self-renew and specifically differentiate in response to the target bimolecular environment. Here, we discuss how advanced biomedical devices can be developed by combining SCs with properly engineered biomaterials and computational models. Examples include composite skin substitutes and bioactive dressings with controlled porosity and surface topography for controlling the infiltration and differentiation of the cells. In this scenario, mathematical frameworks for the simulation of cell population growth can provide support for the design of bioconstructs, reducing the need of expensive, time-consuming, and ethically controversial animal experimentation.

Computational Modeling, Formal Analysis, and Tools for Systems Biology

As the amount of biological data in the public domain grows, so does the range of modeling and analysis techniques employed in systems biology. In recent years, a number of theoretical computer science developments have enabled modeling methodology to keep pace. The growing interest in systems biology in executable models and their analysis has necessitated the borrowing of terms and methods from computer science, such as formal analysis, model checking, static analysis, and runtime verification. Here, we discuss the most important and exciting computational methods and tools currently available to systems biologists. We believe that a deeper understanding of the concepts and theory highlighted in this review will produce better software practice, improved investigation of complex biological processes, and even new ideas and better feedback into computer science.

An Analysis of the Truncated Bid- and ROS-dependent Spatial Propagation of Mitochondrial Permeabilization Waves during Apoptosis

Apoptosis is a form of programmed cell death that is essential for the efficient elimination of surplus, damaged, and transformed cells during metazoan embryonic development and adult tissue homeostasis. Situated at the interface of apoptosis initiation and execution, mitochondrial outer membrane permeabilization (MOMP) represents one of the most fundamental processes during apoptosis signal transduction. It was shown that MOMP can spatiotemporally propagate through cells, in particular in response to extrinsic apoptosis induction. Based on apparently contradictory experimental evidence, two distinct molecular mechanisms have been proposed to underlie the propagation of MOMP signals, namely a reaction-diffusion mechanism governed by anisotropies in the production of the MOMP-inducer truncated Bid (tBid), or a process that drives the spatial propagation of MOMP by sequential bursts of reactive oxygen species. We therefore generated mathematical models for both scenarios and performed in silico simulations of spatiotemporal MOMP signaling to identify which one of the two mechanisms is capable of qualitatively and quantitatively reproducing the existing data. We found that the explanatory power of each model was limited in that only a subset of experimental findings could be replicated. However, the integration of both models into a combined mathematical description of spatiotemporal tBid and reactive oxygen species signaling accurately reproduced all available experimental data and furthermore, provided robustness to spatial MOMP propagation when mitochondria are spatially separated. Our study therefore provides a theoretical framework that is sufficient to describe and mechanistically explain the spatiotemporal propagation of one of the most fundamental processes during apoptotic cell death.

Multiscale Model of Colorectal Cancer Using the Cellular Potts Framework

Colorectal cancer (CRC) is one of the major causes of death in the developed world and forms a canonical example of tumorigenesis. CRC arises from a string of mutations of individual cells in the colorectal crypt, making it particularly suited for multiscale multicellular modeling, where mutations of individual cells can be clearly represented and their effects readily tracked. In this paper, we present a multicellular model of the onset of colorectal cancer, utilizing the cellular Potts model (CPM). We use the model to investigate how, through the modification of their mechanical properties, mutant cells colonize the crypt. Moreover, we study the influence of mutations on the shape of cells in the crypt, suggesting possible cell- and tissue-level indicators for identifying early-stage cancerous crypts. Crucially, we discuss the effect that the motility parameters of the model (key factors in the behavior of the CPM) have on the distribution of cells within a homeostatic crypt, resulting in an optimal parameter regime that accurately reflects biological assumptions. In summary, the key results of this paper are 1) how to couple the CPM with processes occurring on other spatial scales, using the example of the crypt to motivate suitable motility parameters; 2) modeling mutant cells with the CPM; 3) and investigating how mutations influence the shape of cells in the crypt.

Simulating tissue morphogenesis and signaling

During embryonic development tissue morphogenesis and signaling are tightly coupled. It is therefore important to simulate both tissue morphogenesis and signaling simultaneously in in silico models of developmental processes. The resolution of the processes depends on the questions of interest. As part of this chapter we introduce different descriptions of tissue morphogenesi s. In the simplest approximation tissue is a continuous domain and tissue expansion is described according to a predefined function of time (and possibly space). In a slightly more advanced version the expansion speed and direction of the tissue may depend on a signaling variable that evolves on the domain. Both versions will be referred to as "prescribed growth." Alternatively tissue can be regarded as incompressible fluid and can be described with Navier-Stokes equations. Local cell expansion, proliferation, and death are then incorporated by a source term. In other applications the cell boundaries may be important and cell-based models must be introduced. Finally, cells may move within the tissue, a process best described by agent-based models.

Variable cell morphology approach for individual-based modeling of microbial communities

An individual-based, mass-spring modeling framework has been developed to investigate the effect of cell properties on the structure of biofilms and microbial aggregates through Lagrangian modeling. Key features that distinguish this model are variable cell morphology described by a collection of particles connected by springs and a mechanical representation of deformable intracellular, intercellular, and cell-substratum links. A first case study describes the colony formation of a rod-shaped species on a planar substratum. This case shows the importance of mechanical interactions in a community of growing and dividing rod-shaped cells (i.e., bacilli). Cell-substratum links promote formation of mounds as opposed to single-layer biofilms, whereas filial links affect the roundness of the biofilm. A second case study describes the formation of flocs and development of external filaments in a mixed-culture activated sludge community. It is shown by modeling that distinct cell-cell links, microbial morphology, and growth kinetics can lead to excessive filamentous proliferation and interfloc bridging, possible causes for detrimental sludge bulking. This methodology has been extended to more advanced microbial morphologies such as filament branching and proves to be a very powerful tool in determining how fundamental controlling mechanisms determine diverse microbial colony architectures.

Cell resolved, multiparticle model of plastic tissue deformations and morphogenesis

We propose a three-dimensional mechanical model of embryonic tissue dynamics. Mechanically coupled adherent cells are represented as particles interconnected with elastic beams which can exert non-central forces and torques. Tissue plasticity is modeled by a stochastic process consisting of a connectivity change (addition or removal of a single link) followed by a complete relaxation to mechanical equilibrium. In particular, we assume that (i) two non-connected, but adjacent particles can form a new link; and (ii) the lifetime of links is reduced by tensile forces. We demonstrate that the proposed model yields a realistic macroscopic elasto-plastic behavior and we establish how microscopic model parameters determine material properties at the macroscopic scale. Based on these results, microscopic parameter values can be inferred from tissue thickness, macroscopic elastic modulus and the magnitude and dynamics of intercellular adhesion forces. In addition to their mechanical role, model particles can also act as simulation agents and actively modulate their connectivity according to specific rules. As an example, anisotropic link insertion and removal probabilities can give rise to local cell intercalation and large scale convergent extension movements. The proposed stochastic simulation of cell activities yields fluctuating tissue movements which exhibit the same autocorrelation properties as empirical data from avian embryos.

Multiscale computational models in physical systems biology of intracellular trafficking

In intracellular trafficking, a definitive understanding of the interplay between protein binding and membrane morphology remains incomplete. The authors describe a computational approach by integrating coarse-grained molecular dynamics (CGMD) simulations with continuum Monte Carlo (CM) simulations of the membrane to study protein-membrane interactions and the ensuing membrane curvature. They relate the curvature field strength discerned from the molecular level to its effect at the cellular length-scale. They perform thermodynamic integration on the CM model to describe the free energy landscape of vesiculation in clathrin-mediated endocytosis. The method presented here delineates membrane morphologies and maps out the free energy changes associated with membrane remodeling due to varying coat sizes, coat curvature strengths, membrane bending rigidities, and tensions; furthermore several constraints on mechanisms underlying clathrin-mediated endocytosis have also been identified, Their CGMD simulations have revealed the importance of PIP2 for stable binding of proteins essential for curvature induction in the bilayer and have provided a molecular basis for the positive curvature induction by the epsin N-terminal homology (EIMTH) domain. Calculation of the free energy landscape for vesicle budding has identified the critical size and curvature strength of a clathrin coat required for nucleation and stabilisation of a mature vesicle.

USNCTAM perspectives on mechanics in medicine

Over decades, the theoretical and applied mechanics community has developed sophisticated approaches for analysing the behaviour of complex engineering systems. Most of these approaches have targeted systems in the transportation, materials, defence and energy industries. Applying and further developing engineering approaches for understanding, predicting and modulating the response of complicated biomedical processes not only holds great promise in meeting societal needs, but also poses serious challenges. This report, prepared for the US National Committee on Theoretical and Applied Mechanics, aims to identify the most pressing challenges in biological sciences and medicine that can be tackled within the broad field of mechanics. This echoes and complements a number of national and international initiatives aiming at fostering interdisciplinary biomedical research. This report also comments on cultural/educational challenges. Specifically, this report focuses on three major thrusts in which we believe mechanics has and will continue to have a substantial impact. (i) Rationally engineering injectable nano/microdevices for imaging and therapy of disease. Within this context, we discuss nanoparticle carrier design, vascular transport and adhesion, endocytosis and tumour growth in response to therapy, as well as uncertainty quantification techniques to better connect models and experiments. (ii) Design of biomedical devices, including point-of-care diagnostic systems, model organ and multi-organ microdevices, and pulsatile ventricular assistant devices. (iii) Mechanics of cellular processes, including mechanosensing and mechanotransduction, improved characterization of cellular constitutive behaviour, and microfluidic systems for single-cell studies.

Biocellion: accelerating computer simulation of multicellular biological system models

MOTIVATION

Biological system behaviors are often the outcome of complex interactions among a large number of cells and their biotic and abiotic environment. Computational biologists attempt to understand, predict and manipulate biological system behavior through mathematical modeling and computer simulation. Discrete agent-based modeling (in combination with high-resolution grids to model the extracellular environment) is a popular approach for building biological system models. However, the computational complexity of this approach forces computational biologists to resort to coarser resolution approaches to simulate large biological systems. High-performance parallel computers have the potential to address the computing challenge, but writing efficient software for parallel computers is difficult and time-consuming.

RESULTS

We have developed Biocellion, a high-performance software framework, to solve this computing challenge using parallel computers. To support a wide range of multicellular biological system models, Biocellion asks users to provide their model specifics by filling the function body of pre-defined model routines. Using Biocellion, modelers without parallel computing expertise can efficiently exploit parallel computers with less effort than writing sequential programs from scratch. We simulate cell sorting, microbial patterning and a bacterial system in soil aggregate as case studies.

AVAILABILITY AND IMPLEMENTATION

Biocellion runs on x86 compatible systems with the 64 bit Linux operating system and is freely available for academic use. Visit http://biocellion.com for additional information.

Cell division orientation on biospecific peptide gradients

An assay was developed for determining cell division orientation on gradients. The methodology is based on permeating microfluidic devices with alkanethiols and subsequent printing of cell adhesive peptide gradient self-assembled monolayers (SAMs) for examining oriented cell divisions. To our knowledge, there has been no study examining the correlation between cell division orientations based on an underlying ligand gradient. These results implicate an important role for how the extracellular matrix may control cell division. These surfaces would allow for a range of cell behavior (polarization, migration, division, differentiation) studies on tailored biospecific gradients and as a potential biotechnological platform to assess small molecule perturbations of cell function.

Effects of biomechanical properties of the bone-implant interface on dental implant stability: from in silico approaches to the patient's mouth

Dental implants have become a routinely used technique in dentistry for replacing teeth. However, risks of failure are still experienced and remain difficult to anticipate. Multiscale phenomena occurring around the implant interface determine the implant outcome. The aim of this review is to provide an understanding of the biomechanical behavior of the interface between a dental implant and the region of bone adjacent to it (the bone-implant interface) as a function of the interface's environment. First, we describe the determinants of implant stability in relation to the different multiscale simulation approaches used to model the evolution of the bone-implant interface. Then, we review the various aspects of osseointegration in relation to implant stability. Next, we describe the different approaches used in the literature to measure implant stability in vitro and in vivo. Last, we review various factors affecting the evolution of the bone-implant interface properties.