Multi-scale modeling of tissues using CompuCell3D

Rheological transition driven by matrix makes cancer spheroids resilient under confinement

Cancer metastasis through confining peritoneal microenvironments is mediated by spheroids: clusters of disseminated cells. Ovarian cancer spheroids are frequently cavitated; such blastuloid morphologies possess an outer ECM coat. We investigated the effects of these spheroidal morphological traits on their mechanical integrity. Atomic force microscopy showed blastuloids were elastic compared with their prefiguring lumenless moruloid counterparts. Moruloids flowed through microfluidic setups mimicking peritoneal confinement, exhibited asymmetric cell flows during entry, were frequently disintegrated, and showed an incomplete and slow shape recovery upon exit. In contrast, blastuloids exhibited size-uncorrelated transit kinetics, rapid and efficient shape recovery upon exit, symmetric cell flows, and lesser disintegration. Blastuloid ECM debridement phenocopied moruloid traits including lumen loss and greater disintegration. Multiscale computer simulations predicted that higher intercellular adhesion and dynamical lumen make blastuloids resilient. Blastuloids showed higher E-cadherin expression, and their ECM removal decreased membrane E-cadherin localization. E-cadherin knockdown also decreased lumen formation and increased spheroid disintegration. Thus, the spheroidal ECM drives its transition from a labile viscoplastic to a resilient elastic phenotype, facilitating their survival within spatially constrained peritoneal flows.

Intercellular contractile force attenuates chemosensitivity through Notch-MVP-mediated nuclear drug export

Resistance to chemotherapeutics is one major challenge to clinical effectiveness of cancer treatment and is primarily interpreted by various biochemical mechanisms. This study establishes an inverse correlation between tumor cell contractility and chemosensitivity. In both clinical biopsies and cancer cell lines, high/low actomyosin-mediated contractile force attenuates/enhances the vulnerability to chemotherapy, which depends on intercellular force propagation. Cell-cell interaction force activates the mechanosensitive Notch signaling that upregulates the downstream effector major vault protein, which facilitates the export of chemotherapy drugs from nuclei, leading to the reduction of chemosensitivity. Cellular contractility promotes the tolerance of tumor xenografts to chemotherapy and sustains tumor growth in vivo, which can be reversed by the inhibition of contractile force, Notch signaling, or major vault protein. Further, the actomyosin-Notch signaling is associated with drug resistance and cancer recurrence of patients. These findings unveil a regulatory role of intercellular force in chemosensitivity, which could be harnessed as a promising target for cancer mechanotherapeutics.

Towards an integrated view and understanding of embryonic signalling during murine gastrulation

At the onset of mammalian gastrulation, secreted signalling molecules belonging to the Bmp, Wnt, Nodal and Fgf signalling pathways induce and pattern the primitive streak, marking the start for the cellular rearrangements that generate the body plan. Our current understanding of how signalling specifies and organises the germ layers in three dimensions, was mainly derived from genetic experimentation using mouse embryos performed over many decades. However, the exact spatiotemporal sequence of events is still poorly understood, both because of a lack of tractable models that allow for real time visualisation of signalling and differentiation and because of the molecular and cellular complexity of these early developmental events. In recent years, a new wave of in vitro embryo models has begun to shed light on the dynamics of signalling during primitive streak formation. Here we discuss the similarities and differences between a widely adopted mouse embryo model, termed gastruloids, and real embryos from a signalling perspective. We focus on the gene regulatory networks that underlie signalling pathway interactions and outline some of the challenges ahead. Finally, we provide a perspective on how embryo models may be used to advance our understanding of signalling dynamics through computational modelling.

Protrusion force and cell-cell adhesion-induced polarity alignment govern collective migration modes

Collective migration refers to the coordinated movement of cells as a single unit during migration. Although collective migration enhances invasive and metastatic potential in cancer, the mechanisms driving this behavior and regulating tumor migration plasticity remain poorly understood. This study provides a mechanistic model explaining the emergence of different modes of collective migration under hypoxia-induced secretome. We focus on the interplay between cellular protrusion force and cell-cell adhesion using collectively migrating three-dimensional microtumors as models with well-defined microenvironments. Large microtumors show directional migration due to intrinsic hypoxia, whereas small microtumors exhibit radial migration when exposed to hypoxic secretome. Here, we developed an in silico multi-scale microtumor model based on the cellular Potts model and implemented in CompuCell3D to elucidate underlying mechanisms. We identified distinct migration modes within specific regions of protrusion force and cell-cell adhesion parameter space and studied these modes using in vitro experimental microtumor models. We show that sufficient cellular protrusion force is crucial for radial and directional collective microtumor migration. Radial migration emerges when sufficient cellular protrusion force is generated, driving neighboring cells to move collectively in diverse directions. Within migrating tumors, strong cell-cell adhesion enhances the alignment of cell polarity, breaking the symmetric angular distribution of protrusion forces and leading to directional microtumor migration. The integrated results from the experimental and computational models provide fundamental insights into collective migration in response to different microenvironmental stimuli. Our computational and experimental models can adapt to various scenarios, providing valuable insights into cancer migration mechanisms.

A hybrid computational model of cancer spheroid growth with ribose-induced collagen stiffening

Metastasis, the leading cause of death in cancer patients, arises when cancer cells disseminate from a primary solid tumour to distant organs. Growth and invasion of the solid tumour often involve collective cell migration, which is profoundly influenced by cell-cell interactions and the extracellular matrix (ECM). The ECM's biochemical composition and mechanical properties, such as stiffness, regulate cancer cell behaviour and migration dynamics. Mathematical modelling serves as a pivotal tool for studying and predicting these complex dynamics, with hybrid discrete-continuous models offering a powerful approach by combining agent-based representations of cells with continuum descriptions of the surrounding microenvironment. In this study, we investigate the impact of ECM stiffness, modulated via ribose-induced collagen cross-linking, on cancer spheroid growth and invasion. We employed a hybrid discrete-continuous model implemented in PhysiCell to simulate spheroid dynamics, successfully replicating three-dimensional in vitro experiments. The model incorporates detailed representations of cell-cell and cell-ECM interactions, ECM remodelling, and cell proliferation. Our simulations align with experimental observations of two breast cancer cell lines, non-invasive MCF7 and invasive HCC 1954, under varying ECM stiffness conditions. The results demonstrate that increased ECM stiffness due to ribose-induced cross-linking inhibits spheroid invasion in invasive cells, whereas non-invasive cells remain largely unaffected. Furthermore, our simulations show that higher ECM degradation by the cells not only enables spheroid growth and invasion but also facilitates the formation of multicellular protrusions. Conversely, increasing the maximum speed that cells can reach due to cell-ECM interactions enhances spheroid growth while promoting single-cell invasion. This hybrid modelling approach enhances our understanding of the interplay between cancer cell migration, proliferation, and ECM mechanical properties, paving the way for future studies incorporating additional ECM characteristics and microenvironmental conditions.

In silico modelling of organ-on-a-chip devices: an overview

An organ-on-a-chip (OOAC) is a microscale device designed to mimic the functions and complexity of in vivo human physiology. Different from traditional culture systems, OOACs are capable of replicating the biochemical microenvironment, tissue-tissue interactions, and mechanical dynamics of organs thanks to the precise control offered by microfluidic technology. Diverse OOAC devices specific to different organs have been proposed for experimental research and applications such as disease modelling, personalized medicine and drug screening. Previous studies have demonstrated that the mathematical modelling of OOAC can facilitate the optimization of chips' microenvironments, serving as an essential tool to design and improve microdevices which allow reproducible growth of cell culture, reducing the time and cost of experimental testing. Here, we review recent modelling approaches for various OOAC devices, categorized according to the type of organs. We discuss the opportunities for integrating multiphysics with multicellular computational models to better characterize and predict cell culture dynamics. Additionally, we explore how developing more detailed OOAC models would support a more rapid and effective development of microdevices, and the design of robust protocols to grow and control cell cultures.

Improving 3D deep learning segmentation with biophysically motivated cell synthesis

Biomedical research increasingly relies on three-dimensional (3D) cell culture models and artificial-intelligence-based analysis can potentially facilitate a detailed and accurate feature extraction on a single-cell level. However, this requires for a precise segmentation of 3D cell datasets, which in turn demands high-quality ground truth for training. Manual annotation, the gold standard for ground truth data, is too time-consuming and thus not feasible for the generation of large 3D training datasets. To address this, we present a framework for generating 3D training data, which integrates biophysical modeling for realistic cell shape and alignment. Our approach allows the in silico generation of coherent membrane and nuclei signals, that enable the training of segmentation models utilizing both channels for improved performance. Furthermore, we present a generative adversarial network (GAN) training scheme that generates not only image data but also matching labels. Quantitative evaluation shows superior performance of biophysical motivated synthetic training data, even outperforming manual annotation and pretrained models. This underscores the potential of incorporating biophysical modeling for enhancing synthetic training data quality.

Improving neuroendocrine tumor treatments with mathematical modeling: lessons from other endocrine cancers

Neuroendocrine tumors (NETs) occur sporadically or as part of rare endocrine tumor syndromes (RETSs) such as multiple endocrine neoplasia 1 and von Hippel-Lindau syndromes. Due to their relative rarity and lack of model systems, NETs and RETSs are difficult to study, hindering advancements in therapeutic development. Causal or mechanistic mathematical modeling is widely deployed in disease areas such as breast and prostate cancers, aiding the understanding of observations and streamlining in vitro and in vivo modeling efforts. Mathematical modeling, while not yet widely utilized in NET research, offers an opportunity to accelerate NET research and therapy development. To illustrate this, we highlight examples of how mathematical modeling associated with more common endocrine cancers has been successfully used in the preclinical, translational and clinical settings. We also provide a scope of the limited work that has been done in NETs and map how these techniques can be utilized in NET research to address specific outstanding challenges in the field. Finally, we include practical details such as hardware and data requirements, present advantages and disadvantages of various mathematical modeling approaches and discuss challenges of using mathematical modeling. Through a cross-disciplinary approach, we believe that many currently difficult problems can be made more tractable by applying mathematical modeling and that the field of rare diseases in endocrine oncology is well poised to take advantage of these techniques.

Optimal control of agent-based models via surrogate modeling

This paper describes and validates an algorithm to solve optimal control problems for agent-based models (ABMs). For a given ABM and a given optimal control problem, the algorithm derives a surrogate model, typically lower-dimensional, in the form of a system of ordinary differential equations (ODEs), solves the control problem for the surrogate model, and then transfers the solution back to the original ABM. It applies to quite general ABMs and offers several options for the ODE structure, depending on what information about the ABM is to be used. There is a broad range of applications for such an algorithm, since ABMs are used widely in the life sciences, such as ecology, epidemiology, and biomedicine and healthcare, areas where optimal control is an important purpose for modeling, such as for medical digital twin technology.

A computational dynamic systems model for in silico prediction of neural tube closure defects

Neural tube closure is a critical morphogenetic event during early vertebrate development. This complex process is susceptible to perturbation by genetic errors and chemical disruption, which can induce severe neural tube defects (NTDs) such as spina bifida. We built a computational agent-based model (ABM) of neural tube development based on the known biology of morphogenetic signals and cellular biomechanics underlying neural fold elevation, bending and fusion. The computer model functionalizes cell signals and responses to render a dynamic representation of neural tube closure. Perturbations in the control network can then be introduced synthetically or from biological data to yield quantitative simulation and probabilistic prediction of NTDs by incidence and degree of defect. Translational applications of the model include mechanistic understanding of how singular or combinatorial alterations in gene-environmental interactions and animal-free assessment of developmental toxicity for an important human birth defect (spina bifida) and potentially other neurological problems linked to development of the brain and spinal cord.

A Multicellular Mechanochemical Model to Investigate Tumor Microenvironment Remodeling and Pre-Metastatic Niche Formation

Introduction

Colorectal cancer (CRC) is a major cause of cancer related deaths in the United States, with CRC metastasis to the liver being a common occurrence. The development of an optimal metastatic environment is essential process prior to tumor metastasis. This process, called pre-metastatic niche (PMN) formation, involves activation of key resident liver cells, including fibroblast-like stellate cells and macrophages such as Kupffer cells. Tumor-mediated factors introduced to this environment transform resident cells that secrete additional growth factors and remodel the extracellular matrix (ECM), which is thought to promote tumor colonization and metastasis in the secondary environment.

Methods

To investigate the underlying mechanisms of these dynamics, we developed a multicellular computational model to characterize the spatiotemporal dynamics of the PMN formation in tissue. This modeling framework integrates intracellular and extracellular signaling, and traction and junctional forces into a Cellular Potts model, and represents multiple cell types with varying levels of cellular activation. We perform numerical experiments to investigate the role of key factors in PMN formation and tumor invasiveness, including growth factor concentration, timing of tumor arrival, relative composition of resident cells, and the size of invading tumor cluster.

Results

These parameter studies identified growth factor availability and ECM concentration in the environment as two of the key determinants of tumor invasiveness. We further predict that both the ECM concentration potential and growth factor sensitivity of the stellate cells are key drivers of the PMN formation and associated ECM concentration.

Conclusions

Overall, this modeling framework represents a significant step towards simulating cancer metastasis and investigating the role of key factors on PMN formation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-024-00831-0.

Modelling the effect of cell motility on mixing and invasion in epithelial monolayers

Collective cell invasion underlies several biological processes such as wound healing, embryonic development, and cancerous invasion. Here, we investigate the impact of cell motility on invasion in epithelial monolayers and its coupling to cellular mechanical properties, such as cell-cell adhesion and cortex contractility. We develop a two-dimensional computational model for cells with active motility based on the cellular Potts model, which predicts that the cellular invasion speed is mainly determined by active cell motility and is independent of the biological and mechanical properties of the cells. We also find that, in general, motile cells out-compete and invade non-motile cells, however, this can be reversed by differential cell proliferation. Stable coexistence of motile and static cell types is also possible for certain parameter regimes.

Foundations of a Compositional Systems Biology

Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure or dynamics of specific subsystems in controlled conditions, compositional systems biology aims to connect these models, asking critical questions about the space between models: What variables should a submodel expose through its interface? How do coupled models connect and translate across scales? How do domain-specific models connect across biological and physical disciplines to drive the synthesis of new knowledge? This approach requires robust software to integrate diverse datasets and submodels, providing researchers with tools to flexibly recombine, iteratively refine, and collaboratively expand their models. This article offers a comprehensive framework to support this vision, including: a conceptual and graphical framework to define interfaces and composition patterns; standardized schemas that facilitate modular data and model assembly; biological templates that integrate detailed submodels that connect molecular processes to the emergence of the cellular interface; and user-friendly software interfaces that empower research communities to construct and improve multiscale models of cellular systems. By addressing these needs, compositional systems biology will foster a unified and scalable approach to understanding complex cellular systems.

Personalizing computational models to construct medical digital twins

Digital twin technology, pioneered for engineering applications, is being adapted to biomedicine and healthcare; however, several problems need to be solved in the process. One major problem is that of dynamically calibrating a computational model to an individual patient, using data collected from that patient over time. This kind of calibration is crucial for improving model-based forecasts and realizing personalized medicine. The underlying computational model often focuses on a particular part of human biology, combines different modeling paradigms at different scales, and is both stochastic and spatially heterogeneous. A commonly used modeling framework is that of an agent-based model, a computational model for simulating autonomous agents such as cells, which captures how system-level properties are affected by local interactions. There are no standard personalization methods that can be readily applied to such models. The key challenge for any such algorithm is to bridge the gap between the clinically measurable quantities (the macrostate) and the fine-grained data at different physiological scales which are required to run the model (the microstate). In this paper we develop an algorithm which applies a classic data assimilation technique, the ensemble Kalman filter, at the macrostate level. We then link the Kalman update at the macrostate level to an update at the microstate level that produces microstates which are not only compatible with desired macrostates but also highly likely with respect to model dynamics.

An adaptive numerical method for multi-cellular simulations of tissue development and maintenance

In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it's efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge-Kutta 4 and multi-step methods like Adams-Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between L∞ error and run-time is to use Runge-Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10-60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step.

Tumor growth and vascular redistribution contributes to the dosimetric preferential effect of microbeam radiotherapy: a Monte Carlo study

The radiobiological mechanisms behind the favorable response of tissues to microbeam radiation therapy (MRT) are not fully described yet. Among other factors, the differential action to tumor and normal tissue vasculature is considered to contribute to MRT efficacy. This computational study evaluates the relevance of tumor growth stage and associated vascular redistribution to this effect. A multiscale approach was employed with two simulation softwares: TOPAS and CompuCell3D. Segmentation images of the angioarchitecture of a non-bearing tumor mouse brain were used. The tumor vasculature at different tumor growth stages was obtained by simulating the tumor proliferation and spatial vascular redistribution. The radiation-induced damage to vascular cells and consequent change in oxygen perfusion were simulated for normal and tumor tissues. The multiscale model showed that oxygen perfusion to tissues and vessels decreased as a function of the tumor proliferation stage, and with the decrease in uniformity of the vasculature spatial distribution in the tumor tissue. This led to an increase in the fraction of hypoxic (up to 60%) and necrotic (10%) tumor cells at advanced tumor stages, whereas normal tissues remained normoxic. These results showed that tumor stage and spatial vascular distribution contribute to the preferential effect of MRT in tumors.

The cellular Potts model on disordered lattices

The cellular Potts model, also known as the Glazier-Graner-Hogeweg model, is a lattice-based approach by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying lattice structure is assumed for two-dimensional systems, and this is known to introduce artifacts in the structure and dynamics of the model tissues. That is, on regular lattices, cells can assume shapes that are dictated by the symmetries of the underlying lattice. Here, we developed a variant of this method that can be applied to a broad class of (ir)regular lattices. We show that on an irregular lattice deriving from a fluid-like configuration, two types of artifacts can be removed. We further report on the transition between a fluid-like disordered and a solid-like hexagonally ordered phase present for monodisperse confluent cells as a function of their surface tension. This transition shows the hallmarks of a first-order phase transition and is different from the glass/jamming transitions commonly reported for the vertex and active Voronoi models. We emphasize this by analyzing the distribution of shape parameters found in our state space. Our analysis provides a useful reference for the future study of epithelia using the (ir)regular cellular Potts model.

Towards verifiable cancer digital twins: tissue level modeling protocol for precision medicine

Cancer exhibits substantial heterogeneity, manifesting as distinct morphological and molecular variations across tumors, which frequently undermines the efficacy of conventional oncological treatments. Developments in multiomics and sequencing technologies have paved the way for unraveling this heterogeneity. Nevertheless, the complexity of the data gathered from these methods cannot be fully interpreted through multimodal data analysis alone. Mathematical modeling plays a crucial role in delineating the underlying mechanisms to explain sources of heterogeneity using patient-specific data. Intra-tumoral diversity necessitates the development of precision oncology therapies utilizing multiphysics, multiscale mathematical models for cancer. This review discusses recent advancements in computational methodologies for precision oncology, highlighting the potential of cancer digital twins to enhance patient-specific decision-making in clinical settings. We review computational efforts in building patient-informed cellular and tissue-level models for cancer and propose a computational framework that utilizes agent-based modeling as an effective conduit to integrate cancer systems models that encode signaling at the cellular scale with digital twin models that predict tissue-level response in a tumor microenvironment customized to patient information. Furthermore, we discuss machine learning approaches to building surrogates for these complex mathematical models. These surrogates can potentially be used to conduct sensitivity analysis, verification, validation, and uncertainty quantification, which is especially important for tumor studies due to their dynamic nature.

A clustering tool for generating biological geometries for computational modeling in radiobiology

Objective.To develop a computational tool that converts biological images into geometries compatible with computational software dedicated to the Monte Carlo simulation of radiation transport (TOPAS), and subsequent biological tissue responses (CompuCell3D). The depiction of individual biological entities from segmentation images is essential in computational radiobiological modeling for two reasons: image pixels or voxels representing a biological structure, like a cell, should behave as a single entity when simulating biological processes, and the action of radiation in tissues is described by the association of biological endpoints to physical quantities, as radiation dose, scored the entire group of voxels assembling a cell.Approach.The tool is capable of cropping and resizing the images and performing clustering of image voxels to create independent entities (clusters) by assigning a unique identifier to these voxels conforming to the same cluster. The clustering algorithm is based on the adjacency of voxels with image values above an intensity threshold to others already assigned to a cluster. The performance of the tool to generate geometries that reproduced original images was evaluated by the dice similarity coefficient (DSC), and by the number of individual entities in both geometries. A set of tests consisting of segmentation images of cultured neuroblastoma cells, two cell nucleus populations, and the vasculature of a mouse brain were used.Main results.The DSC was 1.0 in all images, indicating that original and generated geometries were identical, and the number of individual entities in both geometries agreed, proving the ability of the tool to cluster voxels effectively following user-defined specifications. The potential of this tool in computational radiobiological modeling, was shown by evaluating the spatial distribution of DNA double-strand-breaks after microbeam irradiation in a segmentation image of a cell culture.Significance.This tool enables the use of realistic biological geometries in computational radiobiological studies.

Probability of early infection extinction depends linearly on the virus clearance rate

We provide an in silico study of stochastic viral infection extinction from a pharmacokinetical viewpoint. Our work considers a non-specific antiviral drug that increases the virus clearance rate, and we investigate the effect of this drug on early infection extinction. Infection extinction data are generated by a hybrid multiscale framework that applies both continuous and discrete mathematical approaches. The central result of our paper is the observation, analysis and explanation of a linear relationship between the virus clearance rate and the probability of early infection extinction. The derivation behind this simple relationship is given by merging different mathematical toolboxes.

Building multiscale models with PhysiBoSS, an agent-based modeling tool

Multiscale models provide a unique tool for analyzing complex processes that study events occurring at different scales across space and time. In the context of biological systems, such models can simulate mechanisms happening at the intracellular level such as signaling, and at the extracellular level where cells communicate and coordinate with other cells. These models aim to understand the impact of genetic or environmental deregulation observed in complex diseases, describe the interplay between a pathological tissue and the immune system, and suggest strategies to revert the diseased phenotypes. The construction of these multiscale models remains a very complex task, including the choice of the components to consider, the level of details of the processes to simulate, or the fitting of the parameters to the data. One additional difficulty is the expert knowledge needed to program these models in languages such as C++ or Python, which may discourage the participation of non-experts. Simplifying this process through structured description formalisms-coupled with a graphical interface-is crucial in making modeling more accessible to the broader scientific community, as well as streamlining the process for advanced users. This article introduces three examples of multiscale models which rely on the framework PhysiBoSS, an add-on of PhysiCell that includes intracellular descriptions as continuous time Boolean models to the agent-based approach. The article demonstrates how to construct these models more easily, relying on PhysiCell Studio, the PhysiCell Graphical User Interface. A step-by-step tutorial is provided as Supplementary Material and all models are provided at https://physiboss.github.io/tutorial/.

Algorithms for Autonomous Formation of Multicellular Shapes from Single Cells

Multicellular organisms originate from a single cell, ultimately giving rise to mature organisms of heterogeneous cell type composition in complex structures. Recent work in the areas of stem cell biology and tissue engineering has laid major groundwork in the ability to convert certain types of cells into other types, but there has been limited progress in the ability to control the morphology of cellular masses as they grow. Contemporary approaches to this problem have included the use of artificial scaffolds, 3D bioprinting, and complex media formulations; however, there are no existing approaches to controlling this process purely through genetics and from a single-cell starting point. Here we describe a computer-aided design approach, called CellArchitect, for designing recombinase-based genetic circuits for controlling the formation of multicellular masses into arbitrary shapes in human cells.

TOPAS-Tissue: A Framework for the Simulation of the Biological Response to Ionizing Radiation at the Multi-Cellular Level

This work aims to develop and validate a framework for the multiscale simulation of the biological response to ionizing radiation in a population of cells forming a tissue. We present TOPAS-Tissue, a framework to allow coupling two Monte Carlo (MC) codes: TOPAS with the TOPAS-nBio extension, capable of handling the track-structure simulation and subsequent chemistry, and CompuCell3D, an agent-based model simulator for biological and environmental behavior of a population of cells. We verified the implementation by simulating the experimental conditions for a clonogenic survival assay of a 2-D PC-3 cell culture model (10 cells in 10,000 µm2) irradiated by MV X-rays at several absorbed dose values from 0-8 Gy. The simulation considered cell growth and division, irradiation, DSB induction, DNA repair, and cellular response. The survival was obtained by counting the number of colonies, defined as a surviving primary (or seeded) cell with progeny, at 2.7 simulated days after irradiation. DNA repair was simulated with an MC implementation of the two-lesion kinetic model and the cell response with a p53 protein-pulse model. The simulated survival curve followed the theoretical linear-quadratic response with dose. The fitted coefficients α = 0.280 ± 0.025/Gy and β = 0.042 ± 0.006/Gy2 agreed with published experimental data within two standard deviations. TOPAS-Tissue extends previous works by simulating in an end-to-end way the effects of radiation in a cell population, from irradiation and DNA damage leading to the cell fate. In conclusion, TOPAS-Tissue offers an extensible all-in-one simulation framework that successfully couples Compucell3D and TOPAS for multiscale simulation of the biological response to radiation.

From in vitro to in silico: a pipeline for generating virtual tissue simulations from real image data

3D cell culture models replicate tissue complexity and aim to study cellular interactions and responses in a more physiologically relevant environment compared to traditional 2D cultures. However, the spherical structure of these models makes it difficult to extract meaningful data, necessitating advanced techniques for proper analysis. In silico simulations enhance research by predicting cellular behaviors and therapeutic responses, providing a powerful tool to complement experimental approaches. Despite their potential, these simulations often require advanced computational skills and significant resources, which creates a barrier for many researchers. To address these challenges, we developed an accessible pipeline using open-source software to facilitate virtual tissue simulations. Our approach employs the Cellular Potts Model, a versatile framework for simulating cellular behaviors in tissues. The simulations are constructed from real world 3D image stacks of cancer spheroids, ensuring that the virtual models are rooted in experimental data. By introducing a new metric for parameter optimization, we enable the creation of realistic simulations without requiring extensive computational expertise. This pipeline benefits researchers wanting to incorporate computational biology into their methods, even if they do not possess extensive expertise in this area. By reducing the technical barriers associated with advanced computational modeling, our pipeline enables more researchers to utilize these powerful tools. Our approach aims to foster a broader use of in silico methods in disease research, contributing to a deeper understanding of disease biology and the refinement of therapeutic interventions.

Bidirectionally validated in silico and in vitro formation of specific depth zone-derived chondrocyte spheroids and clusters

3D multicellular self-organized cluster models, e.g., organoids are promising tools for developing new therapeutic modalities including gene and cell therapies, pharmacological mechanistic and screening assays. Various applications of these models have been used extensively for decades, however, the mechanisms of cluster formation, maintenance, and degradation of these models are not even known over in-vitro-life-time. To explore such advantageous models mimicking native tissues or organs, it is necessary to understand aforementioned mechanisms. Herein, we intend to clarify the mechanisms of the formation of cell clusters. We previously demonstrated that primary chondrocytes isolated from distinct longitudinal depth zones in articular cartilage formed zone-specific spherical multicellular clusters in vitro. To elucidate the mechanisms of such cluster formation, we simulated it using the computational Cellular Potts Model with parameters were translated from gene expression levels and histological characteristics corresponding to interactions between cell and extracellular matrix. This simulation in silico was validated morphologically with cluster formation in vitro and vice versa. Since zone specific chondrocyte cluster models in silico showed similarity with corresponding in vitro model, the in silico has a potential to be used for prediction of the 3D multicellular in vitro models used for development, disease, and therapeutic models.

Modeling the roles of cohesotaxis, cell-intercalation, and tissue geometry in collective cell migration of Xenopus mesendoderm

Collectively migrating Xenopus mesendoderm cells are arranged into leader and follower rows with distinct adhesive properties and protrusive behaviors. In vivo, leading row mesendoderm cells extend polarized protrusions and migrate along a fibronectin matrix assembled by blastocoel roof cells. Traction stresses generated at the leading row result in the pulling forward of attached follower row cells. Mesendoderm explants removed from embryos provide an experimentally tractable system for characterizing collective cell movements and behaviors, yet the cellular mechanisms responsible for this mode of migration remain elusive. We introduce a novel agent-based computational model of migrating mesendoderm in the Cellular-Potts computational framework to investigate the respective contributions of multiple parameters specific to the behaviors of leader and follower row cells. Sensitivity analyses identify cohesotaxis, tissue geometry, and cell intercalation as key parameters affecting the migration velocity of collectively migrating cells. The model predicts that cohesotaxis and tissue geometry in combination promote cooperative migration of leader cells resulting in increased migration velocity of the collective. Radial intercalation of cells towards the substrate is an additional mechanism contributing to an increase in migratory speed of the tissue. Model outcomes are validated experimentally using mesendoderm tissue explants.

Galvanotactic directionality of cell groups depends on group size

Motile cells migrate directionally in the electric field in a process known as galvanotaxis, important and under-investigated phenomenon in wound healing and development. We previously reported that individual fish keratocyte cells migrate to the cathode in electric fields, that inhibition of PI3 kinase reverses single cells to the anode, and that large cohesive groups of either unperturbed or PI3K-inhibited cells migrate to the cathode. Here we find that small uninhibited cell groups move to the cathode, while small groups of PI3K-inhibited cells move to the anode. Small groups move faster than large groups, and groups of unperturbed cells move faster than PI3K-inhibited cell groups of comparable sizes. Shapes and sizes of large groups change little when they start migrating, while size and shapes of small groups change significantly, lamellipodia disappear from the rear edges of these groups, and their shapes start to resemble giant single cells. Our results are consistent with the computational model, according to which cells inside and at the edge of the groups pool their propulsive forces to move but interpret directional signals differently. Namely, cells in the group interior are directed to the cathode independently of their chemical state. Meanwhile, the edge cells behave like individual cells: they are directed to the cathode/anode in uninhibited/PI3K-inhibited groups, respectively. As a result, all cells drive uninhibited groups to the cathode, while larger PI3K-inhibited groups are directed by cell majority in the group interior to the cathode, while majority of the edge cells in small groups win the tug-of-war driving these groups to the anode.

Kiphynet: an online network simulation tool connecting cellular kinetics and physiological transport

INTRODUCTION

Human metabolism is sustained by functional networks that operate at diverse scales. Capturing local and global dynamics in the human body by hierarchically bridging multi-scale functional networks is a major challenge in physiological modeling.

OBJECTIVES

To develop an interactive, user-friendly web application that facilitates the simulation and visualization of advection-dispersion transport in three-dimensional (3D) microvascular networks, biochemical exchange, and metabolic reactions in the tissue layer surrounding the vasculature.

METHODS

To help modelers combine and simulate biochemical processes occurring at multiple scales, KiPhyNet deploys our discrete graph-based modeling framework that bridges functional networks existing at diverse scales. KiPhyNet is implemented in Python based on Apache web server using MATLAB as the simulator engine. KiPhyNet provides the functionality to assimilate multi-omics data from clinical and experimental studies as well as vascular data from imaging studies to investigate the role of structural changes in vascular topology on the functional response of the tissue.

RESULTS

With the network topology, its biophysical attributes, values of initial and boundary conditions, parameterized kinetic constants, biochemical species-specific transport properties such as diffusivity as inputs, a user can use our application to simulate and view the simulation results. The results of steady-state velocity and pressure fields and dynamic concentration fields can be interactively examined.

CONCLUSION

KiPhyNet provides barrier-free access to perform time-course simulation experiments by building multi-scale models of microvascular networks in physiology, using a discrete modeling framework. KiPhyNet is freely accessible at   http://pallab.cds.iisc.ac.in/kiphynet/ and the documentation is available at   https://deepamahm.github.io/kiphynet_docs/ .

Modelling the spatiotemporal dynamics of senescent cells in wound healing, chronic wounds, and fibrosis

Cellular senescence is known to drive age-related pathology through the senescence-associated secretory phenotype (SASP). However, it also plays important physiological roles such as cancer suppression, embryogenesis and wound healing. Wound healing is a tightly regulated process which when disrupted results in conditions such as fibrosis and chronic wounds. Senescent cells appear during the proliferation phase of the healing process where the SASP is involved in maintaining tissue homeostasis after damage. Interestingly, SASP composition and functionality was recently found to be temporally regulated, with distinct SASP profiles involved: a fibrogenic, followed by a fibrolytic SASP, which could have important implications for the role of senescent cells in wound healing. Given the number of factors at play a full understanding requires addressing the multiple levels of complexity, pertaining to the various cell behaviours, individually followed by investigating the interactions and influence each of these elements have on each other and the system as a whole. Here, a systems biology approach was adopted whereby a multi-scale model of wound healing that includes the dynamics of senescent cell behaviour and corresponding SASP composition within the wound microenvironment was developed. The model was built using the software CompuCell3D, which is based on a Cellular Potts modelling framework. We used an existing body of data on healthy wound healing to calibrate the model and validation was done on known disease conditions. The model provides understanding of the spatiotemporal dynamics of different senescent cell phenotypes and the roles they play within the wound healing process. The model also shows how an overall disruption of tissue-level coordination due to age-related changes results in different disease states including fibrosis and chronic wounds. Further specific data to increase model confidence could be used to explore senolytic treatments in wound disorders.

Competing mechanisms in bacterial invasion of human colon mucus probed with agent-based modeling

The gastrointestinal tract is inhabited by a vast community of microorganisms, termed the gut microbiota. Large colonies can pose a health threat, but the gastrointestinal mucus system protects epithelial cells from microbiota invasion. The human colon features a bilayer of mucus lining. Due to imbalances in intestinal homeostasis, bacteria may successfully penetrate the inner mucus layer, which can lead to severe gut diseases. However, it is hard to tease apart the competing mechanisms that lead to this penetration. To probe the conditions that permit bacteria penetration into the inner mucus layer, we develop an agent-based model consisting of bacteria and an inner mucus layer subject to a constant flux of nutrient fields feeding the bacteria. We find that there are three important variables that determine bacterial invasion: the bacterial reproduction rate, the contact energy between bacteria and mucus, and the rate of bacteria degrading the mucus. Under healthy conditions, all bacteria are naturally eliminated by the constant removal of mucus. In diseased states, imbalances between the rates of bacterial degradation and mucus secretion lead to bacterial invasion at certain junctures. We conduct uncertainty quantification and sensitivity analysis to compare the relative impact between these parameters. The contact energy has the strongest influence on bacterial penetration, which, in combination with bacterial degradation rate and growth rate, greatly accelerates bacterial invasion of the human gut mucus lining. Our findings will serve as predictive indicators for the etiology of intestinal diseases and highlight important considerations when developing gut therapeutics.

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.

PhysiCell Studio: a graphical tool to make agent-based modeling more accessible

Defining a multicellular model can be challenging. There may be hundreds of parameters that specify the attributes and behaviors of objects. In the best case, the model will be defined using some format specification - a markup language - that will provide easy model sharing (and a minimal step toward reproducibility). PhysiCell is an open-source, physics-based multicellular simulation framework with an active and growing user community. It uses XML to define a model and, traditionally, users needed to manually edit the XML to modify the model. PhysiCell Studio is a tool to make this task easier. It provides a GUI that allows editing the XML model definition, including the creation and deletion of fundamental objects: cell types and substrates in the microenvironment. It also lets users build their model by defining initial conditions and biological rules, run simulations, and view results interactively. PhysiCell Studio has evolved over multiple workshops and academic courses in recent years, which has led to many improvements. There is both a desktop and cloud version. Its design and development has benefited from an active undergraduate and graduate research program. Like PhysiCell, the Studio is open-source software and contributions from the community are encouraged.

Spatial heterogeneity in tumor adhesion qualifies collective cell invasion

Collective cell invasion (CCI), a canon of most invasive solid tumors, is an emergent property of the interactions between cancer cells and their surrounding extracellular matrix (ECM). However, tumor populations invariably consist of cells expressing variable levels of adhesive proteins that mediate such interactions, disallowing an intuitive understanding of how tumor invasiveness at a multicellular scale is influenced by spatial heterogeneity of cell-cell and cell-ECM adhesion. Here, we have used a Cellular Potts model-based multiscale computational framework that is constructed on the histopathological principles of glandular cancers. In earlier efforts on homogenous cancer cell populations, this framework revealed the relative ranges of interactions, including cell-cell and cell-ECM adhesion that drove collective, dispersed, and mixed multimodal invasion. Here, we constitute a tumor core of two separate cell subsets showing distinct intra- and inter-subset cell-cell or cell-ECM adhesion strengths. These two subsets of cells are arranged to varying extents of spatial intermingling, which we call the heterogeneity index (HI). We observe that low and high inter-subset cell adhesion favors invasion of high-HI and low-HI intermingled populations with distinct intra-subset cell-cell adhesion strengths, respectively. In addition, for explored values of cell-ECM adhesion strengths, populations with high HI values collectively invade better than those with lower HI values. We then asked how spatial invasion is regulated by progressively intermingled cellular subsets that are epithelial, i.e., showed high cell-cell but poor cell-ECM adhesion, and mesenchymal, i.e., with reversed adhesion strengths to the former. Here too, inter-subset adhesion plays an important role in contextualizing the proportionate relationship between HI and invasion. An exception to this relationship is seen for cases of heterogeneous cell-ECM adhesion where sub-maximal HI patterns with higher outer localization of cells with stronger ECM adhesion collectively invade better than their relatively higher-HI counterparts. Our simulations also reveal how adhesion heterogeneity qualifies collective invasion, when either cell-cell or cell-ECM adhesion type is varied but results in an invasive dispersion when both adhesion types are simultaneously altered.

Poissonian Cellular Potts Models Reveal Nonequilibrium Kinetics of Cell Sorting

Cellular Potts models are broadly applied across developmental biology and cancer research. We overcome limitations of the traditional approach, which reinterprets a modified Metropolis sampling as ad hoc dynamics, by introducing a physical timescale through Poissonian kinetics and by applying principles of stochastic thermodynamics to separate thermal and relaxation effects from athermal noise and nonconservative forces. Our method accurately describes cell-sorting dynamics in mouse-embryo development and identifies the distinct contributions of nonequilibrium processes, e.g., cell growth and active fluctuations.

Agent-based model demonstrates the impact of nonlinear, complex interactions between cytokinces on muscle regeneration

Muscle regeneration is a complex process due to dynamic and multiscale biochemical and cellular interactions, making it difficult to identify microenvironmental conditions that are beneficial to muscle recovery from injury using experimental approaches alone. To understand the degree to which individual cellular behaviors impact endogenous mechanisms of muscle recovery, we developed an agent-based model (ABM) using the Cellular-Potts framework to simulate the dynamic microenvironment of a cross-section of murine skeletal muscle tissue. We referenced more than 100 published studies to define over 100 parameters and rules that dictate the behavior of muscle fibers, satellite stem cells (SSCs), fibroblasts, neutrophils, macrophages, microvessels, and lymphatic vessels, as well as their interactions with each other and the microenvironment. We utilized parameter density estimation to calibrate the model to temporal biological datasets describing cross-sectional area (CSA) recovery, SSC, and fibroblast cell counts at multiple timepoints following injury. The calibrated model was validated by comparison of other model outputs (macrophage, neutrophil, and capillaries counts) to experimental observations. Predictions for eight model perturbations that varied cell or cytokine input conditions were compared to published experimental studies to validate model predictive capabilities. We used Latin hypercube sampling and partial rank correlation coefficient to identify in silico perturbations of cytokine diffusion coefficients and decay rates to enhance CSA recovery. This analysis suggests that combined alterations of specific cytokine decay and diffusion parameters result in greater fibroblast and SSC proliferation compared to individual perturbations with a 13% increase in CSA recovery compared to unaltered regeneration at 28 days. These results enable guided development of therapeutic strategies that similarly alter muscle physiology (i.e. converting extracellular matrix [ECM]-bound cytokines into freely diffusible forms as studied in cancer therapeutics or delivery of exogenous cytokines) during regeneration to enhance muscle recovery after injury.

A multiscale spatial modeling framework for the germinal center response

The germinal center response or reaction (GCR) is a hallmark event of adaptive humoral immunity. Unfolding in the B cell follicles of the secondary lymphoid organs, a GC culminates in the production of high-affinity antibody-secreting plasma cells along with memory B cells. By interacting with follicular dendritic cells (FDC) and T follicular helper (Tfh) cells, GC B cells exhibit complex spatiotemporal dynamics. Driving the B cell dynamics are the intracellular signal transduction and gene regulatory network that responds to cell surface signaling molecules, cytokines, and chemokines. As our knowledge of the GC continues to expand in depth and in scope, mathematical modeling has become an important tool to help disentangle the intricacy of the GCR and inform novel mechanistic and clinical insights. While the GC has been modeled at different granularities, a multiscale spatial simulation framework - integrating molecular, cellular, and tissue-level responses - is still rare. Here, we report our recent progress toward this end with a hybrid stochastic GC framework developed on the Cellular Potts Model-based CompuCell3D platform. Tellurium is used to simulate the B cell intracellular molecular network comprising NF-κB, FOXO1, MYC, AP4, CXCR4, and BLIMP1 that responds to B cell receptor (BCR) and CD40-mediated signaling. The molecular outputs of the network drive the spatiotemporal behaviors of B cells, including cyclic migration between the dark zone (DZ) and light zone (LZ) via chemotaxis; clonal proliferative bursts, somatic hypermutation, and DNA damage-induced apoptosis in the DZ; and positive selection, apoptosis via a death timer, and emergence of plasma cells in the LZ. Our simulations are able to recapitulate key molecular, cellular, and morphological GC events, including B cell population growth, affinity maturation, and clonal dominance. This novel modeling framework provides an open-source, customizable, and multiscale virtual GC simulation platform that enables qualitative and quantitative in silico investigations of a range of mechanistic and applied research questions on the adaptive humoral immune response in the future.

Morphological basis of the lung adenocarcinoma subtypes

Lung adenocarcinoma (LUAD), which accounts for a large proportion of lung cancers, is divided into five major subtypes based on histologic characteristics. The clinical characteristics, prognosis, and responses to treatments vary among subtypes. Here, we demonstrate that the variations of cell-cell contact energy result in the LUAD subtype-specific morphogenesis. We reproduced the morphologies of the papillary LUAD subtypes with the cellular Potts Model (CPM). Simulations and experimental validations revealed modifications of cell-cell contact energy changed the morphology from a papillary-like structure to micropapillary or solid subtype-like structures. Remarkably, differential gene expression analysis revealed subtype-specific expressions of genes relating to cell adhesion. Knockdown experiments of the micropapillary upregulated ITGA11 gene resulted in the morphological changes of the spheroids produced from an LUAD cell line PC9. This work shows the consequences of gene mutations and gene expressions on patient prognosis through differences in tissue composing physical forces among LUAD subtypes.

Graph topological transformations in space-filling cell aggregates

Cell rearrangements are fundamental mechanisms driving large-scale deformations of living tissues. In three-dimensional (3D) space-filling cell aggregates, cells rearrange through local topological transitions of the network of cell-cell interfaces, which is most conveniently described by the vertex model. Since these transitions are not yet mathematically properly formulated, the 3D vertex model is generally difficult to implement. The few existing implementations rely on highly customized and complex software-engineering solutions, which cannot be transparently delineated and are thus mostly non-reproducible. To solve this outstanding problem, we propose a reformulation of the vertex model. Our approach, called Graph Vertex Model (GVM), is based on storing the topology of the cell network into a knowledge graph with a particular data structure that allows performing cell-rearrangement events by simple graph transformations. Importantly, when these same transformations are applied to a two-dimensional (2D) polygonal cell aggregate, they reduce to a well-known T1 transition, thereby generalizing cell-rearrangements in 2D and 3D space-filling packings. This result suggests that the GVM's graph data structure may be the most natural representation of cell aggregates and tissues. We also develop a Python package that implements GVM, relying on a graph-database-management framework Neo4j. We use this package to characterize an order-disorder transition in 3D cell aggregates, driven by active noise and we find aggregates undergoing efficient ordering close to the transition point. In all, our work showcases knowledge graphs as particularly suitable data models for structured storage, analysis, and manipulation of tissue data.

A seven-step guide to spatial, agent-based modelling of tumour evolution

Spatial agent-based models are frequently used to investigate the evolution of solid tumours subject to localized cell-cell interactions and microenvironmental heterogeneity. As spatial genomic, transcriptomic and proteomic technologies gain traction, spatial computational models are predicted to become ever more necessary for making sense of complex clinical and experimental data sets, for predicting clinical outcomes, and for optimizing treatment strategies. Here we present a non-technical step by step guide to developing such a model from first principles. Stressing the importance of tailoring the model structure to that of the biological system, we describe methods of increasing complexity, from the basic Eden growth model up to off-lattice simulations with diffusible factors. We examine choices that unavoidably arise in model design, such as implementation, parameterization, visualization and reproducibility. Each topic is illustrated with examples drawn from recent research studies and state of the art modelling platforms. We emphasize the benefits of simpler models that aim to match the complexity of the phenomena of interest, rather than that of the entire biological system. Our guide is aimed at both aspiring modellers and other biologists and oncologists who wish to understand the assumptions and limitations of the models on which major cancer studies now so often depend.

Machine learning approach for recognition and morphological analysis of isolated astrocytes in phase contrast microscopy

Astrocytes are glycolytically active cells in the central nervous system playing a crucial role in various brain processes from homeostasis to neurotransmission. Astrocytes possess a complex branched morphology, frequently examined by fluorescent microscopy. However, staining and fixation may impact the properties of astrocytes, thereby affecting the accuracy of the experimental data of astrocytes dynamics and morphology. On the other hand, phase contrast microscopy can be used to study astrocytes morphology without affecting them, but the post-processing of the resulting low-contrast images is challenging. The main result of this work is a novel approach for recognition and morphological analysis of unstained astrocytes based on machine-learning recognition of microscopic images. We conducted a series of experiments involving the cultivation of isolated astrocytes from the rat brain cortex followed by microscopy. Using the proposed approach, we tracked the temporal evolution of the average total length of branches, branching, and area per astrocyte in our experiments. We believe that the proposed approach and the obtained experimental data will be of interest and benefit to the scientific communities in cell biology, biophysics, and machine learning.

Integrating multiplexed imaging and multiscale modeling identifies tumor phenotype conversion as a critical component of therapeutic T cell efficacy

Cancer progression is a complex process involving interactions that unfold across molecular, cellular, and tissue scales. These multiscale interactions have been difficult to measure and to simulate. Here, we integrated CODEX multiplexed tissue imaging with multiscale modeling software to model key action points that influence the outcome of T cell therapies with cancer. The initial phenotype of therapeutic T cells influences the ability of T cells to convert tumor cells to an inflammatory, anti-proliferative phenotype. This T cell phenotype could be preserved by structural reprogramming to facilitate continual tumor phenotype conversion and killing. One takeaway is that controlling the rate of cancer phenotype conversion is critical for control of tumor growth. The results suggest new design criteria and patient selection metrics for T cell therapies, call for a rethinking of T cell therapeutic implementation, and provide a foundation for synergistically integrating multiplexed imaging data with multiscale modeling of the cancer-immune interface. A record of this paper's transparent peer review process is included in the supplemental information.

Mechanical control of cell proliferation patterns in growing epithelial monolayers

Cell proliferation plays a crucial role in regulating tissue homeostasis and development. However, our understanding of how cell proliferation is controlled in densely packed tissues is limited. Here we develop a computational framework to predict the patterns of cell proliferation in growing epithelial tissues, connecting single-cell behaviors and cell-cell interactions to tissue-level growth. Our model incorporates probabilistic rules governing cell growth, division, and elimination, also taking into account their feedback with tissue mechanics. In particular, cell growth is suppressed and apoptosis is enhanced in regions of high cell density. With these rules and model parameters calibrated using experimental data for epithelial monolayers, we predict how tissue confinement influences cell size and proliferation dynamics and how single-cell physical properties influence the spatiotemporal patterns of tissue growth. In this model, mechanical feedback between tissue confinement and cell growth leads to enhanced cell proliferation at tissue boundaries, whereas cell growth in the bulk is arrested, recapitulating experimental observations in epithelial tissues. By tuning cellular elasticity and contact inhibition of proliferation we can regulate the emergent patterns of cell proliferation, ranging from uniform growth at low contact inhibition to localized growth at higher contact inhibition. We show that the cell size threshold at G1/S transition governs the homeostatic cell density and tissue turnover rate, whereas the mechanical state of the tissue governs the dynamics of tissue growth. In particular, we find that the cellular parameters affecting tissue pressure play a significant role in determining the overall growth rate. Our computational study thus underscores the impact of cell mechanical properties on the spatiotemporal patterns of cell proliferation in growing epithelial tissues.

Multiscale computational modeling of aortic valve calcification

Calcific aortic valve disease (CAVD) is a common cardiovascular disease that affects millions of people worldwide. The disease is characterized by the formation of calcium nodules on the aortic valve leaflets, which can lead to stenosis and heart failure if left untreated. The pathogenesis of CAVD is still not well understood, but involves several signaling pathways, including the transforming growth factor beta (TGF β ) pathway. In this study, we developed a multiscale computational model for TGF β -stimulated CAVD. The model framework comprises cellular behavior dynamics, subcellular signaling pathways, and tissue-level diffusion fields of pertinent chemical species, where information is shared among different scales. Processes such as endothelial to mesenchymal transition (EndMT), fibrosis, and calcification are incorporated. The results indicate that the majority of myofibroblasts and osteoblast-like cells ultimately die due to lack of nutrients as they become trapped in areas with higher levels of fibrosis or calcification, and they subsequently act as sources for calcium nodules, which contribute to a polydispersed nodule size distribution. Additionally, fibrosis and calcification processes occur more frequently in regions closer to the endothelial layer where the cell activity is higher. Our results provide insights into the mechanisms of CAVD and TGF β signaling and could aid in the development of novel therapeutic approaches for CAVD and other related diseases such as cancer. More broadly, this type of modeling framework can pave the way for unraveling the complexity of biological systems by incorporating several signaling pathways in subcellular models to simulate tissue remodeling in diseases involving cellular mechanobiology.

Modelling cell shape in 3D structured environments: A quantitative comparison with experiments

Cell shape plays a fundamental role in many biological processes, including adhesion, migration, division and development, but it is not clear which shape model best predicts three-dimensional cell shape in structured environments. Here, we compare different modelling approaches with experimental data. The shapes of single mesenchymal cells cultured in custom-made 3D scaffolds were compared by a Fourier method with surfaces that minimize area under the given adhesion and volume constraints. For the minimized surface model, we found marked differences to the experimentally observed cell shapes, which necessitated the use of more advanced shape models. We used different variants of the cellular Potts model, which effectively includes both surface and bulk contributions. The simulations revealed that the Hamiltonian with linear area energy outperformed the elastic area constraint in accurately modelling the 3D shapes of cells in structured environments. Explicit modelling the nucleus did not improve the accuracy of the simulated cell shapes. Overall, our work identifies effective methods for accurately modelling cellular shapes in complex environments.

Agent-based model demonstrates the impact of nonlinear, complex interactions between cytokines on muscle regeneration

Muscle regeneration is a complex process due to dynamic and multiscale biochemical and cellular interactions, making it difficult to identify microenvironmental conditions that are beneficial to muscle recovery from injury using experimental approaches alone. To understand the degree to which individual cellular behaviors impact endogenous mechanisms of muscle recovery, we developed an agent-based model (ABM) using the Cellular Potts framework to simulate the dynamic microenvironment of a cross-section of murine skeletal muscle tissue. We referenced more than 100 published studies to define over 100 parameters and rules that dictate the behavior of muscle fibers, satellite stem cells (SSC), fibroblasts, neutrophils, macrophages, microvessels, and lymphatic vessels, as well as their interactions with each other and the microenvironment. We utilized parameter density estimation to calibrate the model to temporal biological datasets describing cross-sectional area (CSA) recovery, SSC, and fibroblast cell counts at multiple time points following injury. The calibrated model was validated by comparison of other model outputs (macrophage, neutrophil, and capillaries counts) to experimental observations. Predictions for eight model perturbations that varied cell or cytokine input conditions were compared to published experimental studies to validate model predictive capabilities. We used Latin hypercube sampling and partial rank correlation coefficient to identify in silico perturbations of cytokine diffusion coefficients and decay rates to enhance CSA recovery. This analysis suggests that combined alterations of specific cytokine decay and diffusion parameters result in greater fibroblast and SSC proliferation compared to individual perturbations with a 13% increase in CSA recovery compared to unaltered regeneration at 28 days. These results enable guided development of therapeutic strategies that similarly alter muscle physiology (i.e. converting ECM-bound cytokines into freely diffusible forms as studied in cancer therapeutics or delivery of exogenous cytokines) during regeneration to enhance muscle recovery after injury.

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.

A Cellular Potts Model of the interplay of synchronization and aggregation

We investigate the behavior of systems of cells with intracellular molecular oscillators ("clocks") where cell-cell adhesion is mediated by differences in clock phase between neighbors. This is motivated by phenomena in developmental biology and in aggregative multicellularity of unicellular organisms. In such systems, aggregation co-occurs with clock synchronization. To account for the effects of spatially extended cells, we use the Cellular Potts Model (CPM), a lattice agent-based model. We find four distinct possible phases: global synchronization, local synchronization, incoherence, and anti-synchronization (checkerboard patterns). We characterize these phases via order parameters. In the case of global synchrony, the speed of synchronization depends on the adhesive effects of the clocks. Synchronization happens fastest when cells in opposite phases adhere the strongest ("opposites attract"). When cells of the same clock phase adhere the strongest ("like attracts like"), synchronization is slower. Surprisingly, the slowest synchronization happens in the diffusive mixing case, where cell-cell adhesion is independent of clock phase. We briefly discuss potential applications of the model, such as pattern formation in the auditory sensory epithelium.

Enhanced perfusion following exposure to radiotherapy: A theoretical investigation

Tumour angiogenesis leads to the formation of blood vessels that are structurally and spatially heterogeneous. Poor blood perfusion, in conjunction with increased hypoxia and oxygen heterogeneity, impairs a tumour's response to radiotherapy. The optimal strategy for enhancing tumour perfusion remains unclear, preventing its regular deployment in combination therapies. In this work, we first identify vascular architectural features that correlate with enhanced perfusion following radiotherapy, using in vivo imaging data from vascular tumours. Then, we present a novel computational model to determine the relationship between these architectural features and blood perfusion in silico. If perfusion is defined to be the proportion of vessels that support blood flow, we find that vascular networks with small mean diameters and large numbers of angiogenic sprouts show the largest increases in perfusion post-irradiation for both biological and synthetic tumours. We also identify cases where perfusion increases due to the pruning of hypoperfused vessels, rather than blood being rerouted. These results indicate the importance of considering network composition when determining the optimal irradiation strategy. In the future, we aim to use our findings to identify tumours that are good candidates for perfusion enhancement and to improve the efficacy of combination therapies.

Is it selfish to be filamentous in biofilms? Individual-based modeling links microbial growth strategies with morphology using the new and modular iDynoMiCS 2.0

Microbial communities are found in all habitable environments and often occur in assemblages with self-organized spatial structures developing over time. This complexity can only be understood, predicted, and managed by combining experiments with mathematical modeling. Individual-based models are particularly suited if individual heterogeneity, local interactions, and adaptive behavior are of interest. Here we present the completely overhauled software platform, the individual-based Dynamics of Microbial Communities Simulator, iDynoMiCS 2.0, which enables researchers to specify a range of different models without having to program. Key new features and improvements are: (1) Substantially enhanced ease of use (graphical user interface, editor for model specification, unit conversions, data analysis and visualization and more). (2) Increased performance and scalability enabling simulations of up to 10 million agents in 3D biofilms. (3) Kinetics can be specified with any arithmetic function. (4) Agent properties can be assembled from orthogonal modules for pick and mix flexibility. (5) Force-based mechanical interaction framework enabling attractive forces and non-spherical agent morphologies as an alternative to the shoving algorithm. The new iDynoMiCS 2.0 has undergone intensive testing, from unit tests to a suite of increasingly complex numerical tests and the standard Benchmark 3 based on nitrifying biofilms. A second test case was based on the "biofilms promote altruism" study previously implemented in BacSim because competition outcomes are highly sensitive to the developing spatial structures due to positive feedback between cooperative individuals. We extended this case study by adding morphology to find that (i) filamentous bacteria outcompete spherical bacteria regardless of growth strategy and (ii) non-cooperating filaments outcompete cooperating filaments because filaments can escape the stronger competition between themselves. In conclusion, the new substantially improved iDynoMiCS 2.0 joins a growing number of platforms for individual-based modeling of microbial communities with specific advantages and disadvantages that we discuss, giving users a wider choice.

A Multiscale Spatial Modeling Framework for the Germinal Center Response

The germinal center response or reaction (GCR) is a hallmark event of adaptive humoral immunity. Unfolding in the B cell follicles of the secondary lymph organs, a GC culminates in the production of high-affinity antibody-secreting plasma cells along with memory B cells. By interacting with follicular dendritic cells (FDC) and T follicular helper (Tfh) cells, GC B cells exhibit complex spatiotemporal dynamics. Driving the B cell dynamics are the intracellular signal transduction and gene regulatory network that responds to cell surface signaling molecules, cytokines, and chemokines. As our knowledge of the GC continues to expand in depth and in scope, mathematical modeling has become an important tool to help disentangle the intricacy of the GCR and inform novel mechanistic and clinical insights. While the GC has been modeled at different granularities, a multiscale spatial simulation framework - integrating molecular, cellular, and tissue-level responses - is still rare. Here, we report our recent progress toward this end with a hybrid stochastic GC framework developed on the Cellular Potts Model-based CompuCell3D platform. Tellurium is used to simulate the B cell intracellular molecular network comprising NF-κB, FOXO1, MYC, AP4, CXCR4, and BLIMP1 that responds to B cell receptor (BCR) and CD40-mediated signaling. The molecular outputs of the network drive the spatiotemporal behaviors of B cells, including cyclic migration between the dark zone (DZ) and light zone (LZ) via chemotaxis; clonal proliferative bursts, somatic hypermutation, and DNA damage-induced apoptosis in the DZ; and positive selection, apoptosis via a death timer, and emergence of plasma cells in the LZ. Our simulations are able to recapitulate key molecular, cellular, and morphological GC events including B cell population growth, affinity maturation, and clonal dominance. This novel modeling framework provides an open-source, customizable, and multiscale virtual GC simulation platform that enables qualitative and quantitative in silico investigations of a range of mechanic and applied research questions in future.