Quantifying the relationship between cell division angle and morphogenesis through computational modeling

Mechanical response of cardiac microtissues to acute localized injury

After a myocardial infarction (MI), the heart undergoes changes including local remodeling that can lead to regional abnormalities in mechanical and electrical properties, ultimately increasing the risk of arrythmias and heart failure. While these responses have been successfully recapitulated in animal models of MI, local changes in tissue and cell-level mechanics caused by MI remain difficult to study in vivo. Here, we developed an in vitro cardiac microtissue (CMT) injury system which through acute focal injury recapitulates aspects of the regional responses seen following an MI. Using a pulsed laser, cell death was induced in the center of the microtissue causing a loss of calcium signaling and a complete loss of contractile function in the injured region and resulting in a 39% reduction in the CMT's overall force production. After 7 days, the injured area remained void of CMs and showed increased expression of vimentin and fibronectin, two markers for fibrotic remodeling. Interestingly, while the injured region showed minimal recovery, calcium amplitudes in uninjured regions returned to levels comparable to control. Furthermore, overall force production returned to pre-injury levels despite the lack of contractile function in the injured region. Instead, uninjured regions exhibited elevated contractile function, compensating for the loss of function in the injured region, drawing parallels to changes in tissue-level mechanics seen in vivo. Overall, this work presents a new in vitro model to study cardiac tissue remodeling and electromechanical changes after injury.

Computable early Caenorhabditis elegans embryo with a phase field model

Morphogenesis is a precise and robust dynamic process during metazoan embryogenesis, consisting of both cell proliferation and cell migration. Despite the fact that much is known about specific regulations at molecular level, how cell proliferation and migration together drive the morphogenesis at cellular and organismic levels is not well understood. Using Caenorhabditis elegans as the model animal, we present a phase field model to compute early embryonic morphogenesis within a confined eggshell. With physical information about cell division obtained from three-dimensional time-lapse cellular imaging experiments, the model can precisely reproduce the early morphogenesis process as seen in vivo, including time evolution of location and morphology of each cell. Furthermore, the model can be used to reveal key cell-cell attractions critical to the development of C. elegans embryo. Our work demonstrates how genetic programming and physical forces collaborate to drive morphogenesis and provides a predictive model to decipher the underlying mechanism.

Embryonic development is a precise process involving cell division, cell-cell interaction, and cell migration. During the process, how each cell reaches its supposed location and be in contact with the right neighbors, and what roles genetic factors and physical forces play are important and fascinating questions. Using the worm Caenorhabditis elegans as a model system, we build a phase field model to simulate early morphogenesis. With a few physical inputs, the model can precisely reproduce the early morphological development of the worm. Such an accurate simulator can not only teach us how physical forces work together with genetic factors to shape up the complex process of development, but also make predictions, such as key cell-cell attractions critical in the process.

Sarc-Graph: Automated segmentation, tracking, and analysis of sarcomeres in hiPSC-derived cardiomyocytes

A better fundamental understanding of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) has the potential to advance applications ranging from drug discovery to cardiac repair. Automated quantitative analysis of beating hiPSC-CMs is an important and fast developing component of the hiPSC-CM research pipeline. Here we introduce “Sarc-Graph,” a computational framework to segment, track, and analyze sarcomeres in fluorescently tagged hiPSC-CMs. Our framework includes functions to segment z-discs and sarcomeres, track z-discs and sarcomeres in beating cells, and perform automated spatiotemporal analysis and data visualization. In addition to reporting good performance for sarcomere segmentation and tracking with little to no parameter tuning and a short runtime, we introduce two novel analysis approaches. First, we construct spatial graphs where z-discs correspond to nodes and sarcomeres correspond to edges. This makes measuring the network distance between each sarcomere (i.e., the number of connecting sarcomeres separating each sarcomere pair) straightforward. Second, we treat tracked and segmented components as fiducial markers and use them to compute the approximate deformation gradient of the entire tracked population. This represents a new quantitative descriptor of hiPSC-CM function. We showcase and validate our approach with both synthetic and experimental movies of beating hiPSC-CMs. By publishing Sarc-Graph, we aim to make automated quantitative analysis of hiPSC-CM behavior more accessible to the broader research community.

Heart disease is the leading cause of death worldwide. Because of this, many researchers are studying heart cells in the lab and trying to create artificial heart tissue. Recently, there has been a growing focus on human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs). These are cells that are safely sampled from living humans, for example from the blood or skin, that are then transformed into human heart muscle cells. One active research goal is to use these cells to repair the damaged heart. Another active research goal is to test new drugs on these cells before testing them in animals and humans. However, one major challenge is that hiPSC-CMs often have an irregular internal structure that is difficult to analyze. At present, their behavior is far from fully understood. To address this, we have created software to automatically analyze movies of beating hiPSC-CMs. With our software, it is possible to quantify properties such as the amount and direction of beating cell contraction, and the variation in behavior across different parts of each cell. These tools will enable further quantitative analysis of hiPSC-CMs. With these tools, it will be easier to understand, control, and optimize artificial heart tissue created with hiPSC-CMs, and quantify the effects of drugs on hiPSC-CM behavior.

FM-Track: A fiducial marker tracking software for studying cell mechanics in a three-dimensional environment

Tracking the deformation of fiducial markers in the vicinity of living cells embedded in compliant synthetic or biological gels is a powerful means to study cell mechanics and mechanobiology in three-dimensional environments. However, current approaches to track and quantify three-dimensional (3D) fiducial marker displacements remain ad-hoc, can be difficult to implement, and may not produce reliable results. Herein, we present a compact software package entitled "FM-Track," written in the popular Python language, to facilitate feature-based particle tracking tailored for 3D cell micromechanical environment studies. FM-Track contains functions for pre-processing images, running fiducial marker tracking, and post-processing and visualization. FM-Track can thus aid the study of cellular mechanics and mechanobiology by providing an extensible software platform to more reliably extract complex local 3D cell contractile information in transparent compliant gel systems.

Analyzing valve interstitial cell mechanics and geometry with spatial statistics

Understanding cell geometric and mechanical properties is crucial to understanding how cells sense and respond to their local environment. Moreover, changes to cell mechanical properties under varied micro-environmental conditions can both influence and indicate fundamental changes to cell behavior. Atomic Force Microscopy (AFM) is a well established, powerful tool to capture geometric and mechanical properties of cells. We have previously demonstrated substantial functional and behavioral differences between aortic and pulmonary valve interstitial cells (VIC) using AFM and subsequent models of VIC mechanical response. In the present work, we extend these studies by demonstrating that to best interpret the spatially distributed AFM data, the use of spatial statistics is required. Spatial statistics includes formal techniques to analyze spatially distributed data, and has been used successfully in the analysis of geographic data. Thus, spatially mapped AFM studies of cell geometry and mechanics are analogous to more traditional forms of geospatial data. We are able to compare the spatial autocorrelation of stiffness in aortic and pulmonary valve interstitial cells, and more accurately capture cell geometry from height recordings. Specifically, we showed that pulmonary valve interstitial cells display higher levels of spatial autocorrelation of stiffness than aortic valve interstitial cells. This suggests that aortic VICs form different stress fiber structures than their pulmonary counterparts, in addition to being more highly expressed and stiffer on average. Thus, the addition of spatial statistics can contribute to our fundamental understanding of the differences between cell types. Moving forward, we anticipate that this work will be meaningful to enhance direct analysis of experimental data and for constructing high fidelity computational of VICs and other cell models.

Understanding the mechanical link between oriented cell division and cerebellar morphogenesis

The cerebellum is a tightly folded structure located at the back of the head. Unlike the folds of the cerebrum, the folds of the cerebellum are aligned such that the external surface appears to be covered in parallel grooves. Experiments have shown that anchoring center initiation drives cerebellar foliation. However, the mechanism guiding the location of these anchoring centers, and subsequently cerebellar morphology, remains poorly understood. In particular, there is no definitive mechanistic explanation for the preferential emergence of parallel folds instead of an irregular folding pattern like in the cerebral cortex. Here we use mechanical modeling on the cellular and tissue scales to show that the oriented granule cell division observed in the experimental setting leads to the characteristic parallel folding pattern of the cerebellum. Specifically, we propose an agent-based model of cell clones, a strategy for propagating information from our in silico cell clones to the tissue scale, and an analytical solution backed by numerical results to understand how differential growth between the cerebellar layers drives geometric instability in three dimensional space on the tissue scale. This proposed mechanical model provides further insight into the process of anchoring center initiation and establishes a framework for future multiscale mechanical analysis of developing organs.

Understanding the relationship between cell death and tissue shrinkage via a stochastic agent-based model

Cell death, a process which can occur both naturally and in response to insult, is both a complex and diverse phenomenon. Under some circumstances, dying cells actively contract and cause their neighbors to rearrange and maintain tissue integrity. Under other circumstances, dying cells leave behind gaps, which results in tissue separation. A better understanding of how the cellular scale features of cell death manifest on the population scale has implications ranging from morphogenesis to tumor response to treatment. However, the mechanistic relationship between cell death and population scale shrinkage is not well understood, and computational methods for studying these relationships are not well established. Here we propose a mechanically robust agent-based cell model designed to capture the implications of cell death on the population scale. In our agent-based model, algorithmic rules applied on the cellular level emerge on the population scale where their effects are quantified. To better quantify model uncertainty and parameter interactions, we implement a recently developed technique for conducting a variance-based sensitivity analysis on the stochastic model. From this analysis and subsequent investigation, we find that cellular scale shrinkage has the largest influence of all model parameters tested, and that by adjusting cellular scale shrinkage population shrinkage varies widely even across simulations which contain the same fraction of dying cells. We anticipate that the methods and results presented here are a starting point for significant future investigation toward quantifying the implications of different mechanisms of cell death on population and tissue scale behavior.

Modeling mechanical inhomogeneities in small populations of proliferating monolayers and spheroids

Understanding the mechanical behavior of multicellular monolayers and spheroids is fundamental to tissue culture, organism development, and the early stages of tumor growth. Proliferating cells in monolayers and spheroids experience mechanical forces as they grow and divide and local inhomogeneities in the mechanical microenvironment can cause individual cells within the multicellular system to grow and divide at different rates. This differential growth, combined with cell division and reorganization, leads to residual stress. Multiple different modeling approaches have been taken to understand and predict the residual stresses that arise in growing multicellular systems, particularly tumor spheroids. Here, we show that by using a mechanically robust agent-based model constructed with the peridynamic framework, we gain a better understanding of residual stresses in multicellular systems as they grow from a single cell. In particular, we focus on small populations of cells (1-100 s) where population behavior is highly stochastic and prior investigation has been limited. We compare the average strain energy density of cells in monolayers and spheroids using different growth and division rules and find that, on average, cells in spheroids have a higher strain energy density than cells in monolayers. We also find that cells in the interior of a growing spheroid are, on average, in compression. Finally, we demonstrate the importance of accounting for stochastic fluctuations in the mechanical environment, particularly when the cellular response to mechanical cues is nonlinear. The results presented here serve as a starting point for both further investigation with agent-based models, and for the incorporation of major findings from agent-based models into continuum scale models when explicit representation of individual cells is not computationally feasible.