Multi-scale modeling of a wound-healing cell migration assay

Dynamics of angiogenesis during wound healing: a coupled in vivo and in silico study

OBJECTIVE

The most critical determinant of restoration of tissue structure during wound healing is the re-establishment of a functional vasculature, which largely occurs via angiogenesis, specifically endothelial sprouting from the pre-existing vasculature.

MATERIALS AND METHODS

We used confocal microscopy to capture sequential images of perfused vascular segments within the injured panniculus carnosus muscle in the mouse dorsal skin-fold window chamber to quantify a range of microcirculatory parameters during the first nine days of healing. This data was used to inform a mathematical model of sequential growth of the vascular plexus. The modeling framework mirrored the experimental circular wound domain and incorporated capillary sprouting and endothelial cell (EC) sensing of vascular endothelial growth factor gradients.

RESULTS

Wound areas, vessel densities and vessel junction densities obtained from the corresponding virtual wound were in excellent agreement both temporally and spatially with data measured during the in vivo healing process. Moreover, by perturbing the proliferative ability of ECs in the mathematical model, this leads to a severe reduction in vascular growth and poor healing. Quantitative measures from this second set of simulations were found to correlate extremely well with experimental data obtained from animals treated with an agent that targets endothelial proliferation (TNP-470).

CONCLUSION

Our direct combination and comparison of in vivo longitudinal analysis (over time in the same animal) and mathematical modeling employed in this study establishes a useful new paradigm. The virtual wound created in this study can be used to investigate a wide range of experimental hypotheses associated with wound healing, including disorders characterized by aberrant angiogenesis (e.g., diabetic models) and the effects of vascular enhancing/disrupting agents or therapeutic interventions such as hyperbaric oxygen.

Spatial organization of mesenchymal stem cells in vitro--results from a new individual cell-based model with podia

Therapeutic application of mesenchymal stem cells (MSC) requires their extensive in vitro expansion. MSC in culture typically grow to confluence within a few weeks. They show spindle-shaped fibroblastoid morphology and align to each other in characteristic spatial patterns at high cell density. We present an individual cell-based model (IBM) that is able to quantitatively describe the spatio-temporal organization of MSC in culture. Our model substantially improves on previous models by explicitly representing cell podia and their dynamics. It employs podia-generated forces for cell movement and adjusts cell behavior in response to cell density. At the same time, it is simple enough to simulate thousands of cells with reasonable computational effort. Experimental sheep MSC cultures were monitored under standard conditions. Automated image analysis was used to determine the location and orientation of individual cells. Our simulations quantitatively reproduced the observed growth dynamics and cell-cell alignment assuming cell density-dependent proliferation, migration, and morphology. In addition to cell growth on plain substrates our model captured cell alignment on micro-structured surfaces. We propose a specific surface micro-structure that according to our simulations can substantially enlarge cell culture harvest. The 'tool box' of cell migratory behavior newly introduced in this study significantly enhances the bandwidth of IBM. Our approach is capable of accommodating individual cell behavior and collective cell dynamics of a variety of cell types and tissues in computational systems biology.

Probing the invasiveness of prostate cancer cells in a 3D microfabricated landscape

The metastatic invasion of cancer cells from primary tumors to distant ecological niches, rather than the primary tumors, is the cause of much cancer mortality [Zhang QB, et al. (2010) Int J Cancer 126:2534-2541; Chambers AF, Goss PE (2008) Breast Cancer Res 10:114]. Metastasis is a three-dimensional invasion process where cells spread from their site of origin and colonize distant microenvironmental niches. It is critical to be able to assess quantitatively the metastatic potential of cancer cells [Harma V, et al. (2010) PLoS ONE 5:e10431]. We have constructed a microfabricated chip with a three-dimensional topology consisting of lowlands and isolated square highlands (Tepuis), which stand hundreds of microns above the lowlands, in order to assess cancer cell metastatic potential as they invade the highlands. As a test case, the invasive ascents of the Tepui by highly metastatic PC-3 and noninvasive LNCaP prostate cancer cells were used. The vertical ascent by prostate cancer cells from the lowlands to the tops of the Tepui was imaged using confocal microscopy and used as a measure of the relative invasiveness. The less-metastatic cells (LNCaP) never populated all available tops, leaving about 15% of them unoccupied, whereas the more metastatic PC-3 cells occupied all available Tepuis. We argue that this distinct difference in invasiveness is due to contact inhibition.

Crawling cells can close wounds without purse strings or signaling

When a gash or gouge is made in a confluent layer of epithelial cells, the cells move to fill in the “wound.” In some cases, such as in wounded embryonic chick wing buds, the movement of the cells is driven by cortical actin contraction (i.e., a purse string mechanism). In adult tissue, though, cells apparently crawl to close wounds. At the single cell level, this crawling is driven by the dynamics of the cell's actin cytoskeleton, which is regulated by a complex biochemical network, and cell signaling has been proposed to play a significant role in directing cells to move into the denuded area. However, wounds made in monolayers of Madin-Darby canine kidney (MDCK) cells still close even when a row of cells is deactivated at the periphery of the wound, and recent experiments show complex, highly-correlated cellular motions that extend tens of cell lengths away from the boundary. These experiments suggest a dominant role for mechanics in wound healing. Here we present a biophysical description of the collective migration of epithelial cells during wound healing based on the basic motility of single cells and cell-cell interactions. This model quantitatively captures the dynamics of wound closure and reproduces the complex cellular flows that are observed. These results suggest that wound healing is predominantly a mechanical process that is modified, but not produced, by cell-cell signaling.

Wound healing is driven by the collective migration of groups of epithelial cells. Experiments have shown that the motions of cells during wound healing are not as simple as had once been thought. Indeed, cells do not just move out to fill in the wounded area but rather undergo a number of complex but coordinated motions. Furthermore, wound healing is not just a response to chemical cues and can be driven by cells that are not immediately at the edge of the wound. In this paper, we develop a mathematical model based on the mechanical behavior of single crawling cells and also includes cell-cell adhesion. We show that this model is capable of explaining quantitatively the dynamics that occur during wound healing assays. This suggests that wound healing is largely a mechanical process where chemical signaling merely acts to augment the overall behavior.

Spatially directed guidance of stem cell population migration by immobilized patterns of growth factors

We investigated how engineered gradients of exogenous growth factors, immobilized to an extracellular matrix material, influence collective guidance of stem cell populations over extended time (>1 day) and length (>1 mm) scales in vitro. Patterns of low-to-high, high-to-low, and uniform concentrations of heparin-binding epidermal growth factor-like growth factor were inkjet printed at precise locations on fibrin substrates. Proliferation and migration responses of mesenchymal stem cells seeded at pattern origins were observed with time-lapse video microscopy and analyzed using both manual and automated computer vision-based cell tracking techniques. Based on results of established chemotaxis studies, we expected that the low-to-high gradient would most effectively direct cell guidance away from the cell source. All printed patterns, however, were found to direct net collective cell guidance with comparable responses. Our analysis revealed that collective "cell diffusion" down a cell-to-cell confinement gradient originating at the cell starting lines and not the net sum of directed individual cell migration up a growth factor concentration gradient is the principal driving force for directing mesenchymal stem cell population outgrowth from a cell source. These results suggest that simple uniform distributions of growth factors immobilized to an extracellular matrix material may be as effective in directing cell migration into a wound site as more complex patterns with concentration gradients.

Monitoring impedance changes associated with motility and mitosis of a single cell

We present a device enabling impedance measurements that probe the motility and mitosis of a single adherent cell in a controlled way. The micrometre-sized electrodes are designed for adhesion of an isolated cell and enhanced sensitivity to cell motion. The electrode surface is switched electro-chemically to favour cell adhesion, and single cells are attracted to the electrode using positive dielectrophoresis. Periods of linear variation in impedance with time correspond to the motility of a single cell adherent to the surface estimated at 0.6 μm h(-1). In the course of our study we observed the impedance changes associated with mitosis of a single cell. Electrical measurements, carried out concomitantly with optical observations, revealed three phases, prophase, metaphase and anaphase in the time variation of the impedance during cell division. Maximal impedance was observed at metaphase with a 20% increase of the impedance. We argue that at mitosis, the changes detected were due to the charge density distribution at the cell surface. Our data demonstrate subtle electrical changes associated with cell motility and for the first time with division at the single-cell level. We speculate that this could open up new avenues for characterizing healthy and pathological cells.

Migration of breast cancer cells: understanding the roles of volume exclusion and cell-to-cell adhesion

We study MCF-7 breast cancer cell movement in a transwell apparatus. Various experimental conditions lead to a variety of monotone and nonmonotone responses which are difficult to interpret. We anticipate that the experimental results could be caused by cell-to-cell adhesion or volume exclusion. Without any modeling, it is impossible to understand the relative roles played by these two mechanisms. A lattice-based exclusion process random-walk model incorporating agent-to-agent adhesion is applied to the experimental system. Our combined experimental and modeling approach shows that a low value of cell-to-cell adhesion strength provides the best explanation of the experimental data suggesting that volume exclusion plays a more important role than cell-to-cell adhesion. This combined experimental and modeling study gives insight into the cell-level details and design of transwell assays.

Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms

BACKGROUND

Simulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models.

RESULTS

We construct a 3D model of epidermal development and provide a set of GPU algorithms that executes significantly faster than sequential central processing unit (CPU) code. We provide a parallel implementation of the subcellular element method for individual cells residing in a lattice-free spatial environment. Each cell in our epidermal model includes an internal gene network, which integrates cellular interaction of Notch signaling together with environmental interaction of basement membrane adhesion, to specify cellular state and behaviors such as growth and division. We take a pedagogical approach to describing how modeling methods are efficiently implemented on the GPU including memory layout of data structures and functional decomposition. We discuss various programmatic issues and provide a set of design guidelines for GPU programming that are instructive to avoid common pitfalls as well as to extract performance from the GPU architecture.

CONCLUSIONS

We demonstrate that GPU algorithms represent a significant technological advance for the simulation of complex biological models. We further demonstrate with our epidermal model that the integration of multiple complex modeling methods for heterogeneous multicellular biological processes is both feasible and computationally tractable using this new technology. We hope that the provided algorithms and source code will be a starting point for modelers to develop their own GPU implementations, and encourage others to implement their modeling methods on the GPU and to make that code available to the wider community.

Phenotype and genotype of pancreatic cancer cell lines

The dismal prognosis of pancreatic adenocarcinoma is due in part to a lack of molecular information regarding disease development. Established cell lines remain a useful tool for investigating these molecular events. Here we present a review of available information on commonly used pancreatic adenocarcinoma cell lines as a resource to help investigators select the cell lines most appropriate for their particular research needs. Information on clinical history; in vitro and in vivo growth characteristics; phenotypic characteristics, such as adhesion, invasion, migration, and tumorigenesis; and genotypic status of commonly altered genes (KRAS, p53, p16, and SMAD4) was evaluated. Identification of both consensus and discrepant information in the literature suggests careful evaluation before selection of cell lines and attention be given to cell line authentication.

Simulation of lung alveolar epithelial wound healing in vitro

The mechanisms that enable and regulate alveolar type II (AT II) epithelial cell wound healing in vitro and in vivo remain largely unknown and need further elucidation. We used an in silico AT II cell-mimetic analogue to explore and better understand plausible wound healing mechanisms for two conditions: cyst repair in three-dimensional cultures and monolayer wound healing. Starting with the analogue that validated for key features of AT II cystogenesis in vitro, we devised an additional cell rearrangement action enabling cyst repair. Monolayer repair was enabled by providing 'cells' a control mechanism to switch automatically to a repair mode in the presence of a distress signal. In cyst wound simulations, the revised analogue closed wounds by adhering to essentially the same axioms available for alveolar-like cystogenesis. In silico cell proliferation was not needed. The analogue recovered within a few simulation cycles but required a longer recovery time for larger or multiple wounds. In simulated monolayer wound repair, diffusive factor-mediated 'cell' migration led to repair patterns comparable to those of in vitro cultures exposed to different growth factors. Simulations predicted directional cell locomotion to be critical for successful in vitro wound repair. We anticipate that with further use and refinement, the methods used will develop as a rigorous, extensible means of unravelling mechanisms of lung alveolar repair and regeneration.

Physical model of the dynamic instability in an expanding cell culture

Collective cell migration is of great significance in many biological processes. The goal of this work is to give a physical model for the dynamics of cell migration during the wound healing response. Experiments demonstrate that an initially uniform cell-culture monolayer expands in a nonuniform manner, developing fingerlike shapes. These fingerlike shapes of the cell culture front are composed of columns of cells that move collectively. We propose a physical model to explain this phenomenon, based on the notion of dynamic instability. In this model, we treat the first layers of cells at the front of the moving cell culture as a continuous one-dimensional membrane (contour), with the usual elasticity of a membrane: curvature and surface-tension. This membrane is active, due to the forces of cellular motility of the cells, and we propose that this motility is related to the local curvature of the culture interface; larger convex curvature correlates with a stronger cellular motility force. This shape-force relation gives rise to a dynamic instability, which we then compare to the patterns observed in the wound healing experiments.

Stochastic collective movement of cells and fingering morphology: no maverick cells

The classical approach to model collective biological cell movement is through coupled nonlinear reaction-diffusion equations for biological cells and diffusive chemicals that interact with the biological cells. This approach takes into account the diffusion of cells, proliferation, death of cells, and chemotaxis. Whereas the classical approach has many advantages, it fails to consider many factors that affect multicell movement. In this work, a multiscale approach, the Glazier-Graner-Hogeweg model, is used. This model is implemented for biological cells coupled with the finite element method for a diffusive chemical. The Glazier-Graner-Hogeweg model takes the biological cell state as discrete and allows it to include cohesive forces between biological cells, deformation of cells, following the path of a single cell, and stochastic behavior of the cells. Where the continuity of the tissue at the epidermis is violated, biological cells regenerate skin to heal the wound. We assume that the cells secrete a diffusive chemical when they feel a wounded region and that the cells are attracted by the chemical they release (chemotaxis). Under certain parameters, the front encounters a fingering morphology, and two fronts progressing against each other are attracted and correlated. Cell flow exhibits interesting patterns, and a drift effect on the chemical may influence the cells' motion. The effects of a polarized substrate are also discussed.

At the biological modeling and simulation frontier

We provide a rationale for and describe examples of synthetic modeling and simulation (M&S) of biological systems. We explain how synthetic methods are distinct from familiar inductive methods. Synthetic M&S is a means to better understand the mechanisms that generate normal and disease-related phenomena observed in research, and how compounds of interest interact with them to alter phenomena. An objective is to build better, working hypotheses of plausible mechanisms. A synthetic model is an extant hypothesis: execution produces an observable mechanism and phenomena. Mobile objects representing compounds carry information enabling components to distinguish between them and react accordingly when different compounds are studied simultaneously. We argue that the familiar inductive approaches contribute to the general inefficiencies being experienced by pharmaceutical R&D, and that use of synthetic approaches accelerates and improves R&D decision-making and thus the drug development process. A reason is that synthetic models encourage and facilitate abductive scientific reasoning, a primary means of knowledge creation and creative cognition. When synthetic models are executed, we observe different aspects of knowledge in action from different perspectives. These models can be tuned to reflect differences in experimental conditions and individuals, making translational research more concrete while moving us closer to personalized medicine.

A cell migration device that maintains a defined surface with no cellular damage during wound edge generation

Studying the rate of cell migration provides insight into fundamental cell biology as well as a tool to assess the functionality of synthetic surfaces and soluble environments used in tissue engineering. The traditional tools used to study cell migration include the fence and wound healing assays. In this paper we describe the development of a microchannel based device for the study of cell migration on defined surfaces. We demonstrate that this device provides a superior tool, relative to the previously mentioned assays, for assessing the propagation rate of cell wave fronts. The significant advantage provided by this technology is the ability to maintain a virgin surface prior to the commencement of the cell migration assay. Here, the device is used to assess rates of mouse fibroblasts (NIH 3T3) and human osteosarcoma (SaOS2) cell migration on surfaces functionalized with various extracellular matrix proteins as a demonstration that confining cell migration within a microchannel produces consistent and robust data. The device design enables rapid and simplistic assessment of multiple repeats on a single chip, where surfaces have not been previously exposed to cells or cellular secretions.

A three species model to simulate application of Hyperbaric Oxygen Therapy to chronic wounds

Chronic wounds are a significant socioeconomic problem for governments worldwide. Approximately 15% of people who suffer from diabetes will experience a lower-limb ulcer at some stage of their lives, and 24% of these wounds will ultimately result in amputation of the lower limb. Hyperbaric Oxygen Therapy (HBOT) has been shown to aid the healing of chronic wounds; however, the causal reasons for the improved healing remain unclear and hence current HBOT protocols remain empirical. Here we develop a three-species mathematical model of wound healing that is used to simulate the application of hyperbaric oxygen therapy in the treatment of wounds. Based on our modelling, we predict that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds. Furthermore, treatment should continue until healing is complete, and HBOT will not stimulate healing under all circumstances, leading us to conclude that finding the right protocol for an individual patient is crucial if HBOT is to be effective. We provide constraints that depend on the model parameters for the range of HBOT protocols that will stimulate healing. More specifically, we predict that patients with a poor arterial supply of oxygen, high consumption of oxygen by the wound tissue, chronically hypoxic wounds, and/or a dysfunctional endothelial cell response to oxygen are at risk of nonresponsiveness to HBOT. The work of this paper can, in some way, highlight which patients are most likely to respond well to HBOT (for example, those with a good arterial supply), and thus has the potential to assist in improving both the success rate and hence the cost-effectiveness of this therapy.

Pathlines in exclusion processes

Trajectory data from observations of a random-walk process are often used to characterize macroscopic transport coefficients and to make inferences about motility mechanisms. Continuum equations describing the average moments of the position of an agent in an exclusion process are derived and validated with simulation data. Unlike standard noninteracting random walks, the moment equations for the exclusion process explicitly represent the interaction of agents since they depend on the averaged macroscopic agent density. Key issues associated with the validity of the continuum equations and interpretation of experimental data are discussed.

An automatic and quantitative on-chip cell migration assay using self-assembled monolayers combined with real-time cellular impedance sensing

Cell migration is crucial in many physiological and pathological processes including embryonic development, immune response and cancer metastasis. Traditional methods for cell migration detection such as wound healing assay usually involve physical scraping of a cell monolayer followed by an optical observation of cell movement. However, these methods require hand-operation with low repeatability. Moreover, it's a qualitative observation not a quantitative measurement, which is hard to scale up to a high-throughput manner. In this article, a novel and reliable on-chip cell migration detection method integrating surface chemical modification of gold electrodes using self-assembled monolayers (SAMs) and real-time cellular impedance sensing is presented. The SAMs are used to inhibit cell adherence forming an area devoid of cells, which could effectively mimic wounds in a cell monolayer. After a DC electrical signal was applied, the SAMs were desorbed from the electrodes and cells started to migrate. The process of cell migration was monitored by real-time impedance sensing. This demonstrates the first occurrence of integrating cellular impedance sensing and wound-forming with SAMs, which makes cell migration assay being real-time, quantitative and fully automatic. We believe this method could be used for high-throughput anti-migratory drug screening and drug discovery.

Cell population-based model of dermal wound invasion with heterogeneous intracellular signaling properties

A deterministic model of dermal wound invasion, which accounts for the platelet-derived growth factor (PDGF) gradient sensing mechanism in fibroblasts mediated by cell surface receptors and the phosphoinositide 3-kinase (PI3K) signal transduction pathway, was previously described (Biophys J 2006; 90:2297-308). Here, we extend that work and implement a hybrid modeling strategy that treats fibroblasts as discrete entities endowed with heterogeneous properties, namely receptor, PI3K and 3' phosphoinositide phosphatase expression levels. Analysis of the model suggests that the wound environment fosters the advancement of cells within the population that are better fit to migrate and/or proliferate in response to PDGF stimulation. Thus, cell-to-cell variability results in a significantly higher rate of wound invasion as compared with the deterministic model, in a manner that depends on the way in which individual cell properties are sampled or inherited upon cell division.

Experimental characterization and computational modelling of two-dimensional cell spreading for skeletal regeneration

Limited cell ingrowth is a major problem for tissue engineering and the clinical application of porous biomaterials as bone substitutes. As a first step, migration and proliferation of an interacting cell population can be studied in two-dimensional culture. Mathematical modelling is essential to generalize the results of these experiments and to derive the intrinsic parameters that can be used for predictions. However, a more thorough evaluation of theoretical models is hampered by limited experimental observations. In this study, experiments and image analysis methods were developed to provide a detailed spatial and temporal picture of how cell distributions evolve. These methods were used to quantify the migration and proliferation of skeletal cell types including MG63 and human bone marrow stromal cells (HBMSCs). The high level of detail with which the cell distributions were mapped enabled a precise assessment of the correspondence between experimental results and theoretical model predictions. This analysis revealed that the standard Fisher equation is appropriate for describing the migration behaviour of the HBMSC population, while for the MG63 cells a sharp front model is more appropriate. In combination with experiments, this type of mathematical model will prove useful in predicting cell ingrowth and improving strategies and control of skeletal tissue regeneration.

Simulating invasion with cellular automata: connecting cell-scale and population-scale properties

Interpretive and predictive tools are needed to assist in the understanding of cell invasion processes. Cell invasion involves cell motility and proliferation, and is central to many biological processes including developmental morphogenesis and tumor invasion. Experimental data can be collected across a wide range of scales, from the population scale to the individual cell scale. Standard continuum or discrete models used in isolation are insufficient to capture this wide range of data. We develop a discrete cellular automata model of invasion with experimentally motivated rules. The cellular automata algorithm is applied to a narrow two-dimensional lattice and simulations reveal the formation of invasion waves moving with constant speed. The simulation results are averaged in one dimension-these data are used to identify the time history of the leading edge to characterize the population-scale wave speed. This allows the relationship between the population-scale wave speed and the cell-scale parameters to be determined. This relationship is analogous to well-known continuum results for Fisher's equation. The cellular automata algorithm also produces individual cell trajectories within the invasion wave that are analogous to cell trajectories obtained with new experimental techniques. Our approach allows both the cell-scale and population-scale properties of invasion to be predicted in a way that is consistent with multiscale experimental data. Furthermore we suggest that the cellular automata algorithm can be used in conjunction with individual data to overcome limitations associated with identifying cell motility mechanisms using continuum models alone.

Travelling Waves of Attached and Detached Cells in a Wound-Healing Cell Migration Assay

During a wound-healing cell migration assay experiment, cells are observed to detach and undergo mitosis before reattaching as a pair of cells on the substrate. During experiments with mice 3T3 fibroblasts, cell detachment can be confined to the wavefront region or it can occur over the whole wave profile. A multi-species continuum approach to modelling a wound-healing assay is taken to account for this phenomenon. The first cell population is composed of attached motile cells, while the second population is composed of detached immotile cells undergoing mitosis and returning to the migrating population after successful division. The first model describes cell division occurring only in the wavefront region, while a second model describes cell division over the whole of the scrape wound. The first model reverts to the Fisher equation when the reattachment rate relative to the detachment rate is large, while the second case does not revert to the Fisher equation in any limit. The models yield travelling wave solutions. The minimum wave speed is slower than the minimum Fisher wave speed and its dependence on the cell detachment and reattachment rate parameters is analysed. Approximate travelling wave profiles of the two cell populations are determined asymptotically under certain parameter regimes.