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

Modeling the mechanosensitive collective migration of cells on the surface and the interior of morphing soft tissues

Cellular contractility, migration, and extracellular matrix (ECM) mechanics are critical for a wide range of biological processes including embryonic development, wound healing, tissue morphogenesis, and regeneration. Even though the distinct response of cells near the tissue periphery has been previously observed in cell-laden microtissues, including faster kinetics and more prominent cell-ECM interactions, there are currently no models that can fully combine coupled surface and bulk mechanics and kinetics to recapitulate the morphogenic response of these constructs. Mailand et al. (Biophys J 117(5):975-986, 2019) had shown the importance of active elastocapillarity in cell-laden microtissues, but modeling the distinct mechanosensitive migration of cells on the periphery and the interior of highly deforming tissues has not been possible thus far, especially in the presence of active elastocapillary effects. This paper presents a framework for understanding the interplay between cellular contractility, migration, and ECM mechanics in dynamically morphing soft tissues accounting for distinct cellular responses in the bulk and the surface of tissues. The major novelty of this approach is that it enables modeling the distinct migratory and contractile response of cells residing on the tissue surface and the bulk, where concurrently the morphing soft tissues undergo large deformations driven by cell contractility. Additionally, the simulation results capture the changes in shape and cell concentration for wounded and intact microtissues, enabling the interpretation of experimental data. The numerical procedure that accounts for mechanosensitive stress generation, large deformations, diffusive migration in the bulk and a distinct mechanism for diffusive migration on deforming surfaces is inspired from recent work on bulk and surface poroelasticity of hydrogels involving elastocapillary effects, but in this work, a two-field weak form is proposed and is able to alleviate numerical instabilities that were observed in the original method that utilized a three-field mixed finite element formulation.

Modelling count data with partial differential equation models in biology

Partial differential equation (PDE) models are often used to study biological phenomena involving movement-birth-death processes, including ecological population dynamics and the invasion of populations of biological cells. Count data, by definition, is non-negative, and count data relating to biological populations is often bounded above by some carrying capacity that arises through biological competition for space or nutrients. Parameter estimation, parameter identifiability, and making model predictions usually involves working with a measurement error model that explicitly relating experimental measurements with the solution of a mathematical model. In many biological applications, a typical approach is to assume the data are normally distributed about the solution of the mathematical model. Despite the widespread use of the standard additive Gaussian measurement error model, the assumptions inherent in this approach are rarely explicitly considered or compared with other options. Here, we interpret scratch assay data, involving migration, proliferation and delays in a population of cancer cells using a reaction-diffusion PDE model. We consider relating experimental measurements to the PDE solution using a standard additive Gaussian measurement error model alongside a comparison to a more biologically realistic binomial measurement error model. While estimates of model parameters are relatively insensitive to the choice of measurement error model, model predictions for data realisations are very sensitive. The standard additive Gaussian measurement error model leads to biologically inconsistent predictions, such as negative counts and counts that exceed the carrying capacity across a relatively large spatial region within the experiment. Furthermore, the standard additive Gaussian measurement error model requires estimating an additional parameter compared to the binomial measurement error model. In contrast, the binomial measurement error model leads to biologically plausible predictions and is simpler to implement. We provide open source Julia software on GitHub to replicate all calculations in this work, and we explain how to generalise our approach to deal with coupled PDE models with several dependent variables through a multinomial measurement error model, as well as pointing out other potential generalisations by linking our work with established practices in the field of generalised linear models.

Exploring Cell Migration Mechanisms in Cancer: From Wound Healing Assays to Cellular Automata Models

PURPOSE

Cell migration is a critical driver of metastatic tumor spread, contributing significantly to cancer-related mortality. Yet, our understanding of the underlying mechanisms remains incomplete.

METHODS

In this study, a wound healing assay was employed to investigate cancer cell migratory behavior, with the aim of utilizing migration as a biomarker for invasiveness. To gain a comprehensive understanding of this complex system, we developed a computational model based on cellular automata (CA) and rigorously calibrated and validated it using in vitro data, including both tumoral and non-tumoral cell lines. Harnessing this CA-based framework, extensive numerical experiments were conducted and supported by local and global sensitivity analyses in order to identify the key biological parameters governing this process.

RESULTS

Our analyses led to the formulation of a power law equation derived from just a few input parameters that accurately describes the governing mechanism of wound healing. This groundbreaking research provides a powerful tool for the pharmaceutical industry. In fact, this approach proves invaluable for the discovery of novel compounds aimed at disrupting cell migration, assessing the efficacy of prospective drugs designed to impede cancer invasion, and evaluating the immune system's responses.

Semi-autonomous wound invasion via matrix-deposited, haptotactic cues

Proper wound healing relies on invasion of fibroblasts via directed migration. While the related experimental and mathematical modeling literature has mainly focused on cell migration directed by soluble cues (chemotaxis), there is ample evidence that fibroblast migration is also directed by insoluble, matrix-bound cues (haptotaxis). Furthermore, numerous studies indicate that fibronectin (FN), a haptotactic ligand for fibroblasts, is present and dynamic in the provisional matrix throughout the proliferative phase of wound healing. In the present work, we show the plausibility of a hypothesis that fibroblasts themselves form and maintain haptotactic gradients in a semi-autonomous fashion. As a precursor to this, we examine the positive control scenario where FN is pre-deposited in the wound matrix, and fibroblasts maintain haptotaxis by removing FN at an appropriate rate. After developing conceptual and quantitative understanding of this scenario, we consider two cases in which fibroblasts activate the latent form of a matrix-loaded cytokine, TGFβ, which upregulates the fibroblasts' own secretion of FN. In the first of these, the latent cytokine is pre-patterned and released by the fibroblasts. In the second, fibroblasts in the wound produce the latent TGFβ, with the presence of the wound providing the only instruction. In all cases, wound invasion is more effective than a negative control model with haptotaxis disabled; however, there is a trade-off between the degree of fibroblast autonomy and the rate of invasion.

Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data

Reaction-diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates; however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models' performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k-means clustering to predict the number of subpopulations based on the recovered distributions.

Identification of lactylation related model to predict prognostic, tumor infiltrating immunocytes and response of immunotherapy in gastric cancer

Background

The epigenetic regulatory chemical lactate is a product of glycolysis. It can regulate gene expression through histone lactylation, thereby promoting tumor proliferation, metastasis, and immunosuppression.

Methods

In this study, a lactylation-related model for gastric cancer (GC) was constructed, and its relationships to prognosis, immune cell infiltration, and immunotherapy were investigated. By contrasting normal tissues and tumor tissues, four lactylation-related pathways that were substantially expressed in GC tissues were found in the GSEA database. Six lactylation-related genes were screened for bioinformatic analysis. The GC data sets from the TCGA and GEO databases were downloaded and integrated to perform cluster analysis, and the lactylation related model was constructed by secondary clustering.

Results

The fingding demonstrated that the lactylation score has a strong correlation with the overall survival rate from GC and the progression of GC. Mechanistic experiments showed that abundant immune cell infiltration (macrophages showed the highest degree of infiltration) and increased genetic instability are traits of high lactylation scores. Immune checkpoint inhibitors (ICIs) demonstrated a reduced response rate in GC with high lactylation scores. At the same time, tumors with high lactylation scores had high Tumor Immune Dysfunction and Exclusion scores, which means that they had a higher risk of immune evasion and dysfunction.

Discussion

These findings indicate that the lactylation score can be used to predict the malignant progression and immune evasion of GC. This model also can guide the treatment response to ICIs of GC. The constructed model of the lactate gene is also expected to become a potential therapeutic target for GC and diagnostic marker.

How quickly does a wound heal? Bayesian calibration of a mathematical model of venous leg ulcer healing

Chronic wounds, such as venous leg ulcers, are difficult to treat and can reduce the quality of life for patients. Clinical trials have been conducted to identify the most effective venous leg ulcer treatments and the clinical factors that may indicate whether a wound will successfully heal. More recently, mathematical modelling has been used to gain insight into biological factors that may affect treatment success but are difficult to measure clinically, such as the rate of oxygen flow into wounded tissue. In this work, we calibrate an existing mathematical model using a Bayesian approach with clinical data for individual patients to explore which clinical factors may impact the rate of wound healing for individuals. Although the model describes group-level behaviour well, it is not able to capture individual-level responses in all cases. From the individual-level analysis, we propose distributions for coefficients of clinical factors in a linear regression model, but ultimately find that it is difficult to draw conclusions about which factors lead to faster wound healing based on the existing model and data. This work highlights the challenges of using Bayesian methods to calibrate partial differential equation models to individual patient clinical data. However, the methods used in this work may be modified and extended to calibrate spatiotemporal mathematical models to multiple data sets, such as clinical trials with several patients, to extract additional information from the model and answer outstanding biological questions.

A Model for Cell Proliferation in a Developing Organism

In mathematical biology, there is a great deal of interest in producing continuum models by scaling discrete agent-based models governed by local stochastic rules. We discuss a particular example of this approach: a model for the proliferation of neural crest cells that can help us understand the development of Hirschprung's disease, a potentially-fatal condition in which the enteric nervous system of a new-born child does not extend all the way through the intestine and colon. Our starting point is a discrete-state, continuous-time Markov chain model proposed by Hywood et al. (2013a) for the location of the neural crest cells that make up the enteric nervous system. Hywood et al. (2013a) scaled their model to derive an approximate second order partial differential equation describing how the limiting expected number of neural crest cells evolve in space and time. In contrast, we exploit the relationship between the above-mentioned Markov chain model and the well-known Yule-Furry process to derive the exact form of the scaled version of the process. Furthermore, we provide expressions for other features of the domain agent occupancy process, such as the variance of the marginal occupancy at a particular site, the distribution of the number of agents that are yet to reach a given site and a stochastic description of the process itself.

Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework

Understanding whether a population will survive or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction–diffusion equations, where migration is usually represented as a linear diffusion term, and birth–death is represented with a nonlinear source term. While linear diffusion is most commonly employed to study migration, there are several limitations of this approach, such as the inability of linear diffusion-based models to predict a well-defined population front. One way to overcome this is to generalize the constant diffusivity, D, to a nonlinear diffusivity function D(C), where C>0 is the population density. While the choice of D(C) affects long-term survival or extinction of a bistable population, working solely in a continuum framework makes it difficult to understand how the choice of D(C) affects survival or extinction. We address this question by working with a discrete simulation model that is easy to interpret. This approach provides clear insight into how the choice of D(C) either encourages or suppresses population extinction relative to the classical linear diffusion model.

Immunomodulatory Efficacy-Mediated Anti-HCV and Anti-HBV Potential of Kefir Grains; Unveiling the In Vitro Antibacterial, Antifungal, and Wound Healing Activities

The utilization of fermented foods with health-promoting properties is becoming more popular around the world. Consequently, kefir, a fermented milk beverage made from kefir grains, was shown in numerous studies to be a probiotic product providing significant health benefits. Herein, we assessed the antibacterial and antifungal potential of kefir against a variety of pathogenic bacteria and fungi. This study also showed the effectiveness of kefir in healing wounds in human gastric epithelial cells (GES-1) by (80.78%) compared with control (55.75%) within 48 h. The quantitative polymerase chain reaction (qPCR) results of kefir-treated HCV- or HBV- infected cells found that 200 µg/mL of kefir can eliminate 92.36% of HCV and 75.71% of HBV relative to the untreated infected cells, whereas 800 µg/mL (the highest concentration) completely eradicated HCV and HBV. Moreover, the estimated IC₅₀ values of kefir, at which HCV and HBV were eradicated by 50%, were 63.84 ± 5.81 µg/mL and 224.02 ± 14.36 µg/mL, correspondingly. Kefir can significantly suppress the elevation of TNF-α and upregulate IL-10 and INF-γ in both treated HCV- and HBV-infected cells. High-performance liquid chromatography (HPLC) and gas chromatography-mass spectrometry (GC-MS) analysis of kefir revealed the presence of numerous active metabolites which mainly contribute to the antimicrobial, antiviral, and immunomodulatory activities. This study demonstrated, for the first time, the anti-HBV efficacy of kefir while also illustrating the immunomodulatory impact in the treated HBV-infected cells. Accordingly, kefir represents a potent antiviral agent against both viral hepatitis C and B, as well as having antimicrobial and wound healing potential.

Lung adenocarcinoma-derived vWF promotes tumor metastasis by regulating PHKG1-mediated glycogen metabolism

Tumor metastasis is a series of complicated biological events. Hematogenous metastasis mediated by von Willebrand factor (vWF) is critical in tumor metastasis. However, the source of vWF and its role in tumor metastasis are controversial, and the further mechanism involved in mediating tumor metastasis is still unclear. In this study, we first demonstrated that lung adenocarcinoma cells could express vWF de novo and promotes tumor metastasis. Through the analysis of transcriptome sequencing, metastasis promotion effect of vWF may be related to phosphorylase kinase subunit G1 (PHKG1), a catalytic subtype of phosphorylase kinase PhK. PHKG1 was highly expressed in lung adenocarcinoma patients and led to poor prognosis. Further experiments found that lung adenocarcinoma-derived vWF induced the up-regulation of PHKG1 through the PI3K/AKT pathway to promote glycogenolysis. Glycogen was funneled into glycolysis, leading to increased metastasis. Tumor metastasis assayed in vitro and in vivo showed that knockdown of PHKG1 or synergistic injection of phosphorylase inhibition based on the overexpression of vWF could inhibit metastasis. In summary, our research proved that lung adenocarcinoma-derived vWF may mediate tumor metastasis by regulating PHKG1 to promote glycogen metabolism, and suggested potential targets for inhibition of lung adenocarcinoma metastasis.

A 3D Mathematical Model of Coupled Stem Cell-Nutrient Dynamics in Myocardial Regeneration Therapy

Stem cell therapy is a promising treatment for the regeneration of myocardial tissue injured by an ischemic event. Mathematical modeling of myocardial regeneration via stem cell therapy is a challenging task, since the mechanisms underlying the processes involved in the treatment are not yet fully understood. Many aspects must be accounted for, such as the spread of stem cells and nutrients, chemoattraction, cell proliferation, stages of cell maturation, differentiation, angiogenesis, stochastic effects, just to name a few. In this paper we propose a 3D mathematical model with a free boundary that aims to provide a qualitative description of some main aspects of the stem cell regenerative therapy in a simplified scenario. The paper mainly focuses on the description of the shrinking of the necrotic core during treatment. The stem cell and nutrients dynamics are described through coupled reaction-diffusion problems. Proliferation, chemoattraction, tissue regeneration and nutrient consumption are included in the model.

PAR1 and PAR4 exert opposite effects on tumor growth and metastasis of esophageal squamous cell carcinoma via STAT3 and NF-κB signaling pathways

BACKGROUND

Esophageal carcinogenesis is a multifactorial process in which genetic and environmental factors interact to activate intracellular signals, leading to the uncontrolled survival and growth of esophageal squamous cell carcinoma (ESCC) cells. The intracellular pathways of ESCC cells could be regulated by proteinase activated-receptors (PARs), which are comprised of four receptors (i.e., PAR-1, PAR-2, PAR-3, and PAR-4). Therefore, the function and possible mechanism of PAR1 and PAR4 in the progression of ECSS were explored in our study.

METHODS

First, we detected the expression levels of PAR1 and PAR4 in 27 cases of ESCC specimens and cell lines by RT-qPCR, IHC and western blot. Meanwhile, the correlation between PAR1/PAR4 expression levels, clinicopathological characteristics, and disease free survival was analyzed. Then, we constructed PAR1/PAR4 knockdown cell models and investigated the role of PAR1/PAR4 knockdown on the proliferation, apoptosis, changes of calcium flow, and metastasis of ESCC cells via MTT, flow cytometry, transwell and wound healing assays in vitro. Further, an experimental metastasis model in vivo was established to explore the role of stable PAR1/PAR4 knockdown on the growth and metastasis of ESCC cells. Finally, the role of nSMase2 in the activation of NF-κB induced by PAR4 and the role of NF-κB and STAT3 signaling pathways in the PAR1/PAR4-mediated tumor promoting or suppressive functions were measured by immunoprecipitation, western blot and immunofluorescence assays.

RESULTS

First, the integrated results demonstrated the expression levels of PAR1 and PAR4 are inversely proportional in ESCC. PAR1 potently enhanced tumor growth and metastasis, while PAR4 had an inhibitory effect. Further, the co-activation of STAT3 and NF-κB was involved in the PAR1 activation-induced tumor promoting effect, while only NF-κB participated in the PAR4 activation-induced tumor inhibitory effect in ESCC. To be specific, FAK/PI3K/AKT/STAT3/NF-κB signaling mediated PAR1 activation-induced tumor promoting effect and nSMase2/MAPK/NF-κB signaling mediated PAR4 activation-induced tumor inhibitory effect.

CONCLUSIONS

Overall, the study has provided new insights into the potential implication of PAR1 and PAR4 in the pathogenesis of ESCC. Besides, FAK/PI3K/AKT/STAT3/NF-κB and nSMase2/MAPK/NF-κB pathways may be novel targets for regulating tumor growth and metastasis in ESCC patients.

Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using approximate Bayesian computation

We develop a parameter estimation method based on approximate Bayesian computation (ABC) for a stochastic cell invasion model using fluorescent cell cycle labelling with proliferation, migration and crowding effects. Previously, inference has been performed on a deterministic version of the model fitted to cell density data, and not all parameters were identifiable. Considering the stochastic model allows us to harness more features of experimental data, including cell trajectories and cell count data, which we show overcomes the parameter identifiability problem. We demonstrate that, while difficult to collect, cell trajectory data can provide more information about the parameters of the cell invasion model. To handle the intractability of the likelihood function of the stochastic model, we use an efficient ABC algorithm based on sequential Monte Carlo. Rcpp and MATLAB implementations of the simulation model and ABC algorithm used in this study are available at https://github.com/michaelcarr-stats/FUCCI.

Model-based data analysis of tissue growth in thin 3D printed scaffolds

Tissue growth in three-dimensional (3D) printed scaffolds enables exploration and control of cell behaviour in more biologically realistic geometries than that allowed by traditional 2D cell culture. Cell proliferation and migration in these experiments have yet to be explicitly characterised, limiting the ability of experimentalists to determine the effects of various experimental conditions, such as scaffold geometry, on cell behaviour. We consider tissue growth by osteoblastic cells in melt electro-written scaffolds that comprise thin square pores with sizes that were deliberately increased between experiments. We collect highly detailed temporal measurements of the average cell density, tissue coverage, and tissue geometry. To quantify tissue growth in terms of the underlying cell proliferation and migration processes, we introduce and calibrate a mechanistic mathematical model based on the Porous-Fisher reaction-diffusion equation. Parameter estimates and uncertainty quantification through profile likelihood analysis reveal consistency in the rate of cell proliferation and steady-state cell density between pore sizes. This analysis also serves as an important model verification tool: while the use of reaction-diffusion models in biology is widespread, the appropriateness of these models to describe tissue growth in 3D scaffolds has yet to be explored. We find that the Porous-Fisher model is able to capture features relating to the cell density and tissue coverage, but is not able to capture geometric features relating to the circularity of the tissue interface. Our analysis identifies two distinct stages of tissue growth, suggests several areas for model refinement, and provides guidance for future experimental work that explores tissue growth in 3D printed scaffolds.

Mathematical Modeling Can Advance Wound Healing Research

Significance: For over 30 years, there has been sustained interest in the development of mathematical models for investigating the complex mechanisms underlying each stage of the wound healing process. Despite the immense associated challenges, such models have helped usher in a paradigm shift in wound healing research. Recent Advances: In this article, we review contributions in the field that span epidermal, dermal, and corneal wound healing, and treatments of nonhealing wounds. The recent influence of mathematical models on biological experiments is detailed, with a focus on wound healing assays and fibroblast-populated collagen lattices. Critical Issues: We provide an overview of the field of mathematical modeling of wound healing, highlighting key advances made in recent decades, and discuss how such models have contributed to the development of improved treatment strategies and/or an enhanced understanding of the tightly regulated steps that comprise the healing process. Future Directions: We detail some of the open problems in the field that could be addressed through a combination of theoretical and/or experimental approaches. To move the field forward, we need to have a common language between scientists to facilitate cross-collaboration, which we hope this review can support by highlighting progress to date.

A novel mathematical model of heterogeneous cell proliferation

We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two cellular processes, asymmetric cell division and induced switching between proliferative states, which are important determinants for the heterogeneity of a cell population. As motivation for our model we provide experimental data that illustrate the induced-switching process. Our model consists of a system of two coupled delay differential equations with distributed time delays and the cell densities as functions of time. The distributed delays are bounded and allow for the choice of delay kernel. We analyse the model and prove the nonnegativity and boundedness of solutions, the existence and uniqueness of solutions, and the local stability characteristics of the equilibrium points. We find that the parameters for induced switching are bifurcation parameters and therefore determine the long-term behaviour of the model. Numerical simulations illustrate and support the theoretical findings, and demonstrate the primary importance of transient dynamics for understanding the evolution of many experimental cell populations.

Modelling cell guidance and curvature control in evolving biological tissues

Tissue geometry is an important influence on the evolution of many biological tissues. The local curvature of an evolving tissue induces tissue crowding or spreading, which leads to differential tissue growth rates, and to changes in cellular tension, which can influence cell behaviour. Here, we investigate how directed cell motion interacts with curvature control in evolving biological tissues. Directed cell motion is involved in the generation of angled tissue growth and anisotropic tissue material properties, such as tissue fibre orientation. We develop a new cell-based mathematical model of tissue growth that includes both curvature control and cell guidance mechanisms to investigate their interplay. The model is based on conservation principles applied to the density of tissue synthesising cells at or near the tissue's moving boundary. The resulting mathematical model is a partial differential equation for cell density on a moving boundary, which is solved numerically using a hybrid front-tracking method called the cell-based particle method. The inclusion of directed cell motion allows us to model new types of biological growth, where tangential cell motion is important for the evolution of the interface, or for the generation of anisotropic tissue properties. We illustrate such situations by applying the model to simulate both the resorption and infilling components of the bone remodelling process, and to simulate root hair growth. We also provide user-friendly MATLAB code to implement the algorithms.

Invading and Receding Sharp-Fronted Travelling Waves

Biological invasion, whereby populations of motile and proliferative individuals lead to moving fronts that invade vacant regions, is routinely studied using partial differential equation models based upon the classical Fisher-KPP equation. While the Fisher-KPP model and extensions have been successfully used to model a range of invasive phenomena, including ecological and cellular invasion, an often-overlooked limitation of the Fisher-KPP model is that it cannot be used to model biological recession where the spatial extent of the population decreases with time. In this work, we study the Fisher-Stefan model, which is a generalisation of the Fisher-KPP model obtained by reformulating the Fisher-KPP model as a moving boundary problem. The nondimensional Fisher-Stefan model involves just one parameter, [Formula: see text], which relates the shape of the density front at the moving boundary to the speed of the associated travelling wave, c. Using numerical simulation, phase plane and perturbation analysis, we construct approximate solutions of the Fisher-Stefan model for both slowly invading and receding travelling waves, as well as for rapidly receding travelling waves. These approximations allow us to determine the relationship between c and [Formula: see text] so that commonly reported experimental estimates of c can be used to provide estimates of the unknown parameter [Formula: see text]. Interestingly, when we reinterpret the Fisher-KPP model as a moving boundary problem, many overlooked features of the classical Fisher-KPP phase plane take on a new interpretation since travelling waves solutions with [Formula: see text] are normally disregarded. This means that our analysis of the Fisher-Stefan model has both practical value and an inherent mathematical value.

Design, Synthesis and Biological Evaluation of Dimethyl Cardamonin (DMC) Derivatives as P-glycoprotein-mediated Multidrug Resistance Reversal Agents

Background:

P-glycoprotein (P-gp) has been regarded as an important factor in the multidrug resistance (MDR) of tumor cells within the last decade, which can be solved by inhibiting Pgp to reverse MDR. Thus, it is an effective strategy to develop inhibitor of P-gp.

Objective:

In this study, the synthesis of a series of derivatives had been carried out by bioisosterism design on the basis of Dimethyl Cardamonin (DMC). Subsequently, we evaluated their reversal activities as potential P-glycoprotein (P-gp)-mediated Multidrug Resistance (MDR) agents.

Methods:

Dimethyl cardamonin derivatives were synthesized from acetophenones and the corresponding benzaldehydes in the presence of 40% KOH by Claisen-Schmidt reaction. Their cytotoxicity and reversal activities in vitro were assessed with MTT. Moreover, the compound B4 was evaluated by Doxorubicin (DOX) accumulation, Western blot and wound-healing assays deeply.

Results and Conclusion:

The results showed that compounds B2, B4 and B6 had the potency of MDR reversers with little intrinsic cytotoxicity. Meanwhile, these compounds also demonstrated the capability to inhibit MCF-7 and MCF-7/DOX cells migration. Besides, the most compound B4 was selected for further study, which promoted the accumulation of DOX in MCF-7/DOX cells and inhibited the expressionof P-gp at protein levels.

Conclusion:

The above findings may provide new insights for the research and development of Pgp- mediated MDR reversal agents.

Scratch assay microscopy: A reaction-diffusion equation approach for common instruments and data

Scratch assay is an easy and widely used "in vitro" technique to study cell migration and proliferation. In this work we focus on its modelling and on the capability to distinguish between these two phenomena that the simpler and common models are not able to disentangle. We adapted a model based on reaction-diffusion equation for being used with common microscopy instruments/data and therefore taking place in the gap between simpler modelling approaches and complex ones. An optimized image analysis pipeline and numerical least-squares fit provide estimates of the scratch proliferation and diffusion coefficients l and D. This work is intended as a first of a series in which the model is tested and its robustness and reproducibility are evaluated. Test samples were NIH3T3 cells scratch assays with proliferation and migration stimulated by varying the foetal bovine serum amount in the culture medium (10%, 7.5%, 5% and 2.5%). Results demonstrate, notwithstanding an expected l-D anticorrelation, the model capability to disentangle them. The 7.5% serum treatment can be identified as the model sensitivity limit. Treat-control l and D variations showed an intra-experiment reproducibility (∼±0.05∕h and ∼±200μm²∕h respectively) consistent with single fit typical uncertainties (∼±0.02∕h and ∼±300μm²∕h respectively).

Cell proliferation and migration explain pore bridging dynamics in 3D printed scaffolds of different pore size

Tissue growth in bioscaffolds is influenced significantly by pore geometry, but how this geometric dependence emerges from dynamic cellular processes such as cell proliferation and cell migration remains poorly understood. Here we investigate the influence of pore size on the time required to bridge pores in thin 3D-printed scaffolds. Experimentally, new tissue infills the pores continually from their perimeter under strong curvature control, which leads the tissue front to round off with time. Despite the varied shapes assumed by the tissue during this evolution, we find that time to bridge a pore simply increases linearly with the overall pore size. To disentangle the biological influence of cell behaviour and the mechanistic influence of geometry in this experimental observation, we propose a simple reaction-diffusion model of tissue growth based on Porous-Fisher invasion of cells into the pores. First, this model provides a good qualitative representation of the evolution of the tissue; new tissue in the model grows at an effective rate that depends on the local curvature of the tissue substrate. Second, the model suggests that a linear dependence of bridging time with pore size arises due to geometric reasons alone, not to differences in cell behaviours across pores of different sizes. Our analysis suggests that tissue growth dynamics in these experimental constructs is dominated by mechanistic crowding effects that influence collective cell proliferation and migration processes, and that can be predicted by simple reaction-diffusion models of cells that have robust, consistent behaviours.

A multiphase model of growth factor-regulated atherosclerotic cap formation

Atherosclerosis is characterised by the growth of fatty plaques in the inner artery wall. In mature plaques, vascular smooth muscle cells (SMCs) are recruited from adjacent tissue to deposit a collagenous cap over the fatty plaque core. This cap isolates the thrombogenic plaque content from the bloodstream and prevents the clotting cascade that leads to myocardial infarction or stroke. Despite the protective role of the cap, the mechanisms that regulate cap formation and maintenance are not well understood. It remains unclear why some caps become stable, while others become vulnerable to rupture. We develop a multiphase PDE model with non-standard boundary conditions to investigate collagen cap formation by SMCs in response to diffusible growth factor signals from the endothelium. Platelet-derived growth factor stimulates SMC migration, proliferation and collagen degradation, while transforming growth factor (TGF)-[Formula: see text] stimulates SMC collagen synthesis and inhibits collagen degradation. The model SMCs respond haptotactically to gradients in the collagen phase and have reduced rates of migration and proliferation in dense collagenous tissue. The model, which is parameterised using in vivo and in vitro experimental data, reproduces several observations from plaque growth in mice. Numerical and analytical results demonstrate that a stable cap can be formed by a relatively small SMC population and emphasise the critical role of TGF-[Formula: see text] in effective cap formation. These findings provide unique insight into the mechanisms that may lead to plaque destabilisation and rupture. This work represents an important step towards the development of a comprehensive in silico plaque model.

Identifying density-dependent interactions in collective cell behaviour

Scratch assays are routinely used to study collective cell behaviour in vitro. Typical experimental protocols do not vary the initial density of cells, and typical mathematical modelling approaches describe cell motility and proliferation based on assumptions of linear diffusion and logistic growth. Jin et al. (Jin et al. 2016 J. Theor. Biol. 390, 136-145 (doi:10.1016/j.jtbi.2015.10.040)) find that the behaviour of cells in scratch assays is density-dependent, and show that standard modelling approaches cannot simultaneously describe data initiated across a range of initial densities. To address this limitation, we calibrate an individual-based model to scratch assay data across a large range of initial densities. Our model allows proliferation, motility, and a direction bias to depend on interactions between neighbouring cells. By considering a hierarchy of models where we systematically and sequentially remove interactions, we perform model selection analysis to identify the minimum interactions required for the model to simultaneously describe data across all initial densities. The calibrated model is able to match the experimental data across all densities using a single parameter distribution, and captures details about the spatial structure of cells. Our results provide strong evidence to suggest that motility is density-dependent in these experiments. On the other hand, we do not see the effect of crowding on proliferation in these experiments. These results are significant as they are precisely the opposite of the assumptions in standard continuum models, such as the Fisher-Kolmogorov equation and its generalizations.

Examining Go-or-Grow Using Fluorescent Cell-Cycle Indicators and Cell-Cycle-Inhibiting Drugs

The go-or-grow hypothesis states that adherent cells undergo reversible phenotype switching between migratory and proliferative states, with cells in the migratory state being more motile than cells in the proliferative state. Here, we examine go-or-grow in two-dimensional in vitro assays using melanoma cells with fluorescent cell-cycle indicators and cell-cycle-inhibiting drugs. We analyze the experimental data using single-cell tracking to calculate mean diffusivities and compare motility between cells in different cell-cycle phases and in cell-cycle arrest. Unequivocally, our analysis does not support the go-or-grow hypothesis. We present clear evidence that cell motility is independent of the cell-cycle phase and that nonproliferative arrested cells have the same motility as cycling cells.

Progress in Animal Models of Pancreatic Ductal Adenocarcinoma

As a common gastrointestinal tumor, the incidence of pancreatic cancer has been increasing in recent years. The disease shows multi-gene, multi-step complex evolution from occurrence to dissemination. Furthermore, pancreatic cancer has an insidious onset and an extremely poor prognosis, so it is difficult to obtain cinical specimens at different stages of the disease, and it is, therefore, difficult to observe tumorigenesis and tumor development in patients with pancreatic cancer. At present, no standard protocols stipulate clinical treatment of pancreatic cancer, and the benefit rate of new targeted therapies is low. For this reason, a well-established preclinical model of pancreatic cancer must be established to allow further exploration of the occurrence, development, invasion, and metastasis mechanism of pancreatic cancer, as well as to facilitate research into new therapeutic targets. A large number of animal models of pancreatic cancer are currently available, including a cancer cell line-based xenograft, a patient-derived xenograft, several mouse models (including transgenic mice), and organoid models. These models have their own characteristics, but they still cannot perfectly predict the clinical outcome of the new treatment. In this paper, we present the distinctive features of the currently popular pancreatic cancer models, and discuss their preparation methods, clinical relations, scientific purposes and limitations.

PD-L1 Expression Is Regulated By NF-κB During EMT Signaling In Gastric Carcinoma

Purpose

The aim of this study was to investigate the influence of epithelial-mesenchymal transition (EMT) occurring in gastric carcinoma cells and the involvement of programmed death ligand 1 (PD-L1) expression in tumor cells that undergo EMT. The mechanisms underlying PD-L1 expression during EMT in gastric carcinoma cells were also explored.

Methods

The capacities of migration and invasion were tested by cell scratch-wound assay and transwell chamber assay. PD-L1 expression by SGC7901 cell line and related mechanism were measured by Western blot and QRT-PCR.

Results

Treating with TGF-β1 promotes the motility of SGC7901 and PD-L1 expression in vitro, while activating the NF-κB signal pathway.

Conclusion

EMT increases the capacities of migration and invasion in gastric cancer cells, which resulted in up-regulation of PD-L1 expression via a mechanism that is dependent on NF-κB activation.

Connecting gene expression to cellular movement: A transport model for cell migration

The adhesion properties and the mobility of biological cells play key roles in the propagation of cancer. These properties are expected to depend on intracellular processes and on the concentrations of chemicals inside the cell. While most existing reaction-diffusion models for cell migration consider that cell mobility and proliferation rate are constant or depend on an external diffusing species, they do not include the gene expression dynamics taking place in moving cells that affect cellular transport. In this work, we propose a multiscale model where mobility and proliferation depend explicitly on the cell's internal state. We focus more specifically on the case of cellular mobility in epithelial tissues. Wound-healing experiments have demonstrated that the loss of a key protein, E-cadherin, results in a significant increase in both mobility and invasiveness of epithelial cells, with dramatic consequences on cancer progression. We can reproduce the results of these experiments under various genetic conditions with a single set of parameters.

Accurate and efficient discretizations for stochastic models providing near agent-based spatial resolution at low computational cost

Understanding how cells proliferate, migrate and die in various environments is essential in determining how organisms develop and repair themselves. Continuum mathematical models, such as the logistic equation and the Fisher-Kolmogorov equation, can describe the global characteristics observed in commonly used cell biology assays, such as proliferation and scratch assays. However, these continuum models do not account for single-cell-level mechanics observed in high-throughput experiments. Mathematical modelling frameworks that represent individual cells, often called agent-based models, can successfully describe key single-cell-level features of these assays but are computationally infeasible when dealing with large populations. In this work, we propose an agent-based model with crowding effects that is computationally efficient and matches the logistic and Fisher-Kolmogorov equations in parameter regimes relevant to proliferation and scratch assays, respectively. This stochastic agent-based model allows multiple agents to be contained within compartments on an underlying lattice, thereby reducing the computational storage compared to existing agent-based models that allow one agent per site only. We propose a systematic method to determine a suitable compartment size. Implementing this compartment-based model with this compartment size provides a balance between computational storage, local resolution of agent behaviour and agreement with classical continuum descriptions.

Revisiting the Fisher-Kolmogorov-Petrovsky-Piskunov equation to interpret the spreading-extinction dichotomy

The Fisher-Kolmogorov-Petrovsky-Piskunov model, also known as the Fisher-KPP model, supports travelling wave solutions that are successfully used to model numerous invasive phenomena with applications in biology, ecology and combustion theory. However, there are certain phenomena that the Fisher-KPP model cannot replicate, such as the extinction of invasive populations. The Fisher-Stefan model is an adaptation of the Fisher-KPP model to include a moving boundary whose evolution is governed by a Stefan condition. The Fisher-Stefan model also supports travelling wave solutions; however, a key additional feature of the Fisher-Stefan model is that it is able to simulate population extinction, giving rise to a spreading-extinction dichotomy. In this work, we revisit travelling wave solutions of the Fisher-KPP model and show that these results provide new insight into travelling wave solutions of the Fisher-Stefan model and the spreading-extinction dichotomy. Using a combination of phase plane analysis, perturbation analysis and linearization, we establish a concrete relationship between travelling wave solutions of the Fisher-Stefan model and often-neglected travelling wave solutions of the Fisher-KPP model. Furthermore, we give closed-form approximate expressions for the shape of the travelling wave solutions of the Fisher-Stefan model in the limit of slow travelling wave speeds, c≪1.

Continuum descriptions of spatial spreading for heterogeneous cell populations: Theory and experiment

Variability in cell populations is frequently observed in both in vitro and in vivo settings. Intrinsic differences within populations of cells, such as differences in cell sizes or differences in rates of cell motility, can be present even within a population of cells from the same cell line. We refer to this variability as cell heterogeneity. Mathematical models of cell migration, for example, in the context of tumour growth and metastatic invasion, often account for both undirected (random) migration and directed migration that is mediated by cell-to-cell contacts and cell-to-cell adhesion. A key feature of standard models is that they often assume that the population is composed of identical cells with constant properties. This leads to relatively simple single-species homogeneous models that neglect the role of heterogeneity. In this work, we use a continuum modelling approach to explore the role of heterogeneity in spatial spreading of cell populations. We employ a three-species heterogeneous model of cell motility that explicitly incorporates different types of experimentally-motivated heterogeneity in cell sizes: (i) monotonically decreasing; (ii) uniform; (iii) non-monotonic; and (iv) monotonically increasing distributions of cell size. Comparing the density profiles generated by the three-species heterogeneous model with density profiles predicted by a more standard single-species homogeneous model reveals that when we are dealing with monotonically decreasing and uniform distributions a simple and computationally efficient single-species homogeneous model can be remarkably accurate in describing the evolution of a heterogeneous cell population. In contrast, we find that the simpler single-species homogeneous model performs relatively poorly when applied to non-monotonic and monotonically increasing distributions of cell sizes. Additional results for heterogeneity in parameters describing both undirected and directed cell migration are also considered, and we find that similar results apply.

Design, synthesis and biological evaluation of chalcones as reversers of P-glycoprotein-mediated multidrug resistance

Overexpression of P-glycoprotein (P-gp) is one of the major causes for multidrug resistance (MDR), which has become a major obstacle in cancer therapy. One hopeful approach to reverse the MDR is to develop inhibitors of P-gp in expression and/or function. Here, we designed and synthesized a series of chalcone derivatives as P-gp inhibitors and evaluated their potential reversal activities against MDR. Among them, the most active compound MY3 had little intrinsic cytotoxicity and showed the highest activity (RF = 50.19) in reversing DOX resistance in MCF-7/DOX cells. Further studies demonstrated that MY3 could increase intracellular accumulation of DOX and inhibit expression of P-gp at mRNA and protein levels. More importantly, MY3 significantly enhanced the efficacy of DOX against the tumor xenografts bearing MCF-7/DOX cells with the precondition of unchanged body weight. Therefore, MY3 might represent a promising lead to develop MDR reversal agents for cancer chemotherapy.

Colloidal Silver Induces Cytoskeleton Reorganization and E-Cadherin Recruitment at Cell-Cell Contacts in HaCaT Cells

Up until the first half of the 20th century, silver found significant employment in medical applications, particularly in the healing of open wounds, thanks to its antibacterial and antifungal properties. Wound repair is a complex and dynamic biological process regulated by several pathways that cooperate to restore tissue integrity and homeostasis. To facilitate healing, injuries need to be promptly treated. Recently, the interest in alternatives to antibiotics has been raised given the widespread phenomenon of antibiotic resistance. Among these alternatives, the use of silver appears to be a valid option, so a resurgence in its use has been recently observed. In particular, in contrast to ionic silver, colloidal silver, a suspension of metallic silver particles, shows antibacterial activity displaying less or no toxicity. However, the human health risks associated with exposure to silver nanoparticles (NP) appear to be conflicted, and some studies have suggested that it could be toxic in different cellular contexts. These potentially harmful effects of silver NP depend on various parameters including NP size, which commonly range from 1 to 100 nm. In this study, we analyzed the effect of a colloidal silver preparation composed of very small and homogeneous nanoparticles of 0.62 nm size, smaller than those previously tested. We found no adverse effect on the cell proliferation of HaCaT cells, even at high NP concentration. Time-lapse microscopy and indirect immunofluorescence experiments demonstrated that this preparation of colloidal silver strongly increased cell migration, re-modeled the cytoskeleton, and caused recruitment of E-cadherin at cell-cell junctions of human cultured keratinocytes.

A free boundary model of epithelial dynamics

In this work we analyse a one-dimensional, cell-based model of an epithelial sheet. In the model, cells interact with their nearest neighbouring cells and move deterministically. Cells also proliferate stochastically, with the rate of proliferation specified as a function of the cell length. This mechanical model of cell dynamics gives rise to a free boundary problem. We construct a corresponding continuum-limit description where the variables in the continuum limit description are expanded in powers of the small parameter 1/N, where N is the number of cells in the population. By carefully constructing the continuum limit description we obtain a free boundary partial differential equation description governing the density of the cells within the evolving domain, as well as a free boundary condition that governs the evolution of the domain. We show that care must be taken to arrive at a free boundary condition that conserves mass. By comparing averaged realisations of the cell-based model with the numerical solution of the free boundary partial differential equation, we show that the new mass-conserving boundary condition enables the coarse-grained partial differential equation model to provide very accurate predictions of the behaviour of the cell-based model, including both evolution of the cell density, and the position of the free boundary, across a range of interaction potentials and proliferation functions in the cell based model.

Extended live-tracking and quantitative characterization of wound healing and cell migration with SiR-Hoechst

Cell migration is essential to many life processes, including immune response, tissue repair, and cancer progression. A reliable quantitative characterization of the cell migration can therefore aid in the high throughput screening of drug efficacy in wound healing and cancer treatments. In this work, we report what we believe is the first use of SiR-Hoechst for extended live tracking and automated analysis of cell migration and wound healing. We showed through rigorous statistical comparisons that this far-red label does not affect migratory behavior. We observed excellent automated tracking of random cell migration, in which the motility parameters (speed, displacement, path length, directionality ratio, persistence time, and direction autocorrelation) obtained closely match those obtained from manual tracking. We also present an analysis framework to characterize the healing of a scratch wound from the perspective of single cells. The use of SiR-Hoechst is advantageous for the crowded environments in wound healing assays because as long as cell nuclei do not overlap, continuous tracking can be maintained even if there is cell-cell contact. In this paper, we report wound recovery based on the number of cells migrating into the wound over time, normalized by the initial cell count prior to the infliction of the wound. This normalized cell count approach is impervious to operator bias during the arbitration of wound edges and is also robust against variability that arises due to differences in the cell density of different samples. Additional wound healing characteristics were also defined based on the evolution of cell speed and directionality during healing. Not unexpected, the wound healing cells exhibited much higher tendency to maintain the same migratory direction in comparison to the randomly migrating cells. The use of SiR-Hoechst thus greatly simplified the automation of single cell and whole population analysis with high spatial and temporal resolution over extended periods of time.

A Bayesian Sequential Learning Framework to Parameterise Continuum Models of Melanoma Invasion into Human Skin

We present a novel framework to parameterise a mathematical model of cell invasion that describes how a population of melanoma cells invades into human skin tissue. Using simple experimental data extracted from complex experimental images, we estimate three model parameters: (i) the melanoma cell proliferation rate, [Formula: see text]; (ii) the melanoma cell diffusivity, D; and (iii) [Formula: see text], a constant that determines the rate that melanoma cells degrade the skin tissue. The Bayesian sequential learning framework involves a sequence of increasingly sophisticated experimental data from: (i) a spatially uniform cell proliferation assay; (ii) a two-dimensional circular barrier assay; and (iii) a three-dimensional invasion assay. The Bayesian sequential learning approach leads to well-defined parameter estimates. In contrast, taking a naive approach that attempts to estimate all parameters from a single set of images from the same experiment fails to produce meaningful results. Overall, our approach to inference is simple-to-implement, computationally efficient, and well suited for many cell biology phenomena that can be described by low-dimensional continuum models using ordinary differential equations and partial differential equations. We anticipate that this Bayesian sequential learning framework will be relevant in other biological contexts where it is challenging to extract detailed, quantitative biological measurements from experimental images and so we must rely on using relatively simple measurements from complex images.

A two-phase model of early fibrous cap formation in atherosclerosis

Atherosclerotic plaque growth is characterised by chronic, non-resolving inflammation that promotes the accumulation of cellular debris and extracellular fat in the inner artery wall. This material is highly thrombogenic, and plaque rupture can lead to the formation of blood clots that occlude major arteries and cause myocardial infarction or stroke. In advanced plaques, vascular smooth muscle cells (SMCs) are recruited from deeper in the artery wall to synthesise a cap of fibrous tissue that stabilises the plaque and sequesters the thrombogenic plaque content from the bloodstream. The fibrous cap provides crucial protection against the clinical consequences of atherosclerosis, but the mechanisms of cap formation are poorly understood. In particular, it is unclear why certain plaques become stable and robust while others become fragile and dangerously vulnerable to rupture. We develop a multiphase model with non-standard boundary conditions to investigate early fibrous cap formation in the atherosclerotic plaque. The model is parameterised using data from a range of in vitro and in vivo studies, and includes highly nonlinear mechanisms of SMC proliferation and migration in response to an endothelium-derived chemical signal. We demonstrate that the model SMC population naturally evolves towards a steady-state, and predict a rate of cap formation and a final plaque SMC content consistent with experimental observations in mice. Parameter sensitivity simulations show that SMC proliferation makes a limited contribution to cap formation, and demonstrate that stable cap formation relies primarily on a critical balance between the rates of SMC recruitment to the plaque, chemotactic SMC migration within the plaque and SMC loss by apoptosis or phenotype change. This model represents the first detailed in silico study of fibrous cap formation in atherosclerosis, and establishes a multiphase modelling framework that can be readily extended to investigate many other aspects of plaque development.

The impact of experimental design choices on parameter inference for models of growing cell colonies

To better understand development, repair and disease progression, it is useful to quantify the behaviour of proliferative and motile cell populations as they grow and expand to fill their local environment. Inferring parameters associated with mechanistic models of cell colony growth using quantitative data collected from carefully designed experiments provides a natural means to elucidate the relative contributions of various processes to the growth of the colony. In this work, we explore how experimental design impacts our ability to infer parameters for simple models of the growth of proliferative and motile cell populations. We adopt a Bayesian approach, which allows us to characterize the uncertainty associated with estimates of the model parameters. Our results suggest that experimental designs that incorporate initial spatial heterogeneities in cell positions facilitate parameter inference without the requirement of cell tracking, while designs that involve uniform initial placement of cells require cell tracking for accurate parameter inference. As cell tracking is an experimental bottleneck in many studies of this type, our recommendations for experimental design provide for significant potential time and cost savings in the analysis of cell colony growth.

INVESTIGATION OF A STRUCTURED FISHER'S EQUATION WITH APPLICATIONS IN BIOCHEMISTRY

Recent biological research has sought to understand how biochemical signaling pathways, such as the mitogen-activated protein kinase (MAPK) family, influence the migration of a population of cells during wound healing. Fisher's Equation has been used extensively to model experimental wound healing assays due to its simple nature and known traveling wave solutions. This partial differential equation with independent variables of time and space cannot account for the effects of biochemical activity on wound healing, however. To this end, we derive a structured Fisher's Equation with independent variables of time, space, and biochemical pathway activity level and prove the existence of a self-similar traveling wave solution to this equation. We exhibit that these methods also apply to a general structured reaction-diffusion equation and a chemotaxis equation. We also consider a more complicated model with different phenotypes based on MAPK activation and numerically investigate how various temporal patterns of biochemical activity can lead to increased and decreased rates of population migration.

PTBP3 contributes to the metastasis of gastric cancer by mediating CAV1 alternative splicing

Polypyrimidine tract-binding protein 3 (PTBP3) is an essential RNA-binding protein with roles in RNA splicing, 3' end processing and translation. Although increasing evidence implicates PTBP3 in several cancers, its role in gastric cancer metastasis remains poorly explored. In this study, we found that PTBP3 was upregulated in the gastric cancer tissues of patients with lymph node metastasis. Patients with high PTBP3 expression levels had significantly shorter survival than those with low PTBP3 expression. Overexpression/knockdown of PTBP3 expression had no effect on proliferation, whereas it regulated migration and invasion in vitro. In addition, when a mouse xenotransplant model of MKN45 was established, knockdown of PTBP3 in MKN45 cells caused the formation of tumours that were smaller in size than their counterparts, with suppression of tumour lymphangiogenesis and metastasis to regional lymph nodes. Furthermore, we identified caveolin 1 (CAV1) as a downstream target of PTBP3. RNA immunoprecipitation (RIP) assays and dual-luciferase reporter gene assays indicated that PTBP3 interacted with the CU-rich region of the CAV1 gene to downregulate CAV1α expression. Knockdown of CAV1α abrogated the reduction of FAK and Src induced by PTBP3 knockdown. In summary, our findings provide experimental evidence that PTBP3 may function as a metastatic gene in gastric cancer by regulating CAV1 through alternative splicing.

Distinguishing cell shoving mechanisms

Motivated by in vitro time–lapse images of ovarian cancer spheroids inducing mesothelial cell clearance, the traditional agent–based model of cell migration, based on simple volume exclusion, was extended to include the possibility that a cell seeking to move into an occupied location may push the resident cell, and any cells neighbouring it, out of the way to occupy that location. In traditional discrete models of motile cells with volume exclusion such a move would be aborted. We introduce a new shoving mechanism which allows cells to choose the direction to shove cells that expends the least amount of shoving effort (to account for the likely resistance of cells to being pushed). We call this motility rule ‘smart shoving’. We examine whether agent–based simulations of different shoving mechanisms can be distinguished on the basis of single realisations and averages over many realisations. We emphasise the difficulty in distinguishing cell mechanisms from cellular automata simulations based on snap–shots of cell distributions, site–occupancy averages and the evolution of the number of cells of each species averaged over many realisations. This difficulty suggests the need for higher resolution cell tracking.

Extended logistic growth model for heterogeneous populations

Cell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

3D TECA hydrogel reduces cellular senescence and enhances fibroblasts migration in wound healing

This study was designed to investigate the effect of 3D TECA hydrogel on the inflammatory-induced senescence marker, and to assess the influence of the gel on the periodontal ligament fibroblasts (PDLFs) migration in wound healing in vitro. PDLFs were cultured with 20 ng/ml TNF-α to induce inflammation in the presence and absence of 50 µM 3D TECA gel for 14 d. The gel effect on the senescence maker secretory associated-β-galactosidase (SA-β-gal) activity was measured by a histochemical staining. Chromatin condensation and DNA synthesis of the cells were assessed by 4′,6-diamidino-2-phenylindole and 5-ethynyl-2′-deoxyuridine fluorescent staining respectively. For evaluating fibroblasts migration, scratch wound healing assay and Pro-Plus Imaging software were used. The activity of senescence marker, SA-β-gal, was positive in the samples with TNF-α-induced inflammation. SA-β-gal percentage is suppressed (>65%, P < 0.05) in the treated cells with TECA gel as compared to the non-treated cells. Chromatin foci were obvious in the non-treated samples. DNA synthesis was markedly recognized by the fluorescent staining in the treated compared to non-treated cultures. Scratch wound test indicated that the cells migration rate was significantly higher (14.9 µm²/h, P < 0.05) in the treated versus (11 µm²/h) for control PDLFs. The new formula of 3D TECA suppresses the inflammatory-mediated cellular senescence and enhanced fibroblasts proliferation and migration. Therefore, 3D TECA may be used as an adjunct to accelerate repair and healing of periodontal tissues.

Linking biological and physical aging: Dynamical scaling of multicellular regeneration

The fight against biological aging (bio-aging) is long-standing, with the focus of intense research aimed at maintaining high rates of tissue regeneration to promote health and longevity. Nevertheless, there are overwhelming complexities associated with the quantitative analysis of aging. In this study, we sought to quantify bio-aging based on physical aging, by mapping instances of multicellular regeneration to the relaxation of physical systems. An experiment of delayed wound healing assays was devised to obtain delay-dependent healing data. The experiment confirmed the slowdown of healing events, which fitted dynamical scaling just as relaxation events do in physical aging. The scaling exponent, which describes the aging rate in physics, is here similarly proposed as an indicator of the deterioration rate of tissue-regenerative power. Parallel equation-based and cell-based simulations also revealed that asymmetric cell cycle-regulatory mechanisms under strong growth-inhibitory conditions predominantly control the critical slowdown of healing analogous to physical criticality. By establishing a direct link between physical aging and biological aging, we are able to estimate the aging rate of tissues and to achieve an integrated understanding of bio-aging mechanism which may improve the modulation of regeneration for clinical use.

Growth of adult spinal cord in knifefish: Development and parametrization of a distributed model

The study of indeterminate-growing organisms such as teleost fish presents a unique opportunity for improving our understanding of central nervous tissue growth during adulthood. Integrating the existing experimental data associated with this process into a theoretical framework through mathematical or computational modeling provides further research avenues through sensitivity analysis and optimization. While this type of approach has been used extensively in investigations of tumor growth, wound healing, and bone regeneration, the development of nervous tissue has been rarely studied within a modeling framework. To address this gap, the present work introduces a distributed model of spinal cord growth in the knifefish Apteronotus leptorhynchus, an established teleostean model of adult growth in the central nervous system. The proposed model incorporates two mechanisms, cell proliferation by active stem/progenitor cells and cell drift due to population pressure, both of which are subject to global constraints. A coupled reaction-diffusion equation approach was adopted to represent the densities of actively-proliferating and non-proliferating cells along the longitudinal axis of the spinal cord. Computer simulations using this model yielded biologically-feasible growth trajectories. Subsequent comparisons with whole-organism growth curves allowed the estimation of previously-unknown parameters, such as relative growth rates.