A Macroscopic Mathematical Model for Cell Migration Assays Using a Real-Time Cell Analysis

A Model for Membrane Degradation Using a Gelatin Invadopodia Assay

One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix metalloproteinases (MMPs), enzymes capable of degrading a type of collagen abundant in the basal membrane separating the epithelial tissue from the connective one. In this work, we employ a synergistic experimental and mathematical modelling approach to explore the invasion process of tumor cells. A mathematical model composed of reaction-diffusion equations describing the evolution of the tumor cells density on a gelatin substrate, MMPs enzymes concentration and the degradation of the gelatin is proposed. This is completed with a calibration strategy. We perform a sensitivity analysis and explore a parameter estimation technique both on synthetic and experimental data in order to find the optimal parameters that describe the in vitro experiments. A comparison between numerical and experimental solutions ends the work.

Generating Patient-Derived HCC Cell Lines Suitable for Predictive In Vitro and In Vivo Drug Screening by Orthotopic Transplantation

Hepatocellular carcinoma (HCC) results in high mortality due to ineffective systemic therapy. Human immortalized cell lines are commonly used to study anti-tumor effects in the context of new anti-tumor therapies and tumor biology. As immortalized cell lines have limited biological relevance and heterogeneity compared to primary cells, patient-derived tumor tissues, and corresponding immune cells are the gold standards for studying the complexity of individual tumor entities. However, culturing primary HCC cells has a low success rate. Here, we aimed to establish a reproducible approach to preserve the patient-derived liver cancer cells for in vitro and in vivo studies. The underlying study aimed to establish an in vitro pre-screening platform to test treatment options' effectivity and dosage, e.g., for new substances, autologous modified immune cells, or combined therapies in HCC. We initially employed 15 surgical resection specimens from patients with different HCC entities for isolation and preservation. The isolated liver cancer cells from four HCC-diagnosed patients were used for orthotopic transplantation into the healthy liver of immunodeficient mice, allowing them to grow for six months before human liver cancer cells were isolated and cultured. As a result, we generated and characterized four new primary-like liver cancer cell lines. Compared to immortalized HCC cell lines, freshly generated liver cancer cells displayed individual morphologies and heterogeneous protein-level characteristics. We assessed their ability to proliferate, migrate, form spheroids, and react to common medications compared to immortalized HCC cell lines. All four liver cancer cell lines exhibit strong migration and colony-forming characteristics in vitro, comparable to extensively investigated immortalized HCC cell lines. Moreover, the four etiological different liver cancer cell lines displayed differences in the response to 5-FU, Sorafenib, Axitinib, and interferon-alpha treatment, ranking from non-responders to responders depending on the applicated medication. In sum, we generated individual patient-derived liver cancer cell lines suitable for predictive in vitro drug screenings and for xenograft transplantations to realize the in vivo investigation of drug candidates. We overcame the low cultivation success rate of liver cancer cells derived from patients and analyzed their potential to serve a pre-clinical model.

The Mathematical modeling of Cancer growth and angiogenesis by an individual based interacting system

We present a mathematical model for the complex system for the growth of a solid tumor. The system embeds proliferation of cells depending on the surrounding oxygen field, hypoxia caused by insufficient oxygen when the tumor reaches a certain size, consequent VEGF release and angiogenic new vasculature growth, re-oxygenation of the tumor and subsequent tumor growth restart. Specifically cancerous cells are represented by individual units, interacting as proliferating particles of a solid body, oxygen, and VEGF are fields with a source and a sink, and new angiogenic vasculature is described by a network of growing curves. The model, as shown by numerical simulations, captures both the time-evolution of the tumor growth before and after angiogenesis and its spatial properties, with different distribution of proliferating and hypoxic cells in the external and deep layers of the tumor, and the spatial structure of the angiogenic network. The microscopic description of the growth opens the possibility of tuning the model to patient-specific scenarios.

YULINK regulates vascular formation in zebrafish and HUVECs

BACKGROUND

The distinct arterial and venous cell fates are dictated by a combination of various genetic factors which form diverse types of blood vessels such as arteries, veins, and capillaries. We report here that YULINK protein is involved in vasculogenesis, especially venous formation.

METHODS

In this manuscript, we employed gene knockdown, yeast two-hybrid, FLIM-FRET, immunoprecipitation, and various imaging technologies to investigate the role of YULINK gene in zebrafish and human umbilical vein endothelial cells (HUVECs).

RESULTS

Knockdown of YULINK during the arterial-venous developmental stage of zebrafish embryos led to the defective venous formation and abnormal vascular plexus formation. Knockdown of YULINK in HUVECs impaired their ability to undergo cell migration and differentiation into a capillary-like tube formation. In addition, the phosphorylated EPHB4 was decreased in YULINK knockdown HUVECs. Yeast two-hybrid, FLIM-FRET, immunoprecipitation, as well as imaging technologies showed that YULINK colocalized with endosome related proteins (EPS15, RAB33B or TICAM2) and markers (Clathrin and RHOB). VEGF-induced VEGFR2 internalization was also compromised in YULINK knockdown HUVECs, demonstrating to the involvement of YULINK.

CONCLUSION

This study suggests that YULINK regulates vasculogenesis, possibly through endocytosis in zebrafish and HUVECs.

Traveling Band Solutions in a System Modeling Hunting Cooperation

A classical Lotka–Volterra model with the logistical growth of prey-and-hunting cooperation in the functional response of predators to prey was extended by introducing advection terms, which included the velocities of animals. The effect of velocity on the kinetics of the problem was analyzed. In order to examine the band behavior of species over time, traveling wave solutions were introduced, and conditions for the coexistence of both populations and/or extinction were found. Numerical simulations illustrating the obtained results were performed.

Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips

The present work is inspired by the recent developments in laboratory experiments made on chips, where the culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis and takes into account the interactions among cell populations and the possibility of drug administration for drug testing effects. Our effort is devoted to the development of a simulation tool that is able to reproduce the chemotactic movement and the interactions between different cell species (immune and cancer cells) living in a microfluidic chip environment. The main issues faced in this work are the introduction of mass-preserving and positivity-preserving conditions, involving the balancing of incoming and outgoing fluxes passing through interfaces between 2D and 1D domains of the chip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2D and 1D domains.

Mathematical modelling of cell migration

The complexity of biological systems creates challenges for fully understanding their behaviour. This is particularly true for cell migration which requires the co-ordinated activity of hundreds of individual components within cells. Mathematical modelling can help understand these complex systems by breaking the system into discrete steps which can then be interrogated in silico. In this review, we highlight scenarios in cell migration where mathematical modelling can be applied and discuss what types of modelling are most suited. Almost any aspect of cell migration is amenable to mathematical modelling from the modelling of intracellular processes such as chemokine receptor signalling and actin filament branching to larger scale processes such as the movement of individual cells or populations of cells through their environment. Two common ways of approaching this modelling are the use of models based on differential equations or agent-based modelling. The application of both these approaches to cell migration are discussed with specific examples along with common software tools to facilitate the process for non-mathematicians. We also highlight the challenges of modelling cell migration and the need for rigorous experimental work to effectively parameterise a model.

Modelling of endothelial cell migration and angiogenesis in microfluidic cell culture systems

Tumour-induced angiogenesis is a complex biological process that involves growth of new blood vessels within the tumour microenvironment and is an important target for cancer therapies. Significant efforts have been undertaken to develop theoretical models as well as in vitro experimental models to study angiogenesis in a highly controllable and accessible manner. Various mathematical models have been developed to study angiogenesis, but these have mostly been applied to in vivo assays. Recently, microfluidic cell culture systems have emerged as useful and powerful tools for studying cell migration and angiogenesis processes, but thus far, mathematical angiogenesis models have not yet been applied to microfluidic geometries. Integrating mathematical and computational modelling with microfluidic-based assays has potential to enable greater control over experimental parameters, provide new insights into fundamental angiogenesis processes and assist in accelerating design and optimization of operating conditions. Here, we describe the development and application of a combined mathematical and computational modelling approach tailored specifically for microfluidic cell culture systems. The objective was to allow optimization of the engineering design of microfluidic systems, where the model may be used to test the impact of various geometric parameters on cell migration and angiogenesis processes, and assist in identifying optimal device dimensions to achieve desired readouts. We employed two separate continuum mathematical models that treated cell density, vessel length density and vascular endothelial growth factor (VEGF) concentration as continuous average variables, and we implemented these models numerically using finite difference discretization and a Method of Lines approach. We examined the average response of cells to VEGF gradients inside our microfluidic device, including the time-dependent changes in cell density and vessel density, and how they were affected by changes in device geometries including the migration port width and length. Our study demonstrated that mathematical modelling can be integrated with microfluidics to offer new perspectives on emerging problems in biomicrofluidics and cancer biology.

Reprogramming miRNAs global expression orchestrates development of drug resistance in BRAF mutated melanoma

Drug resistance imposes severe limitations to the efficacy of targeted therapy in BRAF-mutated metastatic melanoma. Although this issue has been mitigated by the development of combination therapies with BRAF plus MEK inhibitors, drug resistance inevitably occurs with time and results in clinical recurrences and untreatable disease. Hence, there is strong need of developing new combination therapies and non-invasive diagnostics for the early identification of drug-resistant patients. We report here that the development of drug resistance to BRAFi is dominated by a dynamic deregulation of a large population of miRNAs, leading to the alteration of cell intrinsic proliferation and survival pathways, as well as of proinflammatory and proangiogenic cues, where a prominent role is played by the miR-199b-5p/VEGF axis. Significant alterations of miRNA expression levels are detectable in tumor biopsies and plasma from patients after disease recurrence. Targeting these alterations blunts the development of drug resistance.

Urokinase receptor derived peptides as potent inhibitors of the formyl peptide receptor type 1-triggered cell migration

The receptor for the urokinase-type plasminogen activator (uPAR) is a widely recognized master regulator of cell migration. We and others have previously documented that the uPAR(84-95) sequence, interacts with the formyl peptide receptors (FPR)s, henceforth inducing cell migration of several cell lines, including leukocytes, and the synthetic shorter peptide (Ser⁸⁸-Arg-Ser-Arg-Tyr⁹², SRSRY) retains chemotactic activity in vitro and in vivo. Recently, we have developed the head-to-tail cyclic analog [SRSRY], a new potent and stable inhibitor of monocyte trafficking. This prompted us to develop novel cyclic and linear analogs of [SRSRY] with the aim to broaden the knowledge about structure-activity relationships of peptide [SRSRY]. Herein we report their synthesis, effects on cell migration, conformational and docking analyses which served to envisage a new pharmacophore model for inhibitors of FPR1-triggered cell migration.

Retro-inverso Urokinase Receptor Antagonists for the Treatment of Metastatic Sarcomas

The development of metastases is a multistep process that requires the activation of physiological and biochemical processes that govern migration, invasion and entry of metastatic cells into blood vessels. The urokinase receptor (uPAR) promotes cell migration by interacting with the Formyl Peptide Receptors (FPRs). Since both uPAR and FPR1 are involved in tumor progression, the uPAR-FPR1 interaction is an attractive therapeutic target. We previously described peptide antagonists of the uPAR-FPR1 interaction that inhibited cell migration and angiogenesis. To develop enzyme-resistant analogues, we applied here the Retro-Inverso (RI) approach, whereby the topology of the side chains is maintained by inverting the sequence of the peptide and the chirality of all residues. Molecular dynamics suggests that peptide RI-3 adopts the turn structure typical of uPAR-FPR1 antagonists. Accordingly, RI-3 is a nanomolar competitor of N-formyl-Met-Leu-Phe for binding to FPR1 and inhibits migration, invasion, trans-endothelial migration of sarcoma cells and VEGF-triggered endothelial tube formation. When sarcoma cells were subcutaneously injected in nude mice, tumor size, intra-tumoral microvessel density, circulating tumor cells and pulmonary metastases were significantly reduced in animals treated daily with 6 mg/Kg RI-3 as compared to animals treated with vehicle only. Thus, RI-3 represents a promising lead for anti-metastatic drugs.