Stochastic cellular automata model of cell migration, proliferation and differentiation: Validation with in vitro cultures of muscle satellite cells

Morphological switch is associated with increase in cell-cell contacts, ALP, and confluence above a minimum island area to perimeter ratio

During osteogenic differentiation in vitro, stem-like cells seeded at a low-density spread and are isolated. As the cells proliferate and mature, they become more cuboidal in shape with more cell-cell contacts. However, the coordination of this switch in cell morphology from elongated to cuboidal, cell-cell contacts, and differentiation is not known. In this work, we present results from experiments and a simulation of cell proliferation on protein-micropatterned islands that, independent of island size (25-1,000 μm) or shape (circles, squares, and hollow squares), shows a distinct morphological switch that is better described as a function of island confluence than time in culture, the standard measure in cell culture experiments. The simulation and experiments show cell morphology and island cell density versus confluence collapse to a single curve for all islands if the island area to perimeter ratio is ≥25 μm. Cell-cell contacts in the simulation and alkaline phosphatase (ALP) expression in experiments, a common marker for osteogenic differentiation, show exponential growth with confluence, rapidly increasing after the switch at ≈0.5 confluence. Furthermore, cell morphology, density, contacts, and ALP are better predicted by confluence than time in culture. The variability with time in culture leads to challenges in not only interpreting data but also in comparing data across research laboratories. This simulation can be used to predict cell behavior on different size and shape islands and to plan and optimize experiments that explore cell behavior as a function of a wide range of island geometries.

Modeling Living Cells Within Microfluidic Systems Using Cellular Automata Models

Several computational models, both continuum and discrete, allow for the simulation of collective cell behaviors in connection with challenges linked to disease modeling and understanding. Normally, discrete cell modelling employs quasi-infinite or boundary-less 2D lattices, hence modeling collective cell behaviors in Petri dish-like environments. The advent of lab- and organ-on-a-chip devices proves that the information obtained from 2D cell cultures, upon Petri dishes, differs importantly from the results obtained in more biomimetic micro-fluidic environments, made of interconnected chambers and channels. However, discrete cell modelling within lab- and organ-on-a-chip devices, to our knowledge, is not yet found in the literature, although it may prove useful for designing and optimizing these types of systems. Consequently, in this study we focus on the establishment of a direct connection between the computer-aided designs (CAD) of microfluidic systems, especially labs- and organs-on-chips (and their multi-chamber and multi-channel structures), and the lattices for discrete cell modeling approaches aimed at the simulation of collective cell interactions, whose boundaries are defined directly from the CAD models. We illustrate the proposal using a quite straightforward cellular automata model, apply it to simulating cells with different growth rates, within a selected set of microsystem designs, and validate it by tuning the growth rates with the support of cell culture experiments and by checking the results with a real microfluidic system.

Stochastic cellular automata model of neurosphere growth: Roles of proliferative potential, contact inhibition, cell death, and phagocytosis

Neural stem and progenitor cells isolated from the central nervous system form, under specific culture conditions, clonal cell clusters known as neurospheres. The neurosphere assay has proven to be a powerful in vitro system to study the behavior of such cells and the development of their progeny. However, the theory of neurosphere growth has remained poorly understood. To overcome this limitation, we have, in the present paper, developed a cellular automata model, with which we examined the effects of proliferative potential, contact inhibition, cell death, and clearance of dead cells on growth rate, final size, and composition of neurospheres. Simulations based on this model indicated that the proliferative potential of the founder cell and its progenitors has a major influence on neurosphere size. On the other hand, contact inhibition of proliferation limits the final size, and reduces the growth rate, of neurospheres. The effect of this inhibition is particularly dramatic when a stem cell becomes encapsulated by differentiated or other non-proliferating cells, thereby suppressing any further mitotic division - despite the existing proliferative potential of the stem cell. Conversely, clearance of dead cells through phagocytosis is predicted to accelerate growth by reducing contact inhibition. A surprising prediction derived from our model is that cell death, while resulting in a decrease in growth rate and final size of neurospheres, increases the degree of differentiation of neurosphere cells. It is likely that the cellular automata model developed as part of the present investigation is applicable to the study of tissue growth in a wide range of systems.

Isolation, Characterization, and Agent-Based Modeling of Mesenchymal Stem Cells in a Bio-construct for Myocardial Regeneration Scaffold Design

Regenerative medicine involves methods to control and modify normal tissue repair processes. Polymer and cell constructs are under research to create tissue that replaces the affected area in cardiac tissue after myocardial infarction (MI). The aim of the present study is to evaluate the behavior of differentiated and undifferentiated mesenchymal stem cells (MSCs) in vitro and in silico and to compare the results that both offer when it comes to the design process of biodevices for the treatment of infarcted myocardium in biomodels. To assess in vitro behavior, MSCs are isolated from rat bone marrow and seeded undifferentiated and differentiated in multiple scaffolds of a gelled biomaterial. Subsequently, cell behavior is evaluated by trypan blue and fluorescence microscopy, which showed that the cells presented high viability and low cell migration in the biomaterial. An agent-based model intended to reproduce as closely as possible the behavior of individual MSCs by simulating cellular-level processes was developed, where the in vitro results are used to identify parameters in the agent-based model that is developed, and which simulates cellular-level processes: Apoptosis, differentiation, proliferation, and migration. Thanks to the results obtained, suggestions for good results in the design and fabrication of the proposed scaffolds and how an agent-based model can be helpful for testing hypothesis are presented in the discussion. It is concluded that assessment of cell behavior through the observation of viability, proliferation, migration, inflammation reduction, and spatial composition in vitro and in silico, represents an appropriate strategy for scaffold engineering.

Cellular automata model for human articular chondrocytes migration, proliferation and cell death: An in vitro validation

Articular cartilage is characterized by low cell density of only one cell type, chondrocytes, and has limited self-healing properties. When articular cartilage is affected by traumatic injuries, a therapeutic strategy such as autologous chondrocyte implantation is usually proposed for its treatment. This approach requires in vitro chondrocyte expansion to yield high cell number for cell transplantation. To improve the efficiency of this procedure, it is necessary to assess cell dynamics such as migration, proliferation and cell death during culture. Computational models such as cellular automata can be used to simulate cell dynamics in order to enhance the result of cell culture procedures. This methodology has been implemented for several cell types; however, an experimental validation is required for each one. For this reason, in this research a cellular automata model, based on random-walk theory, was devised in order to predict articular chondrocyte behavior in monolayer culture during cell expansion. Results demonstrated that the cellular automata model corresponded to cell dynamics and computed-accurate quantitative results. Moreover, it was possible to observe that cell dynamics depend on weighted probabilities derived from experimental data and cell behavior varies according to the cell culture period. Thus, depending on whether cells were just seeded or proliferated exponentially, culture time probabilities differed in percentages in the CA model. Furthermore, in the experimental assessment a decreased chondrocyte proliferation was observed along with increased passage number. This approach is expected to having other uses as in enhancing articular cartilage therapies based on tissue engineering and regenerative medicine.

Modeling cell adhesion and proliferation: a cellular-automata based approach

BACKGROUND

Cell adhesion is a process that involves the interaction between the cell membrane and another surface, either a cell or a substrate. Unlike experimental tests, computer models can simulate processes and study the result of experiments in a shorter time and lower costs. One of the tools used to simulate biological processes is the cellular automata, which is a dynamic system that is discrete both in space and time.

METHOD

This work describes a computer model based on cellular automata for the adhesion process and cell proliferation to predict the behavior of a cell population in suspension and adhered to a substrate. The values of the simulated system were obtained through experimental tests on fibroblast monolayer cultures.

RESULTS

The results allow us to estimate the cells settling time in culture as well as the adhesion and proliferation time. The change in the cells morphology as the adhesion over the contact surface progress was also observed. The formation of the initial link between cell and the substrate of the adhesion was observed after 100 min where the cell on the substrate retains its spherical morphology during the simulation. The cellular automata model developed is, however, a simplified representation of the steps in the adhesion process and the subsequent proliferation.

CONCLUSION

A combined framework of experimental and computational simulation based on cellular automata was proposed to represent the fibroblast adhesion on substrates and changes in a macro-scale observed in the cell during the adhesion process. The approach showed to be simple and efficient.

ALS-Linked P56S-VAPB Mutation Impairs the Formation of Multinuclear Myotube in C2C12 Cells

Amyotrophic lateral sclerosis (ALS) is a rapidly progressive neurodegenerative disorder that affects upper and lower motor neurons. Since motor neurons target skeletal muscles, the maintenance system of muscles is disturbed in ALS; however, the mechanism by which this occurs is unknown. In the present study, we investigated the effects of ALS-associated P56S-vesicle-associated membrane protein-associated protein B (VAPB) (P56S-VAPB) on the IRE1-XBP1 pathway, which is involved in the unfolded protein response (UPR) of the mouse myoblast cell line (C2C12 cells). Experiments with C2C12 cells transfected with wild-type wt-VAPB and P56S-VAPB expression vectors showed reduced myotube formation and aberrant myonuclear position in cells expressing P56S-VAPB. Activity of the IRE1-XBP1 pathway in the cells visualized with the ERAI system revealed that the pathway was disrupted in cells expressing P56S-VAPB, whereas the IRE1-XBP1 pathway activity was enhanced in the differentiation process of normal C2C12 cells. These results suggest that disruption of the IRE1-XBP1 pathway is a cause for the reduced myotube formation in P56S-VAPB-expressing cells. The expression level of the VAPB protein has been reported to be reduced in the neurons of patients with ALS. Therefore, it is expected that the IRE1-XBP1 pathway is also impaired in muscle tissues of patients with ALS, which causes a disturbance in the muscle maintenance system.