Proliferation of anchorage-dependent contact-inhibited cells: I. Development of theoretical models based on cellular automata

Biomaterialomics: Data science-driven pathways to develop fourth-generation biomaterials

Conventional approaches to developing biomaterials and implants require intuitive tailoring of manufacturing protocols and biocompatibility assessment. This leads to longer development cycles, and high costs. To meet existing and unmet clinical needs, it is critical to accelerate the production of implantable biomaterials, implants and biomedical devices. Building on the Materials Genome Initiative, we define the concept 'biomaterialomics' as the integration of multi-omics data and high-dimensional analysis with artificial intelligence (AI) tools throughout the entire pipeline of biomaterials development. The Data Science-driven approach is envisioned to bring together on a single platform, the computational tools, databases, experimental methods, machine learning, and advanced manufacturing (e.g., 3D printing) to develop the fourth-generation biomaterials and implants, whose clinical performance will be predicted using 'digital twins'. While analysing the key elements of the concept of 'biomaterialomics', significant emphasis has been put forward to effectively utilize high-throughput biocompatibility data together with multiscale physics-based models, E-platform/online databases of clinical studies, data science approaches, including metadata management, AI/ Machine Learning (ML) algorithms and uncertainty predictions. Such integrated formulation will allow one to adopt cross-disciplinary approaches to establish processing-structure-property (PSP) linkages. A few published studies from the lead author's research group serve as representative examples to illustrate the formulation and relevance of the 'Biomaterialomics' approaches for three emerging research themes, i.e. patient-specific implants, additive manufacturing, and bioelectronic medicine. The increased adaptability of AI/ML tools in biomaterials science along with the training of the next generation researchers in data science are strongly recommended. STATEMENT OF SIGNIFICANCE: This leading opinion review paper emphasizes the need to integrate the concepts and algorithms of the data science with biomaterials science. Also, this paper emphasizes the need to establish a mathematically rigorous cross-disciplinary framework that will allow a systematic quantitative exploration and curation of critical biomaterials knowledge needed to drive objectively the innovation efforts within a suitable uncertainty quantification framework, as embodied in 'biomaterialomics' concept, which integrates multi-omics data and high-dimensional analysis with artificial intelligence (AI) tools, like machine learning. The formulation of this approach has been demonstrated for patient-specific implants, additive manufacturing, and bioelectronic medicine.

Anchorage-Dependent Living Supramolecular Self-Assembly of Polymeric Micelles

Anchorage-dependent contact-inhibited growth usually refers to on-surface cell proliferation inhibited by the proximity of other cells. This phenomenon, prominent in nature, has yet to be achieved with polymeric micelles. Here, we report the control living supra-macromolecular self-assembly of elongated micelles with a liquid crystalline core onto a hydrophobic substrate via the synergetic interactions between the substrate and aggregates dispersed in solution. In this system, seed formation is a transient phenomenon induced by the adsorption and rearrangement of the core-swollen aggregates. The seeds then trigger the growth of elongated micelles onto the substrate in a living controllable manner until the contact with the substrate is disrupted. Brownian dynamic simulations show that this unique behavior is due to the fusion of the aggregates onto both ends of the anchored seeds. More important, the micelle length can be tuned by varying the substrate hydrophobicity, a key step toward the fabrication of intricate structures.

Organ-specific isogenic metastatic breast cancer cell lines exhibit distinct Raman spectral signatures and metabolomes

Molecular characterization of organ-specific metastatic lesions, which distinguish them from the primary tumor, will provide a better understanding of tissue specific adaptations that regulate metastatic progression. Using an orthotopic xenograft model, we have isolated isogenic metastatic human breast cancer cell lines directly from organ explants that are phenotypically distinct from the primary tumor cell line. Label-free Raman spectroscopy was used and informative spectral bands were ascertained as differentiators of organ-specific metastases as opposed to the presence of a single universal marker. Decision algorithms derived from the Raman spectra unambiguously identified these isogenic cell lines as unique biological entities – a finding reinforced through metabolomic analyses that indicated tissue of origin metabolite distinctions between the cell lines. Notably, complementarity of the metabolomics and Raman datasets was found. Our findings provide evidence that metastatic spread generates tissue-specific adaptations at the molecular level within cancer cells, which can be differentiated with Raman spectroscopy.

In silico characterization of cell-cell interactions using a cellular automata model of cell culture

BACKGROUND

Cell proliferation is a key characteristic of eukaryotic cells. During cell proliferation, cells interact with each other. In this study, we developed a cellular automata model to estimate cell-cell interactions using experimentally obtained images of cultured cells.

RESULTS

We used four types of cells; HeLa cells, human osteosarcoma (HOS) cells, rat mesenchymal stem cells (MSCs), and rat smooth muscle A7r5 cells. These cells were cultured and stained daily. The obtained cell images were binarized and clipped into squares containing about 10⁴ cells. These cells showed characteristic cell proliferation patterns. The growth curves of these cells were generated from the cell proliferation images and we determined the doubling time of these cells from the growth curves. We developed a simple cellular automata system with an easily accessible graphical user interface. This system has five variable parameters, namely, initial cell number, doubling time, motility, cell-cell adhesion, and cell-cell contact inhibition (of proliferation). Within these parameters, we obtained initial cell numbers and doubling times experimentally. We set the motility at a constant value because the effect of the parameter for our simulation was restricted. Therefore, we simulated cell proliferation behavior with cell-cell adhesion and cell-cell contact inhibition as variables. By comparing growth curves and proliferation cell images, we succeeded in determining the cell-cell interaction properties of each cell. Simulated HeLa and HOS cells exhibited low cell-cell adhesion and weak cell-cell contact inhibition. Simulated MSCs exhibited high cell-cell adhesion and positive cell-cell contact inhibition. Simulated A7r5 cells exhibited low cell-cell adhesion and strong cell-cell contact inhibition. These simulated results correlated with the experimental growth curves and proliferation images.

CONCLUSIONS

Our simulation approach is an easy method for evaluating the cell-cell interaction properties of cells.

An in silico prediction tool for the expansion culture of human skeletal muscle myoblasts

Regenerative therapy using autologous skeletal myoblasts requires a large number of cells to be prepared for high-level secretion of cytokines and chemokines to induce good regeneration of damaged regions. However, myoblast expansion culture is hindered by a reduction in growth rate owing to cellular quiescence and differentiation, therefore optimization is required. We have developed a kinetic computational model describing skeletal myoblast proliferation and differentiation, which can be used as a prediction tool for the expansion process. In the model, myoblasts migrate, divide, quiesce and differentiate as observed during in vitro culture. We assumed cell differentiation initiates following cell-cell attachment for a defined time period. The model parameter values were estimated by fitting to several predetermined experimental datasets. Using an additional experimental dataset, we confirmed validity of the developed model. We then executed simulations using the developed model under several culture conditions and quantitatively predicted that non-uniform cell seeding had adverse effects on the expansion culture, mainly by reducing the existing ratio of proliferative cells. The proposed model is expected to be useful for predicting myoblast behaviours and in designing efficient expansion culture conditions for these cells.

An agent-based model approach to multi-phase life-cycle for contact inhibited, anchorage dependent cells

Cellular agent-based models are a technique that can be easily adapted to describe nuances of a particular cell type. Within we have concentrated on the cellular particularities of the human Endothelial Cell, explicitly the effects both of anchorage dependency and of heightened scaffold binding on the total confluence time of a system. By expansion of a discrete, homogeneous, asynchronous cellular model to account for several states per cell (phases within a cell's life); we accommodate and track dependencies of confluence time and population dynamics on these factors. Increasing the total motility time, analogous to weakening the binding between lattice and cell, affects the system in unique ways from increasing the average cellular velocity; each degree of freedom allows for control over the time length the system achieves logistic growth and confluence. These additional factors may allow for greater control over behaviors of the system. Examinations of system's dependence on both seed state velocity and binding are also enclosed.

Analysis of endothelial cell locomotion: Differential effects of motility and contact inhibition

Video microscopy and digital time-lapse recording were used to monitor locomotion and proliferation of bovine pulmonary artery endothelial (BPAE) cells cultured with varying concentrations of basic fibroblast growth factor (bFGF). Cell trajectories were reconstructed using a generalized nearest-neighbor algorithm and analyzed to determine how cell motility is affected by cell-cell collisions, cell divisions, and increasing cell density. The temporal evolution patterns of the average speed of locomotion for all cells in a culture were computed and the effects of varying bFGF concentrations were analyzed. Intermediate concentrations of bFGF (30 and 50 ng/mL) significantly increased the speed of locomotion above the levels we observed with 0 and 100 ng/mL concentrations of bFGF. Increases in cell density due to proliferation were immediately accompanied by a decrease in the average speed of locomotion of the cell population. Finally, the effect of bFGF concentration on the overall cell proliferation rates was assessed. With the addition of 30 or 50 ng/mL of bFGF to the culture media, the observed cell proliferation rates increased significantly. The proliferation rates decreased when the bFGF concentration increased to 100 ng/mL. These results show that bFGF concentrations that increase the motility of BPAE cells also increase the observed cell proliferation rates. (c) 1994 John Wiley & Sons, Inc.

Quantification and regulation of cell migration

Cell migration is essential for many physiological and pathological processes that include embryonic development, the immune response, wound healing, angiogenesis, and cancer metastasis. It is also important for emerging tissue engineering applications such as tissue reconstitution and the colonization of biomedical implants. By summarizing results from recent experimental and theoretical studies, this review outlines the role played by growth factors or substrate-adhesion molecules in modulating cell motility and shows that cell motility can be an important factor in determining the rates of tissue formation. The application of cell motility assays and the use of theoretical models for analyzing cell migration and proliferation are also discussed.

Growth behavior of number distributed adherent MDCK cells for optimization in microcarrier cultures

An assay for measuring the number of adherent cells on microcarriers that is independent from dilution errors in sample preparation was used to investigate attachment dynamics and cell growth. It could be shown that the recovery of seeded cells is a function of the specific rates of cell attachment and cell death, and finally a function of the initial cell-to-bead ratio. An unstructured, segregated population balance model was developed that considers individual classes of microcarriers covered by 1-220 cells/bead. The model describes the distribution of initially attached cells and their growth in a microcarrier system. The model distinguishes between subpopulations of dividing and nondividing cells and describes in a detailed way cell attachment, cell growth, density-dependent growth inhibition, and basic metabolism of Madin-Darby canine kidney cells used in influenza vaccine manufacturing. To obtain a model approach that is suitable for process control applications, a reduced growth model without cell subpopulations, but with a formulation of the specific cell growth rate as a function of the initial cell distribution on microcarriers after seeding was developed. With both model approaches, the fraction of growth-inhibited cells could be predicted. Simulation results of two cultivations with a different number of initially seeded cells showed that the growth kinetics of adherent cells at the given cultivation conditions is mainly determined by the range of disparity in the initial distribution of cells on microcarriers after attachment.

Hybrid cellular automaton modeling of nutrient modulated cell growth in tissue engineering constructs

Mathematic models help interpret experimental results and accelerate tissue engineering developments. We develop in this paper a hybrid cellular automata model that combines the differential nutrient transport equation to investigate the nutrient limited cell construct development for cartilage tissue engineering. Individual cell behaviors of migration, contact inhibition and cell collision, coupled with the cell proliferation regulated by oxygen concentration were carefully studied. Simplified two-dimensional simulations were performed. Using this model, we investigated the influence of cell migration speed on the overall cell growth within in vitro cell scaffolds. It was found that intense cell motility can enhance initial cell growth rates. However, since cell growth is also significantly modulated by the nutrient contents, intense cell motility with conventional uniform cell seeding method may lead to declined cell growth in the final time because concentrated cell population has been growing around the scaffold periphery to block the nutrient transport from outside culture media. Therefore, homogeneous cell seeding may not be a good way of gaining large and uniform cell densities for the final results. We then compared cell growth in scaffolds with various seeding modes, and proposed a seeding mode with cells initially residing in the middle area of the scaffold that may efficiently reduce the nutrient blockage and result in a better cell amount and uniform cell distribution for tissue engineering construct developments.

The virtual cell--a candidate co-ordinator for 'middle-out' modelling of biological systems

Understanding the functioning of biological systems depends on tackling complexity spanning spatial scales from genome to organ to whole organism. The basic unit of life, the cell, acts to co-ordinate information received across these scales and processes the myriad of signals to produce an integrated cellular response. Cells interact with and respond to other cells through direct or indirect contact, resulting in emergent structure and function of tissues and organs. Systems biology has traditionally used either a 'top-down' or 'bottom-up' approach. However, neither approach takes account of heterogeneity or 'noise', which is an inherent feature of cellular behaviour and may have significant impact on system level behaviour. We review existing approaches to modelling that use cellular automata or agent-based methodologies, where individual cells are represented as equivalent virtual entities governed by simple rules. These paradigms allow a direct one-to-one mapping between real and virtual cells that can be exploited in terms of acquiring parameters from experimental systems, or for model validation. Such models are inherently extensible and can be integrated with other modelling modalities (e.g. partial or ordinary differential equations) to model multi-scale phenomena. Alternatively, hierarchical agent models may be used to explore the functions of biological systems across temporal and spatial scales. This review examines individual-based models and the application of the paradigm to explore multi-scale phenomena in biology. In so doing, it demonstrates how cellular-based models have begun to play an important role in the development of 'middle-out' models, but with considerable potential for future development.

Optimal design of metabolic flux analysis experiments for anchorage-dependent mammalian cells using a cellular automaton model

Metabolic flux analysis (MFA) is widely used to quantify metabolic pathway activity. Typical applications involve isotopically labeled substrates, which require both metabolic and isotopic steady states for simplified data analysis. For bacterial systems, these steady states are readily achieved in chemostat cultures. However, mammalian cells are often anchorage dependent and experiments are typically conducted in batch or fed-batch systems, such as tissue culture dishes or microcarrier-containing bioreactors. Surface adherence may cause deviations from exponential growth, resulting in metabolically heterogeneous populations and a varying number of cellular "nearest neighbors" that may affect the observed metabolism. Here, we discuss different growth models suitable for deconvoluting these effects and their application to the design and optimization of MFA experiments employing surface-adherent mammalian cells. We describe a stochastic two-dimensional (2D) cellular automaton model, with empirical descriptions of cell number and non-growing cell fraction, suitable for easy application to most anchorage-dependent mammalian cell cultures. Model utility was verified by studying the impact of contact inhibition on the growth rate, specific extracellular flux rates, and isotopic labeling in lactate for MCF7 cells, a commonly studied breast cancer cell line. The model successfully defined the time over which exponential growth and a metabolically homogeneous growing cell population could be assumed. The cellular automaton model developed is shown to be a useful tool in designing optimal MFA experiments.

Cell population dynamics modulate the rates of tissue growth processes

The development and testing of a discrete model describing the dynamic process of tissue growth in three-dimensional scaffolds is presented. The model considers populations of cells that execute persistent random walks on the computational grid, collide, and proliferate until they reach confluence. To isolate the effect of population dynamics on tissue growth, the model assumes that nutrient and growth factor concentrations remain constant in space and time. Simulations start either by distributing the seed cells uniformly and randomly throughout the scaffold, or from an initial condition designed to simulate the migration and cell proliferation phase of wound healing. Simulations with uniform seeding show that cell migration enhances tissue growth by counterbalancing the adverse effects of contact inhibition. This beneficial effect, however, diminishes and disappears completely for large migration speeds. By contrast, simulations with the "wound" seeding mode show a continual enhancement of tissue regeneration rates with increasing cell migration speeds. We conclude that cell locomotory parameters and the spatial distribution of seed cells can have profound effects on the dynamics of the process and, consequently, on the pattern and rates of tissue growth. These results can guide the design of experiments for testing the effectiveness of biomimetic modifications for stimulating tissue growth.

Valuation of growth parameters in monolayer keratinocyte cultures based on a two-dimensional cell placement model

The influence of inoculum size on the growth of keratinocyte cells was investigated in a monolayer culture with serum-free medium. A growth model of cell placement was applied to the expression of the cell adhesion phase after the inoculation, lag phase, exponential growth phase, and stationary phase because of contact inhibition at high cell densities. Based on the model, the lag time until the onset of cell division was shortened in proportion to the logarithm of the inoculum cell size, resulting in the enhancement of overall cell propagation. It was verified that the proposed model is valid for the determination of the optimal inoculum size to realize the efficient growth of keratinocytes, indicating that the model is a useful tool to predict an optimal culture scheme for the production of skin grafts.

Development and validation of computational models of cellular interaction

In this paper we take the view that computational models of biological systems should satisfy two conditions - they should be able to predict function at a systems biology level, and robust techniques of validation against biological models must be available. A modelling paradigm for developing a predictive computational model of cellular interaction is described, and methods of providing robust validation against biological models are explored, followed by a consideration of software issues.

Analysis of cell growth kinetics and substrate diffusion in a polymer scaffold

The cultivation of cartilage cells (chondrocytes) in polymer scaffolds leads to implants that may potentially be used to repair damaged joint cartilage or for reconstructive surgery. For this technique to be medically applicable, the physical parameters that govern cell growth in a polymer scaffold must be understood. This understanding of cell behavior under in vitro conditions, where diffusion is the primary mode of transport of nutrients, may aid in the scale-up of the cartilage generation process. A mathematical model of chondrocyte generation and nutrient consumption is developed here to analyze the behavior of cell growth in a biodegradable polymer matrix for a series of different thickness polymers. Recent literature has implied that the diffusion of nutrients is a major factor that limits cell growth (Freed et al., 1994). In the present paper, a mathematical model is developed to directly relate the effects of increasing cell mass in the polymer matrix on the transport of nutrients. Reaction and diffusion of nutrients in the cell-polymer system are described using the fundamental species continuity equations and the volume averaging method. The volume averaging method is utilized to derive a single averaged nutrient continuity equation that includes the effective transport properties. This approach allows for the derivation of effective diffusion and rate coefficients as functions of the cell volume fraction. The cell volume fraction as a function of time is determined by solution of a material balance on cell mass. Growth functions including the Moser, a modified Contois, and an nth-order heterogeneous growth kinetic model are evaluated through a parameter analysis, and the results are compared to experimental data found in the literature. The results indicate that cellular functions in conjunction with mass transfer processes can account partially for the general trends in the cell growth behavior for various thickness polymers. The Contois growth function appeared to describe the data more accurately in terms of the lag period at early times and the long time limits. However, all kinetic growth functions required variations in the kinetic parameters to fully describe the effects of polymer thickness. This result implies that restricted diffusion of nutrients is not the sole factor limiting cell growth when the thickness of the polymer is changed. Therefore, further experimental data and model improvements are needed to accurately describe the cell growth process.

Biomaterials in tissue engineering

Biomaterials play a pivotal role in field of tissue engineering. Biomimetic synthetic polymers have been created to elicit specific cellular functions and to direct cell-cell interactions both in implants that are initially cell-free, which may serve as matrices to conduct tissue regeneration, and in implants to support cell transplantation. Biomimetic approaches have been based on polymers endowed with bioadhesive receptor-binding peptides and mono- and oligosaccharides. These materials have been patterned in two- and three-dimensions to generate model multicellular tissue architectures, and this approach may be useful in future efforts to generate complex organizations of multiple cell types. Natural polymers have also played an important role in these efforts, and recombinant polymers that combine the beneficial aspects of natural polymers with many of the desirable features of synthetic polymers have been designed and produced. Biomaterials have been employed to conduct and accelerate otherwise naturally occurring phenomena, such as tissue regeneration in wound healing in the otherwise healthy subject; to induce cellular responses that might not be normally present, such as healing in a diseased subject or the generation of a new vascular bed to receive a subsequent cell transplant; and to block natural phenomena, such as the immune rejection of cell transplants from other species or the transmission of growth factor signals that stimulate scar formation. This review introduces the biomaterials and describes their application in the engineering of new tissues and the manipulation of tissue responses.

Cell cycle dynamics of microcarrier cultures

In anchorage-dependent cell microcarrier cultures knowledge of the cell's growth kinetics is necessary in order to design and successfully operate bioreactors, particularly on a large scale. However, in addition to growth kinetics, an understanding of the physiological state of the culture is also important. In this paper the cell cycle progression of Vero and MRC-5 microcarrier cultures have been observed utilizing a flow cytometer. Flow cytometry analysis enabled the differentiation of the various phases of the cell cycle as the culture moved from initial inoculation to the stationary, or confluent stage. Not only was the flow cytometer able to distinguish contact inhibited cells from noncontact inhibited cells, but the measured fraction of contact inhibition cells were found to be in agreement with fractions predicted from a previously developed cellular automation model for microcarrier cultures. Further, the data from the stationary phase was used to quantify the death rate in microcarrier cultures.

Modeling of cell culture processes

Models of cell processes can be particularly useful in simulating, optimizing and controlling cell culture systems. Models reported in the literature are of various degrees of biological structure and mathematical complexity and describe cell growth, death, metabolism, and product formation, alone or in combination with each other. This paper reviews these modeling efforts, discusses their results, potential and limitations, and identifies areas where future modeling studies may be especially valuable.