Dynamics of the cell and its extracellular matrix-a simple mathematical approach

Fuzzy Recurrence Exponents of Subcellular-Nanostructure Dynamics in Time-lapse Confocal Imaging

Studying the dynamics of nanostructures in the intracellular space is important because it allows gaining insights into the mechanism of complex biological functions of organelles. Understanding such dynamical processes can contribute to the development of nanomedicine for the diagnosis and treatment of many diseases caused by the interaction of multiple genes and environmental factors. Here a quantitative measure of spatial-temporal dynamics of nanostructures within a cell line in the context of nonlinear dynamics is introduced, where early endosomes, late endosomes, and lysosomes recorded by time-lapse confocal imaging are examined. The mathematical derivation of the proposed technique is based on the concept of recurrence dynamics and sequential rate of change over time. The quantification introduced as fuzzy recurrence exponents can be generalized for characterizing the dynamics of experimental evolutions in other nanostructures of living cells captured under the optical microscope.

Relevant biological processes for tissue development with stem cells and their mechanistic modeling: A review

A potential alternative for tissue transplants is tissue engineering, in which the interaction of cells and biomaterials can be optimized. Tissue development in vitro depends on the complex interaction of several biological processes such as extracellular matrix synthesis, vascularization and cell proliferation, adhesion, migration, death, and differentiation. The complexity of an individual phenomenon or of the combination of these processes can be studied with phenomenological modeling techniques. This work reviews the main biological phenomena in tissue development and their mathematical modeling, focusing on mesenchymal stem cell growth in three-dimensional scaffolds.

Extracellular Matrix Deposition in Engineered Micromass Cartilage Pellet Cultures: Measurements and Modelling

This article explores possible mechanisms governing extracellular matrix deposition in engineered cartilaginous cell pellets. A theoretical investigation is carried out alongside an experimental study measuring proteoglycan and collagen volume fractions within murine chondrogenic (ATDC-5) cell pellets. The simple mathematical model, which adopts a nutrient-dependent proteoglycan production rate, successfully reproduces the periphery-dominated proteoglycan deposition, characteristic of the growth pattern observed experimentally within pellets after 21 days of culture. The results suggest that this inhomogeneous proteoglycan production is due to nutrient deficiencies at the pellet centre. Our model analysis further indicates that a spatially uniform distribution of proteoglycan matrix could be maintained by initiating the culture process with a smaller-sized pellet. Finally, possible extensions are put forward with an aim to improve the model predictions for the early behaviour, where different mechanisms appear to dominate the matrix production within the pellets.

Relationships between degradability of silk scaffolds and osteogenesis

Bone repairs represent a major focus in orthopedic medicine with biomaterials as a critical aspect of the regenerative process. However, only a limited set of biomaterials are utilized today and few studies relate biomaterial scaffold design to degradation rate and new bone formation. Matching biomaterial remodeling rate towards new bone formation is important in terms of the overall rate and quality of bone regeneration outcomes. We report on the osteogenesis and metabolism of human bone marrow derived mesenchymal stem cells (hMSCs) in 3D silk scaffolds. The scaffolds were prepared with two different degradation rates in order to study relationships between matrix degradation, cell metabolism and bone tissue formation in vitro. SEM, histology, chemical assays, real-time PCR and metabolic analyses were assessed to investigate these relationships. More extensively mineralized ECM formed in the scaffolds designed to degrade more rapidly, based on SEM, von Kossa and type I collagen staining and calcium content. Measures of osteogenic ECM were significantly higher in the more rapidly degrading scaffolds than in the more slowly degrading scaffolds over 56 days of study in vitro. Metabolic analysis, including glucose and lactate levels, confirmed the degradation rate differences with the two types of scaffolds, with the more rapidly degrading scaffolds supporting higher levels of glucose consumption and lactate synthesis by the hMSCs upon osteogenesis, in comparison to the more slowly degrading scaffolds. The results demonstrate that scaffold degradation rates directly impact the metabolism of hMSCs, and in turn the rate of osteogenesis. An understanding of the interplay between cellular metabolism and scaffold degradability should aid in the more rational design of scaffolds for bone regeneration needs both in vitro and in vivo.

Extracellular matrix remodeling--methods to quantify cell-matrix interactions

Tissue turnover during wound healing, regeneration or integration of biomedical materials depends on the rate and extent of materials trafficking into and out of cells involved in extracellular matrix (ECM) remodeling. To exploit these processes, we report the first model for matrix trafficking in which these issues are quantitatively assessed for cells grown on both native collagen (normal tissue) and denatured collagen (wound state) substrates. Human fibroblasts more rapidly remodeled denatured versus normal collagen type I to form new ECM. Fluxes to and from the cells from the collagen substrates and the formation of new ECM were quantified using radioactively labeled substrates. The model can be employed for the systematic and quantitative study of the impact of a broad range of physiological factors and disease states on tissue remodeling, integrating extracellular matrix structures and cell biology.

Dynamic matrix composition in engineered cartilage with stochastic supplementation of growth factors

Dynamic extracellular matrix (ECM) synthesis is explored in a hypothesized engineered cartilage construct. Growth (alpha) and decay (beta) rate parameters are developed from a previous engineered cartilage model. The presented mathematical model was constructed from the parameterized experimental data using a deterministic and stochastic examination of ECM synthesis based on a negative feedback control mechanism. A growth factor supplementation is incorporated in a probabilistic mathematical approach. The growth factor component modified an initial deterministic model through a Gaussian white noise fluctuation. As the primary constituents of ECM, the mathematical tool is intended to characterize the probable steady state distribution of glycosaminoglycan (GAG) and collagen molecules as well as mean mass accumulation at homeostasis. Computer simulation of the models is applied to reported data from four similar chondrocyte-polymer construct culture systems. The range in rate ratios reflect the differing nature of GAG and collagen synthesis (alphaGAG/betaGAG = 4.2 to 148.6; alphacollagen/betacollagen = 8.1 to 2590.4). This technique reduced the influencing synthesis factors to a few key descriptive parameters. Additional anabolic and catabolic factors may further be built into the models.

A kinetic modeling of chondrocyte culture for manufacture of tissue-engineered cartilage

For repairing articular cartilage defects, innovative techniques based on tissue engineering have been developed and are now entering into the practical stage of clinical application by means of grafting in vitro cultured products. A variety of natural and artificial materials available for scaffolds, which permit chondrocyte cells to aggregate, have been designed for their ability to promote cell growth and differentiation. From the viewpoint of the manufacturing process for tissue-engineered cartilage, the diverse nature of raw materials (seeding cells) and end products (cultured cartilage) oblige us to design a tailor-made process with less reproducibility, which is an obstacle to establishing a production doctrine based on bioengineering knowledge concerning growth kinetics and modeling as well as designs of bioreactors and culture operations for certification of high product quality. In this article, we review the recent advances in the manufacturing of tissue-engineered cartilage. After outlining the manufacturing processes for tissue-engineered cartilage in the first section, the second and third sections, respectively, describe the three-dimensional culture of chondrocytes with Aterocollagen gel and kinetic model consideration as a tool for evaluating this culture process. In the final section, culture strategy is discussed in terms of the combined processes of monolayer growth (ex vivo chondrocyte cell expansion) and three-dimensional growth (construction of cultured cartilage in the gel).