Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Bioengineered 3D platform to explore cell-ECM interactions and drug resistance of epithelial ovarian cancer cells

The behaviour of cells cultured within three-dimensional (3D) structures rather than onto two-dimensional (2D) culture plastic more closely reflects their in vivo responses. Consequently, 3D culture systems are becoming crucial scientific tools in cancer cell research. We used a novel 3D culture concept to assess cell-matrix interactions implicated in carcinogenesis: a synthetic hydrogel matrix equipped with key biomimetic features, namely incorporated cell integrin-binding motifs (e.g. RGD peptides) and the ability of being degraded by cell-secreted proteases (e.g. matrix metalloproteases). As a cell model, we chose epithelial ovarian cancer, an aggressive disease typically diagnosed at an advanced stage when chemoresistance occurs. Both cell lines used (OV-MZ-6, SKOV-3) proliferated similarly in 2D, but not in 3D. Spheroid formation was observed exclusively in 3D when cells were embedded within hydrogels. By exploiting the design flexibility of the hydrogel characteristics, we showed that proliferation in 3D was dependent on cell-integrin engagement and the ability of cells to proteolytically remodel their extracellular microenvironment. Higher survival rates after exposure to the anti-cancer drug paclitaxel were observed in cell spheroids grown in hydrogels (40-60%) compared to cell monolayers in 2D (20%). Thus, 2D evaluation of chemosensitivity may not reflect pathophysiological events seen in patients. Because of the design flexibility of their characteristics and their stability in long-term cultures (28 days), these biomimetic hydrogels represent alternative culture systems for the increasing demand in cancer research for more versatile, physiologically relevant and reproducible 3D matrices.

Engineering an Ecosystem : Taking Cues from Nature’s Paradigm to Build Tissue in the Lab and the Body

This manuscript took a 'top down' approach to understanding survival of inhabitant cells in the ecosystem bone, working from higher to lower length and time scales through the hierarchical ecosystem of bone. Our working hypothesis is that nature “engineered” the skeleton using a 'bottom up' approach,where mechanical properties of cells emerge from their adaptation to their local me-chanical milieu. Cell aggregation and formation of higher order anisotropic struc- ture results in emergent architectures through cell differentiation and extracellular matrix secretion. These emergent properties, including mechanical properties and architecture, result in mechanical adaptation at length scales and longer time scales which are most relevant for the survival of the vertebrate organism [Knothe Tate and von Recum 2009]. We are currently using insights from this approach to har-ness nature’s regeneration potential and to engineer novel mechanoactive materials [Knothe Tate et al. 2007, Knothe Tate et al. 2009]. In addition to potential applications of these exciting insights, these studies may provide important clues to evolution and development of vertebrate animals. For instance, one might ask why mesenchymal stem cells condense at all? There is a putative advantage to self-assembly and cooperation, but this advantage is somewhat outweighed by the need for infrastructural complexity (e.g., circulatory systems comprised of specific differentiated cell types which in turn form conduits and pumps to overcome limitations of mass transport via diffusion, for example; dif-fusion is untenable for multicellular organisms larger than 250 microns in diameter. A better question might be: Why do cells build skeletal tissue? Once cooperatingcells in tissues begin to deplete local sources of food in their aquatic environment, those that have evolved a means to locomote likely have an evolutionary advantage. Once the environment becomes less aquarian and more terrestrial, self-assembled organisms with the ability to move on land might have conferred evolutionary ad-vantages as well. So did the cytoskeleton evolve several length scales, enabling the emergence of skeletal architecture for vertebrate animals? Did the evolutionary advantage of motility over noncompliant terrestrial substrates (walking on land) favor adaptations including emergence of intracellular architecture (changes in the cytoskeleton and upregulation of structural protein manufacture), inter-cellular con- densation, mineralization of tissues, and emergence of higher order architectures?How far does evolutionary Darwinism extend and how can we exploit this knowl- edge to engineer smart materials and architectures on Earth and new, exploratory environments?[Knothe Tate et al. 2008]. We are limited only by our ability to imagine. Ultimately, we aim to understand nature, mimic nature, guide nature and/or exploit nature’s engineering paradigms without engineer-ing ourselves out of existence.

Generalized binomial Tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise

The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol.2, 117–E (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various τ-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial τ- DSSA method that extends the τ-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial τ-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.

Inverse expression states of the BRN2 and MITF transcription factors in melanoma spheres and tumour xenografts regulate the NOTCH pathway

The use of adherent monolayer cultures have produced many insights into melanoma cell growth and differentiation, but often novel therapeutics demonstrated to act on these cells are not active in vivo. It is imperative that new methods of growing melanoma cells that reflect growth in vivo are investigated. To this end, a range of human melanoma cell lines passaged as adherent cultures or induced to form melanoma spheres (melanospheres) in stem cell media have been studied to compare cellular characteristics and protein expression. Melanoma spheres and tumours grown from cell lines as mouse xenografts had increased heterogeneity when compared with adherent cells and 3D-spheroids in agar (aggregates). Furthermore, cells within the melanoma spheres and mouse xenografts each displayed a high level of reciprocal BRN2 or MITF expression, which matched more closely the pattern seen in human melanoma tumours in situ, rather than the propensity for co-expression of these important melanocytic transcription factors seen in adherent cells and 3D-spheroids. Notably, when the levels of the BRN2 and MITF proteins were each independently repressed using siRNA treatment of adherent melanoma cells, members of the NOTCH pathway responded by decreasing or increasing expression, respectively. This links BRN2 as an activator, and conversely, MITF as a repressor of the NOTCH pathway in melanoma cells. Loss of the BRN2-MITF axis in antisense-ablated cell lines decreased the melanoma sphere-forming capability, cell adhesion during 3D-spheroid formation and invasion through a collagen matrix. Combined, this evidence suggests that the melanoma sphere-culture system induces subpopulations of cells that may more accurately portray the in vivo disease, than the growth as adherent melanoma cells.

Development of a 3D culture system to study the skeletal metastasis of prostate cancer

In the cancer research field, most in vitro studies still rely on two-dimensional (2D) cultures. However, the trend is rapidly shifting towards using a three-dimensional (3D) culture system. This is because 3D models better recapitulate the microenvironment of cells, and therefore, yield cellular and molecular responses that more accurately describe the pathophysiology of cancer. By adopting technology platforms established by the tissue engineering discipline, it is now possible to grow cancer cells in extracellular matrix (ECM)-like environments and dictate the biophysical and biochemical properties of the matrix. In addition, 3D models can be modified to recapitulate different stages of cancer progression for instance from the initial development of tumor to metastasis. Inevitably, to recapitulate a heterotypic condition, comprising more than one cell type, it requires a more complex 3D model. To date, 3D models that are available for studying the prostate cancer (CaP)-bone interactions are still lacking. Therefore, the aim of this study is to establish a co-culture model that allows investigation of direct and indirect CaP-bone interactions. Prior to that, 3D polyethylene glycol (PEG)-based hydrogel cultures for CaP cells were first developed and growth conditions were optimised. Characterization of the 3D hydrogel cultures show that LNCaP cells form a multicellular mass that resembles avascular tumor. In comparison to 2D cultures, besides the difference in cell morphology, the response of LNCaP cells to the androgen analogue (R1881) stimulation is different compared to the cells in 2D cultures. This discrepancy between 2D and 3D cultures is likely associated with the cell-cell contact, density and ligand-receptor interactions. Following the 3D monoculture study, a 3D direct co-culture model of CaP cells and the human tissue engineered bone (hTEBC) construct was developed. Interactions between the CaP cells and human osteoblasts (hOBs) resulted in elevation of Matrix Metalloproteinase 9 (MMP9) for PC-3 cells and Prostate Specific Antigen (PSA) for LNCaP cells. To further investigate the paracrine interaction of CaP cells and (hOBs), a 3D indirect co-culture model was developed, where LNCaP cells embedded within PEG hydrogels were co-cultured with hTEBC. It was found that the cellular changes observed reflect the early event of CaP colonizing the bone site. In the absence of androgens, interestingly, up-regulation of PSA and other kallikreins is also detected in the co-culture compared to the LNCaP monoculture. This non androgenic stimulation could be triggered by the soluble factors secreted by the hOB such as Interleukin-6. There are also decrease in alkaline phosphatase (ALP) activity and down-regulation of genes of the hOB when co-cultured with LNCaP cells that have not been previously described. These genes include transforming growth factor β1 (TGFβ1), osteocalcin and Vimentin. However, no changes to epithelial markers (e.g E-cadherin, Cytokeratin 8) were observed in both cell types from the co-culture. Some of these intriguing changes observed in the co-cultures that had not been previously described have enriched the basic knowledge of the CaP cell-bone interaction. From this study, we have shown evidence of the feasibility and versatility of our established 3D models. These models can be adapted to test various hypotheses for studies pertaining to underlying mechanisms of bone metastasis and could provide a vehicle for anticancer drug screening purposes in the future.

Polarized fluid movement and not cell death, creates luminal spaces in adult prostate epithelium

There are two predominant theories for lumen formation in tissue morphogenesis: cavitation driven by cell death, and membrane separation driven by epithelial polarity. To define the mechanism of lumen formation in prostate acini, we examined both theories in several cell lines grown in three-dimensional (3D) Matrigel culture. Lumen formation occurred early in culture and preceded the expression of cell death markers for apoptosis (active caspase 3) and autophagy (LC-3). Active caspase 3 was expressed by very few cells and inhibition of apoptosis did not suppress lumen formation. Despite LC-3 expression in all cells within a spheroid, this was not associated with cell death. However, expression of a prostate-secretory protein coincided with lumen formation and subsequent disruption of polarized fluid movement led to significant inhibition of lumen formation. This work indicates that lumen formation is driven by the polarized movement of fluids and proteins in 3D prostate epithelial models and not by cavitation.

Cell death control : the interplay of apoptosis and autophagy in the pathogenicity of sclerotinia sclerotiorum

Programmed cell death is characterized by a cascade of tightly controlled events that culminate in the orchestrated death of the cell. In multicellular organisms autophagy and apoptosis are recognized as two principal means by which these genetically determined cell deaths occur. During plant-microbe interactions cell death programs can mediate both resistant and susceptible events. Via oxalic acid (OA), the necrotrophic phytopathogen Sclerotinia sclerotiorum hijacks host pathways and induces cell death in host plant tissue resulting in hallmark apoptotic features in a time and dose dependent manner. OA-deficient mutants are non-pathogenic and trigger a restricted cell death phenotype in the host that unexpectedly exhibits markers associated with the plant hypersensitive response including callose deposition and a pronounced oxidative burst, suggesting the plant can recognize and in this case respond, defensively. The details of this plant directed restrictive cell death associated with OA deficient mutants is the focus of this work. Using a combination of electron and fluorescence microscopy, chemical effectors and reverse genetics, we show that this restricted cell death is autophagic. Inhibition of autophagy rescued the non-pathogenic mutant phenotype. These findings indicate that autophagy is a defense response in this necrotrophic fungus/plant interaction and suggest a novel function associated with OA; namely, the suppression of autophagy. These data suggest that not all cell deaths are equivalent, and though programmed cell death occurs in both situations, the outcome is predicated on who is in control of the cell death machinery. Based on our data, we suggest that it is not cell death per se that dictates the outcome of certain plant-microbe interactions, but the manner by which cell death occurs that is crucial.

The evolution and diversification of Dicers in plants

Most multicellular organisms regulate developmental transitions by microRNAs, which are generated by an enzyme, Dicer. Insects and fungi have two Dicer-like genes, and many animals have only one, yet the plant, Arabidopsis, has four. Examining the poplar and rice genomes revealed that they contain five and six Dicer-like genes, respectively. Analysis of these genes suggests that plants require a basic set of four Dicer types which were present before the divergence of mono- and dicotyledonous plants (∼200 million years ago), but after the divergence of plants from green algae. A fifth type of Dicer seems to have evolved in monocots. © 2006 Federation of European Biochemical Societies.

Metastasis of ovarian cancer is mediated by kallikrein related peptidases

Ovarian cancer, in particular epithelial ovarian cancer (EOC), is commonly diagnosed when the tumor has metastasized into the abdominal cavity with an accumulation of ascites fluid. Combining histopathology and genetic variations, EOC can be sub-grouped into Type-I and Type-II tumors, of which the latter are more aggressive and metastatic. Metastasis and chemoresistance are the key events associated with the tumor microenvironment that lead to a poor patient outcome. Kallikrein-related peptidases (KLKs) are aberrantly expressed in EOC, in particular, in the more metastatic Type-II tumors. KLKs are a family of 15 serine proteases that are expressed in diverse human tissues and involved in various patho-physiological processes. As extracellular enzymes, KLKs function in the hydrolysis of growth factors, proteases, cell membrane bound receptors, adhesion proteins, and cytokines initiating intracellular signaling pathways and their downstream events. High KLK levels are differentially associated with the prognosis of ovarian cancer patients, suggesting that they not only have application as biomarkers but also function in disease progression, and therefore are potential therapeutic targets. Recent studies have demonstrated the function of these proteases in promoting and/or suppressing the invasive behavior of ovarian cancer cells in metastasis in vitro and in vivo. Both conventional cell culture methods and three-dimensional platforms have been applied to mimic the ovarian cancer microenvironment of patients, such as the solid stromal matrix and ascites fluid. Here we summarize published studies to provide an overview of our understanding of the role of KLKs in EOC, and to lay the foundation for future research directions.

A multiscale road map of cancer spheroids : incorporating experimental and mathematical modelling to understand cancer progression

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.

Hepatocyte growth factor stimulates invasion across reconstituted basement membranes by a new human small intestinal cell line

Hepatocyte growth factor/scatter factor (HGF/SF) is a protein growth factor whose pleiotropic effects on epithelial cells include the stimulation of motility, mitosis and tubulogenesis. These responses are mediated by the cell surface tyrosine kinase receptor c-met. Because both the cytokine and receptor are found in the gastrointestinal tract, we have studied the effects of HGF/SF on transformed gut epithelial cells which express c-met. Here we describe the response of a new transformed human jejunal epithelioid cell line (HIE-7) to HGF/SF. Morphologically HIE-7 cells are immature. Their epithelial lineage was confirmed by reactivity with the epithelial specific antibodies AE1/AE3, Cam 5.2, Ber-EP4 and anti-EMA and is consistent with their expression of c-met mRNA and protein. In addition, electron microscopic analysis revealed the presence of primitive junctions and rudimentary microvilli, but features of polarization were absent. When grown on reconstituted basement membranes, HIE-7 cells formed closely associated multicellular cord-like structures adjacent to acellular spaces. However, the cells did not mature structurally, form lumen-like structures or express disaccharidase mRNA, even in the presence of recombinant HGF (rHGF). On the other hand, rHGF induced HIE-7 cells to scatter and stimulated their rapid migration in a modified wound assay. To determine whether the motogenic effect caused by rHGF is associated with HIE-7 cell invasiveness across reconstituted basement membranes, a Boyden chamber chemoinvasion assay was performed. rHGF stimulated a 10-fold increase in the number of HIE-7 cells that crossed the basement membrane barrier, while only stimulating a small increase in chemotaxis across a collagen IV matrix, suggesting that the cytokine activates matrix penetration by these cells. rHGF also stimulated the invasion of basement membranes by an undifferentiated rat intestinal cell line (IEC-6) and by two human colon cancer cell lines which are poorly differentiated (DLD-1 and SW 948). In contrast, two moderately well differentiated colon cancer cell lines (Caco-2 and HT-29) did not manifest an invasive response when exposed to rHGF. These results suggest that HGF/SF may play a significant role in the invasive behavior of anaplastic and poorly differentiated gut epithelial tumors.

Control of cell cycle progression by phosphorylation of cyclin-dependent kinase (CDK) substrates

The eukaryotic cell cycle is a fundamental evolutionarily conserved process that regulates cell division from simple unicellular organisms, such as yeast, through to higher multicellular organisms, such as humans. The cell cycle comprises several phases, including the S-phase (DNA synthesis phase) and M-phase (mitotic phase). During S-phase, the genetic material is replicated, and is then segregated into two identical daughter cells following mitotic M-phase and cytokinesis. The S- and M-phases are separated by two gap phases (G1 and G2) that govern the readiness of cells to enter S- or M-phase. Genetic and biochemical studies demonstrate that cell division in eukaryotes is mediated by CDKs (cyclin-dependent kinases). Active CDKs comprise a protein kinase subunit whose catalytic activity is dependent on association with a regulatory cyclin subunit. Cell-cycle-stage-dependent accumulation and proteolytic degradation of different cyclin subunits regulates their association with CDKs to control different stages of cell division. CDKs promote cell cycle progression by phosphorylating critical downstream substrates to alter their activity. Here, we will review some of the well-characterized CDK substrates to provide mechanistic insights into how these kinases control different stages of cell division.

Three dimensional in-vitro models for studying cancer angiogenesis

Introduction Hydrogels prepared from star-shaped poly(ethylene glycol) (PEG) and maleimide-functionalized heparin provide a potential matrix for use in developing three dimensional (3D) models. We have previously demonstrated that these hydrogels support the cultivation of human umbilical vein endothelial cells (HUVECs). We extend this body of work to study the ability to create an extracellular matrix (ECM)-like model to study breast and prostate cancer cell growth in 3D. Also, we investigate the ability to produce a tri-culture mimicking tumour angiogenesis with cancer spheroids, HUVECs and mesenchymal stem cells (MSCs). Materials and Methods The breast cancer cell lines, MCF-7 and MDA-MB-231, and prostate cancer cell lines, LNCaP and PC3, were seeded into starPEG-heparin hydrogels and grown for 14 Days to analyze the effects of varying hydrogel stiffness on spheroid development. Resulting hydrogel constructs were analyzed via proliferation assays, light microscopy, and immunostaining. Cancer cell lines were then seeded into starPEG-heparin hydrogels functionalized with growth factors as spheroids with HUVECs and MSCs and grown as a tri-culture. Cultures were analyzed via immunostaining and observed using confocal microscopy. Results Cultures prepared in MMP-cleavable starPEG-heparin hydrogels display spheroid formation in contrast to adherent growth on tissue culture plastic. Small differences were visualized in cancer spheroid growth between different gel stiffness across the range of cell lines. Cancer cell lines were able to be co-cultivated with HUVECs and MSC. Interaction was visualized between tumours and HUVECs via confocal microscopy. Further studies intend to further optimize and mimic the ECM environment of in-situ tumour angiogenesis. Discussion Our results confirm the suitability of hydrogels constructed from starPEG-heparin for HUVEC and MSC co-cultivation with cancer cell lines to study cell-cell and cell-matrix interactions in a 3D environment. This represents a step forward in the development of 3D culture models to study the pathomechanisms of breast and prostate cancer.