A cellular automata model to investigate immune cell–tumor cell interactions in growing tumors in two spatial dimensions

We develop a hybrid cellular automata model to describe the effect of the immune system and chemokines on a growing tumor. The hybrid cellular automata model consists of partial differential equations to model chemokine concentrations, and discrete cellular automata to model cell–cell interactions and changes. The computational implementation overlays these two components on the same spatial region. We present representative simulations of the model and show that increasing the number of immature dendritic cells (DCs) in the domain causes a decrease in the number of tumor cells. This result strongly supports the hypothesis that DCs can be used as a cancer treatment. Furthermore, we also use the hybrid cellular automata model to investigate the growth of a tumor in a number of computational “cancer patients.” Using these virtual patients, the model can explain that increasing the number of DCs in the domain causes longer “survival.” Not surprisingly, the model also reflects the fact that the parameter related to tumor division rate plays an important role in tumor metastasis.

A hybrid cellular automata model of multicellular tumour spheroid growth in hypoxic microenvironment

A three-dimensional hybrid cellular automata (CA) model is developed to study the dynamic process of multicellular tumour spheroid (MTS) growth by introducing hypoxia as an important microenvironment factor which influences cell migration and cell phenotype expression. The model enables us to examine the effects of different hypoxic environments on the growth history of the MTS and to study the dynamic interactions between MTS growth and chemical environments. The results include the spatial distribution of different phenotypes of tumour cells and associated oxygen concentration distributions under hypoxic conditions. The discussion of the model system responses to the varied hypoxic conditions reveals that the improvement of the resistance of tumour cells to a hypoxic environment may be important in the tumour normalization therapy.

An improved model of tumour-immune system interactions

The immune system plays an important role in defending the body against tumours and other threats. Currently, mechanisms involved in immune system interactions with tumour cells are not fully understood. Here we develop a mathematical tool that can be used in aiding to address this shortfall in understanding. This paper de- scribes a hybrid cellular automata model of the interaction between a growing tumour and cells of the innate and specific immune system including the effects of chemokines that builds on previous models of tumour-immune system interactions. In particular, the model is focused on the response of immune cells to tumour cells and how the dynamics of the tumour cells change due to the immune system of the host. We present results and predictions of in silico experiments including simulations of Kaplan-Meier survival-like curves.

On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Chlamydial infection and spatial ascension of the female genital tract : a novel hybrid cellular automata and continuum mathematical model

Sexually transmitted chlamydial infection initially establishes in the endocervix in females, but if the infection ascends the genital tract, significant disease, including infertility, can result. Many of the mechanisms associated with chlamydial infection kinetics and disease ascension are unknown. We attempt to elucidate some of these processes by developing a novel mathematical model, using a cellular automata–partial differential equation model. We matched our model outputs to experimental data of chlamydial infection of the guinea-pig cervix and carried out sensitivity analyses to determine the relative influence of model parameters. We found that the rate of recruitment and action of innate immune cells to clear extracellular chlamydial particles and the rate of passive movement of chlamydial particles are the dominant factors in determining the early course of infection, magnitude of the peak chlamydial time course and the time of the peak. The rate of passive movement was found to be the most important factor in determining whether infection would ascend to the upper genital tract. This study highlights the importance of early innate immunity in the control of chlamydial infection and the significance of motility-diffusive properties and the adaptive immune response in the magnitude of infection and in its ascension.

Perfusion model system to generate engineered grafts with controlled cellular distributions

Engineered tissue grafts, which mimic the spatial variations of cell density and extracellular matrix present in native tissues, could facilitate more efficient tissue regeneration and integration. We previously demonstrated that cells could be uniformly seeded throughout a 3D scaffold having a random pore architecture using a perfusion bioreactor2. In this work, we aimed to generate 3D constructs with defined cell distributions based on rapid prototyped scaffolds manufactured with a controlled gradient in porosity. Computational models were developed to assess the influence of fluid flow, associated with pore architecture and perfusion regime, on the resulting cell distribution.

Cellular model systems to study the tumor biological role of kallikrein-related peptidases in ovarian and prostate cancer

Since the identification of the gene family of kallikrein related peptidases (KLKs), their function has been robustly studied at the biochemical level. In vitro biochemical studies have shown that KLK proteases are involved in a number of extracellular processes that initiate intracellular signaling pathways by hydrolysis, as reviewed in Chapters 8, 9, and 15, Volume 1. These events have been associated with more invasive phenotypes of ovarian, prostate, and other cancers. Concomitantly, aberrant expression of KLKs has been associated with poor prognosis of patients with ovarian and prostate cancer (Borgoño and Diamandis, 2004; Clements et al., 2004; Yousef and Diamandis, 2009), with prostate-specific antigen (PSA, KLK3) being a long standing, clinically employed biomarker for prostate cancer (Lilja et al., 2008). Data generated from patient samples in clinical studies, alongwith biochemical activity, suggests that KLKs function in the development and progression of these diseases. To bridge the gap between their function at the molecular level and the clinical need for efficacious treatment and prognostic biomarkers, functional assessment at the in vitro cellular level, using various culture models, is increasing, particularly in a three-dimensional (3D) context (Abbott, 2003; Bissell and Radisky, 2001; Pampaloni et al., 2007; Yamada and Cukierman, 2007).

Infection and cellular defense dynamics in a novel 17beta-estradiol murine model of chronic human group B streptococcus genital tract colonization reveal a role for hemolysin in persistence and neutrophil accumulation

Genital tract carriage of group B streptococcus (GBS) is prevalent among adult women; however, the dynamics of chronic GBS genital tract carriage, including how GBS persists in this immunologically active host niche long term, are not well defined. To our knowledge, in this study, we report the first animal model of chronic GBS genital tract colonization using female mice synchronized into estrus by delivery of 17β-estradiol prior to intravaginal challenge with wild-type GBS 874391. Cervicovaginal swabs, which were used to measure bacterial persistence, showed that GBS colonized the vaginal mucosa of mice at high numbers (106–107 CFU/swab) for at least 90 d. Cellular and histological analyses showed that chronic GBS colonization of the murine genital tract caused significant lymphocyte and PMN cell infiltrates, which were localized to the vaginal mucosal surface. Long-term colonization was independent of regular hormone cycling. Immunological analyses of 23 soluble proteins related to chemotaxis and inflammation showed that the host response to GBS in the genital tract comprised markers of innate immune activation including cytokines such as GM-CSF and TNF-α. A nonhemolytic isogenic mutant of GBS 874391, Δcyle9, was impaired for colonization and was associated with amplified local PMN responses. Induction of DNA neutrophil extracellular traps, which was observed in GBS-infected human PMNs in vitro in a hemolysin-dependent manner, appeared to be part of this response. Overall, this study defines key infection dynamics in a novel murine model of chronic GBS genital tract colonization and establishes previously unknown cellular and soluble defense responses to GBS in the female genital tract.

A model to explain specific cellular communications and cellular harmony: - a hypothesis of coupled cells and interactive coupling molecules

Background The various cell types and their relative numbers in multicellular organisms are controlled by growth factors and related extracellular molecules which affect genetic expression pathways. However, these substances may have both/either inhibitory and/or stimulatory effects on cell division and cell differentiation depending on the cellular environment. It is not known how cells respond to these substances in such an ambiguous way. Many cellular effects have been investigated and reported using cell culture from cancer cell lines in an effort to define normal cellular behaviour using these abnormal cells. A model is offered to explain the harmony of cellular life in multicellular organisms involving interacting extracellular substances. Methods A basic model was proposed based on asymmetric cell division and evidence to support the hypothetical model was accumulated from the literature. In particular, relevant evidence was selected for the Insulin-Like Growth Factor system from the published data, especially from certain cell lines, to support the model. The evidence has been selective in an attempt to provide a picture of normal cellular responses, derived from the cell lines. Results The formation of a pair of coupled cells by asymmetric cell division is an integral part of the model as is the interaction of couplet molecules derived from these cells. Each couplet cell will have a receptor to measure the amount of the couplet molecule produced by the other cell; each cell will be receptor-positive or receptor-negative for the respective receptors. The couplet molecules will form a binary complex whose level is also measured by the cell. The hypothesis is heavily supported by selective collection of circumstantial evidence and by some direct evidence. The basic model can be expanded to other cellular interactions. Conclusions These couplet cells and interacting couplet molecules can be viewed as a mechanism that provides a controlled and balanced division-of-labour between the two progeny cells, and, in turn, their progeny. The presence or absence of a particular receptor for a couplet molecule will define a cell type and the presence or absence of many such receptors will define the cell types of the progeny within cell lineages.

A natural model for architecture : the nature of the evolutionary model 1995

John Frazer's architectural work is inspired by living and generative processes. Both evolutionary and revolutionary, it explores informatin ecologies and the dynamics of the spaces between objects. Fuelled by an interest in the cybernetic work of Gordon Pask and Norbert Wiener, and the possibilities of the computer and the "new science" it has facilitated, Frazer and his team of collaborators have conducted a series of experiments that utilize genetic algorithms, cellular automata, emergent behaviour, complexity and feedback loops to create a truly dynamic architecture. Frazer studied at the Architectural Association (AA) in London from 1963 to 1969, and later became unit master of Diploma Unit 11 there. He was subsequently Director of Computer-Aided Design at the University of Ulter - a post he held while writing An Evolutionary Architecture in 1995 - and a lecturer at the University of Cambridge. In 1983 he co-founded Autographics Software Ltd, which pioneered microprocessor graphics. Frazer was awarded a person chair at the University of Ulster in 1984. In Frazer's hands, architecture becomes machine-readable, formally open-ended and responsive. His work as computer consultant to Cedric Price's Generator Project of 1976 (see P84)led to the development of a series of tools and processes; these have resulted in projects such as the Calbuild Kit (1985) and the Universal Constructor (1990). These subsequent computer-orientated architectural machines are makers of architectural form beyond the full control of the architect-programmer. Frazer makes much reference to the multi-celled relationships found in nature, and their ongoing morphosis in response to continually changing contextual criteria. He defines the elements that describe his evolutionary architectural model thus: "A genetic code script, rules for the development of the code, mapping of the code to a virtual model, the nature of the environment for the development of the model and, most importantly, the criteria for selection. In setting out these parameters for designing evolutionary architectures, Frazer goes beyond the usual notions of architectural beauty and aesthetics. Nevertheless his work is not without an aesthetic: some pieces are a frenzy of mad wire, while others have a modularity that is reminiscent of biological form. Algorithms form the basis of Frazer's designs. These algorithms determine a variety of formal results dependent on the nature of the information they are given. His work, therefore, is always dynamic, always evolving and always different. Designing with algorithms is also critical to other architects featured in this book, such as Marcos Novak (see p150). Frazer has made an unparalleled contribution to defining architectural possibilities for the twenty-first century, and remains an inspiration to architects seeking to create responsive environments. Architects were initially slow to pick up on the opportunities that the computer provides. These opportunities are both representational and spatial: computers can help architects draw buildings and, more importantly, they can help architects create varied spaces, both virtual and actual. Frazer's work was groundbreaking in this respect, and well before its time.

A two-compartment mechanochemical model of the roles of transforming growth factor-beta and tissue tension in dermal wound healing

The repair of dermal tissue is a complex process of interconnected phenomena, where cellular, chemical and mechanical aspects all play a role, both in an autocrine and in a paracrine fashion. Recent experimental results have shown that transforming growth factor-beta (TGF-beta) and tissue mechanics play roles in regulating cell proliferation, differentiation and the production of extracellular materials. We have developed a 1D mathematical model that considers the interaction between the cellular, chemical and mechanical phenomena, allowing the combination of TGF-beta and tissue stress to inform the activation of fibroblasts to myofibroblasts. Additionally, our model incorporates the observed feature of residual stress by considering the changing zero-stress state in the formulation for effective strain. Using this model, we predict that the continued presence of TGF-beta in dermal wounds will produce contractures due to the persistence of myofibroblasts; in contrast, early elimination of TGF-beta significantly reduces the myofibroblast numbers resulting in an increase in wound size. Similar results were obtained by varying the rate at which fibroblasts differentiate to myofibroblasts and by changing the myofibroblast apoptotic rate. Taken together, the implication is that elevated levels of myofibroblasts is the key factor behind wounds healing with excessive contraction, suggesting that clinical strategies which aim to reduce the myofibroblast density may reduce the appearance of contractures.

Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion : a continuum model of matrix metabolism and transport

The functional properties of cartilaginous tissues are determined predominantly by the content, distribution, and organization of proteoglycan and collagen in the extracellular matrix. Extracellular matrix accumulates in tissue-engineered cartilage constructs by metabolism and transport of matrix molecules, processes that are modulated by physical and chemical factors. Constructs incubated under free-swelling conditions with freely permeable or highly permeable membranes exhibit symmetric surface regions of soft tissue. The variation in tissue properties with depth from the surfaces suggests the hypothesis that the transport processes mediated by the boundary conditions govern the distribution of proteoglycan in such constructs. A continuum model (DiMicco and Sah in Transport Porus Med 50:57-73, 2003) was extended to test the effects of membrane permeability and perfusion on proteoglycan accumulation in tissue-engineered cartilage. The concentrations of soluble, bound, and degraded proteoglycan were analyzed as functions of time, space, and non-dimensional parameters for several experimental configurations. The results of the model suggest that the boundary condition at the membrane surface and the rate of perfusion, described by non-dimensional parameters, are important determinants of the pattern of proteoglycan accumulation. With perfusion, the proteoglycan profile is skewed, and decreases or increases in magnitude depending on the level of flow-based stimulation. Utilization of a semi-permeable membrane with or without unidirectional flow may lead to tissues with depth-increasing proteoglycan content, resembling native articular cartilage.