Chemotaxis-based spatial self-organization algorithms

Self-organization is a process that increases the order of a system as a result of local interactions among low-level, simple components, without the guidance of an outside source. Spatial self-organization is a process in which shapes and structures emerge at a global level from collective movements of low level shape primitives. Spatial self-organization is a stochastic process, and the outcome of the aggregation cannot necessarily be guaranteed. Despite the inherent ambiguity, self-organizing complex systems arise everywhere in nature. Motivated by the ability of living cells to form specific shapes and structures, we develop two self-organizing systems towards the ultimate goal of directing the spatial self-organizing process. We first develop a self-sorting system composed of a mixture of cells. The system consistently produces a sorted structure. We then extend the sorting system to a general shape formation system. To do so, we introduce morphogenetic primitives (MP), defined as software agents, which enable self-organizing shape formation of user-defined structures through a chemotaxis paradigm. One challenge that arises from the shape formation process is that the process may form two or more stable final configurations. In order to direct the self-organizing process, we find a way to characterize the macroscopic configuration of the MP swarm. We demonstrate that statistical moments of the primitives' locations can successfully capture the macroscopic structure of the aggregated shape. We do so by predicting the final configurations produced by our spatial self-organization system at an early stage in the process using features based on the statistical moments. At the next stage, we focus on developing a technique to control the outcome of bifurcating aggregations. We identify thresholds of the moments and generate biased initial conditions whose statistical moments meet the thresholds. By starting simulations with biased, random initial configurations, we successfully control the aggregation for a number of swarms produced by the agent-based shape formation system. This thesis demonstrates that chemotaxis can be used as a paradigm to create an agent- based spatial self-organization system. Furthermore, statistical moments of the swarm can be used to robustly predict and control the outcomes of the aggregation process.Ph.D., Computer Science -- Drexel University, 201

Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles

The description of the cell spatial pattern and characteristic distances is fundamental in a wide range of physio-pathological biological phenomena, from morphogenesis to cancer growth. Discrete particle models are widely used in this field, since they are focused on the cell-level of abstraction and are able to preserve the identity of single individuals reproducing their behavior. In particular, a fundamental role in determining the usefulness and the realism of a particle mathematical approach is played by the choice of the intercellular pairwise interaction kernel and by the estimate of its parameters. The aim of the paper is to demonstrate how the concept of H-stability, deriving from statistical mechanics, can have important implications in this respect. For any given interaction kernel, it in fact allows to a priori predict the regions of the free parameter space that result in stable configurations of the system characterized by a finite and strictly positive minimal interparticle distance, which is fundamental when dealing with biological phenomena. The proposed analytical arguments are indeed able to restrict the range of possible variations of selected model coefficients, whose exact estimate however requires further investigations (e.g., fitting with empirical data), as illustrated in this paper by series of representative simulations dealing with cell colony reorganization, sorting phenomena and zebrafish embryonic development

Self-organized collective cell behaviors as design principles for synthetic developmental biology

Over the past two decades, molecular cell biology has graduated from a mostly analytic science to one with substantial synthetic capability. This success is built on a deep understanding of the structure and function of biomolecules and molecular mechanisms. For synthetic biology to achieve similar success at the scale of tissues and organs, an equally deep understanding of the principles of development is required. Here, we review some of the central concepts and recent progress in tissue patterning, morphogenesis and collective cell migration and discuss their value for synthetic developmental biology, emphasizing in particular the power of (guided) self-organization and the role of theoretical advances in making developmental insights applicable in synthesis

Lattice-Gas Cellular Automata In Modeling Biological Pattern Formation

There are several phenomena present in the physical world which can be defined or predicted by specific models. Cellular automata are basic mathematical models for characterization of natural systems by generating simple components and their local interactions. These models are specified on simple updating rules yet demonstrate complex behavior of physical phenomena. Besides this, lattice-gas cellular automata models go one step further and differ from cellular automata by having split updating rule into two parts as collision and propagation. In this study, the goal is to analyze hexagonal lattice-gas cellular automata with single cell type by using agent-based modeling and simulate the model with NetLogo to observe pattern formation. The model examination is focused on the two parameters for stability analysis. The results show that if there is a pattern formation in the model, the system is unstable, and if the patches are smaller and lighter patches, it is stable. Furthermore, the analysis for the choice of particle density and adhesion coefficient displayed that they are the main decision-mechanisms for general structure

Bioengineering strategies for cancer therapy and modelling

Tese de doutoramento em Engenharia de Tecidos, Medicina Regenerativa e Células EstaminaisCancer is a global pandemic with a high incidence among the world population and effective treatments are for the most part elusive. The tumor microenvironment is a highly complex and heterotypic mixture of cells that interact to regulate central control mechanisms, driving immunosuppression and promoting both survival and invasion of cancer cells into surrounding tissues. It has been this complexity that has made finding effective therapeutics such a demanding task and therefore cancer still remains a burden worldwide in health as well as in economic terms. While the progression in the field of cancer research has been clear over the years, there are still several challenges that need to be addressed. Herein, two different sides to this disease are explored: treatment and in vitro models. Adoptive T cell therapy has shown impressive results, however not without its limitations. The use of the T cell mitogen IL-2 within culture systems is known to lead to early exhaustion of T cell subsets while high density of co-stimulating molecules has been linked to undesired immune responses. As an alternative, a nanoparticle system based on the natural polymer gellan-gum was proposed, with tailorable surface functionalization with co-stimulatory molecules. High levels of T cell expansion were observed over the studied period, with secreted IL-2 levels overcoming those of commercial alternatives. With this system, increased expression of cytotoxic molecules Granzyme B and Perforin were also detected in vitro. On the other spectrum, 3D cancer models have sustained a great number of developments observed by an increase in similarity towards native tissues; however, a requirement for even more complex architectures capable of better mimicking cellular interactions is still present. Therefore, an assembloid-based approach was proposed to develop a 3D in vitro melanoma model to further study cellular interactions. These heterotypic tumor assembloids presented a complex architecture capable of sustaining endothelial cell function as well as a high expression of stemness-related markers. These models were subjected to functionality assays where they showed a capacity for “cooperative invasion” which was coincident with an observed increased production of MMP-2. To further unravel the role of stromal cells in the invasive potential of cancer cells a 3D chemotaxis chamber was developed to study cellular interactions observed in the tumor microenvironment, where stem cells and fibroblasts showed to have a crucial role. Ultimately, this thesis allowed to explore biomedical engineering approaches to further contribute to the knowledge in the field opening new doors to be explored in the future.O cancro é uma pandemia global com uma elevada incidência e cujo desenvolvimento de tratamentos eficazes continua a ser difícil. O microambiente tumoral é uma mistura altamente complexa e heterotípica de células que interagem para regular mecanismos centrais que provocam imunossupressão promovendo a sobrevivência e invasão de células tumorais para os tecidos circundantes. É esta complexidade que tem tornado desafiante encontrar terapias eficazes, tornando esta doença um fardo a nível global em termos de saúde e economia. Enquanto a progressão na área da investigação oncológica tem sido clara ao longo dos anos, existem ainda vários desafios que precisam de serem encarados para permitir futuros desenvolvimentos. Aqui, foram exploradas duas vertentes diferentes desta doença: o tratamento e os modelos in vitro. A terapia celular adotiva tem demonstrado resultados impressionantes, no entanto não sem as suas limitações. O uso do mitogénio IL-2 nestes sistemas de cultura é conhecido por levar rapidamente à exaustão das células T, enquanto o uso de moléculas co-estimulatórias em elevadas densidades está associado a respostas imunes não desejadas. Como alternativa, foi proposto um sistema de nanopartículas baseado no polímero natural goma gelana e funcionalizado com moléculas co estimulatórias. Foram observados elevados níveis de expansão de células T e quantidade de IL-2 secretada superior à de alternativas comerciais. Foi ainda verificado in vitro um aumento de expressão das moléculas citotóxicas Grazima B e Perforina. No outro espectro, têm sido desenvolvidos modelos tumorais 3D com uma cada vez maior similaridade para tecidos nativos; no entanto, a necessidade de arquiteturas ainda mais complexas capazes de melhor representar interações celulares persiste. Assim, foi proposta uma abordagem baseada em “assemblóides” para obter modelos 3D in vitro de melanoma para estudar interações celulares. Estes “assemblóides” tumorais heterotípicos apresentaram uma arquitetura complexa capaz de suportar a função de células endoteliais, bem como a elevada expressão de marcadores de pluripotência. Estes modelos foram sujeitos a ensaios de funcionalidade onde mostraram a capacidade de “invasão cooperativa” que foi coincidente com uma produção aumentada de MMP-2. Para tornar mais claro o papel das células estaminais no potencial invasivo de células tumorais, uma câmara 3D de quimiotaxia foi desenvolvida para estudar as interações celulares observadas no microambiente tumoral onde as células estaminais e fibroblastos mostraram ter um papel determinante. Em última análise, esta tese permitiu explorar abordagens da engenharia biomédica de forma a contribuir para o conhecimento da área e abrir novas portas a serem exploradas no futuro

Using Differential Adhesion to Control Self-Assembly and Self-Repair of Collections of Modular Mobile Robots

Institute of Perception, Action and BehaviourThis thesis presents a novel distributed control method which allows a collection of independently mobile robotic units, with two or three dimensional movement, to self-assemble into self-repairing hierarchical structures. The proposed method utilises a simple model of the cellular adhesion mechanisms observed in biological cells, allowing the robotic units to form virtually bonded aggregates which behave as predicted by Steinberg’s differential adhesion hypothesis. Simulated robotic units based on the design of the subaquatic HYDRON module are introduced as a possible platform on which the model can be implemented. The units are used to carry out a detailed investigation of the model behaviour and parameter space focusing on the two main tasks of rounding and sorting in both two and three dimensions. These tasks assess the model’s ability to reach a thermodynamically stable configuration when the aggregates consist of either a single population of units or multiple populations of units with differing adhesive properties. The results are analysed in detail with particular attention given to the role of random movements in determining the overall performance, and demonstrate that this model provides a very robust solution to these complex tasks. Finally, a possible extension of this work is presented in which the original model is combined with a genetic regulatory network controller. The performance of this composite is evaluated, and the benefits of this hybrid approach, in which a powerful control system manipulates a robust self-organising behaviour, are discussed

Multi-scale models of ovarian cancer

In ovarian cancer, disease and treatment can be examined across multiple spatial scales including molecules, cells, intra-tumor vasculature, and body-scale dynamics of circulating drugs. Survival of primary tumor cells and their development into disseminated tumors is related to adhesion between the cells, attachment, and invasion. Growth of new tumors depends on the delivery of nutrients, which depends on the tumor diameter and the tumors vasculature. Drug delivery also depends on tumor diameter and vasculature, and molecular- and gross-scale drug processes. A cellular Potts simulation integrated data at these multiple scales to model microscopic residual disease during relapse after a primary surgery. The model generated new hypotheses about tumor cell behavior, and the effectiveness of drug delivery to tumors disseminated in the peritoneal cavity. First, the model required high intra-tumor adhesion in ovarian tumors, the existence of an unknown factor that drew tumor cells to vessels, a threshold of vascular endothelial growth factor (VEGF) for initiation of endothelial sprouting, and constitutive expression of angiogenic chemical messengers by tumor cells prior to needing oxygen. Alteration of the model incorporated drug delivery by the two standard routes, intraperitoneal and intravenous, from tumor vasculature parameterized from real patient data. Delivery of both small- and large-molecular weight therapies was superior during intraperitoneal therapy. Finally, empirical and theoretical distributions of vessel radii were considered. Samples from tumors with each type of vascular morphology were run as though too distant from the peritoneal cavity to receive peritoneal delivery, with three results: first, intravenous delivery was superior to the secondary delivery into the circulatory system from a primary intraperitoneal delivery. Second, small molecules penetrated homogeneously across all cells, regardless of vascular volume or morphology, while antibodies penetrated heterogeneously, particularly in low-vessel-volume samples. Third, when each of the whole tumors was considered, this heterogeneity resulted in a large sub-population of cells that accumulated non-therapeutic levels of antibody, even during the best delivery scenario (IV). Fourth, delivery of antibodies was poorest in the empirical distribution. Finally, hypotheses were generated about the impact of heterogeneity of drug delivery, to be addressed as future questions

Creation of a Pioneer-Neuron Axonal Pathfinding Model for Future Applications in Developmental Neurotoxicity Testing

The developing central nervous system is a unique target for environmental toxicants both pre- and postnatal. Exposure to industrial chemical toxicants at various stages throughout development are known to contribute to injuries that result in autism, attention-deficit hyperactivity disorder (ADHD), dyslexia, and other cognitive impairments [81]. The damage caused by these exposures is often untreatable and frequently permanent, resulting in reduced intelligence (expressed in terms of lost IQ points) or behavioral abnormalities. It is now reported that 10-15% of all births are associated with disorders of neurobehavioral development [81], where 1 in 68 children in the United States is diagnosed with some form of an autism spectrum disorder (ASD) [7, 93, 188] and 14% of the roughly 4 million children born each year suffer from ADHD [124]. It is estimated that 3% of developmental disabilities are the direct result of environmental exposure, and that another 25% stem from interactions between environmental factors and genetic susceptibility [80, 146]. With more diagnosed cases and rising costs, the identification of the chemicals responsible for the deleterious effects on the developing nervous system has become significant topic of research. Current developmental neurotoxicity (DNT) testing relies heavily on whole animal approaches for hazard identification and dose-response evaluations. These methods are not practical for screening the over 82,000 chemicals already used in commerce with an additional 700 new chemicals introduced annually [24]. Following the first workshop on “Incorporating In Vitro Alternative Methods for Developmental Neurotoxicity (DNT) Testing into International Hazard and Risk Assessment Strategies†in 2005, it was determined that in vitro DNT testing methods should be included as part of a tiered approach to help create a reference list of potential developmentally neurotoxic chemicals and catalog the effects they have on various developmental mechanistic endpoints [40, 127]. Using directionality of pioneer-neuron axonal pathfinding as the mechanism for evaluation, we developed a biochip-based single-neuron axonal pathfinding assay to subjugate extending axons to simultaneous geometric and chemical guidance. To achieve this we devised a laser cell-micropatterning system to facilitate the placement of individual-neurons to exact locations on a PDMS substrate. The cell-culture conditions were optimized to promote single-neuron axonal extension through and beyond the confinements of a geometric guidance microchannel. Evaluation of the pathfinding direction in response to geometric guidance was compared to that of geometric and chemical stimuli. We found using our system that the addition of a chemical guidance component 1) increased the number of individual-neurons extending an axon at least 20 µm beyond the end of a guidance microchannel structure and 2) showed the potential to elicit a growth cone turning event by abruptly changing the initial pathfinding trajectory of an axon. Based on our previous study that single-neuron axonal pathfinding under geometric guidance is one order of magnitude more sensitive to a chemical toxicant, our research data demonstrate that we have created a platform that can be used to test the possible effects that low dose (nM concentrations) chemical exposures may have on pioneer-neuron axonal pathfinding

Spatial quantification and mathematical modelling of tissue development

In this thesis, we study biological tissue development, during which cells organise themselves into structures which perform a specific function. Understanding how particular types of mechanisms lead to the emergence of various cell patterns in tissues is the main motivation of this research. Quantifying the tissue patterns is a first step towards understanding which mechanisms are at work in particular experiments. For this purpose, we develop pair-correlation functions (PCFs) which quantify how a spatial distribution of cells deviates from complete spatial randomness over specified directions. We evaluate the usefulness of PCFs for studying the three-dimensional organisation of cells in tumour spheroids and show that the PCFs robustly reveal information about their spatial structure. In particular, we demonstrate that the boundary that separates the necrotic and viable zones in the tumour spheroids can be detected using the PCF with a high degree of accuracy. We then turn to development of mathematical models to investigate the types of patterns that can arise from simple hypothesised interactions between cells. We begin in Chapter 3 by developing an on-lattice agent-based model (ABM) to investigate tumour spheroid growth using two different culture methods: suspension culture, and culture within a microgel. Our results suggest that stratifying the seeded cells into multiple layers and also reducing cell death are the key effects of the microgel that enable it to produce more uniformly-sized spheroids. In Chapter 4, we extend the ABM to study systems with two interacting species. A huge variety of aggregation patterns can arise in these systems, depending upon the underlying attractive-repulsive mechanisms. More specifically, we show that the run-and chase mechanism can produce a striped pattern, similar to that observed on the skin of zebrafish. Finally, we develop a non-local continuous model, approximating the mean behaviour of the ABM. This provides a connection between the cell-level and population-level models of tissue development. A linear stability analysis of the continuous model allows us to investigate parameter regimes that produce striped patterns. Importantly, we also point out the disparities that may arise between the behaviours of the continuous and discrete models, which highlights the importance of considering the underlying biological constraints in using the continuous approximated models. In particular, we show that the derivation of the approximate continuum model from the ABM introduces terms representing cell-size effects. These terms can lead to the emergence of stripes in cases where they would not be predicted in the similar continuum model of Painter et al. (2015), which does not include these terms. The combination of spatial quantification and mathematical modelling (using both continuous and discrete methods) developed in this work helps us to gain a better understanding of tissue development. Our approach provides a novel means to investigate the underpinning mechanisms of tissue development by combining model simulations with analysis of biological and synthetic data using the pair-correlation functions.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 201

Cell adhesion and cell mechanics during zebrafish development

During vertebrate development, gastrulation leads to the formation of three distinct germlayers. In zebrafish a central process is the delamination and the ingression of single cells from a common ancestor tissue - that will lead to the formation of the germlayers. Several molecules have been identified to regulate this process but the precise cellular mechanisms are poorly understood. Differential adhesiveness, a concept first introduced by Steinberg over 40 years ago, has been proposed to represent a key phenomena by which single hypoblast cells separate from the epiblast to form the mesendoderm at later stages. In this work it is shown that differential adhesion among the germlayer progenitor cells alone cannot predict germlayer formation. It is a combination of several mechanical properties such as cell cortex tension, cell adhesion and membrane mechanical properties that influence the migratory behavior of the constituent cells