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

Investigating biocomplexity through the agent-based paradigm.

Capturing the dynamism that pervades biological systems requires a computational approach that can accommodate both the continuous features of the system environment as well as the flexible and heterogeneous nature of component interactions. This presents a serious challenge for the more traditional mathematical approaches that assume component homogeneity to relate system observables using mathematical equations. While the homogeneity condition does not lead to loss of accuracy while simulating various continua, it fails to offer detailed solutions when applied to systems with dynamically interacting heterogeneous components. As the functionality and architecture of most biological systems is a product of multi-faceted individual interactions at the sub-system level, continuum models rarely offer much beyond qualitative similarity. Agent-based modelling is a class of algorithmic computational approaches that rely on interactions between Turing-complete finite-state machines--or agents--to simulate, from the bottom-up, macroscopic properties of a system. In recognizing the heterogeneity condition, they offer suitable ontologies to the system components being modelled, thereby succeeding where their continuum counterparts tend to struggle. Furthermore, being inherently hierarchical, they are quite amenable to coupling with other computational paradigms. The integration of any agent-based framework with continuum models is arguably the most elegant and precise way of representing biological systems. Although in its nascence, agent-based modelling has been utilized to model biological complexity across a broad range of biological scales (from cells to societies). In this article, we explore the reasons that make agent-based modelling the most precise approach to model biological systems that tend to be non-linear and complex

Selection and competition of somatic mutations in normal epithelia

Tumourigenesis occurs when a series of genome alterations occur in the same group of cells and cause uncontrolled cell proliferation. Therefore, to understand the journey from healthy to cancerous tissue, it is important to study the accumulation and spread of mutations in pre- cancerous normal tissues. Recent studies have shown that apparently normal epithelium contains a high burden of mutations in cancer-associated genes. This thesis explores the behaviour of mutant clones in normal epithelium and how this affects cancer development. The nature of mutant clonal growth and competition in normal epidermis has been a subject of debate. A study found that mutant clone sizes inferred from DNA sequencing of normal human eyelid skin were consistent with a mathematical model of neutral cell dynamics, appearing to contradict a genetic analysis of the same dataset that found several genes under positive selection. I investigate this debate using computational modelling that takes into account the tissue structure and experimental tissue-sampling methods. The results show that mutant clone sizes in skin and oesophagus are consistent with non-neutral clonal competition. Further evidence for non-neutral selection in normal epithelium is found in patterns of mutations detected by DNA sequencing. By adapting a statistical method used for driver gene discovery, I look for enrichment or depletion of structural categories of missense mutations and find biologically meaningful patterns of selection in several proteins. The method can associate changes to protein structure or function with cell fitness, even in the absence of hotspot mutations and in the presence of passenger mutations. I demonstrate how the method is flexible and could be widely applicable, but can also produce misleading results if confounding sources of selection are not accounted for. Clonal competition in normal oesophageal epithelium is dominated by Notch1 loss-of- function mutations. I fit stochastic models of clonal dynamics to lineage tracing data to show that haploinsufficiency greatly accelerates Notch1 mutant expansion and that the loss of the second Notch1 allele provides a further strong selective advantage, consistent with the high frequency of NOTCH1 loss-of-heterozygosity events observed in human oesophagus. Finally, I examine a consequence of the spread of these highly fit mutant clones in the normal tissue. I use a mathematical model to analyse the results of a series of experiments in mutagen-treated mouse oesophagus, finding that microscopic tumours can be eliminated by highly fit clones in the surrounding normal tissue.Harrison Watson Fund at Clare College, Cambridg

Models of self-organization in biological development

Bibliography: p. 297-320.In this thesis we thus wish to consider the concept of self-organization as an overall paradigm within which various theoretical approaches to the study of development may be described and evaluated. In the process, an attempt is made to give a fair and reasonably comprehensive overview of leading modelling approaches in developmental biology, with particular reference to self-organization. The work proceeds from a physical or mathematical perspective, but not unduly so - the major mathematical derivations and results are relegated to appendices - and attempts to fill a perceived gap in the extant review literature, in its breadth and attempted impartiality of scope. A characteristic of the present account is its markedly interdisciplinary approach: it seeks to place self-organization models that have been proposed for biological pattern formation and morphogenesis both within the necessary experimentally-derived biological framework, and in the wider physical context of self-organization and the mathematical techniques that may be employed in its study. Hence the thesis begins with appropriate introductory chapters to provide the necessary background, before proceeding to a discussion of the models themselves. It should be noted that the work is structured so as to be read sequentially, from beginning to end; and that the chapters in the main text were designed to be understood essentially independently of the appendices, although frequent references to the latter are given. In view of the vastness of the available information and literature on developmental biology, a working knowledge of embryological principles must be assumed. Consequently, rather than attempting a comprehensive introduction to experimental embryology, chapter 2 presents just a few biological preliminaries, to 'set the scene', outlining some of the major issues that we are dealing with, and sketching an indication of the current status of knowledge and research on development. The chapter is aimed at furnishing the necessary biological, experimental background, in the light of which the rest of the thesis should be read, and which should indeed underpin and motivate any theoretical discussions. We encounter the different hierarchical levels of description in this chapter, as well as some of the model systems whose experimental study has proved most fruitful, some of the concepts of experimental embryology, and a brief reference to some questions that will not be addressed in this work. With chapter 3, we temporarily move away from developmental biology, and consider the wider physical and mathematical concepts related to the study of self-organization. Here we encounter physical and chemical examples of spontaneous structure formation, thermodynamic considerations, and different approaches to the description of complexity. Mathematical approaches to the dynamical study of self-organization are also introduced, with specific reference to reaction-diffusion equations, and we consider some possible chemical and biochemical realizations of self-organizing kinetics. The chapter may be read in conjunction with appendix A, which gives a somewhat more in-depth study of reaction-diffusion equations, their analysis and properties, as an example of the approach to the analysis of self-organizing dynamical systems and mathematically-formulated models. Appendix B contains a more detailed discussion of the Belousov-Zhabotinskii reaction, which provides a vivid chemical paradigm for the concepts of symmetry-breaking and self-organization. Chapter 3 concludes with a brief discussion of a model biological system, the cellular slime mould, which displays rudimentary development and has thus proved amenable to detailed study and modelling. The following two chapters form the core of the thesis, as they contain discussions of the detailed application of theoretical concepts and models, largely based on self-organization, to various developmental situations. We encounter a diversity of models which has arisen largely in the last quarter century, each of which attempts to account for some aspect of biological pattern formation and morphogenesis; an aim of the discussion is to assess the extent of the underlying unity of these models in terms of the self-organization paradigm. In chapter 4 chemical pre-patterns and positional information are considered, without the overt involvement of cells in the patterning. In chapter 5, on the other hand, cellular interactions and activities are explicitly taken into account; this chapter should be read together with appendix C, which contains a brief introduction to the mathematical formulation and analysis of some of the models discussed. The penultimate chapter, 6, considers two other approaches to the study of development; one of these has faded away, while the other is still apparently in the ascendant. The assumptions underlying catastrophe theory, the value of its applications to developmental biology and the reasons for its decline in popularity, are considered. Lastly, discrete approaches, including the recently fashionable cellular automata, are dealt with, and the possible roles of rule-based interactions, such as of the so-called L-systems, and of fractals and chaos are evaluated. Chapter 7 then concludes the thesis with a brief assessment of the value of the self-organization concept to the study of biological development

Modeling The Spatiotemporal Dynamics Of Cells In The Lung

Multiple research problems related to the lung involve a need to take into account the spatiotemporal dynamics of the underlying component cells. Two such problems involve better understanding the nature of the allergic inflammatory response to explore what might cause chronic inflammatory diseases such as asthma, and determining the rules underlying stem cells used to engraft decellularized lung scaffolds in the hopes of growing new lungs for transplantation. For both problems, we model the systems computationally using agent-based modeling, a tool that enables us to capture these spatiotemporal dynamics by modeling any biological system as a collection of agents (cells) interacting with each other and within their environment. This allows to test the most important pieces of biological systems together rather than in isolation, and thus rapidly derive biological insights from resulting complex behavior that could not have been predicted beforehand, which we can then use to guide wet lab experimentation. For the allergic response, we hypothesized that stimulation of the allergic response with antigen results in a response with formal similarity to a muscle twitch or an action potential, with an inflammatory phase followed by a resolution phase that returns the system to baseline. We prepared an agent-based model (ABM) of the allergic inflammatory response and determined that antigen stimulation indeed results in a twitch-like response. To determine what might cause chronic inflammatory diseases where the twitch presumably cannot resolve back to baseline, we then tested multiple potential defects to the model. We observed that while most of these potential changes lessen the magnitude of the response but do not affect its overall behavior, extending the lifespan of activated pro-inflammatory cells such as neutrophils and eosinophil results in a prolonged inflammatory response that does not resolve to baseline. Finally, we performed a series of experiments involving continual antigen stimulation in mice, determining that there is evidence in the cytokine, cellular and physiologic (mechanical) response consistent with our hypothesis of a finite twitch and an associated refractory period. For stem cells, we made a 3-D ABM of a decellularized scaffold section seeded with a generic stem cell type. We then programmed in different sets of rules that could conceivably underlie the cell\u27s behavior, and observed the change in engraftment patterns in the scaffold over selected timepoints. We compared the change in those patterns against the change in experimental scaffold images seeded with C10 epithelial cells and mesenchymal stem cells, two cell types whose behaviors are not well understood, in order to determine which rulesets more closely match each cell type. Our model indicates that C10s are more likely to survive on regions of higher substrate while MSCs are more likely to proliferate on regions of higher substrate

Overcoming conventional modeling limitations using image- driven lattice-boltzmann method simulations for biophysical applications

The challenges involved in modeling biological systems are significant and push the boundaries of conventional modeling. This is because biological systems are distinctly complex, and their emergent properties are results of the interplay of numerous components/processes. Unfortunately, conventional modeling approaches are often limited by their inability to capture all these complexities. By using in vivo data derived from biomedical imaging, image-based modeling is able to overcome this limitation. In this work, a combination of imaging data with the Lattice-Boltzmann Method for computational fluid dynamics (CFD) is applied to tissue engineering and thrombogenesis. Using this approach, some of the unanswered questions in both application areas are resolved. In the first application, numerical differences between two types of boundary conditions: “wall boundary condition” (WBC) and “periodic boundary condition” (PBC), which are commonly utilized for approximating shear stresses in tissue engineering scaffold simulations is investigated. Surface stresses in 3D scaffold reconstructions, obtained from high resolution microcomputed tomography images are calculated for both boundary condition types and compared with the actual whole scaffold values via image-based CFD simulations. It is found that, both boundary conditions follow the same spatial surface stress patterns as the whole scaffold simulations. However, they under-predict the absolute stress values approximately by a factor of two. Moreover, it is found that the error grows with higher scaffold porosity. Additionally, it is found that the PBC always resulted in a lower error than the WBC. In a second tissue engineering study, the dependence of culture time on the distribution and magnitude of fluid shear in tissue scaffolds cultured under flow perfusion is investigated. In the study, constructs are destructively evaluated with assays for cellularity and calcium deposition, imaged using µCT and reconstructed for CFD simulations. It is found that both the shear stress distributions within scaffolds consistently increase with culture time and correlate with increasing levels of mineralized tissues within the scaffold constructs as seen in calcium deposition data and µCT reconstructions. In the thrombogenesis application, detailed analysis of time lapse microscopy images showing yielding of thrombi in live mouse microvasculature is performed. Using these images, image-based CFD modeling is performed to calculate the fluid-induced shear stresses imposed on the thrombi’s surfaces by the surrounding blood flow. From the results, estimates of the yield stress (A critical parameter for quantifying the extent to which thrombi material can resist deformation and breakage) are obtained for different blood vessels. Further, it is shown that the yielding observed in thrombi occurs mostly in the outer shell region while the inner core remains intact. This suggests that the core material is different from the shell. To that end, we propose an alternative mechanism of thrombogenesis which could help explain this difference. Overall, the findings from this work reveal that image-based modeling is a versatile approach which can be applied to different biomedical application areas while overcoming the difficulties associated with conventional modeling

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented