848 research outputs found
Using mathematical models to help understand biological pattern formation
No full textOne of the characteristics of biological systems is their ability to produce and sustain spatial and spatio-temporal pattern. Elucidating the underlying mechanisms responsible for this phenomenon has been the goal of much experimental and theoretical research. This paper illustrates this area of research by presenting some of the mathematical models that have been proposed to account for pattern formation in biology and considering their implications.To cite this article: P.K. Maini, C. R. Biologies 327 (2004)
Growth and adaptation mechanisms of tumour spheroids with time-dependent oxygen availability
No full textTumours are subject to external environmental variability. However, in vitro tumour spheroid experiments, used to understand cancer progression and develop cancer therapies, have been routinely performed for the past fifty years in constant external environments. Furthermore, spheroids are typically grown in ambient atmospheric oxygen (normoxia), whereas most in vivo tumours exist in hypoxic environments. Therefore, there are clear discrepancies between in vitro and in vivo conditions. We explore these discrepancies by combining tools from experimental biology, mathematical modelling, and statistical uncertainty quantification. Focusing on oxygen variability to develop our framework, we reveal key biological mechanisms governing tumour spheroid growth. Growing spheroids in time-dependent conditions, we identify and quantify novel biological adaptation mechanisms, including unexpected necrotic core removal, and transient reversal of the tumour spheroid growth phases
On the foundations of cancer modelling: selected topics, speculations, & perspectives
No full textThis paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution
Reptile scale paradigm: Evo-Devo, pattern formation and regeneration
No full textThe purpose of this perspective is to highlight the merit of the reptile integument as an experimental model. Reptiles represent the first amniotes. From stem reptiles, extant reptiles, birds and mammals have evolved. Mammal hairs and feathers evolved from Therapsid and Sauropsid reptiles, respectively. The early reptilian integument had to adapt to the challenges of terrestrial life, developing a multi-layered stratum corneum capable of barrier function and ultraviolet protection. For better mechanical protection, diverse reptilian scale types have evolved. The evolution of endothermy has driven the convergent evolution of hair and feather follicles: both form multiple localized growth units with stem cells and transient amplifying cells protected in the proximal follicle. This topological arrangement allows them to elongate, molt and regenerate without structural constraints. Another unique feature of reptile skin is the exquisite arrangement of scales and pigment patterns, making them testable models for mechanisms of pattern formation. Since they face the constant threat of damage on land, different strategies were developed to accommodate skin homeostasis and regeneration. Temporally, they can be under continuous renewal or sloughing cycles. Spatially, they can be diffuse or form discrete localized growth units (follicles). To understand how gene regulatory networks evolved to produce increasingly complex ectodermal organs, we have to study how prototypic scale-forming pathways in reptiles are modulated to produce appendage novelties. Despite the fact that there are numerous studies of reptile scales, molecular analyses have lagged behind. Here, we underscore how further development of this novel experimental model will be valuable in filling the gaps of our understanding of the Evo-Devo of amniote integuments
Cancer disease: integrative modelling approaches
No full textCancer is a complex disease in which a variety of phenomena interact over a wide range of spatial and temporal scales. In this article a theoretical framework will be introduced that is capable of linking together such processes to produce a detailed model of vascular tumour growth. The model is formulated as a hybrid cellular automaton and contains submodels that describe subcellular, cellular and tissue level features. Model simulations will be presented to illustrate the effect that coupling between these different elements has on the tumour's evolution and its response to chemotherapy
A mathematical investigation of a clock and wavefront model for somitogenesis
No full textAbstract Somites are transient blocks of cells that form sequentially along the antero-posterior axis of vertebrate embryos. They give rise to the vertebrae, ribs and other associated features of the trunk. In this work we develop and analyse a mathematical formulation of a version of the Clock and Wavefront model for somite formation, where the clock controls when the boundaries of the somites form and the wavefront determines where they form. Our analysis indicates that this interaction between a segmentation clock and a wavefront can explain the periodic pattern of somites observed in normal embryos. We can also show that a simplification of the model provides a mechanism for predicting the anomalies resulting from perturbation of the wavefront
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