624,876 research outputs found
Applications of mathematical modelling to biological pattern formation,
The formation of spatiotemporal patterning in biology has intrigued experimentalists and theoreticians for many generations. Here we present a brief review of some mathematical models for pattern formation and then focus on three models which use the phenomenon of chemotaxis to generate pattern
Editorial: pattern formation in biology
Over the past two decades, the study of pattern formation in biology has attracted the attention of many scientists from diverse fields, ranging from developmental biology, cell biology and synthetic biology, to physics, mathematics and computer science. Quantitative and interdisciplinary approaches have become essential for understanding these challenging phenomena.
This Research Topic contains a collection of articles and reviews that use quantitative and interdisciplinary perspectives to understand the underlying mechanisms driving biological pattern formation. Modeling morphogenetic processes, gene regulatory network dynamics and morphogen gradients link the articles of this Research Topic, with a focus on three research areas: 1) underlying mechanisms of patterning processes; 2) cross-talk of morphogenetic and pattern formation processes, and 3) mathematical methods for modeling and quantifying biological patterning and morphogenesis. Below, each of the present Research Topic papers is briefly discussed.Centro Regional de Estudios Genómico
Pigmentation pattern formation in butterflies: experiments and models
Butterfly pigmentation patterns are one of the most spectacular and vivid examples of pattern formation in biology. They have attracted much attention from experimentalists and theoreticians, who have tried to understand the underlying genetic, chemical and physical processes that lead to patterning. In this paper, we present a brief review of this field by first considering the generation of the localised, eyespot, patterns and then the formation of more globally controlled patterns. We present some new results applied to pattern formation on the wing of the mimetic butterfly Papilio dardanus. To cite this article: H.F. Nijhout et al., C. R. Biologies 326 (2003)
What is the biological basis of pattern formation of skin lesions?
Pattern recognition is at the heart of clinical dermatology and dermatopathology. Yet, while every practitioner of the art of dermatological diagnosis recognizes the supreme value of diagnostic cues provided by defined patterns of 'efflorescences', few contemplate on the biological basis of pattern formation in and of skin lesions. Vice versa, developmental and theoretical biologists, who would be best prepared to study skin lesion patterns, are lamentably slow to discover this field as a uniquely instructive testing ground for probing theoretical concepts on pattern generation in the human system. As a result, we have at best scraped the surface of understanding the biological basis of pattern formation of skin lesions, and widely open questions dominate over definitive answer. As a symmetry-breaking force, pattern formation represents one of the most fundamental principles that nature enlists for system organization. Thus, the peculiar and often characteristic arrangements that skin lesions display provide a unique opportunity to reflect upon – and to experimentally dissect – the powerful organizing principles at the crossroads of developmental, skin and theoretical biology, genetics, and clinical dermatology that underlie these – increasingly less enigmatic – phenomena. The current 'Controversies' feature offers a range of different perspectives on how pattern formation of skin lesions can be approached. With this, we hope to encourage more systematic interdisciplinary research efforts geared at unraveling the many unsolved, yet utterly fascinating mysteries of dermatological pattern formation. In short: never a dull pattern
Using mathematical models to help understand biological pattern formation
One 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)
Models for pattern formation in somitogenesis: a marriage of cellular and molecular biology
Somitogenesis, the process by which a bilaterally symmetric pattern of cell aggregations is laid down in a cranio-caudal sequence in early vertebrate development, provides an excellent model study for the coupling of interactions at the molecular and cellular level. Here, we review some of the key experimental results and theoretical models related to this process. We extend a recent chemical pre-pattern model based on the cell cycle Journal of Theoretical Biology 207 (2000) 305-316, by including cell movement and show that the resultant model exhibits the correct spatio-temporal dynamics of cell aggregation. We also postulate a model to account for the recently observed spatio-temporal dynamics at the molecular level
Mathematical modelling of pattern formation in developmental biology
The transformation from a single cell to the adult form is one of the remarkable
wonders of nature. However, the fundamental mechanisms and interactions involved
in this metamorphic change still remain elusive. Due to the complexity of the process,
researchers have attempted to exploit simpler systems and, in particular, have
focussed on the emergence of varied and spectacular patterns in nature. A number
of mathematical models have been proposed to study this problem with one of the
most well studied and prominent being the novel concept provided by A.M. Turing in
1952. Turing's simple yet elegant idea consisted of a system of interacting chemicals
that reacted and di used such that, under certain conditions, spatial patterns can
arise from near homogeneity. However, the implicit assumption that cells respond
to respective chemical levels, di erentiating accordingly, is an oversimpli cation and
may not capture the true extent of the biology. Here, we propose mathematical models
that explicitly introduce cell dynamics into pattern formation mechanisms. The
models presented are formulated based on Turing's classical mechanism and are used
to gain insight into the signi cance and impact that cells may have in biological phenomena.
The rst part of this work considers cell di erentiation and incorporates
two conceptually di erent cell commitment processes: asymmetric precursor di erentiation
and precursor speci cation. A variety of possible feedback mechanisms are
considered with the results of direct activator upregulation suggesting a relaxation of
the two species Turing Instability requirement of long range inhibition, short range
activation. Moreover, the results also suggest that the type of feedback mechanism
should be considered to explain observed biological results. In a separate model, cell
signalling is investigated using a discrete mathematical model that is derived from
Turing's classical continuous framework. Within this, two types of cell signalling are
considered, namely autocrine and juxtacrine signalling, with both showing the attainability
of a variety of wavelength patterns that are illustrated and explainable through
individual cell activity levels of receptor, ligand and inhibitor. Together with the full
system, a reduced two species system is investigated that permits a direct comparison
to the classical activator-inhibitor model and the results produce pattern formation
in systems considering both one and two di usible species together with an autocrine
and/or juxtacrine signalling mechanism. Formulating the model in this way shows a
greater applicability to biology with fundamental cell signalling and the interactions
involved in Turing type patterning described using clear and concise variables
Editorial: pattern formation in biology
Over the past two decades, the study of pattern formation in biology has attracted the attention of many scientists from diverse fields, ranging from developmental biology, cell biology and synthetic biology, to physics, mathematics and computer science. Quantitative and interdisciplinary approaches have become essential for understanding these challenging phenomena.
This Research Topic contains a collection of articles and reviews that use quantitative and interdisciplinary perspectives to understand the underlying mechanisms driving biological pattern formation. Modeling morphogenetic processes, gene regulatory network dynamics and morphogen gradients link the articles of this Research Topic, with a focus on three research areas: 1) underlying mechanisms of patterning processes; 2) cross-talk of morphogenetic and pattern formation processes, and 3) mathematical methods for modeling and quantifying biological patterning and morphogenesis. Below, each of the present Research Topic papers is briefly discussed.Centro Regional de Estudios Genómico
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