Biology by Numbers: Mathematical Modelling in Developmental Biology

Department of Aeronautics and Astronautics , Stanford University, Stanford, California, United States
Nature Reviews Genetics (Impact Factor: 36.98). 06/2007; 8(5):331-40. DOI: 10.1038/nrg2098
Source: PubMed


In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.

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    • "In recent years, various research methods, including mathematical modeling, statistical analysis, computer simulation and visualization, have been employed to investigate the dynamic or statistical properties of regulatory networks. In particular, mathematical models have been widely used to describe the dynamics of complex systems inside the cell, including genetic regulatory networks, cell signalling transduction pathways and metabolic pathways [1][2]. However, these substantial progresses have further raised a number of fundamental and challenging issues that require to be addressed imperatively. "
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    ABSTRACT: A fundamental issue in systems biology is how to design simplified mathematical models for describing the dynamics of complex biochemical reaction systems. Among them, a key question is how to use simplified reactions to describe the chemical events of multi-step reactions that are ubiquitous in biochemistry and biophysics. To address this issue, a widely used approach in literature is to use one-step reaction to represent the multi-step chemical events. In recent years, a number of modelling methods have been designed to improve the accuracy of the one-step reaction method, including the use of reactions with time delay. However, our recent research results suggested that there are still deviations between the dynamics of delayed reactions and that of the multi-step reactions. Therefore, more sophisticated modelling methods are needed to accurately describe the complex biological systems in an efficient way. This work designs a two-variable model to simplify chemical events of multi-step reactions. In addition to the total molecule number of a species, we first introduce a new concept regarding the location of molecules in the multi-step reactions, which is the second variable to represent the system dynamics. Then we propose a simulation algorithm to compute the probability for the firing of the last step reaction in the multi-step events. This probability function is evaluated using a deterministic model of ordinary differential equations and a stochastic model in the framework of the stochastic simulation algorithm. The efficiency of the proposed two-variable model is demonstrated by the realization of mRNA degradation process based on the experimentally measured data. Numerical results suggest that the proposed new two-variable model produces predictions that match the multi-step chemical reactions very well. The successful realization of the mRNA degradation dynamics indicates that the proposed method is a promising approach to reduce the complexity of biological systems.
    Full-text · Article · Oct 2013 · BMC Systems Biology
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    • "Mathematical modelling has long played a key role in developmental biology [46,47]. Models allow us to formalise our understanding of a given system and validate that formalisation by testing whether our knowledge is consistent with the modelling framework. "
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    ABSTRACT: Background Cells in some tissues acquire a polarisation in the plane of the tissue in addition to apical-basal polarity. This polarisation is commonly known as planar cell polarity and has been found to be important in developmental processes, as planar polarity is required to define the in-plane tissue coordinate system at the cellular level. Results We have built an in-silico functional model of cellular polarisation that includes cellular asymmetry, cell-cell signalling and a response to a global cue. The model has been validated and parameterised against domineering non-autonomous wing hair phenotypes in Drosophila. Conclusions We have carried out a systematic comparison of in-silico polarity phenotypes with patterns observed in vivo under different genetic manipulations in the wing. This has allowed us to classify the specific functional roles of proteins involved in generating cell polarity, providing new hypotheses about their specific functions, in particular for Pk and Dsh. The predictions from the model allow direct assignment of functional roles of genes from genetic mosaic analysis of Drosophila wings.
    Full-text · Article · May 2013 · BMC Developmental Biology
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    • "(b) Expression of segment polarity genes, wingless (wg; green) and engrailed (en; red). Courtesy of C. Tomlin and J.D. Axelrod (Tomlin and Axelrod, 2007). (c) Expression of seven Hox genes at the extended germ band stage (Courtesy of Dave Kosman, UCSD). "
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    ABSTRACT: The tissues of multicellular organisms are made of differentiated cells arranged in organized patterns. This organization emerges during development from the coupling of dynamic intra- and intercellular regulatory networks. This work applies the methods of information theory to understand how regulatory network structure both within and between cells relates to the complexity of spatial patterns that emerge as a consequence of network operation. A computational study was performed in which undifferentiated cells were arranged in a two dimensional lattice, with gene expression in each cell regulated by identical intracellular randomly generated Boolean networks. Cell-cell contact signalling between embryonic cells is modeled as coupling among intracellular networks so that gene expression in one cell can influence the expression of genes in adjacent cells. In this system, the initially identical cells differentiate and form patterns of different cell types. The complexity of network structure, temporal dynamics and spatial organization is quantified through the Kolmogorov-based measures of normalized compression distance and set complexity. Results over sets of random networks that operate in the ordered, critical and chaotic domains demonstrate that: (1) Ordered and critical networks tend to create the most information-rich patterns; (2) signalling configurations in which cell-to-cell communication is non-directional mostly produce simple patterns irrespective of the internal network domain; and (3) directional signalling configurations, similar to those that function in planar cell polarity, produce the most complex patterns, but only when the intracellular networks function in non-chaotic domains.
    Full-text · Article · Mar 2013 · Bio Systems
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