Spatially Distributed Morphogen Production and Morphogen Gradient Formation

Lander, Arthur D.; Nie, Qing; Wan, Frederic Y. M.

doi:10.3934/mbe.2005.2.239

Cited by 37 publications

(202 citation statements)

References 4 publications

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“…In Drosophila, BMP diffusion occurs within a thin, bounded compartment surrounding a roughly ellipsoidal embryo; DV gradient formation is readily simulated as a reaction-diffusion problem in one dimension, with little loss of accuracy (Eldar et al, 2002;Lander et al, 2002;Eldar et al, 2003;Lander et al, 2006;Lou et al, 2004;Lander et al, 2005Lander et al, , 2007Lou et al, 2005;Mizutani et al, 2005;Shimmi et al, 2005). In view of the more complex arrangement of the zebrafish embryo, we chose here to carry out fully three-dimensional simulations, which are computationally much more costly.…”

Section: Article In Pressmentioning

confidence: 99%

“…BMP activity is regulated by several secreted factors including the antagonist chordin or its invertebrate homologue, short gastrulation (Sog). Recently, mathematical models have provided useful insights into the establishment and function of the BMP activity gradient in Drosophila embryo and its imaginal discs (Eldar et al, 2002;Lander et al, 2002;Eldar et al, 2003;Lander et al, 2006;Lou et al, 2004;Lander et al, 2005Lander et al, , 2007Lou et al, 2005;Mizutani et al, 2005;Shimmi et al, 2005). In the embryo, the functions of BMPs (Dpp, Scw and their heterodimers) are inhibited by the binding of Sog (together with the secreted protein twisted gastrulation (Tsg)) and this inhibition is relieved by the cleavage of BMP-bound Sog by the Tolloid (Tld) protease, which releases free Dpp.…”

Section: Introductionmentioning

confidence: 99%

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Computational analysis of BMP gradients in dorsal-ventral patterning of the zebrafish embryo

Zhang

Lander

Nie

2007

Journal of Theoretical Biology

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The genetic network controlling early dorsal-ventral (DV) patterning has been extensively studied and modeled in the fruit fly Drosophila. This patterning is driven by signals coming from bone morphogenetic proteins (BMPs), and regulated by interactions of BMPs with secreted factors such as the antagonist short gastrulation (Sog). Experimental studies suggest that the DV patterning of vertebrates is controlled by a similar network of BMPs and antagonists (such as Chordin, a homologue of Sog), but differences exist in how the two systems are organized, and a quantitative comparison of pattern formation in them has not been made. Here, we develop a computational model in three dimensions of the zebrafish embryo and use it to study molecular interactions in the formation of BMP morphogen gradients in early DV patterning. Simulation results are presented on the dynamics BMP gradient formation, the cooperative action of two feedback loops from BMP signaling to BMP and Chordin synthesis, and pattern sensitivity with respect to BMP and Chordin dosage. Computational analysis shows that, unlike the case in Drosophila, synergy of the two feedback loops in the zygotic control of BMP and Chordin expression, along with early initiation of localized Chordin expression, is critical for establishment and maintenance of a stable and appropriate BMP gradient in the zebrafish embryo. r

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Section: Article In Pressmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computational analysis of BMP gradients in dorsal-ventral patterning of the zebrafish embryo

Zhang

Lander

Nie

2007

Journal of Theoretical Biology

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“…In particular, the second order approximation of (19) leads to the second order IIF scheme (cIIF2) (20) Like the one-dimensional form [8], the nonlinear reaction term at t n+1 in (20) is decoupled from the diffusion terms. As a result, only a local nonlinear system needs to be solved at each spatial grid point.…”

Section: Two-dimensionsmentioning

confidence: 99%

“…Morphogens are signaling molecules that, when bound to cell receptors, assign different cell fates at different concentrations [15,16]. This role of morphogens has been the prevailing thought in tissue patterning for over half a century; but only recently have there been sufficient experimental data and adequate modeling for us to begin to understand how various morphogens interact and patterns emerge [17][18][19].…”

Section: A Two-dimensional Model For Dorsal-ventral Patterning-formentioning

confidence: 99%

Compact integration factor methods in high spatial dimensions

Nie

Wan

Zhang

et al. 2008

Journal of Computational Physics

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The dominant cost for integration factor (IF) or exponential time differencing (ETD) methods is the repeated vector-matrix multiplications involving exponentials of discretization matrices of differential operators. Although the discretization matrices usually are sparse, their exponentials are not, unless the discretization matrices are diagonal. For example, a two-dimensional system of N × N spatial points, the exponential matrix is of a size of N 2 × N 2 based on direct representations. The vector-matrix multiplication is of O(N 4 ), and the storage of such matrix is usually prohibitive even for a moderate size N. In this paper, we introduce a compact representation of the discretized differential operators for the IF and ETD methods in both two-and three-dimensions. In this approach, the storage and CPU cost are significantly reduced for both IF and ETD methods such that the use of this type of methods becomes possible and attractive for two-or three-dimensional systems. For the case of two-dimensional systems, the required storage and CPU cost are reduced to O(N 2 ) and O(N 3 ), respectively. The improvement on three-dimensional systems is even more significant. We analyze and apply this technique to a class of semi-implicit integration factor method recently developed for stiff reaction-diffusion equations. Direct simulations on test equations along with applications to a morphogen system in two-dimensions and an intra-cellular signaling system in three-dimensions demonstrate an excellent efficiency of the new approach.

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“…This minimal morphogen gradient model fits many features of the Dpp and Wg gradients of the Drosophila wing disc [37].…”

Section: Mathematical Modelmentioning

confidence: 99%

Robust and precise morphogen-mediated patterning: trade-offs, constraints and mechanisms

Zhou

Wan

et al. 2015

J. R. Soc. Interface.

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The patterning of many developing tissues is organized by morphogens. Genetic and environmental perturbations of gene expression, protein synthesis and ligand binding are among the sources of unreliability that limit the accuracy and precision of morphogen-mediated patterning. While it has been found that the robustness of morphogen gradients to the perturbation of morphogen synthesis can be enhanced by particular mechanisms, how such mechanisms affect robustness to other perturbations, such as to receptor synthesis for the same morphogen, has been little explored. Here, we investigate the interplay between the robustness of patterning to the changes in receptor synthesis and morphogen synthesis and to the effects of cell-to-cell variability. Our analysis elucidates the trade-offs and constraints that arise as a result of achieving these three performance objectives simultaneously in the context of simple, steady-state morphogen gradients formed by diffusion and receptormediated uptake. Analysis of the interdependence between length scales of patterning and these performance objectives reveals several potential mechanisms for mitigating such trade-offs and constraints. One involves downregulation of receptor synthesis in the morphogen source, while another involves the presence of non-signalling cell-surface morphogen-binding molecules. Both of these mechanisms occur in Drosophila wing discs during their patterning. We computationally elucidate how these mechanisms improve the robustness and precision of morphogen-mediated patterning.

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Spatially Distributed Morphogen Production and Morphogen Gradient Formation

Cited by 37 publications

References 4 publications

Computational analysis of BMP gradients in dorsal-ventral patterning of the zebrafish embryo

Computational analysis of BMP gradients in dorsal-ventral patterning of the zebrafish embryo

Compact integration factor methods in high spatial dimensions

Robust and precise morphogen-mediated patterning: trade-offs, constraints and mechanisms

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