An Adjoint-Based Parameter Identification Algorithm Applied to Planar Cell Polarity Signaling

Raffard, R.L.; Amonlirdviman, Keith; Axelrod, Jeffrey; Tomlin, Claire J.

doi:10.1109/tac.2007.911362

Cited by 31 publications

(10 citation statements)

References 14 publications

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“…Two models for PCP, focusing on the wing of the fruit fly, have been developed by Amonlirdviman et al ( [2], [12]) and Le Garrec et al [8] (applied to the Drosophila eye in [7]). Both models centre around the idea of amplification of polarity via asymmetric complex formation of the core proteins.…”

Section: Introductionmentioning

confidence: 99%

Modelling and Analysis of Planar Cell Polarity

et al. 2009

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Access from the University of Nottingham repository:http://eprints.nottingham.ac.uk/1002/1/ms_schamberg_PCP.pdf Copyright and reuse:The Nottingham ePrints service makes this work by researchers of the University of Nottingham available open access under the following conditions. This article is made available under the University of Nottingham End User licence and may be reused according to the conditions of the licence. For more details see: http://eprints.nottingham.ac.uk/end_user_agreement.pdf A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. Abstract Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles and feathers; physiologically, it can organise ciliary beating. Here we present two approaches to modelling this phenomenon. The aim is to discover the basic mechanisms that drive PCP, while keeping the models mathematically tractable. We present a feedback and diffusion model, in which adjacent cell sides of neighbouring cells are coupled by a negative feedback loop and diffusion acts within the cell. This approach can give rise to polarity, but also to period two patterns. Polarisation arises via an instability provided a sufficiently strong feedback and sufficiently weak diffusion. Moreover, we discuss a conservative model in which proteins within a cell are redistributed depending on the amount of proteins in the neighbouring cells, coupled with intracellular diffusion. In this case polarity can arise from weakly polarised initial conditions or via a wave provided the diffusion is weak enough. Both models can overcome small anomalies in the initial conditions. Furthermore, the range of the effects of groups of cells with different properties than the surrounding cells depends on the strength of the initial global cue and the intracellular diffusion.

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Section: Introductionmentioning

confidence: 99%

Modelling and Analysis of Planar Cell Polarity

et al. 2009

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“…(14) Note that the second constraint represents the discretized PDE with the ghost points correctly implemented at the link exit boundary. As revealed by our study, while problem (7) or its discrete counterpart (16) is convex in theory, a simple implementation of these programs which does not take into account specific features of the numerical schemes often results in (numerical) infeasibility or meaningless solutions. This occurs even when physically meaningful solutions exist for the continuous programs.…”

Section: B Computational Resultsmentioning

confidence: 94%

“…We represent each link k on a path as a segment [0, L] and denote by u(x, t) the number of aircraft between distances 0 and x at time t. We can define the density of aircraft as the weak derivative of u(x, t) with respect to x : ρ(x, t) = ∂u(x,t) ∂x . The aircraft density is a solution of the partial differential equation: [7], [8], [16] into a convex problem, a feature which was previously unknown. If the previously mentioned constraints are imposed along with the network PDE model, the optimization program for a single junction becomes:…”

Section: A Pde Network Modelmentioning

confidence: 99%

Convex formulations of aggregate network air traffic flow optimization problems

Work

Bayen

2008

2008 47th IEEE Conference on Decision and Control

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The problem of regulating air traffic in the en route airspace of the National Airspace System is studied using an Eulerian network model to describe air traffic flow. The evolution of traffic on each edge of the network is modeled by a modified Lighthill-Whitham-Richards partial differential equation. We pose the problem of optimal traffic flow regulation as a continuous optimization program in which the partial differential equation appears in the constraints. The equation is transformed with a variable change which removes the nonlinearity in the control variables and enables us to use linear finite difference schemes to discretize the problem. Corresponding linear programming and quadratic programming based solutions to this convex optimization program yield a globally optimal solution. The technique is applied for a network scenario in the Oakland Air Route Traffic Control Center.

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“…Several mathematical and computational approaches have been applied to study PCP signalling. In order to understand how the core proteins interact to produce domineering non-autonomy in Drosophila wing, Amonlirdviman et al [1] (extended in [26]) built a model by applying partial differential equations (PDEs) and reaction-diffusion equations which abstract from the spatial dimensions of the PDE model by discretising each cell into a triangular mesh and used periodic boundary conditions to select the grid of cells. Agent-based Modelling (ABM) with stochastic differential equations was used to create a computational model which includes the mechanism in which a Frizzled gradient occurs through feedback-reinforced formation of Flamingo-based asymmetric intercellular complexes in Le Garrec's research [20] (applied to the Drosophila eye in [19]).…”

Section: Related Workmentioning

confidence: 99%

A multiscale approach to modelling planar cell polarity in Drosophila wing using hierarchically coloured Petri nets

Gao

Liu

Gilbert

et al. 2011

Proceedings of the 9th International Conference on Computational Methods in Systems Biology

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Modelling across multiple scales is a current challenge in Systems Biology, especially when applied to multicellular organisms. In this paper we present an approach to model at different spatial scales, using the new concept of hierarchically coloured Petri Nets (HCPN). We apply HCPN to model a tissue comprising multiple cells hexagonally packed in a honeycomb formation in order to describe the phenomenon of Planar Cell Polarity (PCP) signalling in Drosophila wing. We illustrate different levels of abstraction that can be used in order to assist the systematic modelling of such a complex system involving intra-and inter-cellular signalling mechanisms, and we provide a design pattern for similar modelling problems. Our initial model describes normal, wild-type PCP signalling, and we illustrate the power of our approach by easily adapting it to various tissue sizes and to describe the phenotype of a well-documented genetic mutation in Drosophila. We have performed a series of analyses on our models which require computational experiments over very large underlying models. All results are reproducible.

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An Adjoint-Based Parameter Identification Algorithm Applied to Planar Cell Polarity Signaling

Cited by 31 publications

References 14 publications

Modelling and Analysis of Planar Cell Polarity

Modelling and Analysis of Planar Cell Polarity

Convex formulations of aggregate network air traffic flow optimization problems

A multiscale approach to modelling planar cell polarity in Drosophila wing using hierarchically coloured Petri nets

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