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Mathematical modelling of vein patterns during leaf development

Mathematical modelling of vein patterns during leaf development. Biological motivation : leaf development. We are using are using leaf development to study the effects of growth on pattern formation . The veins of mature leaves form a reticulated pattern .

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Mathematical modelling of vein patterns during leaf development

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  1. Mathematicalmodelling of veinpatternsduringleafdevelopment

  2. Biologicalmotivation: leafdevelopment • Weareusingareusingleafdevelopment to studytheeffects of growth on patternformation. • Theveins of matureleaves form a reticulatedpattern. • These form in a specificsequence, startingwiththeformation of themidline. Thisisfollowedbytheformation of loopsthatconnect to pre-existingvasculature.

  3. The hormone auxin is a key regulator of plant development • Auxin(IAA) is a hormone that can move from cell to cell and regulate a number of processes in plants. • Since auxin is a weak acid, it can become trapped inside cells (‘acid trapped’). • Thus it requires efflux transporters, such as PINs, to leave the cell. • Auxin can enter cells either though active transport (by AUX1/LAX proteins) or diffusion. • Thus, transport of auxin is highly regulated. AUX1/LAX influx transporters PIN efflux transporters

  4. Local-auxin synthesis • Leaves synthesize auxin. • Sites of synthesis are highly localised and coincide with vein branch points. 3D old leaves 6D old leaf Complete loss of auxin synthesis blocks vein formation.

  5. Vertex-based approach to modelling plant tissue growth • We have developed a vertex based model which can be used to investigate the interplay between growth, auxin transport and synthesis.

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