Abstract
Using a partial differential equation model derived from the ideas of the Meyerowitz and Traas groups on the role of the growth hormone auxin and those of Green and his group on the role compressive stresses can play in plants, we demonstrate how all features of spiral phyllotaxis can be recovered by the passage of a pushed pattern forming front. The front is generated primarily by a PIN1 mediated instability of a uniform auxin concentration and leaves in its wake an auxin fluctuation field at whose maxima new primordia are assumed to be initiated. Because it propagates through a slowly changing metric, the patterns have to make transitions between spirals enumerated by decreasing parastichy numbers. The point configurations of maxima coincide almost exactly with those configurations generated by the use of discrete algorithms based on optimal packing ideas which suggests that pushed pattern forming fronts may be a general mechanism by which natural organisms can follow optimal strategies. We also describe in detail a numerical method that is used to efficiently and accurately integrate the model equations while preserving the variational structure from which they are derived.
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Claims 6
Claim · model-written summary
The pushed-front model reproduced all features of spiral phyllotaxis.
- Taxon
- plantsViridiplantaee1
- Outcome
- all features of spiral phyllotaxise0
- Comparator
- pushed pattern forming fronte0
Verbatim
e0“all features of spiral phyllotaxis can be recovered by the passage of a pushed pattern forming front”
e1“in plants”
Claim · model-written summary
A PIN1-mediated instability of uniform auxin concentration primarily generated the front.
- Taxon
- plantsViridiplantaee1
- Gene
- PIN1e0
- Outcome
- front is generatede0
- Qualifier
- instability of a uniform auxin concentratione0
Verbatim
e0“The front is generated primarily by a PIN1 mediated instability of a uniform auxin concentration”
e1“in plants”
Claim · model-written summary
Modelled auxin fluctuation maxima were assumed to initiate new primordia.
- Taxon
- plantsViridiplantaee1
- Outcome
- new primordia are assumed to be initiatede0
- Qualifier
- auxin fluctuation field at whose maximae0
Verbatim
e0“an auxin fluctuation field at whose maxima new primordia are assumed to be initiated”
e1“in plants”
Claim · model-written summary
Slowly changing metric forced transitions between spirals with decreasing parastichy numbers.
- Taxon
- plantsViridiplantaee1
- Outcome
- transitions between spirals enumerated by decreasing parastichy numberse0
- Qualifier
- slowly changing metrice0
Verbatim
e0“Because it propagates through a slowly changing metric, the patterns have to make transitions between spirals enumerated by decreasing parastichy numbers”
e1“in plants”
Claim · model-written summary
Front maxima configurations almost exactly coincided with discrete optimal-packing algorithm configurations.
- Taxon
- plantsViridiplantaee1
- Outcome
- point configurations of maxima coincide almost exactlye0
- Comparator
- configurations generated by the use of discrete algorithmse0
Verbatim
e0“point configurations of maxima coincide almost exactly with those configurations generated by the use of discrete algorithms based on optimal packing ideas”
e1“in plants”
Claim · model-written summary
The authors described a numerical integration method that preserves the equations’ variational structure.
- Taxon
- plantsViridiplantaee1
- Outcome
- efficiently and accurately integrate the model equationse0
- Comparator
- variational structuree0
Verbatim
e0“a numerical method that is used to efficiently and accurately integrate the model equations while preserving the variational structure from which they are derived”
e1“in plants”