Tendril Coiling Dynamics Project Proposal

Tendril Coiling Dynamics Project Proposal

Christina Cogdell

Spring 2012

a)Primary project goals and what I want to learn:I would like to measure a real biological “system” (passion flower tendril free coiling) using computational mechanics in order to see what I can learn about the system’s state space, dynamics, and intrinsic computation. What does computational mechanics offer me that is new and changes my insights into the biological system?This dynamical system relates to an architectural project I did in London, where tendrils were the core subject of study for our biomimicry seminar. I am hoping be able to carry through one project in this cross-disciplinary way in order to have diverse insights into a single a architectural/biological system, in particular to better understand nonlinear system dynamics. I would love it if computational mechanics suggests ways to predict future tendril growth patterns, and also to compare the results I get from real experimental data and computational mechanics with two other models (one physical, one digital in Python/Rhino) I have already worked on to see if the parameters and process are the same. In this way I get to compare real tendrils to digital simulations, mathematical analysis, and physical modeling, in order to learn about the usefulness of the different and combined modeling methods.

b)How is the dynamical system nonlinear and time-dependent?

The above picture shows new and old free-coiling tendrils (meaning, they are not coiling around something, just coiling in open air) from the same passion flower vine in my garden. The variety of coils, especially in the old ones that are fixed, reveals that coiling has both regularity and differentiation. These show different radii of the coil, different periodicity between successive coils (in terms of whether they touch the previous coil or how far away it is), and both clockwise and counterclockwise rotation (often both in the same coil). (hmmm – sometimes change in rotation direction is also a change in coiling angle, so perhaps that’s one more parameter). They also show different thickness of the tendril, which I plan to not pay attention to owing to its relation to abundance of water at time of growth, most likely, and not a difference in coiling). The 100+ samples I have show both randomness and structural regularity as two fundamental dynamics of the coiling process.

Tendrils are organs that vines have that are separate from the usual vine-growth process. Coiling usually starts once the tendril is about 4-5inches long, or longer; in other words, it does not coil only through curved growth extension at the tip of the tendril, but rather, while some growth may continue to happen, the curvature stems from processes internal to the mid-growth (phase 2) time period maturity of the tendril. (Tendril growth has been classified as phase 1 – youngest - , phase 2 – mid - , and phase 3 – mature and fixed). Passion flower tendrils exhibit bi-directional coiling, which means that inside they have a ring of gelatinous fibers (the blue area in this diagram) all around the tendril that uses differential water absorption and swelling to elongate one side of the tendril while compressing the other side, after which the g-fibers lignify and hold the coil in place. Whereas many vines coil only in response to contact (in order to coil around the things contacted), free coiling happens without visible physical contact (I need to do more research on free coiling, as opposed to contact-based coiling).

What is the state space?In its favor, the state space I think is one-dimensional (or at least, low dimensional, especially compared to the other two architectural projects I was considering analyzing). It is therefore relatively easy to measure and analyze, even if time-consuming.

What’s the dynamic?Coiling is a complex system, dependent upon chemical processes plus mechanical forces deriving from motion with relation to the sun (heliotropism), contact stimulation (thigmotropism), growth/elongation, plus differential absorption/lignification. While my group wanted to include as much of this complex system in our models (made for the biomimetics architectural seminar) as possible, we were told to limit our study to mechanical forces only (by the tutors, in the interest of time and ease of modeling). However, since I have since learned that it is ok to define a system as bounded by wherever I deem fit, I am declaring that my “system” is the mechanical process of free coiling in tendrils, apart from chemical reactions.

In our group study, we isolated two forces that together produce coiling (twist + bend, or rephrased, rotation + compression), which we then modeled as one single diagonal compressive force. We built both physical and digital models of coiling, and learned a lot about the strength that coiling imparts even to flimsy bendable materials. The most interesting digital simulation of coiling we made is a Python script run with Grasshopper in Rhino that has only 2 parameters of curvature + growth (so growth, first angle of rotation, second angle of rotation), and by altering the two parameters (varying the 2 angles of rotation in relation to each other), we achieved a remarkable complexity of coiling that seems to closely replicate the patterns observed in natural coiling.

The mechanical dynamics of coiling in all its richness, therefore, may be determined by as few as two parameters of rotation angle following a basic simple rule.

Why is it interesting?Coiling is interesting because of its combination of randomness and structure, or regularity plus variation in the pattern. It is also of interest because the plant uses coiling as a very strong, but minimal, method of supporting itself against gravity, even when the vines get to be very large. The strength of coiling comes from the curvature + friction + lignification/fixity of the coil. They are also beautiful and very cool, so I won’t be bored looking at hundreds of coils. How many do I have to measure, by the way, in order to have a reasonable sample for statistical measurement, if I use four symbols: radii range, periodicity range, directionality of coil, and consistence of these three across the coil’s full length? 500?

c)What dynamical properties will I investigate?Coiling regularity and randomness with regard to direction and reversals, and radii and periodicity variation (possibly also coil angle changes?).

d)What information processing (intrinsic computation) properties will I investigate? Good question. The tendril obviously coils in different ways even when free coiling in open air. I want to know if there is a simple structure/mechanism/information architecture that produces this great variety even if the basic rules/parameters remain the same, just different in their input. While I can’t experimentally determine just what those inputs are (especially apart from including chemical reactions in my ‘system’, and environmental conditions like wind and shade which may affect the coil even if the coil isn’t touching anything), perhaps I can determine if a simple state space with a few parameters results when coils are studied using computational mechanics. In this way, I can compare an experimental result and mathematical model/analysis with our foregoing digital simulation.

e)What methods will I use? Why are they appropriate? I will harvest a lot of tendril coils, using only free coils as my samples. Please let me know an appropriate sample size to obtain decent results using computational mechanics. Then, I will measure and classify each tendril by 4 categories (whose ranges will be determined from reasonable observation of the variation): Radii range (sm-md-lg?), Periodicity (tightness of coiling in terms of distance to nearest coil), Directionality of coil (clockwise, counterclockwise, both), and Consistency of these across the full length of the coil. This data will form the basis of my strings, so that rather than having 0s and 1s, I will have Rs, Ps, Ds, and Cs (say…).

Also, while I imagine using a micrometer to measure these distances, I am wondering, and plan to brainstorm with Paul, about how to perhaps measure two degrees of rotation/curvature, to see if there might be a way to closer approximate the 2-parameter digital simulation I already have. Or, perhaps it’s better to use our method as stated above to independently determine what kind of structure/information architecture we find in the system.

f)What is my current guess as to what I will find?I don’t know from the real tendril data, but I already have a hunch based upon the digital simulation we already made. What I don’t understand is how this translates into state space, and mathematical nonlinearity (as in, could we write an equation, Paul??? ), in order for me to connect our findings with my knowledge from real observation (somewhat like the van der Pol oscillator and the human heartbeat study, which makes much more sense to me now after doing that project). I’d like to have a similar illumination from this project.

g)List the appropriate steps for my investigation, with time estimates for each step:

-research/read literature (done + ongoing)

-write simulator – (done - Python model)

-fieldwork to obtain samples (ongoing over this week for up to 500 samples? I already have 120)

-**mathematical analysis (2 weeks starting this week if we agree on this method?)

-**estimate properties from mathematical analysis (I am slow at this, Paul is good at this; together, ??? I’m sure this depends on the number of symbols we pick – the 4 I have seem sound to me, but I’m not sure how the different range data will complicate the string analysis.)

-compare to simulation model (easy to compare once we have the e-machine)

-write up report (2-3 days)

-** is slowest 2 steps.

Tendrils Bibliography by Major Method – I have already read most of these.

General Sources

Darwin, The Movements and Habits of Climbing Plants (1876) – ordered through interlibrary loan.

Putz, Francis and H. A. Mooney, eds., The Biology of Vines (1991), with a chapter on biomechamics.

MacDougal, D. T., “The Mechanism of Curvature in Tendrils,” Oxford Journals (1896).

Adhesion + Blep/Mechanoreceptor Cells in Tendrils

**Engelberth, Jurgen, Gerhard Wanner, Beate Groth, Elmar Weiler, “Funcational Anatomy of the mechanoreceptor in tendrils of Bryonia dioica Jacq.,” Planta 196 (1995): 539-550.

Bowling, A. J., and K.C. Vaughn, “Structural and immunocytochemical characterization of the adhesive tendril of Virginia Creeper,” Protoplasma 232 (2008): 153-63.

Endress, Anton, and William Thomson, “Adhesion of the Boston Ivy Tendril,” Canadian Journal of Botany 55 (1977): 918-924.

Gelatinous Fibers in tendrils for coiling

**Bowling, Andrew and Kevin Vaughn, “Gelatinous Fibers are Widespread in Coiling Tendrils and Twining Vines,” American Journal of Botany 96(4) (2009): 719-727.

Meloche, Christopher, J. Paul Knox, Kevin Vaughn, “A cortical band of gelatinous fibers causes the coiling of redvine tendrils: a model based upon cytochemical and immunocytochemical studies,” Planta 225 (2007): 485-98.

Thigmotropic behavior only in Stage 2 development of tendril cells (ventral vs dorsal size, elongation, curvature)

**Gerrath, Jean, Richard Cote, and Melissa Farquhar, “Pea (Pisum sativum L.) Tendril-Surface Changes are Correlated with Changes in Functional Development,” International Journal of Plant Sciences Vol. 160, no. 2 (March 1999), 261-274.

* Carrington, CMS, and J Esnard, “Kinetics of thigmocurvature in two tendril-bearing climbers,” Plant, Cell and Environment 12 (1989): 449-454.

Larson, Katherine, “Circumnutation Behavior of an Exotic Honeysuckle Vine and Its Native Congener: Influence on Clonal Mobility,” American Journal of Botany 87(4) (2000): 533-538.

**Junker, Steffen, “A Scanning Electron Microscopic Study on the Development of Tendrils of Parthenocissus tricuspidata Sieb.& Zucc.,” New Phytologist 77:3 (November 1976): 741-746.

Vine Morphologies and Growth Patterns within Environmental Contexts

** den Dubbleden, KC and B. Oosterbeek, “The Availability of External Supports Affects Allocation Patterns and Morphology of Herbaceous Climbing Plants,” Functional Ecology 9:4 (August 1995): 628-634.

Krings, Michael, Hans Kerp, Thomas Taylor and Edith Taylor, “How Paleozoic Vines and Lianas Got off the Ground: On Scrambling and Climbing Carboniferous-Early Permian Pteridosperms,” The Botanical Review 69(2) (2003): 204-224.

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