Fitting Fibrils A geometrical approach to plant cell wall development

Anne-Mie EmonsMiriam AkkermanPlant Cell BiologyWageningen University, NL

Bela MulderFOM Institute AMOLFAmsterdam, NL

• Introduction to plant cell wall morphology

• The current paradigm

• The geometrical theory

• Results

• Conclusions

Why study the cell wall ?

Cell walls provide protection and allow plants to exploit turgor pressure to raise themselves against gravity

• Plants make up 99% of the biomass of earth.

• 10% of this biomass is fixed in plant cells.

• Important source of raw materials: wood, paper, fibers …

Example cell: root hair Cross-section

Zooming in on the cell wall

Surface section Shadow-cast EM image

Cellulose microfibrils in a polysaccharide matrix

2-4 nm

CMF

Cell wall textures are regular

The helicoidal cell wall

Real world analogues

Fibre-laminates are both tough and flexible

Helicoidally wound strings pack efficiently

CMF synthases or “rosettes”

The mechanism of CMF synthesis

Certain:

CMF synthases channel UDP glucose from inside the cell, and “spin” the CMF.

Brown et al. (1997)Arioli et al. (1999)

Plausible:

The CMF synthases are propelled forward by the polymerization force and move in the plasma membrane.

Motion from chemical energy: Polymerisation ratchets

The current paradigm

The so-called microtubule/microfibril paradigm (Giddins&Staehelin [1991])

The CMF synthases are “guided” by the cortical microtubules.

However …

• The hypothesis is mainly supported by the the co-alignment of

CMFs and MTs in expanding cells, where forces are exerted.

• In many non-expanding cells there is no co-alignment between

MTs and CMFs (Emons [1983,->])

• New Arabidopsis mutants show normal wall development even

when the cortical MT organization is disrupted (Wasteneys et al.)

• It begs the question of how the cortical MTs are (re)organized.

Background to the geometrical model

CMFs are deposited by CMF synthases that move in the plasma membrane.

Deposition takes place in the limited space between the cell membrane and the already extant wall.

• The CMFs appear closely packed with a spacing of ~20nm

• CMFs are long L >> 1 m

cell interior

CMF

synthase

exis

tin

g w

all

membrane

Ingredient 1: Geometry

cylindrical cell membrane

track of synthase microfibril number of microfibrils

R

Nd

2sin

Geometrical “close packing” rule(Emons, 1994)

Production of synthases

Golgi apparatus

vesicle

cell wall

synthase

membrane

exocytosis

Ingredient 2: space

New synthases created in localised insertion domains along the cell by the Golgi-apparatus and brought to the plasma membrane by exocytosis of Golgi-vesicles

L

rate of synthase creationdepends on number of synthases already present =N

),( tN

d

RNNtN

20),( max

constraint

Ingredient 3: time

insertion domain moves with velocity v

possible sources of movement:

•Cytoplasmic streaming: physical transport of Golgi apparatus

•Calcium waves: activation/deactivation of exocytosis

synthase moves with linear speed ww

v

synthase is “born” ( t = 0 )

synthase “dies” ( t = t†)

Putting it all together: a developmental model

z dz

Fundamental variable:

N(z,t) = the density of active synthases at given location along the cell

Desired result:

(z,t) = the local angle of deposition of microfibrils

i.e. the cell wall texture

geometrical rule

R

dtzNtz

2

),(),(sin

Dynamics of the local synthase density

sources of change

motion of synthases birth and death of synthases

The evolution equation for the synthase density

†( , ) ( , )( , ) ( , , ) ( , , )

2

N z t wd N z tN z t N z t N z t

t R z

motion of the synthases activation deactivation

•The formula make all our assumptions operational.

•It can be used as a “virtual laboratory” in which “experiments” are performed under different conditions = values of the parameters of the model.

Results I: the helicoidal wall

Depends on matching of the size and the speed of the insertion domain and the synthase production rate to the synthase life time.

Results II: the crossed polylammelate wall

Essentially a helicoidal wall in the case that the synthase production is initially very fast, leading to an alternation between layers with a low and a high microfibril angle

Results III: the helical wall

Results when the lifetime of synthases is much larger than the time it takes the insertion domain to travel a distance equal to its length. Most common wall type of wood.

Results IV: the axial wall

In essence a helical wall with a large microfibril angle. Highly likely when the radius of the lumen of the cell is small and hence the maximum number of CMFs that can be accommodated is small.

… But is it true ?

Experimental verification:

• Identification of insertion domains. (Miriam Akkerman, Wageningen)

• Direct visualization of cellulose synthesis and synthase dynamics in vitro (FOM/ALW Physical Biology programme II, vacancy)

• GFP tagging of synthases(exploring collaboration with PRI)

Theoretical elaboration:

• Study the role of physical interactions between synthases(FOM/ALW Physical Biology programme II, vacancy)

• Generalization to cells with inequivalent facets, cell wall deposition at the poles of cells, … (future)

Do insertion domains exist? Dynamics of GFP-tagged Golgi

What is the physical origin of the CMF packing?

Interactions between the CMFs-synthases:

•Hydrodynamical:

? unknown

•Fluctuation induced (Casimir):

attractive

•Elastic:

repulsive

Conclusions

• The geometrical theory provides a unified conceptual

framework for understanding cell wall architecture

• It can describe the formation of all known cell wall types

• It is a quantitative model that explicitly allows experimental

verification/falsification.

• Is an example of fruitful interaction between biology and

theoretical/computational sciences.

The evolution equation for the rosette density

†( , ) ( , )( , ) ( , , ) ( , , )

N z t N z tW z t N z t N z t

t z

motion of the rosettes activation deactivation

( , ) sin ( , ) ( , )2

wdW z t w z t N z t

R

Local axial speed:

Solution:

1

22

11224arcsin

2

1102arcsin

)(2

2

Conditions for helicoid:

211 †

Solutions of the modelHelicoidal case, single Insertion Domain, =0

Full solution: “gluing” together a train of Insertion Domains

v

inter domain-spacing

12

2

v

v