Forming a rodThe mechanics of rod-s

Forming a rod
The mechanics of rod-shaped thin shells
Rod-shaped growth ultimately requires a breaking of symmetry,
which can arise from directionality in the material
properties of the cell wall, stresses, the organization of the
synthesis machinery, or any combination of these. Physical
models for the morphogenesis of walled cells regard the
cell as a thin viscoelastic shell, which is uniformly inflated
from within by turgor pressure. To predict the cell shape
resulting from a given mechanism of growth, it is critical
to consider the distribution of forces due to turgor pressure,
the counterbalancing forces of the wall stretching,
and how the material properties of the wall couple those
forces to the degree of extension. For a linear elastic material,
stress σ (force per unit area) is related to the mechanical
strain ε (fractional stretching) via Young’s modulus:
E ¼ σ=ε; ð1Þ
a measure of the intrinsic stiffness of the material similar
to the force constant k of a spring (for which Hooke’s
law dictates that k = F/x, where F is the force required
for stretching the spring by an amount x). In an elastic
thin shell, the stresses should increase with increasing
cell radius r and with turgor pressure P, and decrease
with larger cell wall thickness d. In a spherical shell, the
stresses are equal in every direction. In contrast, the
geometry of a cylindrical shell dictates that the circumferential
stresses (σr) are twice as large as the longitudinal
stresses (σl) (Figure 1c):
σr ¼ 2σl ¼ Pr
d
: ð2Þ
Combining equations 1 and 2, these model relationships
predict that the circumferential and longitudinal strains
(εr and εl, respectively) should be linearly dependent on
width and turgor pressure and inversely dependent on
wall thickness. If Young’s modulus is equal in every direction
(mechanically isotropic), then εr should be twice
as large as εl.
This relationship between the strains in different directions
has been used to probe the mechanical properties
of the cell wall of rod-shaped cells. In fission yeast,
measuring the degree of shrinkage of cells when turgor
pressure is reduced reveals this predicted 2:1 strain ratio,
suggesting that the cell wall in these cells behaves as an
isotropic material (Atilgan and Chang, unpublished observations).
In contrast, in rod-shaped bacteria such as
E. coli and B. subtilis, cells exhibit a higher degree of
longitudinal rather than radial stretching [10], indicating
mechanical anisotropy (or directional dependence), with
greater stiffness in the circumferential relative to the
longitudinal direction [11]. These observations are consistent
with cryo-electron tomograms showing that the

ผลลัพธ์ (แอฟริกา) 1:

Vorming van 'n Rod
die meganika van staafvormige dun doppe
staafvormige groei vereis uiteindelik 'n verbreking van Simmetrie,
wat van rigting in die materiaal kan ontstaan
​​Properties van die selwand, spanning, die organisering van die
sintese masjinerie, of enige kombinasie van hierdie. . Fisiese
modelle vir die morfogenese selle ommuurde beskou die
sel as 'n visco dun dop, wat eenvormig opgeblaas
van binne deur turgordruk. Te voorspel die selvorm
gevolg van 'n Gegewe meganisme van groei, is dit krities
te oorweeg die verdeling van magte Weens turgordruk,
Die teenbalansering Magte van The Wall strek,
en hoe die materiaal eienskappe van Wall paartjie diegene
Magte van die graad van. uitbreiding. Vir 'n Lineêre elastiese materiaal aan,
is stres Sigma (krag per eenheid area) met betrekking tot die meganiese
Strain epsilon (fraksionele strek) via Young se modulus:
E ¼ Sigma = epsilon; Ð1Þ
n maatstaf van die intrinsieke styfheid van die materiaal soortgelyk
aan die krag van 'n veer konstante k (waarvoor Hooke se
wet bepaal dat K = F / x, waar F die krag wat nodig
vir die strek van die lente met 'n bedrag x). In 'n Elastiese
dun dop, moet die spanning verhoog met toenemende
Cell Radius R en P met turgordruk en verminder
met groter Cell wanddikte D. In 'n sferiese Shell, Die
spanning is gelyk in elke rigting. In teenstelling hiermee het die
meetkunde van 'n silindriese Shell dikteer dat Die sirkumferensiele
spanning (Σr) is twee keer so groot soos die longitudinale
spanning (Σl) (Figuur 1C):
Σr ¼ 2σl ¼ Pr
D
: Ð2Þ
Kombinasie Vergelykings 1 en 2, is hierdie model verhoudings.
Die sirkumferensiele en longitudinale stamme wat voorspel
(Εr en Εl, onderskeidelik) moet wees lineêr afhanklik
breedte en turgordruk en omgekeerd afhanklik
wanddikte. Indien Young se modulus is gelyk in elke rigting
(meganies isotropies), dan moet Εr twee keer
so groot soos Εl.
Hierdie verhouding tussen die stamme in verskillende rigtings
is gebruik om te ondersoek Die meganiese eienskappe
van die selwand van staafvormige selle. In fisie Yeast,
meet Die Graad inkrimping van selle Wanneer turgor
druk verminder openbaar hierdie voorspel 2: 1 Strain verhouding,
wat daarop dui dat die selwand in hierdie selle optree As 'n
. isotropies Materiaal (Atilgan en Chang, Ongepubliseerde waarnemings)
In teenstelling ,. Sulke bakterieë in staafvormige As
E. coli en B. subtilis, selle 'n hoër mate van
radiale longitudinale Eerder as strek [10], wat aandui
meganiese anisotropie (of Directional afhanklikheid), met
'n groter styfheid in Die sirkumferensiele relatief tot die
lengte rigting [11]. Hierdie waarnemings is in ooreenstemming
met die Cryo-Electron tomogram wat wys dat die.