Advances in Bioscience and Biotechnology, 2013, 4, 930-936 ABB
http://dx.doi.org/10.4236/abb.2013.410122 Published Online October 2013 (http://www.scirp.org/journal/abb/)
Analysis of a single soybean microtubule’s persistence
length
Mitra Shojania Feizabadi*, Jimmy Barrientos, Carly Winton
Department of Physics, Seton Hall University, South Orange, USA
Received 30 June 2013; revised 20 July 2013; accepted 15 August 2013
Copyright © 2013 Mitra Shojania Feizabadi et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
In this study, we have reported for the first time the
persistence length of a single soybean microtubule in
vitro. The measurement is based on analysis of ther-
mal bending of a single soybean microtubule. Similar
to mammalian microtubules, the length dependency
of the persistence length was also observed for this
species of plant microtubule. The identification of two
intrinsic aspects of plant microtubules: the persis-
tence length and the compositional structure in terms
of variety of beta tubulin isotypes, and the potential
correlation between these two factors, provides evi-
dence for the functionality mechanism of plant micro-
tubules. In this work, these two fundamental factors
have been further discussed for our case study: single
soybean microtubule.
Keywords: Microtubule; Soybean; Persistence Length;
β Tubulin Isotype
1. INTRODUCTION
Microtubules are key components of the cytoskeleton. In
connection with other intracellular components, they are
involved in many functions ranging from cell division,
cell shape, chromosome movement during mitosis, and
intracellular transport [1,2]. These hollow shaped poly-
mers are dynamic and their unique mechanical and dy-
namic properties generate structure and forces that are
essential to support the cellular functions [3,4]. The evi-
dence indicates that mammalian and plant microtubules
are distinguished from one another in terms of their in-
volvements in intracellular functionality. For example
unlike mammalian microtubules, plant microtubules are
less engaged in intracellular transportation, while having
a major role in cell expansion and cell shape. Further,
microtubules are the dominant component of the plasma
membrane in plant cells while actin filaments play a
similar role in mammalian cells, which indicates the key
role of microtubules in plants’ cell [5-8].
Microtubules are composed of α and β tubulins. These
bio filaments are intrinsically dynamic polymers that
express a non-equilibrium behavior called dynamic in-
stability, where they randomly switch between a growing
and a shrinking phase, both in vitro and in vivo. This dy-
namic is recognized by the following parameters: grow-
ing and shrinking rates, which represent assembly and
disassembly rates during the phases of growth and shrink-
age, and the frequency of catastrophe and frequency of
rescue, which represent the recurrence of switching from
growing to shrinking and vice versa, respectively. Micro-
tubules’ dynamic instability, which has been the subject
of many studies, has been confirmed both in mammalian
and plant microtubules [4,9-13].
While this dynamic is common, the results of study by
Moore et al. have shown that parameters of dynamic
instability are different between plant and neural mam-
malian microtubules [7]. In that study, supported by the
results of a study conducted by Panda et al. that indicates
that microtubule dynamics are regulated by different
isotype composition, different dynamic characterization
of plant microtubules has been also associated with dif-
ferent isoforms from which microtubule is structured [7,
14]. Later, the correlation between dynamic instability
and compositional structure was again confirmed by the
reported result of a study conducted by Newton et al.
[15]. This study focused on measuring dynamic parame-
ters of specific non-neural mammalian microtubules po-
lymerized from HeLa Cell tubulin in vitro, and reported
different dynamic parameters and a slower dynamic in-
stability as compared with Bovine brain microtubules. In
addition, they reported that, unlike Bovine brain, HeLa
Cell microtubules consist of a significantly different β
tubulin isotype distribution, and concluded that the slow-
er dynamic instability can be a result of the diverse tubu-
lin distribution.
*Corresponding author.

M. S. Feizabadi et al. / Advances in Bioscience and Biotechnology 4 (2013) 930-936 931
Different dynamic parameters of plant and mammalian
microtubules are not the only factor which distinguishes
them from one another. It is also notable that plant and
mammalian microtubules show different sensitivity while
interacting with anti-mitotic drugs. Different pharma-
cological properties across different mammalian micro-
tubules and plant microtubules have also been associated
with their diverse protein and compositional structure
[16]. For example, the resistance to docetaxel in some of
the breast cancer (MCF7) cells has been associated with
the alteration of β tubulin isotypes in the structure of
MCF7 microtubules [17-20].
Many multi-dimensional research studies have been
conducted to further clarify the differences between mam-
malian and plant microtubules. In these studies, however,
more weight has been given to researches focused on
dynamics of microtubules. In light of evidence provided
by the outcomes of these studies the major differences
between mammalian and plant microtubules are revealed.
However, a number of questions are still open for further
investigation concerning the better understanding of me-
chanical properties of microtubules in mammalian and
non-mammalian microtubules.
Rigidity of microtubules is one of the mechanical
properties dominant in functionality of a cell. The rigid-
ity of neural microtubules has been measured by differ-
ent methods [21-30]. The recent result of our study, on
rigidity of a single microtubule polymerized from MCF7
tubulin with different beta tubulin structure, indicated a
slight difference in rigidity of a single Bovine brain mi-
crotubule as a sample of neural microtubule, and MCF7
microtubule as a sample of non-neural microtubule, with
different structural composition [31].
To further advance our knowledge about plant micro-
tubules, the focus of this study is to measure the persis-
tence length of a single soybean microtubule in vitro as
species of a plant microtubule with different tubulin di-
versity in its structure, as compared to mammalian mi-
crotubules. Similar to our previous study, we chose to
measure the rigidity of a single soybean microtubule
based on monitoring the fluctuation of an individual mi-
crotubule in response to temperature, implementing the
image analysis techniques.
2. MATERIALS AND METHOD
2.1. Sample Preparation
Microtubules were polymerized from soybean tubulin
(Cytoskeleton, Denver, CO, Cat. TP005). As indicated,
the tubulin is 90% purified in this kit. The tubulin at 5
mg/ml was polymerized via incubation in BRB80 (80
mM PIPES, pH 7.0, 0.5 mM EGTA, and 1 mM MgCl2,
and 1.0 mM GTP with 10% Glycerol) at 37˚C. We ob-
served the nucleation development and polymerization of
soybean tubulin in a real-time sequence of 30 minutes.
To make an appropriate contrast, we also polymerized
Bovine brain tubulin at 5 mg/ml (Cytoskeleton, Denver,
CO, Cat. TL238). The tubulin purification in this kit is
99%, with 10% Glycerol at the 37˚C, and observed on a
regular basis over time.
10 mg/ml BSA was used to inhibit the microtubules
from adhering to glass surfaces. To make a sample of
polymerized microtubule after incubation, a few micro-
liters, usually between 5 µl to 7 µl, of this solution were
pipetted onto a microscope slide (75 × 25 × 1 mm), with
a 22 × 22 mm cover slip (thickness No.1) placed on top.
Pressure was applied to the top of the coverslip to reduce
the thickness. The result was a solution depth of less than
4 micrometers. This state constrained the microtubules to
move only in two dimensions. The edges of the coverslip
were sealed by hot candle wax to avoid any fluid evapo-
ration. All the experiments were conducted at room tem-
perature (24˚C - 25˚C).
2.2. Video Enhanced Differential Interference
Contrast Microscopy and Image Analysis
We visualized the samples using a differential interfer-
ence contrast (DIC) microscope (Diphot 200, Nikon,
Tokyo, Japan) equipped with a 100X oil-immersion ob-
jective lens (NA = 1.25). The images and videos were
recorded with a Sentech USB 2.0 camera (USA). The
digitalized images were then taken at a rate of 1 frame
every 10 s.
The images were then analyzed by Image J (Rasband,
W. S., Image J, US National Institutes of Health, Be-
thesda, Maryland, USA, http://rsb.info.nih.gov/ij/, 1997-
2009). This software was used to adjust the enhance con-
trast between an individual microtubule and the back-
ground. It was used also to measure and monitor the co-
ordinates of points along an individual microtubule in
real time as part of the steps required for measuring the
persistence length. The visualized soybean microtubules
had lengths ranging from 15 to 21 µm.
2.3. Mode Analysis and Bending Rigidity
As expressed in the introduction, the rigidity of a single
microtubule has been measured and reported through
different methods. In our study we implemented a me-
thod introduced by Gittes et al. [21]. In this approach, the
bending rigidity of a single microtubule is calculated by
analyzing the shape fluctuation using the Fourier de-
composition method. The method includes the estimation
of errors correlated to the measurements. Following this
method and to measure the length of a single microtubule,
we first need to specify M + 1 points along each indi-
vidual microtubule. The pixel coordinates for each point
are (xm, ym). The length of each segment is determined

M. S. Feizabadi et al. / Advances in Bioscience and Biotechnology 4 (2013) 930-936 932
using the following equation:

1/2
2
11mmm mm
Sxxyy


 

2


(1)
The tangent angle at each point will be found using the
equation
 
1
11
tan
mmmm
Syyx 





m
x


S
(2)
The length of a microtubule can be calculated by:
1
M
m
m
L


 (3)
Since the fluctuations occur freely, the tangent angle
can be decomposed to a large number of cosine Fourier
modes:
 
00
2π
cos
nn
nn
n
s
sa
LL




 


S


(4)
where an are the amplitudes. A single microtubule has an
intrinsic curvature:

0
0
0
2π
cos
n
n
n
s
a
LL






S


(5)
where is the mode amplitude corresponding to the
filament intrinsic curvature. Therefore the mean ampli-
tude is not zero.
0
n
a
The bending energy of a curved microtubule can be
calculated by:
2
0
0
1d
2
L
Uk SS









s
(6)

22
0
1
1π
2nn
n
n
Uk aa
L








 (7)
where k = kB × T and kB is Boltzmann’s Constant, T is the
temperature, and Lp is the persistence length. Also based
on the equi-partition theorem <U> = 1/2 kBT, we can
calculate the persistence length based on:

2
22
πVar
p
n
L
Lna  (8)
where


2
0
Var nnn aaa (9)
The Fourier coefficients can be calculated as:
1
2π
cos
Nmid
nkk
k
n
aS
LL





k
S


(10)
where
12 1
1
2
mid
k
SSS S

  k
k
S (11)
As explained by Gittes, the measured length of a
microtubule consists of an error due to the quality of our
images, which is associated to the microscope resolution
as well as the sample preparation. The uncertainly in
measuring a length can also be associated to the possible
drift of microtubules in the sample during the recording
of the videos taken from our different samples. The un-
certainly in microtubules’ length can be obtained from
the deviation from the real position along a microtubule.
It can be expressed by a random distance ε, and the error
in estimating the filament length can be calculated as:
2
1
0
11 0
1
12
NN
kk
k
kk
Ls ss










 







 (12)
And
2
2
0
1k
L
L
s


 (13)
The technique to calculate k

is explicitly ex-
plained in Gittes [21]. In brief, it can be shown that



2
22
Var
14 π
11sin
π2
n
k
P
a
Ln
M
nLL M



 

 


 


(14)
and the 2
k

can be calculated by the least-square curve
fitting of


Var n a as a function of n. This error is dif-
ferent from one microtubule to another. In our study this
error is measured and discussed in the following section.
3. RESULTS
To measure the persistence length of a single soybean
microtubule in vitro, we incubated soybean tubulin with
10% Glycerol at 37˚C and noticed that the time required
for polymerization of soybean tubulin to reach to a typi-
cal length beyond 15 µm is longer than the time for Bo-
vine brain tubulin at the same experimental condition.
Bovine brain tubulin with 10% Glycerol can be polym-
erized to long microtubules after incubation for 30 min-
utes. In contrast, we didn’t observe any signs of polym-
erization initiation after 30 minutes of incubation in soy-
bean samples. The focus of this study was not measuring
the polymerization and dynamic parameters of a single
soybean microtubule. However, we observed that soy-
bean microtubules with longer length are reachable after
incubation for two hours. Also, as compared with Bovine
brain, the samples of soybean microtubules were much
less populated, although tubulin was polymerized from
the concentration of 5 mg/ml. All this evidence supports
the hypothesis that the nucleation and polymerization
specifications of a soybean microtubule are different from
those in Bovine brain. Therefore, as we observed, single
soybean microtubules could freely fluctuate in response
to the temperature in our samples without further dilution.

M. S. Feizabadi et al. / Advances in Bioscience and Biotechnology 4 (2013) 930-936 933
So, unlike similar previous studies in measuring the
flexural rigidity of microtubules, our microtubule sam-
ples were not stabilized, or the samples were not diluted
with an antimitotic stabilizer agent such as paclitaxel.
Figure 1 shows a single soybean microtubule viewed in
one of our samples. The same soybean microtubule is
viewed again in a different frame of the movie taken
from the same sample. The two frames located side by
side clearly show the bending of soybean microtubules.
This is a small bending as in general microtubules are
stiff.
To illustrate the microtubules’ shape and monitor the
deflection as a result of their response to the temperature,
several points were selected along single microtubules,
and the positions of digitalized points were monitored
over time. To be consistent with the Gittes method in
selecting the number of the digitalized points along a
single microtubule, we assured that the length of each
segment between two points did not exceed 4 µm. As
explained by Gittes et al., for stiff bio-filaments such as
microtubules that show small curvature as a result of
thermal fluctuations, this segment length is appropriate
to precisely reflect the bending. Therefore, as we set the
limit for the average segment length to be almost 4 µm,
we selected 7 points (n = 1, ···, 7) along an individual
microtubule in our different samples. The coordinates
associated to the positions of these points were recorded
every 10 seconds. In this study we calculated the persis-
tence length of seven individual soybean microtubules
with different lengths.
The length of each microtubule and the error associ-
ated to each microtubule’s length were calculated im-
plementing Eqs.3 and 13. The Fourier coefficients, an =
a1, ···, a4, and as a last step the persistence length of the
single microtubule, were obtained using Eqs.8- 10 . The
results are summarized in Table 1.
In calculating the persistence length, the behavior of
the variance of each mode was observed to be random,
which indicates that our measurement was not associated
with experimental noise. The typical behavior of the va-
riance of modes that is expressed in Figure 2 shows an
initial reduction in its value (solid dots) before rising. As
the variance does not express a monotonic increase, the
Figure 1. Represents two images of a single soybean micro-
tubule in vitro taken by DIC microscopy at two different times.
The above image consists of two selected images to demon-
strate the shape of thermal fluctuations of a single microtubule
in the field of view of the microscope.
Table 1. Persistence length of soybean microtubules with the
different length between 15.71 µm - 20.07 µm polymerized
from pure soybean tubulin in the presence of 10% Glycerol in
27˚C measured from thermal fluctuations in shape method is
estimated. In the second row, the value of the persistence length
calculated from the first mode is expressed. Considering Eq.12,
the relative difference between true length and the measured
length can be calculated as

2
2
0
k
LL
L


 
. The 2
k

can be
calculated by the least-square curve fitting of Var(an) as a func-
tion of n as can be expressed in Figure 2. Also, as explained,
the overall average segment length ∆s0 is 4 µm. The average of
the length difference for our seven samples is 0.06%. This per-
cent difference is ignorable and has no significant effect on
measuring the persistence length.
MT Length (µm) Persistence Length Mode 1 (mm)
15.71 2.84
17.19 6.19
17.94 3.42
19.34 4.23
19.97 8.02
20.07 4.38
20.02 7.51
Figure 2. Solid dots: the variance of mode amplitude versus
mode numbers. The dashed curve is the least square fit of
Eq.14 essential for measuring errors in microtubules’ length.
The random behavior of the variance indicates that the bending
is due to the microtubules’ thermal fluctuations.
bending is related to the thermal fluctuations and not
experimental noise.
Also, as expressed in Table 1, we measured the per-
sistence length of seven soybean microtubules with the
length between of 15 µm - 21 µm and obtained a persis-
tence length between 2.8 mm - 8 mm. The length de-
pendency of persistence length and the liner fit is shown
in Figure 3.

M. S. Feizabadi et al. / Advances in Bioscience and Biotechnology 4 (2013) 930-936 934
Figure 3. The solid dots represent the persistence length of 7
soybean microtubules plotted as a function of the length of
each microtubule and the solid line is the linear fit.
4. DISCUSSION
While microtubules have been subject of many studies,
the focus of many of the biomechanical researches has
been on mammalian and neural microtubules rather than
plant microtubules. To date, we know of many similari-
ties among plant and mammalian microtubules such as
stochastic behavior that can be observed in the dynamic
of both types of microtubules [7,32]. However, plant
microtubules are distinguished from mammalian micro-
tubules in different areas, such as their unique pharma-
cological properties, different dynamic parameters, or
different interaction with MAP [33]. Many of these con-
trasts are associated to significant differences and diver-
sity of tubulin isotypes in the structure of plant micro-
tubules as compared to mammalian microtubules.
The functional diversity of plant microtubules still
needs to be further investigated from other perspectives.
We chose to study one of the important mechanical
properties of plant microtubules by examining the rigid-
ity of a single soybean microtubule in vitro. Soybean
microtubules are significant because they have a unique
compositional structure in terms of β tubulin isotypes.
Although the β tubulin isotype structure of soybean tubu-
lin has not been accurately reported, the existence of
three different beta isotypes (β-I, β-II and pGE23) is con-
firmed [34]. In comparison with a mammalian neural
tubulin such as Bovine Brain with 3% β-I, 58% β-II,
25% β-III, and 13% β-IV, or a non-neural mammalian
tubulin such as MCF7 cell tubulin with 22% β-I, 0% β-II,
51% β-III, and 24% β-IV, soybean tubulin has a different
structural composition. As we run a parallel experiment
with Bovine Brain tubulin, in the first step we noticed
polymerization differences between these two types of
tubulin (unpublished results).
We measured the persistence length of 7 single soy-
bean microtubules with different lengths in vitro, through
a thermally driven fluctuation method in curvature. As
reflected in Table 1, the experimental error associated
with the length of each single soybean microtubule is
small. Therefore, the variation in calculated persistence
length is not significant. The estimated persistence length
for soybean microtubules shows a length dependency as
expressed in Figure 3. The average persistence length
obtained from the first mode is 5.22 mm. This value is
higher than the average persistence length we measured
in our previous study for the MCF7 and bovine brain
microtubules under the same experimental condition [31].
In contrast with our previous study, the soybean micro-
tubules’ length changes broadly between 15 - 10 µm in
our different exponential samples. Considering the length
dependency of the persistence length of microtubules,
the higher value of the average persistence length can be
linked to the fact that length of microtubules changes up
to 4.5 µm from one another. The different value of the
persistence length in soybean microtubules can be asso-
ciated to the different beta isotype structure of soybean
microtubules. So far, many differences in functionality of
plant microtubules, ranging from their dynamic charac-
ters to their mechanism of interacting with anti-mitotic
drugs, are linked to the existence of different beta tubulin
isotypes in their structure. It is reasonable that differ-
ences in the rigidity of soybean microtubules can also be
caused by these compositional differences. In addition,
the origin of the difference between persistence length in
Bovine brain, MCF7, and soybean microtubules can be
associated with the different number of proto-filaments
in the structure of a single soybean microtubule as com-
pared to mammalian microtubules. While the architec-
ture of soybean microtubules in terms of the number of
proto-filament still needs to be investigated, the higher
value of the persistence length can be the result of the
higher number of protofilaments in the structure of mi-
crotubules. Another possible source of differences in
rigidity can be correlated to the existence of the impurity
in soybean tubulin used in this experiment. The Kit of
soybean tubulin consisted of tubulin with 90% purifica-
tion. The existence of impurity, including MAPs, can
cause a difference in persistence length as compared with
those in the Bovine brain percentage of purification.
This study measures the persistence length of a single
soybean microtubule as one of the plant species. This
measurement can support the distinguished role of β tu-
bulin isotypes’ compositional diversity in the functional
diversity of microtubules, which is not limited to the
change in dynamic characters, but includes the mechani-
cal properties as well.
One of the features distinguishing plants is the cell
walls. Unlike animals in which actin filaments are in-
volved in cell shape and plasma membrane, microtubules
are dominant elements in plasma membrane in plant cells
[35,36]. The persistence length of a single soybean’s

M. S. Feizabadi et al. / Advances in Bioscience and Biotechnology 4 (2013) 930-936 935
microtubules measured in this study and the length de-
pendency observed in this study can be significant for
development of the plant cell walls and therefore plant
cell shape.
Our results suggest that the diversity in the composi-
tional structure of microtubules can not only regulate the
dynamic of microtubules, but affect the mechanical prop-
erties as well, and support the fundamental differences
between plant and mammalian microtubules which are
required for their different functionality. While this study
was conducted in vitro, for a better understanding of me-
chanical properties of soybean microtubules, further ex-
periments are required to measure this rigidity in vivo.
The results can be further confirmed by implementing
different methods such as measuring the thermal fluctua-
tion of grafted microtubules or optical trapping tech-
niques. Applying different methods of measuring the per-
sistence length together with examining the structure of
soybean microtubules by the method of electron micros-
copy can reveal the possible source of differences among
soybean and other microtubules [37].
5. ACKNOWLEDGEMENTS
This research was funded by the Physics Department of Seton Hall
University.
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