Golding and Cox: Supplementary Material
Includes:
1. Materials and Methods
2. Table 1
3. Figure 3
Supplementary material: Materials and Methods
Bacterial strains and genetic constructs: The bacterial strain was DH5PRO,
transformed with plasmids carrying the RNA target and tagging protein, as described
previously [1, 2]. Additional strains used were: PA340-129 (MreB deficient) and its
isogenic wild type PA340, gift of Masaaki Wachi [3]; EC309 (FtsZ84(ts)) and its
isogenic wild type EC294, gift of David Weiss [4]. These strains were rendered electrocompetent by a standard protocol [5] and transformed with plasmids carrying the genetic
constructs. Temperature-sensitive phenotype of the EC309 mutant was induced by
growing the cells at 43oC for 1 hour.
Growth and treatment: The basic procedure for growing and inducing the cells was
described previously [1, 2]. In short, cells from a fresh overnight culture were grown in
LB medium at 37°C to an optical density (OD) of ≈ 0.3–0.5. Induction of the tagging
protein and the RNA target was achieved by adding anhydrotetracycline (100 ng/ml) and
isopropyl-beta-D-thiogalactopyranoside (1 mM) for ~ 45-60 minutes. To obtain a slower
growth rate, cells were also grown in minimal medium (M63 with casamino acids and
glucose [6]). The following chemicals were tested for their effect on RNA motion, by
adding the amounts below to an exponentially growing culture: Tetracycline (50 g/ml,
cells examined after 45 minutes), Chloramphenicol (340 g /ml, cells examined after 45
minutes), Nalidixic acid (250 g /ml, cells examined after 120 minutes).
Isolation of tagged RNA molecules for in vitro measurements was performed using the
native protein purification protocol and reagents from Clontech (Mountain View, CA)[7].
Particle motion was tracked in the elution buffer and in 70% glycerol.
Microscopy and image processing: The microscopy system and analysis methods have
been described previously [1, 2]. In a typical experiment, ~ l from an induced culture
was placed under a thin agar slice. Cells were imaged with an inverted epifluorescence
microscope (Nikon Eclipse, model TE2000-U), under a 60X objective.
Time-lapse
movies were taken with a high sensitivity camera (Cascade:512B, Roper Scientific,
Trenton, NJ) for up to 30 minutes at 1 frame/second, 200msec exposure time. For
analysis, movies were read into Matlab software (Mathworks, Natick, MA). The
fluorescent particles were automatically recognized and followed, to yield a time-series
of particle coordinates r(t) = (x(t),y(t)) for each RNA molecule. This vector was used to
calculate the mean square displacement as a function of time interval: ‹2()›, where  =
|r(t + ) – r(t)| and averaging is performed over all pairs of points at time interval  from
each other. In addition, we also calculated P(f), the power spectrum density of the
coordinates x(t) and y(t), using the Welch method as implemented in Matlab (see Matlab
documentation for details of the algorithm:
http://www.mathworks.com/access/helpdesk/help/toolbox/signal/pwelch.html).
Numerical controls for the effects of 2D imaging: One can envision cases where
normal diffusion, in a unique geometry, when projected onto two dimensions, might be
misinterpreted as sub-diffusion. In order to rule out such a scenario we performed
stochastic simulations of particle diffusion in the following geometries, and made certain
that these cases could be differentiated our experimental observations:
(1) Diffusion on the surface of a cell. A motion of that type could arise if RNA movement
were coupled to the cell membrane in some way. We simulated normal two-dimensional
diffusion on a sphero-cylinder with dimensions of a typical E. coli cell, using the
algorithm of Holyst et al [8].
(2) Diffusion inside the cell. In that case we performed a Monte-Carlo simulation with
infinite potential conditions outside a sphero-cylidrical cell [9].
Both these types of movement lead to a distortion of r(t), and therefore of 2() and P(f),
compared to diffusion in free space. However, they do not yield the power-law behaviour
distinctive of the sub-diffusing particles.
Estimation of particle size: We used several independent methods to estimate the size of
the diffusing particle.

Theoretically, the size of a polymer can be estimated by R ~ lp N where lp is the
persistence length, N is the number of segments (of size lp), and  is the scaling exponent.
In our case, we estimate lp ~ 5-10 nm based on the size of the tagging protein (MS2GFP) and the length of the RNA recognition sequence [1]. The number of tagged
monomers is N ~ 100. Assuming an ideal chain behaviour (= 0.5, [10]) one obtains R ~
50-100 nm. A self-avoiding behaviour ( ≈ 0.58) or an extended chain ( = 1) will
yielded a larger size.

A similar expression describes the spatial fluctuations of a tethered polymer [11], and
indeed the tethered molecules observed in our system exhibit fluctuations of the order 50200 nm [1].

By measuring the diffusion coefficient of the fluorescent particle in aqueous buffer (D
≈ 1 m2/sec, viscosity = 9x10-4 kg/m/sec) and in 70% glycerol (D ≈ 0.025 m2/sec,  ≈
0.018 kg/m/sec), and using the Stokes relation between diffusion coefficient and particle
radius R, D = kbT/6R, we obtain an estimate for the hydrodynamic radius of the tagged
RNA molecule, R ~ 200-400 nm. However, it is quite possible that the molecules have a
different conformation (and therefore a different radius) in the cytoplasm.

The observed size of the tagged RNA molecules under the microscope is in the range
200-500 nm (the upper range is probably due to defocusing effects when imaged out of
the focal plane). However, one has to remember that these dimensions, as well as the
estimates above, are all close to the optical resolution limit, given by the Airy radius RAiry
= 0.6 /NA, where  is the light wavelength and NA = numerical aperture of the optical
system. In our system RAiry ~ 200 nm.
Supplementary material: Table 1
Changes in coefficient and sub-diffusion exponent  under varying experimental
conditions.
Changes in coefficient 
Parameter change
ratio
#
Details
trajectories
Absence of ribosome-binding site
~1.4
50
P value < 0.1
Slow growth rate
~2.2
80
P < 0.05
Fast growth medium: LB, generation
time = 50 min. Slow growth medium:
minimal medium, generation time =
90 min.
Changes in exponent 
Parameter change
ratio
#
Details
trajectories
Absence of ribosome-binding site
1.01±0.12
49
Half sized RNA molecule
1.07±0.06
35
Half sized molecule comprised of 48
MS2 binding sites.
Slow growth rate
0.93±0.07
80
Fast growth medium: LB, generation
time = 50 min. Slow growth medium:
minimal medium, generation time =
90 min.
Presence of Tetracycline1
1.03±0.08
13
50 g/ml, 45 minutes
Presence of Chloramphenicol2
0.85±0.11
19
340 g/ml, 45 minutes
Presence of Nalidixic acid3
0.95±0.07
25
250 g/ml, 120 minutes
MreB mutant4
1.00±0.07
52
Strains PA340-129 and PA340 (wt)
FtsZ mutant5
1.05±0.07
19
Strain EC309
1
Tetracycline inhibits protein synthesis by blocking ribosomal binding of aminoacyl-tRNA [5]
J.
Sambrook, and D. W. Russell, Molecular cloning : a laboratory manual (Cold Spring Harbor Laboratory
Press, Cold Spring Harbor, N.Y., 2001)..
2
Chloramphrenicol inhibits translation by blocking peptidyl transferase [5]
Ibid..
3
Nalidixic acid inhibits DNA supercoiling by binding to DNA gyrase [12]
F. C. Neidhardt, J. L.
Ingraham, and M. Schaechter, Physiology of the bacterial cell : a molecular approach (Sinauer Associates,
Sunderland, Mass., 1990), pp. xii..
4
MreB mutants are spherical, thus the stability of  does not represent a weak phenotype of these
mutations.
5
FtsZ mutants are very elongated, thus the stability of  does not represent a weak phenotype of these
mutations.
Supplementary material: Figure 3
Schematic description of the dependence of the sub-diffusion exponent  on the volume
fraction occupied by obstacles. The two solid lines represent the dependence
found in vitro [13],  = l + (1-l)e-/0 , where l = 0.740.02 is the asymptotic value.
is plotted for two arbitrary values of the critical density, 0 = 0.05 and 0.1. The
presumed position of our system in the (plane is indicated by an asterisk and a
rectangle: The excluded volume in an E. coli cell was estimated to be in the range ~
0.34-0.44 [14], whereas our study shows that ≈ 0.70-0.77. The fact that is very close
to the asymptotic value l , and is very robust to changes in the physiological parameters,
suggests that for the RNA molecules studied here, the system is far above the threshold
density, i.e. >> 0.
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