Download Diffusion Modeling of snRNP Dynamics

WDS'08 Proceedings of Contributed Papers, Part III, 142–146, 2008.
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Diffusion Modeling of snRNP Dynamics
M. Blažíková, P. Heřman
Charles University Prague, Faculty of Mathematics and Physics, Prague, Czech Republic.
D. Staněk
Institute of Molecular Genetics ASCR, v.v.i., Vídeňská 1083,142 20 Prague 4, Czech Republic.
J. Malínský
Institute of Experimental Medicine ASCR, v.v.i., Vídeňská 1083, 142 20 Prague 4, Czech Republic.
Abstract. Small nuclear ribonucleoprotein particles (snRNPs) are essential
supramolecular complexes mediating a process of pre-mRNA splicing. The particles
undergo complex assembly steps in a highly dynamic nuclear compartment called the
Cajal body. Since the dynamics of the assembly and a movement of snRNPs inside the
nucleus is poorly understood, we tested the in vivo snRNP dynamics in the frame of a
simple diffusion model. SmB proteins, which are integral parts of most snRNPs were
tagged with a photoactivable GFP and used for visualization of the snRNP movement.
A simple diffusion model was used to fit experimental values. Our results indicate
that the simple diffusion model is not consistent with the experimental data. A
correction of the model is proposed and its biological relevance is discussed.
Introduction
Cajal bodies (CBs) are evolutionary conserved nuclear domains found in metabolically active
cells [Boudonck et al., 1998; Pena et al., 2001]. Most somatic cells contain 2-4 CBs, 0.5-1 µm in
diameter [Klinglauf et al., 2006]. The CBs contain factors involved in the pre-mRNA splicing, the
histone pre-mRNA maturation, and in the pre-rRNA processing [Gall, 2000; Matera and Shpargel,
2006; Stanek and Neugebauer, 2006].
The pre-mRNA splicing is a two-step trans-esterification reaction catalyzed by spliceosomes that
are large complexes of small nuclear ribonucleoprotein particles (snRNPs), namely U1, U2, U4, U5
and U6. Spliceosomes contain hundreds of other proteins as well [Jurica and Moore, 2003]. All
spliceosomal snRNPs except the U6 snRNP contain Sm proteins. The U6 snRNA interacts with
similar Like-Sm (LSm) proteins [Stanek and Neugebauer, 2006]. Both the Sm and the LSm proteins
assemble into snRNPs during maturation and stay stably associated with them during the whole
snRNP "life".
Cajal bodies were shown to be sites of the snRNPs assembly and according to current models
U4/U6•U5 and U2 snRNP assembly occurs in this location [Schaffert et al., 2004, Stanek and
Neugebauer, 2004, Nesic et al., 2004]. The U4/U6•U5 tri-snRNPs together with the U1 and U2
components form an active spliceosome that allow the pre-mRNA splicing to proceed. During the
splicing process, active spliceosomes become inactivated and disassemble for further rounds of
splicing. Recently it has been shown that the snRNPs reassemble in CBs after splicing [Stanek et al.,
2008]. Formation of the U4/U6·U5 tri-snRNP is therefore a complex cyclic reaction that should be
affected by local interactions of the snRNPs and certainly depends on their movement in the
nucleoplasm.
Currently there is not available any model that would describe dynamics of the spliceosomal
snRNPs in vivo. Many studies pointed to a lack of metabolic energy necessary for an active movement
of intra-nuclear proteins and RNAs [e.g. Dundr et al., 2004]. Considering this knowledge, we tested
whether a simple model based on a free diffusion of snRNPs would satisfactorily describe movement
of the particles in the nucleus. Comparison of modeled diffusion kinetics with fluorescence
microscopy data from living HeLa cells revealed inability of the free diffusion model to accurately
describe dynamics of snRNPs in the cell nucleus.
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Materials and methods
Live cell imaging
HeLa cells were co-transfected with two kinds of fluorescently labeled proteins. The first one was
the SART3 protein tagged with the cyan fluorescent protein (SART3:CFP). Because the SART3 is
known to accumulate in CBs, fluorescence of the SART3:CFP construct served for visualization and
localization of the CBs in the cell nucleus. The second protein, SmB, carried a photoactivable green
fluorescent protein tag (PA-GFP) that can be converted to fluorescent form by illumination near 400
nm. [Patterson and Lippincott-Schwarz, 2002]. It has been reported that the fluorescently labeled SmB
proteins (SmB:PA-GFP) remain stably associated with the snRNP complex after its formation. As a
consequence, spreading and distribution of the complex can be followed by SmB:PA-GFP
fluorescence after its local photoactivation by a short laser pulse [Stanek et al., 2008]. In our
experiments the cells were imaged by the Zeiss 510 confocal microscope equipped with a 60x/1.2 NA
water immersion objective. For each time-lapse imaging, three images were averaged before the
photoactivation. Then the SmB:PA-GFP localized in a selected CB was photoconverted to a
fluorescent form by a short laser pulse at 405 nm and series of fluorescent images were acquired for 5
minutes with 15s time increments. SmB:PA-GFP and SART3:CFP were excited at 488 nm and 458
nm, respectively. Emission of SmB:PA-GFP and SART3:CFP was collected through the long-pass
LP505 and the band-pass BP470-500 filters, respectively. Images were processed using Matlab (The
MathWorksTM) software.
Determination of the diffusion coefficient
Diffusion of snRNP was described by a diffusion equation. For simplicity we used its onedimensional form with a spatially invariant diffusion coefficient D:
∂c( x, t )
∂ 2 c ( x, t )
=D
,
∂t
∂x 2
(1)
where x is a space coordinate, t denotes time, and c is a concentration of diffusing particles.
Photoactivation was modeled by an initial condition of c( x,0) = δ ( x − x0 ) that simulates a point
source generated at the coordinate x0. and at the time t = 0 s. Then the fundamental solution F of
Eq.(1) can be written as [Itô, 1992]:
F ( x − x0 , t ) =
1
2 πDt
e
−
( x − x0 ) 2
4 Dt
,
(2)
We used Eq. (2) for a non-linear least squares fitting [Bevington and Robinson, 2002] of the
experimental data obtained by the time-lapse imaging. In order to fit raw (unnormalized) fluorescence
intensities, a multiplicative parameter k describing fluorescence brightness of SmB:PA-GFP in the cell
was added to Eq.(2). The fitting was performed in the Matlab software and as a result we obtained
optimized parameters D and k for each single dataset.
In the global fitting approach [Eisenfeld and Ford, 1979; Knutson et al., 1983; Beechem at al.,
1983] all experimental curves acquired at different locations of the nucleus were fitted simultaneously
and an overall χ2 was minimized. The diffusion coefficient D was kept common (global) for all
curves. This approach helped to over-determine the model by reduction of the number of fitted
parameters. Scaling fluorescence amplitudes k were kept local for each curve.
Results and Discussion
Spliceosomal snRNPs in the cell nucleus represent a rather inhomogeneous population of particles
in different states of assembly, re-assembly and splicing. To overcome this obstacle, we took
advantage of the fact that CBs serve as snRNP assembly sites and all snRNPs leaving CBs are formed
and activated for splicing. Moreover, concentration of the snRNPs in the CB is substantially higher
than in the nucleoplasm [Klingauf et al., 2006]. We monitored movements of Cajal body-accumulated
spliceosome components snRNPs throughout the cell nucleus. In the cells co-expressing a Cajal body
marker SART3:CFP [Stanek et al., 2008] and protein components of snRNP complexes, SmB, tagged
with the photoactivable GFP variant (PA-GFP) [Patterson and Lippincott-Schwarz, 2002], a
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BLAŽÍKOVÁ ET AL.: DIFFUSION IN THE CELL NUCLEUS
population of the snRNPs confined to a selected Cajal body (CB) was photoactivated. Afterwards, a
movement of the photoactivated protein fraction was followed by the time lapse imaging. Fig. 1 shows
an arrangement of the experiment. The fluorescent complex diffused out of the CB and spread through
the nucleoplasm. A time course of its diffusion was measured at a selected nucleoplasmic area (NP).
We acquired 97 data sets at different locations of nucleoplasm. To obtain representative data
independent of individual cell properties, we measured 50 cell nuclei. An example of the data is
presented in Fig.2. As expected from Eq.(2), characteristics of the fluorescence intensity profiles
strongly depend on the distance between the activation and the measurement area. Fitting of data from
Fig.2 to Eq.(2) indicates that the spreading of the photoactivated SmB:PA-GFP has a diffusion
character.
The hypothesis of a free diffusion of SmB:PA-GFP from the photoactivated area assumes
essentially noninteracting SmB particles and macroscopically isotropic physical properties of the
nucleoplasm. Under these assumptions we expect the diffusion coefficient D to be spatially
Figure 1. Arrangement of the photoactivation experiment. Diffusion of the snRNP complexes inside
the nucleus (green delimited area) was visualized by the SmB:PA-GFP fluorescent fusion protein. PAGFP was converted from the nonfluorescent to the fluorescent form within the circular area
corresponding to the Cajal body CB. A consecutive spreading of the photoactivated complexes was
measured in the nucleoplasmic region NP (yellow arrow).
Figure 2. Example of data from photoactivation experiments measured at different distances (d) from
the photoactivated CB: (closed circles) d1 = 2.3 μm; (open circles) d2 = 10.9 μm. Lines represent the
best fit of the data to Eq. (2).
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independent and a single value should fit all data sets. In order to test this hypothesis we used a global
fitting when all 97 measurements acquired at different distances from the photoactivated spot were
fitted simultaneously (see methods). Since the model is heavily overdetermined, the global fitting is a
robust method for verification whether a single diffusion coefficient can fit all the data sets. Fit quality
can be judged from the fit residuals, i.e. from differences between the fitted curve and the measured
values. For a good fit the residuals should randomly oscillate around zero, systematic deviations
indicate poor fit and inconsistency of the model with data.
Result of the best global fitting is shown in Fig. 3A. It is seen that most of the residuals exhibit
significant systematic deviations from zero and we conclude that the free-diffusion model with a
spatially uniform diffusion coefficient cannot explain dynamics of the snRNP particles in the
nucleoplasm.
To release the strong constraint of the constant diffusion coefficient we evaluated D individually
for each measurement. We have found that all 97 curves can be satisfactorily fitted in this case.
Improvement of the fit quality is demonstrated in Fig. 3B where independently of the measurement
location, the fit residuals are randomly distributed along the timeline and the χ2 decreased by factor
2.2. Resulting distance dependence of the diffusion coefficient is shown in Fig. 4. It can be seen that
the value of the diffusion coefficient gradually increases with an increasing radial distance of the
measured area from the photoactivated CB. In the first approximation, a dependence of D(x) on the
radial distance x can be obtained by a linear regression D ( x) = D0 + ΔD ⋅ x , where D0 =
(4.7±5.4)×10-14 m2/s and ΔD =(3.7±0.6)×10-8 m/s. Similar effect was observed when evaluating the
diffusion coefficient in one cell nucleus for different distances (data not shown).
Currently, mechanisms causing the observed spatial dependence of the diffusion coefficient are
unknown. We propose that it could be a detention of snRNPs due to their reversible interactions with
large macromolecular components with low diffusion mobility. Since these interactions are certainly
dependent on a spatial concentration of the interacting partners, the interaction should modulate value
of the apparent diffusion coefficient observed at different locations in the nucleus. A significant
detention of the diffusing particles could be caused e.g. by a reaction of snRNPs with the pre-mRNA
template during the splicing in the nucleoplasm.
Conclusion
Our study of the snRNP dynamics has shown that the snRNP motion in the nucleus is a complex
process that cannot be explained by a simple diffusion model. Importantly, we have presented a novel
evidence that an apparent diffusion coefficient of SmB:PA-GFP has a significant dependence on the
radial distance from the Cajal body that could result from interactions of the diffusing particles with
nuclear matrix. Development of a model that includes such interactions is in progress.
Figure 3. Residuals (deviations of the fitted curve from the measured values) for 6 selected
nucleoplasm measurements performed at the distance of 2.3 µm; 4.8 µm; 7.1 µm; 9.2 µm; 12.6 µm;
14.8 µm from the photoactivated CB (from top to bottom). a) Result of the global fitting. b) Result of
the analysis of individual curves from the same data set.
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BLAŽÍKOVÁ ET AL.: DIFFUSION IN THE CELL NUCLEUS
Figure 4. Dependence of the diffusion coefficient on the radial distance from the photoactivated CB.
The solid line is a linear regression of the data. Diffusion coefficients in the graph represent results of
97 single curve analyses.
Acknowledgements. This work was supported by the Grant Agency of the Czech Republic (204/07/0133),
by the Grant Agency of Charles University (79508, to M.B.) and by the Ministry of Education, Youth and Sports
of the Czech Republic (MSM 0021620835, to P.H.).
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