Enhancement of U4/U6 small nuclear ribonucleoprotein particle association in Cajal bodies predicted by mathematical modeling

Abstract

Spliceosomal small nuclear ribonucleoprotein particles (snRNPs) undergo specific assembly steps in Cajal bodies (CBs), nonmembrane-bound compartments within cell nuclei. An example is the U4/U6 di-snRNP, assembled from U4 and U6 monomers. These snRNPs can also assemble in the nucleoplasm when cells lack CBs. Here, we address the hypothesis that snRNP concentration in CBs facilitates assembly, by comparing the predicted rates of U4 and U6 snRNP association in nuclei with and without CBs. This was accomplished by a random walk-and-capture simulation applied to a three-dimensional model of the HeLa cell nucleus, derived from measurements of living cells. Results of the simulations indicated that snRNP capture is optimal when nuclei contain three to four CBs. Interestingly, this is the observed number of CBs in most cells. Microinjection experiments showed that U4 snRNA targeting to CBs was U6 snRNP independent and that snRNA concentration in CBs is approximately 20-fold higher than in nucleoplasm. Finally, combination of the simulation with calculated association rates predicted that the presence of CBs enhances U4 and U6 snRNP association by up to 11-fold, largely owing to this concentration difference. This provides a chemical foundation for the proposal that these and other cellular compartments promote molecular interactions, by increasing the local concentration of individual components.

Figure 1.

Flow chart of simulation in a nucleus with up to five CBs. Chart is showing the main program on the left and the subprogram Random Walk on the right side.

Figure 2.

Three-dimensional modeling of an average, living HeLa cell nucleus. (A) HeLa cells were transfected with SART3-GFP. Twenty-four hours posttransfection, live cells were imaged using a Zeiss LSM 510 microscope. Approximately 100 sections in the z-direction were taken. An image created by MetaView software (Carl Zeiss) shows sections of a cell in the xz plane (top green box), yz plane (right red box) and xy plane (big blue box). The distance tool was used in this environment to determine the dimensions of HeLa cell nuclei. SART3-GFP is almost entirely found in the nucleoplasm, concentrated in CBs (arrowheads), and excluded from nucleoli. The display window shows an area of 73 × 73 μm and includes cells expressing different levels of SART3-GFP. (B) Three-dimensional projection of the average HeLa cell nucleus including one nucleolus and CBs. Axis scale in micrometers.

Figure 3.

Secondary structure of U4 snRNA. The Sm protein and U6 binding sites are indicated by black brackets. In the U4SubSm mutant, the U-rich sequence of the Sm protein binding site was mutated by replacing it with a C- and G-rich region. In the U4Δ1-18/56-63 snRNA mutant, the U6 binding site was completely deleted, indicated by red lines. Modified from (Gerbi et al., 2003).

Figure 4.

Microinjected U4 snRNA localizes specifically and independently to CBs. HeLa cells were microinjected into the cytoplasm with either U4wt snRNA (A); U4Δ1-18/56-63 snRNA, lacking sequences required for base-pairing with U6 snRNA (B), or U4subSm snRNA, lacking sequences required for Sm protein assembly (C). After 1-h recovery and fixation, cells were stained with anti-coilin antibody. The fluorescein isothiocyanate channel (green) shows Alexa 488-labeled snRNA, and the Cy5 channel (red) anti-coilin immunostaining. DAPI staining is shown in blue. Bar, 5 μm.

Figure 5.

Influence of Cajal bodies on mean first passage time averaged over all initial positions [<τ(r₀)>]. The random walk simulation was executed in an average HeLa cell nucleus with different numbers of CBs. Light gray bars show [<τ(r₀)>] for a particle, with a diffusion coefficient of 0.5 μm²/s, to find a CB in an average HeLa cell nucleus. Dark gray bar shows the analytical solution for a simplified spherical model possessing the same accessible volume with one CB in the center (Kuthan, 2003).

Figure 6.

Concentration of U4 snRNA in the CB versus nucleoplasm. (A) Relative concentrations of U4 snRNA in CBs versus nucleoplasm. The cytoplasm of HeLa cells was microinjected with either U4wt (n = 40) or U4Δ1-18/56-63 (n = 37) snRNAs. After recovery and fixing, cells were stained with anti-coilin antibody. Fluorescent intensities in CBs, nucleoplasm, and background were measured and normalized. The ratios of each cell were averaged. The boxplot represents the pooled data of three independent experiments, each 11–15 cells. The graph depicts the 5–95 percentile distribution (whiskers) with the SE and mean represented by the box and horizontal line, respectively. The data points are scattered along the x-axis for visibility. A two-tailed Mann–Whitney test confirmed a highly significant difference (p < 0.0001) between the values for the two injected RNAs. (B and C) Intensity ratio CB/NP is not affected by the amount of injected fluorescent RNA. The sections of each injected cell were projected in one plane. The integrated intensity of the whole cell, including cytoplasm, was measured, and the signal of a similar area devoid of cells on the same slide was subtracted as background. Graphs show integrated intensities measured over individual cells (x-axis) versus corresponding CB/NP ratios (y-axis) for U4wt snRNA (B) and U4Δ1-18/56-63 snRNA (C). Linear least squares fitting showed that injected intensities are highly uncorrelated to the observed intensity ratio CB/NP (p = 0.83 and 0.831, where p is the probability that R = 0).

Figure 7.

Cajal bodies enhance U4/U6 snRNP assembly over a plausible range in snRNA concentrations and CB numbers and sizes. Combining the simulation data with estimated association rates leads to a prediction of productive hits between U4 and U6 snRNPs, depicted here as time in seconds for one particle to have a productive hit. (A) Variation in association rates in model nuclei, containing one to four CBs in which snRNP targets are concentrated 20-fold over nucleoplasm. Independent solutions are shown for CBs of radius 0.5 (black bars) or 0.25 μm (light gray bars), compared with a cell without a CB (dark gray bar). (B) Variation in association rates in model nuclei, containing three CBs, in which snRNP targets are concentrated 5-, 10-, and 20-fold over nucleoplasm. Note that variation among the predicted values shown in the figure was <5%. (C) Dependence of productive hit rates on polar angle (δ) and resulting difference in overall di-snRNP assembly in a nucleus without CB compared with cell with three CBs. The solid line represents time for productive hits in seconds, in a nucleus with three CBs. The dashed line represents nucleus time for productive hits in seconds, in a nucleus without CBs. Gray bars represent the -fold difference in time to productive hit in a cell with three CBs compared with a cell with none. Parameters are D = 0.5 μm²/s, three CBs (0.5-μm radius), and 20 times concentration difference CB/NP.