Role of the nuclear membrane protein Emerin in front-rear polarity of the nucleus

Cell polarity refers to the intrinsic asymmetry of cells, including the orientation of the cytoskeleton. It affects cell shape and structure as well as the distribution of proteins and organelles. In migratory cells, front-rear polarity is essential and dictates movement direction. While the link between the cytoskeleton and nucleus is well-studied, we aim to investigate if front-rear polarity can be transmitted to the nucleus. We show that the knock-down of emerin, an integral protein of the nuclear envelope, abolishes preferential localization of several nuclear proteins. We propose that the frontally biased localization of the endoplasmic reticulum, through which emerin reaches the nuclear envelope, is sufficient to generate its observed bias. In primary emerin-deficient myoblasts, its expression partially rescues the polarity of the nucleus. Our results demonstrate that front-rear cell polarity is transmitted to the nucleus and that emerin is an important determinant of nuclear polarity.

a Protein distribution plots of normalized density, corresponding to maps in Figure 2c, 2e-j. ***P<0.001 **P<0.01 *P<0.05, ns -not significant. b Representative image of a single cell stained for emerin. c Representative images of single cells stained for LEM domain containing proteins, control (left) and EMD knock-down (right). d Representative images of single cells stained for LINC-complex proteins, control (left) and EMD knock-down (right). e Representative images of single cells stained for lamins (LMN), LMN A/C Ser22 -Ser22 phosphorylated lamin A/C, control (left) and EMD knock-down (right). f Representative images of single cells stained for transcription-related markers, nActin -nuclear actin, RNAPII Ser5P -Ser5 phosphorylated RNA polymerase II, control (left) and EMD knock-down (right). g Representative images of single cells after performing FISH for chromosome 3, control (left) and EMD knock-down (right), the magenta outline indicates nucleus border.

Supplementary Text
In combination with the direct stochastic simulations described in the methods, we designed a minimal mathematical description representing the emerin transfer from the ER to the NE via a diffusive process (Supplementary Information Fig. 1) under the assumptions that (1) the rate of emerin appearance in the ER is proportional to the ER surface (due to surface-coupled synthesis and/or a surface-limited adsorption process), and (2) the emerin diffusion in the NE is slow enough to be neglected.
Since "transverse" diffusion along the ER does not affect he scaling of the mean rate of arrival into the NE by diffusion, the problem is effectively one-dimensional, and the average dynamics of NER and NE (number of emerin molecules in the ER and in the NE, respectively) can be mathematically described by the following two-dimensional dynamical system (1): Where the dots represent time derivatives, b is the synthesis or appearance rate of emerin molecules on the ER surface per unit of surface, d their decay rate (assumed equal in ER and in the NE), k the rate of transfer from ER to NE due to diffusion, assumed to be due to a simple diffusion process, neglecting edge effects (2): where D is the diffusion coefficient of emerin molecules in the ER. We can also express the number of emerin molecules at steady state ( → +∞) in the ER and in the NE as a function of the parameters of the model (5,6): The total number of emerin molecules at steady state is then (7): which provides a way to estimate the synthesis rate b by a measurement of emerin numbers/concentration. Finally, the fraction of emerin molecules in the nuclear envelope is given by (8): We now consider the ER being interspaced by the NE (Fig. 4g; Supplementary Figure 6h), and suppose that the relative position between ER and NE may change, resulting in a differential volume of ER at the two opposite sides of the nucleus. We can at first consider the ER to have uniform width, so to treat its length = 1 + 2 as a proxy for surface.
We are interested in studying the effect of the 1 2 ⁄ asymmetry on the emerin intake at the front and rear sides of the nuclear envelope, under the aforementioned hypotheses. We can thus compute the front/rear ratio in the number of emerin molecules which, at steady-state, reach the NE as a function of the front and back ER lengths 1 , 2 (9): .
To understand which one of the two regimes applies to our experimental system, we can estimate the ⁄ = 2 2 ⁄ ratio in the case of emerin diffusion in the ER. The emerin diffusion coefficient in ER can be approximated with that of GFP in ER ( ≃ 10 2 ⁄ )1. Emerin decay time under the considered experimental conditions was observed to be around −1 ≃ 50 ℎ. The total length of the ER (and thus that of the front and rear fractions) is of the order of 100 . This yields (12): = 2 1,2 2 ≈ 20 2 10 4 2 (50 * 3600 ) −1 ≃ 360 ≫ 1.
In other words, the estimates lead to the conclusion that in the case of emerin diffusion in ER we are in the "high" ⁄ regime, which yields (13): (1) (2) = 1 2 .
These analytical predictions of the mathematical model are in very good agreement with the direct stochastic simulations of the birth/death diffusion process ( Fig. 4g; Supplementary Figure 6h).
In the model described so far we neglected all the possibility of active and directed processes that would transport emerin molecules towards the nucleus, but these processes may also be present. Their relevance will depend on the comparison between the diffusion characteristic time scale and the time scales of active ("ballistic") transport (14) where is the typical speed resulting from the action of molecular motors. In the "ballistic" limit case ( ≪ , ≫ 2 ⁄ ), the characteristic time to reach the nuclear envelope scales as rather than as 2 (15): The front/back ratio in the number of emerin molecules at steady-state has two different regimes (16): (1) (2) = { Hence, as in the diffusive model the emerin front/back ratio at the two opposite sides of the nuclear envelope corresponds to the ER front/rear ratio when the endocytosis velocity is not too high with respect to the decay rate of the molecule ( ⁄ ≫ ). Thus, in this regime, the two models are not distinguishable. On the contrary, the prediction of the ballistic case differs from that of the diffusive case in the regime of high decay / low velocity ( ⁄ ≪ ), where the former would predict an equal distribution of emerin at the two sides of the nuclear envelope irrespective of 1 , 2 .
Finally, we considered the case where the assumption of emerin synthesis/adsorption proportional to the ER surface is relaxed. In this case, the scaling of the front/rear emerin ratio is not compatible with the experimental observations. The front/rear ratio in the number of emerin molecules which, at steady-state, reach the NE as a function of the front and back ER lengths 1 , 2 is then (19): (1) (2) = .
Again, at fixed 1 2 ⁄ ratios, we can obtain two different regimes depending on the ⁄ ratio (20): In other words, the front-rear steady-state ratio in the number of emerin at the NE is never proportional to the length ratio (as observed experimentally) in this model variant where emerin synthesis/adsorption is not proportional to ER surface.

Supplementary Figure 8 Schematic representation of mathematical model
Variants of the proposed mathematical model, based on different assumptions, yield different emerin front-to-back ratios. a Our current model predicts the emerin front-to-back ratio to scale linearly with the ER front-to-back ratio. b A much lower diffusivity (at least 5 orders of magnitude than that of emerin) would cause the front-to-back ratio to be negatively proportional to the amount of ER present on each side. c-d Finally, by relaxing the assumption that EMD synthesis is proportional to the ER surface, or by considering a ballistic model (where we considered endocytic processes that dragging emerin molecules towards the nucleus) would result in a front-to-back ratio equal to 1. Color legend: light blue circles: newly synthesized EMD; purple circles: EMD free in the ER; green circles: EMD reaching the nuclear envelope.