Active diffusion and microtubule-based transport oppose myosin forces to position organelles in cells

Even distribution of peroxisomes (POs) and lipid droplets (LDs) is critical to their role in lipid and reactive oxygen species homeostasis. How even distribution is achieved remains elusive, but diffusive motion and directed motility may play a role. Here we show that in the fungus Ustilago maydis ∼95% of POs and LDs undergo diffusive motions. These movements require ATP and involve bidirectional early endosome motility, indicating that microtubule-associated membrane trafficking enhances diffusion of organelles. When early endosome transport is abolished, POs and LDs drift slowly towards the growing cell end. This pole-ward drift is facilitated by anterograde delivery of secretory cargo to the cell tip by myosin-5. Modelling reveals that microtubule-based directed transport and active diffusion support distribution, mobility and mixing of POs. In mammalian COS-7 cells, microtubules and F-actin also counteract each other to distribute POs. This highlights the importance of opposing cytoskeletal forces in organelle positioning in eukaryotes.


Supplementary Figures and Legends
b, Distribution of LDs in a hok1 null mutant. Note that cells showed occasionally also subapical clustering. This was rare and excluded as considered artificial 2 . Scale bar, 5 µm. c, Average intensity scans over the apical 30 µm in wild-type and a ∆hok1 mutant cells. Each data point represents mean ± SEM, n=40 cells. d, Average intensity scans over the apical 30 µm in wild-type cells treated with benomyl (+Ben) and simultaneously with benomyl and latrunculin A (+Ben/LatA).
Each data point represents mean ± SEM, n=40 cells.

Supplementary
The net drift velocity ‫ݒ‬ was estimated via fitting density profile from the model (S0) to experimental measured intensity for ∆kin3 mutant cells. 1.9 √ √ n/a n/a n/a ‫ݓ‬ : (s -1 ) 0.0034

Supplementary
0.12 √ √ n/a n/a n/a '√': indicates the value from the control data and its specific values are in Supplementary Table 1  Analysis PO distribution Fig. 1b, Supplementary Fig. 1a AB33∆Kin3_Kin3 ts _paGSKL Analysis of PO pole-ward shifting Fig. 1d,e

Mean square displacement analysis and diffusion rate estimation
To analyse the spatial-temporal spreading of LDs and POs, the mean square To classify the behaviour, for ߙ > 1.6 the motion was classified as directed, while for ߙ < 1.6 it was classified as diffusive. The ‫)ݐ(ܦܵܯ‬ curves were calculated using an ensemble average over the entire trajectories of all tracked diffusive organelles and the exponents ߙ were obtained by fitting the ‫)ݐ(ܦܵܯ‬ to the form ‫ݐܣ‬ ఈ in a time interval 0 − 2.5 s (Fig. 4c, 7d, Supplementary Fig. 3b) and in a time interval 0 − 20 s ( Supplementary Fig. 1e), The diffusion coefficients ‫ܦ‬ were estimated by fitting ‫)ݐ(ܦܵܯ‬ to a linear function ‫ݐܦ4‬ in a time interval 0 − 1.8s for each tracked diffusive-like PO (Fig. 4e, 4g) and LD ( Supplementary Fig. 3c) in Ustilago hyphal cells and in a time interval 0 − 3s for each tracked diffusive PO in COS-7 cells (Fig. 7e). Mean and standard errors were calculated for the diffusion rates and student-t tests were performed to detect significant differences between experiments. For the axial and radial diffusion coefficients in Fig. 2d, as well as for the control experiments used in the mathematical modelling, the cell axis was determined through an automatic imaging process (described in the method part) and each trajectory (t) was rotated so that its first and second components correspond to axial and radial directions; the ‫)ݐ(ܦܵܯ‬ in the axial (respectively radial) direction was calculated using an ensemble average of tracked diffusive POs for the first (respectively second) component of (t). These 1-dimensional ‫)ݐ(ܦܵܯ‬ were fitted to a linear function ‫ݐܦ2‬ in a time interval 0 − 3s to get the best fit for the diffusion rate ‫.ܦ‬ An F-test was performed for the significant difference between the best fitting diffusion coefficients in axial and radial direction (Fig. 2d). Nonlinear curve regression and F tests for diffusion coefficient comparison were performed using the software Prism 5.03 (GraphPad Software, San Diego, USA).

Modelling the distribution of peroxisomes in mutant ∆kin3
The situation for the mutant ∆kin3 is simpler than the wild type -there appears to be no fast long-range directed motion of early endosomes. We took a simple drift diffusion model with no flux at the ends:

Modelling the distribution of peroxisomes in wild type cells
In order to understand the coordination between the mechanisms that are transporting POs within the wild type cells, we construct an extension of the dynamical model (S0) for the distribution of POs along a portion of the cell ‫ݔ‬ ≤ ‫ݔ‬ ≤ ‫ݔ‬ . We postulate that POs move between three populations: ߩ ଵ(ଶ) ‫,ݔ(‬ ‫)ݐ‬ is the density of POs that are propagating actively and rapidly away from the tip (to the tip) carried by early endosomes (EEs, ref. 2), while ߩ ଷ ‫,ݔ(‬ ‫)ݐ‬ is the density of POs within the cytoplasm and that is undergoing both diffusion with rate ‫ܦ‬ and a slow but deterministic drift with velocity ‫ݒ‬ towards the tip. We assume that the propagation of the direct-transported POs is at velocity ‫ݑ‬ in the respective direction and changes direction with a rate ‫;ݓ‬ we assume POs in directed transport unbind from EEs at a rate ‫ݓ‬ ௗ and those in cytoplasm bind to EEs and move in directly along MTs with a rate ‫ݓ‬ . Thus the dynamics of the three populations is modelled by the following system of coupled partial differential equations: Persistence of directed transport could lead to accumulation at the ends 3,4 . However, in the context of POs in Usilago hyphal cells, the directed motion of POs is driven by EE motion and, consequently, the behaviour of POs at the ends reflects that of EEs.
It has been shown in Usilago hyphal cells that EEs do not typically fall off the track 5 , or form clusters at the cell tip 6 . Instead, they rapidly move away from the tip due to dynein activity. Therefore, at the ends of the domain, we assume that the directly-    Table 2), during directed transport is characterised by α ~2, and thus is not diffusive.

Model validation for mutant cells (∆ ∆ ∆ ∆hok1)
For the ∆hok1 mutant cells, we measured the axial diffusion rate as ‫ܦ‬ = 0.0034 ± 0.00002 ‫ݏ‬ ିଵ from ‫)ݐ(ܦܵܯ‬ analysis. Using the drift velocity shown in Supplementary   Table 2 and measured axial diffusion rate, and assuming the same background intensity as in ∆kin3 mutant, the model (S0) predicted the intensity profile for POs in the ∆hok1 mutant cells as shown in Fig. 5c.

Hypothetical scenarios: model predictions
We used the model to explore the hypothetical scenarios shown in Supplementary   Table 3 some of which were currently unable to be explored experimentally. The model allows us to examine the importance of the various processes in achieving an even distribution of POs along the cell as well as the speed of mixing for these scenarios. The speed of mixing was characterized using the first arrival time of a PO to a distance distal from the hyphal tip. This was estimated using simulations of PO motility starting at the hyphal tip, averaged over a number of simulations (n=100-2000); random motility of individual POs along cell axis was simulated according to the parameters in Supplementary Table 3