Active diffusion and advection in the Drosophila ooplasm result from the interplay of the actin and microtubule cytoskeletons

Transport in cells occurs via a delicate interplay of passive and active processes, including diffusion, directed transport and advection. Despite progresses in super-resolution microscopy, discriminating and quantifying these processes is a challenge, requiring tracking of rapidly moving, sub-diffraction objects in a crowded, noisy environment. Here we use Differential Dynamic Microscopy with different contrast mechanisms to provide a thorough characterization of the dynamics in the Drosophila oocyte. We study the movement of vesicles and the elusive motion of a cytoplasmic F-actin mesh, a known regulator of cytoplasmic flows. We find that cytoplasmic motility constitutes a combination of directed motion and random diffusion. While advection is mainly attributed to microtubules, we find that active diffusion is driven by the actin cytoskeleton, although it is also enhanced by the flow. We also find that an important dynamic link exists between vesicles and cytoplasmic F-actin motion, as recently suggested in mouse oocytes.


INTRODUCTION
The spatial distribution and organization of cytoplasmic content, like proteins or protein complexes, nucleic acids, and whole organelles require the combined action of passive and active biophysical processes. In fact, thermal-based diffusion is not sufficiently fast and effective in redistributing large organelles, like vesicles, within the cell 1 . This is due to their large size, which makes their diffusion coefficient small, as well as to the typically crowded and viscous environment that is found inside cells. Active transport mechanisms mitigate the ineffectiveness of thermal diffusion. Molecular motor proteins carry attached cargos (such as organelles and vesicles) along cytoskeletal filaments, which act as tracks for directed transport across the cell 2 . In addition, in larger cells, it is likely that the transport of such cargoes causes a large-scale net flow, known as cytoplasmic streaming 3,4 . As a result of the viscous drag, caused by a translocating motor, streaming leads to a circulation of the cytoplasm and its efficient remixing 5,6 . Finally, recent studies demonstrate that ATPdependent processes are responsible for the presence of random force fluctuations within the cytoplasm, whose effects lead to the displacement of tracer particles in a diffusive-like manner -named active diffusion -that is more efficient than thermal-based diffusion [7][8][9][10][11] .
Understanding the details of the subtle interplay between all these processes is a demanding task, due to the many time-and length-scales and the multiple molecular pathways involved.
In this work, we investigate the interactions between different mechanisms of motion in the Drosophila oocyte. Drosophila oogenesis is well studied from a genetic point of view and this large cell can be probed with a variety of chemical treatments and microscopic tools. In the oocyte, microtubules and kinesin-1 are essential for both the transport of cargos and cytoplasmic streaming 12,13 . At mid-oogenesis (stage 9, st9), the topology and speed of cytoplasmic flows directly correlates with the topology of the microtubule cytoskeleton and the speed of kinesin, respectively 14 . In addition, a cytoplasmic network of actin filaments (Factin) -known as the actin mesh -is present within the oocyte and acts as a negative regulator of the microtubule/kinesin-dependent flow 15 . However, much remains to be uncovered about the interplay between the actin mesh and the microtubule cytoskeleton in regulating the motion of material within the ooplasm. The recent discovery of a link between cytoplasmic actin and vesicle dynamics in mouse oocytes already suggests a close relationship between vesicle transport, motor activity and the actin cytoskeleton 16 . However, it remains unclear whether this observation represents a general feature, also present in other eukaryotic cells.
To gain insight on these issues we developed a methodology to simultaneously probe the dynamics of both, cytoplasmic F-actin and vesicles in wild type oocytes, as well as in oocytes with aberrant cytoskeletons and different cytoplasmic streaming conditions. We did so by combining particle image velocimetry (PIV) with Differential Dynamic Microscopy (DDM) 17,18 . In contrast to PIV, DDM probes the sample dynamics not in the direct space, but in the Fourier domain, with the bonus of being able to analyze densely distributed objects, whose size is well below the diffraction limit of the microscope, and in the presence of substantial amounts of noise. DDM can be employed with different imaging mechanisms, providing information on various labeled and unlabeled dynamic structures. These properties are used here for the first time to characterize the crowded interior of a living cell. This is done by combining confocal imaging of labeled F-actin, with simultaneous Differential Interference Contrast (DIC) imaging of unlabeled intracellular vesicles.
Using chemical treatment and genetic manipulation we can show that the dynamics of vesicles result from two contributes: a persistent ballistic motion due to cytoplasmic flows and a diffusion process of active nature. Surprisingly, we found that a similar combination of ballistic and diffusive movements also captures the motility of F-actin, showing a strong correlation between the motion of the actin network and the vesicles. This result provides an important link between the active diffusion of vesicles and the underlying fluctuating nonequilibrium actin network, of which we quantify the overall dynamics by focusing on the diffusive-like component. We discuss our results considering a recently proposed model for the dynamics of a particle embedded in a living cell, where both thermal fluctuations and non-equilibrium activity coexist 19 .
Finally, we demonstrate that, in our system, active diffusion constitutes an ATPdependent process, with at least two distinct ingredients. On one hand the actin mesh itself seems to be a major source of active diffusion. However, we also find that microtubule based flows enhance active diffusion, and only depletion of both cytoskeletons results in the abrogation of this random motion. As shown before, our data outlines a key role of the dynamic cytoplasmic F-actin in facilitating active diffusion. Importantly, we now demonstrate that microtubules substantially contribute to the diffusive motion of both vesicles and the cytoplasmic actin network as well.
In summary, our work sheds new light on the dynamic interplay between ATPdependent forces and cytoplasmic mechanics to regulate intracellular motility. We show that: 1) the major ATP-dependent entities responsible for advection and active diffusion are the microtubule and cytoplasmic F-actin networks, and 2) an important dynamic link exists between vesicles and cytoplasmic F-actin motion.
Under a more methodological perspective, we establish DDM as a powerful tool for all biologists interested in problems involving the motion and the rearrangement dynamics of different structures within the cell, as it allows to extract a robust quantitative information even in conditions where more traditional image processing methods fail.

Ooplasmic vesicle dynamics consist of persistent and diffusive motion
The asymmetric localization of developmental determinants by microtubule motors (such as kinesin-1) in the Drosophila st9 oocyte is a key event for the specification of the body axes of the embryo 20 . In addition, the translocation of cargos by kinesin-1 induces bulk movements of the cytoplasm -called cytoplasmic streaming or flows. These flows can be measured by particle image velocimetry (PIV), using endogenous vesicles as tracer particles 14 . However, while PIV gives an accurate description of flow velocities and topology, it is unsuitable to describe non-persistent, diffusive motion. Therefore, we used Differential Dynamic Microscopy (DDM) to monitor and characterize cytoplasmic movements in more detail ( Fig.   1) 18,21 . Analyzing DIC time-lapse movies of living oocytes by DDM (DIC-DDM) unveiled a more complex dynamic behavior, which is not fully captured by PIV. In fact, DIC-DDM analysis shows that ooplasmic vesicles move in a ballistic, persistent, as well as in a random, diffusive manner ( Fig. 1a,b).
In DDM experiments, the information about the sample dynamics is encoded in the so called intermediate scattering function (ISF) !(#, ∆&), which describes the relaxation of density fluctuations with wave vector # as a function of the delay time ∆& (Fig. 1c) 18,22 . Initial attempts of fitting our experimental ISFs to the prediction of an advection model, inspired by previous PIV results, failed. Our ISFs were clearly suggesting a more complex, long-time dynamics. However, we obtained a successful description of our ISFs, by using a simple advection-diffusion model, given by ! (, )& = + , -. # )& / 01 2 (3)45 (1) in which, in addition to a directional, ballistic motion with rate -. # , the vesicles are also subjected to a random, diffusive motion with rate -6 (#) . We found a good agreement between our model and the experimental data by considering that each vesicle bears the same diffusivity 7 89: ("ves" stands for vesicles), but a different velocity drawn from a prescribed probability distribution function, whose Fourier transform + , appears in Eq.1 (see also Materials and Methods). In fact, once the average vesicle speed ; 89: is calculated, one has -. # = ; 89: # and -6 # = 7 89: # 6 . Fitting the experimental intermediate scattering functions (Fig. 1c) to Eq. (1), confirmed the validity of our model and allowed us to simultaneously determine -. and -6 for each # (Fig. 1d), both exhibiting the expected ballistic or diffusive scaling, respectively. By repeating this analysis on < = 7 cells (with an average of 1500 vesicles per cell contributing to the DIC-DDM signal) we obtained ; 89: = 36 ± 15 nm/s and 7 89: = (3 ± 1) 10 0E µm 2 /s, where in both cases the deviation from the average represents the standard deviation of the population ( Table 1).
The ratio F = 67 89: /; 89: ≃ 500 nm corresponds to a characteristic length scale that separates two distinct regimes: over distances larger than F, advection is the most efficient transport mechanism, while on smaller length scales diffusion prevails. Of note, in our case F is roughly of the order of the vesicle radius. Therefore, it is not surprising that PIV, which operates over a coarse-grained grid with a resolution much larger than the size of the tracers, Methods for details). Comparable information can also be extracted by PIV analysis of movies, imaging the light reflected by vesicles at 561 nm 14 . We find that each vesicle in the DIC images reflects light at 561 nm from its center (Fig. 1b), and therefore, it is not surprising that they display the same motion ( Supplementary Fig. 1). More importantly, the nearly identical velocity values obtained by DIC-PIV and DIC-DDM support the hypothesis that the persistent component of the vesicle's motion captured by DIC-DDM corresponds to the microtubule-dependent flow previously described by PIV only 14 . However, compared to reflection imaging, DIC has three advantages for general studies on motion of cytoplasmic components. Firstly, the focal plane with DIC is thicker. Secondly, there is no need to use a specific laser line to acquire DIC images, and thus the number of fluorophores that can be combined with DIC is higher. And thirdly, DIC can theoretically be applied to any cell type.
In conclusion, we have shown that DDM can quantitatively separate the persistent, ballistic motion from the random, diffusive-like movement experienced by the same set of vesicles. Importantly, this is obtained through a simple and fully automated procedure, that does not require the accurate localization, tracking and trajectory reconstruction of single tracer particles on which direct-space methods typically rely [23][24][25] . This makes the results obtained by DDM analysis particularly robust and user-independent, as they are not affected by the selection bias or by the strong dependence on external parameters that are often associated with manual and automated particle tracking. In addition, our method is noninvasive, as no tracer particles need to be injected into the cells, and, furthermore, we do not need to apply any external force to characterize the motion of cytoplasmic components.
Our approach can be of use in a variety of biological problems, involving the characterization of the motion and the restructuring dynamics of different cytoplasmic components, as it provides a detailed and statistically robust description, even in conditions where single particles and trajectories cannot even be resolved or identified.

The motility of cytoplasmic actin filaments directly correlates with vesicle motion
The cytoplasm constitutes a densely packed environment, containing not only organelles, but also highly dynamic actin filaments. After successfully using DIC-DDM to quantify the motion of vesicles, we applied it to monitor the motility of the cytoplasmic F-actin network traversing the oocyte cytoplasm. This task is made difficult due to the small size of the filaments, their fast and random movement, their crowding, and finally a low signal-to-noise ratio 8,[26][27][28] .
To understand the overall cytoplasmic dynamics in oocytes, we imaged vesicles (DIC) and F-actin simultaneously ( Fig. 2a and Supplementary Fig. 2). In st9 oocytes, a three-dimensional F-actin network traverses the entire ooplasm ( Furthermore, fluorophore-tagged Act5C has a dominant-negative effect, preventing the formation of the actin mesh and inducing fast cytoplasmic flows 32 (and data not shown).
Thus, in order to study the actin mesh in living cells, we used the F-actin binding protein UTRN.GFP, ubiquitously expressed under the sqh promotor (Fig. 2c,c') 33 . UTRN.GFP consists of the calponin homology domain of human Utrophin fused to GFP, strongly binding to actin filaments, but not actin monomers 34 . Based on fixed samples, UTRN.GFP has no effect on the morphology of the F-actin network, or on the timing of its formation and disappearance ( Supplementary Fig. 2c). Thus UTRN.GFP constitutes a suitable probe to visualize cytoplasmic F-actin in living oocytes.
Visual inspection of the movies revealed that cytoplasmic actin filaments are highly motile and seem to be dragged through the ooplasm in a random, "flowing" manner (Supplementary Movie 1). Those movies also suggest that this F-actin structure does not constitute an interconnected stable meshwork of filaments, but rather resembles a network of constantly assembling and disassembling filaments, that may intertwine when in close proximity (Supplementary Movie 1). Attempts to quantify the dynamic behavior of the actin network by particle tracking or PIV were unsuccessful, mainly because of the large level of noise and crowding of the structure. Therefore, we combined DDM with confocal imaging (Con-DDM) 35 to assess its motility. Notably, the same advection-diffusion model used for interpreting the motion of the vesicles is also found to accurately describe the motion of cytoplasmic F-actin (Fig. 2d). Fitting of the q-dependent relaxation rates -. # = ; LM5 #, and -6 # = 7 LM5 # 6 provides an estimate for the characteristic large-scale velocity ; LM5 = 36 ± 15 µm/s and for the effective diffusivity 7 LM5 = (6 ± 1.5) 10 0E µm 2 /s of the actin filaments (where "act" stands for actin, Fig. 2e, Table 1 . This result indicates that both F-actin and vesicles move in a persistent manner by advection, most likely driven by microtubuledependent flows. In addition, we found a remarkable correlation between the diffusion coefficient of vesicles and the effective diffusivity of F-actin, as 7 LM5 ≅ 27 89: (Fig. 2g). This correlation, which will be discussed in more detail below, suggests the existence of an important dynamic link between vesicles and cytoplasmic F-actin motion. This hypothesis is compatible with recent findings in mouse oocytes, where it was found that cytoplasmic actin filaments seem to polymerize from the surface of vesicles 16,36 . However, a comprehensive comparison of all motions (persistent and diffusive) displayed by vesicles (DIC) and the actin network (confocal) was not performed in these studies.

Microtubule-dependent flow enhances active diffusion
Our results suggest that the diffusive motion of vesicles and actin filaments results from the Notably, the flow-independent diffusion coefficient 7 89:,, is significantly larger than the thermal diffusion coefficient 7 QR = 3.1 10 0S µm 2 /s (TH for thermal) that can be estimated for vesicles in the oocyte (average size 1 ± 0.2 µm) and based on previous measurement of the viscosity (T = 1.4 Pa s) for these oocytes (horizontal dotted line in Fig. 2h) 14 . We can thus conclude that 7 89:,, describes an active diffusion process, devoid of any flow contributions.
Similar results were also found for actin, since the effective diffusivity 7 LM5 = 7 LM5,, 1 + P LM5 ; LM5 is made of an intrinsic and a flow-dependent contribution, with 7 LM5,, = (3 ± 1) 10 0E µm 2 /s and P LM5 = (3 ± 1) 10 06 s/µm (Fig. 2h). This suggests that both vesicles and the cytoplasmic F-actin display an active diffusive motion, with a component that depends on cytoplasmic streaming, and a component that does not.
To further assess the influence of flows on cytoplasmic dynamics we first attempted to eliminate kinesin-1, the motor responsible for flows 13,37 . However, the morphology of the actin mesh was massively disturbed in oocytes lacking kinesin, and large aggregations of Factin were observed instead ( Supplementary Fig. 3a,b) 38 . However, it is known that the mesh is present in oocytes that lack microtubules 15 Table 1). Together, these results demonstrate that microtubule-dependent flows significantly contribute to active diffusion.
A final interesting correlation, valid also when microtubules are depolymerized, is that the diffusivity of actin is always faster than the diffusivity of the vesicles, and can be described as 7 LM5 ≅ 27 89: (Fig. 2g,h and Fig. 3c). The active diffusion of vesicles is seemingly locked to the actin mesh, suggesting that the active diffusive motion of the vesicles might originate from an intrinsic activity of the F-actin network. Our results qualitatively agree with a recent model 19 , in which vesicles are caged in the cytoskeleton and the latter act as an actively rearranging harmonic trap for the former. Unfortunately, the rearrangement dynamics of the F-actin network in this model was not explicitly described, as its effect on a tracer particle is described as an effective random force. However, as long as the tracer particle is larger than the actin mesh size, the model predicts that the particle mean square displacement (and so its effective diffusion coefficient 7 9WW ) is inversely proportional to its size. In general, we can thus expect in our experiments that a vesicle of size Y 89: larger than the actin mesh size Z LM5 will have an effective diffusion coefficient lower than the diffusivity of F-actin (7 9WW < 7 LM5 ), with the limiting case being that the size of the vesicle is similar to the mesh size (Y 89: ≅ Z LM5 ), for which we expect an effective diffusion coefficient of the vesicles similar to the effective diffusion coefficient of F-actin (7 9WW ≅ 7 LM5 ).
In this condition, the vesicle size substantially matches the relevant structural length scale of the network and the particle displacement is expected to closely follow the restructuring dynamics of the trapping mesh. The above arguments are compatible with a simple scaling relation between the diffusivities of F-actin and vesicles: 7 9WW ≅ 7 LM5 (Z LM5 /Y 89: ) . We experimentally found that F-actin diffuses approximately two times faster than the vesicles   (Fig. 4a,b and Supplementary Fig. 4a) 29 . To verify that F-actin concentrations are also higher in the oocyte, we stained for F-actin in fixed cells, using TRITC-labeled phalloidin, and measured the mean fluorescence intensities. We found that the fluorescence intensities in SpireB overexpressing cells are increased by about 1.4-fold compared to controls, showing that the overall amount of actin filaments is increased (Supplementary Fig. 4b). We also measured the mean distance between bright actin filaments as an indicator of the mesh size in the same cells and found no apparent difference between the genotypes (data not shown).
We then analyzed how the overexpression of SpireB and the higher content of actin filaments affect cytoplasmic motility. The most striking effect we found was a strong reduction of cytoplasmic streaming. The ballistic contribution to the overall dynamics was so small that for some cells it could not be reliably measured. Overall, DIC-DDM and Con-DDM analyses provide the following upper bound for the streaming speed: ; 89:,`abc9de ≅ ; LM5,`abc9de < 2 nm/s (where SpireOE stands for Spire "over-expression"), a value that is at least one order of magnitude smaller than the typical streaming speed obtained for the control cells. For these Spire over-expressing oocytes, the dynamics are thus substantially diffusive-like, with diffusivities: 7 89:,`abc9de = (1.4 ± 0.5) 10 0E µm 2 /s and 7 LM5,`abc9de = (2.3 ± 0.8) 10 0E µm 2 /s ( Table 1). These values are similar to the ones obtained when microtubules are depolymerized, and flows are abrogated. However, in the present case we were not able to reliably study the connection between the dynamics and the spatial correlation properties of actin and vesicles, since SpireB over-expression causes a marked cell-to-cell variability in vesicle size that prevents a meaningful sizing with the available data. Despite this, our data confirm that both flows and active diffusion depend on a well-regulated concentration of cytoplasmic F-actin, and further support a close link between the motion of cytoplasmic Factin and vesicles.
It is important to note that by over-expressing SpireB in a spire mutant background, the mesh is less sensitive to Latrunculin A (LatA) treatment 29 . LatA is a G-actin sequestering substance that not only inhibits de novo formation of actin filaments, but also causes the depolymerization of dynamic actin filaments. In wild type oocytes, LatA treatment leads to the destruction of the actin mesh 15 , even within minutes of exposure to the drug 15,40 .
However, in oocytes where SpireB expression is driven by an artificial promotor (as in our experiment), LatA treatment remains without any effect 29 . Thus, in SpireB over-expressing oocytes, the aberrant mesh appears to have more, but less dynamic, filaments. This suggests that actin turnover contributes to active diffusion, and it might explain why the diffusive motion of F-actin and vesicles drops in SpireB over-expressing oocytes. Of note, the ectopic expression of Capuccino, a formin jointly working with Spire in forming the actin mesh, also increases the number of actin filaments but does not affect cytoplasmic flows (as measured by PIV) 41 . It is not known why expression of those actin nucleators has a different impact on cytoplasmic flows. However, these observations suggest that a higher concentration of F-actin in the cytoplasm is not enough to substantially inhibit flows.
Finally, we asked how the motion of vesicles changes in oocytes lacking cytoplasmic F-actin. spire mutant oocytes do not show any obvious defects in cortical actin organization, but lack the cytoplasmic F-actin network and display premature fast streaming (Fig. 4c,

Movie 4). This value is about five times smaller than the value measured in control cells and
is twice the thermal diffusion coefficient 7 QR = 3.1 10 0S µm 2 /s, estimated by using the viscosity value obtained in 14 . The diffusivity 7 89:,`abc9 obtained for colchicine treated spire mutants is about six times larger than the diffusivity 7 89:,]Q^_ = (1 ± 0.5) 10 0S µm 2 /s measured in ATP depleted cells. This difference might either be due to the presence of microtubule and F-actin independent residual active processes, or by changes in the cytoplasmic viscosity due to the lack of both microtubules and F-actin.

CONCLUDING REMARKS
In the Drosophila oocyte, streaming promotes the mixing and transport of cytoplasmic components 13,43 and is required for essential events for embryogenesis, such as the localization of mitochondria 4 and of the developmental determinant nanos mRNA 5,45 . Not surprisingly, streaming is more efficient than thermal diffusion in transporting large organelles (e.g. vesicles) over long distances 46 . However, recent studies in cells, which probably lack microtubule-dependent streaming, outlined the important role of active diffusion mechanisms, that at least in mouse oocytes are seemingly dependent on a recently discovered cytoplasmic F-actin cytoskeleton 10,26,27,47 . It is thus worth assessing whether diffusion still plays a role in the presence of streaming and, if that is the case, characterizing the interplay between directed and random motion. In this work, we have developed a robust methodology allowing, for the first time, to separate the persistent motion -due to cytoplasmic flow -from the random motion due to diffusion inside a cell. We have explored how a cytoplasmic F-actin cytoskeleton affects particle dynamics, a question that is largely unknown. In particular, we used Differential Dynamic Microscopy with different contrast mechanisms (DIC and confocal imaging) in combination with genetic and chemical manipulations of the cytoskeletons in the oocyte. Compared to existing techniques, like particle tracking or PIV, the strength of our approach, lies in the ability to quantitatively discriminate between diffusive and persistent motions, without the need of precise tracking (Fig. 5). This enables us to analyze the dynamic behavior of complex, intracellular structures, like the F-actin mesh, which was not possible before. We found that both vesicles and cytoplasmic actin filaments move in a persistent manner by advection, mainly as a result of microtubule-dependent flows. In addition, they display a non-thermal, active diffusion that is dependent on cytoplasmic, but not cortical actin filaments. In fact, we speculate that cytoplasmic F-actin is the major driving force behind active diffusion in the Drosophila oocyte. However, we also found that active diffusion is reduced in oocytes without microtubules. This novel finding suggests that microtubules are not only essential for transport and cytoplasmic streaming, but also substantially contribute to active diffusion.
This may constitute a difference to murine oocytes, as well as various cultured cells where active fluctuations have been measured 8,28,48 . However, the involvement of microtubules in the cytoplasmic motion of cultured cells was not investigated in detail in these studies, and thus this novel function for microtubules modulating diffusion might be conserved in other systems as well.
Our study sheds light on the link between the motion of different cytoplasmic components, in particular between large vesicles and cytoplasmic F-actin, which are found to exhibit the same advection-diffusion dynamics. This link is robust upon perturbation of cytoplasmic streaming, and our findings suggest that cytoplasmic F-actin, a dense nonequilibrium fluctuating mesh, is the source of active diffusion for the vesicles. Even though previous cell biological and biophysical observations pointed out that vesicles and the actin network were functionally linked in other cells, our work is the first one to measure and compare the diffusive-like motion of both vesicles and the cytoplasmic F-actin network, finding a quantitative relation between the parameters describing the dynamics of the two structures. In the future, this link will need to be studied in more depth, for instance by performing a more detailed analysis of the correlation between the size of the actin mesh and of the vesicles that we found here. For instance, it would be of interest to study such correlation as a function of the vesicle size. Cerbino

Fly stocks and genetics:
If not stated otherwise, all flies where kept on standard cornmeal agar at room temperature.

Drug treatment:
Depolymerization of microtubules was achieved by either feeding (Fig. 3) or treatment of dissected egg chambers (Fig. 4). For the feeding experiment, 200 µg/ml colchicine were diluted in yeast paste and fed to female flies for 16h at 25˚C. For short-term treatment, flies were fattened overnight, ovaries dissected in dissection medium (1x Schneider's medium + 2% DMSO) and treated in 20 µg/ml colchicine in dissection medium for 5 min at room temperature (Fig. 4). Ovaries were washed once in a drop of dissection medium and dissected in halocarbon oil. Imaging was performed as described above. ATP was depleted by treating dissected ovaries in 0.4 mM NaN3 and 2 mM 2-Deoxy-D-glucose in dissection medium for 5.5 minutes at room temperature ( Fig. 3 and Supplementary Fig. 3f-h . Here Å is a shape parameter (set to 2 in our case) and ; is the average speed: where -. # = ;# is #-dependent decorrelation rate.
If a 2D projection of the motion is considered, the speed distribution reads where d is the Dirac delta function. This is the quantity that is typically measured with PIV. It is important to note that, in general, the mean value of the 2D projected velocity field: does not coincide with ; . For example, in our case (Schulz distribution with Å=2), it can be shown that I = 0.566;.
The choice of the Schulz distribution is motivated by the simplicity of its analytical form, that makes the fitting procedure of the experimental intermediate scattering function particularly simple and robust, and it is supported by the good agreement with the 2D speed distribution measured with PIV (Fig.1d).
The accessible #-range for DDM analysis is given, in principle by [2~/Ö,~/P] where Ö is the size of the considered region of interest and a is the effective pixel size (typically Ö = 33 µm, P = 0.13 µm). In practice, this range can be significantly reduced. This can be due, at low #, to the presence of very slow dynamics that cannot be fully captured during the finite duration of the image acquisition and, at high #, mainly to the loss of signal due to the microscope transfer function (that depress higher spatial frequencies in the image) and to the presence of dynamics that are too fast to be sampled with the experimental frame rate. Overall, in most of the experiments presented in this work, the effective q-range roughly corresponds to [2,20] µm -1 . In the direct space, this corresponds to considering density fluctuations on length scales comprised approximately between 0.3 µm and 3 µm. It is worth noting that, when flow is present inside the oocyte, the velocity field exhibits some spatial heterogeneity, especially close to the cell edges. For this reason, we considered only regions of interest far from these edges, which we imaged long enough to guarantee that the average velocity was rather homogeneous across the field of view.

Particle Image Velocimetry (PIV):
Maps        Color code as in panel (f). Compared to controls, the dynamics of ATP depleted cells is more than one order of magnitude slower. (c,d) spire mutant oocytes were incubated in control DMSO-containing medium (c) or in colchicine-containing medium (d). As expected, spire mutants do not form an actin mesh. a key information about the nature of the transport mechanism and allows to determine the relevant parameters. The lower left panel pictorially represents the simple and important case where G has a power-law dependence on q (log-log scale). This occurs, for example, when the underlying dynamic is diffusive (a=2 and D a is the diffusivity) or ballistic (a=1 and D a coincides with a characteristic speed).