Fanny Chenillat
email: fanny.chenillat@univ-brest.fr

Thierry Huck

Christophe Maes

Nicolas Grima

Bruno Blanke

Fate of floating plastic debris released along the coasts in a global ocean model

come

Introduction

Marine pollution from plastics is a global issue and challenge (persistence of plastics at sea, consequences for marine life and potentially human health) that infests the ocean from coastal regions (e.g., [START_REF] Bergmann | Citizen scientists reveal: Marine litter pollutes Arctic beaches and affects wild life[END_REF][START_REF] Napper | Plastic Debris in the Marine Environment: History and Future Challenges[END_REF] to the open sea [START_REF] Barnes | Accumulation and fragmentation of plastic debris in global environments[END_REF][START_REF] Law | Plastic accumulation in the North Atlantic subtropical gyre[END_REF]Cozar et al., 2014;van Sebille et al., 2015;[START_REF] Lebreton | Evidence that the Great Pacific Garbage Patch is rapidly accumulating plastic[END_REF].

According to [START_REF] Geyer | Production, use, and fate of all plastics ever made[END_REF], about half of the plastic debris produced is less dense than seawater and, consequently, is expected to float at the sea surface. This floating pollution either accumulates in the center of subtropical gyres (e.g., the Pacific Garbage Patch) or is discharged onto coasts and beaches. Transport of plastic is affected by a variety of physical processes (van Sebille et al., 2020;[START_REF] Dobler | Large impact of Stokes drift on the fate of surface floating debris in the South Indian Basin[END_REF] characterized by different temporal and spatial variability. The pathways and fate of plastic debris in the oceans are still uncertain for many reasons, including a misperception of their sources, both in terms of quantity and distribution [START_REF] Viatte | Air Pollution and Sea Pollution Seen from Space[END_REF]. Indeed, observations are still limited, and the origins of the plastic collected at sea and along coasts remain completely impossible a challenge to identify or assess.

Most of the projects on this issue are nowadays oriented toward a particular region or theme [START_REF] Black | A Geography of Marine Plastics[END_REF], whereas plastic pollution must be considered as a global concern (Maes et al., 2019). Understanding the main pathway and fate of plastic debris remains fundamental to better manage and reduce plastic pollution from an environmental and economic perspective. Indeed, [START_REF] Lau | Evaluating scenarios toward zero plastic pollution[END_REF] have shown that if no plastic pollution reduction strategy is undertaken, plastic pollution will triple by 2040. Despite the multiplicity of plastic pollution sources and the large uncertainties about the contribution of land-based plastic pollution (Horton and Dixon, 2017), according to van Sebille et al. (2020), it is today recognized that coastal pollution is one of the largest sources of ocean plastic waste globally, with 5 to 12 million tons year -1 [START_REF] Jambeck | Plastic waste inputs from land into the ocean[END_REF]. As estimated by [START_REF] Faris | Seas of Debris: A Summary of the Third International Conference on Marine Debris[END_REF], 80% of marine litter enters the ocean by land, with the remaining 20% assumed to come from marine activities such as commercial and recreational fishing, cruises, and shipping [START_REF] Lebreton | Numerical modelling of floating debris in the World's Ocean[END_REF]. Given the scarcity of available data and observations on marine litter and plastic pollution (Cozar et al., 2014), numerical models appear to be one of the most adequate tools for understanding the transport and dispersion of plastic in the ocean [START_REF] Hardesty | Using numerical model simulations to improve the understanding of micro-plastic distribution and pathways in the marine environment[END_REF], especially in a Lagrangian framework (van Sebille et al., 2018). Given the scarcity of available data and observations on marine litter and plastic pollution [START_REF] Galgani | Are litter, plastic and microplastic quantities increasing in the ocean?[END_REF], numerical simulation can be used 'to fill in the gap' between these observations, and to test hypotheses about how plastic particles behave in the ocean" as explained in van Sebille et al. (2020). Indeed, numerical models are proper tools for understanding the transport and dispersion of plastic in the ocean [START_REF] Hardesty | Using numerical model simulations to improve the understanding of micro-plastic distribution and pathways in the marine environment[END_REF], especially in a Lagrangian framework (van Sebille et al., 2018).

For instance, [START_REF] Lebreton | Numerical modelling of floating debris in the World's Ocean[END_REF] studied the relative contributions of plastics from impervious watersheds, coastal population and shipping inputs to different accumulation zones. In their study, they estimated that between 28% and 40% of the released particles were beached, depending on the input scenario.

Using a similar numerical methodology, we study hereafter the fate of floating plastic pollution in the ocean as discharged along the coasts. We compare two different types scenario of sources in the global ocean: one based on river inputs, and the other based on population density along the coasts and waste management. We use a Lagrangian numerical analysis in conjunction with surface currents from a reanalysis of a global ocean circulation model with a horizontal resolution of 1/12˚. In both scenarios, we find the five persistent convergence zones located in the subtropical gyres, also known as garbage patches [START_REF] Kubota | A Mechanism for the Accumulation of Floating Marine Debris North of Hawaii[END_REF][START_REF] Maximenko | Pathways of marine debris from trajectories of Lagrangian drifters[END_REF], but with different characteristics. More generally, particles ending up at sea represent less than half of the particles released (and less than 20 % in the convergence zones), whereas more than 50% end up at the coast. We discuss how the use of different scenarios helps to understand ocean connectivity and plastic pollution on a global scale. This study also highlights the importance of considering accurate coastal inputs or sources, in particular littering from coastal populations, and provides insight into future strategies for monitoring and mitigating plastic debris. This study fits well within the main research priorities on marine plastic litter raised by the scientific community [START_REF] Nikolai | Toward the Integrated Marine Debris Observing System[END_REF], in response to the G7 Science Ministers meeting in Berlin in October 2015 [START_REF] Williamson | Future of the Ocean and its Seas: a non-governmental scientific perspective on seven marine research issues of G7 interest[END_REF], such as understand the pathways "establishing connections between sources and sinks for different types of debris", and understand the sinks, "including accumulation in remote locations".

Section 2 presents the material and methods. Results for particles ending up at sea and in the convergence zones are given in section 3, whereas the specific analysis of particles ending up along the coast (beaching) is presented in section 4. Section 5 is the concluding section.

2.

Material and methods

Global surface ocean circulation model

For this study, we use the sea surface current of the Global Oceanic Circulation Model GLORYS12V1, a leading global reanalysis of ocean circulation and physics [START_REF] Lellouche | Recent updates to the Copernicus Marine Service global ocean monitoring and forecasting real-time 1/12 highresolution system[END_REF]. [START_REF] Karina Von Schuckmann | The Copernicus Marine Environment Monitoring Service Ocean State Report[END_REF]. This reanalysis covers the 1993-2018 altimetry era with a daily frequency, and provides not only a higher horizontal resolution compared to previous versions, but also improvements and corrections [START_REF] Lellouche | Recent updates to the Copernicus Marine Service global ocean monitoring and forecasting real-time 1/12 highresolution system[END_REF]. In the following, we use the daily mean surface currents from the upper layer of the model with a thickness of 1 m, from 1 January 1993 to 31 December 2015 (GLOBAL REANALYSIS PHY_001_030 product downloaded from https://resources.marine.copernicus.eu). The products of the Copernicus reanalysis being provided on a regular grid (A-grid in [START_REF] Arakawa | Computational Design of the Basic Dynamical Process of the UCLA General Circulation Model[END_REF] classification), we interpolated the velocities on the ORCA 1/12° native C-grid to run the Lagrangian experiments.

Coastal plastic source scenarios

In this study, we compare two distinct scenarios of coastal sources of plastic particles: one based on inputs from the world's main rivers and the other based on the coastal population (Fig. S1), which we will identify as the river scenario and population scenario hereafter.

The river scenario comes from the model developed by [START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF]. This global model of plastic inputs from rivers into the oceans is based on waste management, population density and hydrological information. It estimates that about 2 million tons of plastic waste enters the ocean every year from 40,760 rivers. The 20 most polluting rivers are mainly located along the western North Pacific and account for 71% of the total (Fig. 1). Both scenarios are projected and discretized on our model grid. The finite number of total particles released along the experiment, and the rounding-of to an integer number of particles released each month in sources grid cells, reduces the effective number of source points as follows. For the rivers scenario, the finite number of particles released each month (20,000)

reduces the effective number of source points to 522 grid cells (Fig. S1). There are very large sources, with about 10 rivers releasing more than 500 particles per month (representing altogether more than 58% of the total), with the Yangtze River peaking at about 5000 particles (25% of the total). For the population scenario, out of the 2633 source points provided by Erik van Sebille (pers. comm., 2018) on a 1°x1° grid, the finite number of particles released each month reduces the effective number of source grid cells to 1196 in our experiment (i.e., more than twice that of the rivers scenario). There are no sources as extreme as in the rivers scenario, the peak values are about 350 particles per month (barely 2% of the total), with 23 sources releasing more than 100 particles per month (representing altogether 19% of the total).

Our objective is to diagnose how differences in input scenarios affect the fate of floating plastic debris on a global scale. Thus, to make the two scenarios comparable, we choose to ignore the difference in the total amount of plastic mass released in each scenario. For simplicity, we also choose to ignore the temporal variability of coastal inputs in the two scenarios (e.g., river discharge depends on rainfall variability). Thus, we consider that a mean equivalent amount of plastic is released every month over the 23 years of simulation from their coastal positions (see next section) in both scenarios (river and population).

Lagrangian analysis

To study the fate and pathway of floating plastic debris in the global ocean, we use a Lagrangian approach with the Ariane methodology [START_REF] Blanke | Kinematics of the Pacific equatorial undercurrent: An eulerian and lagrangian approach from GCM results[END_REF]. As detailed in [START_REF] Maes | A surface "superconvergence" pathway connecting the South Indian Ocean to the subtropical South Pacific gyre[END_REF] or [START_REF] Dobler | Large impact of Stokes drift on the fate of surface floating debris in the South Indian Basin[END_REF], the Ariane tool has been used so that the numerical particles are horizontally advected by surface currents and do not experience vertical motion. The plastic input data for both scenarios were gridded on the ORCA native grid at a resolution of 1/12˚ at the nearest ocean grid point, i.e. each source point is associated with a single grid cell of the model. The initial particle positions are determined randomly within the grid cell. Note that the population density proxy data set was available at a resolution of 1˚x1˚; for this reason, some final positions on the 1/12˚ grid are not initialized exactly at the coast (as strictly defined by the land-sea mask of the model) but near the coast. Two experiments are run according to the coastal input scenario (see previous section) with equivalent total particle numbers: 5,589,080 particles for the river scenario, and 5,571,720 particles for the population scenario (the particle numbers are slightly different due to rounding to an integer number of particles released each month). About 20,000 particles are thus released each month during the 23-year period from 1993 to 2015 (i.e., about 240,000 particles released per year). Particles released at the same location are subject to turbulent, seasonal and interannual variability of the surface current.

Particles released at close locations within the same grid cell are subject to turbulent, seasonal and interannual variability of the surface current that will lead to dispersion in their trajectories. The positions of the particles are recorded with a monthly frequency. There are no explicit sinks in our approach i.e., the released particles stay indefinitely at the surface in the model, still moving or stuck along the coasts.

Particle behavior

We have diagnosed that particles can experience a different fate depending on their position and trajectory in the ocean:

 case a: the particle leaves the coastline and travels within the ocean domain until the end of the experiment;

 case b: the particle leaves the coastline, travels in the open ocean but ends up along the coast: we will define these particles as "beached";

 case c: the particle never leaves the coastline but rather travels alongshore;

 case d: the particle never leaves its initial grid cell. More precisely, the particle can barely move but never leaves the grid point associated to its initial position. Such behavior results from a conjunction between the initial positioning (indented coastline)

and the dynamics (convergence), which creates unfavorable conditions for moving to another grid cell. Note that this behavior concerns a very small fraction of the initialized particles (<1%, see section 3) and will be considered as a "rare cases" category.

Note that, in absolute terms, cases b and c could refer to a similar category of beaching and thus to the same local pollution by plastic debris. However, we choose to distinguish these two cases because of the possible role of river mouth dynamics in such behavior.

Open ocean convergence zones

The scenarios have similarities and differences (Fig. 2). In both scenarios, surface plastics cover a large portion of the ocean between 45˚S and 45˚N. Particles seem to accumulate in bays, gulfs and seas surrounded by high-flow rivers (river inputs) and densely populated coastlines (population inputs), e.g., in the Bay of Bengal, Gulf of Guinea and China Sea [START_REF] Reisser | Marine plastic pollution in the waters around Australia: Characteristics, concentrations and pathways[END_REF][START_REF] Hinojosa | Floating marine debris in fjords, gulfs and channels of southern Chile[END_REF][START_REF] Collignon | Neustonic microplastic and zooplankton in the North Western Mediterranean Sea[END_REF][START_REF] Ryan | A simple technique for counting marine debris at sea reveals steep litter gradients between the Straits of Malacca and the Bay of Bengal[END_REF], similarly in both scenarios.

Other regions of accumulation are in the centers of the subtropical gyres, regions known as CVZ (Convergence Zones), where plastic accumulates through Ekman transport [START_REF] Kubota | A Mechanism for the Accumulation of Floating Marine Debris North of Hawaii[END_REF][START_REF] Maximenko | Pathways of marine debris from trajectories of Lagrangian drifters[END_REF][START_REF] Van Sebille | The oceans' accumulating plastic garbage[END_REF], mainly in the North Pacific and South Indian basins.

Concentrations differ strongly between scenarios in the South Atlantic, North Atlantic, South Pacific, and Arctic, but also in some coastal regions (e.g., off Europe and Brazil). Another difference between the scenarios is the lower concentration of particles in the equatorial Pacific and equatorial Atlantic in the river scenario compared to the population scenario. These discrepancies between the scenarios are only due to the relative input of particles (as the dynamics are the same in both experiments). Compared to the in situ observations (see figure 1 "standardized data" of van Sebille et al., 2015), the population scenario seems to show better agreement than the river scenario in terms of relative amplitude and global distribution of surface plastic debris, mostly because of the higher concentrations in the North Atlantic, South Atlantic and South Pacific CVZs. It should be mentioned that no scenario exactly satisfies the relative concentrations of particles in the different regions, especially since the syntheses of the observations do not agree with each other. This must might be due to the fact that particles inputs are more widely distributed along the coast in the population scenario than in the river scenario, as described in section 2.2.

To determine the origins of these discrepancies and to untangle the fate and pathways of the particles, now we modify the standard way of analyzing the fate of our particles. Instead of merely looking at the position of particles at time t, which mixes particles of different ages (such as Fig. 2), we choose to focus on the position of particles as a function of their age, i.e., the time elapsed since their release. We can thus follow a cohort of particle traveling from their release position to their final position (Fig. 3). For this section, we focus on particles from case a, i.e., particles ending up at sea. Since particles may be released at the same location at different times, they may experience different dynamics; thus, such an analysis provides much more consistent statistics on the plastic fate at the ocean surface. In addition to the local contribution of plastic pollution in the main gyres, there is a strong remote influence due to there is also a remote contribution allowed by the connectivity between sub-basins. This connectivity depends on the strength and extent of the attraction basins [START_REF] Froyland | How well connected is the surface of the global ocean?[END_REF]. To study this connectivity from coastal regions to the open ocean, we determine the temporal accumulation of particles in the main gyres (Fig. 4) and establish a connectivity matrix from the coastal inputs of particles -i.e., the initial position of the particles -to their final position at sea (Fig. 5) between the sub-regions defined in Fig. S2 (see also the mapped initial positions given in Figs. S3 andS4). To better capture the open-ocean signal of the particles attracted (Fig. 4), we limit the extension of the CVZs to their core -where particles accumulate over time (van Sebille et al., 2020) -and focus on the five main CVZs (see the colored boxes in Fig. 3). The slope of the curve indicates whether particles accumulate mostly in an attractive CVZ (positive slope), whether particles escape mostly from a leaky CVZ (negative slope), or whether an equilibrium is reached between sources and sinks in an attractive but still leaky CVZ (null slope). Sinks may represent particles that move to other regions or that beach.

The rate at which a CVZ attracts particles provides an indication of the origin of the particles:

the faster the early rate, the younger the particles are, the less they travel (and vice versa for a slower rate).

In both rivers and population scenarios, the Indian CVZ is the region where plastics accumulate the most and very rapidly: in 10 years up to 5.0% and 5.9% accumulate in the river and population scenarios, respectively, with concentrations that continue to increase up to 15 years of simulation. This results from the multiplicity of large sources converging to the Indian basin (see IND.S in Figs. 5, S3 and S4), from local sources (all Indian) to remote sources (from the Pacific and Atlantic shores). This is in line with [START_REF] Lebreton | Numerical modelling of floating debris in the World's Ocean[END_REF] who found that in the Indian CVZ, the main contributors are Southeast Asia/Indonesia, Africa and India. Overall, the South Indian is the most heterogeneously and widely impacted region, with particles coming from all origins with the population inputs (except the Mediterranean) and from all over the North Pacific and South Atlantic with the river inputs (Fig. 5). In this case, particles likely crossed the equator, e.g. between the South and the North Indian during the intermonsoon season as recently documented by van der Mheen et al. ( 2020). This result contrasts with that of [START_REF] Lebreton | Numerical modelling of floating debris in the World's Ocean[END_REF] who identified the greatest diversity of particle origins in the Southeast Pacific. This discrepancy must might be due to differences in input scenarios. Interestingly, the North Indian feeds the Southeast Pacific (Fig. 5). This connection has already been documented as the surface "superconvergence" pathway linking the south Indian Ocean to the subtropical south Pacific gyre through the Great Australian Bight [START_REF] Maes | A surface "superconvergence" pathway connecting the South Indian Ocean to the subtropical South Pacific gyre[END_REF].

The North Pacific is the second region where plastics are accumulating the most and very rapidly. The North Pacific CVZ starts to significantly attract particles after 2 years of simulation and accumulates approximately the same number of particles in both scenarios, up to ~4% in about 5 years (Fig. 4). Particles traveled for 2 years from the Pacific and Indian shores before ending up in the CVZ (see PAC.NE in Figs. 5, S3 andS4). An equilibrium is reached between sources and sinks in the population scenario. However, in the river scenario, the equilibrium shows a dip from year 7 to year 15 (i.e., 2000 to 2008), which is not observed in the population scenario. This difference may be due to interannual variability in the dynamics linking one of the sources to the CVZ. Indeed, in the river scenario, some of the sources involved in the In the South Atlantic, there is a rapid accumulation of particles, followed by a slower increase over the rest of the simulation with the population scenario (Fig. 4), due to the larger sources all around the basin, mostly from Southeastern America (Figs. 3, S1 and S3). However, with river inputs, the particle concentration in the South Atlantic CVZ increases slowly over the whole period because particles come from very remote sources, from all over the Indian and NW Pacific (see ATL.S. in Figs. 5 andS4).

Accumulations in the North Atlantic CVZ vary significantly according to the input scenario, as in [START_REF] Lebreton | Numerical modelling of floating debris in the World's Ocean[END_REF]. In the river scenario, very few particles accumulate, and an equilibrium of ~0.1% is rapidly reached (Fig. 4), with particles being attracted only from the local shores (see ATL.N in Fig. 5). In the population scenario, a maximum is rapidly reached (1% in less than a year), followed by a decrease and a further increase toward an equilibrium of ~1.1% in 5 years (Fig. 4). In this case, there is a clear balance between the sources (North and South Atlantic shores) and the open waters of the North Atlantic (Fig. 5), with the dispersion of particles from the core in the North Atlantic waters.

In the South Pacific CVZ, particles accumulate very slowly and the maximum concentration of about 0.1 and 1% is reached in 15 years (ten times slower than in the North Atlantic CVZ) with rivers and population inputs, respectively. This is consistent with [START_REF] Lebreton | Numerical modelling of floating debris in the World's Ocean[END_REF] who identified that "particles originating from South Atlantic and identified in the South Pacific Gyre took more than 15 years to make the journey". In both scenarios, the locations of sources are similar, but the concentration of inputs from the Eastern and Southwestern Pacific shores is higher in the population scenario (see the PAC.SE position in Fig. 5), as in [START_REF] Lebreton | Numerical modelling of floating debris in the World's Ocean[END_REF].

In terms of the contribution of coastal sources to open ocean pollution, we evaluate that 28% (~470,000 particles) and 49% (~1,200,000 particles) of the particles ending at sea have a local origin in the river and population scenarios, respectively (these figures are computed as the sum of the diagonal terms in the connectivity matrix, Fig. 5). Thus, 72% and 51% of the particles ending at sea have a remote origin in the river and population scenarios, respectively, with our definition of regions. In terms of open ocean pollution (particles in case a, ending at sea), we evaluate that 28% (~470,000 particles) have a local origin in the river scenario, against 49% (~1,200,000 particles) in the population scenario (these numbers are computed as the sum of the diagonal terms in the connectivity matrix, Fig. 5). Thus, the remaining portions of the particles have a remote origin (with our definition of regions), respectively 72% in the river and 51% in population scenarios. The NW Pacific shores represent the largest source of pollution at sea in both scenarios (Fig. 1): particles reach mostly the South Indian (4.5 10 5 and 3.8 10 5 particles, i.e., 8% and 6.8% of released particles) and the NE Pacific (4.0 10 5 and 3.0 10 5 particles, i.e., 7.2% and 5.4% of released particles), then the South Atlantic (6.0 10 4 and 5.8 10 4 particles, i.e., 1.1% and 1.0% of released particles) (numbers are given for river and population inputs, respectively). Within these regions are the three main CVZ in terms of total number of particles in cores. The NW Pacific is also a significant source of local pollution with 1.9 10 5 and 1.2 10 5 particles (i.e., 3.4% and 2.2% of released particles) for the river and population inputs, respectively. The remaining number of particles (3.7 10 4 and 1.8 10 4 particles, i.e., 0.7% and 0.3% of released particles) ends up in the South Pacific (E and W) and North Indian.

In summary, these results emphasize the importance of the input of coastal sources in the total accumulation and composition of the 5 CVZ, and the possible exchanges between these regions. Our results show similarities and differences with those of [START_REF] Lebreton | Numerical modelling of floating debris in the World's Ocean[END_REF] (see above for more details) who performed a similar analysis. Although we found the same 5 CVZ, one of the most divergent results is that they find that northern CVZs accumulate more particles than southern CVZs (~25% in northern hemisphere CVZs compared to ~10% in southern hemisphere CVZs), which is not our case (we find that 5% of the particles accumulates in northern hemisphere CVZs versus ~8% in southern hemisphere CVZs). This discrepancy may be due to differences in the input scenarios, the numerical tools (from surface current products to Lagrangian experiments), and the methodology (definition of regions). However, it remains difficult to validate the most realistic solution due to the lack of in situ observations in these regions, especially in the southern hemisphere.

In total, in both scenarios, CVZs do not attract more than 20% of the total particles released at the coast after a few years of simulation (Fig. 4). While the defined CVZs cover only a fraction of the patches in the gyres, i.e., the core, we found that only 29/45% of the particles end up in the open ocean, away from the coast, for the river and population scenarios, respectively (Fig. 6).

The majority of the particles thus end up along the coast, 71/55% respectively, and we now examine in detail the behavior of these beached particles.

Beaching

As noted in many previous studies (e.g., [START_REF] Maximenko | Pathways of marine debris from trajectories of Lagrangian drifters[END_REF]van Sebille et al., 2015), coastal deposit of plastic debris represents an important reservoir in the total budget. In the present estimation of the model dispersion, a significant proportion of the particles released at the coast does not end up in the open ocean (case a). Indeed, 36 and 43 % of them end up on beaches (case b) while 34 and 11 % travel alongshore (case c), in the river and population scenarios, respectively (Fig. 6). In total, 70% and 54% of the particles end up on the coasts (sum of case b and case c) in the river and population scenarios, respectively. This is in good agreement with Lebreton et al. (2019) who showed that 67% of the world's plastic washed up on the coasts. Note that a small proportion of particles, ~1%, do not move from the grid cell where they were released. Details on these categories are given hereafter. Overall, the broad spatial spreading of beachings along the coasts (Fig. 7) is not strikingly different between the two scenarios (except for a few areas), especially when compared to the very contrasted input functions (Fig. S1).

In terms of sources, in both scenarios, coastal pollution originates mainly from the NW Pacific, North Indian and North Atlantic shorelines, mainly because these are the main sources of particles (Fig. 6). In the population scenario, the Mediterranean also represents a major source of beached particles. In the population scenario, most of particles released from the Mediterranean shores actually beached. Depending on the region, the balance of open-oceanfate (case a) and coastal-fate (case b and c) is variable (Fig. S5). Some regions are mainly sources of coastal pollution for cases b and c (i.e., they contribute to >50% of the total pollution) The following regions contribute to more than 50% of the total coastal pollution, as diagnosed in cases b and c: North Indian (56%), NW and SE Pacific (70% and 96%), North Atlantic (93%) and Mediterranean (97%) with the river scenario; and NW Pacific (57%), North Atlantic (65%) and Mediterranean (96%) with the population scenario (Fig. S5).

The origin of the particles that accumulate along the coast is mostly local (Figs. 7, 8, S6 and S7),

i.e., the initial and final positions are in the same region (this is also true for the particles that stay on the coast in case c, Fig. S8). In both scenarios, we estimate that 85% (~2,000,000 particles) of the beached particles have a local origin (this number is computed as the sum of the diagonal terms of the connectivity matrix, Fig. 8) likely due to coastal retention and coastal recirculation. That is especially true for the NW Pacific, North Indian and North Atlantic in both scenarios, and additionally for the Mediterranean in the population scenario. It is not surprising that in the river scenario, the positioning of local beaching pollution corresponds to the river areas, i.e., the Niger, the Amazon, the Ganges and rivers of the NW Pacific region (Mekong, Yangtze, etc.) (Figs. 7 and S6). Rivers also appear to be hotspots for particle retention on coasts (with 34% of particles in case c, Fig. 6 andS8). With regard to the population scenario, where sources are more widely distributed, beaching locations appear to be widespread along the shores and, to a lesser extent, even in divergent regions such as coastal upwelling areas like California, Peru or NW Africa (Fig. 7).

Coastal pollution is not, exclusively and totally, local, and the beaching process may in fact occur after a long distance traveled. In both scenarios, we find that ~27% of the beached particles traveled less than 500 km, ~66% between 500 km and 5000 km, and ~7% more than 5000 km (Fig. 9). This highlights the shore-to-shore connectivity between remote regions (Fig. 8 and S9). For example, particles from the NW Pacific, which is the main source of coastal pollution, can reach the Pacific, Indian or South Atlantic. Conversely, in the population scenario, particles from the Atlantic shores can reach the West Pacific, South Indian, and also Arctic shores. The Indian shores are also a source of beaching for older particles in the West Pacific, in both scenarios.

To summarize, the impact of local pollution on beaching is even greater with population inputs rather than with river inputs. This result deserves more attention and, due to uncertainties and gaps in the observations of plastic waste, it remains challenging to predict plastic sources and fate in coastal systems as mentionned recently by [START_REF] Galgani | Are litter, plastic and microplastic quantities increasing in the ocean?[END_REF]. As for the particles at sea in the CVZs, the differences between the two scenarios appear mainly in the North Atlantic and SE Pacific, where the sources are very different (Fig. S1). In the North Atlantic, river inputs tend to stay locally on the coast (mostly from the Amazon and Niger), whereas population inputs represent a high source of beached and offshore pollution (from Europe and North America). In the SE Pacific, this local pollution is represented by a significant proportion of offshore pollution with population inputs. The Mediterranean and NE Atlantic are largely affected by beaching and coastal retention (Fig. 6 and Fig. S8) with population inputs.

Interestingly, these results highlight the disparity between regions in terms of plastic pollution: some regions are strongly affected by coastal pollution (e.g., the North Pacific), due to coastal retention and coastal recirculation, while others have a significant proportion of particles staying offshore (e.g., North Indian and NW Pacific). In contrast to local pollution, there are a significant number of beached particles that have traveled long distances in both scenarios and this study highlights the main pathways of plastic debris between coastal regions and their ability to travel long distances before ending up at the coast. Note that the geographic differences found in the final positions of particles between the two scenarios are directly related to the location of input sources and differences in concentration. Given these differences between the input scenarios, the particles may encounter different oceanographic features and dynamics that are likely to influence their final positions. However, the statistical robustness of our approach relies on the use of several million particles to diagnose the main pathways from the initial positions to the final positions, overcoming the effect of small scales.

Moreover, Note, however, that in our simulations, the particles do not sink, whereas in reality, such old particles would most likely fall down the water column [START_REF] Egger | First evidence of plastic fallout from the North Pacific Garbage Patch[END_REF][START_REF] Pabortsava | High concentrations of plastic hidden beneath the surface of the Atlantic Ocean[END_REF] under the action of biology (biofouling, ingestion, or aggregation) (e.g., [START_REF] Kooi | Ups and Downs in the Ocean: Effects of Biofouling on Vertical Transport of Microplastics[END_REF]van Sebille et al., 2020).

A qualitative comparison with global beaching patterns, as compiled for instance in the LITTERBASE database (https://litterbase.awi.de/litter, [START_REF] Tekman | LITTERBASE; Alfred Wegener Institute for Polar and Marine Research[END_REF], generally shows relatively good agreement, except for some regions. For instance, the database reports no beachings along the east coast of Africa from Somalia to Mozambique, and along the coasts of Oman and Yemen, probably due to a lack of observations.

A striking difference between the 2 scenarios is the complete absence of beachings along the Pacific coast of South America. Coastal plastic and other debris reported along the Chilean coast suggest that the river input scenario is not sufficient to supply plastic particles to the South Pacific, and in this respect the population scenario is more satisfactory (as reported in LITTERBASE from [START_REF] Thiel | Floating marine debris in coastal waters of the SE-Pacific (Chile)[END_REF][START_REF] Hinojosa | Floating marine debris in fjords, gulfs and channels of southern Chile[END_REF][START_REF] Hinojosa | Temporal and spatial distribution of floating objects in coastal waters of central-southern Chile and Patagonian fjords[END_REF][START_REF] Thiel | Anthropogenic marine debris in the coastal environment: A multi-year comparison between coastal waters and local shores[END_REF][START_REF] Miranda-Urbina | Litter and seabirds found across a longitudinal gradient in the South Pacific Ocean[END_REF], Hidalgo-Ruiz et al., 2018). Similarly, the 2 scenarios differ greatly along the East coast of America, where the river scenario leads to almost no beaching north of Florida. This is not the case in LITTERBASE, confirming once again the need for

Conclusions

The aim of this study is to investigate the pathway and fate of floating plastic debris, a key issue that remains fundamental to better manage and reduce plastic pollution. We diagnose the fate Our study remains an idealized case from several aspects, and from our point of view, the main approximations are the "oversimplified" beaching process and the related dynamical processes.

Indeed, beaching of plastics is a complex process that is strongly influenced by small-scale coastal ocean dynamics [START_REF] Isobe | Selective transport of microplastics and mesoplastics by drifting in coastal waters[END_REF], and by the local morphology of the coastline [START_REF] Zhang | Transport of microplastics in coastal seas[END_REF]. Including Stokes-drift, waves or tides can also influence the number of particles stuck to the coast, and increase it by more than three times [START_REF] Dobler | Large impact of Stokes drift on the fate of surface floating debris in the South Indian Basin[END_REF]. Another key point is the definition that can be given to the term "beaching". Using a 1/12˚ eddy-resolving ocean model, our definition is purely probabilistic since we define as beached particles those that are at a certain distance from the coast (i.e., one grid point) (as similar studies e.g., van der Mheen et al. ( 2020)).

Although this study is still based on available scenarios for plastic sources, it provides new insights on connectivity between regions, on offshore pollution with CVZ composition and on coastal pollution in terms of beaching. There are many ways to add complexity to these processes. Indeed, for the sake of simplicity, we have neglected many key factors such as the temporal/seasonal variability of coastal inputs that could change with rainfall (e.g., Lebreton et al., 2017;[START_REF] Van Der Mheen | Beaching patterns of plastic debris along the Indian Ocean rim[END_REF], and also the significant worldwide increase in plastic inputs to the sea in relation to population growth and the rapid increase in plastic production [START_REF] Ostle | The rise in ocean plastics evidenced from a 60-year time series[END_REF]. We have also ignored sources contribution of of pollution from maritime inputs on global shipping route or fishery activities (e.g., [START_REF] Lebreton | Numerical modelling of floating debris in the World's Ocean[END_REF]. With the 1/12˚

eddy-resolving ocean model used, one might have expected to find particles crossing the Antarctic Polar Front and reaching the Southern Ocean (Fraser et al., 2018), but it is likely that the absence of extreme events and Stokes drift (driven by surface winds) does not allow such connectivity. Finally, we focus on floating debris that could experience vertical motion in response to physical or biological processes (van Sebille et al., 2020). It could be interesting to implement models that allow interaction with the marine ecosystem -e.g., processes such as ingestion by plankton and fish, sedimentation by biofouling [START_REF] Kooi | Ups and Downs in the Ocean: Effects of Biofouling on Vertical Transport of Microplastics[END_REF] which could represent an important sink for particles toward the deep ocean (van Sebille et al., 2020).

Indeed, it has recently been documented by [START_REF] Egger | First evidence of plastic fallout from the North Pacific Garbage Patch[END_REF] that we can find below the surface (5 m depth) to 2,000 meters about 56%-80% of what is seen at the surface.

Marine plastic pollution represents an increasing threat to the environment. Because of their serious detrimental effects on marine ecosystems (see examples in Napper and Thomson, (2020)) and given the huge cost of removing this pollution from beaches (e.g., Burt et al., 2020;[START_REF] Cruz | Beach cleaning costs[END_REF]Napper and Thomson, 2020), it is today fundamental to understand the fate and pathway of marine plastic debris. Such studies are needed to better inform and guide the stakeholders involved in the reduction of plastic pollution and waste management decision makers. However, a consensus is needed among researchers and a major step forward will be to improve the quality of information available on beached marine debris, which would require standardization of data sets (e.g., reporting metrics and sampling methods) [START_REF] Serra-Gonçalves | Global Review of Beach Debris Monitoring and Future Recommendations[END_REF][START_REF] Galgani | Are litter, plastic and microplastic quantities increasing in the ocean?[END_REF].

  particles are released continuously in both experiments. After a few years of Lagrangian advection, the particles spread almost everywhere in the global ocean, from the coast to the open ocean. After a few years of Lagrangian advection, the particles have spread almost all over the global ocean, from the coast to the open ocean. Only a few regions remain free of particles: the Southern Ocean (because of the strong northward Ekman transport), the Atlantic and Pacific equatorial region (because of the strong Ekman transport divergence), and also the northern North Pacific and Chukchi Sea in the Arctic. Figure 2 represents what could be roughly observed in terms of relative surface plastic pollution from space at any given time. The two

  Figure3shows both the quasi-initial position of the particles (i.e., one month after their release at the coast), and their position after 22 years. The one-month-old particles have experienced one month of dynamics and are still relatively close to their release position: such a representation gives a good approximation of the initialization of particles in terms of position and concentration. It also explicitly illustrates the main input differences between the scenarios: with the exception of the tropical areas of the West Pacific and Northeast Indian Oceans, all other shores show significant differences. As explained in section 2b, the population scenario is more widely spread, especially in relation to the American, European and African population. Most of the older particles, which have been drifting with the currents for 20 years, aggregate in the centers of the gyres (while a few others are still drifting in highly dynamical regions such as the Agulhas Current or between the subtropical region of the South Indian Ocean and the southwestern Pacific Ocean). After drifting with the currents for 20 years, particles aggregate in the centers of the gyres (while others are still drifting in highly dynamical regions such as the Agulhas Current or between the subtropical region of the South Indian Ocean and the southwestern Pacific Ocean).

Figure 3

 3 Figure3highlights the importance of sources for accumulation in CVZs and, specifically, the local influence of plastic pollution in the main gyres. By the term "local" we define the particles that originate and end in the same region, as defined in figureS2. Whereas the North Pacific and South Indian CVZs show quite similar concentrations and positions to the first order in both scenarios, the concentration of particles in the South Pacific, North and South Atlantic CVZs is much lower in the river scenario than in the population scenario. Indeed, the sources around the latter basins are much lower in the river scenario (Fig.1) indicating that particles have mostly a local origin in many regions: particles initialized in one region are likely to stay in this region (e.g., North and South Atlantic, Southeast Pacific and Mediterranean). Outside the CVZs, particle concentrations are much lower (e.g.,[START_REF] Maximenko | Pathways of marine debris from trajectories of Lagrangian drifters[END_REF][START_REF] Law | Distribution of surface plastic debris in the Eastern Pacific Ocean from an 11-year data set[END_REF]. In all basins, there is a very intense divergence of particles around the equator, due to the poleward Ekman transport associated with trade winds, such that particles from a sub-basin (North or South) are very likely to remain in their region of origin. As already highlighted by[START_REF] Lebreton | Numerical modelling of floating debris in the World's Ocean[END_REF], because (i) there are little exchanges between hemispheres across the equator (except in few coastal regions), and (ii) the particles are mostly released in the northern hemisphere in the river scenario, there are significantly less particles that end up in the South Atlantic and South Pacific gyres compared to their northern hemisphere counterparts. In the Indian basin, however, there is a seasonal north-south flush of particles along the eastern boundary (van der[START_REF] Van Der Mheen | Beaching patterns of plastic debris along the Indian Ocean rim[END_REF].

  feeding of the North Pacific CVZ in the population scenario must be missing (e.g., from the Eastern Pacific). Toward the end of the simulation, after 15 years (i.e., from 2008), there is a second increase in both scenarios, showing that the dynamics have favored the accumulation of common sources -i.e., from North Pacific or South Indian -in the North Pacific CVZ. Interestingly, the period 2000 to 2015 corresponds to a cool phase of the Pacific Decadal Oscillation (PDO) and a positive phase of the North Pacific Gyre Oscillation (NPGO). Such interannual variability is beyond the scope of this paper, but additional attention could be given to linking particle accumulation to different modes of climate indices in future research projects.

  population inputs. Beaching patterns around the Indian basin and along the West Pacific coasts are not significantly different between the 2 scenarios, and are in good agreement with previously published results (van der Mheen et al., 2020). Beaching patterns around Australia (PAC. SW in Fig. 8) differ from the 2 scenarios and the population scenario is in better agreement with recent studies (Galaiduk et al. 2020) with significant input from local and northwest Pacific shores.

  of plastic pollution discharged along the coasts by comparing two different types of sources in the global ocean: one based on rivers and the other on the population density along the coasts. We use a Lagrangian numerical analysis (forward particle tracking) based on surface currents from reanalysis of a global ocean circulation model with a resolution of 1/12˚. Our results highlight the importance of the input scenario for the concentration of dispersed particles in the open ocean, in specific subtropical convergence zones for instance, and the number of particles beaching around oceanic basins, such as the Mediterranean Sea. The concentration of particles at sea in certain convergence zones is particularly sensitive to the input scenario. More precisely, population-related inputs are critical to feed convergence zones of the South Pacific and North Atlantic. Connectivity between coastal sources and open ocean regions also indicates that the Indian region is the most heterogeneous in terms of pollution with population-related inputs. More generally, particles ending up at sea represent less than half of the particles released (and less than 20 % in the convergence zones), whereas more than 50% end up at the coast.A large fraction of the total particles released ends up along the coast, between 54% in the population scenario and 70% in the river scenario. The number of particles that beach in certain areas also depends particularly on the input scenario, such as the European West Coast, the Mediterranean Sea, and African East Coast with the population input. Rivers represent a large source of local coastal pollution, probably due to the retention and recirculation of coastal waters. Regardless the input scenario, some regions are more subject to offshore pollution such as the South Atlantic and the NE Pacific, while others are more largely affected by coastal pollution (beaching) such as the NW Pacific, North Atlantic and Mediterranean shores. We have found that particles can travel up to several thousand kilometers, allowing remote connectivity between coastal regions. This property is of interest for the application to other types of floating pollution or any conservative biogeochemical properties, or viruses and pathogens.

  This reanalysis is part of the Copernicus Marine Environment Monitoring Service (CMEMS) with a new global eddy-resolving resolution and an ocean model with 50 vertical

levels. The model component is the NEMO platform, forced at its surface by the ERA-Interim atmospheric reanalysis of the European Center for Medium-range Weather Forecast. These products are part of international efforts to give a better estimate of the global state of the oceans

Acknowledgements

FC was supported by postdoctoral funding from CNRS/INSU. We thank gratefully Laurent Lebreton and Erik van Sebille for providing their data sets for the source scenarios.


domain: chim spi

text:
Jean-Baptiste Fleury
email: jean-baptiste.fleury@physik.uni-saarland.de

Marco Werner

Xavier Le Guével

Vladimir A Baulin
email: vladimir.baulin@urv.cat

Protein corona modulates interaction of spiky nanoparticles with lipid bilayers

The impact of protein corona on the interactions of nanoparticles (NPs) with cells remains an open question. This question is particularly relevant to NPs which sizes, ranging from tens to hundreds nanometers, are comparable to the sizes of most abundant proteins in plasma. Protein sizes match with typical thickness of various coatings and ligands layers, usually present at the surfaces of larger NPs. Such size match may affect the properties and the designed function of NPs. We offer a direct demonstration of how protein corona can dramatically change the interaction mode between NPs and 1 lipid bilayers. To this end, we choose the most extreme case of NP surface modification: nanostructures in the form of rigid spikes of 10-20 nm length at the surface of gold nanoparticles. In the absence of proteins we observe the formation of reversible pores when spiky NPs absorb on lipid bilayers. In contrast, the presence of bovine serum albumin (BSA) proteins adsorbed at the surface of spiked NPs, effectively reduce the length of spikes exposed to the interaction with lipid bilayers. Thus, protein corona changes qualitatively the dynamics of pore formation, which is completely suppressed at high protein concentrations. These results suggest that protein corona can not only be critical for interaction of NPs with membranes, it may change their mode of interaction, thus offsetting the role of surface chemistry and ligands.

Introduction

Gold nanoparticles (NPs) are used in many biomedical applications ranging from drug delivery 1,2 and medical imaging 3 to cancer treatment. [4][5][6] The size, shape and surface of gold NPs define most of their physico-chemical properties. 7,8 The behavior of gold NPs is well controlled by their physico-chemical properties. While NPs are dispersed in biological fluids, their behavior is more ambiguous. 9 Proteins and biopolymers, abundantly present in plasma and other biological fluids, tend to aggregate and adsorb at NPs surface, forming a layer of water-soluble proteins (or biopolymers), called protein corona (PC). 10,11 This protein layer is not static, but dynamically exchanging proteins with the bulk while its complex kinetics depends on the size and the structure of proteins present in the bulk. 12 As a result, PC may change properties of NPs, for example, PC can suppresses most of the functional properties of ligand-functionalized well-controlled NPs and even trigger immune reaction. 13 Thus, PC may screen, alter and suppress the contribute prepared in the lab and validated in vitro, NPs may not work in vivo: more than 95 % of the administered NPs end up at sites other than targeted tumors. 14 Thus, PC plays an important role in cellular uptake, targeting, clearance and possible nanotoxicity of these NPs. [START_REF] Corbo | Tasciotti[END_REF]16 with the bio/nano-interface during the last decade. 17 The difficulties reside in the dynamic nature of PC and that in biological media it consists of a myriad of different biomolecules. [START_REF] Corbo | Tasciotti[END_REF][16][17] Large number of proteins, lipids or ligands (such as carbohydrates) that can cover NPs to prevent the PC formation were explored. 10,18,19 However, prevention of PC may also alter or inhibit the NPs functionality. 10,18,19 Some of these strategies even lead to paradoxical results, for example, coating NPs surfaces with hydrophilic polymers can prevent proteins from adsorbing, but, in turn, it can enhance the recognition of the NPs by the immune system. 17,20,21 It is usually considered that the effect of PC is directly proportional to the NP surface area available for the adsorption, 22,23 while the surface area strongly depends on the size and shape of NPs. With this, apart from the surface modification strategy, the shape of NPs has been also considered as a possible way to modulate the PC formation. Recent results show that rod-like NPs can accommodate significantly larger amounts of serum proteins compared to spherical NPs or specific nanostar-shaped NPs. 22,23 To demonstrate significant change of properties of NPs due to adsorption of proteins and even qualitative change of the behavior when interacting with lipid bilayers, in this manuscript we adopt the most radical form of surface modification of NPs, namely NPs with the shape in form of rigid spikes, so called spiky nanoparticles (SNs). These objects are of particular importance for interaction with proteins, since the sizes of spikes of few nanometers are of the order of magnitude of the sizes of most proteins in plasma. 24,25 Thus, these objects are at the crossover between large NPs covered with protein corona and small NPs or nanoclusters with high curvatures and sizes comparable to protein sizes. Due to a particular shape, SNs have recently attracted interest as potential candidate to prevent the PC formation 23,26 and the shape of spikes can be very broad. 23,26,27 This makes SNs the ideal objects to study the effects of adsorbed proteins also in other systems. It is noteworthy, that SNs have the shape similar viral particles. 28,29 Surprisingly, viruses share many biophysical properties with artificial SNs in extracellular environments. 29 In particular, PC formation is occurring on the viral particle surface and this layer is critical for viral-host interactions. 29 Thus, it is interesting to investigate how the shape of a SN could prevent, or affect, the formation of a protein corona on the viral particle surface as well as study interaction of NPs with model cell membranes. 30,31 In the first section we describe the physico-chemical properties and the geometry of SNs.

Then we study the interaction of SNs of different shapes and sizes with lipid bilayers. The spikes at the surfaces of SNs which are comparable in length with the thickness of the bilayers induce pores in the bilayers, which are studied with patch-clamp technique and theoretically with bond-fluctuation model within Monte Carlo simulations. Next chapter describes the effect of protein corona adsorbed on SNs, which is manifested in the effective screening of spikes length, that change qualitatively the behavior of SNs and suppresses pore formation.

Characterization of spiky nanoparticles

SNs were prepared by a standard seed-mediated growth method 32 starting from either 3 nm (Types A and B) or 15 nm (Types C and D) gold seeds (see Materials and Methods for details). This protocol results in SNs with gradually changing sizes and variable spike numbers from Type A to D. We chose this synthesis protocol because it provides SNs at a high yield, high monodispersity and with a precise control of spike numbers and spike lengths. 33 The sizes and geometry of the spikes were determined from TEM images at the same magnifications for a large number of SNs (see Fig. 1A-D and additionally Fig. S1-S4).

All dimensions of the four types of SNs are reported in Table 1. Full size corresponding to the average size of SNs including the metal core and the spikes. SNs of Type A and B were obtained from 3 nm seeds, resulting in full sizes of 44 ± 4.7 nm for Type A and 66.5 ± 8.9 nm for Type B (Fig. 1 and Table 1). SNs of Type A are not only smaller, they have less spikes in average 7 ± 2 compared to 10 ± 2 for Type B and SNs of Type C and Type D were obtained from the 15 nm gold seeds and result in full sizes of 103 ± 11.9 nm and 140.9 ± 7.7 nm, respectively. We observed an increase of spike numbers but no significant changes of spike lengths from Type C to D. The angle between spikes and the distance between spikes have similar values as SNs of Type B. Noteworthy, that gold core has constantly increased for all types of SNs during the synthesis. This could be explained by the reaction of gold salt that reacted on gold seeds to produce bigger sizes and also to form spikes due to the presence of PVP. 34 In addition, we observed that SNs exhibit a broad near-infrared plasmon band typical of anisotropic gold NPs 32 (Fig. S5).

The synthesized SNs were functionalized with thioctic bidentate sulfobetaine zwitterionic molecule (see Materials and Methods) to prevent aggregation and insure colloidal stability in the solution. Non-homogeneous distribution of the coating results in hydrophilic interiors of the SN between the spikes and hydrophobic tips of the spikes. The hydrophobicity of the tips allows for spikes to anchor the lipid bilayer and affects the protein adhesion locally.

The detailed geometrical parameters of each type of SNs obtained from TEM images, allow for the 3D reconstruction of an average SN of each type, as illustrated in Fig. 1A-D.

The reconstruction, in turn, allows to estimate additional geometrical parameters: the total volume of an average SN of each type is gradually growing from Type A to D, Fig. 1E;

the excess area, defined as the total area of SN divided by the projected area of the core, is smaller for Type A, while for B, C, D has similar values, Fig. 1F; the surface-area-to-volume ratio is gradually decreasing from Type A to D, Fig. 1G. This data is further used for Monte Carlo simulations and for the model of protein adsorption.

Pore formation

In this section we study the interaction between SNs and a free-standing bilayer and demonstrate that SNs with spikes long enough to pierce the lipid bilayer can induce reversible pores.

An horizontal free-standing bilayer was formed in a microfluidic chip at a desired location 35,36 The resulting bilayer is stable for at least ≈ 0.5 -2 hours. B) Visualization under dark-field microscopy of an horizontal lipid bilayer in the presence of spiky nanoparticles (100 nm diameter). SNs are depicted in orange, due to their plasmonic properties.

Microfluidic setup allows not only to directly visualize the interaction of nanoparticles with lipid bilayers, it permits simultaneously measure electrical signals across the membrane that are associated with interactions of individual nanoparticles. 37 A planar lipid bilayer without inclusions and in the absence of nanoparticles represents a planar dielectric sheet, where its hydrophobic core is not permeable for ions from the buffer. Thus, if the voltage is applied between two sides of the bilayer, it represents a planar capacitor with nanometersize thickness. Using a patch-clamp setup, one can measure a specific capacitance C s of this capacitor, which yields C s ≈ 3.9 mF/m 2 for a DOPC free standing bilayer. Once the nanoparticles put in contact with the surface of the bilayer, the mechanical interaction changes the capacitance of the bilayer, thus providing a measurable electric signature of this interaction.

It is noteworthy to mention the influence on the measurements of the electric capacity of a golden ring formed at large concentrations of SNs (100 µg gold/mL). For that purpose, SNs were dispersed via the bottom channel of the microfluidic device. Once the golden ring was formed at the edge of the bilayer, the bilayer was rinsed by diluting the surrounding phase around the bilayer by adding a buffer solution until the bulk concentration of SNs drops to zero, while SNs are present only at the bilayer edge. It turns out that the difference of the measured specific capacity C s with that of a pure DOPC lipid bilayer is negligible.

Thus, one can conclude that the ring practically does not contribute to the measurements of the capacitance and the presence of the ring can be neglected. Nevertheless, the following part of our study corresponds to low concentrations of SNs where the ring does not form.

Following the dispersion of SNs in the bottom channel at ≈ 30 min after the bilayer formation, the capacitance and the conductance of the lipid bilayer in the presence of the SNs was measured as a function of time for different types of SNs, Fig. 3A-D). The specific capacitance of the bilayer is drastically reduced in presence of SNs, while the conductance of the bilayer exhibits massive increase, which is attributed to the poration of the bilayer by individual SNs. It is noteworthy that no significant conductance traces were measured without SNs. The size of the resulting nanopores formed by individual SN in contact with the bilayer can be determined by performing highly sensitive conductance measurements.

To this end, the conductance of the bilayer in the presence of SNs was measured at ultralow concentrations, 1 ng/ml. The corresponding conductance trace is showing well-defined conductance jumps with a characteristic conductance amplitude. A characteristic time of the jumps corresponds to the pore opening and closing events and indicates that the poration induced by SNs are reversible, while the amplitude is related to the the pore size. Indeed, the radius of the pore (in nm) is r = Gd/(πk), where d ∼ 4 nm is the DOPC bilayer thickness, k = 1, 15 S/m is the bulk electrolyte conductivity (measured for 100 mM NaCl at 30 • C), and G is the conductance (in nS). We find that the size of the resulting pore r and its lifetime depend on the particular geometry of the SNs. For example, the biggest SNs of Type D induce long-lived (from 100 ms to a few seconds) conductance jumps with an amplitude corresponding to a pore radius of around ≈ 1.7 nm. Smaller SNs induce shorter-lived and smaller pores. The average radius of the pores is 0.88 for Type A, 1.52 for Type B, 0.95 for Type C, 1.7 nm for Type D. The size of the pores is not in the order of the size of SNs, which is gradually increasing from A to D, see Table 1, but most probably corresponds to the geometry of the spikes at the surface of the SNs. The 3D reconstruction of an average SN of each type suggests that Types A may contact with the bilayer with 3 or 4 spikes, while Types B and C may contact with 4

spikes and Type D with more than 4 spikes. This would suggest a gradual increase of pore sizes, however, the observed discrepancy in the order of the sizes could be attributed to the polydispersity of spike shapes that are formed randomly at the surfaces of the gold cores and spike sharpness. Nevertheless, the differences in the sizes is less than 1 nm, which is close to detection limit.

Noteworthy, the measured pores sizes correspond to the minimum pores sizes induced by SNs. Bigger pores lead to bilayer rupture and thus are not observed. Thus, these pore sizes can be considered pre-critical, i.e. before the bilayer rupture: the measured pore radii are close to the critical pore radius of rupture of the bilayer r c = σ/Γ ≈ 2.5 nm. 37 σ ≈ 20 pN is the line tension of the pore edge corresponding to Γ ≈ 8 mN/m (see Materials and Methods). The pore line tension for a DOPC bilayer is estimated from Akimov et al. 38 Recently, the interaction of a spherical gold NPs coated with ZwBuEta with a lipid bilayer was reported. 36 Based on electrophysiological experiments, it appears that these NPs do not create spontaneous pores for NPs diameters between 20 nm to 100 nm. This result can be used as a control for no spikes nanoparticles.

The difference between pores and the ability of an individual SN to break the bilayer is related to nanospikes geometry and hydrophobicity of the spikes. If the spikes are long enough and attractive, e.g. uniformly hydrophobic or hydrophilic, the bilayer would adsorb to reach the core of the spike and thus, then it has bigger chances to induce a rupture of the bilayer by area consumption. In contrast, if the spike is hydrophobic only at the tip or the spikes are not long, the SNs only anchoring the bilayer, making small pores without rupturing it. This was confirmed by Monte Carlo simulations using Bond Fluctuation Model (5) there). For a value of H X = 0, the component is hydrophilic, whereas for H = 1 the component is hydrophobic. while The spikes are modeled as rigid and attractive truncated cones with spherical caps at the tips and variable distances between the centers, Fig. 4A).

We define a total spike height of h = 52a with a being the lattice constant, a radius of the cap R c = 15a, and an opening angle α = 25 • . The height of the corresponding full cone, h 0 , and the boundary height h b between conic and spherical part are given by

h 0 = h + R c 1 sin(α) - 1
h b = h + R c [sin(α) -1] (1)
Above the cap boundary height, h b , monomers are defines as hydrophobic (H A = 1).

Below h b , monomers are defined super-hydrophilic H B = -0.16, i.e. only weakly attractive for the lipid head groups according to Eq. ( 5) in Ref. 43. Spikes are generated in the simulation box of cubic size 128a by occupying the volume with immobile monomers. Three spikes are positioned in an equilateral distance of 60a between the tips. The spikes are grafted to a substrate layer (immobile) with the same hydrophilic property H A . A number of 1200 lipids has been arranged in the simulation box in form of a bilayer above the spikes as well as an explicit solvent such that the volume occupancy in the mobile zones of the simulation box is 0.5. A fluctuation mode analysis for patches of 300 lipids with the same area per lipid revealed that the membrane is under slight tension of γ = 0.0142 k B T /(a 2 ) 44 .

Using an estimate, a ∼ 0.154 nm 42 for the lattice constant, the tension can be referred to an order of magnitude near γ ∼ 2.5 mN/m.

Since the diameter of the spikes tips is much larger than the bilayer thickness, the spikes do not pierce the bilayer, but due to adsorption of the bilayer on the spikes, the bilayer eventually becomes over-stretched in the zone between the spikes depending on the size of membrane-spike contact area. In addition, since pillar tips are hydrophobic, they are typically covered by lipid monolayer patches, that are connected to the remaining bilayer fraction between the tips. A defect in form of a boundary between monolayer and bilayer may act as a nucleation point for pores. If the stretching is large, it can induce a pore that is formedDepending on the interplay between stretching, induced defects and bilayer fluctuations, a pore may form in the zone between spikes, Fig. 4B). In that respect, this mechanism is similar to the mechanism of pore formation described for nanostructured surfaces. 45 Similarly, strong adsorption leads to the rupture of the lipid bilayer, see Fig. 4(D),

where a larger surface-head attraction was applied by using H B = -0.32.

Screening of spikes by protein corona

Once nanoparticles or biomaterials are introduced into biological media, within seconds they get coated by proteins. 46 Dynamic exchange of proteins between the media and the surface of nanoparticles leads to the formation of PC, which is also changing with time. 47 This process is very complex due to large diversity of proteins present in media, variability in kinetics and physico-chemical characteristics. PC not only interacts with the surfaces, it can also drastically modify the surface properties, screen the biomolecules present at the surfaces and screen or alter the action of ligands and coatings. To illustrate significant changes provoked by the adsorption of proteins in a well controlled microfluidic system, SNs of four types were placed in media with a model protein, bovine serum albumin, BSA. The coating with the protein lead to quantitative change of the interactions with lipid bilayers shown in previous section. Later, to confirm our findings that the protein effect is found not only for BSA protein, SNs were placed in blood serum media, containing large variety of proteins. Addition of water-soluble BSA proteins to the solution of SNs leads to the formation of a protein corona. It is manifested in effective reduction of the length of spikes exposed to the interaction with lipid bilayers. To estimate the effect of BSA on a complex nanostructured surface of SNs of each type and calculate the maximal load of proteins per spike and per SN, we used the same approach that was applied for protein adsorption on planar nanostructured surfaces with spikes and pillars. 46 The kinetics of protein adsorption was modeled assuming irreversible adsorption of BSA protein, represented as a sphere of 7 nm diameter, on a shape of spike geometry given in Table 1 for each type of SN. Within Random Sequential Adsorption (RSA) approximation, 48 the adsorption kinetics is expressed as a fraction of covered area θ (occupancy) as a function of time t via

dθ dt = k a nB(θ) -k d θ (2)
In this equation the blocking function B(θ) is defined as the probability to adsorb a protein to the surface for a given occupancy θ, while k a and k d are the rates of adsorption and desorption, respectively and n is the concentration of proteins in the bulk. The pristine surface θ = 0 corresponds to the blocking function B(0) = 1. Assuming irreversible adsorption of proteins within RSA approximation, the blocking function for a given geometry can be accessed directly with Monte Carlo simulations as B(θ) = N succ /N tot , where N succ is the number of potentially successful attempts and N tot is the total number of attempts. 46 Using Gaussian approximation for the spikes shape

f (x, y) = L exp - x 2 + y 2 2w ( 3
)
where L is the length of a spike, w is the Gaussian variance, related with the width of the spike. The results are present in Fig. 5A) for spikes and 5B) for SNs using the geometrical parameters of Table 1. It gives an estimate of a maximal number of proteins per spike and per SN. The protein load follow the order A-B-C-D, which is also consistent with their sizes and number of spikes per SN. This load leads to effective reduction of the spikes lengths and makes the SNs more round-shaped.

Microfluidic experiment confirms that addition of sufficiently high concentration of BSA proteins to the solution with SNs suppresses the pore formation. The formation of PC on the surface of SNs hinders the spikes and this results in the recovery of the bilayer original insulator properties similar to a pure lipid bilayer, regardless the presence of SNs on its surface. As expected, the screening effect of PC depends on both the geometry of the SNs and the BSA concentration. At a high protein concentration, above a threshold value for each type of SN, the pore formation is suppressed for all types of SNs. Nevertheless, the geometry of the spikes strongly influences the threshold value of the BSA concentration when the pores are no longer observed, Fig. 5C).

Another observation is that the pore happens in a narrow concentration range close to the threshold value. This is probably due to the fact that the pores are created when the SNs are rolling on the surface and only by spikes in direct contact with the bilayer. Thus, although the accumulation of proteins can be a gradual process as a function of the bulk protein concentration, the suppression is happening only when all spikes are covered on all sides, which corresponds to the threshold value. The values of threshold concentrations follow the order A-B-C-D, which is consistent with the evaluation of maximal protein load from RSA. SNs of Type A do not induce pores in the bilayer at BSA bulk concentrations slightly below 20% and the threshold concentration for SNs of Type B is 25%. This is supported by electrophysiological measurements as no conductance traces are measured. SNs of of Type C and Type D require higher concentrations of BSA in solutions, 40% for Type C and 85%

for Type D since they have larger areas and larger number of spikes to cover with proteins and these values are very high.

Thus, RSA estimations together with this result indicates that formation of PC around such nanoparticles is mainly determined by the geometry of nanoparticles, namely by the surface area and the number of spikes.

However, the threshold concentrations are much lower for serum proteins, red curves in Fig. 5C). This is due to the fact that serum contains large number of proteins of different types, that can fill the gaps between the spikes and at the surface of SNs more efficiently than globular-shaped BSA. Slightly hydrophobic surfaces of water-soluble SNs may also diminish serum protein adsorption. SNs of Type A and Type C, suppress pores formation when the buffer is containing 10% of serum. SNs of Types B and Type D, suppress pores at 20% and 30% of serum, correspondingly. It results that the spike geometry may hinder proteins adsorption and, thus, the formation of protein corona.

The geometry of the spikes strongly influences the threshold values of serum concentration leading to pores suppression. In particular, the sharpest spikes, i.e. SNs of type B and D, require higher serum concentration to recover the standard bilayer dielectric properties and thus, the interaction between the SNs and the bilayer is highly dependant on serum concentration. If we use the analogy of SNs with virus particles, that have the same sizes, one may expect that the serum and other proteins can screen the viruses from the interaction with bilayers, which may lead to various effects, e.g. escape from recognition by immune cells.

It would be interesting to explore such effects with viral particles in separate experiments.

Materials and Methods

Synthesis of nanoparticles. 4 types of gold spiky nanoparticles (SNs) with different core size and spike lengths (Types A, B,C, D, Fig. 1 ) were synthesized following a modification of the protocol described elsewhere. Microfluidic setup for horizontal bilayer formation. The formation of DOPC freestanding lipid bilayer in squalene oil was done as following. A PDMS 3D-chip was produced with a thin rectangular channel connected with a conical hole, made with a 3D printed method as detailed in. 35,36,52 The bottom micro-channel of the PDMS chip was filled with a drop of oil+lipid followed by the delay of 5 min for spreading. Then a water droplet was added to the conical hole. The oily phase into the bottom channel was replaced by a water phase following the delay for the bilayer formation. The time to form the bilayer depends on the volume of the oil that separate the two water phases. Drainage of the oil happens in 1-2 hours, after that period of time the bilayer forms. Bilayer ideally forms at the intersection point where the upper conical wall and the bottom channel meet. The resulting formed bilayer is stable at least for 2 hours. The µ-chip was then placed under a dark-field microscope (Leica DM2700) for visualization with the camera DFC450 (Leica).

Surface tension and bilayer tension measurements. Surface tensions of the various lipid monolayers at the oil/water interfaces were measured with the pendant drop method using a commercial measurement device (OCA 20, DataPhysics Instruments GmbH, Filderstadt, Germany). An oil solution with a concentration of 5 mg/ml DOPC was produced by introducing a droplet from a steel needle into the surrounding oil phase. The shapes of all droplets were fitted with the Young-Laplace equation to obtain their interfacial tension.

After the initial formation of a droplet, the DOPC lipids adsorb to the interface, leading to a reduction in interfacial tension. This decrease was recorded over several minutes until a plateau was reached. From the values of the surface tension and the bilayer contact angle θ, which were obtained from pendant drop measurements or optical micrographs, respectively, the bilayer tension can be calculated using the Young equation:

Γ = 2γ cos(θ). (4)
For a DOPC bilayer formed at a squalene oil/water interface, the associated bilayer tension could be estimated between Γ ≈ 8 mN/m. Nevertheless, it is worth to mention that this value may vary from a DOPC batch to another.

Patch Clamping. Ag/AgCl electrodes were prepared by inserting a platinium electrode (HEKA, germany) in a borosilicate glass pipette (outer diameter 1.5 mm, inner diameter 0.86 mm, Vendor) containing an electrolyte agarose solution. Lipid membrane conductance was measured using the standard function provided by the patch clamp amplifier EPC 10 USB (Heka-Electronics). A 10 mV sinusoidal wave with a frequency of 20 kHz was used as an excitation signal. The electrodes are carefully introduced into the aqueous compartment of the Sylgard 184 device using micromanipulator. The specific capacitance C s = C/A is define by the ratio between the total capacitance C and the bilayer area A.

Conclusions

On the example of spiky nanoparticles interacting with lipid bilayer we demonstrate how protein corona can change qualitatively the behavior of nanoparticles. Four types of watersoluble gold SNs coated with zwitterionic molecules with different core size and spikes geometries were synthesized. The geometry of synthetized SNs has a high a large surface-areato-volume ratio and high curvature such that the nano-spikes. As a result, SNs dispersed near a lipid bilayer induce nanopores, which dimensions appear to be directly linked to SNs geometry. Monte Carlo simulations show that the pores are formed between the spikes anchoring into the bilayer, while the adsorption of the lipids at the surface of the spikes leads to the stretching of the bilayer between the spikes open a pore.

The presence of proteins in the solution change the behavior of SNs. PC formed around SNs hinders the effect of nanoparticle shape by reducing effectively the length of spikes and when the protein concentration reaches the threshold value, SNs do not induce pores.

The threshold concentration appears to be directly linked to spikes geometry, which have dimensions comparable with the size of the proteins.

Authors Contribution

All the authors designed the research. J.-B.F performed the microfluidic experiments. X.L.G

Figure 1 :

 1 Figure 1: A), B), C), D): TEM images of SNs of types A, B, C, D and their 3D reconstructions, correspondingly. E) The calculated volume of each 3D model of SNs, F) Excess area of each 3D model, the total surface area, divided by the projected area, A/A 0 . G) Surface-area-to-volume ratio of SNs of types A, B, C, D.

(

  see Materials and Methods). SNs of each type A, B, C, D were dispersed on one side in a buffer phase. SNs can be visualized and tracked by dark-field microscopy thanks to their plasmonic and scattering properties: the SNs are diffusing and bouncing on the bilayer surface, Fig.2. The observation of SNs at the surface of the bilayer shows that none of these SNs are able to translocate through the lipid bilayer whatever the geometry of SNs. The average contact time of a SN with the bilayer is around a few seconds before SN detaches from the bilayer and moves in the solution. The SNs do not aggregate on the bilayer surface and are homogeneously distributed at the surface except at the edges of the bilayer, where we observe accumulation of SNs with non-negligible number of immobile SNs. These are clusters of SNs, which becomes much more visible for large concentrations of SNs, forming a golden ring at the edges of the bilayer, which is clearly seen under the microscope. The clustering at the edges demonstrates that the SNs are slightly hydrophobic, even if they are fully water-soluble and insoluble in oil. Such an effect can be related either to the presence of polyvinylpyrolidone on the surface of SN or to the Van der Walls interaction between the hydrophilic zwiterionic ligands coated on SNs (see Materials and Methods).

Figure 2 :

 2 Figure2: A) Schematic illustration of the bilayer formation from a mixture of lipid+oil (DOPC + Squalene) sandwiched between two water droplets: the bilayer forms after drainage of the oil, in 10-15 minutes.35,36 The resulting bilayer is stable for at least ≈ 0.5 -2 hours. B) Visualization under dark-field microscopy of an horizontal lipid bilayer in the presence of spiky nanoparticles (100 nm diameter). SNs are depicted in orange, due to their plasmonic properties.

Figure 3 :

 3 Figure 3: A)-D) Conductance traces from the poration of a DOPC bilayer in contact with SNs of Types A, B, C, D, correspondingly.

Figure 4 :

 4 Figure 4: A) Spike geometry and notations in the coarse grained simulation model. Monte Carlo simulation snapshot of a bilayer for hydrophilicity H B = -0.16 (B,C) and H B = -0.32 (D) of the B-type substrate: B) initial contact with spikes, side view; C) pore formation (red arrow), top-and side views, typical pore radius for a period 8 × 10 7 . . . 2 × 10 8 MCS was r = (22 ± 4)a; D) rupture of the bilayer due to full adsorption on the spikes for the stronger head-substrate attraction. The simulation time is given below each snapshot in units of Monte Carlo Steps (MCS).

Figure 5 :

 5 Figure 5: A) Bloking function of BSA proteins adsorbed on a spike of model SNs of types A-D, with the spike geometries described in Table 1. Inset: Illustration of a maximum load of BSA on Type A spike. B) Blocking function of BSA proteins per SN of Types A-D. They are deduced from A) and the number of spikes per partice. C) Specific capacitance of a DOPC bilayer in contact with the solution of SNs with BSA (blue) or with serum (red) as a function of BSA or serum concentration.

Table 1 :

 1 Measured geometrical parameters of SNs obtained from an average of 100 NPs TEM images.

		Core	Full	Number of	Spike	Spike	Radius for	Angles between Distance between	Spikes thickness
		size (nm) size (nm)	spikes	length (nm) angles ( • ) spikes angle ( • )	spikes ( • )	spikes (nm)	at half-height (nm)
	Type A	16± 2	44±4	7±2	9.7±2	51.6±1	5.1±1	120.8±18	23.4±5	9±1
	Type B	27.8±4	66.5±9	10±2	17.4±4	35.4±7	5.4±2	71.9±15	21.8±4	10.2±1
	Type C	42.4±4 103.9±12	14±2	18.2±3	40.1±9	6.2±2	87.6±20	19±3	11.1±2
	Type D	58±5	140.9±8	19±3	21±4	38.7±7	5.9±2	60.5±15	17.4±3	12.1±1

  39,40 of a lipid bilayer interacting with three rigid spikes. The model of a lipid bilayer and the corresponding parameters are similar to Refs 41-43, where hydrophilic hydrophobic effects are mediated by short-range interactions. A hydrophobicity scale, H X , for a component "X" is defined relative to the lipid tail-and head group repulsion according Ref.43 (Eq.

  32 SNs of types A and B were made with 3 nm gold seeds, which were first formed by adding 22 µL of HAuCl 4 • 3 H 20 (100 mM) to a PVP (MW 10.000; 36 µM; 47.5 mL) solution prepared in the mixture DMF/water (v/v= 18/1). After 5 min under vigorous stirring, a freshly prepared NaBH 4 aqueous solution (10 mM; 2.5 mL) was added quickly to the previous solution, which changed quickly from yellowish to pale pink color and kept stirred for another 2 hours. Solution was stored 24 hours before use. Type A and B differed only by the amount of 3 nm gold seeds added to the growth solution. In a typical synthesis, 82 µL of HAuCl 4 • 3 H 20 (50 mM) was added to 15 mL of PVP solution (Mw 10.000; 10 mM) in DMF. Following this procedure, either 20 µL or 5 µL of the 3 nm gold seeds sol was added to the growth solution to prepare Au SNs type A and type B respectively. SNs were obtained within 2 hours with color change from yellowish to dark blue. SNs were washed 3 times to remove the PVP in excess and resuspended in water at 250 µg Au/mL. SNs Types C and D were made with 15 nm gold seeds, which were prepared by the citrate method adding 5 mL of citrate solution (1 wt%) to a boiling aqueous solution of HAuCl 4 (100 mL, 0.5 mM) and allowed to react for 15 min and then cooled down at room temperature. Following this procedure, 5 mL of PVP (Mw 10.000; 0.1 mM) was added drop-wise to the previous solution and allowed to react overnight. The particles were then centrifuged at 8000 rpm for 30 min and redispersed in ethanol. Using the same protocol to prepare SNs type A and B, 82 µL of HAuCl 4 • 3 H 20 (50 mM) was added to 15 mL of PVP solution (Mw 10.000; 10mM) in DMF. Following this, either 50 µL or 15 µL of the 15 nm gold seeds was added to the growth solution to prepare SNs Type C and Type D, respectively. SNs were obtained within 2 hours with color change from yellowish to blue/grey. SNs were washed 3 times to remove the PVP in excess and resuspended in water at 250 µg Au/mL.

	Transmission Electron Microscopy (TEM). Au SNs images were obtained on an
	FEI Tecnai G2 Twin TEM at 200 kV. TEM samples were prepared by placing a drop of SNs
	solution onto a copper grid covered with holey carbon films. Absorption spectra over a 190-
	900 nm range were collected using a Cary 100Bio UV-visible spectrophotometer (Varian).

Nanoparticle coating. All type of gold nanoparticles were coated with a thioctic bidentate sulfobetaine zwitterionic molecule

49

(Zw, 412 µg/mol) to provide the same surface chemistry and known to enhance colloidal stability.

50,51

Briefly, in 10 mL of gold particles (100 µg Au/mL), 40 µL of NaOH (1 M) was added following by 100 µL of Zw (0.5 mM) and stirred for 6 hours. Zw-coated particles were washed three times using centrifugation method (10.000 rpm for 20 min) to remove the free Zw. Sols were stored in water at 250 µg Au/mL.

Acknowledgments

J.-B.F acknowledges funding from SFB 1027 (DFG), project B4.