Aline Grein-Iankovski

Alain Graillot

Milad Radiom

Watson Loh
email: wloh@unicamp.br

Jean- François Berret
email: jean-francois.berret@univ-paris-diderot.fr

Template-Free Preparation of Thermoresponsive Magnetic Cilia Compatible with Biological Conditions

Bio-inspired materials are commonly used in the development of functional devices. The fabrication of artificial cilia mimicking the biological functions has emerged as a promising strategy for fluid manipulation in miniaturized systems. In this study, we propose a different physicochemical insight for the preparation of magnetic cilia based on the temperature-triggered reversible assembly of coated iron oxide nanoparticles in a biocompatible template-free approach. The length of the prepared cilia could be tuned between 10 -100 µm reaching aspect ratios up to 100 in a very dense array of flexible structures with persistence lengths around 8 µm. Magnetic actuation of the cilia revealed robust structures (over several hours of actuation) with a wide range of bending amplitudes resulting from high susceptibility of the filaments. The results demonstrate that the proposed strategy is an efficient and versatile alternative for templated fabrication methods and producing cilia with remarkable characteristics and dimensions within the template-free approaches.

Introduction

Nature has plenty of complex processes and remarkable structures whose performances in-spire the development of new materials and innovative functional devices. Cilia and flagella are examples of essential structures that provide a range of vital functions in varied biological organisms. [START_REF] Sleigh | The biology of cilia and flagella[END_REF] Generally, these structures present high aspect ratios (ratio of the length to the diameter) with diameter around 0.15 -0.30 µm and lengths varying from few micrometers up to millimeter range. [START_REF] Sleigh | The biology of cilia and flagella[END_REF] In bacteria, these surface-attached organelles are intrinsically related to motility in different ways, including propulsion, self-locomotion and fluid transportation inside the human body. [START_REF] Khan | Functions and Evolution of Archaella, Flagella and Cilia[END_REF] In the bronchial region of the lungs, the collective beating motion and the hydrodynamic coupling of cilia through the cell membrane generates a wave-like pattern, called metachronal waves, whose beating moves mucus towards the pharynx and expel it from the airways. [START_REF] Sleigh | The biology of cilia and flagella[END_REF][START_REF] Gilpin | The multiscale physics of cilia and flagella[END_REF] Inspired by the efficiency of these biological cilia, a variety of artificial structures have been proposed to mimic their behavior in many applications, for example, for fluids manipulation in minia-turized devices, in microfluidic and lab-on-a-chip devices. [START_REF] Fahrni | Micro-fluidic actuation using magnetic artificial cilia[END_REF][START_REF] Zhou | Magnetoresponsive Surfaces for Manipulation of Non-magnetic Liquids: Design and Applications[END_REF] Among the strategies explored to induce motion in these ciliary arrays, we emphasize the magnetic actuation due to their rapid response and efficient non-contact and non-intrusive control over the system. Several theoretical approaches have already investigated the mechanism of the ciliary synchronized motion and demonstrated the possibility of artificial cilia to effectively generate a directional flow for controlling the motion in fluid environments. [START_REF] Gauger | Fluid transport at low Reynolds number with magnetically actuated artificial cilia[END_REF][START_REF] Elgeti | Emergence of metachronal waves in cilia arrays[END_REF] Notable experimental efforts have been made in this direction to prepare biomimetic magnetic cilia using different types of magnetic particles embedded in a soft matrix by different fabrication approaches. A range of nicely shaped cilia arrays with controlled magnetic actuation have been fabricated, many of them displaying great potential for fluid and particle manipulation. However, most of these studies are based on patterning, lithography or rather tedious fabrication processes, even requiring additional steps for the mold preparation. Also, the geometry of the cilia is limited to the pattern of the available mold and to its fabrication boundaries, especially regarding the size, restricting the adjustment of the structures in the array. Therefore, the current limitations regarding cilia size, aspect ratio and density, combined with the desirable search for versatile preparation procedures offer opportunities to explore and contribute to improvements in this field.

In this work, we propose a novel insight within the template-free strategies for the preparation of magnetic cilia exploring the thermoresponsive phase transition of polymer decorated magnetic nanoparticles to induce an oriented assembly. When an external magnetic field is applied over a colloidal suspension of magnetic particles it orients the individual magnetic moment carried by the nanoparticles inducing dipole-dipole interparticle attraction, leading to chain formation. [START_REF] Promislow | Aggregation kinetics of paramagnetic colloidal particles[END_REF][START_REF] Biswal | Mechanics of semiflexible chains formed by poly(ethylene glycol)-linked paramagnetic particles[END_REF][START_REF] Goubault | Flexible Magnetic Filaments as Micromechanical Sensors[END_REF][START_REF] Dreyfus | Micro-scopic artificial swimmers[END_REF][START_REF] Martínez-Pedrero | Forma-tion of magnetic filaments: A kinetic study[END_REF][START_REF] Corr | Linear Assemblies of Magnetic Nanoparticles as MRI Contrast Agents[END_REF] By orienting this assembly perpendicular to a substrate, connecting the particles and anchoring the formed chains on the surface it is possible to produce a magnetic ciliary array. So far, a couple of template-free approaches have been proposed base on the alignment of magnetic beads, [START_REF] Singh | Synthesis of Flexible Magnetic Nanowires of Permanently Linked Accepted at Journal of Physical Chemistry C Friday[END_REF][START_REF] Babataheri | Tethered fleximags as artificial cilia[END_REF][START_REF] Wang | Out of the cleanroom, self-assembled magnetic artificial cilia[END_REF] carbonyl iron particles, [START_REF] Huang | A Switchable Cross-Species Liquid Repellent Surface[END_REF][START_REF] Lu | A bioinspired multilegged soft millirobot that functions in both dry and wet conditions[END_REF][START_REF] Yang | Magnetically Responsive Superhydrophobic Surface: In Situ Reversible Switching of Water Droplet Wettability and Adhesion for Droplet Manipu-lation[END_REF] and cobalt particles, [START_REF] Timonen | A Facile Template-Free Approach to Magnetodriven, Multifunctional Artificial Cilia[END_REF][START_REF] Sun | Bio-inspired artificial cilia with magnetic dynamic properties[END_REF][START_REF] Cao | Unidirectional Wet-ting Properties on Multi-Bioinspired Magnetocontrollable Slippery Microcilia[END_REF] or nanoparticles, [START_REF] Benkoski | Dipolar assembly of ferromagnetic nanoparticles into magnetically driven artificial cilia[END_REF] for example. The explored strategies for linking these particles varied from covalent binding via amidation chemistry, [START_REF] Singh | Synthesis of Flexible Magnetic Nanowires of Permanently Linked Accepted at Journal of Physical Chemistry C Friday[END_REF][START_REF] Benkoski | Dipolar assembly of ferromagnetic nanoparticles into magnetically driven artificial cilia[END_REF] electrostatic attraction, [START_REF] Babataheri | Tethered fleximags as artificial cilia[END_REF][START_REF] Wang | Out of the cleanroom, self-assembled magnetic artificial cilia[END_REF][START_REF] Yan | Growth mechanism of nanostructured superparam-agnetic rods obtained by electrostatic co-assembly[END_REF] dipolar assembly, [START_REF] Benkoski | Dipolar assembly of ferromagnetic nanoparticles into magnetically driven artificial cilia[END_REF] and incorporation in an elastomeric matrix. [START_REF] Timonen | A Facile Template-Free Approach to Magnetodriven, Multifunctional Artificial Cilia[END_REF][START_REF] Sun | Bio-inspired artificial cilia with magnetic dynamic properties[END_REF][START_REF] Kim | Remote Manipulation of Droplets on a Flexible Magnetically Responsive Film[END_REF][START_REF] Cao | Unidirectional Wet-ting Properties on Multi-Bioinspired Magnetocontrollable Slippery Microcilia[END_REF][START_REF] Huang | A Switchable Cross-Species Liquid Repellent Surface[END_REF][START_REF] Lu | A bioinspired multilegged soft millirobot that functions in both dry and wet conditions[END_REF][START_REF] Yang | Magnetically Responsive Superhydrophobic Surface: In Situ Reversible Switching of Water Droplet Wettability and Adhesion for Droplet Manipu-lation[END_REF] . The moldless state of magnetic fabrication enables the preparation of cilia with much higher aspect ratios and the rough adjustment of their dimensions and density by modulating the magnetic field, by varying the particles concentration or the particles size. [START_REF] Timonen | A Facile Template-Free Approach to Magnetodriven, Multifunctional Artificial Cilia[END_REF][START_REF] Benkoski | Dipolar assembly of ferromagnetic nanoparticles into magnetically driven artificial cilia[END_REF][START_REF] Babataheri | Tethered fleximags as artificial cilia[END_REF][START_REF] Sun | Bio-inspired artificial cilia with magnetic dynamic properties[END_REF][START_REF] Kim | Remote Manipulation of Droplets on a Flexible Magnetically Responsive Film[END_REF][START_REF] Wang | Artificial cilia fabricated using magnetic fiber drawing generate substantial fluid flow[END_REF] Cilia with lengths up to 6000 µm with an average aspect ratio of 120 were obtained, [START_REF] Timonen | A Facile Template-Free Approach to Magnetodriven, Multifunctional Artificial Cilia[END_REF] although, cilia with sub-micrometer diameters, within the size range of biological cilia, are only achievable employing nanometer size particles. [START_REF] Benkoski | Dipolar assembly of ferromagnetic nanoparticles into magnetically driven artificial cilia[END_REF] Our contribution accomplishes the temperature-triggered fabrication of high aspect ratio cilia composed of polymer-coated iron oxide nanoparticles. The thermoresponsive polymer at the nanoparticle surface acts as a linker, promoting upon heating nanoparticle binding into elongated filaments. The transition occurs at biological compatible temperature (around 37 °C) and ionic strength (0.1 -0.2 M) and within a broad pH range (2 -8). The resulting magnetic cilia present remarkable flexibility with persistence lengths around 8 µm and aspect ratios up to 100 with submicrometer diameters. Their lengths can vary from 10 -100 µm by increasing the concentration of the nanoparticles, which also results in a higher coverage density (up to 0.1 filament/µm 2 ).

Experimental section Materials

The superparamagnetic maghemite nanoparticles (γ-Fe2O3) with mean diameters of 8 nm and 14 nm were previously synthesized by the coprecipitation method. [START_REF] Fresnais | Poly(acrylic acid)-coated iron oxide nanoparticles: Quantitative evaluation of the coating properties and applications for the removal of a pollutant dye[END_REF] The statistical propylacrylamide copolymer bearing phosphonic acid groups (PAmPh) was custom synthesized by Specific Polymers (Montpellier, France). The synthesis was performed by free radical polymerization using AIBN as radical initiator and the details can be found in the work of Graillot et al. [START_REF] Graillot | How to eas-ily adapt cloud points of statistical thermosensitive polyacrylamide-based copolymers knowing reactivity ratios[END_REF] The copolymer is composed by thermosensitive N-n-propylacrylamide monomers (NnPAAm [25999-13-7] -SP43-0-002) and dimethoxyphosphoryl)methyl 2-methylacrylate (MAPC1, [86242-61-7] -SP41-003) monomers in the molar ratio (0.98:0.02), respectively. The copolymer chemical structure is presented in the Fig. S1 (Supporting In-formation). The number-averaged molecular weight of the copolymer is Mn = 49500 g mol -1 with a dispersity of Ð= 2.8, rendering an average of 8 phosphonic acid groups per polymer chain. Phosphate buffered saline (PBS), nitric acid (HNO3), ammonium hydroxide (NH4OH) and Pluronic F-127 were purchased from Sigma-Aldrich. Purified water was obtained with a Milli-Q purification system.

Preparation of thermoresponsive magnetic nanoparticles

The (γ-Fe2O3) nanoparticles were coated exploring the binding affinity of phosphonic acid groups to metal oxide surfaces. [START_REF] Pujari | Covalent Surface Modification of Oxide Surfaces[END_REF] Initially, 0.1 wt% solutions of both the copolymer PAmPh and γ-Fe2O3 nanoparticles were prepared at pH 2.0 (adjusted with HNO3) and filtered with a 0.22 µm pore membrane (Millipore). All the preparation procedure was temperature controlled under 10 °C to avoid the thermal transition and aggregation of the copolymer. The γ-Fe2O3 solution was added dropwise to the copolymer solution under vigorous stirring until reach a mixing volume ratio of 0.5, ensuring enough polymer chains to well cover all the nanoparticles surface. In the sequence, the pH was raised to 7.5 with the addition of NH4OH and the hybrid γ-Fe2O3@PAmPh nanoparticles were dialyzed in 100 kDa tubing membranes (Spectra/PorTM) for four days at 4 °C to remove the excess of non-linked copolymers. The dialyzed nanoparticles were finally centrifuged at 4000 rpm in 100 kDa centrifuging filters (Merck) to reach a final concentration of 0.1 wt% γ-Fe2O3@PAmPh. The colloidal stability of the γ-Fe2O3@PAmPh and their thermal transition were characterized by dynamic light scattering and zeta potential measurements using a Malvern NanoZS Zetasizer instrument.

Fabrication of magnetic cilia

For the preparation of magnetic cilia, 0.005 wt%, 0.01 wt% and 0.05 wt% γ-Fe2O3@PAmPh dispersions were prepared in cold phosphate buffered saline (PBS, pH 7.4, 0.01 M phosphate buffer, 0.0027 M potassium chloride and 0.137 M sodium chloride) and kept refrigerated under 10 °C until usage. 25 µL of the γ-Fe2O3@PAmPh solution were deposited on glass slides containing an adhesive Gene Frame (Abgene) of 1 cm x 1 cm dimensions and 250 µm thickness, and then sealed with a cover slip. The prepared glass slide containing the sample was placed on the center of a 10 cm x 10 cm x 1 cm Ferrite magnet and an identical magnet was placed over it keeping a gap of 0.6 cm. The resulting field is 40 mT in the center of the magnet. The setup was heated to 50 °C for 30 minutes, cooled down to room temperature before removing the sample from the magnetic field. It is noteworthy that the formation of the elongated structures is already observed at temperatures around 37 °C in less than 10 minutes. Higher temperatures and longer times favor a stronger assembly between the nanoparticles, prolonging the cilia lifetime and facilitating their characterization. A schematic representation of the experimental setup and assembly steps for the preparation of cilia is presented in Fig. 1.

Figure 1: Scheme of the experimental steps used for the cilia preparation using thermoresponsive iron oxide nanoparticles γ-Fe2O3@PAmPh (top) and a microscopic illustrative representation of the transition the system undergoes upon heating in the presence of a magnetic field (bottom).

Characterization

The prepared cilia were analyzed using an IX73 Olympus inverted microscope equipped with 40× objective lens coupled with a CCD camera (QImaging, EXi Blue). The images and videos were captured in the phase contrast mode supported by the software Metaview (Universal Imaging) and analyzed using the ImageJ software. The magnetic actuation of the cilia was induced by controlling the position of a permanent Neodymium magnet (0.4 T at the magnet surface) around the sample (3 -6 cm apart). The transmission electron microscopy (TEM) images were obtained on a Jeol-100 CX microscope. The nanoparticle and filament dispersions were deposited on 400 mesh copper grids (Ted Pella) and air dried. Scanning electron microscopy (SEM) analysis were performed at 5K kV using a Zeiss Supra 40 MEB-FEG instrument. For the calculation of cilia persistence lengths (LP ) we imaged several isolated filaments prepared at c = 0.01 wt% and freely adsorbed on glass surfaces. The data was analyzed with MATLAB software (MathWorks Inc.), where the contour of the filaments were traced and the LP values were calculated using the tangent vector correlation function (Eq. 1).

〈cos 𝜃 ',')* 〉 = 𝑒𝑥𝑝 0 1* 2* 3 4 ( 1
)
where θ is the angle between tangent vectors at points s and s+L, by averaging s along the contour. [START_REF] Jiang | Effects of Hfq on the conformation and compaction of DNA[END_REF][START_REF] Kozhuharov | Persistence Length of Poly(vinylamine): Quantitative Image Analysis versus Single Molecule Force Response[END_REF] The cilia robustness against an imposed flux was investigated in a flow cell, prepared by adapting an inlet and outlet channels in both sides of the framed glass slide. The cilia were prepared in the closed cell and afterwards the inlet channel connected to a syringe pump (New Era, NE-1000). A controlled water flux was applied at different rates and the robustness of the cilia analyzed by optical microscopy.

The ability of the magnetic cilia to remotely induce motion of a fluid was investigated. In one experiment an aqueous dispersion of 5 µm silica particles (Kromasil, 100 Å pore size) was injected (flux of 10 µL min -1 ) in the cell containing a fresh prepared cilia (0.005 wt%). Similarly, in a second approach 25 µm emulsion droplets of silicon oil in water (stabilized by Pluronic F-127) were injected over a cilia array (0.005 wt%). Afterwards, the cilia arrays containing the solid particles and oil droplets were actuated using a permanent Neodymium magnet (0.4 T at the magnet surface) in horizontal oscillating movements over the sample (3 -6 cm apart) and simultaneously analyzed in the optical microscope as specified before.

Results and discussion

The thermoresponsive magnetic nanoparticles were prepared using a multiphosphonic acid coating strategy previously established in our group. [START_REF] Chanteau | Electrosteric Enhanced Stability of Functional Sub-10 nm Cerium and Iron Oxide Particles in Cell Culture Medium[END_REF] This method is based on the affinity of the phosphonic acid groups to readily bind to the surface of the iron oxide nanoparticles directing the interaction to form a polymer shell. [START_REF] Grein-Iankovski | Modulating the interfacial properties of magnetic nanoparticles through surface modification with a binary polymer mixture towards stabilization of double emulsions[END_REF] The presence of multiple binding sites along the polymer chain confer a resilient coating and long-term stability to the modified particles. [START_REF] Baldim | Monophosphonic versus Mul-tiphosphonic Acid Based PEGylated Polymers for Functionalization and Stabilization of Metal[END_REF] The prepared γ-Fe2O3@PAmPh presented an average hydrodynamic diameter of 100 nm (PDI = 0.12) and 110 nm (PDI = 0.13) for the samples prepared with 8 nm and 14 nm γ-Fe2O3 cores, respectively (Fig. S2 -Supporting Information). They displayed a negative surface charge at pH values above 2, indicating the presence of non-linked phosphonic acid groups that deprotonate at higher pH values (pKa1 = 2.13, pKa2 = 7.06). 48 At pH 7.4 the zeta potential of γ-Fe2O3@PAmPh aqueous solution is -30 ± 2 mV and when the nanoparticles are dispersed in PBS solution this value drops to -7 ± 1 mV. The addition of salts minimizes the electrostatic repulsion between the nanoparticles, strengthening their assembly upon heating. Besides, the temperature-induced assembly of γ-Fe2O3@PAmPh can be performed in a broad pH range, from 2 -8 in saline media (0.1 -0.2 M).

The propylacrylamide monomers confer the thermoresponsive properties to the copolymer. [START_REF] Graillot | How to eas-ily adapt cloud points of statistical thermosensitive polyacrylamide-based copolymers knowing reactivity ratios[END_REF] The characteristic low critical solution temperature (LCST) transition of this copolymer when immobilized at the γ-Fe2O3 nanoparticles surface is around 25 o C in PBS (Fig. S3 -Supporting Information). Below LCST, the formation of a structured hydration layer around the polymer chains stabilizes the nanoparticles, conferring colloidal stability to the γ-Fe2O3@PAmPh dispersion at low temperature. As the temperature increases above its LCST, this surrounding water network is no longer stable and the hydrophobic inter-actions between the polymer monomers become dominant causing a coil-to-globule phase transition. 49 The collapse of the polymer shell leads to the nanoparticle aggregation and the attachment of the formed filaments to the surface. Their adhesion to glass is promoted by physical adsorption and reinforced by hydrogen bonding and hydrophobic interaction as the polymer collapse upon heating. In addition, the magnetic attraction force pulls the filaments towards the hot surface strengthening their interaction.

Fig. 2 shows electron microscopy images of the system at different stages of the assembly process towards the formation of elongated filaments. Initially, the γ-Fe2O3@PAmPh nanoparticles are well dispersed below the polymer LCST with an average core diameter of 8 nm (Fig. 2a). The observed nanoparticle clusters are a drying artifact. As the system is heated to 37 • C, above the LCST, the higher contrast of the collapsed polymer around the nanoparticles is clearly observed, connecting them into larger aggregates (Fig. 2b). When the heating process is performed concomitant with the application of magnetic field, the preformed clusters dis-playing larger magnetic moments assemble together along the field direction growing into elongated filaments (Fig. 2c). These filaments may present some voids and irregularities along their structure, which probably contribute to their flexibility (Fig. 2d). It is note-worthy that it is possible to form the filaments with both 8 nm or 14 nm iron oxide cores and the ciliated surfaces likewise. However, the cilia results shown later in optical microscopy were prepared using 14 nm nanoparticles because they displayed greater contrast, facilitating their visualization. By changing the concentration of the initial nanoparticle dispersion in the same preparation setup, it is possible to modulate the size of cilia and their coverage density. This is a versatile approach that enables the adjustment of the cilia features according to the required application, to the length scale of the objects to manipulate, to the size of the compartment where they will be inserted, etc. Fig. 3a shows optical microscopy images of the cilia obtained from 0.005 wt%, 0.01 wt% and 0.05 wt% γ-Fe2O3@PAmPh. These images clearly show a sequential growth of the filaments as the nanoparticle concentration increases, as well as the filament crowding on the surface. The insets in the pictures are a top view of the filaments in upright position, showing the difference in the number of attaching spots resulting from a higher coverage density at higher concentrations. We estimate an average increase on the surface coverage density from 0.02 to 0.04 filament/µm 2 when the nanoparticle concentration increased from 0.005 to 0.01 wt% and reached up to 0.1 filament/µm 2 at the highest concentration 0.05 wt%. Estimates of the cilia lengths and thicknesses were calculated by measuring 100 -200 individual cilium and these values are presented in Figs. 3b and3c, respectively. These estimates show an average increase of 130 % and 350 % in the length and 26 % and 45 % in the thickness of the produced filaments when their concentration increased by 2x and 10x, respectively. The average length of 0.05 wt% might be slightly underestimated due to difficulties to focus the entire filaments given their length and crowding. Therefore, these results demonstrate the possibility to obtain cilia with very high aspect ratios, up to 100 in these conditions. The achievable density and aspect ratio ranges obtained in our work are very significant comparing to other magnetic cilia structures reported so far in the literature. Most of the coverage densities obtained for magnetic cilia were below 0.02 filament/µm 2 . [START_REF] Singh | Synthesis of Flexible Magnetic Nanowires of Permanently Linked Accepted at Journal of Physical Chemistry C Friday[END_REF][START_REF] Evans | Magnetically Actuated Nanorod Arrays as Biomimetic Cilia[END_REF][START_REF] Timonen | A Facile Template-Free Approach to Magnetodriven, Multifunctional Artificial Cilia[END_REF][START_REF] Babataheri | Tethered fleximags as artificial cilia[END_REF] In contrast, Luo et al. [START_REF] Luo | Active Periodic Magnetic Nanos-tructures with High Aspect Ratio and Ultrahigh Pillar Density[END_REF] obtained a density of 0.25 filament/µm 2 for templated cilia with aspect ratios up to 11 and Benkoski et al. [START_REF] Benkoski | Dipolar assembly of ferromagnetic nanoparticles into magnetically driven artificial cilia[END_REF] prepared 10 µm long cilia with a remarkable aspect ratio of 435 and densities up to 1 filament/µm 2 . In the present work, we were able to arrange up to 0.1 filament/µm 2 , with lengths between 10 -100 µm and aspect ratios up to 100, which are among the highest obtained for magnetic cilia within this lenghtscale. [START_REF] Singh | Synthesis of Flexible Magnetic Nanowires of Permanently Linked Accepted at Journal of Physical Chemistry C Friday[END_REF][START_REF] Evans | Magnetically Actuated Nanorod Arrays as Biomimetic Cilia[END_REF][START_REF] Benkoski | Dipolar assembly of ferromagnetic nanoparticles into magnetically driven artificial cilia[END_REF][START_REF] Luo | Active Periodic Magnetic Nanos-tructures with High Aspect Ratio and Ultrahigh Pillar Density[END_REF] High aspect ratios and high coverage densities usually improve the performance and amplitude of the cilia actuation, making them to behave as a continuous array with high compliance. [START_REF] Luo | Active Periodic Magnetic Nanos-tructures with High Aspect Ratio and Ultrahigh Pillar Density[END_REF] These cilia quickly react to an external magnetic stimulus. Their motion can be easily driven ac-cording to the magnetic field direction as can be observed in the Movies 1, 2 and 3 (provided as Supplementary Material) and summarized in Fig. 4. In this case, a permanent neodymium magnet (0.4 T at the magnet surface) was approached to the samples with a gentle oscillating movement, which the cilia promptly followed. As soon as the external field is removed the system relaxes, the cilia structures soften, slowly bend and settle randomly as shown in Movie 4. To estimate the mechanical properties of the cilia we determined their persistence length (LP), which is a characteristic length scale related to the bending rigidity of the material. 50 Fig. 5 shows a representative analysis of an isolated filament (Fig. 5a) with the experimental data and fitted tangent correlation function according to Equation 1 (Fig. 5b). The inverse of the exponential decay results in the LP value. From tracing 36 individual filaments we estimate an average LP of 7.6 µm ± 2.9 (Fig. 5c), within the same range of values observed in biological actin filaments, for example. 51 The flexibility of our magnetic cilia originates from the polymeric junctions in between the nanoparticles. Besides, the assembly driving force via hydrophobic attraction also plays a role. In contrast, magnetic wires formed by electrostatic induced assembly presented much stiffer structures with LP values up to 1 m. 52 Analyzing the filaments tip displacement relative to their base in rotating movements (Movie 5 and Movie 6) clearly demonstrates their wide range of bending amplitudes in all directions.

Accepted at Journal of Physical Chemistry C Friday, November 6, 2020

Flexibility and high bending amplitude are important for the purpose of mimicking the biological structures due to their intrinsic capability of generating metachronal waves. In our case, flexible structures were also observed in the denser sample with high aspect ratio cilia, as emphasized in the Movie 7. The temperature induced assembly of γ-Fe2O3@PAmPh nanoparticles is a reversible process, although it presents a significant hysteresis on heating/cooling cycles depending on the magnitude of the stimulus employed, with both temperature and time. These cilia, when assembled at 50 • C for 30 minutes, remain functional for a couple of hours after the system is cooled to room temperature. Any movement restriction related to increasing rigidity that could signal flexural fatigue was observed after several cycles of excitation. However, we observed a significant disintegration of the filaments after about 24 hours. Still, their lifetime can be prolonged if the system is maintained above its LCST after preparation. When kept in this condition the cilia remained active for at least 24 hours.

Despite their flexibility, this system can stand the flow of liquids. It is possible to pump water or aqueous solutions through the cilia, for instance, a flux of 10 µL min -1 . We observed that higher fluxes can cause the entanglement of the cilia and tipping over due to their high aspect ratio. Cilia with a U-shaped geometry are observed in some cases, when the filaments bend and adhere to the surface from their tip extremity. The cilia display leaching out resistance against a flux of 100 µL/min -1 for 30 minutes, although significant entanglements and surface adherence were observed in this case. Even though these systems are not permanent, their versatile preparation method compatible with biological conditions is a remarkable advantage, enabling one to envisage the cilia formation in different devices, potentially among living cells and the scaling up of the preparation to larger coverage areas. Also, preliminary experimental evidences confirmed the formation of similar cilia over a metallic film of gold, indicating the possibility to explore different substrates. Using this method, by simply injecting the initial nanoparticles dispersion inside the compartment and locally applying a homogeneous magnetic field and heating, the cilia are promptly formed in a few minutes and are ready for actuation.

In addition, the cilia array was tested for its capacity to impart motion. To demonstrate this, in one experiment a dispersion of 5 µm silica particles and in another experiment an emulsion of 25 µm silicon oil droplets in water were injected over the cilia array formed by 0.05 wt% γ-Fe2O3@PAmPh.

The cilia arrays were actuated by an oscillating magnetic field and the imparted motions of the solid particles and oil droplets were monitored by optical microscopy. Exemplary Movie 8 shows that cilia move a silica particle in their direction of motion. Similarly, Movie 9 shows the same effect for a silicon oil droplet. However, for an effective displacement, one should optimize the conditions to avoid adhesion to the array.

Conclusions

In summary, we propose an original approach for the preparation of magnetic cilia based on the temperature induced assembly of iron oxide nanoparticles at biological compatible conditions. This is a versatile template-free methodology that offers the possibility to easily tune the size and coverage density of the cilia by varying the concentration of the nanoparticle dispersion. Structures with lengths between 10 -100 µm and aspect ratios up to 100 were obtained in a dense array of around 0.1 filament/µm 2 , among the highest parameters regarding currently reported similar systems. The cilia are obtained in a few minutes and are reproducible and rather robust towards changes in environmental conditions and flux. The structures display high flexibility with persistence lengths around 8 µm and large bending amplitude when actuated by a magnetic field, being able to potentially induce particle motion. This simple protocol could be used over other substrates such as metallic gold, providing a versatile methodology for preparation of responsive magnetic cilia for varied purposes

Figure 2 :

 2 Figure 2: Steps of the assembly process towards the formation of filaments. TEM images of (a) magnetic γ-Fe2O3@PAmPh dispersion below LCST, (b) γ-Fe2O3@PAmPhh heated to 37°C, (c) γ-Fe2O3@PAmPh aligned and assembled in a magnetic field during heating, Scale bars 100 nm. (d) SEM image of a filament exhibiting local voids in the structure, Scale bar300 nm.

Figure 3 :

 3 Figure 3: Effect of nanoparticles concentration on the dimensions of the formed cilia. (a) Optical microscopy images of the cilia prepared from 0.005 wt%, 0.01 wt% and 0.05 wt% γ-Fe2O3@PAmPh. Scale bars 20 µm. The insets show a top of the filaments in upright position. Measured cilia size in each case: (b) Cilia length distribution, (c) Average cilia thickness (diameter).

Figure 4 :

 4 Figure 4: Sequential frames taken from the movies 1, 2 and 3 showing the motion of the cilia in response to the movement of an external magnet. From top to bottom: cilia obtained from 0.005 wt%, 0.01 wt% and 0.05 wt% γ-Fe2O3@PAmPh, respectively. Scale bars 20 µm.

Figure 5 :

 5 Figure 5: Analysis of the persistence length of the magnetic filaments. (a) Optical microscopy image of an isolated filament adsorbed on glass used to trace its contour length. Scale bar 10 µm. (b) A representative plot of cos θs,s+L as a function of the separation L along the contour and the respective exponential fitting. (c) Persistence length distribution obtained from the fitting of individual magnetic filaments.

Acknowledgement

The authors thank the financial support provided by the São Paulo Research Foundation (FAPESP, grant numbers 2015-25406-5, 2017/04571-3 and 2018/16330-3), ANR (Agence Nationale de la Recherche) and CGI (Commissariat à l'Investissement d'Avenir) through Labex SEAM (Science and Engineering for Advanced Materials and devices) ANR 11 LABX 086, ANR 11 IDEX 05 02. We acknowledge the ImagoSeine facility (Jacques Monod Institute, Paris, France), and the France BioImaging infra-

Supporting Information Available

The following files are available free of charge.

• Supporting information: Additional characterization results and detailed captions of the movie files.

Graphical TOC Entry


Samson Chota
email: samson.chota@googlemail.com

Phillipe Marque

Rufin Vanrullen

Occipital Alpha-TMS causally modulates Temporal Order Judgements: Evidence for discrete temporal windows in vision Abbreviated Title: Alpha-TMS modulates TOJ

Recent advances in neuroscience have challenged the view of conscious visual perception as a continuous process. Behavioral performance, reaction times and some visual illusions all undergo periodic fluctuations that can be traced back to oscillatory activity in the brain. These findings have given rise to the idea of a discrete sampling mechanism in the visual system. In this study we seek to investigate the causal relationship between occipital alpha oscillations and Temporal Order Judgements using neural entrainment via rhythmic TMS. We find that certain phases of the entrained oscillation facilitate temporal order perception of two visual stimuli, whereas others hinder it. Our findings support the idea that the visual system periodically compresses information into discrete packages within which temporal order information is lost.

Significance Statement

Correlational evidence for a relationship between brain states and perception is abundant. However, in order to truly understand the causal relationship between the two, we need to be able to manipulate one and observe changes in the other. Neural entrainment via TMS serves as a valuable tool to interfere with cortical rhythms and observe changes in perception. Here, using rhythmic TMS-pulses at 10 Hz, we investigate the effect of the phase of entrained oscillations on performance in a temporal order judgement (TOJ) task. We observe that the causally entrained oscillation indeed modulates time perception rhythmically. On top of previous work on discrete perception we were able to 1. causally influence brain rhythms in a far more direct fashion using TMS, and 2. show that previous work on discrete perception cannot simply be explained by rhythmic fluctuations in visibility. In conclusion our findings support the long discussed idea that the temporal organization of visual processing is discrete rather than continuous, and is causally modulated by cortical rhythms. To our knowledge, this is the first study providing causal evidence via TMS for an endogenous periodic modulation of time perception.

Introduction

Among neural oscillations, the occipital alpha rhythm is the most easily observed one [START_REF] Berger | Über das Elektrenkephalogramm des Menschen[END_REF].

Since its discovery, it has been implicated in a vast number of cognitive functions such as attention, memory and inhibition (Bonnefond & Jensen, 2012;[START_REF] Foxe | The Role of Alpha-Band Brain Oscillations as a Sensory Suppression Mechanism during Selective Attention[END_REF][START_REF] Jensen | An oscillatory mechanism for prioritizing salient unattended stimuli[END_REF][START_REF] Jensen | Shaping Functional Architecture by Oscillatory Alpha Activity: Gating by Inhibition[END_REF][START_REF] Jokisch | Modulation of Gamma and Alpha Activity during a Working Memory Task Engaging the Dorsal or Ventral Stream[END_REF][START_REF] Klimesch | EEG alpha and theta oscillations reflect cognitive and memory performance: A review and analysis[END_REF][START_REF] Klimesch | α-band oscillations, attention, and controlled access to stored information[END_REF][START_REF] Klimesch | EEG alpha oscillations: The inhibition-timing hypothesis[END_REF][START_REF] Tuladhar | Parieto-occipital sources account for the increase in alpha activity with working memory load[END_REF]. A large body of literature investigates the effects of alpha amplitude on perception, linking high alpha power to high inhibition. More specifically, alpha power has been shown to increase in task irrelevant areas, whereas it decreases in task relevant areas, demonstrating its role in spatial attention [START_REF] Foxe | The Role of Alpha-Band Brain Oscillations as a Sensory Suppression Mechanism during Selective Attention[END_REF][START_REF] Kelly | Increases in Alpha Oscillatory Power Reflect an Active Retinotopic Mechanism for Distracter Suppression During Sustained Visuospatial Attention[END_REF][START_REF] Sauseng | A shift of visual spatial attention is selectively associated with human EEG alpha activity[END_REF]. Alpha oscillations play an even more dynamic role in the context of temporal attention, decreasing/increasing its amplitude at the moment when a target/distractor is expected [START_REF] Rohenkohl | Alpha Oscillations Related to Anticipatory Attention Follow Temporal Expectations[END_REF][START_REF] Van Diepen | Attention and temporal expectations modulate power, not phase, of ongoing alpha oscillations[END_REF]. On an even finer temporal scale we find that the phase of ongoing oscillations in the 5-15 Hz range influences perception. Busch et al. and Mathewson et al. (2009) demonstrated that the phase of occipital alpha oscillations is predictive of stimulus detection performance, implying that excitability in the visual cortex oscillates at around 10 Hz [START_REF] Busch | The phase of ongoing EEG oscillations predicts visual perception[END_REF][START_REF] Mathewson | To See or Not to See: Prestimulus α Phase Predicts Visual Awareness[END_REF]. These findings have been replicated several times using rhythmic entrainment at ~10 Hz via periodic visual stimuli or alpha-TMS [START_REF] Dugué | Transcranial Magnetic Stimulation Reveals Intrinsic Perceptual and Attentional Rhythms[END_REF]Mathewson et al., 2010a;[START_REF] Romei | On the Role of Prestimulus Alpha Rhythms over Occipito-Parietal Areas in Visual Input Regulation: Correlation or Causation[END_REF][START_REF] Spaak | Local Entrainment of Alpha Oscillations by Visual Stimuli Causes Cyclic Modulation of Perception[END_REF][START_REF] Thut | Rhythmic TMS Causes Local Entrainment of Natural Oscillatory Signatures[END_REF].

Many questions however remain. What is the exact relationship between rhythmic activity and perception? Are these periodicities mere changes in excitability, leading to fluctuations in detection probabilities or perceived intensities? Or do they impose discrete, non-overlapping windows, quantizing incoming visual information, akin to the snapshots of a camera? The former can be thought of as a "soft" version of periodic temporal perception whereas the latter can be thought of as a stricter "hard version" of periodic temporal perception.

The idea of a strictly discrete sampling mechanism (or "hard" version of discrete temporal perception (DTP)) states that the brain periodically divides the visual input into discrete windows or "perceptual moments" [START_REF] Busch | The phase of ongoing EEG oscillations predicts visual perception[END_REF][START_REF] Haegens | α-Oscillations in the monkey sensorimotor network influence discrimination performance by rhythmical inhibition of neuronal spiking[END_REF][START_REF] Lőrincz | Temporal Framing of Thalamic Relay-Mode Firing by Phasic Inhibition during the Alpha Rhythm[END_REF][START_REF] Samaha | The Speed of Alpha-Band Oscillations Predicts the Temporal Resolution of Visual Perception[END_REF][START_REF] Vanrullen | Is perception discrete or continuous? Trends in Cognitive Sciences[END_REF][START_REF] Vijayan | Thalamic model of awake alpha oscillations and implications for stimulus processing[END_REF]. Latterly the idea has gained support by psychophysiological and electrophysiological studies linking it to the occipital alpha rhythm [START_REF] Vanrullen | Perceptual Cycles[END_REF]. Recently it was shown that participant's individual alpha peak frequencies are predictive of performance in a two-flash fusion task [START_REF] Samaha | The Speed of Alpha-Band Oscillations Predicts the Temporal Resolution of Visual Perception[END_REF]. Following these lines it was demonstrated that visuo-auditory entrainment at the individual alpha frequency ± 2 Hz could facilitate or impair performance in a temporal segregation/integration task [START_REF] Ronconi | Alpha-band sensory entrainment alters the duration of temporal windows in visual perception[END_REF].

Further evidence comes from studies investigating the flash-lag effect (FLE), a visual illusion that has been suggested to arise from discrete sampling in the visual system [START_REF] Chakravarthi | Conscious updating is a rhythmic process[END_REF][START_REF] Schneider | The Flash-Lag, Fröhlich and Related Motion Illusions Are Natural Consequences of Discrete Sampling in the Visual System[END_REF]. We demonstrated that visual entrainment at 10 Hz leads to a periodic modulation of temporal perception in the FLE [START_REF] Chota | Visual Entrainment at 10 Hz Causes Periodic Modulation of the Flash Lag Illusion[END_REF]. A key finding in the studies described above is that there is not only a fluctuation of perception (detection probabilities, perceived intensities), which is predicted by the soft version of DTP, but also a fluctuation of time perception itself (relative timing, temporal integration/segregation) which is the key prediction of the hard version of DTP. Given the findings described above we propose that the visual system discretely samples the visual scene at a ~10 Hz rhythm, analogous to the "hard" version of periodic perception [START_REF] Vanrullen | Perceptual Cycles[END_REF]. To test this hypothesis we utilized TMS to manipulate the occipital alpha rhythm and probed temporal order judgment (TOJ) at different phases of the entrained oscillation.

Materials and Methods

Participants

25 participants (aged 18-31, 9 females) with normal or corrected to normal vision enrolled in the experiment. 7 participants had to be excluded during the first phosphene localization session because of their inability to see TMS-induced phosphenes, leaving 18 participants for the complete experiment and the final analysis. Note that this number of subjects excluded for this reason is very common in the TMS literature. Dropout rates of 40% due to inability to perceive phosphenes (at medial stimulation intensities) are commonly reported. Informed consent forms were signed before the experiment. The experiment was carried out in accordance with the protocol approved by the Centre National de la Recherché Scientifique ethical committee and followed the Code of Ethics of the World Medical Association (Declaration of Helsinki).

TMS apparatus, parameters and phosphene localization

The TMS stimulation was performed using a Magstim Rapid 2 stimulator of 3.5 tesla, producing a biphasic current. At the beginning of the first session participants were tested on their ability to detect TMS-induced phosphenes. TMS stimulation was initiated at 55% of the maximum stimulator output applying 7 pulses at 20 Hz over occipital cortex. At the beginning of each phosphene localization trial participants were asked to fixate a central cross. Participants closed their eyes without changing the direction of their gaze. TMS was applied, participants opened their eyes and used the mouse to draw the outline and location of the perceived phosphene onto the screen. If no phosphene was perceived the coil position or stimulation intensity were changed manually and the procedure was repeated.

When a reliable phosphene was found the coil was fixated using an armed pedestal. We successfully elicited phosphenes in 18 out of 25 subject in the right (N = 9) or left (N = 9) visual field (Figure 1). Later, we used the phosphene location to place stimuli and scale them according to the cortical magnification factor (see section Stimuli below). Using a two-down one-up staircase procedure, we then determined the individual phosphene perception intensity threshold. Mean phosphene perception intensity threshold was 54.3% of maximum stimulator output. During the experimental TMS sessions we adjusted the TMS intensity to 75% of the individual phosphene perception intensity threshold (no subject reported perceiving a phosphene during the test trials).

Stimuli

Stimuli were presented at a distance of 57 cm with a LCD display (1920 x 1080 resolution, 120 Hz refresh rate) using the Psychophysics Toolbox [START_REF] Brainard | The Psychophysics Toolbox[END_REF] running in MATLAB (MathWorks).

Stimuli consisted of a central fixation cross (diameter = 0.3°), a square placeholder (black, 4°*4°), Gabor patches (Stim A and Stim B) of two orientations (45° and 135°, diameter = 3°, spatial frequency = 1.076 cycles/degree) as well as a mask in the form of a plaid (diameter = 3°), (Figure 2A). We included a masking stimulus in order to prevent subjects from using the persistence or the afterimage of Stimulus B to solve the TOJ task. Stimulus A will always be referring to the first stimulus of the sequence, whereas Stimulus B or "target" will be referring to the second stimulus of the sequence, irrespective of their orientation. During the task Stimulus A and B were presented in quick succession and participants gave Temporal Order Judgements by identifying the orientation of stimulus B.

Additionally we included a single stimulus condition where only one stimulus (Stimulus A or Stimulus B) was presented. Participants reported these trials using a third button. The single stimulus condition was included in order to control for the possibility that TMS entrainment could lead to a significant decrease in stimulus visibility for one of the two stimuli (A or B). In that case we would expect an increase in single stimulus reports. We will show later in the behavioral results that this was not the case.

The experiment consisted of a training condition and a TMS condition. We included a rather extensive training session in order to minimize any potential practice effects that could influence our TMS sessions and to reduce potential biases towards stimulus visibility, as we will explain later. The training condition was run with the parameters described above. The location of placeholder and stimulus sequence was fixed in the lower right or left visual field with equal probability (eccentricity 7°). The stimulus parameters in the TMS condition were identical to the training condition except for the size and position of the stimuli and placeholder which were adjusted based on the phosphene location acquired during the phosphene localization described in the previous paragraph. The location of the stimuli was chosen to be within the reported phosphene area, and as close to the position of the training stimuli as possible (Figure 1). This ensured that stimuli in the TMS condition were not presented further than 7° visual angle from the position of the training stimuli in 96% of trials to keep training and TMS conditions comparable. The stimuli were scaled based on their eccentricity according to cortical magnification [START_REF] Horton | The Representation of the Visual Field in Human Striate Cortex: A Revision of the Classic Holmes Map[END_REF] in order to match the cortical representation of the stimulus to the actual cortical stimulation site during TMS. For example, the stimulus diameter measured 3° at 7° eccentricity and 3.78° at 10° of eccentricity. The contralateral stimulus position was determined by flipping the ipsilateral position around the central y-axis. Left and right stimulus trials were matched pseudo-randomly. Stimuli were presented on a gray background.

We modulated the contrast of our stimuli in a subset of trials. This was done for two reasons. First of all, it allowed us to control for the potential effects of TMS on the visibility of the stimuli. We hypothesized that any detrimental effects of TMS on visibility should be maximal when target contrast is minimal. More specifically, this potential confound should manifest as a reduction in performance for stimuli that were presented on the hemisphere contralateral to TMS, with high contrast stimuli being least and low contrast stimuli being most affected. As we will show later in the Results section, this was not the case. Second, by having stimuli vary in contrast, we aimed to discourage participants from basing their TOJ judgments on visibility (e.g. always judging the most visible stimulus as occurring first or last), by making stimulus visibility inconsistent across trials while at the same time providing feedback. Therefore, even if the entrainment oscillatory phase should affect visibility, participants are actively encouraged to neglect visibility cues and base their decision purely on the perceived temporal order. For this second reason we decided to include several intermediate contrast conditions to better simulate perceptual ambiguity and increase the sense of unreliability of stimulus visibility. 5 Contrast conditions were used (Figure 2C indicates the hemisphere of stimulation. The mouse was used by the subject to draw the outline of the perceived phosphene on the screen. Stimuli (here represented as superimposed white disks) were positioned inside the phosphene regions and scaled according to the cortical magnification factor [START_REF] Horton | The Representation of the Visual Field in Human Striate Cortex: A Revision of the Classic Holmes Map[END_REF]. Note that due to slight changes in head position, the location of the phosphenes could change during the experiment. We re-localized phosphenes and adjusted the stimulus position at the beginning of every block.] On the first session only, participants performed an extensive training consisting of 253 trials without TMS, with feedback and with a predefined stimulus location. Afterwards the main experiment was performed consisting of 5 repetitions of the Block sequence indicated in the figure. These 5 repetitions were repeated on session 2 and 3. C. In order to control for an effect of TMS on the visibility of the stimuli we used 5 different contrast conditions. In a subset of trials the contrast of the stimuli in the sequence was separately reduced to either 10%, 25%, 75% or 90%. The contrast of the Mask was identical in all conditions. Additionally we included a single stimulus condition where one stimulus was omitted.] Afterwards subjects performed the main experimental procedure, which was repeated on session 2 and session 3. In the main experimental procedure participants performed 19 blocks ( 15 (normal contrast), Mask] (See Figure 2C). During the phosphene localization and the experiment, the participants head was fixed between a chinrest and the TMS coil, leading to a stable position. In total, a maximum of 2215 TMS pulses were administered per session.

Data Analysis

We analyzed the data collected during the training blocks and the TMS-blocks separately. The 11 pretraining blocks at the beginning of session 1, which were included to prevent visibility biases, were not included in the analysis because of potential practice effects. Only training blocks that were collected during the main experimental procedure (interleaved with the TMS blocks) are included in this analysis (3 × 5 blocks of 23 trials per subject).

Training Blocks mean performance

Due to the significantly smaller number of trials collected in the training blocks compared to the TMSblocks we did not analyze the time course of TOJ performance during training but looked at the overall performance for all 6 conditions (normal contrast condition, 4 low contrast conditions, single stimulus condition). The 4 low contrast conditions (Figure 2C) were merged into two groups based on the contrast of the stimulus B (target), separating them into a low target contrast group (Stimulus B contrast 10% and 25%) and high target contrast group (Stimulus B contrast (75% and 90%). Note that the major aim of including several fine grained contrast conditions in the first place was to counteract potential visibility biases, by preventing subjects from relying on visibility instead of TOJ. The separation based on Stimulus B contrast was done to control for possible effects of TMS on Stimulus B (target) visibility which should be maximal for the low contrast stimuli (for which orientation was reported) in the low target contrast group. Mean performance (Hits/Misses) was averaged within each subject for 1. normal contrast, 2. low target contrast (low contrast 10%, low contrast 25%), 3. high target contrast (low contrast 75%, low contrast 90%) and 4. single stimulus conditions separately. For the low contrast conditions we acquired 41.9 trials (low target contrast) and 42.2 trials (high target contrast) on average per subject. For the normal contrast and the single stimulus conditions on average 81.3 and 29.5 trials were collected per subject. The behavioral performance for each condition during training was quantified using a repeated measures ANOVA.

TMS Blocks

Analysis of mean performance

The analysis of the mean performance for the 6 conditions (normal contrast condition, 4 low contrast conditions, single stimulus condition) was done similarly to the analysis in the previous section by merging low contrast conditions into 2 groups (low target contrast, high target contrast). Mean performance per subject in the resulting 4 conditions and for each visual field (contraTMS and ipsiTMS) was analyzed using a repeated measures ANOVA.

Analysis of TOJ time-series

For our main results, the effect of TMS on subsequent TOJ-performance was analyzed as a function of the delay between the last TMS-pulse and presentation of the first stimulus of the sequence. Since the other contrast conditions only served to ensure that participants engaged in unbiased TOJ judgments only the normal contrast condition (66.3% of trials) was included in this analysis. We removed all responses where subjects erroneously reported single stimuli (5.4%), counting only left/right responses (making chance performance 50%) .We probed TOJ performance at 9 time points (SOA's) after TMS (25 ms, 41.7 ms, 58.3 ms, 75 ms, 91.7 ms, 108.3 ms, 125 ms, 141.7 ms, 158.3 ms). On average 712.5 trials (24.2 SEM) were collected per subject. Performance (Hits/Total number of trials) was averaged within each subject at each of 9 SOA's for stimuli presented contralateral and ipsilateral to TMS respectively. The resulting time series were normalized by subtracting the mean and averaged over subjects, resulting in a grand average contralateral (contraTMS) and ipsilateral (IpsiTMS) time series.

In an additional analysis the individual 133 ms long TOJ time-series were subtracted on a subject by subject basis in order to calculate the difference waves between the two conditions. These difference waves were averaged resulting in the grand average difference wave (contraTMS minus ipsiTMS). Time-series were zero-padded to a length of 6 times the original window length (6*133.3 ms) and analyzed in the frequency domain using FFT (frequency resolution 1.1 Hz). 9 SOA's at 60 Hz allowed for a Nyquist frequency of 30 Hz. The complex FFT coefficients were squared to obtain oscillatory power at each frequency. To statistically test if the time-series contain significant oscillatory power we calculated 1.000.000 surrogates by shuffling the SOA-labels between trials for every subject, and repeating all analysis steps for each surrogate. The original power-spectrum was then compared to the surrogate distribution and p-values were corrected for multiple comparisons using the False Discovery Rate. The FFT revealed a peak at 10 Hz for contraTMS and a peak at 7.8 Hz for the ipsiTMS condition. For the phase analysis, we therefore decided to extract individual phase angles from the center frequency 8.9 Hz component of the FFT of the down-sampled and normalized contraTMS and ipsiTMS time-courses as well as the contraTMS minus ipsiTMS difference wave. Individual contraTMS and ipsiTMS phase angles were subtracted (contra minus ipsi, pairwise subtraction) to investigate the phase relationship in individuals. Rayleigh's test for non-uniformity was used to statistically test if individual phases were significantly coherent.

Results

In this study we seek to provide causal evidence for the hard theory of discrete perception. Specifically we aim to show that discrete perception entails a periodic compression of time information. Our hypothesis therefore states that within a perceptual moment, perception of the temporal order of events is impaired. To test this hypothesis we entrained participants' alpha oscillations using 10 Hz-TMS over early visual areas. We probed TOJ performance, an index of perception of relative timing, at different phases of the entrained oscillation after stimulation. A significant oscillatory component at 10 Hz at the entrained location (as measured by a frequency analysis on the average TOJ time-course) would suggest a rhythmic modulation of time perception.

Mean performance and low contrast control conditions

Mean performance in the normal and low contrast conditions was compared between Training blocks (no-TMS) and TMS blocks. During Training the mean performance across subjects and visual fields was 63.14% (±3.5% SEM) for the normal condition, 56.4% (±4.4% SEM) for the low target contrast condition, 63.1% (±3.4% SEM) for the high target contrast condition and 49.9% (±6.6% SEM) for the single stimulus condition. In the TMS blocks the mean TOJ performance across observers in the normal contrast condition was 64.4% (± 2.6% SEM) for stimuli contralateral and 62.4% (± 2.5% SEM) for stimuli ipsilateral to the cortical entrainment site. For the single stimulus condition performance was 54.7% (± 5.8% SEM) for stimuli contralateral and 53.3% (±7.1% SEM) for stimuli ipsilateral to the cortical stimulation site. In the low target contrast condition average performance was 63.6% (±3.3% SEM) for the contraTMS condition and 57.4% (±3.7% SEM) for the ipsiTMS condition. Last, in the high target contrast condition performance was 65.8% (±3% SEM) for the contraTMS and 62.1% (±1.8% SEM) for the ipsiTMS condition.

The proportion of "single-stimulus" responses is an indicator of subjects' ability to discern the presence of two stimuli, and therefore to perform genuine temporal order judgments rather than base their responses on the most visible stimulus. We calculated d' by comparing the proportion of singlestimulus responses in the single-stimulus condition (hits: 51.9%) to the proportion of single-stimulus responses in the normal contrast condition (false positives: 5.4%). Sensitivity was d' = 1.7 indicating that participants were well able to differentiate between 2 stimuli and 1 stimulus conditions. Furthermore, the single stimulus report rate of 5.4% in the normal contrast condition indicates that participants could perceive the 2 stimuli in the vast majority (94.6%) of normal contrast trials, and suggests that TMS-induced performance fluctuations stem from fluctuations in temporal order perception, rather than stimulus detection.

To reinforce this conclusion, both TMS blocks and Training blocks were analyzed using a repeated measures ANOVA with factors TMS (TMS versus Training), hemisphere (contra versus ipsilateral to TMS) and contrast (normal, low target contrast, high target contrast, single stimulus). We were particularly interested in verifying that any possible TMS-induced changes in TOJ performance were not mediated by a modulation of the visibility of the stimuli (and specifically, the target stimulus), as this could have been a confounding factor. We hypothesized that if TMS had a detrimental effect on stimulus visibility, this should be reflected in average performance differences when comparing TMS and Training (no-TMS) trials. Furthermore, these differences should be even more pronounced in low contrast conditions, where the target visibility is closer to the visibility threshold. The repeated measures ANOVA revealed a main effect of hemisphere (F(1,17) = 7.6, p = 0.013) but not of TMS (p = 0.38) or contrast (p = 0.1). Post hoc tests revealed significantly higher performance in the contralateral compared to the ipsilateral condition (p = 0.01), in both visual fields for TMS and Training conditions. The increased contralateral performance might be the result of a general attentional bias towards the hemisphere where the phosphene was located, irrespective of TMS stimulation. Most importantly we did not find an interaction effect between factors TMS and hemisphere (p = 0.55) or TMS, hemisphere and contrast (p = 0.73) speaking against the possibility that TMS might influence target visibility. Finally we also investigated the relative number of single stimulus responses for all conditions. We hypothesized that if TMS leads to an occlusion of a single stimulus this should be apparent in an increase in the ratio of single-stimulus responses. Moreover this should especially be the case for stimuli presented contralateral to TMS. The repeated measures ANOVA revealed a main effect of contrast (F(3,51) = 71.1, p < 0.005) but not of TMS (p = 0.12) or hemisphere (p = 0.69). Post hoc tests revealed significantly different ratios of single stimulus reports between all contrast conditions (Normal contrast: 5.4%, high target contrast: 10.9%, low target contrast: 28.8%, single stimulus condition: 51.9%, p<0.05 respectively). This finding comes as no surprise and shows that our contrast manipulation successfully created distinct levels of target visibility. Importantly however no interaction effect between TMS and hemisphere (p = 0.2), TMS and contrast (p = 0.73) or TMS, contrast and hemisphere (p = 0.1) was found, indicating that TMS did not lead to a higher number of single stimulus responses. To avoid confusion, we would like to mention again that, although an increase in single stimulus responses should lead to a decrease in overall performance, the results of both ANOVA's are not contradictory, since in the first ANOVA the singlestimulus reports were removed in all but the single stimulus condition.

We interpret the above presented findings as evidence that TMS did not have a general, timeunspecific effect on target visibility or detection, which could have indirectly led to a modulation of TOJ performance, but rather modulated perceived relative timing of the stimuli.

α-TMS leads to periodic modulation of TOJ performance

In order to verify that TOJ performance was rhythmically modulated by α-TMS we calculated the average TOJ time-series over individuals. This was done by calculating the average performance for each of the 9 SOA's. Performance was analyzed separately for sequences presented contralateral (contraTMS) and ipsilateral (ipsiTMS) to α-TMS. Only normal contrast trials (66.3% of all trials) were included in this analysis, in order to discard any possible influence of contrast differences on stimulus visibility. For this analysis we excluded trials in which participants reported only a single stimulus: when both stimuli are visible, we can reasonably assume that subjects' reports reflect their perceived temporal order, as per the task instructions. TOJ time-series were normalized by subtracting the individual mean before applying the FFT. Figure 3A shows the original, un-normalized timeseries. Initial inspection of the time course for contraTMS indicates a strong oscillation in the TOJ performance lasting for more than 158 ms. To quantify this effect we performed a frequency analysis on the average TOJ-time -series. The resulting power spectrum revealed a dominant oscillation at 10 Hz (Figure 3D). For statistical validation of this peak we created 1.000.000 surrogates by shuffling the 9 SOA-bin labels within subjects and recalculated the power spectrum of the resulting TOJ time series. P-values were computed as the percentile of the mean power values within the bootstrapping distribution. This allowed us to test the null-hypothesis that the power spectrum of the average TOJ time-series does not show a peak at a specific frequency. The TOJ time-series power at 10 Hz was significantly higher compared to the surrogate distribution (Figure 3D, 10 Hz: p = 0.00006, FDR corrected). We analyzed the ipsiTMS TOJ time-series in an identical fashion. Initial inspection indicated a slightly weaker oscillation peaking at a lower frequency of 8 Hz (Figure 3B). The frequency analysis and statistical analysis of the ipsiTMS time-series showed significantly more power compared to the surrogate distribution (Figure 3E). Power peaked at 8 Hz (p = 0.0039, FDR corrected) but was still significant at the entrainment frequency of 10 Hz (p = 0.015, FDR corrected).

To test if the oscillation in the ipsiTMS time-series is caused by a non-specific effect of TMS on both hemispheres, we tested whether oscillations in contra and ipsilateral TOJ time-series were consistent in phase. We therefore subtracted ipsiTMS time-series from the contraTMS time-series for each subject individually. Should both fluctuations in the time-series be caused by the same non-specific effect of TMS they should cancel out and the resulting contraTMS minus ipsiTMS time-series should show reduced amplitude. On the contrary, the resulting difference wave showed markedly higher fluctuations (71% increase in range) compared to the contraTMS time-series. By performing another frequency analysis, this time on the contraTMS minus ipsiTMS time-series, we could attribute this increase to a strong oscillatory component in the 9 Hz range (Figure 3F, 9 Hz: p < 0.00005, FDR corrected). The increase in oscillatory power in the difference wave is likely a result of subtracting two oscillations that share a common (or neighboring) frequency but are in anti-phasic relationship. spectrum of the contraTMS time-series. We compared the peak at 10 Hz to a surrogate distribution (1.000.000 surrogates) which revealed a significantly higher power at this frequency compared to other frequencies after correcting for multiple comparisons (p = 0.00006, FDR-corrected: p = 0.005).

Colored areas: Dark gray: Mean of the surrogate distribution; Light gray: 95% Confidence Interval; 99% CI; 99.9% CI; 99.99% CI; 99.999% CI; 99.9999% CI; White: >99.9999% CI. E. Power spectrum of the ipsiTMS time-series. We observed a relatively strong oscillatory component at around 8 Hz.

Analogous to (D) we analyzed oscillatory power at 8 Hz and found significantly more power compared to the surrogate distribution (p = 0.00038, FDR-corrected: p = 0.0039). F. Power spectrum of the contraTMS minus ipsiTMS time-series. Oscillatory peak was at 9 Hz and showed significant power (p < 0.0005, FDR-corrected: p = 0.0005). Note that 9 Hz oscillatory power was 71% higher in amplitude compared to the 10 Hz oscillation in the contraTMS condition, indicating an anti-phasic relationship.]

10 Hz Phase analysis

To test this hypothesis we analyzed the 9 Hz phase angles of the ipsiTMS and contraTMS time-series (Figure 4A) as well as the difference wave across subjects. The frequency of 9 Hz was chosen because it lies right within the frequency ranges of the contra and ipsilateral peak components and both time series show highly significant power at this frequency (contraTMS: p = 0.00017; ipsiTMS: p = 0.0039). Additionally we performed a pairwise subtraction of the individual contraTMS and ipsiTMS phase angles (phase domain difference) to test if a possible anti-phasic relationship is visible on the single subject level. The complex FFT coefficients at 9 Hz were extracted to calculate individual phase angles (Figure 4B). We then compared these angles using Rayleigh's test for non-uniformity testing the null hypothesis that the phase angles are randomly distributed. Phase angles were significantly clustered in ipsilateral as well as contralateral TOJ time-series (Figure 4B, contralateral: p = 0.000062, ipsilateral: p = 0.0017). We were further interested in the phase relationship between 9 Hz oscillations in contraTMS and ipsiTMS time-series (time domain difference). To test the two sets for phase opposition we subtracted the phase angles for each subject and performed Rayleigh's test for nonuniformity on the resulting phase differences. Phase difference angles were significantly clustered at 180 degrees, indicating anti-phasic oscillations at opposing hemispheres (CI lower bound: 120.5 degrees, upper bound: 199.8 degrees, mean: 160.2 degrees, p < 0.01). The difference wave was analyzed in an identical fashion as contraTMS and ipsiTMS time-series, showing highly significant 9 Hz phase clustering (p=0.000001).

[Figure 4. 9 Hz Phase Analysis. A. Time Course of normalized contraTMS (stimulated hemifield) and ipsiTMS (non-stimulated hemifield) time courses for direct comparison. Note the clear antiphasic relationship between the two. B. 9 Hz phase angles of contraTMS (blue) and ipsiTMS (red) timeseries. Rayleigh's test reveals significant phase clustering for both conditions. C. Pairwise subtraction of 9 Hz contraTMS minus ipsiTMS phase angles (phase domain difference). Phase angles were significantly clustered around 180 degrees indicating an antiphasic relationship between individual contraTMS and ipsiTMS time-series. D. 9 Hz Phase analysis of the difference wave (contraTMS minus ipsiTMS, time domain difference). Phase angles were significantly clustered.]

Discussion

We tested the influence of α-TMS on subsequent temporal order judgements at varying SOA's. 5

Pulses at 10 Hz were administered over left or right occipital cortex. α-TMS was intended to entrain α-oscillations in a local neural population. We probed temporal order perception of two Gabor patches, at the spatial location presumably affected by the TMS entrainment, at 9 SOA's between 25 ms and 158 ms after the last TMS-pulse. Behavioral performance at every SOA was averaged to obtain a 133 ms long TOJ time-series. The frequency analysis of the TOJ time-series contralateral to TMS revealed a strong oscillation at our entrainment frequency of 10 Hz. We found no evidence of potentially confounding effects of TMS on stimulus visibility in our control conditions. In line with previous accounts of discrete perception we hypothesize that the rhythmic modulation in TOJ was caused by a TMS-evoked entrainment of occipital α-oscillations. The phase of α-oscillations has previously been related to so-called "perceptual windows" that serve to discretize visual input into compressed packages. Here we specifically tested the hypothesis that this compression leads to a deterioration of temporal order information. Depending on the relative timing to the last TMS pulse (SOA) the two stimuli fall either in the same or separate perceptual windows, leading to decreased or enhanced TOJ performance respectively. Our findings are in line with a "hard" theory of discrete perception suggesting that temporal order information is limited within perceptual windows. We provide causal evidence for an involvement of occipital alpha oscillations in this process.

The idea of discrete sampling in the visual system has received growing interest in the last years.

Correlational evidence for an involvement of the occipital α-rhythm in the discretization of visual input is frequent [START_REF] Busch | The phase of ongoing EEG oscillations predicts visual perception[END_REF][START_REF] Haegens | α-Oscillations in the monkey sensorimotor network influence discrimination performance by rhythmical inhibition of neuronal spiking[END_REF][START_REF] Lőrincz | Temporal Framing of Thalamic Relay-Mode Firing by Phasic Inhibition during the Alpha Rhythm[END_REF][START_REF] Milton | The phase of pre-stimulus alpha oscillations influences the visual perception of stimulus timing[END_REF][START_REF] Samaha | The Speed of Alpha-Band Oscillations Predicts the Temporal Resolution of Visual Perception[END_REF][START_REF] Valera | Perceptual framing and cortical alpha rhythm[END_REF][START_REF] Vanrullen | Perceptual Cycles[END_REF][START_REF] Vanrullen | Is perception discrete or continuous? Trends in Cognitive Sciences[END_REF][START_REF] Vijayan | Thalamic model of awake alpha oscillations and implications for stimulus processing[END_REF]). Yet it was not clear if the α-rhythm merely modulates excitability, leading to continuous fluctuations in i.e. visual performance or if it implements discrete nonoverlapping perceptual windows. These two notions can be thought of as "soft" and "hard" versions of the discrete perception idea [START_REF] Vanrullen | Perceptual Cycles[END_REF]. Evidence for the latter exists but is rarely of causal nature [START_REF] Chakravarthi | Conscious updating is a rhythmic process[END_REF][START_REF] Milton | The phase of pre-stimulus alpha oscillations influences the visual perception of stimulus timing[END_REF][START_REF] Morand | Temporal framing in apparent motion perception cycles with a 12Hz (alpha) rhythm[END_REF][START_REF] Samaha | The Speed of Alpha-Band Oscillations Predicts the Temporal Resolution of Visual Perception[END_REF][START_REF] Valera | Perceptual framing and cortical alpha rhythm[END_REF][START_REF] Wutz | Temporal Windows in Visual Processing: "Prestimulus Brain State" and "Poststimulus Phase Reset" Segregate Visual Transients on Different Temporal Scales[END_REF]. Recent work shows that the α-rhythm can be causally modulated via visual entrainment, leading to fluctuations in temporal parsing performance [START_REF] Ronconi | Alpha-band sensory entrainment alters the duration of temporal windows in visual perception[END_REF][START_REF] Chota | Visual Entrainment at 10 Hz Causes Periodic Modulation of the Flash Lag Illusion[END_REF]. While these studies help to link αoscillations and perception, they are limited since a visual entrainer passes various processing stages e.g. the LGN before arriving at the primary visual cortex. The LGN is hypothesized to project not only to V1, but also directly to higher cortical areas like V2 and V3 [START_REF] Schmid | Blindsight depends on the lateral geniculate nucleus[END_REF]. Strictly speaking every possible target of visual entrainment could serve as a potential source for the behavioral observations previously reported (Mathewson et al., 2010;[START_REF] Ronconi | Alpha-band sensory entrainment alters the duration of temporal windows in visual perception[END_REF][START_REF] Spaak | Local Entrainment of Alpha Oscillations by Visual Stimuli Causes Cyclic Modulation of Perception[END_REF][START_REF] Chota | Visual Entrainment at 10 Hz Causes Periodic Modulation of the Flash Lag Illusion[END_REF]. TMS allows for a direct and locally confined interaction with endogenous cortical rhythms [START_REF] Romei | On the Role of Prestimulus Alpha Rhythms over Occipito-Parietal Areas in Visual Input Regulation: Correlation or Causation[END_REF][START_REF] Thut | Rhythmic TMS Causes Local Entrainment of Natural Oscillatory Signatures[END_REF]. As the target of our entrainment is confined to the early occipital cortex we can say with relative certainty that the occipital α-rhythm gives rise to the perceptual effects demonstrated in this study. We therefore provide a direct link between occipital α-oscillations and temporal order judgements.

Former experiments have mostly used integration versus segregation tasks (IvS), such as the two-flash fusion paradigm, to quantify temporal parsing performance [START_REF] Ronconi | Alpha-band sensory entrainment alters the duration of temporal windows in visual perception[END_REF][START_REF] Samaha | The Speed of Alpha-Band Oscillations Predicts the Temporal Resolution of Visual Perception[END_REF][START_REF] Valera | Perceptual framing and cortical alpha rhythm[END_REF]. These tasks present two stimuli in quick succession and subsequently probe participants temporal segregation abilities (simultaneous vs. non-simultaneous, one vs. two).

Perceptually it is principally sufficient to detect changes in luminance over time, irrespective of the stimulus characteristics. Flicker fusion experiments show that temporal changes can be detected at far higher frequencies than 10 Hz [START_REF] Simonson | Flicker fusion frequency; background and applications[END_REF]). TOJ's however require precise perception of temporal relationships between individual stimuli and cannot be solved purely by identifying transient changes in luminance. Our findings suggest that fine grained temporal changes are detected at earlier stages of visual processing (e.g. LGN), whereas in early visual cortex (our target of entrainment) temporal order is resolved.

Another complicating factor of IvS tasks is that the oscillatory phase facilitatates or inhibits stimulus detection and ERP latencies, potentially biasing responses by hiding stimuli from perception or delaying their entry into consciousness [START_REF] Busch | The phase of ongoing EEG oscillations predicts visual perception[END_REF][START_REF] Fellinger | Pre-stimulus alpha phase-alignment predicts P1-amplitude[END_REF]. This raises the possibility that effects of phase on IvS performance are caused by inhibitory effects on single stimuli rather than time distortion effects caused by discrete sampling. One could also forward this objection against our paradigm.We therefore implemented several control conditions into our task. We hypothesized that if our findings were the result of phase-dependent α-inhibition, this should lead to a general reduction in the visibility of the target stimulus and reduce performance especially for low contrast conditions. Furthermore, such an effect would likely result in an increase in single stimulus reports for stimuli contralateral to TMS. Our control conditions however demonstrate that performance was comparable between TMS and Training conditions as well as contra and ipsilateral hemispheres in all contrast conditions, indicating that temporal order judgments could be performed under conditions of reduced visibility even under the effect of TMS. Even if one of the stimuli was occasionally hidden from perception entirely, we would remove them from the main TOJ-analysis as single stimulus reports. From our control results we conclude that modulations of stimulus visibility were not the main determinant of TOJ performance fluctuations.

While the effect of α-TMS on the contralateral visual field was somewhat expected we were surprised to find an oscillatory pattern also in the ipsilateral visual field. The ipsiTMS time-series showed a relatively weaker amplitude, oscillated at around 8 Hz and seemed to fluctuate in antiphase compared to its contralateral counterpart for at least 160 ms. We consider it unlikely that the TMS-pulse directly interacted with the contralateral hemisphere because first, all subjects reported phosphenes only in the contralateral visual field, and second, TMS pulses seemed to have opposing effects depending on the stimulus location. Previous work has shown that α-TMS can affect target detection performance in the visual field contra-and ipsilateral to the entrainment site, possibly explained by a transcallosal "push-pull" effect [START_REF] Romei | On the Role of Prestimulus Alpha Rhythms over Occipito-Parietal Areas in Visual Input Regulation: Correlation or Causation[END_REF]. Our findings suggest that α-phase is modulated by this network effect, potentially releasing one hemisphere from inhibition when the other hemisphere enters a state of inhibition. One possible interpretation of the frequency difference is that the ipsilateral oscillation reflects a slower attentional rhythm that is usually placed in the 3 to 8 Hz range [START_REF] Fiebelkorn | A Dynamic Interplay within the Frontoparietal Network Underlies Rhythmic Spatial Attention[END_REF][START_REF] Fiebelkorn | A rhythmic theory of attention[END_REF][START_REF] Vanrullen | Visual Attention: A Rhythmic Process?[END_REF][START_REF] Vanrullen | The blinking spotlight of attention[END_REF]. Another possibility is that the change in frequency relates to differences in α-power between hemispheres. As mentioned before a push-pull effect might lead to a significant reduction in 10 Hz power in the ipsilateral hemisphere [START_REF] Romei | On the Role of Prestimulus Alpha Rhythms over Occipito-Parietal Areas in Visual Input Regulation: Correlation or Causation[END_REF]. Since this oscillatory frequency is likely relevant for stimulus processing the brain might try to compensate by modulating excitability at a lower frequency. Of course this is highly hypothetical and warrants further investigation.

The phase of α-oscillations is predictive of cortical excitability [START_REF] Busch | The phase of ongoing EEG oscillations predicts visual perception[END_REF][START_REF] Dugué | The phase of ongoing oscillations mediates the causal relation between brain excitation and visual perception[END_REF], of neuronal firing rates [START_REF] Haegens | α-Oscillations in the monkey sensorimotor network influence discrimination performance by rhythmical inhibition of neuronal spiking[END_REF][START_REF] Lőrincz | Temporal Framing of Thalamic Relay-Mode Firing by Phasic Inhibition during the Alpha Rhythm[END_REF][START_REF] Vijayan | Thalamic model of awake alpha oscillations and implications for stimulus processing[END_REF] and of the amplitude of gamma oscillations [START_REF] Osipova | Gamma power is phase-locked to posterior alpha activity[END_REF][START_REF] Voytek | Shifts in Gamma Phase-Amplitude Coupling Frequency from Theta to Alpha Over Posterior Cortex During Visual Tasks[END_REF]. As these neural signatures have been implicated in neuronal processing it seems logical that visual processing is concentrated on specific reoccurring intervals. The brain might use these naturally occurring periodicities, in the form of oscillations, to reduce the complexity of incoming information by compressing it into discrete packages. Our findings suggest that this compression results in the loss of temporal relationship between two stimuli. Note that the visual system is very robust to subsampling in the 100 ms range [START_REF] Vanrullen | Is perception discrete or continuous? Trends in Cognitive Sciences[END_REF]. Presumably because visual information is highly redundant, allowing the visual system to reduce complexity via periodic discretization without losing too much relevant information.

In this study we successfully demonstrated that TMS entrainment at 10 Hz leads to a causal rhythmic modulation of temporal order judgements. This modulation was evident in the majority of subjects, shown by a strong inter-individual phase coherence in individual TOJ time-series. Furthermore we found that ipsilateral TOJ time-series were modulated in antiphase to their contralateral counterparts; this cross-hemispheric effect is unlikely to be caused directly by the TMS, but may result from a secondary trans-callosal pathway. We hypothesize that the visual system periodically discards temporal order information in order to reduce the complexity of incoming visual information. Further, we hypothesize that this mechanism is implemented by occipital oscillations in the α-range.

  ): Normal (100% contrast for A and B), low contrast 10% (Stimulus A: 90% contrast, Stimulus B: 10% contrast), low contrast 90% (Stimulus A: 10% contrast, Stimulus B: 90% contrast), low contrast 25% (Stimulus A: 75% contrast, Stimulus B: 25% contrast), low contrast 75% (Stimulus A: 25% contrast, Stimulus B: 75% contrast). Condition names (e.g. low contrast 75%) refer to the contrast value of the second stimulus of the sequence (Orientation of Stimulus B which had to be identified in the TOJ task) and will be used for later reference. Low percentage values represent low contrast or small difference to background luminance. The percentage values represent the Michelson contrast, defined as the ratio between the minimal/maximal luminance value of the stimulus and the gray background ((max. Luminance -min. Luminance)/(max. Luminance + min. Luminance)). [Figure 1. Stimulus locations for all subjects. The stimulus locations during the TMS blocks were determined during the phosphene localization. Participants had their eyes closed and received 7 TMS pulses at 20 Hz either over left or right occipital cortex. The red coil symbol over the blue head inset

  session only, participants performed an extensive pre-training consisting of 12 Training Blocks (23 trials each). Training blocks were identical to the TMS blocks with few exceptions. No TMS-pulses were applied during training and the placeholder as well as sequence presentation was in the lower right or left (equally balanced) visual field. Participants received positive or negative feedback in the form of the fixation cross turning green or red. One goal of the Training Blocks was to prevent participants from basing their TOJ judgements on the visibility of stimuli by making the contrast maximally uninformative as described above. Furthermore, it served to keep performance on a steady level by providing frequent feedback to the participant. In the training blocks 44.3% of trials were low contrast trials, 22.3% were single stimulus trials and 33.3% were normal contrast trials. [Figure 2. Paradigm. A. Experimental Design. Participant's initiated trials via button press while fixating at a central fixation cross. After 1000 ms 5 TMS pulses at 10 Hz were administered. We probed TOJ performance at nine time points between 25 ms and 158 ms after the last TMS pulse. This was done by presenting a sequence of two Gabor patches with different orientation (Stim A and Stim B, 45° or 135°, stimulus length: 42 ms, ISI 58 ms), followed by a mask to prevent stimulus persistence or long afterimages. Participants had to identify the orientation of the second stimulus which was different on every trial. Alternatively participants could report (using a different key) a single stimulus condition where either the first or second stimulus was omitted (see C.). In the TMS Blocks no feedback was provided. B. Protocol. The experiment was performed on 3 separate days within 5 days.

  TMS blocks, 5 Training blocks) with 23 trials per block (In the last TMS block only 20 trials were collected). 3 TMS blocks were interleaved with 1 Training Block. Over the course of 3 sessions this resulted in 1035 trials in the TMS and 345 trials in the training condition per subject (50% trials contralateral to TMS, 50% trials ipsilateral to TMS). Per SOA and per visual field 57 trials were collected. Before each of the 45 TMS blocks participants performed a phosphene localization to make sure that the coil position had not changed and the correct cortical area was stimulated. Trials started with the central fixation cross and the placeholder on either side of the screen (Figure 2 A). The placeholder served as a cue to indicate location of the stimulus sequence with 100% cue validity. This served to avoid potential attentional confounds by always directing attention to the precise location of the upcoming stimuli. Participants initiated the trial via button press. 1000 ms after the button press 5 TMS pulses (100 ms between pulses) were administered over the course of 400 ms. Starting with the last TMS pulse, after a variable delay (25 -158 ms in steps of 16.7 ms) the stimulus sequence was presented inside the square placeholder. The orientation of Stim A and Stim B was pseudo-randomly chosen every trial (45° and 135° or vice versa).The presentation length for Stim A, Stim B and the mask was 42 ms each. The ISI between Stim A and Stim B was 16 ms. The ISI between Stim B and the mask was slightly longer with 24 ms. During Piloting we observed a forward and backwards masking effect on the second stimulus which we compensated by shifting the onset of the mask to a later time-point. This was done to equalize visibility between Stim A and Stim B which we verified during piloting in 4 subjects. After a delay of 1000 ms participants reported either the orientation of Stimulus B (arrow key left or right) or reported perceiving a single stimulus (arrow key up). Trials were randomly chosen from the normal condition (66.3% probability) [Stim A (normal contrast), Stim B (normal contrast), Mask], low contrast condition (22.3% probability) [Stim A (low contrast), Stim B (low contrast), Mask] or a single stimulus condition (11.3% probability) [Stim A (normal contrast), omitted, Mask] or [omitted, Stim B

[Figure 3 .

 3 Main findings. A. Average TOJ time-series (N = 18) for stimuli presented contralateral to TMS. Error bars represent standard error of mean. The vertical gray line indicates the hypothetical time point of the next TMS pulse if the entraining sequence had continued. B. TOJ time-series for ipsilateral stimuli. C. Difference wave between contraTMS and ipsiTMS time series. D. Power

Funding

This work was funded by an ERC Consolidator Grant P-Cycles number 614244 and an ANR OSCIDEEP number ANR-19-NEUC-0004.