domain: chim phys spi

text:
Magdalena Waszkielewicz

Joanna Olesiak-Banska
email: joanna.olesiak-banska@pwr.edu.pl

Clothilde Comby-Zerbino

Franck Bertorelle

Xavier Dagany

Ashu K Bansal

Muhammad T Sajjad

Ifor D W Samuel

Zeljka Sanader

Miroslawa Rozycka

Magdalena Wojtas

Katarzyna Matczyszyn

Vlasta Bonacic- Koutecky

Rodolphe Antoine

Andrzej Ozyhar

Marek Samoc

pH-induced transformation of ligated Au 25 to brighter Au 23 nanoclusters

Thiolate-protected gold nanoclusters have recently attracted considerable attention due to their size-dependent luminescence characterized by a long lifetime and large Stokes shift. However, the optimization of nanocluster properties such as the luminescence quantum yield is still a challenge. We report here transformation of Au25Capt18 (Capt labels captopril) nanoclusters occurring at low pH and yielding a product with much increased luminescence quantum yield which we have identified as Au23Capt17. We applied a simple method of treatment with HCl to accomplish this transformation and we characterized the absorption and emission of the newly-created nanoclusters as well as their morphology. Based on DFT calculations we show which Au nanocluster size transformations can lead to the highly luminescent species such as Au23Capt17.

Introduction

A new class of metallic nanomaterials containing thiolated gold nanoclusters (Au NCs) has been found to exhibit attractive physical and chemical properties. [1][2][3][4][5][6][START_REF] Antoine | Towards a new class of nonlinear optical nanomaterials[END_REF] Au NCs, containing a few up to several hundreds of gold atoms in the core surrounded by various ligands exhibit size-dependent luminescence, in the visible and/or NIR range of wavelengths . [START_REF] Chen | [END_REF]9 The presence of emission in the NIR (in the biological transparency window region) is essential for applications of gold nanoclusters in biology and medicine. As most of biomolecules have low absorption coefficients in this range, a risk of irritation of normal metabolism is limited and the autofluorescence of the biological material is minimized as well as deep penetration (>1 cm) of the tissue is possible. 10 Although strategies based on silver doping 11 or rigidifying the ligand shell have been proposed to enhance the photoluminescence quantum yield of the clusters both in the linear 12 and nonlinear optical regime 13 , it is usually rather low, and has been found to be strongly cluster size dependent. [START_REF] Chen | [END_REF] The ligands may play an important role in fluorescence enhancement, 14 and both the ligands and the nanocluster size may determine the activity and biodistribution in context of applications in vivo. Therefore, a precise choice of the stabilizing ligands is required, as well as the control of the quantum cluster size with the "atomic precision".

Major synthetic breakthroughs have been achieved using two systematic approaches: size-focusing methodology 15 and ligand exchange-induced size/structure transformation (LEIST) methodology. 16 However, a transformation consisting in removing one or two metal atoms and/or ligands from a stable nanocluster size remains challenging. Core etching 17 or using reductive conditions 18 have permitted size conversion of AuNCs from Au25 to Au22 and Au23. Recently, an elegant strategy using a two-step metal exchange method has allowed for the "resection" of two surface gold atoms leading to the transformation from Au23 to Au21 NCs 19 . Another sizecontrolled synthesis of aqueous nanoclusters can be obtained through pH control. Xie and co-workers achieved a size-tunable synthesis of Au10-12, Au15, Au18, and Au25 nanoclusters, under pH adjustment utilizing carbon monoxide (CO) as a mild reducing agent. 20 In this contribution, we report making of highly fluorescent NCs by size transformation of well-characterized Au25 stabilized by This journal is © The Royal Society of Chemistry 20xx

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Results

The captopril protected gold (AuCapt) nanoclusters were synthesized according to a literature procedure 21 and dispersed in water (pH=7). They exhibited absorption bands at 800, 675, 550, 505, 445and 400 nm (Fig. 1a), similar to the Au25(PET)18 (where PET -phenylethanethiol) clusters reported by Jin and co-workers. 22 After transferring the nanoclusters to buffers with pH ranging from 2 to 10, no change has been initially observed in the absorption spectra. However, after several hours the absorption spectra for NCs in pH=2 lost the features characteristic of Au25 NCs i.e. absorption bands at 800, 670 nm and 450 nm gradually decreased. Additionally, a small shoulder at 550 nm developed into a band (Fig. 1a). For pH=3 the leading features of the absorption spectrum were also partly lost, but for other pH values (between 4 to 10) no changes occurred (see SI Fig. S1).

The photoluminescence (PL) spectra measured upon treatment with low pH revealed enhancement in the nanoclusters emission with a maximum at 700 nm (when excited at 550 nm, corresponding to Stokes shift of 0.12 eV). In order to compare the PL intensities, the data were normalized with respect to the same absorbance at the excitation wavelength. The PL intensity of NCs at pH = 2 was found to be an order of magnitude higher than that reported for nanoclusters at pH = 7 (Fig. 1b). The PL quantum yield (QY) of the nanoclusters was calculated by comparing their emission with fluorescence of a standard which was Oxazine 170. 23 AuCapt NCs at pH= 7 have QY = 0.37% whereas at pH = 2 the QY increased ~10 times, up to 3.9%. This dramatic increase of the brightness of the nanoclusters needs therefore to be understood in terms of the possible structural changes. One of the possibilities considered was the formation of Au(I)-Capt which is an intermediate in the synthesis of Au25Capt18. Since Au(I) complexes are known to fluoresce 24 , it might be assumed that the observed emission enhancement is connected with the presence of a significant amount of this Au(I)-Capt polymer. To investigate the potential impact of the polymer on emission of the NC solution at pH=2, we recorded separately its emission spectrum. The fluorescence was observed in the range between 400 and 660 nm with the maximum at 465 nm, which does not provide explanation of the emission enhancement of the nanoclusters (see SI Fig. S2).

To clarify if the observed changes arise due the presence of protonation or to chloride ions in the buffer solution, the neutral and concentrated solution of AuCapt was dissolved in HCl and HNO3, both corresponding to pH = 2. The samples emission and absorption were monitored over 24 hours, as well as after 72 hours. The comparison of the absorption and emission spectra is presented in Figs. S3-S4, which show that a restructuration of the spectra has occurred. The process was identical in the case of samples with the pH = 2 buffer and with HCl, and was completed in 5 hours. In contrast, in the sample with HNO3, different features are observed (SI Fig. S3). Please do not adjust margins

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The luminescence decays were measured and fitted with double exponential function (Fig. 2). The PL lifetimes were found to depend only slightly on the pH, in case of the sample in pH = 7, they were τ1 = 264 (0.09) and τ2 = 1778 ns (0.91) with the average 1753 ns. For the sample in pH = 2, τ1 = 207 (0.18) and τ2 = 1516 ns (0.82), giving average of 1462 ns. The corresponding lifetime values are presented in Table 1. # average lifetime <τ> = (a1τ1 2 +a2τ2 2 )/(a1τ1+a2τ2)

In order to test the reversibility of changes induced by low pH, we dried and redissolved the samples in a buffer of pH = 7. In the case of AuCapt at pH = 2, the absorption and emission spectra were preserved (SI Fig. S5). However, an increase of the PL lifetime was observed, and the value of the long component changed from ~1500 ns to ~1750 ns, which is a value similar to the lifetime of AuNC at pH = 7 (see Fig. 2). For AuCapt at pH = 7 the lifetimes did not change after drying and redissolving the sample.

Since the absorption of NCs at pH=2 did not unambiguously correspond to any reported absorption spectrum in the literature 25 , we checked whether we obtained a mixture of the products. For this reason the polyacrylamide gel electrophoresis (PAGE) was conducted and two separated bands were observed (see Fig. 3a). In order to identify the responsible species, the ESI-MS was carried out for the desalted product mixture as well as for AuCapt before the low pH treatment (Fig. 3b andc, and Fig. S6). The corresponding ESI deconvolution spectrum leads to Au25Capt18 before and after the low pH treatment leads to several peaks with smaller masses, which correspond to a mixture of Au24Capt16and Au23Capt16 and Au23Capt17 and Au22Capt17.

The separated NCs, extracted from a gel, were characterized by UV/Vis spectroscopy (Fig. S7). The absorption spectrum of upper fraction presents two bands at 460 and 575 nm. Similarly, the band of lower fraction was located at 575 nm with a shoulder at 460 nm. The emission spectra of separated fractions were blue-shifted by 6 nm with respect to the one for NCs in pH=2. However, more important findings are that the lower fraction has much higher luminescence quantum yield equal to ~5 % , when compared to the upper fraction which is ~0.1 %.

Discussion

In our experiments, the originally synthesized nanoclusters exhibited the absorption spectra with all the bands characteristic for Au25(SR)18. Based on the absorption spectra and ESI-MS results, we can confirm the formation of Au25(Capt)18 nanoclusters, with no need for post-synthesis separation.

Au25 PL decay times reported in the literature depend on the emission wavelength and stabilizing ligands. Link et al. reported biexponential decays for AuSG NCs, with lifetime values ranging from 177 ns/1380 ns for emission at 700 nm to 341 ns/1480 ns for emission at 800 nm. 26 Wu et al. obtained single PL lifetimes of about 500-700ns for Au25 with -SC2H4Ph, -SC12H25, and -SC6H13 ligands as well as two PL lifetimes of 247 ns/1240 ns for Au25SG18 NCs. 27 These data are in a good agreement with our results of PL decays. AuCapt functionalized clusters presented lifetimes of 210 ns/1790 ns (table 1), similar to those for other ligands with electron-rich groups.

It has been shown in some reports that gold nanoclusters exhibit good stability under pH although results on the influence of pH on PL intensity evolution differ considerably 28,29,30 Our work shows that after an incubation with HCl (pH = 2), the nanoclusters transform into species with increased luminescence. Based on the MS analysis and on the agreement This journal is © The Royal Society of Chemistry 20xx

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Please do not adjust margins between experimental and theoretical absorption spectra for Au23L17 (see Fig. 4), we recognized the transformation as being from Au25(SR)18 to Au23Capt17 (Au23). The proposed composition of Au23SR17 was reported in the literature as possibly emitting bright red PL. 31 In this contribution, we show that application of low pH in the presence of Cl -ions is a new method of transformation from one stable size of nanoclusters to another, with the nanoclusters being produced with the same ligand, in water. On the contrary, previous protocols required thermal treatment and high excess of the thiol that substitute the outgoing ligand. 16 Moreover, the incoming ligand was required to be significantly different from the original one. In early work simple ions like Cl -or OH -were used to stabilize the nanoclusters, but they exhibited low stability in drying process. Other studies showed the charge conversion of [Au25(SCH2CH2Ph)18] 0 clusters into anionic form in the presence of halide ions. 32 In our studies comparison of HCl and HNO3 treatment shows that the presence of Cl -ions is important for the size transformation. On the other hand, application of nitric acid leads to the protonation of clusters.

Relative intensities of 800 nm/630 nm and 450 nm/400 nm absorption peaks might be connected with the change of the charge of ligated Au25 nanoclusters. High intensity of 800 nm and 450 nm peaks, as observed in our samples before treatment, is characteristic for anionic clusters. 33 After HNO3 treatment the changes in absorption spectra shown in Fig. S3a are characteristic for the neutral cluster [Au25SR18] 0 . 33 A similar absorption spectrum is observed at pH=3 with HCl.

Thus, one can suggest that the acidic treatment leads to at least two-step transformation process: The first stage could be explained on the basis of the pKa value for carboxylic group of captopril, which is equal to 3.35 ± 0.04 (for the structure of ligand see Fig. S9) 34 . The protonation of NCs occurs in pH ~ 3 and lower.

The degradation of NCs in the presence of halides was reported before by Zu et al. 32 In that case two types of salts were used -NaX and TOAX (where X -halide), but only NaX caused decomposition. Also in our work chloride ions played crucial role in the second stage of the transformation process. Although Au25(Capt)18 were stabilized with TOA + during whole process, the dramatically low pH could shift the equilibrium in our system. In pH = 2, TOA + had limited stabilizing activity on protonated NCs and as a result partial decomposition of nanoparticles with Cl -anions was possible. A Cl -ion, due to its higher electronegativity, acts as an acceptor of electrons and, when in contact with Au surface, electronic charge transfer from gold ions to chloride ions occurs. Additionally, the protonation of carboxylic groups decreases the electron density in the outer layer of NCs and thus chloride -gold interactions become more prominent. On the other hand, NO3 -has never One notes that the pH-induced transformation described here, has some similarity with the recently reported results from Jin et al. where [Au25(SePh)18] -nanoclusters were transformed into the [Au23(SePh)16] -nanocluster in the presence of NaBH4. 18 In fact our computational results show that the transformation from Au23L16 to Au23L17 is more favorable than from Au25L18 to Au23L17. In the former case, addition of ligand to Au23L16 which is also stable produces the most stable Au23L17 with structure containing core of 12 Au atoms as shown in Fig. 4a), for which the calculated absorption spectrum is in a good agreement with experimental findings. In contrast, the structure of Au23L17 derived from Au25L18 by removing two gold atoms and one ligand is higher in energy and the TDDFT calculated absorption spectrum is not in agreement with experimental findings as shown in Fig. 4b). Although the core contains 12 atoms, its structure is different with respect to the one obtained starting from Au23L16. Since the excitation within the core is responsible for absorption spectra, its structural properties are responsible

Please do not adjust margins Please do not adjust margins for the leading features. The above results show that the removal of the gold atoms and ligand versus addition of a ligand cause a reconstruction of the core which is responsible for the optical properties including fluorescence.

Conclusions

We presented here a new approach to transform Au nanoclusters of one size into another. In our simple method a low pH treatment (with HCl) was successfully applied for the nanoclusters transformation from Au25Capt18 to very fluorescent Au23Capt17. We monitored the changes of nanocluster absorption and emission spectra in the course of the transformation and measured the fluorescence decay times of the substrates and products. We observed enhancement of the fluorescence by up to 13 times when the nanocluster size changed. In fact, changes of optical properties by changing number of Au atoms and ligands occur due to structural changes, as shown by our theoretical findings. The final nanoclusters were stable after the transition from low to neutral pH. Because Au25 are the most easily obtained nanoclusters, our findings about their pH sensitivity and size transformation with corresponding fluorescence enhancement provide significant information useful for their further applications. Moreover, our approach gives a relatively simple procedure for the preparation of highly fluorescent Au23 nanoclusters from Au25. It may also be possible to obtain other sizes by using other monodispersed nanoclusters as a substrate.

Experimental

Chemicals. All of the chemicals were commercially available and used without further purification. Gold(III) chloride trihydrate (HAuCl4•3H2O, 99.999%), captopril (Capt, 98%), sodium borohydride (NaBH4, 98%) and tetraoctylammonium bromide (TOABr, 98%) were purchased from Sigma-Aldrich. Aqueous 40% acrylamide and bisacrylamide stock solution N,N,N',N'tetramethylethylenediamine (TEMED, 99%), N,N'-methylene bisacrylamide (Bis, >98%) and 10x concentrated SDS-PAGE running buffer (SDS) were supplied from Carl Roth. Ammonium persulfate (APS, 98%), 0.5 M Tris-HCl buffer pH 6.8, and 1.5M Tris-HCl buffer pH 8.8 were purchased from BIO-RAD.The universal buffer solutions (pH 2 -10) were supplied from Avantor Performance Materials Poland. The deionized water with the resistivity of 18 MΩ•cm was used in the studies.

Instrumentation and protocols. High-resolution transmission electron microscopy (TEM) was conducted with a FEI Tecnai G2 20 X-TWIN. TEM images of AuCapt nanoclusters in pH = 2, 3 and 7 are presented in Fig. S8 in SI. The absorption and fluorescence measurements were recorded on a JASCO V-670 spectrophotometer and a Hitachi F-4500 spectrofluorometer, respectively. Excited state lifetimes were measured with an Edinburgh Instruments FLS980 Fluorescence Spectrometer. All samples were excited at 379 nm with a PicoQuant pulsed laser and emission was detected at 720 nm using time-correlated single-photon counting (TCSPC). The experimental data was fitted with two exponential decays.

Evolution of the gold NC size without and with acid treatment was determined by electrospray ionization on a commercial quadrupole time-of-flight (micro-qTOF, Bruker-Daltonics, Bremen, Germany, mass resolution 10 000). AuCapt NCs without acid treatment and the same sample after the treatment (HCl, pH = 2) were prepared to a final concentration approximately of 50μM in water. The samples were analysed in negative ion mode: each data point was the summation of spectra over 5 min. External calibration was carried out with a set of synthetic peptides. We used our Au25Capt18 NCs to optimize the mass spectrometer and define the measurement uncertainties. Due to the huge amount of sodium adducts observed in ESI-MS, we decided to perform desalting procedure before MS analysis. The AuNC was dissolved in 1mL of methanol (or water). Then 1mL of glacial acetic acid was added and precipitation was induced by adding THF. Then the sample was centrifuged and dried.

A multiplicative correlation algorithm (MCA) was used to estimate the mass of nanoparticles from the mass-to-charge spectra produced by electrospray ionization mass spectrometry. 35,36 Preparation of AuCapt Clusters. Captopril-protected Au25 clusters were prepared using a modified Kumar one-pot procedure. 21 Briefly, TOABr (0.23 mmol, 126.8 mg) was dissolved in 10 mL of methanolic solution of HAuCl4•3H2O (0.02 M) and stirred vigorously. After 20 min, 1 mmol of captopril (217.2 mg) was dissolved in 5 mL of methanol and rapidly added into the reaction mixture under stirring. After 30 min, 5 mL of aqueous solution of NaBH4 (0.4 M), cooled to 4°C, was rapidly poured to the reaction mixture under vigorous stirring. The solution was allowed to react for 8 h in an ice bath. The suspension was centrifuged to remove unreacted, insoluble Au(I):SR polymers. The supernatant was collected and concentrated in water bath at 45°C. The clusters were precipitated with ethanol and repeatedly washed with methanol and ethanol. The final precipitate was dried in 45°C.

Polyacrylamide Gel Electrophoresis (PAGE)

The electrophoresis in a discontinuous gel system was carried out by using a PROTEAN II XL Cell slab gel electrophoresis unit (BIO-RAD). The separating and stacking gels were prepared from acrylamide monomers with the final concentrations of 18.3 %T; 4.2 %C (separating) and 7.5 %T; 2.6 %C (stacking), where %T -total monomer (acrylamide + bisacrylamide) concentration and %Cconcentration of the cross-linking. The clusters were dissolved in a 5% (v/v) glycerol/water solution. The electrophoresis was carried out for 13 h at a constant voltage mode (150 V) at 4°C. Finally, the separating gel was cut into bands and the particular fractions were eluted with water.

Theoretical This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins Density functional theory (DFT) has been used to determine the properties of the liganded gold structures employing the SVP atomic orbital basis set for all atoms 37 and the relativistic effective core potential (RECP) of the Stuttgart group for gold atoms. 38 The search for structures was performed using simulated annealing simulations as implemented in Turbomole quantum chemistry program. 39 Coordinates for starting structures were taken from crystal structures of Au23L16 -40 and Au25L18 41 where different ligands were replaced by SCH3.

The found structures were subsequently reoptimized using PBE functional. 42,43 The absorption spectra were computed using Perdew-Burke-Ernzerhof exchange-correlation functional (PBE0). 43

Figure 1 .

 1 Figure 1. Absorption (a) and emission (b) spectra of AuCapt measured after several hours of incubation in buffers of various pH. The samples were excited with 550 nm. captopril (Capt) ligand occurring on treatment with low pH. The transformation of Au25 NCs into Au23 NCs is confirmed by electrospray ionization mass spectrometry and qualitative theoretical explanation based on DFT calculations.

Figure 2 .

 2 Figure 2. PL decays of AuCapt in pH = 7 (black), AuCapt in pH = 2 (green) and nanoclusters after treatment (drying and redissolving in pH = 7 buffer): AuCapt pH = 7 after treatment (red) and AuCapt pH = 2 after treatment (blue). IRFinstrument response function.

Figure 3 .

 3 Figure 3. a) Polyacrylamide gel electrophoresis of the product allowed to obtain two bands (left side), where the upper one is very similar to the basic sample Au25 (right side). ESI-MS analysis showed a detailed composition of the product. Well defined Au25Capt18 was used as control. Deconvoluted deconvoluted ESI-MS spectrum of AuCapt NCs before (b) and after pH=2 treatment (c). The corresponding ESI-MS spectra are given in Fig. S6 in SI.

  (1) pH=3, conversion process of the [Au25SR18] -anionic cluster into a charge neutral cluster [Au25(SR)18] 0 and (2) pH=2, degradation of the NCs with a loss of Au2SR or Au3SR, leading to fluorescent Au23(SR)17 and other sizes.

Figure 4 .Scheme 1 .

 41 Figure 4. Comparison between experimental (red line) and TDDFT calculated apsorption spectra (blue lines) for a) lowest energy structure of Au23Capt17 obtained by adding one ligand to Au23Capt16 and b) for higher energy structure (by 0.5eV) of Au23Capt17 obtained by removing two Au atoms and one ligand from Au25Capt18. Captopril ligands are replaced by -SCH3 groups in the calculations, for DFT calculations pbe0 functional and def2svp AO basis have been used.

Table 1 .

 1 PL lifetimes and QY of AuCapt in pH = 7 and 2 and after treatment (drying and redissolving in pH=7 buffer).

	AuCapt pH=7		pH=7	pH=2	pH=2 after
		(QY	=	after	(QY =	treatment
		0.37%)		treatment	3.9%)
	τ1 [ns]	264		200	207	250
		(0.09)		(0.08)	(0.18)	(0.12)
	τ2 [ns]	1778		1809	1516	1757 (0.88)
		(0.91)		(0.92)	(0.82)
	<τ>	1753		1794	1462	1728
	[ns] #

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 3

Acknowledgements

This work was supported by the National Science Centre under grants DEC-2013/10/A/ST4/00114 and DEC-2013/09/B/ST5/03417 and by a statutory activity subsidy from the Polish Ministry of Science and Higher Education for the Faculty of Chemistry of Wroclaw University of Science and Technology. We would like to acknowledge financial support of the French-Croatian project. "International Laboratory for Nano Clusters and Biological Aging, LIA NCBA. IDWS acknowledges support from a Royal Society Wolfson Research Merit Award. This research was supported by STIM -REI, a project funded by European Union from European Structural and Investment Funds 2014. -2020., Contract Number KK.01.1.1.01.0003.

Notes and references

Contributions

JOB conceived the initial idea and coordinated the work, MWa prepared the nanoparticles, MWa and JOB measured optical properties, MWa, JOB, MS analyzed the results. CCZ, FB, XD, RA performed and analyzed ESI-MS experiments. AKB, MTS, IDWS performed and analyzed PL lifetime measurements. ZS, VBK performed and analyzed DFT simulations. MR, MWa, MWo performed PAGE separation experiments. MS, RA, VBK, KM, IDWS, AO supervised and financed the project. JOB, MWa, RA, VBK wrote the paper. All the authors provided critical feedback and helped to shape the final manuscript.


N Briot

G Chagnon

C Masri

E Girard

Y Payan

Ex-Vivo Mechanical Characterisation of the Breast Cooper's Ligaments

Keywords: breast, Cooper's ligament, hyperelasticity

Introduction

Biomechanical modelling of human breast tissues has been widely studied for various medical applications such as surgical procedure training, pre-operative planning, diagnosis and clinical biopsy or imageguided surgery. Most research teams have designed subject-specific Finite Element (FE) models that are for example used to simulate breast deformations due to repositioning, compressions between plaques during mammography or tissue deformations due to needle biopsies. Such FE models usually include various breast tissues such as the skin, the mammary gland, adipose tissue and pectoral muscles. Mira and colleagues recently showed the importance of also including some suspensory ligaments as well as the superficial and deep fascia in these FE models [START_REF] Carton | A biomechanical breast model evaluated with respect to MRI data collected in three different positions[END_REF]. Among the suspensory ligaments, the net of Cooper's ligaments [START_REF] Gaskin | The fibro-adipose structure of the female breast : a dissection study[END_REF] probably plays a role in the global deformation of the breast. However, to the better of our knowledge, these ligaments have never been included in any biomechanical model. This is probably due to the fact that the constitutive behaviour of such ligaments has never been investigated, because (1) of the difficulty to extract them from a specimen and (2) of their extreme fragility once extracted, which makes any experimental characterisation complicated. This paper addresses this issue with samples of Cooper's ligament that were extracted and tested ex vivo in uniaxial tension. The results of the tests were fitted with an original hyperelastic constitutive equation. The variations of the parameters of that equation are highlighted.

Methods

Cooper's Ligaments Specimens

Cooper's ligaments are described as a mesh or a threedimensional net containing the fatty tissue and the mammary gland. They are attached to the dermis and pectoral muscle and merge on fascia layers. To sample Cooper's ligaments from a cadaver, the technique consists in making a lateral incision at the level of the ribs until reaching the pectoral muscles and the intercostal muscles and thus being able to access the breast from below going up toward the dermis. This allows a clear reading of the tissues found. Our sampling of Cooper's ligaments was distributed over the entire volume of the breast of one cadaver. Sizes of samples varied between 13.9 mm and 15.1 mm long, 1.4 mm and 4.9 mm wide and 0.04 mm and 0.3 mm thick. Each sample was cut in the direction of the main fibres visible to the naked eye. The sample should be cut in such a way to respect the dimensions of the uniaxial tensile specimens as well as possible, by respecting a ratio of approximately four between the length and the width of the sample. The uniaxial tensile tests were performed on an MTS model C42.503 machine with 25 N sensors (see panel on figure 1). To reproduce physiological conditions, each sample was placed on the tensile machine with a bath filled with a physiological serum heated to a temperature of 37°C (Masri et al, 2018). A tensile fracture test was performed on each sample.

Results and discussion

Figure 1 shows the results of the uniaxial tensile tests performed on 28 Cooper's ligament samples. The amplitudes of rupture stress and rupture strain during these tests are plotted on that figure. A relatively strong dispersion can be observed. The rupture stresses range from 250 kPa to 13 MPa with an average of 2.0 MPa. Rupture strains range from 1% to 16% with an average of 8.6%. The panel shows a ligament during a tensile test

The experimental curves present a horizontal step before a strain hardening. We propose to use a Neo-Hookean model [START_REF] Treolar | The elasticity of the network of long chain moleculus[END_REF] to describe the horizontal step and to use a power function to describe the hardening, thus assuming the strain-energy density function W with: 𝑊 = 𝐶 1 (𝐼 1 -3) + 𝐶 2 (𝐼 1 -3) 𝐶 3 (1) where I1 is the first invariant of the left Cauchy-Green tensor. The model has three parameters, C1 describing the initial slope and C2 and C3 describing the hardening. For each curve, an optimization process estimates the values of these three parameters to fit the experimental data. Figure 2 provides the range of variation of the three parameters estimated from experimental data on the 28 samples. The C1 parameter varies between 230 kPa and 2.5 MPa, with a median of 710 kPa, 50% of the population being between 480 kPa and 1.2 MPa. The C2 parameter varies between 1.3 MPa and 110 MPa, with a median of 16 MPa, 50% of the population being between 7.6 MPa and 33 MPa. The C3 parameter varies between 1.4 and 2.2, with a median of 1,7, 50% of the population being between 1.5 and 1.7. Table 1 gathers the average, maximal, minimal and standard deviation values for the rupture strain, rupture stress and Young modulus estimated from all the tests. The Young modulus was computed as E=6×C1 (assuming ligaments as quasi-incompressible).

The first point raised by table 1 is the high values for the equivalent Young modulus of Cooper's ligaments (two to three orders of magnitude stiffer than most breast soft tissue). The other point is the dispersion of the data (high standard deviations) as observed on the experimental curves. This can be explained in several ways: the freshness of the tissue (the cadaver was conserved in formalin), errors in section measurements (samples were sectioned by hand) or the various location of the tissue (the localisation can affect results). However, this is to our knowledge the first time that many samples of Cooper's ligaments were extracted and experimentally characterised by a tensile test.

Conclusions

Uniaxial tensile tests were performed on 28 Cooper's ligaments of a single cadaver. A wide dispersion of the results was observed for the rupture stress, the rupture strain and the Young modulus. Surprisingly, the stiffness of these Cooper's ligament is two to three orders of magnitude higher than the stiffness of most breast soft tissue. An original constitutive law was proposed to model the hyperelastic behaviour of the ligaments with an accurate approximation of the stress-strain curve during the uniaxial traction. As a perspective, other mechanical tests such as plane traction or channel compression could be used to check the behaviour of the model in these different cases of stress. Especially the anisotropy of Cooper's ligaments will have to be investigated.

Figure 1 .

 1 Figure 1. The uniaxial tensile tests on 28 Cooper ligaments.The panel shows a ligament during a tensile test

Figure 2 .

 2 Figure 2. Summary of all parameters obtained for the 28 Cooper ligaments (C1 and C2 are in MPa)

Table 1 .

 1 Summary of the mechanical values estimated from the 28 experimental tests

		Average Max Min Standard
					deviation
	Young Modulus	5.8	15	1,4	4.2
	in MPa
	Rupture Strain	8.6	16	1.0	4.2
	in %
	Rupture Stress	1.9	13	0.25 2.5
	in MPa


Aurèle ; Boussard

Adrian Fessel

Christina Oettmeier

Léa Briard

Hans-Gunther Dobereiner

Audrey Dussutour
email: audrey.dussutour@univ-tlse3.fr

Boussard Aurèle

Briard Léa

Döbereiner Hans-Günther

Dussutour Audrey

Adaptive behavior and learning in slime moulds: the role of oscillations

Keywords: Physarum polycephalum, Slime mould, Learning, Cognition, Oscillations, Synchronisation Physarum polycephalum, Slime mould, Learning, Cognition, Oscillations, Synchronisation 15 16 17 18

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Every living organism uses sensory and information-processing mechanisms to evaluate and interact with both 35 its internal milieu and its surroundings . Most processes underlying environmental monitoring, signal propagation or 36 integration of motor and sensory functions are evolutionary conserved between single-celled organisms and animals.

37

In this special issue, we emphasize that cognitive abilities such as perception, problem solving and learning are not 38 restricted to the animal kingdom, but have evolved in all organisms to satisfy the existential needs for survival [START_REF]Individuality, subjectivity, and minimal cognition[END_REF][START_REF] Van Duijn | Principles of minimal cognition: Casting cognition as sensorimotor coordination[END_REF][START_REF] Lyon | The cognitive cell: bacterial behavior reconsidered[END_REF][START_REF] Lyon | Of what is "minimal cognition" the half-baked version?[END_REF][START_REF] Garzón | Plants: Adaptive behavior, root-brains, and minimal cognition[END_REF][START_REF] Baluška | On Having No Head: Cognition throughout Biological Systems[END_REF].

39

As Bourgine & Stewart [START_REF] Bourgine | Autopoiesis and cognition[END_REF] stated, "A system is cognitive if and only if sensory inputs serve to trigger actions in a 40 specific way, so as to satisfy a viability constraint". Cognitive abilities rely on recursive chemical communication of 41 intracellular signalling networks which are highly organized in space and time and which depend on historical and 42 environmental context [START_REF] Koseska | Cell signaling as a cognitive process[END_REF]. The functional link between dynamic processes in cells and their cognitive abilities 43 remains to be elucidated. One of the recurrent patterns observed in cells are self-sustained oscillations which can 44 encode various information [START_REF] Behar | Understanding the temporal codes of intra-cellular signals[END_REF][START_REF] Purvis | Encoding and decoding cellular information through signaling dynamics[END_REF][START_REF] Levine | Functional roles of pulsing in genetic circuits[END_REF][START_REF] Isomura | Ultradian oscillations and pulses: coordinating cellular responses and cell fate decisions[END_REF]. The aim of this review is to discuss how learning in a unicellular organism might 45 rely on self-sustained oscillations. Our model system is the acellular slime mould Physarum polycephalum which 46 shows various oscillatory phenomena whose cognitive significance has yet to be demonstrated. [START_REF] Schenz | Uni-cellular integration of complex spatial information in slime moulds and ciliates[END_REF] Learning, defined as the modification of behavior by experience, is one of the major innovations in the 48 evolution of life. Using past experiences is often critical for optimal decision-making in a fluctuating environment and 49 is involved in every aspect of an organism's life, including foraging and interacting with other individuals. We usually 50 think of learning as a trait that is limited to Neurozoans (i.e., organisms with a central nervous system). Indeed, learning 51 is often equated with neuronal changes like synaptic plasticity, implicitly precluding its existence in aneural organisms 52 such as plants and unicellulars [START_REF] Dukas | Learning: mechanisms, ecology and evolution[END_REF]. While the evolutionary benefits of learning are clear, very little is known about 53 its origins. Even the simplest organisms must adapt to changing environments, raising the possibility that mechanisms 54 for learning might pre-date the evolution of nervous systems, possibly existing in a breadth of as-yet unstudied 55 organisms [START_REF] Lyon | The cognitive cell: bacterial behavior reconsidered[END_REF][START_REF] Garzón | Plants: Adaptive behavior, root-brains, and minimal cognition[END_REF][START_REF] Baluška | On Having No Head: Cognition throughout Biological Systems[END_REF][START_REF] Fernando | Molecular circuits for associative learning in single-celled organisms[END_REF][START_REF] Ginsburg | Epigenetic learning in non-neural organisms[END_REF][START_REF] Mcgregor | Evolution of associative learning in chemical networks[END_REF][START_REF] Westerhoff H V | Macromolecular networks and intelligence in microorganisms[END_REF][START_REF] Gagliano | Plants learn and remember: lets get used to it[END_REF][19]. Evidence for learning in single-celled organisms remains scant and, to date, only few 56 unequivocal reports of such processes have been described. Learning in single-celled organisms has been investigated 57 mainly in ciliates and acellular slime moulds, and there are several reliable reports documenting learning in Stentor 58 sp. [START_REF] Wood | Learning and adaptive plasticity in unicellular organisms[END_REF], Paramecium sp. [START_REF] Hennessey | Classical conditioning in paramecia[END_REF], Tetrahymena sp. [START_REF] Kunita | A ciliate memorizes the geometry of a swimming arena[END_REF] and P. polycephalum [START_REF] Boisseau | Habituation in non-neural organisms: evidence from slime moulds[END_REF]. 59 One of the most fundamental questions in cognitive science is: how can information inferred from interaction [START_REF] Manicka | The Cognitive Lens: a primer on conceptual tools for analysing information processing in developmental and regenerative morphogenesis[END_REF] with the physical world be encoded in physical/chemical changes in an organism, and how is it decoded as future 61 recall? Although many fundamental processes in the brain have been understood, the current state of the art in 62 neuroscience is still far from providing a complete picture. In particular, there exists no coherent explanation for how 63 higher cognitive function arises from the interplay of elementary biological mechanisms. To truly understand the most 64 fundamental mechanisms underlying learning and memory, it is essential to study the origins of cognition in 65 unicellular organisms that implement learning in a non-neural substrate.

66

Due to its comparably simple structure in relation to its behavioural complexity and due to the ease with which 67 it can be cultivated and manipulated, P. polycephalum presents itself as an ideal model system for relating basal 68 cognitive functions to biological mechanisms [START_REF] Oettmeier | Physarum polycephalum -a new take on a classic model system[END_REF][START_REF] Vallverdú | Slime mould: the fundamental mechanisms of biological cognition[END_REF][START_REF] Adamatzky | Thirty seven things to do with live slime mould[END_REF]. In principle, all processes are accessible, in many cases even 69 without disrupting the system and with spatiotemporal resolution constrained only by the experimental setup. In this 70 review, we explore how a simple physical process integrating oscillators could mechanistically explain complex The slime mould P. polycephalum is a remarkable organism belonging to the Amoebozoa. It is often used as a 75 model system to study problem-solving in aneural biological systems (Figure 1) [START_REF] Oettmeier | Physarum polycephalum -a new take on a classic model system[END_REF][START_REF] Vallverdú | Slime mould: the fundamental mechanisms of biological cognition[END_REF][START_REF] Adamatzky | Thirty seven things to do with live slime mould[END_REF][START_REF] Reid | Information integration and multiattribute decision making in non-neuronal organisms[END_REF]. Its vegetative state, the 76 plasmodium, is a giant mobile cell, whose basic structure consists of a syncytium of nuclei and an intracellular 77 cytoskeleton that forms a complex cytoplasmic network of veins (Figure 1). The plasmodium can extend to up to 78 hundreds of square centimetres and can be severed into viable and structurally similar yet smaller subunits. Upon 79 contact, plasmodia can fuse with each other, giving rise to the (re-)formation of a giant plasmodium [START_REF] Aldrich | Cell biology of Physarum and Didymium V1: organisms, nucleus, and cell cycle[END_REF]. P.

80

polycephalum can be reared and maintained in a liquid-shaking culture as micrometre-sized fragments 81 (microplasmodia) or as macroplasmodia on a solid substrate. Lastly, a starving plasmodium can encapsulate and enter 82 a dormant stage called sclerotium (Figure 1). P polycephalum can turn back from this resting stage to a plasmodium 83 within 24 hours after transfer to fresh food medium.

84

Both P. polycephalum's motion and its behaviour rely on its internal architecture. Its cytoplasm consists of a 85 visco-elastic (gel, also named ectoplasm) and a liquid (sol, also named endoplasm) phase [START_REF] Aldrich | Cell biology of Physarum and Didymium V1: organisms, nucleus, and cell cycle[END_REF]. This compartmentation 86 is due to a sharp concentration change of the fibrous proteins forming the cytoskeleton [START_REF] Radszuweit | An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum[END_REF]. Ecto-and endoplasm are 87 convertible into each other. The cell body of P. polycephalum is a transport network consisting of interconnected tubes 88 (Figure 1). Ectoplasm, which contains actin and myosin, forms the contractile walls of the tubes (Figure 1). Within 89 these veins flows the endoplasm, which contains organelles such as nuclei and mitochondria (movies S1 & S2). The 90 veins contract and relax periodically, causing the endoplasm to flow back and forth, a phenomenon termed "shuttle 91 streaming" [START_REF] Matsumoto | Locomotive mechanism of Physarum plasmodia based on spatiotemporal analysis of protoplasmic streaming[END_REF]. The vein network of P. polycephalum bears two analogies with the vertebrates' circulatory systems.

92

First, like the vasculature, the veins transport and distribute the endoplasm throughout the cell body. Second, the veins 93 are pore-like capillaries, allowing respiratory gases, molecules and organelles to be exchanged with the surrounding 94 cytoplasm [START_REF] Oettmeier | Form follows function: ultrastructure of different morphotypes of Physarum polycephalum[END_REF]. This open network allows to maintain homeostasis in cells ranging from 10 square micrometres to 10 95 square meters. The spatial structuration of P. polycephalum's vein network and its dynamics allows an efficient 96 regulation of the cytoplasmic flow within the entire cell [START_REF] Alim | Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual[END_REF][START_REF] Baumgarten | Functional organization of the vascular network of Physarum polycephalum[END_REF]. This vein network and the interactions between 97 ectoplasm and the endoplasm have been studied extensively by numerous biophysicists [START_REF] Nakagaki | Intelligent behaviors of amoeboid movement based on complex dynamics of soft matter[END_REF][START_REF] Alim | Fluid flows shaping organism morphology[END_REF].

98

The vein network is also responsible for cellular motility. P. polycephalum can migrate at a speed of up to 4 99 cm per hour [START_REF] Alim | Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual[END_REF] through the interplay of intracellular flow, adhesion and rhythmic contractions of the intracellular 100 actomyosin cytoskeleton [START_REF] Matsumoto | Locomotive mechanism of Physarum plasmodia based on spatiotemporal analysis of protoplasmic streaming[END_REF][START_REF] Alim | Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual[END_REF]. These contractions produce a pressure gradient that pushes the endoplasm towards 101 the cell periphery where the veins vanish and the endoplasm can flow freely. Local cytoskeletal reorganization and 102 local alteration of the actin-myosin cortex lead to the formation of pseudopods or fan shaped leading fronts which 103 extend and retract in synchrony with the shuttle streaming of the endoplasm [START_REF] Matsumoto | Locomotive mechanism of Physarum plasmodia based on spatiotemporal analysis of protoplasmic streaming[END_REF][START_REF] Lewis | Coordination of contractility, adhesion and flow in migrating Physarum amoebae[END_REF][START_REF] Baumgarten | Dynamics of frontal extension of an amoeboid cell[END_REF]. Based on internal and external 104 cues, P. polycephalum can adapt and alter its shape, size and motion. The frequency and the amplitude of the 105 cytoskeleton contractions depend on the quality of the environment [START_REF] Durham | Control of chemotaxis in Physarum polycephalum[END_REF][START_REF] Miyake | Relationship between intracellular period modulation and external environment change in Physarum plasmodium[END_REF][START_REF] Matsumoto | Propagation of phase wave in relation to tactic responses by the plasmodium of Physarum polycephalum[END_REF]. For instance, higher frequencies are 106 observed in response to attractive, high-quality resources [START_REF] Ray | Information transfer during food choice in the slime mold Physarum polycephalum[END_REF], whereas lower frequencies are recorded when P.

107 polycephalum encounters repulsive stimuli such as chemical repellents [START_REF] Matsumoto | Propagation of phase wave in relation to tactic responses by the plasmodium of Physarum polycephalum[END_REF]. As a result, slime moulds migrate toward 108 or away from a variety of external stimuli such as chemicals [START_REF] Durham | Control of chemotaxis in Physarum polycephalum[END_REF], light [START_REF] Marwan | Photomovement and photomorphogenesis in Physarum polycephalum: targeting of cytoskeleton and gene expression by light[END_REF], temperature [START_REF] Wolf | Thermotaxis and protoplasmic oscillations in Physarum plasmodia analysed in a novel device generating stable linear temperature gradients[END_REF], humidity [START_REF] Rakoczy | The myxomycete Physarum nudum as a model organism for photobiological studies[END_REF], gravity 109 [START_REF] Block | Gravitational response of the slime mold Physarum[END_REF] or substrate distortion [START_REF] Murugan | Mechanosensation Mediates Long-Range Spatial Decision-Making in an Aneural Organism[END_REF].

F o r R e v i e w O n l y b) P.

polycephalum's learning abilities

111 Although slime moulds lack the complex dedicated neural hardware of Neurozoans, the environment they 112 evolved in is no less complex and they face the same challenges: they must search for and choose between resources, 113 adapt to changing conditions, avoid dangers and find suitable microclimates to inhabit. P. polycephalum demonstrates 114 key aspects of complex decision making [START_REF] Oettmeier | Physarum polycephalum -a new take on a classic model system[END_REF][START_REF] Vallverdú | Slime mould: the fundamental mechanisms of biological cognition[END_REF][START_REF] Adamatzky | Thirty seven things to do with live slime mould[END_REF][START_REF] Reid | Information integration and multiattribute decision making in non-neuronal organisms[END_REF][START_REF] Schenz | Uni-cellular integration of complex spatial information in slime moulds and ciliates[END_REF][START_REF] Gao | Does being multi-headed make you better at solving problems? A survey of Physarum-based models and computations[END_REF] (Figure 1). It can find its way in a maze [START_REF] Nakagaki | Mazesolving by an amoeboid organism[END_REF], construct efficient 115 transport networks [50], distinguish how different masses distort the substrate [START_REF] Murugan | Mechanosensation Mediates Long-Range Spatial Decision-Making in an Aneural Organism[END_REF], avoid obstacles [START_REF] Reid | Slime mold uses an externalized spatial "memory" to navigate in complex environments[END_REF] and risky 116 environments [START_REF] Latty | Food quality and the risk of light exposure affect patch-choice decisions in the slime mold Physarum polycephalum[END_REF], optimize its nutrient intake [START_REF] Dussutour | Amoeboid organism solves complex nutritional challenges[END_REF][START_REF] Reid | Decision-making without a brain: how an amoeboid organism solves the twoarmed bandit[END_REF], and use conspecifics' cues to choose what substrate to exploit 117 [START_REF] Vogel | Phenotypic variability in unicellular organisms: from calcium signalling to social behaviour[END_REF][START_REF] Briard | Stress signalling in acellular slime moulds and its detection by conspecifics[END_REF]. All these feats rely on the abilities of P. polycephalum to sense and respond simultaneously to a wide range 118 of biotic and abiotic stimuli [START_REF] Durham | Control of chemotaxis in Physarum polycephalum[END_REF][START_REF] Miyake | Relationship between intracellular period modulation and external environment change in Physarum plasmodium[END_REF][START_REF] Matsumoto | Propagation of phase wave in relation to tactic responses by the plasmodium of Physarum polycephalum[END_REF][START_REF] Ray | Information transfer during food choice in the slime mold Physarum polycephalum[END_REF][START_REF] Marwan | Photomovement and photomorphogenesis in Physarum polycephalum: targeting of cytoskeleton and gene expression by light[END_REF][START_REF] Wolf | Thermotaxis and protoplasmic oscillations in Physarum plasmodia analysed in a novel device generating stable linear temperature gradients[END_REF][START_REF] Rakoczy | The myxomycete Physarum nudum as a model organism for photobiological studies[END_REF][START_REF] Block | Gravitational response of the slime mold Physarum[END_REF].

119 Despite their increasing recognition as a model for the study of complex behaviours in unicellular organisms, 120 surprisingly little attention has been paid to the ability of slime moulds to learn and to modify their behaviour 121 accordingly. Four studies have shown that P. polycephalum displays the capacity to learn [START_REF] Boisseau | Habituation in non-neural organisms: evidence from slime moulds[END_REF][START_REF] Saigusa | Amoebae anticipate periodic events[END_REF][START_REF] Vogel | Direct transfer of learned behaviour via cell fusion in non-neural organisms[END_REF][59]. In the first study, 122 Saigusa et al. [START_REF] Saigusa | Amoebae anticipate periodic events[END_REF] showed primitive anticipatory and recall behaviours. Individuals exposed to periodically occurring 123 negative stimuli were found to reduce their locomotive speed in response to each stimulus. When the negative stimuli 124 were withdrawn, the slime moulds spontaneously reduced their locomotive speed at the point in time when the next 125 negative stimulus would have occurred, i.e, they learned the periodicity. Once the spontaneous slowdowns stopped, 126 they could be induced again by a single negative stimulus, which implies recall of the memorized periodicity. This 127 study has sparked several models considering the involvement of oscillations in aneural learning, as will be further 128 discussed in section 4. In the second study, Boisseau et al. [START_REF] Boisseau | Habituation in non-neural organisms: evidence from slime moulds[END_REF] demonstrated habituation, the simplest form of learning, 129 in P. polycephalum. Habituation is a progressive decrease in the magnitude of a behavioural response to an iterative 130 stimulus. Using locomotion as the behavioural output and diverse chemicals as repellent stimuli, the authors showed 131 that P. polycephalum learned to ignore a chemical when it was encountered repeatedly for 5 days (habituation), but 132 responded again when the chemical was withheld for a certain time (spontaneous recovery). They also demonstrated 133 stimulus specificity and ruled out sensory and motor fatigue, often mistaken for habituation. In the third study, Vogel 134 & Dussutour [START_REF] Vogel | Direct transfer of learned behaviour via cell fusion in non-neural organisms[END_REF] showed that non-habituated slime moulds were able to directly acquire a learned behaviour from a 135 habituated slime mould via cell fusion. They revealed that the transfer of learned behaviour was effective only when 136 the vein networks merged and the cytoplasm streamed back and forth between the fused individuals. In the last study, 137 Boussard et al. [59] showed that the memory of habituation can be stored for a month during the dormant stage and 138 retrieved once the slime mould is revived. Chemical analyses indicated an uptake of repellent during the process of 139 habituation and its retention throughout the dormant stage. The authors showed a strong correlation between the level 140 of intracellular repellent and the habituation performance, and revealed that constrained absorption of the repellent 141 induced habituation in 2 hours. This study proposed that P. polycephalum absorbs the repellent and uses it as a 142 "circulating memory".

c) Inferring learning from motion analysis

144 Motion is straightforward to capture in almost any living system. In this regard, time scale is the only difference 145 between the wing flapping of hummingbirds and the pulsatile movement of P. polycephalum. While it is easy to detect 146 motion, given the right sampling frequency, it is much harder to infer intent from movement [START_REF] Manicka | The Cognitive Lens: a primer on conceptual tools for analysing information processing in developmental and regenerative morphogenesis[END_REF]. This highlights the 147 difficulty of designing experiments addressing cognitive abilities in aneural organisms. In other words, when do we 148 interpret a moving system as cognitive, as opposed to a purely biochemical or biomechanical process? Regardless of

F o r R e v i e w O n l y
149 the organism, at the microscopic scale, motion results from simple biological processes. In most cells, diverse 150 organization of the actin cytoskeleton can produce pushing, pulling, and resistance forces responsible for the whole 151 cell shape and migration [START_REF] Svitkina | The actin cytoskeleton and actinbased motility[END_REF]. Studies investigating learning or decision making in P. polycephalum interpret motion 152 as behaviours. For instance, Boisseau et al. [START_REF] Boisseau | Habituation in non-neural organisms: evidence from slime moulds[END_REF] measured the migration speed of P. polycephalum when facing a 153 repellent and concluded that habituation occurs when the speed ceased to be affected by the repellent. Thus, they 154 implied that motion can reflect cellular "memory" to previous stimuli. One can question the relevance of interpreting 155 motion as a cognitive output as opposed to simple biochemical processes.

156 Contrary to motion, demonstrating a cognitive ability in any living organism requires testable criteria.

157

Cognition can be defined as the individual capacity to perceive, process and use information. Despite numerous 158 evidence showing that cognitive abilities such as sensing, communication, memory, learning, decision making, etc.

159 are found in prokaryotes, single-celled eukaryotes, plants and fungi [START_REF] Westerhoff H V | Macromolecular networks and intelligence in microorganisms[END_REF], some authors restrict the existence of 160 cognition to neural organisms. For instance, Dukas [START_REF] Dukas | Evolutionary biology of animal cognition[END_REF] defines cognition as "the neuronal processes concerned with 161 the acquisition, retention, and use of information". Yet, a cognitive ability observed in several organisms could either 162 rely on similar mechanisms and share a common evolutionary origin or result from an evolutionary convergence [START_REF] Van Duijn | Phylogenetic origins of biological cognition: convergent patterns in the early evolution of learning[END_REF].

163 For instance, in Neurozoans, habituation results from the decreased release of chemical neurotransmitters at synaptic 164 terminals which modulate the weights of certain neural connections. However, in P. polycephalum and other single-165 celled organisms, habituation cannot be encoded in a neural network. Yet, a detailed analysis of P. polycephalum's 166 behaviour [START_REF] Boisseau | Habituation in non-neural organisms: evidence from slime moulds[END_REF] suggests that this organism is capable of habituation as it fulfils all the criteria that define a habituation 167 phenomenon [START_REF] Rankin | Habituation revisited: an updated and revised description of the behavioral characteristics of habituation[END_REF]. Thus, should we restrict a cognitive ability to its underlying mechanisms, and by doing so, preclude 168 its existence in many systems or should we consider together its biological function and its implementation [START_REF] Lyon | Of what is "minimal cognition" the half-baked version?[END_REF]? As 169 suggested by Marr [START_REF] Marr | Vision. A Computational Investigation into the Human Representation and Processing of Visual Information[END_REF], to study a cognitive system we need to answer three questions: what problem is the system 170 trying to solve? How does the system solve the problem at the behavioural level? and what are the mechanisms 171 underlying the behavioural response? The accumulating evidence supporting the existence of cognitive abilities in 172 slime moulds challenge us to understand what kind of physical systems underlie such abilities. One of the hypotheses 173 we make is that learning in slime moulds might result from intracellular oscillators, as oscillations can encode 174 information in their frequency, amplitude or duration. We especially focus on how the coordination of relatively 175 simple oscillatory processes at the cell and molecular levels results in the emergence of learning in P. polycephalum.

Oscillations in Physarum polycephalum

177 Oscillation occurs when "the values of variables characterizing the behaviour of a system repeatedly rise and 178 fall" [START_REF] Bechtel | Thinking dynamically about biological mechanisms: Networks of coupled oscillators[END_REF]. The minimal requirements for regular biological oscillations are the existence of a negative feedback loop, 179 a time delay in the occurrence of this feedback and the nonlinear interactions involved in this feedback [START_REF] Lenz | Temporal and spatial oscillations in bacteria[END_REF]. Longer

347

In biology, in artificial intelligence, and in physics, a system requires a certain level of complexity to process 348 time-variant information presented by multiple inputs while recalling and adjusting past experiences. This complexity 349 may be driven by the complexity of the system's microscopic units themselves, or/and by the nature and topology of 350 their interactions in conjunction with the system size. Systems of interacting oscillators are known to self-organize 351 their dynamics into diverse spatiotemporal patterns, possibly providing the required complexity. Once all differences 352 in structure, function and complexity between nervous systems and the tubular network of P. polycephalum are put 353 aside, what remains are biological systems that self-organize their structure as complex networks and their function 354 as interacting and oscillatory units that give rise to emergent properties, resulting in well-controlled behaviours.

355 Physics procures universal frameworks to apprehend the complexity of such biological systems, and in 356 particular unraveling the working principles of information processing in Neurozoans has seen significant progress in 357 the recent past. In this section, as a perspective for future research, we raise the question whether similar microscopic 358 interactions result in similar capacities among seemingly very different organisms. To lay the basis for developing 359 this perspective further, we provide in section 4.a a brief overview of synchronization phenomena. In section 4.b we 360 explore how integration of environmental information can be facilitated by oscillating systems via the modification 361 of an attentive resting state, and candidate mechanisms that can generate and maintain such a state are discussed in 362 section 4.c. Interestingly, the very same mechanisms support adaptation and learning in artificial and non-artificial 363 systems. This is addressed in section 4.d.

a) Synchronisation, a prerequisite

365 Synchronization, a phenomenon arising from the interaction of two or more oscillators, can be observed in 366 many biological systems. The position of an oscillator in its cycle can be described in terms of its phase, which 367 advances at a pace set by the oscillator's natural frequency. Interacting oscillators influence each other's phase 368 progression (Figure 2). A paradigm for synchronization is a population of globally coupled oscillators (i.e each 369 oscillator in the population is affected by the dynamics of the rest) in which the natural frequencies are initially 370 heterogeneously distributed. As time progresses, the oscillators minimize their pairwise phase differences, resulting 371 in a pattern known as full synchronisation, where all oscillators operate at the same instantaneous frequency and phase.

b) Integration of environmental information

403 Both in nerves and in P. polycephalum's veins, chemical oscillations are responsible for conveying macro-404 oscillations as well as transport or motion at the organism scale. What we call macro-oscillations might be the rhythmic 405 movement of the human legs, the wings of a bird, as well as the centre of gravity of a P. polycephalum plasmodium 406 [START_REF] Matsumoto | Locomotive mechanism of Physarum plasmodia based on spatiotemporal analysis of protoplasmic streaming[END_REF]. Why are these motions rhythmic? An enticing argument arises from a neuroscience perspective, stating that 407 rhythmicity provides a powerful tool for organisms to infer easily from their environment. Buzsáki [START_REF] Buzsaki | Rhythms of the Brain[END_REF]

  We hypothesize that, as in the brain, modulation of spontaneous oscillations may sustain learning 32 in slime mould.

2 .

 2 Cognitive abilities of Physarum polycephalum a) P. polycephalum: a unique model 74

  320activators and inhibitors. The oscillations in CDK activity, in complex with regulatory cyclin subunits drive the cell-321 division cycle. In parallel to experimental measurements, mathematical modeling of the cell cycle has proved helpful 322 in unravelling how interacting proteins such as Cyclin and their partner CDK control the dynamics of cell-division.323These models contributed to the modern understanding of the cell as a complex dynamical system [109-111].324Cyclins and CDK are present in all eukaryotes, including P. polycephalum(Schaap). In P. polycephalum,325the vigorous actomyosin-driven cytoplasmic streaming described earlier ensures that local accumulation of 326 Cyclin/Cdk complexes diffuses and triggers the activation of Cyclin/Cdk complexes in neighboring nuclei [112], 327 maintaining mitotic synchrony [113]. Until now, Yeasts have historically been a major model system to understand 328 the control of the cell-division cycle in animals, taking advantage of their powerful genetics and rapid duplication 329 times. However, many otherwise conserved cell cycle regulators have been lost in this organism. In contrast the 330 complete set of Physarum cell cycle regulatory molecules has been identified [112]. Hence, with new options for 331 experimental manipulation and in conjunction with mathematical modeling, P. polycephalum could become once 332 more an attractive model organism to study cycle regulation at the regulatory complexity of a mammalian cell. 333 Mitotic and genetic oscillators are relevant to understanding learning and memory in P. polycephalum not only 334 due to their oscillatory nature, but also because they provide a way to encode past experiences as epigenetic changes. 335 The concept of epigenetic memory was defined by D'Urso & Brickner [114] as "a stable propagation of a change in 336 gene expression induced by developmental or environmental stimuli". Epigenetic memory impacts gene expression 337 and their associated feedback loops over both short and long timescales. Several evidence suggest that epigenetic 338 mechanisms can regulate the ability to store long-term memories in Neurozoans, it might also be true for aneural 339 organisms [115].

340 4 .

 4 From oscillations to learning341Biological systems of very different architecture and complexity, representatively the (central) nervous system 342 and the slime mould P. polycephalum, possess the ability to orchestrate complex behavioural patterns. This includes the dynamics of both systems reveals that they share a basal feature: they show rich oscillatory 346 dynamics (section 3).

  sees leg 408 movements as an oscillating system in which perturbations indicate an environmental change. Considering leg 409 movement, a change of the floor topology will disturb the movement rhythmicity and therefore will become a piece 410 of integrated information allowing motion continuation. 411 Hence, an environmentally-driven behavioural change can be seen as integration of environmental information 412 through change in the oscillatory pattern. A prominent example is found in rats, in which active movement of the 413 whiskers generates the sense of touch. The perturbation of the whisker movements following a contact with an object 414 elicits a sensory signal that carries information about the object. In rats, whisker motion over a texture produces a 415 specific temporal profile of velocity, which is encoded in the temporal pattern of neural activity, for instance rougher 416 surfaces evoke higher firing rates [125].

Figure 1 :

 1 Figure 1: These pictures illustrate a) a macroplasmodium; the vegetative phase of P. polycephalum, b) a sclerotium, the dormant stage, c) a slime mold making a decision between different food sources varying in quality, d) a vein network, e) a magnified vein and d) the nuclei stained with DAPI within the plasmodium.

Figure 2 :

 2 Figure 2: Oscillations, coupling & synchronization: a) the (instantaneous) phase indicates the state of an oscillator, b) the change of phase is driven by the natural frequency and coupling, c) coupling can be global or local, mediated by a network topology, d-f) states of a random planar network of Kuramoto oscillators, see supp. movies 3&4, d) desynchronization, e) dynamical wave synchronization (local coupling), f) full synchronization (global coupling).

Short-period oscillations in P. polycephalum: the contraction cycle 212

  When facing a repellent in its environment, P. polycephalum reduces its migration speed. However, as 213 mentioned earlier, constrained absorption of the repellent quickly attenuates this behaviour, and the slime mould 214 behaves almost as if the repellent was absent (habituation)[START_REF] Boisseau | Habituation in non-neural organisms: evidence from slime moulds[END_REF]. Thus, the entry of repellents into the cell might interact 215 with the shuttle streaming responsible for the migration of the organism[59]. In P. polycephalum, several well-defined 216 chemical oscillators control regular relaxation-contraction patterns which locally drive the intracellular flow and are 217 at the root of further large-scale patterns such as migration and cell shape. In turn, the shape and motion of the cell 226 most important examples of cellular rhythm in most organisms. In P. polycephalum, free intracellular [Ca2+] is 227 directly linked to actomyosin contraction [77-79]. [Ca2+] and actomyosin contractions oscillate with a similar period 228 but in approximate anti-phase [80,81], because the actin-myosin interaction is inhibited by [Ca2+] [82]. In the resting 229 state, the cytoplasmic concentration of [Ca2+] is kept as low as possible. Excess [Ca2+] is either extruded via the cell 230 membrane or sequestered in mitochondria and cytoplasmic vesicles. When the cell is stimulated, [Ca2+] increases due 231 to its release from storage or the entry of extracellular [Ca2+]. This transient increase is used by the cell as a secondary 232 messenger to regulate the interaction between actin and myosin. However, in contrast to animal cells, in P.

	187 266 305	The human brain self-generates numerous oscillations, i.e., regular fluctuations in electrical potential occurring [93]. When irradiated with UV light, the contractions can be stopped without affecting the rhythmic variation of hours, followed by a long G2 phase and 30 minutes mitosis (the nuclear division itself) [28]. In P polycephalum, gene
	188 267 306	simultaneously in many neurons, whose frequencies range from infraslow <0.01Hz to ultrafast 600 Hz [69]. NAD(P)H. Thus, the NAD(P)H oscillator works independently of the rhythmic contractile system, but seems to be transcription, and in particular mRNA transcription, goes from zero during mitosis to a maximum in early S-phase
	189 268 307	Neuroscientists categorize these oscillations according to their frequency (from the slowest to the fastest: slow-wave entrained with it. A continuous energy production in the form of ATP appears to be necessary for oscillatory [103]. Remarkably, the plasmodium exhibits synchronous mitotic division of its entire population of nuclei and
	190 269 308	sleep, delta, theta, alpha, beta, gamma, and ripples oscillations). At a global scale, slow oscillations generate large and contractions. Both glycolysis, an oscillatory process in itself, and mitochondrial respiration influence the regulation therefore, the number of nuclei doubles every cell cycle [28]. Pieces cut off from a plasmodium maintain this
	191 270 309	synchronous membrane potential fluctuations in large populations of neurons whereas, at a local scale, fast oscillations of the contraction oscillations. synchrony for a certain time and two asynchronous plasmodia can synchronise their mitotic rhythm after fusion [104,
	192 271 310	produce such fluctuations in smaller populations of neurons [70]. Indeed, contrary to what occurs in a computer, where In addition to the chemical oscillators, it should be mentioned that spatiotemporal oscillations can also originate from 105]. Experiments on the cell cycle, particularly those employing fusion techniques in P. polycephalum [104, 105]
	193 272 311	communication is equally fast between close and distant units, in the brain, fast oscillations are limited to local mechano-chemical properties of an active material [94-96]. Spatial coordination can be achieved by mechanical gave rise to pioneering theoretical models [106, 107] that presented the mitotic oscillator as a dynamical system and
	194 233 273 312	assemblies of neurons, due to biological constraints (i.e. axonal conduction delays) [70]. Hence, brains use a complex polycephalum intracellular [Ca2+] is an inhibitor [83]. High [Ca2+] coincides with relaxation whereas low [Ca2+] interactions between different regions (e.g. [97]), and local positive feedback between deformation and contraction of suggested that synchronous mitotic division emerges from dynamic interactions of regulatory molecules. P.
	195 234 274 313	system of multiple oscillators for its operations when a computer only uses one. These different oscillators in the brain induces contraction. The [Ca2+] oscillator was first modelled by Smith & Saldana [84], using a phosphorylation-the contractile apparatus induces the observed characteristic contractile behavior by hydrodynamic interaction alone polycephalum was considered as the ideal organism to study the cell cycle in the seventies. However, due to the lack
	196 235 275 314	coexist and interact with each other hierarchically: the slower oscillators often modulate the faster ones, a phenomenon dephosphorylation cycle of myosin light chain kinase. [Ca2+] waves travel at approximately 5 µm/s, suggesting that via the streaming of endoplasm. However, more realistic models combine the interaction of mechanical and chemical of tools to disrupt gene function in P. polycephalum, in the eighties most researchers turned to other model systems
	197 236 276 315	referred to as cross-frequency coupling [71]. Using this coupling, brains can integrate distributed local processes into they are not propagated by shuttle streaming [85], which is much faster (up to several mm/s). Furthermore, in absence oscillations. It was found that the temporal frequency is set by the chemical oscillator, whereas wavelength is in which they could test their hypothesis.
	198 237 238 239 240 241 277 316 278 317 279 280 318 319	F o r F o r of external stimulations, [Ca2+] is not homogeneously distributed within the cell but forms a gradient throughout the globally ordered states. plasmodium [86], the mean concentration at the front is higher than that at the rear, establishing cellular polarization during migration. Both repellents and attractants change the spatio temporal pattern of [Ca2+]. A stimulation with an attractant at the rear, increases the frequency of [Ca2+] oscillations, raising [Ca2+] at the stimulation site, whereas a repellent has the opposite effect. F o r In the last decades, numerous independent genetic and biochemical studies using different organisms such as determined by a mechanochemical instability [98]. In addition, only a combined model such as ([98], [94]) F xenopus and yeast identified a major evolutionarily conserved regulatory network for cell-division cycle (i.e mitosis) allows for migration of microplasmodia. Radszuweit and coworkers ([96]) proposed a model for the oscillations which is based on both chemical (i.e. exchange of calcium between the cytosol and storage vessels) and mechanical factors (i.e., flow and deformation). regulation [108]. This network includes a cyclin that is periodically synthesized and degraded at specific cell cycle o r phases and a kinase (cyclin-dependent kinases CDK) that is regulated by phosphorylation and interaction with
		R R R R
		e v i e w e v i e w e v i e w e v i e w
		O O O O
		n l n l n l n l
		y y y y
	253	Oscillations of H+ and cAMP also accompany the oscillatory contractility of P. polycephalum [91]. Cytosolic
	254	H+ oscillations are a by-product of oxidative phosphorylation and are in phase with ATP oscillations; they are related
	255	to the energy metabolism [91]. cAMP oscillates ~ 60° ahead of the [Ca2+] oscillations [85,88], and is also involved
	256	in cell polarization. It forms a gradient from front to back, with the back showing several times higher concentrations
	257	than the front. Knowing that ATP and H+ trigger contraction and oscillate in phase whereas cAMP and [Ca2+] are
	180 218 258	time delays in the feedback cause longer periods of oscillation. Oscillations are ubiquitous in biology from the influence these local oscillations [73-75]. Relaxation-contraction patterns are generated through intrinsic nonlinear responsible for the relaxation, Ueda et al. [88] proposed that a feedback loop consisting of ATP, H+, cAMP and [Ca2+]
	181 219 259	intracellular chemical level to the ecological level. They vary in time scale from seconds (ion transport or calcium oscillatory phenomena in the plasmodium supported by complicated mechanochemical reactions among intracellular controls the contraction cycle. They postulated that a negative feedback occurs from [Ca2+] to ATP-H+ in the
	182 220 260	release), to minutes (changes in protein levels during the cell cycle), to hours or days (changes in cell morphology), chemicals such as ATP, free intracellular calcium ([Ca2+]) and actin, but also among organelles. These oscillators are mitochondria where ATP is produced due to H+ influx and Ca2+ entrance in exchange of H+. Ueda et al. [88]
	221 261	interconnected, often coupled, and partially dependent on each other [76]. Most of the observed chemical oscillators suggested that these interactions between [Ca2+], ATP and H+ are involved in the time-keeping of the rhythmic
	222 262	are associated with energy metabolism and respiration, with mitochondria being most prominently involved at the oscillations.

183

and up to years (generation time). The most universal oscillator is the circadian clock which is found in a variety of 184 living organisms, including mammals, insects, plants, fungi, and cyanobacteria

[START_REF] Young | Time zones: a comparative genetics of circadian clocks[END_REF]

. The pervasiveness of oscillations 185 stresses the importance of thinking dynamically about the mechanisms underlying the behaviour of a biological 186 system. Hence, a good appreciation of the timescale of this system is crucial for understanding its behaviour. 199 In the human brain, specific oscillation signatures are related to learning and memory processes. For instance, 200 theta and gamma oscillations are mainly observed during learning processes. Slow-wave sleep and sharp-wave ripples 201 are instrumental in consolidation of memories [72]. Neuronal oscillators are complex but rely nonetheless on 202 principles that are comparable to those of oscillators in other biological systems. Similarly to the brain, P. 203 polycephalum is organized at multiple temporal and spatial levels and it is tempting to relate this spatiotemporal 204 architecture to its cognitive abilities. Our goal in this review is to understand the potential link between the oscillations 205 observed in P. polycephalum and its learning capacities. In the next section, we will describe the variety of oscillations 206 reported in P. polycephalum. We will highlight how oscillators play an important role in diverse organismal functions 207 on a continuum of time scales. We will first focus on the relaxation-contraction cycle which relies on short-period 208 oscillations (90 sec). Then, we will present the nuclear division and gene expression cycle which are characterized 209 by long-period oscillations (few hours). Short-period oscillations could support short-term memory whereas longer-210 scale oscillations could be involved in long-lasting memories. a) 242 Another oscillatory compound is ATP, which is distributed in patterns throughout the plasmodium [87] and 243 exhibits oscillations in phase with the relaxation-contraction cycle [76,80]. ATP efflux increases during the contracting 244 phase whereas it decreases during the relaxing phase. In a migrating plasmodium, ATP concentrations are 245 approximately twice as high at the front [88] than at the rear. ATP provides energy for the contraction of the 246 actomyosin cytoskeleton, which in turn generates cytoplasmic streaming. The ATP producing pathways, e.g., 247 glycolysis in the cytoplasm and biological oxidation in mitochondria, influence directly the contractile activity of P. 248 polycephalum. Hence, there is a strong link between energy metabolism and locomotion. When the plasmodium is 249 starved, ATP synthesis is impacted and the slime mould is constrained to switch to different energy-generating 250 mechanisms [89] or initiate more drastic measures (e.g. sclerotization or sporulation). Inhibition of both ATP synthesis 251 and respiration in mitochondria stop locomotion but inhibition of ATP synthesis alone does not. Thus, it was suggested 252 that another mitochondrial function, such as [Ca2+] regulation, controls the rhythmic contractions [76,90]. 263 Experimental and theoretical evidence indicates that mitochondrial energetic variables oscillate autonomously 264 as part of a network of coupled oscillators

[START_REF] Aon | Mitochondrial oscillations in physiology and pathophysiology[END_REF]

. The concentration of intracellular NAD(P)H in plasmodia of P.

265

polycephalum was found to oscillate with the same period as the rhythmic contractions, but a third of the period ahead 281

We can assume that the contraction cycle in P. polycephalum relies on a feedback system between the 282 contractile apparatus (i.e. the actomyosin system), the calcium regulatory system, and the energy metabolism

[START_REF] Satoh | Primary oscillator of contractional rhythm in the plasmodium of Physarum polycephalum: role of mitochondria[END_REF]100]

.

283

It stands to reason that, since all of these oscillators are highly interconnected, they must be synchronised in some 284 manner to produce coordinated behaviours as a function of environmental conditions (e.g. [101]). These oscillators 285 might be involved in learning and memory as any encounter with a stimuli could be encoded and stored as changes 286 in the contraction cycle and by extension as modifications of the vein network architecture.

  a random planar network. Indeed, synchrony in a population of oscillators is crucially affected by the 385 topology of their network (regular lattice, random network, small-world network, etc.). This lies as the foundation of 386 diverse dynamics observed in biological networks, such as the central nervous system. Synchrony in the brain supports 387 neural communication and neural plasticity and is relevant for many cognitive processes[119]. Similarly,

	384 movie 4 for 388 synchronisation phenomena observed in the plasmodium's intrinsic cellular oscillations have been suggested to
	389	support complex behavior in P. polycephalum [120].
	390	As described previously (section 3.a), transport of cytoplasm in P. polycephalum is actively driven by rhythmic
	391	contractions associated with biochemical oscillations. The rhythmic contractions typically organize as traveling waves
	392	[32, 121], but other patterns such as rotating spirals are observed [122]. Although a variety of active materials is
	393	capable of generating such patterns, they can also be indicative of locally coupled oscillator systems. Unlike neural
	394	networks or cardiac cells, the plasmodium of P. polycephalum is not composed of discrete, interacting units but instead
	395	forms a continuous yet inhomogeneous material (section 2.a). It has been shown that P. polycephalum reproduces the
	396	F dynamics of coupled oscillators at large spatial scales when introducing an artificial discretization by shaping the
	397 398	plasmodium into extended patches connected by thin veins [73, 123]. In this setting, due to the imposed asymmetry, o r the connections were largely passive. In contrast, in naturally-grown plasmodia the connecting veins contribute
	399 400 401	actively to the oscillatory dynamics. Here, it appears necessary to move to smaller spatial scales by regarding the R w e i v plasmodium as a continuum of oscillators coupled locally via diffusion, advection of chemicals through active e transport, and through mechanical interaction. This approach has been pioneered by Kobayashi et al. [124].
		O
		n l
		y
	372	This is described mathematically by the canonical Kuramoto model [116], which predicts a phase transition between
	373	desynchronised and synchronised states, based on the global coupling strength (Figure 2.d and 2f, Supplementary
	374	movie 3). Synchronous mitosis in P. polycephalum illustrates such global coupling leading to a state of full
	375	synchronisation. Here, nuclear division is robustly controlled across the entire organism and occurs when the ratio of
	376	DNA to cytoplasm in the plasmodium drops below a certain value due to an increase of the cellular volume [117].
	377	Modifications of the Kuramoto model give access to a much richer spectrum of synchronisation patterns as
	378	observed in many biological systems such as cardiac cells, populations of fireflies or assemblies of neurons.
	379	Strikingly, employing local instead of global coupling or combinations thereof can lead to the emergence of complex
	380	spatiotemporal patterns. These patterns range from full synchronisation or desynchronisation to spiral waves, traveling
	381	waves (Figure 2.e), and even to curious chimera states [118], where part of the population is synchronised and part is

  423P. polycephalum responds first by adjusting its oscillation frequency and amplitude locally. This change then spreads 424 over the entire network [126] and finally the morphology of the slime mould adapts to the environment [127]. Positive 425 stimuli such as chemoattractants lead to increased frequencies whereas negative stimuli such as chemical repellents 426 lead to a decrease (section 3.a.). Consequently, it appears reasonable to assume that the stimulated regions in-or We do not have the answer yet, but we believe that the process of habituation in P. Natsume K, Miyake Y, Yano M, Shimizu H. 1992 Development of spatio-temporal pattern of Ca 2+ on the chemotactic behaviour of Physarum plasmodium.

		polycephalum. In International review of cytology, pp. 102. Hernandez PJ, Abel T. 2008 The role of
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		83. Kohama K. 2016 Calcium inhibition as an amid decades of debate. Neurobiol. Learn. Mem. 89,
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	427	decrease their importance for the global oscillation pattern: positively stimulated fronts act as pacemakers, whereas Jpn. Acad., Series B 92, 478-498. 103. Sauer HW. 1978 Regulation of gene
	428 429 430 431	negatively stimulated regions concede. Indeed, it is observed in small fragments [121] and in macroplasmodia expression in the cell cycle of Physarum. In Cell cycle 84. Smith DA, Saldana R. 1992 Model of the Ca2+ (personal observation), that travelling waves responsible for mass displacement are directed towards those fronts regulation (eds., Jeter JR, JL Cameron, Padilla GM, oscillator for shuttle streaming in Physarum where the slime mould extends, underlining the plausibility of this concept. Hence, an encounter with an external Zimmermann, AM), pp.149-166. Academic Press, New polycephalum. Biophys. J. 61, 368-380. stimulus could be memorized as a change in the spatiotemporal dynamics of the system. Returning to the results of York.
	432	Boisseau et al [23], we might wonder: how does the global oscillation pattern change in response to repetitive 85. Mayne R. 2016 Biology of the Physarum
	433 stimulations to allow habituation? 434 polycephalum plasmodium: 104. Rusch HP, Sachsenmaier W, Behrens K, preliminaries for Polycephalum relies on both an attentive resting state and mechanisms to adapt the oscillation patterns to changing unconventional computing. In Advances in Physarum Gruter V. 1966 Synchronization of mitosis by the
	435 443	F o r R e v i e w F o r R e v i e w F o r R e v i e w F o r R e v i e w F o r R e v i e w F o r R e v i e w F o r R e v i e w F o r R e v i e w F o r R e v i e w Machines, pp. 3-22. Springer. environments. this article. F o r R fusion of the plasmodia of Physarum polycephalum. J. F F F Cell Biol. 31, 204. 105. Guttes E, Guttes S. 1964 Mitotic synchrony in the plasmodia of Physarum polycephalum and mitotic synchronization by coalescence of microplasmodia. o r R o r R o r R 86. Protoplasma 166, 55-60. 87. Ueda T, Mori Y, Kobatake Y. 1987 Patterns in the distribution of intracellular ATP concentration in relation to coordination of amoeboid cell behavior in Physarum polycephalum. Exp. Cell Res. 169, 191-201. 88. Ueda T, Matsumoto K, Akitaya T, Kobatake Y. e v i e w Methods Cell. Biol. 1, 43-54. 106. Tyson J, Kauffman S. 1975 Control of mitosis by a continuous biochemical oscillation: synchronization; spatially inhomogeneous oscillations. e v i e w e v i e w e v i e w	proposed in
	444 445 446 447 448 449 450 451	O n l y Resting state activity in the brain is not immediately related to any motor task or sensory input. It represents spontaneous activity that is closely related to the functional organization of the neural network and encompasses both, sub-threshold membrane potential oscillations and patterns of neural spiking activity. By assisting spike-timing dependent plasticity (see section 4.d), synchronisation of the sub-threshold activity facilitates reliable and precise section 4.b). slime mold Physarum polycephalum. Protoplasma functions, such as different states of consciousness and focus [129, 130]. Finally, it interacts with external inputs (see numbers increase during glucose deprivation in the optimization of the learning process, network development in the brain and is believed to be implicated in higher 89. Oettmeier C, Döbereiner H-G. 2019 Mitochondrial adaptation of synaptic strengths [128]. Therefore, the resting state is involved in organization of the neural activity, O n l y O n l y O n l y O n l y O n l y O n l y O n l y O n l y 1986 Spatial and temporal organization of intracellular O O O O adenine nucleotides and cyclic nucleotides in relation to rhythmic motility in Physarum plasmodium. Exp. n l n l n l n l Cell Res. 162, 486-494. y y y y
	452	Recent results suggest that the observed resting state patterns indicate a state at which the brain is stable yet
	453	responsive. This is summarized as the critical brain hypothesis [131], stating that the brain operates, controlled by a
	454	self-organizing process, in a subcritical regime, yet close to the critical point [132], where it is most excitable.
	455	Hence, the information given by mechanoreceptors is directly encoded into a Criticality is an umbrella term that denotes the behaviour of a system perched between order and disorder. In the brain,
	417 456	new oscillatory pattern in the brain. This kind of functioning pervades the neural sensing of external stimuli, and the subcritical regime is considered as unexcitable, whereas the critical regime displays cascades of activity unrelated
	418 457	changes in oscillatory patterns are likely to be a common mechanism by which Neurozoans integrate and store to any input. Neither regime is favourable for normal brain function and excitations lead to a controlled response only
	419 458	information. slightly below the critical point.
	420	P. polycephalum's biochemical and cytoplasmic oscillations may have a similar purpose and might offer a

c) Maintaining excitability: resting state activity & self-organized criticality 437 As outlined in the previous section, disturbance of an oscillatory resting state via an input is an efficient 438 mechanism for integrating environmental information. This mechanism is extensively used in Neurozoans' central 439 nervous systems. Here, we describe how the resting state affects neural functioning and introduce a number of 440 advanced mechanisms that can maintain or modify the resting state of an oscillatory system. These mechanisms have 441 proven to be relevant in the context of self-organization or adaptive control, in particular in neural systems. Their 442 involvement in P. polycephalum is unclear yet appears to be entirely possible in the light of the analogy 459 Evidence suggests that the phase transition associated with the critical point in question is in fact the transition 460 between desynchronisation and synchronisation [133] (see also section 4.a), highlighting once more that 461 synchronisation, a very basic feature of coupled oscillatory systems, is at the very heart of coordination of complex

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organelle level. In the following, we will present the chemical oscillators that have been described in P. polycephalum.

[START_REF] Aldrich | Cell biology of Physarum and Didymium V1: organisms, nucleus, and cell cycle[END_REF]. In contrast to most cells, mitosis is not followed by cytokinesis and it occurs within the nuclear membrane (closed

possible explanation for the organism's ability to process, integrate and store information. P. polycephalum exhibits

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