Boris Maletckii
email: maletckii@ipgp.fr

Elvira Astafyeva

Determining spatio-temporal characteristics of Coseismic Travelling Ionospheric Disturbances (CTID) in near real-time

Keywords: ionosphere, GNSS, earthquakes, TEC, TIDs, real-time

Earthquakes are known to generate ionospheric disturbances that are commonly referred to as co-seismic travelling ionospheric disturbances (CTID). In this work, for the first time, we present a novel method that enables to automatically detect CTID in ionospheric GNSS-data, and to determine their spatio-temporal characteristics (velocity and azimuth of propagation) in near-real time (NRT), i.e., less than 15 minutes after an earthquake. The obtained instantaneous velocities allow us to understand the evolution of CTID and to estimate the location of the CTID source in NRT. Furthermore, also for the first time, we developed a concept of real-time traveltime diagrams that aid to verify the correlation with the source and to estimate additionally the propagation speed of the observed CTID. We apply our methods to the Mw7.4 Sanriku earthquake of 09/03/2011 and the Mw9.0 Tohoku earthquake of 11/03/2011, and we make a NRT analysis of the dynamics of CTID driven by these seismic events. We show that the best results are achieved with high-rate 1Hz data. While the first tests are made on CTID, our method is also applicable for detection and determining of spatio-temporal characteristics of other travelling ionospheric disturbances that often occur in the ionosphere driven by many geophysical phenomena.

Introduction

It is known that natural hazard events, such as earthquakes, tsunamis and/or volcanic eruptions generate acoustic and gravity waves that propagate upward in the atmosphere and ionosphere [e.g., 1; 2 ;3 ;4 ;5 ;6 ;7]. Earthquake-driven ionospheric disturbances are called co-seismic travelling ionospheric disturbances (CTID). The first CTID are generated directly by the ground or the seafloor via acoustic waves, they reach the ionospheric altitudes (~200-350 km) in only 7-9 minutes. They are followed by acoustic waves generated by the surface Rayleigh waves, tsunami gravity waves. Nowadays, with the development of permanent networks of dualfrequency Global Navigation Satellite Systems (GNSS) receivers, the detection of CTID and other Natural-Hazard-driven (NH-driven) ionospheric perturbations has nowadays become quite regular [e.g., 8; 9; 10; 11; 5; 12].

Recently, it has been suggested that NH-driven ionospheric disturbances can be used for more advanced purposes: to localize NH and to estimate the characteristics of the source [e.g., 13; 9; 4; 14; 15; 16; 17; 18; 19]. Kamogawa et al. [START_REF] Kamogawa | A possible space-based tsunami early warning system using observations of the tsunami ionospheric hole[END_REF] suggested a method based on observations of a "tsunami-ionospheric hole", ionospheric depletion that often occurs after major earthquakes over the epicentral area. Based on the analysis of seven tsunamigenic earthquakes in Japan and Chile, Kamogawa et al. [START_REF] Kamogawa | A possible space-based tsunami early warning system using observations of the tsunami ionospheric hole[END_REF] found a quantitative relationship between the initial tsunami height and the TEC depression rate. Manta et al. [START_REF] Manta | Rapid identification of tsunamigenic earthquakes using GNSS ionospheric sounding[END_REF] developed a new ionospheric tsunami power index based on measurements of CTID. They showed that the ionospheric index scales with the volume of water displaced due to an earthquake. However, neither of these methods is real-time compatible. As near-real-time (NRT) mode, we refer to as 10-15 minutes after an earthquake. Going further towards NRT, Savastano et al. [START_REF] Savastano | Real-time detection of tsunami ionospheric disturbances with a stand-alone GNSS-receiver: a preliminary feasibility demonstration[END_REF] made the first preliminary feasibility demonstration for ionospheric monitoring by GNSS, by developing a software VARION that can derive TEC in NRT. Their technique has been implemented at several GNSS-receivers around the Pacific Ocean (https://iono2la.gdgps.net), and is aiming -in the future -to detect traveling ionospheric disturbances (TIDs) associated with tsunamis. Shrivastava et al. [START_REF] Shrivastava | Tsunami detection by GPS-derived ionospheric total electron content[END_REF] demonstrated the possibility of tsunami detection by GPS-derived TEC, however, no discussion on the real-time use was provided.

Ravanelli et al. [START_REF] Ravanelli | GNSS total variometric approach: first demonstration of a tool for real-time tsunami genesis estimation[END_REF] claimed to provide the first real-time ionosphere-based tsunami risk assessment by data GNSS receivers in Chile. However, they analyse 2 hours of data and used 8th order polynom, i.e., their approach requires stacking of about 2 hours of data. Therefore, this approach is not NRT-compatible by our definition.

Therefore, recent seismo-ionospheric results show a big potential for the future use of ionospheric measurements for natural hazard risk assessment. However, before such methods could be applied in real-time, several major developments are yet to be implemented. Going toward real-time applications, the first step is to automatically detect CTID in near-real-time and to analyze their features in order to prove their relation to earthquakes. In this work, we introduce, for the first time, nearreal-time compatible methods for determining the spatio-temporal characteristics of CTID.

Methods

Estimation of Total Electron Content (TEC) from GNSS

GNSS allows to estimate the ionospheric total electron content (TEC), which is an integral parameter equal to the number of electrons along a line-of-sight (LOS) between a satellite and a receiver. The LOS TEC is often called slant TEC (sTEC).

The TEC is usually measured in TEC units (TECU), with 1 TECU equal to 10 16 electrons/m 2 . To calculate the TEC, one needs phase and code measurements performed by dual-frequency receivers [i.e., 25]. However, the code measurements are only needed to remove the inter-frequency bias. While, the co-seismic signatures and other disturbances can be retrieved from phase TEC estimated solely from phase measurements: [START_REF] Astafyeva | Ionospheric detection of natural hazards[END_REF] where A = 40.308 m 3 /s 2 , L 1 and L 2 are phase measurements, 1 and 2 are wavelengths at the two Global Positioning System (GPS) frequencies (1227,60 and 1575,42 MHz). Therefore, in near-real-time approach approach, we will only use these phase measurements that can be easily transferred in very short time (Figure 1). The first data point is removed from the whole data series as the unknown bias.

In order to determine the position of ionospheric disturbances, we estimate the coordinates of so-called sub-ionospheric points (SIP) that represent the intersection points between the LOS and the ionospheric thin shell. The satellite orbit information can be rapidly transferred in NRT from the IGS in navigation RINEX files (Figure 1), or it can be forecasted very precisely based on the current known satellite coordinates. Otherwise, ultra-rapid orbits can be used. The shell altitude Hion is not known but presumed from physical principles: we expect the observed perturbation to be concentrated at the altitude of the ionization maximum (HmF2). In NRT, the value of HmF2 can be obtained either from nearest ionosonde stations, or from empirical ionospheric models, such as NeQuick [START_REF] Nava | A near-real-time modelassisted ionosphere electron density retrieval method[END_REF] or International Reference Ionosphere (IRI) [START_REF] Bilitza | International Reference Ionosphere 2016: From ionospheric climate to real-time weather predictions[END_REF]. Here we take Hion = 250 km, which is close to the HmF2 on the days of the earthquakes [15; 28].

It should be noted that in the vast majority of previous studies of ionospheric response to earthquakes the researchers used band-pass filters, such as running mean, polynomial fitting, high order Butterworth, etc. [e.g., 29; 30; 31]. However, in a real-time scenario one cannot use such filters because of the impossibility to stack long series of data (up to 30-60 min) and due to the lack of time. In addition, the band-pass filtering would induce artefacts and will affect the properties of the detected signals (arrival time, amplitude, spectral components). Therefore, here we suggest to analyze the rate of TEC change (dTEC/dt) instead of the sTEC. Such a derivative procedure works as a high-pass filter and removes the bias and trend caused by the satellite orbit motion. In addition, our dTEC/dt approach will not modify the amplitude of CTID.

Below we use 1Hz GNSS data for our real-time scenario.

Real-time detection of co-seismic travelling ionospheric disturbances from TEC data series

The concept of the developed method is presented in Figure 2. CTID is detected by analysing the sTEC data series by 5-sec centered moving averaged over a 5-min window. The averaging prevents detection of random peaks in data. The window duration is chosen to be NRT-compatible and, at the same time, it allows more thorough analysis of CTIDs characteristics in multiple data series at later steps.

Within the selected time window, we search for a local maximum value (LMV) that must exceed every other value within the window.

At step #2, within the window, we switch from sTEC to dTEC/dt. With such an approach, we focus on sudden strong co-seismic TEC signatures that are analogous to the peak ground displacements [START_REF] Melgar | Earthquake magnitude calculation without saturation from the scaling of peak ground displacement[END_REF]. Figure 3 detected by GPS stations 0980, 3007 after the 2011 Tohoku-oki earthquake (1Hz data). The co-seismic signatures in sTEC data series (panels a, b) are quite significant, however, the presence of the trend makes it difficult to calculate the correlation function and the time shift between the data series that are necessary at later steps. In turn, in the dTEC/dt data series, the CTID signatures are visible, but the trend is removed (Figure 3c). The chosen 5-minute window is enough to compute the correlation, since it catches the CTID signatures and they prevail in the time span.

At step #3, we compute the cross-correlation function for two data series in order to obtain the time shifts in the signal arrivals. The latter is found based on the maximum of the cross-correlation function. In addition, the cross-correlation can correct possible errors in finding the LMV. Finally, from the obtained maximum values, it can select 3 GNSS stations for the D1-technique, as explained below in P.3.

To calculate the cross-correlation function, we use Fast Fourier Transformation (FFT), which is a rapid procedure and suitable for NRT applications. Figure 3d shows an example of the cross-correlation function between dTEC/dt data series at two GPS receivers.

The threshold for the correlated data series depends on the standard deviation of dTEC/dt series: [START_REF] Meng | Upper atmospheric responses to surface disturbances: An observational perspective[END_REF] where -the standard deviation of dTEC/dt series at GNSS sites. The standard deviation is an indicator of data noisiness. The noisier the data the more difficult it is to detect CTID because of a lower correlation coefficient. Therefore, our approach will adaptively consider the data noise level. Another issue in determining the threshold T is linked with different data cadences. The dTEC/dt values will increase with data cadence. Consequently, to adapt the threshold estimation to different data sampling, we introduce a normalizing coefficient K. For 1-Hz data, the K is chosen to be 10 TECu -1 based on data analysis. Such an adaptive approach makes our method adjustable to the scale of an ionospheric response and aids to automate the triangle selection process (at a later step). It is known that smaller earthquakes generate CTID of smaller amplitudes [START_REF] Astafyeva | Parameters of seismic source as deduced from 1Hz ionospheric GPS data: case-study of the 2011 Tohoku-oki event[END_REF]. When the response is weaker, the threshold is smaller due to smaller the standard deviation of dTEC/dt series and vice versa. (Figure S1). Setting a constant threshold may affect the results and that there is a need for an adaptive algorithm for this problem.

Real-time estimation/determining of spatio-temporal parameters. D1-GNSS-RT method

To determine spatio-temporal parameters of CTID, such as the horizontal velocity and the azimuth of propagation, we use a so-called "D1" method. This is an interferometric approach that was introduced by Afraimovich et al. [START_REF] Afraimovich | GPS radio interferometry of travelling ionospheric disturbances[END_REF] to analyze and detect TIDs, of which CTIDs are a subclass. Originally, this method was based on use of GPS-measurements only [33; 34]. Our method works with all GNSS data, and it is real-time compatible, therefore, we refer to it as "D1-GNSS-RT".

The disturbances detected by a system of three spatially separated receivers, that act as an interferometric system, are considered to be parts of the same wavefront (Fig. 4a). Then, by analysing the wave characteristics (such as phase, frequency, signal amplitude) of the observed disturbances, we determine the time shift between CTID arrivals at the detection "triangle". Three assumptions are used in the subsequent calculations: 1) the wave front is plane, i.e., the distance between the receivers is less than the horizontal dimensions of CTID; 2) the wave front is homogenous; 3) the CTID propagates horizontally i.e. the GNSS-receivers detect the perturbations at the same altitude (Hion).

At the "0" time moment, a disturbance with horizontal velocity v h and azimuth α is approaching the "A-B-C" interferometric system. At the moment "I", the CTID is detected by the receiver "A", and it is further moving to other receivers of the system.

It is important to note that the consideration of the wave front as plane and homogeneous means that both v h and α would not change when the CTID arrives at the other points of the given system. Garrison et al. [START_REF] Garrison | A method for detecting ionospheric disturbances and estimating their propagation speed and direction using a large GPS network[END_REF] showed the correctness of such an assumption for small-scale (3-10 minutes) TIDs, based on the dense network of receivers in the limited space. At moment "II", the CTID has already passed receiver "A", and arrived at receiver "B". At "III", the CTID arrives at receiver "C". Only after this step, one can compute the characteristics of the perturbation. The velocity v h and the azimuth α are then estimated by using the following formulas [START_REF] Afraimovich | GPS monitoring of the Earth's upper atmosphere[END_REF]:

( (

For better spatial representation, the location of the obtained horizontal velocity vector is placed at the point with the first arrival of the disturbance (point A in Figure 4a). While, in the temporal domain, the obtained velocity is linked with the arrival time of the disturbance at point C.

As mentioned before, the D1-method is only applicable to a TID with a plain waveform. It is known however that, in most cases, the wave front of CTID is circular [e.g., 5; 37]. Therefore, the farther are the stations from one other, the worse is the plain wave condition fulfilled. Also, larger distance between the stations will lower the maximum of the cross-correlation function. Consequently, the D1-GNSS-RT can only be used on a very small segment of the circular wavefront. This limitation requires additional analysis of the positions of the A, B, C receivers with respect to the wavefront. To do that, here we use the cross-correlation function that is the criterion of the similarity of multiple data series. It should be noted that the waveform of the CTID largely depends on the conditions of observations, such as magnetic field configuration in the epicentral area, geometry of GNSS-sounding and the background ionization [e.g., 37; 38; 39; 40]. Therefore, only perturbations registered close to one another will have similar waveforms.

Localization of the source of ionospheric disturbances

The velocity field obtained by the D1-GNSS-RT method can further be used to locate the source of TIDs. The source is defined as a point in the ionosphere where the CTID generated and starts to propagate. We switch to Latitude-Longitude coordinate system, where x-axis is directed from West to East and y-axis is directed from North to South (Fig. 4b). We take the azimuths (α i ) and the values (v i ) of the velocities, as well as the coordinates ( and ) of the velocity "vectors" from the output of the D1-GNSS-RT. This gives us a linear system, where the coordinates ( and ) of the source of ionospheric disturbances are unknown. There are two additional restrictions on the system solutions: 1) the horizontal distance between the vectors should be less than 50 km and 2) the difference in the arrival times between points A-B and A-C should be less than 30%. These restrictions are thought to avoid the location of velocity vectors to be on the same segment of the CTID wavefront in order to fulfill the condition of the plain wavefront.

For one velocity vector the distance to the source is defined by the following equation (Fig. 4b):

Where, and the coordinates of the source, and -that of the given velocity vector, α ithe azimuth of the velocity vector. Similarly, for two vectors we obtain:

Based on the system above, the coordinates of the intersection of the two vectors can be estimated as:

Once the source location is known, along with the velocity vector location and its value, the onset time of the source is estimated as follows: [START_REF] Afraimovich | Near-field TEC response to the main shock of the 2008 Wenchuan earthquake[END_REF] Where, is the time of the velocity vector and is defined by: (

Where, is the distance between the source location and the velocity vector location. If the difference in determination of the source onset time from the two given velocities is less than the sampling interval, we consider this pair of velocities as a possible solution for a specific moment of time and location of the source.

Results

We apply our newly developed methods to the cases of two shallow (~32km) earthquakes that occurred in March 2011 off the east coast of Honshu, Japan. The first one is the great M9. 5b). This smaller event lasted 30-40 seconds and provoked a 2 m co-seismic slip on the north-west from the epicentre (Figure 5b) [START_REF] Shao | Rupture process of the 9 March[END_REF].

To analyze the CTID activity, in both cases, we apply our method to 1Hz GNSS ionospheric data from the Japan GNSS Earth Observation Network (GEONET, https://www.gsi.go.jp).

The velocity field and ionospheric localisation of the 2011 M9.1 Tohokuoki earthquake

The ionospheric response to the Tohoku earthquake was studied in detail by numerous research teams [e.g., 6; 5; 14; 15; 19]. As shown in Figure 3, the nearfield TEC response showed very complex waveforms, with several peaks in TEC data. The amplitude of this response was also quite significant as compared to other earthquakes and was detected by ten GPS satellites [45; 46; 47]. Here we work with data of GPS satellite 26 that showed the largest and the clearest co-seismic signatures.

The CTID velocity field maps for the first CTID arrivals following the Tohoku earthquake are shown in Figures 6a-d The CTID propagation speed can be verified by plotting so-called travel-time diagrams (TTD), that present 3-D diagrams with the distance from the source versus time after the source onset, and the amplitude of CTID is shown in color. TTD also enable to confirm the correlation of the observed perturbations with the source. In retrospective studies, a band-pass filter was applied in order to better extract the coseismic signatures and to clearly see the correlation with the source. In NRT mode, and with the impossibility to use such a filter, we suggest using dTEC/dt parameter, and we call such diagrams near-real-time TTD (NRT-TTD). This is the first NRTcompatible method proposed for obtaining the TTD. As a source, at the first approximation, we can take the epicentre position that should be known from seismological data several minutes after the earthquake. However, the epicentre is the point where the rupture starts, and its position does not always correspond (especially for large earthquakes) to the position of the co-seismic crustal uplift that generates CTID as well as tsunamis. The problem lies, however, in the fact that in NRT, it is very difficult to know the position of the uplift or the slip. Therefore, we can take the position of the source estimated from our ionospheric methods.

The NRT-TTD for the Tohoku event, G26 satellite, plotted for the source located at the epicentre, the center of the maximum slip (38.64; 143.35) and the "ionospheric source" (37.944; 143.153) are presented in Figure 7a,b,c, respectively.

It should be noted that the Tohoku earthquake produced significant displacement of the ground on a large area (the approximative fault size is about 300*80km) and, strictly speaking, taking a single point as the source is an approximation. However, we proceed with such an assumption to plot the NRT-TTD. The correlation is seen when CTID propagates "linearly" from the source. Comparison of Figures 7a, 7b and 7c reveals that the best correlation is obtained for the slip maximum (Figure 7b) and for the ionospherically-determined source (Figure 7c). While, the perturbation is not well-aligned when the diagram is plotted with respect to the epicentre (Figure 7a).

The propagation speed of the observed CTID can be estimated from the slopes on the TTD. We find the speeds to be ~2.3-2.6 km/s, which is in line with previous retrospective observations for the ionospheric response to the Tohoku earthquake [e.g., 6; 5; 14; 15].

The velocity field and ionospheric localisation of the 2011 M7.3 Sanrikuoki earthquake

Ionospheric response to the Sanriku earthquake was studied previously by Thomas et al. [START_REF] Thomas | Revelation of early detection of co-seismic ionospheric perturbations in GPS-TEC from realistic modelling approach: Case study[END_REF] and Astafyeva & Shults [START_REF] Astafyeva | Ionospheric GNSS imagery of seismic source: possibilities, difficulties, challenges[END_REF]. The co-seismic TEC signatures were detected by satellites G07 and G10. Here we only focus on CTID registered by GPS satellite G07. Contrary to the CTID generated by the Mw9.0 Tohoku earthquake, the ionospheric TEC response to this smaller earthquake presented the commonly known N-wave signatures with smaller amplitudes. However, even despite the smaller amplitude of CTID, our method detects these disturbances.

The instantaneous velocity field maps are presented in Figure 8a-d. One can notice that the picture of the velocity field for the CTID generated by the Sanriku event is much simpler that the one for the Tohoku event. The first velocity vector is shown at 02:55:08UT, i.e. 588 seconds after the earthquake onset time. At that instant, the CTID starts to propagate south-westward at the velocity of about 850 m/s (Figure 9a). Within the next minute, we observe south-westward propagation of ionospheric disturbances at ~850-1100 m/s (Figures 8b-c). At 02:56:08UT, we further observe further southwestward propagation of CTID (Figure 8d). From these first velocity fields, we estimate the location of the source to be on the south-east from the epicentre (Figures 8e-h). Overall, one can notice significant difference in the velocity field and CTID evolution during this smaller earthquake. The CTID has lower velocities, and the velocity field is much less complex as compared to the Tohoku earthquake.

The corresponding RT-TTD calculated with respect to the epicentre, the maximum slip point (38.5; 142.7), and the ionospherically determined (38.335; 143.442) source are presented in Figure 7d,e,f, respectively. The best alignment is achieved for the ionospheric source (Figure 7e), where we also see concurrent northward and southward propagation from the source. While, for the two other sources one cannot clearly see this effect (Figures 7a and7e). Therefore, our results suggest that the source was located on the south-east from the epicentre. The worst alignment is obtained for the epicentre as the source of CTIDs (Figure 7d). The CTID propagation speed is estimated to be 1.2-1.6 km/s, which is close to the estimation in after-earthquake analysis by Astafyeva and Shults [START_REF] Astafyeva | Ionospheric GNSS imagery of seismic source: possibilities, difficulties, challenges[END_REF].

Discussions

Above we demonstrated the possibility to calculate in NRT spatio-temporal characteristics of CTIDs on the example of two earthquake events that occurred in Japan in March 2011. For both earthquakes, we also localized in NRT the source of the observed CTIDs. It should be reminded that the CTID coordinates and, consequently, the estimated position of ionospheric sources will change if we vary the altitude of detection Hion. In this work, we took Hion = 250km, which is close to the ionization maximum in the epicentral areas during the earthquakes, and is the right choice from a physical point of view. However, recently it has been suggested that the actual GNSS detection of CTID may take place at lower altitudes [48; 28; 19]. Therefore, strictly speaking, the Hion should be determined each time for the correct estimation of the CTID coordinates. Our method is fully operational independently on the Hion value, however, its results and the accuracy of the ionospheric source localization might be improved if/when we know the real Hion.

Determining the exact altitude of detection is out of the scope of the current work.

Here we used 1Hz GNSS TEC data from the Japanese network of GPS receivers GEONET, i.e. a network with good spatial coverage with 20-km distance between the receivers, and we demonstrated that in such observational conditions, our NRT-compatible methods provide good results both in terms of the source localisation and determining of CTID spatio-temporal characteristics. In our method, the accuracy of localisation seems lower than that by seismic stations that invert the position of the epicentre based on detection of seismic waves. The seismic source can also be localized by other non-seismic instrumentation, such as by balloon pressure sensors via detection of infrasound signals due to earthquakes. For instance, Krishnamoorthy et al. [START_REF] Krishnamoorthy | Aerial Seismology Using Balloon-Based Barometers[END_REF] showed that the source can be localized with 90% probability within an ellipse with a semimajor axis approximately 80 m under the perfect conditions. They used 26 shots that is equal to the usage of a 26-balloon array to solve this task. It should be noted, however, that this result was obtained by a-posteriori analysis, therefore it might be quite challenging to repeat such quality in NRT.

Further, we discuss how lower or much lower spatial and temporal resolutions of GNSS ionospheric data could affect the output of our methods. Also, the accuracy of estimation of the velocities and the source location should be determined.

With regards to the data sampling, for both earthquakes, we tested our methods on 30-sec data that are available from the GSI (http://datahouse1.gsi.go.jp/terras/terras_english.html). We have found that such a resolution is not enough because of two main reasons. First, fewer data within the selected window duration of 5 min will smooth the dTEC/dt values, which, in turn, will erase the specific features of CTIDs that characterize different segments of the wavefront. As mentioned before, the D1-GNSS-RT method can only be used on a small part of a wavefront, because it is only applicable to the plain wave. Therefore, with 30-sec data sampling, it is difficult to control this condition in terms of the correlation between data series, especially for smaller earthquakes, for which the response is smaller in amplitude and duration [START_REF] Astafyeva | Ionospheric response to earthquakes of different magnitudes: larger quakes perturb the ionosphere stronger and longer[END_REF]. Second, 30-sec data rate will introduce ±15-sec error in the LMV determining within the window, and, consequently, it will lead to errors in the arrival time at each point of a triangle. The impact of such ±15-sec error can be seen in Figure 9a-b, where we present the normalized number of the time shifts between points A-B (red, T 1 ) and A-C (blue,

T 2 ) of a triangle for the Tohoku (a) and Sanriku (b) earthquakes. For both events, the distribution of T 1 and T 2 have the same shape and look quite similar, but are shifted for ~5 seconds. This emphasizes the fact that a CTID arrives at points B and C at close moments of time, that is only possible if the arrivals belong to the same segment on a circular disturbance wavefront. One can also notice that, for both events, the majority of arrivals are registered within a narrow period of time, 20 to 40 seconds for the Sanriku event (Figure 9a) and 25 to 60 seconds for the Tohoku event (Figure 9b). This means that lower time steps in data will lead to errors in the correct detection of the moment of arrival would occur, and, consequently will eventually impact the velocity values and the azimuths.

To further analyze the applicability of our method to lower cadence data, we downsampled the initial 1Hz data to 5-, 10-and 15-sec cadence. Figure 10 shows how different data cadences impact the distribution of calculated velocities. One can see a significant difference in the results for 1sec and 30 sec data. Therefore, for better performance of our methods we suggest the use of GNSS-data with 1Hz

sampling.

With respect to the accuracy of our method, we analyzed how an error of ±0.5 seconds in arrival times affects the computation of the velocity values and azimuths.

The normalized number of error cases versus the absolute error percentage is shown in Figure 9c. One can see that ~80% of both velocities and azimuths have less than 2.5% of errors and ~95% -less than 5%. These results also confirm the advantage of high-rate data.

The use of different orbital information can impact the accuracy of our method, because the coordinates of CTID depend on the position of a satellite as well as of that of a GNSS station. The commonly used ephemerides are those transferred in the RINEX navigation file. Alternatively, ultra-rapid orbits can be used. We compared the amplitude and direction of the obtained velocity vectors based on ultra-rapid orbits with those calculated based on the use of the RINEX navigation files (Fig 11a,b). Then, we computed source locations based on these velocities and estimated the error in position (Fig 11c,d). This analysis was made both for the Tohoku and the Sanriku cases. One can see that the majority of both velocities and azimuths have less than 0.05% of differences. This fact can be explained by the high quality (cm-accuracy) of the real-time IGS products [START_REF] Hadas | IGS RTS precise orbits and clocks verification and quality degradation over time[END_REF]. However, the radar diagrams of error positioning show worse results (Figure 11c,d).

Finally, we would like to note that our methods can be used for detection of TIDs of other origins in addition to CTID and, therefore, it is useful for real-time Space Weather applications. The D1-GNSS-RT will automatically catch all CTID and TID with high dTEC/dt values, where the maximum disturbance amplitude exceeds the noise level by at least 4 times (Figure S4a). Such disturbances could be generated by acoustic or gravito-acoustic waves (earthquakes, volcanic eruptions, rocket launches), or by enhanced EUV radiation (solar flares) that produces rapid growth of the ionization in the ionosphere (Figure 12). It should be emphasized that for the detection, the absolute amplitude of CTID and TID is less important than the dTEC/dt. For instance, it is known that smaller earthquakes generate smaller disturbances in the ionosphere [15; 47]. Therefore, it is of interest to apply our technique to the smallest earthquake ever recorded in the ionospherethe M6. 6 16 July 2007 Chuetsu earthquake in Japan [START_REF] Cahyadi | Coseismic ionospheric disturbance of the large strikeslip earthquakes in North Sumatra in 2012: M w dependence of the disturbance amplitudes[END_REF]. The Chuetsu earthquake produced a very small-amplitude TEC disturbance that was registered by satellite G26 and by a few GPS-stations in the near-epicentral region, and the only data available were of 30-sec cadence. Unfortunately, the latter factors did not allow us to compute the velocities and the localization by using the D1-GNSS-RT technique. However, our method successfully found the LMV even for such a small CTID but with sufficient dTEC/dt rate (Figure S5b,c). Also, Figure S5 demonstrates that we could track the CTID propagation with respect to the source in NRT by using our RT-TTD technique.

On the other hand, disturbances with lower sTEC derivative or/and higher noise level might appear undetectable or the D1 triangles will not be formed because of low cross-correlation between data series. For instance, we did not manage to catch CTID registered by satellites G27 (during the Tohoku earthquake) and G10

(during the Sanriku earthquake), because they had low dTEC/dt. Another example is the ionospheric response to the M7.8 2016 Kaikoura earthquake that occurred on 13

November 2016 in New Zealand, for which we also analysed high-rate 1Hz data. The latter TEC variations presented more noise and the amplitude of the detected CTID did not grow up as fast as for the Tohoku and Sanriku cases (Figure S4). For such less pronounced disturbances, other more sophisticated methods should be developed, which is a subject of a future separate work.

Conclusions

For the first time, we introduce a NRT-compatible method that allows very rapid determining of spatio-temporal parameters of travelling ionospheric disturbances. By using our method, one can obtain instantaneous velocity maps for ionospheric perturbations, and to estimate the position of the source. In addition, also for the first time, we present real-time travel-time diagrams. We demonstrate the performance of our methods on CTID generated by the Tohoku-oki Earthquake of 11

March 2011 and the Sanriku-oki Earthquake of 9 March 2011. We use high-rate 1Hz GPS data from the Japan network GEONET for these two earthquakes, and we observe the evolution of the CTID over the source area as it could have been seen in real-time. We show that there is a significant difference between CTID generated by M9 and M7.3 earthquakes in terms of CTID velocities and evolution: the giant Tohoku earthquake generated a massive TEC response in both amplitude and spatial extent, and such a difference can be clearly seen in our results.

It is important to emphasize that, besides CTID, our method can detect and analyze other TID that often occur and propagate in the ionosphere. Therefore, the D1-GNSS-RT method can be used for near-real-time Space Weather applications.

  (a) shows examples of CTID ESSOAr | https://doi.org/10.1002/essoar.10507883.1 | CC_BY_4.0 | First posted online: Thu, 2 Sep 2021 10:13:33 | This content has not been peer reviewed.

( 4 )

 4 ESSOAr | https://doi.org/10.1002/essoar.10507883.1 | CC_BY_4.0 | First posted online: Thu, 2 Sep 2021 10:13:33 | This content has not been peer reviewed.

  Figure 6e-h. It should be noted that, in principle, we can calculate the CTID characteristics for multiple periods of time, as long as the perturbations are detected. For the Tohoku event, instantaneous velocity maps for the first 2 minutes of CTID detection can be found in Animation S1 (available as supplementary material), and the localization results are shown in Animation S2 (supplementary material).Figure

  ESSOAr | https://doi.org/10.1002/essoar.10507883.1 | CC_BY_4.0 | First posted online: Thu, 2 Sep 2021 10:13:33 | This content has not been peer reviewed.

  ESSOAr | https://doi.org/10.1002/essoar.10507883.1 | CC_BY_4.0 | First posted online: Thu, 2 Sep 2021 10:13:33 | This content has not been peer reviewed.

FiguresFigure 1 .

 1 Figures

  Figure 1. Real-time collection of GNSS phase data and orbit parameters. Networked Transport of RTCM [51] via Internet Protocol (NTRIP)[START_REF]Networked Transport of RTCM via Internet Protocol[END_REF] could be used to provide the real-time data stream from the given stations. The main goal of the protocol is Real Time Kinematics (RTK), but it is also suitable for our purposes since it transfers dual-frequency phase and pseudo-range data in real time. RTKLib[START_REF] Takasu | RTKLIB: an open source program package for GNSS positioning[END_REF] software could be used to convert binary information from NTRIP data stream. The International GNSS Service (IGS) ultra-rapid orbit[START_REF] Noll | The Crustal Dynamics Data Information System: A resource to support scientific analysis using space geodesy[END_REF] is used to obtain the information about the elevation angle and the azimuth. BINEX -Binary INdependent EXchange format for files that is used in real-time.

Figure 2 .

 2 Figure 2. The concept of the near-real-time detection of CTID and TID, and explanation of the main steps of the procedure.

Figure 3 .

 3 Figure 3. (a) Variations of slant TEC registered by GPS satellite 26 at stations 0980 and 3007 following the Tohoku earthquake of 11 March 2011. The earthquake time is indicated by vertical black line. Gray shaded rectangles denote 5-min time window, which is used for further cross-correlation analysis; (b) sTEC variations within 5-min time window; (c) dTEC/dt within 5-min time window. Black point shows the LMV determined from the sTEC data. The data are 1Hz; (d) Cross-correlation function for the two dTEC/dt time series

Figure 4 .

 4 Figure 4. (a) Explanation of D1 technique. A, B, C -GNSS stations that are used to determine the CSID parameters: horizontal velocity (v h ) and azimuth (α). 0, I, II, III mark the moments of time when the perturbation approaches the detection triangle (0) and when the perturbation is detected at points A, B, and C, respectively. The wavefront is considered to be plain; (b) Ionospheric localization of CTIDs based on the known location and values of two velocity vectors V 1 and V 2 .

Figure 5 .

 5 Figure 5. Maps for the Mw9.0 Tohoku earthquake of 11 March 2011 (a) and the M7.3 Sanriku earthquake of 9 March 2011 (b).Black star shows the epicenter, black dots show GPS receivers, and the colored squares depict the amplitude of the coseismic slip that occurred due to the earthquakes as calculated by the NEIC USGS[START_REF] Rolland | Discriminating the tectonic and non-tectonic contributions in the ionospheric signature of the 2011, M w 7.1, dip-slip Van earthquake, Eastern Turkey[END_REF]. The corresponding color scale is shown on the bottom. The dotted curve shows

Figure 7 .

 7 Figure 7. Near-real-time travel time diagram (NRT-TTD) plotted by using dTEC/dt data for the Tohoku (a, b, c) earthquake (satellite G26) andSanriku (d, e, f) earthquake (satellite G07). In panels (a, d) the distance is calculated with respect to the earthquakes' epicenters as estimated by the USGS, in panels (b, e)with respect to the maximum co-seismic uplifts; (c, f) -with respect to the ionospheric localization as shown in Figures5(d-e) and 6(d-e). The color scale is shown on the right.

Figure 8 .

 8 Figure 8. (a-d) CTID velocity field calculated from the first CTID detected by GPS satellite PRN 07 following the Sanriku earthquake. The dotted curve shows the position of the Japan Trench, black star depicts the epicenter. The gray arrow corresponds to 1,1 km/s; (e-h) localization of the seismic source as estimated from the first velocity vectors shown on panels (a-d).

Figure 9 .

 9 Figure 9. (a-b) Distribution of normalized number of the time shifts between points A-B (red, T 1 ) and A-C (blue, T 2 ) of a triangle for the Tohoku (a) and Sanriku (b) earthquakes; (c) impact of an error of ±0.5 seconds on arrival times affects the computation of the velocities values and azimuths.

Figure 10 .

 10 Figure 10. Distribution of velocity values calculated from data of different temporal cadences: 1-(red), 5-(green), 10-(blue), 15-(gray), 30-(brown) seconds.

Figure 11 .

 11 Figure 11. Accuracy comparison based on different sources of the orbits: navigational RINEX file and ultra-rapid orbits. Panel (a) -distribution of percentage difference of amplitude and azimuth of propagation for the Tohoku case (y-axis logarithmic scale); panel (b) -distribution of percentage difference of amplitude and azimuth of propagation for the Sanriku case (y-axis logarithmic scale); panel (c) -

Figure 12 .

 12 Figure 12. Examples of TEC disturbances of different origin that are detectable by our approach. Panel (a)slant TEC values characterized by high changes, panel (b) -Rate of TEC of the exact data series.

ESSOAr | https://doi.org/10.1002/essoar.10507883.1 | CC_BY_4.0 | First posted online: Thu, 2 Sep 2021 10:13:33 | This content has not been peer reviewed.

Acknowledgements

We thank the French Space Agency (CNES, Project "IMAGION") for the support. BM additionally thanks the CNES and the IPGP for the PhD fellowship and the support of the RFBR, grant No. 19-05-00889, and partly by budgetary funding of Basic Research Program II.16.

Data availability

The data are available from the GeoSpatial Authority of Japan (GSI, terras.go.jp). http://datahouse1.gsi.go.jp/terras/terras_english.html

Competing interests

The authors declare no competing interests.

Competing financial interests:

The authors declare no competing financial interests.


Chinnaswamy Jagannath

Jere W Mcbride

Isabelle Vergne
email: isabelle.vergne@ipbs.fr

The Autophagy Pathway: Bacterial Pathogen Immunity and Evasion 1 2

Keywords: Autophagy, lysosomes, mTOR, TFEB, immunometabolism, Mycobacterium tuberculosis, 14 Staphylococcus aureus, Salmonella typhimurium, Listeria monocytogenes, Anaplasmataceae, 15 Ehrlichia, Anaplasma, host-directed therapies 16

17

Overview 18

Autophagy is a lysosomal degradative pathway which plays important roles in innate immunity 19 against bacterial pathogens (1). Autophagy enables autophagosomes to engulf and deliver 20 intracellular pathogens to the lysosomes for degradation. In addition, autophagy is implicated in the 21 regulation of inflammation by modulating cytokine production. Not surprisingly, bacterial pathogens 22 have developed multiple strategies to manipulate autophagy in order to survive inside the host [START_REF] Bah | Macrophage Autophagy and Bacterial Infections[END_REF]. 23

Although our knowledge of the interplay between bacterial pathogens and autophagy has 24 considerably improved in the past fifteen years, many questions remain. In this Research Topic, we 25 have assembled several research articles and reviews that respond to some of those questions in 26 regard to the host and bacterial factors involved in autophagy regulation, the crosstalk between 27 autophagy and other host defense mechanisms, and the manipulation of autophagy for host-directed 28 therapies. 29

Autophagy as a host defense mechanism 30

The role of autophagy in innate immunity is well conserved across eukaryotic kingdoms. Several 31 vertebrate models such as mice and zebrafish have been essential for our understanding of the role 32 of autophagy, in vivo, in bacterial infection [START_REF] Levine | Autophagy in immunity and inflammation[END_REF][START_REF] Munoz-Sanchez | Autophagy and Lc3-95 Associated Phagocytosis in Zebrafish Models of Bacterial Infections[END_REF] the specific role of autophagy in such cells was not elucidated [START_REF] Mulcahy | Manipulation of Autophagy and Apoptosis Facilitates Intracellular Survival of 124 Staphylococcus aureus in Human Neutrophils[END_REF]. Importantly, the last stage of 65 autophagy is blocked in both phagocytes and non-phagocytes. Overall, these findings bring novel 66 molecular insights on how diverse bacterial pathogens can avoid or, in contrast, use autophagy to 67 persist and flourish in their host. 68

Autophagy as a target for host-directed therapies 69

With the continuous rise of bacterial multidrug resistance, alternative approaches to combat such 70 pathogens has become a top priority. One promising avenue is to boost host immune responses 71 including autophagy. This approach is particularly relevant for pathogens that are susceptible to 72 autophagy such as M. tuberculosis [START_REF] Kilinc | Host-directed therapy to 126 combat mycobacterial infections[END_REF]

  Both processes appear to be connected by two key 39 kinases, mTOR and AMPK, which regulate TFEB, a central transcriptional factor of autophagy and 40 lysosome machinery. A central role of mTOR in immune responses was further highlighted by Etna et 41 al. who found that rapamycin, an mTOR inhibitor and autophagy activator, modulates expression of 42 regulatory cytokines in Mycobacterium tuberculosis-infected dendritic cells (7). Lastly, Gauron et al.

	. Recently, the yellow mealworm beetle (Tenebrio molitor) model has also been developed to study Listeria monocytogenes infection (Jo et al.) (5). In this model, authors have found a possible dialogue between autophagy and the NF-B pathway as unveiled an important function of another kinase PKC which inhibits autophagy in the context of Staphylococcus aureus (8). Besides kinases, microRNAs extensively regulate bacterial autophagy (9). Liu et al. found that microRNA-106a dampens autophagy by repressing ULK1, ATG7 and ATG16L1 during mycobacterial infection (10). Taken together, these articles underscore the multiple roles of host kinases and microRNAs in autophagy regulation and their dialogue with other host defense mechanisms. Autophagy manipulation by bacterial pathogens Several intracellular bacterial pathogens can evade autophagy including M. tuberculosis, L. monocytogenes and Salmonella typhimurium (2). However, the underlying molecular mechanisms are not fully characterized. Zhou et al. found that Salmonella SpvC blocks autophagosome formation through its phosphothreonine lyase activity (11). Interestingly, Rao et al. observed a reduction of TFEB and lysosomal expression during Salmonella infection of macrophages, possibly through caspase-1 activation (12). Whether SpvC is implicated in that process remains to be investigated. In contrast to Salmonella, other bacterial pathogens exploit autophagy to persist and proliferate in host observed by others 43 33 34 35 44 45 46 47 48 49 50 51 52 53 54 55 56 57 cells.

in mammalian cells. Autophagy is well known to extensively crosstalk with other 36 innate immune responses including the inflammasome and type I interferon-mediated responses (1). 37 In this Research Topic Paik et al. review the relationship between autophagy and immunometabolism in defense against mycobacterial infection (6). Patterson et al. review our current knowledge of the interplay between autophagy and 58 Anaplasmataceae (13). Members of this family exploit autophagy to acquire nutrients while avoiding 59 lysosomal degradation. Interestingly, Bechelli et al. report that Rickettsia australis triggers Atg5-60 dependent autophagy to suppress inflammatory cytokines at both transcriptional and post-61 transcriptional levels, which favors pathogen survival (14). In non-phagocytic cells, autophagy is 62 essential for intracellular survival of Staphylococcus aureus (Gauron et al.) (8). Mulcahy et al. found 63 that S. aureus intracellular survival also requires autophagy in primary human neutrophils, although, 64

  Overall, this Research Topic highlights the intricate interplay between autophagy and various 84 bacterial pathogens. A better understanding of the role and regulation of autophagy in various 85 cellular niches and relevant animal models, as well as its crosstalk with other host defense 86 mechanisms is essential if one wants to harness autophagy for therapeutic purposes. 87

	73	. Strong et al. discuss in depth the opportunities and
	74	limitations of autophagy-based therapies against mycobacterial infections (17). The authors have
	75	compiled a list of autophagy-inducing compounds that have been tested on cellular and animal
	76	models of mycobacterial infection. Notably, some, if not all of these compounds may also modulate
	77	other immune responses as Paik et al. and Etna et al. have pointed out (6,7). Thus, a comprehensive
	78	analysis of the immune responses to infection after treatment with autophagy-inducing molecules
	79	may be extremely informative. Importantly, the involvement of autophagy in the control of bacterial
	80	infections should be evaluated in detail using in vivo models. In conclusion, autophagy appears to be
	81	a promising target for treating mycobacterial infections and, thus, it would be worth examining its
	82	potential in the context of other bacterial infections.
		Perspective and future directions

Author contributions 132

IV conceived and wrote the first draft of this Editorial. CJ The authors declare that the research was conducted in the absence of any commercial or financial 141 relationships that could be construed as a potential conflict of interest. 142


Yuan Zhang

Benjamin Ourri

Pierre-Thomas Skowron

Emeric Jeamet

Ana Belenguer

Nicolas Vanthuyne

Olivier Cala

Pradeep Mandal

Christian Duchamp

Elise Dumont

Encoding stereochemical molecular information on cyclophanes using non-directional interactions and achiral building blocks

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

Encoding stereochemical molecular information on cyclophanes using non-directional interactions and achiral building blocks

Yuan Zhang, Benjamin Ourri, Pierre-Thomas Skowron, Emeric Jeamet, Ana M. Belenguer, Nicolas Vanthuyne, Olivier Cala, Pradeep K. Mandal, Christian Duchamp, Elise Dumont, Florent Perret, Laurent Vial, Ivan Huc, Julien Leclaire,

The stereoselective assembly of achiral constituents through a single spontaneous process into complex covalent architectures bearing multiple stereogenic elements currently seems out of reach to the synthetic chemist. It even seems beyond what nature itself has managed to attain through evolution. Here, we show that such an extreme level of control can be achieved by molecular programming, i.e. by implementing stereo-electronic information on synthetic organic building blocks and exploiting the features of the covalent reactions and interactions, whose interplay acts as a powerful assembling algorithm. Remarkably, we show that non-directional bonds and interactions can reliably transfer this information, delivering in near to physiological conditions, high-molecular weight macrocyclic species carrying up to 8-bits of conformational and configuration information. Beyond the field of supramolecular chemistry, this proof of concept should stimulate the on-demand production of highly structured polyfunctional architectures.

Introduction. The concept of Molecular

Information emerged with the rise of supramolecular chemistry [1][START_REF] Lehn | Perspectives in Supramolecular Chemistry-From Molecular Recognition towards Molecular Information Processing and Self-Organization[END_REF][START_REF] Lehn | Programmed Chemical Systems: Multiple Subprograms and Multiple Processing/Expression of Molecular Information[END_REF] . For instance, complementary molecular information is what underpins the host and guest binding in the lock and key paradigm. When combined to a reliable algorithm (the set of assembling covalent and non-covalent bonds), the molecular information borne by small building blocks can propagate at the nanoscopic level though information transfer, yielding highly ordered and organized architectures such as grids, MOFs or interlocked systems [START_REF] Funeriu | Multiple Expression of Molecular Information: Enforced Generation of Different Supramolecular Inorganic Architectures by Processing of the Same Ligand Information through Specific Coordination Algorithms[END_REF][START_REF] Ayme | Simultaneous Generation of a [2 × 2] Grid-Like Complex and a Linear Double Helicate: a Three-Level Self-Sorting Process[END_REF][START_REF] Wang | A Study of the Morphology, Dynamics, and Folding Pathways of Ring Polymers with Supramolecular Topological Constraints Using Molecular Simulation and Nonlinear Manifold Learning[END_REF][7][START_REF] Dong | Supramolecular Chirality in Metal-Organic Complexes[END_REF][START_REF] Jędrzejewska | Making a Right or Left Choice: Chiral Self-Sorting as a Tool for the Formation of Discrete Complex Structures[END_REF] . One of the key features of the algorithm lies in the reversibility of the linkages, which enables error correction [START_REF] Stewart | Stable and ordered amide frameworks synthesised under reversible conditions which facilitate error checking[END_REF][START_REF] Segura | Post-synthetic modification of covalent organic frameworks[END_REF] .

A seminal example of information transfer was brought by J.M. Lehn, with the self-assembling of circular metal helicates (figure 1a) [START_REF] Hasenknopf | Kinetic and Thermodynamic Control in Self-Assembly: Sequential Formation of Linear and Circular Helicates[END_REF][START_REF] Hasenknopf | Self-Assembly of Tetraand Hexanuclear Circular Helicates[END_REF][START_REF] Hasenknopf | Self-Assembly of a Circular Double Helicate[END_REF] . The first level of information is compositional, with the chloride anion templating the formation of a hosting pentagonal cavity among all possible sizes and topologies (grids, helices) of organometallic architectures. The second level, which remains poorly commented, even in revisited versions of this work [START_REF] Ayme | A synthetic molecular pentafoil knot[END_REF] , is stereochemical. The coordination requirement from the metal cation, the poly-denticity and the rigidity of the tris(bipyridine) strands are three inputs which are translated at the supramolecular level by the metal-ligand assembling chemistry (the algorithm). The first two inputs are encoded into chiral Werner-like complexes involving three different ligand strands on the edges of the cavity. Their  (respectively ) central configuration is stereoselectively interrelated (as a translation of the third input) to windings of M (respectively P) neighbouring helices at the vertices of the pentagone. Remarkably, this process stereoselectively yields the (-)(-P) mixture among all possible pentameric systems. Thus, supramolecular chirality, defined as the nonsymmetric arrangement of constituents in a noncovalent assembly [START_REF] Suárez | Supramolecular Chirality: Chiral hydrogenbonded supermolecules from achiral molecular components[END_REF] , has spontaneously emerged as an information output. This seminal example allows for the formulation of the following take-home messages First, stereochemical information (in this example, the (-P)5 and (-M)5 configurational sequence) can be encoded at the supramolecular level, from simple achiral constituents. To reliably encode and propagate this stereochemical information, directional and reversible linkages (herein metalligand, the coding algorithm) enable error correction. In fact, nanoscopic self-organization of MOFs, helicates, nucleic acids, cages and knots is mostly involving directional reversible linkages such as hydrogen bonds, azomethine connections and/or metal-ligand interactions [START_REF] Stewart | Stable and ordered amide frameworks synthesised under reversible conditions which facilitate error checking[END_REF][START_REF] Nitschke | Substitution, and Sorting of Metallo-organic Structures via Subcomponent Self-Assembly[END_REF][START_REF] Langner | Self-recognition and selfselection in multicomponent supramolecular coordination networks on surfaces[END_REF] . The last message is that, although the linear topography was more frequently chosen by nature and man (to engineer natural and synthetic foldamers), molecular information can also be efficiently encoded within (pseudo) macrocyclic species displaying a welldefined cavity [START_REF] Rota Martir | Homochiral Emissive Λ8and Δ8-[Ir8Pd4]16+ Supramolecular Cages[END_REF][START_REF] Nierengarten | A mannosylated pillar[5]arene derivative: chiral information transfer and antiadhesive properties against uropathogenic bacteria[END_REF] .

Despite their central role in molecular recognition, cavitands and cyclophanes have rarely been considered as substrates for the encryption, propagation and storage of molecular information. During their assembly, most attention is focused on the control of their size (the compositional level). Yet, two recent blockbusters, namely pillar[n]arenes and cucurbiturils, display striking examples of stereoconvergent assembly [START_REF] Pavlović | From Selection to Instruction and Back: Competing Conformational Selection and Induced Fit Pathways in Abiotic Hosts[END_REF][START_REF] Han | Stereoselective Synthesis of Pillar[END_REF][START_REF] Ogoshi | Pillar-Shaped Macrocyclic Hosts Pillar[n]arenes: New Key Players for Supramolecular Chemistry[END_REF][START_REF] Xue | A New Class of Macrocycles for Supramolecular Chemistry[END_REF][START_REF] Vinciguerra | Synthesis and Self-Assembly Processes of Monofunctionalized Cucurbit[END_REF][START_REF] Zhang | Differentially functionalized acyclic cucurbiturils: synthesis, self-assembly and CB[6]-induced allosteric guest binding[END_REF][START_REF] Day | Controlling Factors in the Synthesis of Cucurbituril and Its Homologues[END_REF][START_REF] Wang | Conformationally adaptive macrocycles with flipping aromatic sidewalls[END_REF] . For pillar[n]arenes, although there are two equiprobable pR and pS configurations for each monomeric unit (figure 1b), potentially yielding n (n-1)/2 stereoisomers, only the homochiral pair is obtained [START_REF] Fa | Conformation and Planar Chirality of Pillar[n]arenes[END_REF] . The information input (prochiral flat monomer with lateral hindrance in future positions 2 and 5) is encoded by the assembling chemistry (methylene bridging through reversible Friedel Craft reactions [START_REF] Holler | The high yielding synthesis of pillar[5]arenes under Friedel-Crafts conditions explained by dynamic covalent bond formation[END_REF][START_REF] Li | arenes: Synthesis, Structure, Complexation, and Guest-Induced Circularly Polarized Luminescence Property[END_REF][START_REF] Sala | An intramolecularly selftemplated synthesis of macrocycles: self-filling effects on the formation of prismarenes[END_REF] ) into a homochiral output, which minimizes the steric hindrance on both rims (figure 1b, blue arrow and highlight). Similarly, while the convex/concave glycosuril faces can potentially be oriented toward the cavity or toward the outer medium, the hindrance of the axial CH protons stands as the input, which is encoded by the same assembling algorithm (figure 1b, blue arrow and highlight) into the fully concave output, limiting inverted cucurbiturils to trace amounts [START_REF] Isaacs | The Inverted Cucurbit[n]uril Family[END_REF][START_REF] Stancl | Glycoluril Dimer Isomerization under Aqueous Acidic Conditions Related to Cucurbituril Formation[END_REF][START_REF] Huang | Chiral Recognition inside a Chiral Cucurbituril[END_REF] . In both cases, a posteriori analyses indicate that the stereoreselectivity of the assembling process is guided by steric interactions which propagates (figure 1b, blue arrow and highlight) either during chain growth (cucurbiturils) or ring closure (pillararenes) 36 . In the field of disulfide based cavitands, which can be assembled by dynamic combinatorial strategies, examples of stereoselective assembling remain scarce and almost systematically involve chiral building blocks [START_REF] Gianga | Structurally divergent dynamic combinatorial chemistry on racemic mixtures[END_REF][START_REF] Corbett | Diastereoselective Amplification of an Induced-Fit Receptor from a Dynamic Combinatorial Library[END_REF][START_REF] Ten Cate | Disulfide Exchange in Hydrogen-Bonded Cyclic Assemblies: Stereochemical Self-Selection by Double Dynamic Chemistry[END_REF][START_REF] Lam | Amplification of Acetylcholine-Binding Catenanes from Dynamic Combinatorial Libraries[END_REF] . Template-induced (by casting and/or molding) selection and amplification of different facial stereoisomers of polydisulfide cyclotetramers was reported by Otto et al. [START_REF] Corbett | Diastereoselective Amplification of an Induced-Fit Receptor from a Dynamic Combinatorial Library[END_REF][START_REF] Li | An Allosteric Receptor by Simultaneous "Casting" and "Molding" in a Dynamic Combinatorial Library[END_REF] Yet, the rationale enabling to program on demand the configuration and conformation of a macrocycle by exploiting the stereochemical features of its building blocks and of the template used has remained out of reached so far. In particular, the role and relative configuration of the disulphide linkage between two stereogenic monomeric units have never been explored, even within protein architectures. [START_REF] Panijpan | Chirality of the disulfide bond in biomolecules[END_REF][START_REF] Carmack | Chirality of the Disulfide in the Prion Proteins[END_REF] During the past decade, we have designed and studied the disulfidebased analogues of pilla[n]rarenes named dyn[n]arenes (figure 1c up) [START_REF] Carmack | Chirality of the Disulfide in the Prion Proteins[END_REF] . Interestingly, thiol-to disulphide cyclooligomerization is accompanied by the creation of two classes of stereogenic elements: the monomeric faces and the disulphide bridges linking them. Once the covalent assembling is complete, the constitutional lability (disulphide exchange) is frozen and the only potential remaining exchange processes are of conformational nature. A central question is how to control these stereogenic elements formed i.e. how to program beforehand their configuration and how to preserve them from racemization over time.

We herein report the straightforward encryption and storage of up to 8-bits of stereochemical supramolecular information within such macrocyclic architectures. We show that this process can be directed either by a template or by the design of the building blocks themselves. Remarkably, we demonstrate that non-directional reversible linkages and steric interaction can indeed be powerful algorithm to reliably translate and propagate information from the molecular to the supramolecular level.

Result and discussion

Template-assisted stereochemical information encoding. Recently, we showed that the diversity of the libraries generated from building block A, both in terms of macrocycle ring size and facial stereoisomers (figure 2), is largely underestimated by chromatographic analyses [START_REF] Skowron | On-Demand Cyclophanes: Substituent-Directed Self-Assembling, Folding, and Binding[END_REF] . Although this technique is universally adopted for disulfide-based DCLs, it only enables to detect the trace amount of the homochiral tetramer A4-a (i.e., the strict analogue of pillar[n]arene) within a mixture which is in reality, highly dominated by the homochiral trimer A3 and heterochiral tetramers A4 (each including at least one pR-M-pS sequence as in scheme 1c). The first question that we addressed within the framework of the present study was to assess whether the stereogenic elements of these selfassembled cyclophanes (facial pR/pS configurations vs M/P disulfide bridge conformations, figure 2) were interrelated, similarly to what was observed in Lehn's helicates [START_REF] Hasenknopf | Kinetic and Thermodynamic Control in Self-Assembly: Sequential Formation of Linear and Circular Helicates[END_REF][START_REF] Hasenknopf | Self-Assembly of Tetraand Hexanuclear Circular Helicates[END_REF][START_REF] Hasenknopf | Self-Assembly of a Circular Double Helicate[END_REF] . This issue is truly central, as it probes the potential propagation of stereochemical information between monomer faces and linkages during the reversible oligomerization process. The structure of the cyclotetramers of pR4/pS4, pR3pS/pS3pR, (pR)2(pS)2 configurations noted respectively A4-a, A4-b and A4-c (no (pSpR)2 tetramer could be detected upon thiol-to-disulfide oxidation of A), were modelled by a combination of DFT and MD calculations (supporting section II.1.e). These two classes of simulations respectively yielded the populations of most stable conformers corresponding to each configuration as well as an evaluation of their conformational flexibility. The structures obtained and the repartition of the dihedral angles of the disulfide bridges of each species are gathered in tables S4-S9). The first main information which could be extracted from the calculations was that heterochiral species A4-b and A4-c have a marked tendency to adopt a flattened conformation wherein the cavity is too narrow to be accessed by any guest whatever its size (figure S10-S11).

Figure 2. Guest-induced stereochemical information transfer. Combination of pR and pS configurations arising from the positioning of prochiral monomer faces in-or outward with respect to the cavity (horizontal coordinates) with P and M configuration of the disulfide bridges (vertical coordinates) afford a virtual combinatorial system of 16 tetramers. Templating by an -diammonium guest such as cadaverine quantitatively yields the (pS-P)4 and (pR-M)4 racemic mixture, i.e. encodes 8 bits of stereochemical information on the host (i). Top and side view of the crystallographic structure (with Van der Waals radii in contact) reveals contacts between substituents of the phenyl rings (ii), and crystalizes into a conglomerate (iii) wherein homochiral packing occurs (i.e. (PpR)4 and (MpS)4 species self-sort). This fully agrees with the external binding mode observed experimentally with polyamine partners [START_REF] Skowron | On-Demand Cyclophanes: Substituent-Directed Self-Assembling, Folding, and Binding[END_REF] . It also indicates that the formation of a pseudorotaxane by complex guest inclusion does not represent a sufficient energetic benefit to compensate the unfavourable flattened-to-open induced fit. The second main observation we made is that all stereoisomers A4-x (x= a-c), despite splitting each into several conformers A4-x,n (n = 1-4) of various stability, share a common configurational-conformational inter-dependence: pR-P and pS-M facial-dihedral combinations seem to be systematically the most stable for steric reasons. When conflicts arise (a disulfide bridge surrounded by a pR and a pS face), it forces the -S-S-linkage to adopt a cis conformation, which eventually explains the flattened shaped observed on heterochiral species A4-b and A4-c. While the virtual sub-library of cyclotetramers potentially encompasses 16 combinations of configurations and conformations, this stereochemical inter-dependence guides the real library toward the (x,n) = (a,1), (b,2), (c,3) diagonal on the gridded landscape in figure 2.

The interconnection between the two levels of stereochemical information borne by dyn [4]arenes was confirmed experimentally on the homochiral pR4/pS4 species A4-a. As previously reported [START_REF] Carmack | Chirality of the Disulfide in the Prion Proteins[END_REF] , this cavitand can be quantitatively and stereoselectively self-assembled, at the expense of other ring sizes and stereochemistries, using biogenic polyamines such as spermine and spermidine as templates (figures S4-S5). Such an object combines the ideal cavity size and carboxylate group layout (at the vertices of its parallelepipedal structure) to optimize the binding of polyammoniums by salt bridges (figure 2i). Previously published optimized procedures [START_REF] Carmack | Chirality of the Disulfide in the Prion Proteins[END_REF] enable to obtain on demand either the pure polyamine A4-a pseudo-rotaxane complex or the free host upon guest departure. Both architectures were submitted to a crystallogenesis campaign, which eventually afforded samples eligible for structural elucidation by X-ray diffraction analyses. Guest-containing and free structures (figures S6-S7) support and validate a posteriori the modelling data (figure 2ii). As expected, diammonium guests transfer their stereochemical information (a cylindrical linear backbone terminated by two electron poor moieties) to the host building block, by templating (the algorithm) its assembly into a parallelepipedal structure which displays the optimal carboxylate groups layout (at the vertices of the parallelepiped, i.e. corresponding to the homochiral configuration).

From this intermolecular guest-to-host information transfer, which selects the homochiral A4-a species among all cyclotri-to penta-meric combinations, a second level of information is intramolecularly encrypted. In fact, the steric hindrance of the carboxylate groups propagates along the vertical edges of the parallelepidic cavity, positioning each S-S linkage right in the axis formed by the two neighbouring carboxylates (figure 2ii). Eventually, only the pR-P and pS-R pairs of stereoisomers are observed, in full agreement with the computational model. Remarkably, not only a simple guest such as an -diammonium can transfer up to 8 bits of stereochemical information (coded as (pR-P)4 or (pS-M)4) to the self-assembled host, but this information is recorded, i.e. remains implemented into the host upon guest departure, as confirmed by the X-ray structure of the free host (figures S6-S7). Fortuitously, the informational input initiated by the guest propagates beyond the individual host as conglomerate crystals are obtained (figure 2iii), i.e. crystals in which (pR-P)4 and (pS-M)4) segregate. This indeed means that a third stereoselective selfassembling process takes place consecutively to the templation step: the self-sorting of nearest neighbour cavitands of identical configuration. In other words, -polyamines encode the encryption of (pR-P)4 and (pS-M)4) 8-letter words. Upon, guest departure and supersaturation, these 8-letter words subsequently self-sort into 1-word sentences (the homochiral [(pR-P)4]n and [(pS-M)4]n aggregates).

Template-free stereochemical information encoding. From this first example of guest-to-host transfer and storage of 8-bits of stereochemical information, we envisaged the possibility of extending the concept to guest-free systems. To do so, information should be entirely encoded into the building blocks themselves, through their stereochemical features, i.e. by synthetic design. In the first generation of dynarenes based on A, the stereochemical information was able to propagate along the edges of the monomeric faces through steric interactions (figure 1c, blue highlight).

In a second-generation system, the same class of challenging non-directional interaction was conserved but implemented into three moieties located at different positions of the building blocks (named B and C, figure 3). The profile of these building blocks was inspired from Schraders's molecular tweezers which are equipped with benzene walls and norbornadiene edges [START_REF] Dumartin | The dark side of disulfide-based dynamic combinatorial chemistry[END_REF] . With this design, three groups differing in bulkiness are borne by the cis and trans staircase-shaped monomers B and C: the pair of axial protons Ha found at the edge between the norbornene and cyclobutene rings is the bulkiest class of C-H protons (figure 3i-ii, cyan), the methylene CH2b bridge of the norbornene is slightly less hindered and ranks second (figure 3i groups restrict disulfide dihedral rotation (ii and iv). Out of 24 possible tetrameric combinations of In and Out facial configurations (arising from the positioning of concave/convex monomer faces in-or outward with respect to the cavity, horizontal coordinate) and P or M disulfide bridges conformation (vertical coordinate), B is programmed to selectively deliver a meso alternate MPMP conformation and (In)4 configuration. DFT modelling at the M06 level (v and vi: with Van der Waals surface) supports the design.

To enable the quantitative formation of discrete cyclic species rather than polymers [START_REF] Holler | The high yielding synthesis of pillar[5]arenes under Friedel-Crafts conditions explained by dynamic covalent bond formation[END_REF] , libraries were set in the millimolar range from building block B or C. Slightly acidic pH (5.5) was chosen so that the monomeric units were mono(de)protonated at each dicarboxylic end (figure 4d), thereby yields soluble oligomers within which hydrogen bonds may potentially be shared between nearest monomeric neighbours. This intermediate protonation state was verified a posteriori by the potentiometric titration of the isolated cyclooligomers obtained (figure S120-121). Monitoring of the aerobic thiols-todisulfide based cyclo-oligomerization by (-)-ESI-MS allowed us to qualitatively validate our design. In the case of building block B, disulfide-based linear species were detected during the first 4 hours, followed by the rise of their macrocyclic homologues and the concomitant decline of linear species (figure S97-100). A similar first regime of thiol-to-disulfide-based chain growth was observed on C, which then diverged during the second regime from the mild oxidation pathway. In fact, ring closure was replaced by overoxidation of the disulfides linkages (into thiolsulfinates) on the linear strands, which subsequently underwent cleavage into smaller linear fragments and further overoxidation (from sulfenic to sulfonic acids, figure S101-105). Remarkably, no trace of such overoxidized species could be detected by ESI-MS from libraries based on B. Beyond the qualitative validation of our design, this preliminary analysis seems to indicate that the disulfide oxidation state may be metastable in some circumstances and therefore require additional stabilization sources, which are herein provided by intramolecular noncovalent interactions within the macrocyclic species Bn.

In-depth compositional and structural analyses of the architectures formed from monomer B were conducted by a combination of computational and experimental techniques. UPLC-UV/ESI-MS monitoring over time first provided a quantitative assessment of populations of linear and cyclic objects produced throughout the oxidation process (figure 4a, S106-109). It appeared that linear species of increasing chain length (from dimer B-B to tetramer B-B-B-B) are progressively generated from monomer B during the first 24 hours while the cyclic species, although detectable in ESI-MS by direct infusion (vide infra), remain limited to trace amounts. In fact, the macrocyclization regime by ring closure or dimerization (eq. (c) and (d), figure 4a) effectively takes over the elongation phase (eq. (e)-(e"), figure 4a) after 24h, yielding quantitatively a cyclotetrameric product noted B4. Intriguingly, the corresponding mass spectra, indicated the presence of B8-3H 3-and B8-5H 5-ions (figure S116). Careful examination of the isotopic patterns corresponding to B4-2H 2-and B4-3H [START_REF] Lehn | Programmed Chemical Systems: Multiple Subprograms and Multiple Processing/Expression of Molecular Information[END_REF]-also reveal that their isotopic pattern was respectively interfered with those of B8-4H 4-and B8-6H 6-(figure S115). Given the octaanionic nature of B4 at pH 5.5, formation of a non-covalent dimeric B4-B4 complex which may survive to the ionization process seemed highly unlikely 1 . Although a single and relatively sharp peak is obtained in UPLC after equilibration (and remains stable over more than two weeks), it was ascribed to the co-elution of the cyclic tetramer B4 and octamer B8 (figure 4a-c andS108). MS/MS fragmentation of the B8-3H 3-ion systematically delivered the B-H -monomeric species, which is consistent with a covalent octamer (figure S117). Despite a thorough screening of all currently available chromatographic phases, any attempt to separate these two species, which are presumably obtained from the same tetrameric linear parent B-B-B-B by ring closure (figure 4a, eq. (c)) or cyclodimerization (figure 4a, eq. (d')), remained fruitless. Similarly, our generic procedure of dynarene isolation by controlled acidic precipitation proved to be ineffective to separate both species. The mixture obtained upon equilibration was thus analyzed by multi-nuclear and multi-dimensional NMR (supporting section S.II.2.f). Quantitative 1 H and [START_REF] Hasenknopf | Self-Assembly of Tetraand Hexanuclear Circular Helicates[END_REF] C spectra in the presence of an internal standard indicated the present of a single wellresolved major species (approx. 80 % molar, figure S132), involving two sets of Ha-c magnetically different protons (figure 4d and4e, noted I and II). COSY and NOESY experiments confirmed that these two sets are geometrically isolated, while heteronuclear 2D experiments (HSQC, HMBC) enabled to assign the signals within each set to one of the Ha-c class (figures S122-129). Finally, DOSY confirmed that these two sets belong to the same molecular entity, which displays a hydrodynamic radius of 9.08 +/-0.75 Å (as a comparison, A4-a's radius is 8.30 +/-0.80 Å and the radius of monomer B is measured by the same technique around 5.71 +/-0.07 Å in the same conditions, see figures S87 and S130 and table S10-11). These analyses enabled to narrow the scope of B4 cyclotetramer candidates (those displaying two geometrically distinct Ha-c units) to the meso-(In-M-In-P)2, the (Out-M-Out-P)2 species and the homochiral racemic (In-P-Out-P)2 (In-M-Out-M)2 mixture. These three stereochemical combinations are located on the gridded landscape of all possible configurations and conformations summarized in figure 3 at the (a,4), (f,4) and (d,1) coordinates respectively. Structurally speaking, they strongly differ in terms of degree of exposure of the Ha and Hb protons to the outer solution.

Experimentally, it appears that macrocyclization of B induces the shielding and deshielding of Ha and Hb protons, with a splitting within each class (figure 4e). This supports the hypothesis of a B4 stereoisomer bearing Ha (and Hb protons) which all point outward (respectively inward) with respect to the macrocyclic cavity, wherein two distinct local environments can be found. Assessment of the stability of each member of the virtual combinatorial sub-library of cyclotetramer stereoisomers gathered on the map displayed in figure 3 was performed by DFT calculations (structure optimization with three alternative functionals, followed by single point (SP) energy calculation, see section S.I.8 and table S12). Comparison of the energy levels, which are displayed in figure S139 unambiguously reveal that, the (In-M-In-P)2 stereoisomer is the most stable species and should experimentally dominate the sublibrary of B4 stereoisomers obtained from B. In addition to complementing and refining the NMR analyses, this modelling campaign also provided some insight on the main contributions to the stability of the species. In agreement with our design, it appears that orienting the Ha-bearing concave faces toward the cavity (i.e. the Out configuration) destabilizes the corresponding architectures for steric reason. Stabilizing London dispersion forces follow the same evolution (increasing in strength with the number of Out facial configurations) but their amplitude is insufficient and fail to compensate the repulsion. To minimize steric clash between Hb protons of facing monomeric units (which are in Van der Waals contact, see figure 3iii and iv), the structure adopts distorted octahedral shape. Finally, Hb and Hc protons play their ascribed role of disulfide bridge instructors. Energy calculation validates a posteriori the encoding process i.e. the effective translation of the stereochemical information borne by B by the assembling algorithm (the concomitant disulfide bond formation/exchange operating under the guidance of steric interactions). DFT modelling indeed confirm that the MPMP conformation is systematically favoured within each configurational series. On the most stable and selectively obtained B4, this conformation minimizes the hindrance between Hb protons from neighbouring monomeric units. Finally, molecular dynamics confirm that Hc provide sufficient hindrance in the vicinity of the S-S bridges to freeze and lock their conformation (see figure 5i and ii), at least on the millisecond NMR timescale.

At this stage, it should be mentioned that NMR spectra of equilibrated libraries either analysed directly (in situ) or after acid-induced precipitation and redissolution (ex situ) both display sharp signals corresponding to meso-(In-M-In-P)2-B4 which account for 80% of the total material, while the remaining 20% imputed to a B8 adduct, are dispatched into broad signals buried in the baseline (figure S). We first investigated the impact of the amphoteric salt used for pH regulation, by changing either the anion or cation while maintaining the pH of the library at 5.5). UPLC-analysis did not reveal any deviation from the scenario of B4/B8 selective co-production (figure S106). To rule out the possibility of precipitation-induced interconversion between B4 and B8, which would remain undetectable upon redissolution, we then analysed the material collected by precipitation by NMR and MALDI-MS spectroscopy in the solid state (figures S118-119). Apart from the line broadening, solid and liquid state spectra can be superimposed, thereby ruling out this hypothesis. As B4 and B8 should result from the same B-B-B-B precursors through a monomolecular (ring closure) or bimolecular (dimerization) pathway, we reasoned that experimental parameters affecting the assembling process such as temperature, stirring rate or concentration may affect the final proportions of B4 and B8 within the libraries.

Increasing incubation temperature (from 25° to 75 °C) or stirring rate (from 0 to 1000 rpm) accelerated the elongation and cyclization regime, resulting in faster equilibration but final mixtures of identical compositions (see figure S109 for UPLC-MS analyses). Increasing the concentration of the starting material from 4 to 32 mM induced a similar accelerating effect but also resulted into the formation of solid material after several hours (above 15 mM, see figure S96). This solid, which was filtered and dried, accounted at best for 10 % of the total mass. It proved to be insoluble in all conventional solvents and no data could be extracted from ESI-MS or liquid-state NMR analyses. Solid state NMR delivered a [START_REF] Hasenknopf | Self-Assembly of Tetraand Hexanuclear Circular Helicates[END_REF] C CP-MAS spectra displaying broad peaks (figure S138), indicating that this sample differs from the B4+B8 fraction collected upon acidification at least in terms of tridimensional organization.

As the analysis of the supernatant by ESI-MS and multinuclear NMR were similarly inconclusive (detection of the B8-3H 3-, B8-5H 5-and B4-3H 3-ions for the latter and faint broad signals merged with the baseline accompanying the sharp peaks corresponding to B4, see figure S123 andS131), we performed some semi-quantitative ESI-MS sampling during the assembling process. Quantification of the intensities and areas of the isotopic patterns of identical m/z corresponding to B4-nH n-and B8-2nH 2n-with time was performed after a preliminary validation by calibration (figure S133-136), i.e. injection of precise and increasing amounts of B4/B8 mixtures whose proportions had been determined first by NMR analyses (figure S132). This kinetic monitoring revealed that the B8/B4 proportion is increasing with time during the cyclization regime, reaching the 0.25 asymptotic value measured by NMR, for libraries whose concentration was below the 15 mM threshold value. In contrast, more concentrated sample lead to higher proportions of B8 (up to 0.45), which abruptly dropped to the same asymptote amount (0.25) upon precipitation (figure S137). These observations provided the framework for crystallogenesis campaign based on supersaturated solution prepared by dissolution of the solid B4+B8 material collected after thiol to disulfide assembling in dilute conditions and acid precipitation. To our delight, single crystals eligible for structural elucidation by X-ray diffraction analysis could be collected after screening (figure S140). It should be noted that attempt to isolate them from the mother liquor lead to their collapse and prevented us from recording MS or NMR spectra in the liquid state. The tridimensional structure of the solid material obtained from supersaturated mixtures of B4 and B8 is shown in figure 5. In agreement with ESI-MS monitoring or the assembling and CP-MAS NMR, this analysis confirms that the insoluble material corresponds to a covalent octamer B8 (and rules out the unlikely hypothesis of a complex between two B4 species). The shared filiation of B4 and B8 with B-B-B-B is confirmed by the eight-shaped profile of B8 whose octahedral subunits (figure 5a, grey) almost perfectly superimpose with B4 (figure 5a, pink). This solid-state structure also reveals how the molecular information we encoded into the monomer is handled during the dimerization of B-B-B-B into B8, which competes with the ring closure into B4, i.e. when two tetramers are to be fused. As for B4, the sterochemical information encoded into the monomeric unit is stereoselectively translated into the cyclooctamer both at the configurational and conformational levels. An all-In facial configuration, wherein the bulkiest Ha protons point toward the outer medium (figure 5b, cyan) and the slightly less bulky Hb (figure 5b, green) are oriented inward is indeed observed. Regarding disulfide bridge conformation, it is confirmed that the M/P alternance is the only combination which accommodates the hindrance borne by the building blocks, even on a larger ring size. (figure 5c andS141). As in B4, the unusual eight-shaped folding finds its origin in the interplay between intramolecular attractive and repulsive interactions. Yet, careful examination of the packing between (M-In-P-In)4-B8 homologues reveal that intermolecular interactions in the solid lattice should act here as an additional folding driving force. In the equatorial plane of the macrocyclic ring, contacts between B8 molecules occur at the tip of their long sides, i.e. between the monomeric units which are not engaged into the junctions between B4 subunits, though unexpected stacking of their Ha-bearing cyclobutene moieties (figure 5d). At each pole of the B8 structure, 2 monomers are paired through this unusual interaction with a different B8 neighbour (figure S143). Repetition of this pattern along the xy plane yields cyclotrimeric and hexameric superstructures displaying respectively triangular and circular cavities (figures 5e and S142). In the z-direction, stacking of the B8-layers occurs through H-bond pairing between the carboxylic moieties of homologous monomers (figure 5d, red). The carboxylic paring concerns the four central building blocks of the 8-shaped B8 ring, i.e. the zone resulting from the cyclodimerization of two linear BBBB tetramers. This analysis reveals that stacking in the solid phase, especially along the z axis, may be the driving force underpinning the unexpected formation and selection of a large ring size, which in the absence of enthalpic driving force, is entropically unfavoured. [START_REF] Corbett | Exploring the Relation between Amplification and Binding in Dynamic Combinatorial Libraries of Macrocyclic Synthetic Receptors in Water[END_REF] Despite this unexpected powerful driving force, 8 and 16-bits of (In-M-In-P)n stereochemical sequences could be successfully and simultaneously encoded into dyn [4]-and dyn [8]arene, respectively in solution and in the solid state.

Conclusion

We have brought here the proof of feasibility of multi-bit stereochemical information encoding into disulfide-based cyclophanes. More specifically we could show that the steric hindrance borne by simple methylene and methine moieties on achiral dithiophenol building blocks can serve as informational input. This input can be translated, by a non-directional assembling algorithm (disulfide bridge formation and steric hindrance minimization) with or without the assistance of a template, into a specific stereochemical output (the configurational and conformational sequence of the assembled product). Monomers and connecting linkages can be viewed as two channels wherein two alternative letters/values may be encoded, their inter-relation depending on the input i.e. on the nature of the building block. Encryption is therefore underpinned by design and of the starting material (input) and the choice of the assembling chemistry and interactions at work (the algorithm). The readout requires structural analysis (herein provided by NMR and Xray crystallography), which currently limits the potential applicability of this innovative concept in molecular informatics. The scope of synthetic application of templating and folding, well known driving forces for compositional selection and amplification in DCC was herein extended to stereochemistry. Unexpectedly, the third driving force, namely aggregation and crystal packing can also influence the stereochemical selection by reinforcing (in the case of A4-a) or perturbing (in the case of B8) the encoding process. This conceptual toolbox should therefore be of great value, enabling the community to program on demand the stereoselective assembling of sophisticated architectures from very simple components.

Figure 1 :

 1 Figure 1: Information transfer during macrocyclization: a) seminal example of anion-templated

Figure 3 .

 3 Figure 3. Principle of stereochemical information encoding by self-assembling of hindered dithiophenol monomers B and C (i and ii: schematic representation). Axial protons (cyan: methine C-Ha; green: methylene C-Hb) hinder the concave face of B and both faces of C, preventing the cyclooligomerization of the latter. Axial C-Hb (green) and equatorial C-Hc (grey)

Figure 4 .

 4 Figure 4. UPLC-MS analysis of the dynamic combinatorial library generated from monomer B (4 mM) in 50 mM AcONH4 at pH 5.5. a) Schematic representation of the linear and cyclic species quantified and characterized by UPLC-UV/ESI-MS (b and c), d) monomeric unit displaying two sets of Ha-c protons (I and II) and e) snapshot of the 1 H NMR spectra of starting material B and final product B4+B8.

Figure 5 .

 5 Figure 5. Structural elucidation of B8 octamer by X-ray diffraction crystallography. a): comparison of B4 and B8 structures obtained in silico and experimentally by X-ray diffraction respectively (pink: B4, grey: B8, framed: zoom on the junction between tetrameric subunits), c) :analysis of the facial configuration (green: Ha: cyan Hb ) and d) : disulphide conformation ( yellow : P-SS, red : M-SS) and d) intermolecular packing between four B8 molecules (blue and red: Van der Waals contact between cyclobutene and carboxylic moieties, with a framed zoom of the former) from two xy layers displayed in e)

Acknowledgements We thank the CCSM, CRMN and CCRMN for assistance on Mass Spectrometry, DOSY, High field liquid and solid-state NMR analyses respectively. We acknowledge the contribution of SFR Biosciences (UMS3444/CNRS, US8/Inserm, ENS de Lyon, UCBL) facilities: Protein Science Facility -Frédéric DELOLME for performing MALDI-TOF-MS analysis. We are grateful to S. Vidal for providing access to his UPLC facility (ANR-17-CE07-0054). Financial support from the Chinese Scholarship council (Y. Z scholarship) and UCB Biopharma (P.T.S and B.O scholarships) and the IR-RMN-THC Fr3050 CNRS is gratefully acknowledged. This work was supported by the LABEX iMUST (ANR-10-LABX-0064) of Université de Lyon, within the program "Investissements d'Avenir" operated by the French National Research Agency (ANR).

Data availability statement "Crystallographic data for the structures reported in this Article have been deposited at the Cambridge Crystallographic Data Centre, under deposition numbers CCDC 1554744, 2003290, 2001333, 2003509 for A4-a, A4-a-Cadav, A4-a-Put and B8 respectively. Copies of the data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures/. All other data supporting the findings of this study, including synthetic and analytical procedures are available within the Article and its Supplementary Information, or from the corresponding author upon reasonable request."