Dr Hervé Quintard
email: quintard.h@chu-nice.fr

Lionel Velly

Salah Boussen

Xavier Chiosi

Marie-Eve Amoretti

Élodie Cervantes

Carole Ichai

Elodie Cervantes

Value of assessment of multivoxel proton chemical shift imaging to predict long term outcome in patients after out-of-hospital cardiac arrest: A preliminary prospective observational study

Keywords: Cardiac arrest, outcome, prognosis, magnetic resonance imaging, chemical shift imaging, magnetic resonance spectroscopic, hypoxic ischemic encephalopathy, diffusion weighted imaging 3

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Out-of-hospital cardiac arrest (OHCA) is a major cause of death and disability with an annual incidence of 60 for 100,000 habitants [START_REF] Stecker | Public Health Burden of Sudden Cardiac Death in the United States[END_REF]. Numerous efforts have been made to develop tools that help in detecting injury severity and subsequent outcomes. The more-commonly used indicators of OHCA severity include the initial cardiac rhythm, the length of resuscitation, the initial Glasgow Coma Scale, and the presence of nonreactive pupils [START_REF] Perman | Timing of neuroprognostication in postcardiac arrest therapeutic hypothermia*[END_REF].

However the clinical course of neurological recovery is obscured by sedation and hypothermia [START_REF] Taccone | How to assess prognosis after cardiac arrest and therapeutic hypothermia[END_REF]. An early assessment of unfavorable prognosis based on the sole clinical examination may contribute to withdrawal of life sustaining therapy in nearly 20% of patients who may otherwise have shown complete neurological recovery [START_REF] Perman | Timing of neuroprognostication in postcardiac arrest therapeutic hypothermia*[END_REF]. The development of additional prediction tools, including electrophysiological examinations (electroencephalography and somatosensory evoked potentials), neuroimaging and chemical biomarkers as protein S100β or Neuron Specific Enolase may help to evaluate the extent of brain injury [START_REF] Taccone | How to assess prognosis after cardiac arrest and therapeutic hypothermia[END_REF]. Considering the limits of sensitivity and specificity of these predictive tools, last published guidelines on OHCA recommend delaying prognostication after therapeutic hypothermia and using multiple prognostic tools [START_REF] Cronberg | Neurological prognostication after cardiac arrest-Recommendations from the Swedish Resuscitation Council[END_REF][START_REF] Sandroni | Prognostication in comatose survivors of cardiac arrest: An advisory statement from the European Resuscitation Council and the European Society of Intensive Care Medicine[END_REF][START_REF] Nolan | European Resuscitation Council and European Society of Intensive Care Medicine Guidelines for Post-resuscitation Care 2015[END_REF].

Advances in MRI-based neuroimaging techniques, as diffusion tensor imaging, magnetisation transfer ratio, and perfusion imaging offer new potential to brain injury prognosis [START_REF] Shenton | A review of magnetic resonance imaging and diffusion tensor imaging findings in mild traumatic brain injury[END_REF].

Multivoxel in vivo proton chemical shift imaging ( 1 H-CSI) known as magnetic resonance spectroscopic (MRS) imaging has also the advantage of being a unique noninvasive method to quantify the magnitude and regional distribution of injury [START_REF] Castillo | Clinical applications of proton MR spectroscopy[END_REF]. 1 H-CSI enables to measure levels of several metabolites markers of neuronal integrity and cell membrane turnover [START_REF] Moffett | N-Acetylaspartate in the CNS: From neurodiagnostics to neurobiology[END_REF]. N-acetylaspartate (NAA) levels are commonly used as a marker for neuronal loss after traumatic or hypoxic-ischemic brain injury, Creatinin and phosphocreatine (Cr) resonance levels may represent gliosis, Choline (Cho) resonance represents cell membrane turnover [START_REF] Castillo | Clinical applications of proton MR spectroscopy[END_REF]. Althought several studies have been conducted using this technique in TBI patients with inconsistent results [START_REF] Croall | Magnetic resonance spectroscopy for traumatic brain injury[END_REF], few data are available for post ischemic patients, especially following OHCA. Most of the studies have been conducted in perinatal hypoxia preterm or term newborn with consistent results on the prognosis value of the NAA/Cr ratio mesured in striatum [START_REF] Zarifi | Prediction of Adverse Outcome with Cerebral Lactate Level and Apparent Diffusion Coefficient in Infants with Perinatal Asphyxia[END_REF][START_REF] Boichot | Term neonate prognoses after perinatal asphyxia: contributions of MR imaging, MR spectroscopy, relaxation times, and apparent diffusion coefficients[END_REF][START_REF] Ancora | Prognostic value of brain proton MR spectroscopy and diffusion tensor imaging in newborns with hypoxic-ischemic encephalopathy treated by brain cooling[END_REF]. In adults patients after OHCA, limited data on 1 H-CSI have been reported to assess prognosis [START_REF] Martin | Nuclear magnetic resonance spectroscopy study of human brain after cardiac resuscitation[END_REF][START_REF] Berek | Early determination of neurological outcome after prehospital cardiopulmonary resuscitation[END_REF][START_REF] Kano | Neuronal cell injury in patients after cardiopulmonary resuscitation: evaluation by diffusion-weighted imaging and magnetic resonance spectroscopy[END_REF].

The goal of this study was to assess and validate the prognostic performance of 1 H-CSI in the subacute phase (7 to 14 days post insult) of hypoxic-ischemic brain injury in OHCA patients.

MATERIALS AND METHODS

Study population

All comatose patients (Glasgow Coma Scale, GCS < 9) on admission aged 18 to 80 years admitted from January 1st 2011 to December 31st 2013, for OHCA from cardiac or respiratory causes were eligible. Pregnant women, and patient with contraindication to magnetic exposure were excluded from the study. The study protocol was approved by the local institutional ethics committee (Comité de Protection des Personnes Sud Méditerrranée V, study no. 2011-A00683-38), written informed consent was obtained from the next-of-kin before enrolment. When possible, patient's consent was obtained in case of favorable neurologic outcome in accordance with the French law.

Patient management

Patients were treated according to a standardised institutional protocol that complied with the International Liaison Committee On Resuscitation recommendations [START_REF] Nolan | European Resuscitation Council and European Society of Intensive Care Medicine Guidelines for Post-resuscitation Care 2015[END_REF] and has been described elsewhere [START_REF] Orban | Association of serum lactate with outcome after out-of-hospital cardiac arrest treated with therapeutic hypothermia[END_REF]. Briefly, after return of spontaneous circulation obtained by the medical prehospital team, coronary angiography and percutaneous coronary intervention were performed if needed. Then patients were admitted in our 40 beds intensive care unit (ICU) of our tertiary care university hospital. All comatose OHCA patients were treated with a target body temperature for 24 h according to guidelines, were sedated with an association of midazolam and fentanyl during hypothermia and paralyzed using continuous infusion of cisatracurium. All patients were intubated and mechanically ventilated aiming at a PaO 2 between 75 and 100 mmHg and PaCO 2 between 35 and 45 mmHg. A central venous catheter and an arterial line were inserted for monitoring respectively central venous and arterial blood pressure, and blood sampling. Therapeutic goals were a mean arterial pressure > 80mmHg and urine output > 0.5 mL/kg/hr. These goals were reached by giving fluid infusion or dobutamine or norepinephrine according to hemodynamic monitoring data.

Glucose was maintained between 0.8 and 1.2 g/dL by continuous insulin infusion according to a local protocol.

Data collection

Demographic and clinical informations were collected prospectively with an Utstein-style data [START_REF] Jacobs | Cardiac arrest and cardiopulmonary resuscitation outcome reports: update and simplification of the Utstein templates for resuscitation registries[END_REF]. Glasgow Coma Scale [START_REF] Teasdale | The Description of 'Conscious Level': A Case for the Glasgow Coma Scale[END_REF] was assessed at hospital admission, and day of MRI acquisition and arterial blood lactate levels on admission and at 24 hours later, OHCA score [START_REF] Adrie | Predicting survival with good neurological recovery at hospital admission after successful resuscitation of out-of-hospital cardiac arrest: the OHCA score[END_REF] was computed for each patient (Supplemental, additional file 1). The severity of disease was characterized by the Simplified Acute Physiology Score II [START_REF] Gall | A new Simplified Acute Physiology Score (SAPS II) based on a European/North American multicenter study[END_REF] on the first day after admission. Structural MRI acquisition took about 20 min, depending on the number of slices required to cover the brain. Multivoxel 1 H-CSI was acquired using the point-resolved proton spectroscopy sequence (PRESS) with the following parameters: slice thickness, 20 mm; TR/TE, 1000/144 ms; matrix, 16x16; FOV, 240 mm; number of excitation, 1. The axial 1 H-MRS covering a region from the head of striatum to the thalamus. This acquisition took 11 min.

MR Imaging Data Acquisition

The MR images were retrieved in DICOM (Digital Imaging and Communications in Medicine) format from picture archiving and communication system servers at the hospitals.

Image Processing

Brain MR images were reviewed by a board-certified blinded radiologist (ME.A, with 10 years of postfellowship experience) to evaluate possible structural abnormalities. Participants with any evidence of territorial stroke of any age, intracranial hemorrhage, or intracranial mass lesions were excluded; in addition, any subject with head motion greater than 2 mm across the imaging session was excluded. MR imaging morphologic analysis was accomplished using a validated score on the basis of a visual rating. In the FLAIR-DWI scoring (Supplemental, additional file 2) proposed by Hirsch et al., [START_REF] Hirsch | Prognostic Value of A Qualitative Brain MRI Scoring System After Cardiac Arrest: Prognostic value of qualitative MRI after cardiac arrest[END_REF] developed in a similar population with OHCA, the anatomic location and degree of signal abnormality on FLAIR images and DWI sequences is rated from 0 (normal) to 4 (severe), and composite tissue signal change is then calculated in cortical, basal ganglia and thalamus, brainstem, and cerebellar structures. The sum of scores in cortical, basal ganglia, and all structures is referred to as the "cortex", "deep gray nuclei", and "overall score", respectively. The sum or all scores recorded by using FLAIR and DWI is known as the DWI-FLAIR score, respectively [START_REF] Hirsch | Prognostic Value of A Qualitative Brain MRI Scoring System After Cardiac Arrest: Prognostic value of qualitative MRI after cardiac arrest[END_REF].

Multivoxel 1 H-CSI data processing was performed by an expert radiologist allowing to measure the area under the curve by standard manufacturer software dedicated to MR spectroscopy post-processing (Advantage Windows for General Electric). The volume of interest was placed carefully to avoid contact with cerebral spinal fluid on non-angled FLAIR images after coregistration of spectroscopic data and FLAIR volume (Figure 1). The spectra were analyzed to determine the concentration of metabolites in the lenticular cores (right and left side) and thalami (right and left side): NAA (at 2.0 ppm), Cho (at 3.2 ppm) and Cr (at 3.0 ppm). The quality of the selected spectra was visually inspected and was considered acceptable only if Cho and Cr signals were clearly separated. The spectra were also rejected if MR spectroscopists detected artefacts such as large baseline distortions, exceptionally broadened metabolite peaks, insufficient removal of the water line, large phase errors, and signals originating from outside the voxel as conventionally used in clinical practice. In all cases, peak surface area was used to calculate metabolite ratios for metabolite quantification. The worst value of bilateral lenticular cores and thalami were analysed except in cases of some non interpretable voxels. In this case, the sole side with spectra of good quality was taken into account.

Outcome

Physicians in charge of the patients were blinded to 1 H-CSI but had access to conventional MRI sequences (without FLAIR-DWI scoring) as well as all clinical, biological, and electrophysiological data. All clinical decisions remained at the discretion of the treating team.

Neurologic performance was assessed at 6 months according to Glasgow-Pittsburgh Cerebral Performance Categories (CPC; Supplemental, additional file 3) [START_REF]I Study Group*. Randomized Clinical Study of Thiopental Loading in Comatose Survivors of Cardiac Arrest[END_REF] based on data issued from medical files or from telephone calls. Briefly, CPC 1 as normal, CPC 2 as moderate disability, CPC 3 as severe disability, CPC 4 as persistent vegetative state, and CPC 5 as death.

CPC at 6 months was the primary outcome measure for stratifying patients into favorable outcomes (CPC 1-2) and unfavorable outcome (CPC 3-5).

Statistical analysis

Data were tested for normality and are presented as mean±standard deviation or median [interquartile range (IQR)] for continuous variables when appropriate. Categorical variables are presented as n (%). Comparisons between groups according to outcome at 6 months were performed using Mann-Whitney U test or χ2 test when appropriate. Univariate logistic regression models were used to examine the predictive value of each variable. Additional details of odds ratios are available in the appendix (Supplemental). For each predictive variable (P<0.05), a receiver-operating-characteristic curve was plotted, and the corresponding area under the curve (ROCAUC) was computed. An optimal cutoff was defined as the value leading to the maximal sensitivity at 100% specificity. For this optimal cutoff, specificity, sensitivity, and positive and negative predictive values were computed, with 95% Confidence Interval (CI) computed by bootstrap. The ROCAUC and sensitivity of each variable were compared using the method described by DeLong et al. [START_REF] Delong | Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach[END_REF] and Fisher's exact test, respectively. All these statistics were also computed for three multivariate logistic regression models. Multivariate analysis was performed using backward stepwise logistic regression to enter variables that yielded P values smaller than <0.1 in the univariate analysis to identify factors that independently predicted the 6 months outcome P<0.05 was considered statistically significant. Statistical analysis was performed using MATLAB R2017a and Statistics and Machine Learning Toolbox 11.1 (The MathWorks Inc., Natick, MA).

RESULTS

During the selected period, 40 patients admitted in our intensive care unit after a OHCA met the inclusion criteria, 29 were included in the analysis with an interpretable multi-modal MRI (see consort diagram Figure 2); 8 (28%) had a favorable neurologic outcome (5 with a CPC score of 1 and 3 with a CPC of 2). Unfavorable outcome was reported in 21 patients: 17 (81%) died during hospital stay with a median survival time of 16 days (IQR 12 to 40 days), at 6 months; one patient had CPC 4 and 20 CPC 5 (see Data in Brief, Table 1). Withdrawal or limitation-of-care decisions were taken for 15 patients (52%). Characteristics of patients are summarized in Table 1. At baseline, there was no significant difference between patients with favorable or unfavorable outcome in terms of proportion of shockable rhythm or time to return of spontaneous circulation. Patients with a favorable outcome were younger (P=0.03) and had a lower serum lactate level at H24 (P=0.04).

Median time to MRI was not significantly different in unfavorable-and favorable-outcome patients (7 (IQR 7 to 9 days) vs. 8 (IQR 6 to 12 days) days; P=0.66). The GCS was significantly lower in the unfavorable group compared to favorable one on the MRI-day (10 (IQR 9 to 12) vs. 3 (IQR 3 to 6); p=0.005; Table 2). FLAIR-DWI deep nuclei scores were significantly higher (i.e. worse) in the unfavorable outcome group (2 (IQR 0 to 13) vs. 1 (IQR 0 to 2); p=0.05; Table 2). FLAIR or DWI images showed mild-to-severe signal abnormalities in cortex in 4 patients with a favorable outcome.

In total, 11 (27%) 1 H-CSI spectra were not interpretable. The worst NAA/Cr ratios in lenticular cores was significantly lower in the unfavorablevs. favorable-outcome patients (1.12±0.37 vs. 1.62±0.34 respectively; P=0.002; see Table 2). There was no significant difference between group in Naa/Cr ratios in the thalamus (1.75±0.45 vs. 1.71±0.64 respectively; P=0.87; see Table 2). The NAA/Cho ratio measured in lenticular cores and thalami was not significantly different between groups (respectively P=0.08 and 0.67; see Table 2).

Figure 3 summarizes the results of ROC curves for the principal predictors of unfavorable outcome. Table 3 shows the cutoff value predictive of unfavorable outcome with a specificity of 100%, the sensitivity value corresponding to this cutoff value and ROCAUC for each predictor. The optimal cutoff value of worst NAA/Cr in lenticulair cores was <1.32 with a specificity of 100% (sensitivity 80%). The same cutoff value, similar specificity and sensitivity were obtained in adjusted analyses of the subpopulation excluding patients with withdrawal or limitation of care (see Data in Brief article Table 3).

Multivariate analyses and specific results are shown in Data in Brief article (Data in Brief

article Table 2 and Figure 1). Briefly, in the first model, significant selected variables were SAPS II and Glasgow Coma Scale at MRI. The ROCAUC was 0.85 (95% CI, 0.71 to 0.99). The second model, which included the FLAIR-DWI DNG score, increased the ROCAUC to 0.86 (95% CI, 0.73 to 0.99). Finally, the third model, which included worst NAA/Cr in lenticular cores, increased the ROCAUC to 0.95 (95% CI, 0.87 to 1.00), with a specificity of 100% (95% CI, 63% to 100%) and a sensitivity of 90% (95% CI, 70% to 99%).

DISCUSSION

The major findings of this prospective preliminary study sugget as follow: 1) The DWI-FLAIR "deep gray nuclei" score could be predictive prognostic factor in patient 7 days after OHCA.

2) The Worst NAA/Cr ratio measured in lenticular cores seems to be a feasible predictive factor also in this setting. 3) The association of clinical data (SAPS II and GCS at MRI time), and MRI data as the "deep gray nuclei" score and NAA/Cr ratio measured in lenticular core seems to be an accurate prognostic factor for patient after CA associating an excellent sensitivity (90%) for a specificity of 100%.

Anoxic or hypoxic-ischemic-encephalopathy (HIE) is difficult to predict on clinical grounds.

Few studies recorded both MRI findings and long-term outcome [START_REF] Sandroni | Prognostication in comatose survivors of cardiac arrest: An advisory statement from the European Resuscitation Council and the European Society of Intensive Care Medicine[END_REF]. Diffuse cortical abnormality by DWI in the acute phase following OHCA appears to be of unfavorable prognostic significance [START_REF] Choi | Diffusion-weighted magnetic resonance imaging for predicting the clinical outcome of comatose survivors after cardiac arrest: a cohort study[END_REF]. The Hirsh score has been described recently as an accurate scoring after cardiac arrest [START_REF] Hirsch | Prognostic Value of A Qualitative Brain MRI Scoring System After Cardiac Arrest: Prognostic value of qualitative MRI after cardiac arrest[END_REF]. Using DWI and FLAIR sequences, Hirsch et al. [START_REF] Hirsch | Prognostic Value of A Qualitative Brain MRI Scoring System After Cardiac Arrest: Prognostic value of qualitative MRI after cardiac arrest[END_REF] developed a score according to the importance of lesion in different cerebral areas. They reported a specificity of 100% and a sensitivity 50-60%. Our data show a sensitivity of 57% with a specificity of 100% for a threshold of 8 in "deep gray nuclei" score. Such variation in accuracy could be explained by the delayed MRI exam in our study compared to Hirsch et al. one in which the median time to MRI was early, between 72-96h after cardiac arrest. In our study, the median time to MRI was later, approximately 7 days corresponding to a subacute phase after injury. Indeed, an evolution of MRI brain variables over time has been recently reported in a newborn population after hypoxic lesion, especially within the first 72h after injury [START_REF] Gano | Evolution of pattern of injury and quantitative MRI on days 1 and 3 in term newborns with hypoxic-ischemic encephalopathy[END_REF]. Greer et al., [START_REF] Greer | Serial MRI changes in comatose cardiac arrest patients[END_REF] using serial MRI after adult cardiac arrest showed that in patient with unfavorable outcome there was a worsening in the signal abnormalities between the early phase (days 1-5) and the subacute period (days 6-12) with substantial new white matter changes on imaging, more often seen on DWI (100%) than FLAIR (60%). We decided to propose MRI exam 7 days after OHCA because in clinical practice, most discussions on therapeutic limitation take place during this period. Moreover, OHCA patients are commonly critical care patient with haemodynamic and respiratory instability, and MRI exam could be difficult at the early time following OHCA. Although Hirsh et al. described several patients with impossibility to undergo MRI exam because of agitation or haemodynamic instability, we report only 4 patients with movement artefact in our group.

The presence of the amino acid derivative N-acetylaspartate (NAA) is almost exclusive to neurons and their processes and is, therefore, an accepted marker of their health [START_REF] Simmons | Immunocytochemical localization of N-acetyl-aspartate with monoclonal antibodies[END_REF][START_REF] Jenkins | Nonlinear decrease over time in N-acetyl aspartate levels in the absence of neuronal loss and increases in glutamine and glucose in transgenic Huntington's disease mice[END_REF][START_REF] Moffett | N-Acetylaspartate in the CNS: from neurodiagnostics to neurobiology[END_REF] and, as such, its concentration will decrease with increasing damage to the brain [START_REF] Rigotti | Whole-brain N-acetylaspartate as a surrogate marker of neuronal damage in diffuse neurologic disorders[END_REF]. We can also suggest that the 7 days delay for monitoring NAA concentration, a specific marker of neuronal damage, support the possibility of brain lesion detection. 1 H-CSI was found to correlate with outcome of traumatic brain injury [START_REF] Croall | Magnetic resonance spectroscopy for traumatic brain injury[END_REF][START_REF] Weiss | Clinical review: prognostic value of magnetic resonance imaging in acute brain injury and coma[END_REF] but has not been already well studied in adults after OHCA. In neonatal HIE, 1 H-CSI of the basal ganglia and thalamus has been used to predict an adverse outcome [START_REF] Peden | Proton spectroscopy of the neonatal brain following hypoxic-ischaemic injury[END_REF]. Boichot et al. described a decrease in NAA/Cr ratio in severe neonatal HIE with unfavorable prognosis [START_REF] Boichot | Term neonate prognoses after perinatal asphyxia: contributions of MR imaging, MR spectroscopy, relaxation times, and apparent diffusion coefficients[END_REF]. This decrease seems not to be influenced by hypothermia as reported later [START_REF] Ancora | Prognostic value of brain proton MR spectroscopy and diffusion tensor imaging in newborns with hypoxic-ischemic encephalopathy treated by brain cooling[END_REF]. In a recent meta-analysis, 1 H-CSI was considered as the most accurate quantitative MRI biomarker within the neonatal period for prediction of neurodevelopmental outcome after HIE [START_REF] Thayyil | Cerebral Magnetic Resonance Biomarkers in Neonatal Encephalopathy: A Meta-analysis[END_REF]. In adults, very few data are available, mostly case reports using the single voxel spectroscopy in central white matter [START_REF] Martin | Nuclear magnetic resonance spectroscopy study of human brain after cardiac resuscitation[END_REF][START_REF] Berek | Early determination of neurological outcome after prehospital cardiopulmonary resuscitation[END_REF][START_REF] Kano | Neuronal cell injury in patients after cardiopulmonary resuscitation: evaluation by diffusion-weighted imaging and magnetic resonance spectroscopy[END_REF]. Wartenberg et al. described the case of a OHCA patient who was investigated 7 days after injury with encouraging data of 1 H-CSI compared to other prognostic assessment techniques such as electroencephalography, or clinical evaluation [START_REF] Wartenberg | Is Magnetic Resonance Spectroscopy Superior to Conventional Diagnostic Tools in Hypoxic-Ischemic Encephalopathy?[END_REF]. To our knowledge, our study is the first to assess 1 H-CSI of lenticular cores and thalamus in a prospective cohort of OHCA. In our study, the clinically relevant values of NAA/Cr ratio is 1.32, a threshold below which the probability of unfavorable outcome is close to 100.

Our findings should be interpreted in light of the following potential limitations. First, we decided to perform 1 H-CSI more than 6 days after OHCA. Most case reports studies have been conducted in the acute phase after CA (24-48h after CA) and focused on cerebral lactate measurement [START_REF] Martin | Nuclear magnetic resonance spectroscopy study of human brain after cardiac resuscitation[END_REF][START_REF] Kano | Neuronal cell injury in patients after cardiopulmonary resuscitation: evaluation by diffusion-weighted imaging and magnetic resonance spectroscopy[END_REF]. It is likely that metabolite concentration in the brain is likely to change over time after HIE and lactate doublet peak is likely to disappear as reported in newborns [START_REF] Gano | Evolution of pattern of injury and quantitative MRI on days 1 and 3 in term newborns with hypoxic-ischemic encephalopathy[END_REF]. However, delaying MRI examination has several advantages. It allows a better hemodynamic and respiratory stabilization of the patients, improving patient safety during transport and MRI, an important concern for an exam without short-term benefit. In addition, the data are obtained after the period of rapidly changing neurodegenerative changes, improving the consistency of the data. Delayed 1 H-CSI has been used to predict prognosis after brain trauma with a good sensitivity when MRI was performed 24 days after the injury [START_REF] Tollard | Experience of diffusion tensor imaging and 1H spectroscopy for outcome prediction in severe traumatic brain injury: Preliminary results[END_REF]. Finally, patient recovery is often delayed for a few days due to the practice of hypothermia and sedation. Patients often regain consciousness between day 2 and day 5 and early 1 H-CSI would lead to unnecessary studies. In our study, the mean Glasgow score in good recovery group at the MRI time, at 7 days, was only 10. Despite allowing several days for stabilization in the ICU, we could obtain interpretable 1 H-CSI in only 73 % of our patients. This can probably be improved with increasing experience. Second, as in all others studies using MRS which is limited to the selected region of interest represents also a limitation. This point must be underlined because the neurochemical profile was reported to be variable across brain regions after an experimental focal ischemic lesion [START_REF] Alf | High-resolution spatial mapping of changes in the neurochemical profile after focal ischemia in mice: HIGH-RESOLUTION MRSI AFTER FOCAL ISCHEMIA[END_REF]. We chose to perform 1 H-CSI measurements in 2 different regions of the brain (Lenticular core and thalamus) in order to limit the bias related to sampling choice. In fact, 1 H-CSI in the thalami did not improve prognosis accuracy. We chose these 2 regions because they are easy to recognize and less prone to errors due to inaccurate positioning of voxel samples. They were also associated with prognosis in trauma patients [START_REF] Carpentier | Early Morphologic and Spectroscopic Magnetic Resonance in Severe Traumatic Brain Injuries Can Detect "Invisible Brain Stem Damage" and Predict "Vegetative States[END_REF] but the metabolic pathways of brain injury after brain trauma and OHCA are not similar. Neostriatal structures (putamen and caudate nucleus) are particularly sensitive to ischemia compared to globus pallidus or thalamus [START_REF] Falini | Progressive brain failure after diffuse hypoxic ischemic brain injury: a serial MR and proton MR spectroscopic study[END_REF]. Thus, it is not surprising to find that 1 H-CSI in the lenticular cores was associated with the best prognosis value in our study. Third, our methodological choices for 1 H-CSI can be discussed. We used Cr as the reference metabolite concentration because it is the most stable one across patients. Although its concentration may vary in the early period after OHCA and hypothermia, probably delayed imaging limits the amplitude of this change between patients. Because of our short-time of echo, we were not able to study lactate ratio, which has been used for assessment of prognosis in previous studies. We chose to limit the duration of MRI scanning for safety reasons but it could be interesting to evaluate brain lactate changes after OHCA. Finally, we cannot exclude misclassification of outcome due to "self-fulfilling" prophecies arising from premature decisions of withdrawal and limitation of life-sustaining treatments. However, even if we exclude all patients who died from care withdrawal, the cutoff for NAA/Cr ratios measured in lenticular cores and AUC did not vary significantly (Table 3 Data in Brief).

In conclusion, according our results we suggest that in adult patients after cardiac arrest that 1 H-CSI measured on lenticular cores at the subacute phase of hypoxic-ischemic brain injury is feasible in most patients and may predict long-term recovery. This evidence requires statistical confirmation from future large-scale trials in association with other ancillary tests (EEG, SSEP, pupillometry…) with strict protocol of withdrawal or limitation-of-care decisions.

  MR imaging was performed mean 7 days after OHCA, according to tolerance of transport of such patients. Structural MRI and 1 H-MRS, were performed on 1.5-T Signa HDxt imager (GE Healthcare, Milwaukee, WI, USA). Pulse sequences included a T2-weighted sequence (axial; slice thickness, 5 mm; TR/TE, 6,400/105 ms; bandwidth, 122 Hz; flip angle, 90°; matrix, 512x320; field of view (FOV), 240 mm), T2*-weighted sequence (axial; slice thickness, 5 mm; TR/TE, 640/18 ms; bandwidth, 57 Hz; flip angle, 20°; matrix, 352x224; FOV, 250 mm), fluidattenuated inversion recovery (FLAIR; axial; slice thickness, 5 mm; TR/TE/TI, 9,000/160/2,250 ms; bandwidth, 122 Hz; flip angle, 90°; matrix, 256x192; FOV, 250 mm), and diffusionweighted imaging (DWI; axial; slice thickness, 3 mm; TR/TE, 6,150/102 ms; max b value of 1,000 s/mm2; bandwidth, 1953 Hz; flip angle, 90°; matrix, 128x128; FOV, 250 mm).

Conflict of interest statement:

The authors declare that they have no competing interests.

Author contributions: HQ was the lead intensivist and contributed to the protocol development, study design and concept, conduct, data acquisition and coordination, data interpretation, writing and revising it critically, and reviewing the report. He takes responsibility for the integrity of the data and the accuracy of the data analysis. LV was involved in data interpretation, writing and reviewing the report. SB was involved in data analysis, contribution to the statistical analysis plan, statistical analysis. XC was involved in data collection and preparation of the report. MEA, EC were involved in data acquisition, data analysis, and revising the report. CI was involved in data interpretation, and revising the report critically. All authors approved the final version.

LEGEND OF FIGURES


Teva Vernoux
email: teva.vernoux@ens-lyon.fr

Fabrice Besnard

Christophe Godin

What shoots can teach about theories of plant form

Plants generate a large variety of shoot forms with regular geometries. These forms emerge primarily from the activity of a stem cell niche at the shoot tip. Recent efforts have established a theoretical framework of form emergence at the shoot tip, that has empowered the use of modelling hand in hand with biological approaches to start disentangling the biochemical and physical mechanisms canalizing form development at the shoot tip. We discuss here how these advances get us closer to identifying the construction principles of plant shoot tips. Considering the current limits of our knowledge, we propose a roadmap for developing a general theory of form development at the shoot tip.

Main text: (4573 words)

Introduction

How organisms shape themselves has been a fascinating and challenging question for centuries. Alan Turing's pioneering work on self-organized pattern formation through diffusion of chemical signals exemplifies the central contribution of mathematical modelling and the impact of a theory on the understanding of developmental biology 1 . However, understanding the construction of a form goes beyond patterning (the establishment of the spatial distribution of different cell identities) and must account for the geometry of the living object and the biophysical mechanisms driving geometry changes. The complexity of the problems raised by such integration was already recognized by Alan Turing: " … the description of the [biological system's] state consists of two parts, the mechanical and the chemical. [...] Determining the changes of state [...] is a problem of formidable mathematical complexity. [...] The interdependence of the chemical and mechanical data adds enormously to the difficulty" [START_REF] Turing | The chemical basis of morphogenesis[END_REF] . In recent years, a massive increase in computational power has finally provided opportunities to tackle this challenge and to test our understanding by creating models that reproduce form development in silico, as an emergent property.

Understanding plant forms presents challenges of its own. At the structural level, cell walls as resistant as steel surround plant cells and preclude cell movement. Plants have also unique developmental features that underlie dynamic changes in their post-embryonic form, including continuous apical growth of their axes and reiterative production of new organs and axes throughout their life, and that must be accounted for to understand the emergence of their form.

Here we discuss our understanding of form emergence in the tissue that generates the entire aerial architecture of plants, the shoot apical meristem (SAM; Fig. 1). A stem cell niche in the SAM sustains continuous organogenesis. Recent studies of the SAM and aerial organ development have been instrumental for understanding the dynamics of plant morphogenesis at the tissue scale. We review first how computational models have helped establishing the principles of a theoretical framework for morphogenesis at the SAM. Then, we consider recent analyses of how patterns and forms emerge in the shoot apical meristem, focusing on the ones that, combining modelling and in planta experiments, have explored and challenged the biophysical mechanisms at play. Finally, we highlight what are in our view the main limitations of the current theoretical view of SAM morphogenesis in order to draw up a possible roadmap for future developments. In complement, we also refer the readers to Box 1 for a short companion guide on how to best use and critically assess computational models such as the ones discussed in this perspective.

A theory of shoot apical meristem morphogenesis

The classical view of morphogenesis in biology assumes a two-phase process initiated by patterning and followed by deformation [START_REF] Jaeger | Regulative feedback in pattern formation: towards a general relativistic theory of positional information[END_REF] . These two phases correspond to processes of different bio-physical origins and proposed to act at different temporal scales. In the patterning phase, often considered more rapid than deformation, bio-physical processes create region-defining fields of molecular and physical cues. In the deformation phase, cells read out this patterning information and modify their bio-physical properties accordingly. Patterning thus induces deformation, which in turn, feeds back on patterning by modifying the geometry of the tissue, suggesting that these two processes are deeply interdependent. It also indicates that the classical paradigm of patterning and deformation acting at different time scales needs to be considered with caution. In the SAM, two such phases can readily be identified. They respectively correspond to the dynamic patterning process specifying the initiation sites of primordia of leaves and flowers at the shoot apex, called phyllotaxis, and to the subsequent outgrowth of the organ that generates the typical geometry of the tissue (Fig. 1). In recent years, the elements of a theory integrating the causality between processes controlling form emergence at the SAM have emerged. They are organized according to four main principles (Fig. 2): Principle 1: "Mobile reference points dynamically organize positional information around a stable central zone to pattern the SAM" Phyllotaxis is a remarkable example of self-organized patterning. Dynamic positional information is believed to be predominantly responsible for the emergence of the remarkable symmetry of lateral organ arrangement, which is frequently helicoidal (Fig. 1a). No organ can form at the very tip of the plant, which is defined as the meristem central zone. Around the central zone, primordia can spontaneously emerge in an annular region called the peripheral zone. However, it was postulated early on that primordia within the peripheral zone inhibit the initiation of new primordia in their immediate vicinity (For review: 3 ), preventing organ "crowding". However, growth progressively pushes young primordia away from the peripheral zone, periodically leaving space for new initiations. Remarkably, abstract models of this dynamic process on continuous templates can recapitulate the frequency and position of these initiations and can generate many of the organ patterns that are observed on plant stems and flower heads [START_REF] Douady | Phyllotaxis as a dynamical self-organizing process .2. The spontaneous formation of a periodicity and the coexistence of spiral and whorled patterns[END_REF][START_REF] Refahi | A stochastic multicellular model identifies biological watermarks from disorders in self-organized patterns of phyllotaxis[END_REF][START_REF] Godin | Phyllotaxis as geometric canalization during plant development[END_REF] . The central zone acts as a stable reference relative to which the position of the different primordia can be defined. Organs in turn become secondary mobile reference points with respect to the central zone, that refine the positioning of future organs in space and time.

Together they act as a dynamic reference system that continuously reorganizes positional information prescribing the position and initiation time of subsequent organs (Fig. 3).

Principle 2: "Turgor pressure and cell wall remodelling drives growth and deformation"

Once initiated, primordia start to grow. In recent years, efforts to understand the outgrowth mechanism have focused on the origin and role of mechanical forces in driving the changes of form in plant tissues. It was proposed early on that tissue deformation and growth is fuelled by osmosis-driven cell turgor (Fig. 4) [START_REF] Sachs | A Text-Book of Botany: Morphological and Physiological[END_REF] . Cells have low water potential (mainly due to high osmotic potential), driving extracellular water uptake to generate high internal turgor pressures. Turgor compresses the cell membrane against the rigid cell walls, which resist both by deforming and by building up internal mechanical stresses. When pressure is moderate, walls deform in a reversible (elastic) manner, but yield irreversibly and are remodelled if the pressure is high enough, leading to growth [START_REF] Kutschera | Regulation of Cell Expansion. The Cytoskeletal Basis of Plant Growth and Form 85-99[END_REF] . In a pioneering work, James Lockhart proposed a simple model for this irreversible mechanism applied to an idealized 1-dimensional (1-D) cell [START_REF] Lockhart | An analysis of irreversible plant cell elongation[END_REF] . In this model, turgor pressure is a property emerging from the equilibrium that takes place between the osmotic forces that attract water and deform the cell wall, which in turn resists water ingress [START_REF] Ray | Role of turgor in plant cell growth[END_REF] .

The extension of this model to multicellular 3-D structures only emerged recently. First attempts representing 2-D tissues [START_REF] Dupuy | A system for modelling cellcell interactions during plant morphogenesis[END_REF] , then 3D tissues [START_REF] Hamant | Developmental patterning by mechanical signals in Arabidopsis[END_REF] , were carried out by modelling wall elements as 1-D springs, and then generalized with elastic surface elements able to better represent wall anisotropy in 2 or 3 dimensions [START_REF] Boudon | A computational framework for 3D mechanical modeling of plant morphogenesis with cellular resolution[END_REF][START_REF] Bozorg | A continuous growth model for plant tissue[END_REF] . Using these more general tissue representations, Lockhart's growth equation could be extended to accurately account for potential directional differences in tissue mechanical properties in 3-D, supporting a pivotal role for turgor pressure and cell walls in regulating growth and deformation of complex tissues such as the SAM (Fig. 4).

Principle 3: "Patterns instruct tissue deformation by regulating cell wall properties and turgor pressure"

To link patterns to form emergence, a conceptual framework building on several pioneering attempts [START_REF] Erickson | Modeling of plant growth[END_REF][START_REF] Silk | Quantitative Descriptions of Development[END_REF] was proposed, marking a key step towards a theory coupling patterning and growth [START_REF] Coen | The genetics of geometry[END_REF] . Based on the mathematical fact that any deformation can be expressed using three elementary deformation parameters for each small region (growth rate, growth direction i.e. the principal direction of growth, growth anisotropy i.e. the degree to which growth occurs in any preferential direction), this framework postulated that, at an abstract level, molecular and biophysical cues established during the patterning phase might locally prescribe a "growth plan" in terms of these parameters. In the same way that words can all be constructed from a finite alphabet, elementary deformation instructions could thus be assembled by cells to achieve tissue growth. Here, the intensity of elementary deformations is directly prescribed by genes, either through scalar values (e.g. molecule concentration) or polarizing factors (e.g. oriented flows or gradients of molecules, cell polarization) [START_REF] Abley | An intracellular partitioning-based framework for tissue cell polarity in plants and animals[END_REF] , and mechanics is used to resolve potential conflicts between neighbouring regions instructed to develop at different paces, and thus to prevent tissues from being torn apart [START_REF] Coen | The genetics of geometry[END_REF] . Several studies then attempted to account for local deformations as the result of cellular processes in a more mechanistic way. A first study in virtual cellularised embryos [START_REF] Bassel | Mechanical constraints imposed by 3D cellular geometry and arrangement modulate growth patterns in the Arabidopsis embryo[END_REF] hypothesized that growth results from two independent pathways, one acting on relaxation of cell walls deformed by turgor pressure and a second one that would directly control a hypothetical growth factor locally mediating through yet unknown mechanisms the effect of genes as in [START_REF] Coen | The genetics of geometry[END_REF] . By contrast, other approaches modelled growth uniquely as a result of a cell wall relaxation pathway in tissues with SAM geometry [START_REF] Boudon | A computational framework for 3D mechanical modeling of plant morphogenesis with cellular resolution[END_REF][START_REF] Bozorg | A continuous growth model for plant tissue[END_REF] . Here, genes regulate growth by affecting either cell wall rheological properties or cell turgor. The deformation of each wall segment is locally governed by a growth law, corresponding to the Lockhart equation generalized to 3-D (see Principle 2), and whose parameters depend on regional gene expression. This latter view provides a mechanistic framework for the biochemical and genetic control of form emergence in the SAM, positioning the cell wall and turgor pressure as physical actuators controlled by genes (Fig. 4).

Principle 4: "Tissue deformation feeds back on patterns"

However, connections between patterning and growth are not one-way only. In the last decade, it has been discovered that cells in the SAM may sense the mechanical stresses induced by turgor forces in their wall. At the SAM surface, these stresses are a read-out of the local wall geometry that is used by cells to locally modify their biochemical and rheological properties 12 .

To explore how specific forms can emerge in the SAM from such an intricate interaction and study its properties, further computational models have been developed. They integrate organ geometry, wall rheology, cell turgidity and growth laws with mechanical feedback and have made it possible to simulate forms resulting from different combinations of these factors [START_REF] Bozorg | Stress and strain provide positional and directional cues in development[END_REF][START_REF] Oliveri | Regulation of plant cell wall stiffness by mechanical stress: a mesoscale physical model[END_REF] . These computational models have been and will continue to be instrumental in understanding the properties of complex plant tissues, such as the SAM [START_REF] Bozorg | Stress and strain provide positional and directional cues in development[END_REF][START_REF] Oliveri | Regulation of plant cell wall stiffness by mechanical stress: a mesoscale physical model[END_REF] and in further exploring the general principle that morphogenesis is finely regulated by a feedback loop between patterning and deformation (Fig. 2,4). As pointed out previously, this last principle implies that patterning and deformation cannot be easily temporally separated.

Identifying mechanisms to test the theory

Recent studies combining modelling and in planta experiments have been essential in identifying molecular mechanisms linking signals, genes and form emergence, and at the same time for testing the current theoretical framework for morphogenesis at the SAM.

The stem cell niche acts as a stable reference point

In Principle 1 of the theory, the tip of the SAM acts as a stable reference, essential for defining the coordinates of future growth axes and thus for form emergence. Functionally, this reference is the central domain of the SAM containing the stem cell niche (Fig. 1b). The stem cells are located in the SAM in the external cell layers at the very tip of the stem axis. An organizing centre that maintains the niche is located below. These two domains control each other through a homeostatic feedback loop (Fig. 5a; for review: [START_REF] Gaillochet | Where Art Thou? The mechanisms of shoot meristem patterning[END_REF] ). Organizing centre cells produce the WUSCHEL (WUS) transcription factor, which moves and activates the CLAVATA3 (CLV3) gene. CLV3 peptides then diffuse to inhibit WUS. Beyond its apparent simplicity, this regulatory loop raises a difficult question: how are CLV3 and WUS expression domains maintained in a growing tissue one on top of the other? Models of the WUS/CLV3 pattern on a static template provide a basic understanding [START_REF] Jönsson | Modeling the organization of the WUSCHEL expression domain in the shoot apical meristem[END_REF][START_REF] Hohm | A Dynamic Model for Stem Cell Homeostasis and Patterning in Arabidopsis Meristems[END_REF][START_REF] Yadav | Plant stem cell maintenance involves direct transcriptional repression of differentiation program[END_REF][START_REF] Gruel | An epidermis-driven mechanism positions and scales stem cell niches in plants[END_REF][START_REF] Adibi | Centering the Organizing Center in the Arabidopsis thaliana Shoot Apical Meristem by a Combination of Cytokinin Signaling and Self-Organization[END_REF][START_REF] Zhou | HAIRY MERISTEM with WUSCHEL confines CLAVATA3 expression to the outer apical meristem layers[END_REF][START_REF] Gruel | The interaction of transcription factors controls the spatial layout of plant aerial stem cell niches[END_REF] . The WUS-CLV3 loop recalls the activatorinhibitor couple in a Turing system 1 , but with the activator and inhibitor produced by different cells. The fact that CLV3 is always expressed above WUS within the shoot tip can be explained by including epidermal-derived signals (Fig. 5a). Conversion of cytokinin precursors into bioactive cytokinins (for review: [START_REF] Gaillochet | Where Art Thou? The mechanisms of shoot meristem patterning[END_REF] ) and/or a mobile miRNA 30 are candidate mechanisms. Direct interaction of WUS with the HAIRY MERISTEM (HAM) transcription factors could inhibit the capacity of WUS to induce CLV3 in the organizing centre, allowing WUS to activate CLV3 only when it moves in the outermost layers where HAMs are absent. HAM activity could thus also participate in the separation of WUS and CLV3 expression domains and to the confinement of CLV3 to the outer domain [START_REF] Zhou | HAIRY MERISTEM with WUSCHEL confines CLAVATA3 expression to the outer apical meristem layers[END_REF][START_REF] Gruel | The interaction of transcription factors controls the spatial layout of plant aerial stem cell niches[END_REF] . HAM expression patterns could again depend on epidermal signals. The most recent models have included this idea and, using realistic 3-D growing templates, suggest that epidermal signals could indeed ensure that the WUS-CLV3 pattern remains stable despite shoot growth (Fig. 5b) [START_REF] Zhou | HAIRY MERISTEM with WUSCHEL confines CLAVATA3 expression to the outer apical meristem layers[END_REF][START_REF] Gruel | The interaction of transcription factors controls the spatial layout of plant aerial stem cell niches[END_REF] .

To act as a stable reference, the stem cell niche must not respond to organogenetic signals. As in other plant tissues [START_REF] Benkova | A morphogenetic trigger: is there an emerging concept in plant developmental biology?[END_REF][START_REF] Paque | Auxin: the plant molecule that influences almost anything[END_REF] , the plant hormone auxin is an instructive signal driving patterning in the SAM. Auxin is polarly transported from cell to cell. While auxin distribution in the SAM sets the locations of lateral organ initiation (see below), auxin is also present at high concentration in the central stem cells niche (Fig. 5c) [START_REF] Vernoux | The auxin signalling network translates dynamic input into robust patterning at the shoot apex[END_REF][START_REF] De Reuille | Computer simulations reveal properties of the cell-cell signaling network at the shoot apex in Arabidopsis[END_REF][START_REF] Galvan-Ampudia | Temporal integration of auxin information for the regulation of patterning[END_REF] . However stem cells are largely insensitive to auxin [START_REF] De Reuille | Computer simulations reveal properties of the cell-cell signaling network at the shoot apex in Arabidopsis[END_REF][START_REF] Reinhardt | Auxin regulates the initiation and radial position of plant lateral organs[END_REF] , likely due to a down regulation of auxin signalling transcriptional effectors, the Auxin Response Factors (ARF), in the centre of the SAM [START_REF] Vernoux | The auxin signalling network translates dynamic input into robust patterning at the shoot apex[END_REF][START_REF] Zhao | Hormonal control of the shoot stem-cell niche[END_REF] . Ordinary differential equation modelling of the ARF-dependent signalling network confirms that differential expression of ARFs could lower sensitivity of the stem cells to auxin [START_REF] Vernoux | The auxin signalling network translates dynamic input into robust patterning at the shoot apex[END_REF] and ARF mis-expression in the stem cells shows that this spatial sensitivity pattern is essential for phyllotaxis [START_REF] Zhao | Hormonal control of the shoot stem-cell niche[END_REF] . Stem cell auxin sensitivity regulation depends on WUS, which, together with other transcription factors, gates auxin signalling through gene repression [START_REF] Ma | WUSCHEL acts as an auxin response rheostat to maintain apical stem cells in Arabidopsis[END_REF][START_REF] Truskina | A network of transcriptional repressors modulates auxin responses[END_REF] . The maintenance of a SAM reference point for patterning is thus intricately linked to a spatio-temporal regulation of responses to developmental signals. Collectively, these studies identify multiple biochemical signals and gene expression regulation systems that establish the SAM central reference point hypothesized in Principle 1 of the theory.

Auxin gradients patterns the shoot apical meristem

Spatio-temporal regulation of auxin distribution appears to be the main biological mechanism both explaining lateral inhibition by organs and triggering growth of new organs outside the SAM central domain [START_REF] Vernoux | The auxin signalling network translates dynamic input into robust patterning at the shoot apex[END_REF][START_REF] Galvan-Ampudia | Temporal integration of auxin information for the regulation of patterning[END_REF][START_REF] Reinhardt | Auxin regulates the initiation and radial position of plant lateral organs[END_REF][START_REF] Vernoux | PIN-FORMED 1 regulates cell fate at the periphery of the shoot apical meristem[END_REF][START_REF] Reinhardt | Regulation of phyllotaxis by polar auxin transport[END_REF][START_REF] Heisler | Patterns of auxin transport and gene expression during primordium development revealed by live imaging of the Arabidopsis inflorescence meristem[END_REF] . Cooperatively with other auxin carriers [START_REF] Reinhardt | Regulation of phyllotaxis by polar auxin transport[END_REF][START_REF] Bainbridge | Auxin influx carriers stabilize phyllotactic patterning[END_REF] , the efflux carrier PIN-FORMED1 (PIN1) is a polar protein essential to the control of polar auxin transport. PIN1mediated supra-cellular fluxes in the SAM are essential for organ formation and for phyllotaxis [START_REF] Reinhardt | Regulation of phyllotaxis by polar auxin transport[END_REF] . Live-imaging of PIN1 polarities and auxin distribution in several plant species, and extensive modelling work, suggest that self-organization of PIN1 polarities allows not only the local accumulation of auxin, specifying new organ sites, but also the emergence of inhibitory fields, by depleting auxin in surrounding cells [START_REF] Vernoux | The auxin signalling network translates dynamic input into robust patterning at the shoot apex[END_REF][START_REF] De Reuille | Computer simulations reveal properties of the cell-cell signaling network at the shoot apex in Arabidopsis[END_REF][START_REF] Galvan-Ampudia | Temporal integration of auxin information for the regulation of patterning[END_REF][START_REF] Jönsson | An auxin-driven polarized transport model for phyllotaxis[END_REF][START_REF] Smith | A plausible model of phyllotaxis[END_REF][START_REF] Stoma | Flux-based transport enhancement as a plausible unifying mechanism for auxin transport in meristem development[END_REF][START_REF] Bayer | Integration of transport-based models for phyllotaxis and midvein formation[END_REF][START_REF] Van Berkel | Polar auxin transport: models and mechanisms[END_REF][START_REF] O'connor | A division in PIN-mediated auxin patterning during organ initiation in grasses[END_REF][START_REF] Hartmann | Toward a 3D model of phyllotaxis based on a biochemically plausible auxin-transport mechanism[END_REF][START_REF] Brunoud | A novel sensor to map auxin response and distribution at high spatio-temporal resolution[END_REF] . Thus, positional information hypothesized in Principle 1 of the theory is provided by auxin (Fig. 5c). However, the mechanisms organizing PIN1 polarities are still elusive. Computational models based on two different mechanisms, auxin flux sensing or auxin cellular concentration sensing, can both reproduce realistic PIN1 polarity patterns [START_REF] Van Berkel | Polar auxin transport: models and mechanisms[END_REF][START_REF] Abley | Formation of polarity convergences underlying shoot outgrowths[END_REF] , making it difficult to pinpoint how PIN1 polarities are coordinated within the SAM. Also, adaxial-abaxial patterning of lateral organs might feedback on auxin polarities [START_REF] Caggiano | Cell type boundaries organize plant development[END_REF] , raising the interesting possibility that identity specification during the development of lateral organs dynamically changes their influence on PIN1 polarities. A recent study that quantitively mapped PIN1 polarities and auxin distribution in 4-D now provides opportunities to re-evaluate and extend existing models [START_REF] Galvan-Ampudia | Temporal integration of auxin information for the regulation of patterning[END_REF] . This study further revealed that cells in the peripheral zone integrate auxin information over time to trigger organ initiation (Fig. 5c). Temporal integration of auxin information was predicted by a recent inhibitory field model with stochastic induction of organ initiation 5 developed to explain the occurrence of perturbed phyllotactic patterns [START_REF] Besnard | Cytokinin signalling inhibitory fields provide robustness to phyllotaxis[END_REF] , but still needs to be integrated into cellular models with precise SAM geometry. Furthermore, existing mechanistic models do not explicitly take into account the high auxin concentrations present at the centre of the SAM. This appears to be an important missing element since a recent study combining live imaging with a simplified compartment model to represent functional subdomains of the meristem, showed that high auxin levels in the centre of the SAM are essential for maintenance of stem cell niche size, and that lateral organs are required to maintain these high auxin levels [START_REF] Shi | Feedback from Lateral Organs Controls Shoot Apical Meristem Growth by Modulating Auxin Transport[END_REF] . The recent identification of young flower primordia as putative sites of auxin biosynthesis and the demonstration that PIN1-mediated fluxes could converge globally towards the central zone auxin maximum 35 corroborate this finding. Together, these studies highlight the role of auxin in defining the central zone as a stable reference and in establishing lateral organs as secondary mobile reference points as postulated in Principle 1. These two properties are thus interdependent and emerge from auxin-dependent regulations that are still under investigation (Fig. 5c).

Cell wall mechanical properties are modified during organ growth

How does pattern become form? Principles 2 and 3 of the theory predict a central role for the cell wall. Cell wall anisotropy is directly linked to cellulose microfiber orientation [START_REF] Baskin | Anisotropic expansion of the plant cell wall[END_REF] . In their absence, cells tend to grow isotropically, like soap bubbles [START_REF] Corson | Turning a plant tissue into a living cell froth through isotropic growth[END_REF] . The extracellular deposition of cellulose microfibers by Cellulose Synthase (CESA) transmembrane proteins is directed by dynamic cortical microtubules (for review: [START_REF] Landrein | How mechanical stress controls microtubule behavior and morphogenesis in plants: history, experiments and revisited theories[END_REF] ). Cellulose microfibril patterns thus resemble those of microtubules in SAM cells [START_REF] Sampathkumar | Primary wall cellulose synthase regulates shoot apical meristem mechanics and growth[END_REF] . Auxin has been shown to induce a loss of microtubule anisotropy prior to lateral organ initiation [START_REF] Sassi | An auxin-mediated shift toward growth isotropy promotes organ formation at the shoot meristem in Arabidopsis[END_REF] . Numerical simulations using cell-based models predict that changing both cell wall anisotropy and stiffness is required for organ emergence [START_REF] Sassi | An auxin-mediated shift toward growth isotropy promotes organ formation at the shoot meristem in Arabidopsis[END_REF][START_REF] Armezzani | Transcriptional induction of cell wall remodelling genes is coupled to microtubule-driven growth isotropy at the shoot apex in Arabidopsis[END_REF] . Indeed, loss of cell wall anisotropy is tightly coupled to the induction of cell wall-loosening enzymes, through an yet unknown mechanism [START_REF] Armezzani | Transcriptional induction of cell wall remodelling genes is coupled to microtubule-driven growth isotropy at the shoot apex in Arabidopsis[END_REF] . This cell wall anisotropy/loosening module creates a direct molecular link between cell identity specification and the regulation of cell wall mechanical properties (Fig. 6). The loosening could be mediated by enzymes that modify cell wall polysaccharides, notably those that compose the celluloseembedding visco-elastic matrix. Accordingly, micromanipulations and mutants in genes encoding several such enzymes perturb phyllotaxis [START_REF] Fleming | Induction of leaf primordia by the cell wall protein expansin[END_REF][START_REF] Peaucelle | Arabidopsis phyllotaxis is controlled by the methylesterification status of cell-wall pectins[END_REF][START_REF] Peaucelle | Pectin-induced changes in cell wall mechanics underlie organ initiation in Arabidopsis[END_REF][START_REF] Zhao | Xyloglucans and Microtubules Synergistically Maintain Meristem Geometry and Phyllotaxis[END_REF] . Physical measurements using atomic force microscopy, or manipulation of osmotic pressure, show differences in stiffness and elasticity between the SAM centre and periphery [START_REF] Peaucelle | Pectin-induced changes in cell wall mechanics underlie organ initiation in Arabidopsis[END_REF][START_REF] Milani | In vivo analysis of local wall stiffness at the shoot apical meristem in Arabidopsis using atomic force microscopy[END_REF][START_REF] Kierzkowski | Elastic Domains Regulate Growth and Organogenesis in the Plant Shoot Apical Meristem[END_REF] , indicating differences in cell wall mechanical properties matching SAM functional zonation. Although genetic approaches have not identified all the enzymes responsible (possibly due to functional redundancy), these data nonetheless support the hypothesis that changing cell wall mechanical properties (stiffness, elasticity, anisotropy) is a primary function of genes driving form emergence (Principle 3).

Mechanical feedbacks monitor form changes

The existence of mechanical feedbacks from Principle 4 of the theory was first highlighted by a combination of imaging, genetics and modelling that demonstrated that cortical microtubules align with the direction of maximal tensile stresses in the SAM [START_REF] Hamant | Developmental patterning by mechanical signals in Arabidopsis[END_REF] . Modelling confirms that axial growth is consistent with a feedback law in which tissues produced by the SAM rigidify preferentially in the maximal tensile stress direction, and is incompatible with a law where tissues rigidify in the direction of maximum elongation [START_REF] Hamant | Developmental patterning by mechanical signals in Arabidopsis[END_REF][START_REF] Bozorg | Stress and strain provide positional and directional cues in development[END_REF] . How mechanical stresses are sensed in the SAM remains unclear, although the microtubules could themselves act as sensors [START_REF] Hamant | Are microtubules tension sensors?[END_REF] .

Microtubule anisotropy results in cell wall and thus growth anisotropy. This is in turn reinforced in response to mechanical stresses resulting from changes in form. Interfering with this feedback affects meristem geometry and particularly crease formation at the boundary between SAM and new organs [START_REF] Uyttewaal | Mechanical Stress Acts via Katanin to Amplify Differences in Growth Rate between Adjacent Cells in Arabidopsis[END_REF] . Furthermore a combination of live-imaging and modelling suggests that PIN1 polarity distribution can be affected by mechanical stresses [START_REF] Heisler | Alignment between PIN1 polarity and microtubule orientation in the shoot apical meristem reveals a tight coupling between morphogenesis and auxin transport[END_REF] . Analysis of cesa mutants reveals that impairing cellulose synthesis alters both microtubule organization and the auxin-dependent expression of PIN1 [START_REF] Sampathkumar | Primary wall cellulose synthase regulates shoot apical meristem mechanics and growth[END_REF] . Inducing changes in cell wall mechanical properties through enzymatic modification of the pectin matrix affects PIN1 polarity distribution [START_REF] Braybrook | Mechano-chemical aspects of organ formation in Arabidopsis thaliana: the relationship between auxin and pectin[END_REF] .

Osmotic treatments and modelling also demonstrated that mechanical strain positively regulates the amount of PIN1 present in membranes, notably in lateral organs at the SAM [START_REF] Nakayama | Mechanical regulation of auxin-mediated growth[END_REF] . Together these data strongly support an essential role for mechanical feedbacks in allowing constant form monitoring and pinpoint auxin as a key mediator linking mechanics of the tissue to cell/tissue physiology. Nonetheless, other mechanisms still need to be considered in the future, e.g. involving other hormones. In addition, form can also feedback on the expression of meristematic genes, likely via auxin-independent mechanisms [START_REF] Gruel | An epidermis-driven mechanism positions and scales stem cell niches in plants[END_REF][START_REF] Landrein | Mechanical stress contributes to the expression of the STM homeobox gene in Arabidopsis shoot meristems[END_REF] .

The limits of the theory

Missing elements in the theory

Combining biological and modelling approaches, has permitted a significant step change in our understanding of SAM form emergence over the last decade. Our conceptual understanding of form emergence nonetheless remains fragmented. Biochemical and mechanical mechanisms have largely been considered independently, as have patterning and form acquisition. A key challenge is now to quantitatively analyse coupling of biochemical and mechanical regulations to build a more integrated theory of form emergence. Auxin is a common regulator acting at multiple scales in these mechanisms and provides a possible entry point to a unifying biophysical vision of form emergence at the SAM. Analysis of coupling between biochemistry and mechanics at the SAM will also be key to understand form robustness, i.e. reproducibility between SAMs despite the existence of noise. There are now clear examples of how noise is buffered or contributes to form emergence in the SAM. Noise in the rhythmicity of organ patterning [START_REF] Refahi | A stochastic multicellular model identifies biological watermarks from disorders in self-organized patterns of phyllotaxis[END_REF][START_REF] Mirabet | Noise and robustness in phyllotaxis[END_REF][START_REF] Besnard | Cytokinin signalling inhibitory fields provide robustness to phyllotaxis[END_REF] can perturb form. At the same time, mechanical feedback mediated by microtubules amplifies growth differences, generating variability in cell size and maintaining a robust form at the SAM [START_REF] Uyttewaal | Mechanical Stress Acts via Katanin to Amplify Differences in Growth Rate between Adjacent Cells in Arabidopsis[END_REF] . A role for mechanical resistance to growth of the epidermis has also been proposed in generating robust tissue shapes [START_REF] Zhou | Epidermal restriction confers robustness to organ shapes[END_REF] . A plausible hypothesis is that form emergence is not only influenced by, but also uses both structured and random changes in geometry and mechanical stress distribution as cues for the dynamic generation of form.

Integrating noise into the theoretical framework of SAM form emergence will allow this idea to be tested.

Further development of a theory of morphogenesis dynamics at the SAM requires a deeper understanding of the cellular mechanisms that drive cell growth and division in a tissue context.

Progresses in quantitative imaging have permitted to test the influence of cell geometry on division plane orientation in various tissues [START_REF] Rasmussen | An overview of plant division-plane orientation[END_REF] . In the SAM, mechanical signals have been proposed to contribute to division plane orientation (notably in the organ boundary region; Fig 1b) in addition to geometry, thus providing an understanding of how the tissue context can act on this process [START_REF] Louveaux | Cell division plane orientation based on tensile stress in Arabidopsis thaliana[END_REF][START_REF] Sahlin | A modeling study on how cell division affects properties of epithelial tissues under isotropic growth[END_REF] . Two studies have also explored the control of cell division and expansion in the SAM, demonstrating that cells do not simply divide when they reach a critical size (a simple hypothesis often used in models), but that there is instead a flexibility in the cell size reached at division [START_REF] Jones | Cell-size dependent progression of the cell cycle creates homeostasis and flexibility of plant cell size[END_REF][START_REF] Willis | Cell size and growth regulation in the Arabidopsis thaliana apical stem cell niche[END_REF] . However, we know very little about either the role of cell division orientation or indeed even of how subdivision of tissues into cells can influence the biophysical properties of tissues and thus form emergence. These questions have just started to be addressed [START_REF] Zhao | Microtubule-Mediated Wall Anisotropy Contributes to Leaf Blade Flattening[END_REF] (building on earlier work: [START_REF] Wyrzykowska | Manipulation of leaf shape by modulation of cell division[END_REF] ) and require further experimental and theoretical analysis. Variation in SAM form between genetic variants has been genetically associated with genes regulating either cell division or expansion, highlighting the importance of considering the cellular scale in a theory of form emergence at the SAM [START_REF] Leiboff | Genetic control of morphometric diversity in the maize shoot apical meristem[END_REF] . Also, the recent demonstration that cell contact topology in the SAM depends on microtubule-mediated mechanical feedback, and could determine the transport network topology of auxin [START_REF] Jackson | Global Topological Order Emerges through Local Mechanical Control of Cell Divisions in the Arabidopsis Shoot Apical Meristem[END_REF] , provides a first possible mechanism for coupling geometric/chemical/mechanical feedbacks acting on cells to tissuewide patterning and form emergence.

Understanding the control of the mechanical properties of the SAM and their dynamics remains challenging. Atomic force microscopy and a physical model of pressurized cells have recently been used to measure turgor pressure in the SAM epidermis, opening the possibility of direct evaluation of the contribution of turgor pressure to form emergence [START_REF] Long | Cellular Heterogeneity in Pressure and Growth Emerges from Tissue Topology and Geometry[END_REF] . Turgor pressure is dependent on both cell wall elasticity and water fluxes between cells. Both this study and a theoretical analysis suggest that water fluxes provide a coupling mechanism between cells that can regulate growth and form emergence [START_REF] Long | Cellular Heterogeneity in Pressure and Growth Emerges from Tissue Topology and Geometry[END_REF][START_REF] Cheddadi | Coupling water fluxes with cell wall mechanics in a multicellular model of plant development[END_REF] . Several studies have suggested the existence of developmentally-regulated symplastic sub-domains in the SAM [START_REF] Gisel | Temporal and spatial regulation of symplastic trafficking during development in Arabidopsis thaliana apices[END_REF][START_REF] Rinne | Symplasmic fields in the tunica of the shoot apical meristem coordinate morphogenetic events[END_REF] , where plasmodesmata connectivity could allow for movement of solutes and water between cells. Symplastic connectivity could have a significant impact on turgor pressure regulation and turgor and mechanical forces in general have been suggested to influence plasmodesmata aperture ( [START_REF] Oparka | Direct evidence for pressure-generated closure of plasmodesmata[END_REF][START_REF] Schulz | Plasmodesmal widening accompanies the short-term increase in symplasmic phloem unloading in pea root tips under osmotic stress[END_REF][START_REF] Park | Controlling intercellular flow through mechanosensitive plasmodesmata nanopores[END_REF] ; see also [START_REF] Hernández-Hernández | Interplay between turgor pressure and plasmodesmata during plant development[END_REF] for further discussion). Understanding turgor pressure regulation during form emergence in the SAM will thus likely require considering a combination of inter-dependent apoplastic and symplastic regulations. In relation to this, most analyses have concentrated on the epidermal layer. However, mechanical properties of the internal layers could be important for organogenesis [START_REF] Peaucelle | Pectin-induced changes in cell wall mechanics underlie organ initiation in Arabidopsis[END_REF] and the establishment of the vasculature in the internal tissue might also affect the hydraulic properties of the SAM, in addition to a potential involvement in regulating auxin distribution [START_REF] Bayer | Integration of transport-based models for phyllotaxis and midvein formation[END_REF][START_REF] O'connor | A division in PIN-mediated auxin patterning during organ initiation in grasses[END_REF][START_REF] Hartmann | Toward a 3D model of phyllotaxis based on a biochemically plausible auxin-transport mechanism[END_REF] .

Finally, very recent data on leaf pavement cells suggest that the self-organization properties of pectin polymers in the cell wall could contribute to cellular growth, due to their orientation and to a swelling independent of turgor pressure [START_REF] Haas | Pectin homogalacturonan nanofilament expansion drives morphogenesis in plant epidermal cells[END_REF] . This idea is quite intriguing and will need to be consolidated, both from the experimental and theoretical point of view (see [START_REF] Cosgrove | Plant Cell Growth: Do Pectins Drive Lobe Formation in Arabidopsis Pavement Cells?[END_REF] for an in depth discussion). Nevertheless, it points to the importance of expanding our understanding of the biochemistry of the cell wall (which is still a challenge), in addition to the exploration of the turgor pressure regulation. Future advances will thus require model development allowing further quantitative analyses, the inclusion of water hydraulics, ions and osmoregulation, cell connectivity and a more detailed 3D tissue representation taking into account the cell wall structure in a theoretical framework.

A need for new modelling and biological tools

As illustrated by the work discussed in this perspective, the elaboration of a general theory of plant morphogenesis increasingly relies on the development of intensive computer simulations 97 . They make it possible to predict what forms may emerge from putative laws driving the interaction between plant constituents or cells. To proceed further, new simulation platforms will need to be developed to program and simulate the development of complex forms in a flexible environment, and would be the counterpart for multi-cellular tissues of the successful approaches used for modelling the development of plant architectures with Lsystems at a more macroscopic scale [START_REF] Prusinkiewicz | The Algorithmic Beauty of Plants[END_REF][START_REF] Boudon | L-py: an Lsystem simulation framework for modeling plant architecture development based on a dynamic language[END_REF][100][101] . These platforms should provide ready-to-use highlevel tools to describe forms or infer them from microscope data, to write and run development simulation programs on them, to visualize the simulated forms and their properties at various scales and to assess the simulation results against real data.

Complementary to this and as highlighted in Box 1, it is indeed essential to be able to quantify biological parameters in order to properly build and evaluate the validity of model predictions.

Pushing the frontiers of our understanding of form development is then dependent on the generation of new biological tools, imaging and image analysis methods. We have for example discussed how biosensors have allowed quantifying the spatio-temporal distribution of auxin [START_REF] Galvan-Ampudia | Temporal integration of auxin information for the regulation of patterning[END_REF] .

Numerous biosensors allowing to follow the distribution of a variety of biochemical components in cells and tissues are already available and more are undoubtedly to come. This constitutes a unique toolbox that still needs to be used to its full potential. On the contrary, biological tools allowing direct measurement of mechanical forces at the cellular and tissular scales are largely missing in plants. Fluorescent sensors for mechanical parameters, including turgor pressure, have been developed in animal systems 102 and similar approaches could be considered in plants to extend the available toolset to measure mechanical properties of plant living tissues.

Finally, most of the work considered here used Arabidopsis thaliana for wet experiments.

Generating a general theory of plant shoot forms will require extending the number of species that can be used experimentally and modelled, which is an important challenge for the entire plant developmental biology community. A schematic meristem with a dome geometry is depicted without organs to show how primordium form emergence is regulated and changes mechanical stress distribution (arrows indicate relative intensity and direction of stress anisotropy). Left: at the site of P0 emergence, a region of auxin maximum (red) appears next to a region of auxin minimum (blue). In each region, zooms of a cell and cell wall are shown. The intensity and direction of mechanical stress is the same in the two regions. At the auxin minimum, microtubules align to the principal stress direction, guiding cellulose synthesis by CESA and precluding growth in the main stress direction. At the auxin maximum, auxin uncouples microtubule orientation from stress direction, so that new microfibrils are deposited in all directions. Wall-loosening enzymes, induced by auxin and other factors, reduce the stiffness of the cell wall matrix. Cell growth is then faster and isotropic in the high auxin region (Right). The emergence of the primordium changes mechanical stress distribution, feeding back on primordium development.

Box 1 (650 words)

A short guide to computational models: strengths and limits Like all models, computational models are simplified representations of the reality with which one can reason or operate. They are a convenient tool to think the real, without being overwhelmed by its intrinsic complexity.

Computational models have both a structure and parameters. The structure reflects the main hypotheses used to construct the model: biological elements described as components or compartments of the model, type of interaction laws between these elements, dependence/independence of processes, time and space scales, etc. The parameters make it possible to adapt the structure to the modelled object: kinetic constants of molecular interactions, thresholds, material stiffness and/or viscosity, coupling constants between biophysical mechanisms, transport coefficients, etc.

The most sensible question when evaluating a model is not whether it is right but whether it is useful. This can be for different reasons. First, the design of a model's structure can be instructive as it can pinpoint the lack of knowledge in parts of the modelled system, and suggest new experiments. Second, simulations can show that no parameter of the chosen structure may account for the observations. This also is informative as it leads to reconsider the model's structure and hypotheses (for instance replace a 2D model of organ geometry with a 3D one).

Alternatively, the model can confirm that there exists a plausible range of parameters that shows that the hypothesized model structure does capture the observations well enough. The various models of auxin transport in the SAM (see main text) for instance, successfully confirmed that phyllotaxis patterns can emerge from putative rules controlling PIN1 allocation to membranes in a growing tissue as a function of auxin fluxes and local concentrations.

Another essential consideration to judge the usefulness of a computational model is whether it is a faithful representation of the observed phenomenon. Arguments may rely on its parsimony (i.e. its structure captures the studied phenomenon in a concise but efficient manner), on the fact that its structure reflects that of underlying physical/chemical mechanisms and that the used parameters have been measured or estimated in a realistic range, on whether its emerging mathematical or numerical properties reflect correctly those of the observed phenomenon or on its predictive power, i.e. its ability to predict observations that have not been used to construct the model and that possibly have not yet been observed.

One must however be cautious: reproducing real observations in silico is a necessary, but not sufficient, condition to be a useful model or to say something about the real. It may be that the phenomenon could be reproduced with a model that does not reflect the actual underlying physical or chemical processes. For example, it is still possible that yet another set of rules controlling PIN1 polarization, not yet identified, provides convincing simulations and better reflect what actually happens in a growing SAM. It may also be that the number of parameters is so large, that one does not learn much on the observed system as it is always possible to simulate sufficiently well a phenomenon by using a sufficiently high number of parameters. To avoid this, different techniques are used e.g. define parameters so that they can be measured experimentally or use known observations to find parameter values that can explain the observations (called model inversion and correspond to a form of indirect, model-assisted measurement, e.g. used in [START_REF] Jönsson | An auxin-driven polarized transport model for phyllotaxis[END_REF] ). Finally, the model may also only partially reproduce known facts: as pointed out in the main text for example, none of the models of auxin transport in the SAM currently reproduces the observed accumulation of auxin in the CZ.

Like microscopes are necessary tools to see the invisible, computational models are powerful tools to disentangle the complexity of a system. They contribute to exploring the real, pinpoint new questions, suggest experiments and help reasoning and testing hypotheses but the interpretation of their results must always be critically assessed.

Figure 1 :

 1 Figure 1: Morphology and functional organization of the shoot apical meristem. The SAM of the main inflorescence of Arabidopsis thaliana is shown. (a) Top view (z-projection) image of a SAM with fluorescently-stained cell walls obtained using confocal laser scanning microscopy. The round structures bulging at the periphery in a regular arrangement are the growing flower primordia (P), numbered from youngest to oldest (P0-10). (b) Reconstruction of a longitudinal section going through P0 and P4 (dashed white line in (a)) showing the clonal organization of cells in layers and the typical dome-geometry of the SAM. The stem cells (yellow), primordia (blue) and primordium-meristem boundaries (red) are shown.

Figure 2 :

 2 Figure 2: Principles of dynamical form emergence at the shoot apical meristem. The SAM changes over time with the development of new flowers on its flank while maintaining a central dome where the stem cells are located. The green longitudinal sections on both sides illustrate the changes. In the centre, boxes identify the four principles guiding the dynamic self-organized emergence of this complex shape (see text).

Figure 3 :

 3 Figure 3: Inhibitory field-based model of phyllotactic patterning at the shoot apex. Phyllotaxis can be modelled with organ-centered inhibitory fields (blue discs, radius=d) moving away at the surface of a growing meristem with a dome geometry (green); top views: a-c; lateral views: b-d. Lateral organs are numbered from the youngest one. The specification of P0 at the boundary of the stem-cell domain (yellow, radius R) as a result of growth is illustrated.

Figure 4 :

 4 Figure 4: Theoretical multiscale view of form emergence at the shoot apex. A schematic Arabidopsis SAM bearing two primordia is depicted during the initiation of a new primordium (P0). Zooms of the P0 area and of a cell and its cell walls are shown. Form emerges from several biochemical/physiological (here morphogen gradients and gene expression) and physical (here mechanical stresses; arrows indicate intensity and direction of stress anisotropy) signals influencing growth. These signals feedback on each other and collectively create a dynamical biophysical positional information field instructing cell deformation, controlling changes in cell wall rheology and possibly turgor pressure. A simplified representation of mechanical stress in cell walls is shown using springs.

Figure 5 :

 5 Figure 5: Molecular mechanisms of patterning at the shoot apical meristem. (a-b) The shoot stem cell niche is stably positioned at the shoot tip despite constant apical growth. (a) WUS (purple) and CLV3 (yellow) interact through a regulatory feedback loop. Two cells in the

Figure 6 :

 6 Figure 6: Molecular processes acting in tissue deformation during primordium initiation.

ACKNOWLEDGEMENTS

We thank Gwyneth Ingram, Olivier Hamant, Yvon Jaillais, Yoan Coudert for comments on the manuscript. We thank the colleagues of the RDP laboratory for fruitful discussions on the topic of this review. We thank Carlos S. Galvan-Ampudia for providing the confocal microscope images for the figures. Funding: This work was supported by European union's Horizon 2020 Robotic for Microfarms project (ROMI; grant agreement No 773875) to T.V., F.B and C.G., ANR-18-CE12-0014-02 (ChromAuxi) to T.V. Competing interests: The authors declare no

CORRESPONDING AUTHOR

Correspondence to Teva Vernoux