Association of plasma tryptophan concentration with periaqueductal gray matter functional connectivity in migraine patients

Altered periaqueductal gray matter (PAG) functional connectivity contributes to brain hyperexcitability in migraine. Although tryptophan modulates neurotransmission in PAG projections through its metabolic pathways, the effect of plasma tryptophan on PAG functional connectivity (PAG-FC) in migraine has not been investigated yet. In this study, using a matched case-control design PAG-FC was measured during a resting-state functional magnetic resonance imaging session in migraine without aura patients (n = 27) and healthy controls (n = 27), and its relationship with plasma tryptophan concentration (TRP) was assessed. In addition, correlations of PAG-FC with age at migraine onset, migraine frequency, trait-anxiety and depressive symptoms were tested and the effect of TRP on these correlations was explored. Our results demonstrated that migraineurs had higher TRP compared to controls. In addition, altered PAG-FC in regions responsible for fear-cascade and pain modulation correlated with TRP only in migraineurs. There was no significant correlation in controls. It suggests increased sensitivity to TRP in migraine patients compared to controls. Trait-anxiety and depressive symptoms correlated with PAG-FC in migraine patients, and these correlations were modulated by TRP in regions responsible for emotional aspects of pain processing, but TRP did not interfere with processes that contribute to migraine attack generation or attack frequency.

The mean tryptophan level was significantly higher (F(1,63) = 6.82, p = 0.012) in migraine patients (mean[µg/ ml] ± SD: 9.16 ± 2.35) compared to healthy controls (mean [µg/ml] ± SD: 7.46 ± 2.53) after correction for age, sex and plasma LNAA level. Plasma tryptophan concentration positively correlated with trait anxiety (r = 0.410, p = 0.034) and depressive symptoms (r = 0.392, p = 0.043) in the migraine group, but they did not show correlation in healthy controls (trait anxiety: r = −0.078, p = 0.698; depressive symptoms: r = −0.056, p = 0.781). Migraine attack frequency (rho = −0.059, p = 0.770) and the age at migraine onset (r = 0.127, p = 0.528) did not correlate with plasma tryptophan concentration.  Supplementary  Table S2. Both seed regions demonstrated significant positive functional connectivity with nearby brainstem structures and thalamus, right PAG showed additional positive functional connectivity with cerebellum. No significant negative correlations were detected in our sample. The results of the extended sample (64 subjects) are also shown in Supplementary Table S6.
Intrinsic functional connectivity of PAG comparing migraine patients with healthy controls. In migraine and control group comparison, significantly increased functional resting-state connectivity (Peak-T value = 4.09 at cluster-level p FWE < 0.05, cluster size: 285 voxels) was revealed between left PAG and left postcentral gyrus in migraine patients compared to controls. The region of the postcentral gyrus that showed increased connectivity with the left PAG corresponds to the head and neck area of sensory homunculus. Right PAG showed increased functional connectivity with left orbital part of superior frontal gyrus (Peak-T value = 6.65 at clusterlevel p FWE < 0.05, cluster size: 137 voxels) in migraine patients compared to controls. There was no significantly increased functional resting-state PAG connectivity in controls compared to migraineurs.
Tryptophan effect on intrinsic functional connectivity of PAG: effect of diagnosis. Tryptophan did not show main effect on PAG intrinsic functional connectivity in the whole study population (n = 54). Meanwhile, tryptophan showed diagnosis dependent association with PAG intrinsic functional connectivity. Namely, when migraine group was compared to the control group there was a significant difference between the plasma tryptophan concentration effect on left PAG intrinsic functional connectivity with middle and occipital gyri and fusiform gyrus and left cerebellum (Table 1). Tryptophan concentration also showed significantly different effect on right PAG intrinsic functional connectivity with left fusiform gyrus, left superior and middle occipital gyrus when migraine patients were compared to controls ( Table 1).
Correlation of plasma tryptophan concentration with intrinsic functional connectivity of PAG in migraine patients. Separately analysing the migraine group (Table 2 and Fig. 1), plasma tryptophan concentration positively correlated with the strength of intrinsic functional connectivity between both side of PAG and the superior and superior medial part of frontal gyrus. Significant negative correlations were found between plasma tryptophan concentration and intrinsic functional connectivity of left PAG with left and right fusiform gyrus, right cerebellum, both side of middle part of occipital gyrus and left superior occipital gyrus. Furthermore, significant negative correlation was found in the case of right PAG with left fusiform gyrus. Separately analysing the control group, there were no significant associations between the plasma tryptophan concentration and functional intrinsic connectivity of PAG.
Correlations of PAG intrinsic functional connectivity with migraine indicators, trait anxiety and depressive symptoms. The frequency of migraine attacks and the age of migraine onset significantly correlated with connectivity of PAG, but tryptophan concentration did not affect these associations (Supplementary Table S3).
Trait-anxiety level showed significant positive correlation with connectivity of left PAG and left middle frontal gyrus (Peak-T value = 5.33 at cluster-level p FWE < 0.05). In case of right PAG, trait-anxiety also positively correlated with connectivity of right PAG and left middle (Peak-T value = 5.73 at cluster-level p FWE < 0.05) and superior medial frontal gyrus (Peak-T value = 5.09 at cluster-level p FWE < 0.05). After correction for plasma tryptophan  Table S3). Depressive symptoms significantly positively correlated with connectivity of PAG and middle frontal gyrus (Peak-T value = 6.65 at cluster-level p FWE < 0.05). In addition, a negative correlation with connectivity of right PAG and right fusiform gyrus (Peak-T value = −4.89 at cluster-level p FWE < 0.05) and parahippocampal gyrus (Peak-T value = −4.14 at cluster-level p FWE < 0.05) was found. After correction for plasma tryptophan concentration (also corrected for LNAA) there was no significant correlation between depressive symptoms and connectivity of PAG with middle frontal gyrus, fusiform gyrus or parahippocampal gyrus. However, depressive symptoms negatively correlated with left PAG and left precuneus (Peak-T value = −4.44 at cluster-level p FWE < 0.05), right middle cingulum (Peak-T value = −4.08 at cluster-level p FWE < 0.05) connectivity after correction for plasma tryptophan concentration (Supplementary Table S3).
To test the potential confounding effect of correlation between plasma tryptophan concentration and trait anxiety/depressive symptoms in migraineurs we re-tested the plasma tryptophan concentration correlation with PAG connectivity after correction for trait-anxiety level and depressive symptoms, see Supplementary Table S4.
In healthy controls, trait-anxiety level and depressive symptoms showed no correlation with PAG-FC.

Discussion
Our study demonstrated an elevated plasma tryptophan concentration in episodic migraine patients without aura that modulated PAG intrinsic functional connectivity only in migraineurs but not in healthy controls. In addition, plasma tryptophan concentration also modified the relationship between PAG intrinsic functional connectivity and trait-anxiety and depressive symptoms in migraine patients.

Increased plasma tryptophan concentration in migraine.
In this study, we found elevated plasma tryptophan concentration during two independent blood sampling in interictal episodic migraine patients without aura compared to healthy controls. This finding is in concordance with a previous study of Alam et al. 46 , who demonstrated increased tryptophan concentration in episodic migraine, only in patients without aura.
Another study showed trend level increase in plasma tryptophan concentration in migraine with or without aura patients 47 . Elevated serum tryptophan concentration and kynurenine pathway metabolites' abnormalities are also present in chronic migraine 36 . Nonetheless, opposite results, namely lower serum tryptophan concentration and the role of serotonin metabolism, have also been reported in migraine without aura 44 . Accumulating data suggest that the migraine attack itself can contribute to the elevated plasma tryptophan concentration in several ways 48,49 . The stress effect of the approaching or repeated attacks can increase cortisol secretion which will in turn increase proteolysis and plasma tryptophan concentration 35,49 . In general, decreased protein and increased carbohydrate intake, or fasting are able to increase the free plasma tryptophan concentration and promote the tryptophan uptake to the brain 35,48 . These processes can enhance coping with stress by increasing serotonin synthesis. However, prolonged stress eventually will shift the tryptophan metabolism towards the "kynurenine shunt" that might contribute to brain hypersensitivity and maladaptive stress response in migraine patients 35,38,50 .
In our study, a significant positive correlation was found between plasma tryptophan concentration and trait-anxiety and depressive symptoms, but only in the migraine group. Thus, specifically migraineurs showed increased sensitivity to tryptophan plasma concentrations, as can be seen in patients with depression 51 . In line with the acute tryptophan depletion literature 34,51 , in the control subjects we have not found any correlation between plasma tryptophan concentration and trait-anxiety and depressive symptoms. Regarding the positive direction of association between plasma tryptophan concentration and trait-anxiety and depressive symptoms in migraineurs, our finding may seem contradictory to the widely accepted theory, that acute tryptophan depletion induced decrease in serotonin concentration contributes to low mood and probably to anxiety 34 . However, our participants' plasma tryptophan concentration was in the physiological range, during the experiment they followed their regular diet without any manipulations (depletion or supplementation). In addition, our migraine patients had no psychiatric disorders, and showed similar trait-anxiety and depressive symptom scores as the control participants. Thus, in migraineurs we could not exclude that plasma tryptophan elevation might be a part of a self-remediation process, elicited either by stress or by changes in diet, as discussed above.
Interestingly, we have not found significant correlation between plasma tryptophan concentration and age at migraine onset or migraine frequency despite that migraine patients thought to be sensitive to tryptophan intake 32 and depletion as well 28 . However, tryptophan supplementation as a promising migraine treatment failed in previous studies 52,53 which may support our observation that tryptophan concentration is associated with the emotional symptoms of migraine patients but does not interfere with processes that contribute to attack generation or attack frequency. Indeed, L-tryptophan administration alone cannot exert analgesic property 54 .

Tryptophan modulates PAG intrinsic connectivity in migraine.
Our study was the first to investigate tryptophan modulatory effect on PAG functional connectivity in migraine. Plasma tryptophan concentration showed a diagnosis dependent effect. In healthy control group, there was no correlation between plasma tryptophan concentration and PAG intrinsic connectivity. Meanwhile, in migraine patients increased plasma tryptophan concentration was associated with a reduced functional connectivity between PAG and fusiform gyrus, middle occipital gyrus and cerebellum; and increased connectivity of PAG with superior and superior medial part of frontal gyrus (more precisely with dorsolateral-dlPFC, and dorsomedial prefrontal cortex-dmPFC) in migraine. This PAG functional connectivity pattern that was associated with tryptophan concentration shows opposite direction of connectivity pattern compared to previous studies that investigated PAG connectivity during pain-task 18 , and during resting state fMRI studies in migraineurs with increased anxiety and depressive symptoms 55 or in a mixed group of migraineurs with and without aura 17 . These studies observed an increased PAG connectivity to nociceptive and somatosensory processing pathways and decreased PAG connectivity to top-down pain and emotion modulating areas that might be counterbalanced by the elevated plasma tryptophan concentration in our study. In agreement with this hypothesis, our episodic migraine subjects without aura and with similar trait-anxiety and depressive symptom scores as controls only showed significantly increased PAG connectivity in the region of the postcentral gyrus corresponding to the head and neck area of sensory homunculus in comparison with healthy controls.
Most of the regions that showed altered PAG-FC among migraineurs after taking into account plasma tryptophan concentration are part of the defence cascade 56 and play a role in survival salience 12 . One such region is the fusiform gyrus that is functionally connected to PAG and has a main role in evaluating the environment (movements, vocalizations, and faces) to identify potentially dangerous signals 57 . In case of threatening environment PAG activation occurs, while the fusiform gyrus provides top-down inhibitory control on defensive responses to fear when the situation is safe 58 . Previous studies demonstrated both positive and negative connectivity between PAG and fusiform gyrus depending of which PAG subregion was observed 17,59 . In migraine, a recent study reported that during painful stimuli fusiform gyrus showed increased PAG connectivity compared to controls 18  www.nature.com/scientificreports/ that in rest the PAG-fusiform gyrus intrinsic functional connectivity decreases with higher plasma tryptophan concentration. These results might indicate that in absence of any pain there is a decrease in feeling of threat due to less active fear cascade in migraine patients with elevated plasma tryptophan concentration.
In line with this hypothesis, our results showed an increasing dlPFC and dmPFC connectivity with PAG in parallel with higher plasma tryptophan concentration. The dlPFC and dmPFC have integrative roles in selecting and maintaining appropriate emotional behaviour 60 and also controlling pain perception 61 . For example, contextual fear discrimination, the process which uses previous experiences to evaluate the perceived threats of the current situation, is highly dependent on the connectivity between the dmPFC and PAG 62 . Thus, the strength of this connection is crucial to determine the appropriate defensive or exploratory behaviour. Previous studies separately demonstrated positive PAG connectivity with dmPFC and dlPFC in healthy controls 59 and migraine patients 17 . But they suggested weaker PAG connectivity with dmPFC and dlPFC in migraine patients compared to controls 17,18,55 that may contribute to impaired top-down control of pain and fear responses. Based on our results, increasing plasma tryptophan concentration may strengthen PAG connectivity with dmPFC/dlPFC that helps in optimising cortical control on fear cascade.
Another important brain structure in the defence cascade is the cerebellum that has rich anatomical connections to the PAG 63 , serves as an anatomical substrate to the fear-evoked freezing behaviour 56,64 , and has been increasingly implicated in migraine pathophysiology 65,66 . Beside its important role in motor function, cerebellum is involved in encoding of aversive stimuli such as pain and unpleasant images 67 . Previous studies reported a positive functional resting-state correlation between PAG and cerebellum in healthy people 59,68 . Furthermore, migraineurs compared to healthy controls showed decreased functional correlation between PAG and cerebellum during heat pain stimuli 18,67 . Nevertheless in migraineurs, PAG-cerebellum IV-VI connectivity negatively meanwhile PAG-cerebellum crus 1 and IX positively correlated with migraine attack frequency during painful stimulus showing the complexity of the PAG-cerebellum relationship in pain processing 18 . Indeed, based on previous studies, between PAG and cerebellum, direct and indirect connections exist which functions are dependent on the subregions observed 63 . We did not find correlation between migraine indicators and PAG-cerebellum connectivity during resting-state without pain. In our study, increasing plasma tryptophan concentration was associated with decreasing PAG-cerebellum IV-VI intrinsic functional connectivity in migraineurs. That might suggest a decreasing fear cascade activation with increasing plasma tryptophan concentration, but direct comparison with previous findings is difficult because this field is relatively unexplored.
The middle occipital gyrus is part of the multisensory processing brain regions where spatial localisation of visual, tactile and auditory stimuli occurs 69 . It has extensive negative intrinsic functional connectivity with PAG in healthy people based on previous studies 59, 68 and showed increased activity during mind wandering away from pain 70 . However, it also showed greater activity during the activation of the defence cascade by viewing threatening images compared to less arousing stimuli 71 . Solstrand et al. 18 reported decreased pain-induced PAG-middle occipital gyrus functional connectivity in migraineurs compared to controls and negative correlation between migraine attack frequency and PAG-middle occipital gyrus intrinsic functional connectivity. Contrary to this, we did not find correlation between migraine indicators and PAG-middle occipital gyrus functional connectivity. Thus, although the exact role of the PAG-middle occipital gyrus intrinsic functional connectivity in the defence cascade is not known it can be hypothesised that the decreased intrinsic functional connectivity between these regions, associated with increased plasma tryptophan concentration, may again contribute to decreased pain related fear response.

Migraine indicators not, but trait-anxiety and depressive symptoms are associated with tryptophan correlated PAG connectivity in migraine.
Migraine attack frequency and age at onset although showed positive association with PAG intrinsic functional connectivity in regions previously implicated in migraine (triangular part of inferior frontal gyrus and middle frontal gyrus) 17,18,55 these connections remained unchanged after correcting for the effect of plasma tryptophan concentration. These results correspond well to previous observations that dietary tryptophan manipulation to increase brain serotonin synthesis was not associated with decreased migraine attack frequency in most of the patients 52,53 .
In contrary to this, the positive correlation between trait-anxiety and PAG connectivity with left dlPFC and dmPFC in migraine patients disappeared after correction for plasma tryptophan (and LNAA) concentration. Impaired defensive behaviour is a main psychopathological root of anxiety disorders and, as we discussed above, PAG-dmPFC connectivity plays a pivotal role in contextual fear discrimination 56,62 . In a recent animal study, Yin et al. demonstrated that the activation of excitatory descending pathway from dmPFC to vlPAG has analgesic and antianxiety effects 72 . Our results might suggest that tryptophan and its metabolites actively modulate the functional coupling of PAG and the dmPFC/dlPFC. Thus, increased strength of PAG-dmPFC/dlPFC connectivity with elevated plasma tryptophan concentration might contribute to analgesic and anxiolytic effect in migraineurs. Accordingly, our migraine patients had episodic migraine with relatively low attack frequency and the mean trait-anxiety symptom scores were in comparable range of controls.
Similarly to trait-anxiety, depressive symptoms showed positive correlation with PAG-dlPFC connectivity in migraine patients that was diminished after correcting for plasma tryptophan concentration. PAG is an active participant in cognitive processes, through its afferent and efferent connections with prefrontal cortex it affects negative emotions and pain related autonomic and behavioural responses 73 . Although PAG-dlPFC connectivity changes has not been investigated in depression but hypoactivity of dlPFC was reported in depressed patients and an increase in its activity after treatment 74 . Our results suggest, that elevated tryptophan concentration by enhancing PAG-dlPFC connectivity may be beneficial in migraineurs by decreasing pain induced negative affect and improving emotion processing 75,76 . Again, we have to emphasize that our migraine subjects had no psychiatric disorders and their depressive symptoms scores were not significantly different from controls. Previous www.nature.com/scientificreports/ studies demonstrated no mood lowering effect of tryptophan depletion in never-depressed healthy people, but predisposing factors such as high familial risk for depression or remitted depression make people susceptible to depressive symptoms due to tryptophan concentration changes 51 . Our study is in concordance with these observations, in control subjects, tryptophan plasma concentration neither showed significant association with depressive and trait-anxiety symptoms scores, nor influenced PAG connectivity pattern. In case of depressive symptoms, we also demonstrated negative correlation with PAG connectivity with the right fusiform gyrus and right parahippocampal gyrus that diminished after correction for plasma tryptophan concentration. In a previous study, right fusiform gyrus showed increased intrinsic brain activity in depressed migraine patients compared to non-depressed migraineurs 77 , which is in line with the fear cascade mechanisms we discussed above. Our study suggest that tryptophan might interfere with fear processing through influencing PAG-fusiform gyrus connectivity that can decrease the activity of fear cascade 58 . Regarding parahippocampal gyrus, a positive functional connectivity between PAG-parahippocampal gyrus was found both in migraineurs and in controls 17 , but the exact role of PAG-parahippocampal gyrus connectivity in depressive symptoms is not known yet.

Limitations.
Our study has some important limitations. More women participated in the study than men, but it is in accordance with the disease prevalence sex distribution and all reported results were controlled for age and sex. Plasma tryptophan concentration may have a cyclic variation throughout the menstrual cycle 78 . In our study, there was no significant difference (χ 2 = 0.071 p = 0.790) between the control (11 women were in the follicular phase, and 8 were in the luteal phase) and migraine group (8 women were in the follicular phase, and 7 were in the luteal phase) regarding the menstruation cycle but more migraine patients used oral contraceptives than controls (2 controls, 6 migraineurs) that could influence the plasma tryptophan level. To ensure that our results are not driven by sex imbalance, we carried out the analysis in sex matched subgroups (27-27 migraineurs vs. controls with 21 female and 6 male participants). However, the extended sex imbalanced sample showed very similar results suggesting that our results are stable, representing differences between migraine patients and controls. Another limitation of the study is the determination of the seed region, that is an important step in every seed-to-voxel connectivity analysis. In the literature, both right and left side coordinates are reported to localise PAG 12 and in our analysis there is a difference between the connectivity pattern of the two sides, so we decided to separately analyse the right and left PAG seeds. However, results from the analysis with merged PAG seed are reported in the Supplementary information that also supported our major findings and conclusions (Supplementary Tables S8-S10). Furthermore, we measured peripheral potential biomarker, thus we cannot detect the exact biochemical changes in brain areas. However, the repeated measure of plasma tryptophan concentration provided a better estimation of the average tryptophan concentration in the body, and the correction for other LNAA may improve the detection of its effect on brain mechanisms. In addition, combination of resting-state fMRI with biological and psychological data, as in our study, could be a way forward to investigate a complex, multifactorial disorder and identify migraine subgroups with different underlying pathological mechanisms.

Conclusions
Our study demonstrated a correlation between plasma tryptophan concentration and PAG-FC in migraine for the first time. This correlation was associated with the emotional symptoms of migraine patients but did not interfere with processes that contribute to attack generation or attack frequency. Plasma tryptophan concentration through a more optimal PAG connectivity network might contribute to a better top-down cortical control on contextual fear discrimination and a dampened defence cascade response. These mechanisms might enhance coping strategies in migraine patients. Whether these patients consume tryptophan rich diet as a self-medication or this increased plasma tryptophan concentration is the result of increased stress, as we mentioned above, should be investigated in future studies.

Methods
Participants. Eighty-two subjects were included in the study, 34 episodic migraine patients without aura (mean age (SD) = 26.53 years (4.70); 28 women) and 48 healthy controls (mean age (SD) = 25.69 years (4.05); 29 women). The participants were recruited via university advertisements, newspaper articles and from Headache Clinics. All participants' mental health was checked using the Mini-International Neuropsychiatric Interview 79 by senior researchers. Exclusion criteria was having any past or current serious medical, neurologic (except migraine without aura) or psychiatric disorders. Use of any daily medication, except contraceptives was exclusion criteria for both patients and controls. Blood samplings and fMRI scans were carried out if the patients and controls were medication-free for at least 48 h before the examination. In case of migraine patients, blood samplings and fMRI scans were carried out if they were headache-free for at least 48 h before the examination. Only those patients were included into the analyses who were also headache free for at least 24 h after the examination. Both patients and controls refrained from caffeine 4 h before taking blood sample. Participants were all right handed according to the Edinburgh Handedness Inventory 80 . On the fMRI examination day, participants completed the State-Trait Anxiety Inventory (STAI) 81 and the 20-item Zung Self-Rating Depression Scale 82 about depressive symptoms.
Episodic migraine without aura was diagnosed by expert neurologists using International Classification of Headache Disorders-III criteria (Headache Classification Committee of the IHS 2013). Patients were asked about the acute migraine medication usually used and clinical indicators of migraine, age of disease onset and frequency of attacks per month ( Blood samples. Two separate blood samples were collected at least 28 days apart to evaluate the average tryptophan intake. 74 participants' (31 migraine patients, 43 controls) first blood samples and 68 participants' (27 migraine patients, 41 controls) second blood samples were successfully acquired. The blood samples were collected into 3 mL K3EDTA tubes and immediately centrifuged. Plasma samples were frozen and kept at − 80 °C until the assay. LC-MS/MS method already published by Virág et al. 83 was used for the quantitative determination of total tryptophan and other large amino acids (valine, leucine, isoleucine, phenylalanine, tyrosine) concentration.
Imaging data acquisition. After the second blood sample collection, participants underwent a 6-min resting-state fMRI session using a 3 T MRI scanner (Achieva 3 T, Philips Medical System). They were instructed to close their eyes, but remain awake. The imaging dataset acquisition parameters of T2*-weighted echo-planar (EPI) pulse-sequence were: repetition time (TR) = 2.500 ms, echo time (TE) = 30 ms, field of view (FOV) = 240 × 240 mm 2 ; with 3 × 3 × 3 mm 3 resolution. High-resolution structural data were acquired before the resting-state acquisition using T1-weighted 3D turbo field echo (TFE) sequence and 1 × 1 × 1 mm 3 resolution. Data analysis. Participants characteristics, self-reported data and amino acid levels were analysed with SPSS (IBM Corp. SPSS Statistics for Windows, Version 25.0). Pearson chi-square test was applied to investigate sex difference between migraine and control groups. Mann-Whitney tests were used to determine any differences between migraine and control groups regarding tryptophan concentration or age. The sum of LNAA affecting tryptophan blood-brain-barrier crossing was calculated (namely tyrosine, phenylalanine, leucine, isoleucine and valine) 27 and also estimated for any difference between migraineurs and controls. Spearman correlation was used to determine the relationship between age and tryptophan concentration. Wilcoxon signed-rank test was applied to determine any difference between the first and second blood samples. Since, there was no difference in plasma tryptophan concentration between the first and second blood samples, the mean tryptophan concentration was used to characterize the mean tryptophan intake that showed normal distribution. Univariate ANOVA was applied to determine the difference between migraine and control group regarding the mean tryptophan Table 3. Clinical data of migraine patients. Triptan: sumatriptan (50 mg or 100 mg), in one case zolmitriptan.

Subject
Age of migraine onset (years) Migraine frequency (per month) Triptan Acute migraine medication www.nature.com/scientificreports/ concentration corrected for age, sex and LNAA. Independent t-test was applied to determine whether migraine patients and controls differed in trait-anxiety and depressive symptoms scores. Pearson correlation was calculated to determine the association between tryptophan concentration and anxiety or depressive symptoms. Significance threshold was set at p < 0.05. Two healthy controls did not complete the psychological questionnaires.
Resting-state fMRI data analysis. State of the art preprocessing steps were carried out on the data according to an optimized pipeline which is shown in detail in Supplementary information. The final sample for the functional connectivity analysis consisted of 64 subjects (37 controls and 27 migraineurs) with usable biological and resting-state fMRI data. However, to correct for sex imbalance we report the results of a sex-matched case control analysis of 27 migraine and 27 control subjects (21 females and 6 males in each group) in the main manuscript. Results based on the full 64 subject were provided in the Supplementary information.
Seed regions were defined after Mainero et al. 17 (peak coordinates in MNI space: Left PAG = −2; −28; −6; Right PAG = 4; −28; −6; radius: 3 mm). The fslmaths command of FSL was used to create spherical masks within a 6 mm radius of these two regions for seed selection in a seed-based correlation analysis. For time-series data extraction, followed by voxel-wise connectivity analysis computations NiBabel (v2.3.1) 84 and NumPy (v1.15.4) 85 modules of the Python programming language were utilized. The seed-based connectivity map of each subject, based on voxel-wise Pearson correlation with averaged seed region data, was transformed to Z-scores using Fisher transformation.
These Z maps of each individual were used in within-and between-group comparisons in Statistical Parametric Mapping (SPM12) software package (Wellcome Department of Imaging Neuroscience, Institute of Neurology, London, UK; http:// www. fil. ion. ucl. ac. uk/ spm12/) implemented in Matlab 2016a (Math Works, Natick, MA). First, PAG intrinsic functional connectivity was determined in whole group analysis using one sample t-test. Next, two sample t-test was conducted to compare PAG connectivity between migraine and control groups. Correlation between plasma tryptophan and PAG connectivity in the whole population was determined by including the mean tryptophan concentration as a regressor. Tryptophan correlation with PAG connectivity based on diagnosis was performed by using F-contrast.
To follow up the F-contrast results, the mean plasma tryptophan concentration effect on PAG intrinsic functional connectivity was investigated in the migraine and control group separately using one sample t-tests. In addition, trait-anxiety level (STAI-T) and depressive symptoms (ZUNG) scores and migraine indicators (attack frequency and age of onset) in the migraine group were investigated whether PAG connectivity and these variables show correlation using them as regressors in t-tests to replicate previous findings. Next, tryptophan concentration was used as covariate in order to determine whether it alters the correlation between PAG connectivity and migraine indicators, and trait-anxiety level or depressive symptoms.
All models contained motion correction parameters, age and sex as covariates of no interest. All tryptophan related analyses were corrected for LNAA levels by including plasma LNAA concentration as a regressor of no interest.
An initial threshold of p < 0.001 uncorrected for multiple comparison and at least twenty contiguous voxels 86 was used in the analyses. All reported results survived family-wise error correction at a cluster-level threshold of p FWE < 0.05.

Data visualization.
For visualization of statistical maps, significant clusters were downloaded from SPM12 program and used as overlay on the MNI 152 template brain in MRIcroGL 87 .
Ethics statements. The study was approved by the Scientific and Research Ethics Committee of the Medical Research Council (Hungary). Each participant gave a written informed consent before entering the study in accordance with the Declaration of Helsinki.

Data availability
The datasets generated during the analysis are available in the Open Science Framework repository (https:// osf. io/ etj7h/).