dataesr/scientific-paragraphs-categorization huggingface dataset:
(  1 ). We have introduced the parameter λ = 1 1+∆ 2 : in practical applications, the error ∆ may not be known, and the parameter 0 ≤ λ < 1 allows to weigh data sources differently. For λ = 0 (i. e. large noise), the standard inverse Ising problem is recovered: optimal parameters are such that the model exactly reproduces magnetizations and correlations of the sample. For λ > 0, the second dataset containing quantitative data is taken into account: whenever energies computed from the Hamiltonian H do not match the measured ones, the model statistics deviates from the sample statistics. Both log-likelihood terms in (8) are concave, and thus their sum: Eq. (  9 ) has a unique solution. Noiseless measurements. The case of noiseless energy measurements in Eq. (  5 ) (i. e. λ → 1) has to be treated separately.
First, energies have to be perfectly fitted by the model, by solving the following linear problem: X H = E , (10) where we have introduced a N(N + 1)/2 dimensional vectorial representation H = (h 1 ,. , h N , J 12 ,. , J N,N-1 ) T of the model parameters, and E = (E 1 ,. , E P ) T contains the exactly measured energies. The matrix X =    σ 1 1 • • • σ 1 N (σ 1 1 σ 1 2 ) • • • (σ 1 N-1 σ 1 N ). σ P 1 • • • σ P N (σ P 1 σ P 2 ) • • • (σ P N-1 σ P N )    (11) specifies which parameters contribute to the energies of configurations in the second dataset. If K = N(N +1)/2-rank(X) > 0, the parameters cannot be uniquely determined from the measurements: The sample D eq can be used to remove the resulting degeneracy. To do so, we parametrize the set of solutions of Eq. (  10 ) as follows: H = H nh + K ∑ k=1 α k O k (12) where H nh is any particular solution of the non homogeneous Eq.
Artificial data We first evaluate our method on artificial data (Materials and Methods). Random couplings J 0 and fields h 0 are chosen for a system of N = 32 spins. Dataset D eq is created by Markov chain Monte Carlo (MCMC) sampling, resulting in M = 100 equilibrium configurations. To mimic a protein 'mutagenesis' experiment, one of these configurations is chosen at random as the reference sequence, and the energies of all N configurations differing by a single spin flip from the reference (thereafter referred to as single mutants) are calculated, resulting in dataset D E (after adding noise of standard deviation ∆ 0 ). Datasets D E and D eq will subsequently called "local" and "global" data respectively. Equations (  9 ) are solved using steepest ascent, updating parameters J and h in direction of the gradient of the joint loglikelihood (8).
e. to correct the measurement noise using the equilibrium sample D eq. For every λ , J and h are inferred and used to compute predicted energies of the N configurations in D E. The linear correlation between such predicted energies (measured with the inferred Hamiltonian) and the true energies (measured with the true Hamiltonian) is plotted as a function of λ in Fig. 2. In the very low noise regime, ∆ 0 ≃ 0, the top curve in Figure  2  reaches its peak at λ ≃ 1, which is expected as local data is then sufficient to accurately "predict" energies from single mutants. On the contrary, in the high noise regime, the maximum is located close to λ = 0, pointing to the fact that local data is of little use in this case. Between those two extremes, an optimal integration strength can be found, yielding a better prediction of energies in D E as for any of the datasets taken individually.
It is interesting to notice that even for highly noisy data, integrating the two sources of information with the right weight λ results in an improved modeling. The insert of Fig. 2  shows the integration strength λ at which the best correlation is reached, against the corresponding theoretical value λ 0 = 1/(1 + ∆ 2 0 ) for different realizations. On average, optimal integration is reached close to the theoretical case of equation (  8 ). This result highlights the possibility of using this integrative approach to correct measurement errors in the energies of single mutants. If a dataset such as D eq provides global information about the energy landscape, and the measurement noise ∆ 0 can be estimated, an appropriate integration can then be used to infer more accurately the energies of the single mutants.
where M K is the number of sampled configurations in D H and D 0. The inferred model undoubtedly benefits from the integration, as a minimal divergence between the generating and the inferred probability distributions is found for an intermediate value of λ , outperforming both datasets taken individually (Figure  3 ). It has to be noted that even in the noiseless case ∆ 0 = 0, the minimum in Σ(P 0 , P) obtained at λ = 1 depends crucially on the availability of the equilibrium sample D eq. The local data D E are not sufficient to fix uniquely all model parameters, and the degeneracy in parametrization is resolved using D eq as explained at the end of Sec. As a comparison, the same analysis is done using an independent modeling that uses only fields h, and no couplings. The inset of Figure  3  clearly shows that the pairwise modeling outperforms the independent one.
Biological data To demonstrate the practical utility of our integrative framework, we apply it to the challenging problem of predicting the effect of amino-acid mutations in proteins. To do so, we use three types of data: (i) Multiple-sequence alignments (MSA) of homologous proteins containing large collections of sequences with shared evolutionary ancestry and conserved structure and function; they are obtained using HMMer 29 using profile models from the Pfam database  30. Due to their considerable sequence divergence (typical Hamming distance ∼ 0. 8N), they provide a global sampling of the underlying fitness landscape. (ii) Computational predictions of the impact of all single amino-acid mutations on a protein's structural stability  31  are used to locally characterize the fitness landscape around a given protein.
The noise term ξ a represents the limited accuracy of this predictor, and the uncertainty in using structural stability as a proxy of protein fitness. (iii) Mutagenesis experiments have Independent Pairwise Figure 3. Symmetric Kullback-Leibler divergence Σ between true and integrated pairwise models versus strength of integration λ , estimated from M K = 3 • 10 6 MCMC samples. Different curves correspond to different noise levels added to single mutants energies used for integration, so that datasets D E are the same as in Fig. 2. Insert -Comparison with an independent model using only fields h, with the same methodology. been used before to simultaneously quantify the fitness effects of thousands of mutants  22, 23. While datasets (i) and (ii) play the role of D eq and D E in inference, dataset (iii) is used to assess the quality of our predictions (ideally one would use the most informative datasets (i) and (iii) to have maximally accurate predictions, but no complementary dataset to test predictions would be available in that case).
Conclusion In this paper, we have introduced an integrative Bayesian framework for the inverse Ising problem. In difference to the standard setting, which uses only a global sample of independent equilibrium configurations to reconstruct the Hamiltonian of an Ising model, we also consider a local quantification of the energy function around a reference configuration. Using simulated data, we show that the integrated approach outperforms inference based on each single dataset alone. The gain over the standard setting of the inverse Ising problem is particularly large when the equilibrium sample is too small to allow for accurate inference. This undersampled situation is particularly important in the context of biological data. The prediction of mutational effects in proteins is of enormous importance in various bio-medical applications, as it could help understanding complex and multifactorial genetic diseases, the onset and the proliferation of cancer, or the evolution of antibiotic drug resistance.
However, the sequence samples provided by genomic databases, like the multiple-sequence alignments of homologous proteins considered here, are typically of limited size, including even in the most favorable situations rarely more than 10 3 -10 5 alignable sequences. Fortunately, such sequence data are increasingly complemented by quantitative mutagenesis experiments, which use experimental high-throughput approaches to quantify the effect of thousands of mutants. While it might be tempting to use these data directly to measure mutational landscapes from experiments, it has to be noted that current experimental techniques miss at least 2-3 orders of magnitude in the number of measurable mutants to actually reconstruct the mutational landscape. In such situations, where no single dataset is sufficient for accurate inference, integrative methods like the one proposed here will be of major benefit.
Acknowledgements MW acknowledges funding by the  ANR  project  COEVSTAT  ( ANR-13-BS04-0012-01 ). This work undertaken partially in the framework of CALSIMLAB, supported by the grant  ANR-11-LABX-0037-01  as part of the  "Investissements d'Avenir" program  ( ANR-11-IDEX-0004-02 ).
Artificial data For a system of N = 32 binary spins, couplings J 0 and fields h 0 are chosen from a Gaussian distribution with zero mean, and standard deviation ∼ 0. 8/ √ N for J and 0. 2 for h (analogous results are obtained for other parameter choices, as long as these correspond to a paramagnetic phase). Dataset D eq is created by Markov chain Monte Carlo (MCMC) simulation, resulting in M = 100 equilibrium configurations. A large number (∼ 10 5 ) of MCMC steps are done between each of those configurations to ensure that they are independent. One of these configurations is chosen at random as the reference sequence ("wild-type"), and the energies of all N configurations differing by a single spin flip from the reference are computed ("single mutants"). Gaussian noise of variance ∆ 2 0 can be added to these energies, resulting in dataset D E.
Incidentally, this is also one of the most polymorphic G-quadruplex forming sequences  (21). Here, we investigated the intramolecular folding of telomeric sequences with four tracts of guanines, in the presence of K + cations. All sequences contain the central d((GGGTTA) 3 GGG) core, but the final topology depends on the flanking bases. In 100 mM K + (NMR conditions), a hybrid-1 type G-quadruplex structure was observed for the sequence d(TT(GGGTTA) 3 GGGA) (abbreviated 24TTG, PDB ID: 2GKU  (22) , Figure  1A , see Table  1  for abbreviations) and for d(TA(GGGTTA) 3 GGG) (23TAG, PDB ID: 2JSM  (23) ), the latter being slightly more polymorphic. The sequence d(TTA(GGGTTA) 3 GGGTT) (26TTA, PDB ID: 2JPZ  (24) , Figure  1B ) folds into a hybrid-2 type Gquadruplex. The hybrid topologies differ by the order of the loops: in the hybrid-1 the loops are respectively 5 -propeller-lateral-lateral-3 type.
For the hybrid-2 the loops are 5 -lateral-lateral-propeller-3. The sequence d((GGGTTA) 3 GGGT)) (22GT, PDB ID: 2KF8  (25) , Figure  1C ) folds predominantly (∼70%) into another topology, called the hybrid-3. Here, only two quartets are formed. The structure is further stabilized by a triplet of guanines, and the circular dichroism spectrum therefore resembles that of the other hybrid structures  (26). 22AG (d(A(GGGTTA) 3 GGG)), a sequence very frequently used for drug binding assays, folds in an antiparallel structure in sodium (Figure  1D )  (27)  but is polymorphic in KCl  (28) (29) (30). The structure of 21G (d((GGGTTA) 3 GGG)) has not been solved by NMR, most likely because it is also polymorphic. It is the shortest possible human telomeric sequence containing four tracks of guanines, and it is frequently used in FRET (F örster Resonance Energy Transfer) melting assays with the FAM and TAMRA dyes at the 5 and 3 ends  (31).
21G, with and without the fluorescent tags, have also been included in the present study, as well as the FRET homologue of 26TTA. The modified human telomeric DNA 22CTA (d(A(GGGCTA) 3 GGG), PDB ID: 2KM3 (32), Figure  1E ) was also included. This G-quadruplex structure contains two G-quartets plus a G:C:G:C platform. Telomeric sequences form intramolecular parallel folds only in the crystal state or in molecular crowing conditions, but this species is not significantly populated in dilute aqueous solution  (33, 34). To include a parallel quadruplex in our panel, we also studied the sequence Pu24 (d(TGAG 3 TG 4 AG 3 TG 4 A 2 G 2 ), PDB ID: 2A5P  (35) , Figure  1F ), a variant of the c-myc oncogene promoter nuclease hypersensitivity element. The structural polymorphism of G-quadruplexes complicates their biophysical studies.
K D determination and kinetic model evaluation The concentrations of the species detected by mass spectrometry were obtained after integration of the peaks and subtraction of the nonspecific adducts. We also verified that all complexes have the same response factors. The detailed procedure is reported in the supplementary materials and methods (Supplementary Figures  S1-S10 ). Both K D determination and kinetic model evaluation were carried out using the DynaFit software (4. 05. 103 BioKin Ltd Watertown, MA, USA)  (60). The concentrations of specific complexes of each stoichiometry were fitted as function of the potassium concentration with the chemical Equations (1b) and (2b), correlated to the chemical equilibria (1a) and (2a), respectively. DNA + K + DNA • K (1a) K D1 = [DNA][K + ]/[DNA • K] (1b) DNA • K + K + DNA • 2K (2a) K D2 = [DNA • K][K + ]/[DNA • 2K] (2b) The DynaFit software works by iteration on the two K D values in order to fit all the concentrations of the three sto-ichiometries as a function of total KCl added.
The K D-Glob is defined by the product of K D1 by K D2. K D-glob = K D1 × K D2 = [DNA][K + ] 2 /[DNA • 2K] (3) For the kinetics experiments, we fitted altogether the kinetic data obtained for the 0-K + , specific 1-K + and 2-K + ensembles at four different KCl concentrations (100, 200, 500 and 1000 M), i. e. a total of 12 curves. The chemical reaction models are an input for Dynafit, and the software derives the kinetic differential equations linked with each chemical model, and fits the data. Over 20 different reaction models were tested and ranked using the Akaike information criterion (AIC)  (61). The AIC is applicable when the experiments depend on a multitude of parameters, and one is searching for the most useful model to describe the experimental set  (62). Several starting initial parameters were tested, and converged to the same results.
CD experiments were carried out on solutions prepared exactly as for ESI-MS. Experiments were run on a Jasco J-815 spectrophotometer at 20 • C (unless otherwise mentioned)--see supporting information for the instrumental details. CD data were normalized to molar circulardichroic absoption ( ⑀) based on DNA concentration using Equation (  4 ), ε = θ/(32980 × C × l) ( 4 ) where is the CD ellipticity in milidegrees, C is the DNA concentration in mol/l (in this work: 10 -5 mol/l) and l is the pathlength in cm (0. 2 cm). The concentrations used for CD are the same as those for MS, to allow direct comparison of the results. The DynaFit software was used to obtain the molar ellipticity coefficient of each ensemble defined based on ESI-MS, as a function of the wavelength (here, each 5 nm). The software uses the equilibrium or rate constants to calculate the concentration of each ensemble, and then determines the molar response (here the molar ellipticity coefficient) of each ensemble (see supporting information for the data processing details).
The generated CD spectra are shown in Figure  3D -F and Supporting Supplementary Figure  S24. For 24TTG and Pu24, the CD spectra for the 1-K + structures were not deconvoluted because of the low population of 1-K + ensemble (see for example Figure  3A  for 24TTG). Also, given that the titration involves only two main states, the CD titration data can be fitted using Equation (3). The K D-Glob obtained by fitting the CD titration agrees with the one obtained by fitting the ESI-MS titration (2. 69 × 10 -9 M 2 versus 2. 70 × 10 -9 M 2 , respectively) (Table  1 ), and this also validates the quantitative mathematical treatment of the ESI-MS data. For all the human telomeric sequences in which it is significantly populated, the 1-K + ensemble has clearly an antiparallel-type CD spectrum. For 22GT, based on the published structure (PDB ID: 2KF8 (  25 )), we interpret the results as follows.
ACKNOWLEDGEMENTS The authors acknowledge  Miho Takematsu  for technical assistance and  Frédéric Rosu  for technical support and reading the manuscript. We thank the  Structural Biophysical Chemistry platform of the Institut Européen de Chimie et Biologie  ( CNRS UMS 3033/Inserm US001 / Univ. Bordeaux)  for access to the mass spectrometers. FUNDING  Inserm [ATIP-Avenir Grant  no. R12086GS ];  Conseil Régional Aquitaine  [20121304005];  EU   Seventh Framework Programme  [ FP7-PEOPLE-2012-CIG-333611 ]. Funding for open access charge:  FP7 Marie Curie Career Integration Grant  'BIOPHYMS'.
41, 42 ene expression profiling of CTCs also revealed several surprising findings. 6] [47]  These surprising results must be further investigated. Due to the low number of CTC-positive patients in this study we performed an additional data analysis using the TCGA data package (The Cancer Genome Atlas, freely accessible database) to compare the gene signature of CTCs (our data) with the gene signature of metastasis and primary tumors (TCGA data). In total, we analyzed 1,090 primary tumors and 7 metastasis, all from breast cancer patients. The analysis revealed similar differential expression of HDAC2, TP53, and UPA (Fig. 5 ). HDAC2 and TP53 were downregulated in metastasis compared with primary tumors, which is consistent with our data obtained from CTC-positive patients. UPA was overexpressed in primary tumors compared to metastasis and also overexpressed in our CTC-positive patients.
In order to evaluate the prognostic relevance of the gene signature of CTCs we correlated high expression of these genes and patients survival in the independent cohorts of patients (TGCA data set), by performing Kaplan-Meier analyses using the third quartile of the gene's expression as a cut-off value. Among the 27 genes examined, high expression of 5 genes (CD24, HDAC2, KRAS, PIK3CA, RAD51), was associated with significantly shorter overall-survival (p < 0. 05, log-rank test), and high expression of RAD51 was significantly associated with shorter relapse-free survival (Fig. 6 ). Strikingly, not a single gene examined was associated with a favorable outcome. Epithelial to mesenchymal transition is not the only prerequisite for a successful formation of metastasis. CTCs need to have mechanisms that allow them to survive both in the blood stream and at the site of implantation.
Patient characteristics The study has received ethical approval by the Multicentric Ethics Committee of the University Hospital Motol (approved Figure  5. TCGA data analysis of primary tumors and metastasis. Volcano plot filtering shows differentially expressed genes between primary tumors (n D 1,090) and metastasis (n D 7). Three genes (HDAC2, TP53, UPA), that are highlighted above the horizontal line (statistical significance boundary of p < 0. 05) were significantly upregulated in primary tumors. A total of 147 breast cancer patients were enrolled in this study between 2011 and 2014. The presence of a tumor was confirmed histologically. The patients were distributed into four groups according to tumor stage (stage I to IV), which was determined by a pathologist in compliance with common standards.
Statistical analysis PCR data were analyzed by unpaired Student's t-test using GenEx software (MultiD Analyses). Relative gene expression levels were calculated using the DDCt method and were normalized to the expression levels of reference genes selected by Normfinder. All values are presented as the mean § SEM. Differences were considered significant at p 0. 05. The differential expression of genes according to clinical parameters was assessed by Student's t-test or ANOVA.
and Ambispora sp. (Figure  1 ). An expected 700 bp fragment was amplified from each morphotype. Both BLAST and phylogenetic analyses allowed the identification of the morphotype LBVM01 as A. colombiana (Genbank accession number KX168435) and the other LBVM02 as A. appendicula (Genbank accession number KX168436) (Table  3 ; Figure  2 ). AB, Abengourou; AZ, Azaguié; YA, Yamoussoukro; Field number, 1-2-3-4. -, absent (0 spore/g); +, present (1-2 spores/g); ++, abundant (3-5 spores/g); + + +, highly abundant (6-8 spores/g). bold indicates abundant and ubiquitous AMF species in both field soils and trapped culture.
Identification of candidate ATG8 interacting motifs in PexRD54 ATG8 interacting motif (AIM), also known as LC3 interacting region (LIR), mediates interaction of cargo receptors or adaptors with ATG8 proteins anchored in autophagosome membranes  (Birgisdottir et al. , 2013). It follows the W/F/Y-xx-L/I/V amino acid consensus. Initially, we identified two AIM candidates in PexRD54, AIM1 and AIM2 based on the manual search of the consensus sequence mentioned earlier. Then, we confirmed these AIM candidates using the recently published iLIR software  (Kalvari et al. , 2014). This software assigned AIM1 with an iLIR score of 12 (1. 1e -1 ) and AIM2 with an iLIR score of 23 (3. 2e -3 ).
Sequence analyses and identification of ATG8CL To determine the ATG8 variant(s) specifically targeted by PexRD54 among various host ATG8 family members, we performed a BLASTP search  (Altschul et al. , 1990)  against solanaceous plant proteomes including Solanum tuberosum (potato), Solanum lycopersicum (tomato) and Nicotiana benthamiana using Arabidopsis thaliana ATG8C as the query protein sequence. We found nine ATG8 members in S. tuberosum, seven in S. lycopersicum, and eight in N. benthamiana. To verify the gene calls and open reading frame predictions of the putative orthologs in these three species, we performed a sequence alignment of the family members in each species using the Clustal X program (v2)  (Larkin et al. , 2007)  and compared it to the published A. thaliana ATG8 sequences.
We found evidence of misannotation for two S. lycopersicum sequences (Solyc10g006270 and Sol-yc08g078820) and three others in N. benthamiana (NbS00015425g0005, NbS00003316g0005 and NbS00003005g0010). The two S. lycopersium sequences and the NbS00003005g0010 sequence from N. benthamiana carried extra nucleotides before the likely start codon, which were corrected accordingly. A TBLASTN search against the N. benthamiana scaffolds followed by a BLASTP search of the different exons allowed curation of the two other sequences. Clustal X program was used for multiple sequence alignment of ATG8 variants. Boxshade server (http://embnet. vital-it. ch/software/ BOX_form. html) was used to visualize the sequence alignment.
, UK) as described previously  (Petre et al. , 2015). LC-MS/MS data processing and protein identification were done as described previously  (Petre et al. , 2015). In planta association of PexRD54 and Joka2 with either ATG8CL, ATG8CLD or ATG8IL constructs was tested by co-IP assays as follows: constructs were transiently co-expressed in N. benthamiana leaves by agroinfiltration followed by protein extraction 2-3 days post infiltrations. Protein extraction, purification and western blot analysis steps were performed as described previously   (Saunders et al. , 2012; Bozkurt et al. , 2011; Oh et al. , 2009). Monoclonal FLAG M2 antibody (Sigma-Aldrich, UK), polyclonal GFP/RFP antibodies (Invitrogen, UK), and polyclonal HA (Sigma-Aldrich, UK) antibody were used as primary antibodies, and anti-mouse antibody (Sigma-Aldrich, UK) and anti-rat (Sigma-Aldrich, UK) antibodies were used as secondary antibodies.