dataesr/scientific-paragraphs-categorization huggingface dataset:
(crosses). c Experimental data Y k E , such as the average distance between loci A and B measured by imaging, 〈d AB E 〉, are compared to the predictions 〈d AB Π 〉 for all Π. d, e Similarly, contact frequencies between chromosomes i and j are predicted for all Π (here i=j) (d) and compared to measurements from Hi-C experiments (e). f, g Parameter inference: given an experimental dataset, using the Bayes rule and Markov chain Monte Carlo sampling, we calculate the posterior probability density of any subset of parameters, such as (P, C). Isocontour lines enclose the region of high probability. This can be done for individual experimental data, e. g. 〈d AB E 〉 (f), or for a combination of multiple datasets, e. g. mean distances between loci and chromosome contact frequencies (g). The maximum a posteriori estimate of the parameters (MAP) defines a model that provides the best match to the experimental data nucleus (Additional file 1: Figure  S1a, b ), we used Langevin dynamics to simulate their movements, i.
Compilation of experimental data on yeast chromatin architecture We gathered a large amount of quantitative measurements on yeast nuclear architecture based on light microscopy in live or fixed cells and on Hi-C. The microscopy data contained mostly distances between pairs of loci on the same chromosome (cis) or on different chromosomes (trans), which were typically measured in hundreds or thousands of individual cells  [35, 39, 50, 51]. We also added newly measured distances between 12 pairs of loci along the right arm of chromosome 4, spanning pericentromeric, internal, and subtelomeric regions (Additional file 1: Supplementary Methods). The Hi-C data provided genome-wide maps of contact frequencies between DNA segments averaged over millions of cells  [29, 30]. Most of the imaging and Hi-C data were acquired and quantified by independent groups  [29, 30, 35, 39, 50, 51].
While these data contain many thousands of individual measurements, we chose to condense them into a more manageable set of summary statistics. For example, instead of the entire distribution of distances between two loci, we only considered the mean (or median) distance over all cells. Similarly, we reduced the Hi-C data to the following quantities: (1) average contact frequencies of each chromosome with itself; (2) average contact frequencies of each chromosome with all other chromosomes; (3) intrachromosomal contact frequencies for different genomic distances, averaged over the entire genome; (4) intrachromosomal contact frequencies relative to the centromere, averaged over all chromosomes. Table  2  summarizes the experimental datasets and summary statistics. Additional file 3 provides a detailed list of all imagebased measurements we have used.
Determining the probability density of chromatin parameters by Bayesian inference We aimed to explore the space of chromatin parameters Π and to assign a probabilistic score to all possible values of Π based on how accurately the corresponding model M(Π) predicted a given experimental dataset D. This approach is more informative than an optimization method, which would only determine a single parameter value Π*, irrespective of how well the model explains the data for Π ≠ Π*. Our method employed two main ingredients: (1) a Bayesian formulation that computes the (posterior) probability of an assumed parameter value Π given the data D; and (2) a Monte Carlo Markov Chain algorithm that samples the space of parameters Π. The Bayes rule provides the posterior probability of Π given D by: p(Π|D) ∝ p(D|Π)p(Π), where p indicates probability density and p(A|B) the probability density of A conditioned on B.
Let us consider an experimental dataset D = (Y 1 E , …, Y N E ) consisting of N independent measurements Y k E. For example, Y k E might represent the mean distance between two loci A and B (Fig. 1c ). For each data point Y k E , and for a given parameter value Π, the corresponding model M(Π) provides a single predicted counterpart Y k M(Π) (Fig. 1b, d ). Both the experimental measurements Y k E and the model predictions Y k M(Π) are, however, affected by noise: distances measured from images are necessarily corrupted by random localization errors  [50, 52, 53] , while Hi-C data suffer from counting noise due to limited sequencing depth, random ligations, and other factors  [54, 55]. Our model predictions are also subject to random errors because they are computed from finite samples of stochastic simulations (Fig.
Thus, for any assumed value of the structural and nuisance parameters Π and Ξ, and for a given dataset D, the above formulation yielded a posterior probability p(Π, Ξ|D) (to within a normalization constant). In order to estimate p(Π, Ξ|D) over the entire parameter space, we used a Monte Carlo Markov Chain ensemble sampler that efficiently concentrated the exploration of the high-dimensional parameter space (Π, Ξ) to the region of high posterior probability  [58]. The posterior probability over the structural parameters, p(Π|D) was then readily obtained by integrating p(Π, Ξ|D) over the nuisance parameters Ξ. Similarly, the posterior probability for a single parameter, e. g. chromatin compaction, p(C|D), or the joint probability for a subset of parameters, e. g. p(P, C|D), were obtained by integrating over the remaining parameters (Fig.
e. the parameter values P; Ĉ À Á for which the estimated posterior probability density is maximum. Panels a-e were obtained from simulations with low levels of added noise, panels f-j from simulations with high noise (Additional file 1: Supplementary Methods). Panel pairs (a, f), (b, g), (c, h), (d, i), and (e, j) each correspond to a different subset of simulated observables. Panels a, f: probability densities obtained from distances between the pairs of loci corresponding to the experimental dataset O6 (see Table  2  and Additional file 3). Panels b, g: the same, for distances between pairs of telomeres (observable O1). Panels c, h: the same, for all locus positioning data, corresponding to observables O1-O7 combined. Panels d, i: the same, for contact frequencies between chromosomes (observables O8 or O9).
Panels e, j: the same, for all distance and contact data combined (all observables, O1-O9). k, l: Errors of MAP estimates relative to the simulated ground truth for chromatin persistence length P (k) and compaction C (l). The root mean square (RMS) error is plotted for three different levels of noise and for five distinct simulated models (corresponding to five different values of the parameters), as indicated in the legend The posterior probability densities for persistence length P and compaction C estimated by our method are shown in Fig. 3 , for different subsets of the data (Fig. 3a-f ), and all datasets combined (Fig. 3g ). Intrachromosomal distances alone constrained the compaction C and persistence length P to the vicinity of a curve given by: C ∝ P 0. 7 (Fig. 3a ), but these data could not separately determine C and P on their own, as expected from the above simulation results (Fig.
2a ). By contrast, also as expected (Fig. 2b ), distances between telomeres allowed to constrain both parameters to a much smaller range, namely C = 61 ± 6 bp/nm and P = 56 ± 10 nm (mean ± standard deviation) (Fig. 3b ). When all imaging data were combined, a similar posterior probability density was obtained, with C = 60 ± 5 bp/nm and P = 63 ± 11 nm (Fig. 3d ). Interestingly, imaging data obtained in live and fixed cells resulted in similar probability densities, despite the potential artefacts caused by fixation  [50, 60]  (Fig. 3c ). We next analyzed two independent Hi-C datasets [29, 30] and found that they again led to very similar probability densities (Fig. 3e ). This is remarkable, given that these data were obtained using different experimental protocols and that both led to rather narrow densities.
The probability density obtained when combining both Hi-C datasets is shown in Fig. 3f. Although the joint density obtained from Hi-C does not strictly overlap with that determined by imaging, it is relatively close (Fig. 3d, f ). For the compaction C, the posterior density derived from the Hi-C data is 55 ± 2 bp/nm and overlaps substantially with that derived from the imaging data (Fig. 3h ). For the persistence length P, the Hi-C data yielded an estimate of P = 83 ± 2 nm, an approximately 30% increase relative to the range P = 63 ± 11 nm determined by imaging (Fig. 3i ). This discrepancy can potentially arise from multiple sources, including estimation errors due to mismatch of other parameters (see above), measurement errors exceeding our estimates, differences in data processing, or biological differences related to the different experimental protocols used in imaging or Hi-C.
For example, a fixation-induced shrinkage of the nucleus without alteration of chromatin properties should result in an underestimation of compaction and an overestimation of persistence length. This might explain why the Hi-C data alone predicted lower C and higher P than the imaging data alone (Fig. 3h, i ). If we ignored these discrepancies and combined all 266 experimental data points, we obtained the posterior density shown in Fig. 3g , based on which the Fig. 3  Yeast chromatin parameters inferred from imaging and Hi-C data. This figure shows the posterior probability densities of chromatin compaction C and persistence length P as inferred from a variety of experimental datasets. a-g joint posterior probability densities for (P, C) obtained for different subsets of experimental data (a-f) or the whole experimental dataset (g), as detailed below.
The two contour lines shown enclose 68% and 95% of the probability mass. Individual panels correspond to the following experimental datasets: (a) modes of 3D distances between eight pairs of loci on chromosome 14 measured by imaging in fixed cells (observable O6, Table  2 ). The dashed yellow curve has C ∝ P 0. 7. b Median 3D distances between 62 pairs of telomeres measured by imaging in live cells  [50]  (O1). c Combined set of data from imaging, in live cell or fixed cell experiments. Solid lines: combined data from live cell imaging (111 data points, O1-O4); dotted lines: combined data from imaging fixed cells (28 data points, observables O5-O7). d All imaging data from fixed and live cells pooled together (O1-O7; 139 data points). e Summary statistics from genome-wide contact frequencies measured by Hi-C data (see Table  2  and Additional file 1: Supplementary Methods).
Solid lines: Hi-C data from  [29]  (56 data points; O8). Dotted lines: Hi-C data from  [30]  (56 data points; O9). f Combination of the two Hi-C datasets  [29, 30]  (116 data points; O8, O9). g Combination of all experimental data from imaging and Hi-C (266 data points; O1-O9). h, i Probability densities for C (h) and P (i), obtained either from all the imaging data as in (d) (green), from the two Hi-C datasets as in (f) (blue) or from the combination of imaging and Hi-C data as in (g) (red) compaction and persistence lengths are most likely to fall within the following ranges: C = 61 ± 4 bp/nm, P = 88 ± 4 nm (Fig. 3h, i ). More conservative estimations were obtained when taking into consideration the discrepancy between the Hi-C and the imaging data, which our method does not account for, and using parameter ranges that span the above confidence intervals determined from both datasets separately.
Improved predictions of genome-wide contact maps We also compared the predicted genome-wide contact frequency maps to the two Hi-C datasets used for parameter inference above  [29, 30]  (Fig. 4d, e , Additional file 1: Figure  S9a-c ). When the contacts were binned at the highest resolution of 5 Kb, our improved model achieved a correlation of r = 0. 65 or r = 0. 85, with these data  [29, 30]  (Additional file 1: Figure  S9f  ). This exceeded the correlation between the two Hi-C datasets themselves (r = 0. 6) (Additional file 1: Figure  S9f  ). The correlation of predicted contacts with either Hi-C dataset further improved when increasing the genomic bin, and exceeded r = 0. 9 for bins of 70 Kb (Additional file 1: Figure  S9f  ). To better assess our model's predictive power, we further tested it against two additional genome-wide contact maps: a distinct Hi-C study by Belton et al.
[62]  (Fig. 4f ), and a dataset obtained using Micro-C XL, a recently described variation of the Hi-C technique that uses alternative cross-linking agents instead of formaldehyde and DNA digestion by micrococcal nuclease instead of restriction enzymes  [63]  (Additional file 1: Figure  S9e ). Correlations between model and data were even higher for the Belton et al. Hi-C data and were only slightly lower for the Micro-C XL data (Additional file 1: Figure  S9f ). Since these two datasets were not used for parameter inference, this comparison further demonstrates the predictive power of our model. The predicted mean contact frequencies among the 16 chromosomes also agreed very well with measurements from the three Hi-C data (Additional file 1: Figure  S10a-d, f-h ). We also analyzed the intrachromosomal contact frequencies as function of genomic distance.
92 and the RMS error is 9 degrees. d-f Genome-wide contact frequency matrices, binned at 30 Kb, as predicted by the model (d) or obtained from Hi-C experiments in  [30]  (e) and  [62]  (f). Bright pixels indicate high frequencies, dark pixels indicate low frequencies. A logarithmic scaling was applied to reveal lower frequency contact patterns In order to map simulation time to physical time, we fitted a single scaling parameter once for each of the three datasets  [64] [65] [66]. Figure  5a  shows the predicted and measured MSD between 1 s and 150 s or between 1 s and 10 s for seven different loci on the right arm of chromosome 4 (4R) and for the MAT locus on chromosome 3  [65, 66]. The distances of loci to the centromere were in the range of 12-985 Kb, spanning over 90% of the 1050 Kb long chromosome arm 4R except for the immediate vicinity of the centromere and telomere.
As apparent from Fig. 5a , the model approximately reproduced the measured MSD and recapitulated the observed ordering, i. e. the fact that loci at larger genomic distance from the centromere moved over longer distances during the same time interval. Figure  5b-e  shows measured MSD for four loci on four different chromosomes (including the rDNA-carrying chromosome 12, whose spatial configuration is quite different from the other chromosomes  [64] ) over time intervals in the range of 16 ms to 100 s. As previously pointed out, the MSD obeyed a subdiffusive power law with an exponent ~0. 5, roughly consistent with the Rouse polymer model  [18, 37, 41, 44, 64]. The model reproduced this behavior relatively well over almost four orders of magnitude of time. Discrepancies between predictions and measurements were similar to or smaller than internal discrepancies within the experimental datasets (Fig.
Discussion In this paper, we described a new approach to infer mechanical parameters of chromatin using a whole nucleus simulation of chromosomes. Compared to methods that estimate hundreds or thousands (or more) parameters to reproduce Hi-C contact data or other genome-wide data  [17, 24, 25, 67, 68] , our model assumes only a small number of structural parameters, giving it high predictive power. Our Bayesian formulation and sampling approach allow to determine the region of parameter space consistent with the data and to assign probabilities to parameter values. This approach thereby provides information about the uncertainties associated to the inferred parameters for each dataset or, equivalently, about how strongly the data constrain the parameters. We applied our method to a large set of experimental data on yeast nuclear architecture.
This analysis led to two main outcomes: new constraints on yeast chromatin and a better model of yeast nuclear organization. First, we derived new constraints on yeast chromatin compaction and rigidity, with implications for chromatin structure. Although several previous studies have attempted to determine these parameters from imaging or Hi-C data  [5, [39] [40] [41] [42] , they typically used either a single experimental dataset (e. g. only distances between ) or 1-10 s (inset, data from  [66] ). For each of the two datasets, a single time step parameter was fitted once to align simulation time with experimental time. The genomic distance of each locus to the centromere is indicated in the legend. b-e MSD of four loci on four different chromosomes, over time intervals in the range of 16 ms to 100 s, on a double logarithmic scale.
The chromosome number and the genomic distance of the locus to the centromere are indicated on top of each panel. Data (dots) are measurements from time-lapse microscopy in  [64]. Green curves are model predictions. Dashed black lines show a subdiffusive power law MSD ∝ t 0. 5 as expected from the Rouse model  [22, 37, 41]  loci, which are insufficient to unambiguously determine compaction and rigidity simultaneously, as shown in Figs. 2a  and 3a ) and/or used simpler polymer models that ignored important aspects of nuclear organization, such as tethering of centromeres and telomeres, or entropic repulsion between chromosomes. Accordingly, estimates of compaction C and persistence length P from previous studies spanned a wide range: 30-150 bp/nm and <30-200 nm, respectively. By contrast, our analysis is based on a much more varied and complete dataset compiled from multiple independent studies, which include distances between loci in cis and trans, nuclear locus territories, and two Hi-C datasets.
Nonetheless, future heterogeneous models that avoid overfitting might leverage state-of-the art genomic contact data and high resolution imaging data to shed more light on potential structural variations of the chromatin fiber  [12, 24, 42, 60, 76]. In addition to new insights into average yeast chromatin structure, our analysis yielded a set of models that provide a better explanation of experimental data than our previous model  [35]. In particular, for parameters that maximize the posterior probability, the model agrees well with measured distances between loci (means and distributions), intranuclear gene territory positions, and several aspects of Hi-C data, including Hi-C data that were not used for parameter estimation. Moreover, unlike Monte-Carlo simulations or structural ensembles obtained by optimization  [24, 36] , our model can predict the dynamic behavior of chromatin, in good agreement with observations.
Acknowledgements We thank the  IT service of Institut Pasteur  for access to the computing cluster and relevant assistance. We thank  O. Gadal ,  A. Bancaud , and  K. Bystricky  for providing data,  J. Parmar  for help with Hi-C data analysis and proofreading, and  M. Woringer  for comments on the manuscript. We thank the anonymous reviewers for their constructive criticism of our manuscript, which led to important improvements. C. Z. acknowledges support from the  Siebel Stem Cell Foundation  during a visit to  UC Berkeley , where a part of this paper was completed.
Funding This work was funded by  Institut Pasteur ,  Agence Nationale de la Recherche  (grant  ANR-11-MONU-020-02  to C. Z. ),  Fondation pour la Recherche Médicale (Equipe FRM   DEQ20150331762  grant to C. Z. ) and a  Labex Who am I grant  ( EE-2013  to E. F). J-M. A. was recipient of a  Pasteur-Roux fellowship  from  Institut Pasteur.
Acknowledgements We would like to thank staff of the  Mary Lyon Centre (MLC)  for animal husbandry support and advice, in particular  Jackie Harrison ,  Lee Kent ,  Gemma Atkins ,  Alison Gallop  and  Anju Paudyal. We thank staff of the MLC histology facility for sectioning, staff of the  GEMS facility  for genotyping and sequencing, and  Martin Fray  and his staff in the FESA Core. We thank  Dagmar Wilhelm  and  Makoto Tachibana  for the kind gift of antibodies. We thank staff in the laboratory of  Azim Surani , and in particular Ufuk Gu ¨nesdogan, for their help in establishing the low cell number ChIP protocol. Finally, we also thank other members of the  Greenfield lab at Harwell  for their advice and support.
| Data collection and analysis The study focussed on the layer duck value chain, including table eggs, hatching eggs and spent layer ducks. Duck farms were divided into two groups, raising short-distance free-grazing ducks and longdistance free-grazing ducks, respectively, according to definitions previously used  (Henning et al. , 2013) : short-distance free-grazing ducks graze within the home commune and are kept in confinement on the farm at night, while long-distance free-grazing ducks graze on rice paddies within or outside the home commune and do not return to the farm for extended periods of time. In Vietnam, a commune is a small administrative unit encompassing a central village and a varying number of hamlets. The value chains were investigated in the RRD and the MRD, which constitute the two main duck production regions in Vietnam.
| RESULTS A total of 12 group interviews were conducted in each study province in 2015, with a total of 188 stakeholders from different levels of the value chain (Table  1 ). The demographics of the 145 stakeholders who were interviewed individually are described in the following sections. As the interviewed stakeholders and the methods employed in the two types of exercises were different, some of the results obtained from each exercise slightly differed with each other. The origin of the data (group or individual interviews) is clearly indicated in the table and figure headings. Fifty-one of the 62 farmers interviewed in An Giang (82%) practised long-distance free grazing, while the other practised short-distance free grazing. The long-distance farmers practised full-time scavenging with their duck flocks (except for young flocks less than 2 months old).
| Governance Two main themes linked to the governance of the spent layer duck value chain were identified during the group and individual interviews: the major role of collectors and wholesalers, respectively. As insufficient data were collected on the governance of the egg value chain, they are not presented here. In both provinces, collectors have access to essential information about both the current availability of and demand for spent layer ducks and duck eggs in terms of volume, location and timing. Collectors may have trade contacts with wholesalers and retailers in the provincial urban centres where the demand is higher than it is in rural areas. They have an important role as brokers, influence the product prices and form a key link between the farmers and other actors such as wholesalers in terms of sharing of information on demand and supply.
was used in order to analyse the governance structure and dynamics of the value chains. The group interview notes and individual interview notes were reviewed carefully and the data of potential relevance to HPAI epidemiology and management were structured into codes, which were translated into English. The codes identified were sorted into themes that were used to structure the narrative of this analysis. Data collected via paper format questionnaires during the individual interviews were entered into an Excel database, checked, cleaned and translated into English. The quality of the translation was verified by one of the authors (DXT). Quantitative data were analysed in R (R Core Team 2014), while qualitative data were summarized and analysed manually. The Kruskal-Wallis test (and Dunn's test for post hoc comparisons), chi-squared test of independence and Fisher's test were used to assess the statistical significance between stakeholders from different locations (Hai Phong and An Giang), different systems (short-and long-distance) or different functions (e.
Acknowledgments This work was supported by the  Region of Franche-Comté , the  French RENATECH network  and performed in cooperation with the  Labex ACTION program  (contract  ANR-11-LABX-01-01 ). This research was also sponsored by the  French National Agency for Research (ANR)  funds through the  PHEMTO  project. The authors also thank the  BQR ENSMM  for financial support through the  COSET  project.