Investigating the 3D structure of the genome with Hi-C data analysis

Investigating the 3D structure of the genome withHi-C data analysis

Sylvain Foissac & Nathalie Villa-Vialaneix

[email protected]

Séminaire MIAT - Toulouse, 2 juin 2017

SF & NV2 | Hi-C data analysis 1/28

Sommaire

1 Normalization

2 TAD identification

3 A/B compartments

4 Differential analysis


Sommaire

1 Normalization


3 A/B compartments



Purpose of normalization

1 within matrix normalization: make bins comparable within a matrix(not needed for differential analysis)

2 between matrix normalization: make the same bin pair comparablebetween two matrices (needed for differential analysis)


Purpose of normalization

1 within matrix normalization: make bins comparable within a matrix(not needed for differential analysis)

2 between matrix normalization: make the same bin pair comparablebetween two matrices (needed for differential analysis)


Different within matrix normalizationsto correct technical biases

(GC content, mappability...)

explicit correction [Yaffe and Tanay, 2011, Hu et al., 2012]: every factorcausing bais is identified and estimated

non parametric correction ICE correction using matrix balancing[Imakaev et al., 2012]

K = b>K̃b for a K st ∀ i = 1, . . . , p,p∑

j=1

Kij is constant



(GC content, mappability...)

explicit correction [Yaffe and Tanay, 2011, Hu et al., 2012]: every factorcausing bais is identified and estimated

non parametric correction ICE correction using matrix balancing[Imakaev et al., 2012]

K = b>K̃b for a K st ∀ i = 1, . . . , p,p∑

j=1

Kij is constant



picture from [Schmitt et al., 2016]


Different within matrix normalizationsto take distances into account

theoretical distribution taken from [Belton et al., 2012]

K̃dij =

Kij − Kd(i,j)

σ(Dd(i,j))with

{Kd average counts at distance dσ(Dd) standard deviation

available in HiTC [Servant et al., 2012]


Between matrix normalizationcorrect for differences in sequencing depth

standard approach: similar to RNA-seq normalization

However...

density adjustment by LOESS fit [Robinson and Oshlack, 2010]

(implemented in csaw)



standard approach: similar to RNA-seq normalizationHowever...





standard approach: similar to RNA-seq normalizationHowever...




Sommaire

1 Normalization


3 A/B compartments



Topologically Associated Domains (TADs)

[Rao et al., 2014]


TAD method jungleDirectionality index [Dixon et al., 2012]: compute divergence betweenup/downstream interaction counts + HMM to identify TADs

armatus [Filippova et al., 2013]: maximize a criteria which evaluate awithin/between count ratio + combine multi-resolution results in aconsensual segmentationsegmentation method [Brault et al., 2017]: block boundary estimation inmatrix... (many others), interestingly, very few provides a hierarchicalclusteringComparisons in: [Fotuhi Siahpirani et al., 2016, Dali and Blanchette, 2017]


TAD method jungleDirectionality index [Dixon et al., 2012]: compute divergence betweenup/downstream interaction counts + HMM to identify TADsarmatus [Filippova et al., 2013]: maximize a criteria which evaluate awithin/between count ratio + combine multi-resolution results in aconsensual segmentation

segmentation method [Brault et al., 2017]: block boundary estimation inmatrix... (many others), interestingly, very few provides a hierarchicalclusteringComparisons in: [Fotuhi Siahpirani et al., 2016, Dali and Blanchette, 2017]


TAD method jungleDirectionality index [Dixon et al., 2012]: compute divergence betweenup/downstream interaction counts + HMM to identify TADsarmatus [Filippova et al., 2013]: maximize a criteria which evaluate awithin/between count ratio + combine multi-resolution results in aconsensual segmentationsegmentation method [Brault et al., 2017]: block boundary estimation inmatrix

... (many others), interestingly, very few provides a hierarchicalclusteringComparisons in: [Fotuhi Siahpirani et al., 2016, Dali and Blanchette, 2017]


TAD method jungleDirectionality index [Dixon et al., 2012]: compute divergence betweenup/downstream interaction counts + HMM to identify TADsarmatus [Filippova et al., 2013]: maximize a criteria which evaluate awithin/between count ratio + combine multi-resolution results in aconsensual segmentationsegmentation method [Brault et al., 2017]: block boundary estimation inmatrix... (many others), interestingly, very few provides a hierarchicalclusteringComparisons in: [Fotuhi Siahpirani et al., 2016, Dali and Blanchette, 2017]


DI evolution with respect to armatus TADs


CTCF at TAD boundaries


Enrichment of genomic features around TAD boundariesHomo Sapiens [Dixon et al., 2012]

Sus Scrofa (PORCINET project)


Current methodological developmentConstrained HAC as a way to compare/combine TADs between samplesContrained HAC: Hierarchical clustering with contiguity constrains

Challenges (currently under development with Pierre Neuvial and MarieChavent):

methodological issues: what happens when using Ward’s linkagecriterion with a non Euclidean similarity (counts of the Hi-C matrix)?what happens when adding constrains to HAC? (partially solved)development of the R package adjclust (Google Summer of Codeselected project)


Current methodological developmentConstrained HAC as a way to compare/combine TADs between samplesContrained HAC: Hierarchical clustering with contiguity constrains

Challenges (currently under development with Pierre Neuvial and MarieChavent):

methodological issues: what happens when using Ward’s linkagecriterion with a non Euclidean similarity (counts of the Hi-C matrix)?what happens when adding constrains to HAC? (partially solved)development of the R package adjclust (Google Summer of Codeselected project)


Sommaire

1 Normalization


3 A/B compartments



A/B compartments

[Lieberman-Aiden et al., 2009]

[Giorgetti et al., 2013]

Method (in theory):

compute Pearson correlations between bins(using interaction counts with all the other binsof the same chromosome)

compute eigenvectors (or perform PCA) on thiscorrelation matrix

affect A/B compartments to +/- values of PCs


A/B compartments in practiceafter ICED and distance-based normalizations

Method:

differentiate between A/B using sign of the correlation between PCsand diagonal counts

choose a relevant PC and method maximizing − log10(p − value)between diagonal counts in +/- PC (2-group comparison Student test)


A/B compartments in practice

after ICED and distance-based normalizations

Method:

differentiate between A/B using sign of the correlation between PCsand diagonal counts

choose a relevant PC and method maximizing − log10(p − value)between diagonal counts in +/- PC (2-group comparison Student test)


Biological validation


Sommaire

1 Normalization


3 A/B compartments



FilteringIn differential analysis of sequencing data, filtering is a crucial step:

removing low count features (that are little or no chance to be founddifferential) improves the test power (leverage the multiple testingcorrection effect) and can save unnecessary computational time

can be performed 1/ at the beginning of the analysis or after theestimation of the parameters of the model used for differentialanalysis

; 2/ can be fixed to an arbitrary value (minimum total countper sample) or automated from the data

500 kb - automatic filter (filters counts<∼ 5) - 96.4% of pairs filtered out

before filtering after filtering



removing low count features (that are little or no chance to be founddifferential) improves the test power (leverage the multiple testingcorrection effect) and can save unnecessary computational timecan be performed 1/ at the beginning of the analysis or after theestimation of the parameters of the model used for differentialanalysis

; 2/ can be fixed to an arbitrary value (minimum total countper sample) or automated from the data





removing low count features (that are little or no chance to be founddifferential) improves the test power (leverage the multiple testingcorrection effect) and can save unnecessary computational timecan be performed 1/ at the beginning of the analysis or after theestimation of the parameters of the model used for differentialanalysis; 2/ can be fixed to an arbitrary value (minimum total countper sample) or automated from the data






for Hi-C data:filtering was performed at the beginning of the analysis (to limit thecomputation burden)was performed by using an arbitrary threshold or a threshold basedon the estimation of the noise background by a quantile ofinter-chromosomal counts (as in R package diffHic)









Exploratory analysis (500kb bins)chromosome 1

1 0.911

1

0.8886

0.8866

1

0.8566

0.8651

0.8288

1

0.8973

0.9118

0.8912

0.8692

1

0.8935

0.9032

0.8818

0.8799

0.906

1

LW90−160216−GCCAAT

LW90−160223−CTTGTA

LW90−160308−AGTTCC

LW110−160307−CGATGT

LW110−160308−AGTCAA

LW110−160517−ACAGTG

LW90

−160

216−

GCCAAT

LW90

−160

223−

CTTGTA

LW90

−160

308−

AGTTCC

LW11

0−16

0307

−CGAT

GT

LW11

0−16

0308

−AGTCAA

LW11

0−16

0517

−ACAGTG

−1.0 −0.5 0.0 0.5 1.0

Cosinus (Frobenius norm)

good reproducibility betweenexperiments

no clear organization with respect tothe condition

all data after filtering and betweenmatrix normalization (LOESS)

2 outliers but PC1 is organized withrespect to the condition


Exploratory analysis (500kb bins)chromosome 1

1 0.911

1

0.8886

0.8866

1

0.8566

0.8651

0.8288

1

0.8973

0.9118

0.8912

0.8692

1

0.8935

0.9032

0.8818

0.8799

0.906

1

LW90−160216−GCCAAT

LW90−160223−CTTGTA

LW90−160308−AGTTCC

LW110−160307−CGATGT

LW110−160308−AGTCAA

LW110−160517−ACAGTG

LW90

−160

216−

GCCAAT

LW90

−160

223−

CTTGTA

LW90

−160

308−

AGTTCC

LW11

0−16

0307

−CGAT

GT

LW11

0−16

0308

−AGTCAA

LW11

0−16

0517

−ACAGTG

−1.0 −0.5 0.0 0.5 1.0

Cosinus (Frobenius norm)

good reproducibility betweenexperiments

no clear organization with respect tothe condition

all data after filtering and betweenmatrix normalization (LOESS)

2 outliers but PC1 is organized withrespect to the condition


Methods for differential analysis of Hi-CSimilar to RNA-seq [Lun and Smyth, 2015] and R package diffHic(essentially a wrapper for edgeR):

count data modeled by Binomial Negative distribution

parameters (mean, variance per gene) are estimated from data: avariance vs mean relationship is modeled

test is performed using an exact test (similar to Fisher) or alog-likelihood ratio test (GLM model)












Complementary remarks about DE analysis

Hi-C data contain more zeros than RNA-seq data: some peoplepropose to use Zero Inflated BN distribution (unpublished as far as Iknow)

provides a p-value for every pair of bins:I analysis based on a very large number of bins for finer resolutions

(500kb after filtering: 998 623 pairs of bins; without filtering:13 509 221 pairs of bins): problem solved for 500kb bins but still understudy for 40kb bins

I tests are performed as if bin pairs were independant whereas they arespatially correlated

: estimation of model parameters might be improvedif 1/ smoothed with respect to spatial proximity (similar to what issometimes performed methylation data analysis); 2/ performedindependantly for pairs of bins at a given distance (future work).

post-analysis of spatial distribution of p-values, work-in-progress withPierre Neuvial (submitted CNRS project)






















I tests are performed as if bin pairs were independant whereas they arespatially correlated: estimation of model parameters might be improvedif 1/ smoothed with respect to spatial proximity (similar to what issometimes performed methylation data analysis); 2/ performedindependantly for pairs of bins at a given distance (future work).



because last page had no pictureprobably not suited for the youngest


Preliminary results

913 bin pairs found differential (after multiple testing correction)

most of them are related to 3 chromosomes

parameter setting (filters...) and biological analysis are work-in-progress...


Differential TADs (state-of-the-art)Detecting differential domains between the two conditionsExisting approaches:

[Fraser et al., 2015] (3 conditions, no replicate)I HMM on TAD boundaries (with a tolerance threshold) to identify

different TAD boundaries between samplesI HAC on TADs, cophenetic distance to obtain local conserved structure

by using a z-score approach

R package diffHic computes up/down-stream counts (with ± 100Kb)and uses the GLM model implemented in edgeR with an interactionbetween stream direction (up/down) and condition.

However, the first approach does not take biological variability into account(no replicate) and the second uses only a very aggregated criterion.
















Differential TADs (perspectives)Ideas for future workUsing constrained HAC, are we able to:

compute a consensus dendrogram using several biological replicates;

differentiate branches significantly (in which sense?) differentbetween conditions taking into account the within condition variability?


Differential TADs (perspectives)Ideas for future workUsing constrained HAC, are we able to:

compute a consensus dendrogram using several biological replicates;

differentiate branches significantly (in which sense?) differentbetween conditions taking into account the within condition variability?


Conclusions and perspectives

Honnestly, it’s late and I really do not believe that I will have enough time tomake a conclusion and discuss perspectives so...

Questions?


ReferencesBelton, J., Patton MacCord, R., Harmen Gibcus, J., Naumova, N., Zhan, Y., and Dekker, J. (2012).Hi-C: a comprehensive technique to capture the conformation of genomes.Methods, 58:268–276.

Brault, V., Chiquet, J., and Lévy-Leduc, C. (2017).Efficient block boundaries estimation in block-wise constant matrices: an application to HiC data.Electronic Journal of Statistics, 11(1):1570–1599.

Dali, R. and Blanchette, M. (2017).A critical assessment of topologically associating domain prediction tools.Nucleic Acid Research, 45(6):2994–3005.

Dixon, J., Selvaraj, S., Yue, F., Kim, A., Li, Y., Shen, Y., Hu, M., Liu, J., and Ren, B. (2012).Topological domains in mammalian genomes identified by analysis of chromatin interactions.Nature, 485:376–380.

Filippova, D., Patro, R., Duggal, G., and Kingsford, C. (2013).Identification of alternative topological domains in chromatin.Algorithms for Molecular Biology, 9:14.

Fotuhi Siahpirani, A., Ay, F., and Roy, S. (2016).A multi-task graph-clustering approach for chromosome conformation capture data sets identifies conserved modules ofchromosomal interactions.Genome Biology, 17:114.

Fraser, J., Ferrai, C., Chiariello, A., Schueler, M., Rito, T., Laudanno, G., Barbieri, M., Moore, B., Kraemer, D., Aitken, S., Xie, S.,Morris, K., Itoh, M., Kawaji, H., Jaeger, I., Hayashizaki, Y., Carninci, P., Forrest, A., The FANTOM Consortium, Semple, C.,Dostie, J., Pombo, A., and Nicodemi, M. (2015).Hierarchical folding and reorganization of chromosomes are linked to transcriptional changes in cellular differentiation.Molecular Systems Biology, 11:852.

Giorgetti, L., Servant, N., and Heard, E. (2013).Changes in the organization of the genome during the mammalian cell cycle.


Genome Biology, 14:142.

Hu, M., Deng, K., Selvaraj, S., Qin, Z., Ren, B., and Liu, J. (2012).HiCNorm: removing biases in Hi-C data via Poisson regression.Bioinformatics, 28(23):3131–3133.

Imakaev, M., Fudenberg, G., McCord, R., Naumova, N., Goloborodko, A., Lajoie, B., Dekker, J., and Mirny, L. (2012).Iterative correction of Hi-C data reveals hallmarks of chromosome organization.Nature Methods, 9:999–1003.

Lieberman-Aiden, E., van Berkum, N., Williams, L., Imakaev, M., Ragoczy, T., Telling, A., Amit, I., Lajoie, B., Sabo, P., Dorschner,M., Sandstrom, R., Bernstein, B., Bender, M., Groudine, M., Gnirke, A., Stamatoyannopoulos, J., Mirny, L., Lander, E., andDekker, J. (2009).Comprehensive mapping of long-range interactions reveals folding principles of the human genome.Science, 326(5950):289–293.

Lun, A. and Smyth, G. (2015).diffHic: a Bioconductor package to detect differential genomic interactions in Hi-C data.BMC Bioinformatics, 16:258.

Rao, S., Huntley, M., Durand, N., Stamenova, E., Bochkov, I., Robinson, J., Sanborn, A., Machol, I., Omer, A., Lander, E., andLieberman Aiden, E. (2014).A 3D map of the human genome at kilobase resolution reveals principle of chromatin looping.Cell, 159(7):1665–1680.

Robinson, M. and Oshlack, A. (2010).A scaling normalization method for differential expression analysis of RNA-seq data.Genome Biology, 11:R25.

Schmitt, A., Hu, M., and Ren, B. (2016).Genome-wide mapping and analysis of chromosome architecture.Nature Reviews, 17(12):743–755.

Servant, N., Lajoie, B., Nora, E., Giorgetti, L., Chen, C., Heard, E., Dekker, J., and Barillot, E. (2012).


HiTC: exploration of high-throughput ‘C’ experiments.Bioinformatics, 28(21):2843–2844.

Yaffe, E. and Tanay, A. (2011).Probabilistic modeling of Hi-C contact maps eliminates systematic biases to characterize global chromosomal architecture.Nature Genetics, 43:1059–1065.
