Annotation of genomics data using bidirectional hidden Markov
Contents
1. to account for constraints 5 and 3 This leads to the modified target function Q Gi k 1 log 2 e o molk logn IM Q 9 7 0 Il m k l Soa laza A 1 27 n l k 5G k L log pki So So n i k log Ty kl t 1 k tal S k log Tk ie n Z eu A Z7 p T 1 f z XG k 1 log pri X X e k log me kl t 1 k t 1 n Z ou 1 27 k 1 k 5 Zp log Pkl 5 Gr log Tk k l k pe m Eon a 1 Yom k l k with the constant terms Z pre 16 k l and Gk DE j tak Taking into account that pzz pij and 7 7 the partial derivatives of Q with respect to Ti and pij become 82 a gold a uita 2A ifs Ai 8 On Se 4 pmi ifi i and 7 we A OQ aan J p a iE pij po ii ifi j For ease of notation let zi Zij Zj and gi Gi Gj Setting the partial derivatives to zero we obtain 1 i A 5 mta 2 10 2 Ti and Hi 15 Pig ij 11 note that Equations 10 and 11 also hold if i and if i j Summing over i and j in 11 yields Xom pig 5 05 dS oF X zj i j j i ij X mmt m 27 i j X uate T 12 k Moreover SoG X Gi G T 1 T 1 VM x gt 22 i t 1 t 1 XT 1 13 Multiplying 10 by 7 and summing over i yields s Jon 1 z Dog mime uati gi 1 1 1 32 gt 5d mm 5 aT 12 13 1 1 1 27T 1 T T 2 2 T 2 1 14 Substituting A 1 back into 10 and rearranging terms we get wet2. 3 Moreover a is a stochastic if and only if sum_ i pi_i 1 Thus we are left with three equality constraints 3 and 4 and two sum constraints and From this point it is easy to check that Q in terms of the new parameters is equal to Q of eq 23 and that the maximum of this function is as given in eq 27 Thus the authors are performing exact EM where the internal optimization step has a unique solution i e is convex 1st Revision authors response 24 October 2014 European Molecular Biology Organization We thank the referees for their thorough and generally positive review We are confident that we could address their concerns and we changed the manuscript accordingly Please find below our point to point responses to the reviewers We are looking forward to your decision Sincerely Achim Tresch Editorial comments e We think that in this case it would be better to present the Supplementary Information in the single PDF file format The Supplementary Information has been converted into one single PDF file e We would also like to ask you to provide A doc file for the main manuscript text Since our manuscript contains many mathematical formulas we found it more appropriate to use the MSB TEX template for the revised manuscript We provide the TEX file and a pdf file generated from it e A standfirst text summarizing the study in one or two sentences approximately 250 character
3. To not introduce further biases towards the k means initialization and allow the EM to explore solutions which are further from it covariance matrices were initially set to the covariance of the whole data and transition and initial state probabilities were initialized uniform For the yeast data the strand specific expression data was first split into regions expressed on either the or strand and unexpressed regions Directed states were initialized as a k means clustering from the expressed regions while undirected states were initialized using k means on the unexpressed regions In the absence of strand specific data and without directionality annotation it is non trivial to determine whether a state is directed or not In order to minimize the amount of manual intervention we introduced the directionality score that can be used as a posterior criterion to merge twin states into one undirected state see the bdHMM application to the human data The merged model can then be used as an initialization to another round of bdHMM learning We comment on this in section Genomic state annotation results in a global strand specific transcription map in the main text and added a section Initialization of bdHMMs in Materials and Methods All pre and post processing steps are well documented in the STAN package vignette e A useful initialization can be based on standard HMM learning Learn a model and then introduce directional s
4. equilibrium conditions than the initial state My understanding is that the initial state distribution reflects the probabilities of the various states just before entering the beginning of a chromosomal arm It would be good to see some explanation of why these initial state probabilities should obey detailed balance or the initiation symmetry condition Thanks for pointing this out The two first symmetry conditions are a consequence that at any position of the Markov chain observing state i followed by state j has the same probability as observing the respective conjugate states bar i and bar j in reversed order It might be surprising that the initial probabilities are constrained to match the steady state probabilities This is however fine on practical applications for two reasons First complex regions unassembled regions repeat regions telomeres centromeres etc leads to frequent large stretches of missing values Hence the model is not run on complete chromosomes but on the remaining stretches with enough data For these stretches the biology of the first base differ Hence taking the steady state probability as initial probability is a reasonable modeling assumption Second the stretches are typically long enough so that the influence of the initial probability is minor on the genomic state annotation The Semantic of bdHMMs paragraph has been extended to explain this point e Figure 5c is the novel CUT simply an
5. pg B 240 15 Zee pag tg p oa u uz Cy m ij Ayp po 16 Ni Nj Pi Us 2 1 Se Tij Zij Pij ng tT 4 4 17 J for 7 and hence determine p We guess an approximate solution Ti re Ti i T as gi Yoli yr i Note that by choosing this specific solution we are able to guarantee that the updated parameters satisfy all constraints of a bdHMM see below However we cannot guarantee that the updated parameter set will have a marginal like lihood larger or equal to the previous parameter set 6 7 With this choice for p condition 5 is fulfilled T yi XO Zy Zi gt GG 5 0 0 J J T Sov i y i t T 1 i i yli yr ywli G G yr i gi yli yr i 20 And consequently gt A gi IOF yr i x ae ey The solution p m therefore satisfies all conditions of a bdHMM In case of convergence so far we have not seen an exception but we have not checked extensively yoli m m yr i and the approximation in 18 becomes an exact solution We have then found a local maximum 9
6. that these variables form a first order Markov chain e Same paragraph as above it may be better to use posterior probabilities of states for genome annotation rather than using the Viterbi path Perhaps the authors could comment on this point Are they using the Viterbi path because annotating genomic bins by their posterior probabilities could cause the inferred state to flip back and forth in an unstable manner Thanks we added a comment in section Genomic state annotation results in a global strand specific transcription map It is true that Viterbi path is less subject to state flipping in theory However we did not see any relevant difference in the state annotation of our data 97 of genomic positions are annotated with the same state when comparing Viterbi and posterior decoded state paths Posteriors are useful in other applications an example being our directionality score The STAN package provides both Viterbi and posterior decoding e End of Page 9 it s not exactly clear what is meant by binary data Is this a reference to discretization of the ChIP seq profiles into present absent within each bin Correct we use the binarization provided in the ChromHMM paper We made this clearer in the text and put an additional reference to the original ChromHMM paper by Ernst and Kellis Nat Methods 2012 e End of Page 10 what is the rationale behind the first two symmetry conditions These look more appropriate for describing
7. to another optimization strategy whose computational complexity is identical to our algorithm However the strategy chosen in the manuscript has an intuitive motivation as a lower bound maximization which the other approximation is lacking Therefore we decided to keep our solution Since we would highly appreciate Reveiwer 3 s further input on bdHMM learning we kindly ask you to encourage Reviewer 3 to reveal his identity to us Additionally the revised submission includes a zip file containing the R package STAN together with its vignette and user manual We changed the manuscript title to Annotation of genomics data using bidirectional hidden Markov models unveils variations in Pol II transcription cycle We went through the abstract and synopsis accepting essentially all suggested changes Thank you for your kind assistance in the review process Sincerely Achim Tresch An alternative optimization strategy for the M step in the Baum Welch algorithm The original target function Q is T Q 0 0 5 5 G k 1 log ak 5 yolk log const 1 k k lEK t 1 As suggested by reviewer 3 let pij Tiaij Then p and 7 satisfy the conditions mi 0 iEK 2 iEK yes X tiaj 1 5 j j Pij Pji 6 It follows that A and 7 satisfy all conditions of a bdHMM if and only if p and a satisfy the five conditions above We therefore We substitute a by pij T and introduce Lagrange multipliers ug k E K and
8. Molecular Systems Biology Peer Review Process File molecular systems biology Annotation of genomics data using bidirectional hidden Markov models unveils variations in Pol Il transcription cycle Benedikt Zacher Michael Lidschreiber Patrick Cramer Julien Gagneur and Achim Tresch Corresponding author Achim Tresch Max Planck Institute for Plant Breeding Research Review timeline Submission date 04 August 2014 Editorial Decision 26 September 2014 Revision received 24 October 2014 Editorial Decision 17 November 2014 Revision received 19 November 2014 Accepted 21 November 2014 Editor Maria Polychronidou Transaction Report Note With the exception of the correction of typographical or spelling errors that could be a source of ambiguity letters and reports are not edited The original formatting of letters and referee reports may not be reflected in this compilation 1st Editorial Decision 26 September 2014 Thank you again for submitting your work to Molecular Systems Biology We have now heard back from two of the three referees who agreed to evaluate your manuscript Unfortunately after several reminders we have still not received a report from reviewer 2 Since the recommendations of reviewers 1 and 3 are similar I prefer to make a decision now rather than further delaying the process As you will see from the reports below the referees acknowledge that the presented approach is potentially interestin
9. adable software package with acceptable running time They apply the method to the yeast genome and also the human genome with a focus on annotating the molecular transitions observed at transcribed genes In doing so they uncover a very interesting and fundamental diversity of gene types Specifically they find that promoter escape and transcriptional elongation are regulated very differently at genes from different classes They also find that nucleosome depletion which was previously thought to be a feature of transcription termination sites in yeast may actually only mark termination sites that coincide with the promoter of another gene Overall the manuscript describes a timely new method that can be used on a number of different genomic profiling datasets and also shed new light on basic molecular mechanisms of transcription We thank the reviewer for his her appreciation of the mathematical idea behind bdHMMs and its utility for genomics Major comments e If nucleosome occupancy has been profiled in CD4 T cells and I think it has it would be very useful confirm that the conclusions from yeast transcription termination site analysis are also valid in human In our study the analysis of the human dataset is performed to compare bdHMM against HMM To this end we have used the exact same data and data representation binary discretization as in the original study by Ernst and Kellis A thorough analysis of termination in human is
10. carried out simulations from the model learned on the yeast data set Parameters were recovered with high accuracy confirming the validity and stability of our model and EM algorithm We added a Figure Supplementary Figure 9 showing the results of the simulations and refer to it in section Genomic state annotation results in a global strand specific transcription map We are thankful for this suggestion which improved the quality of the manuscript Technical comment e The authors go into length in presentation of the EM convergence analysis and discussion of approximate version believe the following will simplify the presentation and prove the correctness of this approximation First note that while EM with constraints is generally hard equality constraint are easy theta_i theta_j since we can write the likelihood or Q in terms of reduced parameter set that do not contain redundancies Second we can reparameterize a bdHMM with the following parameters theta_ i j a_ ij pi_i and the vector pi To see this not that whenever a_ i j appears in the likelihood simply replace with a_ i j pi_i Given the constraints 2 amp 3 we can formulate the constrains on theta_ i j theta_ i j theta_ j i pi_i sum_j theta_ i j It is also easy to verify that if theta and pi satisfy amp then a and pi satisfy 2 amp 3 Moreover a is a stochastic if and only if sum_ i pi_i 1 Thu
11. certainly interesting However this would require the analysis of an additional data set including nucleosome data and promoter associated transcription factors in human similar to the yeast data we used here We also anticipate that modeling assumptions including the binarization should be reconsidered Altogether we think that the inclusion of another data set and its analysis goes beyond the scope of the manuscript e The comparison to conventional HMM modeling is good because it shows how transcriptional directionality can be inferred by the bdHMM model However it was limited to state transition probabilities because emission probabilities were kept fixed To convince the research community to use this method it would be good to allow emission probabilities to differ that is how the programs will actually be run by users The purpose of fixing all but the transition parameters was to illustrate the conceptual difference between HMMs and bdHMMs that arises from the bdHMM transition constraints only To compare of bdHMM and HMM without any parameter fixing we have now included a quantitative evaluation of its performance for gene boundary prediction on the yeast data set showing that bdHMM outperforms HMM in terms of accuracy of genome annotation see below for details e Also it would be important to see a comparison of annotation accuracy does the bdHMM approach produce more accurate genome annotations than conventional HMMs We t
12. ciated with ribosome biogenesis translation and other house keeping functions More strikingly we found the DNA binding motif of SFP1 a regulator of ribosomal protein and ribosome biogenesis genes to be enriched in promoter state P T1 which is a frequent promoter state of cluster 14 and 38 genes e As far as I can tell the authors do not discuss how they initialized the model number of directional undirectional states or how many random initialization points where used They discuss this in the context of the simulation but it is unclear whether the same procedure was used on the genomic data It seems that this requires non trivial manual tuning to get good results which is worrisome As Referee 1 confirms there is no reliable automatic way to set the number of states For the yeast data the number of directed and undirected states was set manually after experimenting with different state numbers Be aware that bdHMM is used as an exploratory tool in this context As with all unsupervised discretization methods the appropriate number of states depends on the amount of detail one wants to see Indeed parameter initialization is important We found that initialization by k means works very well and generally converges to a higher likelihood than multiple random starts in agreement with Rabiner 1989 reference in the manuscript We therefore advise to use k means for parameter initialization which does not require manual tuning
13. e biochemical literature as well identify events that were missed by direct observations have some technical issues with the presentation of the methods and a comment that believe will simplify that section see below also would appreciate more insights into the biology uncovered by the analysis This will substantially strengthen the confidence in this approach and its usefulness See detailed comments below We thank the Reviewer 3 for carefully studying the mathematical details of the bdHMM and the thoughtful suggestions on their learning which substantially improved the presentation of the model e would appreciate some more insight on the results of the analysis What are the genes that fall into different clusters Do we have a reason to believe they are co regulated e g bet that ribosomal protein genes appear as one cluster And if so does the specific sequence state and their associated observations match the known biology on these regulatory strategies e g SAGA dependent promoters vs TFIlID dependent promoters understand that some answers appear in the supplement I did not read it believe that they should be made more pronounced in the main text We added a short paragraph in section The transcription cycle shows gene specific variation with additional references to the Supplementary Information to underline the biological significance of our findings Indeed cluster 14 and 38 are enriched in genes asso
14. eard back from the two referees who agreed to evaluate your manuscript As you will see from the reports below the referees are overall satisfied with the modifications made and they think that the study is now suitable for publication Reviewer 3 has included a file attached below related to the technical issue raised in his her review of the initial version of the manuscript As such we would ask you to include a comment on this point in a revision of the manuscript Thank you for submitting this paper to Molecular Systems Biology Yours sincerely Reviewer 1 The authors have satisfactorily addressed my comments Reviewer 3 The attached note which I believe resolves their technical issue can be forwarded to the authors I apologize for the typo in my review that lead them to a dead end 2nd Revision authors response 19 November 2014 see next page European Molecular Biology Organization Dear Mrs Polychronidou We are delighted by the acceptance of the paper We thank Reviewer 3 again for his efforts in solving the EM algorithm for bdHMMs analytically Following his suggestions in the previous review we thoroughly investigated a change of variables in the objective function It is encouraging to see that our ansatz is identical to the one proposed by reviewer 3 in his current comment As detailed below it turns out that the Lagrange multiplier approach does not lead to an exact analytical solution Yet it leads
15. erred by the bdHMM model However it was limited to state transition probabilities because emission probabilities were kept fixed To convince the research community to use this method it would be good to allow emission probabilities to differ that is how the programs will actually be run by users Also it would be important to see a comparison of annotation accuracy does the bd HMM approach produce more accurate genome annotations than conventional HMMs Minor comments I completely agree that there is no point in trying to use information theoretic criteria BIC AIC etc to estimate the true number of HMM states Information theoretic approaches typically overestimate the number of states because of over fitting to technical artifacts Trial and error is the only reasonable option Page 2 second paragraph Metagene analysis in spite of this hypothesis It s not clear which hypothesis this sentence refers to After reading the abstract and the first two paragraphs of the Background I did not get a clear idea of which exact problem this paper solves This became clearer only after I was well into the manuscript Perhaps the introductory portions could be reworded for clarity Page 3 The hidden variables form a Markov chain which means that the probability for observing st depends only on st 1 the transition probability Pr st st 1 This is true only for first order Markov chains Same paragraph as above it may be be
16. extension of CUT007 Is CUTO07 already known We have now realized that a large part of this CUT is actually the protein coding gene FUS3 which is expressed in haploid cells The transcription data on which the transcriptome annotation is based YPD Xu et al 2009 stems from diploid cells whereas all remaining data are from haploid cells No there is a short region between transcripts showing no expression CUTO007 is already known We changed the Figure to avoid confusion e Figure 5d Does the SUT not have a well defined termination site Is it polyadenylated Do the authors have a guess for why it was not discovered earlier The SUT is polyadenylated and shows detectable expression but at a too low level for Xu et al 2009 criteria The termination site of this SUT is not very well defined Reviewer 3 e The authors introduce a variant of HMMs suitable for genomic annotation where some states are directional but can appear in either or strand They show how to apply their method to annotate high dimensional genomic data RNA ChIP etc to find the footprint of processes taking place on the genome like the approach There is a nice straightforward thinking about the issues involved in genome annotations for directed processes e g transcription The authors present a useful and lucid analysis of the yeast transcription cycle that highlights locations that deviate from the canonical sequence of events described in th
17. g However they raise a series of concerns and make suggestions for modifications which we would ask you to carefully address in a revision of the manuscript The referees recommendations are clear in this regard On a more editorial level we would like to mention that while we generally encourage the submission of individual Supplementary Figure Table files in exceptional cases and depending on the nature of information provided we allow the use of a single PDF file including a Table of Contents We think that in this case it would be better to present the Supplementary Information in the single PDF file format Thank you for submitting this paper to Molecular Systems Biology Reviewer 1 In this manuscript Zacher et al introduce the concept of bidirectional hidden Markov models European Molecular Biology Organization Molecular Systems Biology Peer Review Process File bdHMMs for inferring the sequence of states that a transcriptional complex for example passes through as it goes from the promoter to the transcription termination site A bdHMM is a special type of HMM that allows identification of pairs of equivalent states that differ only in their directionality This is an excellent idea because the molecular processes occurring on the forward and reverse strands of chromosomes are identical and differ only in direction It makes much more sense to model the genome using bd HMMs Conventional HMMs ignore directionality a
18. hank the reviewer for this suggestion We now compare the accuracy of transcription start site and polyadenylation site annotation of HMMs and bdHMMs on the yeast data set bdHMMs substantially improve TSS annotation whereas pA site annotation is virtually unchanged This analysis clearly confirms the superiority of bdHMM over HMM for genomics data We added a new Figure 3D and discuss these results in section bdHMM state annotation recovers annotated genomic features with high accuracy of the main text Minor comments e Page 2 second paragraph Metagene analysis in spite of this hypothesis It s not clear which hypothesis this sentence refers to We restructured the introduction and removed this sentence e After reading the abstract and the first two paragraphs of the Background I did not get a clear idea of which exact problem this paper solves This became clearer only after was well into the manuscript Perhaps the introductory portions could be reworded for clarity The Introduction Background section was re written in order to present it more clearly e Page 3 The hidden variables form a Markov chain which means that the probability for observing S depends only on S the transition probability Pr s s 1 This is true only for first order Markov chains True although many authors tacitly refer to first order Markov chains when they use the term Markov chain We made this sentence more precise by saying
19. nd therefore necessarily have unrealistic state transition probabilities The authors go to impressive lengths to construct the mathematical framework of bh HMMs which is not at all trivial I would consider this a major conceptual advance They also provide their method as a downloadable software package with acceptable running time They apply the method to the yeast genome and also the human genome with a focus on annotating the molecular transitions observed at transcribed genes In doing so they uncover a very interesting and fundamental diversity of gene types Specifically they find that promoter escape and transcriptional elongation are regulated very differently at genes from different classes They also find that nucleosome depletion which was previously thought to be a feature of transcription termination sites in yeast may actually only mark termination sites that coincide with the promoter of another gene Overall the manuscript describes a timely new method that can be used on a number of different genomic profiling datasets and also shed new light on basic molecular mechanisms of transcription Major comments If nucleosome occupancy has been profiled in CD4 T cells and I think it has it would be very useful confirm that the conclusions from yeast transcription termination site analysis are also valid in human The comparison to conventional HMM modeling is good because it shows how transcriptional directionality can be inf
20. pes the saddle point defined by the uniform distribution it might not be enough to explore solutions that are further from it I would appreciate simulations also from the model learned from the genome That is take the model learned from yeast for example generate data from it and then try to learn from it This simulation will give some intuition how hard it is learn a model such as the one you learned and will give you confidence estimate in the parameters the procedure is essentially parametric jackknife Technical comment The authors go into length in presentation of the EM convergence analysis and discussion of approximate version I believe the following will simplify the presentation and prove the correctness of this approximation First note that while EM with constraints is generally hard equality constraint are easy theta_i theta_j since we can write the likelihood or Q in terms of reduced parameter set that do not contain redundancies Second we can reparameterize a bdHMM with the following parameters theta_ ij a_ ij pi_i and the vector pi To see this not that whenever a_ i j appears in the likelihood simply replace with a_ ij pi_i Given the constraints 2 amp 3 we can formulate the constrains on theta_ ij theta_ i j theta_ j i pi_i sum_j theta_ i j It is also easy to verify that if theta and pi satisfy amp then a and pi satisfy 2 amp
21. s three to four bullet points highlighting the main findings and a thumbnail image 211x157 pixels jpeg format to highlight the paper on our homepage More information is available at http msb embopress org authorguide a4 4 gt The 250 character summary and three bullet points have been included in the header of the revised manuscript The thumbnail image has been uploaded as a part of the resubmission We further went through the MSB checklist and included it in the completed submission form Reviewer 1 e In this manuscript Zacher et al introduce the concept of bidirectional hidden Markov models bdHMMs for inferring the sequence of states that a transcriptional complex for example passes through as it goes from the promoter to the transcription termination site A bdHMM is a special type of HMM that allows identification of pairs of equivalent states that differ only in their directionality This is an excellent idea because the molecular processes occurring on the forward and reverse strands of chromosomes are identical and differ only in direction It makes much more sense to model the genome using bdHMMs Conventional HMMs ignore directionality and therefore necessarily have unrealistic state transition probabilities The authors go to impressive lengths to construct the mathematical framework of boOHMMs which is not at all trivial would consider this a major conceptual advance They also provide their method as a downlo
22. s we are left with three equality constraints 3 and 4 and two sum constraints and From this point it is easy to check that Q in terms of the new parameters is equal to Q of eq 23 and that the maximum of this function is as given in eq 27 Thus the authors are performing exact EM where the internal optimization step has a unique solution i e is convex The reparametrization of the optimization problem by replacing a_ij through theta_ij is a brilliant idea because it removes the generalized reversibility constraints We assume that the reparametrization by theta_ij a_ij pi_i is a typo because it does not satisfy equation We use theta_ij a_ij pi_j instead division by pi_j instead of pi_i Unfortunately the solution procedure proposed by the reviewer does not lead to our approximate update formula because a the approximate update provably does not always return values that exactly satisfy the bdHMM constraints just check numerically and b using theta_ij a_ij pi_j equation does not hold due to the swap of pi_i and pi_j We still think that the suggested reparametrization could lead to an exact solution however we were unable to find such in the short time available We therefore kept our original solution Molecular Systems Biology Peer Review Process File 2nd Editorial Decision 17 November 2014 Thank you again for submitting your work to Molecular Systems Biology We have now h
23. tates i j k to represent state j appearing after i and before k This defines an obvious conjunction function ij k k ij and provides a nice initialization for the model Of course this initialization comes at the price of cubic number of states but these can be easily trimmed down removing rare triplets or simplified by state merging This is an interesting idea for a definition of directed states However it will probably not be practical due to the large number of states that is introduced even after merging Additionally the most likely triplets will be i i i i i k k i i or i k i do not give rise to meaningful directed states Even worse triplets of the kind i j k have an increased chance of being erroneous since the Viterbi path annotation of the HMM should be smooth Finally it is unclear how to initialize the bdHMM emission distributions of a triple i j k The most obvious choice the HMM emission distribution of the state j would produce many states with initially identical emissions We therefore like to stick to our elimination procedure based on k means clustering and the merging of directed states based on the directionality score which works well in practice e Regarding the initialization in that simulation section the authors initialize from a slightly perturbed uniform distribution While this initialization escapes the saddle point defined by the uniform distribution it might not be enough
24. ter and if so does the specific sequence state and their associated observations match the known biology on these regulatory strategies e g SAGA dependent promoters vs TFIJD dependent promoters I understand that some answers appear in the supplement I did not read it I believe that they should be made more pronounced in the main text As far as I can tell the authors do not discuss how they initialized the model number of directional undirectional states or how many random initialization points where used They discuss this in the context of the simulation but it is unclear whether the same procedure was used on the genomic data It seems that this requires non trivial manual tuning to get good results which is wotrisome A useful initialization can be based on standard HMM learning Learn a model and then introduce directional states i j K to represent state j appearing after i and before k This defines an obvious conjunction function i j k k i j and provides a nice initialization for the model Of course this European Molecular Biology Organization Molecular Systems Biology Peer Review Process File initialization comes at the price of cubic number of states but these can be easily trimmed down removing rare triplets or simplified by state merging Regarding the initialization in that simulation section the authors initialize from a slightly perturbed uniform distribution While this initialization esca
25. to explore solutions that are further from it In fact we do not even perturb the uniform distribution transitions and initial state probabilities are initialized exactly uniform The initialization by a uniform distribution for the transition matrix and the initial state is uncritical in particular it does not define a saddle point of the likelihood function for the following reason In case of a uniform transition matrix the forward and backward probabilities in the E step of the EM algorithm entirely depend on the emission distributions The transition probabilities are then updated in the M step based on these forward and backward probabilities This is equivalent to initializing the transition matrix with empirical transition frequencies obtained from a clustering Nonetheless this is a fair concern We provide now more information about the initialization procedure section Initialization of bd HMMs in Materials and Methods Moreover the new simulations see below demonstrate the overall stability of the inference procedure e would appreciate simulations also from the model learned from the genome That is take the model learned from yeast for example generate data from it and then try to learn from it This simulation will give some intuition how hard it is to learn a model such as the one you learned and will give you confidence estimate in the parameters the procedure is essentially parametric jackknife We have now
26. tter to use posterior probabilities of states for genome annotation rather than using the Viterbi path Perhaps the authors could comment on this point Are they using the Viterbi path because annotating genomic bins by their posterior probabilities could cause the inferred state to flip back and forth in an unstable manner End of Page 9 it s not exactly clear what is meant by binary data Is this a reference to discretization European Molecular Biology Organization Molecular Systems Biology Peer Review Process File of the ChIP seq profiles into present absent within each bin End of Page 10 what is the rationale behind the first two symmetry conditions These look more appropriate for describing equilibrium conditions than the initial state My understanding is that the initial state distribution reflects the probabilities of the various states just before entering the beginning of a chromosomal arm It would be good to see some explanation of why these initial state probabilities should obey detailed balance or the initiation symmetry condition Figure 5c is the novel CUT simply an extension of CUT007 Is CUT007 already known Figure 5d Does the SUT not have a well defined termination site Is it polyadenylated Do the authors have a guess for why it was not discovered earlier Reviewer 3 Review of Zacher et al Annotation of genomics data by the bidirectional hidden Markov model variations in Pol II transcription cycle S
27. ummary The authors introduce a variant of HMMs suitable for genomic annotation where some states are directional but can appear in either or strand They show how to apply their method to annotate high dimensional genomic data RNA ChIP etc to find the footprint of processes taking place on the genome Discussion I like the approach There is a nice straightforward thinking about the issues involved in genome annotations for directed processes e g transcription The authors present a useful and lucid analysis of the yeast transcription cycle that highlights locations that deviate from the canonical sequence of events described in the biochemical literature as well identify events that were missed by direct observations I have some technical issues with the presentation of the methods and a comment that I believe will simplify that section see below I also would appreciate more insights into the biology uncovered by the analysis This will substantially strengthen the confidence in this approach and its usefulness See detailed comments below With these caveats in mind and believing that the authors can address them rather easily I recommend acceptance of this paper to MSB Comments I would appreciate some more insight on the results of the analysis What are the genes that fall into different clusters do we have a reason to believe they are co regulated e g I bet that ribosomal protein genes appear as one clus
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