> y{x{ ,bjbjzz .m$$$$d$ "$z||||||$A"$>9&^z 0`pnJ0 1%1% &1%F 1% : To the Editor of peerJ:
We would like to thank both the Editor and the Reviewers for their thoughtful and constructive comments (#2013:04:431:0:0:REVIEW). Based on these, we have made several important changes to the manuscript, and now believe it better represents the kind of careful research published in peerJ. Below we have parsed out and enumerated the comments from the Editor and the two Reviewers. We have addressed each comment separately, and included changes to the text in the response when possible. These changes can also be found in the resubmitted manuscript, per instructions given to us by Jacqueline Thai.
Editors Comments
-E1. Most importantly, I am concerned that the work is not well embedded in the recent literature on the topic. To my understanding, the k-order Markov models you use are equivalent to (k+1)-mer word frequency counting---the representation most commonly used in related previous work. Yet many such relevant studies that are not covered. In particular, there has been previous work identifying the optimal Markov order for phylogenetic inference and numerous results identifying biases beyond trinucleotides.
Thank you for bringing to our attention several additional relevant papers. In our previous submission, we attempted to focus our introduction on patterns only in DNA sequences but, after considering the references you provided, we extended it to include both DNA and protein sequences in our resubmission. Therefore, we have enhanced the introduction and included several additional references. Please note that this comment and our response has significant conceptual overlap with reviewer 2 comments listed under Experimental design. Please see that section for additional discussion on this topic.
Text in the introduction now reads:
Markov models are defined by a transition matrix, which stores the conditional probabilities of the kth symbol following the previous k-1 symbols in a word of length k; they are akin to word frequency counts. Applying this type of analysis to a complete genome sequence provides information about dynamic and stationary statistics that cannot be captured from a single gene or set of genes. One of the first applications of Markov models to the analysis of genetic sequences was their use as a method to identify sequence bias. Pioneering work by researchers including Phillips ADDIN EN.CITE Phillips198755(51)555517Phillips, Gregory J.Arnold, JonathanIvarie, RobertMono-through hexanucleotide composition of the Escherichia coli genome: a Markov chain analysisNucleic Acids ResearchNucleic Acids Research2611-26261561987March 25, 1987http://nar.oxfordjournals.org/content/15/6/2611.abstract10.1093/nar/15.6.2611( HYPERLINK \l "_ENREF_51" \o "Phillips, 1987 #55" 51) Rocha ADDIN EN.CITE Rocha199856(55)565617Rocha, Eduardo P. C.Viari, AlainDanchin, AntoineOligonucleotide bias in Bacillus subtilis: General trends and taxonomic comparisonsNucleic Acids ResearchNucleic Acids Research2971-298026121998June 1, 1998http://nar.oxfordjournals.org/content/26/12/2971.abstract10.1093/nar/26.12.2971( HYPERLINK \l "_ENREF_55" \o "Rocha, 1998 #56" 55), and Burge and Karlin ADDIN EN.CITE Burge199254(13)545417Burge, C.Campbell, A. M.Karlin, S.Department of Mathematics, Stanford University, CA 94305.Over- and under-representation of short oligonucleotides in DNA sequencesProc Natl Acad Sci U S AProc Natl Acad Sci U S A1358-628941992/02/15AnimalsBase Composition*Base SequenceDNA/*chemistryDNA, Bacterial/chemistryDNA, Mitochondrial/chemistryDNA, Viral/chemistryHumansMolecular Sequence DataOligodeoxyribonucleotides/chemistry1992Feb 150027-8424 (Print)
0027-8424 (Linking)1741388http://www.ncbi.nlm.nih.gov/pubmed/174138848449eng( HYPERLINK \l "_ENREF_13" \o "Burge, 1992 #54" 13) established that Markov analysis of DNA sequences can be useful in identifying over- and under-represented sequences. Work by Elhai ADDIN EN.CITE Elhai200157(20)575717Elhai, J.Elhai, J
Univ Richmond, Dept Biol, Richmond, VA 23173 USA
Univ Richmond, Dept Biol, Richmond, VA 23173 USA
Univ Richmond, Dept Biol, Richmond, VA 23173 USADetermination of bias in the relative abundance of oligonucleotides in DNA sequencesJournal of Computational BiologyJ Comput BiolJournal of Computational BiologyJ Comput BiolJournal of Computational BiologyJ Comput Biol151-17582compositional biasgenomegc compositionpalindromerestriction/modificationwordsrestrictiongenomesbacterialsystemscounts20011066-5277ISI:000169793200004<Go to ISI>://000169793200004Doi 10.1089/106652701300312922English( HYPERLINK \l "_ENREF_20" \o "Elhai, 2001 #57" 20) compared several different statistical methods of finding bias in the relative abundance of oligonucleotides in DNA sequences. All these methods were based on comparing observed oligonucleotide frequencies to their expectation under several models, and all concluded that Markov model based methods underperformed some more complex methods, when the purpose of the method was to determine abundance.
Determining relative abundance is not the only reason for examining DNA sequences, however, and when looking for other patterns an empirically derived Markov model does contain valuable information...
In addition, we included additional comparisons to previous studies to the Results section of the manuscript.
E2. On page 11 "similarity trees constructed on matrices derived from these correlations are in good agreement with 16S RNA trees". Given that the agreement is at best for ~25% of the split, this is an overstatement.
We believe that we did not clearly state our hypothesis and the reasons for performing the comparison between trees. Our comparison was meant to test if the two trees were completely unrelated, or if there was any statistically significant overlap between the trees that would indicate a relationship. Our original hypothesis was that the two trees would be related, but that the overlap would be small enough that we would have to provide rigorous statistical proof to support our conclusions. We never expected the two trees to be anything close to identical, and in fact a ~25% overlap was much better than our highest expectations. We believe that our own enthusiasm for these better-than-expected data influenced our description.
In the manuscript we did attempt to carefully explain our observations (see Determination of tree similarity in Methods for this explanation). We stated the following A direct method of assessing tree similarity comes from set theory and is referred to as the symmetric difference ADDIN EN.CITE Robinson1981168(52)16816817Robinson, D. F.Foulds, L. R.Robinson, Df
Univ Canterbury,Dept Math,Christchurch,New Zealand
Univ Canterbury,Dept Math,Christchurch,New ZealandComparison of Phylogenetic TreesMathematical BiosciencesMath Biosci131-147531-219810025-5564ISI:A1981LB66300008<Go to ISI>://A1981LB66300008English(52). The symmetric difference of a tree structure is the total number of partitions that differ between the two trees. We used the percent symmetric difference, which is the symmetric difference (Ds) divided by the maximum symmetric difference (Dmax), with Dmax H" 2n-6 for n-number of taxa. The significance of Ds for a given number of taxa can be estimated empirically, and is shown to be asymptotic, with a convergence rate dependent on n ADDIN EN.CITE Steel1993147(60)14714717Steel, Mike A.Penny, DavidDistributions of Tree Comparison Metrics--Some New ResultsSyst Biol126-1414221993June 1, 1993http://sysbio.oxfordjournals.org/cgi/content/abstract/42/2/12610.1093/sysbio/42.2.126(60). For n = 30, any Ds < (Dmax - 2) is significant, with p < 0.01. We did not change this text because we believe it to be accurate.
However, we have re-stated our observations to read similarity trees constructed on matrices derived from these correlations have a statistically significant overlap with 16S rRNA trees". We believe this more accurately reflects the data and analysis.
Typos:
Our sincere apologies. Clearly, we (the authors) had re-read this paper enough times that we were skipping over our own typos. We have had the re-submitted manuscript proofread by a third party, and hopefully we have removed any remaining typos.
________________________________________
Reviewer Comments
Reviewer 1
Comments for the author
The paper performs a large-scale Markovian analysis of 906 bacterial genome sequences. The main conclusion is that the genome sequences exhibit Markov property beyond the second-order, which places significant constraints on probable bacterial nucleotide sequences.
Overall, the technique employed is sound and the conclusion is valid. While the study of sequence comparison in bacteria is not new and the conclusion is not surprising, the few results on the differences between the tree constructed from 16S rRNA sequences and the transition tree constructed from whole genome sequences are interesting.
We are glad that Reviewer 1 thought our techniques and conclusions were valid. We agree with Reviewer 1 that sequence comparison by these methods is not novel, and we tried to provide sufficient background in the Introduction so that the reader would understand this manuscript within the context of the substantial amount of previous work. However, almost all of that work was done when there was much less sequence available, and we believe our re-analysis provides some important insight. We believe that is what Reviewer 1 meant in the last sentence of the review.
Reviewer 2
Basic reporting
In general the manuscript is readable but there are some problems with clarity. For example
R2-1: L147 "accepted trace of phylogeny" - What is a "trace of phylogeny" is it not just the accepted phylogeny?
This now reads Branching patterns of trees based on alignments of 16S ribosomal RNAs are an accepted method to represent phylogeny
R2-2: L75 "and for a review (28)" - this does not make sense in the rest of the sentence
Further some things have not been fully described, for example sequence length for the bacterial sequences is not given.
We have made L75 a complete sentence, and Supplemental Material S1 now includes sequence length.
R2-3: There are also a few typos
The re-submitted manuscript was proofread by a third party. Please refer to the response to Editors comments for additional discussion.
Experimental design
R2-4: It is not clear why Markov Chains of different orders have been chosen to model this data. The previous study by Pride uses a 0th order model built on tetramers. This is basically a k-mer counting approach which has also been used previously for phylogenetic tree building. There is no explanation in the manuscript why the different order Markov Chain models would be better than k-mer counting for different k values. As the different order Markov Chains shown here have not been shown to be used elsewhere or shown to be better than previous methods it would be useful to show simulations exhibiting that this is a viable method, and indeed that it is better than a k-mer counting method (or citations which show this).
We have added the following paragraph to the Result and Discussion section in an effort to clarify the our original hypotheses and the intent of the work
The goal of this work is not to devise a new or improved method of phylogenetic inference, or to imply that Markov models are superior to other methods. Rather, our goal is to address the following three questions 1) is there a universal Markov property present in whole bacterial DNA sequences; 2) to what extent (order) does this property hold true; and 3) is the existence of the Markov property biologically relevant.
Our choice of simple Markov models (based on conditional probabilities of k-mer counts), as opposed to those normalized to remove bias answered 1. The exploration of different order Markov models answered 2. Our application of the transition matricies to creating a phylogenetic tree was in response to 3.
R2-5: It is also not shown whether the sequence lengths of the bacterial chromosomes (which are not given) have an effect on the accuracy of the model, and then a further effect on the tree.
The Markov models are derived from the sequences themselves, they are not estimated. In order to infer a meaningful tree, it is necessary to have a rich distance matrix, which in turn, requires rich transition matrices. There are two conditions that can lead to a sparse transition matrix. First, insufficiently long sequence length (a lot of missing k-mers) and second, a heavily biased sequences ( a lot of missing k-mers with biased G+C content). Of course, the worst case is sequences with property one and two (e.g. Buchnera aphidicola), even in those cases, a practical third-order Markov model exists. We have abated these conditions by using both strands of DNA, and by limiting the analysis to a maximal order model of 5th. The choice to terminate the analysis at k=5 is not arbitrary. The statistical analyses of the models are based on the chi-square statistic, which is appropriate for count data with a minimum expected frequency of 5. Even the shortest sequence in this study (Candidatus hodgkinia cicadicola) has an expected frequency of ~35.
R2-6: It is not clearly explained why if the order of the Markov models was increased indefinitely then the subsequent tree topologies would eventually converge. And equally it is not clear what they would converge to. I would have thought that increasing the order of the Markov models will lead to sparse transition matrices (as suggested on line 142) which may make building trees from them difficult.
This statement clearly had interpretations that were not intended. We have modified the paragraph for better clarity. It now reads
Of course, if we continued to increase the order of the Markov models indefinitely, the subsequent tree topologies produced by k-1 and k order models would eventually converge. This is due to the increasingly sparse transition matrices. For a given sequence, the transition matrix would approach the null set, with only two elements populated (that corresponding to (1n-1) and to (2n) for a sequence of length n) with a frequency count of 1.The resulting distance matrix, based on the sparse transition matrices, will reach steady-state..
R2-7: The methods used for building the 16S rRNA tree have not been justified, for example why has the F84 distance measure been chosen. I assume neighbor-joining was used due to the large number of sequences but this has not been stated. As it is known that different bacteria have different GC contents then it may make sense to use a phylogenetic method that takes this, or other known features, into account.
We have modified the Materials and Methods section by adding the following:
We chose to use the F84 distance method because, unlike other methods (e.g. Jukes and Cantor's ADDIN EN.CITE Jukes196964(33)646417Jukes, TH.Cantor, CR.Evolution of Protein MoleculesNew York: Academic PressNew York: Academic Press21-1321969( HYPERLINK \l "_ENREF_33" \o "Jukes, 1969 #64" 33) and K80 ADDIN EN.CITE Kimura198061(40)616117Kimura, M.Kimura, M
Natl Inst Genet,Mishima,Shizuoka 411,Japan
Natl Inst Genet,Mishima,Shizuoka 411,JapanA Simple Method for Estimating Evolutionary Rates of Base Substitutions through Comparative Studies of Nucleotide-SequencesJournal of Molecular EvolutionJ Mol EvolJournal of Molecular EvolutionJ Mol EvolJournal of Molecular EvolutionJ Mol Evol111-12016219800022-2844ISI:A1980KW57300003<Go to ISI>://A1980KW57300003Doi 10.1007/Bf01731581English( HYPERLINK \l "_ENREF_40" \o "Kimura, 1980 #61" 40), it allows for both unequal base frequencies and unequal transition/transversion probabilities. The base frequencies and transition/transversion probabilities are estimated from the data, and the distances can be interpreted as a maximum likelihood estimate of the divergence time; this provides an accurate representation of bacterial sequence dynamics. Each replicated distance matrix was clustered using the Neighbor-joining method ADDIN EN.CITE Saitou1987243(56)24324317Saitou, NNei, MThe neighbor-joining method: a new method for reconstructing phylogenetic treesMol Biol Evol406-425441987July 1, 1987http://mbe.oxfordjournals.org/cgi/content/abstract/4/4/406( HYPERLINK \l "_ENREF_56" \o "Saitou, 1987 #243" 56). Neighbor-joining was used because of its speed and accuracy when given a correct distance matrix.
Validity of the findings
R2-8: There are two big claims in the manuscript. Firstly that "the existence of a third order Markov Process in bacterial chromosomes is most likely universal", and secondly that "transition matrix usage is conserved in taxa". The first claim does not seem to be justified by the data in the manuscript. The fact that a 3rd order model gives a transition tree a lot closer to the phylogenetic tree than a lower order model, and that then increasing the order further does not make greater improvements, does not show that "in nearly all bacterial chromosomes there is a significant long-range nucleotide correlation that extends beyond the 2nd order". This shows as a whole there is evidence of 3rd order effects, but there is no way of knowing that all bacterial chromosomes show this effect.
These claims were justified in the text, and we are not certain if the reviewer is challenging these justifications, or if the explanations of the methods were unclear to the reviewer. The claim that "the existence of a third order Markov Process in bacterial chromosomes is most likely universal" is based on the Statistical rule of three, which gives a 95% confidence interval for the rate of occurrence of an event in a population based on the rate of occurrence in a sample. Formally, if the rate of occurrence of an event (r) in n subjects is zero, then the 95% CI is [0, 3/n]. In terms of the data described in the manuscript, n=906, r=906 so we can be 95% confident that fewer than 1 in 906/3 will not have the Markov property, or alternately no less than 301 in 302 will have the property.
The rule of three is based on rigorous statistics, and is applicable in cases where a significant majority of the data is not available (such as ours).
The Conclusions section discusses this in the following statement:
Using the statistical rule of three, we can be 95% confident that the rate of this phenomenon is no less frequent than 301 in 302 bacterial chromosomes
The claim that transition matrix usage is conserved in taxa". Is based on the comparative analysis of he phylogenetic trees. The basis of which is the very significant overlap between the 16S rRNA tree and the transition tree. Please see our response to Editors comments for additional discussion on this topic.
R2-9: The manuscript later acknowledges that testing Markovidity in this data is very difficult but they have done some statistical tests to show Markovidity. They have however not shown any data for this. As the Markov property is the crux of all their claims much more evidence needs to be shown to prove they have indeed found it. Also the fact that proving Markovidity is difficult should be acknowledged when large claims are made and not only mentioned later on.
We have added the following subsection to the Materials and Methods section Testing for Markovity which describes the statistical theory and procedures used in this work to substantiate our claims about Markovity. We have also included the results of this analysis.
R2-10: A number of the biological explanations for differences between the 16S rRNA phylogeny and the 3rd order transition tree are unconvincing. Why does the fact that Shigella and Escheria sequences are homologous explain the fact that they are shuffled in 16s rRNA tree and not the transition tree. Also why does the nucleic acid content between two groups of Streptococci show up in a 3rd order tree and not in the phylogeny. Dos this indicate that the method used to build the phylogeny could be improved to take this into account?
Whole sequence Markov analysis is more sensitive to biases than 16s rRNA. In fact, 16s rRNA is used for phylogenetic (and other) analyses because it is known to be conserved. The fact that a phylogeny based on whole sequence Markov analysis is able to better discriminate between organisms with distinct sequences biases better than 16s rRNA based methods is an important difference between the two approaches.
We have made the following changes to clarify this:
The 16S rRNA sequences of Shigella and Escherichia are very homologous, and this results in some species from each genera being shuffled within the 16S rRNA tree as opposed to the transition tree, which is more sensitive to sequence bias. This shuffling is not observed in the transition tree
In addition to the changes made to address concerns by the editor and reviewer, we have made wq
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