Estimation of redundancy in microbial genomes

Estimation of redundancy in microbial genomes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Estimation of redundancy in microbial genomes Jon Bohlin, John H.-O. Pettersson, John H.-O. Pettersson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4597889/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background Microbial genomes vary considerably both with respect to size and base composition. While the smallest genomes have less than 200,000 base pairs, or nucleotides, others can consist of millions. The same is true for genomic base composition, often summarized as genomic AT or GC content due to the similar frequencies of (A)denine and (T)hymine on one hand and (C)ytosine and (G)uanine on the other; the most extreme microbes can have genomes with AT content below 25% or above 85%. Genomic AT content influences the frequency of DNA words, or oligonucleotides, consisting of multiple nucleotides. Here we explore to what extent genome size, AT/GC content and genomic oligonucleotide usage variance (OUV) are linked to microbial genome redundancy, or compression rate, as measured using both a DNA based- (MBGC) and a general purpose (ZPAQ) compression algorithm on 4,713 RefSeq genomes. Results We find that genome size (p < 0.001) and OUV (p < 0.001) are both strongly associated with genome redundancy for both types of file compressors. The DNA based MBGC compressor managed to improve compression with approximately 3% on average with respect to ZPAQ. Moreover, MBGC detected a significant (p < 0.001) compression ratio difference between AT poor and AT rich genomes that was not detected with ZPAQ. Conclusion As lack of compressibility is equivalent to the presence of randomness, our findings suggest that small and AT rich genomes may have accumulated more random mutations on average than larger and AT poor/GC rich genomes, which, in turn, were significantly more redundant. Moreover, we find that OUV is a strong proxy for genome compressibility in microbial genomes. The ZPAQ compressor was found to agree with the MBGC compressor, albeit with a poorer performance, except for the compressibility of AT-rich and AT-poor genomes. Figures Figure 1 Figure 2 Figure 3 Figure 4 Background Microbial genomes vary substantially with regards to genome size and base composition [ 1 ]. Due to Chargaff’s parity rules [ 2 ], base composition in microbes can be summarized as the percentage % of (A)denine% + (T)hymine% (%AT), due to their similar frequencies. Alternatively, it can be summarized as 100% - (%AT) = (G)uanine% + (C)ytosine% (%GC). In general, genomic %AT (AT) is negatively associated with genome size [ 3 ]. Within microbial species however, genomic AT has been found to increase with genome size [ 4 ]. While free-living and soil dwelling microbes tend to have larger genomes with less AT (GC rich) [ 5 ] intracellular symbionts [ 6 ], and to a lesser extent pathogens [ 7 ], have small, AT rich genomes due to reductive evolution [ 8 ]. A negative association has also been found between genomic AT content and oligonucleotide frequencies, sometimes referred to as oligonucleotide usage variance (OUV) [ 9 , 10 ], i.e. genome-wide frequencies of ‘DNA words’ consisting of a fixed number of nucleotides (usually 3 (codons) [ 11 ] or 4 (tetranucleotides)) [ 10 ]. OUV is the averaged sum of the squared differences between all possible genomic tetranucleotide frequencies subtracted by their corresponding expected tetranucleotide frequencies. As such, OUV literarily describes the variance of genomic tetranucleotide frequencies. The expected tetranucleotide frequencies are estimated by the respective tetranucleotide word’s individual genomic nucleotide frequencies. That is, if f(AGCT) represents the genomic frequencies of the tetranucleotide word ‘ AGCT ’ then the estimated expected frequency of the word ‘ AGCT ’ will be f(A)f(G)f(C)f(T) . OUV thus represents the average squared difference, or variance, taken over the frequencies of all 4 4 = 256 possible combinations of tetranucleotide words subtracted by the expected occurrence of the corresponding tetranucleotide, e.g. ( f(AGCT) – f(A)f(G)f(C)f(T) ) 2 . Genomes with biased tetranucleotide frequencies, for one reason or another, will have higher OUV as some DNA words will differ greatly from what is expected from the base composition (i.e . AT/GC content) alone. High OUV will thus likely represent genomes having been subjected to strong selective pressures, either positive or negative [ 12 ]. Organisms with low OUV, i.e. oligonucleotides that are more predictable from genomic base composition, have been subjected to more relaxed selective pressures [ 12 ]. It has been shown that AT rich genomes tend to consist of oligonucleotides that are easier to estimate using single nucleotide frequencies and thus tend to have lower OUV than AT poor microbes [ 10 ]. AT poor (sometimes referred to as GC rich) microbes, on the other hand, often have more selective tetranucleotide word usage than AT rich ones resulting in higher OUV [ 12 ]. These discrepancies between AT rich and AT poor genomes, with respect to genome-wide tetranucleotide word frequencies, have been linked to selective pressures [ 10 ]; AT rich genomes appear historically to have been subjected less to selective pressures than AT poor genomes [ 13 , 14 ]. For microbial symbionts, which are often AT rich, this might be, to some extent, explained by easier access to metabolites from the host [ 15 ]. It is also anticipated that genomes being subjected to relaxed selective pressures, such as symbionts, may accumulate genome-wide mutations to a larger degree than organisms subjected to strong selective pressures [ 6 ]. Accumulation of genome-wide random mutations is therefore assumed to result in tetranucleotide word frequencies more in line with AT/GC content [ 16 ]. As mentioned above, AT rich genomes have often been found to be more host associated and pathogenic with the latter having slightly larger genomes. AT poor genomes are often found in environments outside of the host [ 11 ]. Since genomic AT content correlates negatively with nitrogen abundance [ 17 ] many microbial species with AT poor genomes are often found in soil [ 11 ]. Hence, it is assumed that OUV differences are reflective of the selective pressures mediated by the respective environments [ 16 ]. Non-host environments are likely challenging requiring a diverse set of genes for utilizing different types of nutrients for survival. Stronger selective pressures, in particular purifying selection and frequent bottleneck events, may therefore favor species that are more competitive with the ability to survive in diverse and dynamic environments. Under such circumstances, there could be a strong selection for more specific DNA patterns resulting in more biased genome-wide tetranucleotide word frequencies, reflected by higher OUV [ 18 ]. Genome-wide oligonucleotides are more easily compressed if they exhibit some degree of systematic bias. Bias resulting from selection for specific genome-wide DNA patterns is reflected by higher OUV [ 18 ]. The genomes of such organisms could be easier to compress than organisms with low OUV that do not show any genome-wide DNA patterns. In this sense, AT poor genomes, with higher OUV, are expected to have a greater degree of redundancy than more AT-rich genomes. The most common general-purpose compression algorithm (often referred to as LZ after the inventors Abraham Lempel and Jacob Ziv [ 19 ]) attempts to reduce a string of data by searching for repeating patterns or sub-strings and extending these as much as possible. Repeating substrings or patterns are then replaced by smaller symbols, thereby reducing string size. Finally, a dictionary containing the symbols representing specific sub-strings is added to the compressed file for use in decompression. If a string contains many different patterns that require symbols of varying size for representation the Huffman algorithm will ensure that the most frequent patterns, or sub-strings, are assigned progressively shorter representations [ 20 ]. The size of such representations therefore correlates negatively with occurrence frequency. Hence, strings consisting of many repetitive patterns are easier to compress than strings containing fewer such patterns [ 19 ]. Most modern general-purpose compressors consist of several algorithms and steps to reduce the size of a string of data [ 21 ]. Recently, compression algorithms were introduced that take DNA specific properties into account [ 21 ]. In particular, the Multiple Bacterial Genome Compressor (MBGC) considers DNA patterns and their reverse complements as identical [ 22 ]. As such, MBGC achieves a greater compression ratio than other compressors by only requiring one symbol to represent each DNA pattern and its reverse complement. In theoretical computer science, an equivalence relation has been established between compressibility and a definition of randomness [ 23 ]; the more random and unpredictable a string of letters (such as A, G, C and T) is, the harder it is to compress. A string consisting of a few substring patterns is therefore more difficult to compress. As such, by exploring the redundancy of microbial genomes using AT content and OUV, a measure of genomic randomness (i.e. accumulated mutations) is also attained. Since AT content in microbial genomes is, in one way or another, associated with genome size and OUV, the purpose of this project was to explore whether this association could also be extended to genome redundancy. More specifically, is there an association between AT, genome size and OUV on one hand and the compressibility of a microbial genome on the other? To test this hypothesis, 4,713 microbial genomes, representing 1,508 bacterial genera, were downloaded from the NCBI RefSeq database to minimize species- and strain-specific bias. These genomes were compressed using two different algorithms: ZPAQ, which is widely regarded as the best general purpose compression algorithm [ 21 ] and MBGC, a recent compression algorithm specialized for microbial genomes [ 22 ]. The compression rates obtained from both these algorithms for the 4,713 RefSeq genomes were subsequently regressed on corresponding genomic AT content, OUV and genome size. The models were also adjusted for taxonomic relatedness. Results We first explored whether there was any association between genome compression ratio for the ZPAQ algorithm on one hand, and AT content, genome size and OUV on the other (see Fig. 1 ). A generalized additive mixed-effects model (GAMM) was fitted with ZPAQ compression ratio as the outcome and genomic AT content, genome (chromosome) size and OUV as predictors represented by splines, to compensate for putative non-linear trends, for all 4,713 genomes. In addition, taxonomic genus was added as a random effect with respect to genome size, which was established by examining Akaike Information Criterion (AIC) differences between tested models (see Materials and Methods for details). The GAMM model indicated that there was a positive association between ZPAQ compression ratio and the three smooths representing respectively genomic AT content ( p < 0.001 ), genome size ( p < 0.001 ) and OUV ( p 1 indicates non-linearity), with respective edf = 6.3 and edf = 7.1. OUV, on the other hand, did not exhibit any non-linear trends (edf = 1) and was found to be positively associated with ZPAQ compression rate. The AIC for this model was − 3,082 as compared to AIC = -2,053 for the model with the same predictors but without the random slope effects ( i.e. lower AIC is better). The AIC for the null model (the outcome regressed on a constant) was − 725. An additional GAMM model was fitted with the same predictors and random effects as for the ZPAQ compression model above but with the MBGC compression rate as the outcome instead (see Fig. 2 ). Again, both AT content and genome size were found significant ( p < 0.001 ) with considerable non-linear splines: edf = 7.1 and edf = 7.5, respectively. For this model, non-linear trends were also observed for the smooth representing the OUV predictor (edf = 2.0). Once more, the model obtained a better AIC (-2,997) when a random slope of genome size with respect to genus was included in addition to the fixed effect predictors AT, genome size and OUV. For the same model but without the random slope AIC = -1,993 and AIC = 445 for the null model (only outcome). It can be seen from both Figs. 1 and 2 that while there is a clear positive association with respect to genome size and OUV on one hand and for both ZPAQ and MBGC genome compression ratios on the other, the trend with regards to AT content is less clear due to the parabolic trend. Not only does Fig. 3 indicate that MBGC is, on average, better at compressing genomes than the ZPAQ algorithm but also that AT poor/GC rich genomes are considerably better compressed with the MBGC method. To assess the difference between the compression algorithms more formally, the GAMM model with MBGC as the outcome was refitted but now with the ZPAQ compression rate as an additional linear predictor, leaving the rest of the model, as described above, unchanged. AIC improved considerably with − 21378.28 for this model (the AIC null is the same as for the MBGC model described above).. Figure 4 shows an approximate linear relationship between the compression ratios of MBGC and ZPAQ ( p < 0.001 ) and that there is a largely negative association between MBGC compression rate and AT content ( p < 0.001 ), suggesting that compression of AT poor genomes is visibly improved with the MBGC algorithm as compared to the ZPAQ algorithm. Slight improvements over the ZPAQ algorithm can also be observed for genome size and OUV. Excepting the ZPAQ compression ratio, which was assumed to be linear, AT content, genome size and OUV were all non-linear terms with edf equal to 7.7, 8.3 and 4.9, respectively. It can also be noticed in Fig. 4 that the red dashed line, which represents a regression line with slope 1 and intercept 0, was slightly lower than the (blue) regression line, which represents the model intercept ( p < 0.001 ) for the MBGC compression ratio regressed on the ZPAQ compression rate (and adjusted for the other predictors and the random slope effect mentioned above). The model intercept indicates that the MBGC compressor achieves, on average, a 0.15 compression ratio improvement (approximately 3%) over the ZPAQ compressor for microbial genomes. Discussion OUV is a measure of genomic oligonucleotide frequency discrepancy from what is expected based only on the corresponding genomic nucleotide frequencies ( i.e. genomic AT content). Surprisingly, OUV exhibited a strong correlation with both ZPAQ and MBGC compression ratios (see Figs. 1 and 2 ). Higher values of OUV indicate that oligonucleotide frequencies deviate from expected based on the corresponding individual nucleotide frequencies. Low OUV, on the other hand, suggests that oligonucleotide frequencies are more predictive from the corresponding individual nucleotide frequencies. Low OUV may thus be indicative of genomes whose oligonucleotides have historically been subjected to reduced selective pressures as compared to those with high OUV. Alternatively, low OUV may also, at least to some extent, be reflective of genomes with a higher number of accumulated, presumably random, mutations. Systematic bias in oligonucleotide usage may facilitate compression, particularly for the oligonucleotides that occur more frequently than expected. From the results presented here for the MBGC compression rates this appears to be more prevalent in AT poor genomes as seen in Figs. 3 and 4 . Indeed, a negative association has previously been found between OUV and AT content both within [ 24 ] and between genomes [ 10 ]. In general, AT poor/GC rich genomes appear to have more similar oligonucleotide usage [ 25 ]. As mentioned previously, biased genome-wide oligonucleotide usage facilitates compression, something that appears to be reflected in the results presented here. The fact that MBGC compressed AT poor genomes better than ZPAQ indicates that oligonucleotides occur with similar frequency to their reverse complements increasingly more than for AT rich genomes. Hence, biased occurrence of genomic oligonucleotides is increasingly more similar to the occurrence of the corresponding reverse complemented oligonucleotides in genomes with increasingly less genomic AT. As mentioned above, since OUV is lower in AT rich genomes, oligonucleotide frequencies are more similar to individual nucleotide frequencies. In other words, genomic nucleotide frequencies tend to be more predictive of the genomic oligonucleotide frequencies. This could potentially indicate that species with AT rich genomes have historically accumulated more mutations than species with AT poor genomes. Weaker purifying selection may thus have resulted in accumulation of mutations in AT rich genomes to a much larger extent than in AT poor genomes. The performance of the ZPAQ algorithm was on average inferior to the MBGC algorithm and no compression rate differences could be detected between AT rich and AT poor genomes. Both ZPAQ and MBGC algorithms are similar [ 22 ], except for the fact that MBGC treats oligonucleotides and their reverse complements as identical. The difference in compression rate observed with MBGC between AT rich and AT poor genomes must therefore point to trend differences in oligonucleotide usage. More specifically, AT poor genomes appear to have more similar frequencies of abundant oligonucleotides and their reverse complements than AT rich genomes. For both compression algorithms, the lowest compression rates were nevertheless obtained for the genomes with similar AT/GC content ( i.e. %AT/%GC approaching 50%), likely because more oligonucleotide frequencies are less predictable due to the similar nucleotide frequencies. AT rich genomes tend to have smaller genomes. The reason is not completely understood, but as was seen in Figs. 1 and 2 the smaller genomes are also harder to compress, at least those with genome sizes below 2 million base-pairs (mb). Symbionts and pathogens often have such small genomes due to genome reduction [ 6 ]. Reduction in genome size is often preceded by an accumulation of mutations, that go hand in hand with increased AT content and number of pseudogenes [ 6 ]. The reason that mutation accumulation is often positively associated with AT content is that most mutations are in the direction from Cytosine to Thymine [ 13 ]. AT poor genomes, however, are often found outside hosts and have larger genomes with a more diverse set of genes [ 26 ]. An important difference between Adenine and Thymine base-pairs on one hand and Guanine and Cytosine base-pairs on the other is that the latter pair requires three hydrogen bonds instead of two for the former. Hence, G-C base-pairs are stronger than A-T base-pairs but require more stacking energy [ 15 , 27 ]. This suggests that genomic AT content is, at least to some extent, also a manifestation of selective pressures, or lack thereof, having historically acted on a species’ genome [ 26 , 27 ]. Formal definitions of the concept of randomness are relatively recent [ 23 ]. It has been shown that randomness is equivalent with compression [ 28 ]; the more random a string of characters is, the harder it is to compress and vice-versa. Random sequences are also connected to the notion of information. The more random a string of characters is the less information it contains ( i.e. entropy increases) [ 29 ]. It is shown here that microbes with smaller genomes are harder to compress than microbes with larger genomes. Moreover, AT poor genomes are easier to compress than AT rich, at least with the MBGC compression algorithm. Finally, OUV, which is a measure strongly connected to information and entropy [ 18 ], is positively associated with compression rates. As such, smaller AT-rich genomes with lower OUV, appear to contain less information, at least with respect to Shannon entropy [ 18 , 29 ], than larger AT poor/GC rich genomes with higher OUV. Conclusion We demonstrate here that microbes with smaller genomes tend to be harder to compress than microbes with genome sizes approximately above 2 mb. Moreover, we found a clear and surprising positive association between OUV and compression rate suggesting that increasing oligonucleotide usage variance is a proxy for genome redundancy in microbes. Since the OUV measure is related to Shannon entropy, there is a positive association between genome redundancy and information content. The MBGC method compressed microbial genomes to a higher rate than the ZPAQ algorithm, on average. Moreover, MBGC compressed AT poor genomes significantly better than the ZPAQ compressor. The MBGC algorithm's ability to obtain a progressively higher compression rate for genomes with decreasing AT content is likely because the method considered both oligonucleotides and their reverse complements as equals. These findings suggest that organisms with AT poor/GC rich genomes have higher than expected occurrences of particular oligonucleotides and their respective reverse complements than AT rich genomes. Since compression is tightly linked to randomness, smaller, AT rich genomes with low OUV appear to have accumulated more random mutations, on average, and thus exhibit less information potential, than microbes with larger, AT poor genomes and higher OUV. Methods In total 4,829 microbial genomes were downloaded from NCBI’s RefSeq database [ 30 ] ( https://www.ncbi.nlm.nih.gov/refseq/ ) on February 23, 2024. To obtain a prokaryotic population consisting of as representative samples as possible only RefSeq genomes were considered. The genomic data consisted mostly of one genome from each species, excepting only species with substantial genomic differences, within a genus. There were 114 samples of the species Wolbachia endosymbiont , of which 113 were removed to reduce bias from a single species. Three additional genomes were removed due to an unusually high number of repeats resulting in over 30 times compression ratios for both ZPAQ and MBGC compressors. The exceedingly high compression ratios negatively impacted model assumptions and were therefore removed. These included an unnamed endosymbiont of the deep-sea mussel Bathymodiolus septemdierum (accession: AP013042.1), Enterobacter lignolyticus (CP012871.1) and E. ludwigii (CP017279.1). In total, 4,713 genomes were available for analysis. All plasmids were removed from all species/genomes so that only chromosomes were used for the downstream analyses. Genomes consisting of multiple chromosomes were concatenated into one file. All data needed to reproduce the results reported have been included in Additional file 1. The genomes were compressed into ZPAQ format using ‘lrzip’ v.0.651 with the –zpaq option [ 21 ]. For the MBGC compressor, ‘mbgc’ v.1.2.1 [ 22 ] was used ( https://github.com/kowallus/mbgc ). Compression ratio was calculated as genome ( i.e. total chromosome) size / compressed file size for each genome and for both compressors. The AT content, OUV and genome size of these genomes were computed from in-house scripts; AT content as the number of A + T nucleotides / total number of A + T + G + C nucleotides. Genome size was calculated as the total number of nucleotides. OUV was calculated as the average ratio of genomic tetranucleotide frequencies divided by the multiplication of the corresponding nucleotide frequencies. That is, $$OUV={\sum }_{XYZW}^{}\left(\frac{f\left(XYZW\right)}{f\left(X\right)f\left(Y\right)f\left(Z\right)f\left(W\right)}\right)$$ where ‘ XYZW ’ represents nucleotides for every possible genomic tetranucleotide from the alphabet A , G , C and T (e.g. f(ATGC) / f(A)f(T)f(G)f(C) ). To explore whether genomic compression ratio, from either ZPAQ or MBGC algorithms, was associated with genome size, AT content and OUV we employed generalized additive mixed effects models (GAMM) [ 31 ] to account for putative non-linear associations between outcome and predictors and non-constant variance differences between phylogenetic groups. It has previously been demonstrated that adding a taxonomic group below genus level has little impact on the models focusing on genomic base composition in microbes [ 12 , 32 ]. Genus was therefore added as a random intercept effect since there was predominantly only one genome for each species. A random slope effect with respect to genome size resulted in the best fitted model. All models were first estimated using Maximum Likelihood (ML) so that it would be possible to assess goodness-of-fit with the Akaike Information Criterion (AIC) [ 33 ]. The lowest AIC indicates the best model. The best models for both regression models with compression ratio (ZPAQ/MBGC) as outcome and genomic AT content, OUV and genome size as outcome, together with a random slope of genome size with respect to genus, obtained AIC= -3,082 (ZPAQ) / -2,997 (MBGC). Without random effects but the same predictors the models obtained: AIC= -2,053 (ZPAQ) / -1,993 (MBGC). For the null models: -725 (ZPAQ) / 445 (MBGC). To compare the difference between the MBGC compression ratio and the ZPAQ compression ratio with respect to the above-mentioned predictors, the ZPAQ compression rate was added to the MBGC compression rate model described above as a linear predictor. Hence, Fig. 4 shows the remaining effects of the MBGC compression rate model after adjusting away the effects from the ZPAQ compression rate. All final mixed-effect type models were estimated using restricted maximum likelihood (REML) therefore all results presented (except for AIC) are from these models [ 34 ]. All statistical analyses were performed in R v. 4.3.1 [ 35 ], GAM regression was carried out with the ‘mgcv’ library [ 31 ] while the mixed effect GAM (GAMM) was performed with the ‘GAMM4’ library that estimates random effects using the ‘lme4’ library [ 36 ]. All figures were also made with R. Declarations Ethics approval and consent to participate Not applicable Consent for publication Not applicable Availability of data and materials All genomes were downloaded from the NCBI Reference Sequence Database (RefSeq, https://www.ncbi.nlm.nih.gov/refseq/). All data needed to reproduce the findings reported have been included in Additional file 1. Competing interests The authors declare that they have no competing interests. Funding JB is funded by the Norwegian Institute of Public Health. JHOP is funded by the Swedish Research Council VR (grant no.: 2020-02593). Authors' contributions JB: Initiated project, performed bioinformatics and statistical analyses, wrote manuscript. JHOP: Analysis, editing and review. Both authors read and approved the final manuscript. Acknowledgements The authors wish to thank Dr. Sasikiran Kandula for helpful comments and suggestions. References Agashe D, Shankar N. The evolution of bacterial DNA base composition. J Experimental Zool Part B: Mol Dev Evol. 2014;322:517–28. Fariselli P, Taccioli C, Pagani L, Maritan A. DNA sequence symmetries from randomness: the origin of the Chargaff’s second parity rule. Brief Bioinform. 2021;22:2172–81. Mitchell D. GC content and genome length in Chargaff compliant genomes. Biochem Biophys Res Commun. 2007;353:207–10. Bohlin J, Sekse C, Skjerve E, Brynildsrud O. Positive correlations between genomic %AT and genome size within strains of bacterial species. Environ Microbiol Rep. 2014;6:278–86. Foerstner KU, von Mering C, Hooper SD, Bork P. Environments shape the nucleotide composition of genomes. EMBO Rep. 2005;6:1208–13. McCutcheon JP, Moran NA. Extreme genome reduction in symbiotic bacteria. Nat Rev Microbiol. 2012;10:13–26. Weinert LA, Welch JJ. Why Might Bacterial Pathogens Have Small Genomes? Trends Ecol Evol. 2017;32:936–47. Moran NA. Accelerated evolution and Muller’s rachet in endosymbiotic bacteria. Proceedings of the National Academy of Sciences. 1996;93:2873–8. Reva ON, Tümmler B. Global features of sequences of bacterial chromosomes, plasmids and phages revealed by analysis of oligonucleotide usage patterns. BMC Bioinformatics. 2004;5:90. Bohlin J, Skjerve E, Ussery DW. Investigations of Oligonucleotide Usage Variance Within and Between Prokaryotes. PLoS Comput Biol. 2008;4:e1000057. Willenbrock H, Friis C, Juncker AS, Ussery DW. An environmental signature for 323 microbial genomes based on codon adaptation indices. Genome Biol. 2006;7:R114. Bohlin J, Eldholm V, Pettersson JHO, Brynildsrud O, Snipen L. The nucleotide composition of microbial genomes indicates differential patterns of selection on core and accessory genomes. BMC Genomics. 2017;18:151. Hershberg R, Petrov DA. Evidence That Mutation Is Universally Biased towards AT in Bacteria. PLoS Genet. 2010;6:e1001115. Hildebrand F, Meyer A, Eyre-Walker A. Evidence of Selection upon Genomic GC-Content in Bacteria. PLoS Genet. 2010;6:e1001107. Bohlin J, Rose B, Brynildsrud O. Birgitte Freiesleben De Blasio. A simple stochastic model describing genomic evolution over time of GC content in microbial symbionts. J Theor Biol. 2020;503:110389. Bohlin J, Skjerve E, Ussery DW. Analysis of genomic signatures in prokaryotes using multinomial regression and hierarchical clustering. BMC Genomics. 2009;10:487. Seward EA, Kelly S. Dietary nitrogen alters codon bias and genome composition in parasitic microorganisms. Genome Biol. 2016;17:226. Bohlin J, van Passel MW, Snipen L, Kristoffersen AB, Ussery D, Hardy SP. Relative entropy differences in bacterial chromosomes, plasmids, phages and genomic islands. BMC Genomics. 2012;13:66. Ziv J, Lempel A. Compression of individual sequences via variable-rate coding. IEEE Trans Inf Theory. 1978;24:530–6. Huffman DA. A Method for the Construction of Minimum-Redundancy Codes. Proceedings of the IRE. 1952;40:1098–101. Kryukov K, Ueda MT, Nakagawa S, Imanishi T. Sequence Compression Benchmark (SCB) database—A comprehensive evaluation of reference-free compressors for FASTA-formatted sequences. GigaScience. 2020;9:giaa072. Grabowski S, Kowalski TM. MBGC: Multiple Bacteria Genome Compressor. GigaScience. 2022;11:giab099. Martin-Löf P. The definition of random sequences. Inf Control. 1966;9:602–19. Bohlin J, Skjerve E. Examination of Genome Homogeneity in Prokaryotes Using Genomic Signatures. PLoS ONE. 2009;4:e8113. Bohlin J. Genomic Signatures in Microbes—Properties and Applications. Sci World J. 2011;11:715–25. Reichenberger ER, Rosen G, Hershberg U, Hershberg R. Prokaryotic Nucleotide Composition Is Shaped by Both Phylogeny and the Environment. Genome Biol Evol. 2015;7:1380–9. Meyer MM. Revisiting the Relationships Between Genomic G + C Content, RNA Secondary Structures, and Optimal Growth Temperature. J Mol Evol. 2021;89:165–71. Franklin JNY, Porter CP. Key developments in algorithmic randomness. In: Porter CP, Franklin JNY, editors. Algorithmic Randomness: Progress and Prospects. Cambridge: Cambridge University Press; 2020. pp. 1–39. Machta J. Entropy, information, and computation. Am J Phys. 1999;67:1074–7. Pruitt KD, Tatusova T, Maglott DR. NCBI Reference Sequence (RefSeq): a curated non-redundant sequence database of genomes, transcripts and proteins. Nucleic Acids Res. 2005;33 Database issue:D501–4. Wood SN. Generalized Additive Models: An Introduction with R, Second Edition. 2nd edition. New York: Chapman and Hall/CRC; 2017. Maistrenko OM, Mende DR, Luetge M, Hildebrand F, Schmidt TSB, Li SS, et al. Disentangling the impact of environmental and phylogenetic constraints on prokaryotic within-species diversity. ISME J. 2020;14:1247–59. Akaike H. Information Theory and an Extension of the Maximum Likelihood Principle. In: Parzen E, Tanabe K, Kitagawa G, editors. Selected Papers of Hirotugu Akaike. New York, NY: Springer; 1998. pp. 199–213. Pawitan Y. All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press; 2001. Ihaka R, Gentleman R. R: A Language for Data Analysis and Graphics. J Comput Graphical Stat. 1996;5:299–314. Bates D, Mächler M, Bolker B, Walker S. Fitting Linear Mixed-Effects Models Using lme4. J Stat Softw. 2015;67:1–48. Additional Declarations No competing interests reported. Supplementary Files Dataset.xlsx Additional file 1: All data needed to reproduce the findings reported in Excel format. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4597889","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":321971126,"identity":"2af8351c-02d4-4268-ab83-fec68b961f3d","order_by":0,"name":"Jon Bohlin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVRIiWNgGAWjYBACxgYGBmYGhgMybAzMBz4zGJCghYeNgS1xNlFaQACshYGBx3A2ccrbew8wF1Tc4eGT7vnYXFDAkMdP0GE95xKYZ5x5xsMmc3Zj8wwDhmLJBkJaZuQYMPO2HeZhk8jd/pjHgCFxwwHiteQ8bCZZCyORWnrOGByecQakJc0QqEUicSYhvxi29xg+Lqg4LCc/IxnosD82if0EdDAYAs1EdokEIQ0MDPKElYyCUTAKRsGIBwCk2TvNl2tBIAAAAABJRU5ErkJggg==","orcid":"","institution":"Norwegian Institute of Public Health","correspondingAuthor":true,"prefix":"","firstName":"Jon","middleName":"","lastName":"Bohlin","suffix":""},{"id":321971127,"identity":"1a07b729-8501-497b-9f31-457ac2f3c6a3","order_by":1,"name":"John H.-O. Pettersson","email":"","orcid":"","institution":"Uppsala University","correspondingAuthor":false,"prefix":"","firstName":"John","middleName":"H.-O.","lastName":"Pettersson","suffix":""},{"id":321971128,"identity":"a971ba93-f80e-4863-8c5e-87f7aea492f0","order_by":2,"name":"John H.-O. Pettersson","email":"","orcid":"","institution":"Public Health Agency of Sweden","correspondingAuthor":false,"prefix":"","firstName":"John","middleName":"H.-O.","lastName":"Pettersson","suffix":""}],"badges":[],"createdAt":"2024-06-18 06:51:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4597889/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4597889/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":59660881,"identity":"35b62d65-60c4-41ec-933c-9f5c75f17e1e","added_by":"auto","created_at":"2024-07-04 11:52:39","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":30660,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eZPAQ compression rate regressed on genomic AT content, genome size and OUV\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe figure shows the predictors (horizontal axis): AT content (A), genome size (B) and OUV (C), from a GAMM regression model with ZPAQ-based genomic compression rate as the outcome (vertical axis). The model also included a random slope effect of genome size with respect to phylogeny (genus).\u003c/p\u003e","description":"","filename":"Fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-4597889/v1/9368501261908eafd430f792.png"},{"id":59661511,"identity":"e8d09cf7-4f56-45c0-98b3-af7bdf49b550","added_by":"auto","created_at":"2024-07-04 12:00:39","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":29875,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMBGC compression rate regressed on genomic AT content, genome size and OUV\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe figure shows the predictors (horizontal axis): AT content (A), genome size (B) and OUV (C), from a GAMM regression model with MBGC-based genomic compression rate as the outcome (vertical axis). The model also included a random slope effect of genome size with respect to phylogeny (genus).\u003c/p\u003e","description":"","filename":"Fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-4597889/v1/e3920c4fa8819914613e0de6.png"},{"id":59661861,"identity":"24f494ec-b15b-44dd-99d2-ce30c1d66251","added_by":"auto","created_at":"2024-07-04 12:08:39","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":37190,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMBGC and ZPAQ compression rate differences with regards to AT content\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePanel A shows genomic compression ratios (vertical axis) for both MBGC and ZPAQ algorithms plotted against genomic AT content (horizontal axis). Panel B demonstrates the compression rate difference between the two algorithms (vertical axis) with regards to genomic AT content (horizontal axis).\u003c/p\u003e","description":"","filename":"Fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-4597889/v1/81e175b61bae7291f0250068.png"},{"id":59660882,"identity":"c0623e20-ab3b-4d14-9c5c-bf7b5d081440","added_by":"auto","created_at":"2024-07-04 11:52:39","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":69151,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRegression model of compression rate differences\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe figure demonstrates remaining effects of the MBGC compression rate (vertical axis) model after the effects from the ZPAQ compression rate model (horizontal axis) have been adjusted away (Panel A) with a regression line colored in blue (red dashed line has intercept 0 and slope 1). Panel B shows the remaining effect on genomic AT content, Panel C genome size and Panel D OUV. Genome size with respect to phylogeny (genus) was additionally included as a random slope.\u003c/p\u003e","description":"","filename":"Fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-4597889/v1/4964880a83a83a46749bf579.png"},{"id":59975157,"identity":"d81c6be1-3d19-4c02-83d9-7a9f6e85600a","added_by":"auto","created_at":"2024-07-10 04:31:46","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":614211,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4597889/v1/c0f73ce8-1f46-4295-9a6a-f6aef28b4a32.pdf"},{"id":59660884,"identity":"54dc73fc-209c-4b35-9203-decc7d8ad769","added_by":"auto","created_at":"2024-07-04 11:52:39","extension":"xlsx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":497163,"visible":true,"origin":"","legend":"\u003cp\u003eAdditional file 1: All data needed to reproduce the findings reported in Excel format.\u003c/p\u003e","description":"","filename":"Dataset.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-4597889/v1/6023008798761f8f27c2a13c.xlsx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Estimation of redundancy in microbial genomes","fulltext":[{"header":"Background","content":"\u003cp\u003eMicrobial genomes vary substantially with regards to genome size and base composition [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Due to Chargaff\u0026rsquo;s parity rules [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], base composition in microbes can be summarized as the percentage % of (A)denine% + (T)hymine% (%AT), due to their similar frequencies. Alternatively, it can be summarized as 100% - (%AT) = (G)uanine% + (C)ytosine% (%GC). In general, genomic %AT (AT) is negatively associated with genome size [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Within microbial species however, genomic AT has been found to increase with genome size [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. While free-living and soil dwelling microbes tend to have larger genomes with less AT (GC rich) [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] intracellular symbionts [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], and to a lesser extent pathogens [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], have small, AT rich genomes due to reductive evolution [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. A negative association has also been found between genomic AT content and oligonucleotide frequencies, sometimes referred to as oligonucleotide usage variance (OUV) [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], \u003cem\u003ei.e.\u003c/em\u003e genome-wide frequencies of \u0026lsquo;DNA words\u0026rsquo; consisting of a fixed number of nucleotides (usually 3 (codons) [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] or 4 (tetranucleotides)) [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. OUV is the averaged sum of the squared differences between all possible genomic tetranucleotide frequencies subtracted by their corresponding expected tetranucleotide frequencies. As such, OUV literarily describes the variance of genomic tetranucleotide frequencies. The expected tetranucleotide frequencies are estimated by the respective tetranucleotide word\u0026rsquo;s individual genomic nucleotide frequencies. That is, if \u003cem\u003ef(AGCT)\u003c/em\u003e represents the genomic frequencies of the tetranucleotide word \u0026lsquo;\u003cem\u003eAGCT\u003c/em\u003e\u0026rsquo; then the estimated expected frequency of the word \u0026lsquo;\u003cem\u003eAGCT\u003c/em\u003e\u0026rsquo; will be \u003cem\u003ef(A)f(G)f(C)f(T)\u003c/em\u003e. OUV thus represents the average squared difference, or variance, taken over the frequencies of all 4\u003csup\u003e4\u003c/sup\u003e = 256 possible combinations of tetranucleotide words subtracted by the expected occurrence of the corresponding tetranucleotide, \u003cem\u003ee.g.\u003c/em\u003e ( \u003cem\u003ef(AGCT) \u0026ndash; f(A)f(G)f(C)f(T)\u003c/em\u003e )\u003csup\u003e2\u003c/sup\u003e. Genomes with biased tetranucleotide frequencies, for one reason or another, will have higher OUV as some DNA words will differ greatly from what is expected from the base composition \u003cem\u003e(i.e\u003c/em\u003e. AT/GC content) alone. High OUV will thus likely represent genomes having been subjected to strong selective pressures, either positive or negative [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Organisms with low OUV, \u003cem\u003ei.e.\u003c/em\u003e oligonucleotides that are more predictable from genomic base composition, have been subjected to more relaxed selective pressures [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. It has been shown that AT rich genomes tend to consist of oligonucleotides that are easier to estimate using single nucleotide frequencies and thus tend to have lower OUV than AT poor microbes [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. AT poor (sometimes referred to as GC rich) microbes, on the other hand, often have more selective tetranucleotide word usage than AT rich ones resulting in higher OUV [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. These discrepancies between AT rich and AT poor genomes, with respect to genome-wide tetranucleotide word frequencies, have been linked to selective pressures [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]; AT rich genomes appear historically to have been subjected less to selective pressures than AT poor genomes [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. For microbial symbionts, which are often AT rich, this might be, to some extent, explained by easier access to metabolites from the host [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. It is also anticipated that genomes being subjected to relaxed selective pressures, such as symbionts, may accumulate genome-wide mutations to a larger degree than organisms subjected to strong selective pressures [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Accumulation of genome-wide random mutations is therefore assumed to result in tetranucleotide word frequencies more in line with AT/GC content [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAs mentioned above, AT rich genomes have often been found to be more host associated and pathogenic with the latter having slightly larger genomes. AT poor genomes are often found in environments outside of the host [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Since genomic AT content correlates negatively with nitrogen abundance [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] many microbial species with AT poor genomes are often found in soil [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Hence, it is assumed that OUV differences are reflective of the selective pressures mediated by the respective environments [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Non-host environments are likely challenging requiring a diverse set of genes for utilizing different types of nutrients for survival. Stronger selective pressures, in particular purifying selection and frequent bottleneck events, may therefore favor species that are more competitive with the ability to survive in diverse and dynamic environments. Under such circumstances, there could be a strong selection for more specific DNA patterns resulting in more biased genome-wide tetranucleotide word frequencies, reflected by higher OUV [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eGenome-wide oligonucleotides are more easily compressed if they exhibit some degree of systematic bias. Bias resulting from selection for specific genome-wide DNA patterns is reflected by higher OUV [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. The genomes of such organisms could be easier to compress than organisms with low OUV that do not show any genome-wide DNA patterns. In this sense, AT poor genomes, with higher OUV, are expected to have a greater degree of redundancy than more AT-rich genomes.\u003c/p\u003e \u003cp\u003eThe most common general-purpose compression algorithm (often referred to as LZ after the inventors Abraham Lempel and Jacob Ziv [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]) attempts to reduce a string of data by searching for repeating patterns or sub-strings and extending these as much as possible. Repeating substrings or patterns are then replaced by smaller symbols, thereby reducing string size. Finally, a dictionary containing the symbols representing specific sub-strings is added to the compressed file for use in decompression. If a string contains many different patterns that require symbols of varying size for representation the Huffman algorithm will ensure that the most frequent patterns, or sub-strings, are assigned progressively shorter representations [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. The size of such representations therefore correlates negatively with occurrence frequency. Hence, strings consisting of many repetitive patterns are easier to compress than strings containing fewer such patterns [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Most modern general-purpose compressors consist of several algorithms and steps to reduce the size of a string of data [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eRecently, compression algorithms were introduced that take DNA specific properties into account [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. In particular, the Multiple Bacterial Genome Compressor (MBGC) considers DNA patterns and their reverse complements as identical [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. As such, MBGC achieves a greater compression ratio than other compressors by only requiring one symbol to represent each DNA pattern and its reverse complement.\u003c/p\u003e \u003cp\u003eIn theoretical computer science, an equivalence relation has been established between compressibility and a definition of randomness [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]; the more random and unpredictable a string of letters (such as A, G, C and T) is, the harder it is to compress. A string consisting of a few substring patterns is therefore more difficult to compress. As such, by exploring the redundancy of microbial genomes using AT content and OUV, a measure of genomic randomness (i.e. accumulated mutations) is also attained.\u003c/p\u003e \u003cp\u003eSince AT content in microbial genomes is, in one way or another, associated with genome size and OUV, the purpose of this project was to explore whether this association could also be extended to genome redundancy. More specifically, is there an association between AT, genome size and OUV on one hand and the compressibility of a microbial genome on the other? To test this hypothesis, 4,713 microbial genomes, representing 1,508 bacterial genera, were downloaded from the NCBI RefSeq database to minimize species- and strain-specific bias. These genomes were compressed using two different algorithms: ZPAQ, which is widely regarded as the best general purpose compression algorithm [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] and MBGC, a recent compression algorithm specialized for microbial genomes [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. The compression rates obtained from both these algorithms for the 4,713 RefSeq genomes were subsequently regressed on corresponding genomic AT content, OUV and genome size. The models were also adjusted for taxonomic relatedness.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eWe first explored whether there was any association between genome compression ratio for the ZPAQ algorithm on one hand, and AT content, genome size and OUV on the other (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). A generalized additive mixed-effects model (GAMM) was fitted with ZPAQ compression ratio as the outcome and genomic AT content, genome (chromosome) size and OUV as predictors represented by splines, to compensate for putative non-linear trends, for all 4,713 genomes. In addition, taxonomic genus was added as a random effect with respect to genome size, which was established by examining Akaike Information Criterion (AIC) differences between tested models (see Materials and Methods for details).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe GAMM model indicated that there was a positive association between ZPAQ compression ratio and the three smooths representing respectively genomic AT content (\u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/em\u003e), genome size (\u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/em\u003e) and OUV (\u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/em\u003e). Both genomic AT content and genome size exhibited substantial non-linear trends, as measured using effective degrees of freedom (edf, edf\u0026thinsp;\u0026gt;\u0026thinsp;1 indicates non-linearity), with respective edf\u0026thinsp;=\u0026thinsp;6.3 and edf\u0026thinsp;=\u0026thinsp;7.1. OUV, on the other hand, did not exhibit any non-linear trends (edf\u0026thinsp;=\u0026thinsp;1) and was found to be positively associated with ZPAQ compression rate. The AIC for this model was \u0026minus;\u0026thinsp;3,082 as compared to AIC = -2,053 for the model with the same predictors but without the random slope effects (\u003cem\u003ei.e.\u003c/em\u003e lower AIC is better). The AIC for the null model (the outcome regressed on a constant) was \u0026minus;\u0026thinsp;725.\u003c/p\u003e \u003cp\u003eAn additional GAMM model was fitted with the same predictors and random effects as for the ZPAQ compression model above but with the MBGC compression rate as the outcome instead (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Again, both AT content and genome size were found significant (\u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/em\u003e) with considerable non-linear splines: edf\u0026thinsp;=\u0026thinsp;7.1 and edf\u0026thinsp;=\u0026thinsp;7.5, respectively. For this model, non-linear trends were also observed for the smooth representing the OUV predictor (edf\u0026thinsp;=\u0026thinsp;2.0). Once more, the model obtained a better AIC (-2,997) when a random slope of genome size with respect to genus was included in addition to the fixed effect predictors AT, genome size and OUV. For the same model but without the random slope AIC = -1,993 and AIC\u0026thinsp;=\u0026thinsp;445 for the null model (only outcome). It can be seen from both Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e that while there is a clear positive association with respect to genome size and OUV on one hand and for both ZPAQ and MBGC genome compression ratios on the other, the trend with regards to AT content is less clear due to the parabolic trend.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eNot only does Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e indicate that MBGC is, on average, better at compressing genomes than the ZPAQ algorithm but also that AT poor/GC rich genomes are considerably better compressed with the MBGC method. To assess the difference between the compression algorithms more formally, the GAMM model with MBGC as the outcome was refitted but now with the ZPAQ compression rate as an additional linear predictor, leaving the rest of the model, as described above, unchanged. AIC improved considerably with \u0026minus;\u0026thinsp;21378.28 for this model (the AIC null is the same as for the MBGC model described above).. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows an approximate linear relationship between the compression ratios of MBGC and ZPAQ (\u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/em\u003e) and that there is a largely negative association between MBGC compression rate and AT content (\u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/em\u003e), suggesting that compression of AT poor genomes is visibly improved with the MBGC algorithm as compared to the ZPAQ algorithm. Slight improvements over the ZPAQ algorithm can also be observed for genome size and OUV. Excepting the ZPAQ compression ratio, which was assumed to be linear, AT content, genome size and OUV were all non-linear terms with edf equal to 7.7, 8.3 and 4.9, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt can also be noticed in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e that the red dashed line, which represents a regression line with slope 1 and intercept 0, was slightly lower than the (blue) regression line, which represents the model intercept (\u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/em\u003e) for the MBGC compression ratio regressed on the ZPAQ compression rate (and adjusted for the other predictors and the random slope effect mentioned above). The model intercept indicates that the MBGC compressor achieves, on average, a 0.15 compression ratio improvement (approximately 3%) over the ZPAQ compressor for microbial genomes.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eOUV is a measure of genomic oligonucleotide frequency discrepancy from what is expected based only on the corresponding genomic nucleotide frequencies (\u003cem\u003ei.e.\u003c/em\u003e genomic AT content). Surprisingly, OUV exhibited a strong correlation with both ZPAQ and MBGC compression ratios (see Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Higher values of OUV indicate that oligonucleotide frequencies deviate from expected based on the corresponding individual nucleotide frequencies. Low OUV, on the other hand, suggests that oligonucleotide frequencies are more predictive from the corresponding individual nucleotide frequencies. Low OUV may thus be indicative of genomes whose oligonucleotides have historically been subjected to reduced selective pressures as compared to those with high OUV. Alternatively, low OUV may also, at least to some extent, be reflective of genomes with a higher number of accumulated, presumably random, mutations.\u003c/p\u003e \u003cp\u003eSystematic bias in oligonucleotide usage may facilitate compression, particularly for the oligonucleotides that occur more frequently than expected. From the results presented here for the MBGC compression rates this appears to be more prevalent in AT poor genomes as seen in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Indeed, a negative association has previously been found between OUV and AT content both within [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] and between genomes [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. In general, AT poor/GC rich genomes appear to have more similar oligonucleotide usage [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. As mentioned previously, biased genome-wide oligonucleotide usage facilitates compression, something that appears to be reflected in the results presented here. The fact that MBGC compressed AT poor genomes better than ZPAQ indicates that oligonucleotides occur with similar frequency to their reverse complements increasingly more than for AT rich genomes. Hence, biased occurrence of genomic oligonucleotides is increasingly more similar to the occurrence of the corresponding reverse complemented oligonucleotides in genomes with increasingly less genomic AT.\u003c/p\u003e \u003cp\u003eAs mentioned above, since OUV is lower in AT rich genomes, oligonucleotide frequencies are more similar to individual nucleotide frequencies. In other words, genomic nucleotide frequencies tend to be more predictive of the genomic oligonucleotide frequencies. This could potentially indicate that species with AT rich genomes have historically accumulated more mutations than species with AT poor genomes. Weaker purifying selection may thus have resulted in accumulation of mutations in AT rich genomes to a much larger extent than in AT poor genomes.\u003c/p\u003e \u003cp\u003eThe performance of the ZPAQ algorithm was on average inferior to the MBGC algorithm and no compression rate differences could be detected between AT rich and AT poor genomes. Both ZPAQ and MBGC algorithms are similar [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], except for the fact that MBGC treats oligonucleotides and their reverse complements as identical. The difference in compression rate observed with MBGC between AT rich and AT poor genomes must therefore point to trend differences in oligonucleotide usage. More specifically, AT poor genomes appear to have more similar frequencies of abundant oligonucleotides and their reverse complements than AT rich genomes. For both compression algorithms, the lowest compression rates were nevertheless obtained for the genomes with similar AT/GC content (\u003cem\u003ei.e.\u003c/em\u003e %AT/%GC approaching 50%), likely because more oligonucleotide frequencies are less predictable due to the similar nucleotide frequencies.\u003c/p\u003e \u003cp\u003eAT rich genomes tend to have smaller genomes. The reason is not completely understood, but as was seen in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e the smaller genomes are also harder to compress, at least those with genome sizes below 2\u0026nbsp;million base-pairs (mb). Symbionts and pathogens often have such small genomes due to genome reduction [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Reduction in genome size is often preceded by an accumulation of mutations, that go hand in hand with increased AT content and number of pseudogenes [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The reason that mutation accumulation is often positively associated with AT content is that most mutations are in the direction from Cytosine to Thymine [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. AT poor genomes, however, are often found outside hosts and have larger genomes with a more diverse set of genes [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. An important difference between Adenine and Thymine base-pairs on one hand and Guanine and Cytosine base-pairs on the other is that the latter pair requires three hydrogen bonds instead of two for the former. Hence, G-C base-pairs are stronger than A-T base-pairs but require more stacking energy [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. This suggests that genomic AT content is, at least to some extent, also a manifestation of selective pressures, or lack thereof, having historically acted on a species’ genome [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFormal definitions of the concept of randomness are relatively recent [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. It has been shown that randomness is equivalent with compression [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]; the more random a string of characters is, the harder it is to compress and vice-versa. Random sequences are also connected to the notion of information. The more random a string of characters is the less information it contains (\u003cem\u003ei.e.\u003c/em\u003e entropy increases) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. It is shown here that microbes with smaller genomes are harder to compress than microbes with larger genomes. Moreover, AT poor genomes are easier to compress than AT rich, at least with the MBGC compression algorithm. Finally, OUV, which is a measure strongly connected to information and entropy [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], is positively associated with compression rates. As such, smaller AT-rich genomes with lower OUV, appear to contain less information, at least with respect to Shannon entropy [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], than larger AT poor/GC rich genomes with higher OUV.\u003c/p\u003e \u003cp\u003e\u003c/p\u003e "},{"header":"Conclusion","content":"\u003cp\u003eWe demonstrate here that microbes with smaller genomes tend to be harder to compress than microbes with genome sizes approximately above 2 mb. Moreover, we found a clear and surprising positive association between OUV and compression rate suggesting that increasing oligonucleotide usage variance is a proxy for genome redundancy in microbes. Since the OUV measure is related to Shannon entropy, there is a positive association between genome redundancy and information content.\u003c/p\u003e \u003cp\u003eThe MBGC method compressed microbial genomes to a higher rate than the ZPAQ algorithm, on average. Moreover, MBGC compressed AT poor genomes significantly better than the ZPAQ compressor. The MBGC algorithm's ability to obtain a progressively higher compression rate for genomes with decreasing AT content is likely because the method considered both oligonucleotides and their reverse complements as equals. These findings suggest that organisms with AT poor/GC rich genomes have higher than expected occurrences of particular oligonucleotides and their respective reverse complements than AT rich genomes. Since compression is tightly linked to randomness, smaller, AT rich genomes with low OUV appear to have accumulated more random mutations, on average, and thus exhibit less information potential, than microbes with larger, AT poor genomes and higher OUV.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eIn total 4,829 microbial genomes were downloaded from NCBI’s RefSeq database [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.ncbi.nlm.nih.gov/refseq/\u003c/span\u003e\u003cspan address=\"https://www.ncbi.nlm.nih.gov/refseq/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e)\u003c/span\u003e on February 23, 2024. To obtain a prokaryotic population consisting of as representative samples as possible only RefSeq genomes were considered. The genomic data consisted mostly of one genome from each species, excepting only species with substantial genomic differences, within a genus. There were 114 samples of the species \u003cem\u003eWolbachia endosymbiont\u003c/em\u003e, of which 113 were removed to reduce bias from a single species. Three additional genomes were removed due to an unusually high number of repeats resulting in over 30 times compression ratios for both ZPAQ and MBGC compressors. The exceedingly high compression ratios negatively impacted model assumptions and were therefore removed. These included an unnamed endosymbiont of the deep-sea mussel \u003cem\u003eBathymodiolus septemdierum\u003c/em\u003e (accession: AP013042.1), \u003cem\u003eEnterobacter lignolyticus\u003c/em\u003e (CP012871.1) and \u003cem\u003eE. ludwigii\u003c/em\u003e (CP017279.1). In total, 4,713 genomes were available for analysis. All plasmids were removed from all species/genomes so that only chromosomes were used for the downstream analyses. Genomes consisting of multiple chromosomes were concatenated into one file. All data needed to reproduce the results reported have been included in Additional file 1.\u003c/p\u003e\u003cp\u003eThe genomes were compressed into ZPAQ format using ‘lrzip’ v.0.651 with the –zpaq option [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. For the MBGC compressor, ‘mbgc’ v.1.2.1 [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] was used (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/kowallus/mbgc\u003c/span\u003e\u003cspan address=\"https://github.com/kowallus/mbgc\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e).\u003c/span\u003e Compression ratio was calculated as genome (\u003cem\u003ei.e.\u003c/em\u003e total chromosome) size / compressed file size for each genome and for both compressors.\u003c/p\u003e\u003cp\u003eThe AT content, OUV and genome size of these genomes were computed from in-house scripts; AT content as the number of A + T nucleotides / total number of A + T + G + C nucleotides. Genome size was calculated as the total number of nucleotides. OUV was calculated as the average ratio of genomic tetranucleotide frequencies divided by the multiplication of the corresponding nucleotide frequencies. That is,\u003c/p\u003e\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$OUV={\\sum }_{XYZW}^{}\\left(\\frac{f\\left(XYZW\\right)}{f\\left(X\\right)f\\left(Y\\right)f\\left(Z\\right)f\\left(W\\right)}\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cp\u003ewhere ‘\u003cem\u003eXYZW\u003c/em\u003e’ represents nucleotides for every possible genomic tetranucleotide from the alphabet \u003cem\u003eA\u003c/em\u003e, \u003cem\u003eG\u003c/em\u003e, \u003cem\u003eC\u003c/em\u003e and \u003cem\u003eT\u003c/em\u003e (e.g. \u003cem\u003ef(ATGC)\u003c/em\u003e/\u003cem\u003ef(A)f(T)f(G)f(C)\u003c/em\u003e).\u003c/p\u003e\u003cp\u003eTo explore whether genomic compression ratio, from either ZPAQ or MBGC algorithms, was associated with genome size, AT content and OUV we employed generalized additive mixed effects models (GAMM) [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] to account for putative non-linear associations between outcome and predictors and non-constant variance differences between phylogenetic groups. It has previously been demonstrated that adding a taxonomic group below genus level has little impact on the models focusing on genomic base composition in microbes [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Genus was therefore added as a random intercept effect since there was predominantly only one genome for each species. A random slope effect with respect to genome size resulted in the best fitted model. All models were first estimated using Maximum Likelihood (ML) so that it would be possible to assess goodness-of-fit with the Akaike Information Criterion (AIC) [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. The lowest AIC indicates the best model. The best models for both regression models with compression ratio (ZPAQ/MBGC) as outcome and genomic AT content, OUV and genome size as outcome, together with a random slope of genome size with respect to genus, obtained AIC= -3,082 (ZPAQ) / -2,997 (MBGC). Without random effects but the same predictors the models obtained: AIC= -2,053 (ZPAQ) / -1,993 (MBGC). For the null models: -725 (ZPAQ) / 445 (MBGC). To compare the difference between the MBGC compression ratio and the ZPAQ compression ratio with respect to the above-mentioned predictors, the ZPAQ compression rate was added to the MBGC compression rate model described above as a linear predictor. Hence, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the remaining effects of the MBGC compression rate model after adjusting away the effects from the ZPAQ compression rate. All final mixed-effect type models were estimated using restricted maximum likelihood (REML) therefore all results presented (except for AIC) are from these models [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. All statistical analyses were performed in R v. 4.3.1 [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], GAM regression was carried out with the ‘mgcv’ library [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] while the mixed effect GAM (GAMM) was performed with the ‘GAMM4’ library that estimates random effects using the ‘lme4’ library [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. All figures were also made with R.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eEthics approval and consent to participate\u003c/h2\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003ch2\u003eConsent for publication\u003c/h2\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003ch2\u003eAvailability of data and materials\u003c/h2\u003e\n\u003cp\u003eAll genomes were downloaded from the NCBI Reference Sequence Database (RefSeq, https://www.ncbi.nlm.nih.gov/refseq/). All data needed to reproduce the findings reported have been included in Additional file 1.\u003c/p\u003e\n\u003ch2\u003eCompeting interests\u003c/h2\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e\n\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eJB is funded by the Norwegian Institute of Public Health. JHOP is funded by the Swedish Research Council VR (grant no.: 2020-02593).\u003c/p\u003e\n\u003ch2\u003eAuthors\u0026apos; contributions\u003c/h2\u003e\n\u003cp\u003eJB: Initiated project, performed bioinformatics and statistical analyses, wrote manuscript. JHOP: Analysis, editing and review. Both authors read and approved the final manuscript.\u003c/p\u003e\n\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThe authors wish to thank Dr. Sasikiran Kandula for helpful comments and suggestions.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAgashe D, Shankar N. The evolution of bacterial DNA base composition. J Experimental Zool Part B: Mol Dev Evol. 2014;322:517\u0026ndash;28.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFariselli P, Taccioli C, Pagani L, Maritan A. DNA sequence symmetries from randomness: the origin of the Chargaff\u0026rsquo;s second parity rule. Brief Bioinform. 2021;22:2172\u0026ndash;81.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMitchell D. GC content and genome length in Chargaff compliant genomes. Biochem Biophys Res Commun. 2007;353:207\u0026ndash;10.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBohlin J, Sekse C, Skjerve E, Brynildsrud O. Positive correlations between genomic %AT and genome size within strains of bacterial species. Environ Microbiol Rep. 2014;6:278\u0026ndash;86.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFoerstner KU, von Mering C, Hooper SD, Bork P. Environments shape the nucleotide composition of genomes. EMBO Rep. 2005;6:1208\u0026ndash;13.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMcCutcheon JP, Moran NA. Extreme genome reduction in symbiotic bacteria. Nat Rev Microbiol. 2012;10:13\u0026ndash;26.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWeinert LA, Welch JJ. Why Might Bacterial Pathogens Have Small Genomes? Trends Ecol Evol. 2017;32:936\u0026ndash;47.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMoran NA. Accelerated evolution and Muller\u0026rsquo;s rachet in endosymbiotic bacteria. Proceedings of the National Academy of Sciences. 1996;93:2873\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eReva ON, T\u0026uuml;mmler B. Global features of sequences of bacterial chromosomes, plasmids and phages revealed by analysis of oligonucleotide usage patterns. BMC Bioinformatics. 2004;5:90.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBohlin J, Skjerve E, Ussery DW. Investigations of Oligonucleotide Usage Variance Within and Between Prokaryotes. PLoS Comput Biol. 2008;4:e1000057.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWillenbrock H, Friis C, Juncker AS, Ussery DW. An environmental signature for 323 microbial genomes based on codon adaptation indices. Genome Biol. 2006;7:R114.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBohlin J, Eldholm V, Pettersson JHO, Brynildsrud O, Snipen L. The nucleotide composition of microbial genomes indicates differential patterns of selection on core and accessory genomes. BMC Genomics. 2017;18:151.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHershberg R, Petrov DA. Evidence That Mutation Is Universally Biased towards AT in Bacteria. PLoS Genet. 2010;6:e1001115.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHildebrand F, Meyer A, Eyre-Walker A. Evidence of Selection upon Genomic GC-Content in Bacteria. PLoS Genet. 2010;6:e1001107.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBohlin J, Rose B, Brynildsrud O. Birgitte Freiesleben De Blasio. A simple stochastic model describing genomic evolution over time of GC content in microbial symbionts. J Theor Biol. 2020;503:110389.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBohlin J, Skjerve E, Ussery DW. Analysis of genomic signatures in prokaryotes using multinomial regression and hierarchical clustering. BMC Genomics. 2009;10:487.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSeward EA, Kelly S. Dietary nitrogen alters codon bias and genome composition in parasitic microorganisms. Genome Biol. 2016;17:226.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBohlin J, van Passel MW, Snipen L, Kristoffersen AB, Ussery D, Hardy SP. Relative entropy differences in bacterial chromosomes, plasmids, phages and genomic islands. BMC Genomics. 2012;13:66.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZiv J, Lempel A. Compression of individual sequences via variable-rate coding. IEEE Trans Inf Theory. 1978;24:530\u0026ndash;6.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuffman DA. A Method for the Construction of Minimum-Redundancy Codes. Proceedings of the IRE. 1952;40:1098\u0026ndash;101.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKryukov K, Ueda MT, Nakagawa S, Imanishi T. Sequence Compression Benchmark (SCB) database\u0026mdash;A comprehensive evaluation of reference-free compressors for FASTA-formatted sequences. GigaScience. 2020;9:giaa072.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGrabowski S, Kowalski TM. MBGC: Multiple Bacteria Genome Compressor. GigaScience. 2022;11:giab099.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMartin-L\u0026ouml;f P. The definition of random sequences. Inf Control. 1966;9:602\u0026ndash;19.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBohlin J, Skjerve E. Examination of Genome Homogeneity in Prokaryotes Using Genomic Signatures. PLoS ONE. 2009;4:e8113.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBohlin J. Genomic Signatures in Microbes\u0026mdash;Properties and Applications. Sci World J. 2011;11:715\u0026ndash;25.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eReichenberger ER, Rosen G, Hershberg U, Hershberg R. Prokaryotic Nucleotide Composition Is Shaped by Both Phylogeny and the Environment. Genome Biol Evol. 2015;7:1380\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMeyer MM. Revisiting the Relationships Between Genomic G\u0026thinsp;+\u0026thinsp;C Content, RNA Secondary Structures, and Optimal Growth Temperature. J Mol Evol. 2021;89:165\u0026ndash;71.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFranklin JNY, Porter CP. Key developments in algorithmic randomness. In: Porter CP, Franklin JNY, editors. Algorithmic Randomness: Progress and Prospects. Cambridge: Cambridge University Press; 2020. pp. 1\u0026ndash;39.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMachta J. Entropy, information, and computation. Am J Phys. 1999;67:1074\u0026ndash;7.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePruitt KD, Tatusova T, Maglott DR. NCBI Reference Sequence (RefSeq): a curated non-redundant sequence database of genomes, transcripts and proteins. Nucleic Acids Res. 2005;33 Database issue:D501\u0026ndash;4.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWood SN. Generalized Additive Models: An Introduction with R, Second Edition. 2nd edition. New York: Chapman and Hall/CRC; 2017.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMaistrenko OM, Mende DR, Luetge M, Hildebrand F, Schmidt TSB, Li SS, et al. Disentangling the impact of environmental and phylogenetic constraints on prokaryotic within-species diversity. ISME J. 2020;14:1247\u0026ndash;59.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAkaike H. Information Theory and an Extension of the Maximum Likelihood Principle. In: Parzen E, Tanabe K, Kitagawa G, editors. Selected Papers of Hirotugu Akaike. New York, NY: Springer; 1998. pp. 199\u0026ndash;213.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePawitan Y. All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press; 2001.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIhaka R, Gentleman R. R: A Language for Data Analysis and Graphics. J Comput Graphical Stat. 1996;5:299\u0026ndash;314.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBates D, M\u0026auml;chler M, Bolker B, Walker S. Fitting Linear Mixed-Effects Models Using lme4. J Stat Softw. 2015;67:1\u0026ndash;48.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4597889/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4597889/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eMicrobial genomes vary considerably both with respect to size and base composition. While the smallest genomes have less than 200,000 base pairs, or nucleotides, others can consist of millions. The same is true for genomic base composition, often summarized as genomic AT or GC content due to the similar frequencies of (A)denine and (T)hymine on one hand and (C)ytosine and (G)uanine on the other; the most extreme microbes can have genomes with AT content below 25% or above 85%. Genomic AT content influences the frequency of DNA words, or oligonucleotides, consisting of multiple nucleotides. Here we explore to what extent genome size, AT/GC content and genomic oligonucleotide usage variance (OUV) are linked to microbial genome redundancy, or compression rate, as measured using both a DNA based- (MBGC) and a general purpose (ZPAQ) compression algorithm on 4,713 RefSeq genomes.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eWe find that genome size (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) and OUV (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) are both strongly associated with genome redundancy for both types of file compressors. The DNA based MBGC compressor managed to improve compression with approximately 3% on average with respect to ZPAQ. Moreover, MBGC detected a significant (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) compression ratio difference between AT poor and AT rich genomes that was not detected with ZPAQ.\u003c/p\u003e\u003ch2\u003eConclusion\u003c/h2\u003e \u003cp\u003eAs lack of compressibility is equivalent to the presence of randomness, our findings suggest that small and AT rich genomes may have accumulated more random mutations on average than larger and AT poor/GC rich genomes, which, in turn, were significantly more redundant. Moreover, we find that OUV is a strong proxy for genome compressibility in microbial genomes. The ZPAQ compressor was found to agree with the MBGC compressor, albeit with a poorer performance, except for the compressibility of AT-rich and AT-poor genomes.\u003c/p\u003e","manuscriptTitle":"Estimation of redundancy in microbial genomes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-04 11:52:34","doi":"10.21203/rs.3.rs-4597889/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f75bb460-9bd4-452a-8f18-e807b0a7136b","owner":[],"postedDate":"July 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-07-10T04:23:32+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-04 11:52:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4597889","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4597889","identity":"rs-4597889","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}