Genome sequence of the pattern forming Paenibacillus vortex bacterium reveals potential for thriving in complex environments
- Alexandra Sirota-Madi†2, 3,
- Tsviya Olender†3,
- Yael Helman†2, 4,
- Colin Ingham5,
- Ina Brainis1,
- Dalit Roth1, 2,
- Efrat Hagi4,
- Leonid Brodsky1, 6,
- Dena Leshkowitz7,
- Vladimir Galatenko8,
- Vladimir Nikolaev9,
- Raja C Mugasimangalam10,
- Sharron Bransburg-Zabary1, 2,
- David L Gutnick11,
- Doron Lancet3 and
- Eshel Ben-Jacob1, 12Email author
© Sirota-Madi et al; licensee BioMed Central Ltd. 2010
Received: 15 October 2010
Accepted: 17 December 2010
Published: 17 December 2010
The pattern-forming bacterium Paenibacillus vortex is notable for its advanced social behavior, which is reflected in development of colonies with highly intricate architectures. Prior to this study, only two other Paenibacillus species (Paenibacillus sp. JDR-2 and Paenibacillus larvae) have been sequenced. However, no genomic data is available on the Paenibacillus species with pattern-forming and complex social motility. Here we report the de novo genome sequence of this Gram-positive, soil-dwelling, sporulating bacterium.
The complete P. vortex genome was sequenced by a hybrid approach using 454 Life Sciences and Illumina, achieving a total of 289× coverage, with 99.8% sequence identity between the two methods. The sequencing results were validated using a custom designed Agilent microarray expression chip which represented the coding and the non-coding regions. Analysis of the P. vortex genome revealed 6,437 open reading frames (ORFs) and 73 non-coding RNA genes. Comparative genomic analysis with 500 complete bacterial genomes revealed exceptionally high number of two-component system (TCS) genes, transcription factors (TFs), transport and defense related genes. Additionally, we have identified genes involved in the production of antimicrobial compounds and extracellular degrading enzymes.
These findings suggest that P. vortex has advanced faculties to perceive and react to a wide range of signaling molecules and environmental conditions, which could be associated with its ability to reconfigure and replicate complex colony architectures. Additionally, P. vortex is likely to serve as a rich source of genes important for agricultural, medical and industrial applications and it has the potential to advance the study of social microbiology within Gram-positive bacteria.
To face the challenges posed by these environments, Paenibacillus spp. produce a wealth of enzymes and proteases as well as a great variety of antimicrobial substances that affect a wide range of microorganisms [10–12]. The possession of these advanced defensive and offensive strategies render the Paenibacillus spp. bacteria as a rich source of useful genes for agricultural, medical, industrial applications. Despite this potential, genome sequencing of Paenibacillus spp. to date is limited and is currently available only for two species Paenibacillus larvae and Paenibacillus sp. JDR-2.
A successful behavioral strategy utilized by some Paenibacillus spp. is to cooperatively form and develop large and intricately organized colonies of 109-1012 cells. Being part of a large cooperative, the bacteria can better compete for food resources and be protected against antibacterial assaults [3, 13]. Two of the most fascinating pattern-forming Paenibacillus spp. bacteria, are P. vortex[3, 14] and P. dendritiformis[3, 15]. Under laboratory growth conditions, these bacteria can develop, like other social bacteria, colonies that behave much like a multi-cellular organism, with cell differentiation and task distribution [16–19] (see also Additional file 1 section I).
Additional file 2:Movement of a single vortex, 500× magnification and twice the real speed. (WMV 958 KB)
Additional file 3:Early stage of colony organization including the formation of vortices and moving groups of bacteria. The magnification is 50× magnification and 60× rate. (WMV 405 KB)
When grown on hard surfaces, P. vortex generates special aggregates of dense bacteria that are pushed forward by repulsive chemotactic signals sent from the cells at the back (see Additional file 1 section I). These rotating aggregates (termed vortices), are similar to the rotating bacteria groups generated by Paenibacillus alvei and Bacillus circulans, pave the way for the colony to expand. The vortices serve as building blocks of colonies with special modular organization (Figure 1 and Additional file 1 section I).
Accomplishing such intricate cooperative ventures requires sophisticated cell-cell communication [3, 19, 22–24]. Communicating with each other, bacteria exchange information regarding population size, a myriad of individual environmental measurements at different locations, their internal states and their phenotypic and epigenetic adjustments . The bacteria collectively sense the environment and execute distributed information processing to glean and assess relevant information [3, 19, 25]. Next, the bacteria respond accordingly, by reshaping the colony while redistributing tasks and cell differentiations, and turning on defense and offense mechanisms [3, 16–19, 25, 26], thus achieving better adaptability to heterogeneous environments . Such collective, decentralized, adaptive decision making is a form of swarm intelligence, a term originally derived from cybernetics but applicable to some aspects of colonial organisms including ants, birds, humans and bacteria [27–29]. In terms of collective social behaviour, P. vortex has been studied extensively at the level of mathematical modeling [3, 30–32] and now requires a sequenced genome to connect this approach with the underlying genetics.
Comparative genomic analysis revealed that bacteria successful in heterogeneous and competitive environments often contain extensive signal transduction and regulatory networks [33–35]. It is likely that advanced social behavior  and elevated collective adaptability  are underpinned by a highly developed signal transduction system consisting of modular domains forming a network of sensors, transducers and responders [34, 36, 37].
In this report we present the de novo genome sequence of the P. vortex, which was obtained by utilizing a hybrid deep-sequencing approach using 454 and Illumina techniques [38, 39]. We further performed detailed comparative genomic analysis with a dataset of 500 complete bacterial genomes to discover P. vortex unique properties. The results revealed that P. vortex has one of the highest number of signal transduction genes among all the Gram-positive bacteria in the dataset. Only two other Gram-positive bacteria strains, the Paenibacillus sp. JDR-2 and the Geobacillus sp. Y412MC10, have more TCS genes. These two species and P. vortex have equal normalized combined score of TCS, TFs, transport and defense related genes (see material and methods), which is significantly higher than the combined score of all other bacteria in the data set.
The analysis also unveiled genes required for competition over resources (e.g. iron, amino acids and sugars), for producing offensive compounds (antibiotics and lytic enzymes) and for defense (resistance to antibiotics and other toxins). These genes can support traits needed for thriving in the heterogeneous and highly competitive environments.
Sequencing of the P. vortex genome
Summary of the sequencing results obtained from each of the technologies.
Average read length (nt)
Total no. single reads
Total no. paired-end reads
Average depth-coverage of mapped reads
Total contigs (> 500 nt)
Number of scaffolds (> 500 nt) using 454 and Illumina
Assembly accuracy and completeness
To estimate the accuracy and the completeness of the hybrid assembly we performed detailed comparison between the 454 and the Illumina contigs. The results show that the 454 contigs covered 99.93% of the hybrid assembly with an average distance between contigs comprising the hybrid scaffolds of -5 bp and total 890 bp missing from the hybrid assembly (Additional file 1 Figure S6 B, C, D). The Illumina contigs covered 99.81% of the hybrid assembly with average distance between contigs of -10 bp and missing total 4,500 bp (Additional file 1 Table S3). The overall sequence identity between the two technologies was 99.8%. These results and the fact that there were no miss-assemblies demonstrate that although the P. vortex assembly is in several contigs, it provides complete genome coverage and with an extremely high accuracy (Additional file 1 section II).
General genome statistics
Genomic features of the P. vortex genome.
Genome size (nt)
G+C content (%)
Genes with assigned function
Genes with unknown function
Average CDS size (nt)
Percent of coding region
We have identified several types of repetitive sequences: 184 global repeats (sequence that is present in at least two copies in two different locations), 32 local inverted repeats and 231 tandem repeats within the P. vortex genome (Figure 3) (for methods see Additional file 1 section VII). Such sequences were suggested to play an important functional role in genome plasticity , by means of homologous recombination (HR), horizontal transfer or transposition in the genome [46–48]. HR has relevant roles in DNA repair, chromosome segregation and generation of genetic variation. Crossover events might produce genome rearrangements, such as deletions, leading to the loss of all genetic information in that region or duplications which could increase the amount of genetic information . Additionally, repeats located within regulatory regions might constitute an on/off switch of gene expression at the transcriptional level . Similarly, repeats located within coding regions can induce a premature ending of translation when a mutation changes the number of repeats . However, detailed mechanisms and functions of most repeats are still unknown.
Repetitive sequences are the major reason for the difficulty we encountered in finishing the genome assembly into a complete sequence. Analysis of the scaffold ends (100 bp of each end) revealed that 78% of them have repetitive sequences that are on average 37 bp long and could be mapped on average onto 5 different scaffold ends.
We note that some regions in the P. vortex genome have an extremely high coverage (see areas marked in blue, second circle, Figure 3). Although, the assembly algorithms tend to collapse the highly identical repetitive sequences into one copy, high coverage in that specific area might serve as a signature for identifying regions present in several copy numbers in the genome . For example, the ribosomal unit (16 S, 23 S and 5S) has approximately 5 times higher coverage than the average, suggesting that this unit appears approximately 5 times in the P. vortex genome. Interestingly, the Geobacillus sp. Y412MC10 has 8 copies of the ribosomal unit.
Functional validation by custom microarray
We used specially designed Agilent custom microarray submitted to EMBL-EBI [ArrayExpress: E-MEXP-3019] to validate the annotation. The microarray (Additional file 1 section IV) includes 105,000 oligos of 60 bp long, which corresponds to all the predicted ORFs and the intergenic regions.
Hybridization of the genomic DNA validated 91,324 probes (88%) of the total designed probes and no missed regions were found (see Additional file 1 section IV for more details). Hybridization of the pooled RNA from different growth conditions confirmed 4,701 (73%) of the predicted ORFs. The remaining 1,736 (27%) ORFs were not detectable under the tested conditions. Out of those, 1,064 ORFs have an assigned putative function and 672 are hypothetical. Hybridization of predicted 73 non-coding RNAs located within the intergenic regions, confirmed 43 (58%).
We performed detailed comparative analysis between the P. vortex genome and a set of 500 complete bacterial genomes of 2-10 Mbp (Additional file 7). Bacterial genomes available with draft sequence were not included in the analysis. Specifically, we focused on a reduced set of 261 genomes with genome size of 4-8 Mbp (closer to the P. vortex genome size) and a subset of 50 soil bacteria genomes within this group (Additional file 8). The comparison was done with regard to four gene systems which are related to complex bacterial lifestyle and adaptability to fluctuating environments: two-component systems, transcription factors, defense mechanisms and transport systems.
Two-component system (TCS)
Structural classification of the P. vortex RRs according to previously proposed scheme  revealed relatively high number of 37 OmpR family and 30 AraC family DNA-binding response regulators. Class organization of the P. vortex TCS proteins as described in  revealed 150 HK-RR paired, 32 orphaned (isolated) and 21 in complex gene clusters (for more details see Additional file 1 section VII). Neighborhood analysis of the TCS surrounding genes revealed that 101 (30%) are transport related genes, 46 (12.6%) have regulatory functions (mainly consist of transcription factors), and 35 (9.6%) belong to the energy metabolism category (mainly employing biosynthesis and degradation of polysaccharides).
Transcription Factors (TFs)
Using the method described in , we identified a total of 411 TFs in P. vortex genome, which placed it at the upper 5% of the 500 bacteria set (Figure 4C). This number is considerably higher than the average 158 ± 111 TFs among the 500 bacterial genomes and higher than the average 208 ± 92 TFs among the subset of 261 genomes with size 4-8 Mbp sizes. Among the subset of 50 soil bacteria genomes, only two strains, Paenibacillus sp. JDR-2 (7.08 Mbp) and Delftia acidovorans SPH-1 (6.76 Mbp) have a higher number of TFs genes. We note that an overall linear dependence between the TFs and the genome size was found (Figure 4C).
P. vortex encodes an extensive set of 700 transport related genes. Among the 500 bacterial genomes, P. vortex was at the upper 1% of the population (Figure 4B), along with additional five strains Rhizobium leguminobarum bv. viciae (7.75 Mbp), Geobacillus sp. Y412MC10 (7.12 Mbp), Paenibacillus sp. JDR-2 (7.08 Mbp), Sinorhizobium meliloti 1021 (6.7 Mbp) and Sinorhizobium medicae WSM419 (6.8 Mbp). About a third, 258 (35%) of the genes are involved in carbohydrate transport, 42 genes encode components of iron transporters, 23 genes encode components of amino acid transporters and 39 genes encode components of oligo/dipeptide transporters. The latter could be used as nutrient sources, as well as signal molecules regulating bacterial development, virulence, and conjugal plasmid transfer .
The P. vortex genome contains 138 genes related to resistance against inhibitory substances such as antibiotics, copper, aluminium, arsenic and toxic anions (Figure 4D). The proximity of TCS genes to ABC transporters is known to form specific and efficient detoxification units . Out of the 138 genes, 90 are transporter-encoding genes. Non-transport related genes include antibiotic resistance encoding genes such as penicillin binding proteins, beta-lactames, chloramphenicol posphotransferases/acetyltransferases, vanZ and vanW glycopeptide antibiotics resistance genes. Apart from Streptomyces griseus NBRC 13350 (8.54 Mbp), P. vortex harbors the highest number of defense related genes among the 500 analyzed genomes. Additionally, P. vortex has the highest number of these genes compared to the subset of 261 genomes with a 4-8 Mbp genome size (the average for this subset is 60 ± 20).
The combined score
When compiling the four indices into a combined score, P. vortex and two other Gram-positive bacteria strains, the Paenibacillus sp. JDR-2 and the Geobacillus sp. Y412MC10 stand out among the 500 genomes in the dataset (Figure 4E). These two species and P. vortex have equal normalized combined score (Figure 4F), which is significantly higher than the combined score of all other bacteria in the dataset.
Motility and Chemotaxis
Social motility could also be powered by the extension and retraction of type IV pili [61, 62]. P. vortex genome contains several pili-related genes such as pilZ, pilT, flp pilus assembly protein and prepilin type IV. However, we could not identify all the genes known to be involved in biogenesis and motility of type IV pili [63–65]. Furthermore, the fastest known rate of type IV pili related movement does not exceed 50 μm/min [66, 67], whereas, P. vortex has an average movement rate of 300 μm/min (data not shown).
Previous studies suggest that the vortices are formed by attractive interaction between swarming cells which can be mediated via attractive chemotactic signaling and/or physical links . The P. vortex genome contains several chemotaxis related genes, including the cheA, cheB, cheC, cheD, cheW and cheY. Many of the chemotaxis genes are located within the large motility loci (Figure 6 and Additional file 1 Figure S14). Additional 16 MCP (methyl-accepting chemotaxis) genes were found in other locations along the genome.
Sporulation and competence
Formation of spores and uptake of foreign DNA represent an important aspect of bacterial survival strategies. P. vortex genome encodes an extensive set of 153 genes responsible for sporulation including cell division, engulfment, cortex and coat synthesis, maturation and germination (Additional file 9). The identified sporulation genes included one of the conserved PFAM domains [53, 68], TIGR domains , COG categories  or KEGG pathways  associated with sporulation (Additional file 10).
Although, 9 competence-related genes such as comEA, comer and comEC were identified, they represent only a small portion of the complete competence pathway [71–73]. Additionally, we did not identify homologous genes that belong to the Rap system, which plays an important role in the cell decision-making between sporulation and competence [74, 75]. It is therefore possible that the common pathway described for sporulation and competence in other Gram-positive bacteria  is different in P. vortex.
Clusters of Multifunctional Enzymes-Secondary Metabolites
Whole-genome shotgun pyrosequencing has proved remarkably useful for the large-scale sequencing of bacterial genomes [81–83]. High-quality de novo assemblies can be obtained with relatively few errors and gaps when the sequence read coverage redundancy is 15-fold or greater. Closing all the gaps in each genome sequence is time-consuming and costly; therefore, in the near future there will be an excess of draft bacterial sequences versus closed genomes in public databases.
This study presents a de novo assembly of the P. vortex genome utilizing a hybrid deep-sequencing strategy using a Roche 454 Genome Sequencer (GS 20) and an Illumina Genome Analyzer. The use of the two next-generation leading technologies and the combination of the results into a hybrid assembly overcame the drawbacks of each technology and resulted in longer scaffolds. We demonstrated that the sequence identity between the two methods was 99.88%, reflecting the low error rate of both sequences. The genome sequence, the predicted transcripts and the non-coding RNAs were further validated by hybridization to custom microarray.
Notably, even when using several algorithms and an extremely high coverage, the data could not be assembled into a single sequence. Analysis of the ends of contigs revealed that the unassembled contigs have small repetitive sequences at their ends. The existence of high number of repetitive sequences is a generic obstacle that tempers the ability of the assembly algorithms to generate a single version of the complete genome, and more so when working with short reads. It has been shown that sequence repeats have a functional role that can contribute to genomic plasticity which allows rapid adaptation to environmental changes .
P. vortex was originally isolated from colonies of B. subtilis, soil bacteria commonly found in the rhizosphere [84, 85]. The Rhizosphere is characterized by large environmental fluctuations, which act as a selecting force determining the diversity of the microbial community [86–89]. The features identified in the genome of P. vortex suggest that these bacteria can lead a successful lifestyle in the highly competitive environment of the rhizosphere as well as serve as an efficient plant beneficial rhizobacteria (PBR). PBR competitively colonize plant roots and can simultaneously act as biofertilizers and as antagonists (biopesticides) of recognized root pathogens .
Comparative genomics and comparative network biology are emerging as key tools in understanding of how bacteria respond cooperatively to challenging complex environments. In particular, it was previously suggested that bacteria successful in heterogeneous and competitive environments often contain extensive signal transduction and regulatory networks [25, 34, 91]. These observations, and the fact that signal transduction networks afford intracellular information processing , led to the notion that the number and fraction of signal transduction genes can be used as a measure of the "Bacteria IQ" [34, 91]. Detailed comparative genomic analysis revealed that the P. vortex's genome and the genome of the Gram-negative, social and predatory bacterium M. xanthus have exceptionally high number of TCS genes, supporting the notion that they are required for advanced social behavior.
The P. vortex species is marked by its complex spatial organization of the colony, with the bacteria forming different patterns to better cope with the environment [3, 4, 14, 93]. Pattern-formation and self-organization in microbial systems is an intriguing phenomenon that might also provide insights into the evolutionary development of the concerted action of cells in higher organisms . Therefore, sequencing of the P. vortex genome paves the way to understanding of regulatory processes involved in cell-cell communication and colonial patterning and more generally, to understanding of cooperative bacterial response to changing environmental conditions. Such information should facilitate increased exploitation of Paenibacillus spp. in industrial, agricultural and medical fields, as well as help us comprehend the evolutionary development of multicellular organisms.
The P. vortex genome was sequenced using a hybrid deep-sequencing approach resulting in an estimated genome size of 6.3 Mb. A total of 6,437 ORFs were identified and 73% of them confirmed using specially designed Agilent custom microarray chip. The results of the two sequencing methods were compared resulting in 99.88% sequence identity, reflecting low error rate of both sequences. The use of the two next-generation leading technologies and the combination of the results into a hybrid assembly overcame the drawbacks of each technology and resulted in longer scaffolds.
Comparative genomics analysis with 500 complete bacterial genomes revealed that P. vortex has one of the highest number of TCS genes among all the Gram-positive bacteria in the dataset. High numbers of TCS genes were also found in the genome of the social predator M. xanthus, supporting the notion that they are required for advanced social behavior. M. xanthus serves as an important Gram-negative bacterial model for the study of multicellularity in prokaryotes . Similarly, P. vortex may have the potential to provide significant insights on cell-cell interactions, pattern formation and social behavior in Gram-positive bacteria. Additionally, P. vortex encodes an extensive set of TFs, transport and defense related genes. These findings suggest that P. vortex has a highly developed signal transduction system and that these genes can support traits needed for thriving in heterogeneous, fluctuating and highly competitive environments.
The genome sequence of P. vortex provides the basis for understanding of social organization and pattern formation within Gram-positive bacteria. P. vortex is the first sequenced Paenibacillus species reported to show these properties and this work supports the development of genetic approaches to the study of prokaryotic multicellularity and multi-agent decision making (swarm intelligence). Furthermore, this organism is likely to become a valuable resource for exploitation within biotechnology.
P. vortex DNA was prepared at two separate times for the 454 and Illumina sequencing runs following the standard Roche and Illumina protocols respectively. P. vortex was grown in Luria-Bertani (LB) medium, at 37°C with shaking (200 rpm) over night. DNA was extracted from 2 ml cell culture (109/ml), using Qiagen, DNeasy Blood and Tissue Kit, according to the manufacture's protocol with the following modifications; cells were incubated with Lysosyme for 45 minutes prior extraction. Elution from Qiagen column was performed with 200 μl buffer AE (10 mM Tris-HCl, 0.5 mM EDTA pH 9.0).
We used a hybrid sequencing approach that incorporates 454 pyrosequencing with Illumina Genome Analyzer. Sequencing by both methods was performed in compliance with manufacturer's instructions Roche and Illumina accordingly.
The 454 reads were assembled using Newbler Assembler  version number 1.0.53. To obtain optimized results for the assembly of Illumina short reads we tested several algorithms (Additional file 1 Table S2), but eventually selected Velvet . Velvet's algorithm handled single and paired-end reads and produced contigs with highest sequence identity of 99.88% to those produced by the 454. Algorithms used to assemble short reads are Velvet 0.7.28, Edena 2.1.1 and Euler-SR 1.0. Velvet algorithm was used with parameter hash length of 31, insert length of 250 and minimum contig length 50. Edena algorithm was used with a minimum overlap parameter of 23. The final step included the assembly of the Newbler (454) and Velvet (Illumina) contigs using Minimus 2.0.5 .
The DNA sequence was run through JCVI's prokaryotic annotation pipeline (JCVI Annotation Service), which includes gene finding by Glimmer, Blast-extend-repraze (BER) searches, HMM searches, TMHMM searches, SignalP predictions, and automatic annotations from AutoAnnotate. Additionally, the DNA sequence was annotated using NCBI Prokaryotic Genomes Automatic Annotation Pipeline (PGAAP) and the combined annotation was submitted to [GenBank: ADHJ00000000].
Phylogenetic analysis of 16S
The construction of the phylogenetic tree of 22 taxa was based on 16 S rRNA sequences downloaded in fasta format from DNA Data Bank of Japan (DDBJ) ftp://ftp.ddbj.nig.ac.jp/ddbj_database/16S/. The alignment of the chosen sequences was performed using ClustaX  and the construction of the phylegenetic tree using Neighbor-Joining algorithm . The percentage of replicate trees in which the associated taxa clustered together in the bootstrap test (500 replicates) was also calculated . The evolutionary distances were computed using the Maximum Composite Likelihood method  utilizing Mega 4 software .
Identification of Two-Component System and Transcription Factor genes
The approach used to identify putative TCS and TF genes utilized HMM (Hidden Markov Model) profiles found in Pfam database of protein families http://pfam.sanger.ac.uk/. TCS genes were identified similarly to that previously described by  and  and TF genes were identified as described by . The compiled list of Pfam domains that was used to identify TCS and TFs is presented in Additional file 11 and 12 respectfully. Additional methods description is included in Additional file 1 section VII.
Identification of Transporters and Defense related genes
To identify putative transport and defense related genes we utilized Cluster of Orthologous Groups (COG) profiles [42, 43]. The compiled list of COG profiles that were used to identify transport and defense related genes is presented in Additional file 13 and 14 respectfully.
The combined score was calculated as an average of the standard deviation (stdev) of two-component system, transcription factor, transport and defense genes for the dataset of 500 bacterial genomes. The combined score was calculated both as normalized and non-normalized to genome size.
Experiment procedure of P. vortex effect on Verticillium dahlia
V. dahliae was grown on trypsin soy agar plates (TSA), at 28°C. A 10 day old stock plate was used to initiate the experiments as follows: A startup slice of 0.5 mm diameter was cut from the colony edge and placed on a fresh TSA plate. The fungal slice was positioned 1 cm away from the center of a 9 mm Petri dish. Plates were incubated untill V. dahliae colonies reached 1.5 cm diameter (6 days incubation). At this time-point an overnight P. vortex culture, grown in LB, 28°C, with shaking (200 rpm), was inoculated in a 6 cm long line, horizontal to V. dahliae. P. vortex was positioned 2.5 cm away from the V. dahliae colony center. V. dahliae colonies without the inoculation of P. vortex served as control. All tests were carried out in triplicate.
Submission to the international collection deposits
Isolate P. vortex sp. nov. V453 was deposited at the Bacillus Genetic Stock Center (BGSC), Columbus, OH, USA, as strain 31A2T and at the Belgium Coordinated Collection of Microorganisms (BCCM/LMG) as strain LMG 25955.
List of abbreviations
Open Reading Frames
Cluster of Orthologous Groups
Non-Ribosomal Peptide Synthetase
Plant Beneficial Rhizobacteria
Hidden Markov Model
We are thankful to the contribution of the late Vladimir Alexandrovich Drachev during early stage of this research effort. We thank JCVI for providing the JCVI Annotation Service. We thank Relly Foler from DYN-GS. This research has been supported by the Tauber Family Foundation and the Maguy-Glass Chair in Physics of Complex systems at Tel Aviv University and by the National Science Foundation Grants PHY-0216576 and 0225630 at UCSD.
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