Computational Biology and Chemistry 53 (2014) 1–4
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Computational Biology and Chemistry
journal homepage: www.elsevier.com/locate/compbiolchem
Editorial
Editorial: Complexity in genomes
Two years ago, three of us (AP, YA, WL) organized a satellite
meeting in the framework of the European Conference on Complex
Systems (ECCS12) (Gilbert et al., 2014) focusing on genomic complexity.
Although biological life on earth is one of the most complex
systems, the field of complex system studies seems to mainly deal
with physical systems where mathematical description, measurement,
and modelling are traditionally addressed. The idea came
to us that exploration of genomics in the framework of complex
systems theory is needed in print, which led to this special issue.
In the literature, the term complexity (C) in genomes is used
with several meanings. Some people use the number of genes in a
genome to measure its complexity (Hahn and Wray, 2002). The C in
“low complexity” (e.g. Wootton and Federhen, 1993) regions and
the C in “more complex” genomes (e.g. Van Oeveren et al., 2011)
are both caused by repetitive sequences, the only difference being
that the repeat length is shorter in the former whereas the variety
of repeats is larger in the latter case. Biological complexity is also a
much debated concept (McShea, 1996; McShea and Brandon, 2010).
Here we use the C-word more consistently and more generically:
when used on an object, a process, a system, it means that it defies
simple or traditional description – full of surprises, lacking single
universal law, longer (Li and Vitányi, 1997) and/or time-consuming
description (Bennett, 1988) in reproducing a copy, etc.
In biology and in genomics, just when one believes a universal
law should cover all organisms at all time, exceptions are always
discovered. For example, the central dogma (from DNA to mRNA
to protein) was violated with the discovery of reverse transcription
(Temin and Mizutani, 1970). The fact that a continuous stretch of
DNA is transcribed into mRNA and this last is translated to protein
in prokaryotes turned out to be untrue for eukaryotes (Chow et al.,
1977). When it was commonly accepted that all biological functions
are carried out by proteins, and protein-coding genes are the most
meaningful part of the genome, the regulatory role of RNA was
discovered (Fire et al., 1998; Morris and Mattick, 2014), and nonprotein-coding
regions are the focus of intensive studies in recent
years (The ENCODE Project Consortium, 2012). The implication that
evolutionarily conserved non-coding regions (Bejerano et al., 2004)
must have a regulatory function faces the reality of high turnover
rate of these regulatory elements (Dermitzakis and Clark, 2002).
The list goes on.
It would be impossible to cover all hard-to-describe topics in
genomics. What we aim in this special issue is to bring researchers
who are comfortable with the theme of complexity in physical sciences
to discuss genomes. A common thread of all papers here is
the quantitative nature of the analysis, not merely a qualitative
description. As early as 80 years ago, it was proposed that an institute
should be established in which “biologists, chemists, physicists
and mathematicians will cooperate in the future opening, and beneficial
use, of the vast territory of quantitative biology” (Harris,
1933). Though we are still far away from outlining “complexity in
genomes” as a field, just as “quantitative biology” not being a clear
field for over 80 years, at least we bring those with a complex systems
background to study genomics. There are 18 papers in this
special issue, which can be roughly grouped into four categories.
DNA sequences as symbolic sequences: A large group of papers
are treating DNA sequence from genomes as symbolic sequences,
and apply techniques from time series analysis to study them
(Cocho et al., 2014; Melnik and Usatenko, 2014; Papapetrou and
Kugiumtzis, 2014; Provata et al., 2014b; Suvorova et al., 2014;
Wu, 2014). This topic has its own historical surprises: the simplest
description of a symbolic sequence is a random sequence, and
the next simplest one is short-range-correlated sequences. However,
DNA sequences as symbolic sequences were shown to be
much more complicated, exhibiting long-range correlations (Li and
Kaneko, 1992; Peng et al., 1992; Voss, 1992).
Provata et al. (2014b) is an extension of the work on human
genome in Provata et al. (2014a) to other organisms. It exemplifies
a typical approach in studying symbolic sequences: 4-nucleotide
to 2-symbol conversions, dimer frequency and Markov transition
probability, block entropy, symbol persistence properties, etc.
Quantitative markers are extracted as indicatives of evolution,
since organisms with different evolutionary paths are examined
and compared. This collection of the basic statistics from DNA
sequences is more accessible to readers who are less familiar with
biology.
Cocho et al. (2014) attempts to explain the exponential correlation
function observed in bacteria genomes by showing the
roles played by different codon positions, by frame-shift, and by
coding region size distributions. Without mixing statistics from different
codon positions, the correlation between positions will be
much weaker. Without a frame-shift between neighboring coding
sequences, the correlation will not decay at all. And without a broad
distribution of coding sequence length, the correlation function
could be linear instead of exponential.
High-order Markov chains are mathematical models that add
more complexity to the simple first-order Markov chain, with
the goal of better fitting complex sequences. Both Melnik and
Usatenko (2014) and Papapetrou and Kugiumtzis (2014) addressed
http://dx.doi.org/10.1016/j.compbiolchem.2014.08.003
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2 Editorial / Computational Biology and Chemistry 53 (2014) 1–4
high-order Markov models. In Melnik and Usatenko (2014), the
relationship between memory functions and correlation function,
which reduces the number of parameters in high-order Markov
(Usatenko et al., 2009), is applied to DNA sequences.
In Papapetrou and Kugiumtzis (2014), the order of Markov models
in DNA sequences is estimated by a technique proposed in
Papapetrou and Kugiumtzis (2013). This analysis also shows a clear
difference between those DNA sequences which can be modelled
by a higher-order Markov chain, and those which can not (such
as those with power-law correlation). In the latter case, the estimated
Markov chain order does not converge with the increasing
sequence length.
Finding hidden or latent periodicity in DNA sequences has a long
history in bioinformatics, starting from the periodicity-3 signal in
protein-coding regions (Fickett, 1982). Suvorova et al. (2014) compares
the performance of several alternative periodicity-detection
methods. They found that spectra-based methods tend to shift the
signal to a shorter periodicity, whereas a direct matching and test
of a fuzzy motif with a fixed length, called “information decomposition”
(Korotkov et al., 2003), performs better.
Wu (2014) study concerns exact repeats (unlike the latent periodicity
studied in Suvorova et al., 2014) in DNA sequences. In
bioinformatics community, the most common tool in detecting
repeats is the dot-matrix plot (Mount, 2013). In Wu (2014), such
repeats are detected by the recurrence plots borrowed from the
study of dynamical systems (Wu, 2004).
Spatial position and size distribution of functional units: The
second large group of papers concerns the size and/or spacing distribution
of genomic units (Dios et al., 2014; Gao and Miller, 2014;
Mui˜no et al., 2014; Tsiagkas et al., 2014). If the biologically functional
units (e.g. genes) are randomly distributed in the genome,
the gap length follows negative binomial and geometric distribution,
with an exponential trend. On the other hand, if the functional
unit is larger than a single point on the chromosome with its own
size, the simplest description of sizes is still an exponential distribution.
In DNA sequences, the observed distributions for both gap
distances and sizes follow mostly power-laws.
Gao and Miller (2014) focuses on the size distribution of
orthologs obtained from sequence alignment. Such distribution for
human-chimpanzee alignment tends to be exponential, whereas
that for human-mouse alignment or multi-species ultraconserved
regions (Bejerano et al., 2004) tends to be power-law distribution
with an exponent of −4 (Salerno et al., 2006). These can also be compared
to the distribution of paralogs (by genome self-alignment)
which is power-law distribution with exponent −3 (Gao and Miller,
2011; Massip and Arndt, 2013). It is argued in Gao and Miller (2014)
that orthologs from closely related species contain both a component
from self-aligned paralogs and one from orthologs in distant
species, so its distribution is a mixture as well.
In order to detect genome clustering, Dios et al. (2014) compares
gap distances of genomic elements to the geometric distribution,
continuing their earlier work (Hackenberg et al., 2011, 2012). On
average, close to 30% of genomic elements in the human genome
are found to be within clusters. Functional and regulatory elements
(genes, CpG islands, transcription factor binding sites, enhancers)
show higher clustering levels, as compared to DNase sites, repeats
(Alus, LINE1) or SNPs. The clusters for all these elements form in
turn high-level super-clusters, thus revealing a complex genome
landscape dominated by hierarchical clustering.
Mui˜no et al. (2014) studies a clustering of cancer somatic mutations
called “kataegis” (Greek word for “storm”) (Nik-Zainal et al.,
2012). The gap distance between mutations is bimodal, but the
tail of the peaks falls off as a power-law function. Spatial clustering
of somatic mutations may imply mutational hot spots, and the
targeted hypermutated genes may provide new insight on cancer
biology.
Tsiagkas et al. (2014) studies the gap distance between CpG
islands, both those near genes and those away from genes (orphan
CpG islands). Power-law distribution is again obtained similar
to those of other functional units (Sellis et al., 2007; Sellis and
Almirantis, 2009; Klimopoulos et al., 2012; Polychronopoulos et al.,
2014). A simple evolutionary model based on segmental duplication
is used to simulate a possible scenario to explain the
data.
Intricacies in next-generation sequencing: The next group of
papers concern the high-throughput (next-generation) sequencing
(Gallo et al., 2014; Li and Freudenberg, 2014; Zhu and Zheng,
2014). The current sequencing biotechnology involves a mechanical
breakage of genome into fragments, sequencing either the
whole or the two ends of the fragment (the sequenced piece is
called a read), and either aligning the reads back to the reference
genome, if such a reference is available, or “de novo” constructing
the genome sequence from overlapping reads. When one region
of the genome is identical to another, that redundancy creates
tremendous difficulties in either reads alignment or in de novo
assembly.
Gallo et al. (2014) addresses a seldom discussed topic of hidden
parameters in a de novo assembly. Using the SOAPdenovo program
(Luo et al., 2012) as an example, Gallo et al. (2014) shows
that assembly results can be altered if the parameter values are not
chosen optimally, which can be a problem as many users of a de
novo assembly program simply use the default setting. A particular
ignored parameter is the k of k-mer length in the de Bruijn graph.
The optimal choice of k is a function of fragment size, read length,
and the level of redundancy in the genome.
Li and Freudenberg (2014) locates all exact repeats of length
1000 bases (kb) to the human genome, previously identified in Li
et al. (2014). More than 1% of the human genome are covered by
these unmappable 1000-mer reads. The unmappable regions are
compared to those of twenty or so genomic annotations. About
4% of human genes overlap with these unmappable regions. And
more than 90% of the unmappable regions were in the segmental
duplicated regions (Bailey et al., 2002). On the other end, there is
zero overlap between unmappable regions and the ultraconserved
elements (Bejerano et al., 2004).
Zhu and Zheng (2014) does not attempt to align or assemble
reads, but to identify a specific bacterium in a mixture of
many bacteria (i.e., meta-genomes). Their approach is based on
the idea that species-specific codon usage leads to characteristic
k-mer frequencies in six reading frames of the coding region and in
non-coding regions. Collecting k-mer frequencies from the reads,
feeding them as inputs to a learning algorithm (Zheng and Wu,
2003), will indicate the presence or absence of specific types of
bacterial genomes.
Specific biological and genomic topics: These papers are
grouped together as they address specific biological applications:
(Junier, 2014; Nikolaou, 2014; Pratanwanich and Lio, 2014;
Zaghloul et al., 2014; Zuo et al., 2014).
Junier (2014) is an overview of different forces and mechanisms
that shape the organization and structure of bacterial genomes at
different levels. At protein level, interactions between amino acids
determine the co-evolution of protein sequences. At genome level,
genes cluster into operons, with complicated co-regulation and
co-expression for various biological processes (transcription, translation,
replication, cell division). Junier (2014) aims at discussing all
relevant mechanisms in a single work.
Nikolaou (2014) explores biological explanation of a linguisticmotivated
regularity in the genome, the Menzerarth’s law at the
gene-exon-base level (Li, 2012). The Menzerath law in this context
states that if a gene contains more exons, the average exon size
tends to be smaller. This Menzerath law was shown to be true for
human genes (Li, 2012). Using mouse genes, Nikolaou (2014) shows
Editorial / Computational Biology and Chemistry 53 (2014) 1–4 3
that only genes with low conservation tend to follow the Menzerath
law. These genes also tend to have less alternative splicing, fewer
exons, and larger exon sizes.
Profiling genome-wide gene expressions at different conditions
becomes easier by the microarray technology. Besides focusing
on individual genes, more and more analyses focus on collection
of genes such as genes involved in a given biochemical pathway.
Pratanwanich and Lio (2014) investigates yet another method,
called latent Dirichlet allocation (Blai et al., 2003), in the context
of drug treatment, following a similar work using the Bayesian
sparse factor model (Ma and Zhao, 2012). Although this work is
within the scope of machine learning, the topic of multi-scales and
multi-levels remain a favorite in the complex system study.
The finding of strand asymmetry at the replication origin in bacterial
genomes (Lobry, 1996) led to search of GC or AT skew in the
human genome (Brodie Of Brodie et al., 2005). The so-called skew-N
domain is certain pattern in the skew series which is proposed as an
indication of the replication origin (Touchon et al., 2005). Zaghloul
et al. (2014) follows this long line of research to propose a new
type of patterns in the skew series, called skew-split-N domains
which is reminiscent of a letter N but split in half. Skew-N domains
cover 1/3, whereas skew-split-N domains cover 12%, of the human
genome. It is proposed that skew-split-N domains contain random
replication initiations.
Zuo et al. (2014) overviews the authors’ work on alignmentfree
phylogeny using composition vector of k-mers (Hao and Qi,
2004), implemented in the computer program CVTree (Xu and Hao,
2009). The large number of bacterial genomes being sequenced provides
an opportunity to compare alignment-free phylogeny with
the standard Bergey’s Manual of Systematic Bacteriology (Garrity
et al., 2001). The importance of subtracting the expected k-mer frequencies
from (k − 1)-mer data is emphasized. The effect of k on
phylogenetic tree is discussed.
Admittedly, our collection of articles in this special issue is
limited in scopes. We hope to attract more authors from a more
diverse background if we produce a similar special issue in the
future. However, there is no denying that biology is complicated
and genomes are complex. Franc¸ ois Jacob commented in his article
“Evolution and tinkering” (Jacob, 1977): “natural selection does
not work as an engineer works. It works like a tinkerer – a tinkerer
who does not know exactly what he is going to produce but uses
whatever he finds around him...” This ad hoc nature of the evolution,
prolonged tinkering process, and the resulting imperfection,
might be the root cause of complexity in genomes.
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Yannis Almirantis
Theoretical Biology and Computational Genomics
Laboratory, Institute of Biosciences and Applications,
National Center for Scientific Research “Demokritos”,
Athens, Greece
Peter Arndt
Department of Computational Molecular Biology,
Max Planck Institute for Molecular Genetics, Berlin,
Germany
Wentian Li
Robert S Boas Center for Genomics and Human
Genetics, Feinstein Institute for Medical Research,
North Shore LIJ Health Systems, Manhasset, NY, USA
Astero Provata
Statistical Mechanics and Complex Dynamical
Systems Laboratory, Institute of Nanoscience and
Nanotechnology, National Center for Scientific
Research “Demokritos”, Athens, Greece
Available online 19 August 2014