BACKGROUND
hepatitis c virus  infects nearly 3% of the world's population and is a major cause of liver disease worldwide  <cit> .
there is no vaccine against hcv and up to recently standard-of-care therapy involved the combined use of pegylated interferon  and ribavirin .
this combination therapy is expensive, effective in only 50%-60% of patients, and can be associated with frequent and serious adverse side effects in >75% of patients  <cit> .
hcv is genetically very heterogeneous and classified into  <dig> genotypes and numerous subgenotypes  <cit> .
hcv changes continuously during chronic infection, showing a complex dynamics of intra-host viral subpopulations  <cit> .
the most studied hcv region is the hypervariable region  <dig>  located at amino acid  positions 384- <dig> in the structural protein e <dig>  sequence variation in hvr <dig> correlates with neutralization escape and is associated with viral persistence during chronic infection  <cit> .
recent advances in next-generation sequencing  methods allow for analysis of the unprecedented number of hvr <dig> sequence variants from infected patients and present a novel opportunity for understanding intra-host hcv evolution, drug resistance and immune escape  <cit> .
hcv hvr <dig> variants sampled using ngs from infected individuals were studied here.
we report, for the first time, that most variants are organized into large single-mutation connected components.
this finding presents a novel framework for genetic analysis of intra-host hcv populations, relevant to the study of viral transmission, immune escape and drug resistance.
RESULTS
one-step networks
intra-host variants of the e1/e <dig> region were extensively sampled from  <dig> patients chronically infected with hcv genotypes  <dig> or  <dig>  after ngs sequencing error correction, the average number of reads and variants obtained from each sample were  <dig>   and  <dig> , respectively.
in all patients, the average frequency of the major variant was  <dig>  .
the distance between each pair of variants was calculated and networks were created for each patient, where each node is a variant and two nodes are connected by a link if the nucleotide distance between them is  <dig>  the subsequent research was focused only on large components, which were arbitrarily defined as encompassing >5% of all reads.
this threshold was chosen because it defines a small number of large components that still account for most reads found in a patient .
in average, a patient had  <dig>  components , ranging from  <dig> to  <dig> in each patient; each component having in average  <dig>  variants  and a total of  <dig>  reads  .
network topological analysis
all components showed a skewed degree distribution.
although not strictly following a power-law degree distribution, most nodes are incident only to one or two links.
the shortest path distances among all pairs of sequences were estimated, and then the average shortest path distance for each component was calculated.
over all components, the average pairwise distance shortest path was  <dig>  , whereas the diameter was  <dig>  .
interestingly, the nodes in the component did cluster very little .
a low clustering coefficient indicates the absence of triangles in the network.
the only way to form a triangle is to have three sequences that are one mutation away from each other at the same nucleotide position.
the absence of this network motif simply indicates that close sequences of this hcv genomic region often differ at distant positions, instead of differing in states of the same position.
the component distances highly correlated  with the hamming distances between sequences in all patients.
when patristic distances were calculated over a neighbor-joining tree for sequences included in each component, the correlation between the original hamming distances and tree-based distances was lower in all cases, with an average of  <dig>  .
these results indicate that the distances over the component represented the true distances more accurately than the distances over the tree .
in silico sampling robustness
the robustness of each component to sampling bias was evaluated by measuring the decline in component connectivity with reduction of the sample size.
all components were extraordinarily robust to this type of stochastic sampling; even after randomly removing 85% of all reads, the largest connected component in the new subsample still involved  <dig> % of the remaining nodes  .
in vitro reproducibility
for  <dig> of the patients, a second sample which was taken one hour after the first one was available, providing the opportunity to test whether the components found in the first sample were also present in the second sample, an indication of experimental reproducibility.
the results showed that  <dig> % of the components present in the first samples were found in the repeat samples.
for these components found in both samples, we calculated the fraction of reads found in the first sample that were also found in the second sample, obtaining an average over all components of  <dig> %  .
this result suggests that intra-host subpopulations modelled with components are experimentally stable.
all components missing in the second sample had an initial frequency between  <dig> % and  <dig> % of all reads, indicating that the 5% arbitrary frequency cut-off chosen in this work for a component to qualify as "large" is near the limit of experimental replication.
simulated transmission events
we simulated unsafe injection-related transmission events using estimates of the number of virions  that may establish productive infection of liver from contaminated syringes .
in order to simulate the transmission event, a random subsample  of only  <dig> reads was taken from the reads of a given patient .
for each recipient sample, we tested the number of components from the source represented by the sampled reads.
importantly, we found that  <dig> % of all simulated transmission events seeded all components present in the source , indicating that viral variants that have established infection in a recipient after transmission likely represent all components existing in the source, thus allowing for the potential reconstitution of these components from a small but heterogeneous founder population.
differences among components
the components of each patient were well separated, with the average hamming distance between their members  being ~ <dig> times greater than within each component .
for each component, the overall ratio of nonsynonymous  to synonymous changes  was calculated.
most of the patients  harboured only negatively selected components, whereas  <dig> % harboured only positively selected components.
however,  <dig> patients  had a mixture of components under negative or positive selection .
discussion
rna viruses exhibit extremely high mutation rates and given the large population sizes observed in both experimental and natural infections with these viruses, every possible point mutation and many double-mutation combinations could theoretically be generated during each replication cycle within a population.
the mutability of each viral genome means that rna virus populations exist as dynamic mutant networks in which sequences are continuously diversified and regenerated by mutation of related sequences, often known as a quasispecies  <cit> .
connecting viral variants that differ in one mutation provides a natural framework to organize the heterogeneous population of viral variants.
although this has been achieved on theoretical landscapes , here we have built these one-step networks for the first time using viral experimental data, a development just recently enabled by the ngs technology.
analyses conducted using in silico and experimental sampling showed significant robustness of the component to stochastic variation, implying that a true component will not be split into two due to poor sampling.
another advantage of the network framework is that several topological parameters can be calculated  for a given patient and then used to test for differences among different phenotype groupings .
although this topological comparison was not performed in the present research, this network framework provides a new potential tool for comparing viral populations.
the simulated transmission events may seem too simplified, as selective pressure in the new host environment will likely be different, affecting intra-host evolution in a different way.
however, the simulation does not deal with the survival of those seeds, only with their likelihood of being transmitted.
this is in agreement with many reports on hcv outbreaks, where it is very common that newly infected cases share variants and are genetically very close to the transmission source  <cit> .
based on this, the purpose of the simulation was to show a very simple phenomenon: if transmission is purely stochastic , then the variants present in the source will be transmitted to the incident case in proportion to their frequency.
as was shown in the transmission simulation experiments, the high frequency of components allows a small random sample of 20- <dig> variants to represent with high probability all of these components in each intra-host viral population.
this important property facilitates reconstitution of the same component composition of intra-host viral population from the small number of founder variants transmitted from one host to another.
the level of genetic separation among large components indicates that exploration of all the components in each infected host likely cannot be accomplished via a single mutation starting from a single viral variant.
the existence of several subpopulations organized in one-step components in each infected individual studied here suggests that the founder viral population was complex, in agreement with recent findings  <cit> .
the data obtained in this study indicate that the mechanism of stochastic sampling is compatible with the complex founder model and further experiments are underway to resolve this issue.
hcv changes continuously during chronic infection, showing a complex dynamics of intra-host viral subpopulations  <cit> .
large components of hcv variants obtained from follow-up samples could be used to define viral subpopulations, whose shifts in frequency over time can be tracked to pinpoint the sources of drug resistance or immune escape.
the one-step connection provides a simple biological criterion for identifying the genetic structure of viral subpopulations.
when sampling of intra-host viral variants is done using ngs, the one-step components can be generated for clustering closely related variants without any assumption on their ancestral origin.
the genetic space occupied by the variants of a given component will likely be explored very rapidly via single mutations starting from any variant in each component.
the estimation of the amount of time needed for this exploration should take into account the kinetic parameters of hcv infection .
these are currently being investigated in our laboratory.
given that some patients harbour a mixture of positively and negatively selected components, the subpopulations defined by components may experience different selection pressures, accounting for the frequency shifts observed during intra-host evolution in some patients  <cit> .
the distances calculated over the component were found to be almost identical to the hamming distances calculated for all variants, which allows for better visualizing local and global relationships among sequences and among clusters.
it must be noted that other popular representations of the distance matrix, such as hierarchical bifurcating trees or multi-dimensional scaling, reduce dimensionality of data at the cost of accuracy of distance representation among genetic variants.
we have shown here that patristic distances calculated over the neighbor-joining tree have a significantly lower correlation with the distance matrix than the one-step components.
a good phylogenetic tree presents a single most likely history of substitutions, all of which collectively generated the dataset.
however, the key point of our work is that a single history is an over-simplification when the whole quasispecies network is continuously generated over multiple parallel paths.
this network setting fits better the highly dynamic process which is the result of hcv's large population size, high mutation rate and fast doubling time.
although ngs has been instrumental in the acquisition of a massive number of genomic sequences, the contribution of these sequences to understanding intra-host viral evolution have been modest, considering the enormous amount of genetic information generated by the technology  <cit> .
this paradox can, in part, be explained by the shortage of computational methods for verifying the accuracy of generated sequences and accommodating large datasets.
however, extensive sequencing of intra-host viral variants offers also novel opportunities for analysing genetic information, which are not available for small samples of sequences.
one such approach was developed in this study.
we have shown that one-step components represent accurately genetic relationships among the hcv hvr <dig> variants extensively sampled by ngs from infected individuals.
this likely reflects sampling of numerous intermediates and/or co-existent ancestors, which allows the parsimonious reconstruction of the evolutionary process responsible for generation of the intra-host viral population.
CONCLUSIONS
the majority of intra-host hvr <dig> variants form large connected components in infected patients.
these large components preserve true distances among variants, are well separated from each other, are robust to sampling, and are likely seeded during transmission events.
large components identified through ngs-facilitated deep sampling offer a novel evolutionary framework for genetic analysis of intra-host hcv populations to characterise viral factors relevant to transmission, immune escape and drug-resistance.

 hepatitis c virus infects nearly 3% of the world's population and is a major cause of liver disease worldwide. there is no vaccine against hcv and up to recently standard-of-care therapy involved the combined use of pegylated interferon and ribavirin. this combination therapy is expensive, effective in only 50%-60% of patients, and can be associated with frequent and serious adverse side effects in >75% of patients. hcv is genetically very heterogeneous and classified into genotypes and numerous subgenotypes. hcv changes continuously during chronic infection, showing a complex dynamics of intra-host viral subpopulations. the most studied hcv region is the hypervariable region located at amino acid positions 384- in the structural protein e sequence variation in hvr correlates with neutralization escape and is associated with viral persistence during chronic infection. recent advances in next-generation sequencing methods allow for analysis of the unprecedented number of hvr sequence variants from infected patients and present a novel opportunity for understanding intra-host hcv evolution, drug resistance and immune escape. hcv hvr variants sampled using ngs from infected individuals were studied here. we report, for the first time, that most variants are organized into large single-mutation connected components. this finding presents a novel framework for genetic analysis of intra-host hcv populations, relevant to the study of viral transmission, immune escape and drug resistance.  one-step networks intra-host variants of the e1/e region were extensively sampled from patients chronically infected with hcv genotypes or after ngs sequencing error correction, the average number of reads and variants obtained from each sample were and, respectively. in all patients, the average frequency of the major variant was. the distance between each pair of variants was calculated and networks were created for each patient, where each node is a variant and two nodes are connected by a link if the nucleotide distance between them is the subsequent research was focused only on large components, which were arbitrarily defined as encompassing >5% of all reads. this threshold was chosen because it defines a small number of large components that still account for most reads found in a patient. in average, a patient had components, ranging from to in each patient; each component having in average variants and a total of reads. network topological analysis all components showed a skewed degree distribution. although not strictly following a power-law degree distribution, most nodes are incident only to one or two links. the shortest path distances among all pairs of sequences were estimated, and then the average shortest path distance for each component was calculated. over all components, the average pairwise distance shortest path was, whereas the diameter was. interestingly, the nodes in the component did cluster very little. a low clustering coefficient indicates the absence of triangles in the network. the only way to form a triangle is to have three sequences that are one mutation away from each other at the same nucleotide position. the absence of this network motif simply indicates that close sequences of this hcv genomic region often differ at distant positions, instead of differing in states of the same position. the component distances highly correlated with the hamming distances between sequences in all patients. when patristic distances were calculated over a neighbor-joining tree for sequences included in each component, the correlation between the original hamming distances and tree-based distances was lower in all cases, with an average of. these results indicate that the distances over the component represented the true distances more accurately than the distances over the tree. in silico sampling robustness the robustness of each component to sampling bias was evaluated by measuring the decline in component connectivity with reduction of the sample size. all components were extraordinarily robust to this type of stochastic sampling; even after randomly removing 85% of all reads, the largest connected component in the new subsample still involved % of the remaining nodes. in vitro reproducibility for of the patients, a second sample which was taken one hour after the first one was available, providing the opportunity to test whether the components found in the first sample were also present in the second sample, an indication of experimental reproducibility. the results showed that % of the components present in the first samples were found in the repeat samples. for these components found in both samples, we calculated the fraction of reads found in the first sample that were also found in the second sample, obtaining an average over all components of %. this result suggests that intra-host subpopulations modelled with components are experimentally stable. all components missing in the second sample had an initial frequency between % and % of all reads, indicating that the 5% arbitrary frequency cut-off chosen in this work for a component to qualify as "large" is near the limit of experimental replication. simulated transmission events we simulated unsafe injection-related transmission events using estimates of the number of virions that may establish productive infection of liver from contaminated syringes. in order to simulate the transmission event, a random subsample of only reads was taken from the reads of a given patient. for each recipient sample, we tested the number of components from the source represented by the sampled reads. importantly, we found that % of all simulated transmission events seeded all components present in the source, indicating that viral variants that have established infection in a recipient after transmission likely represent all components existing in the source, thus allowing for the potential reconstitution of these components from a small but heterogeneous founder population. differences among components the components of each patient were well separated, with the average hamming distance between their members being ~ times greater than within each component. for each component, the overall ratio of nonsynonymous to synonymous changes was calculated. most of the patients harboured only negatively selected components, whereas % harboured only positively selected components. however, patients had a mixture of components under negative or positive selection. discussion rna viruses exhibit extremely high mutation rates and given the large population sizes observed in both experimental and natural infections with these viruses, every possible point mutation and many double-mutation combinations could theoretically be generated during each replication cycle within a population. the mutability of each viral genome means that rna virus populations exist as dynamic mutant networks in which sequences are continuously diversified and regenerated by mutation of related sequences, often known as a quasispecies. connecting viral variants that differ in one mutation provides a natural framework to organize the heterogeneous population of viral variants. although this has been achieved on theoretical landscapes, here we have built these one-step networks for the first time using viral experimental data, a development just recently enabled by the ngs technology. analyses conducted using in silico and experimental sampling showed significant robustness of the component to stochastic variation, implying that a true component will not be split into two due to poor sampling. another advantage of the network framework is that several topological parameters can be calculated for a given patient and then used to test for differences among different phenotype groupings. although this topological comparison was not performed in the present research, this network framework provides a new potential tool for comparing viral populations. the simulated transmission events may seem too simplified, as selective pressure in the new host environment will likely be different, affecting intra-host evolution in a different way. however, the simulation does not deal with the survival of those seeds, only with their likelihood of being transmitted. this is in agreement with many reports on hcv outbreaks, where it is very common that newly infected cases share variants and are genetically very close to the transmission source. based on this, the purpose of the simulation was to show a very simple phenomenon: if transmission is purely stochastic, then the variants present in the source will be transmitted to the incident case in proportion to their frequency. as was shown in the transmission simulation experiments, the high frequency of components allows a small random sample of 20- variants to represent with high probability all of these components in each intra-host viral population. this important property facilitates reconstitution of the same component composition of intra-host viral population from the small number of founder variants transmitted from one host to another. the level of genetic separation among large components indicates that exploration of all the components in each infected host likely cannot be accomplished via a single mutation starting from a single viral variant. the existence of several subpopulations organized in one-step components in each infected individual studied here suggests that the founder viral population was complex, in agreement with recent findings. the data obtained in this study indicate that the mechanism of stochastic sampling is compatible with the complex founder model and further experiments are underway to resolve this issue. hcv changes continuously during chronic infection, showing a complex dynamics of intra-host viral subpopulations. large components of hcv variants obtained from follow-up samples could be used to define viral subpopulations, whose shifts in frequency over time can be tracked to pinpoint the sources of drug resistance or immune escape. the one-step connection provides a simple biological criterion for identifying the genetic structure of viral subpopulations. when sampling of intra-host viral variants is done using ngs, the one-step components can be generated for clustering closely related variants without any assumption on their ancestral origin. the genetic space occupied by the variants of a given component will likely be explored very rapidly via single mutations starting from any variant in each component. the estimation of the amount of time needed for this exploration should take into account the kinetic parameters of hcv infection. these are currently being investigated in our laboratory. given that some patients harbour a mixture of positively and negatively selected components, the subpopulations defined by components may experience different selection pressures, accounting for the frequency shifts observed during intra-host evolution in some patients. the distances calculated over the component were found to be almost identical to the hamming distances calculated for all variants, which allows for better visualizing local and global relationships among sequences and among clusters. it must be noted that other popular representations of the distance matrix, such as hierarchical bifurcating trees or multi-dimensional scaling, reduce dimensionality of data at the cost of accuracy of distance representation among genetic variants. we have shown here that patristic distances calculated over the neighbor-joining tree have a significantly lower correlation with the distance matrix than the one-step components. a good phylogenetic tree presents a single most likely history of substitutions, all of which collectively generated the dataset. however, the key point of our work is that a single history is an over-simplification when the whole quasispecies network is continuously generated over multiple parallel paths. this network setting fits better the highly dynamic process which is the result of hcv's large population size, high mutation rate and fast doubling time. although ngs has been instrumental in the acquisition of a massive number of genomic sequences, the contribution of these sequences to understanding intra-host viral evolution have been modest, considering the enormous amount of genetic information generated by the technology. this paradox can, in part, be explained by the shortage of computational methods for verifying the accuracy of generated sequences and accommodating large datasets. however, extensive sequencing of intra-host viral variants offers also novel opportunities for analysing genetic information, which are not available for small samples of sequences. one such approach was developed in this study. we have shown that one-step components represent accurately genetic relationships among the hcv hvr variants extensively sampled by ngs from infected individuals. this likely reflects sampling of numerous intermediates and/or co-existent ancestors, which allows the parsimonious reconstruction of the evolutionary process responsible for generation of the intra-host viral population.  the majority of intra-host hvr variants form large connected components in infected patients. these large components preserve true distances among variants, are well separated from each other, are robust to sampling, and are likely seeded during transmission events. large components identified through ngs-facilitated deep sampling offer a novel evolutionary framework for genetic analysis of intra-host hcv populations to characterise viral factors relevant to transmission, immune escape and drug-resistance. 
all components were robust to in silico stochastic sampling; even after randomly removing 85% of all reads, the largest connected component in the new subsample still involved % of remaining nodes. facilitated by ngs, large components offer a novel evolutionary framework for genetic analysis of intra-host viral populations and understanding transmission, immune escape and drug resistance. when syringe-sharing transmission events were simulated, % of all simulated transmission events seeded all components present in the source. most intra-host variants are organized into distinct single-mutation components that are: well separated from each other, represent genetic distances between viral variants, robust to sampling, reproducible and likely seeded during transmission events. the distance between each pair of variants was calculated and networks were created for each patient, where each node is a variant and two nodes are connected by a link if the nucleotide distance between them is the work focused on large components having > 5% of all reads, which in average account for % of all reads found in a patient. this provides a novel opportunity to represent and study the mutational landscape of hepatitis c virus within a single host. after ngs error correction, the average number of reads and variants obtained from each sample were and respectively. the ratio of nonsynonymous to synonymous changes was calculated and some patients showed a mixture of networks under strong negative and positive selection. next-generation sequencing allows for sampling numerous viral variants from infected patients. the distance between any two variants calculated over the component correlated strongly with nucleotide distances, a better correlation than the one obtained with neighbour-joining trees.
 next-generation sequencing allows for sampling numerous viral variants from infected patients. this provides a novel opportunity to represent and study the mutational landscape of hepatitis c virus within a single host.  intra-host variants of the hcv e1/e region were extensively sampled from chronically infected patients. after ngs error correction, the average number of reads and variants obtained from each sample were and respectively. the distance between each pair of variants was calculated and networks were created for each patient, where each node is a variant and two nodes are connected by a link if the nucleotide distance between them is the work focused on large components having > 5% of all reads, which in average account for % of all reads found in a patient. the distance between any two variants calculated over the component correlated strongly with nucleotide distances, a better correlation than the one obtained with neighbour-joining trees. in each patient, components were well separated, with the average distance between being times greater than within each component. the ratio of nonsynonymous to synonymous changes was calculated and some patients showed a mixture of networks under strong negative and positive selection. all components were robust to in silico stochastic sampling; even after randomly removing 85% of all reads, the largest connected component in the new subsample still involved % of remaining nodes. in vitro sampling showed that % of components present in the original sample were also found in experimental replicas, with % of reads found in both. when syringe-sharing transmission events were simulated, % of all simulated transmission events seeded all components present in the source.  most intra-host variants are organized into distinct single-mutation components that are: well separated from each other, represent genetic distances between viral variants, robust to sampling, reproducible and likely seeded during transmission events. facilitated by ngs, large components offer a novel evolutionary framework for genetic analysis of intra-host viral populations and understanding transmission, immune escape and drug resistance. 12- june third ieee international conference on computational advances in bio and medical sciences new orleans, la, usa 