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<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
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<meta name="src" content="canal.tex">
<meta name="date" content="2012-03-05 15:37:00">
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<!--l. 86--><p class="noindent" ><span
class="cmbx-10x-x-109">Background: </span>Since its emergence in 1968, influenza A (H3N2) has evolved extensively in
genotype and antigenic phenotype. However, despite strong pressure to evolve away from human
immunity and to diversify in antigenic phenotype, H3N2 influenza shows paradoxically
limited genetic and antigenic diversity present at any one time. Here, we propose simple
immunity and to diversify in antigenic phenotype, H3N2 influenza shows paradoxically limited
genetic and antigenic diversity present at any one time. Here, we propose a simple
model of antigenic evolution in the influenza virus that accounts for this apparent
discrepancy.
<!--l. 88--><p class="noindent" ><span
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periodic transmission in the tropics. During this time, H3N2 influenza has continually evolved
both genetically and antigenically. Most antigenic drift is thought to be driven by
changes to epitopes in the hemagglutinin (HA) protein <span class="cite">[<a
href="#XNelson07NatRevGenet">2</a>]</span>. Phylogenetic analysis of the
genetic relationships among HA sequences has revealed a distinctive genealogical tree
href="#XNelson07NatRevGenet">2</a>]</span>. Phylogenetic analysis of
the relationships among HA sequences has revealed a distinctive genealogical tree
showing a single predominant trunk lineage and side branches that persist for only 1&#8211;5
years before going extinct <span class="cite">[<a
href="#XFitch97">3</a>]</span>. This tree shape is indicative of serial replacement of
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<!--l. 114--><p class="noindent" >The virus persists over the course of the 40-year simulation, and at the end of most simulations,
there remain only a few closely related viral lineages, indicating that genealogical diversity is
restricted by evolution in the two-dimensional antigenic landscape. Reduced diversity is
substantially more common in models with less mutation or models with less variable mutation
effects (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: param --></a>). At higher mutation rates, viruses may move apart in antigenic phenotype too
rapidly for competition to always eliminate the weaker of two diverging lineages. Similarly, with
high variance in mutational effect, there can sometimes emerge new antigenic types, too distant
from the existing population to suffer limiting competitive pressure. Both these scenarios lead to
coexistence of multiple antigenic phenotypes. We thus restrict the model to parameter regimes
with lower mutation rates and lower mutation effect variances. We primarily focus on
the model with 10<sup><span
substantially more common in models with less mutation or models with less variable
mutation effects (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: param --></a>). At higher mutation rates, viruses may move apart in
antigenic phenotype too rapidly for competition to always eliminate the weaker of two
diverging lineages. Similarly, with high variance in mutational effect, there can sometimes
emerge new antigenic types, too distant from the existing population to suffer limiting
competitive pressure. Both these scenarios lead to coexistence of multiple antigenic
phenotypes. We thus restrict the model to parameter regimes with lower mutation rates and
lower mutation effect variances. We primarily focus on the model with 10<sup><span
class="cmsy-8">-</span><span
class="cmr-8">4</span></sup> mutations per infection per day and standard deviation of 4
antigenic units. In this model, 80 out of the 100 replicate simulations show reduced
genealogical diversity (defined as less than 9 years separating contemporaneous viruses).
class="cmr-8">4</span></sup> mutations
per infection per day and mutation effects with standard deviation of 0.4 antigenic
units. In this model, 80 out of the 100 replicate simulations show reduced genealogical
diversity (defined as less than 9 years of evolution separating contemporaneous viruses).
We conditioned the following analysis on these 80 simulations, compiling summary
statistics across this pool and presenting a detailed analysis of a single representative
simulation.
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<!--l. 124--><p class="noindent" ></div><hr class="endfigure">
<!--l. 126--><p class="noindent" >The model exhibits annual winter epidemics in temperate regions and less periodic epidemics in
the tropics (<a href="#x1-4002r2">Figure 2<!--tex4ht:ref: evol -->A</a>). Across replicate simulations, we observe average yearly attack rates of
6.8% in temperate regions and rates of 7.1% in the tropics, comparable with estimated attack
rates of influenza A (H3N2) of 3&#8211;8% per year <span class="cite">[<a
6.8% in temperate regions and rates of 7.1% in the tropics, comparable with estimated
attack rates of influenza A (H3N2) of 3&#8211;8% per year <span class="cite">[<a
href="#XMonto93">10</a>,&#x00A0;<a
href="#XKoelle09">11</a>]</span>. Over the course of the simulation, the
virus population evolves in antigenic phenotype exhibiting, at any point, a handful of highly
abundant phenotypes sampled repeatedly and a large number of phenotypes appearing at low
abundance (<a href="#x1-4002r2">Figure 2<!--tex4ht:ref: evol -->B</a>). The observed antigenic map of H3N2 influenza includes substantial
experimental noise; replicate strains appear in diverse positions on the observed map. By
including measurement noise on antigenic locations (see Methods), we approximate an
experimental antigenic map of H3N2 influenza (<a href="#x1-4002r2">Figure 2<!--tex4ht:ref: evol -->D</a>). Over the 40-year simulation,
antigenic drift moves the virus population at an average rate across replicates of 1.05 antigenic
units per year, corresponding closely to the empirical rate of 1.2 units per year <span class="cite">[<a
href="#XSmith04">9</a>]</span>. The
appearance of clusters in the antigenic map comes from the regular spacing of high abundance
href="#XKoelle09">11</a>]</span>. Over the course of the
simulation, the virus population evolves in antigenic phenotype exhibiting, at any point, a
handful of highly abundant phenotypes sampled repeatedly and a large number of
phenotypes appearing at low abundance (<a href="#x1-4002r2">Figure 2<!--tex4ht:ref: evol -->B</a>). The observed antigenic map of
H3N2 influenza includes substantial experimental noise; replicate strains appear in
diverse positions on the observed map. By including measurement noise on antigenic
locations (see Methods), we approximate an experimental antigenic map of H3N2
influenza (<a href="#x1-4002r2">Figure 2<!--tex4ht:ref: evol -->D</a>). Over the 40-year simulation, antigenic drift moves the virus
population at an average rate across replicate simulations of 1.05 antigenic units per year,
corresponding closely to the empirical rate of 1.2 units per year <span class="cite">[<a
href="#XSmith04">9</a>]</span>. The appearance
of clusters in the antigenic map comes from the regular spacing of high abundance
phenotypes combined with measurement noise. Over time, clusters of antigenically
similar strains are replaced by novel clusters of more advanced strains (<a href="#x1-4003r3">Figure 3<!--tex4ht:ref: phenotypes -->A</a>).
Across replicate simulations, clusters persist for an average of 5.0 years measured as
Across replicate simulations, clusters persist for an average of 5.0 years, measured as
the time it takes for a new cluster to reach 10% frequency, peak and decline to 10%
frequency. The transition between clusters occurs quickly, taking an average of 1.8
years.
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and genealogical diversity <span class="cite">[<a
href="#XBedfordBMC11">12</a>]</span>.
<!--l. 150--><p class="noindent" >Selective pressures can be examined by comparing which mutations fix, i.e.&#x00A0;are incorporated into
the progenitor trunk lineage, and which mutations are lost, i.e.&#x00A0;incorporated into side branches
bound for extinction. This approach has shown that, in influenza A (H3N2), natural selection
promotes mutations to epitope sites in the HA1 region <span class="cite">[<a
the progenitor trunk lineage, and which mutations are lost, i.e.&#x00A0;incorporated into side
branches bound for extinction. This approach has shown that, in influenza A (H3N2),
natural selection promotes mutations to epitope sites in the HA1 region <span class="cite">[<a
href="#XBush99MBE">13</a>,&#x00A0;<a
href="#XWolf06">14</a>]</span>. By examining antigenic
mutations, we find a corresponding effect in simulated evolutionary trajectories (<a href="#x1-4004r1">Table 1<!--tex4ht:ref: mktable --></a>).
Trunk mutations tend to push antigenic phenotype forward along the line of primary
antigenic variation. Additionally, we find that trunk mutations occur at strikingly
href="#XWolf06">14</a>]</span>. By
examining antigenic mutations, we find a corresponding effect in simulated evolutionary
trajectories (<a href="#x1-4004r1">Table 1<!--tex4ht:ref: mktable --></a>). Additionally, we find that trunk mutations occur at strikingly
regular intervals, with less variation of waiting times than expected under a simple
random process (<a href="#x1-4005r4">Figure 4<!--tex4ht:ref: waittimes --></a>). There is a relative scarcity of mutation events occurring in
intervals under 1 year and a relative excess of a mutation events occurring in 2&#8211;3 year
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seasonal forcing, we would expect trunk proportions of one third for each region. We
calculated rates of migration based on observed event counts across replicate simulations,
separating region-specific rates on side branches from region-specific rates on trunk
branches. We find that migration patterns on side branches are close to symmetric, with
similar rates between all regions, while migration patterns on trunk branches are highly
asymmetric, with high rates of movement between temperate regions and from temperate
regions into the tropics (<a href="#x1-5001r5">Figure 5<!--tex4ht:ref: spatial -->B</a>). Extrapolating from these rates, we arrive at an
expected stationary distribution of trunk location of 76% tropics and 24% temperate
regions, in line with the observed residency patterns of the trunk. It may at first seem
counter-intuitive to see higher rates of movement from the temperate regions into the tropics
along trunk branches, but it makes sense when thought of in terms of conditional
probability. Only those lineages that remain in the tropics, migrate into the tropics or
those lineages which rapidly migrate between the north and south have a chance at
branches. We find that migration patterns on side branches are close to symmetric,
with similar rates between all regions, while migration patterns on trunk branches are
highly asymmetric, with high rates of movement between temperate regions and from
temperate regions into the tropics (<a href="#x1-5001r5">Figure 5<!--tex4ht:ref: spatial -->B</a>). Extrapolating from these rates, we
arrive at an expected stationary distribution of trunk location of 76% tropics and 24%
temperate regions, in line with the observed residency patterns of the trunk. It may at first
seem counter-intuitive to see higher rates of movement from the temperate regions
into the tropics along trunk branches, but it makes sense when thought of in terms of
conditional probability. Only those lineages that remain in the tropics, migrate into
the tropics or which rapidly migrate between the north and south have a chance at
becoming the trunk lineage, while lineages that remain within the temperate regions are
doomed to extinction. Along similar lines, Adams and McHardy <span class="cite">[<a
href="#XAdams11">18</a>]</span> use a modeling
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id="x1-7000"></a>Linear antigenic movement</h3>


<!--l. 205--><p class="noindent" >It would seem likely for one viral lineage to move in one antigenic direction, while another lineage
moves tangentially, eventually resulting in two non-interacting viral lineages. Instead, we find
that movement in a single antigenic direction is favored, resulting in most replicate simulations
showing low standing diversity (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: param --></a>). The origins of this pattern can be seen in the
interaction between virus evolution and host immunity (<a href="#x1-7001r6">Figure 6<!--tex4ht:ref: immunity --></a>). As the virus population
<!--l. 205--><p class="noindent" >It might seem reasonable for one viral lineage to move in one antigenic direction, while another
lineage moves tangentially, eventually resulting in two non-interacting viral lineages. Instead, we
find that movement in a single antigenic direction is favored, resulting in most replicate
simulations showing low standing diversity (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: param --></a>). The origins of this pattern can be seen in
the interaction between virus evolution and host immunity (<a href="#x1-7001r6">Figure 6<!--tex4ht:ref: immunity --></a>). As the virus population
evolves forward it leaves a wake of immunity in the host population, and evolution away from this
immunity results in the canalization of the antigenic phenotype; mutations that continue along
the line of primary antigenic variation will show a transmission advantage compared to more
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genealogical tree <span class="cite">[<a
href="#XFitch97">3</a>]</span> exhibited by influenza A (H3N2). However, for this process to take
hold, the virus population needs to be somewhat mutationally-limited; if functional
antigenic variants of novel phenotype emerge too quickly, then antigenic change will
occur too rapidly for competition to winnow down the virus population to a single
lineage.
antigenic variants of novel phenotype emerge too quickly, then antigenic change will occur
too rapidly for competition to winnow down the virus population to a single lineage
(<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: param --></a>).
<!--l. 217--><p class="noindent" >To consider to what extent these results were contingent on the dimensionality of the
underlying antigenic model, we further implemented our model in a 10-dimensional
antigenic space. Here, mutations occur as 10-spheres, but the distance moved by a
Expand All @@ -622,7 +623,7 @@ <h3 class="likesubsectionHead"><a
and second dimensions of variation account for 87% and 7%, respectively, of the total
variance (<a href="#x1-18003r3">Figure S3<!--tex4ht:ref: 10dgrid --></a>). Thus, our model predicts that future work probing mutational
effects will support an underlying high-dimensional antigenic space, even though a
two-dimensional map is sufficient to explain observed antigenic relationships among
two-dimensional map is sufficient to explain observed antigenic relationships among evolving
strains.
<h3 class="likesubsectionHead"><a
id="x1-8000"></a>Winding back the tape</h3>
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Instead, the viral genealogy is directly recorded. This is made possible by tracking transmission
events connecting infections during the simulation; infections record the ID of their
&#8216;parent&#8217; infection. Proceeding from a sample of infections, their genealogical history can
be reconstructed by following consecutive links to parental infections. During this
be reconstructed by following consecutive links to parental infections. Following this
procedure, lineages coalesce to the ancestral lineages shared by the sampled infections,
eventually arriving at the initial infection introduced at the beginning of the simulation.
Commonly, phylodynamic simulations generate sequences that are subsequently analyzed
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class="cmr-8">0</span></sub> of influenza due to the effects of human immunity.
We assumed <span
class="cmmi-10x-x-109">R</span><sub><span
class="cmr-8">0</span></sub> of 1.8, consistent with the upper range of seasonal estimates. Duration of
infection was chosen based on patterns of viral shedding shown during challenge studies
<span class="cite">[<a
href="#XCarrat08">35</a>]</span>. The linear form of the risk of infection and its increase as a function of antigenic
distance <span
class="cmmi-10x-x-109">s </span>was chosen as 0.07 based on experimental work on equine influenza <span class="cite">[<a
class="cmr-8">0</span></sub> of 1.8, consistent with the upper range of seasonal estimates. Duration
of infection was chosen based on patterns of viral shedding shown during challenge
studies <span class="cite">[<a
href="#XCarrat08">35</a>]</span>. The linear form of the risk of infection and its increase as a function of
antigenic distance <span
class="cmmi-10x-x-109">s </span>= 0<span
class="cmmi-10x-x-109">.</span>07 was based on experimental work on equine influenza <span class="cite">[<a
href="#XPark09">36</a>]</span> and
from studies of vaccine effectiveness <span class="cite">[<a
href="#XGupta06">37</a>]</span>. Between-region contact rate <span
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