Asynchrony between virus diversity and antibody selection limits influenza virus evolution

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Appendix 1—figure 1

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Appendix 1—figure 2

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Appendix 1—figure 3

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Tables

Table 1

Parameter	Meaning	Units	Value	Source or justification
$t_M$	time post-infection of antibody response in experienced hosts	days	2	literature (see review in Appendix Section A2)
$t_N^w$	time post-infection of a novel immune response to the old antigenic variant	days	6	literature (see review in Appendix Section A2)
$p_C$	per-capita growth rate of target cells at low density	$\frac{1}{\text{days}}$	0	ignored on the timescale of a single infection
$C_{\max }$	maximum number of target cells	cells	4 × 108	standard in the modeling literature (Baccam et al., 2006; Luo et al., 2012; Hadjichrysanthou et al., 2016)
${ℛ}_0$	within-host basic reproduction number for the virus	unitless	5	empirical fits of target cell models (Hadjichrysanthou et al., 2016)
$r_w$	average number of infectious virions produced by a cell infected with old antigenic variant virus	virions	100	literature (Frensing et al., 2016)
$r_m$	average number of infectious virions produced by a cell infected with new antigenic variant virus	virions	100	no within-host deleteriousness for new antigenic variants
${\displaystyle {\mu }_{wm}}$	probability of mutation from old variant to new variant	unitless	0.33 × 10–5	literature (Nobusawa and Sato, 2006)
${\displaystyle {\mu }_{mw}}$	probability of mutation from new variant to old variant	unitless	0	back-mutation neglected
$\beta$	rate of infectious contact between virions and target cells per cell per virion	${\displaystyle \frac{1}{\mathrm{v}\mathrm{i}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{s}\mathrm{d}\mathrm{a}\mathrm{y}\mathrm{s}}}$	calculated	from ${ℛ}_0$
${\displaystyle \ell }$	number of target cells lost per infectious contact	cells	1	one cell lost per cell infection
${\displaystyle d_v}$	exponential decay rate of infectious virions	$\frac{1}{\text{days}}$	4	empirical fits of target cell models (Hadjichrysanthou et al., 2016) and modeling literature (Baccam et al., 2006Luo et al., 2012)
$k$	additional per-virion neutralization rate in the presence of a well-matched antibody response	$\frac{1}{\text{days}}$	6	varied to test hypotheses
$c_w$	fractional cross reactivity during viral replication between host antibodies and the old antigenic variant	unitless	0 or 1	naive or homotypically reinfected hosts
$c_m$	fractional cross reactivity during viral replication between host antibodies and the new antigenic variant	unitless	0	full escape variant
${\kappa }_w$	probability that an individual old antigenic variant virion inoculated into an experienced host is neutralized in the respiratory tract mucosa	unitless	set from $z_w$	calculated from Equation 38
${\kappa }_m$	probability that an individual new antigenic variant virion inoculated into an experienced host is neutralized in the respiratory tract mucosa	unitless	$\sigma {\kappa }_w$	reduced relative to ${\displaystyle {\kappa }_w}$ by immune escape
$\sigma$	fractional cross immunity at the sIgA bottleneck between old antigenic variant and new antigenic variant	unitless	0	full escape variant
$v$	number of virions encountering sIgA	virions	10 × b
$b$	size of final/cell infection bottleneck	virions	1	NGS studies (McCrone et al., 2018; Xue and Bloom, 2019)
$V_{50}$	viral load at which there is a fifty percent transmission probability	virions	108	chosen to give realistic transmission window (Tsang et al., 2015) and based on prior modeling studies (Russell et al., 2012)
$\theta$	transmission threshold for threshold model	virions	107	chosen to be consistent with $V_{50}$

Table 2

Parameter	Minimum value	Maximum value
$t_N$	6	9
$C_{\max }$	108	109
${ℛ}_0$	5	15
r	10	500
${\displaystyle {\mu }_{wm}}$	0.33 × 10−6	0.33 × 10−4
dv	2	8
k	3	16
cm	0.5	1
zw	0.70	0.99
$z_m/z_w$	0.5	0.9
${\displaystyle V_{50}}$	107	109
$v/b$	1	50

Appendix 1—table 1

A/H1N1 1999–2008		A/H3N2 2008–2011		A/H3N2 2012–2014
Pre-filter	Final dataset	Pre-filter	Final dataset	Pre-filter	Final dataset
4882	3514	7050	5738	11970	10107

Appendix 1—table 2

Lineage	Geographic composition in first year of co-circulation	Trunk substitutions from MRCA to K140E fixation	Trunk substitutions post- K140E fixation
1	South Asia	Y94H, R188K, E273K	D35N, K145R*, A189T, G185V, N183S, G185S
2	East Asia	Y94H, S36N, A189T, R188M, T193K*	N244S, K82R*, I47K, E68G
3	South-East Asia	Y94H, K73R, V128A*, A128T*	P270S

Appendix 1—table 3

Lineage	Trunk substitutions from MRCA to K158N/N189K fixation	Trunk substitutions post- K158N/N189K fixation
1 (Victoria / 2009-like)		T212A, S45N, T48A, K92R, Q57H, A198S, V223I, N312S, N278K,Q33R, N145S, G5E, E62V, D53N, E280A, I230V, Y94H, I192T, S199A
2 (Perth / 2009-like)	E62K	N144K, R261Q, I260M, P162S, E50K, V213A, N133D, T212A, R142G

Appendix 1—table 4

Lineage	Trunk substitutions from MRCA to F159X fixation	Trunk substitutions post- F159X fixation
F159Y (lineage 1, Clade 3C.2a)	L3I, N225D, Q311H, N144S, K160T	R142K, R261L
F159S (lineage 2, Clade 3C.3a)	R142G, T128A, A138S, N225D

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