What controls the initial dynamics of influenza and HIV

Alan S. Perelson

Theoretical Biology and Biophysics

Los Alamos National Laboratory

Los Alamos, NM

asp@lanl.gov

Acute HIV Infection: Target Cell Limited?

Keele et alPNAS 105:7552 (2008)

Salazar-GonzalezJ Exp Med 206:1273 (2009)

78 of 102 pts had single founder virus

Keele et alJ Exp Med 206:1117 (2009)

Viral stock diverse

10-5

10-4

10-3

10-2

10-1

0

101

102

103

104

105

106

107

108

Transmission

Vir

us

Conce

ntr

ati

on in E

xtr

ace

llula

r Fl

uid

or

Pla

sma (

Copie

s/m

l)

Acute HIV-1 Infection

Time Post Exposure (days)

0 5 10 15 20 30 3525 40 45 50 55 60 65 70

Reservoir

Virus dissemination Transi

t

eclipse?

T0

Acute Phase ReactantsDays -5 to-7

Ab-virus Immune ComplexesDay 9

Onset cytokinesapoptosis, Day 7 Free IgM anti-gp41 Ab, Day 13 (non-neutralizing)

CD8 T CellResponses

CTL Escape

AutologousNeutralizing Antibody

AutologousNeutralizing

Antibody Escape

II TT

k Infection Rate

c

Clearance

pVirions/d

Target Cell

InfectedCell

Death

Model of HIV Infection

+

Model of Viral Infection

cVpIdt

dV

IkVTdt

dI

kVTdTdt

dT

Basic Target Cell-Limited Model T, target CD4 cellsI, infected CellsV, virus

λ, T cell productiond, normal T cell deathk, infectivity constantp, viral productionc, viral clearance, infected cell death

λ = 10,000 cells/μL/dayd = 0.01/dayc = 23/dayδ, k, and p are fit.

Stafford et al. JTB203: 285 (2000)

HIV PrimaryInfection

Target cell limitedmodel can fit HIV RNAdata during early AHI

Stafford et al. JTB203: 285 (2000)

At loner times the target cell limited model mayshow oscillations that arenot in the data and mayoverestimate the HIV RNA level if immune responsesare playing a role

Anti-HIV Antibodies• Plasma samples obtained by CHAVI from blood

bank donors have been analyzed for the presence of HIV RNA as well IgG, IgM and IgA antibody levels. G. Tomaras et al. JVI 82: 12449 (2008) has shown that the earliest antibodies are anti-gp41 and that immune complexes form between these antibodies and HIV.

• The question we want to address is whether the presence of anti-env antibodies impacts viral dynamics.

We Study Three Effects of Antibody

• Opsonize viral particles and increase their rate of clearance.

• Neutralize HIV and decrease rate of infection of cells.

• Bind to infected cells and hasten their destruction either through complement mediated lysis or antibody-dependent cellular cytotoxicity (ADCC).

Results: Fits to the Target Cell Limited Model (First 40 days

after virus detected - T100)

Target Cell Limited Model

Model of Antibody Enhanced Virion Clearance

VtIgGcpIdt

dV

IkVTdt

dI

kVTdTdt

dT

))(1(

T, target CD4 cellsI, infected CellsV, virus

λ, T cell productionδ, normal T cell deathk, infectivity constantp, viral productionc, viral clearance

λ = 10,000 cells/μL/dayd = 0.01/dayc = 23/dayδ, k, p, and α are fit.

The viral clearance term, c, in the target cell-limited modelis assumed to be increased proportional to the Ab conc.

Anti-gp41 IgG antibody term added to c

Model of Antibody Mediated Viral Neutralization

1 ( )

1 ( )

dT kdT VT

dt IgG t

dI kVT I

dt IgG t

dVpI cV

dt

The infectivity term, k, of the target cell-limited model is reduced by Ab

T, target CD4 cellsI, infected CellsV, virus

λ, T cell productiond, normal T cell deathk, infectivity constantp, viral productionc, viral clearance

No improvement in fit is seen except for 9032

Anti-gp41 IgG antibody term added to k

SSR increases as β increases, with k, p, and δ set to the best-fit parameters of the target cell-limited model.

Model of Antibody Enhanced Infected Cell Death

(1 ( ))

dTdT kVT

dtdI

kVT IgG t IdtdV

pI cVdt

T, target CD4 cellsI, infected CellsV, virus

λ, T cell productionδ, normal T cell deathk, infectivity constantp, viral productionc, viral clearance

λ = 10,000 cells/μL/dayd = 0.01/dayc = 23/dayδ, k, p, and α are fit.

The infected cell death rate, , in the target cell-limited model is assumed to be increased proportional to the anti-gp41 concentration.

Again no improvement in fit is seen

PatientClearance Enhanced,

IgG

Clearance Enhanced,

IgM

Clearance Enhanced, IgG+IgM

Infectivity Diminished,

IgG

Infectivity Diminished,

IgM

Infectivity Diminished,

IgG+IgM

Cell death enhanced,

IgG

Cell death enhanced,

IgM

Cell death enhanced, IgG+IgM

6240 0.320 0.326 0.266 0.975 0.977 0.975 0.975 0.975 1.000

6246 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

9032 0.004 0.006 0.001 0.005 0.006 0.006 0.89 0.011 0.923

9077 0.567 0.998 0.687 0.604 0.998 0.623 0.722 0.998 0.991

9079 0.992 0.994 0.960 0.998 0.649 0.992 0.964 0.070 0.598

12008 0.566 0.607 0.590 0.648 0.546 0.657 1.000 1.000 1.000

9077 0.567 0.998 0.687 0.604 0.998 0.623 0.722 0.998 0.991

9079 0.992 0.994 0.960 0.998 0.649 0.992 0.964 0.070 0.598

P-values from F-test comparison of target-cell limited model with antibody-including models for all patients, fitting through day 40. The value in bold indicates the lowest p-value for patient 9032, the only patient better fit by an antibody-including model.

Limitations• One possible limitation of our approach is

that the antibody data we used is the concentration of free anti-gp41 antibody.

• Antibody in immune complexes is being ignored as well as antibodies with other specificities.

• Only looked at first 40 days after virus is detectable.

Viral infectivity may vary with time

May be due to host or virus; Ma et al J Virol. 83: 3288 2009

SIV Infection

CTL Escape

• Gertrude Elion – “An antiviral is a drug that selects for resistance”.

• Similarly, one can assess the potency of a CTL response by asking if it selects for escape mutations.

Escape from CTL pressure

Asquith et al., PLoS Biol 2006

Idea: By examining rate of escape one can estimate the CTL pressure on the virus

Goonetilleke et al. J Exp Med. 2009

Escape from CTL pressure

'

dwaw dw kw

dtdm

a m dmdt

Wildtype virus (infected cells)

Escape mutant (infected cells)

CTL killing

Replication ratea’=a(1-c)

Fitness cost, c=0 no cost, c=1 maximal cost

For WT, =d+k = total rate of killingNote, k/is fraction of killing attributed to CTL

Time course of escape variants

(0)(0)

( ) 1( )

( ) ( ) 1w rtm

m tp t

w t m t e

Proportion of mutant virus over time

We can use this equation to fit McMichael’s data andestimate the rate of escape r.

Model Fits to Kinetics of HIV-1 Escape from CTL Responses in Acute Infection

TW10

TW10

Escape rates and epitopes

Elispot / IFN g staining

Patient Mutations Escape rate

(day-1) t50%

(days)

CD8 T cell

epitope

Confirmed T cell response (HXB2

position)

CH40 Nef S188R/N, R196Q 0.22 15 yes Yes, (Nef185-202)

Gag A120D 0.17 31 no no

Gag I401L, R403K 0.17 31 yes Yes (Gag389-406)

Vpr S84R 0.16 31 yes no

Vif T167I 0.37 38 yes no

Pol K76R 0.015 119 yes Yes, (Pol73-90)

CH77 Env R355K/S/N,T358A 0.36 9 yes Yes, (Env350-368)

Nef R21K/G, R22K/G/,TD23E/N, P25S 0.30 19 yes Yes, (Nef17-34)

Nef K82Q/T/P, A83G, L85H, L87I 0.29 24 yes Yes, (Nef81-98)

Gag I147L 0.035 101 yes Yes, (Gag140-157) IW9

Gag T242N,V247I, G248E/S 0.063 124 yes Yes, (Gag236-253) TW10

CH58 Env Y586H 0.10 21 yes Yes, (Env576-596)

Env F829V/S/L, I830M/L/F, A832T, V833I 0.12 27 no no

Gag T248N, G254E 0.085 60 yes Yes, (Gag236-253) TW10

Gag I147L 0.007 430 yes Yes , (Gag140-157) IW9

SUMA0874 Rev R48K, Q51H, Q53R, S54L, L55I 0.32 30 yes Yes, (Rev47-55)

Median 0.17 30

Results: Median rate of CTL escape = 0.17/d; Maximum rate of CTL escape = 0.37/d Avg death rate of productively-infected cells on HAART = 1/d.

Conclusions• Escapes measured here are faster than previously seen:

– Median r =0.17 day-1, max r =0.37 day-1

– Asquith et al. (2006), median r = 0.04 day-1

• Comparing rate of escape with the death rate of infected cells, = 1 day-1 (HAART data) one sees CTL pressure to one epitope is high and accounts for as much as 37% of the killing rate and on average 17%. However, virus rapidly escapes this pressure.

• Multiple simultaneous responses could account for even more of the loss rate of infected cells (new modeling work is examining this).

Influenza

• Unlike HIV, influenza is generally rapidly cleared.

• Clearance can be due to target-cell limitation as long as target cells do not replenish before the virus is eliminated.– If targets replenish, virus can resurge and an

immune response is needed to ultimately clear virus.

Data: Infection in Humans

Murphy, B. R et al., Evaluation of influenza A/Hong Kong/123/77 (H1N1) ts-1A2 and cold- adapted recombinant viruses in seronegative adult volunteers. Infect. Immun. 29:348-55 1980.

• Exponential growth of virus, peaks day 2-3, then declines and is cleared.

Data

MODEL

Targets Infected

Virus

dTVT

dt

dIVT I

dt

T IrT

dVpI cV

d

T

t

0

(1 )

p

c

11

21 2

2

(3 )

(3 )

(3 )

dTTV a

dtdI

TV kI bdtdI

kI I cdtdV

pI cVdt

Model with Infection Delay

DELAY is dashedBaccam et al. JVI 2006

Double Peaks

2 ( )dF

sI t Fdt

1

2

ˆ(6)

1

ˆ

1

F

pp

F

Interferon Response

Conclusions

• Target cell limited models work well in explaining viral load data obtained early in HIV and influenza infection. As infection progresses immune responses are seen and contribute to the late dynamics. Quantifying the precise contribution of both innate and adaptive responses is ongoing.