doi:10.1016/j.jtbi.2004.12.007
Copyright © 2005 Elsevier Ltd All rights reserved.
Mathematical analysis demonstrates that interferons-β and -γ interact in a multiplicative manner to disrupt herpes simplex virus replication
William P. Halforda,
,
, Keith J. Halfordb and Amy T. Piercea
aDepartment of Microbiology and Immunology, Tulane University Health Sciences Center, New Orleans, LA 70112, USA
bDepartment of Water Resources, United States Geological Survey, Carson City, NV 89706, USA
Received 19 August 2004;
revised 10 November 2004;
accepted 6 December 2004.
Communicated by Robert Root-Bernstein.
Available online 25 January 2005.
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Abstract
Several studies suggest that the innate interferons (IFNs), IFN-α and IFN-β, can act in concert with IFN-γ to synergistically inhibit the replication of cytomegalovirus and herpes simplex virus type 1 (HSV-1). The significance of this observation is not yet agreed upon in large part because the nature and magnitude of the interaction between IFN-α/β and IFN-γ is not well defined. In the current study, we resolve this issue by demonstrating three points. First, the hyperbolic tangent function, tanh (x), can be used to describe the individual effects of IFN-β or IFN-γ on HSV-1 replication over a 320,000-fold range of IFN concentration. Second, pharmacological methods prove that IFN-β and IFN-γ interact in a greater-than-additive manner to inhibit HSV-1 replication. Finally, the potency with which combinations of IFN-β and IFN-γ inhibit HSV-1 replication is accurately predicted by multiplying the individual inhibitory effects of each cytokine. Thus, IFN-β and IFN-γ interact in a multiplicative manner. We infer that a primary antiviral function of IFN-γ lies in its capacity to multiply the potency with which IFN-α/β restricts HSV-1 replication in vivo. This hypothesis has important ramifications for understanding how T lymphocyte-secreted cytokines such as IFN-γ can force herpesviruses into a latent state without destroying the neurons or leukocytes that continue to harbor these viral infections for the lifetime of the host.
Keywords: Interferon; Synergy; Multiplicative interaction; Herpesvirus; Latent infection
Fig. 1. Measurements of HSV-1 DNA yield correlate with viral titers. (A) HSV-1 titers were determined by plaque assay in Vero cells 24 h after inoculation with 0.002 to 4.6 PFU per cell (n=2 per MOI). (B) Dotblots of DNA samples harvested from uninfected Vero cells (MOI=0) and HSV-1 infected Vero cells 24 h after inoculation (n=2 per MOI). Estimates of HSV-1 DNA yield were calculated based on the amount of HSV-specific oligonucleotide that hybridized to each DNA sample. (C) The log (viral DNA yield) is plotted as a function of MOI, and is expressed in terms of log (fold-increase above the lower limit of detection); thus, the value ‘0’ on the y-axis indicates the lower limit of detection of the assay.
Fig. 2. Effect of human IFN-β on HSV-1 replication. (A) and (B) Dotblot of DNA samples harvested (A) 30 or (B) 48 h after inoculation with HSV-1 (MOI=0.1). Vero cells were treated with half-log dilutions of human IFN-β ranging in concentration from 0.03 to 10,000 U/ml (n=2 per concentration). HSV-1 DNA yields were measured based on the efficiency with which an HSV-specific oligonucleotide probe hybridized to each DNA sample. The log (viral DNA yield) measured (C) 30 or (D) 48 h after inoculation is plotted as a function of the log [IFN-β]. Open diamonds and error bars indicate the mean±SD of log (viral DNA yield), which is expressed in terms of log (fold-increase above the lower limit of detection); thus, the value ‘0’ on the y-axis indicates the lower limit of detection.
 |
Fig. 3. Mathematical description of inhibition of HSV-1 replication by IFN-β. (A) The relationship between V (log [viral DNA yield]) and I (log [IFN]) is dictated by 1. ΔI, one-half the width of the difference between Imin and Imax, 2. ΔV, the height of the difference between Vmax and Vmin, and 3. the midpoint of the dose–response curve, I50, V50 (closed circle). The locations of Imin and Imax are denoted by vertical dotted lines and the open circles on the dose–response curve. The upper and lower asymptotes of the hyperbolic tangent function, Vmax and Vmin respectively, are denoted by horizontal dashed lines. (B) and (C) Relationship of log (viral DNA yield) to log [IFN-β] when measured (B) 30 or (C) 48 h after inoculation. Open diamonds and error bars indicate the mean±SD of measured values of log (viral DNA yield), which are expressed as log (HSV-1 DNA). The dashed line indicates the simulated values that were derived by fitting the V(β) equation to visual estimates of Vmin, Vmax, Imin, and Imax. The solid line indicates the simulated values derived by fitting the equation for (B) V(β)30 h and (C) V(β)48 h to their respective data sets by the method of least squares. The maximum reductions in log (viral DNA yield) achieved by IFN-β are denoted by the vertical arrows labeled
and
.
 |
Fig. 4. Effect of human IFN-γ on HSV-1 replication. (A) and (B) Dotblot of DNA samples harvested (A) 30 or (B) 48 h after inoculation (MOI=0.1). Vero cells were treated with half-log dilutions of IFN-γ ranging in concentration from 0.03 to 10,000 U/ml (n=2 per concentration). (C) and (D) Relationship of log (viral DNA yield) to log [IFN-γ] when measured (C) 30 or (D) 48 h after inoculation. Open triangles and error bars indicate the mean±SD of measurements of log (viral DNA yield), which are expressed in terms of log (fold-increase above the lower limit of detection); thus, the value ‘0’ on the y-axis indicates the lower limit of detection. The locations of Imin and Imax are denoted by vertical dotted lines, and Vmax and Vmin are denoted by horizontal dashed lines. The closed circle in the middle of the square indicates the location of I50, V50. The solid line indicates the simulated values derived by fitting the equation for (C) V(γ)30 h or (D) V(γ)48 h to their respective data sets by the method of least squares. The maximum reductions in log (viral DNA yield) achieved by IFN-γ are denoted by the vertical arrows labeled
and
.
 |
Fig. 5. Additive composite curve analysis of the combined effects of IFN-β and IFN-γ. (A) and (B) Dotblot of DNA samples harvested (A) 30 or (B) 48 h after inoculation (MOI=0.1). Vero cells were treated with half-log dilutions of human IFN-β, human IFN-γ, or 1:1 combinations of IFN-β and IFN-γ that ranged in concentration from 0.03 to 10,000 U/ml (n=2 per concentration). (C) and (D) Relationship of log (viral DNA yield) to log [IFN-β] (open diamonds), log [IFN-γ] (open triangles), or log [IFN-β+IFN-γ] (open circles) when measured (C) 30 or (D) 48 h after inoculation. Open symbols and error bars indicate the mean±SD of measurements of log (viral DNA yield), which are expressed in terms of log (fold-increase above the lower limit of detection); thus, the value ‘0’ on the y-axis indicates the lower limit of detection. For the V(β:γ) functions, the locations of Imin and Imax are denoted by vertical dotted lines, Vmax and Vmin are denoted by horizontal dashed lines, and the closed circle denotes the location of I50, V50. The line of X's indicates the reduction in log (viral DNA yield) predicted by the null (dose-additive) hypothesis. The solid black line indicates simulated values derived by fitting the equations (C) V(β:γ)30 h or (D) V(β:γ)48 h to the observed data. The maximum observed reductions in HSV-1 DNA yield achieved by 1:1 combinations of IFN-β+IFN-γ are denoted by the vertical arrows labeled
and
.
 |
Fig. 6. Response surface analysis of the combined effects of IFN-β and IFN-γ. (A) and (D) Dotblot of DNA samples harvested (A) 30 h or (D) 48 h after inoculation (MOI=0.1). Vero cells were treated with a matrix of 1/3rd log dilutions of IFN-β and IFN-γ that ranged in concentration from 0 to 1000 U/ml. (B) and (E) Relationship of log (HSV-1 DNA) to the combined concentration of IFN-β and IFN-γ in cultures treated with increasing doses of IFN-β and constant doses of IFN-γ of either 0, 21, or 100 U/ml, as determined (B) 30 h or (E) 48 h after inoculation. The equations V(β) and V(β:γ) provide reference points for previously observed effects of IFN-β versus 1:1 combinations of IFN-β and IFN-γ, and are based on the terms presented in Table 1. (C) and (F) The three-dimensional response surface of fold-reduction in HSV-1 DNA yield, as determined (C) 30 h or (F) 48 h after inoculation. Fold-reduction is defined as HSV-1 DNA yield in ‘vehicle-treated cells’/‘IFN-treated cells.’ Isoboles (contours) on the response surface occur in 20-fold increments.
 |
Fig. 7. Mathematical models of the interaction between IFN-β and IFN-γ. (A) and (B) Predictions of the dose-additive model (Eq. (5)). Three-dimensional response surfaces of fold-reduction in viral DNA yield predicted to occur (A) 30 h and (B) 48 h after inoculation if IFN-β and IFN-γ interact in a dose-additive manner. Isoboles on the response surface occur in 20-fold increments. (C) and (D) Predictions of the multiplicative interaction model (Eq. (6)). Three-dimensional response surfaces of fold-reduction in viral DNA yield that are predicted to occur (C) 30 h and (D) 48 h after inoculation if IFN-β and IFN-γ interact in a multiplicative manner. (E) and (F) Observed measurements of log (viral DNA yield) obtained (E) 30 h and (F) 48 h p.i. are plotted on the x-axis relative to the values predicted by the dose-additive and multiplicative interaction models (y-axis). The line of unity in each graph denotes the series of points at which there is a perfect correlation between predicted and observed values.
Table 1.
Individual versus combined effects of IFN-β and IFN-γ on HSV-1 replication
a Interferon used in dose–response experiments;
n=the number of independent experiments performed. In each experiment, the range of [IFN] tested was 0.03 to 10,000 U/ml and was based on two replicate measurements at each dilution of IFN.
b The mean±SD of each term, as estimated in individual experiments by fitting Eq.
(1) to the IFN dose–response data. The term Δ
V=maximum reduction in log (viral DNA yield) and Δ
I=1/2(
Imax−
Imin).
c IC50 refers to the concentration at which a 50% reduction in log (HSV-1 DNA) was observed, and equals
10I50. The
IC50 is reported as the range of values that lie between

and

.
d ‘Maximum inhibition’ refers to the maximum observed reduction in log (HSV-1 DNA), and equals
10ΔV. The maximum inhibition is reported as the range of values that lie between

and
