Modeling the acute and chronic phases of Theiler murine encephalomyelitis virus infection

Abstract

Theiler murine encephalomyelitis virus (TMEV) infection of a mouse's central nervous system is biphasic: first the virus infects motor neurons (acute phase), and this is followed by a chronic phase in which the virus infects glial cells (primarily microglia and macrophages [M]) of the spinal cord white matter, leading to inflammation and demyelination. As such, TMEV-induced demyelinating disease in mice provides a highly relevant experimental animal model for multiple sclerosis. Mathematical models have proven valuable in understanding the in vivo dynamics of persistent virus infections, such as HIV-1, hepatitis B virus, and hepatitis C virus infections. However, viral dynamic modeling has not been used for understanding TMEV infection. We constructed the first mathematical model of TMEV-host kinetics during acute and early chronic infections in mice and fit measured viral kinetic data with the model. The data fitting allowed us to estimate several unknown parameters, including the following: the rate of infection of neurons, 0.5 × 10(-8) to 5.6 × 10(-8) day(-1); the percent reduction of the infection rate due to the presence of virus-specific antibodies, which reaches 98.5 to 99.9% after day 15 postinfection (p.i.); the half-life of infected neurons, 0.1 to 1.2 days; and a cytokine-enhanced macrophage source rate of 25 to 350 M/day into the spinal cord starting at 10.9 to 12.9 days p.i. The model presented here is a first step toward building a comprehensive model for TMEV-induced demyelinating disease. Moreover, the model can serve as an important tool in understanding TMEV infectious mechanisms and may prove useful in evaluating antivirals and/or therapeutic modalities to prevent or inhibit demyelination.

Fig 1

Schematic model of TMEV infection during the acute and chronic phases. The acute infection phase is plotted on the left (equations 1 to 3): uninfected motor neurons (T) are infected by free viruses (V) at rate β_nV and become infected neurons (I). After 5 days p.i. virus-specific antibodies block infection with effectiveness η(t) (equations 7 and 8). Free virus is produced at rate constant p_n and cleared at rate constant c. Motor neurons die only after they become infected at rate constant δ_n. The death of infected neurons generate infectious debris, I_D. Within approximately 11 days p.i., TMEV-chemokine-recruited monocytes enter the CNS and differentiate into susceptible macrophages, Mϕ, at rate s(t) (equation 9). Uninfected Mϕ become infected, I_Mϕ, via phagocytosis of infectious debris, I_D, at rate constant b. TMEV infection in Mϕ represents the transition from the acute to chronic phase and is plotted on the right (equations 4 to 6). Uninfected Mϕ, infected Mϕ, and infectious debris die or are lost at rate constants δ_Mϕ, δ_IMϕ, and c_ID, respectively. Loss and death rates are represented by dashed lines.

Fig 2

TMEV kinetics and model simulation. Total TMEV RNA kinetic data (dots) can be patterns divided into 4 stages: (i) viral increase during the first 6 days p.i., (ii) viral decrease 6 to 11 days p.i., (iii) viral increase 11 to 13 days p.i., and (iv) steady state after approximately 15 day p.i. The viral RNA kinetic data were fitted by a mathematical model (equations 1 to 9) using a Monte Carlo filtering approach as described in Materials and Methods and Fig. 4. An example of good fit curve is shown by the solid line. Dots and bars represent means and one standard deviation of log₁₀-transformed vRNA copy equivalents measured in spinal cords of infected mice (9).

Fig 3

TMEV-specific antibody titers and modeling. Serum TMEV-specific antibody titers (dots; data are from reference 9) can be fitted using equation 7 (solid line). Antibody titers increased exponentially on day 5 p.i. and approached saturation (dashed line) by day 15 p.i.

Fig 4

Parameter histograms from 6,000 sets of parameters which fit the data shown in Fig. 2 well using equation 10, as described in Materials and Methods. These histograms were used for the estimation of the range of unknown viral and host parameters (Table 1).

Fig 5

The rate constant (b) of infection of Mϕ by infectious debris via phagocytosis is strongly correlated with the rate constant (c_ID) of clearance of infectious debris.