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Image-Guided Modeling of Virus Growth and Spread

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Abstract

Although many tools of cellular and molecular biology have been used to characterize single intracellular cycles of virus growth, few culture methods exist to study the dynamics of spatially spreading viruses over multiple generations. We have previously developed a method that addresses this need by tracking the spread of focal infections using immunocytochemical labeling and digital imaging. Here, we build reaction–diffusion models to account for spatio-temporal patterns formed by the spreading viral infection front as well as data from a single cycle of virus growth (one-step growth). Systems with and without the interferon-mediated antiviral response of the host cells are considered. Dynamic images of the spreading infections guide iterative model refinement steps that lead to reproduction of all of the salient features contained in the images, not just the velocity of the infection front. The optimal fits provide estimates for key parameters such as virus-host binding and the production rate of interferon. For the examined data, highly-lumped infection models that ignore the one-step growth dynamics provide a comparable fit to models that more accurately account for these dynamics, highlighting the fact that increased model complexity does not necessarily translate to improved fit. This work demonstrates how model building can facilitate the interpretation of experiments by highlighting contributions from both biological and methodological factors.

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Abbreviations

c j :

concentration of species j

\(\bar{c}_{\mathrm{infc}}(\tau)\,d\tau\) :

concentration of infected cells at age τ for the age-segregated model

c unc,0 :

initial concentration of uninfected cells

c vir,0 :

initial concentration of virus

D ifn :

interferon diffusivity

D vir :

virus diffusivity

e :

error vector

h(x k ;θ):

model prediction vector of the measurement

i bgd :

background fluorescence

k j :

rate constant for reaction j

\(\bar{k}_{j}\) :

jth constant for the Hill function fit

k m :

conversion constant from cell concentration to intensity

n unc,0 :

initial number of uninfected cells

n vir,0 :

number of viruses in the initial inoculum

R :

covariance matrix for parameter estimation

R vir(τ):

virus production as a function of the cell age τ

r :

radial dimension

r plate :

radius of the plate

t :

time

V c :

cell volume

x :

state vector

Y:

virus yield per infected cell

y :

measurement vector

y m :

predicted intensity measurement

\(\hat{y}_{m}\) :

unsaturated predicted intensity measurement

λ :

eigenvalue

∇ θ Φ :

gradient of the objective function with respect to the model parameters for parameter estimation

∇ θ θ Φ :

Hessian of the objective function with respect to the model parameters for parameter estimation

Φ :

objective function value for parameter estimation

τ :

age of infection

τ d :

maximum age of infection

θ :

vector of model parameters

dc:

dead cell

ifn:

interferon

infc:

infected cell

inoc:

inoculated cell

unc:

uninfected cell

lsub:

limiting substrate

vir:

virus

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Authors and Affiliations

  1. Department of Chemical and Biological Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, WI, 53706-1607, USA

    Eric L. Haseltine, Vy Lam, John Yin & James B. Rawlings

Authors
  1. Eric L. Haseltine
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  2. Vy Lam
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  3. John Yin
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  4. James B. Rawlings
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Correspondence to James B. Rawlings.

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Haseltine, E.L., Lam, V., Yin, J. et al. Image-Guided Modeling of Virus Growth and Spread. Bull. Math. Biol. 70, 1730–1748 (2008). https://doi.org/10.1007/s11538-008-9316-3

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  • DOI: https://doi.org/10.1007/s11538-008-9316-3

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