Computational Modeling of Virus Growth and Infection Spread

James B. Rawlings and John Yin
Department of Chemical and Biological Engineering
University of Wisconsin-Madison
Madison, WI 53706-1607

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To what extent can the development of computational models serve to enhance our understanding of biology? A grand challenge of biology is to grasp how the information encoded within the genome of an organism informs its growth and development. We approach this daunting challenge by focusing on viruses as model minimal organisms. Viruses are parasites that must infect living cells in order to reproduce. They carry the smallest genomes, encode the fewest genes, and employ biochemical processes that are arguably among the best characterized and most complete of any organism. During infection viruses divert the bio-synthetic machinery and resources of their host cells toward their own growth. We apply principles of chemical reaction engineering to cast known bio-molecular interactions and processes in mathematical terms. The resulting model is a network of coupled reactions that incorporates parameters from our own experiments and the biochemical and biophysical literature. We employ open-source numerical software GNU Octave ( to solve the resulting system of differential and algebraic equations, providing an integrated and mechanistic perspective of the intricately coupled processes that contribute to virus growth.

In the initial phase of our study we have developed a computational model for the single-cycle growth of vesicular stomatitis virus (VSV). VSV is prototypical of a diverse class of non-segmented negative-strand RNA viruses of human health relevance. This class includes respiratory syncytial, rabies, and measles viruses, as well as the highly pathogenic Marburg and Ebola viruses. We have developed our model of VSV growth with the intent that it be tested and refined by quantitative experiments. Moreover, in subsequent phases of this project we envision that the intracellular model may serve as a foundation for understanding: (i) how the genome organization of the virus can quantitatively influence the dynamics of its growth, (ii) how noisy gene expression may contribute to broad distributions in virus yield for single infected cells, and (iii) how activation of host innate defensive responses may impact the development of an anti-viral cellular state.

This website provides a vehicle for dissemination of our software, manuscripts, and publications relating to this project. Complete collections of the M-files for both Matlab and Octave in zip or tar.gz file formats are available for download from the links provided below. Further by clicking on figure thumbnails you may access the code that was used to generate each figure. We encourage users to send us feedback.

Acknowledgment: We are grateful for support for this project from the National Institutes of Health (5R21AI071197-03) Phased Innovation Award (R21/R33) program.

PAPER 1: Stochastic Kinetic Modeling of Vesicular Stomatitis Virus Intracellular Growth

Figure 2a:
Stochastic simulation run including all encapsidation (chain) reactions.
Figure 2b:
Stochastic simulation run including all encapsidation (chain) reactions.
Figure 3:
Mean of the genome levels over time.
Figure 4:
Mean of total mRNA levels versus time.
Figure 5:
Mean of total protein level versus time.
Figure 6a:
Distribution of the (-)RNA molecule level at t = 2.5 hr.
Figure 6b:
Distribution of the (-)RNA molecule level at t = 3 hr.
Figure 6c:
Distribution of the (-)RNA molecule level at t = 4 hr.
Figure 7:
The (-)RNA genome level at 4 hr versus the L mRNA level at 1.5 hr.
Figure 8a:
Distribution of the GFP at t = 3.5 hr.
Figure 8b:
Distribution of the GFP at t = 4 hr.