Modeling population heterogeneity in viral dynamics for chronic hepatitis C infection: Insights from Phase 3 telaprevir clinical studies.

Viral dynamic modelling has proven useful for designing clinical studies and predicting treatment outcomes for patients infected with the hepatitis C virus. Generally these models aim to capture and predict the on-treatment viral load dynamics from a small study of individual patients. Here, we explored extending these models (1) to clinical studies with numerous patients and (2) by incorporating additional data types, including sequence data and prior response to interferon.

Modeling viral evolutionary dynamics after telaprevir-based treatment.

For patients infected with hepatitis C virus (HCV), the combination of the direct-acting antiviral agent telaprevir, pegylated-interferon alfa (Peg-IFN), and ribavirin (RBV) significantly increases the chances of sustained virologic response (SVR) over treatment with Peg-IFN and RBV alone. If patients do not achieve SVR with telaprevir-based treatment, their viral population is often significantly enriched with telaprevir-resistant variants at the end of treatment. We sought to quantify the evolutionary dynamics of these post-treatment resistant variant populations.

The stochastic quasi-steady-state assumption: reducing the model but not the noise.

Highly reactive species at small copy numbers play an important role in many biological reaction networks. We have described previously how these species can be removed from reaction networks using stochastic quasi-steady-state singular perturbation analysis (sQSPA). In this paper we apply sQSPA to three published biological models: the pap operon regulation, a biochemical oscillator, and an intracellular viral infection.

Implications of decoupling the intracellular and extracellular levels in multi-level models of virus growth.

Virus infections are characterized by two distinct levels of detail: the intracellular level describing how viruses hijack the host machinery to replicate, and the extracellular level describing how populations of virus and host cells interact. Deterministic, population balance models for viral infections permit incorporation of both the intracellular and extracellular levels of information. In this work, we identify assumptions that lead to exact, selective decoupling of the interaction between the intracellular and extracellular levels, effectively permitting solution of first the intracellular level, and subsequently the extracellular level.

Image-guided modeling of virus growth and spread.

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).

Implications of rewiring bacterial quorum sensing.

Bacteria employ quorum sensing, a form of cell-cell communication, to sense changes in population density and regulate gene expression accordingly. This work investigated the rewiring of one quorum-sensing module, the lux circuit from the marine bacterium Vibrio fischeri. Steady-state experiments demonstrate that rewiring the network architecture of this module can yield graded, threshold, and bistable gene expression as predicted by a mathematical model.

Two classes of quasi-steady-state model reductions for stochastic kinetics.

The quasi-steady-state approximation (QSSA) is a model reduction technique used to remove highly reactive species from deterministic models of reaction mechanisms. In many reaction networks the highly reactive intermediates (QSSA species) have populations small enough to require a stochastic representation. In this work we apply singular perturbation analysis to remove the QSSA species from the chemical master equation for two classes of problems.

Synthetic gene circuits: design with directed evolution.

Synthetic circuits offer great promise for generating insights into nature's underlying design principles or forward engineering novel biotechnology applications. However, construction of these circuits is not straightforward. Synthetic circuits generally consist of components optimized to function in their natural context, not in the context of the synthetic circuit.

Stochastic simulation of catalytic surface reactions in the fast diffusion limit.

The master equation of a lattice gas reaction tracks the probability of visiting all spatial configurations. The large number of unique spatial configurations on a lattice renders master equation simulations infeasible for even small lattices. In this work, a reduced master equation is derived for the probability distribution of the coverages in the infinite diffusion limit.

On the origins of approximations for stochastic chemical kinetics.

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported.