Evaluation of HIV-1 kinetic models using quantitative discrimination analysis

Global threshold dynamics in an HIV virus model with nonlinear infection rate and distributed invasion and production delays

We consider a mathematical model that describes the interactions of the HIV virus, CD4 cells and CTLs within host, which is a modification of some existing models by incorporating (i) two distributed kernels reflecting the variance of time for virus to invade into cells and the variance of time for invaded virions to reproduce within cells; (ii) a nonlinear incidence function f for virus infections, and (iii) a nonlinear removal rate function h for infected cells. By constructing Lyapunov functionals and subtle estimates of the derivatives of these Lyapunov functionals, we shown that the model has the threshold dynamics: if the basic reproduction number (BRN) is less than or equal to one, then the infection free equilibrium is globally asymptotically stable, meaning that HIV virus will be cleared; whereas if the BRN is larger than one, then there exist an infected equilibrium which is globally asymptotically stable, implying that the HIV-1 infection will persist in the host and the viral concentration will approach a positive constant level. This together with the dependence/independence of the BRN on f and h reveals the effect of the adoption of these nonlinear functions.

The virus as metabolic engineer

Recent genome-wide screens of host genetic requirements for viral infection have reemphasized the critical role of host metabolism in enabling the production of viral particles. In this review, we highlight the metabolic aspects of viral infection found in these studies, and focus on the opportunities these requirements present for metabolic engineers. In particular, the objectives and approaches that metabolic engineers use are readily comparable to the behaviors exhibited by viruses during infection. As a result, metabolic engineers have a unique perspective that could lead to novel and effective methods to combat viral infection.

Bayesian-based selection of metabolic objective functions

MOTIVATION

A critical component of in silico analysis of underdetermined metabolic systems is the identification of the appropriate objective function. A common assumption is that the objective of the cell is to maximize growth. This objective function has been shown to be consistent in a few limited experimental cases, but may not be universally appropriate. Here a method is presented to quantitatively determine the most probable objective function.

RESULTS

The genome-scale metabolism of Escherichia coli growing on succinate was used as a case-study for analysis. Five different objective functions, including maximization of growth rate, were chosen based on biological plausibility. A combination of flux balance analysis and linear programming was used to simulate cellular metabolism, which was then compared to independent experimental data using a Bayesian objective function discrimination technique. After comparing rates of oxygen uptake and acetate production, minimization of the production rate of redox potential was determined to be the most probable objective function. Given the appropriate reaction network and experimental data, the discrimination technique can be applied to any bacterium to test a variety of different possible objective functions.

SUPPLEMENTARY INFORMATION

Additional files, code and a program for carrying out model discrimination are available at http://www.engr.uconn.edu/~srivasta/modisc.html.