Dynamics of an HIV-1 therapy model of fighting a virus with another virus

In this paper, we rigorously analyse an ordinary differential equation system that models fighting the HIV-1 virus with a genetically modified virus. We show that when the basic reproduction ratio ?₀<1, then the infection-free equilibrium E ₀ is globally asymptotically stable; when ?₀>1, E ₀ loses its stability and there is the single-infection equilibrium E _s. If ?₀∈(1, 1+δ) where δ is a positive constant explicitly depending on system parameters, then the single-infection equilibrium E _s that is globally asymptotically stable, while when ?₀>1+δ, E _s becomes unstable and the double-infection equilibrium E _d comes into existence. When ?₀ is slightly larger than 1+δ, E _d is stable and it loses its stability via Hopf bifurcation when ?₀ is further increased in some ways. Through a numerical example and by applying a normal form theory, we demonstrate how to determine the bifurcation direction and stability, as well as the estimates of the amplitudes and the periods of the bifurcated periodic solutions. We also perform numerical simulations which agree with the theoretical results. The approaches we use here are a combination of analysis of characteristic equations, fluctuation lemma, Lyapunov function and normal form theory.     

Fighting a virus with a virus: a dynamic model for HIV-1 therapy

A mathematical model examined a potential therapy for controlling viral infections using genetically modified viruses. The control of the infection is an indirect effect of the selective elimination by an engineered virus of infected cells that are the source of the pathogens. Therefore, this engineered virus could greatly compensate for a dysfunctional immune system compromised by AIDS. In vitro studies using engineered viruses have been shown to decrease the HIV-1 load about 1000-fold. However, the efficacy of this potential treatment for reducing the viral load in AIDS patients is unknown. The present model studied the interactions among the HIV-1 virus, its main host cell (activated CD4+ T cells), and a therapeutic engineered virus in an in vivo context; and it examined the conditions for controlling the pathogen. This model predicted a significant drop in the HIV-1 load, but the treatment does not eradicate HIV. A basic estimation using a currently engineered virus indicated an HIV-1 load reduction of 92% and a recovery of host cells to 17% of their normal level. Greater success (98% HIV reduction, 44% host cells recovery) is expected as more competent engineered viruses are designed. These results suggest that therapy using viruses could be an alternative to extend the survival of AIDS patients.     

Dynamics of HIV-1 Assembly and Release

Assembly and release of human immunodeficiency virus (HIV) occur at the plasma membrane of infected cells and are driven by the Gag polyprotein. Previous studies analyzed viral morphogenesis using biochemical methods and static images, while dynamic and kinetic information has been lacking until very recently. Using a combination of wide-field and total internal reflection fluorescence microscopy, we have investigated the assembly and release of fluorescently labeled HIV-1 at the plasma membrane of living cells with high time resolution. Gag assembled into discrete clusters corresponding to single virions. Formation of multiple particles from the same site was rarely observed. Using a photoconvertible fluorescent protein fused to Gag, we determined that assembly was nucleated preferentially by Gag molecules that had recently attached to the plasma membrane or arrived directly from the cytosol. Both membrane-bound and cytosol derived Gag polyproteins contributed to the growing bud. After their initial appearance, assembly sites accumulated at the plasma membrane of individual cells over 1–2 hours. Assembly kinetics were rapid: the number of Gag molecules at a budding site increased, following a saturating exponential with a rate constant of ∼5×10⁻³ s⁻¹, corresponding to 8–9 min for 90% completion of assembly for a single virion. Release of extracellular particles was observed at ∼1,500±700 s after the onset of assembly. The ability of the virus to recruit components of the cellular ESCRT machinery or to undergo proteolytic maturation, or the absence of Vpu did not significantly alter the assembly kinetics.     

具有时滞的HBV病毒动力学模型稳定性分析

HBV（HePatitis B virus）是一种具有严重传染性的肝炎病毒,迄今为止,人们对它的免疫和慢性化的机制等方面还不甚了解。本文基于相关的病理知识,对应的建立了具有时滞的微分方程数学模型,系统地探讨了肝炎B病毒与宿主细胞之间的关系,利用Lyapunov函数方法研究了病毒动力学模型感染平衡点的局部稳定性和未感染平衡点全局稳定性,并利用数学模拟验证了理论分析。结果表明时滞的存在不会影响到感染平衡点的局部稳定性,但能影响平衡点到达的时间跨度,对于药物治疗的疗程和治疗时机的确定有参考意义。     

Nonlinear control of HIV-1 infection with a singular perturbation model

Using a singular perturbation approximation, a nonlinear state-space model of HIV-1 infection, having as state variables the number of healthy and infected CD4+T cells and the number of virion particles, is simplified and used to design a control law. The control law comprises an inner block that performs feedback linearizing of the virus dynamics and an outer block implementing an LQ regulator that drives the number of virion particles to a number below the specification. A sensitivity analysis of the resulting law is performed with respect to the model parameter to the infection rate, showing that the controlled system remains stable in the presence of significant changes of this parameter with respect to the nominal value.     

A model of HIV-1 pathogenesis that includes an intracellular delay

Mathematical modeling combined with experimental measurements have yielded important insights into HIV-1 pathogenesis. For example, data from experiments in which HIV-infected patients are given potent antiretroviral drugs that perturb the infection process have been used to estimate kinetic parameters underlying HIV infection. Many of the models used to analyze data have assumed drug treatments to be completely efficacious and that upon infection a cell instantly begins producing virus. We consider a model that allows for less then perfect drug effects and which includes a delay in the initiation of virus production. We present detailed analysis of this delay differential equation model and compare the results to a model without delay. Our analysis shows that when drug efficacy is less than 100%, as may be the case in vivo, the predicted rate of decline in plasma virus concentration depends on three factors: the death rate of virus producing cells, the efficacy of therapy, and the length of the delay. Thus, previous estimates of infected cell loss rates can be improved upon by considering more realistic models of viral infection.     

Flap opening dynamics in HIV-1 protease explored with a coarse-grained model

We present a one-bead coarse-grained model that enables dynamical simulations of proteins on the time scale of tens of microseconds. The parameterization of the force field includes accurate conformational terms that allow for fast and reliable exploration of the configurational space. The model is applied to the dynamics of flap opening in HIV-1 protease. The experimental structure of the recently crystallized semi-open conformation of HIV-1 protease is well reproduced in the simulation, which supports the accuracy of our model. Thanks to very long simulations and extensive sampling of opening and closing events, we also investigate the thermodynamics and kinetics of the opening process. We have shown that the effect of the solvent slows down the dynamics to the experimentally observed time scales. The model is found to be reliable for application to substrate docking simulations, which are currently in progress.     

Suppression of human immunodeficiency virus type 1 (HIV-1) replication by an HIV-1-dependent double locked vector with the Cre/loxP system

We previously demonstrated the function of an HIV-1-dependent ribozyme expression vector, with which the site-specific excision of loxP sequences can be achieved by using the Cre-loxP system (ON/OFF) as a molecular switch in an acute HIV-1 infection. However, this expression system also revealed the lower, non-specific expression of the anti-H1V-1 ribozyme in the absence of tat. To circumvent this problem, we used the more efficient HIV-1-dependent Cre recombinase gene expression vector, encoding the LTR-gag-p17 (extending from the 5'-LTR to the middle of the gag gene (pLTR-gag-p17-Cre)). Comparatively, the pLTR-gag-p17-Cre induces a higher Cre-protein expression level in an HIV-1 infection-dependent manner than the minimal pLTR-Cre. Furthermore, we constructed the ploxP-Rz-U5 and pLTR-gag-p17-Cre plasmids and also combined them into a single vector, pLTR-gag-p17-Cre/loxP-Rz-U5, for a comparison of their anti-HIV-1 activities. The resultant simultaneous expression of the Cre protein and the homologous recombination of the two loxP sequences induced a high level of HIV-1 replication inhibition (95%). Significantly, a high steady-state of ribozyme expression was observed in the RT-PCR analysis. These data imply that targeting the HIV-1 genes with the pLTR-gag-p17-Cre/loxP-Rz-U5 vector, which mediates HIV-1-dependent ribozyme expression, would be a useful tool for HIV-1 gene therapy applications.     

Dissecting the Dynamics of HIV-1 Protein Sequence Diversity

The rapid mutation of human immunodeficiency virus-type 1 (HIV-1) and the limited characterization of the composition and incidence of the variant population are major obstacles to the development of an effective HIV-1 vaccine. This issue was addressed by a comprehensive analysis of over 58,000 clade B HIV-1 protein sequences reported over at least 26 years. The sequences were aligned and the 2,874 overlapping nonamer amino acid positions of the viral proteome, each a possible core binding domain for human leukocyte antigen molecules and T-cell receptors, were quantitatively analyzed for four patterns of sequence motifs: (1) “index”, the most prevalent sequence; (2) “major” variant, the most common variant sequence; (3) “minor” variants, multiple different sequences, each with an incidence less than that of the major variant; and (4) “unique” variants, each observed only once in the alignment. The collective incidence of the major, minor, and unique variants at each nonamer position represented the total variant population for the position. Positions with more than 50% total variants contained correspondingly reduced incidences of index and major variant sequences and increased minor and unique variants. Highly diverse positions, with 80 to 98% variant nonamer sequences, were present in each protein, including 5% of Gag, and 27% of Env and Nef, each. The multitude of different variant nonamer sequences (i.e. nonatypes; up to 68%) at the highly diverse positions, represented by the major, multiple minor, and multiple unique variants likely supported variants function both in immune escape and as altered peptide ligands with deleterious T-cell responses. The patterns of mutational change were consistent with the sequences of individual HXB2 and C1P viruses and can be considered applicable to all HIV-1 viruses. This characterization of HIV-1 protein mutation provides a foundation for the design of peptide-based vaccines and therapeutics.