Mathematical model of influenza A virus production in large-scale microcarrier culture

A mathematical model that describes the replication of influenza A virus in animal cells in large-scale microcarrier culture is presented. The virus is produced in a two-step process, which begins with the growth of adherent Madin-Darby canine kidney (MDCK) cells. After several washing steps serum-free virus maintenance medium is added, and the cells are infected with equine influenza virus (A/Equi 2 (H3N8), Newmarket 1/93). A time-delayed model is considered that has three state variables: the number of uninfected cells, infected cells, and free virus particles. It is assumed that uninfected cells adsorb the virus added at the time of infection. The infection rate is proportional to the number of uninfected cells and free virions. Depending on multiplicity of infection (MOI), not necessarily all cells are infected by this first step leading to the production of free virions. Newly produced viruses can infect the remaining uninfected cells in a chain reaction. To follow the time course of virus replication, infected cells were stained with fluorescent antibodies. Quantitation of influenza viruses by a hemagglutination assay (HA) enabled the estimation of the total number of new virions produced, which is relevant for the production of inactivated influenza vaccines. It takes about 4-6 h before visibly infected cells can be identified on the microcarriers followed by a strong increase in HA titers after 15-16 h in the medium. Maximum virus yield Vmax was about 1x10(10) virions/mL (2.4 log HA units/100 microL), which corresponds to a burst size ratio of about 18,755 virus particles produced per cell. The model tracks the time course of uninfected and infected cells as well as virus production. It suggests that small variations (<10%) in initial values and specific rates do not have a significant influence on Vmax. The main parameters relevant for the optimization of virus antigen yields are specific virus replication rate and specific cell death rate due to infection. Simulation studies indicate that a mathematical model that neglects the delay between virus infection and the release of new virions gives similar results with respect to overall virus dynamics compared with a time delayed model.     

Virus evolution within patients increases pathogenicity

Viruses like the human immunodeficiency virus (HIV), the hepatitis B virus (HBV), the hepatitis C virus (HCV) and many others undergo numerous rounds of inaccurate reproduction within an infected host. The resulting viral quasispecies is heterogeneous and sensitive to any selection pressure. Here we extend earlier work by showing that for a wide class of models describing the interaction between the virus population and the immune system, virus evolution has a well-defined direction toward increased pathogenicity. In particular, we study virus-induced impairment of the immune response and certain cross-reactive stimulation of specific immune responses. For eight different mathematical models, we show that virus evolution reduces the equilibrium abundance of uninfected cells and increases the rate at which uninfected cells are infected. Thus, in general, virus evolution makes things worse. An idea for combating HIV infection, however, is constructing a virus mutant that could outcompete the existing infection without being pathogenic itself.     

Assessment of virus infection in cultured cells using metabolic monitoring

A rapid, in-process assessment of virus replication is disired to quickly investigate the effects of process parameters on virus infection, and to monitor consistency of process in routine manufacturing of viral vaccines. Live virus potency assays are generally based on plaque formation, cytopathic effect, or antigen production (TCID₅₀) and can take days to weeks to complete. Interestingly, when infected with viruses, cultured cells undergo changes in cellular metabolism that can be easily measured. These phenomena appear to be common as they has been observed in a variety of virus-host systems, e.g., in insect cells infected with baculovirus, Vero cells infected with Rotavirus, MRC-5 cells infected with Hepatitis A virus, and MRC-5 cells infected with the Varicella Zoster Virus (VZV). In this article, changes in glycolytic metabolism of MRC-5 cells as a result of CVZ infection are described. Both glucose consumption and lactate production in VZV infected MRC-5 cells are significantly elevated in comparison to uninfected cells. Based on this result, a rapid, in-process assay to follow VZV infection has been developed. The relative increase in lactate production in infected cells () increases as the infection progresses and then plateaus as the infection peaks. This plateau correlates with time of peak virus titer and could be used as a harvest triggering parameter in a virus production process.X_u = cell density of uninfected cellsX_i = cell density of infected cellsX_T = total cell densityL_i = cumulative lactate production in infected culturesL_u = cumulative lactate production in uninfected culturesq_Li = specific lactate production of infected cellsq_Lu = specific lactate production of uninfected cellsk₁, K₂ = constantsList of Symbols     

DNA distribution and respiratory activity of Spodoptera frugiperda populations infected with wild-type and recombinant Autographa californica nuclear polyhedrosis virus.

Spodoptera frugiperda cells were infected with a wild-type Autographa californica nuclear polyhedrosis virus and with a recombinant Autographa californica nuclear polyhedrosis virus. The recombinant virus was derived from the wild-type virus and produced beta-galactosidase instead of polyhedrin. The changes in cell size, cell growth, viability, DNA distribution, and respiratory activity were followed through the time course of the infection. The DNA content as measured by flow cytometry of infected cells increased to approximately 1.8 times the value of uninfected cells and the distributions of single-cell DNA content of the infected cells were strongly deformed. Early in the infection the respiratory activity passed through a maximum. The mitochondrial activity based on Rhodamine 123 labelling of cells infected with the recombinant virus, as determined by flow cytometry, also passed through a maximum at 24 h post infection while the mitochondrial activity of cells infected with the wild-type virus continued to increase. Evolution of single-cell mitochondrial activity was different in uninfected populations and in populations infected with wild-type and with recombinant virus. In all experiments performed, the recombinant virus influenced cell behavior and the measured parameters earlier than the wild-type virus. The influence of the multiplicity of infection was stronger for the wild-type virus than for the recombinant virus.     

不同种雏鸭建立鸭乙肝病毒感染模型及抗病毒效果的实验

目的探讨不同种雏鸭建立鸭乙肝病毒感染模型的影响因素,观察应用该模型抗病毒的效果。方法采集鸭血清,应用PCR方法定性检测鸭血清中病毒DNA;定量PCR方法检测鸭血清中病毒DNA载量变化;用抗病毒药物处理,观察其在鸭DHBV感染模型中的抗病毒效果。结果不同种鸭DHBV自然感染率不同,樱桃谷鸭为8.75%,湖北麻鸭两个批次分别为17.80%和10.68%;静脉注射和腹腔注射两途径均能致雏鸭感染DHBV,静脉注射感染率80%,腹腔注射感染率65%;鸭感染DHBV后,体内病毒载量维持在106～108copies/mL,可持续20 d以上;抗病毒药物处理后,在不同DHBV模型中其抗病毒效果变化趋势一致。结论鸭的种类和人工感染途径可影响DHBV感染率;雏鸭感染DHBV后其体内有持续性的病毒血症;DHBV感染模型是药物抗病毒研究较好模型。     

Constraints on the use of lifespan-shortening Wolbachia to control dengue fever

Dengue fever, a viral disease spread by the mosquito Aedes aegypti, affects 50–100 million people a year in many tropical countries. Because the virus must incubate within mosquito hosts for two weeks before being able to transmit the infection, shortening the lifespan of mosquitoes may curtail dengue transmission. We developed a continuous time reaction-diffusion model of the spatial spread of Wolbachia through a population of A. aegypti. This model incorporates the lifespan-shortening effects of Wolbachia on infected A. aegypti and the fitness advantage to infected females due to cytoplasmic incompatibility (CI). We found that local establishment of the Wolbachia infection can occur if the fitness advantage due to CI exceeds the fitness reduction due to lifespan-shortening effects, in accordance with earlier results concerning fecundity reduction. However, spatial spread is possible only if the fitness advantage due to CI is twice as great as the fitness reduction due to lifespan shortening effects. Moreover, lifespan-shortening and fecundity-reduction can have different effects on the speed of wave-retreat. Using data from the literature, we estimated all demographic parameters for infected and uninfected mosquitoes and computed the velocities of spread of infection. Our most optimistic estimates suggest that the spatial spread of lifespan-shortening Wolbachia may be so slow that efficient spatial spread would require a prohibitively large number of point releases. However, as these estimates of demographic parameters may not accurately reflect natural conditions, further research is necessary to corroborate these predictions.     

Parameter estimation and sensitivity analysis in an agent-based model of Leishmania major infection

Computer models of disease take a systems biology approach toward understanding host-pathogen interactions. In particular, data driven computer model calibration is the basis for inference of immunological and pathogen parameters, assessment of model validity, and comparison between alternative models of immune or pathogen behavior. In this paper we describe the calibration and analysis of an agent-based model of Leishmania major infection. A model of macrophage loss following uptake of necrotic tissue is proposed to explain macrophage depletion following peak infection. Using Gaussian processes to approximate the computer code, we perform a sensitivity analysis to identify important parameters and to characterize their influence on the simulated infection. The analysis indicates that increasing growth rate can favor or suppress pathogen loads, depending on the infection stage and the pathogen's ability to avoid detection. Subsequent calibration of the model against previously published biological observations suggests that L. major has a relatively slow growth rate and can replicate for an extended period of time before damaging the host cell.     

A delay-differential equation model of HIV infection of CD4(+) T-cells

A.S. Perelson, D.E. Kirschner and R. De Boer (Math. Biosci. 114 (1993) 81) proposed an ODE model of cell-free viral spread of human immunodeficiency virus (HIV) in a well-mixed compartment such as the bloodstream. Their model consists of four components: uninfected healthy CD4(+) T-cells, latently infected CD4(+) T-cells, actively infected CD4(+) T-cells, and free virus. This model has been important in the field of mathematical modeling of HIV infection and many other models have been proposed which take the model of Perelson, Kirschner and De Boer as their inspiration, so to speak (see a recent survey paper by A.S. Perelson and P.W. Nelson (SIAM Rev. 41 (1999) 3-44)). We first simplify their model into one consisting of only three components: the healthy CD4(+) T-cells, infected CD4(+) T-cells, and free virus and discuss the existence and stability of the infected steady state. Then, we introduce a discrete time delay to the model to describe the time between infection of a CD4(+) T-cell and the emission of viral particles on a cellular level (see A.V.M. Herz, S. Bonhoeffer, R.M. Anderson, R.M. May, M.A. Nowak [Proc. Nat. Acad. Sci. USA 93 (1996) 7247]). We study the effect of the time delay on the stability of the endemically infected equilibrium, criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. Numerical simulations are presented to illustrate the results.     

On the intra-host dynamics of HIV-1 infections

An extension of a previously proposed theory for the pathogenesis of AIDS is presented and analyzed using a mathematical modelling approach. This theory is based on the observation that human immunodeficiency virus type 1 (HIV-1) predominantly infects and replicates in (CD4+)-T cells, and that the infection process within an infected individual is characterized by ongoing generation and selection of HIV variants with increasing reproductive capacity. This evolutionary process is considered to be the reason for the gradual loss of immunocompetence and the final destruction of the immune system observed in most patients. The extension presented here incorporates the effect of the permanently increasing susceptibility of (CD4+)-T cell clones, as a result of the evolutionary process. The presented model reproduces and possibly explains a wide variety of findings about the HIV infection process. Numerical results indicate that the effect of the initial dose is minimal, and restricted to the primary phase of infection. According to the model predictions the impact of the HIV evolutionary speed is crucial for the progression to disease. An important progression determinant is the initial infection rate, being a component of the viral reproductive capacity. An influential role in disease progression seems to be played by the initial (CD4+)-T cell count.     

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.     

Thymidine kinase activity in mouse embryo fibroblast cells infected with murine cytomegalovirus

Thymidine kinase activity was found in whole cell extracts of growing and stationary mouse embryo fibroblast cells after infection with murine cytomegalovirus. Determination of the kinetic constants and heat stability characteristics indicated that the enzyme activity from infected cells was different to that found in uninfected cells in the growth phase. The expression of thymidine kinase activity during virus replication was reflected by the incorporation of (6-³H) thymidine into acid precipitable fractions of infected cell cultures. Preliminary data from kinetic studies showed a reduction in the phosphorylation of thymidine by this enzyme activity in the presence of Acyclovir, a potent inhibitor of herpes virus replication.     

Dispersing hemipteran vectors have reduced arbovirus prevalence

A challenge in managing vector-borne zoonotic diseases in human and wildlife populations is predicting where epidemics or epizootics are likely to occur, and this requires knowing in part the likelihood of infected insect vectors dispersing pathogens from existing infection foci to novel areas. We measured prevalence of an arbovirus, Buggy Creek virus, in dispersing and resident individuals of its exclusive vector, the ectoparasitic swallow bug (Oeciacus vicarius), that occupies cliff swallow (Petrochelidon pyrrhonota) colonies in western Nebraska. Bugs colonizing new colony sites and immigrating into established colonies by clinging to the swallows’ legs and feet had significantly lower virus prevalence than bugs in established colonies and those that were clustering in established colonies before dispersing. The reduced likelihood of infected bugs dispersing to new colony sites indicates that even heavily infected sites may not always export virus to nearby foci at a high rate. Infected arthropods should not be assumed to exhibit the same dispersal or movement behaviour as uninfected individuals, and these differences in dispersal should perhaps be considered in the epidemiology of vector-borne pathogens such as arboviruses.     

The AIDS epidemic: profiles of development

As all HIV-infected subjects become virus carriers, the epidemic will not attain a "steady state" until the number of deletions (from death and other factors) equals or outnumbers that of new cases, i.e. each HIV-infected subject transmits the infection to only one subject in the course of his lifespan. A full stop of all spreading of HIV will most likely require worldwide vaccination. By simple mathematical models it is shown that calculation of the number of HIV infected individuals based on the number of AIDS cases is very uncertain. The ratio of HIV infected subjects to AIDS cases is greatly influenced by the length of the incubation period and the case doubling time. Since the growth of the epidemic is exponential, all efforts to control the epidemic should be continuously intensified as single measures will only retard the rate of spread. The effect of saturation/deletion on the number of susceptible individuals is insignificant in this phase of the epidemic, except in small groups at special risk.     

CYTOPLASMIC INCOMPATIBILITY IN POPULATIONS WITH OVERLAPPING GENERATIONS

Many insects and other arthropods harbor maternally inherited bacteria inducing "cytoplasmic incompatibility" (CI), reduced egg hatch when infected males mate with uninfected females. CI-causing infections produce a frequency-dependent reproductive advantage for infected females. However, many such infections impose fitness costs that lead to unstable equilibrium frequencies below which the infections tend to be eliminated. To understand the unstable equilibria produced by reduced lifespan or lengthened development, overlapping-generation analyses are needed. An idealized model of overlapping generations with age-independent parameters produces a simple expression showing how the unstable point depends on the population growth rate, the intensity of CI, and the infection's effects on development time, longevity, and fecundity. The interpretation of this equilibrium is complicated by age structure. Nevertheless, the unstable equilibrium provides insight into the CI-causing infections found in nature, and it can guide potential manipulations of natural populations, including those that transmit diseases, through the introduction of infections that alter life-table parameters.     

An HBV model with diffusion and time delay

In this paper, a hepatitis B virus (HBV) model with spatial diffusion and saturation response of the infection rate is investigated, in which the intracellular incubation period is modelled by a discrete time delay. By analyzing the corresponding characteristic equations, the local stability of an infected steady state and an uninfected steady state is discussed. By comparison arguments, it is proved that if the basic reproductive number is less than unity, the uninfected steady state is globally asymptotically stable. If the basic reproductive number is greater than unity, by successively modifying the coupled lower-upper solution pairs, sufficient conditions are obtained for the global stability of the infected steady state. Numerical simulations are carried out to illustrate the main results.     

Amplification of tick-borne encephalitis virus infection during co-feeding of ticks

Abstract. Following engorgement of Rhipicephalus appendiculatus larvae on guinea-pigs infected with tick-borne encephalitis (TBE) virus, none of the engorged larvae or emergent nymphs contained detectable infectious virus. However, one of twelve pools, each containing three of the unfed nymphs, was positive when screened by polymerase chain reaction (PCR), indicating a low prevalence of TBE virus infection in the unfed nymphs. After engorgement of the nymphs on four uninfected guinea-pigs, 19/24 (79%) fed nymphs from one guinea-pig and 4/25 (16%) fed nymphs from a second guinea-pig were infected; all the ticks examined from the other two guinea-pigs were uninfected. The results suggest that TBE virus was transmitted from a low proportion of infected nymphs (infected as larvae) to uninfected nymphs as they fed together on an uninfected guinea-pig. Such amplification of the initial infection, at the population level, could play an important role in maintaining TBE virus infections in nature, particularly if there is a low level of vertical transmission from one tick generation to the next.     

Mathematical analysis of delay differential equation models of HIV-1 infection

Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays. We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells. We show that when the drug efficacy is less than perfect the estimated value of the loss rate of productively infected T cells, delta, is increased when data is fit with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of delta. We also provide some general results on the stability of non-linear delay differential equation infection models.     

On the behavior of solutions in viral dynamical models

We consider simple mathematical models for the early population dynamics of the human immunodefficiency type 1 virus (HIV-1). Although these systems of differential equations may be solved by numerical methods, few general theoretical results are available due to nonlinearities. We analyze a model whose components are plasma densities of uninfected CD4+ T-cells and infected cells (assumed in this model to be proportional to virion density). In addition to analyzing the nature of the equilibrium points, we show that there are no periodic or limit-cycle solutions. Depending on the values of the parameters, solutions either tend without oscillation to an equilibrium point with zero virion density or to an equilibrium point in which there are a nonzero number of virions. In the latter case the approach to equilibrium may be through damped oscillations or without oscillation.     

Replication of Coliphage M-13 I. Effects on Host Cells After Synchronized Infection

Techniques have been described for synchronization of bacteriophage M-13 infection of host cells. The latent period in infected cells was 10 min, and no appreciable number of intracellular phage was observed. Phage production proceeded in three phases after release of the starvation block: an initial rapid exponential rate of progeny phage release without cell lysis, a period of rate transition accompanying the resumption of host cell division, and a second, slower exponential rate of phage production which paralleled the rate of host cell division. The size of infected cells was not affected by infection, but the generation time was increased by 25%. Starved infected cells exhibited a much longer lag in attaining an exponential rate of growth upon the addition of nutrients than did an uninfected control culture.