Quantification of in vivo replicative capacity of HIV-1 in different compartments of infected cells

Concentration-response model of rilpivirine in a cohort of HIV-1-infected naive and pre-treated patients

BACKGROUND

Rilpivirine is widely prescribed in people living with HIV. Although trough plasma concentrations have been associated with virological response, the drug pharmacodynamics remain incompletely characterized.

OBJECTIVES

To develop the first pharmacodynamic model of rilpivirine in order to establish the rilpivirine concentration-response relationship for future treatment optimization.

METHODS

A retrospective observational study was conducted in patients receiving the once-daily rilpivirine/tenofovir disoproxil fumarate/emtricitabine regimen. Individual rilpivirine trough plasma concentrations over time were predicted using a previous pharmacokinetic model. An established susceptible, infected, recovered model was used to describe HIV dynamics without assuming disease steady-state. Population analysis was performed with MONOLIX 2018 software. Simulations of the viral load evolution as a function of time and rilpivirine trough plasma concentration were performed.

RESULTS

Overall, 60 naive and 39 pre-treated patients were included with a follow-up ranging from 2 to 37 months. The final model adequately described the data and the pharmacodynamic parameters were estimated with a good precision. The population typical value of rilpivirine EC50 was estimated at 65 ng/mL. A higher infection rate constant of CD4 cells for HIV-1 was obtained in pre-treated patients. Consequently, the time to obtain virological suppression was longer in pre-treated than in naive patients.

CONCLUSIONS

The concentration-response relationship of rilpivirine was satisfactorily described for the first time using an original population pharmacodynamic model. Simulations performed using the final model showed that the currently used 50 ng/mL rilpivirine trough plasma concentration efficacy target might need revision upwards, particularly in pre-treated patients.

HIV dynamics linked to memory CD4+ T cell homeostasis

The dynamics of latent HIV is linked to infection and clearance of resting memory CD4+ T cells. Infection also resides within activated, non-dividing memory cells and can be impacted by antigen-driven and homeostatic proliferation despite suppressive antiretroviral therapy (ART). We investigated whether plasma viral level (pVL) and HIV DNA dynamics could be explained by HIV’s impact on memory CD4+ T cell homeostasis. Median total, 2-LTR and integrated HIV DNA levels per μL of peripheral blood, for 8 primary (PHI) and 8 chronic HIV infected (CHI) individuals enrolled on a raltegravir (RAL) based regimen, exhibited greatest changes over the 1^st year of ART. Dynamics slowed over the following 2 years so that total HIV DNA levels were equivalent to reported values for individuals after 10 years of ART. The mathematical model reproduced the multiphasic dynamics of pVL, and levels of total, 2-LTR and integrated HIV DNA in both PHI and CHI over 3 years of ART. Under these simulations, residual viremia originated from reactivated latently infected cells where most of these cells arose from clonal expansion within the resting phenotype. Since virion production from clonally expanded cells will not be affected by antiretroviral drugs, simulations of ART intensification had little impact on pVL. HIV DNA decay over the first year of ART followed the loss of activated memory cells (120 day half-life) while the 5.9 year half-life of total HIV DNA after this point mirrored the slower decay of resting memory cells. Simulations had difficulty reproducing the fast early HIV DNA dynamics, including 2-LTR levels peaking at week 12, and the later slow loss of total and 2-LTR HIV DNA, suggesting some ongoing infection. In summary, our modelling indicates that much of the dynamical behavior of HIV can be explained by its impact on memory CD4+ T cell homeostasis.

Impact of disease, drug and patient adherence on the effectiveness of antiviral therapy in pediatric HIV

INTRODUCTION

Maintaining effective antiretroviral treatment for life is a major problem in both resource-limited and resource-rich countries. Despite the progress observed in paediatric antiretroviral therapy, approximately 12% of children still experience treatment failure due to drug resistance, inadequate dosing and poor adherence. We explore the current status of antiretroviral therapy in children with focus on the interaction between disease, drug pharmacokinetics and patient behavior, all of which are strongly interconnected and determine treatment outcome. Areas covered: An overview is provided of the viral characteristics and available drug combinations aimed at the prevention of resistance. In this context, the role of patient adherence is scrutinized. A detailed assessment of factors affecting adherence is presented together with the main strategies to enhance treatment response in children. Expert opinion: Using modeling and simulation, a framework for characterizing the forgiveness of non-adherence for specific antiretroviral drugs in children is proposed in which information on pharmacokinetics, pharmacokinetic-pharmacodynamic relationships and viral dynamics is integrated. This approach represents an opportunity for the simplification of dosing regimens taking into account the interaction between these factors. Based on clinical trial simulation scenarios, we envisage the possibility of assessing the impact of variable adherence to antiretroviral drug combinations in HIV-infected children.

HIV-1 resistance to neutralizing antibodies: Determination of antibody concentrations leading to escape mutant evolution

Broadly neutralizing antibodies against human immunodeficiency virus type 1 (HIV-1) are considered vital components of novel therapeutics and blueprints for vaccine research. Yet escape to even the most potent of these antibodies is imminent in natural infection. Measures to define antibody efficacy and prevent mutant selection are thus urgently needed. Here, we derive a mathematical framework to predict the concentration ranges for which antibody escape variants can outcompete their viral ancestors, referred to as mutant selection window (MSW). When determining the MSW, we focus on the differential efficacy of neutralizing antibodies against HIV-1 in two canonical infection routes, free-virus infection and cell-cell transmission. The latter has proven highly effective in vitro suggesting its importance for both in vivo spread as well as for escaping targeted intervention strategies. We observed a range of MSW patterns that highlight the potential of mutants to arise in both transmission pathways and over wide concentration ranges. Most importantly, we found that only when the arising mutant has both, residual sensitivity to the neutralizing antibody and reduced infectivity compared to the parental virus, antibody dosing outside of the MSW to restrict mutant selection is possible. Emergence of mutants that provide complete escape and have no considerable fitness loss cannot be prevented by adjusting antibody doses. The latter may in part explain the ubiquitous resistance to neutralizing antibodies observed in natural infection and antibody treatment. Based on our findings, combinations of antibodies targeting different epitopes should be favored for antibody-based interventions as this may render complete resistance less likely to occur and also increase chances that multiple escapes result in severe fitness loss of the virus making longer-term antibody treatment more feasible.

What do mathematical models tell us about killing rates during HIV-1 infection?

Over the past few decades the extent to which cytotoxic T lymphocytes (CTLs) control human immunodeficiency virus (HIV) replication has been studied extensively, yet their role and mode of action remain controversial. In some studies, CTLs were found to kill a large fraction of the productively infected cells relative to the viral cytopathicity, whereas in others CTLs were suggested to kill only a small fraction of infected cells. In this review, we compile published estimates of CTL-mediated death rates, and examine whether these studies permit determining the rate at which CTLs kill HIV-1 infected cells. We highlight potential misinterpretations of the CTL-killing rates from the escape rates of mutants, and from perturbations of the steady state viral load during chronic infection. Our major conclusion is that CTL-mediated killing rates remain unknown. But contrary to current consensus, we argue that killing rates higher than one per day are perfectly consistent with the experimental data, which would imply that the majority of the productively infected cells could still die from CTL-mediated killing rather than from viral cytopathicity.

Quantifying the turnover of transcriptional subclasses of HIV-1-infected cells

HIV-1-infected cells in peripheral blood can be grouped into different transcriptional subclasses. Quantifying the turnover of these cellular subclasses can provide important insights into the viral life cycle and the generation and maintenance of latently infected cells. We used previously published data from five patients chronically infected with HIV-1 that initiated combination antiretroviral therapy (cART). Patient-matched PCR for unspliced and multiply spliced viral RNAs combined with limiting dilution analysis provided measurements of transcriptional profiles at the single cell level. Furthermore, measurement of intracellular transcripts and extracellular virion-enclosed HIV-1 RNA allowed us to distinguish productive from non-productive cells. We developed a mathematical model describing the dynamics of plasma virus and the transcriptional subclasses of HIV-1-infected cells. Fitting the model to the data allowed us to better understand the phenotype of different transcriptional subclasses and their contribution to the overall turnover of HIV-1 before and during cART. The average number of virus-producing cells in peripheral blood is small during chronic infection. We find that a substantial fraction of cells can become defectively infected. Assuming that the infection is homogenous throughout the body, we estimate an average in vivo viral burst size on the order of 10⁴ virions per cell. Our study provides novel quantitative insights into the turnover and development of different subclasses of HIV-1-infected cells, and indicates that cells containing solely unspliced viral RNA are a good marker for viral latency. The model illustrates how the pool of latently infected cells becomes rapidly established during the first months of acute infection and continues to increase slowly during the first years of chronic infection. Having a detailed understanding of this process will be useful for the evaluation of viral eradication strategies that aim to deplete the latent reservoir of HIV-1.

Gaining a quantitative understanding of the development and turnover of different HIV-1-infected subpopulations of cells is crucial to improve the outcome of patients on combination antiretroviral therapy (cART). The population of latently infected cells is of particular interest as they represent the major barrier to a cure of HIV-1 infection. We developed a mathematical model that describes the dynamics of different transcriptionally active subclasses of HIV-1-infected cells and the viral load in peripheral blood. The model was fitted to previously published data from five chronically HIV-1-infected patients starting cART. This allowed us to estimate critical parameters of the within-host dynamics of HIV-1, such as the the number of virions produced by a single infected cell. The model further allowed investigation of HIV-1 dynamics during the acute phase. Computer simulations illustrate that latently infected cells become rapidly established during the first months of acute infection and continue to increase slowly during the first years of chronic infection. This illustrates the opportunity for strategies that aim to eradicate the virus during early cART as the pool of HIV-1 infected cells is substantially smaller during acute infection than during chronic infection.

Integrated population pharmacokinetic/viral dynamic modelling of lopinavir/ritonavir in HIV-1 treatment-naïve patients

BACKGROUND

Lopinavir (LPV)/ritonavir (RTV) co-formulation (LPV/RTV) is a widely used protease inhibitor (PI)-based regimen to treat HIV-infection. As with all PIs, the trough concentration (C trough) is a primary determinant of response, but the optimum exposure remains poorly defined. The primary objective was to develop an integrated LPV population pharmacokinetic model to investigate the influence of α-1-acid glycoprotein and link total and free LPV exposure to pharmacodynamic changes in HIV-1 RNA and assess viral dynamic and drug efficacy parameters.

METHODS

Data from 35 treatment-naïve HIV-infected patients initiating therapy with LPV/RTV 400/100 mg orally twice daily across two studies were used for model development and simulations using ADAPT. Total LPV (LPVt) and RTV concentrations were measured by high-performance liquid chromatography with ultraviolet (UV) detection. Free LPV (LPVf) concentrations were measured using equilibrium dialysis and mass spectrometry.

RESULTS

The LPVt typical value of clearance (CLLPVt/F) was 4.73 L/h and the distribution volume (VLPVt/F) was 55.7 L. The clearance (CLLPVf/F) and distribution volume (Vf/F) for LPVf were 596 L/h and 6,370 L, respectively. The virion clearance rate was 0.0350 h(-1). The simulated LPVLPVt C trough values at 90% (EC90) and 95% (EC95) of the maximum response were 316 and 726 ng/mL, respectively.

CONCLUSIONS

The pharmacokinetic-pharmacodynamic model provides a useful tool to quantitatively describe the relationship between LPV/RTV exposure and viral response. This comprehensive modelling and simulation approach could be used as a surrogate assessment of antiretroviral (ARV) activity where adequate early-phase dose-ranging studies are lacking in order to define target trough concentrations and possibly refine dosing recommendations.

ESTROGEN REPLACEMENT THERAPY FOR STROKE

Stroke is the third most common cause of death and severe disability among Western populations. Overall, the incidence of stroke is uniformly higher in men than in women. Stroke is rare in women during the reproductive years, and rapidly increases after menopause, strongly suggesting that estrogen (E2) plays an important role in the prevention of stroke. Ongoing studies are currently evaluating both the benefits and risks associated with E2 replacement therapy and hormone replacement therapy in stroke. Equally important is the role of E2 receptor (ER), as studies indicate that ER populations in several tissue sites may significantly change during stress and aging. Such changes may affect the patient's susceptibility to neurological disorders including stroke, and greatly affect the response to selective E2 receptor modulators (SERMs). Replacement therapies may be inefficient with low ER levels. The goal of this review paper is to discuss an animal model that will allow investigations of the potential therapeutic effects of E2 and its derivatives in stroke. We hypothesize that E2 neuroprotection is, in part, receptor mediated. This hypothesis is a proof of principle approach to demonstrate a role for specific ER subtypes in E2 neuroprotection. To accomplish this, we use a retroviral mediated gene transfer strategy that express subtypes of the ER gene in regions of the rat brain most susceptible to neuronal damage, namely the striatum and cortex. The animal model is exposed to experimental stroke conditions involving middle cerebral artery occlusion (MCAo) method, and eventually the extent of neuronal damage will be evaluated. A reduction in neuronal damage is expected when E2 is administered with specific ER subtypes. From this animal model, an optimal E2 dose and treatment regimen can be determined. The animal model can help identify potential E2-like therapeutics in stroke, and screen for beneficial or toxic additives present in commercial E2 preparations that are currently available. Such studies will be informative in designing drug therapies for stroke.

A hunter virus that targets both infected cells and HIV free virions: implications for therapy

The design of ‘hunter’ viruses aimed at destroying human immunodeficiency virus (HIV) infected cells is an active area of research that has produced promising results in vitro. Hunters are designed to target exposed viral envelope proteins in the membranes of infected cells, but there is evidence that the hunter may also target envelope proteins of free HIV, inducing virus-virus fusion. In order to predict the effects of this fusion on therapy outcomes and determine whether fusion ability is advantageous for hunter virus design, we have constructed a model to account for the possibility of hunter-HIV fusion. The study was based on a target cell-limited model of HIV infection and it examined the hunter therapeutic effect on recovering the HIV main target cells, the activated CD4⁺ T lymphocytes. These cells assist in setting up an immune response to opportunistic infections. The study analyzed the hunter dual mechanisms to control infection and because of diverse estimates for viral production and clearance of HIV, simulations were examined at rates spanning an order of magnitude. Results indicate that without hunter-HIV fusion ability, hunters that kill HIV-infected cells lead to a substantial recovery of healthy cell population at both low and high HIV turnover rates. When hunter-HIV fusion is included, cell recovery was particularly enhanced at lower HIV turnover rates. This study shows that the fusion ability, in addition to hunter infection ability, could be a favorable attribute for improving the efficacy of hunter-viral therapy. These results provide support for the potential use of engineered viruses to control HIV and other viral infections.

Quantification system for the viral dynamics of a highly pathogenic simian/human immunodeficiency virus based on an in vitro experiment and a mathematical model

Background

Developing a quantitative understanding of viral kinetics is useful for determining the pathogenesis and transmissibility of the virus, predicting the course of disease, and evaluating the effects of antiviral therapy. The availability of data in clinical, animal, and cell culture studies, however, has been quite limited. Many studies of virus infection kinetics have been based solely on measures of total or infectious virus count. Here, we introduce a new mathematical model which tracks both infectious and total viral load, as well as the fraction of infected and uninfected cells within a cell culture, and apply it to analyze time-course data of an SHIV infection in vitro.

Results

We infected HSC-F cells with SHIV-KS661 and measured the concentration of Nef-negative (target) and Nef-positive (infected) HSC-F cells, the total viral load, and the infectious viral load daily for nine days. The experiments were repeated at four different MOIs, and the model was fitted to the full dataset simultaneously. Our analysis allowed us to extract an infected cell half-life of 14.1 h, a half-life of SHIV-KS661 infectiousness of 17.9 h, a virus burst size of 22.1 thousand RNA copies or 0.19 TCID₅₀, and a basic reproductive number of 62.8. Furthermore, we calculated that SHIV-KS661 virus-infected cells produce at least 1 infectious virion for every 350 virions produced.

Conclusions

Our method, combining in vitro experiments and a mathematical model, provides detailed quantitative insights into the kinetics of the SHIV infection which could be used to significantly improve the understanding of SHIV and HIV-1 pathogenesis. The method could also be applied to other viral infections and used to improve the in vitro determination of the effect and efficacy of antiviral compounds.

Global stability for an HIV-1 infection model including an eclipse stage of infected cells

We consider the mathematical model for the viral dynamics of HIV-1 introduced in Rong et al. (2007) [37]. One main feature of this model is that an eclipse stage for the infected cells is included and cells in this stage may revert to the uninfected class. The viral dynamics is described by four nonlinear ordinary differential equations. In Rong et al. (2007) [37], the stability of the infected equilibrium has been analyzed locally. Here, we perform the global stability analysis using two techniques, the Lyapunov direct method and the geometric approach to stability, based on the higher-order generalization of Bendixson's criterion. We obtain sufficient conditions written in terms of the system parameters. Numerical simulations are also provided to give a more complete representation of the system dynamics.

Non-linear mixed effects modeling of antiretroviral drug response after administration of lopinavir, atazanavir and efavirenz containing regimens to treatment-naïve HIV-1 infected patients

The objective of this analysis was to compare three methods of handling HIV-RNA data below the limit of quantification (LOQ) when describing the time-course of antiretroviral drug response using a drug-disease model. Treatment naïve Scandinavian HIV-positive patients (n = 242) were randomized to one of three study arms. Two nucleoside reverse transcriptase inhibitors were administrated in combination with 400/100 mg lopinavir/ritonavir twice daily, 300/100 mg atazanavir/ritonavir once a day or 600 mg efavirenz once a day. The viral response was monitored at screening, baseline and at 1, 2, 3, 4, 12, 24, 48, 96, 120, and 144 weeks after study initiation. Data up to 400 days was fitted using a viral dynamics non-linear mixed effects drug-disease model in NONMEM. HIV-RNA data below LOQ of 50 copies/ml plasma (39%) was omitted, replaced by LOQ/2 or included in the analysis using a likelihood-based method (M3 method). Including data below LOQ using the M3 method substantially improved the model fit. The drug response parameter expressing the fractional inhibition of viral replication was on average (95% CI) estimated to 0.787 (0.721-0.864) for lopinavir and atazanavir treatment arms and 0.868 (0.796-0.923) for the efavirenz containing regimen. At 400 days after treatment initiation 90% (76-100) of the lopinavir and atazanavir treated patients were predicted to have undetectable viral levels and 96% (89-100%) for the efavirenz containing treatment. Including viral data below the LOQ rather than omitting or replacing data provides advantages such as better model predictions and less biased parameter estimates which are of importance when quantifying antiretroviral drug response.

Maximum likelihood estimation of long-term HIV dynamic models and antiviral response

HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short-term dynamic models, recent works considered more complex long-term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation expectation-maximization) algorithm, a powerful maximum likelihood estimation algorithm, to analyze simultaneously the HIV viral load decrease and the CD4 increase in patients using a long-term HIV dynamic system. We applied the proposed methodology to the prospective COPHAR2-ANRS 111 trial. Very satisfactory results were obtained with a model with latent CD4 cells defined with five differential equations. One parameter was fixed, the 10 remaining parameters (eight with between-patient variability) of this model were well estimated. We showed that the efficacy of nelfinavir was reduced compared to indinavir and lopinavir.

The use of the SAEM algorithm in MONOLIX software for estimation of population pharmacokinetic-pharmacodynamic-viral dynamics parameters of maraviroc in asymptomatic HIV subjects

Using simulated viral load data for a given maraviroc monotherapy study design, the feasibility of different algorithms to perform parameter estimation for a pharmacokinetic-pharmacodynamic-viral dynamics (PKPD-VD) model was assessed. The assessed algorithms are the first-order conditional estimation method with interaction (FOCEI) implemented in NONMEM VI and the SAEM algorithm implemented in MONOLIX version 2.4. Simulated data were also used to test if an effect compartment and/or a lag time could be distinguished to describe an observed delay in onset of viral inhibition using SAEM. The preferred model was then used to describe the observed maraviroc monotherapy plasma concentration and viral load data using SAEM. In this last step, three modelling approaches were compared; (i) sequential PKPD-VD with fixed individual Empirical Bayesian Estimates (EBE) for PK, (ii) sequential PKPD-VD with fixed population PK parameters and including concentrations, and (iii) simultaneous PKPD-VD. Using FOCEI, many convergence problems (56%) were experienced with fitting the sequential PKPD-VD model to the simulated data. For the sequential modelling approach, SAEM (with default settings) took less time to generate population and individual estimates including diagnostics than with FOCEI without diagnostics. For the given maraviroc monotherapy sampling design, it was difficult to separate the viral dynamics system delay from a pharmacokinetic distributional delay or delay due to receptor binding and subsequent cellular signalling. The preferred model included a viral load lag time without inter-individual variability. Parameter estimates from the SAEM analysis of observed data were comparable among the three modelling approaches. For the sequential methods, computation time is approximately 25% less when fixing individual EBE of PK parameters with omission of the concentration data compared with fixed population PK parameters and retention of concentration data in the PD-VD estimation step. Computation times were similar for the sequential method with fixed population PK parameters and the simultaneous PKPD-VD modelling approach. The current analysis demonstrated that the SAEM algorithm in MONOLIX is useful for fitting complex mechanistic models requiring multiple differential equations. The SAEM algorithm allowed simultaneous estimation of PKPD and viral dynamics parameters, as well as investigation of different model sub-components during the model building process. This was not possible with the FOCEI method (NONMEM version VI or below). SAEM provides a more feasible alternative to FOCEI when facing lengthy computation times and convergence problems with complex models.

Effectiveness of a 'hunter' virus in controlling human immunodeficiency virus type 1 infection

Engineered therapeutic viruses provide an alternative method for treating infectious diseases, and mathematical models can clarify the system's dynamics underlying this type of therapy. In particular, this study developed models to evaluate the potential to contain human immunodeficiency virus type 1 (HIV-1) infection using a genetically engineered 'hunter' virus that kills HIV-1-infected cells. First, we constructed a novel model for understanding the progression of HIV infection that predicted the loss of the immune system's CD4(+) T cells across time. Subsequently, it determined the effects of introducing hunter viruses in restoring cell population. The model implemented direct and indirect mechanisms by which HIV-1 may cause cell depletion and an immune response. Results suggest that the slow progression of HIV infection may result from a slowly decaying CTL immune response, leading to a limited but constant removal of uninfected CD4 resting cells through apoptosis - and from resting cell proliferation that reduces the rate of cell depletion over time. Importantly, results show that the hunter virus does restrain HIV infection and has the potential to allow major cell recovery to 'functional' levels. Further, the hunter virus persisted at a reduced HIV load and was effective either early or late in the infection. This study indicates that hunter viruses may halt the progression of the HIV infection by restoring and sustaining high CD4(+) T-cell levels.

Basic PK/PD principles of drug effects in circular/proliferative systems for disease modelling

Disease progression modelling can provide information about the time course and outcome of pharmacological intervention on the disease. The basic PK/PD principles of proliferative and circular systems within the context of modelling disease progression and the effect of treatment thereupon are illustrated with the goal to better understand/predict eventual clinical outcome. Circular/proliferative systems can be very complex. To facilitate the understanding of how a dosing regimen can be defined in such systems we have shown the derivation of a system parameter named the Reproduction Minimum Inhibitory Concentration (RMIC) which represents the critical concentration at which the system switches from growth to extinction. The RMIC depends on two parameters (RMIC = (R₀ − 1) × IC₅₀): the basic reproductive ratio (R₀) a fundamental parameter of the circular/proliferative system that represents the number of offspring produced by one replicating species during its lifespan, and the IC₅₀, the potency of the drug to inhibit the proliferation of the system. The RMIC is constant for a given system and a given drug and represents the lowest concentration that needs to be achieved for eradication of the system. When exposure is higher than the RMIC, success can be expected in the long term. Time varying inhibition of replicating species proliferation is a natural consequence of the time varying inhibitor drug concentrations and when combined with the dynamics of the circular/proliferative system makes it difficult to predict the eventual outcome. Time varying inhibition of proliferative/circular systems can be handled by calculating the equivalent effective constant concentration (ECC), the constant plasma concentration that would give rise to the average inhibition at steady state. When ECC is higher than the RMIC, eradication of the system can be expected. In addition, it is shown that scenarios that have the same steady state ECC whatever the dose, dosage schedule or PK parameters have also the same average R₀ in the presence of the inhibitor (i.e. R_0-INH) and therefore lead to the same outcome. This allows predicting equivalent active doses and dosing schedules in circular and proliferative systems when the IC₅₀ and pharmacokinetic characteristics of the drugs are known. The results from the simulations performed demonstrate that, for a given system (defined by its RMIC), treatment success depends mainly on the pharmacokinetic characteristics of the drug and the dosing schedule.

Quantifying the treatment efficacy of reverse transcriptase inhibitors: new analyses of clinical data based on within-host modeling

Background

Current measures of the clinical efficacy of antiretroviral therapy (ART) in the treatment of HIV include the change in HIV RNA in the plasma and the gain in CD4 cells.

Methods

We propose new measures for evaluating the efficacy of treatment that is based upon combinations of non-nucleoside and nucleoside reverse transcriptase inhibitors. Our efficacy measures are: the CD4 gain per virion eliminated, the potential of CD4 count restoration and the viral reproduction number (R₀). These efficacy measures are based upon a theoretical understanding of the impact of treatment on both viral dynamics and the immune reconstitution. Patient data were obtained from longitudinal HIV clinical cohorts.

Results

We found that the CD4 cell gain per virion eliminated ranged from 10^-2 to 600 CD4 cells/virion, the potential of CD4 count restoration ranged from 60 to 1520 CD4 cells/μl, and the basic reproduction number was reduced from an average of 5.1 before therapy to an average of 1.2 after one year of therapy. There was substantial heterogeneity in these efficacy measures among patients with detectable viral replication. We found that many patients who achieved viral suppression did not have high CD4 cell recovery profiles. Our efficacy measures also enabled us to identify a subgroup of patients who were not virally suppressed but had the potential to reach a high CD4 count and/or achieve viral suppression if they had been switched to a more potent regimen.

Conclusion

We show that our new efficacy measures are useful for analyzing the long-term treatment efficacy of combination reverse transcriptase inhibitors and argue that achieving a low R₀ does not imply achieving viral suppression.

A receptor theory-based semimechanistic PD model for the CCR5 noncompetitive antagonist maraviroc

AIM

To develop a novel combined viral dynamics/operational model of (ant-)agonism that describes the pharmacodynamic effects of maraviroc, a noncompetitive CCR5 inhibitor, on viral load.

METHODS

A common theoretical framework based on receptor theory and the operational model of (ant-)agonism has been developed to describe the binding of maraviroc to the CCR5 receptor and the subsequent decrease in viral load. The anchor point of the operational model in the differential equations of the viral dynamic model is the infection rate constant; this is assumed to be dependent on the number of free activated receptors on each target cell.

RESULTS

The new model provides one explanation for the apparent discrepancy between the in vivo binding of maraviroc to the CCR5 receptor (K(D) = 0.089 ng ml(-1)) and the estimated in vivo inhibition (IC(50) = 8 ng ml(-1)) of the infection rate. The estimated K(E) value of the operational model indicates that only 1.2% of free activated receptors are utilized to elicit 50% of the maximum infection rate.

CONCLUSIONS

The developed model suggests that the target cells, when activated, express more receptors (spare receptors) than needed. In the presence of maraviroc these spare receptors first require blocking before any decrease in the infection rate, and consequently in the viral load at equilibrium, can be detected. The model allows the simultaneous simulation of the binding of maraviroc to the CCR5 receptor and the change in viral load after both short- and long-term treatment.

Leveraging prior quantitative knowledge to guide drug development decisions and regulatory science recommendations: impact of FDA pharmacometrics during 2004-2006

The End-of-Phase 2A meetings are proposed to identify opportunities to make innovative medical products available sooner and to increase the quality of drug applications through early meetings between sponsors and the FDA. This article summarizes the overall experience across 11 pilot End-of-Phase 2A meetings since 2004. Four case studies are presented in more detail to demonstrate the various issues and methods encountered at these meetings. Overall, industry and FDA scientists ranked these meetings to be "very helpful" (average score of 4 on a scale of 1 to 5). In almost all the instances the sponsors changed their drug development plans subsequent to these extensive quantitative analyses-based meetings. A draft Guidance is being developed to be issued in 2008, and we hope this initiative will be resourced by then.

Viral dynamics in transplant patients: implications for disease

Viral infections cause substantial morbidity and mortality in transplant patients. Quantifying viral loads is widely appreciated as a direct means to diagnose and monitor the course of viral infections. Recent studies indicate that the kinetics of viral load changes rather than single viral load measurements better correlate with organ involvement. In this Review, we will summarise the current knowledge regarding the kinetics of viruses relevant to transplantation including cytomegalovirus, Epstein-Barr virus, the herpes viruses 6 and 7, hepatitis C virus, GB virus C, adenovirus, and the emerging human polyomavirus type BK. We discuss the implications of viral kinetics for organ pathology as well as for the evaluation of antiviral interventions in transplant patients.

Costs versus benefits: best possible and best practical treatment regimens for HIV

Current HIV therapy, although highly effective, may cause very serious side effects, making adherence to the prescribed regimen difficult. Mathematical modeling may be used to evaluate alternative treatment regimens by weighing the positive results of treatment, such as higher levels of helper T cells, against the negative consequences, such as side effects and the possibility of resistance mutations. Although estimating the weights assigned to these factors is difficult, current clinical practice offers insight by defining situations in which therapy is considered "worthwhile". We therefore use clinical practice, along with the probability that a drug-resistant mutation is present at the start of therapy, to suggest methods of rationally estimating these weights. In our underlying model, we use ordinary differential equations to describe the time course of in-host HIV infection, and include populations of both activated CD4(+) T cells and CD8(+) T cells. We then determine the best possible treatment regimen, assuming that the effectiveness of the drug can be continually adjusted, and the best practical treatment regimen, evaluating all patterns of a block of days "on" therapy followed by a block of days "off" therapy. We find that when the tolerance for drug-resistant mutations is low, high drug concentrations which maintain low infected cell populations are optimal. In contrast, if the tolerance for drug-resistant mutations is fairly high, the optimal treatment involves periods of reduced drug exposure which consequently boost the immune response through increased antigen exposure. We elucidate the dependence of the optimal treatment regimen on the pharmacokinetic parameters of specific antiviral agents.

A pharmacokinetic-pharmacodynamic model to optimize the phase IIa development program of maraviroc

OBJECTIVES

To use a viral dynamics model to compare the effectiveness of in vivo viral inhibition of several doses of maraviroc (MVC;UK-427,857) and to use a modeling approach to support design decisions for a monotherapy study using various dosing regimens of maraviroc given with and without food.

DESIGN

The pharmacokinetic-pharmacodynamic model was developed using clinical data from a first monotherapy study (study A4001007). This was a randomized, double-blind, placebo-controlled, multicenter study of maraviroc in 44 asymptomatic HIV-1-infected patients. Patients received maraviroc under food restrictions at 25 mg once daily or 50, 100, or 300 mg twice daily, or placebo for 10 days.

METHODS

Antiviral responses were assessed by measuring plasma HIV-1 RNA levels during screening, during randomization, at baseline, and daily during the 10 days of treatment and at days 11 to 15, 19, 22, 25, and 40. An integrated pharmacokinetic-pharmacodynamic model was developed using the mixed effects modeling approach with patients' pharmacokinetic profiles on the last day of treatment, HIV-1 RNA levels over time, and the individual viral susceptibility. The parameters derived from the viral dynamic model were used to calculate average viral inhibition fraction, decay rate of actively infected cells, and basic reproductive ratio for each treatment group. Monte Carlo simulation was then used to determine the distribution of viral load change across simulated patients over time for each regimen to be studied in another monotherapy study, A4001015.

RESULTS

The decline rate in the 300 mg twice daily group was comparable to that induced by potent protease inhibitor monotherapy, but was significantly slower than that in patients receiving combination therapy including both protease inhibitor and reverse transcriptase inhibitors. The efficacy of inhibition in vivo was estimated to range from 0.15 to 0.38 for the 25 mg once daily dose group and from 0.88 to 0.96 for the 300 mg twice daily dose group.

CONCLUSIONS

The model has aided the analysis and interpretation of the clinical data. The use of a model-based approach for selecting doses can accelerate drug development by replacing some arms or trials with simulations.

HIV replication elicits little cytopathic effects in vivo: Analysis of surrogate markers for virus production, cytotoxic T cell response and infected cell death

Several potential mechanisms for viral destruction of HIV-infected cells have been described. The hypothesis was examined that if HIV were cytopathic, a positive relation between the in vivo virus production or CTL activity and infected cell death should be observed. In a regression analysis no significant relation was found between surrogate markers for in vivo virus production or the virus-specific CTL response and death rates of productively infected cells. In a subgroup of patients the hypothesis is rejected that HIV replication elicits a large (R(2) > 0.25) cytopathic effect (P < 0.05, N = 36). It is concluded that HIV replication elicits little cytopathic effect in productively infected cells and that CD4(+) T lymphocytes are eroded by other mechanisms.

Modelling and clinical trials in paediatrics

Clinical trials are more difficult to conduct in children, but they are even more necessary than in adults their scarcity is an ethical scandal. Mathematical models can be built that can describe both the disease process and the mechanism of action of drugs. These models can then be used to simulate the outcome of clinical trials. Inspection of the simulated results then facilitates optimisation of the trial design and proposed methods of analysis. Validation is a crucial issue for the good practice of modelling and simulation. The participants of Round Table No. 6 recommend: (i) that modelling be systematically employed; (ii) that all the required professional personnel be involved, at all phases; (iii) that all data needed are made accessible; (iv) that clinicians be trained; (v) that specialists develop training tool kits; and (vi) that universities provide appropriate training.

Stochastic interplay between mutation and recombination during the acquisition of drug resistance mutations in human immunodeficiency virus type 1

The emergence of drug resistance mutations in human immunodeficiency virus (HIV) has been a major setback in the treatment of infected patients. Besides the high mutation rate, recombination has been conjectured to have an important impact on the emergence of drug resistance. Population genetic theory suggests that in populations limited in size recombination may facilitate the acquisition of beneficial mutations. The viral population in an infected patient may indeed represent such a population limited in size, since current estimates of the effective population size range from 500 to 10(5). To address the effects of limited population size, we therefore expand a previously described deterministic population genetic model of HIV replication by incorporating the stochastic processes that occur in finite populations of infected cells. Using parameter estimates from the literature, we simulate the evolution of drug-resistant viral strains. The simulations show that recombination has only a minor effect on the rate of acquisition of drug resistance mutations in populations with effective population sizes as small as 1,000, since in these populations, viral strains typically fix beneficial mutations sequentially. However, for intermediate effective population sizes (10(4) to 10(5)), recombination can accelerate the evolution of drug resistance by up to 25%. Furthermore, a reduction in population size caused by drug therapy can be overcome by a higher viral mutation rate, leading to a faster evolution of drug resistance.

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.

Evaluation of HIV-1 kinetic models using quantitative discrimination analysis

MOTIVATION

Since the identification of human immunodeficiency virus (HIV) over twenty years ago, many mathematical models of HIV dynamics have been proposed. The purpose of this study was to evaluate intracellular and intercellular scale HIV models that best described the dynamics of viral and cell titers of a person, where parameters were determined using typically available patient data. In this case, 'best' was defined as the model most capable of describing experimental patient data and was determined by Bayesian-based model discrimination analysis and the ability to provide realistic results.

RESULTS

Twenty models of HIV-1 viral dynamics were initially evaluated to determine whether parameters could be obtained from readily available clinical data from established HIV-1 patients with stable disease. Based on this analysis, three models were chosen for further examination and comparison. Parameters were estimated using experimental data from a cohort of 338 people monitored for up to 2484 days. The models were evaluated using a Bayesian technique to determine which model was most probable. The model ultimately selected as most probable was overwhelmingly favored relative to the remaining two models, and it accounted for uninfected cells, infected cells and cytotoxic T lymphocyte dynamics. The authors developed a fourth model for comparison purposes by combining the features of the original three models. Parameters were estimated for the new model and the statistical analysis was repeated for all four models. The model that was initially favored was selected again upon model discrimination analysis.

CONTACT

srivasta@engr.uconn.edu.

Quantification of infectious HIV-1 plasma viral load using a boosted in vitro infection protocol

Methods currently used for HIV-1 viral load measurements are very sensitive, but cannot distinguish between infectious and noninfectious particles. Here we describe the development of a novel, sensitive, and highly reproducible method that allows rapid isolation and quantification of infectious particles from patient plasma. By immobilizing HIV-1 particles in human plasma to platelets using polybrene, we observed a 10- to 1000-fold increase in infectivity over infection protocols using free virus particles. Using this method, we evaluated infectivity in plasma from 52 patients at various disease stages. At plasma viral loads of 1000-10000 HIV-1 RNA copies/ml 18%, at 10,000-50,000 copies/ml 73%, at 50,000-100,000 copies/ml 90%, and above 100,000 copies 96% of cultures were positive. We found that infectious titers among patients vary distinctively but are characteristic for a patient over extended time periods. Furthermore, we demonstrate that by evaluating infectious titers in conjunction with total HIV RNA loads, subtle effects of treatment intervention on viremia levels can be detected. The immobilization procedure does not interfere with viral entry and does not restore the infectivity of neutralized virus. Therefore, this assay system can be utilized to investigate the influence of substances that specifically affect virion infectivity such as neutralizing antibodies, soluble CD4, or protease inhibitors. Measuring viral infectivity may thereby function as an additional, useful marker in monitoring disease progression and evaluating efficacy of antivirals in vivo.