
MBW:HIV DynamicsFrom MathBioThis wiki page summarizes the paper "HIV1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell LifeSpan, and Viral Generation Time’’ by Perelson et al. (1996). A pdf of the paper is available here: http://www.tiem.utk.edu/~mikeg/courses/EID.S07/readings/Perelson.et.al.96.pdf ContentsOverview
Executive SummaryIn the paper "HIV1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell LifeSpan, and Viral Generation Time," Perelson et al. developed a mathematical model to further investigate the dynamics between HIV and an inhibitor drug known as ritonavir, which acts as an HIV1 protease inhibitor. The authors used this model to predict the lifespan of both infected cells and virions, the average total HIV1 virions produced per day, the minimum duration of HIV1 lifecycle in days, and the average generation time of a HIV1 virion. This model and its conclusions about the dynamics between HIV1 and an inhibitor drug increased the understanding of HIV and its interactions with potentially lifesaving drugs. Hopefully this information can be used in the future to refine treatment strategies that maximize survival of those infected by this virus. Background and History of HIV1 and Modeling its DynamicsToday, there are two known strains of HIV, known as HIV1 and HIV2. Scientists have classified HIV1 to be the more dangerous of the two strains of virus, as it is usually proves to be deadlier and more contagious than HIV2. The Spread and Detection of HIVHIV spreads throughout a person’s body with the help of the individual’s own cells. Once a cell has been infected by the virus, the cell is used by the virus to produce more HIV, and the virus continues to spread. To measure a person’s level of infection with HIV1, one draws blood and measures the concentration of CD4 lymphocyes. As the virus progresses, a person has less of these lymphocytes and more HIV in the blood. Two recent tests for HIV are known as HIV Elisa and HIV Western blood tests. These tests identify the HIV by detecting the specific antibodies the human body produces when HIV exists in their system. After what can be years of infection with this virus, both untreated and treated people may develop AIDs (acquired immunodeficiency syndrome), which eventually leads to the carrier’s death. A person with HIV1 develops AIDs after the CD4lymphocyte count in their blood drops below a critical point. At this point, the body can no longer fight off infections, even those as common and harmless as a cold. After the CD4 lymphocyte count drops below a certain level, HIV has suppressed a person’s immune system and death is usually eminent. Treating HIVCurrent medications for HIV are aimed at preventing any complications that may go hand in hand with the disease, as well as delaying the onset of AIDs. Medicines for HIV do one of two things to the virus: interfere with virus’s reverse transcriptase, or interfere with the virus’s protease. The main function of reverse transcriptase of HIV is to change the genetic material of the virus so it can enter cells and the nuclei undetected. If the HIV is able to enter the cell’s nucleus and be detected, it is then able to replicate itself using the cell. The main function of the enzyme protease in HIV is to cut long chains of proteins into more manageable lengths that will then produce new active copies of the virus. Protease inhibitor medicines help to stop the protease from cutting the proteins, so the new copies of the virus do not contain any protein chains, and are therefore noninfectious. For a visual representation of how protease inhibitors work, please see Figure 1. Unfortunately, there is no cure for HIV, and people with the virus will eventually develop AIDs. With no miracle drug on the horizon that cures HIV, the more people know about how the dynamics of the virus work with the human body’s natural responses and current medicines, the better doctors can treat the disease and lengthen the amount of time until a person develops AIDs. Research and Models of HIV DynamicsSince HIV became prevalent around the world in the 1980s, the amount of research on the subject has increased dramatically. Many mathematical models have been developed to study the dynamics between the virus and the drugs people use to combat the disease. The authors have done a previous study on the subject in addition to the study discussed here. Mathematical models of the disease are constantly being updated as more information becomes available and as more precise measuring techniques are developed. Experimental MethodsFive individuals at varying stages of HIV1 were used in this study. Twice a day, 600mg of ritonavir, a known HIV drug, was administered to each of the five individuals. Following the drug regimen, the concentrations of HIV1 RNA in each person’s blood was measured at set times. The concentrations were measured every 2 hours until the sixth hour, and every 6 hours until the second day, then every 24 hours until day 7. In drug treatments, there is usually a lag time between the first dose and when the first druginduced change is seen. This lag was present in this study, and can be attributed to the lag in protease inhibitors. Protease inhibitors do not prevent the production of new virions and do not prevent the infection of new cells by infectious virions that were produced prior to the drug treatment. Protease inhibitors simply cause newly produced virions to be noninfectious. This accounts for the lag time between the administration of the drug and any noticeable effects of the drug. After the lag time, the decay of HIV1 RNA in the blood of each individual followed the mathematical model presented in the next sections. Mathematical ModelsFor this mathematical model, Perelson et al. defined many variables and parameters to be used in differential equations (for a discussion on how some of these parameters are estimated see [MBW:Estimation Of HIV/AIDS Parameters]). For a discussion of additional developments in these parameters see Perelson 2002. These variables and parameters include: = target cells = rate constant at which HIV1 infects target cells = productively infected cells created by the rate constant k = concentration of viral particles in plasma = rate of loss of virusproducing cells = number of new virons produced by each infected cell across its lifetime = rate constant for virion clearance = plasma concentration of virions before the drug treatment (still infectious) = concentration of virions after the drug treatment (noninfectious) = 0 is the time of onset of the drug effect
Full Model and ResultsTo further the above model, it was assumed that the system was at quasi steady state before drug treatment. Also, it was assumed that T, the uninfected cell concentration, remained approximately at , its steadystate value, for one week after a dose of ritonavir was given. It was then concluded, from the above equations, the total concentration of plasma virions, , varies according to:
Nonlinear regression analysis was used to estimate both c and δ for each patient. This was accomplished by fitting the above equation to the plasma HIV1 RNA measurements (Table 1). With the use of the bestfit values of c and δ, the theoretical curves obtained from the above equation provided an exceptional fit to the data for all patients. It was found that the clearance of free virions is the faster process. Values of c ranged from 2.06 to 3.81 per day, while the corresponding values for free virions ranged from 0.18 to 0.34 days. An independent experiment was used to confirm the virion clearance rate. It was found that the loss of infectious virions exhibited a firstorder decay rate. The rate constant was determined to be 3.0 per day. This is within the 68% confidence interval of the estimated value of c.
For a model discussing the dynamics of drug resistant HIV, see MBW:Dynamics of DrugResistant HIV Mutant. Analysis and InterpretationAs a result of the model described above, many characteristics of the replication cycle of HIV1 in vivo can be determined. The parameters c and δ correspond to the decay rate constants of plasma virions and productively infected cells, respectively. Therefore, 1/c and 1/δ correspond to the average lifespans of plasma virions and productively infected cells, respectively. The average lifespan of a virion is approximately 0.3 days. The average lifespan of a productively infected cell is approximately 2.2 days (Table 2). In addition, the average viral generation time is defined to be the time from the release of a virion until the virion infects another cell and initiates the release of a new wave of viral particles. Therefore, is equal to the sum of the average lifespans of a free virion and a productively infected cell. The average value of for the patients in the experiment is approximately 2.6 days (Table 2). Minimal estimates for the average duration of the life cycle of HIV1 and its intracellular phase (from binding to the release of the first progeny) were determined using a heuristic procedure. The parameter S was defined as the life cycle of HIV1. The lag in the decay of HIV1 RNA in plasma after the pharmacological delay is subtracted was used to estimate S. The values of S estimated for each of the patients were quite consistent. The mean of S was approximately 1.2 days. In addition, the average time for infection is given by 1/c. If this average is assumed to be larger than the minimal time for infection, then a minimal estimate of the average length of the intracellular phase of the HIV1 life cycle is determined by S – (1/c) and found to be 0.9 days. In previous studies, a crude estimate of the of viral decay was given without the lifespan of productively infected cells being separated from the lifespan of plasma virions. However, with the results described above, it was calculated that productively infected cells are lost with an average of approximately 1.6 days. Between the five patients, the lifespans of productively infected cells were not significantly different. This is interesting as a person with a low CD4 lymphocyte count typically has a decreased number of virusspecific, major histocompatibility complex class Irestricted cytotoxic T lymphocytes. In addition, the mean lifeexpectancy of a virion in the blood was found to be 0.3 days. As a result, a population of plasma virions is cleared with a of 0.24 days. In other words, on average, every six hours a population of plasma virions is turned over. The estimates for the virion clearance rate and infected cell loss rate are minimal estimates, as a result of the assumption that the antiviral effect of ritonavir was complete and that the target cells did not recover during treatment. Hence, the true value of for a virion may be less than six hours. As a consequence, the total number of virions that are produced and released into the extracellular fluid is at least 10.3 x 10^9 virions per day. This is approximately 15 times the previous minimum estimate. Furthermore, at least 99% of the substantial group of virus is produced by recently infected cells (Fig. 2). Due to the fact that c has similar values for each patient involved in the study, the degree of plasma viremia is a representation of the total virion production, which is proportional to the number of productively infected cells T* and their viral burst size N. As the average generation time of HIV1 is about 2.6 days, the authors suggest that approximately 140 viral replication cycles occur each year. This is about half the number of viral replication cycles estimated by Coffin. With this conclusion, it becomes clear that the repetitive replication of HIV1, shown on the left side of Fig. 2, is responsible for at least 99% of the plasma viruses in infected individuals and causes the high destruction rate of CD4 lymphocytes. For additional information on how HIV interacts with CD4 lymphocytes, see MBW:Modelling Viral Dynamics and Immune System Dynamics. ConclusionThis new insight into the highly dynamic nature of the cyclic process of HIV1 replication provides many theoretical ideas to direct the advancement of treatment. The authors strongly suggest that if an antiviral agent is to be effective, it should detectably lower the viral load in plasma after a few days of treatment. Next, one must take into account the large turnover rate of HIV1 described above. In fact, the failure of the antiviral agents used around 1996 in monotherapy is the result of the HIV1 replication dynamics. The authors argue that an effective treatment must force the virus to mutate simultaneously at multiple positions in one viral genome by means of a combination of multiple, potent antiretroviral agents. Early and aggressive therapeutic attention is necessary to make a clinical impact, especially as the production of mutant viruses is repeated for approximately 140 generations each year. Lastly, although it is apparent that the “raging fire” of HIV1 replication could be extinguished using potent antiretroviral treatments in two to three weeks, the dynamics of other viral compartments must be studied. Even though these viral compartments cause 1% or less of the plasma virus, they have the ability to restart a high rate of viral replication after the therapeutic treatment has concluded. In the future, the decay rate of longlived, virusproducing groups of cells must be determined. The activation rate of latent cell compartments carrying infectious proviruses is also essential to determine. The authors hope that this information will allow a new type of treatment to block de novo HIV1 replication for a long enough period of time for each latent cell compartment to extinguish. References and External LinksCoffin, J.M. 1995. "HIV population dynamics in vivo: Implications for genetic variation, pathogenesis, and therapy." Science 267, 483488. "Combination Therapy for HIV Infection:  The Body." The Body: The Complete HIV/AIDS Resource. Web. 18 Mar. 2010. <http://www.thebody.com/content/art12199.html>. "HIV." Wikipedia, the Free Encyclopedia. Web. 18 Mar. 2010. <http://en.wikipedia.org/wiki/HIV>. "HIV Infection." Google Health. Web. 18 Mar. 2010. <https://health.google.com/health/ref/HIV+infection>. Perelson, A.S., Neumann, A.U., Markowitz, M., Leonard, J.M., Ho, D.D., 1996. "HIV1 dynamics in vivo: Virion clearance rate, infected cell lifespan, and viral generation time." Science 271, 1582–1586. 