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Simple mathematical models do not accurately predict early SIV dynamics.

Noecker C, Schaefer K, Zaccheo K, Yang Y, Day J, Ganusov VV - Viruses (2015)

Bottom Line: First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals.Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production.These results suggest that, in order to appropriately model early HIV/SIV dynamics, additional factors must be considered in the model development.

View Article: PubMed Central - PubMed

Affiliation: National institute for Mathematical and Biological synthesis (NIMBioS), Knoxville, TN 37996, USA. cecilia.noecker@gmail.com.

ABSTRACT
Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1-2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the "standard" mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV). First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral dose. These results suggest that, in order to appropriately model early HIV/SIV dynamics, additional factors must be considered in the model development. These may include variability in monkey susceptibility to infection, within-host competition between different viruses for target cells at the initial site of virus replication in the mucosa, innate immune response, and possibly the inclusion of several different tissue compartments. The sobering news is that while an increase in model complexity is needed to explain the available experimental data, testing and rejection of more complex models may require more quantitative data than is currently available.

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For biologically reasonable parameter values, the mode of virus production by infected cells has little impact on the time to virus detection in deterministic simulations. We solve the mathematical model (Equations (1)–(3)) numerically and plot predicted values for the infectious virus (V), infected cells in the eclipse phase (IE), and virus-producing cells (I). Time courses are shown for the model with continuous-mode virus production (short eclipse phase, left panel), intermediate mode virus production (eclipse phase takes approximately half of the life-span of infected cells, middle panel), and bursting mode of virus production (long eclipse phase, right panel). Parameters used are given in Table 1. All infections are started with V0 = 1. The time of virus detection, tdet, is the time when the virus population reaches Vdet = 104 infectious viruses and is indicated on individual panels.
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viruses-07-01189-f002: For biologically reasonable parameter values, the mode of virus production by infected cells has little impact on the time to virus detection in deterministic simulations. We solve the mathematical model (Equations (1)–(3)) numerically and plot predicted values for the infectious virus (V), infected cells in the eclipse phase (IE), and virus-producing cells (I). Time courses are shown for the model with continuous-mode virus production (short eclipse phase, left panel), intermediate mode virus production (eclipse phase takes approximately half of the life-span of infected cells, middle panel), and bursting mode of virus production (long eclipse phase, right panel). Parameters used are given in Table 1. All infections are started with V0 = 1. The time of virus detection, tdet, is the time when the virus population reaches Vdet = 104 infectious viruses and is indicated on individual panels.

Mentions: To explore the dynamics of our mathematical model (Equations (1)–(3)) we ran a set of deterministic simulations. When starting an infection with one virion, there is an initial decline in the number of virions before it grows exponentially (Figure 2); the rate of exponential decline is approximately given by virus clearance rate c (see Supplement for derivations). Although biologically unrealistic, the deterministic model allows for a fraction of one virus to exist, and thus can rebound from a number less than one. For this set of parameters, the number of infectious viruses present at any time is predicted to be lower than the number of cells in the eclipse phase or the number of virus-producing cells (Figure 2). This arises because our model tracks the dynamics of only infectious viruses and because in our simulations only N = 10 infectious viruses are produced on average by the virus-producing cells. Increasing the burst size results in simulations in which the amount of free virus exceeds the amount of virus-infected cells (Figure S2 in Supplement). Importantly, as expected from the standard model for HIV dynamics [27], the mode of virus production, either bursting or budding, has little impact on the time to virus detection in such deterministic simulations (Figure 2). Interestingly, if infections are started with 1 cell in the eclipse phase or with 1 virus-producing cell, the populations approach the phase of exponential growth more rapidly than when infection starts with a single virion (results not shown).


Simple mathematical models do not accurately predict early SIV dynamics.

Noecker C, Schaefer K, Zaccheo K, Yang Y, Day J, Ganusov VV - Viruses (2015)

For biologically reasonable parameter values, the mode of virus production by infected cells has little impact on the time to virus detection in deterministic simulations. We solve the mathematical model (Equations (1)–(3)) numerically and plot predicted values for the infectious virus (V), infected cells in the eclipse phase (IE), and virus-producing cells (I). Time courses are shown for the model with continuous-mode virus production (short eclipse phase, left panel), intermediate mode virus production (eclipse phase takes approximately half of the life-span of infected cells, middle panel), and bursting mode of virus production (long eclipse phase, right panel). Parameters used are given in Table 1. All infections are started with V0 = 1. The time of virus detection, tdet, is the time when the virus population reaches Vdet = 104 infectious viruses and is indicated on individual panels.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4379566&req=5

viruses-07-01189-f002: For biologically reasonable parameter values, the mode of virus production by infected cells has little impact on the time to virus detection in deterministic simulations. We solve the mathematical model (Equations (1)–(3)) numerically and plot predicted values for the infectious virus (V), infected cells in the eclipse phase (IE), and virus-producing cells (I). Time courses are shown for the model with continuous-mode virus production (short eclipse phase, left panel), intermediate mode virus production (eclipse phase takes approximately half of the life-span of infected cells, middle panel), and bursting mode of virus production (long eclipse phase, right panel). Parameters used are given in Table 1. All infections are started with V0 = 1. The time of virus detection, tdet, is the time when the virus population reaches Vdet = 104 infectious viruses and is indicated on individual panels.
Mentions: To explore the dynamics of our mathematical model (Equations (1)–(3)) we ran a set of deterministic simulations. When starting an infection with one virion, there is an initial decline in the number of virions before it grows exponentially (Figure 2); the rate of exponential decline is approximately given by virus clearance rate c (see Supplement for derivations). Although biologically unrealistic, the deterministic model allows for a fraction of one virus to exist, and thus can rebound from a number less than one. For this set of parameters, the number of infectious viruses present at any time is predicted to be lower than the number of cells in the eclipse phase or the number of virus-producing cells (Figure 2). This arises because our model tracks the dynamics of only infectious viruses and because in our simulations only N = 10 infectious viruses are produced on average by the virus-producing cells. Increasing the burst size results in simulations in which the amount of free virus exceeds the amount of virus-infected cells (Figure S2 in Supplement). Importantly, as expected from the standard model for HIV dynamics [27], the mode of virus production, either bursting or budding, has little impact on the time to virus detection in such deterministic simulations (Figure 2). Interestingly, if infections are started with 1 cell in the eclipse phase or with 1 virus-producing cell, the populations approach the phase of exponential growth more rapidly than when infection starts with a single virion (results not shown).

Bottom Line: First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals.Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production.These results suggest that, in order to appropriately model early HIV/SIV dynamics, additional factors must be considered in the model development.

View Article: PubMed Central - PubMed

Affiliation: National institute for Mathematical and Biological synthesis (NIMBioS), Knoxville, TN 37996, USA. cecilia.noecker@gmail.com.

ABSTRACT
Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1-2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the "standard" mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV). First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral dose. These results suggest that, in order to appropriately model early HIV/SIV dynamics, additional factors must be considered in the model development. These may include variability in monkey susceptibility to infection, within-host competition between different viruses for target cells at the initial site of virus replication in the mucosa, innate immune response, and possibly the inclusion of several different tissue compartments. The sobering news is that while an increase in model complexity is needed to explain the available experimental data, testing and rejection of more complex models may require more quantitative data than is currently available.

Show MeSH
Related in: MedlinePlus