Effect of the CTL proliferation program on virus dynamics
Dominik Wodarz1 and
Allan Randrup Thomsen2
1 Department of Ecology and Evolutionary Biology, 321 Steinhaus Hall, University of California, Irvine, CA 92697, USA
2 Institute of Medical Microbiology and Immunology, Panum Institute, University of Copenhagen, Building 22.5.16, 3C Blegdamsvej, DK-2200 Copenhagen, Denmark
Correspondence to: D. Wodarz; E-mail: dwodarz{at}uci.edu
 |
Abstract
|
---|
Experiments have established that CTLs do not require continuous antigenic stimulation for expansion. Instead, responses develop by a process of programmed proliferation which involves
710 antigen-independent cell divisions, the generation of effector cells and the differentiation into memory cells. The effect of this program on the infection dynamics and the advantages gained by the program have, however, not been explored yet. We investigate this with mathematical models. We find that more programmed divisions can make virus clearance more efficient because CTL division continues to occur independent from antigenic stimulation when virus load drops to low levels. This results in stronger effector activity at low virus loads, and in a higher chance of virus extinction. On the other hand, the more programmed divisions occur, the less efficient the response is at preventing high acute virus loads and thus acute symptoms. The reason is that the programmed divisions are independent from antigenic stimulation, and an increase in virus load does not speed up the rate of CTL expansion. We hypothesize that the 710 programmed divisions observed in vivo represent an optimal solution to this trade-off which maximizes the chances to clear, while preventing excessive acute pathology. If the CTLs fail to clear the virus, however, we find that the properties of the programmed proliferation model are very similar to those derived from models which assume continuous antigenic stimulation. We discuss these results in the context of data from murine virus infections and explore implications for virus dynamics in CD4 helper-deficient hosts.
Keywords: mathematical model, programmed CTL proliferation dynamics, CTL homeostasis, effector molecules, CD4 T cell help
 |
Introduction
|
---|
In recent years, immunological research has given rise to important new insights into the mechanisms by which CTLs respond to infectious agents. It has traditionally been assumed that CTL division and expansion requires constant antigenic stimulation. A series of papers demonstrated, however, that this is not the case (15). Instead, a single encounter with antigen triggers a program of CTL expansion and differentiation which is independent from further antigenic stimulation events. This is referred to as programmed proliferation. It is thought that the CTLs undergo
710 cell divisions which result in the generation of effector cells, and subsequently in the differentiation into memory cells. If this does not result in the clearance of the pathogen, the memory CTLs are reactivated and further expansion occurs. Experimental data (68) have shown that CD4 T cell help is specifically required for the re-stimulation and expansion of the memory CTLs. CD4 cell help is not required for CTL expansion during the primary response.
While these insights have provided a new and better understanding about the way in which CTLs respond to antigenic stimulation, little is known about how programmed proliferation influences the dynamics of viral infections. This is the subject of the paper. We aim to investigate how programmed proliferation influences the kinetics of virus growth and CTL-mediated clearance. Does programmed proliferation enable the host to deal more effectively with pathogens? Why has programmed proliferation evolved? We compare the properties of the programmed proliferation model with those derived from models which assume continuous antigenic stimulation, and discuss the interpretation of experimental data from murine virus infections. Finally, the analysis enables us to gain a better understanding of infection dynamics in helper-deficient hosts which is discussed both from a theoretical and an experimental perspective.
 |
Methods
|
---|
Analysis of the mathematical model
The results presented in this paper are based on a mathematical model of programmed CTL proliferation. So far, only one mathematical paper has been published in the context of programmed CTL proliferation (9), and this study has a very different focus and the model is different. The present mathematical model which describes programmed CTL proliferation contains the following variables: resting and memory CTLs, m; newly activated CTLs, m0; activated CTLs which have undergone i (i = 1,...,n) cell divisions, mi, and effector CTLs, z. It is given by the following set of differential equations.
This is coupled with a basic model of infection dynamics which is given as follows.
where x denotes the population of susceptible host cells, y the population of infected cells and v the population of free virus. Uninfected cells are assumed to be produced at a constant rate
, and die at a rate dx. Without an infection, the abundance of uninfected cells converges to an equilibrium value given by
/d, and this can correspond to tissue. Free virus particles infect susceptible cells at a rate proportional to the product of their abundances, ßxv. The rate constant ß describes the efficacy of this process, including the rate at which virus particles find uninfected cells, the rate of virus entry and the rate of successful infection. Infected cells produce free virus at a rate proportional to their abundance, ky, and die at a rate ay. In addition, infected cells are killed by the CTL response with a rate pyz. The model can be easily modified to include non-lyitc CTL activity, but this would not make a difference in the context of the questions investigated here. Finally, free virus particles decay at a rate uv.
Infection induces CTL expansion.
If the first round of proliferation does not result in virus clearance (reduction of virus load below a defined threshold), the dynamics eventually converge to the following equilibrium outcome.
 |
 |
 |
 |
 |
 |
Mathematical comparison between programmed proliferation and continuous stimulation
We compare the programmed proliferation model studied here with models which assume continuous antigenic stimulation. Assume that upon antigenic stimulation, the program is executed at a very fast rate (high values of r) and that the turnover of activated and effector CTLs is significantly faster than the turnover of memory cells. In this case, the programmed proliferation model can be reduced to a single equation for the memory CTLs. It is given by
This is basically the same equation as the continuous stimulation model (10), where the CTL responsiveness is given by
Therefore, the single CTL population in the continuous stimulation model should be considered as the population of memory CTLs. The effector CTL population can be assumed to be in quasi steady state and is given by z = 2n
ym/(
+
). Consequently, the rate of killing is described by p'y2m, where p' = 2n
/(
+
). The killing term is proportional to the square of virus load (y) because the generation of effector cells from memory cells is proportional to virus load. In the simple continuous stimulation models which have been studied before (10), the killing term is only linearly proportional to virus load because the model does not distinguish between memory and effector CTLs. More complicated continuous stimulation models which distinguish between memory and effector CTLs have the killing term essentially proportional to the square of virus load (11).
 |
Results and discussion
|
---|
Modeling programmed CTL proliferation
A mathematical description of the programmed CTL proliferation concept is given in Methods. In the following, we will summarize the basic assumptions which underlie the model. We start with a population of resting CTLs, denoted by m. Upon antigenic encounter, these cells become activated at a rate
ym. These activated cells are denoted by m0. Following activation, the CTLs undergo n rounds of proliferation, and this is independent of antigenic stimulation. Proliferation occurs with a rate 2rmi, where mi denotes CTLs which have undergone i divisions (i = 1,...,n 1). The nth division gives rise to effector cells, denoted by z. They can kill infected cells (or alternatively have non-lytic activity). Effectors die at a rate
z and differentiate into memory cells at a rate
z. Memory cells are again denoted by m since they are resting. If the virus is not cleared after this first round of programmed proliferation, the memory cells are reactivated according to the same principles as described above and undergo another round of programmed proliferation. The only difference is that memory cells are characterized by an elevated activation and proliferation rate compared with naive cells (higher values of
and r, respectively). Note that the exact mechanisms by which CTLs react in response to re-stimulation are still unclear. This topic is further discussed in Implications for the Role of CD4 Cell Help. The model is easily adapted to assume that effectors are generated after nE cell divisions (nE < n) and that effectors subsequently undergo further divisions until they have divided n times (12). We will consider two scenarios in our analysis. (i) We start with the acute phase of infection; we define this as the dynamics which occur during the first round of programmed CTL proliferation only. (ii) Subsequently, we examine the scenario where virus is not cleared after one round of programmed CTL proliferation and where memory CTLs are reactivated. We refer to this as chronic infection dynamics.
Acute infection dynamics
We ask how host and viral parameters influence the ability of an acute CTL response to clear an infection (Fig. 1). Regarding CTL parameters, we find an optimal rate of CTL activation (
) and proliferation (r) which maximizes the chance of pathogen clearance. Variation in both parameters produces similar trends (Fig. 1). As the rate of CTL activation/proliferation is increased from low to high, the degree of CTL-mediated reduction of virus load becomes stronger (i.e. clearance becomes more likely). The reason obviously is that the immune response becomes more effective. As the rate of CTL activation/proliferation is increased further, however, the degree of virus load reduction by CTLs becomes weaker (i.e. clearance becomes less likely). This is because effector activity is generated fast and the virus can only grow to limited levels. Limited antigenic load reduces the chances to trigger further naive CTLs to expand. This results in the generation of overall fewer effector cells and thus in a reduced chance of clearance. Hence, there is a trade-off between the extent of initial virus growth and the ability of the CTLs to clear the infection. If virus growth is stopped too early and virus load does not reach higher levels, acute pathology is reduced, but fewer CTL effectors are generated. This results in a reduced ability to clear. If virus grows to higher levels, stronger pathology is observed, but the infection is more likely to be cleared. In contrast to this counter-intuitive outcome, the relationship between the rate of anti-viral activity, p, and the chance of clearance is straightforward (Fig. 1): the higher the rate of anti-viral activity, the higher the chances to achieve virus clearance.

View larger version (16K):
[in this window]
[in a new window]
|
Fig. 1. Relationship between host and viral parameters and virus dynamics during acute infection. Among the host parameters, we consider the rate of CTL activation and proliferation ( and r), as well as the rate of CTL-mediated anti-viral activity (p). Among the viral parameters, we consider the replication rate (ß). Two measures are plotted. The minimum virus load is an indicator of the chance that the infection is cleared. The lower the minimum load during acute infection, the higher the chances of clearance. The peak virus load indicates the severity of acute symptoms. (i and ii) As the rate of CTL activation/proliferation is increased from low to high, we first observe a reduction in both minimum and peak virus load. As the rate of CTL activation/proliferation is increased further, we find that minimum virus load becomes higher while peak virus load becomes lower. Thus, while acute symptoms are reduced in this parameter region, the chance to clear is also reduced as a result of lower levels of antigen and stimulation. (iii) The higher the rate of CTL-mediated activity, the lower the minimum and peak virus loads. (iv) A faster viral replication rate leads to higher peak virus loads. The relationship with the minimum virus load is more complicated. At very low rates of viral replication (parameter region where the infection can just about be maintained in the host), increased replication correlates with higher minimum virus load. At slightly faster rates of viral spread, however, faster replication correlates with reduced minimum virus load and higher chances of clearance. This is because faster virus spread leads to higher peak virus loads, and more antigenic stimulation. If the rate of virus spread is still higher, we again observe the opposite: faster virus replication correlates with increased minimum virus loads and reduced chances of clearance. This is because peak virus loads have reached their maximum in this parameter region and increased virus spread only counters the CTLs and does not increase the level of antigenic stimulation. Baseline parameters were chosen as follows. = 10; d = 0.1; ß = 0.05; a = 0.1; r = 5; = 1; = 0.01; = 0.5; p = 0.2 and = 0.001.
|
|
Among viral parameters, the replication kinetics of the virus, ß, significantly determines the chances of virus clearance during the acute phase. We observe an interesting relationship if the viral replication kinetics is changed from low to high (Fig. 1). (i) At first, an increase in viral replication reduces the chances of viral clearance because the virus spreads faster. This corresponds to the parameter region where the basic reproductive ratio of the virus is close to one and the infection can just about be maintained. (ii) A further increase in the viral replication kinetics, however, changes this relationship. Now, faster virus replication leads to higher chances of clearance. This is because faster spread quickly gives rise to higher levels of antigen. While this increases acute pathology, it also induces more naive CTLs to undergo expansion which results in more effectors and more efficient clearance. On the other hand, slower virus spread results in lower levels of antigen. While this reduces acute pathology, it triggers fewer naive CTLs into expansion, fewer effectors are generated and this renders clearance less efficient. The virus can be thought of as sneaking past the CTL response by replicating relatively slowly and thereby providing a weak stimulus. This might be observed with relatively slowly replicating viruses, and has been suggested previously as a reason for the persistence of hepatitis C virus infection (13). Thus, there is again a similar trade-off between the efficacy of clearance and the ability of the response to reduce acute symptoms. (iii) Finally, if the viral replication kinetics is increased further, faster virus spread again decreases the chances of virus clearance. This is because in this parameter region, virus spread is sufficiently fast that at the time of CTL triggering, virus load has already attained the highest possible values. Therefore, a further increase in the viral replication kinetics does not change the level of antigenic stimulation, but merely counters the effect of CTL-mediated anti-viral activity. This is likely to be observed with relatively fast-replicating viruses.
Chronic infection dynamics
Now, we assume that the virus has not been cleared during acute infection and that re-activation of the memory CTLs is required to achieve resolution of the infection. Now, recurring rounds of CTL proliferation will be induced, and the system will eventually converge toward a steady state. (The exact way in which CTL re-stimulation works is still under debate and discussed further in Implications for the Role of CD4 Cell Help.) Virus load at this steady state determines the degree of virus control. If virus load lies below a threshold, this corresponds to clearance in practical terms (reduction to less than one infected cell). Higher virus load indicates persistent infection and reduced levels of virus control. The equilibrium expressions are given in Methods, and their properties are summarized as follows. Virus load is determined by a number of immunological factors. A high activation rate of memory CTLs (high value of
) and a long life span of memory CTLs in the absence of antigen (low value of
) contribute to low virus loads. Also, the higher the number of CTL proliferations (higher value of n), the lower the virus load. The number of CTLs at the steady state is mainly determined by the rate of anti-viral activity, p. The lower the rate of CTL-mediated anti-viral activity, the higher the number of CTLs.
Interestingly, these properties are almost identical to the properties derived from mathematical models which assume that CTL proliferation requires continuous antigenic stimulation (referred to here as continuous stimulation model) (10). In fact, the continuous stimulation model is a special case of the programmed proliferation model in which the program is executed with a very fast rate. This is shown mathematically in Methods.
Why programmed proliferation?
Given the similarities in the steady-state properties of the programmed proliferation and the continuous stimulation models, we ask the question why programmed proliferation exists. The answer is that the equilibrium outcome of the model does not tell the whole story (Fig. 2). We distinguish between two scenarios. First, we assume a strong CTL memory response which gives rise to a very low virus load at equilibrium (clearance). Then, we assume a weaker CTL memory response which correlates with the persistence of higher virus load at equilibrium.
Assume that the CTL response is strong (Fig. 2i). Consider the continuous stimulation model first. Initially, the CTL response can be very efficient at stopping viral growth and reducing virus load. This is because the rate of CTL expansion increases as the level of virus load, and thus antigenic stimulation, grows. As virus load declines, however, the effectiveness of the response becomes greatly diminished. This is because generation of effectors requires constant antigenic stimulation, and the amount of antigen is low. Consequently, the dynamics enter a phase where virus load settles at a level which is significantly higher than the predicted equilibrium and where virus load declines at a very slow rate (Fig. 2i). This behavior has been observed before and has been referred to as a quasi-equilibrium since the real equilibrium is not reached in a realistic period of time (11). Now, consider the programmed proliferation model. In this case, CTL divisions are independent from antigenic stimulation. This provides an initial disadvantage: as virus load grows, the increased level of antigenic stimulation does not result in faster CTL expansion and the virus can more easily grow to high levels and cause acute pathology. As virus load is reduced to low levels by the CTLs, however, the CTLs can keep dividing despite the small amounts of antigenic stimulation. Thus, in contrast to the continuous stimulation model, production of effectors does not slow down abruptly as virus load drops. Consequently, CTL-mediated pressure is maintained at low virus loads and this results in efficient reduction of the virus population to very low levels or extinction. Thus, clearance can occur before the system converges to an equilibrium (Fig. 2i). As a consequence, however, we again observe a trade-off between the ability of the CTLs to clear an infection and to reduce acute phase symptoms. Thus, to optimize the fitness of the host, there should be enough programmed divisions to ensure clearance, but no more such that acute pathology is limited. We hypothesize that the 710 antigen-independent CTL divisions observed in experimental data represent this optimum. In principle, the optimal number of cell divisions for host fitness could be determined in the model. Lack of the appropriate parameter values and uncertainties regarding the exact assumptions about host fitness would, however, prevent us from attaining any further useful insights at this stage.
Now assume a weaker CTL memory response (Fig. 2ii). In this case, equilibrium virus load is higher which can correspond to persistent infection. The same equilibrium is reached, both in the continuous stimulation and the programmed proliferation model. The outcome of the dynamics does not depend significantly on these model differences. Thus, if the CTLs fail to resolve the infection, the continuous stimulation and the programmed proliferation models give rise to similar predictions.
Robustness of previous results: role of effector molecules
Most of the theoretical literature so far has used mathematical models which assume that continuous antigenic stimulation is required for CTL expansion (14). How robust are these results in the context of programmed proliferation? The above discussion has shown that there are both differences and similarities in model predictions. It is clear that details of acute infection dynamics are not accurately represented by continuous stimulation models. This phase is characterized by the activation of naive cells and the subsequent antigen-independent expansion of the activated CTLs; this is only captured in the program model. If antigen is not cleared after one round of programmed proliferation, and if memory CTLs become reactivated, however, the predictions of the continuous stimulation and the program model become similar. This is especially true in the context of prolonged virus persistence. We will elaborate on this in the context of an interesting debate: the role of effector molecules, such as IFN-
and perforin, in determining CTL homeostasis.
In mice deficient of perforin or IFN-
, elevated levels of CTLs are observed. Based on continuous stimulation models, it has been argued that reduced CTL-mediated effector activity results in elevated levels of antigenic stimulation and thus in higher numbers of CTLs (15, 16). On the other hand, it has been argued that this explanation cannot work in the context of programmed proliferation since the program is antigen independent. Hence, it was proposed that the effector molecules somehow directly modulate the CTL response (1719); this would be an additional function of effector molecules which is independent from their role as effectors. While we cannot evaluate this notion with theory, the model presented here shows that programmed proliferation is not at odds with the hypothesis that a difference in effector activity alone can explain the observation. This requires that memory cells become re-stimulated once or more before the infection is cleared. In this context, it is interesting to consider recent results by Christensen et al. (20). They studied CTL dynamics in vesicular stomatitis virus (VSV)-infected mice deficient in perforin and/or IFN-
. In the context of VSV, these molecules do not contribute substantially to effector activity and clearance. The experiments showed that perforin and IFN-
did not significantly regulate the level of virus-specific CTLs. This result supports the notion that effector activity itself may be what drives the regulation of CTL numbers by perforin and IFN-
.
Implications for the role of CD4 cell help
The model has interesting implications for understanding the role of CD4 T cell help. This has been heavily debated in the literature. With some infections, help seems crucial for viral clearance, while with other infections viral clearance can be achieved in the absence of help (2129). Recent experiments suggest that the acute response and memory cells can be generated regardless of help but that the ability of memory CTLs to become activated in response to re-stimulation and to be maintained crucially depends on the availability of help (68). The mechanism which underlies this observation is unclear (7, 8, 30). Some studies suggested that the helper cells somehow program the CTLs during acute infection and that the subsequent availability of help has no influence (7, 8). On the other hand, a recent study indicates that the presence of help may be continuously required to maintain memory in the long term (30).
We would like to point out that the above scenario might only hold in the context of infections which persist. In this case, the memory cells which develop after acute infection need the presence of help in order to become reactivated by the persisting virus. The dependency of CTL memory activation on help can be different in the context of exogenous re-infection. That is, if a host is primed with a virus which is cleared, and subsequently re-infected with the same virus. In this case, the re-activation of memory CTLs could occur in the absence of help, as observed in recent experimental data (31). The reason for this difference could be as follows. If an infection is initiated in a host, whether for the first time or upon re-infection, certain innate responses develop which signal the presence of danger. This allows CTL activation and proliferation to occur at normal levels in the absence of help. On the other hand, in the context of a persisting virus, these innate signals which are present during the initial stages of the infection vanish as the virus remains present. In this case, the re-activation of memory CTLs strictly depends on help.
Here, we concentrate on the dynamics of a virus which has the potential to persist, resulting in the helper-dependent re-activation of the memory CTLs. In terms of our model, we can assume that the absence of help corresponds to the successful execution of only one round of programmed proliferation, without the re-activation of memory cells. On the other hand, the presence of help corresponds to the ability of memory CTLs to become repeatedly reactivated. We have explored the conditions under which a single round of proliferation can or cannot result in virus clearance; these should be the conditions under which helper-deficient hosts can or cannot clear infections.
The model suggests that the main viral parameter which could determine whether help is needed for the resolution of infection is the viral replication rate. As discussed above, the relationship between the viral replication kinetics and the ability of a single round of proliferation to clear the infection is complex. For relatively slowly replicating viruses, it is possible that an increase in the rate of viral spread increases the chances of viral clearance because CTLs receive a higher antigenic stimulus. On the other hand, in the parameter region where viral replication is generally faster, an increase in the rate of viral spread always increases the chance of viral persistence. Therefore, when comparing viruses which are characterized by different replication rates in general, it is difficult to predict how replication kinetics correlates with the need for help to resolve the infection.
The easiest scenario is given by the comparison of viruses which differ in their rate of spread but which all replicate at a relatively fast rate. In this parameter region, the model suggests that increased viral replication kinetics correlates with an inability of CTLs to clear the infection in the absence of help. Moreover, the model suggests the following dynamics in helper-deficient hosts (Fig. 3). The CTL response initially reduces virus load to low or undetectable levels. This is because the acute response does not depend on help. If the viral replication rate is relatively slow, this results in clearance or long-term control. Otherwise, this is followed by a resurge of the virus population after a given period of time, which correlates with the lack of memory CTL responses. The time it takes for the virus to resurge depends on the rate of viral replication. The faster the replication rate, the quicker the virus population grows back (virus load is reduced to a lesser degree and can subsequently grow faster in the absence of memory responses).
Model predictions regarding the dynamics in the absence of help fit well with experimental data from virus infections in helper-deficient mice. Lymphocytic choriomeningitis virus (LCMV) is a good case study. It is a relatively fast-replicating virus, but comes in different strains characterized by different replication kinetics (32). As suggested by the model, if the replication rate of the virus is slower, such as with LCMV Armstrong, absence of help results in the clearance of the infection (33). Faster replicating strains of LCMV (such as Traub), however, result in persistent infection (28, 32, 34, 35). In accord with the model, the experimental data show that the acute CTL response initially reduces virus load to low levels and that the virus population subsequently grows back (28). In addition, virus resurgence is observed earlier with faster replicating viruses (28).
 |
Conclusions
|
---|
We have examined a mathematical model which describes programmed CTL proliferation in response to viral infections. We investigated how the process of programmed proliferation influences the infection dynamics, in particular the ability of the response to clear the virus. Programmed divisions improve the ability of the response to clear an infection, but reduce the ability of the response to catch up with a growing virus population and limit acute symptoms. We hypothesized that the 710 cell divisions observed in experiments represent an optimum: fewer divisions would compromise clearance; more divisions would result in too much acute pathology. In the context of prolonged antigen persistence, we found that predictions derived from the programmed proliferation model were very similar to those derived from the continuous stimulation models. Therefore, many of the previous results regarding persistent infections obtained from continuous stimulation models should remain robust in the context of programmed CTL proliferation. We have discussed the interpretation of experimental data in the context of VSV and LCMV infection. Further experiments will have to be performed in order to examine some model assumptions more accurately. Experimental data have analyzed CTL dynamics during acute infection in much detail. The exact events which occur upon re-stimulation of memory cells are less well established. Experiments should determine whether the proliferation program is simply repeated at every stimulation event (as assumed here), or whether additional complexities need to be taken into consideration. In addition, it would be interesting to compare the number of programmed CTL divisions in different virus infections, and across different host species. The 710 programmed divisions found so far might vary, reflecting the optimal number of divisions required to prevent acute pathology and to maximize the chances of clearance.
 |
Acknowledgements
|
---|
This work was funded by NIH grant R01 AI058153-01A2 (DW).
 |
Abbreviations
|
---|
LCMV | lymphocytic choriomeningitis virus |
VSV | vesicular stomatitis virus |
 |
Notes
|
---|
Transmitting editor: M. Bevan
Received 6 May 2005,
accepted 29 June 2005.
 |
References
|
---|
- Kaech, S. M. and Ahmed, R. 2001. Memory CD8+ T cell differentiation: initial antigen encounter triggers a developmental program in naive cells. Nat. Immunol. 2:415.[ISI][Medline]
- van Stipdonk, M. J., Lemmens, E. E. and Schoenberger, S. P. 2001. Naive CTLs require a single brief period of antigenic stimulation for clonal expansion and differentiation. Nat. Immunol. 2:423.[ISI][Medline]
- van Stipdonk, M. J., Hardenberg, G., Bijker, M. S. et al. 2003. Dynamic programming of CD8+ T lymphocyte responses. Nat. Immunol. 4:361.[CrossRef][ISI][Medline]
- Wong, P. and Pamer, E. G. 2001. Cutting edge: antigen-independent CD8 T cell proliferation. J. Immunol. 166:5864.[Abstract/Free Full Text]
- Badovinac, V. P., Porter, B. B. and Harty, J. T. 2002. Programmed contraction of CD8(+) T cells after infection. Nat. Immunol. 3:619.[ISI][Medline]
- Janssen, E. M., Lemmens, E. E., Wolfe, T., Christen, U., von Herrath, M. G. and Schoenberger, S. P. 2003. CD4+ T cells are required for secondary expansion and memory in CD8+ T lymphocytes. Nature 421:852.[CrossRef][ISI][Medline]
- Sun, J. C. and Bevan, M. J. 2003. Defective CD8 T cell memory following acute infection without CD4 T cell help. Science 300:339.[Abstract/Free Full Text]
- Shedlock, D. J. and Shen, H. 2003. Requirement for CD4 T cell help in generating functional CD8 T cell memory. Science 300:337.[Abstract/Free Full Text]
- Antia, R., Bergstrom, C. T., Pilyugin, S. S., Kaech, S. M. and Ahmed, R. 2003. Models of CD8+ responses: 1. What is the antigen-independent proliferation program. J. Theor. Biol. 221:585.[CrossRef][ISI][Medline]
- Nowak, M. A. and Bangham, C. R. 1996. Population dynamics of immune responses to persistent viruses. Science 272:74.[Abstract]
- Wodarz, D., Page, K. M., Arnaout, R. A., Thomsen, A. R., Lifson, J. D. and Nowak, M. A. 2000. A new theory of cytotoxic T-lymphocyte memory: implications for HIV treatment [In Process Citation]. Philos. Trans. R. Soc. Lond. B Biol. Sci. 355:329.[CrossRef][ISI][Medline]
- Opferman, J. T., Ober, B. T. and Ashton-Rickardt, P. G. 1999. Linear differentiation of cytotoxic effectors into memory T lymphocytes. Science 283:1745.[Abstract/Free Full Text]
- Bocharov, G., Ludewig, B., Bertoletti, A. et al. 2004. Underwhelming the immune response: effect of slow virus growth on CD8+-T-lymphocyte responses. J. Virol. 78:2247.[Abstract/Free Full Text]
- Perelson, A. S. 2002. Modelling viral and immune system dynamics. Nature Rev. Immunol. 2:28.[CrossRef][ISI][Medline]
- Bartholdy, C., Christensen, J. P., Wodarz, D. and Thomsen, A. R. 2000. Persistent virus infection despite chronic cytotoxic T-lymphocyte activation in gamma interferon-deficient mice infected with lymphocytic choriomeningitis virus [In Process Citation]. J. Virol. 74:10304.[Abstract/Free Full Text]
- Wodarz, D. 2001. Mechanisms underlying antigen-specific CD8+ T cell homeostasis. Science 292:595.[CrossRef][Medline]
- Matloubian, M., Suresh, M., Glass, A. et al. 1999. A role for perforin in downregulating T-cell responses during chronic viral infection. J. Virol. 73:2527.[Abstract/Free Full Text]
- Badovinac, V. P., Tvinnereim, A. R. and Harty, J. T. 2000. Regulation of antigen-specific CD8(+) T cell homeostasis by perforin and interferon-gamma. Science 290:1354.[Abstract/Free Full Text]
- Stepp, S. E., Mathew, P. A., Bennett, M., de Saint Basile, G. and Kumar, V. 2000. Perforin: more than just an effector molecule. Immunol. Today 21:254.[CrossRef][ISI][Medline]
- Christensen, J. E., Wodarz, D., Christensen, J. P. and Thomsen, A. R. 2004. Perforin and IFN gamma do not significantly regulate the virus-specific CD8+ T cell response in the absence of antiviral effector activity. Eur. J. Immunol. 34:1389.[CrossRef][ISI][Medline]
- Battegay, M., Moskophidis, D., Rahemtulla, A., Hengartner, H., Mak, T. W. and Zinkernagel, R. M. 1994. Enhanced establishment of a virus carrier state in adult CD4+ T-cell-deficient mice. J. Virol. 68:4700.[Abstract]
- Matloubian, M., Concepcion, R. J. and Ahmed, R. 1994. CD4+ T cells are required to sustain CD8+ cytotoxic T-cell responses during chronic viral infection. J. Virol. 68:8056.[Abstract]
- Sarawar, S. R., Lee, B. J., Reiter, S. K. and Schoenberger, S. P. 2001. Stimulation via CD40 can substitute for CD4 T cell function in preventing reactivation of a latent herpesvirus. Proc. Natl Acad. Sci. USA 98:6325.[Abstract/Free Full Text]
- Doherty, P. C., Topham, D. J., Tripp, R. A., Cardin, R. D., Brooks, J. W. and Stevenson, P. G. 1997. Effector CD4+ and CD8+ T-cell mechanisms in the control of respiratory virus infections. Immunol. Rev. 159:105.[ISI][Medline]
- Borrow, P., Tishon, A., Lee, S. et al. 1996. CD40L-deficient mice show deficits in antiviral immunity and have an impaired memory CD8+ CTL response. J. Exp. Med. 183:2129.[Abstract/Free Full Text]
- Borrow, P., Tough, D. F., Eto, D. et al. 1998. CD40 ligand-mediated interactions are involved in the generation of memory CD8(+) cytotoxic T lymphocytes (CTL) but are not required for the maintenance of CTL memory following virus infection. J. Virol. 72:7440.[Abstract/Free Full Text]
- Thomsen, A. R., Nansen, A., Christensen, J. P., Andreasen, S. O. and Marker, O. 1998. CD40 ligand is pivotal to efficient control of virus replication in mice infected with lymphocytic choriomeningitis virus. J. Immunol. 161:4583.[Abstract/Free Full Text]
- Thomsen, A. R., Johansen, J., Marker, O. and Christensen, J. P. 1996. Exhaustion of CTL memory and recrudescence of viremia in lymphocytic choriomeningitis virus-infected MHC class II-deficient mice and B cell-deficient mice. J. Immunol. 157:3074.[Abstract]
- Belz, G. T., Wodarz, D., Diaz, G., Nowak, M. A. and Doherty, P. C. 2002. Compromised influenza virus-specific CD8(+)-T-cell memory in CD4(+)-T-cell-deficient mice. J. Virol. 76:12388.[Abstract/Free Full Text]
- Sun, J. C., Williams, M. A. and Bevan, M. J. 2004. CD4+ T cells are required for the maintenance, not programming, of memory CD8+ T cells after acute infection. Nat. Immunol. 5:927.[CrossRef][ISI][Medline]
- Marzo, A. L., Vezys, V., Klonowski, K. D., Lee, S. J., Muralimohan, G., Moore, M., Tough, D., Lefrancois, L. 2004. Fully functional memory CD8 T cells in the absence of CD4 T cells. J. Int. Imm. 173:969.
- Thomsen, A. R., Nansen, A., Andreasen, S. O., Wodarz, D. and Christensen, J. P. 2000. Host factors influencing viral persistence. Philos. Trans. R. Soc. Lond. B 355:1031.[CrossRef][ISI][Medline]
- Ahmed, R., Butler, L. D. and Bhatti, L. 1988. T4+ T helper cell function in vivo: differential requirement for induction of antiviral cytotoxic T-cell and antibody responses. J. Virol. 62:2102.[ISI][Medline]
- Christensen, J. P., Bartholdy, C., Wodarz, D. and Thomsen, A. R. 2001. Depletion of CD4+ T cells precipitates immunopathology in immunodeficient mice infected with a noncytocidal virus. J. Immunol. 166:3384.[Abstract/Free Full Text]
- Planz, O., Ehl, S., Furrer, E. et al. 1997. A critical role for neutralizing-antibody-producing B cells, CD4(+) T cells, and interferons in persistent and acute infections of mice with lymphocytic choriomeningitis virus: implications for adoptive immunotherapy of virus carriers. Proc. Natl Acad. Sci. USA 94:6874.[Abstract/Free Full Text]