XW0 yVbcv

pyrCCv

Coexistence of infected and uninfected cells is described by equilibrium E2:

(2) (3k (rcv — b(3 — cvd) — cv (ar — sd) — 6/3 (i— s) zv = .

PyCyT

How do the CTL influence the outcome of treatment? We distinguish between two scenarios.

Slowly replicating virus

Slowly replicating virus

Log virus specific CTL responsiveness, cv

Fig. 12.4 Dependence of overall tumor load on the strength of the virus-specific CTL response. There is an optimal CTL responsiveness at which tumor load is smallest. The faster the rate of virus replication, the higher the optimal strength of the CTL response, and the smaller the minimum tumor load. Parameters were chosen as follows: k=10; r=0.5; s=0.5; d=0.1; b=0.1; p=l; a=0.2; for fast viral replication, /3=J; for slow viral replication ¡3=0.1.

Log virus specific CTL responsiveness, cv

Fig. 12.4 Dependence of overall tumor load on the strength of the virus-specific CTL response. There is an optimal CTL responsiveness at which tumor load is smallest. The faster the rate of virus replication, the higher the optimal strength of the CTL response, and the smaller the minimum tumor load. Parameters were chosen as follows: k=10; r=0.5; s=0.5; d=0.1; b=0.1; p=l; a=0.2; for fast viral replication, /3=J; for slow viral replication ¡3=0.1.

(i) If the virus has established 100% prevalence in the tumor cell population in the absence of the CTL response, the presence of CTL can both be beneficial and detrimental to the patient (Figure 12.4). On one hand, the virus can remain 100% prevalent in the tumor in the presence of CTL. In this case, overall tumor size is given by x + y = b/cv. At this equilibrium, an increase in the CTL responsiveness against the virus decreases the tumor size. On the other hand, if the CTL responsiveness crosses a threshold given by cv > b({3k + r)/[k(r — d)], the virus does not maintain 100% prevalence in the tumor cell population, and the overall tumor size is given by x + y — k[cv(r — d) — b(3}J{cvr). In this case, an increase in the CTL responsiveness to the virus increases tumor load and is detrimental to the patient (Figure 12.4). This is because the CTL response kills the virus faster than it can spread. Hence, the optimal CTL responsiveness is given by copt = b{(3k + r)/[k(r — d)}. At this optimal CTL responsiveness, the tumor size is reduced maximally and is given by [x + y][min] = k(r — d)/(r + ¡3k). The faster the replication rate of the virus, the higher the optimal CTL responsiveness, and the lower the minimum size of the tumor that can be attained by therapy (Figure 12.4). Note that the minimum tumor size that can be achieved is the same as in the previous case where viral cytotoxicity alone was responsible for reducing the tumor. The effect of the CTL response is to modulate the overall death rate of infected cells with the aim of pushing it towards its optimum value. Figure 12.5 shows a simulation of therapy where an intermediate CTL responsiveness results in tumor remis sion, while a stronger CTL response can result in failure of therapy because virus spread is inhibited.

Higher CTL responsiveness, cv

10 15 20 2S 30 35 40

^ Time scale (arbitrary units)

Start of virus therapy

Higher CTL responsiveness, cv

Intermediate CTL responsiveness, cv

10 15 20 2S 30 35 40

^ Time scale (arbitrary units)

Start of virus therapy

Fig. 12.5 Simulation of therapy using an oncolytic viruses in the presence of virus-specific lytic CTL. An intermediate CTL responsiveness results in tumor eradication, while a stronger CTL response results in tumor persistence. Parameters were chosen as follows: k=10; r=0.5; s=0.5; ¡3=0.1; a=0.2; p=l; b=0.1; b=0.1; d=0.1; The intermediate CTL responsiveness is characterized by cv = 0.2625, while the stronger CTL response is characterized by cv = 2.

(ii) If the virus is not 100% prevalent already in the absence of the CTL response, a CTL-mediated increase in the death rate of infected cells can only be detrimental to the patient since it increases tumor load. The system converges to an equilibrium tumor size described by x + y = A;[cv[r — d) — b(3]/cvr.

12.3 Virus infection and the induction of tumor-specific CTL

Previous sections explored how virus infection and the virus-specific CTL response can influence tumor load. However, virus infection might not only induce a CTL response specific for viral antigen displayed on the surface of the tumor cells. In addition, active virus replication could induce a CTL response specific for tumor antigens [Fuchs and Matzinger (1996); Matzinger (1998)]. The reason is that virus replication could result in the release of substances and signals alerting and stimulating the immune system. This could be induced by tumor antigens being released and taken up by pro fessional antigen presenting cells (APC), and/or by other signals released from the infected tumor cells. This is known as the danger signal hypothesis in immunology (and is discussed in more detail in Chapter 11). Normal tumor growth is thought not to evoke such signals, whereas the presence of viruses might evoke danger signals. Here, such a tumor specific CTL response is included in the model. It is assumed that the responsiveness of the tumor-specific CTL requires two signals: (i) the presence of the tumor antigen, and (ii) the presence of infected tumor cells providing immuno-stimulatory signals. In the following, the interactions between the tumor, the virus, and the tumor-specific CTL are investigated.

A model is constructed describing the interactions between the tumor population, the virus population, and a tumor-specific CTL response. It takes into account three variables. Uninfected tumor cells, x, infected tumor cells, y, and tumor-specific CTL, zt- It is given by the following set of differential equations [Wodarz (2001)],

The basic interactions between viral replication and tumor growth are identical to the models described above. The tumor-specific CTL expand in response to tumor antigen, which is displayed both on uninfected and infected cells (x+y), at a rate cy. However, in accord with the danger signal hypothesis, it is assumed that the tumor-specific CTL response only has the potential to expand in the presence of the virus, y. In the model virus load correlates with the ability of the tumor-specific response to expand, since high levels of viral replication result in stronger stimulatory signals. The tumor-specific CTL kill both uninfected and infected tumor cells at a rate pryzr-

If the virus has reached 100% prevalence in the absence of CTL, the tumor-specific CTL response becomes established if ct > bs2/[k(a — s)]2. If infected and uninfected tumor cells coexist in the absence of CTL, the tumor-specific CTL response becomes established if zT = cT(x + y)zT - bzT.

In the presence of the tumor-specific CTL, the virus can again attain 100% prevalence in the tumor cell population, or we may observe the coexistence of infected and uninfected tumor cells. Hundred percent prevalence in the tumor population is described by equilibrium El:

Coexistence of infected and uninfected tumor cells is described by equilibrium E2:

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