The standard leishmaniasis treatments are chemotherapy based, though some new treatments are based on the use of immunotherapy. In our model, the chemotherapeutical agents are those that target parasite destruction (g2) or inhibit proliferation (g1), whereas immunotherapeutic treatment implies changing parameters g3, ... g8 and g3, g4, g6, g8, g9, ...g12. In most cases the exact interaction mechanism of the drug is not yet known, though it is possible to associate them to the corresponding parameters that are being influenced. It is important to mention that if a given therapeutic agent has an influence that is not represented by any of our model's parameters but corresponds with the in- or outflux of a model variable, the effect of this agent can be translated in our model by a change in the respective rate constant γi.
Regarding drug therapy, we have found three parameters which cause parasite load reduction: g1, which describes the influence of parasites on their own proliferation; g6, which represents the influence of lymphocytes on their own proliferation; and γ2, the rate constant for parasite degradation.
Examination of the standard drugs used for leishmaniasis treatment shows that most are aimed at parasite destruction. In our model that translates a an increase in γ2
, the rate of parasite destruction [34
], an observation that is coherent with our model's predictions. This is the case for several standard treatments such as amphotericin B (partially inhibits the completion of the parasite's membrane), antimonials (decrease biosynthesis of energy in the amastigote), and itraconazole and pyrazolopyrimidines (inhibit the parasite growth). Other substances currently under evaluation, such as betle leaves extract (reduces viability of promastigotes), interferon (actives macrophages that reduce parasite load), and IL-12 (stimulates Th1) also increase γ2
. These observations constitute a pragmatic, a posteriori
verification of our model's predictions.
Most of the therapeutic drugs used also seem to inhibit, albeit through different mechanisms, parasite proliferation: aminoglycosides alter parasite messenger RNA, pentamidine inhibits polyamine and DNA synthesis in the parasite, imidazole and itraconazole inhibit demethylation of membrane, and pyrazolopyrimidines block protein synthesis and destroy parasite RNA. All these effects can be interpreted, in terms of our model, as a decrease in g1
. The discrepancy in our model's predictions can be explained by several facts. First, in all cases where a decrease in g1
could be assumed, there is also the concomitant effect of increasing γ2
, as noted above. Thus, a trade-off of these two actions should be previously evaluated in order to have an accurate account of the whole drug effect. Second, it should be taken into account that the effect of a g1
modulation could be different depending on the stage of the disease. It has also been shown that if parasites replicate quickly, the immune system is able to recognize them more easily [13
]. Parasites use mechanisms like inhibition of antigen presentation to escape immune response, however, a high growth rate induces massive macrophage recruitment [13
]. At this point it should be stressed that our model considers the infection from the very initial stage. A third explanation could be that the parasites produce a certain molecule that stimulates an immune response of the body. (While investigating a model of tuberculosis infection [35
], it was also found that the partial rank correlation between growth rate and extracellular bacteria is negative in a certain time interval.)
The factor that increases the influence of parasites on their own proliferation (g1) is crucial according to our model's results; and currently, no pharmaceuticals that increase g1 have been tested against Leishmania. Insuline-like growth factor 1, interferon, and possibly TNF-α cytikine could be considered as potential targets for stimulating parasite replication inside macrophages, and it would be of great interest to test their anti-leishmanial effectiveness. Insuline-like growth factor also increases the number of parasites (γ1) and reduces parasite-toxic production of nitric oxide (γ2).
Furthermore, no existing drug is known to have an effect on g6, which, in our analysis, is also seen as a possible effective pharmaceutical target. This clearly points to the new, potential application of existing and current therapeutic strategies.
The approach used for detecting key processes that must be regulated in order to reduce parasite load also allowed us to identify combinations of two drugs that would eventually be more effective than a single drug treatment. As is showed in Figure , combinations of drugs able to increase g1 or g2 and simultaneously change any other parameter, or, alternatively, combinations of drugs that decrease g1 together with the change in another parameter, would cause significant reduction in the final parasite load. These findings greatly amplify the number of therapeutic options available, although they still remain to be tested. By way of illustration, we could suggest the combination of any of the available drugs that increase g2 (amphotericin B, aminoglycosides, antimonials, pentamidine imidazole, itraconazole, and pyrazolopyrimidines) together with any of the following: interleukin-5,6,13 and MHC class II molecules (both increasing g3), rLmSTI1 (increase in g4), and chemokines (that increase g3 and g2 simultaneously). In the same mouse model we will test the effects on the variables of different drug combinations to verify the model's predictions and to eventually refine and extend the model by including new variables and mechanisms.
A limitation of the present approach is that our model is a simplification and does not include a detailed description of all the factors involved in the interaction mechanism of the drug in the body. However, given that these mechanisms are often not known, the modeling approach constitutes an approximation to the understanding of a complex dynamic system based on available information and informed hypothesis.