The objective of this study was to identify new targets with potential for drug discovery against malaria. Since malaria is a complex disease with plenty of host–parasite interactions, the disease’s dynamics and symptoms (the system emergent properties) can only be understood through an integrated view of parasite infection and host responses. By acting on these targets, including those that only work in vivo, we aim to reduce the parasitemia of the two species of the parasite inside the host.
The proposed model focuses on the modeling of the underlying processes within the host-parasite dynamics of Plasmodium invasion of red blood cells. Its main objective is to allow for the systematic search, by means of an optimization approach, for the most interesting targets for drug research. Given the high number of processes involved and the model’s inherent complexity, we opted for a phenomenological representation that is simple enough to permit the proposed search but at the same time rich enough to provide valuable insight into suitable targets. Based on the results of this search, we would set up the necessary conditions to find, or help to define, therapeutic strategies, including some which are counter-intuitive. These strategies will not necessarily impede infection but will reduce parasitemia and the risk of severe symptoms as well as diminish the risk of drug resistance and selective pressure for resistant Plasmodium strains. The model considered a set of relevant components, processes and interactions. Variables selected for the model were the two phases of the parasite inside the host erythrocytes (mRBC, merozoites, and gRBC, gametocytes), the healthy erythrocytes of the host, hRBC, and the immune activity of the host against the parasite, IS (see ). All the variables of the model were measured in terms of their concentration inside the bloodstream. The values of the variable IS are given by the concentration of IgG1, which serves as the representative component of the mean immune response against the parasite.
We are aware of the fact that we are extrapolating the P. chabaudi model dynamics built from mouse data to the same process with P. falciparum in monkeys and humans and that Plasmodium life cycle lengths differ between hosts and within the erythrocyte between Plasmodium species. But since our approach is phenomenological, we were able to obtain a qualitative verification of the observed general pattern of behavior in monkeys and humans. The approach serves to provide information about the basic mechanism that operates in this type of infection as well as some guidance for new targets for therapeutic drugs.
The proposed model is able to describe the dynamics of the infection by Plasmodium chabaudi
in mice. In addition, the model’s predictions were successfully compared with different experimental scenarios (, and ). shows how the model reproduces the dynamics of the infection in humans after the first peak of parasitemia, predicting the attenuated oscillations and the delay observed between the phases; it also reproduces the final maintenance of the parasite load. The model’s results also correlate well with the observed response to the infection of a vaccinated host (). The model shows the observed retardation and maximum value of the first peak of parasitemia when the host is vaccinated. Since the model is able to reproduce the disease in a third host, it can be concluded that it has captured the essentials of the host–parasite interactions. A further confirmation of the model’s reliability was obtained by comparing its predictions with the experimental measures of merozoite parasitemia in β-artemether treatment of mice infected with Plasmodium chabaudi
() using two different methods of inoculation of the drug. When β-artemether was injected directly into the bloodstream, the observed delayed and lower peak of parasitemia was predicted by the model (). Also, when the drug was inoculated through liposomes, the observed early, reduced peak of parasitemia followed by a second, lower peak was also forecast by the model (). Thus, the ability of the model to reproduce very different malaria infection scenarios (involving different species of Plasmodium
as well as distinct hosts and various treatment methods) makes us confident enough to use it as a reliable tool in the search for effective pharmacological targets.
A set of such targets (single or combined) are presented in the Results section (see ). A first target would consist on decreasing the invasion rate of the erythrocytes by the merozoites; such an intervention would lead to the full recovery of the host (). Decreasing this rate means that free merozoites are less effective in invading red blood cells; thus they will be more exposed to the immune system 
. Although this strategy has already been partially evaluated as a vaccination strategy [2, see also 33], our results suggest that it could also be effective as a pharmacological treatment. In fact, such an approach has been tested through the treatment of infected mice with dextran sulfate 
, a molecule that impairs the invasion of red blood cells by merozoites 
. These authors 
showed the effects of this substance on reducing the parasitemia and the parallel increase in the survival rate of the mice. More recently, Vulliez et al. 
showed, through the use of structural methods, that impairment of the malaria parasite moving junction complex (decreasing the invasion rate of merozoites) is effective as antimalarial treatment. To sum up, our results indicate that decreasing the invasion rate of the red blood cells by merozoites is a target where some drug treatments can be effective against malaria.
The second single target proposed by the model works by increasing the death rate of the gametocytes. This intervention produces a decrease in gametocyte load but an increase in merozoite load, although the maximum peak will be attenuated (). A treatment along these lines will reduce the transmission rate during the initial stages of the disease and can be combined with traditional treatments targeting the asexual phase. Such a strategy has been already used (artemisinin combined treatments, 
), with the predicted effects of a lower transmission rate for the disease.
A third target was to decrease the ability of the gametocytes to activate the immune system. Its effect is to reduce the maximum peaks of both parasite species (), and so it is expected that it would alleviate the symptoms of non-complicated malaria and reduce the transmission rate during the initial stages of the infection. This target also has additional convenient characteristics. Since it does not directly affect the parasites, there is no selective pressure on them and thus the emergence of drug resistance is avoided. Also, if combined with traditional treatments, the doses could be reduced, thereby also reducing the emergence of drug resistance (see 
). Since this target refers to a parasite-host interaction, the only chance to observe its effects would be in in vivo
conditions. Of equal importance is the fact that it is a very counterintuitive solution. All this could explain why this strategy has never been explored. In addition, we are aware of the technical difficulties involved in the design and implementation of such a strategy, where the sensitivity of the immune system towards the presence of one of the parasite forms is to be impaired.
The last single target identified operates by increasing the transformation rate of merozoites into envisaged gametocytes. The effect of this increase is to produce a significant decrease in merozoite load and also a decrease in gametocyte load (see )
. Although it is not surprising that increasing the merozoite transformation rate would produce a decrease in merozoite load, what is not so intuitive is the model’s prediction of a decrease in the gametocyte load. This is a good illustration of how the integration into a mathematical representation of the many non-linear interactions among the variables involved in the relevant processes can lead to the emergence of certain counterintuitive conclusions that cannot be derived from the consideration of the local changes only. This type of intervention has been shown to relax the symptomatology of non-complicated malaria 
and reduce transmission during the initial stages of the infection 
. It is interesting to observe that the activation of the transformation of merozoites into gametocytes has the effect of impairing the pathogen load. A higher gametocyte growth rate yields an initial increase in its population, but this is followed by a greater decrease in such a way that, as a whole, more parasites are eliminated earlier. This behavior has been observed in other parasitic diseases 
and can be explained by stating that a pathogen that proliferates rapidly is more likely to be detected by the immune system. Increasing the gametocytogenesis is a strategy that has never been evaluated by structural drug design methods, and our results propose this target as a promising process where these techniques can be applied for drug design.
Our exploration of the effective combinations of two targets showed that reducing the influence of gametocytes on the activation of the immune system while at the same time decreasing the effect of the immune system on the death rate of the red blood cells (see ) would cause a reduction in both of the parasite forms (). The latter action can be interpreted as making the immune system less efficient in removing old erythrocytes, thus enhancing their half-life. This therapeutic strategy is optimal in order to prevent the emergence of drug resistance in the parasite. These two proposed targets have never been evaluated by structural methods. There should be great interest in examining these two processes in order to design new drugs, because affecting these processes does not generate selective pressure on the parasites; thus, effective drugs will have a low probability of leading to the emergence of resistance, thereby extending their life span. Here we can see again how the systemic approach might shed new light on a well-studied process and help propose a novel combination of targets, none of which aims to directly kill the parasites, but which could reduce the parasitemia. In all these explorations, the magnitudes of target-related parameter changes, although related with the corresponding processes, do not have a direct translation into a particular process. Accordingly, they have to be interpreted as an indication of the magnitude and sense of the intervention that would lead to the desired effect.
The new, potential antimalarial targets proposed here were identified through the use of a mathematical model that reliably reproduces the infection dynamics under different in vivo scenarios of the disease. This model-based strategy can be of assistance in key phases of the drug discovery process, such as the identification of the right targets, since these targets allow us to guide drug design at the molecular level through the systematic use of other means such as structural methods (molecular docking) or data-mining of inhibitor databases. A best-case illustration is provided by the proposed target consisting of decreasing the invasion of red blood cells by merozoites, which relates to the interruption of the interaction between the Apical Membrane Antigen 1 associations with its receptor, the Rhoptry Neck Protein 2. In fact, the structural details of the specific Apical Membrane Antigen 1 with the Rhoptry Neck Protein 2 interaction involved in the invasion mechanism enables the design of molecules with optimal inhibitory properties to treat malarial infection. However, due to the phenomenological character of the model, the proposed targets do not have a direct translation into a concrete, well-defined process. On the contrary, it should be stressed that the contribution of this work is to propose certain processes of the intraerythrocytic cycle of Plasmodium as targets for a more detailed analysis that would eventually lead to the determination of a set of concrete processes where the activity of some drugs will cause the desired global effect. This second iteration would be the natural next step in this project.
Our results suggest that the invasion of erythrocytes by merozoites is a key point where any impairment intervention would cause a decrease in parasitemia. In this case, some work has already been done with respect to structural methods of drug design 
. Furthermore, comparison of the effect on a known drug target (β-artemether administration through liposomes; ) with the new drug target of increasing gametocytogenesis () shows that both reduce the peak of parasitemia (, panel B). When β-artemether is inoculated directly, the same peak of parasitemia is observed, but with several days’ delay (, panel A). Chimanuka et al. 
showed that the liposome inoculation allowed the mice to survive, in contrast with the direct inoculation. We can thus conclude that a drug which increases gametocytogenesis would produce the same effects on parasitemia (which permit survival in mice) as the β-artemether administration through liposomes.
We conclude that focusing on cellular function as a system rather than on the level of the single process or molecule will facilitate the discovery of novel classes of drugs. Through the integration into a model of the in vivo host–pathogen interactions, we can achieve an integrated view of parasite infection and host responses that will allow for an understanding of the host–parasite–drug interactions and the selection of drug combination strategies of therapeutic value, and for controlling the transmission of malaria by anopheline mosquitoes. In addition, the insight obtained from this work already suggests future extensions and refinements. In particular, models with a greater resolution in terms of the mechanisms involved in the novel targets such as those represented by the V6 (γ6, elimination of gRBC), V5, (γ5, gametocytogenesis), V7 (g73, activation of the immune system by the gametocytes) or V2 (g24, recycling of the erythrocytes) would lead to more mechanistically detailed versions of the model that would suggest more precise targets for drug action. We are aware of the difficulties of translating the proposed targets into precise therapies; the aim of this work is to propose targets that would direct the drug search toward certain processes of the intraerythrocytic cycle of Plasmodium.
Moreover, since the systemic approach used here is a general methodology, it can be used in the selection of strategies for controlling a plethora of parasitic diseases. In each case, the specific processes and their corresponding variables and parameters should be considered, but the application of the model to other forms of parasitemia would benefit from the fact that there are many common features shared by all.