Background
Malaria is a major life-threatening disease caused by parasites of the genus
Plasmodium [
1]. The genus
Plasmodium includes parasites of different species that can infect humans as well as nonhuman primates (NHPs), rodents, bats, reptiles and birds [
2].
Plasmodium vivax has a wide geographical distribution and is responsible for almost half of the malarial cases outside of Africa, where
Plasmodium falciparum predominates [
1,
3,
4]. Having been responsible for 8.5 million cases globally in 2016,
P. vivax constitutes a major challenge towards the goals of the World Health Organization and its partners of eliminating malaria from 35 countries and reducing incidence and mortality rates by 90% by 2030 [
1]. Its closely related sister species,
Plasmodium cynomolgi, is a simian malaria parasite that has been an important model for research [
5‐
8] and is now also recognized as a zoonosis [
9].
In the vertebrate host, the infection process begins with a blood-meal by a female
Anopheles mosquito, which typically results in the inoculation of the host with fewer than 100 sporozoites [
10,
11]. Successful sporozoites travel from the skin to the liver, where they infect hepatocytes. From each infected hepatocyte, tens of thousands of merozoites may develop and be released into the bloodstream [
12,
13]. Several species including
P. vivax and
P. cynomolgi have the additional ability to produce hypnozoites during the liver stage, which are dormant forms of the parasite that may be activated and thus able to cause relapse infections weeks to months after the primary infection [
14‐
17].
During the blood stage of the parasite’s life cycle, merozoites exclusively infect red blood cells (RBCs). The productivity of an infected RBC is much lower than that of an infected hepatocyte, with an infected RBC only producing up to 30 new merozoites, depending on the
Plasmodium species. In the case of
P. cynomolgi, the number of released merozoites per infected RBC is on average 16, with a range of 14–20 [
18]. At some point during the blood stage cycle, some merozoites become committed to the production of gametocytes, which, if taken up by a mosquito, begin the arthropod stage of the infection.
Whereas the liver stage of the infection proceeds asymptomatically, the blood stage often presents symptoms that are shared by common viral infections, i.e., headaches, fever, chills, dizziness, myalgia, nausea and vomiting [
19,
20]. On the other end of the clinical spectrum is severe malaria, which is most often caused by
P. falciparum, although
P. vivax may also cause severe disease [
21]. Severe malaria complications can develop very rapidly and progress to death within hours or days [
22]. Disease manifestations can include, among others, respiratory distress, pulmonary oedema, acute renal failure, thrombocytopaenia, and severe anaemia [
23]. With that said, many infections can be asymptomatic, as also shown recently for relapsing [
17] and zoonotic cases [
9] of
P. cynomolgi. Both species exhibit tropism toward reticulocytes, which is nearly strict in the case of
P. vivax and conditional for
P. cynomolgi [
8,
24,
25]. Also, both species produce caveola vesicle complexes in the infected RBCs, which involves remodelling of the host RBC cytoskeleton, and results in increased membrane deformability [
24,
26,
27]. And, as mentioned above, both species produce hypnozoites capable of causing relapses.
To characterize and quantify the RBC dynamics during malaria, various mathematical models have been developed with the particular goal of deconvolving and quantifying the different processes of RBC removal. Models of the malarial host–pathogen interactions have been proposed since the late 1980s [
28] (reviewed in [
29]). Dynamic models for such a purpose are often formulated as sets of ordinary differential equations (ODEs), and in their simplest form are commonly represented with three compartments, namely, RBCs, infected RBCs, and either merozoites or some marker of the immune response [
30‐
33]. More complex models may contain more than three compartments, especially when they focus on antigenic variation, where many parasite variants are considered, and specific and cross-reactive immune responses are included [
29]. Attempts have also been made to model the delays inherent to this system, in which case it was necessary to use delayed differential equations, age-structured ODEs, partial differential equations, or discrete implementations of their continuous analogs. All these approaches have advantages and drawbacks [
34] that should be taken into consideration, depending on the ultimate goals of the model, i.e., whether the model was developed as a tool for further analytical investigations, data fitting, hypothesis generation, or other purposes.
Here, a time-dependent discrete recursive equation (DRE) model with age structure is used. The model has four compartments: reticulocytes, mature RBCs, infected RBCs and merozoites, all of which have an age structure, except for the merozoites. Unlike most other models [
29], the processes here are quantified time-dependently rather than imposing certain kinetic formulations, such as a mass-action representation. This strategy was used to assess the reticulocyte maturation time in circulation, loss of RBCs, and the impact of the immune response. It also permits the time-dependent quantification of the extent of RBC production and of RBC loss through different processes (random death, senescence, parasitization, or bystander effect), as well as an assessment of the reticulocyte timespan in circulation and of the immune response. The result is in each case a personalized model of each macaque’s response to the infection, which is then analysed a posteriori.
The experimental data used in this work were generated from a longitudinal study involving a cohort of Rhesus macaques that were infected with
P. cynomolgi (B/M strain) sporozoites and followed for 100 days, with sampling of blood and bone marrow at different points in time. Of particular importance for the model, complete blood counts (CBCs) and parasitaemia counts were performed. The data are publicly available [
35], and a comprehensive clinical analysis of these infections [
17], as well as multi-omic integrated analyses have been reported [
36].
Discussion
Nonhuman primate model systems hold the greatest potential for understanding malarial host-parasite dynamics and pathogenesis in vivo [
14,
45‐
47]. A new computational model is presented here for the analysis of erythrocyte dynamics during infections with
P. cynomolgi, a relapsing simian malaria parasite that is a zoonosis and can serve as an experimental model for
P. vivax. This computational model was parameterized to reproduce experimental data obtained from
P. cynomolgi infection of Rhesus macaques [
17] and allowed the characterization of the lifespan of reticulocytes in healthy malaria-naïve animals, the interactions between parasite and host, and the host responses during a blood-stage infection.
Process quantification in this model was done by inference of a time-dependent function from the experimental data, rather than assuming that these processes follow a mass-action model in an
ad-
hoc fashion, as it is commonly done in the field [
30‐
33]. By avoiding the assumption of such relationships, it becomes possible to test assumptions and system properties in an unbiased manner. One such property examined was the erythropoietic output, which corresponds to the rate of RBC production and the rate of reticulocyte release from the bone marrow. This property is usually assumed to depend linearly on present or recent anaemia or to be inversely proportional to the present or recent RBC levels [
48,
49]. Yet, the results show no correlation between either, which suggests that the true function is more complex and likely includes delays.
In humans, the maturation time of reticulocytes in circulation is about 24 h [
50,
51], but this period may be increased to as many as 3 days under erythropoietic stress [
52]. Here, the computational model shows that the maturation time of circulating reticulocytes in healthy
Macaca mulatta is about 24 ± 5 h (n = 15). This value is corroborated by an in vitro analysis of the surviving reticulocytes in fresh RBC cultures from healthy macaques. In these cultures, reticulocytes remained detectable for 25 h, as identified by their RNA content. Overall, these results point to a similar reticulocyte kinetics between
Macaca mulatta and humans. From the same analysis, the normal healthy RBC production rate was determined to be 2727 ± 209 cells/h/µL (n = 15) for
Macaca mulatta.
All macaques exhibited a period of elevated reticulocyte levels 11–13 days after the inoculation with sporozoites, which preceded the detection of patent parasitaemia in the blood and occurred concurrently without any change in RBC numbers. Theoretically, an increase in reticulocyte numbers can only be due to one of two processes, or both: (1) increased RBC production and release from the bone marrow; or (2) a shift towards the release of younger reticulocytes, as it has been observed during erythropoietic stress [
52]. The first would lead to increased reticulocyte numbers in circulation, along with an increase in the overall RBC numbers. In the latter, the same total number of RBCs is still being produced, so no increase in RBC numbers would be observed. However, if reticulocytes are released at a younger stage from the bone marrow, these would take a longer time to mature in circulation, thus leading to an increased accumulation of reticulocytes in circulation. Given that an increase in the total number of RBCs was not observed, an increase in the RBC production does not explain the current data. Therefore, the more likely explanation is a shift toward the release of less mature reticulocytes. Under this assumption, this shift would have to occur around days 6–8 to be consistent with the observed changes, which puts this shift at around the time the parasites are coming out of the liver and starting the infection’s blood stage. A plausible explanation may be that during the beginning of the blood-stage infection the parasite releases a factor that ultimately results in the release of younger reticulocytes from the bone marrow. This mechanism would ensure an increase of circulating reticulocytes, which are arguably the parasite’s preferred host cells, although the preference is not exclusive [
8,
24,
25]. The increased number of reticulocytes seems to subside before a subsequent reticulocyte peak occurs due to the host’s response to the anaemia. During the high parasitaemia period, the reticulocyte numbers exhibit oscillations. These seem to be due to the cycles of RBC infection. In this period of the infection, it is difficult for the model to distinguish precisely between the high consumption of reticulocytes and the decrease in maturation time of these cells. However, the decrease in maturation time has to happen during this time period, because the model only fits the reticulocyte peak in response to the anaemia if the reticulocyte maturation time has returned to normal. These observations are interesting as they suggest that
P. cynomolgi parasites may be capable of causing a shift in the age at which reticulocytes are released from the bone marrow. This shift may be advantageous for the parasite as it happens in anticipation of the parasite’s high demand for reticulocytes and, secondarily, red blood cells, and occurs a week after the release from the liver, when the parasite numbers reach their maximum.
It has long been recognized that certain
Plasmodium species show preferences for invading mature RBCs or reticulocytes [
25,
53]. Species like
Plasmodium ovale and
P. vivax have almost strict reticulocyte tropism, whereas
P. coatneyi,
Plasmodium knowlesi and
Plasmodium malariae have mature RBC tropism [
24]. By contrast,
P. falciparum invades both mature and immature RBCs.
P. cynomolgi resembles
P. vivax, which has an almost strict reticulocyte tropism [
24], whereas the tropism appears to be conditional in the case of
P. cynomolgi [
25,
54], thus exhibiting a preference for reticulocytes while maintaining the ability to infect both RBC maturation stages. Using the computational model developed here, the reticulocyte preference calculated for each macaque is about 15, 1, 100 and 10 (RFa14, RMe14, RSb14 and RIc14, respectively), which gives an average of 32 ± 46 (n = 4) or a median of 13 for this cohort. These results are rough estimates, as they depend highly on the level of reticulocytes during peak parasitaemia, a short time span with just about six time points for each macaque. Additionally, the reticulocyte preference parameter also suffers from structural correlation with the reticulocyte maturation time. The model results show that the reticulocyte maturation and release timing returns to normalcy by the time high parasitaemias are observed, which allows averting the issue of structural non-identifiability. The value determined here for the reticulocyte preference is lower than what was measured for
Plasmodium berghei, 153 [
55], and closer to what was recently obtained for
P. berghei ANKA strain, 74 [
56]. Additionally, a recent in vitro study showed that
P. cynomolgi B strain has strict tropism towards human reticulocytes, but this was not evident when testing
Macaca mulatta RBCs [
8]. Unfortunately, this study did not address possible host cell preferences using co-cultures of reticulocytes and RBCs, thus preventing the quantification of
P. cynomolgi preference for
Macaca mulatta reticulocytes. Overall it appears that the reticulocyte preference is an important parameter for the infection dynamics, as it has been shown that the preference may be correlated with parasitaemia levels and ultimately with disease severity [
33,
48,
49].
Analysis of the parasite growth rates within each macaque revealed that the parasite population grew at unexpectedly fast rates, mostly with values in the range of 30–54 merozoites per infected RBC. In the case of the
P. cynomolgi infected macaque RFv13, the computed value actually reached 110 merozoites per infected RBC, which is likewise unrealistic. This monkey had a particularly high peak parasitaemia (19.5%), suffered severe manifestations of the disease and ultimately needed to be euthanized [
7,
17]. A likely explanation of the apparently high growth rates is that not all parasite forms circulate freely but may rather become concealed in venules or tissues [
44], such that parasitaemia readings from peripheral blood smears may not reflect the total parasite load in the blood. If indeed a substantial number of infected RBCs go into concealment for some of their 48-h life cycle, then the parasite population based on blood smear readings may at times appear to grow at a faster rate than what is biologically possible. This hypothesis has been analysed for
P. cynomolgi, where the analysis of in vivo data suggested the existence of a population of non-circulating concealed parasites [
44]. The model here did not consider concealment and accounted only for parasites observed on blood smears. However, as compensation, the parasitaemias were allowed to grow at the observed, seemingly inflated, growth rates, even though these are higher than what would be biologically possible. In this way, the growth of the parasitaemias does take into consideration any non-visible, and thus concealed, parasites, without requiring any assumption regarding possible concealment probabilities, kinetics, or sites.
Analysis of the infection profiles of RFa14 and RIc14 points to a temporal segregation of RBC production and removal (Fig.
5 and Additional file
3: Fig. S2.3), and similar results were found for
P. coatneyi [
38]. Interestingly, RSb14 (Additional file
3: Fig. S2.2) does not fit this pattern, as it shows an increased level of RBC production that lasts 15 days with its maximum at Day 30, during which time losses due to bystander effect and parasite invasion are recorded. Given the limited sample size, all cases are being reported here. In addition to the deconvolution of loss and production of RBCs in RFa14 and RIc14, RBC losses by parasite invasion and bystander effect tend not to occur simultaneously. This observation gives confidence that loss due to bystander effect is real and not due to a miss-calculation of parasite invasion. Additionally, removal by bystander effect is also detected in periods where parasitaemia is low, which further strengthens this point. Yet, the fact that these two losses tend to be segregated from RBC production does suggest that something involved with the RBC losses prevents up-regulation of the erythropoietic system even during periods of anaemia.
For example, the profile of RIc14 contains a period (Days 23–28) where the main parasitaemia peak had subsided, and the erythropoietic production is high. Suddenly, parasitaemia increases again, and the model measures an increase in RBC death, due to both invasion and bystander effect, which is accompanied by a decrease in RBC production. The decrease in production is inferred by the model as a result of the decrease in reticulocyte counts. What the mediator of this effect could be is not known, but the unknown factor could be mediated by the immune system, as suggested by the analysis of the bone marrow transcriptome of this macaque cohort [
36]. Additionally, it is possible that some aspect of the immune response may be the culprit for the bystander effect, which would simultaneously explain uninfected and infected RBC losses and the failure to up-regulate RBC production.
However, the analysis never shows a reduction of the erythropoietic flux during the infection and recovery periods. The healthy baseline RBC production is determined from the RBC status of each macaque during the first 5–7 days of the experiment, and across all infections, the RBC production is never inferred to dip below this healthy level. Thus, anaemia cannot be due to decreased RBC production, but is more likely due to increased RBC destruction, either by parasite invasion and a bystander effect, and to suppression of the erythropoietin-dependent up-regulation of erythropoiesis in response to anaemia, despite elevated levels of erythropoietin in this macaque cohort between Days 20 and 30 [
36]. By contrast, decreased RBC production is observed only after full recovery of the macaques, but that is due to a shift in the age distribution of RBCs which becomes skewed toward a younger than normal population (see Additional file
1). This younger population of RBCs is, therefore, subject to fewer losses due to old age, and the erythropoietic system of these macaques transiently adjusts the production to meet these reduced losses at normal haematocrit levels.
The bystander effect was estimated from all RBCs produced and lost throughout the first 50 days of the infection. This period of 50 days post-inoculation includes the main parasitaemia peak, anaemia, treatment if needed, and recovery, but excludes relapses. As a consequence of the infections, RBC production and removal doubled to 217% (from 3.5 ± 0.3 to 7.6 ± 0.9 million RBCs/µL). During this same period, RBC removal occurred due to normal physiological processes of senescence and random loss (38 ± 4%), invasion by the parasite (23 ± 2%), and the bystander effect (38 ± 6%). These results suggest that the bystander effect accounts for 62 ± 8% of all infection-induced RBC losses.
Bystander removal of RBCs during malaria has been documented in humans [
41,
57,
58], yet accurate measurements are difficult to obtain [
41]. Using a mathematical model similar to the one used here, the bystander removal of RBCs was inferred for
Macaca mulatta during
P. coatneyi infections as 95% [
38], which is similar to values estimated for humans with falciparum malaria (90–92%) [
41,
58]. Bystander loss of RBCs has also been documented in vivax malaria [
58] and may be due to changes in membrane rigidity, although other mechanisms are under investigation [
59,
60]. The present data do not allow inferences regarding the possible underlying causes of the bystander effect, but they do show that proportionally fewer RBCs are removed by the bystander effect in
P. cynomolgi (62%) infections than in
P. coatneyi (95%) [
44]. Whether this difference is indicative of the difference between the human counterparts of these infections (vivax and falciparum, respectively) is yet to be determined.