A computational lens for sexual-stage transmission, reproduction, fitness and kinetics in Plasmodium falciparum

Abstract

Background: The burden of falciparum malaria remains unacceptably high in much of sub-Saharan Africa and massive efforts are underway to eliminate the parasite. While symptoms of malaria are caused by asexual reproduction of the parasite, transmission to new human hosts relies entirely on male and female sexual-stage parasites, known as gametocytes. Successful transmission can be observed at very low gametocyte densities, which raises the question of whether transmission-enhancing mechanisms exist in the human host, the mosquito, or both.

Methods: A new computational model was developed to investigate the probability of fertilization over a range of overdispersion parameters and male gamete exploration rates. Simulations were used to fit a likelihood surface for data on rates of mosquito infection across a wide range of host gametocyte densities.

Results: The best fit simultaneously requires very strong overdispersion and faster gamete exploration than is possible with random swimming in order to explain typical prevalence levels in mosquitoes. Gametocyte overdispersion or clustering in the human host and faster gamete exploration of the mosquito blood meal are highly probably given these results.

Conclusions: Density-dependent gametocyte clustering in the human host, and non-random searching (e.g., chemotaxis) in the mosquito are probable. Future work should aim to discover these mechanisms, as disrupting parasite development in the mosquito will play a critical role in eliminating malaria.

Keywords: Gametocytes; Mathematical model; Plasmodium falciparum.

Fig. 1

Gametocytes are drawn from Poisson (left) or negative binomial (right) distributions, with a mean of 5 gametocytes/µl (the threshold of microscopic detection). Each capillary represents exactly 1 µL of blood and in addition to the male (yellow) and female (purple) gametocytes pictured, also contains 5 million RBCs (represented by the red background). Definite failures to infect are in the bottom capillaries, containing no or single sex gametocytes (2 failures for Poisson, 3 for negative binomial). The female mosquito takes her blood meal from the capillary with a relatively high number of males (7) and females (14), represented in her gut. The red cube zooms in on 1/10th of this meal (0.1 µl). As noted, this cube contains 500,000 RBCs but only 2 females and 1 male. The purple dots in the red cube are the approximate relative size of immotile females in 1/10th of a µL, and the two yellow cubes represent the volume explored by a single male swimming at 5 µm/s (slow) or 50 µm/s (fast). The male gametocyte present in this cube could produce up to 8 male gametes, but it would take 500 slow males or 50 fast males to fully explore this cube

Fig. 2

(Left) Probability of at least one zygote for varying gametocyte densities, a female sex ratio of 0.7, and 2 male gametes per gametocyte. Black is for Poisson gametocyte draws with male gametes exploring 1/10,000 of a blood meal, green is for Poisson gametocyte draws with male gametes exploring 1/1000 of a blood meal, and blue is for an negative binomial gametocyte draw with overdispersion k = 1 and male gametes exploring 1/10,000 of a blood meal. The red shaded bar is the Schneider et al. [10]. fit to data, and the pink shaded bar is an approximation to the Da et al. data. The inset shows the probability of at least one zygote zoomed in at low gametocyte densities. (Right) The distribution, mean and one standard deviation for the number of zygotes for each of the three scenarios simulated on the left. The pink shaded bar is for the Da et al. [11] data on oocysts. The histograms for female gametocytes, male gametocytes, and zygotes in a blood meal for each condition in this Figure can be found in Additional file 1: Figures S1–S3

Fig. 3

Mapping the likelihood of model fitting to Schneider et al. [10] and Da et al. [11] data for varying overdispersion parameter k and blood meal coverage per male gamete. A clear likelihood peak is seen in both dimensions showing that both more efficient exploration of the blood meal and strongly overdispersed clustering are both needed to get the best fit

Fig. 4

(Left) The probability of at least one zygote for the best fitting model parameters (k = 0.6 and blood meal coverage by male gamete of 0.004) is shown in blue–green. Combining the clustering and rapid blood meal search mechanisms creates a close approximation to the Schneider et al. [10] and Da et al. [11] data across all density regimes studied. If the overdispersion parameter k is allowed to vary from 0.5 at low densities, increasing above a gametocyte density of 1/µL at 0.5 per log10 of density, then an even better fit is achieved, as seen in orange for male gamete blood meal coverage of 0.003. (Right) The zygote distributions follow a similar line as the Da et al. [11] data, although the fitting process did not fit to oocyst number. As desired, the mean number of zygotes is almost a full order of magnitude higher than the oocyst counts, with the divergence increasing at higher densities. Note that the varying k plot allows a closer fit to the probability of successful infection while reducing the excessively high zygote counts at the top of the distribution for 100 gc/μl