Simulating within-vector generation of the malaria parasite diversity

Abstract

Plasmodium falciparum, the most virulent human malaria parasite, undergoes asexual reproduction within the human host, but reproduces sexually within its vector host, the Anopheles mosquito. Consequently, the mosquito stage of the parasite life cycle provides an opportunity to create genetically novel parasites in multiply-infected mosquitoes, potentially increasing parasite population diversity. Despite the important implications for disease transmission and malaria control, a quantitative mapping of how parasite diversity entering a mosquito relates to diversity of the parasite exiting, has not been undertaken. To examine the role that vector biology plays in modulating parasite diversity, we develop a two-part model framework that estimates the diversity as a consequence of different bottlenecks and expansion events occurring during the vector-stage of the parasite life cycle. For the underlying framework, we develop the first stochastic model of within-vector P. falciparum parasite dynamics and go on to simulate the dynamics of two parasite subpopulations, emulating multiply infected mosquitoes. We show that incorporating stochasticity is essential to capture the extensive variation in parasite dynamics, particularly in the presence of multiple parasites. In particular, unlike deterministic models, which always predict the most fit parasites to produce the most sporozoites, we find that occasionally only parasites with lower fitness survive to the sporozoite stage. This has important implications for onward transmission. The second part of our framework includes a model of sequence diversity generation resulting from recombination and reassortment between parasites within a mosquito. Our two-part model framework shows that bottlenecks entering the oocyst stage decrease parasite diversity from what is present in the initial gametocyte population in a mosquito's blood meal. However, diversity increases with the possibility for recombination and proliferation in the formation of sporozoites. Furthermore, when we begin with two parasite subpopulations in the initial gametocyte population, the probability of transmitting more than two unique parasites from mosquito to human is over 50% for a wide range of initial gametocyte densities.

Fig 1. Dynamics of the within-vector model.

The temporal dynamics of the deterministic model (black line) and the average dynamics across 1000 stochastic simulations (blue curve) overlays 100 simulations of the single-parasite population CTMC model (gray lines) with initial gametocyte number G₀ = 300 for zygotes (A), ookinetes (B), oocysts (C) and sporozoites (D). Observe that not all simulations produce a positive number of sporozoites. In fact, out of 10,000 simulations, 2.58% produce no sporozoites.

Fig 2. Comparison of life cycle model with published data.

(A) Experimental data (blue circles) extracted (using Plot Digitizer) from Figure 1A in [46] along with the mean number of oocysts per mosquito calculated from our simulation data. The experimental data is scaled to be in units of gametocytes per five μL rather than gametocytes per one μL. A regression line to the log-log experimental data (dashed green) and to a subset of the experimental data over the range of initial gametocyte densities used to parameterize the model (solid green) is shown along with our model simulations (red stars). (B) Experimental data (black circles) from Figure 1 in [47] of oocyst intensity and prevalence (reproduced with permission) compared to results of the simulation starting from 150 (red shading), 300 (green shading) and 450 (blue shading) gametocytes. The colored areas represent the range of oocyst intensity and prevalence observed from simulations.

Fig 3. Comparison of stochastic and deterministic dynamics of oocysts and sporozoites.

(A) Each of the first four rows illustrate the dynamics of the oocyst (left column) and sporozoite (right column) populations from individual simulations of the CTMC model using 50% fitness bias and G₀ = 300. (B) The dynamics of the deterministic model for oocysts (left) and sporozoites (right). Observe the variation in dynamics possible with the CTMC model.

Fig 4. Cumulative and ruptured oocysts.

The mean cumulative number (on day 21) of oocysts formed (A) and the total number of ruptured oocysts (B) resulting from the 10,000 simulations of the two-parasite population CTMC model (dots) and deterministic model (crosses) is illustrated for initial gametocyte number G₀. Here, the CTMC model utilizes a more biologically realistic continuous rupture function for oocyst bursting, compared to the step function used in the deterministic model. (See S4 Fig for the comparison of models both using a step bursting function.) Left to right the columns illustrate the results for 0%, 10% and 50% fitness biases, respectively.

Fig 5. Oocyst intensity and prevalence.

The scatter plots show mean oocyst intensity (x-axis) versus mean oocyst prevalence (y-axis), calculated 1000 times. Oocyst prevalence is defined as the proportion of mosquitoes harboring oocysts (i.e. simulations producing at least one oocyst). Oocyst intensity is defined as the number of oocysts per mosquito (i.e. per simulation). To produce each point, we randomly drew ten mosquitoes (that is, ten stochastic realizations) from our 10,000 simulations of the stochastic model and computed the oocyst prevalence and intensity for these ten mosquitoes on day seven. The histograms show the density of points in the scatter plot for different values of oocyst intensity (horizontal graph) and oocyst prevalence (vertical graph). In the left and right columns, the initial gametocyte number is G₀ = 150 and G₀ = 450, respectively. Top to bottom the rows illustrate the results for 0%, 10% and 50% fitness biases, respectively. Observe that as G₀ increases, the differences in distribution of the genetically distinct parasite populations becomes more pronounced.

Fig 6. Number of unique barcode sequences.

(A) The number of unique barcode sequences from two genetically distinct parasite populations as a function of the number of barcode positions that initially differ. (B) Distribution of the unique barcode sequences when looking at 15 differences between the two initial parasite populations. Colors indicate the number of starting gametocytes with darker colors representing lower initial gametocyte numbers. Left to right the columns illustrate the results for 0%, 10% and 50% fitness biases, respectively. Gray bars in (A) show the similarity in parasite populations for the distributions in (B).

Fig 7. Nucleotide diversity of ruptured oocysts.

Nucleotide diversity, π, by differing number of starting positions between genetically distinct parasite populations. Left to right the columns illustrate the results for 0%, 10% and 50% fitness biases, respectively. Colors refer to the initial gametocyte number with darker colors representing lower gametocyte numbers.

Fig 8. Frequency that multiple genetically distinct parasites are passed in an infectious bite.

The fraction of infectious bites that harbor one (black), two (brown) or multiple (beige) parasites with distinct barcode sequences. When the mosquito is infected with a small number of gametocytes, 34% of infectious bites are composed of a single sequence. At larger initial gametocyte numbers the proportion of infectious bites passing only a single genetically distinct parasite population falls to nearly 0. Ten sporozoites were assumed to be present in a single infectious bite.