Sporozoites

Ross developed and Macdonald modified a mathematical model for the transmission of a vector-borne disease that is a simplified quantitative description of the parasite life cycle [11 ,12 ]. The parameter names, following Macdonald's notation, are given in Table 2. The life-cycle model tracks the fraction of infected humans, X, and the fraction of infectious mosquitoes, Y, over time:
In this system of equations, the parasite persists if R₀ > 1, where
If R₀ > 1, the equilibria are given by the expressions
Since the average mosquito lifespan is short (i.e., 1/g ≈ 10–20 d), but the malaria infections in humans last months (i.e., b/r ≈ 170 d [14 (link)]), the proportion of infectious mosquitoes adjusts rapidly to the proportion of infectious humans, i.e., the sporozoite rate tracks PR when mosquito populations are constant (but see the discussions by Aron and May [52 ] and by Smith et al. [17 (link)]).
Thus, EIR is given by the formula
where V denotes vectorial capacity, following the original definition (see Table 2) [24 (link)]. Solving for V, we get
By our notation R₀ = bcV/r, so we can compute R₀ by solving for vectorial capacity:

Dietz [15 ] and Dye and Hasibeder [16 (link)] have demonstrated that R₀ is higher because of heterogeneous biting:
where α is the squared coefficient of variation of the human biting rate.
In these equations, mortality during sporogony is counted, but the delay for sporogony is not [17 (link)]. These equations give expressions for R₀ and equilibria,
X̄and
Ȳ, that are consistent with the simple assumptions of the classic model. These equations differ slightly from those given by Anderson and May, who write
[9 ], but the equilibrium
would not be consistent with the standard assumptions when mortality during sporogony is incorporated by setting c′ = ce^−gn [27 (link)]. Closely related delay equations are given by Aron and May [52 ]. An alternative approach incorporating a realistic incubation period was modeled by Smith et al. [17 (link)]. All these models assume constant per capita mortality for mosquitoes, and so they ignore important factors such as temperature-dependent mortality and senescence.
Macdonald et al.'s equilibrium method estimates R₀ from the force of infection [23 (link)]; usually, these estimates of h are based on the change in PR with age in cross-sectional surveys:
so

Before performing a Plasmodium specific PCR, every DNA extract was checked for the presence of mosquito DNA by the allele specific PCR for Anopheles dirus complex [20 (link)] or the ITS2 PCR for other mosquito species [21 (link)]. PCR specific for Plasmodium spp. was performed on all CSP-ELISA positive specimens and on all abdomens tested to confirm the presence of sporozoites by using primers PL1473F18 and PL1679R18 targeting the 18SrRNA [22 (link)]. For evaluation of the sensitivity of the CSP-ELISA technique, 299 CSP-ELISA negative An. dirus mosquitoes were tested by Plasmodium specific PCR.
The amplicons of PCR positive samples were cloned and sequenced for confirmation of the Plasmodium species (see below), or the samples were subjected to a more general Haemosporidia PCR [23 (link)] after which the amplicon could be sequenced directly. If the positive CSP-ELISA was not confirmed by Plasmodium specific PCR, this result was considered to be false positive. In this case, four PCR assays were used in order to detect related, possibly zoonotic, and vector-transmitted pathogens: Primers and PCR conditions of the PCR assays to detect parasites belonging to the Haemosporidia [23 (link)], to the Trypanosomatidae [24 (link)], to the Piroplasmida [25 (link)], and to the Haemogregarina [26 (link)] are given in Additional files 3 and 4 respectively.

A natural analytical framework for considering the effects of temperature on malaria transmission intensity is provided by deterministic models for the disease's basic reproductive number, R ₀ , defined formally as the expected number of new cases arising in a naive population after one generation of the parasite from the introduction of a single infectious person [39 -41 ]. These models parameterise malaria transmission in terms of characteristics of, and interactions between, human, vector, and parasite populations [42 -46 (link)]. Those aspects of the transmission cycle affected by temperature are encapsulated in a component of R ₀ known as vectorial capacity [47 (link)], V , which defines the total number of subsequent infectious bites arising from a single person-day of exposure and is classically expressed as:
where m is the number of mosquitoes per human, a is the human feeding rate, p is the daily vector survival rate, and n is the time required for sporogony, the maturation of parasites ingested by mosquitoes during human blood meals into the sporozoite life cycle stage infectious to humans. Expressing vector survival in terms of daily death rate, g where, g = -ln p, and holding constant the rate of adult mosquito recruitment, λ, relative to the human population so that, m = λ/g, vectorial capacity can be rewritten [48 (link)] as:
Temperature can influence all of the terms in this equation. Temperature affects feeding rates, a for example, via effects on vector activity and blood meal digestion [49 -51 ]. Larval ecology and, thus, adult recruitment, λ, are affected by temperatures found in aquatic habitats which play a role in modulating larval development rates and survival [33 (link),34 (link),52 (link),53 ]. Other work has demonstrated how these factors alone can impose limits on habitat suitability for particular anopheline species [53 ]. Adult mosquito recruitment is, however, also driven by a myriad of other climatic and local environmental factors, in particular those associated with the often transitory availability of aquatic oviposition sites. Here we focus on the more pronounced and directly measurable effects of temperature on vectorial capacity: the interaction between vector lifespan, determined by, g and the duration of sporogony, a. Holding a and λ constant, then, we can modify equation (2) to obtain an expression as a function of temperature, T:
Since a and λ are unknown, vectorial capacity cannot be evaluated directly, so we define instead an index of temperature suitability Z(T) that is linearly proportional to V(T) and therefore sufficient for exploring the relative, rather than absolute, effect of temperature on vectorial capacity and, thus, on R ₀ . The index Z(T) can be interpreted as a relative measure of the number of infectious mosquitoes supported in an environment with temperature T, given a constant emergence rate λ. All other things being equal, an environment with, say Z(T), a value of 100 would support twice the vectorial capacity or, equivalently, require half as many vectors to support the same vectorial capacity as one with a Z(T) value of 50. Locations in which Z(T) is zero indicate that no vectors survive long enough to accumulate sufficient degree days for sporogony.

Having determined the relative polarity, the necessary step for combining is finding the relative φ rotation (rotation around the symmetry axis) between individual microtubules. This could be done by aligning each individual particle to a common reference, but would result in a large number of errors due to the low signal to noise ratio. We developed a method analogous to that of Zabeo et al.,^{25 (link)} where the microtubule average volumes are aligned together in order to find their relative φ rotation (Fig. S9 step 4). These φ rotations were then applied to their respective particles and aligned to a common reference. SVA was subsequently performed with volumes binned 4 and 2 times. Only sporozoite data were aligned with unbinned volumes; the final step was to replace volumes reconstructed with the whole sets of tilts by volumes reconstructed with tilts between ±24°. No rotation search was performed with the restricted tilt range. The resulting C1 EM map was anisotropic around the pseudosymmetry axis due to an uneven distribution of microtubule rotational orientations. To address this, particles were separated into classes by orientation and particles with the lowest cross correlation coefficients in the most abundant classes were removed. This reduced the number of particles from 24028 to 13263 in sporozoite and 8377 to 1851 in ookinete datasets.

SPMT doublets were processed in a manner analogous to ookinete and sporozoite data, where average volumes were used to determine relative φ rotations. SPMTs with different numbers of protofilaments in A and B tubules were combined together, resulting in an ensemble average volume.