Mitochondrial DNA is critical for longevity and metabolism of transmission stage Trypanosoma brucei

The sleeping sickness parasite Trypanosoma brucei has a complex life cycle, alternating between a mammalian host and the tsetse fly vector. A tightly controlled developmental programme ensures parasite transmission between hosts as well as survival within them and involves strict regulation of mitochondrial activities. In the glucose-rich bloodstream, the replicative ‘slender’ stage is thought to produce ATP exclusively via glycolysis and uses the mitochondrial F1FO-ATP synthase as an ATP hydrolysis-driven proton pump to generate the mitochondrial membrane potential (ΔΨm). The ‘procyclic’ stage in the glucose-poor tsetse midgut depends on mitochondrial catabolism of amino acids for energy production, which involves oxidative phosphorylation with ATP production via the F1FO-ATP synthase. Both modes of the F1FO enzyme critically depend on FO subunit a, which is encoded in the parasite’s mitochondrial DNA (kinetoplast or kDNA). Comparatively little is known about mitochondrial function and the role of kDNA in non-replicative ‘stumpy’ bloodstream forms, a developmental stage essential for disease transmission. Here we show that the L262P mutation in the nuclear-encoded F1 subunit γ that permits survival of ‘slender’ bloodstream forms lacking kDNA (‘akinetoplastic’ forms), via FO-independent generation of ΔΨm, also permits their differentiation into stumpy forms. However, these akinetoplastic stumpy cells lack a ΔΨm and have a reduced lifespan in vitro and in mice, which significantly alters the within-host dynamics of the parasite. We further show that generation of ΔΨm in stumpy parasites and their ability to use α-ketoglutarate to sustain viability depend on F1-ATPase activity. Surprisingly, however, loss of ΔΨm does not reduce stumpy life span. We conclude that the L262P γ subunit mutation does not enable FO-independent generation of ΔΨm in stumpy cells, most likely as a consequence of mitochondrial ATP production in these cells. In addition, kDNA-encoded genes other than FO subunit a are important for stumpy form viability.


Introduction
The parasitic protist Trypanosoma brucei undergoes a complex life cycle involving stages within the mammalian bloodstream and its tsetse fly vector. In the bloodstream of the mammalian host, the cell population exhibits two major morphotypes: the proliferative long slender bloodstream form (BSF) and the cell cycle-arrested stumpy form. Differentiation from the slender BSF to the stumpy form is triggered upon high slender parasite numbers [1]. The emergence of cell cycle-arrested stumpy forms prevents parasitaemia increasing further, prolonging host survival, and results in the characteristic waves of parasitaemia seen in bloodstream infections in rodents. This density dependent differentiation has been shown to be induced by a stumpy induction factor (SIF) via a form of quorum sensing [2].
The stumpy form is insect-transmissible and is preadapted to survive within the low glucose environment of the tsetse fly midgut, where it differentiates to the procyclic (PCF) tsetse midgut form of the parasite. PCF are able to generate ATP using mitochondrial energy production pathways, involving both oxidative and substrate-level phosphorylation [3][4][5][6]. In contrast, ATP production in the slender BSF is thought to solely involve non-mitochondrial glycolysis, utilising the glucose-rich environment found within the mammalian bloodstream [7,8]. Comparatively little is known about the metabolic requirements of stumpy forms, but studies have demonstrated an increase in the abundance of many mitochondrial proteins in the stumpy life cycle form compared to the slender BSF, including subunits of the mitochondrial respiratory complexes and key mitochondrial metabolic enzyme activities such as pyruvate dehydrogenase, α-ketoglutarate (α-KG) dehydrogenase, acetate:succinate CoA-transferase (ASCT) and succinyl-CoA synthetase (SCoAS) [9][10][11][12]. Accordingly, stumpy forms can utilise both glucose and α-KG as carbon sources for mitochondrial substrate level phosphorylation, at least in vitro [9,10,13]. Cytochromes have not been detected in stumpy forms [10], but the presence of an abbreviated oxidative phosphorylation pathway consisting of respiratory complexes I (cI; NADH:ubiquinone oxidoreductase) and V (F 1 F O -ATP synthase) and the trypanosome alternative oxidase (AOX) has been proposed [14].
The single mitochondrion of T. brucei contains a complex genome, termed kinetoplast DNA or kDNA and comprising of maxicircles and minicircles [15]. The maxicircle line EATRO 1125 (AnTat1.1 90:13) [34] (generating cell line WT/L262Pγ; see Table 1 for a list of cell lines used in this study). This mutation fully compensates for the requirement for kDNA in slender bloodstream form T. brucei [16]. We introduced a wild type version (WTγ) into the same parental cell line to generate an otherwise isogenic control (WT/WTγ). We generated two cell lines lacking kDNA (kDNA 0 #1 and #2) from two distinct clones of genotype WT/L262Pγ (#1 and #2) by treatment with acriflavine [16]; we obtained a third WT/L262Pγ (kDNA 0 ) cell line (#3) fortuitously after spontaneous loss of kDNA. We confirmed absence of kDNA in all three cell lines by PCR and microscopically (S1A and S1B Fig). In vitro, WT/ L262Pγ kDNA + and kDNA 0 cell lines grew at the same rate as the WT/WTγ cell line, showing that both modifications had no effect on the viability of the cells under these conditions (S1C Fig). As expected, cells expressing an L262Pγ allele, regardless of the presence of kDNA, were resistant to 10 nM EtBr [33], unlike cells expressing solely WTγ, which died within 4-5 days of treatment (S1C Fig).
To test the capacity for differentiation to stumpy forms, we infected mice of strain MF1 with cell lines WT/WTγ, WT/L262Pγ #2 and WT/L262Pγ (kDNA 0 #1 and #2) via IP injection. Accurate measures of parasitaemia level and morphology during the first peak of infection were recorded over time for each cell line in four replicate infections. Parasites that were morphologically stumpy were seen in all infections as they progressed (Fig 1A, days [7][8] and were found to express the stumpy-specific protein PAD1 [35] (Fig 1B). This demonstrated that kDNA 0 populations were capable of generating stumpy forms.

Lack of kDNA reduces persistence of stumpy parasites in vivo
We next carried out a detailed comparison between cell lines in terms of the efficiency of the slender to stumpy transition, and the length of time that the parasitaemia was maintained, to judge the effect of kDNA loss on the in vivo dynamics of a mouse infection.
Cell lines WT/WTγ and WT/L262Pγ had first peaks of parasitaemia that were very similar to each other (Fig 2A-2E) and to published data [36]. In contrast, we observed three main differences for the kDNA 0 cell lines: (i) a delayed rise in parasitaemia (Fig 2A-2C); (ii) a more rapid decline in parasitaemia once peak density had been reached (Fig 2A); and (iii) absence of a smaller, second peak in slender form parasitaemia evident in kDNA + cells on days 7-8 post infection (Fig 2D).
Both kDNA 0 clones showed a delayed rise in cell numbers (Fig 2A, days [3][4][5][6], at least in part caused by a slower growth rate up to day 4 ( Fig 2B and 2C), suggesting that a lack of kDNA affects the parasite's ability to proliferate in vivo and/or to persist during the transitions they  (Fig 2F-2H). Here, no consistent differences were observed between kDNA 0 and kDNA + cells. At peak parasitaemia, populations of all cell lines consisted of 80-90% stumpy cells, again demonstrating that kDNA is not required for the differentiation of T. brucei from slender to stumpy forms. Although differentiation of kDNA 0 cell line #1 was delayed by approximately half a day, this was not the case for the other kDNA 0 cell line and therefore unlikely to be a consequence of kDNA loss. The slower growth (and therefore the delayed rise) of these cells could therefore be due to longer cell-cycle times or an increased death rate.
Having reached maximum parasitaemia, total cell numbers for kDNA 0 parasites declined more rapidly than for kDNA + parasites (Fig 2A, days 6-9). When we assessed stumpy form densities, it was evident that kDNA 0 stumpy cells maintained high densities for a shorter period of time than kDNA + stumpy cells (Fig 2E and 2I). To investigate this further, we assessed the lifespan of stumpy forms in vitro. In this experiment we included a third kDNA 0 cell line (#3) that had lost its kDNA spontaneously to address the possibility that stumpy lifespan might have been affected by any non-kinetoplast related mutagenic effects of acriflavine. We harvested populations enriched for the stumpy form parasites from mice and incubated them in HMI-9 medium in the presence of the cytostatic agent α-difluoromethylornithine (DFMO); this prevents contaminating slender cells from proliferating [37][38][39]. We sampled cells every 8 h and determined numbers with a particle counter. We also stained cells with carboxyfluorescein diacetate succinimidyl ester (CFDA-SE) to analyse the proportion of dead cells over time. Consistent with what we observed in vivo (Fig 2I), cell numbers for kDNA 0 stumpy cells dropped more quickly for kDNA 0 than for kDNA + stumpy cells (Fig 3A), with kDNA 0 stumpy cells reaching a threshold of 50% dead cells 40-50 h earlier than the kDNA + populations ( Fig 3B). All kDNA 0 cell lines behaved in a very similar manner, confirming that the decrease in stumpy life span was not due to secondary mutations caused by acriflavine treatment.
Finally, kDNA + cells had a second peak in slender parasitaemia around days 7-8 ( Fig 2D). This second peak was absent in kDNA 0 cells. The presence of the second peak in slender density in kDNA + parasites was confirmed by quantifying the percentage of cells in G 2 phase of the cell cycle in samples taken across the time course, using flow cytometry (S2 Fig). In summary, our mouse infection data demonstrated differences in the within-host infection dynamics for T. brucei parasites with and without a kinetoplast. Most importantly, stumpy cells lacking kDNA had a reduced life span.

Optimisation of a mathematical model for T. brucei infections
Mathematical models allow complex biological systems to be deconstructed into individual components and parameters, and as such are suitable for quantitation, hypothesis generation and testing. We used an existing mathematical model for T. brucei infection dynamics [36] to interpret the experimentally obtained data presented in Fig 2 and to provide us with testable hypotheses as to the differences in the infection dynamics observed between kDNA + and kDNA 0 cells.
The cell types in this model are (i) non-committed replicating slender cells (i.e. slender cells not yet committed to stumpy formation), (ii) committed replicating slender cells, and (iii) non-proliferating differentiated cells, including both stumpy and intermediate cells (Fig 4A). harvested at peak parasitaemia (day 6). 2x10 6   We first compared two models: the published model, where the differentiation rate was proportional to SIF concentration [36], and a modified version of this model, where slender to stumpy differentiation rates are additionally influenced by a SIF-independent differentiation term [40]. The latter reflects a constant background level of slender form differentiation, independent of the concentration of SIF. Hence, each slender cell has a fixed probability of differentiating per cell cycle independently of SIF. The two terms are summed, with both terms acting to affect differentiation, with the SIF-dependent term only having a significant effect at high slender form concentrations due to the accumulation of high SIF levels. We inferred model parameter estimates (mean and confidence interval) by fitting both models to the data for all 16 mice using a Bayesian MC-MC method (S3 Fig).
We next assessed the fit of each model by residual analysis (Fig 4B and S4A Fig). In the model containing SIF-independent differentiation, there was a lower number of outlying residuals, with most within the 95% predictive interval more of the time than in the model containing only SIF-dependent differentiation. This difference was apparent for the slender proportion on day 4. The model with additional SIF-independent differentiation captured the drop in slender proportion from 100% to 90% by day 4 (Fig 4B; S3 Fig,    Schematic of the mathematical model. Slender cells can become committed to differentiation via a SIF dependent route, proportional to SIF concentration, and a SIF independent route. SIF is produced by both committed and non-committed slender forms, and is cleared over time. The concentration of each cell type depends on the replication rate (applicable to slender forms only), the immune clearance rate, the lifespan of that cell type and the differentiation rate (applicable to slender forms only). (B) Standardised residuals (blue circles) of parasite density and slender fraction, by time (dpi, days post infection), of the model fits with SIF-dependent and -independent differentiation to all mice. Under a true model standardised residuals have an approximately standard normal distribution (i.e., zero mean and unit standard deviation (SD)). Inadequate fit of a model is indicated by its residuals deviating from a standard normal distribution (such as residuals further than~3 SD from zero, represented by the lightest grey shading, or a set of residuals consistently above or below zero. The red line shows the average, across all mice, of the residuals at a particular time point. measures the quality of a fit of a mathematical model to a set of data, taking into account the goodness of fit and the number of parameters estimated in the model [41]. The models with and without SIF-independent differentiation had AIC values of 2659 and 3033, respectively, hence the former is preferred as it has the lower AIC. When we reanalysed the infection data from an earlier study [36] by including the additional SIF-independent term, that model was also preferred when mathematically assessed by the AIC (S4B Fig). In conclusion, the mathematical model for within-host infection dynamics of T. brucei provided a better fit to experimental data when it included an additional term for SIF-independent slender-to-stumpy differentiation. This is consistent with the recent identification of a quorum sensing-independent path to stumpy development in this parasite [42].

Infection dynamics as predicted from improved mathematical modelling
We next used the optimised mathematical model to identify and quantitate the parameters predicted to be responsible for these differences between kDNA + and kDNA 0 cell lines. This resulted in two key observations. First, infection with kDNA + parasites resulted in a broader peak of high cell density than infection with kDNA 0 parasites ( Fig 5A). The model predicts that the rise in parasitaemia levels off due to SIF-induced differentiation to the stumpy form: as slender forms proliferate, SIF begins to rise (S3 Fig, pink curves), which increases the rate of differentiation, and stumpy forms begin to emerge (S3 Fig, light orange curves). As the number of slender forms decrease, SIF concentration falls, causing the differentiation rate to fall. Stumpy cells disappear due to an intrinsically limited life span or immune clearance ( Fig  4A). The estimates for total committed lifespan of kDNA + and kDNA 0 cells were 72-77 h and 41-51 h, respectively ( Table 2). The total committed lifespan can be broken down into duration of the committed slender form and the duration of the stumpy form. Committed slender kDNA + cells were estimated to survive longer than kDNA 0 cells; they were predicted to have gone through at least one further cell cycle division than kDNA 0 cells before they entered cell cycle arrest as the intermediate form ( Table 2, 'Committed slender replications'). Stumpy forms with kDNA lived on average for 56-62 h, whereas for kDNA 0 cells the calculated average stumpy lifespan was predicted to be considerably lower, 36-49 h. Interestingly, the model predicted a clear difference between the immune responses to kDNA + and kDNA 0 stumpy cells. While the model estimated similar and consistent clearance rates for WT/WTγ and WT/L262Pγ stumpy cells, at~20% per hour (Table 2), it estimated that immune clearance was not required to explain the disappearance of kDNA 0 stumpy cells. We note that immune response against trypanosomes, although multifactorial, highly complex and incompletely understood, is represented by a simple step function in our model. There is insufficient data to support more realistic representations of the immune response. Nonetheless, our model fitted the experimental data very well and predicted that the narrower peak of high parasitaemia in kDNA 0 parasites (see Fig 5A) was largely due to accelerated cell death of stumpy cells lacking kDNA.
Second, in kDNA + cells, a second peak in parasitaemia emerged around day 7, when a reduced SIF concentration allowed slender cells to proliferate again ( Fig 5B). According to the model, the density fell again due to onset of immune killing (S3A and S3C Fig, yellow curves). Without immune killing the model predicts a continued rise in slender density to a much higher level. The absence of this second peak in kDNA 0 parasites ( Fig 5B)  In summary, an optimised mathematical model for within-host infection dynamics that included an additional SIF-independent parameter for slender-to-stumpy differentiation provided a very good fit to experimental data and captured experimentally observed differences between kDNA + and kDNA 0 parasites. A narrower peak of high parasitaemia in the latter was predicted to be largely due to accelerated cell death of stumpy forms lacking kDNA.

Absence of kDNA is associated with loss of ΔCm in stumpy forms
The shortened lifespan of kDNA 0 stumpy forms (Fig 2 and Fig 3) pointed to loss of critical mitochondrial functions. A hallmark of functional mitochondria is the presence of ΔCm. In BSF T. brucei ΔCm is primarily generated by ATP hydrolysis-driven proton pumping of the F 1 F O -ATPase, whereas PCF T. brucei generate ΔCm by proton pumping of respiratory complexes III and IV and, potentially, cI. It is not clear how the ΔCm is generated in stumpy forms, although it has been reported to be sensitive to cI inhibitors but insensitive to the F 1 F O -ATPase inhibitor oligomycin [14].
To explore the role of kDNA in maintaining ΔCm in stumpy forms, we harvested parasites from all five cell lines (WT/WTγ, WT/L262Pγ, and the three WT/L262Pγ kDNA 0 cell lines) from infected mice at maximum parasitaemia, with a proportion of approximately 90% stumpy cells (S5A Fig), and stained them with the ΔCm probe tetramethylrhodamine ethyl ester (TMRE) under various experimental conditions. First, we assessed ΔCm in WT/WTγ cells in the presence or absence of azide, a specific inhibitor of the F 1 moiety that disrupts ΔCm production in slender BSF cells and kills these cells in 36-48 h [23]. Treatment with 0.1-2 mM azide completely abolished ΔCm (Fig 6A), indicating that F 1 has an essential role in generating the ΔCm in the stumpy form. Although treatment with 0.5 mM azide eliminated ΔCm, it did not reduce the viability of stumpy forms: in the absence of azide, the percentage of dead cells in the population increased from 0.4% to 17.2% after 24 h, and to 25.3% after 48 h, and these percentages were not significantly increased in the presence of azide (  The role of the F 1 ATPase in generating ΔCm could be direct, as described above, or indirect, as in slender BSF kDNA 0 cells. In the latter, the ATP/ADP carrier (AAC) acts to generate ΔCm via the electrogenic exchange of matrix ADP 3for cytosolic ATP 4-. F 1 acts independently of F O by hydrolysing ATP 4to maintain an ATP/ADP ratio across the inner mitochondrial membrane that can sustain AAC activity [16,23]. We investigated whether this F O -independent pathway can function in stumpy forms by assessing ΔCm in WT/L262Pγ (kDNA 0 ) cells purified from mice. Live, freshly isolated kDNA 0 stumpy cells were found to not have a ΔCm (Fig 6C), demonstrating that the kDNA-encoded a subunit of the F o -proton pore is required for ΔCm generation and that this requirement cannot be circumvented by the L262Pγ mutation. Hence, the alternative, F O -independent mechanism of ΔCm generation that functions in kDNA 0 slender T. brucei and in subspecies T. b. evansi and T. b. equiperdum cannot operate in stumpy forms.

kDNA 0 stumpy forms cannot use α-KG to sustain viability
The stumpy life cycle stage is preadapted to differentiation to the PCF in the midgut of the tsetse fly. Stumpy forms can use glycolysis or, alternatively, mitochondrial catabolism of α-KG as energy sources [9,10,13], which reflects the shift in metabolism towards the glucose-deficient environment of the tsetse midgut.
We assessed the ability of kDNA 0 stumpy forms to survive in the presence of glucose or α-KG. Although kDNA 0 stumpy forms in the presence of glucose showed normal viability after 24 h, more than 70% of cells had died after 24 h of incubation with α-KG as sole major carbon source (Fig 7A). When α-KG was provided in addition to glucose it had little, if any, detrimental effects on kDNA 0 cells (S5D Fig). The addition of N-acetyl glucosamine (GlcNAc), a nonmetabolized glucose analog, to prevent uptake of residual glucose present in fetal calf serum  [43] further reduced the number of surviving cells (Fig 7A). The viability of kDNA + control cells was comparable for medium with α-KG vs. glucose as main carbon source, and addition of GlcNAc to medium with α-KG had no negative effects on WT/WTγ cells (S5D Fig), confirming that GlcNAc only interferes with glucose-based energy metabolism. These results demonstrate that, unlike kDNA + stumpy forms, kDNA 0 parasites are unable to use α-KG to sustain viability. Interestingly, stumpy WT/WTγ cells treated with azide to inhibit generation of a ΔCm died within 24 h if α-KG was the sole carbon source, but azide had little effect in the presence of glucose (Fig 7B), indicating that ΔCm may be required for the entry of α-KG into the mitochondrion or for efficient export of mitochondrially produced ATP.
In summary, these experiments suggest that the lack of a ΔCm in stumpy cells without kDNA precludes the use of α-KG to satisfy the energy needs of these cells.

Discussion
The mitochondrion plays essential roles in the life cycle and the cell cycle of T. brucei and is an important target for existing anti-trypanosomatid chemotherapies, but our knowledge of its precise functions in each of the life cycle stages and how these are regulated is far from complete [44]. One gap in knowledge concerns mitochondrial biology, and in particular the role of kDNA-encoded proteins in the so-called stumpy stage, which dominates within-host dynamics and is critical for transmission to the tsetse fly vector [36].
To provide insight into these questions we have introduced a subunit γ allele with the L262P mutation ('L262Pγ') into a pleomorphic (i.e. differentiation competent) T. brucei brucei cell line by in situ replacement of one of the endogenous alleles. This mutation enables slender BSF T. brucei to proliferate without kDNA in vitro and in vivo [16]. From such heterozygous WT/L262Pγ cell lines we obtained kDNA 0 mutants by acriflavine exposure or through accidental loss of the kinetoplast. We then studied within-host dynamics in a mouse model, interpreted the data with the help of mathematical modelling and investigated the molecular basis for the observed phenotypes with cell physiological assays. Our study shows that parasite kDNA is critical for full viability of the transmissible stumpy stage and suggests a model for mitochondrial energy metabolism in these forms (Fig 8).

Slender BSF T. brucei lacking kDNA can differentiate into stumpy forms
Our mouse infections with cell lines with the genotypes WT/WTγ, WT/L262Pγ and WT/ L262Pγ (kDNA 0 ) and quantification of within-host dynamics using mathematical modelling Schematic representation of key functions we propose to be involved in energy metabolism of stumpy form T. brucei, based on data presented in this work and in earlier studies, as cited in the text. Note that energy metabolism in other compartments such as adipose tissue or skin will very likely be different. Transporters in the inner mitochondrial membrane are shown as coloured squares (MPC, mitochondrial pyruvate carrier; KGC, α-KG carrier; AAC, ATP/ ADP carrier). A two-subunit mitochondrial pyruvate carrier, MPC1/2, presumably driven by proton symport, has been identified in T. brucei, but functional studies concluded that at least one additional mitochondrial pyruvate transporter must be present [74], indicated here by a yellow square with a question mark. Enzymes or enzyme complexes associated with the inner membrane are shown as coloured circles (cI, NADH:ubiquinone oxidoreductase; cV, F 1 F O -ATPase, or respiratory complex V; G3P-DH, glycerol-3-phosphate dehydrogenase; AOX, alternative oxidase; NDH2, type 2 NADH dehydrogenase). Functions that directly depend on kDNA-encoded proteins are indicated by red letters and arrows. Key metabolic reactions in the mitochondrial matrix are indicated by numbers in circles: 1, pyruvate dehydrogenase; 2, acetyl-CoA thioesterase; 3, ASCT; 4, SCoAS; 5, α-KG dehydrogenase complex; 6, L-alanine aminotransferase (co-substrate glutamate and co-product alanine omitted for simplicity). Other abbreviations: UQ, ubiquinone; G3P, glycerol-3-phosphate; DHAP, dihydroxyacetone phosphate; ACoA, acetyl-CoA; SucCoA, succinyl-CoA).
https://doi.org/10.1371/journal.ppat.1007195.g008 mtDNA function in stumpy form Trypanosoma brucei showed that lack of kDNA did not affect the rate of differentiation into stumpy forms. The morphological changes we observed during slender to stumpy differentiation were similar for kDNA + and kDNA 0 cells. These results confirm conclusions from an earlier study that had investigated differentiation of kDNA-depleted T. brucei cells obtained by treatment with acriflavine for 24 h [18], but that study could not rule out that some kDNA-encoded factors had persisted after treatment.
As kDNA 0 slender BSF T. brucei are able to transition to the stumpy form as efficiently as cells that have their kDNA intact, we conclude that the absence of kDNA is not the primary reason why the dyskinetoplastic subspecies T. b. evansi and T. b. equiperdum are generally monomorphic [29,31]. A different molecular mechanism must therefore prevent naturally occurring kDNA 0 or kDNA -T. brucei subspecies from differentiating to the stumpy life cycle form, such as loss of function in components of the SIF secretion or stumpy induction pathways [1], in a fashion similar to monomorphic T. b. brucei BSF forms [2]. SIF-dependent differentiation to the stumpy form places a limit on the parasitaemia level, presumably in part to extend the lifespan of the host [1]. As the probability of mechanical transmission of trypanosomes increases with the levels of parasitaemia in the blood [45], preventing slender to stumpy differentiation could thus have been a key event in the evolution of T. b. evansi, as has been discussed elsewhere [46,47]. Genome sequences from a number of T. b. evansi isolates are now available [26,48] and could be mined for candidate mutations in differentiation pathways.
A few T. b. evansi strains have historically been reported to have some limited capacity to produce stumpy forms (for example [30]); this could be due to SIF-independent background differentiation or residual and inefficient SIF-dependent differentiation. We found that a mathematical model including SIF-independent differentiation provided a better fit to the experimental data from both the current study and a previous infection study [36] than a model only including SIF-dependent differentiation. A recent study provided biological evidence for SIF-independent differentiation in trypanosome infections [42] and there is emerging evidence for a background level of random differentiation in Plasmodium and Theileria infections [49][50][51]. Thus, our study supports the view that stochastic, low level differentiation events occurring in parallel to a signal transduction-type of differentiation could be a more broadly conserved aspect of infections with protist parasites.

Loss of kDNA affects within-host infection dynamics of T. brucei
Although kDNA 0 T. brucei differentiated into stumpy forms with the same efficiency as control cells, we observed some important differences in other aspects of their within-host dynamics. Firstly, kDNA 0 cells showed a slightly lower growth rate up to day 4 of infection, resulting in a delayed rise in cell numbers leading up to the first peak of parasitaemia. In contrast, growth rates of kDNA 0 and kDNA + parasites were very similar when cultured in rich medium in vitro. Potential explanations are that kDNA 0 parasites are more affected by the more limiting growth conditions in the host environment, or that they are more sensitive to attack by the host's immune system, or both. Our mathematical model predicts that the immune response does not significantly affect infection dynamics until day 6 or 7 (although there appear to be differences for kDNA 0 vs. kDNA + parasites, see below), but as the action of the immune system during a trypanosome infection is not fully understood, our modelling of this aspect is necessarily an oversimplification. Understanding these differences will require further investigation, for example by comparing growth rates in minimal medium [52] and by investigating infection dynamics in immunosuppressed mice.
Secondly, a second peak in slender parasitaemia was evident in kDNA + cells around days 7-8 post infection, but completely absent in kDNA 0 cells. According to the mathematical model, this second slender peak in infections with kDNA + cells was due to SIF-dependent differentiation causing slender density, and therefore SIF density, to fall around day 6, allowing the remaining slender cells to begin proliferation rather than entering cell cycle arrest. A strong immune response around day 8 then prevented a further rise in parasitaemia. The model predicts that an earlier onset of immune killing in infections with kDNA 0 cells was responsible for completely suppressing this second peak in these parasites. This surprising result requires further investigation; we speculate that kDNA 0 cells could be less efficient at VSG switching or production, allowing more efficient clearance of slender cells in the earlier stage of the infection. Alternatively, kDNA 0 cells could be less able to access potentially immune privileged body compartments [53,54], or they could swim more slowly or in a different way, preventing the efficient clearance of antibody that is mediated by swimming [55].
Finally, and most importantly, we observed a substantially shorter lifespan of kDNA 0 stumpy forms. For kDNA + T. brucei we determined an average value for 'duration of stumpy form' of 56-62 h. This is in good agreement with other reports using a mouse infection model [36,38]. There are no reports on stumpy cell lifespan in other hosts, or how it might be affected by parasite distribution in different tissues [53], but our in vitro survival assay showed that >90% of kDNA + stumpy cells had perished 70 h after isolation from a mouse, i.e. within a time span comparable to the one observed in vivo. In marked contrast, we determined substantially shorter lifespans for kDNA 0 stumpy cells, both in vivo (duration of stumpy forms 36-49 h) as well as in vitro. This indicated that the underlying cause was intrinsic to the parasites, rather than due to faster immune clearance.

Differences in mitochondrial physiology of stumpy stage T. brucei with and without kDNA
The mechanism of cell death in stumpy forms is not understood, but an early event in programmed cell death in other organisms can be loss of ΔCm [56][57][58]. Furthermore, ΔCm is a key indicator of mitochondrial health [59], it is essential for mitochondrial protein import and other transport processes [60], and its generation in both BSF and PCF T. brucei depends on kDNA-encoded proteins [23,44].
In the present study we show that the F 1 -ATPase inhibitor azide completely abolished ΔCm in kDNA + stumpy cells, suggesting its generation by the F 1 F O -ATP synthase functioning as a proton pump, as in slender BSF cells [20,21,23,24]. We propose that the switch in directionality of this enzyme from ATPase to ATP synthase activity occurs during the transition from stumpy BSF parasites to PCF parasites. This is also consistent with the increase of the IF1 protein during that transition measured in a recent proteomics study [61]. IF1 (Tb927.10.2970) is a specific inhibitor of the ATP hydrolase activity of the F 1 F O -ATP synthase [62] and shows strict developmental regulation in T. brucei, with repression in slender BSF and expression in PCF [63].
An earlier study had reported that ΔCm in stumpy forms was sensitive to the cI inhibitor rotenone but insensitive to the F 1 F O -ATP synthase inhibitor oligomycin [14]; the authors of that study had concluded that cI generates ΔCm in stumpy forms, with the F 1 F O -ATP synthase acting in ATP synthesis mode, driven by the proton motive force. One possible explanation for this apparent discrepancy is that the relatively high concentration of rotenone used in the earlier study had caused non-specific effects, as has been argued by others [64]. Future studies with genetic mutants for specific subunits of cI and the F1F O -ATP synthase in a pleomorphic T. brucei strain will be required to investigate this apparent discrepancy further.
We did not detect a ΔCm in kDNA 0 stumpy cells, indicating that the alternative, F O -independent mechanism for generating ΔCm enabled by the L262Pγ mutation in slender T. brucei [16] cannot operate in the stumpy life cycle stage. This alternative mechanism depends on electrogenic exchange of matrix ADP 3for cytosolic ATP 4by the AAC and continued ATP hydrolysis by F 1 , perhaps in vicinity of the AAC, to maintain a suitable ATP/ADP ratio across the inner mitochondrial membrane [16,23,65]. Significant mitochondrial ATP production would be expected to thwart this mechanism, and indeed there is evidence for this occurring in stumpy form T. brucei [10,[12][13][14]. Conceivably this could occur via F 1 F O -ATP synthase activity, as mentioned above, or, more consistent with our data, via substrate level phosphorylation involving SCoAS and, depending on the carbon source, ASCT [3,66,67]. Pyruvate from glycolysis can be catabolised by stumpy cells to acetate, with ATP production via the ASCT / SCoAS cycle (Fig 8) [12]. It was also demonstrated that motility of stumpy cells, but not of slender BSF cells, can be sustained in vitro with α-KG as sole carbon source [9], with mainly succinate as end product [10] and ATP production via SCoAS (Fig 8). A putative mitochondrial α-KG transporter, termed MCP12 (Tb927.10.12840), has been identified and functionally characterised in T. brucei [68,69], and a proteomics study reported~20-fold upregulation of this protein in stumpy cells compared to slender cells [61]. Potentially, pyruvate could be converted to α-KG via L-alanine aminotransferase (Fig 8), an enzyme expressed in BSF and PCF T. brucei [70]. This step would require glutamate as co-substrate, which could be obtained directly from the medium or via proline catabolism.
We confirmed that kDNA + stumpy cells maintain viability for at least 24 h when incubated in minimal medium supplemented with glucose or α-KG. Nearly 100% of kDNA 0 stumpy cells survived for at least 24 h when medium was supplemented with glucose, but the survival rate dropped to~20% when provided with α-KG instead of glucose, and suppressing uptake of residual glucose with GlcNAc resulted in a further drop to less than 10% survivors. We also found that azide, which abolished ΔCm in kDNA + stumpy cells, prevented survival of these cells in minimal medium supplemented with α-KG, while it did not affect survival in the presence of glucose. At least two scenarios that are not mutually exclusive could explain these results. Firstly, ΔCm could be required for mitochondrial uptake of α-KG. The transporter identified in T. brucei was proposed to be an α-KG/malate antiporter [69], analogous to the mammalian enzyme, although this has not yet been confirmed experimentally. In that case α-KG import would not be directly dependent on ΔCm. The E. coli enzyme is an α-KG/proton symporter that depends on a proton motive force [71], but its closest homolog in T. brucei is a myo-inositol/proton symporter in the Golgi [72]. Secondly, α-KG import could be ΔCm-independent and still drive mitochondrial substrate phosphorylation in the absence of kDNA or presence of azide (Fig 8), but in the absence of ΔCm, ATP may not reach the cytosol in sufficient quantities to sustain viability: ATP 4-/ADP 3exchange by the AAC is driven by the concentration gradient of the substrates as well as ΔCm [73,74]. Resolving which of these scenarios, if any, is correct will require further experimental evidence.
In summary, these experiments demonstrate clear differences in physiology and metabolic capacity of stumpy cells with and without kDNA.

What defects in mitochondrial function cause the reduced lifespan of stumpy forms lacking kDNA?
Although we found clear evidence for deficiencies in mitochondrial function in kDNA 0 stumpy cells, correlating any of these deficiencies to the reduced lifespan was not straightforward. The most prominent defect of kDNA 0 stumpy cells that we identified in this study was lack of a ΔCm. However, the ability of stumpy cells lacking a ΔCm (i.e. kDNA 0 cells or kDNA + cells in the presence of azide) to survive for at least 48 h in medium provided with glucose suggests that sufficient amounts of ATP can be produced via glycolysis in the absence of a ΔCm, at least in the short term. In the long term, ΔCm-dependent mitochondrial transport processes such as continued import of the alternative oxidase, are vital for sustained glycolysis in proliferating parasites [7], but this may be less relevant for cell-cycle arrested stumpy forms with their intrinsically limited life span. If loss of ΔCm does not affect viability of kDNA + stumpy cells, what is the cause of the reduced lifespan in kDNA 0 stumpy cells? One possibility is an impaired redox balance in the mitochondrial matrix caused by loss of kDNA. At least seven subunits of cI are kDNA-encoded [75], and therefore kDNA 0 cells will be cI-deficient. Activity of this enzyme is dispensable for slender BSF, at least in vitro and in the bloodstream [75], probably in part due to the presence of an alternative type 2 NADH dehydrogenase [76]. Differentiation into stumpy cells has long been known to be associated with a dramatic increase in 'NAD diaphorase' activity [9] (an assay for NADH dehydrogenase activity), and we note that both pathways for mitochondrial substrate phosphorylation are dependent on recycling of NADH (Fig 8).

Conclusions and outlook
Our study shows that kDNA in the sleeping sickness parasite T. brucei is not required for differentiation into the transmissible stumpy stage, but that it is critical for the longevity of this stage and for generation of its ΔCm. We identified three important differences to slender BSF T. brucei: (i) a L262P mutation in the nuclear-encoded ATPase subunit γ does not enable kDNA-independent generation of ΔCm, most likely because of considerable mitochondrial ATP production; (ii) loss of ΔCm does not affect the life span of stumpy T. brucei, presumably because life span is limited by other factors that come into play before loss of ΔCm-dependent processes can take their toll; and (iii) stumpy form viability depends on kDNA-encoded genes other than F O subunit a. Future studies should, for example, assess the consequences of loss of function of respiratory complex I and the F 1 F O -ATP synthase on stumpy cell viability with specific genetic mutants and seek to identify the intrinsic factors that limit stumpy cell life span.
The ATPase γ subunit gene was amplified from genomic DNA via PCR, allowing direct Sanger sequencing of the gel-extracted PCR product to confirm the presence or absence of the L262Pγ mutation using primers 5'-CGG CGG CCG CAT GTC AGG TAA ACT TCG TCT TTA CAA AG-3' (forward) and 5'-ATA GGA TCC CTA CTT GGT TAC TGC CCC TTC CCA G-3' (reverse).

Generation of kDNA 0 cell lines
WT/L262Pγ cells were treated with 10 nM acriflavine (Sigma) over 3 days; loss of kDNA was assessed by preparing microscope slides and mounting with a cover slip using 50 μl Prolong Gold Antifade with 4', 6-diamidino-2-phenylindole (DAPI; Life Tech.). To confirm loss of maxicircle genes and of a representative minicircle (type A-like) [16,80] by PCR, total DNA was extracted after expanding the cell culture for a further two days in the absence of acriflavine. The PCR assay was carried out exactly as described in Dean et al. (2013).

Growth analysis of T. brucei cell lines in vitro
Cells were grown in the presence or absence of 10 nM ethidium bromide (EtBr; Sigma). Cell counts were performed daily using a Beckmann Z2 Coulter counter, and cultures were split to a concentration of 1x10 5 /ml after counting.

Ethics statement
All animal experiments were carried out in adult MF1 mice after local ethical approval at the University of Edinburgh. All animal experiments were carried out by Caroline Dewar, working under personal license I3997C068 and project licences 60/4373 (Professor Keith Matthews) and 70/8734 (Professor Achim Schnaufer), granted by the UK Home Office under the Animals (Scientific Procedures) Act 1986, section 5.

Mouse infections with T. brucei
Sex-and age-matched MF1 mice were infected with T. brucei EATRO 1125 AnTat1.1 90:13 cells (suspended in 200 μl HMI-9) via intraperitoneal (IP) injection. No immunosuppressant was used. Parasitaemia was monitored by obtaining blood via a tail snip, compressing a drop of blood under a cover slip on a microscope slide, and counting parasites at 400x magnification. Five μl blood was also taken for an immunofluorescence assay and cell cycle analysis. Morphology counts were performed as described [36]. Methanol-fixed blood smear slides were blinded by a colleague with respect to cell line, day and time point to prevent bias. Morphology was scored from these slides independently by two individuals.
Parasitaemia was judged by eye, based on the Rapid Matching method [36,81]. This method entails an upper limit of 64 parasites per field of view, correlating to a density of 2.5x10 8 cells/ ml, above which it becomes difficult to estimate counts accurately.

Mathematical model for T. brucei infection dynamics
A mathematical model described previously [36] was modified to include a parameter for SIFindependent slender to stumpy differentiation.
The model was constructed as follows. Let the concentration of non-committed slender cells at time t be L(t). The initial infection is at time t = 0. Non-committed slender cells replicate at rate α (i.e., a cell-cycle time of ln (2)/α)). They are cleared by a time-dependent immune response at rate r L (t). They become committed to differentiate at rate β b + β f f(t), where f(t) is SIF concentration, β b is the background, SIF independent differentiation rate and β f is the SIF dependent differentiation rate. Therefore, the differential equation that describes the dynamics of non-committed slender forms is: Let the age of differentiated cells since becoming committed to differentiation be a and let d (a,t) be the age density distribution of differentiated cells at time t.
Differentiated cells fall into two classes: i) replicating, committed slender cells, and ii) nonreplicating stumpy cells. Committed slender cells replicate at rate α, are assumed to be cleared by the immune system at the same rate as non-committed slender cells (r L (t)), and develop into stumpy cells at age τ C . Stumpy cells do not replicate, they are assumed to be cleared by the immune response at a different rate r S (t), and they die at age τ S . Thus, the partial differential equation that describes the dynamics of the age density distribution of committed cells is The boundary conditions on these equations are determined by differentiation of non-committed slender cells into age a = 0, i.e., d(0,t) = [β b + β f f(t)]L(t), and stumpy death at age τ S , i.e., d(τ S ,t) = 0.
Let C(t) be the total concentration of committed slender cells, let S(t) be the total concentration of stumpy cells, and let T(t) be the total concentration of all cells. These are given by: TðtÞ ¼ LðtÞ þ CðtÞ þ SðtÞ SIF is produced by both non-committed and committed slender cells. SIF is removed at rate γ. Therefore, the differential equation describing the dynamics of SIF concentration is: Note that, because SIF is not measured, its concentration is on a dimensionless scale. The immune response against trypanosomes is multifactorial and highly complex, and only qualitatively understood at best. A detailed mathematical model of the immune response was, therefore, of little use when no data were available to fit to. Instead, we used a simple step function to represent an immune response switching from an inactive to an active state at a time T post infection. The strengths of the immune responses against slender and stumpy cells are assumed to be different. They are given by the equations ( mtDNA function in stumpy form Trypanosoma brucei and where ϕ L is the removal rate of slender cells and ϕ S is the removal rate of stumpy cells. Naive mice are infected with non-committed slender cells at a concentration L 0 . Therefore the initial conditions are L(0) = L 0 , d(a,0) = 0 for all a and f(0) = 0. These imply C(0) = S(0) = T (0) = 0. All variables and parameters are listed in Table 3.
For particular numerical values of the model parameters, the model was solved numerically for each mouse. In order to quantify the fit of the model with these parameters to the data, the log-likelihood of the model solution at each data point by was calculated. Parasite density was estimated by observing a field of cells and estimating the number of parasites in the field. Due to the difficulty of observing many moving parasites in a microscopic field, density estimates were categorised into 0, 1, 2, 3, 4, 5, 6,8,10,12,16,20,24,32,48,64, and 92 parasites per field. Parameter r t i describes the expected density of parasites at time t i (which is obtained from the model). The volume of blood v, in a microscopic field is v = 25.6 × 10 −8 μl. The expected number of parasites per field therefore is l ¼ vr t i . The number of parasites N in a field is Poisson distributed with parameter λ. If N equals 0 to 5 then the likelihood of r t i is equal to l N e À l N! . If N is greater than 5 then it can be assumed that the number of parasites lies within a range. The start of the range is the midpoint between the previous category and the assigned category. For example, if the number of parasites in a field is estimated to be about 48 parasites, then the assigned category is 48, the start of the range is N l = (32 + 48)/2 = 40 parasites. Similarly, the end of the range is the midpoint between the next category and the assigned category, for example N u = (48 + 64)/2 = 56. The likelihood of r t i is then equal to P N h i¼N l l i e À l i! which equals Q (N h ,λ) − Q(N l ,λ) where Q is the normalised incomplete Gamma function.
The likelihood function also includes the proportion of parasites that are slender forms at a time t i . The number X of parasites that have slender morphology is binomially distributed with parameters M and p, where M is the number of parasites observed and p is the predicted proportion that are slender forms (obtained from the model). Thus, the likelihood of p t i is propor- The parameter posterior distribution was found by multiplying the likelihood, which is the product of likelihoods at each time point, by the prior distributions, which were taken from [36]. The prior on β b was N T (0.01, 0.01 2 ), a normal distribution truncated at 0. Samples from the posterior were drawn using an adaptive population based Markov chain Monte Carlo algorithm with power posteriors [83,84].

In vitro incubation of stumpy forms
Cells were harvested from a mouse infection during peak parasitaemia whilst the population was approximately 90% stumpy form. After purification from blood, parasites were washed in PBS-G (PBS, 6 mM glucose) and resuspended in either HMI-9 containing 10% (v/v) FCS or a modified minimal medium (CMM) [52] containing 10% (v/v) FCS and devoid of glucose. Supplements (25 mM glucose, 25 mM α-KG, 50 mM N-acetyl glucosamine, all from Sigma) were added as required.

Live/Dead staining
Cells were harvested from culture and washed in sterile warm PBS-G. The pellet was resuspended in PBS-G with 10 μM CFDA-SE (ThermoFisher), and incubated for 15 mins at 37˚C. Cells were washed with HMI-9 medium and incubated in HMI-9 for 30 mins at 37˚C. Cells were then washed, and fixed with 3.7% (v/v) formaldehyde for 10 min (a detailed paper on validating CFDA-SE staining as a live/dead assay compatible with fixation of cells will be published elsewhere). Fixative was washed out with PBS-G, and cells were resuspended in PBS-G plus 5 μg/ml Hoechst 33342 (Life Tech.). Samples were analysed with excitation peak of 492 nm and emission peak of 517 nm for CFDA-SE on a BD LSRII instrument.
For propidium iodide (PI) staining, 1 μl 500 ng/ml PI was added to the final resuspension before analysis. Samples were analysed at peak excitation at 488 nm and emission at 695 nm.

Measuring mitochondrial membrane potential (ΔCm)
The TMRE Mitochondrial Membrane Potential kit (Abcam) was used. All samples were supplemented with 100 nM TMRE and left at 37˚C for 20 min. Cells were preincubated with 20 μM carbonyl cyanide-4-(trifluoromethoxy)phenylhydrazone (FCCP) for 10 min or with 0.1-2 mM sodium azide for 2 h. Cells were pelleted, and washed in 0.2% BSA in PBS. Cell pellets were resuspended in 0.2% BSA in PBS containing 5 μg/ml Hoechst 33342 DNA staining dye before analysis on a BD LSRII instrument, with peak excitation at 549 nm and peak emission at 575 nm for TMRE.

Microscopy
Images were captured using a Retiga 2000R Mono Cooled charged-coupled device camera attached to an Axioscope 2 or Axioimager Z2 (Carl Zeiss MicroImaging, Inc.) using either Plan-Apochromat 63x (1.40 NA) or Plan-Apochromat 100x (1.40 NA) phase-contrast objectives. an approximately standard normal distribution (i.e., zero mean and unit standard deviation (SD)). Inadequate fit of a model is indicated by its residuals deviating from a standard normal distribution (such as residuals further than~3 SD from zero, represented by the lightest grey shading, or a set of residuals consistently above or below zero. The red line shows the average, across all mice, of the residuals at a particular time point. (B) Assessment of the quality of fit of the two alternative models to infection data from MacGregor et al., 2011, using the Akaike information criterion (AIC). The AIC measures the quality of a fit of mathematical model to a set of data, taking into account the goodness of fit and the number of parameters estimated in the model. As increasing the number of parameters improves the goodness of fit, AIC penalizes models with more estimated parameters to discourage overfitting. Hence the model with the lowest AIC, i.e. the model with the lowest number of parameters to prevent overfitting, is preferred.