This approach can assess the likelihood that a migrant animal originated from a given location(s) within a continent but requires a robust algorithm linking H isotopes in tissues of interest to an appropriate hydrological isotopic spatio-temporal pattern, such as weighted-annual rainfall. However, a number of factors contribute to or alter expected isotopic patterns in animals. We present results of an extensive investigation into taxonomic and environmental factors influencing feather δ2H patterns across North America.Tracking small migrant organisms worldwide has been hampered by technological and recovery limitations and sampling bias inherent in exogenous markers. Naturally occurring stable isotopes of H (δδ2H, the most parsimonious model explaining 83% of the isotopic variance was found with amount-weighted growing-season precipitation δ2H, foraging substrate and migratory strategy.Stable isotope data were measured from 544 feathers from 40 species and 140 known locations. For δ2H and global hydrologic δ2H patterns, and accounting for variance associated with foraging substrate and migratory strategy, can be used in conservation and research for the purpose of assigning birds and other species to their approximate origin.This extensive H isotopic analysis of known-origin feathers of songbirds in North America and elsewhere reconfirmed the strong coupling between tissue  Conversely, intrinsic, naturally occurring molecular or stable isotope markers of origin are comparatively inexpensive, and are unbiased by the restricted distribution of tagged individuals, hence large samples can be obtained in which every individual can be used to infer origins δ2Hf), has proven particularly successful because well-known and predictable continental patterns of hydrogen isotopes in rainfall (δ2Hp) are often closely reflected in tissue δ2H values. Isotopic locational information is stored in tissues, particularly those that are metabolically inert following growth  in order to infer origins where tissues were grown. For birds, the assignment of individuals and populations to their region of origin using feather δ2Hf isoscapes has proven to be a leading advance in establishing migratory connections, especially for migrant and threatened species in North America Among isotopic markers, stable-hydrogen isotopes in animal tissues, especially feathers of birds (δ2Hf assignment approach δ2Hp isoscapes on which they are based 2H), that underpin H isotopic flow into food webs, is based on long-term averages obtained from a 50-year disparate global record, and that it remains unclear how much interannual differences at any location vary from this long term. Secondly, with ongoing research it became clear that no single global assignment algorithm is appropriate for all species, taxa, or age classes δ2Hf values than their sedentary young δ2Hf values. Further, for some species like carnivores the H isotopes in their tissues have been shown to be almost completely disconnected from the underpinning spatial H isotope patterns Since the first studies demonstrating the potential of the Hobson and Wassenaar Here, we obtained and measured H isotopes in a large collection of feathers from across North America, which included a new group of songbird individuals that were known with certainty to have grown their feathers at specific sites across contiguous North America. Our objective was to construct the best possible calibrated feather isoscape for passerines and other species in North America and to further quantify what biotic and abiotic factors may influence isotopic patterns across large geographic scales.This study was conducted under authority of the Canadian Council for Animal Care as reviewed by the University of Saskatchewan (Permit 20100084). All federal permits for the use of feather material were issued by the Canadian Wildlife Service and the U.S. Fish and Wildlife Service.The majority (n = 434 of 544) of feathers sampled were outer-tail feathers (rectrices) of passerines collected during the breeding season at constant-effort mist-netting sites such as MAPS  molt on the breeding grounds Seiurus auricapilla) for which it was assumed they held the same territory between years. Samples were obtained from 33 recaptured Golden-winged Warblers (Vermivora chrysoptera) from a mark-recapture experiment, and 30 hatching-year Tree Swallows (Tachycineta bicolor) captured near their nesting location. The locations of these sample sites are included in In addition to known origin samples obtained from the CTR sample collection, first primary (P1) samples were obtained from 91 samples collected at 16 sites in Canada. These included 25 samples from after-second year Ovenbirds  flash pyrolysis of 350±10 ug feather subsamples from the distal section of feather vane and keratin standards using continuous-flow isotope-ratio mass spectrometry. Measurement of the three keratin laboratory reference materials  corrected for linear instrumental drift were both accurate and precise with typical mean δ2H ± SD values of −147.4±0.79‰ (n = 5), −187±0.56‰ (n = 5) and −108±0.33‰ (n = 5), respectively. A control keratin reference yielded a 6-month running SD of ±3.3‰ (n = 76). All results are reported for non-exchangeable H expressed in the typical delta notation, in units of per mil (‰), and normalized on the Vienna Standard Mean Ocean Water – Standard Light Antarctic Precipitation (VSMOW-SLAP) standard scale.All feathers were cleaned of surface oils in 2∶1 chloroform∶methanol solvent rinse and prepared for δ2H in rainfall and animal tissues, however, we wished to determine if various life history traits influence this relationship. Thus, life history data was obtained from the Avian Life History Information Database (http://www.on.ec.gc.ca/wildlife/wildspace/project.cfm), or from species accounts in the Birds of North America δ2Hf were based on our expectation that trophic position could influence δ2Hf, that foodwebs associated with the soil-leaf litter interface may be enriched in 2H over the canopy and shrub layers and that migratory strategy is associated with timing of molt and hence period of isotopic integration. Finally, at continental scales, aquatic environments may represent different hydrogen pools available to birds compared to averaged precipitation.Numerous studies have demonstrated the causal link between δ2H of feathers, alternative models of δ2H in the underpinning precipitation isoscapes were examined. Previous work on North American migratory birds largely focused on precipitation amount-weighted growing season average δ2H in precipitation , and this was included as one estimate of local δ2H in precipitation. However, it remains unclear which months of rainfall exert the greatest influence driving H isotopic flow into primary foodwebs that contribute to avian diet and feather growth. Thus, the relationship between δ2Hf and amount-weighted average δ2H in precipitation for the months of May through July (hereafter δ2HpMay–July) time period were also examined. Model-based estimates of δ2Hp were obtained from the geospatial model provided by δ2HpMay–July were obtained from a geospatial model of δ2H in May–July precipitation using IsoMAP δ2H in precipitation. During the preliminary analysis it was observed that δ2Hf was more strongly correlated with δ2Hp  than δ2HpMay–July  thus all subsequent modeling was done using δ2Hp as a linear covariate and δ2HpMay–July was not considered further.Prior to modeling spatial variation in δ2Hf from a calibration set of 544 known origin birds from across North America (Oporornis tolmei) sampled near the Umatilla River in Oregon.General Linear Models (GLM) were used to statistically model variation in  America . A prelia priori candidate GLM models were considered, and the most parsimonious model was selected based on AICc  and on AIC model weights δ2Hp as the predictor variable; but varied with the inclusion of those factors for foraging guild, foraging substrate, migratory guild, and age class (hatching-year and second-year birds versus after hatching-year) and interactions up to the second order.Twenty five δ2Hf were explored using descriptive statistics and testing for spatial autocorrelation using Moran's index of autocorrelation. Furthermore, residuals from our top model were examined for variation related to body size (wing-length (mm), body mass (grams)), year of feather growth, and climatic departures from long-term averages during the year of feather growth (North Atlantic Oscillation Index (NAO) and multivariate El Niño-Southern Oscillation Index (ENSO)).Residuals from our top model for variation in δ2Hf values were regressed against predicted δ2Hf from the top model. In addition, using these same 269 samples, likelihood-based assignment algorithms δ2Hf value could have been generated at a given location given the isoscape predicted value for that location and the level of error inherent in the assignment process. The likelihoods were converted to likely (1) versus unlikely (0) origins by selecting areas associated with a threshold probability density value, based on a user specified odds ratio of being correct versus incorrect We examined how well our top model performed on temporally distinct data from birds of presumed origin from previously published sources δ2Hf and δ2Hp .A strong relationship was observed between nd δ2Hp . Of 25 c support . The mosδ2Hf for birds from a given migratory guild and foraging substrate throughout North America , followed by ground foraging resident species (∼−27.9‰), non-ground foraging Neotropical migrants (−27.1‰), ground foraging short-distance migrants (−23.0‰), ground foraging Neotropical migrants (−17.6‰), and finally by non-ground foraging resident species . Regression of observed versus predicted δ2Hf suggested that our model performed reasonably well  at predicting δ2Hf for the validation data set . Similarly, at 3∶1 odds, the observed frequencies of correct (192) to incorrect (77) classifications did not differ from the expected frequencies of 202 and 67 .Applying likelihood-based assignments to determine origin for the 269 validation samples resulted in classification accuracies similar to those expected given the specified level of risk. Selecting GIS cells within the isoscape that corresponded to 2∶1 odds of correct classification resulted in 172 samples being correctly classified to place of capture, and 97 samples assigned to origins that did not include the place of actual capture. By contrast, the expected frequency of correct to incorrect classifications was 179 to 90 samples, which did not differ from the observed frequencies , compared to the global isotopic range in nature of over 250‰, these differences are significant enough to cause a substantive disparity in correctly assigning birds to previously established spatial isoscape models.The influence of foraging substrate on feather H isotopes, where it was observed that ground foragers generally had comparatively higher δ2Hf values between migrant ground-foraging Ovenbirds and canopy-foraging America Redstarts (Setophaga ruticilla) across several sites in the southern boreal of Canada. Similarly Hylocichla mustelina) in Georgia were more enriched in 2H than expected from the generalized algorithm used by The precise cause of the H isotopic differences among migrant and resident foragers remains speculative, but has been previously observed. Hobson et al. 2H than canopy foraging counterparts must be related to local diet or the diet during the period of feather growth or physiological differences between these foraging guilds. Several inter-related possibilities could account for these differences which ultimately result in enrichment in feather 2H. One possibility is that soil-level invertebrate prey may be comparatively enriched in 2H compared to shrub and canopy insects due to the evapotranspiration that can occur at the soil-atmosphere interface whereby isotopically light water is preferentially lost to the atmosphere compared to deeper water transmitted to leaves 2H enrichment in ground foragers. The effect of evapotranspiration would be expected to be more pronounced in regions of high ambient temperature and/or low humidity. Alternatively, invertebrates used by ground-foraging birds  may simply represent a higher mean trophic level than herbivorous insects associated with the canopy and, if insect δ2H correlates positively with trophic level, ground-foraging birds would be enriched in 2H over canopy foraging birds . Neotropical migrants in North America typically replace flight feathers before migration primarily during July and August. Clearly, possible causal mechanisms underlying the observed differences in δ2Hf due to timing of molt and foraging substrate remain speculative and will require more research.In contrast, resident ground foragers had lower δ2Hp and δ2Hf values for North America are not unexpected δ2Hf and δ2Hp. The results of this study are therefore encouraging and underline the fact that the more one can account for isotopic variability in feathers (and other tissues), the greater precision one might expect in assigning birds and other animals to geographic origin using appropriate empirical algorithms.As several authors have indicated, differences in the algorithms linking δ2Hp and δ2Hf values for North America and its application to geographic assignments to origin. Thus, challenges to the H isotope approach may be unnecessarily alarmist, particularly where North American passerines are concerned 2H will be attenuated by averaging effects within the hydrologic cycle , the foodweb, and the tendency for H isotopic variance to average out at higher trophic levels pre-specified levels of accuracy. Thus, in our opinion, the question instead should be how best to handle known sources of variance in both δ2Hp and δ2Hf when assigning individuals and populations to probability of origin surfaces δ2Hf and δ2Hp, likely provided a better reflection of the true variance inherent in assignments to origin than variation δ2H in precipitation represented in the GNIP isoscape data.This study provides renewed and strong support for the enduring relationship between Table S1δ2Hf.List of species sampled for stable hydrogen isotope analysis of feathers and associated categorical factors used in models examining variation in (DOC)Click here for additional data file.Table S2c based model selection statistics for the 25 a priori candidate models used to examine variation in δ2Hf. K = number of parameters, AICc = Akaike's Information Criterion corrected for small sample size, ΔAICc = difference in AICc between model and highest ranked model, and ωi = AIC weight.AIC(DOC)Click here for additional data file.


Thresht and Threshd) affects the accuracy of reconstructed images, and developed an easy method to select optimal thresholds. We also identified an empirical criterion to evaluate whether an imaging condition is appropriate for accurate superresolution image reconstruction with the clustering algorithm. Both the threshold selection method and imaging condition criterion are easy to implement within existing PALM clustering algorithms and experimental conditions. The main advantage of our method is that it generates a superresolution image and molecule position list that faithfully represents molecule counts and positions within a cellular structure, rather than only summarizing structural properties into ensemble parameters. This feature makes it particularly useful for cellular structures of heterogeneous densities and irregular geometries, and allows a variety of quantitative measurements tailored to specific needs of different biological systems.Localization-based superresolution microscopy techniques such as Photoactivated Localization Microscopy (PALM) and Stochastic Optical Reconstruction Microscopy (STORM) have allowed investigations of cellular structures with unprecedented optical resolutions. One major obstacle to interpreting superresolution images, however, is the overcounting of molecule numbers caused by fluorophore photoblinking. Using both experimental and simulated images, we determined the effects of photoblinking on the accurate reconstruction of superresolution images and on quantitative measurements of structural dimension and molecule density made from those images. We found that structural dimension and relative density measurements can be made reliably from images that contain photoblinking-related overcounting, but accurate absolute density measurements, and consequently faithful representations of molecule counts and positions in cellular structures, require the application of a clustering algorithm to group localizations that originate from the same molecule. We analyzed how applying a simple algorithm with different clustering thresholds ( Localization-based superresolution methods such as Photoactivated Localization Microscopy (PALM), Stochastic Optical Reconstruction Microscopy (STORM), and direct STORM (dSTORM) utilize the stochastic switching of fluorophores between dark and bright emission states to visualize fluorophore-labeled single molecules sequentially from the ensemble pool in-vivo dimensions and molecule density of the Z-ring to deduce the arrangement of FtsZ protofilaments inside the ring Previously, we and other groups employed superresolution imaging to characterize the cytokinetic “Z-ring” formed by the tubulin homolog FtsZ in bacterial cells Caulobacter crescentus chromosomes Other PALM and (d)STORM studies have resolved the dimensions of structures such as the ParA bundles that segregate Many photoactivatable fluorescent proteins have recently been shown to fluoresce intermittently, or “blink”, once activated Escherichia coli cell expressing the FtsZ protein fused to mEos2, a photoactivatable fluorescent protein and a popular choice for PALM imaging To illustrate this point, we show in Thresht and Threshd) – if two localizations occur within Thresht and Threshd, they likely come from the same molecule and should be grouped together Threshd  = 167 nm for our system) and separated by up to one or three frames, respectively, were grouped together Thresht and Threshd values that accurately group localized spots has yet to be developed.In various attempts to account for photoblinking so that each molecule in a superresolution image is represented only once, several studies have employed a simple clustering algorithm to group multiple localizations of a single molecule based on the occurrence of these localizations within certain time and distance thresholds  profiles to Gaussian distributions and extracting the full width at half maximum (FWHM) Thresht and Threshd values to both experimental and simulated data. Using a single experimental dataset obtained with FtsZ-mEos2, we generated a series of superresolution images using different threshold pairs and then measured the Z-ring width in each image , Z-ring width varied approximately 1.5-fold (60–90 nm) with larger threshold values resulting in smaller width measurements. We observed the same trend with measurements made from a simulated dataset (Thresht <1 s and Threshd <100 nm) were within the 95% confidence interval for the fitted Z-ring width in the reference image (94 nm –100 nm), while extremely high threshold values yielded much smaller Z-ring width measurements.To determine the effect of threshold selection on dimension measurement, we applied the clustering algorithm  with varying ch image . Across  dataset  where moThe general decrease in Z-ring width measurement at large thresholds is due to false grouping of localizations that originated from multiple molecules, which affects dimension measurements in two ways. First, because the convolved Z-ring profile is described by a Gaussian distribution, groups that are comprised of multiple molecules have centroid positions weighted toward the center of the Z-ring. Plotting these centroid positions tightens the spatial distribution of the Z-ring and results in smaller width measurements. Second, very large thresholds can cause insufficient sampling of the Z-ring, resulting in further reduced width measurements.Thresht and Threshd values of 0), the Z-ring width measured from the simulated data approximates that measured from the reference image. This can be understood if multiple localizations of the same molecule result in an increased amplitude but unchanged standard deviation of the Z-ring Gaussian distribution. This observation is consistent with previous studies where it was shown that multiple localizations of fluorophores improves the statistical sampling of underlying structures and can increase the apparent spatial resolution of a superresolution image We note that when no clustering is applied  may not be activatable due to misfolding or incomplete fluorophore maturation Thresht and Threshd selection affects three types of measurements: mean density, relative density, and density distribution measurements. Mean density is a bulk measurement of the average number of molecules per unit area; relative density reports the fraction of molecules confined to a particular region of the structure; and the density distribution is described by the histogram of number of molecules detected per unit area. Fluorophore blinking amplifies both mean density and density distributions, which are absolute measurements of molecule counts, but relative density, which is the ratio between molecule counts in different regions, should not be affected if all molecules have the same ensemble blinking properties.Fluorophore blinking results in erroneous amplification of fluorophore density due to repeat localizations. Below we explore how Thresh and dThresh selection on mean density (molecules per unit area) by analyzing how the total number of molecules (N) in the same cell area varies with different tThresh and dThresh pairs. Both experimental (ref)/Nref|, which is plotted in ref) can be achieved by multiple threshold pairs along two valleys that intersect at tThresh ≈ 0.4 s and dThresh ≈ 60 nm.Using the same experimental and simulated datasets shown in the dimension measurement analysis in rimental  and simurimental  datasetsThresh and dThresh selection on relative density measurements by measuring fmidcell, the fraction of molecules detected in the Z-ring relative to the whole cell. Increasing values of both tThresh and dThresh resulted in smaller fmidcell values for both experimental  revealed that images generated with smaller thresholds yielded reasonably accurate relative density measurements (<10% difference for tThresh <1 s and dThresh <105 nm). This is because molecules within and outside the structure of interest have the same blinking properties, allowing the effect of multiple molecule localizations to cancel out in a relative measurement. The underestimation of fmidcell for larger threshold values is due to the greater likelihood of falsely grouping molecules in denser regions such as the Z-ring. These results confirm that, as with the Z-ring width measurement, relative density can be accurately measured from a superresolution image that has not been processed using a clustering algorithm , as long as the structure of interest is sampled sufficiently.Next, we examined the effect of trimental  and simurimental  datasets2 goodness-of-fit test GOF  = 0). This seemingly heterogeneous distribution of molecules inside the Z-ring, as judged by the significant deviation from Poisson distribution, is actually caused by multiple localizations of single molecules due to photoblinking. GOF  = 0.74).While mean and relative molecule densities describe global structural properties, the molecule density distribution provides additional information about the uniformity or heterogeneity of molecule positions within a structure. If molecules are uniformly distributed throughout the structure, the molecule density histogram should be well described by a Poisson distribution. Thresht and Threshd pairs to the distribution from the reference image using the Kolmogorov–Smirnov (KS) test KSp >0.05) along two intersecting ridges .We have shown that the mean molecule density and density histogram measurements are significantly affected by fluorophore blinking, while dimension and relative density measurements are not. However, all four measurements are affected by the selection of The combined error analysis selected a limited threshold range rather than a unique, optimal threshold pair. While this range of thresholds can satisfy all investigated quantitative measurements simultaneously, some threshold pairs in this range may not generate accurate superresolution images in which the molecule counts and positions are correctly identified. This is because each of the measurements described above quantifies an ensemble structural property and may not be sensitive to errors at the individual molecule level.To find the optimal threshold pair that not only provides reliable quantitative measurements, but also an accurate image at the single-molecule level, we further assessed the clustering accuracy of each threshold pair using the Jaccard index Thresht and Threshd  also generates an image that provides accurate quantification of dimension and density.We calculated the Jaccard Index as a function of  dThresh  for the ror plot . This agTo examine whether differences in structural geometry or dimension can alter the observed effects of photoblinking or threshold selection on quantitative measurements, we simulated another type of cellular structure: circular clusters of various sizes (see Methods for simulation details). refN-N)ref/N| plot , resulting from each threshold pair. Then, we identified the minimum-error threshold pair that yielded the lowest allε. In allε generated by the minimum-error threshold pair and the corresponding Jaccard Index achieved by that threshold pair. Across a large range of fluorophore blinking properties and activation rates examined, most Z-ring (blue) and cluster (red) simulations could generate images with low measurement error (<10%) using at least one threshold pair. However, not all of these images achieved high accuracy at the single molecule level (Jaccard index >0.8). This result suggests that achieving accurate ensemble measurements is not sufficient to ensure that the corresponding list of molecule positions is reliable.To further illustrate the relationship between Jaccard index and measurement error under a variety of conditions, we generated simulated datasets with different structural geometries, molecule densities, fluorophore blinking properties, and activation rates (see Table S1 and S2 for parameter ranges). For each simulation, we calculated the combined measurement error, 2 for mEos2 in our imaging condition) becomes comparable to the probability that a molecule blinks back on, it is difficult for the clustering algorithm to discriminate a repeat localization of an activated molecule from the first localization of a new molecule, resulting in separate molecules falsely grouped as single molecules more frequently.As shown by the region where the maximum Jaccard index is <0.8 in maxΔt and repeatΔt. We define maxΔt as the average time between subsequent localizations of all molecules within the diffraction-limited region of highest molecule density in a superresolution image. maxΔt can be easily calculated by dividing the total imaging acquisition time by the number of localizations detected in the maximum density region (see Methods). maxΔt therefore increases when activation is slower given the same fluorophore properties, and serves as a convenient measurement of activation rate. We define repeatΔt as the average time between subsequent localizations of the same molecule, which is determined by fluorophore blinking kinetics, and can be measured from in vitro or in vivo experiments where single fluorophores are clearly identifiable .To understand what combination of fluorophore blinking rate and activation rate ensures a high achievable accuracy in superresolution image reconstruction, we employ two experimentally-measureable parameters, maxΔt and repeatΔt for the simulations analyzed in maxΔt/repeatΔt  can be achieved when the ratio is kept above 40, regardless of the underlying structure. This observation provides a simple criterion for screening imaging conditions, specifically activation rates, in order to reconstruct a highly accurate superresolution image.To explore the relationship between these two parameters and achievable Jaccard index, we calculated Δtrepeat . SimulatThresht and Threshd pair from the plot of Jaccard indices at various Thresht and Threshd values (refN-N)ref/N| plot ref/N| plot and the threshold pair that gives rise to the peak Jaccard index value, we compared the maximum Jaccard index of different simulations with the Jaccard index achieved using the threshold pair at the intersection of valleys in the |(refN-N)ref/N| plot identified by eye . refN-N)ref/N| plot under the ideal experimental conditions described above .To examine the correlation between the intersection of the valleys in the |(refN-N)ref/N| plot requires knowledge of the true number of molecules, refN. This number can be calculated by dividing the total number of localized spots in the unprocessed image (unprocessedN) by the average number of localizations per molecule (α) under a given imaging condition  such that refN  =  unprocessedN/αet al. extracts refN from fitting a semi-empirical equation to the dependence of N on Thresht at a fixed ThreshdGeneration of the | for purified mEos2. Furthermore, using fixed E. coli cells expressing low levels of untagged mEos2 protein at extremely low activation level, we obtained a similar value  , suggesting that the blinking properties of mEos2 are similar in vitro and in fixed cells under the same buffer conditions. Therefore, we combined the datasets to obtain mEos2α = 2.2 , which is within the range of values reported in previous studies under different conditions (mEos2α = 1–3) The parameter izations . Figure mEos2α, we calculated the true refN for the experimental dataset described in refN  =  unprocessedN/mEos2α = 1204/2.2 = 547). We then varied both Thresht and Threshd to generate the plot of |(refN-N)ref/N| (Thresht  = 0.4 s and Threshd  = 60 nm) as the optimal threshold pair, which we used to generate the optimal superresolution image (Thresht  = 0.05 s (1 frame) and Threshd  = 167 nm) /Nref| , which if)/Nref| . From thon image . The ima 167 nm)  and with 167 nm)  exhibit maxΔt  = 87 frames. Using the mEos2 characterization data described above, we measured repeatΔt  = 2.1±3.3 frames  , resulting in the ratio maxΔt/repeatΔt  = 41, which is similar to the criterion provided in maxΔt/repeatΔt >40). Consequently, the Z-ring width, midcellf, and mean molecule density are within 15% of the expected values (Table 1). We also analyzed the Z-ring density distribution from both images using the Poisson goodness-of-fit test. In this case, both the original and the optimal image were well-described by a Poisson distribution . This result suggests that the blinking behavior of mEos2 does not affect the molecule density distribution of the Z-ring significantly at our level of sampling (<molecules/pixel>  = 0.5 in the Z-ring).In addition to identifying real protein clusters in the optimal superresolution image, we performed the four quantitative measurements described above using the optimal superresolution image. This dataset was acquired over 20 minutes, resulting in We have shown that reliable dimension and relative density measurements can be made from superresolution images with multiple fluorophore localizations due to photoblinking. For (d)STORM imaging, it has been shown that multiple localizations of single fluorophores can actually enhance image quality because repetitive sampling of the same molecule averages out the stochasticity in individual localizations, leading to convergence on the true molecule position repeatΔt) If the goal of a superresolution experiment is to count the number of molecules accurately in a cellular structure so that stoichiometric information of molecular components can be obtained, photoactivatable fluorophores that are irreversibly activated and exhibit only a few localizations before permanent photobleaching are desirable. Photoactivatable fluorescent proteins such as mEos2 yield only a few localizations per molecule and provide the benefit of stoichiometric labeling via genetic fusion to a protein of interest, improving the accuracy of counting molecules. We show that photoactivatable fluorescent proteins can yield accurate density measurements if activation is kept adequately slow and a clustering algorithm with carefully-selected thresholds is applied. Because conditions and fluorophores for (d)STORM are often optimized to yield long dark times between reversible switching events ref/N| plot. The optimal values of Thresht and Threshd ensure that most repeat localizations are grouped together, minimizing false identification of repeat localizations as separate molecules. However, we have also shown that successful application of the optimized clustering algorithm requires low activation rates, where the probability that a new molecule will be photoactivated nearby an activated molecule before it is photobleached is low. High activation rates result in false grouping of separate molecules.We have described a method for selecting the optimal values of maxΔt needs to be more than 40-fold longer than repeatΔt . Consequently, a minimum maxΔt of 84 frames between localizations in the 225±225 nm2 square of highest density is required. This criterion can be converted into a maximum detection rate of 0.24 molecules/µm2 per frame in the maximum density region (1/0.05 um2/84 frames), which also satisfies the conditions previously reported to avoid detection of overlapping fluorescent molecules  and the spatial resolution, respectively. Longer <offτ> values require larger values of Thresht to accommodate the longer dark times between spots so that most repeat localizations of the same molecule are grouped into the same cluster . Likewise, the Threshd value increases with the value of spatial resolution , which is defined as the FWHM of Gaussian-distributed fluorophore localizations around the central molecule position, and determines the average distance between repeat molecule localizations (Text S1). The optimal Threshd value is approximately twice the spatial resolution, which is large enough to account for most repeat localizations of the same molecule . The values obtained for the experimental image described above  agree with the <offτ> timescale of mEos2 blinking kinetics observed in our study  and previous studies (0.1–0.4 s) refN-N)ref/N| takes all of these factors into account, while requiring similar effort in fluorophore characterization.Under an imaging condition that allows accurate superresolution reconstruction, the optimal values for repeatΔt, should be compared with the activation rate to identify imaging conditions that are suitable for accurate superresolution image reconstruction as described above. Second, the average number of observations per molecule, α, is required to generate the |(refN-N)ref/N| plot. Both of these parameters should be determined using the same exposure time and excitation intensity as those used for the superresolution imaging. This can be done with either purified fluorophore or, ideally, with a fixed biological sample of low labeling density that is activated extremely slowly. It is also important to characterize a fluorophore under the same buffer conditions used for superresolution imaging because blinking kinetics are highly dependent on a fluorophore's chemical environment Two fluorophore properties need to be determined to implement the method we have described. First, the average time between repeat molecule localizations, onτ, offτ, and blinkn observed from individual mEos2 molecules can be approximated well by the single exponential distributions used in our simulation .The kinetic scheme that we used to described the blinking behavior of mEos2 is relatively simple (see Methods) and has been previously shown to sufficiently describe mEos2 et al. identifies the correct number of molecules (refN ) in a superresolution image by fitting the dependence of N on Thresht to a semi-empirical function refN in a heterogeneous image, our method provides optimal Thresht and Threshd values to generate a reliable image that can be quantified in many different ways, and identified a quantitative criterion (maxΔt/repeatΔt >40) under which optimal image reconstruction is possible.A few recent methods have addressed some of the effects of photoblinking on superresolution images. The method developed by Annibale Other studies have applied pair correlation analyses to images of membrane clusters to extract mean density and cluster size The optimized clustering algorithm we described in this work complements these methods by generating a full superresolution image and accurate list of molecule positions that provide additional qualitative and quantitative information that cannot be described by one or a few global parameters. We have described a few quantitative analyses that can be performed , but each biological system may be characterized by unique quantitative features that can be measured from the images and list of positions our method provides. Additionally, because our method is a simple modification to the superresolution image analysis algorithm first developed for PALM Based on our experimental PALM images Simulations presented in this work were comprised of 1000, 2000, or 5000, total molecules that were distributed with 30%, 50%, or 75% in the midplane population (see Table S1).Each simulation of circular clusters required designation of the following parameters: total number of molecules in a cell, fraction of molecules within clusters, mean number of molecules per cluster, and cluster FWHM (parameter ranges can be found in Table S2). The positions of molecules that were not within clusters (cytoplasmic molecules) were sampled in the same manner as described for the cytoplasmic molecules in the FtsZ simulation.The integer number of clusters in a given simulation was calculated by dividing the total number of molecules in all clusters by the mean number of molecules per cluster. Then, the number of molecules in each cluster was sampled from an exponential distribution. The molecules within each cluster were scattered according to a symmetrical, two-dimensional Gaussian distribution with the designated FWHM, and the center of each cluster was distributed uniformly throughout the cell. Figure S8C shows a representative simulation of distributed clustered (red) and cytoplasmic (blue) molecules.We simulated the kinetics of fluorophore activation and blinking by varying the following parameters:1k): rate at which new molecules are activated; inversely proportional to the number of unactivated molecules remaining.Activation rate (2k): rate at which a molecule is reversibly converted to the transient ‘off’ state.Blink off rate (3k): rate at which a molecule is turned on from the transient ‘off’ state.Blink on rate (4k): rate at which a molecule is irreversibly turned off by photobleaching.Bleaching rate :actτ) was sampled from an exponential probability distribution with expected value of act0τ, which increases as the number of remaining molecules (remainingN) that have not been activated decreases. act0τ is the expected lag time at the initial number of molecules .Lag time between molecule activations (onτ).The duration of each blink (offτ).The duration of dark times between blinks (blinkn).Number of blinks per molecule . Note that the kinetic parameters used in these simulations reflect observed fluorescence time traces that are highly dependent on experimental conditions such as excitation/activation light intensity, pixel size, background noise, frame rate, spot detection algorithm, and spot fitting algorithm. We validated this scheme by verifying that the observed time traces of individual mEos2 molecules under our experimental conditions can be well-described by exponential distributions of onτ, offτ, and blinkn .The actτ distribution. Once activated, the number of blinks for a given molecule was sampled from the blinkn distribution. For each blink event, the on-time was sampled from the onτ distribution and the time until the next blink was sampled from the offτ distribution. The lag time (actτ) until the next molecule activation was calculated from the start of the previously activated molecule such that blinking events from multiple molecules could overlap in time.Molecules were iteratively activated with lag times sampled from the updated blinkn <0.5 (rounded to blinkn  = 0) means that the molecule was activated but never ‘observed’ in the simulation due to fast photobleaching. This was also true for low values of mean on-time (onτ), which resulted in some blinks not being recorded. These properties mimic experimental conditions and highlight the fact that not every activated fluorophore or blinking event will be visualized.For low expected values, sampling from an exponential distribution often resulted in values less than one frame. A value of σ, between 7–37 nm (see Table S1 and S2). For the simulation described in σ = 15 nm, which results in a FWHM spatial resolution of 35 nm. We validated that the position distributions generated by the simulation were similar to those observed for experimental mEos2 localizations by plotting the histograms of distances between repeat localizations of the same molecule that result from the simulation  and from experimental data . The shape and peak position of both distributions are similar, suggesting that the simulation with σ = 15 nm approximates our experimental data.Once the blinking time trace was established for each molecule, its multiple localizations were scattered around the original molecule position according to a two-dimensional normal distribution with a standard deviation, σ equal to the experimental or simulated localization precision. For simulated data, the localization precision was equivalent to the standard deviation, σ, used to simulate the scatter of localizations around the molecule position (see previous paragraph). For experimental data, only molecules with localization precisions smaller than 20 nm were plotted. Superresolution images were pseudocolored using the ‘Red Hot’ lookup table in ImageJ software (NIH).Superresolution images of both simulated and experimental data were generated in MATLAB® with a pixel size of 15 nm. Each localized spot was plotted as a symmetrical 2D Gaussian distribution with total intensity equal to 1 and For density measurements, superresolution molecule density images of both simulated and experimental data were generated in MATLAB® with a pixel size of 15 nm. The intensity of each pixel in the density image represents the number of molecules detected within the pixel's boundaries, and hence represents a two-dimensional histogram of molecule counts. For experimental data, only molecules with localization precisions smaller than 20 nm were included.midcellf) was calculated by dividing the summed intensity within the Z-ring region by the total intensity of the density image . Similarly, relative density within clusters (clusterf) was calculated by dividing the summed intensity within all clusters by the total intensity of the density image. Z-ring density histograms were generated by binning pixels within the Z-ring region by intensity.Boundaries of the Z-ring or cluster regions of each density image were identified as polygons by eye. Relative density within the Z-ring  using the ‘nlfilter’ function in MATLAB with a 17pixel×17pixel sliding window (15 nm pixel size). The maximum density square is centered at the maximum intensity pixel in the filtered image. This calculation is identical for both simulated and experimental data.The average time between molecule activations, Thresht, and distance, Threshd, of a previous spot was grouped into the same cluster as that previous spot . The resulting cluster was assigned a spatial position equal to the centroid position of all the spots included in the cluster.Both simulated and experimental time traces were clustered in MATLAB® using two thresholds: any spot that occurred within time, TP/(TP +FP + FN). TP is the number of pairs of localizations that came from the same molecule, and were grouped into the same cluster; FP is the number of pairs of localizations that did not come from the same molecule, but were grouped into the same cluster; and FN is the number of pairs of localizations that came from the same molecule, but were grouped into different clusters. The Jaccard index varies from 0 to 1, where a value of 1 represents perfect clustering.We calculated the Jaccard index mEos2 gene was amplified using primers GTCGACAATGAGTGCGATTAAGCCAGACAAATT and GCGGCCGCTTATCGTCTGGCATTGTCAGTTAA. The PCR product was restricted using SalI and NotI restriction enzymes (New England Biolabs), and cloned into the same sites of plasmid pT7HMT 600 of 0.8, then induced for 2 hours with 0.5 mM IPTG . Cells were collected at 4100 rpm for 20 min in a Sorvall Legend RT bench top centrifuge at 4°C. Cells were lysed using sonication and repeated freeze thaw cycles and subsequently purified on Ni-NTA beads (Invitrogen) at 4°C according to the ProBond™ native protocol. Protein was buffer-exchanged and concentrated from elution buffer to pH 7.4 phosphate buffer saline using a Vivaspin 500 concentrator  with a 5,000 MW cutoff. Purified his-mEos2 was checked for purity by running Mini-PROTEAN TGX Gels (BIO-RAD), and concentration was determined in a Nanodrop spectrophotometer using absorption coefficient of 5,600 M−1cm−1 at 280 nm The 2 aqueous solution was prepared and filtered to sterilize and remove aggregates. A coverslip was secured via Scotch tape (3 M) to a Mini Mouse II (Denville scientific) centrifuge with the 1.5 mL tube attachment. While spinning at 6000 RPM, 50 µL of the NiCl2 solution was slowly pipetted to the center of the spinning coverslip through a ∼1 cm hole in the plastic cover. The spin coating was visually inspected for evenness. Next, 0.5 µL of purified his-mEos2 sample (1.35 nM) was pipetted to the center of the NiCl2-coated coverslip without spinning. Sample was allowed to dry, then topped with an agarose gel pad to mimic the PALM image acquisition setup described previously A 12% NiClE. coli B/rA cells containing plasmid pCA24N-FtsZ-mEos2 600 of 0.2, then induced with 20 µM IPTG for 2 hrs. Cells were then collected via centrifugation, resuspended in fresh M9 media, grown at 25°C for 90 minutes, and fixed with 4% formaldehyde at 25°C for 40 min. The fixed E. coli cells were mixed with 50 nm gold fiducial beads , then sandwiched between an agarose gel pad and a cleaned coverslip as described previously TM, Coherent, Santa Clara, CA) was used to activate mEos2. The green and red fluorescence of mEos2 was excited via epi-illumination with 488 nm and 561 nm solid state lasers  and emission was collected on an EMCCD camera  after passing through a dual-band emission filter .Images were acquired using an Olympus IX-71 inverted microscope, equipped with a 60×, 1.45 NA TIRFM objective. A 405 nm laser  with a 100pixel ×100pixel imaging area. The intensity of the 405 nm activation laser was increased stepwise as the number of unactivated mEos2 molecules decreased during data acquisition.Molecules were detected and localized as described previously Figure S1Schematic of spot clustering algorithm. After spot identification and localization, the set of spots is processed iteratively such that any previous spot (“forerunner spot”) that occurred within Thresht and Threshd of a given spot (“spot i”) are grouped together. Each group is then plotted only once in the final superresolution image at the calculated centroid position.(TIF)Click here for additional data file.Figure S2Characterization of repeatΔt for mEos2. Histogram of time (in frames) between sequential molecule localizations, repeatΔt, from 1743 molecules resulting in 3815 localized spots and 2072 intervals between sequential localizations of the same molecules. Data from both in vitro samples and fixed cells expressing low levels of mEos2 were combined to generate this histogram. Most repeat localizations occur in consecutive frames , but long dark intervals (>10 frames) are sometimes observed. The sample mean is <repeatΔt>  = 2.1±3.3 frames (0.11±0.17 seconds).(TIF)Click here for additional data file.Figure S3Examples of intersection identification in the |(N – Nref)/Nref| plot. Among the 92 simulations investigated, three categories of plot shapes were observed: symmetric (A), asymmetric (B), and diffuse (C). The optimal threshold pair identified by eye for each example is shown as a blue circle. For symmetric plots, the optimal threshold pair should be selected in the center of the intersection point. For asymmetric plots, the optimal threshold pair should be selected at the inflection point with the longest Thresht value. The identification of the intersection point in diffuse plots (C) may be difficult because the intersection area is broad. However, these plots result from kinetic parameters that yield very broad and high Jaccard peaks such that a broad range of thresholds around the intersection points yield almost equivalent and sufficient accuracy in resulting images. These representative plots were generated from simulated datasets with the following parameters : 500–30%–1,4,1,1 (A), 1000–30% −2,8,1,1 (B), 500–50% –3,4,1,20 (C) – all τ values are reported in frames; 1 frame  = 50 ms).(TIF)Click here for additional data file.Figure S4Characterization of mEos2 in fixed E. coli cells. (A) Representative images from a single E. coli cell expressing mEos2. The brightfield (top left) and green fluorescence (bottom left) images are shown for comparison. The scatter plot (right) shows single molecule localizations  colored by detection time. Localizations that originated from the same molecule are grouped together (large circles). The cell outline is shown in white. (B) Histogram (gray) of localizations per mEos2 molecule (α) in fixed E. coli cells with the corresponding single-exponential fit (red). The fitted mean is 0.5±0.1 localizations per molecule. The ensemble average is 2.1±4.3  localizations per molecule. (C) Histogram (gray) and single-exponential fit (red) calculated after combining in vitro (B) and in vivo (N = 1743) localizations per molecule. in vivo  datasets(TIF)Click here for additional data file.Figure S5Optimal tThresh values are related to the mean off time. Datasets from both Z-ring and cluster simulations were grouped by simulated fluorophore off-time, offτ, then Thresht values at the Jaccard index peak of each simulation were averaged  and plotted against the fluorophore off-time. The two parameters show a clear correlation, suggesting that the optimum Thresht value is largely determined by the mean fluorophore off time . However, the large variation at some offτ values suggest that other experimental factors affect the optimal Thresht value. A list of simulations used in this analysis can be found in Table S1 and S2.(TIF)Click here for additional data file.Figure S6Optimal dThresh values are related to the spatial resolution. Datasets from Z-ring and cluster simulations were grouped by simulated spatial resolution (FWHM), then the Threshd values at the Jaccard index peak of each simulation were averaged  and plotted against the simulated spatial resolution. Spatial resolution was calculated as 2.35σ, where σ is the Gaussian standard deviation used to scatter localizations around the central molecule positions (see Methods and Text S1). The two parameters show a clear correlation, indicating that larger spatial resolutions result in larger values for optimum dThresh . This plot was generated using the same datasets analyzed in Figure S5 (see Table S1 and S2 for parameter list).(TIF)Click here for additional data file.Figure S7Validation of kinetic and spatial simulation parameters. Combined datasets from both in vitro and in vivo characterizations of mEos2 were used to generate histograms of blinkn (A), offτ (B), and onτ(C), which are all described well by single-exponential distributions, validating the simple kinetic scheme used to simulate fluorophore dynamics in this work. Red curves indicate single-exponential fits that yielded mean values of: <blinkn>  = 0.44±0.03 (A), <τoff>  = 2.0±0.2 frames (B), and <onτ>  = 0.56±0.03 frames (C). (D–E) Histograms of the pair-wise distances between repeat localizations of the same molecule for experimental (D) and simulated (E) datasets. The histograms were fit to Equation 2 from σ, of 18±1 nm (D) and 15±1 nm (E), respectively. The experimental dataset is the same combined dataset characterized in (A–C) above. The simulated dataset had a nominal σ of 15 nm, and is the same dataset analyzed in totalN  = 2000 (50% midplane), σ = 15 nm, <blinkn>  = 2, <offτ>  = 1 frame, <onτ>  = 1 frame, <0actτ>  = 5 frames (1 frame  = 50 ms)).(TIF)Click here for additional data file.Figure S8Representative simulations of superresolution images. (A) Representative simulation of FtsZ locations within an E. coli cell. The total number of molecules, N, is 500. Molecules are divided into 50% midplane (red) and 50% cytoplasmic (blue). (B) Superresolution image generated from the data in (A) after simulating the following kinetic parameters: <blinkn>  = 3, <offτ>  = 4 frames, <onτ>  = 1 frame, <0actτ>  = 7 frames, and applying the same clustering algorithm used to generate E. coli cell. The total number of molecules, N, is 2000. Molecules are divided into 50% clustered (red) and 50% cytoplasmic (blue) molecules, with the cluster diameter designated as 50 nm FWHM. The number of molecules per cluster was sampled from an exponential distribution with <molecules/cluster>  = 200. (D) Superresolution image generated from the data in (C) after simulating the following kinetic parameters: <blinkn>  = 2, <offτ>  = 1 frames, <onτ>  = 1 frame, <0actτ>  = 5 frames, but plotting only the first localization of each molecule. Scale bars, 500 nm. Grid size, 30 nm.(TIF)Click here for additional data file.Table S1Simulation parameters for Z-ring simulations.(XLSX)Click here for additional data file.Table S2Simulation parameters for cluster simulations.(XLSX)Click here for additional data file.Text S1Calculation of spatial resolution.(DOCX)Click here for additional data file.


Unraveling the fundamental mechanisms and pathways behind protein misfolding and aggregation is one of the great challenges of current science. The failure of specific proteins to fold correctly or to remain correctly folded and their subsequent self-assembly into dysfunctional or indeed toxic aggregates is associated with a range of highly debilitating and increasingly prevalent pathological conditions.Although the morphology, size, and biological function of parent polypeptides are remarkably diverse, all amyloid fibrils share common structural properties. They consist of highly ordered β-strands that lie perpendicular to a common axis in a so-called cross-β arrangement.In this paper, we show that this phenomenon can be used to track the aggregation of amyloid proteins noninvasively and quantitatively without any need for extrinsic labels. We validate the method against an established assay of protein aggregation and compare the increase in the intrinsic fluorescence emission intensity with the change in Thioflavin T (ThT) fluorescent signal under conditions that give highly reproducible fibril-growth kinetics. We quantify the conversion from the soluble into aggregated forms of two proteins in real time and use atomic force microscopy (AFM) and confocal imaging to probe the identity of the species giving rise to the observed fluorescence signatures. We also show that the assay is compatible with standard confocal microscope setups, so that both spatial  and spectral information can be monitored simultaneously from fibril assemblies. The intrinsic fluorescence assay has an excellent dynamic range, similar to that of ThT fluorescence, but with the significant advantage that no extrinsic labels are required, neither is the presence of aromatic residues necessary;, 10 thusWe have performed detailed spectroscopic measurements on a series of amyloid fibrils, and all exhibited an intrinsic fluorescence, thus suggesting that this is a generic feature of the amyloid form of proteins. We used a purpose-built confocal microscope, equipped with spectral emission imaging and lifetime measurement capability,–13 to alA key problem in the validation of a new assay of amyloid growth is the difficulty of obtaining standardized and calibrated aggregation conditions because the observed growth kinetics are the result of a complex interplay of underlying elementary reaction steps. Amyloid fibrils form through a nucleated growth process,y=y0+A1 exp(−(t/t1))  and recorded the time evolution of the intrinsic fluorescence intensity over several hours , offers a similar dynamic range to traditional assays such as ThT, and reports quantitatively and reproducibly on amyloid fibrillar growth. We have demonstrated the potential of studying the interactions of small-molecule binding to amyloid fibrils through intrinsic fluorescence and shown that this method is more reliable than assays requiring extrinsic dye labels. Given its well-defined nature and straightforward application, we anticipate the widespread use of this method in the study of protein aggregation and in the search for small molecules that are potential therapeutic lead compounds.Materials: All chemicals for the preparation of buffers, as well as the heparin and the lacmoid were purchased from Sigma–Aldrich. The “synthetic” human Aβ(1–42)  was prepared by sequential treatment with trifluoroacetic acid (TFA) and hexafluoroisopropanol (HFIP) to remove small aggregates and stored as a lyophilized film in Eppendorf tubes at −20 °C.Conversion of soluble polypeptides into fibrils: Lyophilized, TFA- and HFIP-treated human Aβ(1–42) were dissolved in 1×PBS buffer (pH 7.4) at 50 μm peptide concentration in Eppendorf tube, and the solutions were incubated at 37 °C for 7 days. A lyophilized  aliquot (≈15 nmol) of recombinant Aβ(1–42) was dissolved in deionized water (150 μL) and left to aggregate at room temperature overnight. K18 (I260C/C291A/C322A) tau  was incubated at 37 °C for 24 h, quiescent, in the presence of heparin . All buffers were made with Milli-Q water and were filtered with 0.20 μm filters (Millipore) before use. Human α-synuclein  was incubated for 50 h at 45 °C under strong stirring with a Teflon-coated stir bar. The fibrils formed were diluted to 70 μm with PBS buffer and sonicated for 4 min with a probe sonicator  at 10 % maximum power and with 30 % cycles.Thioflavin T kinetic assay: Experiments with ThT were carried out in an Optima Fluostar platereader . Samples were prepared that contained monomeric α-synuclein (70 or 35 μm), sonicated seed fibrils (7 or 3.5 μm) and Thioflavin T (100 μm). The experiments with lacmoid were performed by diluting a stock solution of lacmoid (10 mm) in DMSO 100-fold into the above solution of ThT, fibrillar, and monomeric α-synuclein. The control experiment in this case therefore contained 1 % (v/v) DMSO. We used half-area, low-binding, clear-bottom, 96-well plates (Corning). The experiments were performed under quiescent conditions so as to simulate as closely as possible the intrinsic fluorescence time-course measurements.Atomic force microscopy (AFM): AFM images were acquired by using a VEECO Dimension 3100 atomic force microscope (Bruker) and a JPK Nanowizard . The instruments were operated in tapping mode in air by using silicon cantilevers with a resonant frequency of 300 kHz, a spring constant of 40 N m−1 and a tip radius of 10 nm . Images were collected at a scan rate of 1 Hz. Each fibrillar sample (5 μL) was deposited onto freshly cleaved mica surfaces for 2 h for adsorption. The samples were rinsed with Milli-Q water (5×200 μL) and left to dry completely in air before imaging.Confocal microscopy and spectral imaging: Spatially resolved images of the intrinsic fluorescence of amyloid fibrils were obtained with a confocal microscope , with a 405 nm diode laser as the excitation source and a 63-fold, 1.4 NA oil immersion objective. These experiments were performed on the same samples as imaged by AFM. An emission bandwidth of 20 nm was used for the spectral measurements. It was verified that photobleaching was insignificant during image and spectrum acquisition. In the kinetic experiments, the intrinsic fluorescence intensity at each time point was integrated over a defined confocal volume taken at ten different focal (Z) planes.Fluorescence lifetime imaging microscopy (FLIM): All fluorescence lifetime images were recorded on a home-built confocal microscopy platform based on a confocal microscope scanning unit (Olympus FluoView 300) coupled with an Olympus IX70 inverted microscope frame. Details can be found in ref.


Malaria parasites must undergo a round of sexual reproduction in the blood meal of a mosquito vector to be transmitted between hosts. Developing a transmission-blocking intervention to prevent parasites from mating is a major goal of biomedicine, but its effectiveness could be compromised if parasites can compensate by simply adjusting their sex allocation strategies. Recently, the application of evolutionary theory for sex allocation has been supported by experiments demonstrating that malaria parasites adjust their sex ratios in response to infection genetic diversity, precisely as predicted. Theory also predicts that parasites should adjust sex allocation in response to host immunity. Whilst data are supportive, the assumptions underlying this prediction – that host immune responses have differential effects on the mating ability of males and females – have not yet been tested. Here, we combine experimental work with theoretical models in order to investigate whether the development and fertility of male and female parasites is affected by innate immune factors and develop new theory to predict how parasites' sex allocation strategies should evolve in response to the observed effects. Specifically, we demonstrate that reactive nitrogen species impair gametogenesis of males only, but reduce the fertility of both male and female gametes. In contrast, tumour necrosis factor-α does not influence gametogenesis in either sex but impairs zygote development. Therefore, our experiments demonstrate that immune factors have complex effects on each sex, ranging from reducing the ability of gametocytes to develop into gametes, to affecting the viability of offspring. We incorporate these results into theory to predict how the evolutionary trajectories of parasite sex ratio strategies are shaped by sex differences in gamete production, fertility and offspring development. We show that medical interventions targeting offspring development are more likely to be ‘evolution-proof’ than interventions directed at killing males or females. Given the drive to develop medical interventions that interfere with parasite mating, our data and theoretical models have important implications. Malaria and related parasites cause some of the most serious infectious diseases of humans, domestic animals and wildlife. To be transmitted, these parasites produce male and female sexual stages that differentiate into gametes and mate when taken up in a mosquito blood meal. Despite the need to develop a transmission-blocking intervention, remarkably little is understood about the evolution of parasite mating strategies. However, recent research demonstrates that producing the right ratio of male to female stages is central to mating success. Evolutionary theory predicts that sex ratios are adjusted in line with a variety of factors that affect mating success, including host immunity. We test this theory by investigating whether ubiquitous immune factors differentially affect the production and fertility of males and females. Our experiments demonstrate that immune factors have complex, sex-specific effects, from reducing gamete production to affecting offspring viability. We use these results to generate theory predicting how such effects shape the evolutionary trajectories of parasite sex ratio strategies. Given the drive to develop medical interventions that prevent transmission by blocking parasite mating, our results have important implications. Specifically, we suggest that medical interventions targeting offspring development are more likely to be ‘evolution-proof’ than interventions with sex-specific effects. Plasmodium mating biology.Malaria parasites are obliged to undertake a single round of sexual reproduction in the mosquito vector before they can transmit to new hosts, making this stage of their life-cycle a potential target for medical interventions Every asexual replication cycle, a small proportion of parasites differentiate into male and female sexual stages – termed gametocytes – which are developmentally arrested gamete precursors Plasmodium and could play an important role in the response of malaria parasites to medical interventions that aim to reduce mating success Sex allocation is an important fitness-related trait in et al.P. gallinaceum and P. vinckei increase their sex ratio in response to erythropoiesis, which is thought to act as a cue for the appearance of TBI factors. Second, Reece et al.P. chabaudi genotypes is a mechanism to ensure fertility in face of within-host competition, host anaemia and TBI factors. Fertility Insurance currently provides the best explanation for the observed within-infection variation in the sex ratios of malaria parasites. However, the theory is based upon the untested assumption that TBI factors reduce the fertility of males more than females. Here we provide the first direct test of this key assumption by investigating whether reactive nitrogen species and pro-inflammatory cytokines, influence gametogenesis, gamete fertility and ookinete production.Currently, two complementary evolutionary theories predict how and why parasites should adjust their investment into male and female gametocytes to maximise fertilization success. These theories – Fertility Insurance and Local Mate Competition – predict that parasites adjust sex ratios in response to environmental (e.g. transmission-blocking immunity) and social factors (inbreeding rate), respectively Plasmodium gametocytes, across a variety of host-parasite systems P. falciparum and P. vivax gametocytes Plasmodium infections, RNS appears to impair asexual replication, gametogenesis and zygote development P. yoelii infections and reduce ookinete production when either gametocytes or gametes are exposed P. berghei ookinetes P. berghei oocyst burdens in Anopheles mosquitoes Levels of reactive nitrogen species (RNS) and pro-inflammatory cytokines vary during malaria infections. These immune factors, which are ubiquitous components of the innate immune system, have been specifically implied in the sudden loss of infectivity to vectors that occurs during paroxysms and infection crisis Plasmodium berghei to conduct a series of experiments to investigate how RNS and TNF-α influence mating success and ookinete production and develop theoretical models that predict the evolution of sex allocation strategies, given the effects observed in our experiments. Therefore, we use these immune manipulations as ‘proof-of-principle’ for other factors with similar effects on the sexual reproduction and transmission of malaria parasites. Specifically, we test whether: (1) RNS and TNF-α have dose dependent effects on male gametogenesis (exflagellation) and ookinete production; (2) exposure of male and female gametocytes to both RNS and TNF-α influences their sexual development; (3) the greater effect of RNS we observe on male gametogenesis results in sex-specific fertility effects; and (4) the observed effects of RNS depend on the developmental stage at which parasites are exposed. Our results reveal that RNS reduces male but not female gametogenesis and impairs the fertility of both sexes, whereas TNF-α only affects zygote development. The relative importance of reduced gametogenesis, impaired mating ability and reduced post-mating development have not been explicitly considered by Fertility Insurance theory. Therefore we develop a new mathematical model to derive predictions for how the effects of immune factors generated naturally or by a medical intervention are likely to impact upon parasite sex ratio evolution , or conditions that ‘mimicked the host’  All the experiments we describe below were performed  = 16.28, P<0.0001; transformed y = 0.16-0.10x) and ookinetes  = 25.86, P<0.0001; transformed y = 0.17-0.18x). Similarly, TNF-α also caused a significant linear decrease in the densities of exflagellating males  = 6.83, P = 0.012; y = 0.23-0.09x) and ookinetes  = 17.53, P<0.0001 ; transformed y = 0.54-0.37x).We first tested whether RNS and TNF-α influence sexual reproduction by exposing parasites to different concentrations of these factors and assaying exflagellation and ookinete production. We incubated parasites in vector mimicking media across seven concentrations of SIN-1 (ranging from 0 to 1 mg/ml) Having found significant negative effects of RNS and TNF-α on exflagellation and ookinete production we investigated whether these factors interacted with each other to further reduce parasite mating success and if these effects depended on the developmental stage at which parasites were exposed (i.e. in host or vector conditions). For this set of experiments we used a fully cross-factored design, consisting of two RNS and two TNF-α levels see .21 = 2.72, P = 0.099) or TNF-α . In contrast, the proportion of male gametocytes that emerged from RBCs was significantly reduced by RNS  = 81.29; P<0.0001; mean ‘RNS−’ 0.55±0.02; ‘RNS+’ 0.32±0.02) but not by TNF-α . Similarly, the ability of males to exflagellate was significantly reduced by RNS  = 33.40; P<0.0001; mean ‘RNS−’ 0.15±0.01; ‘RNS+’ 0.09±0.01) but not by TNF-α .First, we investigated the effects of RNS and TNF-α on gametocytes by incubating parasites for 60 minutes in host mimicking media. We then replaced treatment media with vector mimicking media (without RNS or TNF-α manipulations) to stimulate gametogenesis and quantified the development of male and female gametocytes into gametes using the following classifications: (a) mature gametocytes still inside their RBC, (b) gametocytes that had emerged from the RBC and (c) exflagellating male gametes see . The pro = 11.24, P = 0.002; mean ‘RNS−’ 0.32±0.06; ‘RNS+’ 0.12±0.03). This effect was enhanced by TNF-α  = 6.67, P = 0.014) but in the absence of RNS, TNF-α had no significant effect  = 1.90, P = 0.175). Conversely, the effect of RNS and TNF-α on ookinete production depended on each others presence  = 14.91, P = 0.001). Specifically, ookinete production was reduced by TNF-α but only in the absence of RNS , whereas RNS reduced ookinete production but only when TNF-α was absent .Second, we investigated the effects of RNS and TNF-α on exflagellation and ookinete production by incubating parasites in culture media mimicking the vector environment . In lineP. berghei lines: Pbs48/45ko and Pbs47ko Experiment 2 revealed that only RNS had a significant effect on gametogenesis, in which male but not female development was impaired. Therefore, we tested whether these effects translated into sex-specific differences in fertility (i.e. whether matings with RNS exposed gametocytes/gametes resulted in fewer ookinetes), when parasites were exposed as gametocytes (in host-mimicking media) or during gametogenesis (in vector-mimicking media). We separately exposed each sex to RNS using two genetically transformed   = 15.87, P = 0.0001; mean ‘RNS−’ 0.30±0.02; ‘RNS+’ 0.20±0.02). In contrast to our predictions, RNS did not have sex-specific effects , nor was this effect influenced by exposing parasites to RNS in host- or vector-mimicking environments . However, across all treatments, parasites exposed in host conditions produced significantly more ookinetes than those exposed in vector conditions  = 10.19, P = 0.0018; mean ‘Host’ 0.29±0.02; ‘Vector’ 0.21±0.02).We observed that RNS exposure significantly reduced fertility of both males and females regardless of whether parasites were exposed as gametocytes or during gametogenesis ; blocking the mating ability of male gametes; and causing damage to gametocytes or gametes such that mating can occur but zygotes are not viable. We term the latter phenomenon, of cryptic damage to gametocytes or gametes that results in a dead zygote, as dysfunction. Note that, although we do not observe all of the effects on all stages and all sexes, we incorporate them all in the model (illustrated in p<1) have no impact on the evolutionarily stable (ES) sex ratio W = ζ(z) p, i.e. fitness is the product of zygote production and zygote viability, where zygote production depends upon sex ratio but zygote viability does not. The direction of selection is given by the derivative of fitness with respect to sex ratio W/dz = (dζ/dz)p. The ES sex ratio z* satisfies dW/dz|z = z* = 0, i.e. selection does not favour an increase or decrease in sex ratio when the population is at the ES sex ratio, and this is equivalent to the condition dζ/dz|z = z* = 0 for all p>0. Since ζ is not a function of p, it follows that z* is not a function of p . An exploration of the ES sex ratio z* across this parameter space is presented in Second, to investigate the impact of model parameters arising from gametocyte or gamete killing on the ES sex ratio, we write an explicit expression for expected fitness:q) increases. We also show that factors causing gametes to become dysfunctional (resulting in inviable zygotes) do not affect the ES sex ratio. Below, we discuss the results of our experiments, explain the evolutionary predictions of our model and its implications for the development of transmission-blocking interventions.Evolutionary theory developed to explain the sex allocation strategies of metazoan taxa has enjoyed huge success. Recently, there has been growing interest in whether this theory could be applied to protozoans, particularly malaria parasites per se is unlikely to be influenced by RNS, the development of fertilized females into zygotes and ookinetes is likely to be affected. For example, damage to stored mRNA and inhibition of protein synthesis or mitochondrial activity (e.g. cytochrome oxidases) would impair meiosis (at ∼3 h after fertilization) and zygote development, but not impair fertilization In our experiments, RNS reduced male but not female gametogenesis while impairing the fertility of both sexes. How can these results be explained? In parasitic infections, high levels of RNS may cause: oxidative damage of DNA (leading to mutations and strand brakes); inhibition of DNA repair and synthesis; inhibition of protein synthesis; inhibition of mitochondrial activity; down- or up-regulation of cytokine (e.g. TNF-α) levels Our experiments show that TNF-α consistently reduces ookinete production and whilst we observed a reduction in exflagellation in some experiments, this effect was inconsistent. Why does TNF-α reduce ookinete production? As TNF-α functions are mainly modulatory and need time to develop, it is possible that gametogenesis and mating occur before the effects of TNF-α manifest. Ookinete development takes about 18–20 hours from fertilization and during this time TNF-α could exert its effects, which could also involve the activation of apoptotic-like death q), number of gametes formed per male gametocyte (0≤χ≤8) and gamete and/or gametocyte mortality. Although, our model makes no assumptions about whether parasites achieve an ES sex ratio through the evolution of facultative or fixed sex allocation strategies, facultative sex allocation is predicted for reasons already outlined in the introduction.The results of our experiments show that TBI factors can affect the sexual development and fertility of male and female parasites and that the stage at which this occurs is sex-specific. As illustrated in q→∞), that behaves deterministically, the ES sex ratio is one that leads to the same number of male and female gametes being present in the mating pool. This is the sex ratio z* that satisfies cz* = 1-z*, i.e. z* = 1/(c+1), where c is the number of male gametes, able to mate, produced per male gametocyte c>1, and male biased if c<1 (q<∞) – that behave stochastically – the expectation of mating success must be calculated over the whole distribution of possible outcomes. This will tend to reduce the extent to which the sex ratio is biased towards the sex favoured in the deterministic case q = 2; the lowest mating group size for which mating success is possible), the ES sex ratio is always z* = 0.5 , to maximise the probability of both sexes being present (χ) – fertility insurance can even lead to a sex ratio bias in the opposite direction . For an infinite gametocyte group size . Put simply, this suggests that zygote mortality or gametocyte/gamete dysfunction will not impose selection on parasite sex allocation strategies as parasites cannot compensate for the loss of reproductive success through sex ratio adjustment. More broadly, other immune factors, such as antibodies or complement, could also impair the sexual reproduction of malaria parasites and the effects of such factors should be easily interpreted in light of our theoretical models.q), parasites should produce a less female biased sex ratio than expected by the inbreeding rate alone. This is due to the stochastic risk of too few males being present in the blood meal to fertilize the females when sex ratios are female biased To bring our mathematical modelling in line with our experiments we have focused on the importance of mortality and dysfunction throughout the sexual development of malaria parasites. However two additional factors have an important impact in sex allocation strategies of malaria parasites: (1) the inbreeding rate and (2) the rate at which asexually replicating parasites commit to gametocyte production (conversion rate). The effect of inbreeding on the ES sex ratio is well understood, with theory  enjoying strong empirical support Our model reveals that an intervention with a sex-specific effect on mating ability will elicit an evolutionary response. However, sex ratio adjustment cannot fully rescue zygote production, given that an increase in the number of male gametocytes comes at the cost of decreasing the number of female gametocytes. Nevertheless, in a scenario of widespread transmission-blocking vaccination or treatment with gametocidal drugs with a sex-specific effect, natural selection will “compare” the fitness of parasites that do, and do not, adjust their sex allocation strategies, leading to an increase in the frequencies of the former. Therefore, quantifying the impact of sex ratio adjustment on rescuing fertility and thus, fitness is now required. In contrast, our model also reveals that a transmission-blocking factor resulting in zygote mortality or gametocyte/gamete dysfunction will be ‘evolution proof’ with respect to parasite sex allocation strategies. Therefore, we suggest that current efforts to prevent fertilization by targeting proteins with sex-specific phenotypes, such as P230, P48/45 (involved in gamete attachment) or Pfg377 , will be less effective than vaccines targeting zygote development (e.g. P28) Given the drive to develop transmission-blocking interventions that disrupt sexual reproduction in malaria parasites, there is an urgent need to evaluate how their short- and long-term success will be influenced by parasite mating strategies. Here, we combined experiments with mathematical modelling to predict how transmission-blocking factors influence parasite sex allocation strategies. Our model predicts that transmission-blocking interventions causing gametocyte/gamete dysfunction and/or zygote mortality will be ‘evolution-proof’ from the perspective of imposing selection on parasite sex ratio strategies, i.e. parasites may still evolve other strategies or traits to cope with a transmission-blocking intervention, but these will have to be independent of sex allocation. Put simply, understanding the behavioural strategies that parasites have evolved to cope with naturally occurring transmission-blocking immune factors, will inform predictions for how they will respond to a transmission-blocking factor. More broadly, understanding how, when and why parasites respond to changes in their in-host environment will facilitate the development of interventions that induce parasites to make decisions that are suboptimal for their transmission success, but that are clinically or epidemiologically beneficial. For efficient progress, synergy between research directed at evolutionary and mechanistic explanations for parasite traits and strategies is required.ad libitum food (RM3(P), DBM Scotland Ltd, UK) and water (supplemented with 0.05% PABA to enhance parasite growth), with a 12 hour light cycle, at 21°C. We initiated infections by intra-peritoneal inoculation of 107 parasitized RBCs in 100 µl carrier consisting of 50% Ringers , 47.5% heat-inactivated foetal bovine serum and 2.5% heparin (5 units ml−1). For experiments 1 and 2, we inoculated female mice, previously (day −3 or −4) treated with 60 mg/kg of phenylhydrazine (PHZ), with P. berghei line 820 P. berghei KO lines: Pbs48/45ko or Pbs47ko P. berghei, which maximises the number of gametocytes that can be harvested for in vitro mating experiments We maintained MF1 mice, aged 8–10 weeks , on All the protocols involving mice passed an ethical review process and were approved by the U.K. Home Office (Project License 60/3481). Work was carried according to the Animals (Scientific Procedures) Act, 1986.−), SIN-1 is likely to act as a donor of either NO or peroxynitrite, depending on the rates at which SIN-1 generates NO and superoxide In order to manipulate the levels of RNS and TNF-α we used the following chemicals: recombinant mouse TNF-α , L-ana  and SIN-1 . We dissolved all chemicals in phospate buffered saline and exposed parasites to treatments in 1 ml cultures with 15 or 20 µl parasitized blood. L-ana is a specific inhibitor of the activity of the enzyme inducible nitric oxide synthase which becomes active in response to infection. SIN-1 donates NO and/or superoxide, in solution, at different rates depending on the specific conditions in which SIN-1 is incubated We set up cultures with vector mimicking media for the following SIN-1 concentrations: 0, 0.00001, 0.0001, 0.001, 0.01, 0.1 and 1 mg/ml We used the following RNS and TNF-α levels: 1 mg/ml SIN-1 (RNS+), 1 mg/ml of L-ana (RNS−), and presence (TNF-α+) or absence (TNF-α−) of 1 µg/ml recombinant mouse TNF-α. Parasites from each of 20 mice were exposed to all four combinations of treatments. We used the following criteria to classify developmental stages of gametogenesis after 15 minutes incubation in vector mimicking media: (1) Mature gametocytes: still inside their RBC; females have blue-purple cytoplasm, small, well defined purple nucleus surrounded by a small nucleolus; males have pink-yellow cytoplasm and large disperse pale-pink nucleus. (2) Emerged females: female gamete condensed into a more circular shape, without a vacuole, cytoplasm staining a more intense blue and a less obvious nucleolus than in a female gametocyte. (3) Emerged male: male gamete with a large circular nucleus in the centre of the cell surrounded by a ring of cytoplasm. (4) Exflagellating male: emerged male gamete progressed to forming up to 8 flagella that protrude from the cell and stain red-purple −5 mg/ml SIN-1, mimicking host (60 min. incubation) or vector conditions (15 min. incubation), to which we added 15 µl of parasites from one of the infections in each pair. These single sex cultures provided ‘exposed’ parasites for fertility testing, and corresponded to the following factorial design: 2 conditions (host/vector)×2 SIN-1 exposures (RNS+/−)×2 sexes . After incubation we replaced media in all cultures with 1 ml vector mimicking media (without any SIN-1 manipulation). While ‘exposed’ parasites were incubating, we collected 60 µl of blood from each infection's pair and added these ‘unexposed’ parasites to 4 ml cultures in vector mimicking media (without SIN-1). Each 1 ml culture of the ‘exposed’ parasites was then added to a 4 ml culture containing its ‘unexposed’ pair and incubated to produce ookinetes (as for Experiment 1). This allowed us to ensure that the mating success of the ‘exposed’ sex would not be limited by the availability of ‘unexposed’ gametocytes from the opposite sex. All the cultures were timed so that ‘exposed’ parasites were added to the cultures containing their ‘unexposed’ mates at the same developmental stage. For example, a final 5 ml culture could contain 15 µl of blood from a RNS exposed Pbs48/45ko infection  and 60 µl of blood from a Pbs47ko infection . We also set up cultures in vector mimicking media to verify that ‘unexposed’ parasites from each line are unable to produce ookinetes on their own. We recorded the densities of ookinetes as described for experiment 1.We infected 38 mice with Pbs47ko (n = 19) or Pbs48/45ko (n = 19). We set up mating cultures following Reece et al. www.R-project.org) because, by treating each infection (or pair of infections in Experiment 3) as a ‘random’ effect, we can account for problems associated with pseudoreplication arising from repeated measurements of each infection. In order to meet the assumptions made by parametric tests we arcsine square root transformed response variables where necessary. We minimised models following stepwise deletion of the least significant term and using log-likelihood ratio (2χ) tests to evaluate the change in model deviance until only significant terms remained, and we present F-ratios for fixed effects remaining in minimal models. We then re-ran minimal models using restricted maximum likelihood to estimate the effect sizes reported in the text. Unless otherwise indicated, data and estimated effect sizes are presented as proportions of the focal parasite stage produced in a given treatment, relative to that produced across all treatments for each infection.We used linear mixed effects models  . Consequently, the number of female gametocytes is q-α. Male and female gametocytes are killed with probability Md and Fd respectively, leaving Γ∼Bi surviving males and φ∼Bi surviving females. We assume every surviving male produces χ gametes, and every surviving female produces a single gamete. We consider that male gametes are killed with probability Mδ, and hence γ∼Bi male gametes enter the mating pool. We assume that all φ female gametes enter the mating pool . Therefore, the number of zygotes is equal to the number of gametes of the limiting sex, i.e. ζ = min. Finally, we assume that only a proportion p of zygotes are viable, due to either: (a) factors that kill each zygote with probability ZΩ; (b) factors acting on gametocytes resulting in the production of dysfunctional gametes at rate MΩ for males and FΩ for females; or (c) factors acting on gametes and causing them to become dysfunctional at rate ϖM for males and ϖF for females, i.e. p = (Z1-Ω)(M1-Ω)(F1-Ω)(M1-ϖ)(F1-ϖ). In this context, we use the term ‘dysfunctional’ to refer to a gamete that achieves fertilisation but carries sufficient damage to render the resulting zygote inviable (i.e. unable to develop as an ookinete). Inviable zygotes will result when one or both of the parental gametes are dysfunctional. Hence, the number of viable zygotes produced by the mating group is W = ζ p, and this is our measure of fitness We assume an infinite host population, divided into infected and uninfected individuals, with infected hosts containing a single infection producing haploid gametocytes that circulate in the blood. We assume that Figure S1Evolutionarily stable sex allocation strategies when sex- and stage-specific mortality rates vary (χ = 1). Effect of male and female gametocyte mortality and male gamete mortality on the ES gametocyte sex ratio (z*), for a clonal population, when the number of gametes per male gametocyte (χ) is 1. On each plot, z* varies with male gamete mortality rate (δM). The coloured lines represent different gametocyte group sizes (q): 2 (grey), 5 (blue), 10 (red), 20 (green) and ∞ (yellow). Every plot depicts different parameter combinations of male gametocyte  and female mortality rate , with dM increasing left to right and dF increasing bottom to top.(0.16 MB PDF)Click here for additional data file.Figure S2Evolutionarily stable sex allocation strategies when sex- and stage-specific mortality rates vary (χ = 4). Effect of male and female gametocyte mortality and male gamete mortality on the ES gametocyte sex ratio (z*), for a clonal population, when the number of gametes per male gametocyte (χ) is 4. On each plot, z* varies with male gamete mortality rate (δM). The coloured lines represent different gametocyte group sizes (q): 2 (grey), 5 (blue), 10 (red), 20 (green) and ∞ (yellow). Every plot depicts different parameter combinations of male gametocyte  and female mortality rate , with dM increasing left to right and dF increasing bottom to top.(0.21 MB PDF)Click here for additional data file.Figure S3Evolutionarily stable sex allocation strategies when sex- and stage-specific mortality rates vary (χ = 8). Effect of male and female gametocyte mortality and male gamete mortality on the ES gametocyte sex ratio (z*), for a clonal population, when the number of gametes per male gametocyte (χ) is 8. On each plot, z* varies with male gamete mortality rate (δM). The coloured lines represent different gametocyte group sizes (q): 2 (grey), 5 (blue), 10 (red), 20 (green) and ∞(yellow). Every plot depicts different parameter combinations of male gametocyte  and female mortality rate , with dM increasing left to right and dF increasing bottom to top.(0.20 MB PDF)Click here for additional data file.