Acrosome

Protein sequences were collected from the Swiss-Prot database at http://www.ebi.ac.uk/swissprot/. The detailed procedures are basically the same as described in [14] (link); the only difference is: in order to establish a more updated benchmark dataset, instead of version 50.7 of the Swiss-Prot database released on 9-Sept-2006, the version 55.3 released on 29-Apr-2008 was adopted. After strictly following the procedures as described in [14] (link), we finally obtained a benchmark dataset containing 7,766 different protein sequences that are distributed among 22 subcellular locations (Fig. 1); i.e., where represents the subset for the subcellular location of “acrosome”, for “cell membrane”, for “cell wall”, and so forth; while represents the symbol for “union” in the set theory. A breakdown of the 7,766 eukaryotic proteins in the benchmark dataset according to their 22 location sites is given in Table 1. To avoid redundancy and homology bias, none of the proteins in has pairwise sequence identity to any other in a same subset. The corresponding accession numbers and protein sequences are given in Online Supporting Information S1.
Because the system investigated now contains both the single-location and the multiple-location proteins, some of the proteins in may occur in two or more location sites. Therefore, it is instructive to introduce the concept of “virtual sample”, as illustrated as follows. A protein sample coexisting at two different location sites will be counted as 2 virtual samples even though they have an identical sequence; if coexisting at three different sites, 3 virtual samples; and so forth. Accordingly, the total number of the different virtual protein samples is generally greater than that of the total different sequence samples. Their relationship can be formulated as follows where is the number of total different virtual protein samples in , the number of total different protein sequences, the number of proteins with one location, the number of proteins with two locations, and so forth; while is the number of total subcellular location sites (for the current case, as shown in Fig. 1 and Table 1).
For the current 7,766 different protein sequences, 6,687 occur in one subcellular location, 1,029 in two locations, 48 in three locations, 2 in four locations, and none in five or more locations. Substituting these data into Eq.2, we have which is fully consistent with the figures in Table 1 and the data in Online Supporting Information S1.
As stated in a recent comprehensive review [20] , to develop a powerful method for statistically predicting protein subcellular localization, one of the most important things is to formulate the sample of a protein with the core features that have intrinsic correlation with its localization in a cell. Since the concept of pseudo amino acid composition (PseAAC) was proposed [16] , it has provided a very flexible mathematical frame for investigators to incorporate their desired information into the representation of protein samples. According to its original definition, the PseAAC is actually formulated by a set of discrete numbers [16] as long as it is different from the classical amino acid composition (AAC) and that it is derived from a protein sequence that is able to harbor some sort of its sequence order and pattern information, or able to reflect some physicochemical and biochemical properties of the constituent amino acids. Since the concept of PseAAC was proposed, it has been widely used to deal with many protein-related problems and sequence-related systems (see, e.g., [21] (link), [22] (link), [23] (link), [24] (link), [25] (link), [26] (link), [27] (link), [28] (link), [29] (link), [30] (link), [31] (link), [32] (link), [33] (link), [34] (link), [35] (link), [36] , [37] (link), [38] (link), [39] , [40] (link), [41] , [42] and a long list of PseAAC-related references cited in a recent review [20] ). As summarized in [20] , until now 16 different PseAAC modes have been used to represent the samples of proteins for predicting their attributes. Each of these modes has its own advantage and disadvantage. In this study, we are to formulate the protein samples by hybridizing the following three different modes of PseAAC.

In this study, let us introduce a novel classifier, called the multi-label KNN or abbreviated as ML-KNN classifier, to predict the subcellular localization for the systems that contain both single-location and multiple-location proteins.
Without losing generality, let us consider a system or dataset that contains eukaryotic proteins classified into subcellular location sites (Fig. 1); i.e.,
where represents the subset for the subcellular location of “acrosome”, for “cell membrane”, for “cell wall”, and so forth (cf Table 1); while represents the symbol for “union” in the set theory. For convenience, hereafter let us just use the subscripts of Eq.17 as the codes of the 22 location sites; i.e., “1” for “acrosome”, “2” for “cell membrane”, “3” for “cell wall”, and so forth (Table 2).
Suppose is the protein in the subset of (Eq.17). Thus, we have where and have the same forms as (Eq.6), and (Eq.15), respectively; the only difference is that the corresponding constituent elements are derived from the amino acid sequence of instead of .
In sequence analysis, there are many different scales to define the distance between two proteins, such as Euclidean distance, Hamming distance [59] , and Mahalanobis distance [51] (link), [60] , [61] . In [40] (link), the distance between and was defined by . However, we found that when the GO descriptor was formulated with real numbers, better results would be obtained by using the Euclidean metric; i.e., the distance between and is defined here by where represents the module of the vector difference between and in the Euclidean space. According to Eq.19, when we have , indicating the distance between these two protein sequences is zero and hence they have perfect or 100% similarity.
Suppose are the K nearest neighbor proteins to the protein that forms a set denoted by , which is a subset of ; i.e., Based on the K nearest neighbor proteins in , let us define an accumulation-layer (AL) scale, given by where where and Note that because a protein may belong to one or more subcellular location sites in the current system.
Now, for a query protein , its subcellular location(s) will be predicted according to the following steps.

In order to compare variability of body measures and sperm traits across the species, coefficients of variation (CV) were calculated as follows: CV = (SD * 100)/ , where SD = standard deviation, and  = mean. Variables were transformed to attain normal distributions. Normal distribution was tested by using a Kolmogorov–Smirnov normality test.
To explore relationships between total sperm number, % normal sperm, % acrosome integrity, % live sperm and % motile sperm, we calculated the effect size r of the correlations between the variables with phylogenetic correction. The level of test significance was adjusted to P<0.05. Using correlation matrix values between sperm numbers and sperm quality traits, we constructed a cluster diagram with single linkage-joining rule (distance metric = 1−r) to identify relationships between sperm traits.
A global measure of sperm quality (“overall sperm quality”) was obtained by means of a principal component analysis (PCA) to reduce potentially correlated variables of sperm quality (% normal sperm, % acrosome integrity, % live sperm, % motile sperm) to a single variable that would summarize the original information. This analysis extracted the first and second eigenvectors that summarized multivariate quality variation and best represented “quality components” [72] .
To test whether different levels of sperm competition were associated with sperm numbers and quality across species, multiple regression analysis were performed using as dependent variables: total sperm number, % normal sperm, % acrosome integrity, % live sperm, % motile sperm and the global measure of sperm quality (“overall sperm quality”) calculated by PCA. Body mass and testes mass were used as predictor variables. Since predictor variables were related to each other (thus non orthogonal), they were added to the multiple regression analysis in the following order: body mass, testes mass, using a sequential (Type I) sum of squares.
As species may share character values as a result of a common ancestry rather than independent evolution [77] , we used a generalized least-squares (GLS) approach in a phylogenetic framework [78] (link) to control for phylogenetic effect on the associations of the variables. This method estimates a phylogenetic scaling parameter lambda (λ), which represents the transformation that makes the data fit the Brownian motion evolutionary model. When λ values are close to 0, variables are likely to have evolved independently of phylogeny, whereas λ values close to 1 indicate that the variables are strongly phylogenetically associated. GLS method allows for a variable degree of phylogenetic correction according to each tested model, accounting for different levels of phylogenetic association between different traits. The estimation of λ values and GLS analyses were performed using a code written by R. Freckleton for the statistical package R v.2.10.1 (R Foundation for Statistical Computing 2010) and the maximum likelihood value of λ was compared against the models with λ = 0 and λ = 1.
We reconstructed a phylogenetic tree of the species used in this study (Fig. S2) from partial phylogenies from the literature that were based on several mitochondrial, nuclear and ribosomal genes [79] (link)–[89] . We also used cytochrome b sequences to clarify relationships among Mus musculus subspecies that were not resolved in previous studies. GenBank accession numbers for the sequences used are: Arvicola terrestris, AF159400; Chionomys nivalis, AY513848; Clethrionomys glareolus, AY309421; Microtus arvalis, AY220789; Microtus cabrerae, AY513788; Microtus duodecimcostatus, AY513796; Microtus lusitanicus, AY513812; Apodemus sylvaticus, AB033695; Mus cookii, AY057813; Mus famulus, AJ698872; Mus macedonicus, AY057808; Mus musculus bactrianus, HQ148567; Mus m. castaneus, AY057805; Mus m. domesticus, AY057807; Mus m. musculus, AY057804; Mus pahari, AY057814; Mus spicilegus, AY057809; Mus spretus, AY057810.
All statistical analyses were conducted with R v.2.10.1 and STATISTICA v.6.0, and P values were considered statistically significant at α<0.05.
In order to plot relative testes mass in the figures we calculated relative testes mass for each species following Kenagy and Trombulak's [58] formula for rodents: Y = 0.031X^0.77, where Y is predicted testes mass in grams for the observed body mass X. Relative testes mass is calculated as the ratio of observed testes mass to the predicted testes mass Y. Relative testes mass was not used in any of the statistical analyses because this measure does not properly account for the allometric relationships between the variables [90] .

Lectins Histochemistry: Wheat germ agglutinin (WGA), peanut agglutinin (PNA), and concanavalin A (ConA) (all from Sigma, USA) were used to detect non-capacitated, acrosome intact, and acrosome-reacted spermatozoa, respectively. The smears of the thawed samples were fixed with 2% paraformaldehyde for 20 min. After washing with phosphate-buffered saline (PBS), the samples were incubated with fluorescein isothiocyanate (FITC)-conjugated lectins at 10 μg/mL dilution for two hours and double stained with Hoechst (Sigma, USA) for five min. The slides were evaluated using the Eclipse E600 fluorescent microscope (Nikon, Japan).
Flow Cytometry: Thawed samples were washed with 800 µL of PBS, centrifuged at 170 g for 10 min, and fixed with 2% paraformaldehyde for 30 min at 4 °C.
Thereafter, the aliquots were centrifuged, and the pellets were resuspended in PBS. The aliquots containing 1×10⁵ cells were exposed to FITC-conjugated lectins
at a dilution of 10 μg/mL for two hours at 37 °C. The samples were assessed using the FL1 channel (wavelengths ≈495 nm) and FL3 channel (wavelength >575 nm)
of the FACSCalibur^TM flow cytometer (BD Biosciences, USA). The data were analyzed using FlowJo software (BD Biosciences, USA).