Robust Accurate Identification and Biomass Estimates of Microorganisms via Tandem Mass Spectrometry

Abstract

Rapid and accurate identification of microorganisms and estimation of their biomasses are of extreme importance to public health. Mass spectrometry has become an important technique for these purposes. Previously we published a workflow named Microorganism Classification and Identification (MiCId v.12.26.2017) that was shown to perform no worse than other workflows. This manuscript presents MiCId v.12.13.2018 that, in comparison with the earlier version v.12.26.2017, allows for biomass estimates, provides more accurate microorganism identifications (better controls the number of false positives), and is robust against database size increase. This significant advance is made possible by several new ingredients introduced: first, we apply a modified expectation-maximization method to compute for each taxon considered a prior probability, which can be used for biomass estimate; second, we introduce a new concept called ownership, through which the participation ratio is computed and use it as the number of taxa to be kept within a cluster of closely related taxa; third, based on confidently identified peptides, we calculate for each taxon its degree of independence from the rest of taxa considered to determine whether or not to split this taxon off the cluster. Using 270 data files, each containing a large number of MS/MS spectra, we show that, in comparison with v.12.26.2017, version v.12.13.2018 yields superior retrieval results. We also show that MiCId v.12.13.2018 can estimate species biomass reasonably well. The new MiCId v.12.13.2018, designed to run in Linux environment, is freely available for download at https://www.ncbi.nlm.nih.gov/CBBresearch/Yu/downloads.html.

Graphical Abstract

1. INTRODUCTION

Rapid and accurate identification of microorganisms, the proteins they express, and their biomass estimates are of extreme importance to public health.^1–3 Reducing the time needed to identify pathogenic microorganisms and the proteins expressed are especially important in clinical setting:⁴ patients infected by a single or multiple pathogens will evidently benefit from a fast and accurate diagnosis. Once the microorganisms causing the infections are identified, along with their antibiotic resistant proteins,⁵ if present, targeted treatment with proper agents can be administered which can increase patients’ survival rate and minimize improper use of antibiotics.^6,7 Trustworthy biomass estimates, on the other hand, are critical for microbial community structure analyses that arise in almost every microbiome study.^8–10

Recently, molecular methods such as polymerase chain reaction (PCR), next-generation sequencing (NGS), and mass spectrometry (MS) have sped up microorganism identifications^11–17 and have been used for biomass estimates.^8,18,19 For a survey of available workflows for analyzing NGS and MS/MS data in meta-omics studies, we refer readers to publications.^20–23 The current manuscript focuses on the identifications and biomass estimates of multiple microorganisms using high-performance liquid chromatography coupled to a high resolution tandem MS (HPLC–MS/MS).

Workflows for identification/classification of microorganisms via HPLC–MS/MS, also known as proteotyping,¹⁵ can be categorized into two main groups: those that utilize confidently identified taxon-specific peptides, i.e., peptides that are unique to a given taxon,^24–27 and those that utilize all confidently identified peptides.^28–30 Methods of the former type usually use the least common ancestor algorithm for taxa identifications. Basically, with a specified cutoff number for taxon-specific peptides, at a given taxonomy level, a taxon is considered identified if it has more taxon-specific peptides than the specified cutoff. However, if the cutoff is set too low, the identifications may be plagued with false positives while if the cutoff is set too high, the sensitivity drops.^5,31 There is also a subtle dependence on the database used since a peptide can be a taxon-specific peptide in a smaller database but become a shared peptide with other taxa in a larger database. In addition, the typical number of identifiable unique peptides may vary with the sample preparation, concentration and complexity. That is, the best cutoff number learned from one case might not be ideal for the other.

Methods of the latter type assess the peptide evidence globally.^28–30 By having a bigger candidate pool for evidence peptides than methods of the former type, methods of this type reduce the influence of a few falsely identified taxa-specific peptides that could have occurred due to sequencing/database errors or random false matches. However, they face a different challenge (that is also shared by the former methods) arising from a high degree of sequence similarity among taxa, especially at the species level and lower, and the scenarios when taxa have a low number of identified peptides due to low abundances or high sample complexity.^21,30 Under these circumstances, the identified taxon-specific peptides can be scarce to meet the cutoff and the majority of evidence peptides are shared among taxa. The former methods will report no identifications at this taxonomy level. For the latter methods, however, the identification is most naturally done with taxa sharing a substantial portion of their evidence peptides clustered together. This may not be considered a specific enough identification in real applications as the number of member taxa could be large. To provide usable information, it is critical to be able to narrow down the number of member taxa in a cluster (unambiguous identification) and to have the right means to split a taxon off a cluster if it has enough independent evidence.

In earlier publications^28,32 we have evaluated our workflow, named Microorganism Classification and Identification (MiCId v.12.26.2017) and demonstrated the following: (1) MiCId can correctly identify microorganisms at the genus and species levels from samples composed of single and multiple microorganisms, (2) our method for assigning statistical confidence to identified microorganisms via combining peptides’ E-values³³ can be used to control false positives without the need of a decoy database,^34–36 (3) using a large published dataset,³⁷ we showed that, in terms of microorganism identifications, MiCId performs no worse than three other workflows (MetaProteome Analyzer (MPA; v.1.0.6) using X!Tandem, MaxQuant (MQ; v.1.5.2.8), and Proteome Discover (PD; v.1.4.1.14) using Sequest-HT and Percolator) that perform taxonomic identification via Unipept,³⁸ and (4) MiCId, when compared directly with Unipept, shows a better true positive rate and stronger control over the number of false positives. A direct comparison against MEGAN²⁴ was not conducted because Unipept was already shown to outperform MEGAN in microorganism identification using MS/MS data.^31,39 We also do not compare with other workflows either because they are, for pragmatic reasons (such as very long run time), limited to using small databases³⁰ or because they rely on Unipept/MEGAN for the identification of microorganisms.^40,41

The new MiCId version presented here outperforms the previous version in multiple aspects. Unlike the previous version, the new version v.12.13.2018 is able to estimate microorganism’s protein biomass contributions. Estimating microorganism’s protein biomass contributions in a microbial community is an important but challenging task. The most popular approach is to first identify peptides, map the identified peptides to proteins, and then map the identified proteins to taxa.⁸ A taxon’s protein biomass is then attained by applying various heuristics to estimate the abundances of taxon-specific proteins.^8,42,43 Errors introduced in any of the steps above will propagate to the next, hence undermining the accuracy of the biomass estimates. As described in ref 8, the challenging protein inference problem arises during the step of mapping peptides to proteins because it is often difficult to control the errors in such mappings. For protein biomass estimates, MiCId v.12.13.2018 does not suffer from the protein inference problem as it bypasses this step and goes directly from all peptides mappable to a taxon to the taxon’s prior, which can be viewed as that taxon’s protein biomass up to an overall proportionality constant that is the sum of protein biomasses from all taxa present. (In other words, the ratio of the protein biomass of taxon $t_{\beta }$ to the protein biomass of taxon $t_{\gamma }$ in an analyzed sample is equal to the ratio of the prior of taxon $t_{\beta }$ to the prior of taxon $t_{\gamma }$.)

In addition to being able to provide biomass estimates of microbes, the MiCId version (v.12.13.2018) presented in this manuscript surpasses the earlier version (v.12.26.2017) in specifying the appropriate number of taxa to be kept in a cluster, in providing a criterion for determining whether a taxon should be split off a cluster, and in significantly reducing the false positives without losing true positives. These significant advances are made possible by the new ingredients described below. First, in section 2.1.1, we show how a modified version of the expectation-maximization (EM) method^44,45 is applied under a simple assumption to establish a recursive formalism to compute for each taxon under consideration its prior probability, which can be used for biomass estimate. Second, in section 2.1.4 we introduce a new concept called ownership, based on which the participation ratio^46,47 is computed to yield the effective number of taxa within a cluster. Third, in section 2.1.5, based on peptides observed, we calculate for each taxon its degree of independence from the rest of taxa considered to determine whether or not to split this taxon off the cluster. Figure 1 and section 2.1 summarize how these important ingredients are put together to improve microorganism identifications and biomass estimates.

Figure 1.

Workflow of MiCId. (A) General workflow of MiCId v.12.13.2018. Steps described in black font around the arrows are present in both the previous version and current version of MiCId; steps described in red fonts are new and only present in the new version of MiCId, v.12.13.2018. (B) Real example of cluster cleaning via the use of ownership and participation ratio. In this example, a data file (DF 228) from an E. coli sample were used to search DB-Largest, and the top ranking cluster contains quite a number of closely related species. However, upon using each species’ ownership to compute the participation ratio for that cluster, we find it has a participation ratio value close to 1, suggesting that one should keep only the taxon with the largest ownership. Following this suggestion and upon recomputing the prior, unified E-value and ownership, one ends up with one taxon (E. coli) identified with dominant prior and ownership values.

The new MiCId v.12.13.2018 is evaluated in four aspects. First, a microbial identification comparison with the earlier version v.12.26.2017 is made by using 87 experimental data files from mixtures of 1, 4, 9, 28, and 32 microbes. Second, the retrieval stability of the new MiCId with respect to the database size increase is assessed. Third, we evaluate the use of the new ingredient “prior” for computing biomass in microbial communities. (This task is not possible for the previous version of MiCId.) To this end, we have amassed from the literature a large number of microbiota data of human stool samples, human saliva samples, and 28/32 organism (corresponding to 24/28 species) mixtures. Fourth, by ignoring taxon-specific peptides or by removing some strains/species from the database, we simulate different scenarios that may arise when analyzing a not-yet-characterized isolate.

Comparing the microbial identifications with the previous version v.12.26.2017, we find that the new version v.12.13.2018 proposed here yields fewer false positives and has a better retrieval performance. In terms of retrieval sensitivity reduction with respect to increasing database size, to the extent we tested, we find the retrieval performance does not worsen as the database size increases. In the case of using our priors to represents the biomass in a microbial community, we show that MiCId performs no worse than the three most commonly used label-free quantification methods mentioned and assessed by Kleiner et al.⁸ Finally, when simulating different extreme scenarios associated with isolate analysis, we observe the following: when the underlying strains (or species) in the samples are removed from the database, MiCId v.12.13.2018 reports most of the time the correct species (or closely related species); what is most surprising is that when the species-specific peptides are ignored, MiCId v.12.13.2018 can still identify the microorganisms at the species level correctly. The new MiCId version v.12.13.2018, designed to run in Linux environment and tested under (i) CentOS Linux release 7.6.1810, (ii) Red Hat Enterprise Linux Server release 7.7, and (iii) Ubuntu release 18.04.3, is freely available for downloaded at https://www.ncbi.nlm.nih.gov/CBBresearch/Yu/downloads.html.

2. METHODS

2.1. Computational Formalism.

Before we summarize our workflow, let us first mention the main quantities/ingredients of the workflow. For previously defined quantities/concepts such as the E-value,³⁴ the database P-value,³⁵ and the resemblance coefficient³² (of taxon $i$ to taxon $j$) ${\rho }_{i\to j}$, we refer the readers to earlier publications. Four new ingredients are introduced in this paper: taxon prior, ownership, participation ratio, and degree of independence. In the paragraphs below, we first provide a nontechnical explanation for each new ingredient. We then provide a pictorial of the workflow in Figure 1 which also highlights the new ingredients, followed by a few paragraphs summarizing in simple terms the technical aspects, and finally in the forthcoming subsections we elaborate on the technical details of the formalism. Readers wishing to skip the technical details can still gain an intuitive understanding of our workflow by reading through the following paragraphs and Figure 1.

For taxon $t\alpha$, its prior, denoted by $p\left(t_{\alpha }\right)$, is the probability for $t_{\alpha }$ to emit any evidence peptide. The $p\left(t_{\alpha }\right)$‘s are obtained by demanding self consistency via a recursive method. A taxon’s ownership $𝒪$, taking values between 0 and 1, measures the propriety of the taxon’s peptide evidence. For example, it admits value 1 if a taxon’s evidence peptides belong only to this taxon and a value 0.5 if all of its evidence peptides belong to two taxa. Taxa sharing significant numbers of peptides are often entangled into a cluster. Based on the ownership number of each taxon in a cluster, one computes the participation ratio $ℛ$ of the cluster. The participation ratio estimates the effective number of taxa needed to explain the evidence peptides of the cluster. For example, for a cluster containing 10 taxa, a computed $ℛ\approx 2$ indicates that only two taxa (two components) are needed (should be kept) to faithfully represent that cluster. Finally, we introduce the new quantity “degree of independence” $𝒤$ that measures how independent a taxon’s peptide evidence is from all other taxa considered. This quantity can be further used to decide whether a taxon should be split off its current cluster, which may lessen the effect of aggressive clustering.

For a less technical summary, we encourage the readers to look into Figure 1, which displays graphically the workflow. We note that steps described in red text in Figure 1A are new ingredients in v.12.13.2018. Figure 1B shows an example of how to use these new ingredients to retain only the most relevant taxa within a cluster.

Starting with peptides identified with E-values less than one, we employ the modified EM method^44,45 described in section 2.1.1 to compute the prior probabilities for all M candidate taxa considered. Any taxon with prior less than ${10}^{-6}$ is then removed from consideration. We then compute, for each of the remaining $M^{\prime }$ taxa, a unified E-value based on the formalism of combining truncated P-values^28,32,33 as described in section 2.1.2. A clustering procedure is then performed to agglomerate taxa with high degree of similarity in terms of peptides observed. To cluster, the $M^{\prime }$ taxa considered are sorted in ascending order of their priors: $t_1,t_2,...,t_{M^{\prime }}$. Starting with the first taxa $t_1$ (of lowest prior), we compute its resemblance coefficients (described in section 2.1.3) to all other taxa, i.e., ${\rho }_{1\to k}$ with $2\le k\le M^{\prime }$. Taxon $t_1$ will be clustered to taxon $t_{\beta }$ provided ${\rho }_{1\to \beta }$ is the largest among $\left\{{\rho }_{1\to k};2\le k\le M^{\prime }\right\}$ and ${\rho }_{1\to \beta }>0.5$. One then proceeds to taxon $t_2$ and checks if taxon $t_2$ can be clustered into taxon $t_k$ (with $3\le k\le M^{\prime }$). This process continues until one reaches the end of the list. A taxon $t_{\alpha }$ that is not clustered may be a singleton or may have other taxa clustered to it. In either case, $t_{\alpha }$ is regarded as the head of the cluster including taxon $t_{\alpha }$ and its other member taxa.

Our next step is to compute a new quantity called ownership that measures how proprietary a taxon’s peptide evidence is and the participation ratio $ℛ$ based on ownership; see section 2.1.4. This enables us to determine the appropriate number $\lfloor ℛ+0.5\rfloor$ of microbes needed in a cluster to explain the majority of the identified peptides mappable to that cluster. We then keep within each cluster only the $\lfloor ℛ+0.5\rfloor$ taxa of highest ownership.

After this procedure, the total number of taxa under consideration reduces to $M^{″}\le M^{\prime }$. If $M^{″}<M^{\prime }$, we first, with the now smaller set of taxa, repeat the steps from 2.1.1 to the computation of ownership but not the participation ratios. This is because we no longer remove taxa from clusters at this stage. Since our clustering procedure is aggressive, a cluster may contain more than one true positive microbe. However, the new similarity measure introduced in section 2.1.5 can be used to determine the taxon’s degree of independence, which can be further used to decide whether the taxon should be split off from its current cluster.

2.1.1. Modified Expectation Maximization Formalism.

We begin by introducing the required notation. In a given HPLC–MS/MS experiment hundreds to thousands of peptides are usually identified.⁴⁸ Let $\mathrm{\Pi }=\left\{{\pi }_1,{\pi }_2,\dots ,{\pi }_N\right\}$ be a set of N non-redundant peptides identified. Assume peptide ${\pi }_i$ has been observed $n_i$ times. We shall label the $M$ taxa included (at a specified taxonomy level) by $\alpha$; i.e., $t_{\alpha }$ represents the $\alpha \mathrm{th}$ taxon. Let us also denote by $d_{\alpha }$ the peptidome of $t_{\alpha }$. Let $p\left({\pi }_i\leftarrow t_{\alpha }\right)\ge 0$ denote the probability for ${\pi }_i$ to come out taxon $t_{\alpha }$. Let $0\le n_{i,\alpha }\le n_i$ denote the number of ${\pi }_i$ coming out of taxon $t_{\alpha }$. Evidently, the requirement ${\sum }_{\alpha } n_{i,\alpha }=n_i$ must be satisfied. Since we don’t know a priori from which taxon ${\pi }_i$ comes about, the $n_{i,\alpha }\mathrm{s}$ are hidden variables while the $n_i\text{s}$ are not. On the other hand, the objective of expectation maximization is to find the parameters $p\left({\pi }_i\leftarrow t_{\alpha }\right)$ that maximize the likelihood of the observed data $\left\{n_i\right\}$. Obviously ${\sum }_{\alpha } p\left({\pi }_i\leftarrow t_{\alpha }\right)I\left({\pi }_i\in d_{\alpha }\right)=p\left({\pi }_i\right)=\frac{n_i}{{\sum }_j n_j}$ where $p\left({\pi }_i\right)$ denotes the prior of peptide ${\pi }_i$ and the indicator function $I\left({\pi }_i\in d_{\alpha }\right)$ equals 1 if ${\pi }_i$ belongs to the peptidome of $t_{\alpha }$ and zero otherwise. Naturally, ${\sum }_{i=1}^N p\left({\pi }_i\right)=1$.

We will now begin describing the formal expectation maximization procedure, followed by our modification and simplification. Assuming independence among peptides’ occurrences, we may write the likelihood for $\left\{n_{i,\alpha }\right\}$ consistent with the observed $\left\{n_i\right\}$ (assuming that $p\left({\pi }_i\leftarrow t_{\alpha }\right)\text{s}$ are known) as

$$\begin{gathered} L\left(\left\{n_{i,\alpha }\right\}\mid \left\{p\left({\pi }_i\leftarrow t_{\alpha }\right)\right\}\right)=\frac{\left({\sum }_{i=1}^N{n}_i\right)!}{{\prod }_{i=1}^N{n}_i!}\frac{{\prod }_{i=1}^N{n}_i!}{{\prod }_{i=1}^N{\prod }_{\alpha =1}^M{n}_{i,\alpha }!} \\ \prod _{i=1}^N\prod _{\alpha =1}^M{\left[p\left({\pi }_i\leftarrow t_{\alpha }\right)\right]}^{n_{i,\alpha }} \end{gathered}$$ (1)

The first step of EM is to compute the expected values of the hidden variables. Because $n_i={\sum }_{\alpha } n_{i,\alpha }I\left({\pi }_i\in d_{\alpha }\right)$, the expected value of $n_{i,\alpha }$ for a fixed $i$ can be easily computed for any $t_{\alpha }$ whose peptidome contain ${\pi }_i$. Let $\varsigma \left(i\right)$ denote a realization of $\left\{n_{i,\alpha }\right\}$ satisfying $n_i={\sum }_{\alpha } n_{i,\alpha }I\left({\pi }_i\in d_{\alpha }\right)$. For example, if $n_1=2$ and ${\pi }_1$ is in peptidomes of $t_1,t_3$, and $t_8$. Then $\left(n_{\mathrm{1,1}},n_{\mathrm{1,3}},n_{\mathrm{1,8}}\right)$ can be $(\mathrm{2,0},0),(\mathrm{0,2},0),(\mathrm{0,0},2),(\mathrm{1,1},0),(\mathrm{1,0},1)$, or $(\mathrm{0,1},1)$. That is, $\varsigma \left(1\right)$ in this case can be any of the six configuration above. Obviously, in this case $n_{1,\alpha }$ can assume non-zero value only when $\alpha$ equals 1, 3, and 8. The expected value of $n_{i,\beta }$ can be written as

$$\begin{gathered} E\left[n_{i,\beta }|\left\{p\left({\pi }_j\leftarrow t_{\alpha }\right)\right\}\right]=\frac{{\sum }_{\zeta (i)}L\left(\left\{n_{k,\alpha }\right\}\mid \left\{p\left({\pi }_j\leftarrow t_{\alpha }\right)\right\}\right)n_{i,\beta }}{{\sum }_{\zeta (i)}L\left(\left\{n_{k,\alpha }\right\}\mid \left\{p\left({\pi }_j\leftarrow t_{\alpha }\right)\right\}\right)} \\ =\frac{\partial \text{ln}\left[{\sum }_{\zeta (i)}L\left(\left\{n_{k,\alpha }\right\}\mid \left\{p\left({\pi }_j\leftarrow t_{\alpha }\right)\right\}\right)\right]}{\partial \text{ln}\left[p\left({\pi }_i\leftarrow t_{\beta }\right)\right]} \end{gathered}$$ (2)

Because

$$\sum _{\zeta (i)}L\left(\left\{n_{i,\alpha }\right\}\mid \left\{p\left({\pi }_j\leftarrow t_{\alpha }\right)\right\}\right)\propto {\left[\sum _{\alpha }p\left({\pi }_i\leftarrow t_{\alpha }\right)I\left({\pi }_i\in d_{\alpha }\right)\right]}^{n_i}$$

we find

$$E\left[n_{i,\beta }\mid \left\{p\left({\pi }_j\leftarrow t_{\alpha }\right)\right\}\right]=n_i\frac{p\left({\pi }_i\leftarrow t_{\beta }\right)I\left({\pi }_i\in d_{\beta }\right)}{{\sum }_{\alpha }p\left({\pi }_i\leftarrow t_{\alpha }\right)I\left({\pi }_i\in d_{\alpha }\right)}$$ (3)

In the second (maximization) step, one finds the next set of $\left\{p^{(l+1)}\left({\pi }_i\leftarrow t_{\alpha }\right)\right\}$ to replace the previous set of $\left\{p^{\left(l\right)}\left({\pi }_i\leftarrow t_{\alpha }\right)\right\}$ that was used to compute the expected values $E\left[n_{i,\beta }\mid \left\{p^{\left(l\right)}\left({\pi }_j\leftarrow t_{\alpha }\right)\right\}\right]$. This is done by maximizing the log likelihood in eq 1, with the $n_{i,\alpha }\text{s}$ replaced by their expected values and treated as known numbers, via differentiation with respect to $\left\{p\left({\pi }_i\leftarrow t_{\alpha }\right)\right\}$. There is of course a constraint that $1={\sum }_{i=1}^N p\left({\pi }_i\right)={\sum }_{i=1}^N {\sum }_{\alpha =1}^M p\left({\pi }_i\leftarrow t_{\alpha }\right)$. Introducing this constraint via a Lagrange multiplier, one ends up having

$$p^{(l+1)}\left({\pi }_i\leftarrow t_{\alpha }\right)=\frac{E\left[n_{i,\alpha }\mid \left\{p^{(l)}\left({\pi }_j\leftarrow t_{\beta }\right)\right\}\right]}{{\sum }_{i=1}^N{\sum }_{\alpha =1}^{M}E\left[n_{i,\alpha }\mid \left\{p^{(l)}\left({\pi }_j\leftarrow t_{\beta }\right)\right\}\right]}$$ (4)

A few considerations lead us to take a simplified form of the above EM procedure. First, it requires a lot of data to faithfully estimate $\left\{p\left({\pi }_i\leftarrow t_{\alpha }\right)\right\}$. Therefore, we make the simple choice that $p\left({\pi }_i\leftarrow t_{\alpha }\right)=p\left(t_{\alpha }\right)p\left({\pi }_i\right)$ to reduce the number of parameters to be fitted. Second, even though peptide ${\pi }_i$ is identified, there is no good way to infer $n_i$. Therefore, we pick $n_i=1$ for all peptides first. This choice makes $\forall jp\left({\pi }_j\right)=1/N$; hence, $p\left({\pi }_i\leftarrow t_{\alpha }\right)=p\left(t_{\alpha }\right)/N$. Now each peptide may have different identification confidence. When the identification is of high confidence (low E-value), we may consider that peptide has prior $1/N$. However, when a peptide is identified with poor significance (high E-value), one may wish to discount $n_i$ (hence $n_{i,\alpha }$) according to the significance of ${\pi }_i$. We use the standardized weighted count as before

$$Z\left[E\left({\pi }_i\right)\right]=\frac{1}{1+E\left({\pi }_i\right)/E_c}\equiv z_i$$ (5)

Basically, we will replace $n_i=1$ by $z_i$ and $n_{i,\alpha }$ by $z_{i,\alpha }$. Here, $E_c$ is the E-value cutoff used to control the expected number of false positives. The expected number of false positive peptides identified is strongly controlled to be no more than 100 by setting $E_c$ equal to 100 divided by the total number of MS/MS spectra.

With the simplifications and modifications above, eq 3 becomes

$$E\left[z_{i,\beta }\mid \left\{p\left(t_{\alpha }\right)\right\}\right]=z_i\frac{p\left(t_{\beta }\right)I\left({\pi }_i\in d_{\beta }\right)}{{\sum }_{\alpha }p\left(t_{\alpha }\right)I\left({\pi }_i\in d_{\alpha }\right)}$$ (6)

Before proceeding to maximization, we first note that the number of variables has decreased substantially under the simplification, and eq 1 becomes

$$L\left(\left\{z_{i,\alpha }\right\}\mid \left\{p\left({\pi }_i\leftarrow t_{\alpha }\right)\right\}\right)=\frac{\text{Γ}\left(1+{\sum }_i{z}_i\right)}{{\prod }_i{\prod }_{\alpha }\text{Γ}\left(z_{i,\alpha }+1\right)}\prod _{\alpha =1}^M{\left[\frac{p\left(t_{\alpha }\right)}{N}\right]}^{{\sum }_{i=1}^N{z}_{i,\alpha }}$$ (7)

Maximization (with the constraint ${\sum }_{\alpha } p\left(t_{\alpha }\right)=1$) now leads to

$$\begin{gathered} p^{(l+1)}\left(t_{\alpha }\right)\propto \sum _{i=1}^{N}E\left[z_{i,\alpha }\mid \left\{p^{(l)}\left(t_{\beta }\right)\right\}\right]\propto \\ \sum _{i=1}^N{z}_i\frac{p^{(l)}\left(t_{\alpha }\right)I\left({\pi }_i\in d_{\alpha }\right)}{{\sum }_{\beta }{p}^{(l)}\left(t_{\beta }\right)I\left({\pi }_i\in d_{\beta }\right)}\equiv C_{\alpha }^{(l+1)} \end{gathered}$$ (8)

The normalization condition then leads to

$$p^{(l+1)}\left(t_{\beta }\right)\Rightarrow \frac{C_{\beta }^{(l+1)}}{{\sum }_{\alpha }{C}_{\alpha }^{(l+1)}}$$ (9)

In the first iteration of the EM algorithm the $p\left(t_{\alpha }\right)$’s are initialized to $1/M$ and the E-step and M-step are repeated until numerical convergence is obtained for the priors $p\left(t_{\alpha }\right)$’s.

2.1.2. Taxon Unified E-Value.

To compute the statistical significance of an identified taxon $t_{\alpha }$, we first find the set of identified peptides which are mappable to that taxon; we then compute the product of those peptides’ P-values (weighted) and compare with the product of a number of independent random variables that are each uniformly distributed over the interval $\left(0,P_c\right]$. Here, $P_c\equiv \left(1-e^{E_c}\right)$ is the database P-value cutoff used to control the expect number of false positive peptides; the number $m_{\text{raw}}\left(t_{\alpha }\right)$ of random variables needed is defined as half of the weighted peptide count

$$m_{\text{raw}}\left(t_{\alpha }\right)\equiv \frac{1}{2}\underset{l\to \infty }{\text{lim}}{C}_{\alpha }^{(l)}$$ (10)

where $C_{\alpha }^{\left(l\right)}$ was defined in eq 8

$$C_{\alpha }^{(l+1)}=\sum _{i=1}^N{z}_i\frac{p^{(l)}\left(t_{\alpha }\right)I\left({\pi }_i\in d_{\alpha }\right)}{{\sum }_{\beta }{p}^{(l)}\left(t_{\beta }\right)I\left({\pi }_i\in d_{\beta }\right)}$$

and $p^{(l+1)}\left(t_{\alpha }\right)$ in eq 9. It is worth noting that when convergence is reached, $C_{\alpha }\equiv {\mathrm{l}\mathrm{i}\mathrm{m}}_{l\to \mathrm{\infty }} C_{\alpha }^{\left(l\right)}$ represents a weighted peptide count. Specifically, we may write

$$C_{\alpha }=\sum _{i=1}^N{z}_i\frac{p\left(t_{\alpha }\right)I\left({\pi }_i\in d_{\alpha }\right)}{{\sum }_{\beta }p\left(t_{\beta }\right)I\left({\pi }_i\in d_{\beta }\right)}$$ (11)

For each taxon $\alpha$, a unified $E$-value $\left(E_u\right)$ is given by

$$E_u=M^{\text{'}}\times P_u\left(\tilde{\tau }\le {\tau }_{\alpha }\mid m_{\alpha },m_{\text{raw}}\left(t_{\alpha }\right)\right)$$ (12)

where $m_{\alpha }=\left[m_{\text{raw}}\left(t_{\alpha }\right)\right]$ is the smallest integer that is greater than or equal to $m_{\text{raw}}\left(t_{\alpha }\right)$, and $M^{\prime }$, the Bonferroni correction factor, is equal to the total number of taxa with priors larger than ${10}^{-6}$ and $P_u\left(\tilde{\tau }\le {\tau }_{\alpha }\mid m,m_{\text{raw}}\right)$ is the conditional probability for the product of truncated P-values:^28,49

$$P_t\left(\tilde{\tau }\le \tau \mid m,m_{\text{raw}}\right)=\frac{\tau }{P_c^{m_{\text{raw}}}}\sum _{s=0}^{m-1}\frac{{\left[m_{\text{raw}}\text{ln}\left(P_c\right)-\text{ln}(\tau )\right]}^s}{s!}$$ (13)

In eq 13, $\tilde{\tau }$ is a stochastic variable, $m\equiv \left[m_{\text{raw}}\right]$ is the smallest integer that is greater than or equal to $m_{\text{raw}},\tau$ is the weighted product of database P-values,^50,51 and for taxon $\alpha$ is given by

$${\tau }_{\alpha }=\prod _{j=1}^N{\left[1-{\text{e}}^{-E\left({\pi }_j\right)}\right]}^{w_{\alpha }\left({\pi }_j\right)}$$

where the taxon-specific peptide weight $w\left({\pi }_j\right)$ is

$$w_{\alpha }\left({\pi }_j\right)=\frac{z_j}{2}\frac{p\left(t_{\alpha }\right)I\left({\pi }_j\in d_{\alpha }\right)}{{\sum }_{\beta =1}^{M}p\left(t_{\beta }\right)I\left({\pi }_j\in d_{\beta }\right)}$$ (14)

An example of how to compute the unified P-value using eq 13 can be found in the supplementary material of an earlier publication.²⁸

2.1.3. Resemblance Coefficient.

The resemblance coefficient of taxon $t_{\beta }$ to taxon $t_{\alpha }$ is defined as

$${\rho }_{\beta \to \alpha }=\frac{{\sum }_{i=1}^N{z}_{i}I\left({\pi }_i\in d_{\alpha }\right)I\left({\pi }_i\in d_{\beta }\right)}{{\sum }_{i=1}^N{z}_{i}I\left({\pi }_i\in d_{\beta }\right)}$$ (15)

In our clustering procedure, one clusters a taxon with a smaller prior $p\left(t_{\beta }\right)$ to a taxon $t_{\alpha }$ with a larger prior $p\left(t_{\alpha }\right)$. The definition of resemblance coefficient above, however, is general and not limited to the condition of $p\left(t_{\beta }\right)\le p\left(t_{\alpha }\right)$. If the resemblance coefficient ${\rho }_{\beta \to \gamma }={\mathrm{m}\mathrm{a}\mathrm{x}}_{\alpha } \left\{{\rho }_{\beta \to \alpha }\right\}$ and ${\rho }_{\beta \to \gamma }$ is greater than 0.5, we cluster $t_{\beta }$ to taxon $t_{\gamma }$.

2.1.4. Ownership and Participation Ratio.

We first define a new quantity called ownership ${𝒪}_{\alpha }$ as follows

$${𝒪}_{\alpha }=\frac{{\sum }_{i=1}^N{z}_i\frac{p\left(t_{\alpha }\right)I\left({\pi }_i\in d_{\alpha }\right)}{{\sum }_{\beta }p\left(t_{\beta }\right)I\left({\pi }_i\in d_{\beta }\right)}}{{\sum }_{j=1}^N{z}_{j}I\left({\pi }_j\in d_{\alpha }\right)}=\frac{2m_{\text{raw}}\left(t_{\alpha }\right)}{{\sum }_{j=1}^N{z}_{j}I\left({\pi }_j\in d_{\alpha }\right)}$$ (16)

The ownership thus reflects the proportion of total weighted count from all peptides mappable to a taxon $t_{\alpha }$ ending up in $m_{\text{raw}}\left(t_{\alpha }\right)$. Note that even when $m_{\text{raw}}\left(t_{\alpha }\right)$ is small, the ownership can be as large as one if all peptides mappable to taxon $t_{\alpha }$ are solely owned by $t_{\alpha }$ (all peptides mappable to taxon $t_{\alpha }$ do not appear in the peptidome of other taxa).

Within a microbe cluster, we need a method to determine the appropriate number of microbes needed to explain the majority of the identified peptides mappable to that cluster. We can compute the ownership of each taxon within a cluster and use these quantities to assess how proprietary a taxon’s peptidome evidence is. We then use the participation ratio $\left(ℛ\right)$ to calculate how many taxa should be kept in an identified cluster. For each identified cluster of $L$ taxa, the participation ratio is given by

$$ℛ=\frac{{\left({\sum }_{\alpha =1}^L{𝒪}_{\alpha }^2\right)}^2}{{\sum }_{\alpha =1}^L{𝒪}_{\alpha }^4}$$ (17)

The value of $ℛ$ provides the number of ${𝒪}_{\alpha }\text{s}$ whose magnitudes are significant,^46,47 namely, the number of representative taxa within a cluster.

2.1.5. Degree of Independence and Similarity to Other Taxa.

We can also define a similar weighted count reflecting the portion of $m_{\text{raw}}\left(t_{\alpha }\right)$ that can be explained by all other taxa. For taxon $t_{\alpha }$, this quantity is defined as

$$S\left(t_{\alpha }\right)=\sum _{i=1}^N{z}_{i}I\left({\pi }_i\in d_{\alpha }\right)\text{min}\left(\frac{p\left(t_{\alpha }\right)}{{\sum }_{\beta }p\left(t_{\beta }\right)I\left({\pi }_i\in d_{\beta }\right)},1-\frac{p\left(t_{\alpha }\right)}{{\sum }_{\beta }p\left(t_{\beta }\right)I\left({\pi }_i\in d_{\beta }\right)}\right)$$ (18)

Note that if a peptide $\pi$ only belongs to $t_{\alpha }$, the ratio $\frac{p\left(t_{\alpha }\right)}{{\sum }_{\beta } p\left(t_{\beta }\right)I\left(\pi \in d_{\beta }\right)}$ equals one and $\mathrm{m}\mathrm{i}\mathrm{n}\left(\frac{p\left(t_{\alpha }\right)}{{\sum }_{\beta } p\left(t_{\beta }\right)I\left(\pi \in d_{\beta }\right)},1-\frac{p\left(t_{\alpha }\right)}{{\sum }_{\beta } p\left(t_{\beta }\right)I\left(\pi \in d_{\beta }\right)}\right)=0$, and thus $\pi$ does not contribute to $S\left(t_{\alpha }\right)$.

We also define the degree of independence $ℐ\left(t_{\alpha }\right)$ of $t_{\alpha }$ as the part of $m_{\text{raw}}\left(t_{\alpha }\right)$ that is not in $S\left(t_{\alpha }\right)$. That is

$$ℐ\left(t_{\alpha }\right)\equiv m_{\text{raw}}\left(t_{\alpha }\right)-\frac{1}{2}S\left(t_{\alpha }\right)$$ (19)

Finally, the resemblance coefficient of taxon $t_{\alpha }$ to all other taxa collectively is then defined as

$${\rho }_{\alpha \to \text{others}}=\frac{S\left(t_{\alpha }\right)}{2m_{\text{raw}}\left(t_{\alpha }\right)}$$ (20)

which allows us to write

$$ℐ\left(t_{\alpha }\right)=m_{\text{raw}}\left(t_{\alpha }\right)\left[1-{\rho }_{\alpha \to \text{others}}\right]$$

The degree of independence $ℐ\left(t_{\alpha }\right)$ is employed for determining whether or not to split taxon $t_{\alpha }$ from the cluster it is in.

2.2. MS/MS Dataset and Databases Used.

For this study, we use in total 294 data files (DFs); 24 of those DFs were already described in ref 32 and thus won’t be listed here. Each DF contains MS/MS spectra from an experimental run and was downloaded from the ProteomeXchange database (http://www.proteomexchange.org/) or from PeptideAtlas (http://www.peptideatlas.org/). In Supplementary Table S1, we list the new DFs used and their pertinent information. These DFs were used for the following studies: (i) identification performance comparison with the previous version, (ii) studying the effects of databases on MiCId retrieval, (iii) assessing MiCId’s priors in estimating the biomass in microbial communities, and (iv) simulating various scenarios when analyzing an environmental isolate (DFs from seven bacterial strains were used).

In terms of databases, there are in total six protein sequence databases used: DB-T2018 (out of which DB-TStR and DB-TSpR are constructed), DB-Largest, DB-Medium, DB-32, DB-HS, and DB-HG. DB-HG, created using the genus list downloaded from MicrobiomeDB (http://microbiomedb.org, EuPathDB release date: MicrobiomeDB 1/31-MAR-17),⁵² consist of protein sequences of microbes found in human gut. DB-HS, downloaded from ProteomeXchange PXD006366,⁸ contains the protein sequences of microbes found in human saliva. DB-32 comprises the protein sequences of the 32 microbes (belonging to 28 species) in ref 8. DB-Medium is composed of protein sequences of microbes in ref 5 along with those of the nine microbes in ref 53 and those of the 32 microbes (belonging to 28 species) in ref 8. DB-Largest includes protein sequences from Homo sapiens, Mus musculus, and from all bacteria, archaea, fungi, and viruses whose genome assembly levels are at the level from chromosome to reference genome (the highest level) as of April 2019. The proteomes of the nine microbes in ref 53 and those of the 32 microbes (belonging to 28 species) in ref 8 are also added in DB-Largest. DB-T2018, constructed in 2018,³² includes protein sequences from H. sapiens, M. musculus, and from all bacteria, archaea, fungi, and viruses whose genome assembly levels are at the level from chromosome to reference genome (the highest level) as of February 2018. DB-TStR (denoting target strains removed) has the bacterial strains in study (ii) above removed from DB-T2018. DB-TSpR (denoting target species removed) has the bacterial species in study (ii) above removed from DB-T2018. We provide in Table 1 pertinent information regarding these databases, including database name, size, etc. In Supplementary File S2, we list the microorganisms included in each database and further information.

Table 1.

Databases Used in This Manuscript

DB-name	sections using this DB	no. of microorganisms	no. of species	no. of nonredundant peptides	size (GB)
DB-Largest	3.1 and 3.2	34960	18175	980429437	61.2
DB-Medium	3.1 and 3.2	2981	1522	233682503	9.8
DB-32	3.2	32	28	6017625	0.2
DB-HG	3.3	5851	981	192539752	14.9
DB-HS	3.3	387	306	43260790	1.5
DB-T2018	3.4	23912	13072	807574956	46.8

In order to train the parameters for the new MiCId v.12.13.2018, we used a blended MS/MS dataset (BMD-A-1) that contains 500 DFs, each from a realization of sampling 1% of each of the 24 single species’ MS/MS spectra, as described in ref 32. Let us briefly describe how to samples p % for taxon $t_{\alpha }$ whose total number of spectra is $N_{\alpha }$: one goes through every one of the $N_{\alpha }$ spectra and generates a random number for each spectrum; if the random number is smaller than or equal to $p/100$, that spectrum is included. (This yields, on average, $N_{\alpha }\times p/100$ spectra.) There is no further normalization. Other authors³⁰ have also used blended MS/MS datasets in other studies.

For comparing the new MiCId with its previous version in terms of microbial identification, DFs 1–87 are used; in terms of databases, DB-Largest and DB-Medium are both employed. DFs 1-87 are from various mixture samples of known microbes, which are natural candidates for identification performance assessment. These DFs are from mixtures of 1, 4, 9, 28, and 32 microbes.^5,8,53

DFs 41-87 are used to assess the effect of databases on MiCId’s retrieval. DFs 41–87 are from three mixture samples of 28 and 32 organisms (corresponding to 24 and 28 species) assembled to mimic a microbial community. Three types of mock microbial communities are included: equal protein masses of 24 species, equal cell numbers of 24 species, and uneven protein/cell amounts of 28 species.⁸ For each mock microbial community type mentioned above, there are four different biological replicates and for each replicate four different runs with different chromotographical times. This should lead to $3\times 4\times 4=48$ DFs. However, one of the data file is missing from the ProteomeXchange database (http://www.proteomexchange.org/); hence, we are left with 47 DFs (DFs 41–87). One thing worth pointing out is that about 2/3 of the DFs are from mixtures of 24 species only.

DFs 41–64 and DFs 88–227 are used to assess how well our new ingredient “priors” reflect species’ biomasses. DFs 41–64 are from mock-microbial-community mixture samples of 28 and 32 organisms⁸ and are queried against DB-32; DFs 88–119 are from saliva samples from four persons (two male, two female)⁴³ and are queried against DB-HS. DFs 120–227 include MS/MS data files from fecal samples from three persons⁵⁴ and are queried against DB-HG;

To simulate various scenarios of analyzing an environmental isolate (strain), DFs $1-6$ and 228–270 from 7 bacteria strains were analyzed using three different databases: DB-T2018, DB-TStR, and DB-TSpR. Using DB-TStR mimics the case when the strain’s proteome is absent from the database but its close relatives’ proteomes are not; using DB-TSpR mimics the case when no close relatives of the same species are present in the database; when species-specific peptides are ignored in DB-T2018, we mimic the scenario that there are so many homologous species under a genus leading to no species-specific peptide.

2.3. Software Parameter Values.

When performing database searches, the digestion rules of trypsin and lys-c were assumed with up to two missed cleavage sites per peptide allowed. Iodocetamide was used as the reduction agent, changing the molecular mass of every cysteine from 103.00919 to 160.030647 Da. The mass error tolerance of 10 ppm was set for both precursor and product ions except when analyzing DFs 88-119 (5 ppm for the precursor ions). (The exception is made because in the original publication⁴³ of those DFs a 4.5 ppm precursor ion mass error is reported.) RAId’s Rscore, using b and y ions as evidence, was used to score peptides. The statistical significance of each peptide was assigned by RAId’s theoretically derived peptide score distribution.³⁴ The largest (cutoff) E-value for a peptide to be reported was set to 1.

The parameters used in MiCId v.12.13.2018 are determined as the follows. Using BMD-A-1 (containing 500 DFs) as queries, we examined the retrieval performance when using various resemblance coefficient cutoffs (0.4, 0.5, 0.6, 0.7, and 0.8), see section 2.1.3, and degree of independence cutoffs (1, 2, 3 and 4), see section 2.1.5. (Coming up with a theoretically firm method to determine appropriate cutoff values is important but deserves a full and separate investigation.) As shown in Supplementary Figure S1, the differences in retrieval performance are small. Regardless of the degree of independence cutoff used, the trend in terms of the resemblance coefficient cutoffs used remains the same: the retrievals are comparable for resemblance coefficient cutoff values 0.5, 0.6 and 0.7; when the cutoff value 0.4 is used, over-clustering worsens the retrieval performance noticeably; when the cutoff value 0.8 is used, the gain in false positives (due to insufficient clustering) lowers the number of identified species at a fixed value of proportion of false discoveries (PFD). When comparing retrievals using different degree of independence cutoffs (but using the same resemblance coefficient cutoff), the cutoff values of 1 and 2 perform comparably, and both are better than other cutoff values. We end up choosing 2 as our degree of independence cutoff and 0.5 as the resemblance coefficient cutoff to avoid occurrences of false positives at the expense of having perhaps slightly fewer true positives reported as cluster heads. These default values are recommended for regular uses. As an illustration, throughout this paper, all DFs, be it from single species samples or from complex microbiota samples, are all analyzed using these default parameters.

3. RESULTS AND DISCUSSION

In this section, we show the evaluation results of the new MiCId v.12.13.2018 in four aspects. First, a microbial identification comparison with the earlier version v.12.26.2017 in terms of retrieval performance is made by using 87 experimental data files from mixtures of 1, 4, 9, 28, and 32 microbes. Second, we use data files from mixtures of 28 and 32 microbes to query DB-Largest and DB-Medium in order to study the effect of databases on MiCId’s retrieval. Third, we evaluate the use of the new ingredient “prior” for computing biomass in microbial communities. (This task is not possible using the previous version of MiCId.) To this end, we have amassed from the literature a large number of microbiota data of human stool samples, human saliva samples, and 28/32 mock organism (corresponding to 24/28 mock species) mixtures. Fourth, using the three databases DB-T2018/DB-TStR/DB-TSpR described in section 2.2, we simulate different scenarios that may arise when analyzing an environmental isolate (strain): using DB-TStR mimics the case when the strain’s proteome is absent from the database but its close relatives’ proteomes are not; using DB-TSpR mimics the case when no close relatives of the same species are present in the database; using DB-T2018 regularly reflects the case when the strain’s proteome is in the database; when species-specific peptides are ignored in DB-T2018, we mimic the scenario that there are so many homologous species under a genus that no species-specific peptide exists.

3.1. Comparison of MiCId v.12.13.2018 with MiCId v.12.26.2017.

We first use DFs 1-87, acquired from samples containing 1, 4, 9, or 24-28 known species, for identification performance comparison between MiCId v.12.13.2018 and MiCId v.12.26.2017. Both DB-Largest and DB-Medium are employed to see if the performance differences are affected by the database size. When analyzing the data, MiCId only considers the head of each taxon cluster. Hence if a head taxon is (not) the correct microorganism, that taxon is considered a true (false) positive in the retrieval analysis. It is possible that a cluster might contain two or more taxa (with participation ratio ≥2) but did not further split into smaller clusters. This case arises when member taxa lack sufficient independence evidence; and even though MiCId only considers them as one entity represented by the head taxon, all member taxa of the cluster will be reported. Clusters 1 and 3 in Figure 1A illustrate such cases. This feature can be helpful for users’ manual inspections of the results as it is possible for multiple microorganisms within the same sample to be also within one cluster.

In Figure 2, panels A, B, and C (D, E, and F) are results from querying DB-Largest (DB-Medium) with DFs 1-87 (DFs 41-87). In panels A and D of Figure 2, we display the retrieval curves (number of species identified versus the PFD). As one may see from both panels, the new MiCId v.12.13.2018 outperforms MiCId v.12.26.2017 in general, especially at the most relevant region for retrieval (the small PFD region). Similarly, panels B and E plots the receiver operating characteristic (ROC) curves. As one may see from both panels, at low number of false positives, the new MiCId v.12.13.2018 outperforms MiCId v.12.26.2017 significantly in terms of number of true positives identified. The other way to interpret panels B and E is by looking at the same number of true positives identified, the new MiCId v.12.13.2018 reports fewer false positives than MiCId v.12.26.2017. Hence, MiCId v.12.13.2018 is more accurate. Panels C and F show the cumulative count of identified peptides with E-value less than specified. The readers may wonder why there is only one histogram per panel, not two. The reason is that the peptides identified are identical for both versions. This can also be seen from the MiCId WorkFlow, Figure 1. As one would have expected, when searching the smaller DB-Medium, there tend to be more significantly identified peptides at a given E-value cutoff.

Figure 2.

Retrieval performance comparison between the previous MiCId version (v.12.26.2017) and the current version (v.12.13.2018). (A–C) Results from querying DB-Largest with DFs 1–87 (from MS/MS of mixtures of 1, 4, 9, and 24–28 species). (D–F) Results from querying DB-Medium with DFs 41–87 (from MS/MS of mixtures of 24–28 species). Panels A and D show the number of identified species versus the PFD; panels B and E exhibit the number of true positives identified versus the number of false positives identified; panels C and F provide the cumulative count of identified peptides with E-values less than specified.

The observed difference in performance can be partially attributed to the heuristics contained in version v.12.26.2017, under which the formation of a taxon cluster is controlled by two factors: (1) the number of confidently identified peptides weighted by their identification E-values (see eq 5) and (2) the number of taxon-specific peptides i.e., peptides that are identified with an E-value less than ${10}^{-4}$ and belonging exclusively to one taxon. In v.12.26.2017, a member taxon $t_{\beta }$ is kept in a cluster headed by $t_{\alpha }$ only when ${\rho }_{\beta \to \alpha }>0.85$ (see eq 15 for the definition of ${\rho }_{\beta \to \alpha }$) or when it has less than three taxon-specific peptides as explained in detail.^28,32 These conditions were obtained by using a BMD to train parameters via maximizing the area under the ROC curve.²⁸ The performance, however, might still be sensitive to the variation of parameter values. This is because in v.12.26.2017, once a taxon is clustered, it can’t split off the cluster. Thus, when clustering too aggressively, one loses true positives as they might become members of other taxa clusters; when clustering too infrequently, one ends up with too many false positives that should be regarded as members of other taxa clusters.

The new MiCId version v.12.13.2018 lessens the effect of the old heuristics by introducing, for each taxon $t_{\alpha }$, two new quantities called the ownership and the degree of independence, denoted respectively by ${𝒪}_{\alpha }$ (eq 16) and $ℐ\left(t_{\alpha }\right)$ (eq 19). The ownership measures how proprietary a taxon’s peptide evidence is and can thus be used as a strong indicator for the presence/absence of that taxon even for samples containing microorganisms with fewer confidently identified peptides. We then use the set of $\left\{{𝒪}_{\alpha }\right\}$ in a given cluster to compute that cluster’s participation ratio $ℛ$ (eq 17). The $ℛ$ value reflects the appropriate number of microbes needed in a cluster to explain the majority of the identified peptides mappable to that cluster, and hence the number of taxa to keep in a cluster when taxa are sorted in descending order of their ownerships. Although the quantity $ℛ$ is known in physics for defining the number of significant components of the electron wavefunction,⁴⁶ only in recent years has it been used to estimate the number of significant nodes in interaction networks⁴⁷ in computational biology. This work is the first to introduce the concept of ${𝒪}_{\alpha }$ and to apply $ℛ$ to estimate the number of significant taxa to keep for each taxon cluster. The quantity $ℐ\left(t_{\alpha }\right)$, which is also new to the existing literature, measures taxon $\alpha$’s degree of independence from the rest of taxa considered and we can use it to determine whether or not to split $t_{\alpha }$ off the cluster. It is this mechanism that makes the new MiCId v.12.13.2018 less sensitive to the resemblance coefficient cutoff needed for clustering.

3.2. Effect of Database on Species Level Identification Using MiCId v.12.13.2018.

The size of the database is expected to impact the retrieval performance. The general trend is that the retrieval performance usually worsens as the database size increases. In this study, we use DFs from the 32 microbe mixture of Kleiner et al.,⁸ 32 of which are from 24 species mixtures and 15 of which are from 28 species mixtures. To investigate this effect under the new MiCId v.12.13.2018, we use DFs 41–87 to query DB-Largest (containing proteomes of H. sapiens, M. musculus, and 34960 microbes and of size 61.2 GB), DB-Medium (containing proteomes of 2,981 microbes and of size 9.8 GB), and DB-32 (containing the proteomes of 32 microbes and of size 200 MB). All databases contain all microorganisms presumably present in the samples yielding DFs 41–87. However, it is worth pointing out that in the samples prepared by Kleiner et al.,⁸ the microorganism Burkholderia xenovorans is found to be contaminated with Staphylococcus epidermidis. Hence the presence of B. xenovorans is not certain. Since DB-32 does not contain S. epidermidis, one is not expected to see S. epidermidis in the list of microbes identified. DB-Largest and DB-Medium, however, both contains S. epidermidis, and in this part of the study we may view S. epidermidis as a true positive from DFs 41-87 when searching DB-Largest or DB-Medium.

The readers may wonder why do we even include DB-32 in this study as it is unrealistic for identification purpose to search a database that contains already only true positives. The reason we include it here is to use it as an indicator for best retrieval possible. The readers might have noticed that the average number of identified species ranges from 18 to 19. Although this may not seem impressive, we should note that in each of the samples there are five phages (Enterobacteria phage ES18, Enterobacteria phage M2, Escherichia virus M13, Salmonella phage FelixO1, and Salmonella virus P22) with very small proteomes and with considerably less protein biomasses (see the “32_Organisms_Sample” sheet of Supplementary File S4 for the actual input biomass composition provided by⁸), making their confident identifications in complex mixtures through mass spectrometry extremely challenging. If one excludes from consideration the 5 phages along with the possible absence of B. xenovorans due to contamination, the maximum number of true positives becomes $18\times 32+22\times 15=906$, averaging 19 species identifiable per sample. Thus, an average of 18 species identified is adequate. When searching DB-Medium and DB-Largest, since they both include the contaminant S. epidermidis, the maximum number of true positives becomes $19\times 32+23\times 15=953$.

As shown in Figure 3A, we see that the retrieval curves for DB-Largest and DB-Medium do start with lower numbers of identified microbes. However, performance difference in using DB-Largest and DB-Medium is not noticeable, indicating robustness of MiCId v.12.13.2018. It is worth noting that if one sets a cutoff E-value around 0.01 for MiCId v.12.13.2018, the PFD is well controlled to be below 5% (see Figure 3B). In the analyses below, we shall use 0.01 as the E-value cutoff when a cutoff is required. To investigate the effect of increasing database sizes, it is thus instructive to compare the retrievals at a fixed E-value cutoff rather than using PFD curves. At taxon unified E-value cutoff 0.01, MiCId v.12.13.2018 achieves 834/837/805 correct species identifications out of 906/953/953, corresponding to a true positive rate of 92%/88%/84%, when searching DB-32/DB-Medium/DB-Largest. The complete list of true positives identified with E-values less than 0.01 can be found in Supplementary File S3. In this file, the readers will notice that the number of species-specific peptides identified per species decreases as the database increases. However, the species identification does not suffer much. For example, the species Agrobacterium fabrum has on average about 56/3/0 species-specific peptides identified when using DB-32/DB-Medium/DB-Largest as the database. If one were to use identification method solely relying on the presence of species-specific peptides, it will be hard to identify this species when searching DB-Medium and DB-Largest. However, MiCId v.12.13.2018 remains robust as it identifies A. fabrum confidently out of 47 samples 47/47/46 times while searching DB-32/DB-Medium/DB-Largest. As another example, although Bacillus subtilis has on average about 28/4/0 species-specific peptides identified when using DB-32/DB-Medium/DB-Largest as the database, it is identified 47 times out of 47 samples regardless which one of the three databases is searched. This again underlines the robustness of MiCId v.12.13.2018.

Figure 3.

Effect of database on MiCId v.12.13.2018. DFs 41-87 (from MS/MS of mixtures of 24–28 species) are used to query DB-Largest, DB-Medium, and DB-32. Curves in orange/purple/green color result from searching DB-Largest/DB-Medium/DB-32. As mentioned in the main text, the result from searching DB-32 is not realistic for microbe identification and only serves as the upper bound for retrieval. Searching DB-Medium and DB-Largest are more in line with real applications. In each sample, there are five phages that have very small proteomes and with considerably less protein biomasses, making their identifications in complex mixture via mass spectrometry very challenging. If one excludes the five phages from consideration, the maximum number of true positives becomes $19\times 32+23\times 15=953$. Thus, in terms of identifying microbes within the mock microbial communities,⁸ MiCId performs reasonably well: near 1% PFD, the number of true/false positive species identified is 776/8 (685/7) corresponding to true positive rates of 81.4% (71.9%) when searching DB-Largest (DB-Medium); near 5% PFD, the number of true/false positive species identified is 793/40 (895/43) corresponding to true positive rates of 83.2% (93.9%) when searching DB-Largest (DB-Medium). The important thing is that there is no significant degradation in identification performance as the database size increases, and interestingly, at any given E-value cutoff, the PFD is better controlled while searching DB-Largest than searching DB-Medium.

What may appear counterintuitive, as shown in Figure 3B, is that one actually obtains a smaller PFD, given the same E-value cutoff, when searching in DB-Largest than in DB-Medium. The complete list of the false positives when searching DB-Largest and DB-Medium (with E-values less than 0.01) is given in Table 2. In this Table, one finds that the false positives, 17 occurrences of 4 species, when searching DB-Medium are more significant (lower average ln(E-values)) than the false positives, 8 occurrences of 3 species, when searching DB-Largest. The three false positives, Salmonella bongori, Enterobacter cloacae, and Enterobacter bacterium.FGI.57 occurred 2, 6, and 7 times respectively, when searching DB-Medium, all are members that split off the true positive cluster headed by Salmonella enterica; the other false positive, Rhizobium etli, occurred 2 times, is a member that splits off the true positive cluster headed by Rhizobium leguminosarum. As for false positives when searching DB-Largest, Cupriavidus pauculus, occurred 6 times, is a member that splits off the true positive cluster headed by Cupriavidus metallidurans; while the two other false positives, Staphylococcus argenteus and Bacillus halodurans, are likely random matches as they have much less significant E-values and each occurred once only. The difference in the false positives identified between searching DB-Largest and DB-Medium suggests that the microbial composition of the database searched plays a significant role in retrieval. Studying the impact of database’s microbial composition on the retrieval is beyond the scope of the current manuscript, but certainly deserves a separate and thorough investigation.

Table 2.

False Positive Lists^a

species	NTI	E[ln(E-value)]	E[NIP]	E[NUP]
(A) False Positives Occurring When Searching DB-Medium
Salmonella bongori	2	−62.02	1159.00	3.00
Rhizobium etli	2	−46.45	392.50	3.50
Enterobacter cloacae	6	−32.22	715.17	3.17
Enterobacter bacterium.FGI.57	7	−31.47	536.57	3.57
(B) False Positives Occurring When Searching DB-Largest
Cupriavidus pauculus	6	−30.54	397.50	3.83
Staphylococcus argenteus	1	−6.66	43.00	1.00
Bacillus halodurans	1	−10.55	22.00	1.00

^aFalse positives obtained when querying DB-Largest and DB-Medium with data from 32 microorganism mixtures (DFs 41–87). NTI is the abbreviation for “number of times identified”, NIP is the “number of identified peptides”, and NUP is the ‘number of identified unique peptides”. The symbol E[•] stands for the average value of •. Taxa identified with an E-value less than 0.01 are kept.

It is also worth pointing out that even when searching a large database, such as DB-Largest, MiCId searches the database in a single pass with PFD accurately computed via the E-values reported;^34,36 it does not use multipass target-decoy heuristics. The latter was designed with the intent to amplify the identification rates, but unfortunately violates the statistical foundations^32,55–58 of the target-decoy approach.

3.3. Priors as the Protein Biomasses.

Reflecting on the definition of the priors, it seems to us that the prior of each taxon can also be viewed as its protein biomass within the sample analyzed. (All taxa share an overall proportionality constant of course.) This is because the prior of a taxon represents the likelihood for a peptide in its peptidome to be sampled (see subsection 2.1); and a taxon with a larger protein biomass has in proportion a larger likelihood for its peptides to be sampled. We thus hypothesize that the prior of each taxon can be regarded as its protein biomass and examine its validity below with comparison to other protein biomass determination methods. The assessment is done in several steps. Using the DFs from artificially assembled microbial communities,⁸ we first establish that our priors can reflect well the protein biomasses of different taxa. We then use the DFs from four human saliva samples⁴³ and contrast our estimated protein biomasses with two other published analyses.^8,43 To further assess biomass distributions in microbial communities, three human stool samples,⁵⁴ each with three technical replicates, are used. For these stool samples, both the identification of microbes along with absolute quantification of protein biomasses are carried out at the genus level.

In order to have a gold standard to compare with, it is important to use a dataset within which the true positives are known and whose complexity is similar to that of an environmental sample. The three artificially assembled microbial communities by Kleiner et al.⁸ serve this purpose exactly. In order to compare with the three most commonly used label-free quantification methods, summarized by Figure 3 of Kleiner et al.,⁸ we use the same data files (DFs 41–64) as Kleiner et al.⁸ to query DB-32. The three communities are assembled in the following manner: one with equal protein masses, one with equal cell numbers, one with uneven protein/cell amounts.⁸ It is believed that these data are most suitable for method development and testing.⁸ The box plots in Figure 4 show the fold deviations, of the protein amounts measured using our priors and three other label-free quantification methods, from the actual protein input amounts. As shown in Figure 4, our priors appear to be most consistent with the actual protein input amounts, indicating that using our priors as the protein biomass is appropriate. In the 32_Organisms_Sample sheet of Supplementary File S4, we provide the list of species identified in those samples along with the data needed for making Figure 4.

Figure 4.

Comparison of species-level protein biomass estimates. Displayed in the three panels are protein biomass quantification assessments (average of two runs each containing four biological replicates) for three different assembled mock communities: (i) a community of 28 microbes ( 24 species) with equal cell amounts per organism (DFs 41–44, 53–56), (ii) a community of 28 microbes (24 species) with equal protein amounts per organism (DFs 45–48, 57–60), and (iii) a community of 32 microbes (28 species) with uneven cell/protein amounts (DFs 49–52, 61–64). Within each mock community, the protein amount associated with each species is assessed by using the priors of MiCId. Within each mock community, the statistics of the relative fold deviations from the actual protein amount, (estimated amount – actual amount)/(actual amount), is collected and shown in the box-whisker plots (with the cross “$x$” location representing the average and the horizontal line “−” location indicating the median). An accurate biomass estimate method thus should have its box centered about 0 and its average close to 0. Plotted along with the MiCId result are species-level fold deviation results from analyzing the same data using the three other most commonly used label-free quantification methods: PSMs, u intensities, and $r+u$ intensities.⁸ Note that in order to obtain the species level fold deviations for these methods, we need to sum the strain level protein biomass estimates by these methods in the supplementary tables of ref 8. We include these tables in the sheet titled “32_Organisms_Sample” of our Supplementary File S4 along with the information on actual protein amount documented by Kleiner et al.⁸ As we see from panels A–C, MiCId provides more accurate protein biomass estimates in comparison to the three commonly used label-free quantification methods.⁸ For MiCId, only taxa identified with an E-value less than 0.01 are kept.

Our second assessment of viewing priors as the protein biomass uses DFs from the four human (two male and two female) saliva samples as in ref 8 to query DB-HS. It was shown in ref 8 that the biomass contributions obtained by ref 8 and ref 43 appear to be quite different. As shown in Figure 5, for female samples, our results agree more with ref 8 in terms of genera identified and inter-sample variability. For male samples, however, an even larger intersample variability is observed in addition to having more identified genera. The genera displayed in Figure 5 are those shown in ref 8. For male sample 1, we have in the “other bacteria” group at least four more genera with nonnegligible biomass proportions ranging from 6.2% to 1.1% : Paenibacillus, Schaalia, Actinobaculum, and Megasphaera; for male sample 3, we have in the “other bacteria” group at least four more genera with nonnegligible biomass proportions ranging from 5.7% to 1.0%: Actinobaculum, Schaalia, Megasphaera, and Stomatobaculum. Although our results are closer to those of ref 8, in terms of the protein biomasses of different genera computed, it is interesting to observe that ref 8 has a larger disagreement with ref 43 than our method. In the Human_Saliva_Sample sheet of Supplementary File S4, we provide the list of genera identified in those samples along with the quantification results (i.e., priors) that form the basis of Figure 5. In this sheet of Supplementary File S4, one may also see that, in terms of genera detected, our results indicate a larger variation between male samples than between female samples.

Figure 5.

Analyses of human saliva samples by three methods. We reanalyze the data from two female samples and two male samples in Grassl et al.⁴³ to assess protein biomasses of different genera present in each sample and contrast our results with the original analysis done in⁴³ and a reanalysis done by Kleiner et al.⁸ In terms of genera identified, our analysis and that of Kleiner et al. are closest. In terms of genera biomass abundance profiles obtained, for each sample, our profile is still closer to that in ref 8, although the similarity between our profile and that in Grassl et al.⁴³ is stronger than the similarity between that in ref 8 and that in ref 43. Grassl et al.⁴³ estimate genera biomass abundances by summing MS intensities of the 10 most abundant peptides per genus; Kleiner et al.⁸ measure the genera biomass abundances by using PSMs of proteins inferred by FidoCT⁶¹ with at least two protein unique peptides; we assess the genera biomass abundances by using the genera priors computed by MiCId. For MiCId, only taxa identified with E-values less than 0.01 are kept.

As a demonstration of applying MiCId v.12.13.2018 to characterize the structures of microbial communities, we use, in our third assessment here, a complex microbiota dataset within which only proteins (but not microbes or their associated protein biomasses) are identified/quantified.⁵⁴ The degree of success for such an endeavor largely depends on the accuracy in microbial identification and protein biomass quantification. The results shown in Figure 4 establish that our protein biomass estimates in general agree the best with the actual protein input amounts, while the results from section 3.1 and in rer 32 show that our microbe identification performance is also among the best. Therefore, applying MiCId v.12.13.2018 to characterize the structures of microbial communities is a natural choice. Three human stool samples, each with three technical replicates, are used⁵⁴ for this assessment. For each sample, the DFs of the technical replicates are merged prior to querying DB-HG. Displayed in Figure 6A are the protein biomass proportions among genera identified within each of the three samples. As shown in Figure 6A, samples 3 and 4 as well as samples 4 and 5 exhibit similar protein biomass proportions among genera present while samples 3 and 5 show rather different microbial biomass proportions. If one were to look at only the genera identified with significant biomass (with priors larger than 1%), however, one would find that the genera identified are largely the same across individuals, see the Venn diagram in Figure 6B which shows overlaps in identified genera with priors larger than 1% among individuals. The Venn diagram in Figure 6C shows overlaps in all genera identified (without prior cutoff) among individuals: given that there are 31, 21, and 22 genera identified for individual 3, 4, and 5 respectively; the number of overlapping genera between individuals 3 and 4 is 18, between 3 and 5 is 19, and between 4 and 5 is 16; the number of genera present in all three individuals is 15. In the Human_Stool_Sample sheet of Supplementary File S4, we provide the list of genera identified in those samples along with the quantification results (i.e., priors) that form the basis of Figure 6.

Figure 6.

Three human stool samples analyzed by MiCId. (A) Bar charts display the genera biomass profiles, computed using MiCId’s priors, of the three individuals. (B) Venn diagram shows overlaps in significantly identified genera with priors larger than 1%. This Venn diagram also shows that in terms of genera of nonnegligible biomasses, all three samples contain similar genera. (C) Overlaps in all genera identified (without prior cutoff) are shown. The symbol “R.1-3” simply means that we merge MS/MS data from replicates 1–3 of each individual’s sample before the analysis. Taxa identified with E-values less than 0.01 are kept.

3.4. Simulating Analyses of Environmental Isolates.

In the previous sections, we have shown that the new MiCId v.12.13.2018 performs well in identifying microbes within a mixture sample and in estimating taxa’s protein biomasses in a microbial community. The assessments, however, were done assuming all the microbes present in the mixture samples or microbial communities are all present in the databases searched. When applying MiCId to analyze a not-yet-characterized isolate, it is possible that the microorganism’s proteome is not in the database searched. In this case, it is difficult but important to know what to expect. (Investigation of this scenario may even help in interpreting the results from analyzing complex microbiota samples where some species are expected to be absent from the database.) In fact, to stress test MiCId, one might even wish to test on other atypical extreme cases as well. Here, we will use the three databases DB-T2018/DB-TStR/DB-TSpR, described in section 2.2, and simulate different extreme scenarios that may arise when analyzing an environmental isolate (strain): using DB-TStR mimics the case when the strain’s proteome is absent from the database; using DB-TSpR mimics the case when no close relatives of the same species are present in the database; using DB-T2018 regularly reflects the case when the strain’s proteome is in the database; when species-specific peptides are ignored in DB-T2018, we mimic the scenario that there are so many homologous species under a genus that no species-specific peptide exists. Some of these scenarios’ impact on microbial identifications was considered and extensively discussed by Karlsson et al.,⁵⁹ while the issues regarding biomass estimate under some of these scenarios were discussed in.⁸ Before we elaborate on these simulated scenarios, however, let us first provide a discussion regarding the sources of difficulty in identifying multiple microbes and their protein biomases estimate within a sample/community.

If a sample contains closely related microorganisms, it can be difficult to identify and separate them as the majority of their peptide evidences will overlap. This difficulty, however, persists even when one uses a single species sample if the database searched contains the proteomes of many microbes that are closely related to the microbe in the sample. When there are closely related strains present in the database, unless there are enough peptides sampled, it is intrinsically difficult to pinpoint which microbe in the database is responsible for producing the observed peptides. As an illustration, we use spectral DFs from single species samples of 7 different microbes to query DB-T2018. The heat maps displayed in Supplementary File S5 indicates that when a database search is performed, numerous closely related microbes shared peptide evidence with the true underlying microbe, making the identification of the microbe and the interpretation of the results challenging.

One possible scenario that might be more common in isolate analysis is that the underlying strain might be missing in the database while other closely related strains are present under the same species. In this case, we expect to have successful species level identifications. To simulate this scenario, we query DFs 1–6 and 228–270 against DB-TStR. Table 3A shows that this is indeed the case. Six out of the seven microbes are correctly identified at the species level without false positives, while false positive species appear from analyzing the 7 DFs of Shewanella oneidensis MR1 due to the fact that S. oneidensis MR1 is the only strain under the species S. oneidensis in DB-T2018. Nevertheless, all of the false positive species from analyzing the 7 DFs of S. oneidensis MR1 are identified with the correct genus Shewanella. In terms of biomass associated with the microbes, since all samples are from a single species, ideally one would expect a prior close to 1 for each identified species. We find this to be true for Salmonella typhimurium, Staphylococcus aureus, and Pseudomonas aeruginosa. For Escherichia coli, the average prior out of 11 identifications is 0.808; nearly 20% of its prior was constantly assigned to Shigella due to the well-known high similarity between Shigella and E. coli.⁶⁰ A similar scenario happens for M. tuberculosis and Yersinia pseudotuberculosis. M. tuberculosis is constantly identified to be the cluster head with members M. canettii, M. africanum, and M. bovis, forming the well-known M. tuberculosis complex; Y. pseudotuberculosis also has closely related species Yersinia pestis. In the case of removing the strain S. oneidensis MR1 from the database, its prior was divided among many other species (although all under the Shewanella genus) as S. oneidensis MR1 is the only strain under the S. oneidensis species.

Table 3.

Simulation of Analyzing Environmental Isolates^a

^aDB-TStR and DB-TSpR are searched with queries being DFs 1-6 and 228-270. These DFs are single strain spectra data from seven strains: E. coli K12, M. tuberculosis H37Rv, Yersinia pseudotuberculosis PB1, S. oneidensis MR-1, S. typhimurium ATCC 14028, S. aureus subsp. aureus NTCTC838, and P. aeruginosa PA01. Each of the seven strains are assigned a different color (as shown in the “True Positives” portion). The false positive species obtained from querying DFs of a strain are colored the same way as that strain. For example, the strain E. coli K12 is colored in light blue. With the strain E. coli K12 removed from DB-T2018, one still obtain E. coli as the species identified without false positive. However, when the species E. coli is removed from DB-T2018, the closest species found by MiCId are false positive species such as Shigella sp.PAMC.28760, Shigella boydii, and Escherichia albertii. These false positive species are also colored in light blue, same as the color assigned to E. coli K12. Regarding other symbols used in the Table: R is the rank of the microorganism identified among other microbes when analyzing one DF; IF stands for identification fraction, whose denominator shows the number of DFs containing the microorganism and the numerator is the number of times that microorganism is identified as the head of the top ranking cluster; NIP stands for ‘number of identified peptides, NUP for ‘number of identified unique peptides’, and CS for cluster size (number of members within the cluster). The symbol E[•] stands for the average value of •. The symbol T_Prior represents the total priors within the cluster headed by the microorganism specified in the left most column. Taxa identified with E-value less than 0.01 are kept.

Another extreme scenario occurs when the species to which the isolate belongs is so poorly represented that the database does not even contain any strain of that species. To simulate this scenario, we use DFs 1–6 and DFs 228–270 as queries and search in DB-TSpR. Here, one would naturally expect to see correct genus level identifications provided that there are enough closely related species under each target genus. Table 3B shows that out of the 49 DFs analyzed, correct genera are always identified although sometimes with false positives. For example, when E. coli is removed from the database, one identifies the Shigella genus every time when analyzing a DF from E. coli. However, this may not be due to the lack of closely related species under the Escherichia genus, but is more likely due to the the well-known problem of whether or not to classify Shigella as a member microbe of the species E. coli.⁶⁰ Another example of false positives occurred when the species S. enterica (containing serovar S. enterica typhimurium which often is abbreviated as Salmonella typhimurium) is removed from DB-T2018. In this case, out of the 7 DFs containing S. typhimurium, MiCId v.12.13.2018 always reports another species S. bongori of the same genus but also reports false positive genera three times: Citrobacter koseri twice and Lelliottia amnigena once. These three false genus level identifications might be because in DB-T2018 there are only two species, S. enterica and S. bongori, under the genus Salmonella. In terms of biomasses etimated, except for the aforementioned Shigella and E. coli case, the priors largely remain within the correct genera.

Using DFs 1–6 and 228–270 (from 7 bacteria strains) as queries and searching in DB-T2018 that contains them, we find that MiCId v.12.13.2018 is able to identify all seven at the species level without false positives, see Table 4A. This reflects the desirable cases when the microbes to be identified are already included in the database searched. In terms of biomass estimates, as one would have expected, the results are largely identical to what one sees when searching DB-TStR (Table 3A). The only difference appears in the result for S. oneidensis MR1 as it is the only strain under the S. oneidensis species.

Table 4.

Another Simulation of Analyzing Environmental Isolates^a

^aDFs 1-6 and 228-270 are used to query DB-T2018. Part A of the table summarize results from regular searches; part B of the table displays the results when taxon-specific peptides are excluded from consideration. See the caption of Table 3 for the meaning of the symbols. Taxa identified with E-values less than 0.01 are kept.

Finally, let us consider another extreme case when the species-specific peptides are not considered. This scenario might be of importance in the following cases: (1) when there are so many database entries under a genus that there are no more species-specific peptides under such a genus, (2) when the proteomes of the target microbes are incomplete, and (3) when there are sequencing/annotation errors. In Supplementary File S3, case (1) can be partially seen for several species whose numbers of identified species-specific peptides decrease as database size increases. For methods relying on taxon-specific peptides, a species level identification is no longer possible in this case. We may ask, however, can the new MiCId v.12.13.2018 identify the species correctly. To simulate this scenario, using DFs 1–6 and 228–270 and searching in DB-T2018, we ignore (at every taxonomy level) all taxon-specific peptides identified in microorganism identification analyses. Interestingly, as shown in Table 4B, MiCId v.12.13.2018 is still able to identify all seven microorganisms at the species level without false positives, albeit with weaker statistical significances. What is even more interesting is that the biomasses estimated (i.e., priors) in this case remain close to 100%, similar to those under regular search (Table 4A). The results above are impossible to achieve for methods relying on taxon-specific peptides for identifications and biomass estimates.

4. CONCLUSION

This manuscript presents the new MiCId v.12.13.2018 that, in comparison with the earlier version v.12.26.2017, is able to estimate biomass, provides more accurate microorganism identifications (by successfully reducing the number of false positives), and is robust against database size increase. This significant advance is made possible by several new ingredients introduced: first, we apply a modified expectation-maximization method to compute for each taxon considered a prior probability, which can be used for biomass estimate; second, we introduce a new concept called ownership, through which the participation ratio is computed and use it as the number of taxa to be kept within a cluster; third, based on confidently identified peptides, we calculate for each taxon its degree of independence from the rest of taxa considered to determine whether or not to split this taxon off the cluster.

Throughout this manuscript, the lowest taxonomy level for real retrieval analyses is always done at the species level or higher. This is because we use the taxonomy classification of the National Center for Biotechnology Information (NCBI) while according to the NCBI taxonomy group they have not yet had a chance to correctly annotate microorganisms below the species level. This might also be the reason that in some studies, investigators have hand-selected their own strains to be included in the databases they used.⁵⁹ Based on our study in sections 3.2 and 3.4, the taxa included in the database may significantly influence the outcomes of microbe identifications and biomass estimates. Our study in section 3.2 also suggests that using a more complete database may have some advantage, in terms of retrieval stability, when the PFD cutoff is set low.

The biomass aspect studied in section 3.4 seems to suggest that a more realistic biomass estimate might be achieved if one sums the priors of the members to the cluster head while analyzing protein biomasses. With $T_{\text{Prior}}$‘s representing such sums, we observe that the expected values of $T_{\text{Prior}}$, recorded in the columns headed by $E\left[T_{\text{Prior}}\right]$ in Tables 3A, 4A, and 4B indeed better reflect the true single-species biomass (100 %) in these studies.

Using a large dataset, we show that, in comparison with v.12.26.2017, version v.12.13.2018 yields superior retrieval results. In addition, we show that MiCId v.12.13.2018 has stable retrieval results as the database size increases. Using a large number of DFs from somewhat complex microbiota samples, we also show that MiCId v.12.13.2018 can estimate species biomass reasonably well. By removing target strains/species or ignoring species-specific peptides, we simulate different extreme scenarios while analyzing an environmental isolate using MiCId v.12.13.2018. We found that MiCId v.12.13.2018 mostly reports results expected but sometimes yields better results than expected. For example, when taxon-specific peptides are ignored from analysis, MiCId v.12.13.2018 is still able to identify the microbes correctly at the species MiCId v.12.13.2018 islevel when analyzing data files containing a single species. Tested under under (i) CentOS Linux release 7.6.1810, (ii) Red Hat Enterprise Linux Server release 7.7, and (iii) Ubuntu release 18.04.3, the new MiCId version (v.12.13.2018), a freely available software for Linux environment, can be downloaded at https://www.ncbi.nlm.nih.gov/CBBresearch/Yu/downloads.html.