Latent class analysis of endoreduplicated nuclei in confocal microscopy

Latent class analysis of endoreduplicated nuclei

in confocal microscopy

Analisi di classi latenti per dati di nuclei endoreduplicati

tramite microscopia confocale

Ivan Sciascia [email protected], Gennaro Carotenuto

[email protected], Andrea Genre [email protected], Università di Torino Dipartimento di Scienze della vita e biologia dei sistemi, viale Mattioli 25, 10125 Torino

Abstract We measured the areas of fluorescently labelled nuclei in confocal

microscopy images and compared manual and semi-automated measurements based on an ImageJ plugin. Assuming such nuclear area data as a manifest variable, we try to collect K latent classes of a categorial latent variable, the ploidy level (nuclear DNA content), which can be represented as the endoreduplication index (2C for diploid, 4C for tetraploid,…etc)

Abstract Abbiamo misurato manualmente e semi-automaticamente (tramite un

plugin Image-J) le dimensioni delle aree dei nuclei evidenziati con fluorescenza in immagini da microscopia confocale. Considerando le aree come variabile manifesta, applichiamo un modello a classi latenti per identificare una variabile latente che assumiamo essere il livello di ploidia ovvero il numero di appartenenza ad una classe di endoreduplicazione (2C = diploide, 4C = tetraploide, etc…).

Key words: Latent class analysis, clustering, area detection, nuclear ploidy, image

analysis

1 Introduction

The topic of our research is the arbuscular mycorrhizal (AM) symbiosis, a beneficial interaction between the majority of plants and a small group of soil fungi, developing arbuscules, the structures devoted to the exchange of mineral nutrients for sugars and lipids [1]. The interaction between symbionts involves the exchange of Carbon, Phosphorus, Nitrogen and water.

2 Sciascia I., Carotenuto G., Genre A.

Recent evidence from our research group shed light on the activation of plant cell cycle-related mechanisms during AM colonization [2] using live microscopic observations, gene expression and flow cytometry analyses. Previous studies have highlighted endoreduplication in several plant-microbe interaction, including AM colonized roots, but the precise location of the endoreduplication events has never been defined for AM. The aim of this research is to provide more solid statistical support to the observed increase in nuclear ploidy (derived from endoreduplication events) in mycorrhizal compared to uninoculated roots, by using a clustering approach based on latent class analysis.

Endoreduplication events have been analyzed through image post-processing analyses from confocal observations to investigate the occurrence of nuclear size increases (related to increases in ploidy) in AM colonized roots of Medicago truncatula [2, 3].

The current presentation combines two image analysis methods, manual and customized ImageJ plugin, applied to mycorrhizal and uninoculated roots, to obtain four sample datasets to be used for the identification of latent classes using the R package poLCA.

2 Confocal microscopy images

1 cm-long root segments from both control and mycorrhizal roots were sectioned using a Vibratome into 100µ thick slices which were then stained with DAPI, a fluorescent dye for DNA, that labels all nuclei.

These samples were then imaged under a confocal microscope, as described by [3]. In each section we identified and measured the size (area) of hundreds of nuclei. We analyzed root sections using two post-processing methods: manual measurement, more precise and reliable, but time consuming, and a customized plugin in Fiji ImageJ environment, faster but more error prone. By combining the two approaches we obtained the required datasets to be used for the detection of latent classes that could correspond to classes of nuclear ploidy.

The manual and automated areas measurements shown a frequency distribution range 15-114 µm2 _{for control samples and 15-149 µm}2 _{for mycorrhizal root sections.}

Due to the relatively small number of cells undergoing endoreduplication, simple descriptive statistics are unable to highlight significant differences between average nuclear areas (Figure 1).

Figure 1: Detection, automated measurements and descriptive statistics

( a ) ( b ) ( c ) ( d ) ( e ) ( f )

Latent class analysis of endoreduplicated nuclei in confocal microscopy 3

For this reason we decided to address the detection of latent classes that could correspond to the endoreduplication index. [3].

3 Latent class data analysis

We analysed four samples of nuclei areas, two deriving from manual and two from automated analysis of nuclear size in control and mycorrhizal roots.

As the poLCA package in R [4] accept only integers and identical vector of measurements we inserted missing values with each mean for each measurements in order to collect 4600 (1150 each) total spots.

Based on our previous analyses, we performed descriptive statistics with SPSS package to arbitrarily identify 8 levels of area dimensions according to 8 point division in equal classes (percentiles) for the frequency distributions.

To identify latent classes we perform poLCA code in R searching for optimal clustering according to information criteria [5]. We then compared control and mycorrhizal groups to check for a similar classification with poLCA.

The area is the manifest variable and ploidy level is assumed to be the latent variable; class membership with only one manifest variable without covariates can be computed in poLCA:

And the density function





 

Where yi are the areas, and rk the class conditional probability that an

observation in class r=1….R produces the k outcome of the area manifest variable and



Then the poLCA use the EM algorithm to maximize the log likelihood function to estimate latent class model:

 







pr

L

ln

ln



After finding latent classes we apply the information criteria: adjusted Bayesian information criterion aBIC, consistent Aikake information Criterion cAIC, log likelihood, and Entropy for finding an optima model both for control and mycorrhizal samples. For every class from k=2 to k=8 we computed the R code and the information criteria.

Models calculation: library(poLCA) data(Control or Myc)

 







K

k

y

rk

i

y

f

1

;

)

(

_

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f<- cbind(CtrManual, CtrPlugin) ~1; CK<-poLCA(f, Control, nclass=K) Information criteria: aBIC<- -2*cK$llik+cKnpar*log((cK$N+2)/24) cAIC<- -2*cK$llik+cKnpar*log(cK$N)+1 log-likelihood<-cK$llik Entropy<-poLCA.entropy(cK)

Latent class analysis of endoreduplicated nuclei in confocal microscopy 5

Searching for lowest aBIC and cAIC, high Entropy and Log-Likelihhod to individuate the optimal classes both for Control and Mycorrhizal samples we found in Control minimum aBIC in k=5 and cAIC in k=7 suggesting no accordance. In Mycorrhizal sample both aBIC and cAIC suggest optimal class for k=6.

Considering that cAIC is more reliable for small samples, we put more focus on the aBIC criterion. This suggests 5 optimal classes for Control sample and 6 optimal classes for Mycorrhizal sample. This result is in agreement with previous evaluations based on flow cytometry, suggesting the existence of 5 ploidy classes in control and 8 ploidy classes in mycorrhizal roots [3]. We speculate that the more restrictive statistical analysis performed by poLCA may underestimate the two top nuclear classes (actually represented by a very small number of measures), but our study provides a strong evidence that image analysis-based measurements of nuclear size (manifest variable) can correlate with actual nuclear DNA content, the ploidy level (latent variable), and convincing support to our previous interpretations of the experimental results [3].

References

1. Gutjahr C, Parniske M. Cell and developmental biology of the arbuscular mycorrhiza symbiosis. Annu. Rev. Cell Dev. Biol. 29: 593–617.2 (2013)

2. Kondorosi E, Roudier F, Gendreau E. Plant cell-size control: growing by ploidy? Curr. Opin. Plant Biol. 3:488–492 (2000)

3. Carotenuto G, Volpe V., Russo G., Politi M., Sciascia I., de Almeida-Engler J., Genre A., Local endoreduplication as a feature of intracellular fungal accommodation in arbuscular mycorrhizas. New Phitol. doi: 10.1111/nph.15763 (2019)

4. Linzer, D.A., Lewis J.B., poLCA: An R Package for Polytomous Variable Latent Class Analysis. J Stat Softw 42(10), 2-29 (2011)

5. Zhang Z., Abarda A., Contractor A.A., Wang J., Dayton C.M., Exploring heterogeneity in clinical trials with latent class analysis. Ann Transl Med 6(7):119 (2018) doi: 10.21037/atm.2018.01.24