Determining nucleolar multiplicity and cell number from sectional data

Abstract

SUMMARY The occurrence of more than one nucleolus within the cellular nucleus (polynucleolarity) is a well‐known phenomenon during the proliferative cell cycle, both under normal and pathological conditions (e.g. neoplasia). It can also be observed in neuronal nuclei at early stages of their maturation. Polynucleolarity merits investigation for cytological reasons. In an histological section, the observed number of nucleoli in a nucleus may be smaller than the actual number. In order to estimate the true distribution of the number of nucleoli per nucleus from the observed distribution, the mathematical relation between these distributions is derived (Section 4) on the basis of rather restrictive (Sections 3 and 11) stereological assumptions (Section 2). It is indicated how these distributions can be estimated from the data available and how the statistical uncertainties involved can be expressed (Sections 5, 6 and 7). This paper arose from making cell counts (Section 1). Two methods may be applied: (1) all visible nuclear profiles are counted, (2) nuclear profiles are only included if at least one nucleolus is visible in the section. We recommend a combination of these two methods (Section 8). An advantage of our theory for determining cell number (Section 9) is that one can often manage without the rather restrictive stereological assumptions needed hitherto. The advantage of expressing statistical uncertainties in estimated nucleolar multiplicity probabilities and cell numbers is indicated (Section 10).

The distributed circuit within the piriform cortex makes odor discrimination robust

“…We were careful to avoid over‐counting by marking only nucleoli. They typically have a radius of 1.5–2 μm, and in 40 μm sections, that reduces the margin of error to less than 5% (Gramsbergen, Kok, Poortema, & Schaafsma, ; Konigsmark, ). We also took care to mark a single nucleolus in those few neurons that had multiple nucleoli (Gramsbergen et al, ).…”

Scaling Principles of Distributed Circuits

“…We were careful to avoid over-counting by marking only nucleoli. They typically have a radius of 1.5-2 m, and in 40 m sections, that reduces the margin of error to less than 5% [63,64]. We also took care to mark a single nucleolus in those few neurons that had multiple nucleoli [63].…”

“…They typically have a radius of 1.5-2 m, and in 40 m sections, that reduces the margin of error to less than 5% [63,64]. We also took care to mark a single nucleolus in those few neurons that had multiple nucleoli [63]. The validation for these counts is presented in Figure S1A for glomeruli and Figure S2C for neurons.…”

A quantitative description of the mouse piriform cortex

“…This brings up an issue of over-counting. We were careful to address this potential issue by marking nucleoli -which typically have a radius of 1.5-2 μ m -in 40 μ m sections, reducing the margin of error to less than 5 % (Konigsmark 1970;Gramsbergen et al 1987). We also took care to mark a single nucleolus in those few neurons that had multiple nucleoli (Gramsbergen et al 1987).…”