Reprint of "Stereology meets electron tomography: towards quantitative 3D electron microscopy" [J. Struct. Biol. 159 (2007) 443-450]

Stereological tools are the gold standard for accurate (i.e., unbiased) and precise quantification of any microscopic sample. The past decades have provided a broad spectrum of tools to estimate a variety of parameters such as volumes, surfaces, lengths, and numbers. Some of them require pairs of parallel sections that can be produced by either physical or optical sectioning, with optical sectioning being much more efficient when applicable. Unfortunately, transmission electron microscopy could not fully profit from these riches, mainly because of the large depth of field. Hence, optical sectioning was a long-time desire for electron microscopists. This desire was fulfilled with the development of electron tomography that yield stacks of slices from electron microscopic sections. Now, parallel optical slices of a previously unimagined small thickness (2-5nm axial resolution) can be produced. These optical slices minimize problems related to overprojection effects, and allow for direct stereological analysis, e.g., volume estimation with the Cavalieri principle and number estimation with the optical disector method. Here, we demonstrate that the symbiosis of stereology and electron tomography is an easy and efficient way for quantitative analysis at the electron microscopic level. We call this approach quantitative 3D electron microscopy.

Prenatal sonographic diagnosis of skeletal dysplasias

OBJECTIVE: To assess the types and numbers of cases, gestational age at specific prenatal diagnosis and diagnostic accuracy of the diagnosis of skeletal dysplasias in a prenatal population from a single tertiary center. METHODS: This was a retrospective database review of type, prenatal and definitive postnatal diagnoses and gestational age at specific prenatal diagnosis of all cases of skeletal dysplasias from a mixed referral and screening population between 1985 and 2007. Prenatal diagnoses were grouped into 'correct ultrasound diagnosis' (complete concordance with postnatal pediatric or pathological findings) or 'partially correct ultrasound diagnosis' (skeletal dysplasias found postnatally to be a different one from that diagnosed prenatally). RESULTS: We included 178 fetuses in this study, of which 176 had a prenatal ultrasound diagnosis of 'skeletal dysplasia'. In 160 cases the prenatal diagnosis of a skeletal dysplasia was confirmed; two cases with skeletal dysplasias identified postnatally had not been diagnosed prenatally, giving 162 fetuses with skeletal dysplasias in total. There were 23 different classifiable types of skeletal dysplasia. The specific diagnoses based on prenatal ultrasound examination alone were correct in 110/162 (67.9%) cases and partially correct in 50/162 (30.9%) cases, (160/162 overall, 98.8%). In 16 cases, skeletal dysplasia was diagnosed prenatally, but was not confirmed postnatally (n = 12 false positives) or the case was lost to follow-up (n = 4). The following skeletal dysplasias were recorded: thanatophoric dysplasia (35 diagnosed correctly prenatally of 40 overall), osteogenesis imperfecta (lethal and non-lethal, 31/35), short-rib dysplasias (5/10), chondroectodermal dysplasia Ellis-van Creveld (4/9), achondroplasia (7/9), achondrogenesis (7/8), campomelic dysplasia (6/8), asphyxiating thoracic dysplasia Jeune (3/7), hypochondrogenesis (1/6), diastrophic dysplasia (2/5), chondrodysplasia punctata (2/2), hypophosphatasia (0/2) as well as a further 7/21 cases with rare or unclassifiable skeletal dysplasias. CONCLUSION: Prenatal diagnosis of skeletal dysplasias can present a considerable diagnostic challenge. However, a meticulous sonographic examination yields high overall detection. In the two most common disorders, thanatophoric dysplasia and osteogenesis imperfecta (25% and 22% of all cases, respectively), typical sonomorphology accounts for the high rates of completely correct prenatal diagnosis (88% and 89%, respectively) at the first diagnostic examination.

An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

Case and partnership reproduction numbers for a curable sexually transmitted infection

Sexually transmitted infections (STIs) are, by definition, transmitted between sexual partners. For curable STIs an infected index case can potentially re-infect the same partner multiple times. Thus, R0, the average number of secondary infections one typical infected individual will produce during his or her infectious period is not necessarily the same as the average number of secondary cases (infected persons). Here we introduce the new concept of the case reproduction number (Rc). In addition, we define the partnership reproduction number (Rp) as the average number of secondary partnerships consisting of two infected individuals one typical infected individual will produce over his or her infectious lifetime. Rp takes into account clearance and re-infection within partnerships, which results in a prolongation of the duration of the infectious period. The two new reproduction numbers were derived for a deterministic pair model with serial monogamous partnerships using infection parameters for Chlamydia trachomatis, an example of a curable STI. We showed that re-infection within partnerships means that curable STIs can be sustained endemically even when the average number of secondary cases a person produces during his or her infectious period is below one.

Phyllotaxis — a new chapter in an old tale about beauty and magic numbers

Phyllotaxis, the regular arrangement of leaves and flowers around the stem, is one of the most fascinating patterning phenomena in biology. Numerous theoretical models, that are based on biochemical, biophysical and other principles, have been proposed to explain the development of the patterns. Recently, auxin has been identified as the inducer of organ formation. An emerging model for phyllotaxis states that polar auxin transport in the plant apex generates local peaks in auxin concentration that determine the site of organ formation and thereby the different phyllotactic patterns found in nature. The PIN proteins play a primary role in auxin transport. These proteins are localized in a polar fashion, reflecting the directionality of polar auxin transport. Recent evidence shows that most aspects of phyllotaxis can be explained by the expression pattern and the dynamic subcellular localization of PIN1.