Incomplete penetrance: The role of stochasticity in developmental cell colonization

Incomplete Penetrance and Variable Expressivity: From Clinical Studies to Population Cohorts

The same genetic variant found in different individuals can cause a range of diverse phenotypes, from no discernible clinical phenotype to severe disease, even among related individuals. Such variants can be said to display incomplete penetrance, a binary phenomenon where the genotype either causes the expected clinical phenotype or it does not, or they can be said to display variable expressivity, in which the same genotype can cause a wide range of clinical symptoms across a spectrum. Both incomplete penetrance and variable expressivity are thought to be caused by a range of factors, including common variants, variants in regulatory regions, epigenetics, environmental factors, and lifestyle. Many thousands of genetic variants have been identified as the cause of monogenic disorders, mostly determined through small clinical studies, and thus, the penetrance and expressivity of these variants may be overestimated when compared to their effect on the general population. With the wealth of population cohort data currently available, the penetrance and expressivity of such genetic variants can be investigated across a much wider contingent, potentially helping to reclassify variants that were previously thought to be completely penetrant. Research into the penetrance and expressivity of such genetic variants is important for clinical classification, both for determining causative mechanisms of disease in the affected population and for providing accurate risk information through genetic counseling. A genotype-based definition of the causes of rare diseases incorporating information from population cohorts and clinical studies is critical for our understanding of incomplete penetrance and variable expressivity. This review examines our current knowledge of the penetrance and expressivity of genetic variants in rare disease and across populations, as well as looking into the potential causes of the variation seen, including genetic modifiers, mosaicism, and polygenic factors, among others. We also considered the challenges that come with investigating penetrance and expressivity.

Random Penetrance of Mutations Among Individuals: A New Type of Genetic Drift in Molecular Evolution

The determinative view of mutation penetrance is a fundamental assumption for the building of molecular evolutionary theory: individuals in the population with the same genotype have the same fitness effect. Since this view has been constantly challenged by experimental evidence, it is desirable to examine to what extent violation of this view could affect our understanding of molecular evolution. To this end, the author formulated a new theory of molecular evolution under a random model of penetrance: for any individual with the same mutational genotype, the coefficient of selection is a random variable. It follows that, in addition to the conventional N _e-genetic drift (N _e is the effective population size), the variance of penetrance among individuals (ε ²) represents a new type of genetic drift, coined by the ε ²-genetic drift. It has been demonstrated that these two genetic drifts together provided new insights on the nearly neutral evolution: the evolutionary rate is inversely related to the log-of-N _e when the ε ²-genetic drift is nontrivial. This log-of-N _e feature of ε ²-genetic drift did explain well why the d _N /d _S ratio (the nonsynonymous rate to the synonymous rate) in humans is only as twofold as that in mice, while the effective population size (N _e) of mice is about two-magnitude larger than that of humans. It was estimated that, for the first time, the variance of random penetrance in mammalian genes was approximately ε ²≈ 5.89 × 10^-3.

Stochastic models for single-cell data: Current challenges and the way forward

Although the quantity and quality of single-cell data have progressed rapidly, making quantitative predictions with single-cell stochastic models remains challenging. The stochastic nature of cellular processes leads to at least three challenges in building models with single-cell data: (a) because variability in single-cell data can be attributed to multiple different sources, it is difficult to rule out conflicting mechanistic models that explain the same data equally well; (b) the distinction between interesting biological variability and experimental variability is sometimes ambiguous; (c) the nonstandard distributions of single-cell data can lead to violations of the assumption of symmetric errors in least-squares fitting. In this review, we first discuss recent studies that overcome some of the challenges or set up a promising direction and then introduce some powerful statistical approaches utilized in these studies. We conclude that applying and developing statistical approaches could lead to further progress in building stochastic models for single-cell data.

Addressing Interdisciplinary Difficulties in Developmental Biology/Mathematical Collaborations: A Neural Crest Example

Mathematical modeling can allow insight into the biological processes that can be difficult to access by conventional biological means alone. Such projects are becoming increasingly attractive with the appearance of faster and more powerful quantitative techniques in both biological data acquisition and data storage, manipulation, and presentation. However, as is frequent in interdisciplinary research, the main hurdles are not within the mindset and techniques of each discipline but are usually encountered in attempting to meld the different disciplines together. Based upon our experience in applying mathematical methods to investigate how neural crest cells interact to form the enteric nervous system, we present our views on how to pursue biomathematical modeling projects, what difficulties to expect, and how to overcome, or at least survive, these hurdles. The main advice being: persevere.

Neural crest migration with continuous cell states

Models of cranial neural crest cell migration in cell-induced (or self-generated) gradients have included a division of labour into leader and follower migratory states, which undergo chemotaxis and contact guidance, respectively. Despite validated utility of these models through experimental perturbation of migration in the chick embryo and gene expression analysis showing relevant heterogeneity at the single cell level, an often raised question has been whether the discrete cell states are necessary, or if a continuum of cell behaviours offers a functionally equivalent description. Here we argue that this picture is supported by recent single-cell transcriptome data. Motivated by this, we implement two versions of a continuous-state model: (1) signal choice and (2) signal combination. We find that the cell population migrates further than in the discrete-state model and than in experimental observations. We further show that the signal combination model, but not the signal choice model, can be successfully adjusted to experimentally plausible regimes by reducing the chemoattractant consumption parameter. Thus we show an equivalently plausible, experimentally motivated, model of neural crest cell migration.

Cartilage-specific deletion of ephrin-B2 in mice results in early developmental defects and an osteoarthritis-like phenotype during aging in vivo

BACKGROUND

Ephrins and their related receptors have been implicated in some developmental events. We have demonstrated that ephrin-B2 (EFNB2) could play a role in knee joint pathology associated with osteoarthritis (OA). Here, we delineate the in vivo role of EFNB2 in musculoskeletal growth, development, and in OA using a cartilage-specific EFNB2 knockout (EFNB2(Col2)KO) mouse model.

METHODS

EFNB2(Col2)KO was generated with Col2a1-Cre transgenic mice. The skeletal development was evaluated using macroscopy, immunohistochemistry, histomorphometry, radiology, densitometry, and micro-computed tomography. Analyses were performed at P0 (birth) and on postnatal days P15, P21, and on 8-week- and 1-year-old mice.

RESULTS

EFNB2(Col2)KO mice exhibited significant reduction in size, weight, length, and in long bones. At P0, the growth plates of EFNB2(Col2)KO mice displayed increased type X collagen, disorganized hyphertrophic zone, and decreased mineralization. At P15, mutant mice demonstrated a significant reduction in VEGF and TRAP at the chondro-osseous junction and a delay in the secondary ossification, including a decrease in bone volume and trabecular thickness. At P21 and 8 weeks old, EFNB2(Col2)KO mice exhibited reduced bone mineral density in the total skeleton, femur and spine. One-year-old EFNB2(Col2)KO mice demonstrated OA phenotypic features in both the knee and hip. By P15, 27 % of the EFNB2(Col2)KO mice developed a hip locomotor phenotype, which further experiments demonstrated reflected the neurological midline abnormality involving the corticospinal tract.

CONCLUSION

This in vivo study demonstrated, for the first time, that EFNB2 is essential for normal long bone growth and development and its absence leads to a knee and hip OA phenotype in aged mice.

Reconciling diverse mammalian pigmentation patterns with a fundamental mathematical model

Bands of colour extending laterally from the dorsal to ventral trunk are a common feature of mouse chimeras. These stripes were originally taken as evidence of the directed dorsoventral migration of melanoblasts (the embryonic precursors of melanocytes) as they colonize the developing skin. Depigmented ‘belly spots' in mice with mutations in the receptor tyrosine kinase Kit are thought to represent a failure of this colonization, either due to impaired migration or proliferation. Tracing of single melanoblast clones, however, has revealed a diffuse distribution with high levels of axial mixing—hard to reconcile with directed migration. Here we construct an agent-based stochastic model calibrated by experimental measurements to investigate the formation of diffuse clones, chimeric stripes and belly spots. Our observations indicate that melanoblast colonization likely proceeds through a process of undirected migration, proliferation and tissue expansion, and that reduced proliferation is the cause of the belly spots in Kit mutants.

How embryonic melanoblast behaviour influences adult pigmentation patterns and causes patterning defects is unclear. Here, Mort et al. construct a stochastic model parameterised experimentally to show that melanoblast migration is undirected and that reduced proliferation causes patterning defects.