Gene tree distributions under the coalescent process

Under the coalescent model for population divergence, lineage sorting can cause considerable variability in gene trees generated from any given species tree. In this paper, we derive a method for computing the distribution of gene tree topologies given a bifurcating species tree for trees with an arbitrary number of taxa in the case that there is one gene sampled per species. Applications for gene tree distributions include determining exact probabilities of topological equivalence between gene trees and species trees and inferring species trees from multiple datasets. In addition, we examine the shapes of gene tree distributions and their sensitivity to changes in branch lengths, species tree shape, and tree size. The method for computing gene tree distributions is implemented in the computer program COAL.     

Stem cells in the embryonic cerebral cortex: Their role in histogenesis and patterning

The cytoarchitectural simplicity of the cerebral cortex makes it an attractive system to study central nervous system (CNS) histogenesis—the process whereby diverse cells are generated in the right numbers at the appropriate place and time. Recently, multipotent stem cells have been implicated in this process, as progenitor cells for diverse types of cortical neurons and glia. Continuous analysis of stem cell clone development reveals stereotyped division patterns within their lineage trees, highly reminiscent of neural lineage trees in arthropods and Caenorhabditis elegans. Given that these division patterns play a critical part in generating diverse neural types in invertebrates, we speculate that they play a similar role in the cortex. Because stereotyped lineage trees can be observed from cells growing at clonal density, cell-intrinsic factors are likely to have a key role in stem cell behavior. Cortical stem cells also respond to environmental signals to alter the types of cells they generate, providing the means for feedback regulation on the germinal zone. Evidence is accumulating that cortical stem cells, influenced by intrinsic programs and environmental signals, actually change with development—for example, by reducing the number and types of neurons they produce. Age-related changes in the stem cell population may have a critical role in orchestrating development; whether these cells truly self-renew is a point of discussion. In summary, we propose that cortical stem cells are the focus of regulatory mechanisms central to the development of the cortical cytoarchitecture. © 1998 John Wiley & Sons, Inc. J Neurobiol 36: 162–174, 1998     

Effects of branch length uncertainty on Bayesian posterior probabilities for phylogenetic hypotheses

In Bayesian phylogenetics, confidence in evolutionary relationships is expressed as posterior probability--the probability that a tree or clade is true given the data, evolutionary model, and prior assumptions about model parameters. Model parameters, such as branch lengths, are never known in advance; Bayesian methods incorporate this uncertainty by integrating over a range of plausible values given an assumed prior probability distribution for each parameter. Little is known about the effects of integrating over branch length uncertainty on posterior probabilities when different priors are assumed. Here, we show that integrating over uncertainty using a wide range of typical prior assumptions strongly affects posterior probabilities, causing them to deviate from those that would be inferred if branch lengths were known in advance; only when there is no uncertainty to integrate over does the average posterior probability of a group of trees accurately predict the proportion of correct trees in the group. The pattern of branch lengths on the true tree determines whether integrating over uncertainty pushes posterior probabilities upward or downward. The magnitude of the effect depends on the specific prior distributions used and the length of the sequences analyzed. Under realistic conditions, however, even extraordinarily long sequences are not enough to prevent frequent inference of incorrect clades with strong support. We found that across a range of conditions, diffuse priors--either flat or exponential distributions with moderate to large means--provide more reliable inferences than small-mean exponential priors. An empirical Bayes approach that fixes branch lengths at their maximum likelihood estimates yields posterior probabilities that more closely match those that would be inferred if the true branch lengths were known in advance and reduces the rate of strongly supported false inferences compared with fully Bayesian integration.     

Stochastic model for multipotent hemopoietic progenitor differentiation

In this study, the authors propose a stochastic model for multipotent hemopoietic progenitor differentiation, which assumes that there is a fixed probability (P) that a progenitor with a potential for differentiation along a particular lineage maintains the potential in each cell division in each daughter cell, and this differentiation process of each lineage proceeds independently. To examine the applicability of this model, a sequential micromanipulation of paired progenitors was carried out and followed by cytological examination of the cells contained in the colonies derived from these progenitors; then calculation was made of the ratio of the number of paired colonies containing cell(s) with a particular lineage to the number of paired colonies in which only one colony contained cell(s) with the lineage at the first and second cell division. The ratios were similar at the first and second cell division within each lineage. Furthermore, the frequences of each lineage in multilineage hemopoietic colonies were calculated using the P values obtained from these micromanipulation experiments. The expected frequencies were similar to those in the actual experiments. These results suggested that the stochastic model was applicable to multipotent hemopoietic progenitor differentiation.     

Allopatry increases the balance of phylogenetic trees during radiation under neutral speciation

The shape of a phylogenetic tree is defined by the sequence of speciation events, represented by its branching points, and extinctions, represented by branch interruptions. In a neutral scenario of parapatry and isolation by distance, species tend to branch off the original population one after the other, leading to highly unbalanced trees. In this case the degree of imbalance, measured by the normalized Sackin index, grows linearly with species richness. Here we claim that moderate values of imbalance for trees with large number of species can occur if the geographic distribution involves more than one deme (allopatry) and speciation is parapatric within demes. The combined values of balance (normalized Sackin index) and species richness provide an estimate of how many demes were involved in the process if it happened in such neutral scenario. We also show that the spatial division in demes moderately slows down the diversification process, portraying a neutral mechanism for structuring the branch length distribution of phylogenetic trees.     

Modeling and Inferring Cleavage Patterns in Proliferating Epithelia

The regulation of cleavage plane orientation is one of the key mechanisms driving epithelial morphogenesis. Still, many aspects of the relationship between local cleavage patterns and tissue-level properties remain poorly understood. Here we develop a topological model that simulates the dynamics of a 2D proliferating epithelium from generation to generation, enabling the exploration of a wide variety of biologically plausible cleavage patterns. We investigate a spectrum of models that incorporate the spatial impact of neighboring cells and the temporal influence of parent cells on the choice of cleavage plane. Our findings show that cleavage patterns generate “signature” equilibrium distributions of polygonal cell shapes. These signatures enable the inference of local cleavage parameters such as neighbor impact, maternal influence, and division symmetry from global observations of the distribution of cell shape. Applying these insights to the proliferating epithelia of five diverse organisms, we find that strong division symmetry and moderate neighbor/maternal influence are required to reproduce the predominance of hexagonal cells and low variability in cell shape seen empirically. Furthermore, we present two distinct cleavage pattern models, one stochastic and one deterministic, that can reproduce the empirical distribution of cell shapes. Although the proliferating epithelia of the five diverse organisms show a highly conserved cell shape distribution, there are multiple plausible cleavage patterns that can generate this distribution, and experimental evidence suggests that indeed plants and fruitflies use distinct division mechanisms.     

Progenitor properties of symmetrically dividing Drosophila neuroblasts during embryonic and larval development

Asymmetric cell division generates two daughter cells of differential gene expression and/or cell shape. Drosophila neuroblasts undergo typical asymmetric divisions with regard to both features; this is achieved by asymmetric segregation of cell fate determinants (such as Prospero) and also by asymmetric spindle formation. The loss of genes involved in these individual asymmetric processes has revealed the roles of each asymmetric feature in neurogenesis, yet little is known about the fate of the neuroblast progeny when asymmetric processes are blocked and the cells divide symmetrically. We genetically created such neuroblasts, and found that in embryos, they were initially mitotic and then gradually differentiated into neurons, frequently forming a clone of cells homogeneous in temporal identity. By contrast, larval neuroblasts with the same genotype continued to proliferate without differentiation. Our results indicate that asymmetric divisions govern lineage length and progeny fate, consequently generating neural diversity, while the progeny fate of symmetrically dividing neuroblasts depends on developmental stages, presumably reflecting differential activities of Prospero in the nucleus.     

Centrosome regulation and function in mammalian cortical neurogenesis

As the primary microtubule-organizing center in animal cells, centrosomes regulate microtubule cytoskeleton to support various cellular behaviors. They also serve as the base for nucleating primary cilia, the hub of diverse signaling pathways. Cells typically possess one centrosome that contains two inequal centrioles and undergoes semi-conservative duplication during cell division, resulting in two centrosomes with an inherent asymmetry in age and properties. While the centrosome is ubiquitously present, mutations of centrosome proteins are strongly associated with human microcephaly characterized by a small cerebral cortex, underscoring the importance of an intact centrosome in supporting cortical neurogenesis. Here we review recent advances on centrosome regulation and function in mammalian cortical neural progenitors and discuss the implications for a better understanding of cortical neurogenesis and related disease mechanisms.     

Tree-based maximal likelihood substitution matrices and hidden Markov models

There has been considerable interest in the problem of making maximum likelihood (ML) evolutionary trees which allow insertions and deletions. This problem is partly one of formulation: how does one define a probabilistic model for such trees which treats insertion and deletion in a biologically plausible manner? A possible answer to this question is proposed here by extending the concept of a hidden Markov model (HMM) to evolutionary trees. The model, called a tree-HMM, allows what may be loosely regarded as learnable affine-type gap penalties for alignments. These penalties are expressed in HMMs as probabilities of transitions between states. In the tree-HMM, this idea is given an evolutionary embodiment by defining trees of transitions. Just as the probability of a tree composed of ungapped sequences is computed, by Felsenstein's method, using matrices representing the probabilities of substitutions of residues along the edges of the tree, so the probabilities in a tree-HMM are computed by substitution matrices for both residues and transitions. How to define these matrices by a ML procedure using an algorithm that learns from a database of protein sequences is shown here. Given these matrices, one can define a tree-HMM likelihood for a set of sequences, assuming a particular tree topology and an alignment of the sequences to the model. If one could efficiently find the alignment which maximizes (or comes close to maximizing) this likelihood, then one could search for the optimal tree topology for the sequences. An alignment algorithm is defined here which, given a particular tree topology, is guaranteed to increase the likelihood of the model. Unfortunately, it fails to find global optima for realistic sequence sets. Thus further research is needed to turn the tree-HMM into a practical phylogenetic tool.     

Estimating trees from filtered data: Identifiability of models for morphological phylogenetics

As an alternative to parsimony analyses, stochastic models have been proposed ( [Lewis, 2001] and [Nylander et al., 2004]) for morphological characters, so that maximum likelihood or Bayesian analyses may be used for phylogenetic inference. A key feature of these models is that they account for ascertainment bias, in that only varying, or parsimony-informative characters are observed. However, statistical consistency of such model-based inference requires that the model parameters be identifiable from the joint distribution they entail, and this issue has not been addressed.Here we prove that parameters for several such models, with finite state spaces of arbitrary size, are identifiable, provided the tree has at least eight leaves. If the tree topology is already known, then seven leaves suffice for identifiability of the numerical parameters. The method of proof involves first inferring a full distribution of both parsimony-informative and non-informative pattern joint probabilities from the parsimony-informative ones, using phylogenetic invariants. The failure of identifiability of the tree parameter for four-taxon trees is also investigated.     

The shape of evolution: systematic tree topology

Three hypotheses that predict probabilities associated with various tree shapes, or topologies, are compared with observed topology frequencies for a large number of 4, 5, 6 and 7-member trees. The united data on these n-member trees demonstrate that both the equiprobable and proportional-to-distinguishable-types hypotheses poorly predict tree topologies, while all observed topology frequencies are similar to predictions of a simple Markovian dichotomous branching hypothesis. Differences in topology frequencies between phenetic and non-phenetic trees are observed, but their statistical significance is uncertain. Relative frequencies of highly asymmetrical topologies are larger, and those of symmetrical topologies are smaller, in phenetic than in non-phenetic trees. The fact that a simple Markovian branching process, which assumes that each species has an equal probability of speciating in each time period, can predict tree topologies offers promise. Refinement of Markovian branching hypotheses to include the possibility of multiple furcations, differential speciation and extinction rates for different groups of organisms as well as for a single group through geological time, hybrid speciation, introgression, and lineage fusion will be necessary to produce realistic models of lineage diversification.     

A basic limitation on inferring phylogenies by pairwise sequence comparisons

Distance-based approaches in phylogenetics such as Neighbor-Joining are a fast and popular approach for building trees. These methods take pairs of sequences, and from them construct a value that, in expectation, is additive under a stochastic model of site substitution. Most models assume a distribution of rates across sites, often based on a gamma distribution. Provided the (shape) parameter of this distribution is known, the method can correctly reconstruct the tree. However, if the shape parameter is not known then we show that topologically different trees, with different shape parameters and associated positive branch lengths, can lead to exactly matching distributions on pairwise site patterns between all pairs of taxa. Thus, one could not distinguish between the two trees using pairs of sequences without some prior knowledge of the shape parameter. More surprisingly, this can happen for any choice of distinct shape parameters on the two trees, and thus the result is not peculiar to a particular or contrived selection of the shape parameters. On a positive note, we point out known conditions where identifiability can be restored (namely, when the branch lengths are clocklike, or if methods such as maximum likelihood are used).     

Uncovering the link between malfunctions in Drosophila neuroblast asymmetric cell division and tumorigenesis

Asymmetric cell division is a developmental process utilized by several organisms. On the most basic level, an asymmetric division produces two daughter cells, each possessing a different identity or fate. Drosophila melanogaster progenitor cells, referred to as neuroblasts, undergo asymmetric division to produce a daughter neuroblast and another cell known as a ganglion mother cell (GMC). There are several features of asymmetric division in Drosophila that make it a very complex process, and these aspects will be discussed at length. The cell fate determinants that play a role in specifying daughter cell fate, as well as the mechanisms behind setting up cortical polarity within neuroblasts, have proved to be essential to ensuring that neurogenesis occurs properly. The role that mitotic spindle orientation plays in coordinating asymmetric division, as well as how cell cycle regulators influence asymmetric division machinery, will also be addressed. Most significantly, malfunctions during asymmetric cell division have shown to be causally linked with neoplastic growth and tumor formation. Therefore, it is imperative that the developmental repercussions as a result of asymmetric cell division gone awry be understood.     

Asymmetric Numb distribution is critical for asymmetric cell division of mouse cerebral cortical stem cells and neuroblasts

Stem cells and neuroblasts derived from mouse embryos undergo repeated asymmetric cell divisions, generating neural lineage trees similar to those of invertebrates. In Drosophila, unequal distribution of Numb protein during mitosis produces asymmetric cell divisions and consequently diverse neural cell fates. We investigated whether a mouse homologue m-numb had a similar role during mouse cortical development. Progenitor cells isolated from the embryonic mouse cortex were followed as they underwent their next cell division in vitro. Numb distribution was predominantly asymmetric during asymmetric cell divisions yielding a beta-tubulin III(-) progenitor and a beta-tubulin III(+) neuronal cell (P/N divisions) and predominantly symmetric during divisions producing two neurons (N/N divisions). Cells from the numb knockout mouse underwent significantly fewer asymmetric P/N divisions compared to wild type, indicating a causal role for Numb. When progenitor cells derived from early (E10) cortex undergo P/N divisions, both daughters express the progenitor marker Nestin, indicating their immature state, and Numb segregates into the P or N daughter with similar frequency. In contrast, when progenitor cells derived from later E13 cortex (during active neurogenesis in vivo) undergo P/N divisions they produce a Nestin(+) progenitor and a Nestin(-) neuronal daughter, and Numb segregates preferentially into the neuronal daughter. Thus during mouse cortical neurogenesis, as in Drosophila neurogenesis, asymmetric segregation of Numb could inhibit Notch activity in one daughter to induce neuronal differentiation. At terminal divisions generating two neurons, Numb was symmetrically distributed in approximately 80% of pairs and asymmetrically in 20%. We found a significant association between Numb distribution and morphology: most sisters of neuron pairs with symmetric Numb were similar and most with asymmetric Numb were different. Developing cortical neurons with Numb had longer processes than those without. Numb is expressed by neuroblasts and stem cells and can be asymmetrically segregated by both. These data indicate Numb has an important role in generating asymmetric cell divisions and diverse cell fates during mouse cortical development.     

Antigen-driven selection in germinal centers as reflected by the shape characteristics of immunoglobulin gene lineage trees: a large-scale simulation study

During the immune response, the generation of memory B lymphocytes in germinal centers involves affinity maturation of the cells’ antigen receptors, based on somatic hypermutation of receptor genes and antigen-driven selection of the resulting mutants. Affinity maturation is vital for immune protection, and is the basis of humoral immune learning and memory. Lineage trees of somatically hypermutated immunoglobulin genes often serve to qualitatively illustrate claims concerning the dynamics of affinity maturation in germinal centers. Here, we derive the quantitative relationships between parameters characterizing affinity maturation dynamics (proliferation, differentiation and mutation rates, initial affinity of the Ig to the antigen, and selection thresholds) and the mathematical properties of lineage trees, using a computer simulation which combines mathematical models for all mature B cell populations, stochastic models of hypermutation and selection, lineage tree generation and measurement of graphical tree characteristics. We identified seven key lineage tree properties, and found correlations of these with initial clone affinity and with the selection threshold. These two parameters were found to be the main factors affecting lineage tree shapes in both primary and secondary response trees. The results also confirm that recycling from centrocytes back to centroblasts is highly likely.     

Cell shape and cell division

The correlation between cell shape elongation and the orientation of the division axis described by early cell biologists is still used as a paradigm in developmental studies. However, analysis of early embryo development and tissue morphogenesis has highlighted the role of the spatial distribution of cortical cues able to guide spindle orientation. In vitro studies of cell division have revealed similar mechanisms. Recent data support the possibility that the orientation of cell division in mammalian cells is dominated by cell adhesion and the associated traction forces developed in interphase. Cell shape is a manifestation of these adhesive and tensional patterns. These patterns control the spatial distribution of cortical signals and thereby guide spindle orientation and daughter cell positioning. From these data, cell division appears to be a continuous transformation ensuring the maintenance of tissue mechanical integrity.     

Genomic variability within an organism exposes its cell lineage tree

What is the lineage relation among the cells of an organism? The answer is sought by developmental biology, immunology, stem cell research, brain research, and cancer research, yet complete cell lineage trees have been reconstructed only for simple organisms such as Caenorhabditis elegans. We discovered that somatic mutations accumulated during normal development of a higher organism implicitly encode its entire cell lineage tree with very high precision. Our mathematical analysis of known mutation rates in microsatellites (MSs) shows that the entire cell lineage tree of a human embryo, or a mouse, in which no cell is a descendent of more than 40 divisions, can be reconstructed from information on somatic MS mutations alone with no errors, with probability greater than 99.95%. Analyzing all approximately 1.5 million MSs of each cell of an organism may not be practical at present, but we also show that in a genetically unstable organism, analyzing only a few hundred MSs may suffice to reconstruct portions of its cell lineage tree. We demonstrate the utility of the approach by reconstructing cell lineage trees from DNA samples of a human cell line displaying MS instability. Our discovery and its associated procedure, which we have automated, may point the way to a future "Human Cell Lineage Project" that would aim to resolve fundamental open questions in biology and medicine by reconstructing ever larger portions of the human cell lineage tree.