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PubMed1996

A biologically-based dose-response model for developmental toxicology.

The methods currently used to evaluate the risk of developmental defects in humans from exposure to potential toxic agents do not reflect biological processes in extrapolating estimated risks to low doses and from test species to humans. We develop a mathematical model to describe aspects of the dynamic process of organogenesis, based on branching process models of cell kinetics. The biological information that can be incorporated into the model includes timing and rates of dynamic cell processes such as differentiation, migration, growth, and replication. The dose-response models produced can explain patterns of malformation rates as a function of both dose and time of exposure, resulting in improvements in risk assessment and understanding of the underlying mechanistic processes. To illustrate the use of the model, we apply it to the prediction of the effects of methylmercury on brain development in rats.

Abnormalities, Drug-Induced↗
PubMed1996

Development of the Drosophila tracheal system occurs by a series of morphologically distinct but genetically coupled branching events.

The tracheal (respiratory) system of Drosophila melanogaster is a branched network of epithelial tubes that ramifies throughout the body and transports oxygen to the tissues. It forms by a series of sequential branching events in each hemisegment from T2 to A8. Here we present a cellular and initial genetic analysis of the branching process. We show that although branching is sequential it is not iterative. The three levels of branching that we distinguish involve different cellular mechanisms of tube formation. Primary branches are multicellular tubes that arise by cell migration and intercalation; secondary branches are unicellular tubes formed by individual tracheal cells; terminal branches are subcellular tubes formed within long cytoplasmic extensions. Each level of branching is accompanied by expression of a different set of enhancer trap markers. These sets of markers are sequentially activated in progressively restricted domains and ultimately individual tracheal cells that are actively forming new branches. A clonal analysis demonstrates that branching fates are not assigned to tracheal cells until after cell division ceases and branching begins. We further show that the breathless FGF receptor, a tracheal gene required for primary branching, is also required to activate expression of markers involved in secondary branching and that the pointed ETS-domain transcription factor is required for secondary branching and also to activate expression of terminal branch markers. The combined morphological, marker expression and genetic data support a model in which successive branching events are mechanistically and genetically distinct but coupled through the action of a tracheal gene regulatory hierarchy.

Animals↗
PubMed2000

Meristem growth dynamics and branching patterns in the Cladoniaceae.

Branching patterns in the lichen family Cladoniaceae are varied and taxonomically important. Branching occurs on the podetium, the erect secondary thallus that characterizes most species in the Cladoniaceae, and is influenced by growth dynamics of the fungal meristem tissue at the apex of the podetium. Branching is primarily the result of meristem divisions, and branching patterns are modified by meristem enlargement, deformation, and torsion. Branching processes are conserved, and early branch ontogeny provides information from which to determine relationships in the Cladoniaceae. Branching is characterized by two major patterns. In one pattern, branches arise from the relatively late divisions of a large meristem (≥100 μm in diameter), whose shape changes during ontogeny. In a second pattern, branches arise from small meristems (<100 μm in diameter), which split early in ontogeny but whose shape does not change. The trend toward reduced meristems that split early in ontogeny is seen as an evolutionary advance in the Cladoniaceae. Some "small meristem" species retain aspects of the "large meristem" habit in early ontogeny, and this provides a clue to their relationships. Patterns of meristem growth dynamics provide a basis for interpreting phylogeny in mycobionts of the Cladoniaceae. Meristem activities in four genera of the Cladoniaceae were compared in order to determine trends in growth dynamics within the family.

Journal Article↗
PubMed1999

Redistribution of MAP2 immunoreactivity in the neurohypophysial astrocytes of adult rats during dehydration.

The low-molecular-weight microtubule-associated protein-2 (LMW MAP2) is expressed in immature and developing brains, and decreases its content dramatically along with maturation of the central nervous system. In our previous studies, we demonstrated through western blots and dual-labeling immunohistochemistry that LMW MAP2 is expressed in the pituicytes, modified astrocytes of the neurohypophysis in adult rats. The present study aimed to examine changes in the MAP2 immunoreactivity within pituicyte in adult rats under various hydration states using quantitative morphometrical analysis to demonstrate in vivo shape conversion of the pituicyte morphology. In well-hydrated control rats, light microscopic observation revealed that MAP2-stained pituicytes ramified long and well-branched processes. At electron microscopic level, MAP2 immunoreactivity was found in the fine process and cell body of all pituicyte cytoplasm, but not in the axonal terminals containing neurosecretory vesicles. The quantitative analysis demonstrated that the cell size and perimeter of MAP2-stained pituicytes were significantly greater as compared with those of cells stained with glial fibrillary acidic protein (GFAP). When the rats were dehydrated with water deprivation or drinking of 2% saline solution, the process of MAP2-stained pituicytes was less branched due to retracting their cellular processes as compared with those of well-hydrated control and rehydrated rats. The quantitative analysis further demonstrated that water deprivation significantly reduced the cell size, perimeter and length of cellular processes of MAP2-stained pituicytes as compared with those of control. The present finding indicates that MAP2 staining is better method for investigating in vivo shape conversion of the pituicyte morphology than GFAP one. Moreover, the finding that hydration states significantly and reversibly alter in vivo pituicyte shape supports the hypothesis that the plastic shape conversion of pituicyte morphology is responsible for morphological plasticity in the neurohypophysis.

Animals↗
PubMed2003

Random variation and concentration effects in PCR.

Even though the efficiency of the polymerase chain reaction (PCR) reaction decreases, analyses are made in terms of Galton-Watson processes, or simple deterministic models with constant replication probability (efficiency). Recently, Schnell and Mendoza have suggested that the form of the efficiency, can be derived from enzyme kinetics. This results in the sequence of molecules numbers forming a stochastic process with the properties of a branching process with population size dependence, which is supercritical, but has a mean reproduction number that approaches one. Such processes display ultimate linear growth, after an initial exponential phase, as is the case in PCR. It is also shown that the resulting stochastic process for a large Michaelis-Menten constant behaves like the deterministic sequence x(n) arising by iterations of the function f(x)=x+x/(1+x).

Genetic Variation↗
PubMed1986

A population dynamics simulation model with application to health planning.

Despite the increasing emphasis on computers and quantitative methods in health services programs, health services administration students are denied access to many of the most powerful tools of systems analysis, including discrete event simulation, because they lack the necessary background in computer programming, simulation methodology, and stochastic processes. This article presents an approach to the modeling of the growth and decline of population groups and their attributes that can be used by students who do not have the extensive quantitative background required to develop the usual discrete event simulation models. The underlying theory, which is based on the behavior of the expectation process of vector Galton-Watson branching processes, can be explained quite easily. An example is presented that uses an age and sex specific model of population growth to investigate policy questions related to the feasibility of the construction of a long-term care facility for a defined population group. Planning decisions are based on the growth and decline of the numbers of individuals in the various age and sex groups. Extensions of the basic methodology are possible that would include projections of the variance-covariance matrix of the population sizes for each year of the projection process. In addition, the model can be extended to include projections of the impact of infectious and communicable diseases on a defined population group together with the effect of categorical disease screening and control programs. Given the basic data utilized in the model, the implementation of the calculations required by the model can be made on modern microcomputer hardware using any of the standard spreadsheet programs.

Health Planning↗
PubMed1989

The morphology of the basal lamina and periepithelial collagen during growth and branching of the embryonic lung of mice (day 14 to 16).

In order to be able to interpret the developmental mechanism of the epithelial branching pattern, we investigated lung development of mouse embryos of gestational days 14 to 16 electron microscopically. Various fixation techniques (Karnovsky, tannic acid, ruthenium red) were employed. Four regions could be distinguished in a growing and branching epithelial bud: 1) the epithelial tube before the site of branching; 2) the actual site and gap of branching; 3) the already formed part of the new buds and 4) the actual leading, i.e., the growing tip. Regions 1 and 3 were characterized by a continuous basal lamina and a more (1) or less (3) thick sheath of accompanying collagen. The site of branching (2) showed a pronounced folding of the basal lamina to which numerous collagenous fibrils were attached. At the distal, i.e., growing site (4) the basal lamina was characterized by numerous interruptions; accompanying collagen was missing. Immunomorphological investigations of regions 1 to 3 revealed all components of a basal lamina and collagen types I, III and V and fibronectin at the border between epithelium and connective tissue. However, this amount was clearly reduced at the growing tip, and collagen type I was missing. These findings help to understand and elucidate the importance of the mesenchyme for the growth and branching process and the development of the branching pattern.

Animals↗
PubMed1986

On three methods for estimating mutation rates indirectly.

Methods for estimating a mutation rate mu has been proposed by Kimura and Ohta; Nei; and Rothman and Adams. It is shown here that all three methods are best applied to rare alleles and that they are all based upon the assumption that all alleles ultimately become extinct. If there is a neutral allele in a growing population, there is conditioning on ultimate extinction, which implies that the underlying stochastic process can be approximated by a branching process for which the mean number of offspring is less than 1. The low numerical values of t0, the mean time to extinction of a line descended from a single mutant, found in two simulation studies, can be attributed to two features. First, the data on which these studies were based came from a fairly rapidly growing population. In such a population, we would expect that extinction, if it does occur, takes place quickly. A second factor is that the effective population size is somewhat lower than the actual number of adults. Population subdivision and migration does not seem to play a significant role. Conservative high and low estimates of mutation rates are computed, and an estimate is obtained for the standard deviation of the estimate of mu. These allow a rough estimate of a 95% confidence interval, which contains estimates of mu found by Neel and Rothman.

Gene Frequency↗
PubMed1979

Morphology of dissociated hippocampal cultures from fetal mice.

Dissociated hippocampal cultures from fetal mice (13--18 days gestational age) can be maintained for up to two months in culture. Cells grow as either isolated neurons or in small neuronal aggregates. Neurons remain small with a soma diameter of 15--20 micrometer even in mature cultures and develop extensively branched processes during the first two weeks in culture. After this time, processes become more difficult to visualize with phase-contrast optics because of a tendency to grow within the underlying non-neuronal cells. However, the presence of processes has been proved by silver-staining which demonstrates an organizational complexity ranging from a loosely reticulated neuropil to fascicles containing many fibers. More detailed study of individual neuronal morphology was carried out in cells filled with the fluorescent dye, Lucifer Yellow CH, in conjunction with the intracellular recording of synaptic and action potentials from dye-containing micropipettes. Dye-filled cells show a well-developed branching morphology. Process specializations include spines, beading, and basket-like endings. Processes tend to emanate from one side of the soma, either originating at the cell body or from a single trunk. Commonly there are 2--4 orders of branching, but up to 6 orders can occur (counted centrifugally from the soma). Electron microscopy revealed synapses distributed predominantly on dendrites with a smaller number on somata. Dendritic spines are present and are contacted principally by asymmetric synaptic junctions. Symmetric synapses are relatively more common on somata and proximal dendrites.

Action Potentials↗
PubMed1989

Visualization of oligodendrocytes and astrocytes in the intact rat optic nerve by intracellular injection of lucifer yellow and horseradish peroxidase.

The morphology of glial cells in the intact rat optic nerve, a central nervous system (CNS) white matter tract, was analysed by filling over 500 macroglial cells intracellularly with horseradish peroxidase (HRP) or Lucifer yellow (LY). Two main cell types were distinguished: fibrous astrocytes and cells presumed to be oligodendrocytes. Intracellularly stained astrocytes were highly complex, with 50-60 long branching processes which passed radially from the cell body and terminated in end-feet at the pial surface or on blood vessels; some processes ended freely in the nerve parenchyma. Astrocytes filled with LY were usually dye-coupled to other astrocytes after the first week of life. Filled oligodendrocytes had a unique appearance that unmistakably distinguished them from astrocytes and were occassionally dye-coupled to nearby oligodendrocytes. These cells had 20-30 longitudinally oriented processes 150-200 microns long, which passed exclusively along the long axis of the nerve parallel to axons; the longitudinal processes were connected to the cell body by thin branches 15-30 microns long. The longitudinal processes probably represent the tongue processes of the internodal myelin sheaths, and thus each oligodendrocyte appears to myelinate 20-30 axons with sheaths that are 150-200 microns in length.

Animals↗
PubMed1988

PC12 cells grown on cellulosic filters differentiate in response to NGF and exhibit a polarity not seen when they are grown on solid substrata.

Studies were performed with cellulosic filters and standard culture plates to compare methods of cell culture and differentiation of the cell line PC12, a clone originating from a rat pheochromocytoma. PC12 cells respond to nerve growth factor (NGF) by flattening of the cell body and subsequent extension of neurite-like processes. When PC12 cells are cultured in dishes without NGF, they have a diameter of approximately 3 to 7 micron and exhibit short processes of no longer than 3 to 5 micron. If PC12 cells are grown on a cellulosic filter they have the same average soma diameter and similar short processes extending laterally, but in addition have branching processes which extend as far as 10 to 15 micron into the filter substrate. When dish-cultured and filter-cultured cells are incubated with 50 ng/ml NGF they both exhibit differentiation-specific ultrastructural changes by 3 d of treatment. In the case of dish-cultured cells, large cytoplasmic processes exhibit an increase in the number of chromaffin cell-like secretory granules by 3 d of treatment. This characteristic is also demonstrated by filter-cultured cells, but the processes containing these granules are found concentrated within the cellulosic meshwork. Thus the timing of the NGF-elicited differentiation program is similar to both filter-cultured and dish-cultured cells, but the ultrastructural consequences are different. The filter-cultured PC12 cells exhibit a polarity not demonstrated by dish-cultured cells. Growing PC12 cells on cellulosic filters is a technique useful for "anchoring" neurons without the complication of the addition of extracellular matrix components. Filter-culture may represent a more in vivo-like method for studying neuronal growth and differentiation.

Adrenal Gland Neoplasms↗
PubMed1996

Progressive remodeling of the oligodendrocyte process arbor during myelinogenesis.

Myelin sheaths develop in the central nervous system (CNS) as elaborations of the processes of oligodendrocytes. Although many details of the spiral wrapping of oligodendrocyte processes around axons and their subsequent transformation into myelin sheaths are known from thin-section electron-microscopic studies, the three-dimensional architecture of the myelin-forming cells is incompletely understood. To characterize this aspect of oligodendrocyte development, we labeled thick (100- to 300-microns) sections of developing murine CNS with oligodendrocyte marker antibodies, recorded individual cells in serial optical sections by confocal microscopy, and created whole-cell reconstructions of oligodendrocytes before and during the initiation of myelination. We distinguish three stages in the maturation of oligodendrocytes, which at all three stages are labeled by the O4, O1 and Ranscht monoclonals and by antibodies against the myelin-specific proteins CNP and myelin basic protein. Premyelinating oligodendrocytes, present before axonal ensheathment begins, emit multiple irregular processes which have predominant radial orientation. These processes, which generally terminate within 50 microns of the cell body, have a surface area 3-8 times or more that of the cell body itself and may represent a mechanism for sampling the local environment of each cell and for identifying target axons. Transitional cells have initiated one or more myelin sheaths; these cells progressively reduce the number of their radial processes as they increase the number of their myelin internodes. The radial processes of each transitional cell are most reduced in parts of the process arbor where ensheathment has begun, suggesting directional control in the elaboration or stability of the radial processes. Mature myelin-bearing oligodendrocytes entirely lack the radial processes and instead emit a few sparsely branching processes which connect cell bodies with myelin internodes. Three-dimensional analysis of the earliest stages in myelin sheath formation reveals two distinct phases. The initiating event in the formation of myelin internodes is the growth of thin unbranched processes, termed 'initiator processes', along axons. The second phase, spiral ensheathment of target axons, begins through the elaboration from each initiator process of lamellar extensions which extend circumferentially around the target axon and thereby form the first turn of its myelin sheath.

Animals↗
PubMed1994

Transforming growth factor-beta 1 and -beta 2 promote neurite sprouting and elongation of cultured rat hippocampal neurons.

Transforming growth factor-beta (TGF-beta) is known as a potent regulator of cell proliferation and differentiation. In the present study, we investigated the effects of TGF-beta 1 and -beta 2 on the survival, neurite sprouting and process elongation of primary cultured hippocampal neurons obtained from rat embryos. Addition of TGF-beta 1 little affected the total number of surviving neurons, but clearly increased the number of neurons bearing processes, indicating that TGF-beta 1 promotes neurite sprouting rather than neuronal survival. Furthermore, TGF-beta 1 significantly promoted the elongation of axon-like processes, but did not affect the process branching and the number of dendrite-like processes. TGF-beta 2 also promoted the neurite sprouting and stimulated the elongation of axons without affecting the branching. The effects of TGF-beta 2 were very similar to those of TGF-beta 1 in terms of both effective concentrations (0.1-1 ng/ml) and maximal effects. It is possible that TGF-beta 1 and -beta 2 play roles in the formation of neuritic networks in the central nervous system.

Animals↗
PubMed2025

Estimation of demography and mutation rates from one million haploid genomes.

As genetic sequencing costs have plummeted, datasets with sizes previously unthinkable have begun to appear. Such datasets present opportunities to learn about evolutionary history, particularly via rare alleles that record the very recent past. However, beyond the computational challenges inherent in the analysis of many large-scale datasets, large population-genetic datasets present theoretical problems. In particular, the majority of population-genetic tools require the assumption that each mutant allele in the sample is the result of a single mutation (the "infinite-sites" assumption), which is violated in large samples. Here, we present DR EVIL, a method for estimating mutation rates and recent demographic history from very large samples. DR EVIL avoids the infinite-sites assumption by using a diffusion approximation to a branching-process model with recurrent mutation. This approach results in tractable likelihoods that are accurate for rare alleles. We show that DR EVIL performs well in simulations and apply it to rare-variant data from one million haploid samples. We identify mutation-rate heterogeneity even after accounting for trinucleotide context and methylation status. We also predict that at modern sample sizes, the alleles at most polymorphic sites with high mutation rates represent the descendants of multiple mutation events.

Haploidy↗
PubMed1978

Genetic and evolutionary fitness.

The advantages and disadvantages of evolutionary fitness (probability that a single mutant line will not become extinct) and genetic fitness (mean fecundity) are compared. For deterministic processes the two are equivalent, but for stochastic branching processes they may be totally unrelated except that an absolute genetic fitness of unity or less implies an evolutionary fitness of zero. To know the variance as well as the mean family size does not in general uniquely determine the evolutionary fitness. Except where genetic fitness is close to unity, the impact of selection is shown to be rapid for the binomial, Poisson, negative binomial, and truncated negative binomial distributions. Evolutionary fitness, though somewhat cumbersome, has greater relevance to evolution, genetic counseling, and voluntary population control; but genetic fitness which is much easier to handle is the more appropriate measure where a large number of mutants is involved. Some empirical data on the transmission of various types of characters from parent to child are analyzed to allow comparison of genetic fitness, Crow's index, and a Malthusian parameter, with evolutionary fitness. There is a fair, but far from perfect, agreement among them. Multiple correlation of evolutionary fitness with mean and variance of family size taken jointly suggests a much more satisfactory approximation. It thus appears that, at the least, the population geneticist cannot afford to ignore the variance (which is not adequately represented in Crow's index). These relationships, based on two sets of data only may be accidental and should be invoked with caution. It seems more than likely that other aspects of the distribution of family size (eg, even higher moments) may contain relevant information in certain cases.

Biological Evolution↗
PubMed1994

Blood monocytes and spleen macrophages differentiate into microglia-like cells on monolayers of astrocytes: morphology.

Several morphological and functional properties of microglial cells, the resident immunoeffector cells of the central nervous system (CNS), differ from those of monocytes/macrophages in other tissues. Microglia are assumed to derive from myelonocytic lineage, possibly as a distinct subpopulation that diverges from a common cell line early in ontogeny, invades the CNS, proliferates, and differentiates into ameboid and then ramified microglia. We tested the hypothesis that some morphological and functional properties of microglia are induced in myelomonocytic cells by nervous tissue, specifically astrocytes. In the present in vitro studies we compared the differentiation of microglia, blood monocytes, and spleen macrophages on acellular substrates and on monolayers of astrocytes and fibroblasts. On acellular substrates, microglial cells at first acquire an ameboid morphology; later they show a few short, unbranched processes. On monolayers of pure astrocytes, microglial cells at first also differentiate into ameboid cells, but after 5 to 7 days they start to develop processes with large lamellopodial tips. These lengthen and branch continuously during the next 2 weeks in vitro, demarcating a round to oval territory around the small ellipsoid cell body. By contrast, on monolayers of fibroblasts the microglial cells develop an ameboid morphology, but do not grow the typical long branched processes of the ramified form. Blood monocytes and spleen macrophages behave indistinguishably from microglia both on acellular and cellular substrates, i.e., on astroglia they develop the ramified form, while on fibroblasts they retain the ameboid shape. When microglia, macrophages, or monocytes are cultured on coverslips on top of astrocytic monolayers, i.e., physically separated from the astroglia, but exposed to the medium conditioned by astrocytes, a significant proportion of them also develop the ramified shape. These findings indicate that the ramified shape of microglia is induced by astrocytes. Since this morphology can also be induced in blood monocytes and macrophages, we take this to be further evidence for the proposition that microglial cells are derived from the myelomonocytic lineage, and, moreover, that properties of resident macrophages are largely determined by tissue components of their host organ.

Animals↗
PubMed2001

Growth of branched actin networks against obstacles.

A method for simulating the growth of branched actin networks against obstacles has been developed. The method is based on simple stochastic events, including addition or removal of monomers at filament ends, capping of filament ends, nucleation of branches from existing filaments, and detachment of branches; the network structure for several different models of the branching process has also been studied. The models differ with regard to their inclusion of effects such as preferred branch orientations, filament uncapping at the obstacle, and preferential branching at filament ends. The actin ultrastructure near the membrane in lamellipodia is reasonably well produced if preferential branching in the direction of the obstacle or barbed-end uncapping effects are included. Uncapping effects cause the structures to have a few very long filaments that are similar to those seen in pathogen-induced "actin tails." The dependence of the growth velocity, branch spacing, and network density on the rate parameters for the various processes is quite different among the branching models. An analytic theory of the growth velocity and branch spacing of the network is described. Experiments are suggested that could distinguish among some of the branching models.

Actin Depolymerizing Factors↗
PubMed1989

GABAergic neurons in brainstem auditory nuclei of the chick: distribution, morphology, and connectivity.

The second- and third-order auditory nuclei in the brainstem of the chicken, nucleus magnocellularis (NM) and nucleus laminaris (NL), receive afferents that are immunoreactive to gamma-aminobutyric acid (GABA). In order to investigate the source(s) of these GABAergic afferents, we examined the distribution, morphology, and connectivity of GABAergic neurons in and adjacent to NM and NL in chicks from 7 days of incubation to 12 days posthatch. Immunocytochemical techniques revealed the presence of approximately 150 GABA-labeled neurons within the neuropil surrounding NM and NL on each side of the brainstem. Most of these neurons are located between NM and NL and along the lateral border of NM. GABAergic neurons are multipolar; their thick dendritic processes branch extensively and give rise to several thin, secondary processes. Frequently, the GABA-labeled processes arborize within NM or NL. The morphology of these non-NM/NL neurons was investigated further with Golgi impregnation and specific neuronal markers (antisera to microtubule-associated protein). Our observations suggest that a considerable portion of GABAergic input to NM and NL originates from local GABAergic neurons. In order to determine other possible sources of GABAergic input to NM and NL, we injected tracers unilaterally into NM/NL. A small number (20-30) of neurons were retrogradely labeled in the trapezoid body, almost exclusively ipsilaterally. No labeled cells were found in other regions of the brainstem, except for the contralateral NM. Unilateral injections of horseradish-peroxidase-labeled wheat germ agglutinin into the paraflocculus revealed only minor terminal labeling in the lateral region of NL bilaterally. The number and distribution of GABAergic terminals in NM and NL appeared normal after transection of the crossed dorsal cochlear tract.

Animals↗