A probability distribution model of small -scale species richness in plant communities

We devised a probability distribution model that best expressed species richness per quadrat in grassland communities, and clarified the mechanism by which the mean richness per quadrat was always larger than the variance among quadrats. Our model will aid in the understanding of community structures, and allow comparisons among different communities. The model was constructed based on relatively simple theoretical assumptions about the mechanisms in play in target communities. We assumed in the model that the number of species occurring in an actual quadrat, j, is the sum of “the fundamental number of species”, k (constant), and “a fluctuating number of species”, i (a Poisson variate with the mean of μ); that is, j = k + i, where i, j and k are non-negative integers. The probability that j species occur in a quadrat is given by a Poisson-like distribution (extended Poisson), with two parameters k and μ. The mean species richness in the probability distribution is expressed by λ (= k + μ), and the variance is λ − k. The proposed model afforded a good fit for the observed frequency distribution of species richness per quadrat. If even one species is common among many quadrats, the mean number of species per quadrat is greater than the variance. The greater the number of common species among quadrats is, the larger is the value of k, and then the more pronounced is the difference between the mean and the variance (although the variance does not change). We fitted the model to 55 datasets collected by ourselves from grasslands in various locations (Tibet, Inner Mongolia, Slovakia, or Japan), with varying quadrat size (0.25, 0.0625, or 0.01 m²), and under differing management status (various stocking densities).     

Space-time decoupling in the branching process in the mutant étoile of the filamentous brown alga Ectocarpus siliculosus

Ectocarpus siliculosus is being developed as a model organism for brown algal genetics and genomics.^1,2 Brown algae are phylogenetically distant from the other multicellular phyla (green lineage, red algae, fungi and metazoan)³ and therefore might offer the opportunity to study novel and alternative developmental processes that lead to the establishment of multicellularity. E. siliculosus develops as uniseriate filaments, thereby displaying one of the simplest architectures among multicellular organisms.⁴ The young sporophyte grows as a primary filament and then branching occurs, preferentially at the center of the filament. We recently described the first morphogenetic mutant étoile (etl) in a brown alga, produced by UVB mutagenesis in E. siliculosus.⁵ We showed that a single recessive mutation was responsible for a defect in both cell differentiation and the very early branching pattern (first and second branch emergences). Here, we supplement this study by reporting the branching defects observed subsequently, i.e. for the later stages corresponding to the emergence of up to the first six secondary filaments, and we show that the branching process is composed of at least two distinct components: time and position.   The developmental pattern of E. siliculosus is characterized by a very high level of morphological plasticity.⁶ Observations followed by statistical analyses allowed analyzing the morphometric features accompanying the establishment of the branching pattern in the mutant étoile, compared with the wild type (WT) organism (strain Ec32). The branching pattern can be deciphered in two main components: (1) the timing of branching and (2) the position of branching.     

The Carboxyl Terminal Residues 220–283 Are Not Required for Voltage Gating of a Chimeric Connexin32 Hemichannel

Connexin hemichannels display two distinct forms of voltage-dependent gating, corresponding to the operation of V_j- or fast gates and loop- or slow gates. The carboxyl terminus (CT) of connexin 32 has been reported to be required for the operation of the V_j (fast) gates, but this conclusion was inferred from the loss of a fast kinetic component in macroscopic currents of CT-truncated intercellular channels elicited by transjunctional voltage. Such inferences are complicated by presence of both fast and slow gates in each hemichannel and the serial head-to-head arrangement of these gates in the intercellular channel. Examination of voltage gating in undocked hemichannels and V_j gate polarity reversal by a negative charge substitution (N2E) in the amino terminal domain allow unequivocal separation of the two gating processes in a Cx32 chimera (Cx32^∗43E1). This chimera expresses currents as an undocked hemichannel in Xenopus oocytes and provides a model system to study the molecular determinants and mechanisms of Cx32 voltage gating. Here, we demonstrate that both V_j- and loop gates are operational in a truncation mutation that removes all but the first four CT residues (ACAR²¹⁹) of the Cx32^∗43E1 hemichannel. We conclude that an operational Cx32 V_j (fast) gate does not require CT residues 220–283, as reported previously by others.     

The Carboxyl Terminal Residues 220–283 Are Not Required for Voltage Gating of a Chimeric Connexin32 Hemichannel

Connexin hemichannels display two distinct forms of voltage-dependent gating, corresponding to the operation of V_j- or fast gates and loop- or slow gates. The carboxyl terminus (CT) of connexin 32 has been reported to be required for the operation of the V_j (fast) gates, but this conclusion was inferred from the loss of a fast kinetic component in macroscopic currents of CT-truncated intercellular channels elicited by transjunctional voltage. Such inferences are complicated by presence of both fast and slow gates in each hemichannel and the serial head-to-head arrangement of these gates in the intercellular channel. Examination of voltage gating in undocked hemichannels and V_j gate polarity reversal by a negative charge substitution (N2E) in the amino terminal domain allow unequivocal separation of the two gating processes in a Cx32 chimera (Cx32^∗43E1). This chimera expresses currents as an undocked hemichannel in Xenopus oocytes and provides a model system to study the molecular determinants and mechanisms of Cx32 voltage gating. Here, we demonstrate that both V_j- and loop gates are operational in a truncation mutation that removes all but the first four CT residues (ACAR²¹⁹) of the Cx32^∗43E1 hemichannel. We conclude that an operational Cx32 V_j (fast) gate does not require CT residues 220–283, as reported previously by others.     

Quantum-chemical and empirical calculations on phospholipids. VI: The stereospecific interaction of Na+ with phosphatidylethanolamine and with phosphatidylcholine layer systems

Using 1-6-12 atom-atom potential functions with a solvent-averaged electrostatic potential U = q_Iq_j/(?D(r)r_1j between the charges q_I and q_j the stereospecific interaction of Na⁺ with clusters of l-glycero-phosphorylethanolamine (GPE) and -choline (GPC) in a two-dimensional planar lattice was calculated. With neutral PE headgroups only a weak attractive interaction of ?140 kJ/mol was found. This should be compensated in PE/water systems by reorientational processes within the Na⁺ hydration shell to get an optimum binding of Na⁺ with the PE headgroup. With a phosphorylethanolamine anion within a neutral PE headgroup environment a stereospecific binding energy of ?500 kJ/mol was calculated. The interaction of Na⁺ or Ca²⁺ with clusters of phosphatidylcholine is always repulsive. These results are in a very good agreement with experimental ones where a binding of Na⁺ with PE bilayers at pH > 7.5, but not with PC bilayers was detected.     

Stochastic continuous time neurite branching models with tree and segment dependent rates

In this paper we introduce a continuous time stochastic neurite branching model closely related to the discrete time stochastic BES-model. The discrete time BES-model is underlying current attempts to simulate cortical development, but is difficult to analyze. The new continuous time formulation facilitates analytical treatment thus allowing us to examine the structure of the model more closely. We derive explicit expressions for the time dependent probabilities p(γ,t) for finding a tree γ at time t, valid for arbitrary continuous time branching models with tree and segment dependent branching rates. We show, for the specific case of the continuous time BES-model, that as expected from our model formulation, the sums needed to evaluate expectation values of functions of the terminal segment number μ(f(n),t) do not depend on the distribution of the total branching probability over the terminal segments. In addition, we derive a system of differential equations for the probabilities p(n,t) of finding n terminal segments at time t. For the continuous BES-model, this system of differential equations gives direct numerical access to functions only depending on the number of terminal segments, and we use this to evaluate the development of the mean and standard deviation of the number of terminal segments at a time t. For comparison we discuss two cases where mean and variance of the number of terminal segments are exactly solvable. Then we discuss the numerical evaluation of the S-dependence of the solutions for the continuous time BES-model. The numerical results show clearly that higher S values, i.e. values such that more proximal terminal segments have higher branching rates than more distal terminal segments, lead to more symmetrical trees as measured by three tree symmetry indicators.     

Genetic hazards of ionizing radiations: cytogenetic extrapolations from mouse to man

The frequencies of X-ray induced asymmetrical interchanges (dicentrics) and acentric fragments (deletions) at several doses were measured in the circullating leukocytes of six species. The leukocytes of the species used had similar DNA contents but different chromosome and chromosome arm numbers. The data for dicentrics were fitted separately for each species by regression analysis to the model Y_j = b_jD + c_jD². All species gave a good fit to this model. As expected, when the dicentric data for all species were pooled and fitted to this model a poor fit was obtained. However, if a term for arm number was included, so that the model Y_j = (N_j?1) (bD+cD²) was fitted, a significant amount of the variation among species could be accounted for. At each dose there was an approximately linear relationship between the yield of dicentrics and the arm number. Man, with an effective arm number of 81, had twice as many dicentrics as the mouse, with an effective arm number of. These results strongly suggest that the chromosome arm number of a species influences the yield of asymmetrica interchanges. The chromosome arm number did not appear to influence the yield of deletions, and the yields induced in the mouse and man at easch dose were equal.These results show that man is twice as sensitive as the mouse to the induction of translocations, whereas the two species are equally sensitive to the indcution of deletions and, in all probability, to the production of mutations.     

A stochastic model for estimation of mutation rates in multiple-replication proliferation processes

In this paper we propose a stochastic model based on the branching process for estimation and comparison of the mutation rates in proliferation processes of cells or microbes. We assume in this model that cells or microbes (the elements of a population) are reproduced by generations and thus the model is more suitably applicable to situations in which the new elements in a population are produced by older elements from the previous generation rather than by newly created elements from the same current generation. Cells and bacteria proliferate by binary replication, whereas the RNA viruses proliferate by multiple replication. The model is in terms of multiple replications, which includes the special case of binary replication. We propose statistical procedures for estimation and comparison of the mutation rates from data of multiple cultures with divergent culture sizes. The mutation rate is defined as the probability of mutation per replication per genome and thus can be assumed constant in the entire proliferation process. We derive the number of cultures for planning experiments to achieve desired accuracy for estimation or desired statistical power for comparing the mutation rates of two strains of microbes. We establish the efficiency of the proposed method by demonstrating how the estimation of mutation rates would be affected when the culture sizes were assumed similar but actually diverge.      

Hs2st mediated kidney mesenchyme induction regulates early ureteric bud branching

Heparan sulfate proteoglycans (HSPGs) are central modulators of developmental processes likely through their interaction with growth factors, such as GDNF, members of the FGF and TGFβ superfamilies, EGF receptor ligands and HGF. Absence of the biosynthetic enzyme, heparan sulfate 2-O-sulfotransferase (Hs2st) leads to kidney agenesis. Using a novel combination of in vivo and in vitro approaches, we have reanalyzed the defect in morphogenesis of the Hs2st^−/− kidney. Utilizing assays that separately model distinct stages of kidney branching morphogenesis, we found that the Hs2st^−/− UB is able to undergo branching and induce mesenchymal-to-epithelial transformation when recombined with control MM, and the isolated Hs2st null UB is able to undergo branching morphogenesis in the presence of exogenous soluble pro-branching growth factors when embedded in an extracellular matrix, indicating that the UB is intrinsically competent. This is in contrast to the prevailing view that the defect underlying the renal agenesis phenotype is due to a primary role for 2-O sulfated HS in UB branching. Unexpectedly, the mutant MM was also fully capable of being induced in recombination experiments with wild-type tissue. Thus, both the mutant UB and mutant MM tissue appear competent in and of themselves, but the combination of mutant tissues fails in vivo and, as we show, in organ culture. We hypothesized a 2OS-dependent defect in the mutual inductive process, which could be on either the UB or MM side, since both progenitor tissues express Hs2st. In light of these observations, we specifically examined the role of the HS 2-O sulfation modification on the morphogenetic capacity of the UB and MM individually. We demonstrate that early UB branching morphogenesis is not primarily modulated by factors that depend on the HS 2-O sulfate modification; however, factors that contribute to MM induction are markedly sensitive to the 2-O sulfation modification. These data suggest that key defect in Hs2st null kidneys is the inability of MM to undergo induction either through a failure of mutual induction or a primary failure of MM morphogenesis. This results in normal UB formation but affects either T-shaped UB formation or iterative branching of the T-shaped UB (possibly two separate stages in collecting system development dependent upon HS). We discuss the possibility that a disruption in the interaction between HS and Wnts (e.g. Wnt 9b) may be an important aspect of the observed phenotype. This appears to be the first example of a defect in the MM preventing advancement of early UB branching past the first bifurcation stage, one of the limiting steps in early kidney development.     

Hypotonic Regulation of Mouse Epithelial Sodium Channel in Xenopus laevis Oocytes

The regulation of the epithelial Na⁺ channel (ENaC) during cell swelling is relevant in cellular processes in which cell volume changes occur, i.e., migration, proliferation and cell absorption. Its sensitivity to hypotonically induced swelling was investigated in the Xenopus oocyte expression system with the injection of the three subunits of mouse ENaC. We used voltage-clamp techniques to study the amiloride-sensitive Na⁺ currents (INa_(amil)) and video microscopic methodologies to assess oocyte volume changes. Under conditions of mild swelling (25 % reduced hypotonicity) inward current amplitude decreased rapidly over 1.5 min. In contrast, there was no change in current amplitude of H₂O-injected oocytes to the osmotic insult. INa_(amil) kinetics analysis revealed a decrease in the slower inactivation time constant during the hypotonic stimuli. Currents from ENaC-injected oocytes were not sensitive to external Cl^? reduction. Neither short- nor long-term cytochalasin D treatment affected the observed response. Oocytes expressing a DEG mutant β-ENaC subunit (β-S518K) with an open probability of 1 had reduced INa_(amil) hypotonic response compared to oocytes injected with wild-type ENaC subunits. Finally, during the hypotonic response ENaC-injected oocytes did not show a cell volume difference compared with water-injected oocytes. On this basis we suggest that hypotonicity-dependent ENaC inhibition is principally mediated through an effect on open probability of channels in the membrane.     

Fixation probabilities and effective population numbers in diploid populations with overlapping generations

A finite diploid population, observed at times t = 0, 1, 2,…, is studied. An individual is said to be in age group i at time t if its age is between i and i + 1 units at that time, where i ? 1. It is assumed that the number of individuals in a particular age-sex class is the same for every t and that the probability that a male offspring was produced by a mating of a male in age group i and a female in age group j is p_ij^m (with a corresponding probability p^f_ij for a female offspring), regardless of when the individual is born. The probability of ultimate fixation of an allele A₁ and the inbreeding effective number, for large populations, is calculated under the further assumptions that A₁ is neutral and that mating is random, given the ages of the mates.     

Magnesium gating of cardiac gap junction channels

We aimed to study kinetics of modulation by intracellular Mg²⁺ of cardiac gap junction (Mg²⁺ gate). Paired myocytes of guinea-pig ventricle were superfused with solutions containing various concentrations of Mg²⁺. In order to rapidly apply Mg²⁺ to one aspect of the gap junction, the non-junctional membrane of one of the pair was perforated at nearly the connecting site by pulses of nitrogen laser beam. The gap junction conductance (G_j) was measured by clamping the membrane potential of the other cell using two-electrode voltage clamp method. The laser perforation immediately increased G_j, followed by slow G_j change with time constant of 3.5 s at 10 mM Mg²⁺. Mg²⁺ more than 1.0 mM attenuated dose-dependently the gap junction conductance and lower Mg²⁺ (0.6 mM) increased G_j with a Hill coefficient of 3.4 and a half-maximum effective concentration of 0.6 mM. The time course of G_j changes was fitted by single exponential function, and the relationship between the reciprocal of time constant and Mg²⁺ concentration was almost linear. Based on the experimental data, a mathematical model of Mg²⁺ gate with one open state and three closed states well reproduced experimental results. One-dimensional cable model of thirty ventricular myocytes connected to the Mg²⁺ gate model suggested a pivotal role of the Mg²⁺ gate of gap junction under pathological conditions.     

Detecting particular genotypes in populations under nonrandom mating

We investigate the time to formation of particular genotypes in populations with nonrandom mating systems. We employ two main techniques. The first is a study of branching processes with “killing”; these are models which behave just like a standard Galton-Watson branching process with the added possibility of being terminated by the occurrence of a special event in the process. In our case, this special event corresponds to formation or detection of a group of individuals carrying a specific genotype. We then use these results and some natural approximation methods to analyze and interpret the gene formation problem in a simple way.     

Separation of Gating Properties from Permeation and Block in mslo Large Conductance Ca-activated K+ Channels

In this and the following paper we have examined the kinetic and steady-state properties of macroscopic mslo Ca-activated K⁺ currents in order to interpret these currents in terms of the gating behavior of the mslo channel. To do so, however, it was necessary to first find conditions by which we could separate the effects that changes in Ca²⁺ concentration or membrane voltage have on channel permeation from the effects these stimuli have on channel gating. In this study we investigate three phenomena which are unrelated to gating but are manifest in macroscopic current records: a saturation of single channel current at high voltage, a rapid voltage-dependent Ca²⁺ block, and a slow voltage-dependent Ba²⁺ block. Where possible methods are described by which these phenomena can be separated from the effects that changes in Ca²⁺ concentration and membrane voltage have on channel gating. Where this is not possible, some assessment of the impact these effects have on gating parameters determined from macroscopic current measurements is provided. We have also found that without considering the effects of Ca²⁺ and voltage on channel permeation and block, macroscopic current measurements suggest that mslo channels do not reach the same maximum open probability at all Ca²⁺ concentrations. Taking into account permeation and blocking effects, however, we find that this is not the case. The maximum open probability of the mslo channel is the same or very similar over a Ca²⁺ concentration range spanning three orders of magnitude indicating that over this range the internal Ca²⁺ concentration does not limit the ability of the channel to be activated by voltage.     

Multi-type branching models to describe cell differentiation programs

Cell proliferation and differentiation is described by a multi-type branching process, a probability model that defines the inheritance of cell type. Cell type is defined by (i) a repression index related to the time required for S-phase entry and (ii) phenotype as determined by cell markers and division history. The inheritance of cell type is expressed as the expected number and type of progeny cells produced by a mother cell given her type. Expressions for the expected number and type of cells produced by a multi-cellular (bulk culture) system are derived from the general model by making the simplifying assumption that cell generation times are independent. The multi-type Smith-Martin model (MSM) makes the further assumption that cell generation times are lag-exponentially distributed with phenotype transitions occurring just before entry into S-phase. The inheritance-modified MSM (IMSM) model includes the influence of generation time memory so that mother and daughter generation times are correlated. The expansion of human cord blood CD34⁺ cells by haematopoietic growth factors was division tracked in bulk culture using carboxyfluorescein diacetate, succinimidyl ester (CFDA-SE). The MSM model was fitted to division tracking data to indentify cell cycle length, and the rates of CD34 antigen down-regulation and apoptosis. The IMSM model was estimated for mouse granulocyte-macrophage progenitors using live cell imaging data. Multi-type branching models describe cell differentiation dynamics at both single- and multi-cell scales, providing a new paradigm for systematic analysis of stem and progenitor cell development.     

A System for ex vivo Culturing of Embryonic Pancreas

The pancreas controls vital functions of our body, including the production of digestive enzymes and regulation of blood sugar levels¹. Although in the past decade many studies have contributed to a solid foundation for understanding pancreatic organogenesis, important gaps persist in our knowledge of early pancreas formation². A complete understanding of these early events will provide insight into the development of this organ, but also into incurable diseases that target the pancreas, such as diabetes or pancreatic cancer. Finally, this information will generate a blueprint for developing cell-replacement therapies in the context of diabetes.During embryogenesis, the pancreas originates from distinct embryonic outgrowths of the dorsal and ventral foregut endoderm at embryonic day (E) 9.5 in the mouse embryo^3,4. Both outgrowths evaginate into the surrounding mesenchyme as solid epithelial buds, which undergo proliferation, branching and differentiation to generate a fully mature organ^2,5,6. Recent evidences have suggested that growth and differentiation of pancreatic cell lineages, including the insulin-producing β-cells, depends on proper tissue-architecture, epithelial remodeling and cell positioning within the branching pancreatic epithelium^7,8. However, how branching morphogenesis occurs and is coordinated with proliferation and differentiation in the pancreas is largely unknown. This is in part due to the fact that current knowledge about these developmental processes has relied almost exclusively on analysis of fixed specimens, while morphogenetic events are highly dynamic.Here, we report a method for dissecting and culturing mouse embryonic pancreatic buds ex vivo on glass bottom dishes, which allow direct visualization of the developing pancreas (Figure 1). This culture system is ideally devised for confocal laser scanning microscopy and, in particular, live-cell imaging. Pancreatic explants can be prepared not only from wild-type mouse embryos, but also from genetically engineered mouse strains (e.g. transgenic or knockout), allowing real-time studies of mutant phenotypes. Moreover, this ex vivo culture system is valuable to study the effects of chemical compounds on pancreatic development, enabling to obtain quantitative data about proliferation and growth, elongation, branching, tubulogenesis and differentiation. In conclusion, the development of an ex vivo pancreatic explant culture method combined with high-resolution imaging provides a strong platform for observing morphogenetic and differentiation events as they occur within the developing mouse embryo.     

Impact of slow K<Superscript>+</Superscript> currents on spike generation can be described by an adaptive threshold model

A neuron that is stimulated by rectangular current injections initially responds with a high firing rate, followed by a decrease in the firing rate. This phenomenon is called spike-frequency adaptation and is usually mediated by slow K⁺ currents, such as the M-type K⁺ current (I _M ) or the Ca²⁺-activated K⁺ current (I _AHP ). It is not clear how the detailed biophysical mechanisms regulate spike generation in a cortical neuron. In this study, we investigated the impact of slow K⁺ currents on spike generation mechanism by reducing a detailed conductance-based neuron model. We showed that the detailed model can be reduced to a multi-timescale adaptive threshold model, and derived the formulae that describe the relationship between slow K⁺ current parameters and reduced model parameters. Our analysis of the reduced model suggests that slow K⁺ currents have a differential effect on the noise tolerance in neural coding.     

More on Nei and Roychoudhury''s Sampling Variances of Heterozygosity and Genetic Distance

The inequality relationship between the expected values of ( j_x-g)² and (ĝ-g) ², where j_x is a biased and ĝ is an unbiased estimate of population homozygosity g, were examined earlier by Nei and Roychoudhury (1974) and later by Mitra (1975). The improvement in the inequality still left much to be desired. In this paper a lower boundary of g has been obtained which may be regarded as ultimate for ensuring a smaller expected value of ( j_x-g)² than the corresponding value of ( ĝ-g)².