Ewens' sampling formula and related formulae: combinatorial proofs, extensions to variable population size and applications to ages of alleles

Ewens' sampling formula, the probability distribution of a configuration of alleles in a sample of genes under the infinitely-many-alleles model of mutation, is proved by a direct combinatorial argument. The distribution is extended to a model where the population size may vary back in time. The distribution of age-ordered frequencies in the population is also derived in the model, extending the GEM distribution of age-ordered frequencies in a model with a constant-sized population. The genealogy of a rare allele is studied using a combinatorial approach. A connection is explored between the distribution of age-ordered frequencies and ladder indices and heights in a sequence of random variables. In a sample of n genes the connection is with ladder heights and indices in a sequence of draws from an urn containing balls labelled 1,2,...,n; and in the population the connection is with ladder heights and indices in a sequence of independent uniform random variables.     

The transfer of J blood-group activity from J-containing bovine serum to J-negative erythrocytes.

The J blood-group activity of bovine serum is contained both in a lipid and in a nonlipid fraction. This is also true for calf serum. It demonstrated that the J determinant is transferred from a serum protein onto the erythrocyte membrane by incubation in vitro. Even though the donor of J activity is a lipid-free serum protein (probably a glycoprotein), the transferred J activity is detectable only in the lipid fraction of erythrocytes. Thus, the J determinant (probably a carbohydrate unit) must have been detached from a serum glycoprotein and transferred to a lipidic receptor (probably a glycosphingolipid) at the erythrocyte membrane. It is suggested than an enzyme system located in or at the erythrocyte membrane is responsible for the transfer of J substance. The transfer of J substance is inhibited by a polar lipid present in bovine serum.     

Effect of binding on melting transitions in polymer–diluent systems

An expression is derived for the melting point of a polymer when in equilibrium with a solution in which binding of low molecular weight compounds to the polymer takes place. Allowance is made for the possibility that the crystalline polymer itself is a complex. The argument is a purely thermodynamic one and is based on a consideration of the change in free energy as a result of a change in binding. Allowance is made also for non-specific polymer–solvent interactions, in which the mixture of low molecular weight solvents is treated as a single solvent. Special attention is paid to “inverted” melting transitions, i.e., cases in which the melting point increases with increasing dilution of the polymer. It is shown that as a rule this is accompanied by a corresponding, inverted effect of the solvent composition on the melting point. It is further shown that-in the absence of binding, “normal” behavior at the critical point (i.e., phase separation is induced by lowering the temperature) is always accompanied by “normal” melting behavior (i.e., a decrease in melting point when the polymer is diluted). Also, “inverted” melting always implies that phase separation at the critical point is induced by heating, but the reverse is not necessarily true.     

A graph theoretic approach to the development of minimal phylogenetic trees

Summary The problem of determining the minimal phylogenetic tree is discussed in relation to graph theory. It is shown that this problem is an example of the Steiner problem in graphs which is to connect a set of points by a minimal length network where new points can be added. There is no reported method of solving realistically-sized Steiner problems in reasonable computing time. A heuristic method of approaching the phylogenetic problem is presented, together with a worked example with 7 mammalian cytochrome c sequences. It is shown in this case that the method develops a phylogenetic tree that has the smallest possible number of amino acid replacements. The potential and limitations of the method are discussed. It is stressed that objective methods must be used for comparing different trees. In particular it should be determined how close a given tree is to a mathematically determined lower bound. A theorem is proved which is used to establish a lower bound on the length of any tree and if a tree is found with a length equal to the lower bound, then no shorter tree can exist.     

Translational-entropy gain of solvent upon protein folding

We show that even in the complete absence of potential energies among the atoms in a protein-aqueous solution system, there is a physical factor that favors the folded state of the protein. It is a gain in the translational entropy (TE) of water originating from the translational movement of water molecules. An elaborate statistical-mechanical theory is employed to analyze the TE of water in which a protein or peptide with a prescribed conformation is immersed. It is shown that if the number of residues is sufficiently large, the TE gain is powerful enough to compete with the conformational-entropy loss upon folding. For protein G we have tested over 100 compact conformations generated by a computer simulation with the all-atom potentials as well as the native structure. A significant finding is that the largest TE is attained in the native structure. The translational movement of water molecules is quite effective in achieving the tight packing in the interior of a natural protein. These results are true only when the solvent is water whose molecular size is the smallest among the ordinary liquids in nature.     

ON THE INFLUENCE OF AGGREGATES ON THE MEMBRANE POTENTIALS AND THE OSMOTIC PRESSURE OF PROTEIN SOLUTIONS

1. It is shown that when part of the gelatin in a solution of gelatin chloride is replaced by particles of powdered gelatin (without change of pH) the membrane potential of the solution is influenced comparatively little. 2. A measurement of the hydrogen ion concentration of the gelatin chloride solution and the outside aqueous solution with which the gelatin solution is in osmotic equilibrium, shows that the membrane potential can be calculated from this difference of hydrogen ion concentration with an accuracy of half a millivolt. This proves that the membrane potential is due to the establishment of a membrane equilibrium and that the powdered particles participate in this membrane equilibrium. 3. It is shown that a Donnan equilibrium is established between powdered particles of gelatin chloride and not too strong a solution of gelatin chloride. This is due to the fact that the powdered gelatin particles may be considered as a solid solution of gelatin with a higher concentration than that of the weak gelatin solution in which they are suspended. It follows from the theory of membrane equilibria that this difference in concentration of protein ions must give rise to potential differences between the solid particles and the weaker gelatin solution. 4. The writer had shown previously that when the gelatin in a solution of gelatin chloride is replaced by powdered gelatin (without a change in pH), the osmotic pressure of the solution is lowered the more the more dissolved gelatin is replaced by powdered gelatin. It is therefore obvious that the powdered particles of gelatin do not participate in the osmotic pressure of the solution in spite of the fact that they participate in the establishment of the Donnan equilibrium and in the membrane potentials. 5. This paradoxical phenomenon finds its explanation in the fact that as a consequence of the participation of each particle in the Donnan equilibrium, a special osmotic pressure is set up in each individual particle of powdered gelatin which leads to a swelling of that particle, and this osmotic pressure is measured by the increase in the cohesion pressure of the powdered particles required to balance the osmotic pressure inside each particle. 6. In a mixture of protein in solution and powdered protein (or protein micellæ) we have therefore two kinds of osmotic pressure, the hydrostatic pressure of the protein which is in true solution, and the cohesion pressure of the aggregates. Since only the former is noticeable in the hydrostatic pressure which serves as a measure of the osmotic pressure of a solution, it is clear why the osmotic pressure of a protein solution must be diminished when part of the protein in true solution is replaced by aggregates.     

Transfer RNA and the formation of the heme and chlorophyll precursor, 5-aminolevulinic acid

5-Aminolevulinic acid is the first committed precursor for the synthesis of porphyrins such as hemes and chlorophylls. In many organisms aminolevulinate is synthesized from glutamate in a three-step pathway (C5 pathway). The key step in this conversion is a tRNA-mediated reduction of glutamate to glutamate-1-semialdehyde. tRNA is a specific cofactor for an NADPH-dependent enzyme, Glu-tRNA reductase, which is capable of sequence-specific recognition of Glu-tRNA(Glu). tRNA(Glu) is a dual-function molecule; it participates both in protein and in aminolevulinate biosynthesis. This reduction reaction represents a novel role for tRNA where it participates in a metabolic conversion of its amino acid into a low molecular weight metabolite which is subsequently not used in peptide bond synthesis.     

Pulse wave velocity as a diagnostic index: the pitfalls of tethering versus stiffening of the arterial wall

Pulse wave velocity (PWV) is often used as a clinical index of aging, vascular disease, or age related hypertension. This practice is based on the assumption that a higher wave speed indicates vascular stiffening. This assumption is well grounded in the physics of pulsatile flow of an incompressible fluid where it is fully established that a pulse wave travels faster in a tube of stiffer wall, the wave speed becoming infinite in the mathematical limit of a rigid wall. However, in this paper we point out that the physical principal of higher pulse wave velocity in a stiffer tube is strictly valid only when the wall is free from outside constraints, which in the physiological setting is present in the form of tethering of the vessel wall. The use of PWV as an index of arterial stiffening may thus lose its validity if tethering is involved. A solution of the problem of vessel wall mechanics as they arise from the physiological pulsatile flow problem is presented for the purpose of resolving this issue. The vessel wall is considered to have finite thickness with or without tethering and with a range of mechanical properties ranging from viscoelastic to stiff. The results show that, indeed, while the wave speed becomes infinite in the mathematical limit of a rigid free wall, the opposite actually happens if the vessel wall is tethered. Here the wave speed actually diminishes as the degree of tethering increases. This dichotomy in the effects of tethering versus stiffening of the arterial wall may clearly lead to error in the interpretation of PWV as an index of vessel wall stiffness. In particular, a normal value of PWV may lead to the conclusion that vessel wall stiffening is absent while this value may in fact have been lowered by tethering. In other words, the diagnostic test may lead to a false negative diagnosis. Our results indicate that the reason for which PWV is lower in a tethered wall compared with that in a free wall of the same stiffness is that the radial movements of the wall are greatly reduced by tethering. More precisely, the results show that PWV depends strongly on the ratio of radial to axial displacements and that this ratio is much lower in a tethered wall than it is in a free wall of the same stiffness.     

Murine numb regulates granule cell maturation in the cerebellum

Notch is a key regulator of vertebrate neurogenesis and the cytoplasmic adaptor protein Numb is a modulator of the Notch signaling pathway. To address the role of murine Numb in development of the central nervous system, we used a conditional gene ablation approach. We show that Numb is involved in the maturation of cerebellar granule cells. Although the specification of neural cell fates in the cerebellum is not affected in the absence of Numb, the transition from a mitotic progenitor to a mature granule cell is aberrant and migration of postmitotic granule cells to the internal granule cell layer is delayed. In some animals, this results in a complete agenesis of granule cells and a strong ataxia. We confirmed these findings in vitro and found that Numb-deficient cerebellar progenitor cells show a marked delay in granule cell maturation. Our results suggest that Numb plays a role in the transition of a mitotic progenitor to a fully differentiated granule cell in the cerebellum. In addition, the maturation of Purkinje cells is also delayed in Numb-deficient mice.     

Bistability Analysis of an Apoptosis Model in the Presence of Nitric Oxide

Bistability in apoptosis, or programmed cell death, is crucial for the healthy functioning of multicellular organisms. The aim in this study is to show the presence of bistability in a mitochondria-dependent apoptosis model under nitric oxide effects using chemical reaction network theory. The model equations are a set of coupled ordinary differential equations arising from the assumed mass action kinetics. Whether these equations have a capacity for bistability (cell survival and apoptosis) is determined using a modular approach in which the model is decomposed into modules. Each module contains only a subset of the whole model and is analyzed separately. It is seen that bistability in a module is preserved throughout the whole model after adding the remaining reactions in the pathway on these modules. It is also found that inhibitor effect of some proteins and the appearance of a reacting protein in a later stage as a product is a desired feature but not sufficient for bistability (in the absence of cooperativity effects). On the whole model, two apoptotic and two cell survival states are obtained depending on the initial cell conditions. The results suggest that the antiapoptotic effects of nitric oxide species are responsible for the bistable character of the apoptotic pathway when cooperativity is not assumed in the apoptosome formation.     

The interactions of the non-specific inhibitor of hyaluronidase with hyaluronidase and proteolytic enzymes in vivo

1. Following intravenous administration of testes hyaluronidase in rabbits and dogs, there is a decrease in the level of the non-specific inhibitor of hyaluronidase in serum. 2. If a large amount of hyaluronidase is injected, the inhibitor level is reduced to zero and hyaluronidase may be present in serum for some time after the injection. The hyaluronidase activity of such samples of serum increases when the serum is incubated with papain. 3. Hyaluronidase activity is found in the livers of the injected animals in large amounts and this activity is increased considerably when the homogenate of this tissue is incubated with papain. 4. Intravenous administration of several proteases or venom produces a decrease in the serum inhibitor level. Intravenous administration of streptokinase produces such a decrease in rabbits but not in dogs. 5. There is a correlation between the depletion of the inhibitor from the serum and the occurrence of a slow, persistent depression of blood pressure upon administration of proteolytic enzymes.     

Molecular Reproduction & Development: Volume 76, Issue 1

The echinoderm larval gut. The image is a projection from a reconstruction of a portion of Strongylocentrolus purpuratus pluteus endoderm. Nuclear DNA is in blue, modifying enzyme is in green and extracellular matrix is shown in red.     

Optimal seasonal timing of univoltine and bivoltine insects

This study examines the optimal seasonal timing of the life cycle for univoltine and bivoltine insects, assuming that resource availability has a peak in the middle of a year and is symmetric around it. Results show that if the growth rate increases in proporrion to the bodyweight, bivoltine life cannot be optimal. If the growth rate is a power function of the bodyweight with a power smaller than unity, a symmetric bivoltine solution can be the optimal provided that the resource availability has a plateau in the middle of the season. If the resource availability has a sharp peak, the optimal pattern is an asymmetric bivoltine solution in which the larval periods of two generations differ in length. The bivoltine life cycle is more likely to be superior to the univoltine one if: growth is fast, suitable growing season is long, biomass loss during nonlarval stages is small, and egg size is small.     

The Influence of Temperature on the Effect of Bacteriostatic Concentrations of Phenol Against Escherichia coli

S ummary . During early exponential growth of Escherichia coli in the absence of phenol there is a natural death rate at 20, 30, and 44° but at the optimum temperature around 37° there is little if any significant death. The influence of a rise in temperature from 20 to 44° is to decrease the generation time and at 44° the lower generation time compensates for a reduced generation index. The main effect of sub-bacteriostatic concentrations of phenol is to increase the generation time but at 30, 37 and 44° there is a significant reduction in the generation index at the higher concentrations resulting in a dynamic bacteriostasis. At 20° bacteriostasis is due mainly to a large generation time but there is a little growth and so bacteriostasis is essentially dynamic. There is also evidence to suggest that the effect of a particular concentration of phenol on the generation index is not merely influenced by the temperature but by the generation time under the particular set of conditions. If phenol is added to rapidly growing cultures of E. coli the effect of a rise in temperature is to reduce the concentration required for bacteriostasis but if it is added during the lag phase there is a maximum in the bacteriostatic concentration between 20 and 37°.     

Fixation probabilities when the population size undergoes cyclic fluctuations

Let us assume that there is a monoecious random mating population that changes cyclically in size. Then, the probability that a nonrecessive favorable mutant is ultimately fixed, if it is originally present in a single heterozygote, is approximately proportional to the harmonic mean of the effective population sizes in the cycle and inversely proportional to the population size when the mutant appears. This approximation works well if the selective advantage s of the mutant is small and the length k of a cycle is small in comparison with the population sizes in a cycle. If k is large the harmonic mean is, in general, replaced by a weighted harmonic mean that puts the largest weights on reciprocals of effective population sizes in the first few generations after the mutant appears.     

Does Computation Reveal Machine Cognition?

This paper seeks to understand machine cognition. The nature of machine cognition has been shrouded in incomprehensibility. We have often encountered familiar arguments in cognitive science that human cognition is still faintly understood. This paper will argue that machine cognition is far less understood than even human cognition despite the fact that a lot about computer architecture and computational operations is known. Even if there have been putative claims about the transparency of the notion of machine computations, these claims do not hold out in unraveling machine cognition, let alone machine consciousness (if there is any such thing). The nature and form of machine cognition remains further confused also because of attempts to explain human cognition in terms of computation and to model/simulate (aspects of) human cognitive processing in machines. Given that these problems in characterizing machine cognition persist, a view of machine cognition that aims to avoid these problems is outlined. The argument that is advanced is that something becomes a computation in machines only when a human interprets it, which is a kind of semiotic causation. From this it follows that a computing machine is not engaged in a computation unless a human interprets what it is doing; instead, it is engaged in machine cognition, which is defined as a member or subset of the set of all possible mappings of inputs to outputs. The human interpretation, which is a semiotic process, gives meaning to what a machine does, and then what it does becomes a computation.     

Rhesus monkey apolipoprotein(a). Sequence, evolution, and sites of synthesis

Human lipoprotein(a) is a low density lipoprotein-like lipoprotein whose concentration in plasma is correlated with atherosclerosis. The characteristic protein component of lipoprotein(a) is apolipoprotein(a) (apo(a)) which is disulfide-linked to apolipoprotein B-100. Sequencing of rhesus monkey apo(a) cDNA suggests that this protein, like human apo(a), is highly similar to plasminogen. Sequence data suggests that a plasminogen-like protease activity and kringle 1-, 2-, 3-, and 5-like domains are unnecessary for apo(a) function, but a highly repeated kringle four-like domain is important. Liver is the major site of apo(a) RNA synthesis; reduced amounts of message were also found in testes and brain. Co-expression with apoB-100 and plasminogen in rhesus tissues is not mandatory.     

Adaptive variation in sex determination in a crustacean, Gammarus duebeni

In some animals sex is determined after conception by environmental factors (environmental sex determination. ESD). In the amphipod Gammarus duebeni sex is reportedly determined by photoperiod: there is a higher proportion of males in broods reared under long-day than under short-day photoperiods. It has been proposed that this is an adaptive response to seasonal population dynamics. A test of the hypothesis would be to demonstrate changes in the degree to which sex is determined by the environment in populations from different latitudes with different dynamics. This study reports such a test. Environmental response is significantly less strong in a southern population with a long breeding season than in a northern one in which breeding is seasonally restricted. Moreover, the threshold of the ESD cue for male or female determination is not defined when the breeding season is weakly seasonal. There is a broad correlation between latitude (and hence breeding seasonality) and the strength of ESD response across a series of population studies. Similarities between the Gammarus system of sex determination and that of the Atlantic silverside Menidia menidia, a fish with thermal ESD, are discussed.     

On statistical inference for the random set generated Cox process with set-marking

Cox point process is a process class for hierarchical modelling of systems of non-interacting points in Rd under environmental heterogeneity which is modelled through a random intensity function. In this work a class of Cox processes is suggested where the random intensity is generated by a random closed set. Such heterogeneity appears for example in forestry where silvicultural treatments like harvesting and site-preparation create geometrical patterns for tree density variation in two different phases. In this paper the second order property, important both in data analysis and in the context of spatial sampling, is derived. The usefulness of the random set generated Cox process is highly increased, if for each point it is observed whether it is included in the random set or not. This additional information is easy and economical to obtain in many cases and is hence of practical value; it leads to marks for the points. The resulting random set marked Cox process is a marked point process where the marks are intensity-dependent. The problem with set-marking is that the marks are not a representative sample from the random set. This paper derives the second order property of the random set marked Cox process and suggests a practical estimation method for area fraction and covariance of the random set and for the point densities within and outside the random set. A simulated example and a forestry example are given.