Random currents through nerve membranes

The linear cable equation with uniform Poisson or white noise input current is employed as a model for the voltage across the membrane of a onedimensional nerve cylinder, which may sometimes represent the dendritic tree of a nerve cell. From the Green's function representation of the solutions, the mean, variance and covariance of the voltage are found. At large times, the voltage becomes asymptotically wide-sense stationary and we find the spectral density functions for various cable lengths and boundary conditions. For large frequencies the voltage exhibits “1/f ^3/2 noise”. Using the Fourier series representation of the voltage we study the moments of the firing times for the diffusion model with numerical techniques, employing a simplified threshold criterion. We also simulate the solution of the stochastic cable equation by two different methods in order to estimate the moments and density of the firing time.     

Discrimination of promoters by <Emphasis Type="Italic">Bacillus subtilis</Emphasis> RNA polymerase σ<Superscript>A</Superscript> and σ<Superscript>H</Superscript> holoenzymes is associated with periodic patterns in promoter nucleotide sequences

Bacillus subtilis promoters recognized by σ^A and σ^H RNA polymerases were found to have different periodic patterns of nucleotide disposition. Using a special version of Fourier analysis for symbolic sequences, Fourier spectra were obtained for the primary structure of promoters used by the two holoenzymes. Stepwise discriminant analysis with jackknife testing was performed for two promoter data sets (small and large). Based on the spectral patterns of the nucleotide sequences, the data sets could be sorted with 100% accuracy into two classes: promoters recognized by Eσ^A and by Eσ^H. Correlations were obtained between the promoter strength and the characteristics of their Fourier spectra. Moreover, perfect separation was achieved even when the “consensus” ?35 and ?10 sites were replaced by sequences of “blank symbols.” Thus, the periodicity in nucleotide distribution along the DNA chain is itself an attribute sufficient for selective recognition of the cognate promoter by RNA polymerase.     

Polymer concentration effects on helix–coil transition widths

A theoretical study of effects of excluded volume intermolecular interactions on the sharpness of helix–coil transitions in solutions of polyamino acids or simple proteins indicates that the transition width may vary appreciably as a function of polymer concentration. The analysis is based on a second virial approximation for the excess free energy of mixing of a solution of polymers of varying degrees of helicity. The virial coefficients involved are roughly estimated on the basis of gross polymer geometry. For large N (degree of polymerization) the transition is found, typically to sharpen with increasing concentration, becoming second order and then first order at sufficiently high concentrations. The critical polymer concentration is found to be roughly of the order N^?1.2 ??₀^?1 for an “all or none” model and of order σ^1/2 N^?0.2 ??₀^?1 for a model with continuously variable degree of helicity (??₀ is the volume of a single helical molecule and σ^1/2 the normalized statistical weight of a helix–coil interface). In the second case for N ～ 10³ and σ ～ 10^?2–10^?4, the predicted critical concentration is in the range 10^?1–10^?3 g/cm.³ Comparison is made with experiments on solutions of poly(γ-benzyl-L glutamate).     

Control by cell interaction of phosphate uptake in 3T3 cells.

Phosphate uptake by monolayers of 3T3 cell decreases when the cultures enter the stationary phase, even when incubated in fresh medium containing 10% serum. However, SV 3T3 cultures retain a high rate of phosphate uptake when the cells reach saturation densities.We have observed that 3T3 cells grown to stationary phase in monolayers and then trypsinized and incubated in suspension, display an increase in phosphate uptake when the cell concentration is decreased from 10⁶ cells/ml to 10⁵ cells/ml. Where the cell concentration is further reduced from 10⁵ cells/ml to 2.5 × 10⁴ cells/ml there is no further increase in the rate of phosphate uptake. We observed, on the contrary, a small decrease.The “concentration effect” (the decrease of phosphate uptake when the cell concentration increases from 10⁵ to 10⁶ cells/ml) is larger when cells originate from a culture in stationary phase than when they originate from a culture in log phase.The “concentration effect” may be observed 10 min after cell incubation but is larger after a lag time of 40 min incubation.Differences in the “concentration effect” may be noted between 3T3 and SV 3T3 cells. In SV 3T3 cells no significant variations of phosphate uptake were observed when the cell concentration was changed. Thus, differences between phosphate uptake in 3T3 and SV 3T3 cells are large when cells are incubated at high concentrations or at high densities and small when they are incubated at low concentrations or at low densities.The “concentration effect” in 3T3 cells supports the assumption that interactions between cells cause the decrease of phosphate metabolism in dense culture. Diffusion of an inhibitor into the medium remains the more plausible explanation of the data.     

Sequence-dependent model of genes with dual σ factor preference

Escherichia coli uses σ factors to quickly control large gene cohorts during stress conditions. While most of its genes respond to a single σ factor, approximately 5% of them have dual σ factor preference. The most common are those responsive to both σ⁷⁰, which controls housekeeping genes, and σ³⁸, which activates genes during stationary growth and stresses. Using RNA-seq and flow-cytometry measurements, we show that ‘σ⁷⁰⁺³⁸ genes’ are nearly as upregulated in stationary growth as ‘σ³⁸ genes’. Moreover, we find a clear quantitative relationship between their promoter sequence and their response strength to changes in σ³⁸ levels. We then propose and validate a sequence dependent model of σ⁷⁰⁺³⁸ genes, with dual sensitivity to σ³⁸ and σ⁷⁰, that is applicable in the exponential and stationary growth phases, as well in the transient period in between. We further propose a general model, applicable to other stresses and σ factor combinations. Given this, promoters controlling σ⁷⁰⁺³⁸ genes (and variants) could become important building blocks of synthetic circuits with predictable, sequence-dependent sensitivity to transitions between the exponential and stationary growth phases.     

A paradoxical effect of hydrated C60-fullerene at an ultralow concentration on the viability and aging of cultured Chinese hamster cells

The effect of an aqueous solution of hydrated C₆₀-fullerene (HyFn) on the growth and “stationary phase aging” (accumulation of “age-related” changes in cultured cells during the slowing down of their proliferation within a single passage and the subsequent “aging” in the stationary phase of growth) of transformed B11-dii FAF28 Chinese hamster cells was studied. The final calculated concentration of HyFn in the growth medium was 10^?19 M. A paradoxical result contrasting the available data on the absence of HyFn cytotoxicity at higher concentrations was obtained in our experiments: namely, HyFn decelerated cell proliferation (estimated by the growth of mass culture, as well as by the efficiency of colony formation) and accelerated the “stationary phase aging” of the cell culture. Moreover, repeated addition of an aqueous solution of HyFn (to the final calculated concentration of 10^?19 M) to the cells that had already reached the stationary phase of growth caused a rapid (within no more than 24 h) death of a significant part of the cell population. The observed effect of HyFn at ultralow concentration is supposed to arise from the alterations in the properties of the water surrounding the fullerene molecule: namely, water becomes a donor and acceptor of electrons and regulates redox processes (especially those involving oxygen) in aqueous systems. This effect of HyFn at an ultralow concentration may be specific for transformed cells, and, therefore, experiments on normal fibroblasts with limited mitotic potential are planned as a continuation of the present study. It is also possible that the reported antiaging effect of HyFn in experimental animals is due to its anticancer, immunostimulatory, antiviral, and antibacterial properties manifested only at the whole-organism level.     

Production models for nonlinear stochastic age-structured fisheries

The overriding feature of stock-recruitment data for most fisheries is the amount of variability involved. Previous production models have assumed either an underlying linear stock-recruitment relationship [11] or an equilibrium condition [23]. Here a production model is derived for an age-structured fishery exhibiting nonlinear stochastic recruitment under nonequilibrium conditions. In the first section deterministic age-structured production models are reviewed, and in the next section corresponding random variable models are presented. Equations for the first and second order moments for each age class, for the stock, and for the yield are then derived using two approaches. The first approach assumes that third and order higher moments associated with the noise can be neglected (thus extending the “small noise” approach in [23]). The second approach assumes that the distributions associated with the random variables can be characterized by a particular two parameter distribution. This latter approximation can be applied to systems with “large noise,” and precision will not be lost for situations where the exact form of the distribution, associated with the stock-recruitment data, is unknown. Equations are derived for the solution under equilibrium recruitment and constant harvesting conditions. Detailed expressions are also obtained for the case where the random variables are assumed to satisfy a gamma distribution.     

Back to log phase: σS as a global regulator in the osmotic control of gene expression in Escherichia coli

It is now well established that the σ^S subunit of RNA polymerase is a master regulator in a complex regulatory network that governs the expression of many stationary-phase-inducible genes in Escherichiacoli. In this review, more recent findings will be summarized that demonstrate that σ^S also acts as a global regulator for the osmotic control of gene expression, and actually does so in exponentially growing cells. Thus, many σ^S-dependent genes are induced during entry into stationary phase as well as in response to osmotic upshift. K⁺ glutamate, which accumulates in hyperosmotically stressed cells, seems to specifically stimulate the activity of σ^S-containing RNA polymerase at σ^S-dependent promoters. Moreover, osmotic upshift results in an elevated cellular σ^S level similar to that observed in stationary-phase cells. This increase is the result of a stimulation of rpoS translation as well as an inhibition of the turnover of σ^S, which in exponentially growing non-stressed cells is a highly unstable protein. Whereas the RNA-binding protein HF-I, previously known as a host factor for the replication of phage Qβ RNA, is essential for rpoS translation, the recently discovered response regulator RssB, and ClpXP protease, have been shown to be required for σ^S degradation. The finding that the histone-like protein H-NS is also involved in the control of rpoS translation and σ^S turnover, sheds new light on the function of this protein in osmoregulation. Finally, preliminary evidence suggests that additional stresses, such as heat shock and acid shock, also result in increased cellular σ^S levels in exponentially growing cells. Taken together, σ^S function is clearly not confined to stationary phase. Rather, σ^S may be regarded as a sigma factor associated with general stress conditions.     

An ordered precipitate of polyadenylic acid formed by freezing at acidic pH: comparison of X-ray diffraction and other properties of the precipitate with those of fibers or direct acid-precipitates

Poly A was found to precipitate upon freezing acidic solutions at p^H values where it is normally soluble; this precipitate tends to have the form of small thin plates of irregular outline (“plates”). The X-ray diffraction pattern and solubility properties of the “plates” were compared with those of poly A precipitated solely by exposure to lower p^H values, and with fibers drawn from acidic solution. There is considerable molecular order in each of these three types of preparation. In all cases, the diffraction patterns are consistent with the presence of the double-stranded helical structure proposed by Rich, Davies, Crick, and Watson (J. Mol. Biol., 3 , 71 (1961)) based on fiber diffraction data. The diffraction pattern from the “plates” is compared in detail with that of the fibers, and is shown to be in accord with a packing scheme having the chain axis of the molecular structure confined to the plane of the “plate,” but oriented randomly in that plane.     

The S-Distribution A Tool for Approximation and Classification of Univariate,Unimodal Probability Distributions

In many statistical applications a data set needs to be evaluated but there is no solid information about which probability distribution might be most appropriate. Typical solutions to this problems are: to make assumptions that facilitate mathematical treatment; to use a family of distribution functions that contains all relevant distributions as special cases; or, to employ nonparametric methods. All three solutions have disadvantages since assumptions are usually difficult to justify, families of distributions contain too many parameters to be of practical use, and nonparametric methods make it difficult to characterize data in a succinct quantitative form. The S-distribution introduced here is a compromise between the conflicting goals of simplicity in analysis and generality in scope. It is characterized by four parameters, one of which reflects its location, the second one its spread, and the remaining two its shape; transformation to a standard form reduces the number of free parameters to two. Cumulatives and densities are computed numerically in fractions of seconds, key features like quantiles and moments are easily obtained, and results can be presented in terms of parameter values. The S-distribution rather accurately models different distribution functions, including central and noncentral distributions, and thus competes in flexibility with some distribution families. As an approximation, the S-distribution provides a graphical method for demonstrating relationships between distributions, such as the relationships between central F, χ² and χ^?2 or central and noncentral t, χ^-1, and normal.     

Thermodynamic approach to biomass distribution in ecological systems

In the derivation of the biomass distribution function for an ecological population critical use is made of an energetic constraint on the maximization of biomass diversity. The nature of this constraint is explored in detail using Kleiber's relation σ(m)=cm ^γ between animal metabolic rate σ(m) and body weightm in conjuction with the Prigogine-Wiame thermodynamic paradigm for specific entropy production in biological stationary states. These two inputs fix the energetic constraint on the maximization of biomass diversity to be the constancy of the mean metabolic rate of the ecosystem. The resulting biomass distribution function is tested against observational data.     

Asynchronous DNA Synthesis in a Duplicated Chromosomal Region of <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>

THERE is a highly ordered temporal sequence in the replication of DNA in the polytene chromosomes of Drosophila^1–10. The mechanism underlying this replicative organization remains unknown, but it has been shown that homologous chromosome regions replicate their DNA synchronously whether or not they are paired¹¹ and, in the one case in which it has been studied, this synchrony remains evident even when one of the two homologous regions is translocated to an abnormal position¹². These observations suggest that an essential part of the system controlling replication pattern is located in each of the small chromosome regions, replication of which can be resolved autoradiographically. The simplest model consistent with these assumptions involves a chromosome constituted of numerous “replicons” with replication times geared to a common control mechanism but are independent of the anatomical ordering of the “replicons” within the genome.     

Incorporation of Tritium from Thymidine-methyl-H3 into DNA,RNA, Lipids and Protein in Logarithmic and Stationary Phase Tetrahymena pyriformis,Strain W*

SYNOPSIS. Numerous reports may be found in the literature on cytoplasmic and non-DNA utilization of tritium from H³-thymidine. Such reports underscore the need to clarify the metabolic fate of H³-thymidine. This investigation outlines the fate of thymidinemethyl-H³ (TMH³) in logarithmic phase and stationary phase Tetrahymena pyriformis, strain W. Isotope identification by liquid scintillation spectrometry in chemically derived fractions of log phase cultures grown thruout the initial 48 hours of population growth with TMH³ revealed the majority of the radioactivity (90% of intracellular recovery) to be in the DNA fraction. The remainder of the intracellular label was recovered in the acid soluble fraction, lipid fraction, and a small amount in the RNA and cell residue. On chromatographs, tritium appeared only in the thymine moiety of the nucleic acid derivatives. Hence in dividing cells, thymidine-methyl-H³ is “essentially” specific for DNA at the dosage used although some incorporation into other compounds was detected. Fractionation of the lipid extract from the above experiment on a florisil column localized most of the label to the triglyceride and phospholipid fractions with some recovery in the cholesterol-esters. Similar scintillation counting of the various fractions of early stationary phase cells incubated for the last 48 hours of culture with TMH³ revealed limited tritium distribution in all fractions.     

Correlation of gene frequencies between neutral linked genes in finite populations

The mean squared correlation (r²) of gene frequencies between two selectively neutral loci in segregating populations is obtained using an approximation based on expanding the formula for r² in terms up to eighth moments. The moments are evaluated for all populations, whether segregating or not, but when combined with the probability of segregation, quite accurate results are obtained. Formulae for the moments and an approximation for the probability of segregation are given for populations of large size (N) and small recombination fraction (c). The method is extended to evaluate the variance of r². The coefficient of variation of r² exceeds unity for a wide range of Nc values.     

How small are small mutation rates?

We consider evolutionary game dynamics in a finite population of size N. When mutations are rare, the population is monomorphic most of the time. Occasionally a mutation arises. It can either reach fixation or go extinct. The evolutionary dynamics of the process under small mutation rates can be approximated by an embedded Markov chain on the pure states. Here we analyze how small the mutation rate should be to make the embedded Markov chain a good approximation by calculating the difference between the real stationary distribution and the approximated one. While for a coexistence game, where the best reply to any strategy is the opposite strategy, it is necessary that the mutation rate μ is less than N ^−1/2exp[−N] to ensure that the approximation is good, for all other games, it is sufficient if the mutation rate is smaller than (N ln N)⁻¹. Our results also hold for a wide class of imitation processes under arbitrary selection intensity.