Periodicity in the fine structure of histograms during nuclear decay

A theoretical explanation is offered for the appearance of periodicity in the fine structure of histograms describing the processes of nuclear decay. This effect is observed in a sample containing nonpolarized radioactive nuclei, with largely isotropic spin distribution over directions. However, because of fluctuations occurring in any real sample, the number of nuclei having spin directed along some isolated axis would differ somewhat from the number of nuclei with spin directed along another axis. The same is immobile relating to the Earth but rotates in space together with it. At the same time, the nuclear spins, owing to quite weak interaction with the environment, keep their directions in space. Therefore, the spin ensemble rotates both relative to the sample itself and relative to the detector of α-particles directed onto the sample. Since fluctuations in the number of nuclei with spins directed at a certain angle relative to the detector direction affect the fine structure of histograms, the latter proves to depend, among other things, of the rotation of the Earth. Consequently, when the Earth makes a full revolution and the distribution of fluctuations in the number of nuclei with given spin direction returns to the initial one, the shape of the fine structure of histograms will be repeated, and repeated over the same definite time intervals.     

Relationship between the fine structure and statistic fluctuations in measurement result distributions

The "near zone effect" described first in the macroscopic fluctuations researches was studied by numerical modeling. Possible mechanisms of its formation were proposed, and the lengths of portions of experimental data that retain the fine structure of histograms necessary for studying the "near zone effect" and provide the minimum level of statistical noise.     

Correlation of fine structures of distributions of amplitudes of a photomultiplier dark current fluctuations with the Earth rotations about its axis

The fine structures of distributions of photomultiplier dark current fluctuations measured in two laboratories 2000 km distant from other: in the international Institute of Biophysics (Neuss, Germany) and in the Moscow State University (Moscow, Russia) were compared. It is shown that similar forms of appropriate histograms are apparently more often realized at both locations at the same local time. This confirms the previous conclusion that the fine structure of distributions correlates with rotation of the Earth about its axis.     

Macroscopic fluctuations of discrete distribution forms as a consequence of the arithmetic and cosmophysical causes

The recent investigations are reviewed of the "macsroscopic fluctuations", i.e. synchronous on local time changes in probability of the appearance of the same detailed structure of distribution (histograms) of the rates of different processes, at the same or at different geographic points. Gravitation nonhomogeneousity is considered as a probable cause of these phenomena.     

Calculation of photon-count number distributions via master equations

Fitting of photon-count number histograms is a way of analysis of fluorescence intensity fluctuations, a successor to fluorescence correlation spectroscopy. First versions of the theory for calculating photon-count number distributions have assumed constant emission intensity by a molecule during a counting time interval. For a long time a question has remained unanswered: to what extent is this assumption violated in experiments? Here we present a theory of photon-count number distributions that takes account of intensity fluctuations during a counting time interval. Theoretical count-number distributions are calculated via a numerical solution of Master equations (ME), which is a set of differential equations describing diffusion, singlet-triplet transitions, and photon emission. Detector afterpulsing and dead-time corrections are also included. The ME-theory is tested by fitting a series of photon-count number histograms corresponding to different lengths of the counting time interval. Compared to the first version of fluorescence intensity multiple distribution analysis theory introduced in 2000, the fit quality is significantly improved. It is discussed how a theory of photon-count number distributions, which assumes constant emission intensity during a counting time interval, may also yield a good fit quality. We argue that the spatial brightness distribution used in calculations of the fit curve is not the true spatial brightness distribution. Instead, a number of dynamic processes, which cause fluorescence intensity fluctuations, are indirectly taken into account via the profile adjustment parameters.     

Morphology,biomass and nutrient status of fine roots of Scots pine (<Emphasis Type="Italic">Pinus sylvestris</Emphasis>) as influenced by seasonal fluctuations in soil moisture and soil solution chemistry

A field monitoring study was carried out to follow the changes of fine root morphology, biomass and nutrient status in relation to seasonal changes in soil solution chemistry and moisture regime in a mature Scots pine stand on acid soil. Seasonal and yearly fluctuations in soil moisture and soil solution chemistry have been observed. Changes in soil moisture accounted for some of the changes in the soil solution chemistry. The results showed that when natural acidification in the soil occurs with low pH (3.5–4.2) and high aluminium concentration in the soil solution (>3–10 mg l^–1), fine root longevity and distribution could be affected. However, fine root growth of Scots pine may not be negatively influenced by adverse soil chemical conditions if soil moisture is not a limiting factor for root growth. In contrast, dry soil conditions increase Scots pine susceptibility to soil acidification and this could significantly reduce fine root growth and increase root mortality. It is therefore important to study seasonal fluctuations of the environmental variables when investigating and modelling cause-effect relationships.     

The contribution of transient counterion imbalances to DNA bending fluctuations

A two-sided model for DNA is employed to analyze fluctuations of the spatial distribution of condensed counterions and the effect of these fluctuations on transient bending. We analyze two classes of fluctuations. In the first, the number of condensed counterions on one side of the DNA remains at its average value, while on the other side, counterions are lost to bulk solution or gained from it. The second class of fluctuations is characterized by movement of some counterions from one side of the DNA to the other. The root-mean-square fluctuation for each class is calculated from counterion condensation theory. The amplitude of the root-mean-square fluctuation depends on the ionic strength as well as the length of the segment considered and is of the order 5-10%. Both classes of fluctuation result in transient bends toward the side of greater counterion density. The bending amplitudes are approximately 15% of the total root-mean-square bends associated with the persistence length of DNA. We are thus led to suggest that asymmetric fluctuations of counterion density contribute modestly but significantly toward the aggregate of thermalized solvent fluctuations that cause bending deformations of DNA free in solution. The calculations support the idea that counterions may exert some modulating influence on the fine structure of DNA.     

Comparing proteins by their unfolding pattern

Single molecule force spectroscopy has evolved into an important and extremely powerful technique for investigating the folding potentials of biomolecules. Mechanical tension is applied to individual molecules, and the subsequent, often stepwise unfolding is recorded in force extension traces. However, because the energy barriers of the folding potentials are often close to the thermal energy, both the extensions and the forces at which these barriers are overcome are subject to marked fluctuations. Therefore, force extension traces are an inadequate representation despite widespread use particularly when large populations of proteins need to be compared and analyzed. We show in this article that contour length, which is independent of fluctuations and alterable experimental parameters, is a more appropriate variable than extension. By transforming force extension traces into contour length space, histograms are obtained that directly represent the energy barriers. In contrast to force extension traces, such barrier position histograms can be averaged to investigate details of the unfolding potential. The cross-superposition of barrier position histograms allows us to detect and visualize the order of unfolding events. We show with this approach that in contrast to the sequential unfolding of bacteriorhodopsin, two main steps in the unfolding of the enzyme titin kinase are independent of each other. The potential of this new method for accurate and automated analysis of force spectroscopy data and for novel automated screening techniques is shown with bacteriorhodopsin and with protein constructs containing GFP and titin kinase.     

A differential amplifier circuit for reducing noise in axial light loss measurements

Simplified electronics have been developed for reducing laser excitation source light intensity fluctuations in flow cytometric axial light loss (extinction) measurements. By continuously monitoring the laser output with a photodiode detector and combining it with the axial light loss signal from a second detector using a high-speed differential amplifier, background interference is reduced 10 to 40 dB. Oscilloscope waveforms and frequency distribution histograms recorded from uniform-size polystyrene latex spheres and human mononuclear blood cells are used to illustrate the noise reduction capabilities.     

Analyzing spatial structure of communities using the two-dimensional poisson lognormal species abundance model

The joint spatial and temporal fluctuations in the community structure of tropical butterflies are analyzed by fitting the bivariate Poisson lognormal distribution to a large number of observations in space and time. By applying multivariate dependent diffusions for describing the fluctuations in the abundances, the environmental variance is estimated to be very large and so is the strength of local density regulation. The variance in the lognormal species abundance distribution is partitioned into components expressing the heterogeneity between the species, independent noise components for the different species, a demographic stochastic component, and a component due to overdispersion in the sampling. In disagreement with the neutral theory, the estimates show that the heterogeneity component is the dominating one, representing 81% of the total variance in the lognormal model. Different spatial components of diversity, the alpha, beta, and gamma diversity, are also estimated. The spatial scale of the autocorrelation function for the community is of order 1 km, while sampling of a quadrat would need to be 10 km on a side to yield the total diversity for the community.     

Forms of histograms constructed from measurements of alpha-decay of 228Ra in Lindau (Germany) and neutron fluxes in Moscow change synchronously according to the local time

In joint experiments performed at Max Plank Institute of Aeronomy (Germany) and the Institute of Theoretical and Experimental Biophysics in Pushchino, the main manifestations of the phenomenon of macroscopic fluctuations were confirmed. An increased probability of the similarity in synchronous histograms in independent measurements performed by two installations in one laboratory and in two laboratories separated by a distance of 2000 km was shown. In the latter case, the similarity of histograms is most probable at the same local time.     

DNA content and survival in mammary carcinoma

In a retrospective study of archival fine needle aspiration biopsy material from 112 patients with primary mammary carcinoma, the DNA distribution patterns of the cancer cell populations were determined. A distinct correlation was found between the occurrence of certain types of DNA distribution histograms and the survival time of the patients. Thus, the data indicate that DNA determinations can give prognostic information, in the individual case, over and above that furnished by clinical staging and morphologic criteria.     

A model of the mechanisms of formation of unit activity

Dependence of the temporal structure of the spike discharge of a neuron in a weakly interacting network on the characteristics of excitatory and inhibitory input flows and on cell parameters was analyzed by a mathematical model. The intensity of communication between individual neurons corresponded to the intensity of synaptic communication between real spinal neurons. The temporal course of trace and accommodation processes in the model was similar to that of these processes in real spinal neurons. Connection of inhibitory inputs and an increase in the intensity of their influences were shown to be equivalent to a decrease in the intensity of excitatory input flows. Changes in cell parameters had a significant effect on the spike discharge only in the case of weak input influences (the ratio of the amplitude of the combined ESP evoked by the input spike train to the threshold value of membrane potential at rest was about 1.2:1.0 to 1.4:1.0). An increase in the input flow intensity led to considerable reorganization of the firing pattern: Mean values of interspike intervals and their fluctuations were reduced, histograms of interspike intervals became more symmetrical, and periodic waves appeared on the autocorrelation histograms. It is concluded on the basis of these results and of data in the literature that the main factor determining reorganization of the temporal structure of unit activity in a network of weakly interacting cells is the intensity of the input flow.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 12, No. 2, pp. 199–207, March–April, 1980.     

Resolving heterogeneity on the single molecular level with the photon-counting histogram

The diffusion of fluorescent particles through a small, illuminated observation volume gives rise to intensity fluctuations caused by particle number fluctuations in the open observation volume and the inhomogeneous excitation-beam profile. The intensity distribution of these fluorescence fluctuations is experimentally captured by the photon-counting histogram (PCH). We recently introduced the theory of the PCH for diffusing particles (Chen et al., Biophys. J., 77:553-567), where we showed that we can uniquely describe the distribution of photon counts with only two parameters for each species: the molecular brightness of the particle and the average number of particles within the observation volume. The PCH is sensitive to the molecular brightness and thus offers the possibility to separate a mixture of fluorescent species into its constituents, based on a difference in their molecular brightness alone. This analysis is complementary to the autocorrelation function, traditionally used in fluorescence fluctuation spectroscopy, which separates a mixture of species by a difference in their diffusion coefficient. The PCH of each individual species is convoluted successively to yield the PCH of the mixture. Successful resolution of the histogram into its components is largely a matter of the signal statistics. Here, we discuss the case of two species in detail and show that a concentration for each species exists, where the signal statistics is optimal. We also discuss the influence of the absolute molecular brightness and the brightness contrast between two species on the resolvability of two species. A binary dye mixture serves as a model system to demonstrate that the molecular brightness and the concentration of each species can be resolved experimentally from a single or from several histograms. We extend our study to biomolecules, where we label proteins with a fluorescent dye and show that a brightness ratio of two can be resolved. The ability to resolve a brightness ratio of two is very important for biological applications.     

关于氮有效性影响细根生产量和周转率的四个假说

在全球变化如氮沉降及温度升高等可能导致土壤氮有效性增加的背景下,细根动态如何变化一直是陆地生态学研究中的一个重要内容.本文综述了前人提出的细根动态响应土壤N有效性提高的4个代表性假说:1)细根生产量和周转率都提高;2)细根生产量和周转率都下降;3)细根生产量下降,周转率提高;4)细根生产量提高,周转率下降.根据2000年以来以微根管方法为主测得的根系动态数据,笔者认为假说1)和假说2)得到的支持最为充分.此外,还探讨了树种、细根异质性、菌根真菌、细根采样方法和施肥方法等对上述各假说检验的影响.     

Deviation from a Poisson distribution in a series of identical tests of E. coli cultures as a result of the effect of correlating factors of exo- and endogenous natures]

Vital cells number (VCN) in the sampling of E. coli populations was experimentally measured and distribution histograms were obtained. In most cases distributions show considerable deviation from Poisson model. VCN distribution histograms are polymodal, dispersion/arithmetical mean ratio may essentially differ from 1. The more essential differences from Poisson distribution were observed for populations with the higher cell concentration. Computer simulation of the VCN histograms indicated that additional parameters (such as those describing cellular interaction of different nature and/or other factors that influence random behaviour of cells) should be introduced into Poisson model to explain observed variations in VCN distribution histograms.     

Fractal dimension and histogram method: Algorithm and some preliminary results of noise-like time series analysis

In the present work a methodological background for the histogram method of time series analysis is developed. Connection between shapes of smoothed histograms constructed on the basis of short segments of time series of fluctuations and the fractal dimension of the segments is studied. It is shown that the fractal dimension possesses all main properties of the histogram method. Based on it a further development of fractal dimension determination algorithm is proposed. This algorithm allows more precision determination of the fractal dimension by using the “all possible combination” method. The application of the method to noise-like time series analysis leads to results, which could be obtained earlier only by means of the histogram method based on human expert comparisons of histograms shapes.     

Disentangling subpopulations in single-molecule FRET and ALEX experiments with photon distribution analysis

Among the advantages of the single-molecule approach when used to study biomolecular structural dynamics and interaction is its ability to distinguish between and independently observe minor subpopulations. In a single-molecule Förster resonance energy transfer (FRET) and alternating laser excitation diffusion experiment, the various populations are apparent in the resultant histograms. However, because histograms are calculated based on the per-burst mean FRET and stoichiometry ratio and not on the internal photon distribution, much of the acquired information is lost, thereby reducing the capabilities of the method. Here we suggest what to our knowledge is a novel statistical analysis tool that significantly enhances these capabilities, and we use it to identify and isolate static and dynamic subpopulations. Based on a kernel density estimator and a proper photon distribution analysis, for each individual burst, we calculate scores that reflect properties of interest. Specifically, we determine the FRET efficiency and brightness ratio distributions and use them to reveal 1), the underlying structure of a two-state DNA-hairpin and a DNA hairpin that is bound to DNA origami; 2), a minor doubly labeled dsDNA subpopulation concealed in a larger singly labeled dsDNA; and 3), functioning DNA origami motors concealed within a larger subpopulation of defective motors. Altogether, these findings demonstrate the usefulness of the proposed approach. The method was developed and tested using simulations, its rationality is described, and a computer algorithm is provided.     

A statistical theory for flow cytometry profiles in terms of the binding of ligands to cell surface receptors and changes in gene expression

Flow cytometry analysis is a technique used for obtaining light scattering and fluorescence intensity data in order to characterise a chosen cell line. From a sample of the data obtained, it is desired to infer the distribution of cell size, cell granularity and occupancy of cell surface receptors, by constructing histograms for the variables of interest. Often an attempt is made, for instance, to account for the changes in shape of these histograms in terms of alterations in gene expression, etc. In this paper we analyse the way that changes in the sample histograms can be interpreted in three frequently encountered situations, namely (a) when there is one cell line exposed to alterations in chemical potential of ligand, (b) when there are two cell lines exposed separately to saturating concentrations of the same ligand, and (c) when two ligands are added in saturating amounts, first separately, then together, to the same cell line. We demonstrate that, under a wide range of assumptions, the change in histogram shape can be accounted for in terms of a proportionate and absolute component and examples are given to illustrate this. Finally, a computer program to analyse experimental data in terms of estimated shift and stretch parameters is described.