Interpretation of tracer data: Some factors which reduce the number of terms in the specific activity functions inn-pool systems

The number of exponential terms in the function which describes the change in the specific activity of a pool following the injection of an isotopically labeled tracer is usually considered to equal the number of pools in which the labeled compound is distributed. However, the number of exponential terms may be smaller than the actual number of pools in the system, even if all pools exchange material with each other. This study is concerned with the derivation of relationships among the fractional rates of transfer between pools which are necessary and sufficient for a reduction in the number of exponential terms for all exchanging pools. The concept of linear dependence among the specific activity functions is basic to this analysis. By considering these relationships, it is possible to interpret the data on the basis of models consisting of a large number of pools which satisfy the condition of fast internal mixing. Such models may be necessary for a meaningful interpretation of tracer data obtained from biological systems.     

The Design of Pooling Experiments for Screening a Clone Map

We consider nonadaptive pooling designs for unique-sequence screening of a 1530-clone map ofAspergillus nidulans.The map has the properties that the clones are, with possibly a few exceptions, ordered and no more than 2 of them cover any point on the genome. We propose two subdesigns of the Steiner systemS(3, 5, 65), one with 65 pools and approximately 118 clones per pool, the other with 54 pools and about 142 clones per pool. Each design allows 1 or 2 positive clones to be detected, even in the presence of substantial experimental error rates. More efficient designs are possible if the overlap information in the map is exploited, if there is no constraint on the number of clones in a pool, and if no error tolerance is required. An information theory lower bound requires at least 12 pools to satisfy these minimal criteria, and an “interleaved binary” design can be constructed on 20 pools, with about 380 clones per pool. However, the designs with more pools have important properties of robustness to various possible errors and general applicability to a wider class of pooling experiments.     

Pools and protein synthesis in mammalian cells.

From the kinetics of incorporation into protein shown by four amino acids and one amino acid analogue in suspension cultured HeLa S-3 cells, two distinctly different patterns were observed under the same experimental conditions. An initial slow exponential incorporation followed by linear kinetics was characteristic of the two non-essential amino acids, glycine and proline, whereas the two essential amino acids studied, phenylalanine and leucine, showed linear kinetics of incorporation with no detectable delay. The analogue amino acid, p-fluorophenylalanine also showed immediate linear kinetics of incorporation. There was a poor correlation between the rate of formation of acid-soluble pools and incorporation kinetics. However, the rate of formation of the freely diffusible pool of amino acids correlated more closely with incorporation kinetics. The lack of direct involvement of the acid-soluble pool in protein synthesis was also demonstrated by pre-loading of pools before treatment of cells with labelled amino acids. The results partially support the hypothesis that precursor amino acids for protein synthesis come from the external medium rather than the acid-soluble pool, but suggest that the amino acid which freely diffuses into the cell from the external medium could also be the source.     

Resolvability of fluorescence lifetime distributions using phase fluorometry.

The analysis of the fluorescence decay using discrete exponential components assumes that a small number of species is present. In the absence of a definite kinetic model or when a large number of species is present, the exponential analysis underestimates the uncertainty of the recovered lifetime values. A different approach to determine the lifetime of a population of molecules is the use of probability density functions and lifetime distributions. Fluorescence decay data from continuous distributions of exponentially decaying components were generated. Different magnitudes of error were added to the data to simulate experimental conditions. The resolvability of the distributional model was studied by fitting the simulated data to one and two exponentials. The maximum width of symmetric distributions (uniform, gaussian, and lorentzian), which cannot be distinguished from single and double exponential fits for statistical errors of 1 and 0.1%, were determined. The width limits are determined by the statistical error of the data. It is also shown that, in the frequency domain, the discrete exponential analysis does not uniformly weights all the components of a distribution. This systematic error is less important when probability and distribution functions are used to recover the decay. Finally, it is shown that real lifetime distributions can be proved using multimodal probability density functions. In the companion paper that follows we propose a physical approach, which provides lifetime distribution functions for the tryptophan decay in proteins. In the third companion paper (Alcala, J.R., E. Gratton, and F.J. Prendergast, 1987, Biophys. J., in press) we use the distribution functions obtained to fit data from the fluorescence decay of single tryptophan proteins.     

Regression models for disease prevalence with diagnostic tests on pools of serum samples

Whether the aim is to diagnose individuals or estimate prevalence, many epidemiological studies have demonstrated the successful use of tests on pooled sera. These tests detect whether at least one sample in the pool is positive. Although originally designed to reduce diagnostic costs, testing pools also lowers false positive and negative rates in low prevalence settings and yields more precise prevalence estimates. Current methods are aimed at estimating the average population risk from diagnostic tests on pools. In this article, we extend the original class of risk estimators to adjust for covariates recorded on individual pool members. Maximum likelihood theory provides a flexible estimation method that handles different covariate values in the pool, different pool sizes, and errors in test results. In special cases, software for generalized linear models can be used. Pool design has a strong impact on precision and cost efficiency, with covariate-homogeneous pools carrying the largest amount of information. We perform joint pool and sample size calculations using information from individual contributors to the pool and show that a good design can severely reduce cost and yet increase precision. The methods are illustrated using data from a Kenyan surveillance study of HIV. Compared to individual testing, age-homogeneous, optimal-sized pools of average size seven reduce cost to 44% of the original price with virtually no loss in precision.     

Case-Control Association Testing of Common Variants from Sequencing of DNA Pools

While genome-wide association studies (GWAS) have been successful in identifying a large number of variants associated with disease, the challenge of locating the underlying causal loci remains. Sequencing of case and control DNA pools provides an inexpensive method for assessing all variation in a genomic region surrounding a significant GWAS result. However, individual variants need to be ranked in terms of the strength of their association to disease in order to prioritise follow-up by individual genotyping. A simple method for testing for case-control association in sequence data from DNA pools is presented that allows the partitioning of the variance in allele frequency estimates into components due to the sampling of chromosomes from the pool during sequencing, sampling individuals from the population and unequal contribution from individuals during pool construction. The utility of this method is demonstrated on a sequence from the alcohol dehydrogenase (ADH) gene cluster on a case-control sample for heavy alcohol consumption.     

Calculation of Steel's cell loss factor and of the parameters of cellular kinetics for a population with an exponential growth of the cell number and cell death at G0 phase with a probability equal to 1

The method of calculation of three cell kinetics parameters (the Steel's cell loss factor phi, the proliferative pool Pc, and the mean number m of the proliferating cells after mitotic division of one cell) was shown to be the same for the exponential growth state of cell number with cell death at the G0-phase, and for the exponential growth state with cell death occurring immediately after mitosis. The value of the mean number delta of non-proliferating cells that appeared after mitotic division of one cell is different for these two models of the exponential growth state with the equal values of the other three parameters (phi, Pc, and m). A method is proposed for calculating the parameter delta on the data of the percentage of labeled cells obtained in the experiments with continuous cultivation of cells in the nutrient medium containing 3H-thymidine. The kinetics of cell line HL-60 (the experimental data of Foa et al., 1982) can be described at the first approximation, by a model of the exponential growth state with the cell death at the G0-phase, with Pc = 0.80, phi = 0.24, m = 1.61, delta = 0.39, and the life time of the non-proliferating cells tQ = 24 hours.     

Determination of SNP allele frequencies in pooled DNAs by primer extension genotyping and denaturing high-performance liquid chromatography

By testing DNA pools rather than single samples the number of tests for a case-control association study can be decreased to only two for each marker: one on the patient and one on the control pool. A fundamental requirement is that each pool represents the frequency of the markers in the corresponding population beyond the influence of experimental errors. Consequently the latter must be carefully determined. To this aim, we prepared pools of different size (49-402 individuals) with accurately quantified DNAs, estimated the allelic frequencies in the pools of two SNPs by primer extension genotyping followed by DHPLC analysis and compared them with the real frequencies determined in the single samples. Our data show that (1) the method is highly reproducible: the standard deviation of repeated determinations was +/-0.014; (2) the experimental error (i.e., the discrepancy between the estimated and real frequencies) was +/-0.013 (95% C.I.: 0.0098-0.0165). The magnitude of this error was not correlated to the pool size or to the type of SNP. The effect of the observed experimental error on the power of the association test was evaluated. We conclude that this method constitutes an efficient tool for high-throughput association screenings provided that the experimental error is low. We therefore recommend that before a pool is used for extensive association studies, its quality, i.e., the experimental error, is verified by determining the difference between estimated and real frequencies for at least one marker.     

Hidden pools,hidden modes,and visible repeated eigenvalues in compartmental models

In compartmental analysis, when time-series data are initially fitted by sums of exponential functions, it is usually assumed that the eigenvalues are real and distinct and the number of pools (compartments) equals the number of exponentials. However, repeated real or complex eigenvalues, although more difficult to detect, may be inherent in the data, and the number of pools may be larger than the number of exponentials. In order to describe compartmental models with such properties, the visible multiplicity of eigenvalues and concepts of hidden pools and visible and hidden modes are defined. It is then shown that if a model is state observable, each mode is visible (not hidden) in the zero-input response for some choice of initial state, but not conversely, and also that the visible multiplicity of eigenvalues is determined by the submodel of input-output connectable compartments. Compartmental models are analyzed, using their decomposition into what we define as strongly connected components. An upper bound is given for the visible multiplicity of eigenvalues in terms of the model's strongly connected components. For models with one input and one output, this bound is shown to be attained for what we call generalized trees.     

Compartmentation of dCTP pools disappears after hydroxyurea or araC treatment in lymphocytes.

The calculated rate of DNA synthesis using [5-3H]TdR was about 4 times higher than in the case of [5-3H]CdR labeling, even after correction for the specific radioactivities of the intracellular pools. These data show a compartmentation of dCTP pools in lymphocytes. Hydroxyurea increased the specific activities of both dTTP and dCTP pools so that the calculated rate of DNA synthesis became equal. The same effect was found for araC treatment, but not for fluorodeoxyuridine. dCTP was supplied from CTP which is the lowest ribonucleotide pool in lymphocytes. Different functions of the two dCTP pools are proposed: one serving DNA replication; the other one supplies phospholipid precursors and DNA repair.     

Multiple glucose 6-phosphate pools or channelling of flux in diverse pathways?

Glucose 6-phosphate is an intermediate of pathways of glucose utilization and production as well as a regulator of enzyme activity and gene expression. Studies on the latter functions are in part based on measurement of the glucose 6-phosphate content in a whole-cell extract. Several studies have suggested that there are multiple subcellular pools of glucose 6-phosphate. It is proposed that this data can be interpreted in terms of channelling of metabolic intermediates through multiple pathways of glucose metabolism with leakage of glucose 6-phosphate from the channels into a single free pool. It is also proposed that measurement of total tissue content of glucose 6-phosphate approximates the free pool.     

Failure of an iterative curve-fitting procedure to successfully estimate two organic N pools

Fitting a double negative exponential function to N mineralization data can be used to characterize two organic nitrogen pools; an easily decomposable (N_dpm) and a resistant one (N_rpm). The relevance of those two calculated N mineralization pools was investigated by adding easily decomposable organic material to soils. Soil amended with crop residues of sugar-beet or bean was mixed with an equal amount of coarse sand, incubated at 35 °C and leached at specific time-intervals. Upon leaching, NH₄ ⁺ and NO₃ ^- were measured in the extracts. A double negative exponential function was fitted to the data and two organic N pools were defined. Fitting a double negative exponential function to N mineralization data to characterize an active and resistant organic N pool was sometimes impossible; the N mineralization data did not always resemble a negative exponential function. Additionally, the size of the two pools calculated were not constant with time and were often meaningless; the N_rpm pool was greater than the soil organic N content, the size of the N_rpm pool was smaller than the N_dpm pool or one of the N pools was negative. Relevant values for both N_rpm and N_dpm which were consistent with incubation time were only obtained when excessive amounts of organic material, normally not dealt with in the field, were applied.     

Separating soil CO2 efflux into C-pool-specific decay rates via inverse analysis of soil incubation data

Soil organic matter (SOM) is heterogeneous in structure and has been considered to consist of various pools with different intrinsic turnover rates. Although those pools have been conceptually expressed in models and analyzed according to soil physical and chemical properties, separation of SOM into component pools is still challenging. In this study, we conducted inverse analyses with data from a long-term (385 days) incubation experiment with two types of soil (from plant interspace and from underneath plants) to deconvolute soil carbon (C) efflux into different source pools. We analyzed the two datasets with one-, two- and three-pool models and used probability density functions as a criterion to judge the best model to fit the datasets. Our results indicated that soil C release trajectories over the 385 days of the incubation study were best modeled with a two-pool C model. For both soil types, released C within the first 10 days of the incubation study originated from the labile pool. Decomposition of C in the recalcitrant pool was modeled to contribute to the total CO₂ efflux by 9–11 % at the beginning of the incubation. At the end of the experiment, 75–85 % of the initial soil organic carbon (SOC) was modeled to be released over the incubation period. Our modeling analysis also indicated that the labile C-pool in the soil underneath plants was larger than that in soil from interspace. This deconvolution analysis was based on information contained in incubation data to separate carbon pools and can facilitate integration of results from incubation experiments into ecosystem models with improved parameterization.     

Breeding habitat selection and larval performance of two anurans in freshwater rock-pools

I studied breeding habitat choice of common toad Bufo bufo and common frog Rana temporaria in 221 freshwater rock-pools on 15 small islands in the southwestern coast of Finland. I monitored tadpole growth rate in a number of rock-pools differing in size, competitors and predator regime. Furthermore, I carried out a short-term field experiment to investigate the effects of different predators on larval survival. Rana bred in pools of virtually all sizes, although the very smallest ones were usually avoided. A logistic regression analysis showed that the amount of aquatic macrophyte vegetation and pool surface area were the most important pool characters for Rana. Bufo preferred the largest pools, and pool surface area was by far the most important habitat variable. Rana avoided pools with the lowest pH. but was more common than expected at pools with pH around 6. In Bufo such an effect was not found, but this may be due to relatively low number of pools occupied by Bufo. In Rana there was a positive correlation between pool area and tadpole body length in early June, but two weeks later this relationship was not significant. In Bufo tadpole body size was not significantly affected by pool area. Presence of predators or presence of the other tadpole species did not affect growth or tadpole body size in either Rana or Bufo. A short-term experiment in wading pools indicated that both species suffered heavy mortality in the presence of a diving beetle larva. In the presence of predatory fish, mortality of Bufo did not differ from controls, whereas mortality was high among Rana tadpoles. It appears that although predators prey heavily on Rana tadpoles, they do not exclude Rana from larger rock-pools. However, it is not evident from this study why Bufo avoids smaller pools.     

Comparing amphibian habitat quality and functional success among natural,restored, and created vernal pools

The fact that several vernal pool restoration and creation attempts in eastern Pennsylvania and New Jersey have been paired with conservation of natural pools in the same area provided a valuable research opportunity to compare amphibian habitat quality between project sites and natural reference pools. To measure desired outcomes, we used successful reproduction and metamorphosis of two vernal pool indicator species, the wood frog and spotted salamander. Although many previous studies indicate that restored and created pools rarely replace function lost in the destruction of natural pools, success of vernal pool indicator species was not necessarily related to pool type in this study. Results indicate a strong correlation between reproductive success for both species and vernal pool size (i.e. mean depth and volume), regardless of pool type. Although overall survival rates of wood frog larvae were significantly higher in natural pools with hydroperiods between 12 and 35 weeks, wood frogs were also successful in one restored and one created vernal pool. Salamander survival rates were highest in two natural and two created pools, which had in common both greater volumes and higher proportions of forest land cover in the surrounding 1,000 m. The documented success of vernal pool indicator species in two well‐established created pools demonstrates that pool creation can sometimes restore communities and ecological functions lost, especially when nearby natural pools are degraded or destroyed.     

Experimental and modeling investigation of the mechanism of synaptic vesicles recycling

Under the condition of microelectrode recording and fluorescence microscopy with dye FM 1-43 the research of exo-/endocytosis of synaptic vesicles in motor nerve terminals (NT) of frog cutaneous pectoris and white mice diaphragm muscles during high frequency stimulation (20 imp/s) was carried out. A mathematical modeling allowed us to conclude that the obtained experimental data can be explained in the following framework. Three pools of synaptic vesicles are involved in neurotransmitter release in the frog motor NT. Recovery of these pools is provided by endocytosis of two types: fast endocytosis with limited capacity and slow endocytosis. Fast-reconstructing vesicles refill the mobilization pool and slow endocytosis recovers the reserve pool. Our modeling investigation has revealed in frog NT independent recruiting of reserve and mobilization pools to the neurotransmitter secretion, i.e. this pools work concurrently. Experimental data, obtained on mice preparations, are well described with the framework of two-pools model including single type of endocytosis (fast endocytosis).     

Inversion of Markov processes to determine rate constants from single-channel data.

The determination of rate constants from single-channel data can be very difficult, in part because the single-channel lifetime distributions commonly analyzed by experimenters often have a complicated mathematical relation to the channel gating mechanism. The standard treatment of channel gating as a Markov process leads to the prediction that lifetime distributions are exponential functions. As the number of states of a channel gating scheme increases, the number of exponential terms in the lifetime distribution increases, and the weights and decay constants of the lifetime distributions become progressively more complicated functions of the underlying rate constants. In the present study a mathematical strategy for inverting these functions is introduced in order to determine rate constants from single-channel lifetime distributions. This inversion is easy for channel gating schemes with two or fewer states of a given conductance, so the present study focuses on schemes with more states. The procedure is to derive explicit equations relating the parameters of the lifetime distribution to the rate constants of the scheme. Such equations can be derived using the equality between symmetric functions of eigenvalues of a matrix and sums over principle minors, as well as expressions for the moments, derivatives, and weights of a lifetime distribution. The rate constants are then obtained as roots to this system of equations. For a gating scheme with three sequential closed states and a single gateway state, exact analytical expressions were found for each rate constant in terms of the parameters of the three-exponential closed-time distribution. For several other gating schemes, systems of equations were found that could be solved numerically to obtain the rate constants. Lifetime distributions were shown to specify a unique set of real rate constants in sequential gating schemes with up to five closed or five open states. For kinetic schemes with multiple gating pathways, the analysis of simulated data revealed multiple solutions. These multiple solutions could be distinguished by examining two-dimensional probability density functions. The utility of the methods introduced here are demonstrated by analyzing published data on nicotinic acetylcholine receptors, GABA(A) receptors, and NMDA receptors.     

Estimating heritability using family-pooled phenotypic and genotypic data: a simulation study applied to aquaculture

Estimating heritability based on individual phenotypic and genotypic measurements can be expensive and labour-intensive in commercial aquaculture breeding. Here, the feasibility of estimating heritability using within-family means of phenotypes and allelic frequencies was investigated. Different numbers of full-sib families and family sizes across ten generations with phenotypic and genotypic information on 10 K SNPs were analysed in ten replicates. Three scenarios, representing differing numbers of pools per family (one, two and five) were considered. The results showed that using one pool per family did not reliably estimate the heritability of family means. Using simulation parameters appropriate for aquaculture, at least 200 families of 60 progeny per family divided equally in two pools per family was required to estimate the heritability of family means effectively. Although application of five pools generated more within- and between- family relationships, it reduced the number of individuals per pool and increased within-family residual variation, hence, decreased the heritability of family means. Moreover, increasing the size of pools resulted in increasing the heritability of family means towards one. In addition, heritability of family mean estimates were higher than family heritabilities obtained from Falconer’s formula due to lower intraclass correlation estimate compared to the coefficient of relationship.Subject terms: Genome evolution     

Computational generation and screening of RNA motifs in large nucleotide sequence pools

Although identification of active motifs in large random sequence pools is central to RNA in vitro selection, no systematic computational equivalent of this process has yet been developed. We develop a computational approach that combines target pool generation, motif scanning and motif screening using secondary structure analysis for applications to 10¹²–10¹⁴-sequence pools; large pool sizes are made possible using program redesign and supercomputing resources. We use the new protocol to search for aptamer and ribozyme motifs in pools up to experimental pool size (10¹⁴ sequences). We show that motif scanning, structure matching and flanking sequence analysis, respectively, reduce the initial sequence pool by 6–8, 1–2 and 1 orders of magnitude, consistent with the rare occurrence of active motifs in random pools. The final yields match the theoretical yields from probability theory for simple motifs and overestimate experimental yields, which constitute lower bounds, for aptamers because screening analyses beyond secondary structure information are not considered systematically. We also show that designed pools using our nucleotide transition probability matrices can produce higher yields for RNA ligase motifs than random pools. Our methods for generating, analyzing and designing large pools can help improve RNA design via simulation of aspects of in vitro selection.