Estimation of microbial densities from dilution count experiments

Although dilution counts have been widely used in quantitative microbiology, their interpretation has always been widely discussed both in microbiology and in applied statistics. Maximum-likelihood (most-probable-number) methods hae generally been used to estimate densities from dilution experiments. It has not been widely recognized that these methods are intrinsically and statistically biased at the sample sizes used in microbiology. This paper presents an analysis of proposed method for correction of such biases, and the method was found to be robust for moderate deviations from Poisson behavior. For analyses at greater variance with the Poisson assumptions, the use of the Spearman-Karber method is analyzed and shown to yield an estimate of density of lesser bias than that produced by the most-probable-number method. Revised methods of constructing confidence limits proposed by Loyer and Hamilton (M.W. Loyer and M.A. Hamilton, Biometrics 40:907-916, 1984) are also discussed, and charts for the three- and four-decimal dilution series with five tubes per dilution are presented.     

Estimation of parrot and hornbill densities using a point count distance sampling method

The suitability of point count distance methods for estimating densities of tropical parrots and hornbills was assessed during surveys in Indonesia. The methods will perform well, so long as the following are considered. (1) Enough bird records must be accumulated to model species' detection curves precisely. For some species, around 2000 point counts may be needed and, in very rare species, the method may not be appropriate. Pooling data across habitats, species or years may increase precision in cases of small sample size. (2) Point counts are likely to be less biased than line transects because bird detection rates close to the recorder may be higher and there may be less chance of double-counting birds. Distances greater than 400 m between census points are unnecessary. (3) Count periods lasting ten minutes may be needed to ensure that most birds close to the recorder are detected. Controlled flushing of concealed birds after the main count period may also be appropriate. (4) The best time of day for census is the period when bird detectability is high but bird mobility low. For many large avian frugivores, this corresponds to the period between one hour after dawn and 10.30 h. (5) Records of flying birds must be excluded from density calculations. In the species studied, between 2% and 20% should be added to density estimates to compensate for the exclusion of flying birds.     

A cautionary note: Examples of possible microbial community dynamics in dilution grazing experiments

Dilution experiments are used commonly to provide estimates of grazing pressure exerted on phytoplankton and bacterioplankton as well as estimate their growth rates. However, very little attention has been given to the dynamics of grazers, especially heterotrophic nanoflagellates (HNF), in such experiments. We found temporal changes in concentrations of ciliates and HNF in a dilution experiment using water from the oligotrophic N.W. Mediterranean Sea. Ciliates decreased markedly over 24 h when held in seawater diluted with particle-free water (60% and 20% final conc whole seawater) while HNF increased in concentration in the same treatments. Using a time-course approach in a second experiment, we monitored changes in HNF and bacterioplankton concentrations in 20% whole seawater (80% particle-free seawater). Both HNF and heterotrophic bacteria displayed stable concentrations for the first 12 h and then grew rapidly, especially HNF, from 12 to 24 h. Examination of bacterial community composition using denaturing gel gradient electrophoresis (DGGE) showed a change in community composition over the 24 h incubation period. Dilution can have differential effects on the distinct components of the marine microbial food web.     

盐度对稀释平板法研究红树林区土壤微生物数量的影响

在使用稀释平板法分离潮间带红树林及其对照光滩土壤微生物以及计数时,多数情况下使用陈海水制作培养基和稀释水,很少考虑培养基和稀释水的盐度对最终计数结果的影响.使用稀释平板法研究了盐度对福建九龙江口红树林区与深圳福田红树林保护区土壤微生物平板计数的影响,结果表明培养基与稀释水盐度对微生物数量有明显的影响.统计分析显示细菌的海水稀释效果优于淡水,而放线菌与真菌则刚好相反(P<0.05,一个例外).海水不适合配制红树林区土壤微生物平板计数的培养基,从0～35,高盐度的平板培养基会降低微生物的数量,尤其是放线菌的数量,尽管培养基的盐度对真菌影响无规律,但细菌数量在低盐度时比在高盐度和不加氯化钠时要多.根据盐度效应,提出了稀释平板技术应用于潮间带的红树林及其相应光滩时的优化方法,认为细菌应该用海水作无菌稀释水,而放线菌和真菌则应用淡水作稀释水;包括光滩在内的红树林区土壤微生物分离与计数的培养基宜控制较低盐度范围.     

Impact of dilution on microbial community structure and functional potential: comparison of numerical simulations and batch culture experiments

A series of microcosm experiments was performed using serial dilutions of a sewage microbial community to inoculate a set of batch cultures in sterile sewage. After inoculation, the dilution-defined communities were allowed to regrow for several days and a number of community attributes were measured in the regrown assemblages. Based upon a set of numerical simulations, community structure was expected to differ along the dilution gradient; the greatest differences in structure were anticipated between the undiluted-low-dilution communities and the communities regrown from the very dilute (more than 10(-4)) inocula. Furthermore, some differences were expected among the lower-dilution treatments (e.g., between undiluted and 10(-1)) depending upon the evenness of the original community. In general, each of the procedures used to examine the experimental community structures separated the communities into at least two, often three, distinct groups. The groupings were consistent with the simulated dilution of a mixture of organisms with a very uneven distribution. Significant differences in community structure were detected with genetic (amplified fragment length polymorphism and terminal restriction fragment length polymorphism), physiological (community level physiological profiling), and culture-based (colony morphology on R2A agar) measurements. Along with differences in community structure, differences in community size (acridine orange direct counting), composition (ratio of sewage medium counts to R2A counts, monitoring of each colony morphology across the treatments), and metabolic redundancy (i.e., generalist versus specialist) were also observed, suggesting that the differences in structure and diversity of communities maintained in the same environment can be manifested as differences in community organization and function.     

Estimation of cell cycle parameters from double labeling experiments

Double labeling of cell populations with radioactive thymidine yields two types of differently labeled nuclei. Their numbers and the number of unlabeled nuclei can be used to estimate doubling times, T, and S-phase lengths, S. As of yet, such estimations have been performed either for stationary populations in which proliferation and losses are in balance, or for exponentially growing populations in which all cells have the same cycle duration. We calculate S and T for the more general type of cell population with arbitrarily distributed frequencies of cycle durations. The calculations do not require more mathematical or computational effort. We obtain three main results: (i) The estimation of T and S does not require explicit knowledge of the frequency distribution of cycle durations; (ii) in particular, equivalent estimates for T and S are obtained for both types of growing cell populations without losses, one with arbitrarily distributed cycle durations and one with the same cycle duration for all cells; and (iii) for small labeling indices, the estimate for S from the general model approaches the S-phase length of a stationary population and the estimate for T from the general model approaches the generation time of a stationary population, multiplied by the constant factor 1n(2). These relationships are valuable tools for reinterpreting results derived under the assumption of stationarity, which are considerably easier to obtain.     

Estimation of relative potency with sequential dilution errors in radioimmunoassay.

Sequential dilution is a very common procedure in radioimmunoassay, in which the dilution error will be accumulated from the highest to the lowest concentration. A simulated example in relative potency determination is used to demonstrate the potentially wrong conclusion that can be drawn, when the dilution error is not properly included in the model. A Bayesian method is used and an alternative approximation via maximum likelihood is proposed. An alternative experimental design is recommended to increase the precision of the inference.     

Predicting stability of mixed microbial cultures from single species experiments: 2. Physiological model

In this paper, we study the equilibria of a physiological model describing the continuous culture in which two microbial populations compete for two substitutable resources. This work is an extension of the stability analysis of the phenomenological model of mixed microbial growth [M.M. Ballyk, G.S.K. Wolkowicz, Exploitative competition in the chemostat for two perfectly substitutable resources, Math. Biosci. 118 (1993) 127-180; S.S. Pilyugin, G.T. Reeves, A. Narang, Predicting stability of mixed microbial cultures from single species experiments: 2. Phenomenological model]. Here, we investigate the influence of the peripheral enzymes that catabolize the substrate uptake on the stability of the mixed culture. We show that, under steady state conditions, an increase in the concentration of one substrate inhibits the uptake of the other substrate(s). We present the criteria for existence, uniqueness, and stability of various types of equilibria. We formulate these criteria in terms of growth isoclines and consumption curves for each of the competing species. Since both types of curves can be obtained from a single species experiment, our approach provides a direct connection between theory and experiment and allows one to infer the dynamics of mixed cultures from the dynamics of single species cultures. By expressing the stability criteria in terms of intracellular properties, the model establishes a link between ecology and molecular biology.     

Predicting stability of mixed microbial cultures from single species experiments: 1. Phenomenological model

The growth of mixed microbial cultures on mixtures of substrates is a fundamental problem of both theoretical and practical interest. On the one hand, the literature is abundant with experimental studies of mixed-substrate phenomena [T. Egli, The ecological and physiological significance of the growth of heterotrophic microorganisms with mixtures of substrates, Adv. Microbiol. Ecol. 14 (1995) 305-386]. On the other hand, a number of mathematical models of mixed-substrate growth have been analyzed in the last three decades. These models typically assume specific kinetic expressions for substrate uptake and biomass growth rates and their predictions are formulated in terms of parameters of the model. In this work, we formulate and analyze a general mathematical model of mixed microbial growth on mixtures of substitutable substrates. Using this model, we study the effect of mutual inhibition of substrate uptake rates on the stability of the equilibria of the model. Specifically, we address the following question: How much of the dynamics exhibited by two competing species can be inferred from single species data? We provide geometric criteria for stability of various types of equilibria corresponding to non-competitive exclusion, competitive exclusion, and coexistence of two competing species in terms of growth isoclines and consumption curves. A growth isocline is a curve in the plane of substrate concentrations corresponding to the zero net growth of a given species. In [G.T. Reeves, A. Narang, S.S. Pilyugin, Growth of mixed cultures on mixtures of substitutable substrates: The operating diagram for a structured model, J. Theor. Biol. 226 (2004) 143-157], we introduced consumption curves as sets of all possible combinations of substrate concentrations corresponding to balanced growth of a single microbial species. Both types of curves can be obtained in single species experiments.     

Myosin step size. Estimation from slow sliding movement of actin over low densities of heavy meromyosin

We have estimated the step size of the myosin cross-bridge (d, displacement of an actin filament per one ATP hydrolysis) in an in vitro motility assay system by measuring the velocity of slowly moving actin filaments over low densities of heavy meromyosin on a nitrocellulose surface. In previous studies, only filaments greater than a minimum length were observed to undergo continuous sliding movement. These filaments moved at the maximum speed (Vo), while shorter filaments dissociated from the surface. We have now modified the assay system by including 0.8% methylcellulose in the ATP solution. Under these conditions, filaments shorter than the previous minimum length move, but significantly slower than Vo, as they are propelled by a limited number of myosin heads. These data are consistent with a model that predicts that the sliding velocity (v) of slowly moving filaments is determined by the product of vo and the fraction of time when at least one myosin head is propelling the filament, that is, v = vo [1-(1-ts/tc)N], where ts is the time the head is strongly bound to actin, tc is the cycle time of ATP hydrolysis, and N is the average number of myosin heads that can interact with the filament. Using this equation, the optimum value of ts/tc to fit the measured relationship between v and N was calculated to be 0.050. Assuming d = vots, the step size was then calculated to be between 10nm and 28 nm per ATP hydrolyzed, the latter value representing the upper limit. This range is within that of geometric constraint for conformational change imposed by the size of the myosin head, and therefore is not inconsistent with the swinging cross-bridge model tightly coupled with ATP hydrolysis.     

Estimation of population firing rates and current source densities from laminar electrode recordings

This model study investigates the validity of methods used to interpret linear (laminar) multielectrode recordings. In computer experiments extracellular potentials from a synaptically activated population of about 1,000 pyramidal neurons are calculated using biologically realistic compartmental neuron models combined with electrostatic forward modeling. The somas of the pyramidal neurons are located in a 0.4 mm high and wide columnar cylinder, mimicking a stimulus-evoked layer-5 population in a neocortical column. Current-source density (CSD) analysis of the low-frequency part (<500 Hz) of the calculated potentials (local field potentials, LFP) based on the ‘inverse’ CSD method is, in contrast to the ‘standard’ CSD method, seen to give excellent estimates of the true underlying CSD. The high-frequency part (>750 Hz) of the potentials (multi-unit activity, MUA) is found to scale approximately as the population firing rate to the power 3/4 and to give excellent estimates of the underlying population firing rate for trial-averaged data. The MUA signal is found to decay much more sharply outside the columnar populations than the LFP.     

An evaluation of isotope dilution effect from conventional data sets of 15N uptake experiments

A practical calculation procedure to correct the underestimatecaused by isotope dilution in ¹⁵N uptake experiments is described.The estimate is based on the experimental observation of ¹⁵Nincorporation into particuUtc organic matter but not on directmeasurement of isotope enrichment in the substrate. Conventionaldata sets of ¹⁵N uptake and an estimate of the ratio of theflux of regeneration and uptake can provide the informationneeded to correct for isotope dilution. Application of thismethod to ¹⁵NH₄⁺ uptake data in the literature showed that theunderestimate is small in open ocean waters but sometimes substantialin coastal or estuarine waters.     

Automated statistical analysis of microbial enumeration by dilution series

Equations are formulated for the standard error and confidence interval for the MPN estimate of microbial density from a general dilution series. A statistical test of homogeneity is presented. This tests whether a handling error in the dilution series may have occurred which would invalidate the density estimate. The analysis may be automated using a Basic computer program which contains a fast algorithm for the solution of the general MPN equation. This allows the calculation of the MPN, standard error, 95% confidence interval and test statistic for any dilution series, with any degree of replication at each dilution level, with variable sample volumes at each dilution level, with variable dilution ratio between levels, and with any number of levels.