Comparison of definitions of the lag phase and the exponential phase in bacterial growth.

Different definitions for the lag time and of the duration of the exponential phase can be used to calculate these quantities from growth models. The conventional definitions were compared with newly proposed definitions. It appeared to be possible to derive values for the lag time and the duration of the exponential phase from the growth models and differences between the various definitions could be quantified. All the different values can be calculated from the growth parameters microm, lambda and alpha. Therefore, it appeared to be unnecessary to use complicated mathematical equations; simple equations were adequate. For the Gompertz model the conventional definition of the lag time did not differ appreciably from the newly proposed definition. The end-point of the exponential phase and thus the duration of the exponential phase differed considerably for the two definitions. For the logistic model the two definitions lead to considerable differences for all quantities. It is recommended that the conventional definition is used for calculating the lag time. For the duration of the exponential phase it is recommended that the new definition is used. The value can be calculated, however, directly from the conventional growth parameters.     

Comparison of definitions of the lag phase and the exponential phase in bacterial growth

M.H. ZWIETERING, F.M. ROMBOUTS AND K. VAN 'T RIET. 1992. Different definitions of the lag time and of the duration of the exponential phase can be used to calculate these quantities from growth models. The conventional definitions were compared with newly proposed definitions. It appeared to be possible to derive values for the lag time and the duration of the exponential phase from the growth models, and differences between the various definitions could be quantified. All the different values can be calculated from the growth parameters μ _m , and a. Therefore, it appeared to be unnecessary to use complicated mathematical equations: simple equations were adequate. For the Gompertz model the conventional definition of the lag time did not differ appreciably from the newly proposed definition. The end-point of the exponential phase and thus the duration of the exponential phase differed considerably for the two definitions. For the logistic model the two definitions lead to considerable differences for all quantities. It is recommended that the conventional definition is used for calculating the lag time. For the duration of the exponential phase it is recommended that the new definition is used. The value can be calculated, however, directly from the conventional growth parameters.     

Diverging times in movement analysis

In movement analysis, more than one measuring system is often used to record biomechanical variables. Usually, it is desired to assign the occurring events to a common time line, which can be accomplished by synchronizing data acquisition, i.e. using a pulse to trigger a sample on all systems. However, this method is not supported by every system. Alternatively, the measurements of different systems can be started by a common trigger signal with no further synchronization of their sampling clocks during acquisition. With that, two systematic errors may be introduced, namely time lag and time drift. The extents of these errors not only depend on the individual system properties, but also depend on the set of systems combined. In this study, we introduce a simple method to determine time lag and time drift for two systems including cameras and force plates. Our results show that both parameters are present and dependent on chosen sampling frequencies. We conclude that in order to avoid misinterpretation of recorded signals the identified time lag and time drift need to be taken into account for trials of all durations.     

When to wake up? The optimal waking-up strategies for starvation-induced persistence

Prolonged lag time can be induced by starvation contributing to the antibiotic tolerance of bacteria. We analyze the optimal lag time to survive and grow the iterative and stochastic application of antibiotics. A simple model shows that the optimal lag time can exhibit a discontinuous transition when the severeness of the antibiotic application, such as the probability to be exposed the antibiotic, the death rate under the exposure, and the duration of the exposure, is increased. This suggests the possibility of reducing tolerant bacteria by controlled usage of antibiotics application. When the bacterial populations are able to have two phenotypes with different lag times, the fraction of the second phenotype that has different lag time shows a continuous transition. We then present a generic framework to investigate the optimal lag time distribution for total population fitness for a given distribution of the antibiotic application duration. The obtained optimal distributions have multiple peaks for a wide range of the antibiotic application duration distributions, including the case where the latter is monotonically decreasing. The analysis supports the advantage in evolving multiple, possibly discrete phenotypes in lag time for bacterial long-term fitness.     

Aminoacyl adenylate, a normal intermediate or a dead end in aminoacylation of transfer ribonucleic acid.

The shape of the time curve for the aminoacylation of tRNA has been investigated using five different amino acid:tRNA ligases. Four of these enzymes showed a lag in the time curve during the early phase of the first catalytic turnover of the enzyme. In each case, the lag period could be abolished by preincubating the ligase with amino acid, ATP, and Mg2+ under conditions known to give an aminoacyl adenylate-enzyme complex. With all five ligases the steady state rate of transfer from the preformed aminoacyl-adenylate complex to tRNA was approximately the same as that of the overall reaction.     

Acetaldehyde addition and pre-adaptation to the stressor together virtually eliminate the ethanol-induced lag phase in Saccharomyces cerevisiae

AIMS: To show that the ethanol-induced lag phase in yeast can be almost eliminated by combining pre-adaptation with acetaldehyde supplementation. METHODS AND RESULTS: Pre-adaptation to noninhibitory concentrations of ethanol and supplementation of unadapted cultures with acetaldehyde each separately reduced the lag phase of ethanol-inhibited cultures by c. 70%. By combining the two methods the ethanol-induced lag phase was virtually eliminated (90% reduction in lag time). CONCLUSIONS: Pre-adaptation to ethanol and acetaldehyde supplementation appear to promote yeast growth through different mechanisms, which are additive when combined. SIGNIFICANCE AND IMPACT OF THE STUDY: The combination of the above procedures is a potentially powerful tool for reducing the lag of stressed cultures, which may have practical applications: e.g. in reducing the lag of yeasts inoculated into lignocellulosic hydrolysates employed in fuel ethanol production.     

Modelling Bacterial Growth of Lactobacillus curvatus as a Function of Acidity and Temperature

Models that describe the effect of acidity, temperature, and the combined effect of these variables on the growth parameters of Lactobacillus curvatus are developed and validated. Growth parameters (lag time, specific growth rate, and maximum population density) were calculated from growth data at different temperature-acidity combinations. Experiments were set up to assess the quantitative effects of temperature and acidity on the growth parameters rather than for parameter estimation solely. The effect of acidity is monitored at several constant temperature values. Models are set up and fitted to the data. The same procedure is used at constant acidity values to model the effect of temperature. For lag time, specific growth rate, and maximum population density, the effect of temperature could be multiplied with the effect of acidity to obtain combinatory models that describe the effect of both controlling factors on the growth parameters. Lag time measurements showed large deviations, and therefore the lag time models developed can only be used to estimate the order of magnitude of lag time.     

Competition between Primary Nucleation and Autocatalysis in Amyloid Fibril Self-Assembly

Kinetic measurements of the self-assembly of proteins into amyloid fibrils are often used to make inferences about molecular mechanisms. In particular, the lag time—the quiescent period before aggregates are detected—is often found to scale with the protein concentration as a power law, whose exponent has been used to infer the presence or absence of autocatalytic growth processes such as fibril fragmentation. Here we show that experimental data for lag time versus protein concentration can show signs of kinks: clear changes in scaling exponent, indicating changes in the dominant molecular mechanism determining the lag time. Classical models for the kinetics of fibril assembly suggest that at least two mechanisms are at play during the lag time: primary nucleation and autocatalytic growth. Using computer simulations and theoretical calculations, we investigate whether the competition between these two processes can account for the kinks which we observe in our and others’ experimental data. We derive theoretical conditions for the crossover between nucleation-dominated and growth-dominated regimes, and analyze their dependence on system volume and autocatalysis mechanism. Comparing these predictions to the data, we find that the experimentally observed kinks cannot be explained by a simple crossover between nucleation-dominated and autocatalytic growth regimes. Our results show that existing kinetic models fail to explain detailed features of lag time versus concentration curves, suggesting that new mechanistic understanding is needed. More broadly, our work demonstrates that care is needed in interpreting lag-time scaling exponents from protein assembly data.     

Mutagenic analysis of the nucleation propensity of oxidized Alzheimer's beta-amyloid peptide

The formation of polypeptide aggregates represents a nucleated polymerization reaction in which an initial nucleation event (lag phase) is followed by the extension of newly formed nuclei into larger aggregates, including fibrils (growth phase). The efficiencies of these reactions relate to the lag time (lag phase) and to the rate of aggregation (growth phase), which can be determined from experimental aggregation curves. Here we present a mutagenic analysis in which we replace valine 18 of the Alzheimer's Abeta (1-40) peptide with 17 different amino acids and determine its effect on the lag time, and therefore, on the propensity of nucleation. Comparison with various physico-chemical properties shows that nucleation is affected in a predictable manner depending on the beta-sheet propensity and hydrophobicity of residue 18. In addition, we observe a direct proportionality between the lag time and the rate of aggregation. These data imply that the two reactions, nucleation and polymerization, are governed by very similar physicochemical principles and that they involve the formation of the same types of noncovalent interactions.     

Plastic inducible morphologies are not always adaptive: The importance of time delays in a stochastic environment

Summary We present a mathematical model for predicting the expected fitness of phenotypically plastic organisms experiencing a variable environment. We assume that individuals experience two discrete environments probabilistically in time (as a Markov process) and that there are two different phenotypic states, each yielding the highest fitness in one of the two environments. We compare the expected fitness of a phenotypically fixed individual to that of an individual whose phenotype is induced to produce the better phenotype in each environment with a time lag between experiencing a new environment and realization of the new phenotype. Such time lags are common in organisms where phenotypically plastic, inducible traits have been documented. We find that although plasticity is generally adaptive when time lags are short (relative to the time scale of environmental variability), plasticity can be disadvantageous for longer lag times. Asymmetries in environmental change probabilities and/or the relative fitnesses of each phenotype strongly influence whether plasticity is favoured. In contrast to other models, our model does not require costs for plasticity to be disadvantageous; costs affect the results quantitatively, not qualitatively.     

Automated image analysis of bacterial colony growth as a tool to study individual lag time distributions of immobilized cells

A method to determine the individual lag time (lag) distributions of immobilized bacteria was presented. The method was based on the image analysis of the bacterial colony growth. The lag distributions were retrieved from the distributions of the detection times (Td) required to form macroscopically visible colonies. Using this method, the lag distributions on agar for Listeria monocytogenes cells previously subjected to two situations reproducing conditions encountered during the contamination of cheese, were determined. The results were presented and compared with lag distributions obtained with an established method based on the time to detection of turbidity in broth. An original method to retrieve lag in broth and agar without any knowledge of the growth rate was also proposed. In order not to bias the distributions of lag on agar the impact of spatial separation between colonies on colony growth rates was quantified. Means and standard deviations of lag distributions for the two different stresses were found to be similar in broth and on agar. Extreme Value type II distributions fitted the best the different datasets of lag distributions.     

Sample sizes based on the log-rank statistic in complex clinical trials

The log-rank test is frequently used to compare survival curves. While sample size estimation for comparison of binomial proportions has been adapted to typical clinical trial conditions such as noncompliance, lag time, and staggered entry, the estimation of sample size when the log-rank statistic is to be used has not been generalized to these types of clinical trial conditions. This paper presents a method of estimating sample sizes for the comparison of survival curves by the log-rank statistic in the presence of unrestricted rates of noncompliance, lag time, and so forth. The method applies to stratified trials in which the above conditions may vary across the different strata, and does not assume proportional hazards. Power and duration, as well as sample sizes, can be estimated. The method also produces estimates for binomial proportions and the Tarone-Ware class of statistics.     

Effects of preculturing conditions on lag time and specific growth rate of Enterobacter sakazakii in reconstituted powdered infant formula

Enterobacter sakazakii can be present, although in low levels, in dry powdered infant formulae, and it has been linked to cases of meningitis in neonates, especially those born prematurely. In order to prevent illness, product contamination at manufacture and during preparation, as well as growth after reconstitution, must be minimized by appropriate control measures. In this publication, several determinants of the growth of E. sakazakii in reconstituted infant formula are reported. The following key growth parameters were determined: lag time, specific growth rate, and maximum population density. Cells were harvested at different phases of growth and spiked into powdered infant formula. After reconstitution in sterile water, E. sakazakii was able to grow at temperatures between 8 and 47 degrees C. The estimated optimal growth temperature was 39.4 degrees C, whereas the optimal specific growth rate was 2.31 h(-1). The effect of temperature on the specific growth rate was described with two secondary growth models. The resulting minimum and maximum temperatures estimated with the secondary Rosso equation were 3.6 degrees C and 47.6 degrees C, respectively. The estimated lag time varied from 83.3 +/- 18.7 h at 10 degrees C to 1.73 +/- 0.43 h at 37 degrees C and could be described with the hyperbolic model and reciprocal square root relation. Cells harvested at different phases of growth did not exhibit significant differences in either specific growth rate or lag time. Strains did not have different lag times, and lag times were short given that the cells had spent several (3 to 10) days in dry powdered infant formula. The growth rates and lag times at various temperatures obtained in this study may help in calculations of the period for which reconstituted infant formula can be stored at a specific temperature without detrimental impact on health.     

Delayed and separate costimulation in vitro supports the evidence of a transient "excited" state of CD8+ T cells during activation

Although the two-signal model for T cell activation states that a signal-1 through the TCR and a costimulatory signal-2 are required for optimal stimulation, it is now clear that the requirement for costimulation can be bypassed under certain conditions. We previously reported that this is the case for naive CD8+ T cells in vitro. In the present study we tested the effect of signal-2 when delivered after signal-1 has been disrupted. Naive CD8+ T cells from TCR transgenic mice were stimulated in vitro by using immobilized recombinant single-chain MHC molecules alone as signal-1. This signal was then stopped after different lengths of time, and anti-CD28 mAb as signal-2 was given either immediately or after a time lag. We found that signal-2 can potentiate a short signal-1 when added sequentially. Moreover, a time lag between the two signals does not abolish this potentiation. If the strength of signal-1, but not its duration, is increased, then the time lag between the delivery of signals 1 and 2 can be lengthen without loss of potentiation. Together, our results indicate that the two signals do not need to be delivered concomitantly to get optimal T cell activation. We suggest that the CD8+ T cells can reach a transient "excited" state after being stimulated with signal-1 alone, characterized by the cell's ability to respond to separate and delayed signal-2.     

Identifying critical interactions in complex competition dynamics between bean beetles

Identifying behavioural basis of competitive relationship is essential to understand outcome of interspecific competition. However, it remains difficult to investigate demographic effect of competitive behaviour, because various kinds of behaviours may co‐occur in the competition and make the dynamics far complicated in nonlinear ways. We report that the behavioural basis of interspecific interaction can be identified, by focusing on the timescale difference from the occurrence of each behaviour to the appearance of its demographic effect. Between two bean beetles, Callosobruchus chinensis and C. maculatus, major interspecific interactions are resource competition (RC) at the larval stage and reproductive interference (RI) at the adult stage. RC has longer time lag than RI, because effect of RC appears in the adult number of the next generation through larval competition while effect of RI appears instantaneously in the adult number through early death of females. If we detect two effects with different time lags from the competition dynamics, an effect with intergenerational time lag and with no time lag would be considered as RC and RI, respectively. We applied empirical dynamic modelling approach, which is a nonlinear time series analysis for detecting causal interactions and the strength, to two published datasets of experimental competition between those beetles. Results showed the significant causality from the winner species to the loser one in both experiments, but the causality time lag differed between experiments: the causality had no time lag in the C. chinensis‐win data, while intergenerational time lag in C. maculatus‐win data. Furthermore, detection of the causality with intergenerational time lag from C. maculatus to C. chinensis in both experiments suggests interplay of constant RC and variable RI which can reverse the outcome. This study is the first successful case study that links behavioural‐level interactions to demographic‐level effects in interspecific competition.     

The Relationship Between Assessments of Jet Lag and Some of Its Symptoms

The power of the symptoms of jet lag in predicting the amount of jet lag measured at the same and different times of the day has been investigated. A total of 85 subjects was studied for 6 days after a flight from the UK to Australia (10 time zones to the east). At 08:00, 12:00, 16:00, 20:00, and 24:00h, the subjects recorded their jet lag and fatigue. At 08:00h, they also assessed their sleep. At 12:00 and 16:00h, they assessed their attitude to a meal, as well as their motivation, commitment, and irritability. On retiring, they recorded bowel activity. Assessments were by visual analog scales. Jet lag was treated as the dependent variable and the symptoms as covariates in ANCOVAs. Fatigue was a powerful predictor of jet lag, provided it was measured at the same time, and some aspects of sleep predicted jet lag measured on retiring or rising. The other symptoms predicted jet lag less powerfully and/or at a wider range of times. It is concluded that, even though jet lag at any time of the day can be predicted from contemporaneous assessments of fatigue and that it can be predicted on retiring or rising from some aspects of changed sleep, jet lag is predicted less reliably from other symptoms, including aspects of mental performance. These findings question exactly what causes jet lag at a particular time of day, and so are relevant to studies which use this measurement to investigate the problems associated with time‐zone transitions, and ways to ameliorate them.     

Impacts of sterilization, microwave and ultrasonication pretreatment on hydrogen producing using waste sludge

Hydrogen production by sterilization, microwave and ultrasonication pretreated waste sludge was investigated in this study. A new strain of Pseudomonas sp. GZ1 (EF551040) was inoculated in pretreated waste sludge to produce hydrogen. The experimental results showed that different pretreated sludge had evident differences in the yield of hydrogen production and lag time. Sterilized sludge had the largest yield of hydrogen production, and the maximum yield was 15.02 ml/gTCOD. The lag time of using sterilized sludge was 15 h, longer than other two pretreated sludge. Using the ultrasonicated sludge, the hydrogen production yield was smallest and lag time was shortest in the three pretreated sludge. Protein and carbohydrate could be released from waste sludge by pretreatment. Protein was the main nutrient used for hydrogen production. The concentration of protein, carbohydrate and SCOD increased after pretreatment and fermentation. The impacts of different pretreatments on hydrogen production were also discussed in detail.     

How quickly do brains catch up with bodies? A comparative method for detecting evolutionary lag.

A trait may be at odds with theoretical expectation because it is still in the process of responding to a recent selective force. Such a situation can be termed evolutionary lag. Although many cases of evolutionary lag have been suggested, almost all of the arguments have focused on trait fitness. An alternative approach is to examine the prediction that trait expression is a function of the time over which the trait could evolve. Here we present a phylogenetic comparative method for using this 'time' approach and we apply the method to a long-standing lag hypothesis: evolutionary changes in brain size lag behind evolutionary changes in body size. We tested the prediction in primates that brain mass contrast residuals, calculated from a regression of pairwise brain mass contrasts on positive pairwise body mass contrasts, are correlated with the time since the paired species diverged. Contrary to the brain size lag hypothesis, time since divergence was not significantly correlated with brain mass contrast residuals. We found the same result when we accounted for socioecology, used alternative body mass estimates and used male rather than female values. These tests do not support the brain size lag hypothesis. Therefore, body mass need not be viewed as a suspect variable in comparative neuroanatomical studies and relative brain size should not be used to infer recent evolutionary changes in body size.     

The relationship between assessments of jet lag and some of its symptoms

The power of the symptoms of jet lag in predicting the amount of jet lag measured at the same and different times of the day has been investigated. A total of 85 subjects was studied for 6 days after a flight from the UK to Australia (10 time zones to the east). At 08:00, 12:00, 16:00, 20:00, and 24:00h, the subjects recorded their jet lag and fatigue. At 08:00h, they also assessed their sleep. At 12:00 and 16:00h, they assessed their attitude to a meal, as well as their motivation, commitment, and irritability. On retiring, they recorded bowel activity. Assessments were by visual analog scales. Jet lag was treated as the dependent variable and the symptoms as covariates in ANCOVAs. Fatigue was a powerful predictor of jet lag, provided it was measured at the same time, and some aspects of sleep predicted jet lag measured on retiring or rising. The other symptoms predicted jet lag less powerfully and/or at a wider range of times. It is concluded that, even though jet lag at any time of the day can be predicted from contemporaneous assessments of fatigue and that it can be predicted on retiring or rising from some aspects of changed sleep, jet lag is predicted less reliably from other symptoms, including aspects of mental performance. These findings question exactly what causes jet lag at a particular time of day, and so are relevant to studies which use this measurement to investigate the problems associated with time-zone transitions, and ways to ameliorate them.     

Electrophotoluminescence and the electrical properties of the photosynthetic membrane. I. Initial kinetics and the charging capacitance of the membrane

Preilluminated chloroplast membranes, and particularly hypotonically swollen vesicles (blebs), give rise to a strong characteristic luminescence (electrophotoluminescence, EPL; Ellenson and Sauer, 1976, Photochem. Photobiol., 23:113-123; Arnold and Azzi, 1971, Photochem. Photobiol., 14:233-240) during the application of a strong external electric field. A detailed kinetic study of EPL was carried out and the initial kinetics from the field onset are reported here. The fast rise time (less than 0.2 mus) of the applied external electric field together with a high instrumental time resolution allowed the observation of a characteristic delay (lag time) between the field onset and the appearance of the induced emission. The lag time decreased with increase in the applied field strength and/or the conductivity of the suspension and is interpreted to be a consequence of (a) the necessity to reach a threshold electrical potential difference in the bleb membrane, below which no emission can be triggered, and (b) the finite time required to attain such a transmembranal field during the charging process of the membrane. A quantitative analysis, connecting the lag time, the controllable experimental parameters, and the membrane electrical characteristics is presented. Its verification was carried out in both size-selected and heterogeneous bleb populations. In the latter, experiments were consistent with the assumption that the lag time reflects the charging of the largest blebs. The results indicate (a) the possibility of directly measuring the specific membrane capacitance, yielding an estimate of Cm = 1.2 +/- 0.3 microF/cm2 (the precision being particle size-homogeneity dependent); (b) A minimal transmembranal potential difference (of approximately 240 mV) is necessary to induce electrophotoluminescence; and (c) the lag duration depends on the time elapsed between the preillumination and the external field application. Correlated with the study of ionophore effects on the lag time, this suggests additivity of the light- and field-induced transmembrane potentials in attaining the threshold for emission.