Connection between stochastic and deterministic modelling of microbial growth

We present in this paper various links between individual and population cell growth. Deterministic models of the lag and subsequent growth of a bacterial population and their connection with stochastic models for the lag and subsequent generation times of individual cells are analysed. We derived the individual lag time distribution inherent in population growth models, which shows that the Baranyi model allows a wide range of shapes for individual lag time distribution. We demonstrate that individual cell lag time distributions cannot be retrieved from population growth data. We also present the results of our investigation on the effect of the mean and variance of the individual lag time and the initial cell number on the mean and variance of the population lag time. These relationships are analysed theoretically, and their consequence for predictive microbiology research is discussed.     

Short Lag Times for Invasive Tropical Plants: Evidence from Experimental Plantings in Hawai'i

Background

The lag time of an invasion is the delay between arrival of an introduced species and its successful spread in a new area. To date, most estimates of lag times for plants have been indirect or anecdotal, and these estimates suggest that plant invasions are often characterized by lag times of 50 years or more. No general estimates are available of lag times for tropical plant invasions. Historical plantings and documentation were used to directly estimate lag times for tropical plant invasions in Hawai''i.

Methodology/Principal Findings

Historical planting records for the Lyon Arboretum dating back to 1920 were examined to identify plants that have since become invasive pests in the Hawaiian Islands. Annual reports describing escape from plantings were then used to determine the lag times between initial plantings and earliest recorded spread of the successful invaders. Among 23 species that eventually became invasive pests, the average lag time between introduction and first evidence of spread was 14 years for woody plants and 5 years for herbaceous plants.

Conclusions/Significance

These direct estimates of lag times are as much as an order of magnitude shorter than previous, indirect estimates, which were mainly based on temperate plants. Tropical invaders may have much shorter lag times than temperate species. A lack of direct and deliberate observations may have also inflated many previous lag time estimates. Although there have been documented cases of long lag times due to delayed arrival of a mutualist or environmental changes over time, this study suggests that most successful invasions are likely to begin shortly after arrival of the plant in a suitable habitat, at least in tropical environments. Short lag times suggest that controlled field trials may be a practical element of risk assessment for plant introductions.     

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.     

Anhydrobiosis in the infective juveniles of Trichostrongylus colubriformis (Nematoda: Trichostrongylidae)

The infective juveniles of Trichostrongylus colubriformis can survive exposure to 0% relative humidity after desiccation at higher relative humidities. During rehydration there is a lag phase before recovery. The infective juveniles are thus capable of anhydrobiosis. Removal of the sheath does not affect desiccation survival but does affect the duration of the lag phase. Morphological changes during the lag phase are described. The appearance of birefringence in the muscle cells during the anomalous shrinkage which occurs during the lag phase is considered to reflect physiological changes necessary for the recovery of normal muscle function.     

Genetic Properties of Mutations at the PEP4 Locus in SACCHAROMYCES CEREVISIAE

Yeast cells that inherit mutations at the PEP4 locus exhibit a pronounced phenotypic lag in the expression of the mutant phenotype imparted by these mutations. This lag appears to extend to all of the enzymes that are affected by the pep4-3 mutation. For at least two of the enzymatic activities, phenotypic lag shows mitotic cosegregation. Phenotypic lag is found for meiotic progeny and for mitotic segregants from heterokaryons. The phenotypic lag in the expression of the carboxypeptidase Y deficiency is abolished by nonsense mutations in either PRC1, the structural gene for carboxypeptidase Y, or PRB1, the structural gene for proteinase B. Models to explain these observations are proposed.     

Homozygous diploid deletion strains of Saccharomyces cerevisiae that determine lag phase and dehydration tolerance

This study identifies genes that determine length of lag phase, using the model eukaryotic organism, Saccharomyces cerevisiae. We report growth of a yeast deletion series following variations in the lag phase induced by variable storage times after drying-down yeast on filters. Using a homozygous diploid deletion pool, lag times ranging from 0 h to 90 h were associated with increased drop-out of mitochondrial genes and increased survival of nuclear genes. Simple linear regression (R² analysis) shows that there are over 500 genes for which >70% of the variation can be explained by lag alone. In the genes with a positive correlation, such that the gene abundance increases with lag and hence the deletion strain is suitable for survival during prolonged storage, there is a strong predominance of nucleonic genes. In the genes with a negative correlation, such that the gene abundance decreases with lag and hence the strain may be critical for getting yeast out of the lag phase, there is a strong predominance of glycoproteins and transmembrane proteins. This study identifies yeast deletion strains with survival advantage on prolonged storage and amplifies our understanding of the genes critical for getting out of the lag phase.     

Comparison of lag times in plant physiology

Abstract Comparison of lag (or latent) times is a useful tool in plant physiology for investigating potential mechanisms involved in a response. There are two main ways of deriving the lag time, but only one of these can be properly used for comparative purposes. The other method is biased by the faster responding plants and may not give a representative estimate for the lag time in the population. The fact that the two methods give different, non-comparable results has been widely overlooked. We suggest more care should be taken for their correct use, and propose two terms which can be used to describe the different estimates of the lag time to avoid confusion.     

On the Distinction Between Lag and Delay in Population Growth

The analysis and results presented in this paper provide conclusive evidence to distinguish between the delay effect and the lag as two biologically distinct phenomena. It therefore dispels the incorrect notion that delay effects represented by delay differential equations are the biological reason behind the lag phase in microorganism growth. The resulting consequence so far is that the only other reason for the lag phase is the existence of unstable stationary states. The latter are a result of accounting for the microbial metabolic mass transfer in the population growth process.     

First jet lag symptoms after travelling across multiple time zones

Jet lag is a consequence of desynchronisation of human endogenous circadian rhythm with respect to the immediate environment. The slower adaptation rate of the internal rhythm in contrast to rapid travel in commercial aircraft results in symptoms such as insomnia or daytime fatigue. A group of 53 travelling subjects answered the Charité Jet Lag Scale (CJLS) questionnaire, the first of its kind in German. The CJLS represents a holistic approach to the individual symptoms of jet lag. Study results indicate a possible enhancement by shortening the CJLS to a morning and evening report. Moreover, our study determined a decreasing exponential gradient for jet lag during the first days after travel. Physical and mental symptoms are identified as the primary predictors of jet lag. The CJLS and its future translations could lead to a consistent interviewing method – one key factor for development of future intervention methods to manage jet lag.     

Kinetic studies of L-aspartase from Escherichia coli: substrate activation

The enzyme L-aspartase from Escherichia coli was observed to have a time lag during the production of aspartic acid from fumarate and ammonia. This time lag is pH dependent, with little lag observed below pH 7.0 and a very extensive lag observed above pH 8.0. This time lag was also found to be dependent on both substrate and divalent metal ion concentrations and on the degree of proteolysis of L-aspartase. The observed lag, in the reaction examined in the amination direction, has been found to be correlated with the nonlinear kinetics seen at higher pH in the deamination direction. Both phenomena are consistent with a model in which there is a separate activator site for the substrate, L-aspartic acid, that is distinct from the enzyme active site. Occupation of this site by the substrate, or by various substrate analogues, eliminates both the nonlinearity and the time lag. The D isomer of aspartic acid, which does not bind at the active site, can bind at this newly identified activator site.     

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.     

Changes in the EPR signal of dinitrogenase from Azotobacter vinelandii during the lag period before hydrogen evolution begins.

During the lag period before H2 is evolved by the nitrogenase system, the EPR signal of dinitrogenase decreases steadily, indicating transfer of electrons into dinitrogenase. The rate constant for the decrease in amplitude of the EPR signal, the steady state rate of H2 evolution from nitrogenase, and the length of the lag period have been measured. The data suggest that H2 is evolved only after dinitrogenase has been reduced by 2 electrons/molybdenum. The electrons that have been transfered into dinitrogenase during the lag period are not evolved as H2 upon denaturation of dinitrogenase. The existence of a lag indicates that the two nitrogenase proteins dissociate after every electron transfer. The lag occurs and the nitrogenase proteins dissociate under a variety of conditions of pH and temperature.     

A significant lag in the induction of ovalbumin messenger RNA by steroid hormones: a receptor translocation hypothesis.

Although ovalbumin and conalbumin mRNA accumulate in the same tubular gland cells of the chick oviduct in response to estrogen or progesterone treatment, the kinetics of induction are markedly different. Conalbumin mRNA begins to accumulate within 30 min after estrogen administration, whereas there is a lag of approximately 3 hr before ovalbumin mRNA begins to accumulate, as measured by three independent assays. The kinetics of estrogen-receptor binding to chromatin indicate that these sites are saturated within 15 min of estrogen administration to the chicks, demonstrating that the lag is not due to slow uptake of the steroid. Suboptimal doses of estrogen produce the same lag, but the resultant rate of ovalbumin mRNA accumulation is lower than with an optimal dose. Partial induction of ovalbumin mRNA by a low dose of estrogen does not shorten the lag with an optimal dose. With progesteone, there is a lag of about 2 hr before either ovalbumin or conalbumin mRNA begins to accumulate. Treatment of chicks with hydroxyurea shortens the lag for ovalbumin induction with either hormone. Inhibition of protein synthesis with emetine does not prevent the accumulation of either ovalbumin or conalbumin mRNA. With cycloheximide, however, ovalbumin mRNA accumulation can be prevented. The existence of a lag suggests that there are intermediate steps between the binding of steroid receptors to chromatin and the induction of ovalbumin mRNA. There are basically two models to explain these delays in response: one involving the accumulation of an essential intermediate, and the other involving a rate-limiting translocation of steroid receptors from initial nonproductive chromatin-binding sites to productive sites. Several aspects of the kinetics of ovalbumin mRNA induction are more consistent with the latter model.     

Hominid taphonomy: Transport of human skeletal parts in an artificial fluviatile environment

Flume experiments demonstrate that human skeletal parts sort into lag and transportable groups in a current flow of 31 cm/sec. Orientations, rates and types of movement, and stable positions are recorded. Density of a skeletal part is correlated with the average rate of movement, whereas wet weight in air, weight in water, and volume are not. Shape is an important but unquantifiable factor. Complete crania are the fastest moving elements; individual cranial fragments are in the lag group. Omo fluviatile deposits show a preponderance of hominid lag elements, whereas Olduvai and East Rudolf perilacustrine deposits present a mixture of transportable and lag elements.     

Individual-based modelling of bacterial cultures to study the microscopic causes of the lag phase

The lag phase has been widely studied for years in an effort to contribute to the improvement of food safety. Many analytical models have been built and tested by several authors. The use of Individual-based Modelling (IbM) allows us to probe deeper into the behaviour of individual cells; it is a bridge between theories and experiments when needed. INDividual DIScrete SIMulation (INDISIM) has been developed and coded by our group as an IbM simulator and used to study bacterial growth, including the microscopic causes of the lag phase. First of all, the evolution of cellular masses, specifically the mean mass and biomass distribution, is shown to be a determining factor in the beginning of the exponential phase. Secondly, whenever there is a need for an enzyme synthesis, its rate has a direct effect on the lag duration. The variability of the lag phase with different factors is also studied. The known decrease of the lag phase with an increase in the temperature is also observed in the simulations. An initial study of the relationship between individual and collective lag phases is presented, as a complement to the studies already published. One important result is the variability of the individual lag times and generation times. It has also been found that the mean of the individual lags is greater than the population lag. This is the first in a series of studies of the lag phase that we are carrying out. Therefore, the present work addresses a generic system by making a simple set of assumptions.     

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.     

Fatty Acid Composition of Escherichia coli as a Possible Controlling Factor of the Minimal Growth Temperature.

Shaw, Maxwell K. (University of California, Davis), and John L. Ingraham. Fatty acid composition of Escherichia coli as a possible controlling factor of the minimal growth temperature. J. Bacteriol. 90:141-146. 1965.-If Escherichia coli ML30 is shifted from 37 to 10 C during exponential growth in glucose minimal medium, a 4.5-hr lag results. During this lag, the proportion of unsaturated fatty acids increases in the cellular lipids. However, the adjustment of the fatty acid composition does not appear to be prerequisite to growth at 10 C. If shifts are made to 10 C into minimal medium containing glucose after starvation for glucose at 37 C for 0.5 and 16 hr, the lag periods at 10 C are 4.5 and 6 hr, respectively. Withholding glucose during the lag periods does not affect the duration of the lag periods, but no change in fatty acid composition occurs if glucose is not present. Supplementing the medium with glucose after the lag period permits immediate growth at 10 C; however, the fatty acid composition is still typical of cells grown at 37 C. It is concluded that the fatty acid composition of cells does not determine the minimal temperature of growth.     

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.     

Bayesian calibration of simultaneity in audiovisual temporal order judgments

After repeated exposures to two successive audiovisual stimuli presented in one frequent order, participants eventually perceive a pair separated by some lag time in the same order as occurring simultaneously (lag adaptation). In contrast, we previously found that perceptual changes occurred in the opposite direction in response to tactile stimuli, conforming to bayesian integration theory (bayesian calibration). We further showed, in theory, that the effect of bayesian calibration cannot be observed when the lag adaptation was fully operational. This led to the hypothesis that bayesian calibration affects judgments regarding the order of audiovisual stimuli, but that this effect is concealed behind the lag adaptation mechanism. In the present study, we showed that lag adaptation is pitch-insensitive using two sounds at 1046 and 1480 Hz. This enabled us to cancel lag adaptation by associating one pitch with sound-first stimuli and the other with light-first stimuli. When we presented each type of stimulus (high- or low-tone) in a different block, the point of simultaneity shifted to "sound-first" for the pitch associated with sound-first stimuli, and to "light-first" for the pitch associated with light-first stimuli. These results are consistent with lag adaptation. In contrast, when we delivered each type of stimulus in a randomized order, the point of simultaneity shifted to "light-first" for the pitch associated with sound-first stimuli, and to "sound-first" for the pitch associated with light-first stimuli. The results clearly show that bayesian calibration is pitch-specific and is at work behind pitch-insensitive lag adaptation during temporal order judgment of audiovisual stimuli.