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.     

Effect of Environmental and Physiological Conditions on the Phase of Adjustment of Pseudomonas fragi

The duration of the phase of adjustment of Pseudomonas fragi was affected by the physiological age and growth temperature of the inoculum, as well as by the temperature at which the growth curve was determined. Cultures in the exponential phase of growth gave shorter lags than stationary-phase and resting-phase inocula. Inocula from the latter phase gave the longest lags. Inocula grown at the temperature at which the growth curve was determined usually gave the shortest lags: the greater the difference between the incubation temperature of the inoculum and the incubation temperature of the growth curve, the longer the lag. Inocula grown at temperatures below the incubation temperature of the culture tended to produce longer lags than inocula grown at temperatures above the incubation temperature. The combined effect of physiological age and incubation temperature of the inoculum was additive. The effect of the incubation temperature of the culture upon the duration of the lag depended upon the method used to determine this phase. Lags that were measured in physical time (i.e., Lockhart's lag) decreased as the incubation temperature of the culture was increased, within the temperatures used. But Monod's lag, which measures physiological time, did not decrease as the temperature of growth increased but rather appeared to vary around some constant value dependent upon the physiological condition of the culture.     

On the lag phase and initial decline of microbial growth curves

The lag phase is generally thought to be a period during which the cells adjust to a new environment before the onset of exponential growth. Characterizing the lag phase in microbial growth curves has importance in food sciences, environmental sciences, bioremediation and in understanding basic cellular processes. The goal of this work is to extend the analysis of cell growth curves and to better estimate the duration of the lag phase. A non-autonomous model is presented that includes actively duplicating cells and two subclasses of non-duplicating cells. The growth curves depend on the growth and death rate of these three subpopulations and on the initial proportion of each. A deterministic and a stochastic model are both developed and give the same results. A notable feature of the model is the decline of cells during the early stage of the growth curve, and the range of parameters when this decline occurs is identified. A limited growth model is also presented that accounts for the lag, exponential growth and stationary phase of microbial growth curves.     

Effect of growth phase on survival of bromegrass suspension cells following cryopreservation and abiotic stresses

BACKGROUND AND AIMS: Cryopreservation is a practical method of preserving plant cell cultures and their genetic integrity. It has long been believed that cryopreservation of plant cell cultures is best performed with cells at the late lag or early exponential growth phase. At these stages the cells are small and non-vacuolated. This belief was based on studies using conventional slow prefreezing protocols and survival determined with fluorescein diacetate staining or 2,3,5-triphenyltetrazolium chloride assays. This classical issue was revisited here to determine the optimum growth phase for cryopreserving a bromegrass (Bromus inermis) suspension culture using more recently developed protocols and regrowth assays for determination of survival. METHODS: Cells at different growth phases were cryopreserved using three protocols: slow prefreezing, rapid prefreezing and vitrification. Stage-dependent trends in cell osmolarity, water content and tolerance to freezing, heat and salt stresses were also determined. In all cases survival was assayed by regrowth of cells following the treatments. KEY RESULTS: Slow prefreezing and rapid prefreezing protocols resulted in higher cell survival compared with the vitrification method. For all the protocols used, the best regrowth was obtained using cells in the late exponential or early stationary phase, whereas lowest survival was obtained for cells in the late lag or early exponential phase. Cells at the late exponential phase were characterized by high water content and high osmolarity and were most tolerant to freezing, heat and salt stresses, whereas cells at the early exponential phase, characterized by low water content and low osmolarity, were least tolerant. CONCLUSIONS: The results are contrary to the classical concept which utilizes cells in the late lag or early exponential growth phase for cryopreservation. The optimal growth phase for cryopreservation may depend upon the species or cell culture being cryopreserved and requires re-investigation for each cell culture. Stage-dependent survival following cryopreservation was proportionally correlated with the levels of abiotic stress tolerance in bromegrass cells.     

Behavior in two-phase aqueous polymer systems of L5178Y mouse leukemic cells : II. The lag and exponential phases of growth

The behavior of lag and exponential growth phase L5178Y mouse leukemic cells under normal and prolonged lag phase conditions with respect to partition in aqueous dextran — polyethylene glycol polymer systems has been studied. ‘Backculture’ of early stationary cells into fresh growth medium is accompanied by a decrease in partition ratio from 0.52 to 0.11. The partition ratio remains depressed for a time considerably longer than the duration of lag phase but rises rapidly and returns to its former value as the cells reach late exponential/early stationary phase. If lag phase is prolonged, the time for which the partition ratio remains depressed is also prolonged. In the exponential phase following a prolonged lag phase, the partition ratio rises at a rate slower than during a normal exponential phase and does not reach the same magnitude for the same position in the cycle. Net negative surface charge as measured by particle microelectrophoresis does not change appreciably throughout the growth cycle. The results suggest that the sequence of events at the cell surface on a populational basis which contribute to the partitioning behavior is possibly predetermined or programmed at the time of transfer into fresh medium. The results further substantiate the technique of aqueous polymer partitioning as being the most sensitive method available for monitoring subtle changes in plasma membrane properties during the cell growth cycle.     

Effect of the development phase and growth rate of a Shigella sonnei population on the reproduction of homologous bacteriophage

This study showed that the minimum latent period (20 minutes) of the intracellular multiplication of dysentery bacteriophage S-9 in the population of S. sonnei substrate strain under the conditions of static heterogeneous surface batch cultivation was observed at the end of the lag phase and at the growth acceleration phase, in the first and second thirds of the exponential curve, while the maximum latent period (35-40 minutes) was observed at the stationary phase. The maximum yield of phage S-9 from one infected bacterial cell (628.3 +/- 116.8) was registered during the first third of the phase of the exponential growth of the bacterial population and the minimum yield (18.66 +/- 6.6), at the beginning of the lag phase. The significant direct correlation between the specific growth rate of the bacterial population and the yield of the phage from one infected bacterial cell at the end of the lag phase, at the growth acceleration and deceleration phases, as well as the significant inverse correlation between the yield of the phage and the time of the generation of the bacterial population at the growth acceleration phase were established.     

Growth and Enzyme Activity of Myxococcus virescens in Liquid Medium

The object of this work was to develop a method for determination of the growth of Myxocuccus virescens in liquid medium. The bacteria were grown in N III-B medium in 100 ml Kjeldahl flasks, which were fixed on a disc forming an angle of 50 degrees with the horizontal plane. The disc was rotated two full revolutions per minute. The total nitrogen content of the washed swarms, developing on the glass walls of the flasks, was used as an expression for the myxobacterial growth. After a lag the bacteria grown in total darkness had a growth phase, approximately exponential, of about 270 hours, which was followed by a steep phase of decline. When the bacteria were illuminated daily for a short period, a lag of 50–200 hours appeared in the middle of the exponential growth phase, after which a new exponential growth phase began. This second growth seemed to depend on variants insensitive to light induced lysis. The increase of enzymes, active on casein and autoclaved aerobacter cells, closely followed the first part of the growth curve. However both activities began to decrease before the growth maximum. No sign of proteolytic activity or lytic activity on autoclaved aerobacter cells could be detected after about 700 hours' incubation. In illuminated flasks it is shown that the production of yellow pigments in culture solution is sharply increased at the end of the exponential growth phase. The lytic enzymes of M. virescens seem to be extracellular, secreted during the exponential phase of growth. No activity was exhibited by washed cell swarms, even if they were sonically disintegrated.     

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.     

Probabilistic neural networks using Bayesian decision strategies and a modified Gompertz model for growth phase classification in the batch culture of Bacillus subtilis

Probabilistic neural networks (PNNs) were used in conjunction with the Gompertz model for bacterial growth to classify the lag, logarithmic, and stationary phases in a batch process. Using the fermentation time and the optical density of diluted cell suspensions, sampled from a culture of Bacillus subtilis, PNNs enabled a reliable determination of the growth phases. Based on a Bayesian decision strategy, the Gompertz based PNN used newly proposed definition of the lag and logarithmic phases to estimate the latent, logarithmic and stationary phases. This network topology has the potential for use with on-line turbidimeter for the automation and control of cultivation processes.     

Identification of genes and proteins induced during the lag and early exponential phase of lager brewing yeasts

AIMS: The aim of the present study is to identify genes and proteins whose expression is induced in lager brewing yeast during the lag phase and early exponential growth. METHODS AND RESULTS: Two-dimensional gel electrophoresis was used to identify proteins induced during the lag and early exponential phase of lager brewing yeast in minimal medium. The identified, early-induced proteins were Ade17p, Eno2p, Ilv5gp, Sam1p, Rps21p and Ssa2p. For most of these proteins, the patterns of induction differed from those of the corresponding genes. However, the genes had similar early expression patterns in minimal medium as observed during lager brewing conditions. The expression of previously identified early-induced genes in Saccharomyces cerevisiae grown in minimal medium, ADO1, ALD6, ASC1, ERG4, GPP1, RPL25, SSB1 and YKL056C, was also early induced in lager yeast under brewing conditions. CONCLUSIONS: The results indicate that the above-mentioned genes in general are induced during the lag phase and early exponential growth in Saccharomyces yeasts. The processes in which these genes take part are likely to play an important role during growth initiation. SIGNIFICANCE AND IMPACT OF THE STUDY: Increased knowledge regarding the early growth phase of lager brewing yeast was obtained. Further, the universality of the identified expression patterns suggests new methodologies for optimization and control of growth initiation during brewing fermentations.     

Fungal melanin inhibitor and related compounds from Penicillium decumbens

In Silene vulgaris (M.) G. cell culture three growth phases were distinguished, namely, a lag phase, an exponential phase and a stationary phase. Pectin termed silenan and an acidic arabinogalactan were isolated as cell wall polysaccharides of S. vulgaris callus at the different growth phases during culture. Production of silenan as the galacturonan (or rhamnogalacturonan) core was observed at the beginning of the exponential phase and at the stationary phase of the callus growth. Arabinogalactan, containing the galacturonic acid residues, is formed at the exponential phase followed by attachment to the core of silenan in the middle of the exponential phase. The arabinogalactan constituent of silenan appeared to be destroyed gradually at the stationary growth phase. The monosaccharide compositions of silenan and arabinogalactan were determined at various phases of the callus growth. Silenan was found to be formed in maximum amounts at the exponential phase of the cell growth. Insignificant alterations of the yields of acidic arabinogalactan were found during culture while total productivity per litre of medium and rate of production per day of arabinogalactan were found to be maximal at the exponential phase of growth.     

Modeling of Bacterial Growth with Shifts in Temperature

The temperature of chilled foods is an important variable for the shelf life of a product in a production and distribution chain. To predict the number of organisms as a function of temperature and time, it is essential to model the growth as a function of temperature. The temperature is often not constant in various stages of distribution. The objective of this research was to determine the effect of shifts in temperature. The suitability and usefulness of several models to describe the growth of Lactobacillus plantarum with fluctuating temperatures was evaluated. It can be assumed that temperature shifts within the lag phase can be handled by adding relative parts of the lag time to be completed and that temperature shifts within the exponential phase result in no lag phase. With these assumptions, the kinetic behavior of temperature shift experiments was reasonably well predicted, and this hypothesis was accepted statistically in 73% of the cases. Only shifts of temperature around the minimum temperature for growth showed very large deviations from the model prediction. The best results were obtained with the assumption that a temperature shift (within the lag phase as well as within the exponential phase) results in an additional lag phase. This hypothesis was accepted statistically in 93% of the cases. The length of the additional lag phase is one-fourth of the lag time normally found at the temperature after the shift.     

Parameter estimation for the distribution of single cell lag times

In Quantitative Microbial Risk Assessment, it is vital to understand how lag times of individual cells are distributed over a bacterial population. Such identified distributions can be used to predict the time by which, in a growth-supporting environment, a few pathogenic cells can multiply to a poisoning concentration level.We model the lag time of a single cell, inoculated into a new environment, by the delay of the growth function characterizing the generated subpopulation. We introduce an easy-to-implement procedure, based on the method of moments, to estimate the parameters of the distribution of single cell lag times. The advantage of the method is especially apparent for cases where the initial number of cells is small and random, and the culture is detectable only in the exponential growth phase.     

Effects of pulse ultrasonic irradiation on the lag phase of Saccharomyces cerevisiae growth

Aims: This paper presents an analysis of lag phase phenomena in Saccharomyces cerevisiae growth as a function of ultrasonic irradiation. Methods and Results: Pulse irradiation treatments were performed by a 20 kHz ultrasonic transducer with different durations and energies. Data obtained from experiments were then employed to estimate growth parameters by specific transfer function. The significance of the different lag times in response to ultrasonic irradiation was analysed. The results showed that the yeast growth in lag phase responded to the irradiated ultrasonic of 20 min more than the 10 min. The ultrasonic energies between 330 and 360 W s m^?3 could decrease lag time up to 1 h compared to the sample without ultrasonic irradiation. Conversely, the treatments with energies higher than 850 W s m^?3 were able to extend the lag time and decrease the yeast growth. Conclusions: The lag durations of S. cerevisiae were changed significantly by different ultrasonic irradiations, energies and durations. In particular, sufficient irradiation energies reduced the lag time, resulting in accelerated yeast growth. In contrast, high energy could inactivate growth by increasing the lag time. Significance and Impact of the Study: This work provides an alternative technique to either accelerate or inactivate the S. cerevisiae lag phase. The approach can be developed in experiment designed to control the yeast growth by ultrasonic irradiation as assistance in the environments.     

Growth Stimulating Substance for Microorganisms Produced by Escherichia coli Causing the Reduction of the Lag Phase in Microbial Growth and Identity of the Substance with Pyrroloquinoline Quinone

The finding that most strains of microbes produce a growth stimulating substance for microorganisms was demonstrated and confirmed with the culture broth of Escherichia coli grown on a glucose-mineral medium. Addition of culture broth of E. coli to the culture media of the others markedly reduced the lag phase in microbial growth but not growth rate in the subsequent exponential phase nor the total cell yield in the stationary phase. The growth stimulation causing reduction of the lag phase was dependent on the amount of culture broth added. Occurrence of cell growth was essential for the excretion of the growth stimulating substance by E. coli. Under identical inoculum size, even with a heavy inoculum, a further reduction of the lag phase was observed by the addition of culture broth of E. coli. The substance was only effective at the initial growth phase but inert when the substance was added to a growing culture at the exponential phase. Finally, the substance was identified as pyrroloquinoline quinone, a newly established coenzyme, through chromatographic, spectroscopic and enzymatic criteria.     

Relation between the damaging effect of surface-active compounds on Escherichia coli cells and the phase of culture growth

The techniques of cell electrophoresis and electro-orientation spectroscopy were used to study the effect of sodium dodecyl sulfate (SDS) and cetyl trimethyl ammonium bromide (CTAB) on Escherichia coli K-12 cells from the culture at the exponential and stationary growth phases. SDS (2 x 10(-4) M) considerably damaged cells at the exponential phase, particularly at pH less than 6.0, whereas cells at the stationary phase were damaged to a less degree and only at pH less than 5.3 or after their treatment with Trilon B. The damaging effect of SDS decreased in an isotonic medium (0.25 M sucrose) as compared to a hypotonic medium (distilled water). CTAB also damaged cells at the exponential phase more than those at the stationary phase, and its damaging action decreased with pH. Mg2+, Ca2+, and Sr2+ cations diminished the degree of cell damage with CTAB, but did not exert any noticeable protection in the case of SDS. The different sensitivity of cells at the exponential and stationary growth phases may be associated with changes in their surface electric charge and with the existence of hydrophobic regions on the cell surface. The higher electric charge of cells at the stationary growth phase is presumed to stem from a rise in the amount of surface lipopolysaccharides which bear a negative electric charge.     

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.     

Cell size distribution as a parameter for the predetermination of exponential growth during repeated batch cultivation of CHO cells

The routine measurement of the cell size distribution of a Chinese hamster ovary (CHO) cell population during a repeated batch process enables the predetermination of exponential growth even 24 h before the population enters the log phase, due to a short but significantly increased cell size during the lag phase. A prolongation of the stationary phase causes to progressive limitation in asparagine, serine, and ethanolamine. Such extended limitation influences the duration of the following lag phase and obviously induces a synchronization of the cell population that can be monitored easily by a fast cell size analyzing technique. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 793-797, 1997.     

Physiological and biochemical characterization of a suspensionculture system for sustained exponential growth of Nicotiana silvestris

A strong approach to understanding the regulation of enzymes in metabolic pathways, such as those responsible for amino acid biosynthesis, is to follow enzyme levels throughout the growth curve of higher plant cells in suspension culture. The rise and fall of enzyme levels can be traced as a function of physiological stage of growth Subculturing, as typically carried out by low-factor dilution of stationary phase cells, yields a system suitable for the study of changes in enzyme and metabolite levels that accompany the transition from stationary-phase physiology to exponential-phase physiology. However, the short duration of exponential growth in such subculture protocols is inadequate to avoid carryover effects from previous stationary-phase physiology. Suspension cultures of Nicotiana silvestris Speg, et Comes (2N = 24) were used to demonstrate substantial carryover levels of acid phosphatase, alkaline phosphatase and protease activities. A subculture routine is described for maintaining cell populations in exponential phase indefinitely. About 10 generations of sustained exponential growth is required to approach a true balanced state of exponential growth. Such exponential phase populations consist of cells termed EE cells. EE-cell populations were similar to cells that have been in exponential phase for only a few generations (E cells), with respect to doubling time (about 40 h) and to minimal density of diluted populations able to resume growth (about 500 cells ml^?1). EE cells possess a high content of soluble protein; they are smaller and more aggregated than are E cells. Upon dilution into fresh medium, EE cells resume exponential growth without a lag. In contrast to E cells, EE cells exhibit properties of balanced growth, since proportionate increases in cell number, dry weight, wet weight and packed-cell volume were observed. E cells, sampled at different elapsed times of growth, are likely to differ in metabolite, enzyme and cell properties, whereas EE cells exhibit near-constant properties.