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.     

Flocculation of lag phase yeast cells ofCandida albicans

Flocculation of the yeast form ofCandida albicans occurs during the early or lag phase of growth. Once a developing culture has entered the logarithmic phase of growth, the cells are no longer capable of flocculating. The flocculation during these early stages in the growth of the culture was studied and appeared to be similar in many physical respects to agglutination of mating strains ofHansenula wingei. Variations in the carbohydrate content, nitrogen content, pH, and temperature of the growth medium did not alter the amount of flocculation. Studies with electrical fields indicated that an electrostatic charge is not involved. Treatment of the surface of the cells with solvents showed that lipid solvents do not inhibit flocculation, but phenol, which removes both carbohydrate and protein material, does inhibit flocculation. Lipases also do not affect flocculation but enzymes that break down carbohydrates or protein such as trypsin, papain, and pancreatin do affect flocculation. Phenol extracts from sonicated, washed cell walls were analyzed by electrophoresis and paper chromatography for proteins, amino acids, and polysaccharides. These analyses confirm earlier reports of constituents of the cell wall but do not show a difference in the types of compounds present in the cell walls of flocculant cells as compared with the cell walls of older non-flocculant cells.     

Synchronous protein cycling in batch cultures of the yeast Saccharomyces cerevisiae at log growth phase

The assumption that cells are temporally organized systems, i.e. showing relevant dynamics of their state variables such as gene expression or protein and metabolite concentration, while tacitly given for granted at the molecular level, is not explicitly taken into account when interpreting biological experimental data. This conundrum stems from the (undemonstrated) assumption that a cell culture, the actual object of biological experimentation, is a population of billions of independent oscillators (cells) randomly experiencing different phases of their cycles and thus not producing relevant coordinated dynamics at the population level. Moreover the fact of considering reproductive cycle as by far the most important cyclic process in a cell resulted in lower attention given to other rhythmic processes. Here we demonstrate that growing yeast cells show a very repeatable and robust cyclic variation of the concentration of proteins with different cellular functions. We also report experimental evidence that the mechanism governing this basic oscillator and the cellular entrainment is resistant to external chemical constraints. Finally, cell growth is accompanied by cyclic dynamics of medium pH. These cycles are observed in batch cultures, different from the usual continuous cultures in which yeast metabolic cycles are known to occur, and suggest the existence of basic, spontaneous, collective and synchronous behaviors of the cell population as a whole.     

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.     

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.     

Significance of the lag phase in K1 killer toxin action on sensitive yeast cells

The minimum period between the addition of killer toxin K1 to sensitive yeast cells and the appearance of first cells stained with bromocresol purple indicating membrane damage, is approximately 20 min. The length of this lag phase depends strongly on toxin concentration, extending sharply at toxin levels lower than 60 lethal units (LU) per cell (about one-tenth of the toxin concentration necessary for saturating all surface receptors). As the binding of the toxin to the cell is virtually complete within 1 min, the rest of the lag phase reflects processes different from actual binding,e.g. combination of several toxin molecules to form a membrane ion channel or pore.     

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.     

Factors affecting mycelial to yeast phase conversion and growth of the yeast phase ofHistoplasma capsulatum

A procedure for rapid induction of mycelial to yeast phase (M→Y) conversion ofHistoplasma capsulatum has been devised. Exposure of mycelial fragments to low oxidation-reduction (O/R) potentials (+5 to+65 mv) either aerobically (ascorbic acid treatment) or anaerobically (nitrogen atmosphere) for 18 to 24 hours at 37° C resulted in induction of the M→Y conversion process whether or not an organic sulfur source was available. However, aerobic conditions and a suitable organic sulfur source, such as cysteine, cystine or lanthionine were found essential for outgrowth and maintenance in the yeastlike 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.     

Phospholipase C and D in the commitment to survival or death in the early lag phase of tetrahymena cultures

We made three kinds of experiments in order to elucidate aspects of physiological mechanisms involved in a series of specific events leading to either cell death or survival in the lag phase of culture growth. We studied the fate of newly inoculated Tetrahymena cells in small droplets at 'high' (more than 1000 cells ml(-1)) and 'low' cell densities (less than 600 cells ml(-1)) in a nutrionally complete, synthetic nutrient medium. Confirming previous results we found that the cells in high-density cultures multiplied to final densities around 500,000 cells ml(-1) and that cells in low-density cultures died before multiplying. The appearance of the cells was recorded with a video camera at 20 frames per second for 6 h or until they died. The results indicated that the death process took place within milliseconds. We also studied the effects of U 73122, an inhibitor of the phosphatidylinositol-specific phospholipase C, on cell survival at low densities. At low inhibitor concentrations low-density cells were rescued from dying. At high inhibitor concentrations all cells died, and phosphatidylinositol - but not phosphatidylserine and phosphatidylcholine - saved them. The results indicate that the paths leading to either cell death or to cell proliferation separate within the first few minutes after subcultivation into a new medium, since the first cells in each culture died within 4-30 min after inoculation. Our results also indicate that some PLC activity was required for stimulation of phospholipase D, and that cell death during the early lag phase is caused by a shortage in phosphatidylinositol before the phospholipase D activity is upregulated. These experiments are shedding light on the lethal consequences of a cellular depletion of the important signalling compound phosphatidylinositol in an in vivo system, and may help to elucidate mechanisms behind the century-old fact that eukaryote cells die when inoculated at too low a cell density to survive.     

Kinetics of biphasic growth of yeast in continuous and fed-batch cultures

The influence of dilution rate on the production of biomass, ethanol, and invertase in an aerobic culture of Saccharomyces carlsbergensis was studied in a glucose-limited chemostat culture. A kinetic model was developed to analyze the biphasic growth of yeast on both the glucose remaining and the ethanol produced in the culture. The model assumes a double effect where glucose regulates the flux of glucose catabolism (respiration and aerobic fermentation) and the ethanol utilization in yeast cells. The model could successfully demonstrate the experimental results of a chemostat culture featuring the monotonic decrease of biomass concentration with an increase of dilution rate higher than 0.2 hr^?1 as well as the maximum ethanol concentration at a particular dilution rate around 0.5 hr^?1. Some supplementary data were collected from an ethanol-limited aerobic chemostat culture and a glucose-limited anaerobic chemostat culture to use in the model calculation. Some parametric constants of cell growth, ethanol production, and invertase formation were determined in batch cultures under aerobic and anaerobic states as summarized in a table in comparison with the chemostat data. Using the constants, a prediction of the optimal control of a glucose fed-batch yeast culture was conducted in connection with an experiment for harvesting a high yield of yeast cells with high invertase activity.