Light-induced division and genomic synchrony in phototrophically growing cultures of Rhodopseudomonas sphaeroides.

An experimental procedure for rapidly obtaining cell populations of phototrophically growing Rhodopseudomonas sphaeroides which display division and genomic synchrony has been developed. The basis of the procedure resides with the normal physiological response displayed by cells of R. sphaeroides that have been subjected to an immediate decrease in incident light intensity. After an abrupt high- to low-light transition of an asynchronously dividing cell population, an immediate cessation of increases in culture turbidity, total cell number, and net accumulations of culture deoxyribonucleic acid and phospholipid occurs. Total cell number remains constant for 2.5 h after the transition to low light, after which time, it undergoes a sharp increase. Reinitiation of high-light conditions of growth 1 h subsequent to this increase in total cell number results in a cell population possessing a high degree of division and genomic synchrony. A characterization of this procedure, together with a demonstration of its utility for studies on intracytoplasmic membrane assembly, is presented.     

SYNCHRONOUS GROWTH OF CHLAMYDOMONAS REINHARDTII (CHLOROPHYCEAE): A REVIEW OF OPTIMAL CONDITIONS1

Chlamydomonas reinhardtii Dangeard was synchronized at optimal growth conditions under a 12:4 LD regime at 35 C and 20,000 lx with serial dilution to a standard starting cell density of (1.4 ± 0.2) × 10⁶ cells/ml. Synchronous growth and division were characterized by measuring cell number, cell volume and size distribution, dry weight, protein, carbon, nitrogen, chlorophyll, carotenoids, nucleic acids, nuclear and cytoplasmic division during the vegetative life cycle. The main properties of the present system are: Exponential growth with high productivity, high degrees of synchrony and reproducibility during repeated life cycles. The degree of synchrony of this light-dark synchronization system was evaluated and compared with those described in the literature using probit analysis of the time course of DNA synthesis, nuclear and cytoplasmic division and sporulation (increase in cell number). The results showed that the degree of synchrony is highest for cells grown under optimal conditions.     

State-vector models of the cell cycle 1. Parametrization and fits to labeled mitoses data

In this paper we study the Hahn model of the cell cycle from the point of view that a cell population's age distribution is more relevant to labeled mitoses data than is the distribution of its transit times.Closed-form relationships are derived between the transition probabilities of the Hahn model and the transit time of the mean of a cohort of labeled cells (with the variance of their transit time through mitosis). Constraints result which define the acceptable values for the number of ages in the state vector and the length of the time step (rarely does the dimension of the state vector equal the number of time steps in the generation time).A generalization to distinct probabilities for G₁, S and G₂M is presented, and the automatic fitting of fraction-labeled mitoses (FLM) data is described. The doubling time of the population is used to define the daughter factor, via the largest eigenvalue of the state transition matrix. The performance of the generalized Hahn model is compared to that of other commonly used fitting methods using two sets of FLM data from the literature. The synthesis of continuous labeling curves is discussed as an independent check of the parametrization. Based on the stable age distribution resulting from fits to experimental FLM data, it is shown that a nonlinear relationship exists between biological age and time.     

On the distribution of state values of reproducing cells

Characterizing a cell state by measuring the degree of gene expression as well as its noise has gathered much attention. The distribution of such state values (e.g., abundances of some proteins) over cells has been measured, and is not only a result of intracellular process, but is also influenced by the growth in cell number that depends on the state. By incorporating the growth-death process into the standard Fokker-Planck equation, a nonlinear temporal evolution equation of distribution is derived and then solved by means of eigenfunction expansions. This general formalism is applied to the linear relaxation case. First, when the growth rate of a cell increases linearly with the state value x, the shift of the average x due to the growth effect is shown to be proportional to the variance of x and the relaxation time, similar to the biological fluctuation-response relationship. Second, when there is a threshold value of x for growth, the existence of a critical growth rate, represented again by the variance and the relaxation time, is demonstrated. The relevance of the results to the analysis of biological data on the distribution of cell states, as obtained for example by flow cytometry, is discussed.     

Potassium Uptake in Synchronous and Synchronized Cultures of Escherichia coli

Criteria are presented for distinguishing between synchronous and synchronized cultures (natural vs. forced synchrony) on the basis of characteristics of growth and division during a single generation. These criteria were applied in an examination of the uptake of potassium during the cell growth and division cycle in synchronous cultures and in a synchronized culture of Escherichia coli. In the synchronous cultures the uptake of ⁴²K doubled synchronously with cell number, corresponding to a constant rate of uptake per cell throughout the cell cycle. In the synchronized culture, uptake rates also remained constant during most of the cycle, but rates doubled abruptly well within the cycle. This constancy of ⁴²K uptake per cell supports an earlier interpretation for steady-state cultures that uptake is limited in each cell by a constant number of functional sites for binding, transport, or accumulation of compounds from the growth medium, and that the average number of such sites doubles late in each cell cycle. The abrupt doubling of the rate of uptake of potassium per cell in the synchronized culture appears because of partial uncoupling of cell division from activation or synthesis of these uptake sites.     

Measurements and models of synchronous growth of fission yeast induced by temperature oscillations

Pulsing of temperature in a fermentor at intervals coincident with cell generation time was used to induce synchrony in a population of the fission yeast Schizosaccharomyces pombe. Measurements of culture protein, RNA, and DNA during synchronous growth confirm continuous synthesis of protein and RNA and discontinuos synthesis of DNA as previously reported. Flow microfluorometry of populations at different times during the synchrony cycle was used to monitor the changes in single-cell protein. RNA, and DNA frequency functions. These measurements illustrate very clearly the degree of synchrony and patterns of macromolecular synthesis and also confirm previous estimates of the cellular protein contents characteristic of dividing cells. Additional insights into single-cell kinetics and division controls are provided by two-parameter flow microfluorometry measurements and by mathematical modeling of population dynamics. Such data are necessary foundations for robust population balance models of microbial processes.     

NUCLEAR SYNCHRONY IN VALONIA MACROPHYSA(CHLOROPHYTA): LIGHT MICROSCOPY AND FLOW CYTOMETRY1

The coenocytic alga Valonia macrophysa Kützing was selected for an investigation of nuclear synchrony in the order Siphonocladales. Light microscopy reveals that nuclear synchrony is evident as patches of nuclei dividing simultaneously. Flow cytometry was utilized for the first time with a macroalga for cell-cycle analysis. Results indicate that nuclei in the entire cell exhibit a high degree of synchrony throughout the cell cycle. Also it appears that cells within a clonal culture are synchronous with each other, in their progression through the cell cycle. The advantages of using flow cytometry for cell-cycle analysis of coenocytic algae include the rapid collection of quantitative data on relative DNA content for a large number of nuclei.     

A general method for modeling cell populations undergoing G1----G0 transitions during development.

The transition from the dividing state to a non-dividing, terminally differentiated state is common to the history of most populations of cells during development. Quantifying such transitions and events related to them is often difficult, even in those cases for which there is a good tissue culture model, because the process is asynchronous and occurs against a background of continued extensive growth. A general model for analyzing these complex population changes is presented here. In the absence of definitive data, the model provides projections of the possible range, under a given set of boundary values, for the rate of terminal differentiation, the overall growth rate, and the degree of cell death. On the other hand, given data on the rate of DNA accumulation, dividing cell fraction, and generation time, the model provides the effective partitioning coefficient between the dividing and non-dividing states averaged over the population, at a given time. These data also allow for an assessment of the degree of actual cell death against a background in which significant numbers of cells are withdrawing from the cell cycle. The types of data required with respect to the model's ability to resolve the nature of a G0 transition "window" within the cell cycle are also discussed.     

Set-back model of division-synchronization: optimal spacing of thermal shocks that accelerate cell cycling.

Monte Carlo simulations have been used to predict the dependence of synchrony on the timing of periodic thermal shocks that synchronize division by cell cycle set-backs. In many of the simulations each set-back augmented the subsequent rate of progression of individual cells through the division cycle. In this study a subtle error in previous synchronization simulations was corrected. The simulations show that whether or not set-backs affect subsequent cell-cycling rates the degree of synchrony attained is acutely dependent on the spacing of thermal shocks administered once per division. Set-back-dependent increases in division-cycling rates usually decrease the difference between maximum and minimum synchrony. According to the simulations the more cell cycle rates between shocks are augmented by set-back the shorter the optimum time span between shocks. Whether or not set-backs affect subsequent division-cycling rates the intershock time span providing maximum synchrony allows cell number to precisely double.     

Kinetic analysis of cell size and DNA content distributions during tumor cell proliferation: Ehrlich ascites tumor study.

In order to study the growth dynamics of proliferating and non-proliferating cells utilizing discrete-time state equations, the cell cycle was divided into a finite number of age compartments. In analysing tumor growth, the kinetic parameters associated with a retardation in the growth rate of tumors were characterized by computer simulation in which the simulated results of the growth curve, the growth fraction, and the mean generation time were adjusted to fit the experimental data. The cell age distibution during the period of growth was obtained and by a linear transformation of the state transition matrices, was employed to specify the cell size and DNA content distributions. In an application of the model, the time-course behavior of cell cycle parameters of Ehrlich ascites tumor is illustrated, and the parameters important for the transition of cells in the proliferating compartment to the non-proliferating compartment are discussed, particularly in relation to the G1-G0 and G2-G0 transitions of non-cycling cells as revealed by the variation of cell size distribution.     

Synchrony induced by double phosphate starvation in a suspension culture of Catharanthus roseus

A synchronous cell division system was established using the double phosphate starvation method, based on the observation that one of the limiting factors in the growth of a suspension culture of Catharanthus roseus (L.) G. Don cells in the medium of Murashige and Skoog was phosphate. In the system, an increase in cell number took place in a short period of only 4 h, while the cell number remained almost constant during other periods of the cell cycle. The synchrony of the culture was confirmed by changes in mitotic index, which increased sharply prior to the increase in cell number. The S phase was determined by measuring incorporation of [³H]-thymidine into the DNA fraction during the cell cycle and synchrony of DNA synthesis was verified likewise. Synchronization by phosphate starvation is discussed in relation to the function of phosphate as a nutrient. The synchronous system thus established will be useful in biochemical studies of the cell cycle in higher plants.     

Generation time statistics of Escherichia coli B measured by synchronous culture techniques.

Synchronous cultures of Escherichia coli B were produced under various environmental conditions. Analysis of the cell number data permitted the characterization of the generation time distribution for these organisms and the estimation of the mother-daughter generation time correlation coefficients. For all growth conditions, the distribution of generation times was found to be symmetrical with a coefficienoefficient was significantly negative at doubling times between 40 and 64 min. However, the results for a culture growing in succinate medium at 37 degrees C, which had a significantly greater generation time, yielded a correlation coefficient close to zero. Within the range of temperatures studied (26 to 37 degrees C), no significant effect on the correlation coefficient was observed.     

Comprehension of attachment and multiplication properties by observing individual cell behaviors in anchorage-dependent culture

The behavioral properties of cell attachment and division were characterized by direct observation of individual cells in the culture of murine fibroblasts. At the cell attachment stage in the culture for early 10 h, the extent of cell spreading, which was defined as a ratio of the projected area of each cell against its saturated value, had a relatively broad distribution at 0.25 h, and it shifted to a higher level with elapsed time up to 10 h with narrowing in the distribution. The critical value of the extent of cell spreading was determined to be 0.54 as a threshold at which a cell is assumed to complete its adhesion to culture surface. The ratio of the number of cells with the extent of cell spreading over 0.54 against the total number of examined cells fairly followed the profile of cell adhesion which was obtained by measuring the number of adherent cells on culture surface.

At the cell growth stage in the culture for 20–64 h, doubling time of cell population increased gradually as the culture progressed toward confluence. Generation times (or cell-dividing spans) of individual cells, however, did not show a discriminating dependency on cell concentration and culture time. To clarify the influence of local congestion on the cell division, the generation time was formulated as a function of the number of contact cells around each target cell. Applying the cell placement growth model to estimating the extent of contact inhibition, the reciprocal value of doubling time could be correlated with the average of reciprocal generation times, implying that the doubling time on a cell-population basis is explained by considering the variation in dividing spans of individual cells affected by local contact environment.     

Synchronization of Drosophila cells in culture.

We synchronized Drosophila cell lines (Schneider's line 2 and Kc) by allowing the cells to enter the stationary phase of growth and then diluting them into fresh culture medium. The cells of both cell lines entered S phase, after an 8- to 14-hr delay, in a state of partial synchrony; 60 to 80% of the cell population accumulated in S phase. Measurements of the cell cycle phases of Schneider's line 2 cells (S = 14 to 16 hr; G2 = 6 to 8 hr; M = 0.4 hr) were similar to those of Kc cells.     

Sloppy size control of the cell division cycle

In an asynchronous, exponentially proliferating cell culture there is a great deal of variability among individual cells in size at birth, size at division and generation time (= age at division). To account for this variability we assume that individual cells grow according to some given growth law and that, after reaching a minimum size, they divide with a certain probability (per unit time) which increases with increasing cell size. This model is called sloppy size control because cell division is assumed to be a random process with size-dependent probability. We derive general equations for the distribution of cell size at division, the distribution of generation time, and the correlations between generation times of closely related cells. Our theoretical results are compared in detail with experimental results (obtained by Miyata and coworkers) for cell division in fission yeast, Schizosaccharomyces pombe. The agreement between theory and experiment is superior to that found for any other simple models of the coordination of cell growth and division.     

Synchronization of division in vitamin B12-starved Euglena gracilis.

Vitamin B12 deficiency arrests cell division in Euglena gracilis. B12 starvation for short periods made it possible to induce synchronous growth by addition of the vitamin. Culture conditions were established to optimize replenishment synchrony. The DNA content of E. gracilis in steady state culture and vitamin B12 deficiency culture was measured by flow cytofluorometry and was consistent with colorimetric determinations. The cell volume and DNA distributions of E. gracilis in synchronous culture were analyzed and the sequential changes during the division cycle were computed. Synchronous culture permits more definitive studies of shifts in cell volume and DNA distributions, in which the biochemical events required for cell division are presumably synchronized.     

Surface-limited growth: a model for the synchronization of a growing bacterial culture through periodic starvation

This article analyses the Surface-Limited Growth Model put forward to explain the very tight synchrony, over more than ten division cycles, obtained experimentally by subjecting a growing bacterial culture to alternating periods of starvation and dilution, using inorganic phosphate as the limiting substrate. The Model states that when an essential nutrient is in limited supply, the rate of growth of an individual cell will be proportional to its surface area (and the current concentration of the limiting substance) rather than to its volume. This decrease in dimensionality from volume to surface is expected to favor the smaller cells and so result ultimately in a narrower size distribution. The Surface-Limited Growth Model deals with cell growth under unusual nutritional conditions, and its predictions depend on how the cell replication cycle is assumed to behave under these same circumstances. Two alternatives are considered: the volume at which cells divide is the same during the starvation phase as during steady-state exponential growth, and the cells adjust immediately to the changing growth rate. In the latter case, we have tested both C + D constant with time and C + D variable (where C + D is the time between initiation of chromosome replication and the corresponding cell division), the incremental value at any instant being computed separately for each individual cell from its current effective growth rate. The simulation results are of two sorts depending on the auxiliary assumptions used. Either the dilution-starvation cycles have no effect whatsoever on the cell volume distribution, or the width of the distribution decreases gradually with time, approaching zero slowly and asymptotically, but the mean cell volume decreases as well--directly contradicting experimental observations. We conclude that the Surface-Limited Growth Model is incapable of explaining the synchronization of cells by periodic starvation of a growing bacterial culture.     

Quantification of cell size distribution as applied to the growth of Corynebacterium glutamicum

It is known that the cell size is related to the physiological state of a cell. Therefore, cell size distribution directly reflects the average physiological properties of the cell culture. Cell size distribution can be enumerated by image analysis, flow cytometry and coulter counter. In this study, image analysis was used to characterize the cell size distribution during the growth of Corynebacterium glutamicum and was further analyzed by a distribution function. The parameters of the distribution function indicate the mean value and spread of the distribution. Analysis demonstrated that the maximum specific growth rate was higher (0.67h(-1)) for the growth obtained through serial dilution of seed as compared to growth from a normal seed culture (0.53h(-1)). This was due to a greater percentage of the cell population being in the state of division for the growth through serial dilution in the mid-log phase. The measurement of the cell size distribution demonstrated that the average cell size decreased during the course of growth. The distribution function was also used to enumerate the average specific growth rate of both the conditions of the culture. The demonstrated methodology can be used to predict an average growth property of a cell culture.     

Perception of timbral analogies.

Recent studies have investigated the structure of perceptual relations among musical instrument timbres by multidimensional scaling (MDS) techniques. These studies have employed both acoustically produced tones and digitally synthesized imitations and hybrids of acoustic instrument tones. The analyses of dissimilarity ratings for all pairs of a set of tones are usually represented as geometrical structures in a two- or three-dimensional Euclidean space in which the shared 'perceptual' axes are shown to have a qualitative correspondence to acoustic properties such as spectral energy distribution, onset characteristics and degree of change in spectral distribution over the duration of the tone. The present study took as a point of departure a MDS analysis for complex, synthetic tones with the aim of testing whether musician and non-musician listeners used the relations defined by the perceptual space to perform an analogies task of the sort: timbre A is to timbre B as timbre C is to which of two possible timbres, D or D'? A parallelogram model was used to select the D timbres: if the relation between A and B is represented as a vector with both magnitude and direction components, then the appropriate D should form a vector with C having similar magnitude and direction in the timbre space. Aside from conceptual difficulties with the task for both non-musicians and composers, choices for both groups provide support for the parallelogram model indicating a capacity in listeners to perceive abstract relations among the timbres of complex sounds without specific training in such a task.     

Loss and stabilization of amplified dihydrofolate reductase genes in mouse sarcoma S-180 cell lines.

We studied the loss and stabilization of dihydrofolate reductase genes in clones of a methotrexate-resistant murine S-180 cell line. These cells contained multiple copies of the dihydrofolate reductase gene which were associated with double minute chromosomes. The growth rate of these cells in the absence of methotrexate was inversely related to the degree of gene amplification (number of double minute chromosomes). Cells could both gain and lose genes as a result of an unequal distribution of double minute chromosomes into daughter cells at mitosis. The loss of amplified dihydrofolate reductase genes during growth in the absence of methotrexate resulted from the continual generation of cells containing lower numbers of double minute chromosomes. Because of the growth advantage of these cells, they became dominant in the population. We also studied an unstably resistant S-180 cell line (clone) that, after 3 years of continuous growth in methotrexate, generated cells containing stably amplified dihydrofolate reductase genes. These genes were present on one or more chromosomes, and they were retained in a stable state.