The basis of synchronization by repetitive dilution of a growing culture

Biomass growth rate during the prokaryote cell cycle

The rate of biomass growth throughout the cell cycle of prokaryotes is important in the study of global regulation. Two limiting cases have generally been considered: the exponential model and the linear model. The exponential model is a logical expectation because protein, the main component of biomass of a bacterial cell, increases continuously during the cell cycle and therefore the means for synthesis of other cell components and metabolites also increases. In addition, during the cell cycle, ribosomes, the means of production of proteins, increase monotonically. As a consequence, the increase of all should be autocatalytic and the content of cell substance should be an exponential function of time. Two cellular components would not be expected to increase exponentially: the DNA and the cell envelope. The former because of the intermittent synthesis of the chromosome, and the latter because of changes in the surface-to-volume ratio with growth and division. In contrast to the exponential model, the linear model of Kubitschek postulates that the cell only increases its membrane transport capability over a brief period during the cell cycle, and, thus limited by transport, all cell components can increase only at a constant linear rate during most of the cell cycle. Other proposed models are intermediate and assume that the growth rate of the cell depends on some cell cycle event, such as the initiation of chromosome replication. The models have relevance to prokaryotes undergoing balanced growth; they may not be relevant to eukaryotic microbes or to eukaryotic cells in tissue culture that have endogenous rhythms or are controlled by protein growth factors. Logically, the models could possibly apply to a free-living cell that does not respond to environmental cues. Even under rigidly constant conditions, however, cells may try to respond to a stimulus that was periodic or regulatory under natural conditions, but is present at a constant level under the experimental culture condition. There are four classes of experiments that have been used to measure the accumulation of dry biomass or its components during the cell cycle of a bacterium, as typified by Escherichia coli. For the first class of experiments, the dimensions of living cells are measured under the microscope. So far, the experiments have been limited by the resolving power of the phase microscope, but adequate resolution should be possible with the confocal scanning light microscope or various video computer systems. Such experiments are called integral because augmentation of cell constituents is followed. The second class involves pulse-chase labeling of cells and then their separation into different phases of the cycle or age groups and measurement of the radioactivity per cell in the fractions. Such experiments are called differential in that the rate is measured directly instead of being deduced by comparing the total size at different times.(ABSTRACT TRUNCATED AT 400 WORDS)

The growth kinetics of B. subtilis

There has been considerable discussion by Kubitschek and Cooper concerning the growth rate of cells of E. coli throughout the cell cycle. Consequently, it is relevant to test Kubitschek's linear model against the exponential model espoused by Cooper (and many others) with another organism and another technique. Burdett et al. measured, by electron microscopy and computer analysis of the microphotographs, the distribution of lengths of a population of cells of Bacillus subtilis grown in 0.4% succinate in a minimal medium. The data were fitted to the extended Collins-Richmond method of Kirkwood & Burdett which subdivided the cell cycle into several phases. I have taken their results and compared them with the linear and exponential growth models for the entire cell cycle after applying correction to the data for the shape of completed and forming poles; i.e., to put the data on a cell-volume basis instead of a cell-length basis. Most of the correction involves no arbitrary assumptions. The conclusion is that global volume growth rate is nearly proportional to cell volume; i.e. growth of Bacillus subtilis is nearly exponential for almost every cell in the growing culture.

State-structure models—A base for efficient control of fermentation processes

The imbedding of state-structure models into the framework of structured segregated models is described. A special type of state-structure models based on delay-differential equations is considered. Some results regarding the description of unbalanced growth processes and the development of efficient periodic control strategies are presented.

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.