Biochemical Engineering Fundamentals Part 1 - Bailey J., Ollis D. 1989

Molecular Genetics and Regulatory Systems
Growth and Self-Reproduction of an Isolated Cell
The Eukaryotic Cell Cycle

First of all, we should recall that a typical Introduction/5.html">Eukaryotic Cell does not actually exist in nature. At the same time, the model of such an imaginary cell is extremely useful when discussing features characteristic of most eukaryotes; it is precisely in this sense that we will use METABOLISM/2.html">THE CONCEPT OF a typical eukaryote in this section.

Potential differences between various types of Eukaryotic Cells are easy to appreciate if we examine, for example, the increase in cell mass during The life cycle of mouse and amoeba cells (Fig. 6.33). While the dry mass of mouse cells increases linearly or exponentially over time, the growth rate of amoeba cells gradually decreases and becomes virtually zero at the moment of division. The second scenario is more typical of eukaryotes in general. Note also the time scale—the Cell Cycle of these eukaryotes lasts about a day. However, some eukaryotic organisms, such as Yeast, can divide approximately once an hour under optimal conditions.

Compared to prokaryotes, the eukaryotic cell cycle is characterized by a high degree of differentiation between its individual periods. A typical eukaryotic cell cycle is depicted in Fig. 6.34. It is subdivided into four periods: G₁, S, G₂, and M, with the relative durations of these periods indicated in the figure. Active synthesis of Proteins and RNA occurs during the G₁ period, while DNA is not synthesized. Chromosome Replication takes place in the subsequent S period. The function of the G₂ period is not yet fully understood. This period is followed by Cell Division (the M period). The complex, highly coordinated process of eukaryotic division is called mitosis. In mitosis, two sets of Chromosomes are separated and distributed to daughter cells. In slowly growing or non-growing cultures, cells enter a resting state designated by the symbol G₀.

Unlike the linear time dependence characteristic of prokaryotes, enzyme synthesis in eukaryotes almost invariably occurs periodically. At a certain point in The Cell cycle, a sharp increase in the concentration of a particular enzyme is observed. Available experimental data suggest that this phenomenon is driven by the sequential nature of DNA Transcription.

As an example illustrating The Structure of the eukaryotic CELL CYCLE AND asymmetric cell division, let us briefly consider the Life Cycle of the budding yeast S. cerevisiae. This microorganism is widely used in brewing, food production, and Genetic Engineering. As shown in Fig. 6.35, the daughter cell grows on the mother cell as a bud. Then, following division, the mother cell rapidly returns to the initial phase of the budding cycle, whereas the daughter cell—typically relatively small—must continue to grow for some time before reaching the state typical of the onset of the budding cycle (the "start").

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FIG. 6.34. Sequence of events in the life cycle of a typical eukaryotic cell.

FIG. 6.35. Cell cycle of the budding yeast S. cerevisiae.

The onset of the S period roughly coincides with the appearance of the bud. All non-budding cells are in the G₁ period. Turning to the DNA distribution in individual S. cerevisiae cells shown in Fig. 6.30, it is reasonable to assume that the first peak corresponds to cells with a single genome, i.e., cells in the G₁ period. The second peak corresponds to cells with two genomes, which may be in either the G₂ or M period. Mathematical analysis of such distributions makes it possible to rapidly determine the relative residence times of S. cerevisiae cells in the G₁, S, and G₂+M periods, thereby facilitating The Study of how genetic alterations and environment affect Cell cycle regulation.

In this section, we have reviewed some KEY FEATURES OF cell cycles. In essence, extremely limited data are currently available regarding them. As our Study of Cellular metabolism showed (Chap. 5), efficient nutrient utilization requires the cell to meticulously coordinate an immensely complex network of Chemical Reactions. While the biochemistry of these reactions is understood in considerable detail, we know almost nothing about how they proceed in vivo. Figure 6.36 presents fascinating data indicating that complex patterns govern the temporal distribution of individual interrelated reactions. Consequently, chemical reactions within the cell are localized not only spatially (for example, through Enzyme Immobilization on a membrane surface) but also temporally. All these complex effects compel us to exercise extreme caution when approaching the mathematical analysis of living cell growth kinetics.

With this, we conclude our Introduction to the biological sciences. Armed with the knowledge gained in this and previous chapters, we should be well-prepared to study living-cell process technology. The subsequent chapters will focus primarily on the analysis, modeling, and design of biological processes. Chapter 7 covers The kinetics of cell growth.

FIG. 6.36. Complex pattern of Changes in the relative content of free Amino Acids during the cell cycle in Chlorella pyrenoidosa. [Reprinted with permission from: Hare T. A., Schmidt R. R., Nitrogen metabolism During Synchronous Growth of Chlorella: II. Free-, Peptide-, and Protein- Amino Acid Distribution, J. Cell Physiol., 75, 73 (1970).]

Exercises

6.1. Mutation rate. Mutations give rise to new species, or mutants. Since DNA is merely a polymer molecule, it presumably undergoes chemical and physical changes during mutation in much the same way as the molecules of any other compound.

a) Based on the data in Fig. 6Q1.1,a, calculate the activation energy of the mutation, E_m, and the pre-exponential factor, k°_m, in the equation k_m = k°_mexp (—E_m/RT). Compare the calculated values with analogous parameters for simpler compounds undergoing chemical transformations. (These data can be found in any organic chemistry textbook.)

b) Radiation absorption obeys the Beer-Lambert law, according to which each component of the target absorbs the same fraction of the radiation incident upon it; consequently, I(x) = I₀e^-ax. Fig. 6Q1.1,b shows the linear dependence of the mutation rate on the radiation intensity I₀. Under what conditions could all cells receive the same radiation dose? Would a linear dependence of mutation rate on dose be expected if not all cells receive the same dose?

FIG. 6Q1.1. The mutation rate of E. coli increases with Temperature and ionizing radiation dose. a — Effect of temperature on the mutation rate of his^- (Histidine-non-synthesizing Bacteria) to his⁺ (histidine-synthesizing organisms); b — effect of X-ray dose on The conversion of met-2^- organisms (Methionine non-synthesizers) into met-2⁺ mutants (methionine synthesizers). (Reprinted from: Sager R., Ryon F. Cell Heredity: An Analysis of the Mechanisms of Hereditary at THE CELLULAR LEVEL, John Wiley and Sons, Inc., New York, 1961.)

c) The data presented in Fig. 6Q1.1 refer to E. coli populations mutating from his^- (unable to synthesize histidine) to his⁺ (Fig. 6Q1.1,a) and from met-2^- (unable to synthesize methionine) to met-2⁺. If any DNA changes occur with the same probability as in these cases, What is the overall mutation rate of E. coli DNA? Justify your answer. Is phenotypic expression characteristic of these mutations?

6.2. Repair and Thermodynamics of mutations. If A large number of organisms is involved in the process, mutation kinetics can be described using the same parameters as those employed in conventional chemical reaction kinetics.

a) In a bacterial population with a cell concentration of 3∙10⁷ mL^-1 (culture volume 1000 L), mutation of the Gene to gene g₂ occurs at a frequency of 10^-8 per cell division, while the reverse mutation of g₂ to g₁ occurs at a frequency of 10^-6 per cell division. Calculate the "equilibrium" concentrations of each mutant.

b) Since cells capable of enzymatically repairing DNA damage possess the relevant specific enzyme, it can be assumed that an equilibrium between normal and damaged DNA also exists in such cases:

Suppose that DNA is also damaged by ultraviolet radiation, and the rate constant of this reaction is k¹. Show that in this case, the equilibrium population of damaged DNA increases from k₁/(k₁+k_-1) to (k¹+k₁) / (k₁+k¹+k_-1).

(c) Show that after turning off the ultraviolet radiation source (assuming that K_m of the repair enzyme significantly exceeds the total DNA concentration), the average concentration of damaged DNA returns to its initial level at a rate proportional to the difference in damaged DNA concentrations in the absence and presence of ultraviolet radiation.

6.3. Simplified model of repressor kinetics. J. M. Smith proposed a simplified kinetic regulation network scheme, shown in Fig. 6U3.1.

FIG. 6U3.1. Simplified model of the repressor action mechanism. (Reprinted from: Smith J. M., Mathematical Ideas in Biology, fig. 30, Cambridge University Press, London, 1971.)

(a) Assuming that the concentrations of P and the gene are stationary, develop a kinetic model describing (after solving the corresponding equations) the time dependence of the concentrations of RNA, M, and Z. Assume that The rate of RNA loss is proportional to its concentration. Try to approach the complete solution for the Transition State as closely as possible.

(b) Based on the material of this and previous chapters, indicate whether diffusion should be taken into account in this case, and note the shortcomings of the model.

6.4. Mutation and The Genetic Code. The Amino Acid Substitutions listed below were found in mutant proteins. Explain which codons underwent changes.

6.5. Organization of intracellular transformations; multienzyme systems. Many reactions in the cell proceed via the conversion of S₁ into S₃ through the intermediate compound S₂, with the equilibrium concentration of S₂ being small compared to S₁ and S₃:

If S3 participates in the subsequent enzyme-catalyzed reaction, the reversibility of the second reaction can be neglected.

(a) Assuming that for each enzyme s_i ≪ K_i and that S₁ and S₂, E₁ and E₂ are distributed uniformly throughout the volume, show that the steady-state reaction rate is determined by the following expression:

(b) Show that if E₁ is immobilized on one side of a permeable plate and E₂ on the other, the steady-state reaction rate will obey the equation

Show also that this value is less than s_{2 e}qullD/L, where L is the distance between the plate surfaces, and s_2,equll is the concentration of S₂ in equilibrium with S₁ at a concentration of the latter equal to s₁.

(c) Typically, the oxygen consumption rate is 10^-8 mol/(s·cm³). Assuming that the rates of each intracellular metabolism stage are approximately equal, calculate the maximum distance between E₁ and E₂ at which the specified oxygen consumption rate would be possible, if the value of s_2,equll ranges from 10^-4 to 10^-12 mol/cm³. [Weisz P. B., Enzymatic Reaction Sequences and Cytological Dimensions, Nature, 195, 772 (1962).]

6.6. Organization of intracellular transformations; synthesis and utilization of

ATP. In an intact cell, there are localized centers (Organelles) designed to supply the entire cell with specific compounds. In this regard, It is interesting to consider bull spermatozoa, in which ATP is synthesized only in the midpiece, while the flagellum consumes a significant portion of ATP for locomotion.

(a) Assuming that the ATP utilization reaction at any point of the flagellum is of zero order and that ATP is distributed uniformly in the midpiece at a concentration c₀, show that The change in ATP concentration in the flagellum can be described by the equation c = 1—z(1 + ^—2/2) + ^—2z²/2, where — is the Thiele modulus of the flagellum, z is a dimensionless parameter characterizing the distance from the flagellum, and c is a dimensionless parameter characterizing the concentration.

(b) Each moving spermatozoon consumes oxygen for motility at a rate of 3.7–5.0·10^-18 mol/s. Using the additional data provided below, calculate the minimum ATP content in a spermatozoon required to maintain its transport into the flagellum by diffusion.

Diffusion coefficient of ATP (determined taking into account the Water content

in the flagellum and tortuosity) 3.6·10^-6 cm²/s

Volume of the midpiece 1.3·10^-12 cm³

Flagellum length: 5∙10^-3 cm

Cross-sectional area of the flagellum (excluding the membrane and fibrils)

ATP yield per mole of O₂ consumed: 6%

c) It was found that a single spermatozoon contains, on average, 200∙10^-18 mol of ATP. It has been estimated that between one-third and one-half of all ATP is consumed by the cell's Mitochondria. Evaluate the results of your calculations from part (b) of this problem in terms of whether it is necessary (or unnecessary) to account for transport mechanisms other than passive diffusion to ensure the appropriate distribution of ATP from the mitochondria localized in the midpiece. [Nevo A. C., Rikmenspoel R., Diffusion of ATP in Sperm Flagella, J. Theoret. Biol., 26, 11 (1970).]

6.7. Target theory. To explain the loss of activity in spores, Viruses, or cells from a molecular-biological perspective, a hypothesis was proposed stating that "in every cell and in every Organism there exists A number of 'targets', and the change in activity is the result of random damage to these targets." (Smith J. M., Mathematical Ideas in Biology, p. 87, Cambridge University Press, London, 1971.) Let us consider the following scenario.

Suppose that a cell containing N targets is irradiated with a dose of K particles. Let the probability of a given target being hit by a given particle be p; clearly, the value of p is very small.

The probability that a given target will not be hit by a given particle is 1 - p.

From this, it follows that the probability of a given target escaping hits from all K particles is

(1 — р)^K ≈ е^-Кр

a) Given that for large K and small p, Kp ≈ (K-1)p ≈ (K-2)p, prove the validity of this approximation for this typical case (large K, small p).

б) Show that if the relative number of damaged cells (where damage implies that a cell has been hit once or more) is small, then the "relative number of damaged cells is equal to NKp, i.e., proportional to the dose." Conversely, if few undamaged cells remain, the fraction s of the latter is given by ln s = -NKp; confirm the validity of this equation.

в) If a cell is damaged only after multiple hits, a similar approach can be used to analyze the situation. "A bacterium is infected by identical Bacteriophages; the number of bacteriophages infecting a single bacterium is r, and each bacteriophage contains N essential genes. A viable bacteriophage can be formed via recombination provided that in each of the N loci, one gene remains undamaged" (see reference above). Show that if the "probability of each target remaining undamaged is small," then ln s = N ln r - NpK (here, targets refer to the number of bacteriophage copies r within the cell at the time of irradiation).

г) Show that the results of the previous exercise 6(c) are consistent with the data plotted in Fig. 6Y7.1,a; estimate all possible parameters. What phenomena might account for the system behavior graphically represented in Fig. 6Y7.1,b?

FIG. 6Y7.1. Experimental dependence of the infection probability S of bacteria by bacteriophage T7 (a) and bacteriophage T2 (b) on the radiation dose at various durations of the period between infection and irradiation. [Based on: Benzer S., Resistance to Ultraviolet Light as an Index to the Reproduction of Bacteriophage, J. Bacteriol., 63, 59 (1952).]

6.8. Fate of a mutant gene in a growing population. Mutations occur frequently in populations. The viability of mutant organisms is remarkably high, whereas the stability of mutant genes is low. For a sexually reproducing population of N diploid organisms at the moment a mutant gene (allele) appears, the mutation frequency is 1/2N. The total number of organisms in the population, N, exceeds the number of breeding organisms, N_e.

a) For a selectively neutral mutation (where the mutant has neither advantages nor disadvantages compared to the parental strain), the average number of generations preceding the loss of the mutant gene is given by t_l = 2(N_e/N)ln 2N, and the average number of generations preceding gene fixation (i.e., the state where the gene frequency reaches 1.0) is t_f = 4N_e. Here, t_l and t_f are averaged only over the parameters of gene loss and fixation, respectively. Assuming N_e/N = 0.5 and a doubling time of 1 h,

calculate t_l and t_f for a population with a concentration of 10⁷ cells per mL in a culture volume of 1 L.

б) The spread of t_f values is small, whereas that of t_l values is large relative to their mean values; you can confirm this fact by calculation using the following expressions:

в) The probability of mutation fixation in a population can be estimated using the equation

where s₁ is the selective advantage of the mutant gene over the wild-type gene. Show that under typical microbial population conditions, u = 2s₁N_e/N. Consequently, even if the selective advantage is large (s₁ = 1% = 10^-2), the probability that the mutant will eventually become dominant in the population is low (Kimura M., Ohta T., Theoretical Aspects of Population Genetics, Princeton University Press, Princeton, N.J., 1971).

6.9. Natural Selection. The relative fitness w of a given genotype x can be defined as The ratio of the survival rate of genotype x to the survival rate of the average population genotype. (Survival rate is understood as the ratio of the number of breeding organisms to the number of offspring born in each generation.) Assume that the fitness of genotype x depends linearly on the mean phenotypic expression such that where a is a measure of the intensity of The Effect of the difference on w(x) (a > 0). By definition, g(x) is the normalized distribution of the initial genotype [ʃ g(x)dx = 1.0]. After one generation, the distribution changes to: g'(x) = w(x)g(x).

a) Express in terms of the mean value and the genetic variance σ². [Recall that the mean is and the variance is

b) Show that in a single generation the change in is proportional to 0%, i.e., "the rate of evolution is proportional to the genetic variance of the population" (Fundamental Theorem of Natural Selection; see Wilson, E. O., Bossert, W. H., Primer of Population Biology, pp. 79–83, Sinauer Associates, Stamford, Conn., 1971).

c) Wilson and Bossert assert that the magnitude of is "in some way proportional to the genotype variance," even when w depends nonlinearly on x. Select a series of reasonable dependencies w = f(x) and demonstrate the validity (or incorrectness) of this statement.

6.10. Multiple operator sites; Regulation of the λP_R promoter. The repressor protein of phage λP_R can bind to three distinct operator sites designated as O_R1, O_R2, and O_R3. As shown in Fig. 6U10.1, repressor binding to any of these sites (except O_R3) blocks the P_R promoter. Assume that the repressor-operator binding reaction is at equilibrium and that the equilibrium constants for binding to the three sites are K₁, K₂, and K₃, respectively.

a) Derive a general equation expressing the fraction of P_R promoters available for RNA polymerase binding in terms of the equilibrium constants, the total amount of repressor protein, and the P_RO_R sequences in the cell.

b) Estimate the fraction of available promoters in a cell containing 25 P_RO_R sequences and 70 repressor molecules. Assume K₁, K₂, and K₃ to be 125∙10⁸, 1.25∙10⁸, and 1∙10⁹ M^-1, respectively. What is the physical significance of your result?

FIG. 6U10.1. Relative positions of the P_R promoter and the three operators O_R1, O_R2, and O_R3 in phage λ.

c) The solutions to the preceding exercises were based on classical thermodynamics. Statistical thermodynamics allows a more precise estimation of the interactions among a small number of different molecules within a cell population. Solve problems 6.10a and 6.10b in light of the theory presented by Berg, O. G., and Blomberg, C., Mass Action Relations in vivo with Application to the Lac Operon; J. Theoret. Biol., 67, 523 (1977).

6.11. DNA replication rates in PROKARYOTES AND EUKARYOTES. a) Replication requires unwinding of the DNA double helix. Assuming There are two unwinding origins (two replication forks), determine the rotational speed at the unwinding origins (in revolutions per minute) for E. coli DNA if the entire chromosome is synthesized in 41 min. b) The S phase of a mammalian cell line with a genome containing 1.1 m of double-stranded DNA lasts 4.8 h. If the DNA Synthesis rate in these cells is identical to that of E. coli, how many replication forks must function simultaneously?

6.12. Recombination of DNA fragments. Two double-stranded DNA molecules, 1 and 2, are cleaved by the restriction endonuclease EcoRI; one strand of each DNA molecule is depicted below. The resulting fragments are mixed, recombined, and treated with DNA ligase, which catalyzes covalent bond formation. List all possible reaction products.

6.13. Restriction maps. The relative positions of restriction sites within DNA fragments are determined by partial or complete Cleavage with restriction Enzymes followed by molecular mass estimation of the resulting fragments via gel Electrophoresis. A HindIII DNA fragment containing 3,000 Base Pairs is treated with EcoRI, BglII, and a mixture of both enzymes. Gel electrophoresis reveals that this yields two fragments of 1,400 and 1,600 base pairs; three fragments of 400, 900, and 1,700 base pairs; and four fragments of 400, 500, 900, and 1,200 base pairs, respectively. Determine the restriction map for HindIII.

6.14. Primer for interferon cDNA. To maximize the probability of cloning the cDNA encoding the Amino Acid Sequence of fibroblast interferon (IFN-β), it is useful to employ an oligodeoxyribonucleotide primer complementary to the 5'-terminal coding sequence of the mRNA. The N-terminal sequence of the protein is Met—Ser—Tyr—Asn. List all possible corresponding mRNA nucleotide sequences and the set of corresponding primers. Pay close attention to identifying the 3' and 5' ends of each primer.

6.15. Intracellular protein production by recombinant cells. Estimating the bioreactor capacity required to produce a specific amount of a cloned gene's expression product accumulating within cells is straightforward. Suppose a recombinant E. coli strain accumulates a foreign protein—the product of a plasmid Gene Expression—at concentrations up to 30% of the total cellular protein. If the maximum allowable cell density is 10⁹ cells/mL, how much protein can be harvested from 1 L of bioreactor volume?

References

Each of the works cited in Chapters 1 and 2 contains valuable information directly relevant to various topics in this chapter. In addition, the following literature is recommended:

1. Stent, G. S., and Calendar, R., Molecular Genetics. An excellent historical Description of the fundamental concepts of molecular genetics, with special emphasis on the experimental validation of currently accepted hypotheses.

2. Lewin, B., Genes, 2nd ed., John Wiley and Sons, New York, 1985. A well-written, highly detailed, and comprehensive Overview of the nature, replication, and Functions of genes.

3. Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., and Watson, J. D., Molecular Biology of the Cell. Cell biology presented from a molecular perspective, highlighting it as one of the most exciting Branches of the biological sciences.

An introduction to the problems of mutagenesis and applied genetics (from the perspective of the microbiological industry) is provided in the following literature:

4. Elander, R. P., Applications of Microbial Genetics to Industrial Fermentation, in Fermentation Advances, Perlman, D. (ed.), Academic Press, Inc., New York, 1969.

5. Demain, A. L., Overproduction of Microbial Metabolites and Enzymes Due to Alteration of Regulation, Adv. Biochem. Eng., 1, 113 (1971).

6. Dobrzanski, W. T., Microbial Genetics in Pharmacy, Chem. Br., 10, 386 (1974).

7. Biology of Industrial Microorganisms, Demain, A. L., and Solomon, N. A. (eds.), Benjamin/Cummings Publishing Co., Menlo Park, CA, 1984. This recently published collection summarizes data on the metabolism, regulatory systems, and genetics of microorganisms currently used in industry. One of the very few books that provides a detailed Treatment of the microbiology of Molds and Streptomyces.

The following articles discuss hybridomas and Cell Fusion techniques applied to the synthesis of Monoclonal Antibodies:

8. Peberdy J. F., Protoplast Fusion — A Tool for Genetic Manipulation and Breeding in Industrial Microorganisms, Enzyme and Microbial Tech., 2, 25 (1980).

9. Milstein C., Monoclonal Antibodies, Scientific American, 243, 66 (1980).

10. Boyd J. E., James K., McClelland D. B. L., Human Monoclonal Antibodies — Production and Potential, Trends in Biotech., 2, 70 (1984).

Selected Examples of the Practical Applications OF microbial genetics are discussed in the following papers from the collection Fermentation Advances, Perlman D. (ed.), Academic Press, Inc., New York, 1969:

11. Pardee A. B., Enzyme Production by Bacteria, p. 3.

12. Ueda К., Some Fundamental Problems of Continuous L-Glutamic Acid Fermentations, p. 43.

13. Furuya A., Misawa M., Nara T., Abe S., Kinoshita S., Metabolic Controls of Accumulations of Amino Acids and NUCLEOTIDES, p. 177.

Due to rapid scientific and technological advances in recent years, an increasing number of publications have been devoted to Recombinant DNA technology.

In the list below, they are arranged in order of increasing complexity, ranging from introductory, general reviews to detailed descriptions of Methods and research results.

14. Cohen S. N., The Manipulation of Genes, Scientific American, 233, 24 (1975).

15. Gilbert W., Villa-Komaroff L., Useful Proteins from Recombinant Bacteria, Scientific American, 242, 74 (1980).

16. Wetzel R., Applications of Recombinant DNA Technology, American Scientist, 68, 664 (1980).

17. Watson J. D., Tooze J., Kurtz D. T., Recombinant DNA: A Short Course, W. H. Freeman and Co., New York, 1983.

18. Glover D. M., Genetic Engineering: Cloning DNA, Chapman and Hall, New York, 1980.

19. Old R. W., Primrose S. B., Principles of Gene Manipulation, 2nd ed., University of California Press, Berkeley, 1981.

20. Rodriguez R. L., Tait R. C., Recombinant DNA Techniques: An Introduction, Addison-Wesley Publishing Co., Reading, Massachusetts, 1983.

21. Recombinant DNA, Methods in Enzymology, vols. 68 (1979), 100, 101 (1983), Academic Press, New York.

22. Sanger F., Nicklen S., Coulson A. R., DNA Sequencing with Chain-Terminating Inhibitors, Proc. Natl. Acad. Sci. USA, 74, 5463 (1977).

23. Gray P. W. et al., Expression of Human Immune Interferon cDNA in E. coli and Monkey Cells, Nature, 295, 503 (1982).

Scientific and public discussions concerning recombinant DNA technology are covered in the book:

24. Watson J. D., Tooze J., The DNA Story, W. H. Freeman and Co., San Francisco, 1981.

Works concerning the study of cell cycles in general and those of E. coli

and S. cerevisiae in particular are reviewed in the following literature:

25. Mitchison J. М., The Biology of the Cell Cycle, Cambridge University Press, London, 1971.

26. Ingraham J. L., Maaløe O., Neidhardt F. C., Growth of the Bacterial Cell, Sinauer Associates, Inc., Sunderland, Massachusetts, 1983.

27. Hartwell L. H., Saccharomyces cerevisiae Cell Cycle, Bad. Rev., 38, 164 (1974).

28. Lievense J. C., Lim H. C., The Growth and Dynamics of Saccharomyces cerevisiae, in Annual Reports on Fermentation Processes, vol. 5, p. 211, Tsao G. T. (ed.), Academic Press, New York, 1982.