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**GROWTH OF CULTURE Population growth**

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**Growth curve of culture**

Semi-log plot Growth phases: lag, exponential, and stationary Real lag phase: spores germination, physiological readjustment Apparent lag phase: turbidometric measurement of growth when inoculum consists of living and dead cells

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**Unrestricted growth Culture grow at a characteristic rate**

No limiting concentration of nutrients and no effective level of toxic compounds Balanced growth Exponential phase

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Balanced growth All cell constituents begin to increase by the same proportion over the same interval The mean cell size remain constant Balanced growth refers to the average behavior of cells in a population, not to that of individual cells (bacteria do not usually grow and divide synchronously) Usually unbalanced for most bacteria under natural conditions

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**Practical advantages in working with balanced growth cultures**

It can be approximated for a considerable time in the laboratory Samples of different time are identical except cell number The relative rate of synthesis of any cellular component becomes known just by measuring the growth rate The most reproducible physiological state of a bacterial culture

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Growth equations (1) dx / dt = μx x: cell number or some specific cellular component per unit volume, μ: instantaneous growth-rate constant or specific growth-rate constant. lnx2 – lnx1 = μ(t2 – t1) (1/ x) dx =μdt, ∫(1/ x) dx =∫μdt then, lnx =μt μ = (logx2 – logx1) / (t2 – t1), lnx = logex = logx / loge = logx / log = logx / = logx

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Growth equations (2) tg(td) = ln2 /μ = /μ tg: generation time or doubling time κ = 1 / tg κ: the growth-rate constant for a batch culture (doublings per hour), μ = 0.693κ

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**Measurement of growth (1)**

Cell mass: Dry weight / Turbidity Light scattering: Nephelometer & Spectrophotometer Lambert-Beer’s law: Absorbance (A) = log(I0/I) = εlc Optical density (OD) Relationship, Fig. 1

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**Measurement of growth (2)**

Cell number Viable count: (1)operational errors: bacterial clumps, true sampling time etc (2)sampling errors: (X±√X) Total count: (1)Bacterial counting chamber / Hemocytometer (2)Electronic counting / Flow cytometer (measure the size distribution and the number) Cellular constituent: Protein or ATP …

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Growth yield Yield coefficient: unitless parameter, dry weight produced per unit weight of limiting nutrient Yglucose: usually about 0.5 for aerobes / may be 100 times greater for a required amino acid or vitamin Used in bioassay of vitamin or biosynthetic intermediates Measurement of YATP is restricted to culture that generate ATP by fermentation

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**Specific oxygen consumption (1)**

Andersen and von Meyenburg (1980) found that the specific oxygen consumption QO2 (mmole h-1 g-1 dry weight) in cultures of E. coli does not vary significantly with the growth rate. QO2 is about 20 in cultures grown in a mineral salts medium with various carbon sources. (μ is 0.3 in acetate, 0.9 in glucose, 1.2 in glucose and casein hydrolysate)

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**Specific oxygen consumption (2)**

If ATP generated per mole of oxygen consumed does not vary with the growth rate, then the total energy available for doubling the cell mass decreases in proportion to the growth rate. How can we interpret the finding? At low growth rates, the cells must make their own building blocks, a demand requiring extra energy.

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**Effect of concentration of nutrients on the growth rate**

Monod equation: μ = μmaxc / (Ks + c) Michaelis-Menten equation: V = VmaxS / (Km + S) Double reciprocal plot (1/μ vs. 1/c)

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**Continuous culture Turbidostat (growth rate is determined internally)**

Chemostat (growth rate is determined externally, vigorous mixing) Useful in studies of bacterial physiology, mutagenesis and evolution

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**Equations in chemostat culture**

Mean resident time, MRT = V / f Dilution rate, D = f / V μ= D (dx / dt =μx – xf / V =μx – Dx = 0 in the chemostat) c = KsD / (μmax – D) (solving Monod equation for c gives the relationship between nutrient concentration in the growth vessel and the dilution rate) Y = x / (cr – c), cr: nutrient conc. in the reservoir dc / dt = Dcr – Dc, dc / dt = (dx / dt) (dc / dx), dx / dt = μx, dc / dx = 1/Y, μx / Y = Dcr – Dc, D = μ

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**Lower limit to the dilution rate in chemostat culture**

If the limiting nutrient is the source of energy, growth ceases at low dilutions and the cells are washed out. If the limiting nutrient is an amino acid or other precursor in macromolecular synthesis, chemostat can be operated at dilution rates leading to a mean residence time of several days or weeks

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Maintenance energy A certain amount of energy used for essential processes other than those leading to increase in mass: (1)the maintenance of a potential across the cytoplasmic membrane, (2)the transport of certain solutes, (3)the constant hydrolysis and resynthesis of certain macromolecules – termed turnover, (4)cell motility, etc. dx /dt = Y‧dc / dt - ax a: the specific maintenance rate, hr-1 for E. coli growing at 37℃ Maintenance coefficient m = a / Yg

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Study questions Calculate the doubling time of a culture if it contains 103 cells at t1 and 108 cells 6 hours later Ans: μ = (8-3) x / 6 = 1.92 hr-1, tg = / 1.92 = 0.36 hr = 21.7 min How to increase the steady-state cell density in the growth vessel of a glucose-limited chemostat? Ans: increase cr or decreas D

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Study questions A technician has isolated a mutant of E. coli that has lost a certain function. When mixed with its parent and grown at low dilution in a glucose-limited chemostat, the mutant persists and the parent disappears. How could this phenomenon be explained? Ans: the mutant blocked a function that contributed to maintenance energy (lowered maintenance energy requirement) Show the profiles of dilution rate vs. cell concentration in a chemostat using glucose, phosphate or ammonium as limiting nutrient.

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