Rate laws cell growth

Zeng AP, Deckwer WD, Hu WS (1998), Determinants and rate laws of growth and death of hybridoma cells in continuous culture, Biotechnol. Bioeng. 57 642-654. 

Chlorophyll a (Chi a) functions as the primary light harvesting pigment in marine oxygenic phototrophs. Even though the C Chl a ratio of photoautotrophic cells varies considerably as a function of environmental conditions and growth rate (Laws et al., 1983), measurements of Chi a have been used extensively to estimate the biomass of photoautotrophic microorganisms in the sea. 

Even more complex is C-isotope fractionation in aquatic plants. Factors that control the of phytoplankton include temperature, availability of C02(aq), light intensity, nutrient availability, pH and physiological factors such as cell size and growth rate (Laws et al. 1995, 1997 Biigare et al. 1997 Popp et al. 1998 and others). In particular the relationship between C-isotope composition of phytoplankton and concentration of oceanic dissolved CO2 has been subject of considerable debate because of its potential as a palaeo-C02 barometer (see discussion). 

The carbon isotopic composition of phytoplankton has been shown to be strongly affected by the />( (>2 of surface waters in the ocean (Rau et al., 1989, 1992). Moreover, fractionation of carbon isotopes by phytoplankton is also correlated with cell growth rate, cell size, cell membrane permeability, and CO2 (aq) (Laws et al., 1995 Rau et al., 1997). 

While many laws exist for the cell growth rate of new cells, that is, cells + substrate ----------------- more cells + product... 

CSTR. The cell growth rate law for this system is... 

Because there is no growth during the stationary phase, it is clear that Equation (7-112) caimotbe used to account for substrate consumption, nor can the rate of product formation be related to the growth rate [e.g.. Equation (7-113)], Many antibiotics, such as peniciUin, are produced in the st onary phase. In this phase, the nutrient consumed for growth has tecome vulually exhausted and a different nutrient, called the secondary nutrients, is used for cell maintenance and to produce the desired product. Usually, the rate law for product formation during the stationary phase is similar in form to the Monad equation, that is,... 

P7-29a a CSTR is being operated at steady state. The cell growth follows the Monod growth law without inhibition. The exiting substrate and cell concentrations are measured as a function of the volumetric flow rate (represented as the dilution rate), and the results are shown below. Of course, measurements are not taken until steady state is achieved after each change in the flow rate. Neglect substrate consumption for maintenance and the death rate, and assume that is zero. For run 4, the entering substrate concentration was 50 g/dia and the volumetric flow rate of the substrate was 2 dmVs,... 

While many laws exist for the cell growth rate of new cells, that is,... 

We turn our attention next to the rate laws and principles of applied reaction kinetics typically associated with various phases of cell growth. 

The ability of Monod s empirical relation to fit kinetic data for biochemical reactions has its foundations in generalizations of two phenomena frequently observed for fermentation processes (1) nature places a cap on the quantity of microorganism that can be achieved during the exponential phase of growth in a bioreactor operating in a batch mode and (2) as the concentration of the limiting substrate approaches zero, the rate laws for biochemical reactions approach pseudo-first-order behavior with respect to that substrate. The cap indicated on the cell growth rate has been associated with the natural limit on the maximum rate at which replication of DNA can be achieved. 

In equation (13.3.2) we have also assumed that the rate at which biomass enters in the original wastewater is negligible (xq = 0) compared to the rate at which biomass enters the contaimnent vessel via the recycle stream. Readers should note the presence of different subscripts on the specific growth rate (p) in equations (13.3.2) and (13.3.3). The subscript net implies the presence of a cell death term, whereas the subscript max does not. For the substrate, the Monod form of the rate law is appropriate for use. 

The kinetics of cell growth are governed by a Monod rate law for which the kinetic parameters at the operating conditions proposed are p = 0.7 h" and Kg = 0.2 g glu-cose/L. 

For purposes of the analysis, you may assume that cell death and cell maintenance metabolism effects are negligible, as is formation of any products other than biomass. The concentration of substrate in the feed is 25 g/L and the yield coefficient x/s is 0.52 g cells (dry weight)/g substrate. The kinetics of cell growth are characterized by a rate law of the Monod form with = 0.6 h" and Kg = 0.5 g/L. The dilution rate for the CSTBR is 0.95 h" and the concentration factor / is 2.5. 

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