A mechanism of microbial cell growth

Abstract

SummaryPresently empirical expressions, especially the Monod equation, are used to quantitatively relate microbial growth rate to limiting substrate concentration in the solution. In this paper microbial growth is postulated to occur by a mechanism involving a mass transfer or assimilation process and an ingestion and cell division process. The assimilation process is assumed to be substrate mass transfer limited and hence proportional to the limiting substrate concentration. The ingestion is assumed independent of limiting substrate concentration and only dependent upon internal reaction rates. The quantitative relationship between limiting substrate and microbial growth rate resulting from this mechanism is developed. Under certain limiting conditions this expression is shown to reduce to the Monod equation and under other conditions it reduces to the LotkaVolterra relationship. This mechanism is applied to batch and continuous cultures and the results obtained are compared qualitatively with experiment.The principal mathematical expression used to relate rate of microbial cell growth to limiting substrate concentration is the Monod equation' which is analogous to the Michaelis-Menten equation for enzymatic reactions. This equation is accepted primarily because it qualitatively resembles the experimentally measured relationship and it is easy to use. However, it is recognized that there are many cases in which observed values of cell concentration do not correspond to those predicted by this equation in batch cultivation. I n particular, this expression does not predict the lag phase, nor does it predict the endogenous phase of batch cultivation. In continuous cultivation, this equation rarely predicts the experimental results, partly because the yield of cell mass from limiting substrate is not

The role of Thiobacillus ferrooxidans in hydrometallurgical processes

“…Despite the fact that most workers [117,126,[129][130][131][132]162] have regarded the specific growth rate of a population as a single function of the concentration of the limiting substrate, others were able to show that it is also a function of the population density [133,134] and the mass transfer or the assimilation processes [135]. These authors [133][134][135] also claim general applicability of their models to both batch and continuous systems. For a single stage continuous culture [ 182] the rate of bacterial growth, dX/dt, and substrate utilization, dS/dt, can be defined as follows:…”

A Mathematical Model of Exoprotein Production in Bacteria

“…The constituents of a simple, unstructured mathematical model for the process described in Section 1 are the bacterial biomass concentration X, the (limiting) substrate (nutrient) density S, and the extracellular product concentration P. The simplest analogous 'reaction' scheme (see Verhoff et al, 1972;Bijkerk & Hall, 1977) to describe this process is »2X X+ ai S_ij;| (2.1)~-…”

“…It has been used as the basic building block of most subsequent models (e.g. Barford & Hall, 1978;Blanch, 1981;Koga, Burg, & Humphrey, 1967;Verhoff, Sundaresan, & Tenney, 1972).…”

“…Perhaps most notable (at least from the mathematical point of view) are the structured models, in which some variation in cell quality is admitted. This can take a number of forms, of which the concept of a structured biomass is the most prevalent; the cell is considered to consist of two or more constituents, each of which has a distinct function (Grenney, Bella, & Curl, 1973;Pamment, Hall, & Barford, 1978;Verhoff et al, 1972;Williams, 1967). Typically there is a component A which is able to take up substrate and convert it into a form which can be used to promote all growth in a second component B.…”

Modelagem e otimização de fermentadores para obtenção de etanol

“…Este modelo foi usado para simular crescimento em batelada usando um inóculo em nutriente exausto, que corresponde a SUNDARESAN (1972) empregaram expressões empíricas, especialmente a de Monod para descrever o crescimento microbiano na limitação de substrato. O crescimento é admitido ocorrer através de um mecanismo envolvendo transferência de massa, assimilação, ingestão e processo de divisão.…”