Abstract
AbstractWe consider how the double-membrane structure of the cell envelope of Gram-negative bacteria affects its functional response, which is the mathematical relationship that expresses how the nutrient uptake flux depends on environmental conditions. We show that, under suitable conditions, the Holling Type I functional response is a plausible model, as opposed to the Holling Type II (rectangular hyperbolic, ‘Michaelis–Menten’) response that is the default model in much of the literature. We investigate both diffusion-limited and capacity-limited regimes. Furthermore, we reconcile our findings with the preponderance in the established literature of hyperbolic models for the growth response, which are generally assumed to be valid, for both Gram-negative and Gram-positive bacteria. Finally, we consider the phenomenon of dynamic adjustment of investment of molecular building blocks in cellular components, and show how this will affect the functional response as observed by the experimenter.
Highlights
The cell envelope of Gram-negative bacteria consists of two concentric lipid bilayer membranes, an inner membrane (IM) and an outer membrane (OM), in contrast to Gram-positive bacteria that have a single cytoplasmic membrane, corresponding to the IM of the Gram-negative cells (Schlegel & Zaborosch, 1993)
−1 u, D pρpo followed by a constant portion Ψ ≈ ρtrψ, with a transition at u ≈ r0/D +−1 ρtrψ. These approximations become better as ρbp increases, and in the limit ρbp → ∞ the Ψ -u graph consists of these two straight line segments, that is, we have obtained the classic Holling Type I functional response
The analysis presented in this paper would suggest that the Holling Type I functional response for nutrient uptake should not be uncommon in Gram-negative bacteria, and yet this response seems to have received little attention in the microbiological literature, despite its status as a standard concept in general ecology (Begon et al, 1990)
Summary
The cell envelope of Gram-negative bacteria consists of two concentric lipid bilayer membranes, an inner membrane (IM) and an outer membrane (OM), in contrast to Gram-positive bacteria that have a single cytoplasmic membrane, corresponding to the IM of the Gram-negative cells (Schlegel & Zaborosch, 1993). The first factor is proportional to the surface density of transporter molecules embedded in the membrane, whereas the second depends on the mechanism of the transporter; a popular choice is the hyperbola that arises in the Michaelis–Menten model (Michaelis & Menten, 1913; Jordy et al, 1996; Button, 1998). In ecology, this hyperbolic response is known as the Holling Type II response (Begon et al, 1990). We shall demonstrate that this is not necessarily the case, in view of adaptations that the cell can make at the whole-organism level
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