Experimental and theoretical bases of specific affinity, a cytoarchitecture-based formulation of nutrient collection proposed to supercede the Michaelis-Menten paradigm of microbial kinetics

Abstract

A theory for solute uptake by whole cells was derived with a focus on the ability of oligobacteria to sequester nutrients. It provided a general relationship that was used to obtain the kinetic constants for in situ marine populations in the presence of naturally occurring substrates. In situ affinities of 0.9 to 400 liters g of cells(-1) h(-1) found were up to 10(3) times smaller than those from a "Marinobacter arcticus " isolate, but springtime values were greatly increased by warming. Affinities of the isolate for usual polar substrates but not for hydrocarbons were diminished by ionophores. A kinetic curve or Monod plot was constructed from the best available data for cytoarchitectural components of the isolate by using the theory together with concepts and calculations from first principles. The order of effect of these components on specific affinity was membrane potential > cytoplasmic enzyme concentration > cytoplasmic enzyme affinity > permease concentration > area of the permease site > translation coefficient > porin concentration. Component balance was influential as well; a small increase in cytoplasmic enzyme concentration gave a large increase in the effect of permease concentration. The effect of permease concentration on specific affinity was large, while the effect on K(m) was small. These results are in contrast to the Michaelis-Menten theory as applied by Monod that has uptake kinetics dependent on the quality of the permease molecules, with K(m) as an independent measure of affinity. Calculations demonstrated that most oligobacteria in the environment must use multiple substrates simultaneously to attain sufficient energy and material for growth, a requirement consistent with communities largely comprising few species.

FIG. 1.

Cytoarchitectural model of nutrient kinetics. Ambient nutrient S diffuses through a porin to periplasmic concentration ([S_P]), where it combines with a proton-empowered permease having an active-site radius of r_s. Transport produces a [S_c] that generates both a proton potential and a concentration-driving force that facilitates substrate flow through an enzyme sequence (E) to produce cell material (X).

FIG. 2.

Monod (A and C) and affinity (B and D) plots of leucine uptake from Resurrection Bay, Alaska, seawater at a 10-m depth in Thumb Cove during June. Panels A and B show apparent rates from the specific activity of the [³H]leucine added; panels C and D show rates corrected for an ambient leucine concentration ([S_n]) of 0.85 μg/liter. Insets expand data near the origin. Both rates were corrected for an incorporation-to-uptake ratio of cell yields (Y) using a value of 0.45 from ¹⁴CO₂ liberation and ³H incorporation rate data. When fit to the equation v = V_m[S]/(K_a + [S]) + k_ind[S], the parameters for observed (A and B) and S_n-corrected (C and D) rates (V_m) were 0.42 and 0.50 μg of leucine mg of cells⁻¹ h⁻¹, and k_ind was 0.002 and 0.003 liters g of cells⁻¹ h⁻¹. The affinity constants (K_a) obtained from [S] at the half-maximal value of v/[S] and the rate v (the affinity plot abscissa) were 1.5 and 1.9 μg/liter from panels B and D, respectively.

FIG. 3.

Uptake of [¹⁴C]leucine by “M. arcticus” in the presence of glutamate. (A) Time course showing effect of leucine concentration on incorporated radioactivity. (B) Lineweaver-Burk plot based on the equation 1/v = a°_S(1/[S]) + 1/V_m, with leucine as the variable substrate and glutamate as the auxiliary substrate. Rates were taken from the best line through the data points independent of the origin. (C) Dependence of the specific affinity for leucine on the concentration of glutamate.

FIG. 4.

Kinetics of alanine uptake by “M. arcticus” to 10 μg/liter. The solid line in each panel shows the base calculation. The effects of changing each parameter by the amounts indicated are shown by the broken lines.

FIG. 5.

Effect of substrate concentration on specific affinity (solid line) calculated from equations 6 through 1010 showing processes postulated to effect major control. Affinities as v/[S] from the Michaelis-Menten hyperbola are shown as a broken line.