Nutrient uptake by microorganisms according to kinetic parameters from theory as related to cytoarchitecture

Abstract

The abilities of organisms to sequester substrate are described by the two kinetic constants specific affinity, a degrees, and maximal velocity Vmax. Specific affinity is derived from the frequency of substrate-molecule collisions with permease sites on the cell surface at subsaturating concentrations of substrates. Vmax is derived from the number of permeases and the effective residence time, tau, of the transported molecule on the permease. The results may be analyzed with affinity plots (v/S versus v, where v is the rate of substrate uptake), which extrapolate to the specific affinity and are usually concave up. A third derived parameter, the affinity constant KA, is similar to KM but is compared to the specific affinity rather than Vmax and is defined as the concentration of substrate necessary to reduce the specific affinity by half. It can be determined in the absence of a maximal velocity measurement and is equal to the Michaelis constant for a system with hyperbolic kinetics. Both are taken as a measure of tau, with departure of KM from KA being affected by permease/enzyme ratios. Compilation of kinetic data indicates a 10(8)-fold range in specific affinities and a smaller (10(3)-fold) range in Vmax values. Data suggest that both specific affinities and maximal velocities can be underestimated by protocols which interrupt nutrient flow prior to kinetic analysis. A previously reported inverse relationship between specific affinity and saturation constants was confirmed. Comparisons of affinities with ambient concentrations of substrates indicated that only the largest a degreesS values are compatible with growth in natural systems.

FIG. 1

Model of substrate uptake kinetics by a cell growing on a single substrate.

FIG. 2

Graphical determination of kinetic constants for substrate uptake. (A) Plot of v against S for leucine uptake by E. coli. The inset shows the complete range of substrate concentrations analyzed. (B) Plot of v/S versus v (affinity plot). The equation of the curves is the sum of equation 13 and a linear function v = dS, where d is an arbitrary constant. The line was visually fit, by use of a plotting program, SigmaPlot, to the three plots simultaneously so that small and large values could be equally weighted. The base value of the specific affinity a^o_s, 0.008 liters mg of cells⁻¹ h⁻¹, was taken from the ordinate intercept of the affinity plot and used to draw the initial slope of the curve of v against S, which gives the specific affinity as well. V_max was indeterminate at >9 μg of substrate mg of cells⁻¹ h⁻¹. The half-maximal value of the specific affinity, a^KA_s, is 0.004 liters mg of cells⁻¹ h⁻¹. The affinity constant K_A is S at a^KA_s or v/a^KA_s and has a value of 2 μg of S mg of cells⁻¹ h⁻¹/0.004 liter mg of cells⁻¹ h⁻¹ or 500 μg of S liter⁻¹. In the plot of v against S, a^KA_s is the value of the abscissa at the intersection of the line with slope a^KA_s and the curve. The Michaelis constant, K_m, remains S at V_max/2 (>7,000 μg liter⁻¹).

FIG. 3

Data trends from Table 2. (A) V_max plotted against specific affinity (inset), with the logarithmic transformation shown in the main figure. (B) Saturation constants plotted against specific affinity (inset), with the logarithmic transformation shown in the main figure. Solid symbols indicate K_m, and open symbols indicate K_A.