A model for inorganic carbon fluxes and photosynthesis in cyanobacterial carboxysomes

A barrier to CO2 diffusion within the cyanobacterial cell has been regarded as essential for the inorganic carbon concentrating mechanism. We present here an extension of our earlier quantitative model demonstrating that it may be unnecessary to postulate any barrier other than the ribulose 1,5-bisphosphate carboxylase/oxygenase (Rubisco) molecules themselves. It is proposed that carbonic anhydrase is located in the interior of the carboxysome and that the CO2 generated is largely fixed as it diffuses outwards past Rubisco sites located along the diffusion path. Equations have been developed, by combining a mass balance equation with Fick's Law and the Michaelis-Menten equation (representing CO2 fixation), estimate the value that must be assigned to the diffusion coefficient for CO2 within the carboxysome if the CO2 concentration is to be reduced to near zero at the carboxysome outer surface. A solution has been obtained for two limiting cases, that where CO2 concentration is nearly saturating and that where it is at the Km(CO2) value or below. These two estimates predict that the permeability constant for the Rubisco zone in the carboxysome would have to be 10−2–10−3 cm∙s−1, a value that we suggest is reasonable for three-dimensional diffusion through a densely packed protein layer. The concentration gradient in the inward direction, for substrates penetrating the carboxysomes from the cytoplasm, is shown to be relatively flat, owing to the concentrating effect experienced by solutes passing from the periphery to the center of a sphere. Key words: cyanobacteria, carboxysomes, inorganic carbon fluxes, photosynthesis, model.