Internalisation rate constant

Once adsorbed, we assume that M is internalised following a first-order kinetic process in each of the sites, with internalisation rate constants k and k2 respectively [9,16-18], For each kind of adsorption site, we have an uptake flux given by ... 

As seen above (equation (5)), the basis of the simple bioaccumulation models is that the metal forms a complex with a carrier or channel protein at the surface of the biological membrane prior to internalisation. In the case of trace metals, it is extremely difficult to determine thermodynamic stability or kinetic rate constants for the adsorption, since for living cells it is nearly impossible to experimentally isolate adsorption to the membrane internalisation sites (equation (3)) from the other processes occurring simultaneously (e.g. mass transport complexation adsorption to other nonspecific sites, Seen, (equation (31)) internalisation). 

In the thermodynamic models (FIAM and BLM), the internalisation flux is assumed to be rate-limiting, and the concentration of carriers or sensitive sites bound by the solute of interest negligible with respect to the total number of carriers (i.e. free carrier concentration constant). The fundamental equations describing the equilibrium models can be summarised as ... 

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