Internalisation sites

Let us consider the uptake of a given species, either a nutrient or a pollutant heavy metal or an organic (macro)molecule, etc., which will be referred to as M. M is present in the bulk of the medium at a concentration, c, ar d we assume that the only relevant mode of transport from the medium to the organism s surface is diffusion. The internalisation sites are taken to be located on the spherical surface of the microorganism or in a semi-spherical surface of a specialised region of the organism with radius ro (see Figure 1). Thus, diffusion prescribes ... 

Figure 2. Evolution of diffusive (Jm, continuous line) and internalisation (/u, circles) fluxes with time for a system with two internalisation sites (Section 2.1.2). Fraction of coverages of each site type, 81 and 82, are indicated with dashed lines. Parameters Dm = 10-9m2 s 1,= l(E4molm 3,r0 = l(E4m,Km,i = l(E5molm 3, Am,2 = 10 3 molm 3,rmax,i = 10 8molm 2,rmax,2 = 10 n molm 2, i = 10 2s 1 and kj = 1 s 1...

Two Sites Site 1 = Adsorption + Internalisation, Site 2 = Adsorption Only. The balances of fluxes can be written ... 

The impact of changing AM,2 on /u (using equation (48)) is seen in Figure 18. Because Am,i CM, no saturation effect of the internalising site 1 can be expected. When Am,2 is larger or similar to Am,i (curves (a) and (b)) the approach of Ju to steady-state follows the usual parabolic behaviour. For low Am,2 (curve (c)) the supplied M is mostly adsorbed on to site 2 (because rm p rmax,i), with adsorption still following practically linear isotherms for both sites with the... 

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). 

Adsorption Sites Coupled to First-Order Internalisation Processes. 150... 

Figure 1. Outline of the uptake model showing the spherical diffusion of species M through the medium towards two different sites where adsorption is followed by internalisation. The radius of the organism is taken as ro...

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 ... 

We deal now with two parallel Langmuir adsorption steps, only one of which is followed by internalisation. Parameters of the site with both adsorption and internalisation will be denoted with subscript 1 (physiologically active site), while the other, with no internalisation, will be denoted with subscript 2 (physiologically inactive site) [2]. 

In the range of linear adsorption behaviour, whatever the number of site types (see Section 2.3.1 for the merging of parameters of two sites), the surface concentration F is related to via an effective linear coefficient, Ah, while the first-order internalisation processes can also be described by an effective first-order constant, k. Thus, equation (39) can be recast, for instance, in terms of r as ... 

The numerical example given above also shows that, for certain sets of parameter values, the assumption of linear adsorption may be violated. Since the sites for adsorption plus internalisation have a higher affinity, they are preferentially filled because they are much lower in number, the nonlinear regime can be surpassed. For the above example, cj, which combined with Kh,2 (for the noninternalisation sites) of O(10-5)m, yields 0(10 l0)molm of occupied sites. If the maximum number of such sites is... 

One Site Adsorbing and Internalising The balance of fluxes (39) can be written in terms of the surface concentration F as ... 

Figure 17. Comparison of Ju versus t plots predicted by different submodels for a system with one type of site (adsorbing and internalising) linear isotherm with dSS approximation (O) applying equation (43) with A)i = 5.2 x 10 6 m Langmuirian isotherm with dSS approximation (continuous line) applying equation (46) Langmuirian isotherm with semi-infinite diffusion (dotted line) by numerically solving integral equation (7)). Other parameters c(, = 5x 10-4 mol m-3, Dm = 8 x 10 10 m2 s-1, Kn = 2 x 10-5 m, k — 5 x 10 4 s 1, ro = 1.8 x 10 6 m, r0 + <5M = 10 5 m, KM — 2.88x 10 3mol m 3, Tmax = 1.5 x 10-8 mol m-2...

If other ions affect the internalisation process via competition for the transport sites [3,5,14,15,37,52,69,93,97-99], then a reasonable starting point is to modify the Langmuir isotherms (3) to ... 

Another factor to take into account in biouptake studies is the possibility that the organism develops strategies of eliminating toxic species by means of efflux [38,52,101]. As a first approach, the efflux rate can be set proportional to the amount of species taken up that has been internalised, thus converting the boundary condition of flux balances for two sites, equation (4), into ... 

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 ... 

From a plot of the internalisation flux against the metal concentration in the bulk solution, it is possible to obtain a value of the Michaelis-Menten constant, Am and a maximum value of the internalisation flux, /max (equation (35)). Under the assumption that kd kml for a nonlimiting diffusive flux, the apparent stability constant for the adsorption at sensitive sites, As, can be calculated from the inverse of the Michaelis-Menten constant (i.e. A 1 = As = kf /kd). The use of thermodynamic constants from flux measurements can be problematic due to both practical and theoretical (see Chapter 4) limitations, including a bias in the values due to nonequilibrium conditions, difficulties in separating bound from free solute or the use of incorrect model assumptions [187,188],... 

The above procedures imply that (1) there is only a single type of site (2) binding occurs only to the transporter site (usually not the case for trace metals), and (3) the internalisation flux is negligible for the equilibration times that are employed [197,198], These conditions are rarely fulfilled for metal transporters. The interpretation of Scatchard plots is especially ambiguous in the presence of several independent sites. On the other hand, in the biomedical literature, where nonspecific adsorption is generally not a problem, values of 104 to 106 carriers per cell (ca. 10-13 to 10 11 carriers cm-2 of cell surface area), with even lower numbers determined for some receptors (e.g. haematopoetic growth factor [199]), are typically reported. 

Depending upon the mechanism that is employed by the organism to accumulate the solute, internalisation fluxes can vary both in direction and order of magnitude. The kinetics of passive transport will be examined in Section 6.1.1. Trace element internalisation via ion channels or carrier-mediated transport, subsequent to the specific binding of a solute to a transport site, will be addressed in Section 6.1.2. Finally, since several substances (e.g. Na+, Ca2+, Zn2+, some sugars and amino acids) can be concentrated in the cell against their electrochemical gradient (active transport systems), the kinetic implications of an active transport mechanism will be examined in Section 6.1.3. Further explanations of the mechanisms themselves can be obtained in Chapters 6 and 7 of this volume [24,245]. 

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