zinc concentration change. This assumption was made for the following reasons: the
steps involved in the formation of a complex include the movement of a zinc ion
toward the site, the binding, and the dissociation from it, the latter occurring after a
conformational change of the bound target. The value of the on-rate constant is
mainly determined by diffusion and binding. The speed of a reaction is largely
determined by the diffusion value, considered for all ions as 10
9 –10
10 s
�1 [57] and,
to some extent, by the rate with which water leaves the ionic solvation sphere. For
zinc, this rate and the on-rate constant are considered to be above 10
7 s
�1 and
10
8 M
�1 s
�1 , respectively [57]. We can now introduce values of on-rate constants
between 10
7 and 10
8 M
�1 s
�1
, in agreement with the values for the NMDA sites used
in the model and the dissociation, IC 50 and EC 50 , values in Table 1. In these cases,
the off-rate constants have values in the range 60 s
�1 to approximately 7000 s
�1
,
which exceed, by two to four orders of magnitude, the off-rate constant (0.6 s
�1
)
for the NMDA 2A reaction. Thus, since for those complexes unbinding occurs
very rapidly, the assumption that they are always in equilibrium with free zinc is
justified.
The computational study led to the representation of a variety of time-varying
curves to illustrate, for different stimuli, the release minus uptake and the concentrations of total and free zinc, as well as of the various zinc complexes formed.
Assuming, in a single release process, a low level of stimulation, causing free zinc to
reach 10 nM in the cleft, the predominant complexes are formed with the highaffinity NMDA 2A glutamate receptor sites and with the lower-affinity and highly
concentrated GLAST glutamate transporters from glial cells [58]. The concentrations of the other complexes are lower by several orders of magnitude. As mentioned before, all ligands for which the reaction rate constants are not known are
assumed to be in equilibrium with free zinc. For this reason all these complexes, and
also those associated with the short and long release events, have a similar time
course to that of free zinc.
If a 10 times higher free zinc concentration, 100 nM, is attained in the cleft,
following the more intense short stimulation, the most abundant zinc complex is
now the GLAST one, followed by the NMDA 2A which lasts longer than any of the
other complexes. This is due to the much higher affinity of the NMDA 2A sites for
zinc. Similar properties apply to the third type of estimated curves, associated with
the existence of 1 μM free zinc in the cleft, produced by a longer stimulus. The main
differences, with respect to the short stimulus situation, are that the concentration
of the NMDA 2A complex remains high for a longer period and all formed complexes have larger amplitudes than in the case of the short stimulus. The fact that
externally applied zinc (100 nM) was found to inhibit postsynaptic NMDA currents, at hippocampal CA3 neurons [27], is in agreement with the idea that zinc
binds to and inhibits the NMDA receptors. The remaining signals, with much
smaller amplitudes, have thus minor or negligible roles in accounting for cleft zinc
removal.
The most intense stimulation considered in this study, which assumed a maximum zinc cleft concentration of 1 μM, reveals that, as observed in the short case,
GLAST is the complex formed in higher concentration. It is followed by the NMDA
2A complex that saturates when all the corresponding zinc sites (about 40 nM) are
bound to zinc. All the other bindings have again much smaller contributions to zinc
clearance, especially the complex formed with L-type VDCCs, with a concentration
in the fM range.
In conclusion, for a single stimulus, the NMDA 2A high-affinity sites are the
most involved in the initial clearance process, while for the stronger stimulations
considered (short and long), this role is taken by the highly abundant GLAST
complexes. In all cases, uptake has a much slower time course.
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Advances in Neural Signal Processing
steps involved in the formation of a complex include the movement of a zinc ion
toward the site, the binding, and the dissociation from it, the latter occurring after a
conformational change of the bound target. The value of the on-rate constant is
mainly determined by diffusion and binding. The speed of a reaction is largely
determined by the diffusion value, considered for all ions as 10
9 –10
10 s
�1 [57] and,
to some extent, by the rate with which water leaves the ionic solvation sphere. For
zinc, this rate and the on-rate constant are considered to be above 10
7 s
�1 and
10
8 M
�1 s
�1 , respectively [57]. We can now introduce values of on-rate constants
between 10
7 and 10
8 M
�1 s
�1
, in agreement with the values for the NMDA sites used
in the model and the dissociation, IC 50 and EC 50 , values in Table 1. In these cases,
the off-rate constants have values in the range 60 s
�1 to approximately 7000 s
�1
,
which exceed, by two to four orders of magnitude, the off-rate constant (0.6 s
�1
)
for the NMDA 2A reaction. Thus, since for those complexes unbinding occurs
very rapidly, the assumption that they are always in equilibrium with free zinc is
justified.
The computational study led to the representation of a variety of time-varying
curves to illustrate, for different stimuli, the release minus uptake and the concentrations of total and free zinc, as well as of the various zinc complexes formed.
Assuming, in a single release process, a low level of stimulation, causing free zinc to
reach 10 nM in the cleft, the predominant complexes are formed with the highaffinity NMDA 2A glutamate receptor sites and with the lower-affinity and highly
concentrated GLAST glutamate transporters from glial cells [58]. The concentrations of the other complexes are lower by several orders of magnitude. As mentioned before, all ligands for which the reaction rate constants are not known are
assumed to be in equilibrium with free zinc. For this reason all these complexes, and
also those associated with the short and long release events, have a similar time
course to that of free zinc.
If a 10 times higher free zinc concentration, 100 nM, is attained in the cleft,
following the more intense short stimulation, the most abundant zinc complex is
now the GLAST one, followed by the NMDA 2A which lasts longer than any of the
other complexes. This is due to the much higher affinity of the NMDA 2A sites for
zinc. Similar properties apply to the third type of estimated curves, associated with
the existence of 1 μM free zinc in the cleft, produced by a longer stimulus. The main
differences, with respect to the short stimulus situation, are that the concentration
of the NMDA 2A complex remains high for a longer period and all formed complexes have larger amplitudes than in the case of the short stimulus. The fact that
externally applied zinc (100 nM) was found to inhibit postsynaptic NMDA currents, at hippocampal CA3 neurons [27], is in agreement with the idea that zinc
binds to and inhibits the NMDA receptors. The remaining signals, with much
smaller amplitudes, have thus minor or negligible roles in accounting for cleft zinc
removal.
The most intense stimulation considered in this study, which assumed a maximum zinc cleft concentration of 1 μM, reveals that, as observed in the short case,
GLAST is the complex formed in higher concentration. It is followed by the NMDA
2A complex that saturates when all the corresponding zinc sites (about 40 nM) are
bound to zinc. All the other bindings have again much smaller contributions to zinc
clearance, especially the complex formed with L-type VDCCs, with a concentration
in the fM range.
In conclusion, for a single stimulus, the NMDA 2A high-affinity sites are the
most involved in the initial clearance process, while for the stronger stimulations
considered (short and long), this role is taken by the highly abundant GLAST
complexes. In all cases, uptake has a much slower time course.
122
Advances in Neural Signal Processing