routine increases the value of ∆t, in order for the calculation to proceed at a faster
pace. If the error is too large, then the result is rejected, and a new attempt is made
with a smaller step.
This method provides the values of the complex concentrations whose dynamics
is described by Eq. (10) after one time step. However, it is also necessary to
calculate the values of the other complex concentrations and of the free zinc concentration. This can be achieved by iterating Eqs. (12) and (14) in the following
way: using the results obtained by the Runge–Kutta method for the reactions for
which the rate constants are known, together with the previous values for the
results obtained for the other complex concentrations in Eq. (14), an approximate
value for the free zinc concentration is obtained. This value can then be used in
Eq. (12), providing new values for the complex concentrations whose rate constants
are not known and which are assumed to be in equilibrium. Then this procedure is
repeated using these new results in Eq. (14) to obtain again a new value for the free
zinc concentration, which is used once more in Eq. (12). The process is repeated
until self-consistency is obtained, i.e., until the change of the concentration values
after one iteration is negligible.
3. Results
The data indicated in Table 1 allowed a variety of estimates of total, free, and
complexed zinc changes at the hippocampal mossy fiber synapses from CA3 area.
The studies considered the release processes in a synaptic cleft, both from a single
and from multiple vesicles, and also the corresponding uptake. Table 2 shows the
data that was used to describe a single vesicle event and two possible multiple
vesicle events which are denoted by short and long, where the latter corresponds to
a longer time before the maximum concentration of free zinc is obtained, as well as
a larger value for that maximum. Table 2 includes also the values of the parameters
Table 1.
Concentrations of the sites and rate and dissociation constants, IC 50 and EC 50 , for the binding reactions
[54, 55]. Source: Reproduced from Quinta-Ferreira et al. [12], with permission from Springer Nature.
117
Computer Simulations of Hippocampal Mossy Fiber Cleft Zinc Movements
DOI: http://dx.doi.org/10.5772/intechopen.90094
pace. If the error is too large, then the result is rejected, and a new attempt is made
with a smaller step.
This method provides the values of the complex concentrations whose dynamics
is described by Eq. (10) after one time step. However, it is also necessary to
calculate the values of the other complex concentrations and of the free zinc concentration. This can be achieved by iterating Eqs. (12) and (14) in the following
way: using the results obtained by the Runge–Kutta method for the reactions for
which the rate constants are known, together with the previous values for the
results obtained for the other complex concentrations in Eq. (14), an approximate
value for the free zinc concentration is obtained. This value can then be used in
Eq. (12), providing new values for the complex concentrations whose rate constants
are not known and which are assumed to be in equilibrium. Then this procedure is
repeated using these new results in Eq. (14) to obtain again a new value for the free
zinc concentration, which is used once more in Eq. (12). The process is repeated
until self-consistency is obtained, i.e., until the change of the concentration values
after one iteration is negligible.
3. Results
The data indicated in Table 1 allowed a variety of estimates of total, free, and
complexed zinc changes at the hippocampal mossy fiber synapses from CA3 area.
The studies considered the release processes in a synaptic cleft, both from a single
and from multiple vesicles, and also the corresponding uptake. Table 2 shows the
data that was used to describe a single vesicle event and two possible multiple
vesicle events which are denoted by short and long, where the latter corresponds to
a longer time before the maximum concentration of free zinc is obtained, as well as
a larger value for that maximum. Table 2 includes also the values of the parameters
Table 1.
Concentrations of the sites and rate and dissociation constants, IC 50 and EC 50 , for the binding reactions
[54, 55]. Source: Reproduced from Quinta-Ferreira et al. [12], with permission from Springer Nature.
117
Computer Simulations of Hippocampal Mossy Fiber Cleft Zinc Movements
DOI: http://dx.doi.org/10.5772/intechopen.90094