Introduction

Gadolinium (Gd³⁺) is a chemical substance belonging to the lanthanide group used in magnetic resonance imaging (MRI) as a contrast agent. The first gadolinium approved as contrast agent appeared in 1988 [ 1 , 2 ]. The reason for using gadolinium as a contrast agent is the quality enhancement of an image of MRI. It typically makes diseased tissue appear brighter than the surrounding tissue. The characteristic of free gadolinium is extremely toxic and can cause central lobular necrosis of the liver, enzyme inhibition, a variety of hematological abnormalities [ 3 ], nephrogenic systemic fibrosis (NSF) [ 4 , 5 ] and many of the voltage calcium channel blocking [ 3 , 6 , 7 ]. Recently, Kanda, T. et al. and Barbieri, S. et al. found that gadolinium accumulates in the brain especially in dentate nuclei and globus pallidus and makes high signal intensity have an effect on unenhanced T1-weighted MR images after multiple injections of gadolinium [ 8 - 10 ].

The presence of gadolinium in the body needs to be alerted because it is a foreign material inserted into the body. Gadolinium has potent to block and competes with Calcium (Ca²⁺) in the body, especially influx to calcium channel [ 6 , 11 ]. Disturbance of the Calcium diffusion can affect the release of neurotransmitters from presynaptic to postsynaptic through the synaptic cleft. Physically, Gadolinium has a similar crystallographic radius as Calcium to be exactly radius Gd³⁺ (0.94 Å) and radius of Ca²⁺ (0.99 Å) [ 11 ].

The mechanism of Ca²⁺ diffusion influx to the presynaptic as the signal transmission at chemical synapses initiated when a potential action invades into presynaptic. The action potential causes the opening of voltage-gated calcium channels in the presynaptic membrane. The opening of these channels causes a rapid influx of Ca²⁺ into the presynaptic terminal because the concentration of Ca²⁺ inside the presynaptic is lower than outside the presynaptic. The existence of Ca²⁺ triggers synaptic vesicle exocytosis, thereby releasing the neurotransmitters contained in the vesicles and initiating synaptic transmission to the synaptic cleft and postsynaptic [ 12 , 13 ].

The magnitude of the potential action at the presynaptic affects the average number of open calcium channels that proportionally affect the amount of Ca²⁺ influx to the presynaptic. With the reduced presynaptic Ca²⁺ influx, the probability of synaptic vesicle fusion also reduced that it results in less neurotransmitter release each presynaptic action potential [ 14 ]. The reduction of neurotransmitters means disruption of chemical transmission from one neuron to the next neuron. One of the causes of the reduced number of Ca²⁺ influx into presynaptic is the presence of Gd³⁺ in the vicinity of calcium channel, which Gd³⁺ is blocking of calcium channel.

This research is an investigated mechanism model of Ca²⁺ influx influenced by the presence of Gd³⁺. The simulation is carried out using Monte Carlo method which capable of giving all the probabilities of ion interaction as Ca²⁺, Gd³⁺, synaptic vesicle, and ions calcium channel, ion membrane, active membrane, and neurotransmitter. The model simulation also shows the effect of the number of Gd³⁺ and calcium channel density on the speed of calcium channel blocking, duration Ca²⁺ in presynaptic and how much synaptic vesicle can release into the synaptic cleft.

Material and Methods

Monte Carlo Cell simulations were carried out using MCell 3.1 (www.mcell.org) [ 15 , 16 ] running on a Lenovo ThinkPad 2.2. GHz Intel Core i7 (Ubuntu 14.10). Visualization of the synapse consisting of presynaptic, postsynaptic, and boundary of the synapse was made from the output of MCell using blender 2.69, which add-on with Cell-blender.

a. Model Synapse

Figure 1 shows the synapse model representing a presynaptic and postsynaptic with Ca²⁺ and Gd³⁺ around presynaptic. Ca²⁺ and Gd³⁺ diffusions are translated from outside to inside presynaptic through calcium channel because both have radius ion size similar. Gd³⁺ cannot diffuse presynaptic influx as a blocker for Ca²⁺ and the presence of Gd³⁺ has disturbed presynaptic Ca²⁺ diffusion influx.

Figure 1. The model of synapse consisting of a presynaptic and a postsynaptic with calcium channel base on Neuroscience [13,17].

The synapse design with blender 2.69 consists of three parts, a presynaptic at the top, a postsynaptic at the bottom which in the middle; there are synaptic cleft and boundary as a frame of the synapse. The presynaptic has volume 0.20 μm³ and surface area 1.85 μm², and the postsynaptic has volume 0.21 μm³ and surface area 2.07 μm².There are 23 calcium channels on the presynaptic with density 10^-4μm² and membrane-active with a function to release neurotransmitter at the bottom surface. The number of calcium channels represents an average open calcium channel for each potential action. Figure 2 displays the visual result of synapse design. Each ion has a different color to distinguish each other.

Figure 2. Synapse design use blender 2.69.

b. Kinematic Schemes

This study used four reaction models to describe the mechanism of Ca²⁺ diffusion from outside presynaptic to neurotransmitter release in the synaptic cleft and that reaction expressed:

$A+b_1\underset{k_{-1}}{\overset{\stackrel{k_1}{\to }}{\leftarrow }}{b}_1+\mathrm{Á}$

$D+b_1\stackrel{k_2}{\to }E$

$\mathrm{Á}{b}_2\stackrel{k_3}{\to }{b}_2+b_3$

$B+b_3\stackrel{k_4}{\to }C$

The first reaction was Ca²⁺ diffusion that presented outside of presynaptic (A) into the presynaptic (A’) through the calcium channel (b₁) with the reversible process. The second reaction, Gd³⁺ (D) and calcium channel as a reactant, produced a product (E) that works as blocking in calcium channel [ 18 ]. The next response was the outcome of the first reaction that Ca²⁺ in presynaptic and membrane at the bottom of presynaptic (b₂) produced an active layer (b₃) to synaptic vesicle docking. The last response was synaptic vesicle (B), and active membrane as reactant generated a neurotransmitter (C) released to the synaptic cleft. Simulations were carried out using a set of standard parameter values in Table 1.

c. Diffusion

The diffusion of calcium, gadolinium, synaptic vesicle, and neurotransmitter can be described mathematically using a Fick’s first law, obtain:

$J_r=-D\frac{\mathrm{\partial C}}{\mathrm{\partial r}}$ (1)

The Fick’s first law has a relation with the diffusive flux to the concentration in steady states condition. The flux goes from high to low level, with a magnitude that is proportional to the slope of the concentration function and the constant of proportionality is –D. The negative sign indicates the particle concentration will decrease as a function of position, whereas the diffusion coefficient D depends on the diffused particle and the medium it passed [ 20 ]. The presynaptic model is built using a spherical base form and considers a spherical absorber of radius one in the medium. Every ion reached the surface of the spherical and absorbed the concentration at the spherical surface was 0, and infinity level was C₀. With these boundary conditions with spherical symmetry has the solution:

$C_r=C_0(1-\frac{a}{r})$ (2)

Moreover, the flux is:

$J_r\left(r\right)=D{C}_0\frac{a}{r^2}$ (3)

The net migration of ions through a spherical surface at a rate equal to the area, 4πa², time the incoming flux, -J_r(a):

$I=\mathrm{4DNs}{C}_0$ (4)

Where D is a diffusion coefficient, s is the surface area of a disk, N is the number of discs, C₀ is initial concentration [ 20 , 21 ]. The diffusion current has linear proportional to a total of the disk surface. In terms of the disk number increases, then-current diffusion will decrease and vice versa.

Results

a. Simulation result

Figure 3 is a simulation result of diffusion time dependence on all ions except Gd³⁺ ion from outside presynaptic to clef synaptic. The black line indicates diffusion of Ca²⁺ from outside to inside presynaptic through the calcium channel on the presynaptic surface without blocking of Gd³⁺. Ca²⁺ in the presynaptic (red line) has two phases, absorption and elimination phase. The absorption phase is from zero to a maximum number of ions, and the elimination phase is from maximum declination to a minimum amount of an ion. During Ca²⁺ diffusion influx presynaptic, Ca²⁺ inside of presynaptic is interacting with ion membrane at the bottom to produce active layer (dark blue line) as docking of a synaptic vesicle (light blue) to release neurotransmitter (pink line) to the synaptic cleft.

Figure 3. Time dependence of Ca²⁺ diffusion at all part of the synapse. The standard parameters (Table 1) used in this simulation.

b. Diffusion of Ca2+ Influx Presynaptic

The presence and absence of Gd³⁺ in presynaptic gives a considerable influence on the Ca²⁺ diffusion process. Ca²⁺ can quickly diffuse influx to presynaptic without Gd³⁺. On the other hand, the presence of Gd³⁺ impairs diffusion process of Ca²⁺ depending on the number of Gd³⁺ outside presynaptic.

Figure 4 shows the Ca²⁺ diffusion into the presynaptic by varying number of Gd³⁺ at outside presynaptic. The Colour lines show the different ratio between Ca²⁺ and Gd³⁺, black, red, dark blue, light blue, and pink are 6:0, 6:1, 6:2, 6:4, 6:6, respectively. The black line indicates diffusion of Ca²⁺, which drops off and then declines gradually and reaches a steady state. More importantly, the black line shows the diffusion of Ca²⁺ with the absence of Gd³⁺ has a half-life (t_0.5) at 0.028 s. In comparison, the red line as Ca²⁺ diffusion with the presence of Gd³⁺, which shows the number of Gd³⁺ is one-sixth of Ca²⁺; time duration declines shorter than the previous result. However, a t_0.5 of Ca²⁺ is longer than the last result at 0.053 s. Then again, the ratio 6:2, 6:4, and 6:6 lead the number of Ca²⁺ of the total Ca²⁺ diffusion to be 36%, 20%, 13% and that happen at 0.056 s, 0.028 s, and 0.016 s, respectively.

Figure 4. Time dependence of diffusion result of Ca²⁺ from outside to inside presynaptic with different number of Gd³⁺.

Moreover, with increasing Gd³⁺ ratio, the number of Ca²⁺ influx to presynaptic will decrease and t_0.5 never achieved, and this happens for a ratio 6:2, 6:4, 6:6, respectively. Hence, the difference in the number of Gd³⁺ has a different effect on the speed of diffusion and the amount of Ca²⁺ diffusion. The Gd³⁺presence has been competing with Ca²⁺, which has a significant role in chemical transmission.

c. Blocking of Gd3+

Ca²⁺ and Gd³⁺ are at the same location that is outside of presynaptic. Each ion will surely move randomly and migrate from high to the low concentration; in this case, it will move from outside to the inside of presynaptic. Ca²⁺ migration to the presynaptic through calcium channel happens, while Gd³⁺ will suspend on the surface of calcium channel. Ca²⁺ and Gd³⁺ compete to reach on the calcium channel surface. However, the presence of Gd³⁺ on the calcium channel surface becomes an impair Ca²⁺ diffusion, and the amount of Gd³⁺ will affect the speed block of calcium channel.

At t = 0.200 s, the Gd³⁺ blocks all calcium channels surface that amounts of Ca²⁺ and Gd³⁺ were as ratio 6:1. Similarly, Gd³⁺ totally blocks calcium channel with variety amount of Gd³⁺, t = 0.060 s, 0.284 s, and 0.019 s with ratio 6:2, 6:4, 6:6, respectively, Figure 5. At initial state to 40% blocked, the speed of blocking calcium channel is linear then follows an exponential function. The fastest blocking is the one with the greatest Gd³⁺. In terms of the number of Gd³⁺ blocking, the calcium channel is extensive. Besides, the increasing number of Gd³⁺ attached to the calcium channel, the area of the calcium channel reduced so that the Ca²⁺ current will be proportional to the calcium channel extent.

Figure 5. The Gd³⁺ blocking calcium channel at variety ratio Ca²⁺ and Gd³⁺ stepwise 20% blocking.

d. The amount, half-life, and Duration of Ca2+ in presynaptic

Figure 6 shows the amount of Ca²⁺ present in presynaptic after diffusion from the outside presynaptic. The amount of Ca²⁺ that influx to the presynaptic greatly influenced by the amount of Gd³⁺ present outside the presynaptic. The black line shows an amount of Ca²⁺ in the absence of Gd³⁺ while red, dark blue, light blue, and pink lines indicate Ca²⁺ in presynaptic due to Gd³⁺ with ratio 6:1, 6:2, 6:4, 6:6, respectively. Each line has two phases; the first phase indicates the absorption phase from the initial state to the maximum amount, and the second phase indicates the elimination phase from the maximum amount to the minimum amount. Furthermore, the increasing amount of Gd³⁺ that exists outside presynaptic influences the amount of Ca²⁺ influx to the presynaptic.

Figure 6. Time-dependent of Ca²⁺ in presynaptic with the variation amount of Gd³⁺.

The maximum amount of Ca²⁺ diffusing into the presynaptic in the presence of Gd³⁺ is 1592, 1308, 831, and 622 Ca²⁺ ions and it occurs at t = 0.017 s, 0.015 s, 0.013 s, and 0.007 s, respectively. This data shows that the presence of Gd³⁺ has reduced the maximum number of diffused Ca²⁺. The decreases in the amount of Ca²⁺ caused the total number of Ca²⁺ and diffused reductions of the Area under the Curve (AUC) of the graph.

Then again, the half-life of Ca²⁺ of the highest to the lowest presence of Gd³⁺ in the elimination phase is t_0.5 = 0.062 s, 0.047 s, 0.038 s, and 0.032 s, respectively. The indicates that a high amount of Ca²⁺ in the presynaptic has a longer half-life of Ca²⁺. This advantage is the high Ca²⁺ amount in presynaptic which provides an opportunity for the formation of an active membrane for the synaptic vesicle docking.

The duration of Ca²⁺ in the presynaptic is another important factor because the longer Ca²⁺ due to the large amount in the presynaptic means the opportunities of the synaptic vesicle docked in the active membrane increases. The meaning of duration, in this case, is from the onset time to half-life. Thus, the duration of Ca²⁺ for each presence Gd³⁺ from higher to lower is ∆t = 0.059 s, 0.045 s, 0.036 s, and 0.031 s.

e. Calcium Channel Density

To sum up, this interference in the rate-limiting steps supported by a simulation in which the density of calcium channel decreased. The t_0.5 values plotted as Figure 7 showed and summarised the result of simulation using the different density of calcium channel that is 0.5 to 2 × 10⁴ µm² stepwise 0.5 × 10⁴ µm² with the t_0.5 = 0.0457 s, 0.0068 s, 0.0076 s, and 0.0083 s, respectively.

Figure 7. The effect of calcium channel density on surface presynaptic. Parameters are the same as shown in Table 1 except for calcium channel density. Amount of Gd³⁺ is equal in 2000.

According to the shape of the curve, a particular moment will experience saturation. Thus, the increase in density after saturation did not change the equilibrium time. With faster the equilibrium time, ion migration time shortened. It has shown that calcium channel density has a vital role in ion migration from higher to lower concentration.

f. Active Membrane

The active membrane is the membrane at the bottom of the presynaptic place for synaptic vesicle docking. It provides a location of the synaptic vesicle to be able to release neurotransmitter. An active layer formed due to the interaction between membrane ions and Ca²⁺. Figure 8 shows the number of active membranes occurs based on the amount of Ca²⁺ in the presynaptic, where the amount of Ca²⁺ depends on the ration Ca²⁺ and Gd³⁺ in the initial state. The formation of the active membrane is higher, too. Because of the higher amount of Ca²⁺ in the presynaptic, the probability of Ca²⁺ interaction with the membrane ion is higher. It can seen from the simulation result that the color sequence of the black line is the lowest Gd³⁺. It shows the highest number of the active membrane followed by red, dark blue and light blue lines, respectively.

Figure 8. Time dependence of active membrane creates by interaction with calcium in presynaptic

g. Neurotransmitter Release

Neurotransmitters are stored in a synaptic vesicle. Furthermore, neurotransmitter release is comparable to the amount of synaptic vesicle docking in the active membrane. The active layer is formed due to the role of calcium in the presynaptic. Therefore, Figure 9 shows the results of neurotransmitter release based on the amount of synaptic vesicle. It can be seen that each color has a different amount of presence Gd³⁺ from the initial state. According to the result, the increase in the amount of Gd³⁺ causes different effects for the amount of synaptic vesicle docking and then releases neurotransmitter into the synaptic cleft. All lines show the same patterns that neurotransmitters released are not abrupt. The length of the time gap depends on the amount of Gd³⁺in the initial state. The black line shows Gd³⁺ absence with a steep slope. It means the speed of synaptic vesicles to release neurotransmitters is high and saturated in the vast amount. The pink line shows the highest presence Gd³⁺ on the initial state with a gentle slope. It has proved that the degree of the slope indicates the level of Gd³⁺ presence at the initial state. The presence of Gd³⁺ in the presynaptic inhibits the docking process of a synaptic vesicle, causing a slow release of neurotransmitters by synaptic vesicles. Complementary, the first 0.05 second for each ratio Ca²⁺ and G3+ from lowest to the highest presence of Gd³⁺ indicates different numbers of neurotransmitters that are 2098, 1868, 1525,884, and 590, respectively.

Figure 9. Time dependence of neurotransmitter release to synaptic cleft due to the influence of the number of Gd³⁺.

Discussion

Patients can receive repeated Gd³⁺ injections for diagnostic MRI, and the results show high signal intensity [ 8 , 9 ]. High signal intensity has indicated that contrast material cannot be all released the patient’s body. The presence of Gd³⁺ in the patient’s body raises serious problems because Gd³⁺ is toxic and has the potential for blocking calcium channels [ 6 , 11 ]. The closure of calcium channels by Gd³⁺ can disrupt the signal system in the patient’s body.

Calcium is an essential ion in the signal system body, especially in the synapse. The calcium influence the number of neurotransmitters released into the synaptic cleft [ 22 ]. The action potential causes the calcium channel to open, and the higher the action potential causes the calcium channel to open to increase. The number of calcium channels strongly influences the amount of calcium that enters the presynaptic.

Gd³⁺ around presynaptic has potential as a barrier to calcium channels, and then calcium cannot diffuse into the presynaptic. Gd³⁺ enters the presynaptic through calcium channel and interact with the wall then it called side binding. Gd³⁺ sticking to the wall of calcium channel causing calcium diffusion is blocked into the presynaptic [ 23 ].

The calcium channel is blocked by Gd³⁺, causing interference of calcium diffusion. The disorder is the amount of calcium can enter the presynaptic reduced. The presence of Gd³⁺ in the signal system occurs because of the accumulation of the patient’s body. This pattern is shown in Figure 4; the diffusion of calcium from outside the presynaptic to the inside of the presynaptic is disrupted by the increasing number of Gd³⁺ outside the presynaptic. The increased amount of Gd³⁺ outside the presynaptic causes the amount of calcium that diffuses into the presynaptic to decrease, as shown in Figure 6. A large amount of Gd³⁺ around the presynaptic causes the amount of calcium present in the presynaptic to decrease. The amount of calcium decreases affects the number of docking synaptic vesicles. Another condition, the half-life of calcium in the presynaptic becomes shorter, which means the docking process occurs in a shorter time. This situation sequentially causes the number of neurotransmitters released into the synaptic gap to decrease, as shown in Figure 9 and the signal process to disrupted.

The number of neurotransmitters released into cleft decreases, causing the action potential at the next synapse to decrease, so the weaker the signal that can be transmitted. The presence of Gd³⁺ around the synapse due to the effect of repeated injections greatly influences signaling in the body. Therefore it is necessary to get serious attention in handling patients using Gd³⁺ contrast both the number of doses given and the number of repetitions.

Conclusion

Gadolinium is a substance that is injected into the body which has the advantage of enhancement images of MRI. Gadolinium can differentiate between healthy and unhealthy tissues. In the beginning, the benefit of gadolinium has caused a new problem in the mechanism of chemical synapses. The presence of gadolinium around synapse has affected the amount of calcium diffusion into presynaptic, which the existence of calcium is significant to synaptic vesicle released neurotransmitter as chemical messengers. Gadolinium and calcium compete with each other across of calcium channel. However, gadolinium is attached to the calcium channel surface as calcium blocker. The presence of gadolinium has caused a chain effect for signal transmission at chemical synapse, which reduces the amount of active membrane, synaptic vesicle docking, and neurotransmitter release.

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