Monte Carlo simulation of spontaneous miniature excitatory ...

Pflügers Arch – Eur J Physiol (1998) 435:193–202

© Springer-Verlag 1998

O R I G I NA L A RT I C L E

&roles:Mladen I. Glavinovi´c · Hamid R. Rabie

Monte Carlo simulation of spontaneous miniature excitatory postsynaptic currents in rat hippocampal synapse in the presence and absence of desensitization &misc:Received: 17 April 1997 / Received: after revision: 11 August 1997 / Accepted: 1 September 1997

&p.1:Abstract Using the Monte Carlo method, spontaneous fast excitatory postsynaptic currents (mEPSCs) at a hippocampal synapse were simulated by releasing 150–20,000 glutamate molecules from a point source centred 15 nm above a rectangular grid of 14 × 14 αamino-3-hydroxy-methyl-isoxazole (AMPA) receptors and assuming the channel kinetics to be as reported by Jonas et al. [J Physiol (Lond) 472:615; 1993]. The relationship between the amplitudes of mEPSCs and their time constants of decay is positive, but not pronounced in physiological conditions (except when the number of molecules released is very high). It increases as desensitization is reduced and becomes highly pronounced when it is eliminated. mEPSCs are prolonged with repeated opening of AMPA channels due to enhancement of two concentration-dependent processes: (1) binding of glutamate molecules by AMPA receptors, and (2) occupancy of both activatable bound states. In contrast, the time constant of decay of the patch currents evoked by a short glutamate pulse is independent of glutamate concentration and current amplitude in control conditions, and only moderately concentration dependent in the absence of desensitization. The fast application protocol thus fails to reproduce synaptic currents reliably when there is repeated binding of glutamate molecules to AMPA receptors. During an mEPSC, the occupancy of desensitized states increases rapidly and it strongly depends on the number of glutamate molecules released. Desensitization reaches its maximum after an mEPSC decays to very low levels, and recovers very slowly (from tens to hundreds of milliseconds), and in a concenM. I. Glavinovi´c Department of Physiology, McGill University, 3655 Drummond Street, Montreal, PQ, H3G IY6, Canada M. I. Glavinovi´c (✉) Department of Anaesthesia Research, McGill University, 3655 Drummond Street, Montreal, PQ H3G 1Y6, Canada H. R. Rabie Department of Chemical Engineering, McGill University, 3655 Drummond Street, Montreal, PQ H3G 1Y6, Canada&/fn-block:

tration-dependent manner. In conclusion, under physiological conditions the desensitization of AMPA receptors plays a major role in shaping the time course of mEPSCs by minimizing the repeated opening of AMPA channels. &kwd:Key words Glutamate · AMPA receptor channels · Desensitization · Buffering · Monte Carlo method&bdy:

Introduction The mechanisms determining the amplitude and the time course of unitary synaptic currents, especially in the central nervous system (CNS), are not well understood [5, 9, 16]. The time course of decay of the fast [i.e. α-amino-3hydroxy-methyl-isoxazole (AMPA) receptor activated] excitatory postsynaptic currents (mEPSCs) has been attributed to the kinetics of postsynaptic channel closure [12, 22], or to some combination of prolonged presence of neurotransmitter in the cleft [2, 6, 23] and channel desensitization [19, 24, 25]. Two comprehensive approaches have been traditionally taken to describe the diffusion of neurotransmitter molecules in the cleft coupled to the kinetic models of channel opening and closing: (1) a numerical solution of partial differential equations [27] – in this method the channel kinetics are driven by the bulk concentration of the transmitter in the synaptic cleft; and (2) a Monte Carlo method, in which each transmitter molecule is followed as it diffuses randomly within the synaptic cleft and interacts with the postsynaptic receptors [3, 26] – this allows us to explore the stochastic properties of both neurotransmitter diffusion and channel kinetics. Following the recent measurements of the fast excitatory currents at the mossy fibre CA3 synapse [7, 17, 20], a kinetic scheme for the ligand-gated channel responsible for the fast excitatory currents was published [17]. In the present study we used this kinetic scheme [17] and Monte Carlo methods to investigate the factors affecting the time course of the spontaneous mEPSCs in the hippocampus. Our simulations show that the time constant of decay of mEPSCs (rd), which is amplitude dependent

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only when the number of molecules released is high in physiological conditions, becomes markedly amplitude dependent for any number of molecules when desensitization is reduced or abolished, because the buffering of glutamate in the synaptic cleft, and the occupancy of the bound activable states by the AMPA receptors are both increased and concentration dependent.

Materials and methods Theory Synaptic transmission in the excitatory synapse in the hippocampus was simulated using a Monte Carlo method [3, 26]. This method was used instead of numerically evaluating the partial differential equations that describe the macroscopic quantities. It enables one to study the fluctuations due to the stochastic nature of the diffusion of the individual transmitter molecules, their interactions with the receptor molecules, and the stochastic nature of the gating of the associated ion channels. At each discrete time step: (1) every transmitter molecule is associated with a position (x,y,z), and is either flagged as free or bound – free molecules move randomly in all three dimensions or interact with receptors; (2) every receptor has a fixed position and is considered to be in one of the states of a given kinetic scheme – every receptor has a finite probability of changing to another state according to the kinetic scheme. The changes of the receptor states were assumed to be Markovian (i.e. they were assumed to depend only on their present position and not on their previous history). Computer simulations All simulations in this paper have been done using MATLAB (MathWorks, Natick Mass., USA) on either a 486 or a Pentium IBM computer. Since the rise time of mEPSCs is of the order of ≈100 µs, we chose the time step in our simulation to be 1 µs (see below; [26]). The distance travelled by a transmitter molecule (in each of three dimensions) was chosen randomly from a Gaussian distribution with mean of 0 and a standard deviation σ given by  σ=√ 2Dδt

(1)

[13, 26], where the δt is the length of the time step and D is the diffusion coefficient of the transmitter molecule. The diffusion coefficient of glutamine (D = 7.6 × 10–6 cm2/s measured in water at 25°C; [18]) was taken to be the diffusion coefficient of glutamate in the synapse. The Q10 for diffusion was assumed to be 1.3 [13]. The random numbers were obtained from a random number generator. The diffusion in a restricted space was simulated by assuming that the transmitter molecules collide elastically with the “walls” of the space (i.e. presynaptic and postsynaptic membranes; [26]). Finally all molecules that reach the edge of the model synapse and diffuse away into the “infinite” space (or return from it into the synaptic cleft) were also followed throughout simulation. According to the kinetic scheme of channel gating (Fig. 1) a receptor can be unbound (C1), in a single- or in a double-bound state (C2 and C3 respectively; these are also called activatable states), open (O4), or in one of the three desensitized states (C5, C6 and C7). Following previous reports [3, 26], we associated with each state of the receptor a surface area and a probability of binding, given that a transmitter molecule “hits” this receptor surface. The inverse of the receptor surface area is taken to be the density of the receptor molecules (σr) at the postsynaptic membrane. The probability (Pb) that a transmitter molecule, after hitting the receptor surface, will bind in a given time step (δt) is related to the macroscopic rate constant by Pb = [(σρκ)/Na]√ (πδ  t) /D

(2)

where Na is Avogadro’s number and κ is the appropriate rate constant of binding (in M–1 s–1). For steps in the kinetic scheme that did not involve binding of the transmitter, the probability (p) that a receptor will move to a new state in a given time step (δt) is related to the macroscopic rate constant by p = 1 –e –k δ t

(3)

where k is the appropriate rate constant (in s –1). The time step (chosen to be 1 µs in all our calculations) was such that the probability of a receptor changing state twice within one time step was < 1 in 100. It has been shown previously that the results do not become more accurate by reducing the time step further [26]. Equation 3 also applies to the situation when a transmitter molecule unbinds from a receptor. We have chosen to move a molecule the mean length of the random jump (0.67σ) perpendicularly away from the receptor surface at unbinding: (1) to ensure that the probability of a given receptor making a transition to a bound state does not depend on the receptor’s previous history; and (2) because such physical separation between the neurotransmitter and the receptor accurately reproduces the macroscopic unbinding rate constant [3]. In all our calculations we used the rate constants of the kinetic scheme of Jonas et al. [17] without restrictions, as these values have been found to be more adequate than those with restrictions (Fig. 1). The rate constants used in the kinetic scheme, however, were adjusted for the difference in temperature (37°C in all our calculations) and assuming a Q10 of 4.0 for all rate constants as done previously [26]. We modelled a typical synapse as one with 196 receptors in the postsynaptic membrane, 14 nm apart in a rectangular array of 14 × 14, and the synaptic cleft as a 15-nm-thick sheet [26]. This choice was made for a “typical” synapse because, assuming a particle density of 3000 particles per µm2 (from CA1 pyramidal cells, [11]), one obtains 600 particles within 0.2 µm2. On the other hand, the lower limit of the number of available fast excitatory channels in a mossy fibre CA3 synapse has been estimated from the average amplitude of quantal events as 20–100 [17]. A simulation of voltage-clamp experiments on an outside-out membrane patch was done by constructing a 100-nm “box” around the receptor grid. We fixed the concentration of glutamate at a given level while keeping the size of the box constant. In order to maintain the concentration of glutamate, any binding or unbinding of glutamate molecules was not associated with removal or addition of glutamate molecules from or to the “box”. The glutamate molecules were distributed randomly within the box at the beginning of the simulation. To simulate abrupt changes in the glutamate concentration (pulses), we distributed additional molecules at random positions in the box or removed a certain number of free molecules.

Results Amplitude dependence of kinetics of synaptic currents in the presence and absence of desensitization To simulate the release of a single vesicle of neurotransmitter, N molecules were simultaneously released into the cleft at a point source on the presynaptic membrane, centred above the postsynaptic receptor grid. The time course of the number of channels in the “open” state (Fig. 1, state O4) simulates mEPSC that might be recorded under conditions of perfect voltage clamp and no dendritic filtering [15]. Figure 2A illustrates such mEPSCs simulated at 37°C. N ranged from 600 to 10,000 as indicated (traces are averages of five and ten simulation runs with different random seeds; two upper and three lower traces, respectively). Note that the decay times of mEPSCs (τd) became clearly longer as N increases.

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Fig. 1 Kinetic scheme for gating of AMPA channels. The constants taken from Jonas et al. [17] assume no restrictions. They are: K+1 = 3.67 × 107 M–1 s–1, k-1 = 3.41 × 104 s—1, K+2 = 22.7 × 107 M–1 s–1, k-2 = 2.61 × 104 s–1, K+3 = 1.02 × 107 M–1 s–1, k-3 = 366 s–1 for glutamate binding; α = 3.39 × 104 s–1, β = 7200 s–1 for channel opening; and α1 = 2.31 × 104 s–1, β1 = 314 s–1, α2 = 1376 s–1, β2 = 5.82 s–1, α3 = 142 s–1, β3 = 32 s–1, α4 = 134.4 s–1, β4 = 1523 s–1 for the desensitization pathway&ig.c:/f

Fig. 2A, B Decay of simulated miniature excitatory postsynaptic currents (mEPSCs) is concentration, and thus amplitude dependent. Two families of simulated mEPSCs are shown, one calculated assuming physiological rate constants for desensitization (A; control), and the other calculated assuming that all desensitized states have been eliminated (B; no desensitization). The number of glutamate molecules released (N) was as indicated. Traces are averages of 5 and 10 simulations runs with different random seeds for the 2 upper and 3 lower traces respectively. The time course of the postsynaptic current is expressed as the fraction of the total number of channels in the open state at any point in time. The decay phase of mEPSCs (τd) increases as N increases and elimination of desensitization prolongs it further&ig.c:/f

Several studies have shown that mEPSCs are prolonged following application of compounds such as aniracetam or cyclothiazide that reduce or abolish desensitization [1, 10, 14, 25]. Furthermore our studies have suggested that the amplitude dependence of τd increases following such a treatment [1, 10]. Since it may be argued that this is due to the presence of different types of AMPA channels at different synapses (with different single-channel conductance, mean open time and sensitivity to desensitization) we simulated the synaptic currents in the presence and in the absence of desensitization to determine what the amplitude dependence of τd is (in the presence and in absence of desensitization) at a synapse being mediated by the same type of AMPA channels. The simulations focused on establishing whether the pu-

Fig. 3A The amplitude dependence of decay times (rd) of mEPSCs increases as desensitization is reduced and becomes very pronounced when it is eliminated (note the semilog scale). B The amplitude dependence of τd in the absence of desensitization, but with the density of AMPA receptors reduced to a half or increased to twice the control value. C The relationship between the number of molecules released (N) and mEPSC amplitude (A); D N versus τd. [Squares Physiological rates of desensitization, upright triangles desensitization reduced by decreasing α1 to one-tenth of the control value, circles all desensitization states eliminated, downward triangles and diamonds, dashed line all desensitization states eliminated and the diffusion constant reduced to a half and a quarter of control value (as indicated), crosses, dotted line closure rate reduced to one-third of the control value]&ig.c:/f

tative amplitude dependence of τd is due to the concentration dependence of channel gating, buffering of glutamate molecules by AMPA receptors or some combination of these. Figure 2B illustrates a family of mEPSCs equivalent to that shown in Fig. 2A but with all desensitized states abolished. mEPSCs are clearly prolonged following abolition of desensitization. To gain an insight into whether other factors, and especially the buffering of glutamate molecules by AMPA receptors, contribute to shaping the time course of mEPSCs, we made additional simulations that were in all respects equivalent, but permitted only a single binding of a glutamate molecule to AMPA receptors. Following the unbinding, the glutamate molecule was taken out of the system. Finally, we also determined the amplitude dependence of τd in the absence of desensitization, but with either half or double the density of AMPA receptors. Figure 3 summarizes these findings showing the amplitude dependence of τd (Fig. 3A), and the relationships between the amplitude of the mEPSC or τd and N (Fig. 3C and D respec-

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tively; the maximal occupancy of the open state was taken to be the amplitude). The relationship between τd and the amplitude of the mEPSC was positive when desensitization rates were at their physiological level, but was not very pronounced, irrespective of whether a single or a multiple binding of glutamate molecules was assumed, except for large values of N. The relationships involving the single binding are not shown to avoid crowding, and were essentially the same as those for multiple binding. When desensitization was reduced (by reducing the rate from the single to the desensitized state), and especially when it was eliminated, τd became markedly amplitude dependent (Fig. 3A, B). A reduction of desensitization, by either a reduction of the rate from the double-bound state to a corresponding desensitized state or alternatively by an increase of the rate leading in the opposite direction, was in all respects similar to the one presented (not shown). The difference in duration of τd for a case of multiple and single binding became clear in the absence of desensitization (Fig. 3D). However, even complete elimination of desensitization altered relationship between the amplitude of the mEPSC and N only modestly (Fig. 3C); in all cases the buffering of glutamate molecules had very little effect on the relationship (not shown). Slower diffusion (i.e. lower diffusion constant) leads to a markedly longer τd. With slower closing of the open channel, the τd versus amplitude relationship was shifted upwards but the slope was not increased (Fig. 3A). Finally, reducing the density of receptors did not lead to less, but rather to more, pronounced amplitude dependence of τd (note that to enable a comparison the amplitude values were multiplied by the number of AMPA receptors; Fig. 3B). These findings argue that buffering of glutamate molecules plays only a minor role in altering either the amplitudes or the time courses of mEPSCs in the absence of desensitization, but plays an important role when desensitization is abolished (especially if the diffusion of glutamate in the cleft is slower than that in solution). These findings, however, also prompt several questions. According to our simulations, the number of glutamate molecules released was typically greater, and in some cases much greater, than the number of AMPA receptors postsynaptically. How could so few AMPA receptors buffer so many glutamate molecules? This is discussed in the following section. Buffering of glutamate in the synaptic cleft – effect of desensitization Buffering was calculated as the difference in glutamate concentration in the synaptic cleft between a case when AMPA receptors were present and a case when they were completely absent. In all simulations, the concentration of glutamate in the cleft was calculated as an average concentration in a volume centred above the receptor grid. We used a volume that covers the postsynaptic grid and overlaps the edges of the grid by 5 nm in every direction (15 × 192 × 192 nm3; [26]). Figure 4A shows the dependence of the cleft glutamate concentration on

Fig. 4A, B The cleft concentration of glutamate is altered significantly because of buffering by AMPA receptors. A The glutamate cleft concentration in the absence of AMPA receptors (filled circles), in their presence and with physiological rates of desensitization (filled downward triangles) or with all desensitization states eliminated (filled upright triangles). The difference between physiological or zero desensitization and no AMPA receptors (open upright or downward triangles respectively). In all cases, the concentration was calculated as an average over an interval of from 0.95 to 1.0 ms from the start of the release. B Time course of glutamate concentration in the synaptic cleft (semilog scale). Three families of three traces each are shown. The number of molecules released is given to the right of the trace. In all cases the upper trace represents the simulation in the absence of desensitization, the middle trace the physiological case and the lower trace simulation in absence of AMPA receptors. The cleft concentration is clearly greater in the absence of desensitization, with the effect increasing with time&ig.c:/f

N. The buffering of glutamate molecules by AMPA receptors was especially important for large values of N (buffering was thus concentration dependent), and was clearly greater throughout when desensitization was abolished. Change of the gating mechanism clearly can alter the buffering of glutamate in the synaptic cleft (the elimination of desensitization of AMPA receptors increases the buffering). Note also that the glutamate concentration increase due to buffering becomes relatively more important with time (Fig. 4B). Occupancy of an unbound and activatable singleand double-bound states – effect of desensitization The occupancy of the activatable double-bound state (state C3; FCdb) and the transition probability from the double-bound to the open state (Tdb,o) determine the frequency of opening of AMPA channels. Similar reasoning applies to the occupancy of the activatable single-bound state (state C2; FCsb), the transition probability from the single-bound to the activatable double-bound state

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Fig. 5A, B The occupancy of AMPA receptors in a single- or a double-bound activatable state increases when desensitization is eliminated. A (Circles Occupancy of the activatable single-bound state, upright triangles the activatable double-bound state, squares their sum.) In all cases open symbols indicate a physiological rate of desensitization and filled symbols the case when all desensitized states are eliminated. All estimates are averages over an interval of from 0.95 to 1.0 ms from the start of the release. B Occupancy ratios (zero/physiological desensitization). Filled circles, upright triangles and squares are the symbols for the activatable, single- or double-bound states, and their sum, respectively. Note that the ratios are always greater than one (straight line), and are especially pronounced for low numbers of molecules released. C The occupancy of the activatable double-bound state is greater in the absence of desensitization throughout the time interval examined. Both traces are the averages of 10 runs&ig.c:/f

(Tsb,db; Tsb,db was, however, strongly dependent on the glutamate concentration in the synaptic cleft) and the frequency of transition from the activatable single-bound to the activatable double-bound state. Figure 5A gives the occupancy of the activatable single-bound and double-bound states as well as their sum. The occupancy ratio is given in Fig. 5B (zero desensitization over control). The ratio, which was always greater than one (straight line), was especially high for low values of N. These ratios are expected to be greater than unity throughout the time interval examined, since over the whole interval the occupancy of the activatable double-bound state was greater in the absence of desensitization (Fig. 5C). To better understand how changes of the glutamate concentration in the synaptic cleft and the occupancy of the activatable bound states affect the transition probability and the frequency of opening of the AMPA channels,

Fig. 6A Occupancy of the unbound state is also affected by the presence or absence of desensitization. The number of molecules released is as indicated. Occupancy was estimated 1 ms from the start of release. B The ratio of the occupancies (FCUnb, NoDes/ FCUnb, Control) has a maximum when approximately 2500 molecules are released, and is approximately four (i.e. four times as many AMPA channels are in an unbound state in the absence of desensitization)&ig.c:/f

we studied a case of physiological and one of zero desensitization. We set N to 1250 and assessed the results 1 ms after the start of release. The transitional probability from the activatable double-bound to the open state was, in the control case, Tdb,o = α/(α + α2 + k–2), and was equal to 0.55; for zero desensitization this gives α/(α + k–2) and 0.57. Since the frequency of transitions to the open state from the activatable double-bound state was equal to FCdb × Tdb,o, and since FCdb was 1.69% for physiological desensitization and 5.81% for zero desensitization, the frequency of transition increases 3.5 times. A similar line of argument applies to a transition from a single-bound to an activatable double-bound state. Tsb,db = K+2/(α1 + K+2 + k–1), and was equal to 0.057 for a control case. For a zero desensitization case this gives Tsb,db = K+2/(K+2 + k–1), which was equal to 0.163. Since the occupancy of the activatable single-bound state was 0.82% and 8.1% for the control and the zero desensitization cases, respectively, the frequency of transition increases 28.3 times. Thus, the increase was so pronounced because of: (1) a much greater FCsb, and (2) a greater Tsb,db (this occurs mainly because of a greater K+2; K+2 was concentration dependent and the glutamate concentration in the cleft increases) and to a much lesser extent because α1 was set to zero). The relationship between Tsb,db and the concentration of glutamate is strongly nonlinear (not shown). As a result, a very small fraction of all transitions occurs between a single-bound and an activatable double-bound state at low concentrations, but essentially all occur at high concentrations (this

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Fig. 7A The occupancy of individual desensitized states (FCDes) and their sum (all determined at 1 ms from the start of release) is strongly concentration dependent, i.e. dependent on the number of glutamate molecules (N) released into the synaptic cleft. Note that AMPA receptors desensitized primarily to state seven for low values of N, and to state six for high values of N. B The relationship between the desensitization maxima (for the sum of all desensitized states) and N does not itself have a maximum. The values are higher than shown in A due to the increase in the occupancy of desensitized states after the mEPSC declined to very low levels. C The time constant of recovery from desensitization does not show either a maximum or a saturation and continues to increase with N&ig.c:/f

change in the level of transitions occurs within a very narrow range of concentrations). When desensitization was abolished the sensitivity of Tsb,db to glutamate concentration increased, i.e. there was a shift to the left. This increase is another reason why a lower desensitization leads to a higher occurrence of reopening of AMPA channels and to a prolongation of mEPSCs but only to marginally greater amplitudes of mEPSCs. Finally the occupancy of the unbound state (state C1) also changed when desensitization was abolished. Figure 6A shows the occupancy of the unbound state 1 ms after the release of the transmitter, as a function of N. Note that irrespective of N more AMPA receptors were in the unbound state in the absence of desensitization than in its presence. However, their ratio (i.e. the ratio of the occupancy in the absence and in the presence of desensitization; Fig. 6B) was about 1 at low values of N. It reached to a maximum of 4 at N ≈ 2500, and decreased to 1 with further increases in N. A higher level of occupancy of the unbound state results in a greater occupancy of the activatable single-bound state as well as of the activatable double-bound and the open states. It also con-

Fig. 8A–D The rates of decay of patch-clamp currents following brief pulses of glutamate (“deactivation rates”) are not concentration dependent in the presence of densitization, but show a modest concentration dependence its absence. Glutamate molecules are positioned randomly in a confined volume above a rectangular grid of 194 unbound AMPA receptors 14 nm apart, and are permitted to diffuse and interact with receptors randomly. After 0.125 ms all unbound molecules are removed from the simulation, as are the rest as soon as they become unbound. Two families of traces of occupancy of the open state are shown, one calculated assuming physiological rates of desensitization (A) and other assuming that all desensitized states are eliminated (B; each trace is an average of 10 runs). The concentration dependence of “deactivation rates” determined from the decay phase of the currents following a 0.125-ms glutamate pulse [C; open circles physiological rates of desensitization, filled circles all desensitized states are abolished (“zero desensitization”)]. D Time course of the occupancy of the activatable double-bound state. Two concentrations of glutamate, i.e. 1 mM (zero desensitization and control; two lower overlapping traces), and 5 mM (zero desensitization and control; the first and the second from the top respectively), were tested&ig.c:/f

tributes to the higher concentration of glutamate in the synaptic cleft (i.e. to greater buffering). Concentration dependence of desensitization of synaptic currents Figure 7A gives the occupancy of different desensitized states, as well as their sum (all calculated 1 ms from the start of release of transmitter) as a function of N. They all exhibit maxima that occur at different values of N. Figure 7B gives the dependence of desensitization maxima on N and Fig. 7C shows the dependence of the time constant of recovery from desensitization (determined

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Fig. 9A–D The rates of decay of patch-clamp currents during pulses of glutamate with intermediate duration (“desensitization rates”) are not concentration dependent. Glutamate molecules are positioned randomly in a confined volume above a rectangular grid of 194 unbound AMPA receptors 14 nm apart, and are permitted to diffuse and interact with receptors randomly. A The family of traces of occupancy of the open state shown was calculated assuming physiological rates of desensitization. B The concentration dependence of “desensitization rates” determined from the decay phase of the currents during 2-ms glutamate pulses. C Corresponding family of traces of occupancy of combined desensitization states (glutamate concentrations were as indicated; 10, 5 and 2 runs were averaged when 0.5–2 mM, 5 mM and 10–20 mM were used, respectively). D The concentration dependence of occupancy of combined desensitization states (determined at the end of glutamate pulse) shows a broad but a clear maximum at ≈0.5 mM

from the decay phases of the desensitization occupancy traces) on N. Both the time constant of desensitization recovery and the desensitization maxima strongly depend on N, but their relationships differ greatly. While the former continues to increase with N, the latter shows saturation with its values approaching the theoretical limit (i.e. almost all AMPA receptors become desensitized following a single mEPSC) even for comparatively low values of N. Simulations of macroscopic patch-clamp currents We simulated macroscopic patch-clamp currents to determine how currents, produced with a glutamate pulse with a well-defined time course and without the contribution of buffering, depend on N or on the abolition of

desensitization. Figure 8 gives two families of open channel traces resulting from 0.125-ms pulses of glutamate (concentration in mM as indicated; semilog scale) followed by 0.875 ms of recovery. Figure 8A shows physiological rates of desensitization, while Fig. 8B shows zero desensitization. The duration of the glutamate pulse was chosen to be this short because the rates in the kinetic scheme were high (due to the high temperature assumed in the present simulation – see Materials and methods). Deactivation rates were essentially concentration independent for physiological rates of desensitization, whereas they were moderately concentration dependent in the absence of desensitization (Fig. 8C). This occurred as a result of the concentration dependence of the occupancy of the open state and a high transition probability between the activatable double-bound and the open states. Both factors favour a repeated and a concentration-dependent opening of AMPA channels, and, as a result, a concentration-dependent occupancy of not only the open but also of the activatable double-bound state. This is illustrated in Fig. 8D in which the time course of the occupancy of the activatable double-bound state is shown for two different concentrations of glutamate: 1 mM (zero desensitization and control; two lower overlapping traces), and 5 mM (zero desensitization and control; the first and the second from the top, respectively). Figure 9 gives two families of traces, one for the occupancy of the open state (A) and the other for the occupancy of all desensitized states (C; concentrations in mM were as indicated). The time constants of desensitization (estimated from fits of a single exponential and a constant to the traces shown in Fig. 9A) did not show a clear concen-

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tration dependence (Fig. 9B). The concentration depen- Buffering of glutamate molecules by AMPA receptors dence of the occupancy of all desensitized states (deter- and occupancy of activatable bound states during mined 1 ms after the beginning of simulation) was obvi- an mEPSC ous, however, peaking at approximately 0.5 mM (Fig. 9D). Initially, the cleft glutamate concentration decreases rapidly in the presence or absence of desensitization and, as Discussion expected during this time interval, the desensitization has a minimal or no effect on the rate of decrease. However, Amplitude and time course of miniature currents at approximately 0.2 ms, when the rate of decrease slows in the presence and absence of desensitization considerably and the desensitization has an important effect on the time course of mEPSCs, the glutamate conIt is still controversial whether a positive (or any) relation- centration is already significantly reduced. Thus, these ship exists between the amplitudes and the kinetics of the findings do not support the interesting recent suggestion fast spontaneous miniature currents. Several reports have [8] that the glutamate concentration has to be high and argued against such a positive relationship [4, 14]. In con- essentially constant for the duration of an mEPSC if detrast, our recent results show that such a positive relation- sensitization is to have a major impact on the time course ship exists, as demonstrated by control recordings, and of mEPSCs. As discussed later, concomitant changes of that it increases dramatically following a reduction of de- the occupancy of the single- and the activatable doublesensitization by aniracetam and cyclothiazide [1, 10]. This bound state, as well as changes of the transition probastudy was undertaken to clarify whether the kinetics of bility from a single- to the double-bound activatable state mEPSCs is amplitude dependent at synapse(s) with the appear to be responsible for these findings. same type of AMPA receptors. The mEPSCs were simuThe increase in the cleft glutamate concentration due lated using Monte Carlo methods. to the buffering (assessed from the concentration differThe amplitude of mEPSCs is not greatly affected by a ence in the presence and absence of AMPA receptors) reduction or a complete abolition of desensitization, irre- depends on the number of glutamate molecules released spective of N values or whether single or repeated bind- – buffering is thus concentration dependent. A relative ing of glutamate molecules is assumed. This is in excel- increase (i.e. the concentration increase due to the bufflent agreement with the experimental findings that neither ering normalized by the glutamate concentration in the means nor CV values of the amplitude change signifi- absence of any AMPA receptors) assessed 1 ms after the cantly following the addition of aniracetam or cyclothi- start of release of glutamate molecules was greater for azide, which profoundly affects their time course [1, 10, low values of N, and was especially pronounced in the 14]. The relationship between the decay time of mEPSCs absence of desensitization: it ranged from 15 to 115% (τd) and its amplitude is positive but not pronounced (ex- and from 46 to 228% for control and zero desensitizacept for large values of N) when the rates of desensitiza- tion, respectively. Buffering of glutamate by AMPA retion are at physiological levels. However, it becomes ceptors clearly and strongly depends on the mechanism markedly so when desensitization is abolished because of gating of AMPA channels. Note, however, that the the prolongation of τd is amplitude dependent. The lower glutamate is not likely to be buffered by AMPA receptors the diffusion constant (i.e. the slower the diffusion) the only. Uptake transporters may also be an important facgreater the amplitude dependence of τd. On the other tor in affecting the kinetics of synaptic currents [2, 21]. hand, the rate of closure of open AMPA receptor chan- If their contribution is highly significant, they may mask nels does not increase the amplitude dependence of τd. the differences in the buffering of glutamate by AMPA When only a single binding of glutamate molecules to receptors. AMPA receptors is permitted to occur τd values are shortProlongation of mEPSCs caused by the frequent reer. However, when the rates of desensitization are at opening of AMPA channels is also due to a greater occuphysiological levels, repeated binding of glutamate mole- pancy of the activatable double-bound state. This may cules has little effect on τd. Its effect becomes very pro- occur either because of the greater occupancy of the actnounced when desensitization is abolished. These find- ivatable single-bound state and/or the greater transition ings all suggest that in the absence of desensitization, probability from the single- to the double-bound activamEPSCs are prolonged because of the repeated opening table state. Both changes occur as N increases and/or as of AMPA channels, itself caused by repeated binding of desensitization is reduced or eliminated; neither is surglutamate molecules to AMPA receptors. A surprising prising. The two rates κ+1 and κ+2, leading to the singlefinding is that in the absence of desensitization, a greater and the double-bound activatable states respectively, are density of AMPA receptor channels is not associated with concentration dependent. Furthermore, with desensitizaa greater, but with a lower, amplitude dependence of τd. tion reduced or eliminated, the occupancy of all nondeGreater amplitude of mEPSCs and the insensitivity of τd sensitized states (i.e. the activatable bound states, the unto higher density of AMPA receptor channels explain bound state and the open state) increases markedly and these findings, which are in contrast to changes observed in a concentration-dependent manner. Almost all AMPA at the neuromuscular junction. This is clearly in contrast receptors become desensitized at physiological rates of desensitization, even for modest values of N. to changes observed at the neuromuscular junction.

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It is beyond the scope of this paper to characterize in detail why altering the density of AMPA receptor channels does not affect τd. However, during the 1-ms time interval starting from the beginning of glutamate release, the glutamate concentration in the cleft was (except at the very beginning) higher in the case of a greater density of AMPA receptor channels, but not four times higher (not shown). As a result, the repeated binding of glutamate molecules per individual AMPA receptor (and the repeated opening of AMPA channels) is less rather than more likely to occur. Occupancy of desensitized states during and after a single mEPSC The occupancy of all desensitized states (during and after a single mEPSC) was found to be concentration dependent. Generally, and not surprisingly, state seven is occupied the most at low concentrations of glutamate. As the glutamate concentration increases, the occupancy of states five and six becomes more important. Maximal desensitization (defined as the maximal occupancy of all desensitized states) is strongly dependent on N, but even for a relatively low N a very high level of desensitization of AMPA channels is reached. The time course of desensitization recovery appears to be monoexponential and slow (with a duration that increases as N increases) and is similar to the time course of the paired pulse depression reported recently [14, 25]. Progressively greater occupancy of states six and five is responsible for this prolongation (their conversion to nondesensitized states and ultimately to the unbound state is slower than that for desensitized state seven). Deactivation and desensitization of patch currents Earlier experimental studies have shown that, for a prolonged application of glutamate pulses, the time constant of decrease of the macroscopic patch currents (a standard measure of desensitization) is essentially concentration independent [7]. Our simulations of patch currents during 2-ms glutamate pulses (2 ms is found to be long enough because the kinetics of gating of AMPA channels is fast due to the high temperature assumed in the present simulation) show a similar concentration independence. This is not unexpected since the kinetic model of AMPA channel gating is as given by Jonas et al. [17], but it serves as additional evidence that our simulations provide an adequate means for assessing the synaptic and patch currents. Furthermore, the time course of the decrease of the current flow through the open channels of the simulated macroscopic patch currents following a short (0.125 ms) glutamate pulse (a standard measure of deactivation) was found to be essentially concentration independent when the rates of desensitization are at physiological levels. A modest concentration dependence is observed when desensitization is abolished.

The agreement between the simulated synaptic currents and the response to short (0.125 ms) glutamate pulses is good when: (1) the synaptic currents result from the release of low number of molecules, and (2) desensitization is at a physiological level. However, whenever the repeated opening of AMPA channels due to the repeated binding of glutamate molecules becomes important, either because of the greater buffering of glutamate molecules in the synaptic cleft, or an elevated occupancy of the activatable bound states or both (as occurs during reduced or no desensitization), the fast application protocol becomes inadequate for reproducing the synaptic currents. Therefore, any conclusion about the synaptic currents drawn from patch currents should be treated with great caution. Thus, this simulation also shows that the time course of deactivation is not insensitive to the level of desensitization, emphasizing the need for caution in using a fast application protocol. Nevertheless, note that the conclusions reached in our simulations of the synaptic currents depend on the kinetic scheme used, and might not hold for other combinations of rate constants or receptor state diagrams. Finally, good agreement between the theoretical calculations of how a reduction or abolition of desensitization affects the amplitude of mEPSCs, τd and their relationship and the actual experimental findings suggests that the experimental findings are due to the events at synapses with the same type of AMPA channels. It is thus not necessary to postulate the existence of AMPA channels with different single-channel conductance, mean open time or sensitivity to desensitization at different synapses. This is an important point since recent evidence indicates that the functional properties of somatic and dendritic glutamate receptors in the CA3 mossy fibre synapses are similar [20]. We did not explore the effect of changes in desensitization on rise times since throughout this study we assumed that release occurs from an instantaneous point source. The release from a vesicle through a fusion pore is not likely to have an important effect on τd but is expected to be a very important factor in determining the duration of τr. In conclusion, this study helps to reconcile the fact that in control recordings the time constant of decay of mEPSCs is essentially the same as that of the deactivation, and the growing evidence that desensitization plays a major role in shaping the time course of mEPSCs. &p.2:Acknowledgements Drs. K. Krnjevic, M. Mackey and L. Glass read the manuscript and made valuable comments. Supported by the Medical Research Council of Canada (M.I.G.).

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