INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The importance of Ca²⁺ flux through voltage-dependent ion channels cannot be overstated. Calcium entering the cell through this pathway participates in muscle contraction, gene expression, synaptic transmission, and various forms of short- and long-term memory (Bito et al. 1997; Tsien and Tsien 1990). It is therefore not surprising that Ca²⁺ channels are subject to control through a myriad of electrical, biochemical, and genetic pathways. In recent years there have been numerous studies on Ca²⁺ channel regulation through G protein signaling (for example, Arnot et al. 2000; Bean 1989; Boland and Bean 1993; Chen and van den Pol 1998; Dittman and Regehr 1996; Garcia et al. 1998; Patil et al. 1996; Ruiz-Velasco and Ikeda 2000; Stanley and Mirotznik 1997; Zamponi and Snutch 1998). Channel regulation may be due to the direct action of activated G proteins or may involve additional second-messenger pathways (Diversé-Pierluissi et al. 2000). The focus of the present study is on functional implications of direct regulation of N-type Ca²⁺ channels, where it has been established that the G subunits of activated G proteins bind directly to the channels at the cytoplasmic linker region between domains I and II of the ₁ subunit and also at the carboxyl terminal region (Herlitze et al. 1996; Ikeda 1996; Zamponi et al. 1997; Zhang et al. 1996). Such binding puts channels into a reluctant state, reducing the net Ca²⁺ flux into the cell (Bean 1989). This inhibition can be relieved by depolarization (Bean 1989), which results in unbinding of G from the channel (Zamponi and Snutch 1998).

Two defining characteristics of voltage-dependent G protein-mediated Ca²⁺ channel inhibition are "kinetic slowing" (Patil et al. 1996), whereby the Ca²⁺ current time course is slowed in the presence of G protein agonists, and "prepulse facilitation" (Boland and Bean 1993), whereby the Ca²⁺ current evoked by a voltage pulse is facilitated if preceded by a depolarizing prepulse. Recent studies have shown that the extent of kinetic slowing and prepulse facilitation depend greatly on the specific G protein  and  subunits involved. This was shown for native N-type Ca²⁺ channels in the presence of transfected G dimers in cervical ganglion cells (Garcia et al. 1998; Ruiz-Velasco and Ikeda 2000) and for N-type (Zhou et al. 2000) or N- and P-type Ca²⁺ channels co-transfected with G dimers in human embryonic kidney cells (Arnot et al. 2000). G specificity raises the possibility that a single agonist, such as glutamate or norepinephrine, can bind to different receptor types and activate several G dimeric isoforms within the same cell or cell compartment, each dimer having a distinct inhibitory action on the Ca²⁺ channels.

Although inhibition of Ca²⁺ channels can have many functional ramifications in neurons, the focus of the present study is the role that G protein inhibition may play in signal processing at the synapse by regulating the probability of synaptic transmitter release. Exocytosis of synaptic transmitters occurs upon binding of Ca²⁺ to proteins associated with the vesicle fusion machinery. The source of this Ca²⁺ is influx through Ca²⁺ channels, primarily N- and P-type, colocalized with synaptic vesicles (Llinás et al. 1992; Simon and Llinás 1985). It has been demonstrated that bath application of G protein agonists reduce transmitter release by inhibiting Ca²⁺ channels (Boehm and Betz 1997; Chen and van den Pol 1997; Dittman and Regehr 1996; Qian et al. 1997; Takahashi et al. 1998; Wu and Saggau 1994). Recently, G subunits were injected directly into the large calyx of Held synapse by whole cell patch pipettes, and shown to inhibit P-type Ca²⁺ channels (Kajikawa et al. 2001). Other studies have shown that facilitation of transmitter release was enhanced by G protein agonists (Brody and Yue 2000; Dittman and Regehr 1997; Dunwiddie and Haas 1985; Isaacson et al. 1993; Shen and Johnson 1997). These latter studies are consistent with data showing that trains of short action potential-like depolarizations can relieve G protein inhibition of N-type channels in central neurons (Williams et al. 1997) and recombinant P/Q-type Ca²⁺ channels in HEK cells (Brody et al. 1997). Taken together, these data provide strong evidence that G protein inhibition and voltage-dependent relief of inhibition may play an important role in short-term synaptic plasticity. This was explored in a computational study, where it was demonstrated that the facilitory effects of residual Ca²⁺ can be compounded by relief of channel inhibition, significantly augmenting short-term synaptic enhancement (Bertram and Behan 1999).

Activation of G proteins is achieved through the binding of hormones or neurotransmitters to G protein-coupled receptors, leading to dissociation of G and G subunits. One intriguing pathway involves the release of neurotransmitters and subsequent binding onto the same presynaptic terminal. Autoinhibition of transmitter release then occurs as the result of the G protein-mediated inhibition of Ca²⁺ channels (Wu and Saggau 1997). In this report, we use computational modeling to address two questions: 1) what is the role of G protein-mediated autoinhibition on synaptic signal processing, and 2) how is signal processing affected by the different G isoforms? We employ a previously developed model for an N-type Ca²⁺ channel (Bertram and Behan 1999; Boland and Bean 1993) with G protein unbinding kinetics modified according to data for different G dimeric isoforms (Fig. 2) (Arnot et al. 2000). Although these data were obtained from HEK cells co-transfected with N-type channels (_1B + ₂   + _1b) and G dimers, the properties of the regulatory mechanism should be similar for similar channels and G proteins expressed in synapses.

Computational studies have shown previously that G protein autoinhibitory feedback on the presynaptic terminal acts like a high-pass filter, allowing high-frequency signals to pass through to the postsynaptic cell while attenuating and essentially filtering out low-frequency signals (Bertram 2001). Experimental support for this was provided by studies of bullfrog sympathetic ganglia, where presynaptic depression was prominent during 1- and 5-Hz stimulation, but not at 20 Hz (Shen and Horn 1996). This filtering is due to the kinetic slowing produced as activated G dimers accumulate. As we show here with 10-ms test pulses, kinetic slowing is expressed as a reduction in the initial slope of the Ca²⁺ current (Fig. 2), which would greatly reduce the amount of Ca²⁺ entering the terminal during an action potential. During high-frequency trains this inhibition is relieved as G dimers unbind from Ca²⁺ channels during the action potentials. Based on the present computational study, we predict that activation of different G isoforms leads to very different filtering properties. In particular, the range of frequencies over which signals are suppressed is different for different G isoforms.

We use network simulations to demonstrate that high-pass filtering removes low-frequency noise from input-layer (i.e., presynaptic) neurons, increasing the signal-to-noise ratio in the output layer (i.e., postsynaptic) neurons and enhancing the spatial contrast of the transmitted "image." Another mechanism for increasing spatial contrast has been described (Shepherd 1998), involving reciprocal inhibitory coupling of neighboring neurons. The novelty of the present mechanism is that no circuitry is required; all that is required is that input-layer neurons possess G protein-mediated autoinhibitory feedback.

We also consider signals produced by the concident firing of two or more high-frequency input cells. The fidelity of this type of signaling is degraded by low-frequency input, which can summate with a postsynaptic response from a high-frequency input to generate a "false positive" response. G protein-mediated autoinhibition reduces the input-layer noise, decreasing the number of false positive output-layer responses and so increasing the fidelity of coincidence detection.

Finally, we emphasize that the filtering characteristics associated with a specific G dimer depend on many biophysical parameters. We demonstrate this by varying the unbinding rate of a transmitter molecule from the presynaptic autoreceptor. Faster unbinding lowers the filter cut while slower unbinding raises the cut. These maneuvers effectively adjust the definitions of "signal" and "noise."

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Experimental

Human embryonic kidney-tsa201 cells (HEK-tsa201) were transiently transfected with cDNAs for N-type Ca²⁺ channels (_1B + ₂   + _1b), the G₂ subunit, and either the G₁ or G₂ subunit. cDNAs encoding calcium channels and G proteins, transient transfection of N-type Ca²⁺ channels, and patch-clamp recordings were the same as those previously described (Arnot et al. 2000). Briefly, currents were elicited by stepping from 100 mV to a test potential of +20 mV. Inhibition of Ca²⁺ channel current by G proteins was assessed by application of a strong depolarizing (+150 mV) prepulse (PP). The degree of inhibition caused by the G protein was determined as the ratio of absolute peak current amplitudes in the presence and absence of the PP (the real facilitation). These real facilitation ratios were obtained by varying the duration between the PP and the test pulse (t₁ = 2, 4, 6, 10, 15, 20, and 1,000 ms, Fig. 2A) and extrapolating to t₁ = 0. Peak amplitudes were normalized to current amplitude after a 1-s interpulse duration. Cells were compensated by 75-85%. Currents were analyzed using Clampfit (Axon Instruments) and fitted in Sigmaplot 4.0 (Jandel Scientific). A semiquantitative measure of activation time constants was established with monoexponential fits to the late rising phase of the raw current using Clampfit.

Presynaptic model

The presynaptic terminal is modeled as a single compartment, with equations for membrane potential, Ca²⁺-dependent transmitter release, transmitter binding to autoreceptors, and Ca²⁺ influx through G protein-regulated channels (Fig. 1). The membrane potential (V) is described by a simplified form of the Hodgkin-Huxley equations (Hodgkin and Huxley 1952; Rinzel and Ermentrout 1989)

(1)

(2)

where C_m = 1 µFcm² is the membrane capacitance, I_Na = 120x(1  n)(V  120), I_K = 36n⁴(V + 77), I_leak = 0.3(V + 54) (µAcm²) are endogenous currents, I_app is an external current applied periodically (40 µAcm²) to evoke action potentials, and n is an activation variable for the K⁺ current, with _n = 0.02(V + 55)/ [1  e^(V+55)/10] and _n = 0.25e^(V+65)/80. Since Ca²⁺ current often has little effect on the action potential in synapses (Sabatini and Regehr 1997; Takahashi et al. 1998), we omit this current from the voltage equation.

View larger version (10K): [in this window] [in a new window]   Fig. 1. Illustration of the presynaptic model. Vesicle fusion and transmitter release occur when a Ca2+ ion binds to a low-affinity binding site (1), binding of a transmitter molecule to a presynaptic autoreceptor activates a G protein (2), the G dimer binds to an N-type Ca2+ channel (3), the bound channel is put into a reluctant state (4).

Flux of Ca²⁺ into the presynaptic terminal is through N-type Ca²⁺ channels. The model used here is based on a model of N-type G protein-regulated channels developed by Boland and Bean (1993), and simplified by Bertram and Behan (1999). This has three G protein bound "reluctant" closed states (C_G1-C_G3), four "willing" closed states (C₁-C₄), and one willing open state (O)
where k = 64k and k = (64)²k. For simplicity, the notations for the state of the system and the probability that the system is in that state are the same. The channel kinetic scheme can be written as differential equations using the law of mass action

(3)

(4)

(5)

(6)

(7)

(8)

(9)

The probability that a channel is open is obtained from the conservation equation O = 1  C₁  C₂  C₃  C₄  C_G1  C_G2  C_G3. The probability that a channel is in a reluctant state will be used later, C_G = C_G1 + C_G2 + C_G3. Voltage-dependent forward () and backward () rates are (in ms¹)

(10)

(11)

The G protein binding rate (k, in ms¹) is chosen to be a sigmoidal function of the fraction (a) of bound autoreceptors

(12)

The unbinding rate, k, is set according to the G dimer simulated, as described later. Detailed descriptions of this channel model are given in Boland and Bean (1993) and Bertram and Behan (1999).

A very simple model is used for transmitter exocytosis, which assumes that Ca²⁺ must bind to a single site for exocytosis to occur. This model purposely omits synaptic enhancement due to the buildup of free or bound Ca²⁺ (Bertram et al. 1996; Zucker 1996) and depression due to the depletion of readily releasable vesicles (Abbott et al. 1997; Zucker 1989). These are omitted so that the effects of G protein inhibition and relief of inhibition can be studied independently of other modulatory mechanisms. The effects of relief of G protein inhibition on synaptic facilitation were addressed in a previous computational study (Bertram and Behan 1999), and a comparison of this form of depression with vesicle depletion was made in Bertram (2001). In the present model, transmitter release probability (R) is given by

(13)

where k = 0.15 µM¹ms¹, k = 2.5 ms¹, and Ca is the average domain Ca²⁺ concentration (in µM) at the mouth of an open Ca²⁺ channel, assumed to be colocalized with the transmitter release site. This depends on the probability that the channel is open (O), the Ca²⁺ concentration at an open channel (Ca_open) and a basal level of bulk Ca²⁺, Ca = OCa_open + 0.1. The steady-state formula from Neher (1986) is used for Ca_open, assuming that no mobile Ca²⁺ buffers are present

(14)

where D_c = 220 µm²s¹ is the Ca²⁺ diffusion coefficient (Allbritton et al. 1992), r = 10 nm is the assumed distance from the channel to the release site, and  = 5.182 · i(V) is the Ca²⁺ flux through the channel. The single-channel current i(V) is described by the Goldman-Hodgkin-Katz formula (Goldman 1943)

(15)

with _Ca = 1.2 pS, P = 6 mVmM¹, RT/F = 26.7 mV, and Ca_ex = 2 mM. The _Ca = 1.2-pS single-channel conductance is used to approximate physiological Ca²⁺ concentrations. The domain Ca²⁺ equations and choice of parameters are discussed in detail in Bertram et al. (1999).

Transmitter concentration in the synaptic cleft is assumed to be proportional to the release probability, T = R, giving concentrations of several hundred micromolar during an action potential. For simulations of superthreshold postsynaptic responses  = 4 mM, while  = 1 mM for simulations of subthreshold responses. Transmitter in the cleft binds to presynaptic autoreceptors with binding and unbinding rates determined from a cerebellar synapse (Dittman and Regehr 1997). The fraction of bound autoreceptors, used in Eq. 12, changes in time according to

(16)

where k = 0.2 mM¹ms¹ and k = 0.0015 ms¹.

Postsynaptic model

The model for postsynaptic membrane potential is similar to that for presynaptic membrane potential, with the addition of a synaptic current and the removal of the external applied current

(17)

(18)

(19)

where _n, _n, and all currents depend on postsynaptic voltage. The synaptic current, I_syn = g_synb(V_post  V_syn), depends also on the fraction of bound postsynaptic receptors, b, which changes in time according to Eq. 19, reflecting first-order binding of transmitter. The binding and unbinding rates are set to give a fast postsynaptic response, k = 2 mM¹ms¹, k = 1 ms¹. The synapse is assumed to be excitatory, with V_syn = 0 and g_syn = 0.2 mScm².

In the simulations shown in Figs. 3, 4, 8, and 9, there is one presynaptic neuron and one postsynaptic neuron. In network simulations, a 5 × 5 grid of "input layer" neurons projects to a 5 × 5 grid of "output layer" neurons. In the simulation shown in Fig. 5, A and B, each input layer cell projects to a single output layer cell; input cell (i, j) projects to output cell (i, j). In Figs. 5, C and D, 6, and 7 input cell (i, j) projects to output cells (i, j), (i  1, j), (i + 1, j), (i, j + 1), and (i, j  1). Input layer cells on the edge of the grid project to fewer cells, and output layer cells on the edge of the grid receive fewer synaptic inputs. For example, output edge cell (1, 2) receives input from input cells (1, 1), (1, 2), (1, 3), and (2, 2) only. Output corner cell (1, 1) receives input from input cells (1, 1), (1, 2), and (2, 1).

In simulations shown in Figs. 3, 4, 5, A and B, and 8,  = 4 mM so that input from a single presynaptic cell can evoke a postsynaptic action potential (in the absence of G protein inhibition). In simulations shown in Figs. 5, C and D, 6 and 7,  = 1 mM, and k = 1.1 mM¹ms¹, k = 0.19 ms¹ so that a single presynaptic cell is incapable of evoking a postsynaptic action potential. To maintain the same level of presynaptic autoreceptor activation, the binding rate is increased by a factor of four to k = 0.8 mM¹ms¹.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Kinetic slowing of N-type channels

With bath application of a G protein agonist, or transient expression of G dimers, a subpopulation of Ca²⁺ channels becomes bound by G and enters a reluctant state. Depolarization is thought to change the channel configuration, reflected in a rightward movement along the channel kinetic diagram, making it more likely that bound G dimers will unbind from reluctant channels. As a result, channels will move from a reluctant closed (RC) to a willing closed (WC) state. If the depolarization is sufficiently long, these channels can open (the willing open or WO state) and contribute to the macroscopic Ca²⁺ current. The extra steps involved in channel opening are the major reason for kinetic slowing. Another contributor to kinetic slowing is the slow opening of channels while in a reluctant state (reluctant openings, the RO state), which has been shown to occur during large depolarizations in N-type Ca²⁺ channels (Colecraft et al. 2000; Lee and Elmslie 2000). Since reluctant openings appear to be a minority of the delayed channel openings (Lee and Elmslie 2000), the RO state is not included in our mathematical model, and kinetic slowing is due entirely to the RC  WC  WO pathway.

Several studies have demonstrated that the degree of inhibition and kinetic slowing depends on the G and G isoforms comprising the activated G dimer (Arnot et al. 2000; Garcia et al. 1998; Ruiz-Velasco and Ikeda 2000; Zhou et al. 2000). To set kinetic parameters for the Ca²⁺ channel model, we focus here on data from Fig. 2 and from Arnot et al. (2000). Here, G₂ and various G subunits are co-transfected with N-type Ca²⁺ channels in HEK-tsa201 cells. A 100-ms test pulse to +20 mV is applied with or without a depolarizing prepulse to +150 mV (Fig. 2A). With the transfected G₁₂ dimer, current recorded in the absence of a prepulse [I(PP)] was significantly reduced compared with that recorded following a prepulse [I(+PP)] (Fig. 2C). The ratio I(+PP) to I(PP) is a measure of the depolarization-induced relief of inhibition, or facilitation. The facilitation is smaller in the G₂₂ transfected cells (Fig. 2C).

View larger version (19K): [in this window] [in a new window]   Fig. 2. Experimental data demonstrating kinetic slowing of an N-type channel. A: pulse protocol used to determine G protein real facilitation ratios after a strong depolarizing prepulse (PP) with t1 varied as described in METHODS. B: slowing of the Ca2+ channel mediated by G12 and G22. Inset: real facilitation ratios in the presence of G12 or G22. C: current traces illustrating kinetic slowing by G12 and G22. Current records were obtained in the absence of a PP or 2 ms following a 50-ms +150-mV PP. Current traces were recorded using a test pulse of +20 mV for 10 ms. Inset: a semiquantitative measure of the activation time constants using monoexponential fits of the activation time course. Error bars represent SE; numbers in parentheses reflect the number of experiments and asterisks denote significance (P < 0.001) relative to G22 values using Student's t-test.

Facilitation decreases exponentially as the time interval between the prepulse and test pulse (t₁, Fig. 2) is increased (Fig. 1 in Arnot et al. 2000). It is at its greatest as t₁  0. The exponential facilitation curve, extrapolated back to t₁ = 0, thus gives a measure of the real facilitation induced by the prepulse. This is shown in the inset to Fig. 2B for cells transfected with the G₁₂ and G₂₂ dimers. The greater real facilitation for G₁₂-transfected cells suggests that G protein-coupled receptor activation of this subunit will have a greater modulatory impact on Ca²⁺ channels and downstream targets of Ca²⁺ influx. Real facilitation ratios for G₃₂, G₄₂, and G₅₂ transfected cells are shown in Fig. 2 of Arnot et al. (2000), and demonstrate that real facilitation is greatest for G₁₂ and G₃₂ transfected cells, followed by G₂₂ and G₄₂. Cells transfected with G₅₂ display no significant facilitation.

Kinetic slowing and prepulse facilitation are related in that both reflect the RC  WC transition, and thus depend on the G protein unbinding rate. Kinetic slowing in cells transfected with either G₁₂ or G₂₂ is illustrated in Fig. 2C. For a G₁₂-transfected cell, channel activation is clearly much slower without a prepulse than with a prepulse. The inset shows exponential fits to the rising phase of the currents, providing a 2.90-ms time constant without prepulse and a 1.10-ms time constant with prepulse. For a G₂₂-transfected cell there is less kinetic slowing, with activation time constants of 1.52 ms (PP) and 1.15 ms (+PP). Kinetic slowing data are summarized in Fig. 2B for 22 cells transfected with G₁₂ and 22 cells with G₂₂. The larger extent of kinetic slowing exhibited by the G₁₂ population is consistent with the greater prepulse facilitation induced by these dimers.

One important consequence of the large activation time constant PP versus +PP is that there will be relatively few Ca²⁺ channel openings at the beginning of a train of action potentials, since each action potential is of very short duration. This is particularly true in the case of activation of G₁₂ dimers (Fig. 2C), where I(PP) is only about 15% of I(+PP) 2 ms after the start of the test pulse. In fact, the prepulse-induced increase of the initial slope of the current is more important physiologically than the increase in the peak current, which may occur 10 ms or more after the start of the test pulse.

Calibration of the model was done by simulating the voltage-clamp protocol used in experiments (Fig. 2A). Since kinetic slowing is due largely to the delay in going from the RC to the WC state, it seems likely that the differential kinetic slowing exhibited by the G₂ dimers is due largely to differences in the G protein unbinding rate, k. Indeed, we found that varying this parameter in the channel model was effective at producing a wide range of activation rates, with smaller values of k leading to more kinetic slowing. Using a fixed value of k = 0.035 (ms¹), the k were calibrated to produce activation time constant ratios similar to those for the G₁₂  G₄₂ dimers (Fig. 3 of Arnot et al.). This is shown in Table 1. Simulations of the G₅₂ dimer are not included since this appears to lead to little or no kinetic slowing. In this and subsequent simulations we assume identical G protein binding rates among the dimers, so that k is the sole parameter distinguishing one dimer from the next.

Frequency-dependent autoinhibition

The frequency dependence of autoinhibition is quite complex. On the one hand, more transmitter will be released at higher stimulus frequencies, yielding more G protein activation. On the other hand, the average presynaptic voltage is higher at higher stimulus frequencies, so there will be more relief of Ca²⁺ channel inhibition. Since Ca²⁺ channel inhibition in turn affects transmitter release probability, this means that both negative and positive feedback loops are present. The dominant feedback depends on the stimulus frequency, as we illustrate below.

A simulation with a single presynaptic and a single postsynaptic cell is shown in Fig. 3, where it is assumed that bound autoreceptors activate G₃₂ dimers. Presynaptic action potentials are evoked (Fig. 3A) by a train of current pulses applied at 10 Hz for 1.5 s. Each action potential releases transmitter that binds to postsynaptic receptors (Fig. 3D), depolarizing the postsynaptic cell to spike threshold during the first half of the pulse train (Fig. 3E). At the same time, transmitter molecules bind to presynaptic autoreceptors (Fig. 3B), activating G proteins and putting Ca²⁺ channels into a reluctant state (Fig. 3C). As the fraction of reluctant channels increases, the average domain Ca²⁺ concentration decreases, and so too does the transmitter release probability. Hence the fraction of postsynaptic receptors activated by presynaptic action potentials declines during the 10-Hz pulse train. Halfway through the train, excitatory postsynaptic currents (EPSCs) elicited by presynaptic action potentials are insufficient to reach the spike threshold, and postsynaptic action potentials are not produced. Hence the postsynaptic cell only responds transiently to the presynaptic impulse train; all later responses are filtered out by the G protein-mediated presynaptic inhibition. The inhibition of postsynaptic responses will remain throughout the duration of the pulse train, so a train of 30 presynaptic impulses will elicit the same postsynaptic response (8 postsynaptic impulses) as the train of 15 impulses.

View larger version (29K): [in this window] [in a new window]   Fig. 3. Simulation with a single presynaptic and a single postsynaptic cell. A: a 10-Hz train of applied current pulses elicits presynaptic action potentials. B: during a 10-Hz or a 30-Hz train, the fraction of bound autoreceptors and the fraction of reluctant Ca2+ channels rise (C). D: the fraction of postsynaptic receptors bound with each evoked release of transmitter declines during the 10-Hz train, so that the postsynaptic voltage reaches spike threshold only during the 1st half of the train (E).

At a higher stimulus frequency (e.g., 30 Hz) one might expect the postsynaptic response to be blunted to a greater extent than during the 10-Hz train, since the increase in transmitter release will result in more binding to presynaptic autoreceptors (Fig. 3B). However, the increased relief of inhibition that accompanies the increase in average presynaptic voltage will more than compensate for this, so that the fraction of reluctant channels will actually be lower than during the 10-Hz train (Fig. 3C). For this reason, the transmitter release is inhibited to a lesser extent during the 30-Hz train. The binding to postsynaptic receptors declines during the 30-Hz train (not shown) as it did during the 10-Hz train (Fig. 3D), but to a lesser extent, and the postsynaptic voltage reaches the spike threshold throughout the pulse train (not shown). Thus the lower-frequency signal is filtered out after a transient response, while the higher-frequency signal is transmitted in its entirety.

To determine the frequency range of input filtered out by autoinhibition, we performed simulations in which the presynaptic cell was stimulated for 10 s at frequencies ranging from 2 to 35 Hz. The number of postsynaptic action potentials generated by the resulting transmitter release was recorded. In the absence of presynaptic autoinhibition, the number of presynaptic and postsynaptic impulses is the same. However, with autoinhibition, the postsynaptic response can be blunted. Figure 4A shows the frequency response using the G protein unbinding rate calibrated for the G₁₂ dimer. For frequencies 35 Hz the input impulse train is transmitted in its entirety to the postsynaptic cell. However, for frequencies 30 Hz the signal is filtered out; the postsynaptic cell generates only a short transient response. Thus the filter cut is between 30 and 35 Hz for the G₁₂ dimer. Autoinhibition with the G₂₂ dimer, which shows little kinetic slowing, allows signals of all frequencies 2 Hz to be transmitted (Fig. 4B), so the filter cut in this case is <2 Hz. Autoinhibition with the G₃₂ dimer filters out input signals 15 Hz, while transmitting signals with frequencies 20 Hz, so the filter cut here is between 15 and 20 Hz. Finally, the unbinding kinetic rate determined for G₄₂ is equal to that determined for G₂₂, so the filtering properties are the same.

View larger version (46K): [in this window] [in a new window]   Fig. 4. Number of postsynaptic action potentials generated by presynaptic spike trains lasting 10 s, for a range of presynaptic stimulus frequencies. In the absence of autoinhibition, the number of postsynaptic spikes equals the number of presynaptic spikes (input, gray). Autoinhibition filters out the low-frequency spike trains, allowing high-frequency trains to pass in their entirety (output, black). The filter cut is different for different G dimers.

In summary, this computational study indicates that 1) G protein-mediated autoinhibition can filter out low-frequency input (presynaptic) signals, thus acting as a high-pass filter, and 2) the range of frequencies filtered out is different for different activated G dimers.

Autoinhibition increases spatial contrast

We now turn to some of the functional implications of the high-pass filtering mediated by autoinhibition. As a first example, we consider a 5 × 5 grid of presynaptic or input neurons projecting to a 5 × 5 grid of postsynaptic or output neurons, with each output neuron receiving input from exactly one input neuron (see METHODS). Each of the input neurons is subject to autoinhibition, acting via G₁₂ dimers. The input neurons at locations (2, 2), (2, 4), (3, 3), (4, 2), and (4, 4) are stimulated at high frequencies, chosen randomly between 41 and 50 Hz, while other input cells are stimulated at low frequencies, chosen randomly between 1 and 10 Hz. The high-frequency input cells carry the "signal," while the low-frequency cells carry "noise." This is illustrated in Fig. 5A, where the number of impulses evoked during a 10-s stimulation is shown for each input cell using color and size coding (see figure caption). The large black squares correspond to the high-frequency signal, while the smaller colored squares correspond to noise at a range of frequencies (smaller squares for lower frequencies). Thus the spatially distributed signal, in the shape of an X, is degraded by surrounding noise.

View larger version (22K): [in this window] [in a new window]   Fig. 5. A: 5 × 5 input layer of neurons stimulated at various frequencies and projecting directly onto a 5 × 5 output layer. B: each output cell receives a synaptic projection from 1 input cell. C and D: the input layer projects with nearest neighbor coupling to output layer cells. In C there is no presynaptic autoinhibition. Number of impulses in 10 s of stimulation (N) is color and size coded, with larger squares representing more impulses. Black, N > 100; red, 70 < N  100; green, 40 < N  70; blue, 10 < N < 40; yellow, N < 10.

A fundamental task of neural circuitry is to extract spatially distributed signals from the background noise. One way to do this is to employ lateral inhibition between input layer cells, so that neighboring cells inhibit one another (Shepherd 1998). High-frequency cells are more effective than low-frequency cells at inhibiting their neighbors, and as a consequence the low-frequency input is filtered out.

A second method for increasing spatial contrast is to employ G protein-mediated autoinhibition. As demonstrated in the previous section, autoinhibition preferentially filters out low-frequency input, while leaving high-frequency input intact. Thus the noise that was present in the input layer (Fig. 5A) is filtered out, and as a result the signal is much more prominent in the output layer (Fig. 5B). One advantage to this method of spatial contrast enhancement is that no circuitry is involved; each input neuron has feedback only onto itself. Another advantage is that the filter cut, and thus the definition of noise, is variable, depending on the G dimer activated by the autoreceptors (among other things). For example, while the G₁₂ dimer used in Fig. 5 is effective at filtering the noise, the G₂₂ dimer has no effect. Also, a 20-Hz signal would be considered noise by G₁₂, and signal by G₃₂. In the DISCUSSION we suggest possible mechanisms for time-dependent filter cuts.

As a second example, we again consider 5 × 5 grids of input and output neurons, but now each input cell projects to the corresponding output cell and its nearest neighbors. Several parameters have been adjusted so that release from a single presynaptic impulse is insufficient to bring a postsynaptic cell to the spike threshold (see METHODS). Instead, spike threshold is reached when two or more neighboring input cells fire at similar times, so that the postsynaptic EPSCs summate. Using the same input impulse distribution as in Fig. 5A, we now see a rather different output pattern even in the absence of autoinhibition (Fig. 5C). Output cells receiving input from two or more high-frequency "signal" input cells produce a high-frequency response, while others respond at low frequency. Thus the nearest-neighbor circuitry and the requirement for coincident inputs to evoke a response transform the spatial signal, and remove some of the noise (fewer red and green squares in Fig. 5C than in Fig. 5A). When G₁₂ autoinhibition is included in the input layer cells, the output signal is as in Fig. 5C, but with reduced noise (Fig. 5D). Hence, even in this case where the circuitry performs a spatial transformation of the input signal, autoinhibition is effective at increasing the spatial contrast.

Autoinhibition increases fidelity of coincidence detection

For some tasks, the timing of synaptic input from several sources is crucial. This appears to be the case, for example, for sound localization and spatial orientation (Hopfield 1995). Associative learning is also thought to depend on action potential timing, in this case the coincident firing of associated pathways (Brown et al. 1990). One mechanism for coincidence detection is the requirement of temporal overlap of EPSCs to evoke a postsynaptic response. For perfect fidelity of coincidence detection, the output cell should fire only when input cells carrying high-frequency signals have coincident action potentials. Noise from low-frequency cells can reduce the fidelity by producing false positives. This occurs when an action potential in a low-frequency cell is coincident with an action potential in a high-frequency cell. We demonstrate here that G protein-mediated autoinhibition can increase the fidelity of coincidence detection.

A scenario is considered in which 10 input cells project to a single output cell. As in Fig. 5, C and D, parameters are adjusted so that EPSCs must overlap to evoke a postsynaptic impulse. Two of the input cells carry high-frequency signals (80 and 100 Hz). The remaining input cells carry low-frequency noise, randomly chosen from 1 to 10 Hz. Autoinhibition is not included in the simulation. Figure 6 shows the voltage response of the single output cell (black) during a 100-ms simulation. Superimposed are excitatory postsynaptic potentials (EPSPs) evoked by transmitter released from the 80-Hz input cell alone and the 100-Hz input cell alone. Of the seven postsynaptic action potentials produced (truncated for clarity), only four are produced as the result of coincident input from the signal cells. These four "true positives," where the red and blue EPSPs overlap in such a way as to generate an impulse, are marked by arrows in the figure. The remaining three postsynaptic impulses, the false positives, are produced by the overlap of EPSCs from a signal cell and from a low-frequency noise cell. Thus the fidelity of coincidence detection of the high-frequency signals is low in this example.

View larger version (24K): [in this window] [in a new window]   Fig. 6. Voltage response of a single output cell to subthreshold synaptic input from 10 input cells, with no autoinhibition. Two input cells fire at high frequencies, while the remaining 8 fire at low frequencies. Four impulses are generated by coincidence of high-frequency input (marked by arrows), 3 are generated by coincidence of low- and high-frequency input. Superimposed are excitatory postsynaptic potentials (EPSPs) from the 80-Hz and 100-Hz cells alone.

High-pass filtering through autoinhibition can increase the fidelity of coincidence detection by reducing the noise. This is demonstrated in Fig. 7 for several combinations of signal frequencies. Here, simulations like the one above are carried out for 1 s of simulation time and the number of output spikes are counted, differentiating between true and false positives. For each simulation, eight of the input cells fire with frequencies between 1 and 10 Hz. The remaining two input cells fire at 40 and 60 Hz, 60 and 80 Hz, or 80 and 100 Hz. Figure 7A shows that, without autoinhibition, a large fraction of the postsynaptic impulses are false positives. When autoinhibition is introduced through activation of the G₁₂ dimer, the number of false positives is greatly reduced (Fig. 7B). This is true for each combination of signal frequencies. The number of true positives is also reduced, since signal EPSCs that are only roughly coincident may not be sufficient to push the cell above the spike threshold without some coincident noise. However, the number of false positives is reduced to a much greater extent. As with spatial contrast enhancement, the increase in coincidence detection fidelity varies with the particular activated G dimer. The effect is maximized with the G₁₂ dimer, and there is little or no effect with the G₂₂ dimer.

View larger version (28K): [in this window] [in a new window]   Fig. 7. True positives () and false positives () generated during a 1-s simulation, for 3 different combinations of signal frequencies. In each case, 8 of the 10 input cells fire at low frequencies between 1 and 10 Hz. A: with no autoinhibition there are many false positives. B: with G12 autoinhibition the fraction of false positives is greatly reduced, increasing the fidelity of coincidence detection.

Filter cut depends on autoreceptor kinetics

An important determinant of the high-pass filter cut is the dynamics of bound autoreceptor accumulation. The accumulation of bound autoreceptors during an impulse train depends on the impulse frequency, the proportionality constant () between transmitter release probability and transmitter concentration in the synaptic cleft, and the autoreceptor binding (k