Synaptic Physiology II: Presynaptic Mechanisms and Quantal Analysis

Introduction

• In the previous unit, we began our study of chemical synaptic transmission by analyzing the responses of the postsynaptic membrane to the opening or closing of ion channels due to direct or indirect actions of transmitters.

• In this unit, we continue our study of chemical synaptic transmission.

• We will describe the techniques used to identify whether a synapse is electrical or chemical, whether the chemical synapse is direct or indirect, the preparations that have been used to analyze synaptic transmission, the ways in which one can distinguish presynaptic from postsynaptic changes in transmission, and then some of the recent work on the molecular mechanisms of transmitter release.

Identifying Chemical Synapses

Figure 1: Recording from a presynaptic neuron (A) and a postsynaptic neuron (B).

Figure 2: A simple three neuron circuit.

Figure 3: Recordings from a three neuron circuit in which the polysynaptic connection works.

Figure 4: Same circuit in high divalent cation solution; polysynaptic connection fails.

• In the previous unit, we saw that it was possible to tell whether a connection was electrical by injecting hyperpolarizing and depolarizing current pulses into the presynaptic neuron. If the connection is electrical, then generally (but not always) the postsynaptic neuron will show similar changes in voltage (hyperpolarization of its voltage in response to hyperpolarizing current pulses, depolarization of its voltage in response to depolarizing pulses).

• As shown in Figure 1, we have an intracellular electrode that is recording and stimulating neuron A, and a second intracellular electrodes that is recording and stimulating neuron B.

• If we put a hyperpolarizing pulse into neuron A, we record no response in neuron B.

• In contrast, if we put a depolarizing pulse into neuron A, if this is sufficient to generate an action potential that propagates to the presynaptic terminal, we see a postsynaptic potential in neuron B.

• Is a chemical synaptic connection direct or indirect? If it is direct, so that there is only one synapse between neurons A and B, i.e., it is monosynaptic, as illustrated schematically in Figure 1, then the connection is likely to persist even if the postsynaptic neuron receives some inhibition.

• In contrast, as shown (for example) in Figure 2, where we are recording intracellularly from three neurons, and neuron B is interposed between neurons A and C, firing neuron A may be able to induce a postsynaptic potential in neuron C. However, it can only do so if it brings neuron B to threshold.

• Recordings shown in Figure 3 illustrate how a polysynaptic connection might work. The input current pulse (bottom trace) induces an action potential in neuron A (second trace from bottom), which in turn successfully induces an action potential in neuron B (third trace from the bottom), and this induces an excitatory postsynaptic potential in neuron C (top trace).

• How can one distinguish monosynaptic from polysynaptic connections? Bathing the nervous system in solutions that are osmotically equivalent to extracellular fluid, and in which electroneutrality is maintained, but have higher than normal concentrations of divalent cations such as magnesium and calcium (often known as Hi Di salines, for short) raise the threshold for firing action potentials (probably by shielding charges near the membrane).

• As a consequence, as shown in Figure 4, in response to the same input current, neuron A induces a postsynaptic potential in neuron B, but because neuron B's threshold is much higher, the postsynaptic potential is no longer sufficient to induce an action potential in neuron B. In turn, neuron C is completely silent, because it is not excited by neuron B.

• Connections that persist in Hi Di salines and show fixed and short latency even when the presynaptic neuron is fired repeatedly at high frequency are usually presumed to be monosynaptic, although to unequivocally establish this, it may be necessary to perform anatomical studies (e.g., using electron microscopy) to show a direct synaptic specialization between two neurons.

• Current clamp techniques are often sufficient to establish patterns of neural connectivity (as illustrated in Figures 3 and 4). Characterizing the biophysical properties of the synapse usually involves a combination of current clamp and voltage clamp (or patch clamp) techniques.

Studying Presynaptic Release

• Two preparations have provided a great deal of insight into synaptic transmission, because of their size: the squid giant synapse (which is made on the squid giant axon, our old friend), and the neuromuscular junction. We will focus first on some of the important lessons learned by studying the squid giant synapse.

• In the squid giant synapse, it was possible to record from both the presynaptic and the postsynaptic terminals.

• Investigators showed that when both sodium and potassium ion channels were blocked, and the presynaptic terminal was depolarized, it was still possible to generate a postsynaptic response. Thus, the process of release was independent of the processes generating the action potential.

• However, if calcium was removed from the medium, the postsynaptic response was blocked. This strongly suggested that calcium influx into the presynaptic terminal was crucial for the actual process of transmitter release.

• Using voltage clamp, stepping the presynaptic terminal to steps 60 mV positive to the resting potential had two effects: little or no change was observed in the postsynaptic potential during the depolarizing step, and then, after the membrane potential was returned to its resting value, a rapid depolarization was observed in the postsynaptic neuron. The effect seen when the membrane was returned to its resting potential is referred to as a tail current. The assumption is that all of the voltage dependent calcium channels have been opened by the initial depolarizing step, but because the step is beyond the reversal potential for calcium ions, they do not flow into the presynaptic terminal. However, when the membrane potential is returned to the resting potential, the calcium ion channels are fully opened, and so calcium ions can rapidly flow in through them. In turn, this induces a rapid release of transmitter and a postsynaptic response. These studies suggested that there were several components to synaptic delay:
  • the time for voltage-dependent calcium channels to open (which was eliminated during the tail current experiments);
  • the time for the influx of calcium to induce transmitter release;
  • the time for transmitter to diffuse across the synaptic cleft;
  • the time for the postsynaptic receptors to bind transmitter and alter ion channel conductances.

• Further evidence for the important role of calcium in transmitter release was provided by injecting aequorin into the presynaptic terminal. Aequorin can bind calcium and generates blue light in response to the resulting conformational changes. Using Aequorin, it was possible to demonstrate significant increases in calcium in the presynaptic terminal with the appropriate time course to induce transmitter release.

• Mathematical models of the squid giant synapse strongly suggested that the amount of calcium that would flow into the presynaptic terminal was very sensitive to the total duration of the action potential invading the presynaptic terminal.

• Studies in a variety of other synapses have confirmed that the following sequence of steps occur during chemical synaptic transmission:
  • An action potential invades the presynaptic terminal, depolarizing it strongly.
  • The depolarization induces voltage-dependent calcium channels to open.
  • Calcium ions rush into the presynaptic terminal along their concentration gradient (calcium ion concentrations within neurons are generally many orders of magnitude lower than the concentrations in the surrounding extracellular fluid).
  • Calcium ion channels are often nearby the pool of readily releasable transmitter vesicles, which are are often docked close to the membrane of the presynaptic terminal.
  • The rise in calcium triggers a cascade of events (described in more detail below) that induce the transmitter vesicle to fuse with the presynaptic membrane.
  • The fusion of the transmitter vesicle leads to the release of transmitter into the synaptic cleft, the gap between the presynaptic and postsynaptic terminals.
  • The transmitter diffuses across the synaptic cleft (this process is usually rapid for conventional transmitters; for some transmitters that do not degrade rapidly, or are diffusible gases, the diffusion may occur more slowly and over a much wider area).
  • Transmitter molecules bind to receptors on the membrane of the postsynaptic terminal.
  • Transmitter action is usually brief, because transmitters may be degraded or inactivated by enzymes within the synaptic cleft, may diffuse away from the synaptic cleft, or may be re-uptaken by the presynaptic or postsynaptic terminal.
  • Receptors act, either directly (ionotropic receptors) or via a molecular cascade (metabotropic receptors) to open or close ion channels, changing the potential of the postsynaptic membrane.

Quantal Analysis: Separating Presynaptic and Postsynaptic Responses

• In the frog neuromuscular junction, after it was partially paralyzed with curare (which blocks the action of the normal transmitter, acetylcholine, on nicotinic receptors), it was possible to make extensive recordings from the muscle fibers, which effectively constituted a giant postsynaptic terminal.

• In the neuromuscular junction, the postsynaptic responses were referred to as end plate potentials (EPPs), and, under conditions of very low release, the smallest responses that were observed were referred to as miniature end plate potentials (mepps). An EPP consists of many mepps.

• In studying the mepps, investigators began to realize that they came in definite units. Experiments showed that one could apply a controlled amount of transmitter (acetylcholine) by passing current through an electrode (this is known as iontophoresis) placed near the postsynaptic terminal of the junction, and thus precisely control the amount of transmitter applied. These experiments showed that the post-synaptic membrane showed a continuously increasing depolarization in response to continuously increasing current (i.e., to continued increases in application of acetylcholine). Thus, the postsynaptic receptors were inherently able to respond to transmitter in a graded fashion.

• In contrast, mepps were observed in essentially fixed unit sizes, as illustrated in Figure 5.

Figure 5. Schematic illustration of recorded mepps in 8 successive trials; stimulation of the nerve innervating the muscle occurs at 30 ms.

• As the figure shows, in the first trial, an event of magnitude one unit occurred (about 10 mV in size); in the next four trials, no response was recorded; in the next two, responses that were twice the magnitude of the unit value were recorded; and in the last trial, a response that was three times the magnitude of the unit response occurred.

• In conjunction with electron microscopic recordings which showed vesicles near the membrane, and studies demonstrating that the amount of transmitter in the vesicle would cause "unit" depolarization in the postsynaptic membrane, researchers concluded that neurotransmitter was not released continuously, but in discrete "packets", corresponding to the fusion of the vesicles with the presynaptic membrane.

• They referred to these units as quanta (following the nomenclature of the physicists), and developed a way of analyzing changes in presynaptic and postsynaptic terminals that they referred to as quantal analysis.

• How does knowing that there are transmitter quanta help analyze synaptic transmission?

• The investigators assumed that there were two key features to transmitter release by vesicles: (1) the underlying distribution of the vesicle release, i.e., the probability that no vesicles, one vesicle, two vesicles, .... n vesicles might be released the next time that the synapse was activated, and (2) the amount of transmitter in each vesicle.

• If a treatment acted primarily on the presynaptic terminal and affected the probability of vesicle release - increased or decreased it - then the release probability would change. The average number released is referred to as the quantal content, and is usually represented by the symbol $m$.

• If a treatment acted primarily on the postsynaptic terminal, and affected the response of the postsynaptic receptors - increased or decreased them - then the unit size would change. The average amount of transmitter released per vesicle is referred to as the quantal size, and is usually represented by the symbol $q.$

• These principles have been shown to apply to many other synapses than the neuromuscular junction. When one is examining a central synapse, for example, the response is a postsynaptic potential (PSP), and the miniature events are referred to as miniature postsynaptic potentials, or mpsps, but the principles are the same.

• An important measure of dispersion is called the coefficient of variation, and is defined as the ratio of the standard deviation to the mean. For a normal (Gaussian distribution) with mean $\mu$ and standard deviation $\sigma$, the coefficient of variation would be defined as $\frac{\sigma}{\mu}$. For the Poisson distribution (which is defined below), the standard deviation is equal to the square root of the mean value, and so the coefficient of variation can be used as another way of estimating the quantal output $m$.

• You now have enough information to begin to analyze a simulated synapse using quantal analysis. As usual, you may wish to open the simulation in a separate window as you work through the problems.

• Question 1. When the probability of release is low, it is possible to model the release process using a Poisson distribution. Thus, if the average number of quanta released is $m$, the probability $P$ of seeing a specific number of quanta $k$ can be represented by the formula $$P_k = \frac{e^{-m} m^k}{k!} \quad\text{(Equation 1)}$$
  • The symbol $k!$, which is read "k factorial", stands for $k \times (k-1) \times \dotsc \times 3 \times 2 \times 1$. Thus, $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$.
  • A concrete example of the use of Equation 1 may clarify how to use it. Let the mean number of quanta released in a single trial be m = 3.2 quanta. To determine the probability of seeing k = 2 quanta released on any given trial, calculate $$\frac{e^{-3.2} 3.2^2}{2!} = 0.2087,$$ so, in 10,000 trials, one would expect to observe the release of 2 quanta about 2087 times.
  • Load the Presynaptic Release Simulation. Click the button that says "Poisson Distribution". If you restart the simulation, you will need to do this again for Questions 1 through 5.
  • The top panel shows several PSPs. The second panel shows the number of failures (PSPs of size zero), and the number of PSPs of different sizes; this is referred to as the PSP distribution histogram. The third panel shows the distributions of the miniature PSP size (mPSP size), which provides a measure of the value of $q$, the size of the postsynaptic response (quantal size). Explore the role of the variation in the PSP size. In the box labeled "CV of Quanta Size" (i.e., the coefficient of variation of the quanta size), set the value to 0. What happens to the mPSP size? What happens to the PSP distribution histogram? What values can the PSPs have? Explain.

• Question 2. Run the simulation again by pressing Run Simulation (still leaving the value of CV of Quanta size to 0). What happens to the sequence of PSPs? What happens to the histogram? Run the simulation several times, and observe the sequence of PSPs, and the histogram. Are the PSPs the same? Is the histogram the same? Explain.

• Question 3. What is the role of the parameter $m$, the quantal content, on the output of the synapse? Leaving the CV at 0, change the value of $m$ to 1.5 (from its default value of 3.5), and run the simulation. Repeat this two or three times. What happens to the PSPs? What happens to the distribution histogram? Now change the value of $m$ to 10, and again run the simulation. Again repeat this two or three times. What happens to the PSPs? What happens to the distribution histogram? Note that the expected PSP size, $v$, is the mean release times the size of the mean quantal size, or $$v = m q. \quad\text{(Equation 2)}$$
  • For example, if the mean release $m$ is equal to 4, and the quantal size $q$ is equal to 5 mV, the predicted release size would be $4 \times 5\ \text{mV} = 20\ \text{mV}$. How well does this equation predict the peak of the distribution histogram as you change the value of $m$? Explain.

• Question 4. Let us now focus on the method of failures for estimating the average number of quanta released, or the quantal content, characterized by the parameter $m$. You have manipulated this parameter already, but now you will estimate its value from the data as if you did not have the number in front of you. Press the Poisson Distribution button (this will restore the value of CV of Quanta to 0.5 and the value of $m$ to 3.5). Measure the number of failures (i.e., right-click the first bar in the PSP distribution histogram); for each "experiment", you can then get an estimate of fraction of failures for that "experiment", where this fraction is $\frac{\text{number of failures}}{\text{total number of stimuli}}$. Do this ten times, and obtain an average failure rate. You can do this one of two ways: average the fractions you determined with each "experiment", or sum up all the failures you observed in the ten "experiments" and divide by the total number of stimuli that were applied to the preparation over the course of the ten "experiments". Use this to estimate the value of $m$. Note that $m$ can be solved for in Equation 1 with $k$ set to 0, and that $P_{0} = \frac{\text{number of failures}}{\text{total number of stimuli}}$. Note that 0! = 1. Solve this equation for $m$, and write down the general form of the equation before filling in the specific numbers you obtained (you will be using this equation several times for later problems). How good an estimate of $m$ do you obtain? Explain.

• Question 5. At many central synapses, the number of release sites may be as low as one, but the probability of release may not be small. Thus, the approximation that allows one to use the Poisson distribution (i.e., the probability of release, $p$, is very small, and the number of release sites, $n$, is very large) may be inaccurate. For these synapses, it may be more appropriate to use the binomial distribution to model the probability of $k$ quanta being released in a single trial. If vesicles are released according to this distribution, the probability of $k$ quanta being released is $$P_{k} = \frac{n!}{k! (n - k)!} p^k (1 - p)^{n - k}. \quad\text{(Equation 3)}$$
  • Once again, a concrete example may make this clearer. Assume that the total number of vesicle release sites at a presynaptic terminal is $n=5$, and the probability for each site to release a vesicle is $p=0.1$. Then the probability of observing $k=2$ quanta released in any given trial will be $$P_{2} = \frac{5!}{2! (5 - 2)!} 0.1^2 (1 - 0.1)^{5 - 2} = 10*(0.1)^2(0.9)^3 = 0.0729.$$
  • Thus, in 10,000 trials, one would expect to see about 729 events in which 2 quanta were released.
  • Load the Presynaptic Release Simulation, and press the Binomial Distribution button.
  • First, let's explore the role of the number of release sites. Change the value of $n$ from 100 to 10. Run the simulation. What happens to the distribution histogram? Now change the value to 1000. Run the simulation. What happens to the distribution histogram? Note that the mean number of quanta that should be released, $m$, is equal to the number of release sites times the probability of release, or $$m = n p. \quad\text{(Equation 4)}$$
  • Using Equations 2 and 4, predict the mean PSP size for both $n = 10$ and $n = 1000$, and explain the changes you saw in the distribution histogram.

• Question 6. Second, let's explore the role of the probability of release at each site. Press the Binomial Distribution button (note that this restores $n$ to its default value). Change the value of $p$ from 0.035 to 0.001. Run the simulation. What happens to the distribution histogram? Now change the value to 0.5. Run the simulation. What happens to the distribution histogram? Again, predict the mean PSP size for both $p = 0.001$ and $p = 0.5$ and explain in terms of the Equations 2 and 4.

• Question 7. When $n$ is large (> 20) and $p$ is small (<0.05), using the Poisson distribution becomes a reasonable approximation for describing synaptic events. Run the simulation using $n$ = 1000 and $p$ = 0.001. Predict the value of $m$ and the peak of the distribution histogram using Equations 2 and 4. Click the Poisson distribution button, and run the simulation again with the calculated $m$ value. Do your results support this claim?
  • As $n$ grows large, and $p$ approaches 0.5, using the Gaussian (or normal) distribution becomes a reasonable approximation for describing synaptic events. Do your results from question 6 support this claim?

• Question 8. Once the underlying principles of quantal release had been established experimentally, it became possible to use them to explore the roles of different drugs that could act presynaptically or postsynaptically to modify the synapse. Assume that the results you see when you click on the Poisson Distribution button constitute the control response of the synapse; change the number of stimuli to 100,000. Write down the mean quantal size $q$ and mean number of quanta released $m$ under these control conditions.
  • Now, click on the button labeled "Drug A". Note that the parameter values are hidden, but that you can still see the PSPs and the distribution histograms. What has happened to the mPSP size? Use the mPSP histogram to estimate the value of $q$.
  • What has happened to the distribution histogram? Using the method of failures, estimate the value of $m$ from the distribution histogram. What has the drug done compared to the baseline values? Is the effect of the drug primarily presynaptic or postsynaptic? Explain your reasoning.

• Question 9. Click on the button labeled "Drug B". What happened to the mPSP size? Use the mPSP histogram to estimate $q$.
  • What has happened to the distribution histogram? Using the method of failures, estimate the value of $m$. What has the drug done compared to the control values (i.e., the parameter values obtained when the Poisson Distribution is pressed)? Is the effect of the drug primarily presynaptic or postsynaptic? Explain your reasoning.

Molecular Mechanisms of Presynaptic Release

• Many details of the molecular mechanisms that underlie the actual release process have been worked out.

• Release occurs by a process known as exocytosis, which is a process used by many cells throughout the body, so that there are commonalities at the molecular level between the process of transmitter release from the presynaptic terminal, and exocytotic processes in many other cell types. We will briefly describe some of the key molecular players for neural transmission.

• A key molecule in the process is synaptotagamin. The influx of calcium ions after the action potential invades the presynaptic terminal and opens voltage-dependent calcium channels is sensed by the binding of calcium to synaptogamin.

• In turn, synaptotagamin bound to calcium can activate the last steps in the molecular cascade leading to vesicle fusion with the membrane, and neurotransmitter release.

• The molecular cascade involves molecules that are known as soluble N-ethylmaleimide-sensitive-factor attachment receptors. The abbreviation for N-ethylmaleimide-sensitive-factor is NSF, and the abbreviation for the attachment receptors, based on the initials, is SNARE proteins.

• Activation of the SNARE proteins, which form a complex, is crucial to allow vesicles to dock, i.e., approach the presynaptic membrane and attach to other molecules that surround release sites.

• Once docked, vesicles can then fuse and release their contents into the synaptic cleft.

• The membrane of the vesicles is often recycled into new vesicles.

• A variety of toxins can act on these molecular mechanisms, and thus block key phases of presynaptic transmission.

• An important preparation for studying synaptic transmission in mammals is found in the auditory nervous system, in the connections between neurons from the ventral cochlear nucleus to the medial nucleus of the trapezoid body. These synapses have a shape similar to flower petals, and were therefore named a calyx by their first describer, Held. These unusually large synapse helps speed transmission in the auditory system, and studies of the calyx of Held have become the basis for a much better understanding of synaptic transmission.

• Injectable compounds that hold onto ("chelate") calcium have been devised that can be induced to rapidly release the calcium in response to a flash of light. This is referred to as the calcium uncaging technique.

• Using calcium uncaging in the calyx of Held, investigators have demonstrated that release occurs in response to extremely brief pulses of calcium (less than half a millisecond) that increase the local concentration of calcium into the micromolar range (resting calcium levels are usually in the nano molar range).

• Moreover, they found that there was some spontaneous release that was present at very low calcium ion levels, and might therefore be calcium ion independent; release of vesicles with a greater than 2 millisecond delay after stimulation of the presynaptic terminal (asynchronous release) that occurred at low to moderate calcium ion concentration; and simultaneous release of up to 1000 vesicles (synchronous release, with delays less than 2 milliseconds after stimulation of the presynaptic terminal) that occurred at high calcium ion levels. A model assuming a spontaneous rate of vesicle fusion whose rate increased geometrically as more and more calcium ions bound the relevant molecules successfully fit the data.

• A recent review, which you can find here, provides more details on the role of synaptogamins in presynaptic transmission in the calyx of Held.