Quantal Analysis Problems

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1 Quantal Analysis Problems 1. Imagine you had performed an experiment on a muscle preparation from a Drosophila larva. In this experiment, intracellular recordings were made from an identified muscle fibre, in response to stimulation of the nerve innervating the segment containing the muscle fibre. Two sets of measurements were obtained after successful microelectrode penetration of the muscle fibre in the vicinity of the neuromuscular junction. First, the nerve supply to the muscle fibre was stimulated at a frequency of 1 Hz, while the stimulus intensity was systematically increased. The mean amplitude and standard deviation of the evoked excitatory junctional potential (EJP) was measured (Table 1). Second, spontaneous miniature EJP's (mejp) were recorded from the fibre in 60 successive time intervals ('sweeps') of 1 second duration and the numbers of sweeps containing between zero and eight mejp s per sweep were recorded (Table 2). The data obtained were as follows: Table 1 Table 2 a. Provide an interpretation of the stepwise increase in the mean amplitude of the evoked EJP shown in Table 1, as stimulus strength was increased. Distinct 'steps' in EJPs as nerve stimulation voltage increases are seen in polyneuronally innervated muscle fibres. For example, the diagram on the right is a recording from neonatal rat muscle stimulated at different potentials. The theory underlying this is that individual neurons have different thresholds of activating potential. Therefore at low stimulating voltages, none or one fibre may be active, producing a consistent EJP associated with release of ACh from that neuron's terminal (i.e. up to 0.4V in table 1). As stimulating voltage is increased additional neurons are recruited, causing an increase in ACh release at their shared NMJ, reflected by an increased EJP (i.e. in table 2, an additional neuron is stimulated at 0.5V, and a third at 0.8V). This produces the stepped pattern of EJPs observed. It is therefore reasonable to assume that the drosophila larval NMJs studied are polyneuronally innervated. b. Use the Variance Method based on the Poisson equation to estimate the mean quantal content of the responses evoked by a stimulating voltage of 0.4V in Table 1 and predict from this the mean quantal size (mejp amplitude). The Variance Method A feature of the Poisson distribution is that its variance is equal to its mean. The distribution of EPPs is essentially the distribution of quantal content multiplied by a factor, the mepp (the EPP generated by a single quanta). If you scale a distribution by multiplying it by a constant factor, the variance scales by the square of that factor. This allows the following to be derived (where m is the mean quantal content):

2 Var(EJP) = mejp + Var(Quantal Size) = mejp + m Mean EJP amplitude = mejp m Without knowing the mejp size, it is possible to calculate m using the following formula: m = (mean EJP amplitude)+ Var(EJP) OR m = < σ(ejp) mean EJP >?+ The first two formulae allow the derivation of this relationship (effectively by cancelling mejp): (mean EJP amplitude) + = Var(EJP) (m mejp)+ m mejp + The equivalent formula involving standard deviation (σ) simply uses the fact that variance is equal to standard deviation squared. The standard deviation divided by the mean is referred to as the coefficient of variation thus the equation can be expressed as m=c.v. 2. Application In this question, at 0.4V the standard deviation of EJP amplitude is 1.5 and the mean is 2.3 (mv). Feeding that in to our equation: m = < >?+ = < σ(ejp) mean EJP >?+ = So the mean quantal content is when stimulating the nerve at 0.4V. To work out the mejp amplitude, we can now simply divide the mean EJP by the mean quantal content (m) as (assuming a linear summation model which is not inaccurate at low quantal contents) mean EJP = mejp x m. mejp = Emean EJP E = 2.3 = mv m = m c. Show how the method of failures, based on the Poisson equation and the number of sweeps containing no occurrences of mejps, could be used to estimate the mean frequencies of mejps in table 2. Assuming mejps are essentially independent and random events which occur with a certain mean frequency over time, their occurrence over a fixed time interval can be modelled by a Poisson distribution. The time interval used in the experiment was 1 second, and 60 samples ('sweeps') were taken. The Poisson equation is: P(x) = e?m m N Where P(x) is the probability of seeing x mejps in a single sweep this is observed as: P(x) = x! Number of sweeps containing x mejps Total number of sweeps performed And m is the mean number of mejps per sweep which we are attempting to calculate. The method of failures relies on the properties of this equation when x=0.

3 As m 0 and 0! are equal to 1: P(0) = e?m m Y = e?m 0! P(0) is observed from the table: Therefore, we can solve for: P(0) = Number of sweeps containing 0 mejps Total number of sweeps performed = = e?m ln = m m = ln = From the look of the table, number of mejps/sweep seems concentrated from 0 2, so we can be confident our answer is in the right range. Since the length of time for each sweep was 1 second, we can say that the mean frequency of mejps is s 1. d. Show quantitatively that the distribution of number of mejps per 1s sweep, given in table 2, is consistent with predictions from a Poisson model of neuromuscular transmission. Having calculated m, we now have a distribution for x, the number of mejps per 1s sweep. P(x) = e?_.+`_ N x! Using this equation, we can calculate predictions for the probability of a sweep containing x mejps. We can then multiply this by 60 to predict the number of sweeps/60 that would contain x mejps and compare our results to the observed values. X (mejp/sweep) Number of sweeps with x mejp Prediction from Poisson Model Illustrating this graphically (which would be difficult in exam conditions!): It is apparent that the values predicted by the Poisson model are very similar to those obtained from the experiment. This suggests the Poisson model is a good fit for modelling mejp frequency.

4 e. Suppose extracellular potassium ionic concentration was increased, with the effect of doubling the mean frequency of mejps. Predict the number of one second sweeps out of 60 containing exactly one mejp. Doubling the mean frequency of mejps essentially means doubling m x 2 = This gives us a new Poisson distribution for x: Thus the probability of a sweep containing 1 mejp is: P(x) = e?+.a N x! P(1) = e?+.a _ 1! = Multiplying this by 60 (number of sweeps) gives a prediction of sweeps containing exactly 1 mejp so our prediction is 12 sweeps. f. By what mechanisms might raising extracellular potassium ion concentration increase the frequency but decrease the amplitude of spontaneous mejps? Suggest experiments that would test experimentally your proposed explanation. mejps are spontaneous events that occur in the absence of nerve stimulation. A single mejp is associated with the release of one vesicle of ACh from the pre synaptic terminal. During nerve excitation, exocytosis of vesicles is driven by an increase in [Ca 2+ ] in the pre synaptic terminal, caused by an influx of Ca 2+ through voltage gated Calcium channels (N type). It could be presumed that mejps are a consequence of random changes in [Ca 2+ ] in a localised fashion so a rise in [Ca 2+ ] near one active zone could trigger singular vesicle fusion at that active zone alone. A possible mechanism by which Ca 2+ concentration could vary might be activity of the voltage gated calcium channels. Ion channels open and close relatively constantly and randomly, but the probability of opening and the time spent open can be modified by numerous factors, such as membrane potential and ligand binding. Membrane potential depends on numerous factors, mostly related to the concentrations of intracellular and extracellular ions and their conductance through the membrane. Potassium has an equilibrium potential described by the Nernst Equation: K o is the extracellular K + concentration, K i the intracellular. E b = 58 log [K g] [K i ] Increasing extracellular K + concentration would drive the equilibrium potential for potassium up (more positive), hence driving the resting potential of the membrane upwards as well. With a higher resting potential, it may be the case that the probability of voltage gated calcium channels opening is increased leading to greater random calcium influxes and greater random release of vesicles manifesting as an increased mejp potential. Regarding the amplitude of mejps, this is determined by both ACh release and subsequent influx of Na + through nicotinic AChR ion channels. The end plate membrane may be similarly affected by K + levels, thus having a slightly higher resting potential. This higher resting potential reduces the electrochemical gradient for Na + entry to the myotube and thus reduces the mejp amplitude (less Na + entry = smaller pot. diff. change). An experiment to test this hypothesis could be to measure the membrane potential of a presynaptic terminal bathed in high [K + ] and to use voltage clamp techniques to hold a presynaptic terminal in physiological saline at the same potential. mejp frequencies could be compared from both experiments, and a control. If the difference in mejp frequency is solely due to membrane potential changes, then both experimental groups should be significantly different from the control group, but not from each other.

5 5. Intracellular recordings of endplate potentials (EPPs) and miniature endplate potentials (MEPPs) were obtained from a muscle fibre in an isolated mouse skeletal muscle bathed in normal physiological saline but in which the Ca2+ concentration was reduced from 2mM to 1mM and the Mg2+ concentration was increased from 1mM to 4 mm. The preparation was then stimulated with 100 trains of four nerve stimuli, delivered at 50Hz with intervals of 10s between each stimulus train. Each stimulus train evoked a corresponding train of four EPPs (EPP1 EPP4). The acetylcholinesterase inhibitor neostigmine (final concentration 3 µm) was then added to the physiological saline. After 20 minutes, recordings were resumed from the same muscle fibre and a further 100 trains of four supramaximal nerve stimuli were applied to the nerve. Other constituents of the bathing solution were unaltered from that of normal physiological saline. The resting membrane potential of the muscle fibre remained steady throughout at 72 mv. The following data were obtained Before and After adding neostigmine. Before adding neostigmine: Mean MEPP amplitude: 1.2 mv Stimulus trials: 100 EPP1 EPP2 EPP3 EPP4 Number of EPP Failures Mean EPP Amplitude (mv) Rise time (ms) Half Decay time (ms) After adding neostigmine: Mean MEPP amplitude: 1.5 mv Stimulus trials: 100 EPP1 EPP2 EPP3 EPP4 Number of EPP Failures Mean EPP Amplitude (mv) Rise time (ms) Half Decay time (ms) A. Describe and explain the responses to nerve stimulation and the effects of neostigmine on amplitude and time course of the EPPs. Sketch their appearance in the trains of four before and after the change in bathing solution. Before adding neostigmine to the bathing solution, nerve stimulation at 50Hz in trains of four produces trains of EPPs with a mean amplitude beginning at 4.3mV (the first EPP) and increasing incrementally to 5.5mV (the last EPP). The rate of failures is 3% for the first EPP, and this drops to 1% for the last EPP. Mean rise time and half decay time of each EPP seem relatively consistent for all 4 EPPs in a train, at around 1.5 and 2.6 ms respectively. This could be taken as a demonstration of the phenomenon of facilitation repeated firing of a nerve with short intervals leads to an increased response in terms of EPP and reduced failure rate. Explanations for this could be that the probability of vesicle release increases with sequential firing, thus quantal content increases, and the probability of failures decreases. This could be due to a raised intracellular calcium concentration in the presynaptic terminal following repetitive stimulation, increasing activation of vesicle release at active zones. The 10s delay between trains is likely sufficient to reset any facilitative mechanisms. When neostigmine is added to the bathing solution, some changes are apparent when comparing results with the pre neostigmine values. The phenomenon of facilitation is still present, and the probability of failures for each EPP is roughly similar, given the small numbers of failures observed, the small differences are likely insignificant. However, mean EPP amplitude is increased slightly and consistently for each EPP in the train of four. The mepp amplitude is also increased. Both rise time and half decay time are greater following neostigmine application. Interestingly, half decay time now seems to increase on subsequent EPPs in a train, whereas previously it was relatively constant for each EPP in a train.

6 Neostigmine is an anticholinesterase and as such inhibits the breakdown of ACh by AChE in the synaptic cleft. This could explain the findings seen here. As AChE activity is reduced, more ACh from the pre synaptic terminal is able to diffuse across the synaptic cleft without being broken down. This leads to increased activation of AChRs on the end plate, thus increasing the amplitude of any one mepp (each quantum will have a greater effect). This increase in quantal size then translates to an increased EPP. The decay of an EPP is related to the inactivation of ACh by its hydrolysis by AChE. Inhibiting AChE will reduce the rate of this breakdown, thus ACh is able to act for longer, at post synaptic AChRs, thus the decay half time is increased. The increase in decay half time in sequential EPPs could be due to ACh concentrations significantly in excess of the AChE saturation point, such that breakdown rate of ACh is no longer proportional to the concentration of ACh thus giving a linear rather than exponential breakdown curve. Not to scale! Top: before neostigmine, Bottom: after neostigmine. B. What would you conclude from quantal analysis of these data and should correction for non linear summation of EPPs be considered? Since we are given both the mepp amplitude and the observed number of failures for each EPP in the train, we can analyse the results quantally using both the method of failures and the direct method. The method of failures is the same as above: P(0) = e?m m Y 0! = e?m m = ln 1 P(0) The direct method is simple, and just involves dividing the mean EPP amplitude by the mepp amplitude as the EPP is made up of the response to n vesicles, which is equivalent to n mepps. m = Mean EPP amplitude mepp amplitude Using both these methods we can calculate m for all EPPs in both trains:

7 Before adding neostigmine: Mean MEPP amplitude: 1.2 mv Stimulus trials: 100 EPP1 EPP2 EPP3 EPP4 Number of EPP Failures Mean EPP Amplitude (mv) M (method of failures) M (direct method) After adding neostigmine: Mean MEPP amplitude: 1.5 mv Stimulus trials: 100 EPP1 EPP2 EPP3 EPP4 Number of EPP Failures Mean EPP Amplitude (mv) M (method of failures) M (direct method) This analysis highlights somewhat the limitations of the method of failures. If the probability of failure is very low, then it is difficult to observe a useful number of failures (out of 100 trails). It also leaves little room for discrimination a number of failures is a very discrete number. If more experiments were done, and an average number of failures was taken, this may be more useful. Our handout gives a rule of thumb that when mean quantal content is greater than 5, the method of failures cannot usually be applied. This experiment is very close to this limit. The results from the failures method are of limited use here. The direct method however, reveals a distinct decrease in in quantal content following neostigmine application (this is not at all distinct using the failures method). This decrease is consistent across all 4 EPPs in the train, which suggests it is not linked to facilitation differences. Regarding correction for non linear summation, since the mean quantal content is less than 5, it is unlikely that non linear summation would have a large impact on these results. The basis behind non linear summation is that each additional vesicle release to form an EPP has slightly less impact on the EPP amplitude than the last. This is because the post synaptic membrane begins to reach reversal potential, where increasing the sodium conductance would not achieve further depolarisation as sodium is at equilibrium at this point. The closer the EPP to this potential (i.e. the greater the quantal content), the more impact non linear summation has. Since the quantal content in these experiments is low, the impact of non linear summation is likely to be low. C. Anticholinesterases may have additional direct effects on properties of presynaptic or post synaptic acetylcholine receptors. Formulate hypotheses to explain the effects of neostigmine on the amplitude and time course of the synaptic potentials, with justification of your reasoning. Thinking about hypotheses, it may be useful to start by listing the effects of neostigmine observed: 1. Increase in mepp amplitude 2. Increase in EPP amplitude 3. Decrease in quantal content (by direct method) suggests 2 is due to the effect of 1 outweighing Increased rise time of EPPs 5. Increase half decay time, which increases on subsequent stimuli in a train of four 1 & 2 can be explained (at least in part) by the action on AChE as above. Of particular interest is number 3 as it is difficult to think of a direct link between AChE inhibition and decrease in quantal content (why would less vesicles be released?). With respect to the amplitude of the EPP, the effect of a reduction in quantal content (in light of an increased mepp) would be to make the increase in amplitude less than would be predicted by the change in mepp size alone.

8 One possible mechanism by which neostigmine may affect quantal content is by an action on presynaptic ACh receptors. ACh receptors on the presynaptic terminal are known to exist, and are muscarinic (G protein coupled) in mode of action. Their function is likely that of negative feedback on ACh release action of ACh on the receptors signals a cascade of protein activation which ultimately results in a lower probability of vesicle release. An action of neostigmine on these receptors could potentiate this effect either by allosteric modification increasing the response to ACh molecules, or direct agonist by neostigmine itself. These receptors may also be less active during membrane depolarisation facilitating mass vesicle release during stimulation of the nerve. Neostigmine could potentially reduce the effect of membrane depolarisation on the inhibition of presynaptic AChR activity, thus reducing vesicle release during stimulation. A suitable hypothesis might be that neostigmine increases the activity of presynaptic AChRs, leading to negative feedback on ACh release and reduced quantal content. Another phenomenon caused by neostigmine that isn t immediately explained by AChE inhibition is the increase in rise time & half decay time of EPPs. These measures are fundamentally due to movement of ions across the postsynaptic membrane, presumably through ion channels (nicotinic AChRs). Therefore, to affect these measurements, neostigmine must have an effect (direct or indirect) on these ion channels. The most obvious indirect effect is reducing ACh breakdown rate, which would lengthen half decay time as mentioned previously. The effect on rise time, however, is more difficult to explain. As rise time is associated with both the rate and amplitude of depolarisation, and amplitude is only marginally increased following neostigmine application, d amplitude is only marginally increased following neostigmine application, it appears that neostigmine decreases the rate of depolarisation. It is possible that neostigmine acts to reduce postsynaptic AChR activity reducing the end plate current but that the increased concentration and duration of ACh action leads to a similar (or greater per quantum mepp) magnitude of depolarisation. D. Suggests how the hypotheses you have proposed might be tested experimentally and what alternative outcomes of these experiments would imply. From the previous question, we have two hypotheses: 1. Neostigmine reduces quantal content by acting on presynaptic ACh receptors to inhibit ACh release. 2. Neostigmine increases rise time of EPPs by reducing the end plate current amplitude but extending its duration. This action is secondary to an inhibiting effect on postsynaptic AChRs. An experiment to test the first hypothesis could be to replicate the conditions from the present experiment (low Ca 2+, high Mg 2+ ) and perform the same recordings on a preparation with 3 different bathing solutions one of which involves an antagonist selective for the presynaptic ACh receptor (or multiple antagonists and combinations if more than one ACh receptor subtype is present on the presynaptic terminal): A control in physiological saline (with calcium/magnesium changes) A neostigmine and saline solution A neostigmine, presynaptic ACh receptor antagonist and saline solution A presynaptic ACh receptor antagonist and saline solution For simplicity, we will assume only one presynaptic AChR subtype, and that the selective antagonist has negligible effects on AChE and postsynaptic nachrs. If the results from the neostigmine and antagonist experiment are not significantly different from the normal control, but the neostigmine alone result gives a significantly lower quantal content than the control, this would provide evidence in favour of our hypothesis. Neostigmine acts on presynaptic ACh receptors to reduce quantal content, and this effect is reversed by application of a presynaptic ACh receptor antagonist. If a significant difference remains even when neostigmine and the antagonist are co applied, then higher doses of antagonist could be tested. Failure to reverse the effect of neostigmine on quantal content with a selective

9 presynaptic AChR antagonist would suggest the hypothesis was incorrect, and that neostigmine affects quantal content by another mechanism. An additional potential confounder would be if the presynaptic receptor antagonist alone increased quantal content under the same conditions. This would raise the possibility of neostigmine and the antagonist having opposite effects but by different mechanisms appearing to 'cancel out' each other. The second hypothesis could initially be tested using voltage clamp techniques to measure the end plate current on nerve stimulation in the presence or absence of neostigmine. If the expected differences in amplitude and duration of the EPC are confirmed, then the second aspect of the hypothesis could be tested. If EPC changes are absent, or not as expected, this would inform further refinement or complete reworking of the hypothesis. To test whether the effect on EPC is due to neostigmine acting on postsynaptic nachrs, and not an artefact of the effect of neostigmine on ACh concentration, breakdown and diffusion across the synaptic cleft, isolated preparations of muscle fibres could be used in absence of nerve terminals. Controlled doses of ACh could be applied to the muscle fibre by iontophoresis in the presence or absence of neostigmine. The resultant EPC in the muscle fibre could then be measured. If neostigmine still produces changes in the EPC, it would suggest that it acts on postsynaptic nachrs as suggested. Clearly, a denervated muscle fibre is not representative of the situation at the normal NMJ, but nachr properties would be similar, and a significant effect of neostigmine in this preparation helps isolate the effect to postsynaptic receptors. This would not, however, rule out action of neostigmine on other postsynaptic receptors that are not nachrs. Lack of a significant effect of neostigmine in this preparation would suggest that changes in EPC following neostigmine application are mostly due to the effect of neostigmine on ACh release, diffusion and breakdown in the synaptic cleft. Michael Lowe for Hons Neuroscience NMJiHaD Course 2012

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