Presented at the Computational Neuroscience Meeting (CNS*00), Brugge, Belgium, July 19, 2000
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1) Introduction. I would like to thank the organizers for giving me the opportunity to describe the collaboration I have had with Dr. Curtis Bell during the past three years. This is a modeling effort that uses both analytic and simulation techniques to combine experimental results from the synaptic level with studies of the whole organism. The results yield a picture of the neural dynamics of this adaptive electrosensory system. However, we believe that these methods have relevance for other systems and can shed light on the synaptic basis of learning and memory. The research will be described in two parts; first and experimental part and then a modeling part. The experimental work has been carried out by Curt Bell and his colleagues for more than 20 years. I'll begin with an introduction to the electrosensory system of mormyrid electric fish. Then I'll present the sensory problem that the fish must solve through adaptation to changing sensory stimuli. Next, I'll present some of the neuroanatomical details that are important to understand adaptation in this system; I will then introduce a spike timing dependent synaptic learning rule (or temporal learning rule) that changes synaptic strength in response to the exact timing of pre- and postsynaptic spikes. Finally, I'll describe the model; first our model of a single neuron, and then show that the presence of mutually inhibitory pairs of neurons increases the adaptation rate. I would like to make clear that I personally have never touched one of these fish. I am indebted to Curt Bell and his colleagues for my involvement in this study, the beautiful experimental data that they provide, and for their ongoing work and discussions. The picture shows the species of mormyrid that is studies in Bell's lab, also called the elephant nose fish because of its protruding lower lip. They grow up to about 15 centimeters in length, and are native to muddy rivers and streams of sub-Sahara Africa. They are generally nocturnal and their electrosensory system allows them to thrive in their habitat.
2) Mormyrid Electric Fish. Mormyrid electric fish have been quite successful and make up about 30% of the fresh water fish species in sub-Sahara Africa. Here is a picture of several other species besides the elephant nose, that were caught with a single toss of the net into a West African river. The picture is from Carl Hopkins' web site and was taken on an expedition in 1998.
3) The electric organ discharge (EOD). All mormyrids have an electric organ; a modified muscle that generates a weak electric field. The fish sends a motor command, like flexing a muscle, to cause the electric organ to discharge in pulses at a resting rate of 2-3 Hz. By detecting distortions caused by external objects in its own electric field, the fish can navigate in the dark. This is analogous to the use of echolocation by bats.
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4) The Electrosensory World. Mormyrids have three types of electroreceptors that serve different functions, and different electroreceptors are used for these tasks. Aside from active electrolocation, these fish use their electric organ to call and challenge each other. Furthermore, the fish have specialized receptors for detecting external sources of electric fields such as other moving organisms. However, because of the electric organ discharge, the fish now has to sense the subtle electric field of a food source like a wiggling worm (lower left), over the background of its own electric discharge. This is not unlike a problem that is solved by our own visual system. When we move our eyes, the visual field moves across our retina, but we don't perceive the visual scene moving. However, if we move our eyes without using our eye muscles, then the scene appears to move. Since the fish generates the signal, the information is available to predict what the sensory image of the electric discharge will be and eliminates the predicted image in order to emphasize subtle novelties in it's environment like worms. The system needs to be adaptive to adjust to changing sensory conditions such as changes in water conductivity.
5) Observing Adaptation... One of the reasons this particular fish makes a good experimental subject is that even if they are paralyzed, they will continue to electrolocate and try to pulse their electric organ. The motor command can be detected and used to trigger and artificial electric field that mimics the fish's discharge. The artificial field can then be manipulated while recording from neurons that respond to external electrosensory signals.
6) Cancellation of Predicted Sensory Image. This is a raster plot of neuron spike activity where each horizontal trace is triggered by the command signal (at time zero on the plot). Each dot represents a spike and each row represents a cycle of the motor command. During each cycle another row of spikes is added. The cycles marked with a black line are paired with the artificial stimulus that simulates the electric organ discharge. We see here that the neuron is responding with a pause followed by a burst of spikes. However, after several minutes of pairing, the responses begin to fade as the neuron adapts to the sensory stimulus. Now when we turn off the stimulus, the cell responds to the command alone, generating a negative image of the expected sensory image. This is an adaptive filter of the electrosensory information.
7) Three Electrosensory Systems. This figure shows a schematic of the three receptor systems used by the electric fish to process electrosensory information: communication, active electrolocation, and the passive electrodetection system. In this complicated figure, we will concentrate on the center (red) system, the passive electrosensory system. To review what we know now using this diagram; the command is sent to the electric organ that responds with an electric pulse, the sensory "re-afferent" information from electroreceptors is sent to the principal neurons that respond as we saw in the raster plot. However, there must exist some kind of expectation generator that responds to a corollary discharge of the command signal. The expected signal is then subtracted from the afferent electrosensory information. This expected pattern is continually updated so that novel signals are emphasized.
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8) Electrosensory Lateral Line Lobe. Now we'll look at the neuroanatomy of the electrosensory system to better understand the expectation generator. The recording shown in the raster plot were made in the electrosensory lateral line lobe, or ELL, the site of first entry of electrosensory afferents to the brain. Electroreceptors in the skin project somatopically, that is, the image on the ELL reflects the image on the skin of the electric field strength. The receptors that we are interested project onto the ventral lateral zone (VLZ) of the ELL.
9) Cell Types of the ELL. Detailed anatomical studies have been made in the ELL that have identified various cell types. Most important about this slide is the laminar structure, the electrosensory afferents enter from the deep layer. There is a layer of large cells, and it is these neurons that show the strongest adaptation to changing sensory images. These medium ganglion cells have basal dendrites that receive the electrosensory afferent input, and apical dendrites that reach in to the molecular layer to receive a variety of synaptic inputs from parallel fibers. The parallel fibers originate externally to the ELL as granule cells that respond to the corollary discharge. There are 2 anatomically distinct types of medium ganglion cells which respond oppositely to sensory stimuli; if one type bursts, the other pauses. Their dendrites are most dense at different layers, and their axons project to the other's dendrites. This suggests that these GABAergic neurons are mutually inhibitory.
10) Electrosensory Pathways. This shows how the ELL sits in the brain, and how the two pathways that we are interested in intersect. The motor command originates in the command nucleus and runs down the spinal chord to the electric organ that generates an electric discharge. The electrosensory afferent fibers then project to the deep layers of the ELL. Simultaneously, a corollary discharge signal enters the ELL through parallel fibers.
11) Medium Ganglion Cell Inputs. Now we can isolate the expectation generator in this anatomy. The medium ganglion cell responses adapt to eliminate the sensory signal. Recordings from granule cells show that they do not respond to the corollary discharge simultaneously, but their responses seem to be distributed in time following the command signal. Corollary discharge information of when the electric discharge arrives through parallel fibers, so a likely candidate for adaptation would be the synapse between the parallel fibers and the apical dendrites. But before we look at the synapse, a special property of the medium ganglion calls is needed.
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12) Two Spike Types. Medium ganglion cells respond to a depolarizing in put with two types of spike: a small narrow spike and a broad large spike when recording from the soma where the broad spike is present at a higher threshold. Experimental evidence suggests that the small spike is axonal and the broad spike propagates into the dendrites. The dendritic spike would be able to inform the parallel fiber synapses of strong depolarization caused by afferent sensory input to the basilar dendrites.
13) The Temporal Learning Rule. To test the synapse for changes in postsynaptic potential, Curt Bell, Victor Han, and colleagues used a slice preparation of the ELL and stimulated the parallel fibers to measure the synaptic strength. Then they stimulatedparallel fibers while depolarizing the medium ganglion cell to generate a broad spike at various delays. The important aspect of this test is to characterize the timing between the pre- and postsynaptic spikes to induce synaptic change. After repeatedly pairing a stimulation with a broad spike at a certain delay they remeasured the strength of the synapse again with postsynaptic potential. Some delays increased the synaptic strength while others decreased it. When all the changes were plotted as a function of the delays, they found that the synapse was depressed if the broad spike immediately follows the stimulation, otherwise the synaptic strength was enhanced. In fact, the depression was in a time window of about the same duration and coincident with the postsynaptic potential.
14) Antisymmetric Biological Learning. For comparison, this slide shows another timing relation for a biological spike-timing dependent learning rule. These data were collected in Mu Ming-Poo's lab, and are taken from the developing frog optic tectum, the hippocampus, and are consistent with the timing relations found in the rat neocortex. Here you can see that there is depression when the postsynaptic spike precedes the presynaptic spike, and there is potentiation when the postsynaptic follows the presynaptic spike. This will lead to very different learning dynamics than the learning rule found in the ELL.
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15) Model of the Medium Ganglion Cell. This is where I entered on the scene. I had previously avoided learning models before because it seemed that with the right choice of learning and architecture, one could teach a model just about anything. But here we have a detailed learning rule and a well characterized architecture. I included the simplest elements in the model; the afferent sensory inputs, and a series of delayed synaptic inputs that can change their strength according to the time dependent learning rule. The series of delayed inputs represent the parallel fiber signals that are the delayed response to the corollary discharge signals. Also, noise is introduced into the model neuron to account for any other inputs that are not correlated with the command.
16) Model Learning Rule. The rule is applied to each epsp by finding a broad spike, and if it is outside the range of the epsp, then the epsp is enhanced by a factor called the non-associative learning rate. Otherwise, if the broad spike is within the postsynaptic potentials of a synaptic input the weight is changed proportionally. The sum of all inputs gives the contribution of the apical dendrites to the average membrane potential. We then add on the sensory image and noise to give a probability of narrow and broad spikes at any time during the cycle. This is a spike response model because it represents the response of the postsynaptic neuron to the presynaptic spikes. This is easily implemented on the computer, but we can also derive analytic results such as the synaptic weight distribution following adaptation and the rate of adaptation. This helps us to see the functional relationship between parameters, and better understand the model's limitations.
17) Adaptation of Sensory Responses. Now if we run the simulation with the same pairing procedure as shown earlier, the results can be compared with experiment. First, only the command signal which brings a series of synaptic inputs to the medium ganglion cell, then during every cycle pair the sensory image of the electric organ discharge with the electrosensory input to get a pause-burst response. After some time, the synapses change:they are relatively enhanced during the pause for a lack of broad spikes, and depressed for many broad spikes. Then when the sensory stimulus is turned off, the negative image is revealed, and slowly fades.
18) MG cell simulation.This movie of a simulation run shows how the system adapts. On the right side is mostly interface, but what will be important is the sensory image that will change to a flat line after 100 cycles. On the left the array of spikes will be laid down every cycle, and below is a color coding on the synaptic weights values. Each color band represents the value of the weight for the epsp that begins at that time step. Warmer colors represent higher values and cooler values represent lower values. Beginning the simulation, you can see the cell respond during each cycle with a pause-burst following the sensory image representing a hyperpolarization followed by a depolarization. Since there is a relative absence of broad spikes in the pause, the non-associative potentiation dominates and the weights increase, seen by the warmer colors. During the burst, where there is a high probability of broad spikes, the associative enhancement dominates and the weights are reduced. At 100 cycles we turn off the sensory image and the negative image is revealed. The system then reverses the adaptation process to flatten out the output again. As the system adapts, the spike probability reaches an equilibrium that is dependent on the ration of the non-associative learning rate to the associative learning rate.
19) Weight Adjustments. An instructive way to look at the system is by watching the weights change. Here is the same type of simulation, but now the weights for the synaptic inputs that begin at each time step are displayed. Again, warm colors are stronger weights and cooler colors are weaker weights. We can see in the pause phase of the response the weights increase and they are depressed in the burst phase.
20) Antisymmetric rule simulation. Now we will repeat the simulation as before, but with the antisymmetric learning rule to see the difference in learning dynamics. The only other difference is that I've reduced the noise a little so you can the effect better. Recall that in this rule there is potentiation when the postsynaptic broad spike in coincident with the epsp, and depression if the broad spike immediately precedes the epsp. The simulation begins with a potentiation where the SLOPE of the sensory image is positive, and depression where the slope is negative. As the membrane potential builds, there is a movement of the peak of the sensory image towards the beginning of the cycle as the learning rule adjusts the weights as a function of the slope of the postsynaptic membrane potential. Thus, this turns out to be a differential-Hebbian rule. In the last cycle, the neuron that responded with a burst late in its cycle, now responds early in the cycle.
21) Negative image of sensory input... Here we display the contribution of the sensory inputs and the apical or parallel fiber inputs following adaptation. The sum is a flat line and the negative image is represented in the parallel fiber inputs.
22) Time Evolution of the Adaptive Response. The difference from a perfect negative image is measured here by a chi-squared analysis. As the number of cycles progresses (to the right) the curve decreases showing that the total membrane potential is level. In this situation, (lowest number) the fish would be most sensitive to any novel external stimuli such as a wiggling worm because its own predictable field is completely filtered out.
23) Instabilities Disrupt the Negative Image. However, any learning rule with associative depression and non-associative enhancement will work for this system. The two rule shown here are unstable and lead to oscillations that follow the command signal. These rules are as bad, if not worse than if there were no adaptation at all because there are bursts and pauses that are completely uncorrelated with external electrical signals. These patterns are a result of the dynamics of the learning rules themselves. The second one we see how the broad spikes depress elsewhere from the action of the synapses, and lead to enhancement where the epsp contributes most So not only is it important that the learning rule generates the negative image, but the learning rule needs to be dynamically stable.
24) Few Learning Rules Converge... Here is a comparison of four learning rules using the chi-squared measure of faithfulness of the negative image. The fifth one is the physiological learning rule with no non-associative enhancement. The instabilities of the symmetric rule are slow to develop; here we see good cancellation of the afferent input, but eventually the value climbs as oscillations set in. The leading decent of all these is a result of the associative depression along with non-associative enhancement. Using analytic methods we found that if the associative depression window is less than four times the duration of the epsp, then the rule is stable. If it is less than the epsp duration, then the rule is unstable. This is done by computing the average weight change. We then take a continuum limit of the expression and test for oscillatory solution with a decay in the number of cycles. We can then solve for the decay constant and if it is negative, there are growing oscillation, and if it is complex, then there are travelling wave solutions.
25) Universality classes of temporal learning rules. The analysis allows us to classify spike-timing dependent learning rules into four universality classes of behaviors. The first approaches a constant output and is associated with anti-Hebbian learning, as found in the ELL. The second generates stable oscillations, and the other two generate travelling waves of activity and can be associated with anti-differential Hebbian and differential Hebbian learning. At the right are examples, but represent families of curves that generate these classes. Three of these rules have been seen in biological preparations, the first and last we have talked about, and the second more recently by Egger and colleagues in the rat barrel cortex. [V. Egger, D. Feldmeyer, B. Sakmann (1999), Coincidence detection and changes of synaptic efficacy in spiny stellate neurons in rat barrel cortex, Nature Neurosci. 2:1098-1105]
26) Model of Mutually Inhibitory MG cells. Now returning to the electric fish, we'll look at how the circuitry on the ELL can affect the adaptation rate. You may recall that I talked about two types of medium ganglion cells each of which responds oppositely to the electric organ discharge. I one type pauses, the other bursts. I also said that their dendrites receive input from different layers in the ELL, and that their axons project so that it is possible that they mutually inhibit. We decided to test the effects of this with the model, primarily the effect on the adaptation rate.
28) Two cell model with mutual inhibition increases adaptation rate. The result in terms of the chi-squared variable is shown here. Trace A is the simple one-neuron model, and the noisier trace is one of the cells in the mutually inhibitory model. The extra noise is due to the response of the neuron to the simple spikes of its pair. In these simulations, the synaptic learning rates were set with data from the slice experiments so we could compare the system adaptation rate with in vivo experiments. The inset in the upper right shows the results of in vivo recordings and the grey region between the two curves has been mapped onto the model results. The single neuron model falls outside the range, but the mutually inhibitory model falls inside.
29) New Dynamics from more complex circuits. However, the ELL is still more complex. Here is the presently hypothesized circuit for the neuron types in the ELL. In the middle are the medium ganglion cells that we have already discussed, and these synapse onto the efferent neurons that are the actual output of the ELL. Also inhibitory stellate in the molecular layer respond to parallel fibers and inhibit the medium ganglion and efferent neurons. The sensory inputs are also more complex than I have modeled here, and all of these circuit are expected to add new dynamics to adaptation of the system that we are beginning to understand.
30) Learning rule + Architecture = Function. But we can draw on these results to other systems and hope to gain insights about their function. What we found in the ELL was that the combination of a particular learning rule in combination with the series of delayed synaptic inputs leads to a cancellation of the predictable sensory image. Other systems appear to have characteristic learning rules, such as the hippocampus and the cortex. In combination with the neural architecture we can begin to make predictions about how the neural system functions. I've put the cerebellum here next to the ELL because the ELL is considered a cerebellum-like structure. However, there is a great deal of controversy about what the corresponding learning rule is, or if there is learning at all at the synapse from the parallel fibers onto Purkinje cells. A project that addresses the question of spike timing dependent learning in the cerebellum is currently underway and is supported in part by a grant from NIMH (R01 MH60364).
31) Collaborators. As our mormyrid ponders the mysteries of electrodynamics, I would like to thank my collaborators. The research was funded in part by a grant from the National Science Foundation (IBN-9808887). Media design by Lindsey Creek Creative.