PROJECT. Synaptic failure: benefit or inefficiency?

Transcription

1 Tartu University Institute of Computer Science Computational Neuroscence Lab MTAT Sissejuhatus arvutuslikku neuroteadusesse PROJECT Synaptic failure: benefit or inefficiency? Project duration: Authors: Oliver Härmson, Rao Pärnpuu Supervisor: Ardi Tampuu Tartu

2 Table of Contents TABLE OF CONTENTS 2 1. INTRODUCTION 3 2. OVERVIEW OF THE LITERATURE 3 3. THE MODEL 7 4. AIMS 9 5. RESULTS 9 6. CONCLUDING REMARKS 16 REFERENCES 17 2

3 1. Introduction The aim of our project was to study the effect of synaptic failure on information transmission. Synaptic failure is a neurobiological phenomenon. In the brain, up to 70% of pre- synaptic signals do not elicit post- synaptic signals. The exact mechanism and reason for this effect has not been conclusively established. In this paper we focus on two parts related to this question. In the first part we explore scientific literature connected to this phenomena, to see what are the possible biological or informational reasons for this type of failure and what are the exact mechanisms in the neuron that initiate this effect. In the second part we use a biologically realistic neuronal model to simulate different experiments. The aim of these experiments is to see whether synaptic failure can benefit the efficiency of information processing. More precisely, we aim to see whether synaptic failure helps to differentiate between the inputs of different pre- synaptic neurons, using machine learning. This can be helpful in explaining the positive aspects of synaptic failure and how it increases the amount of information transferred by also reducing the number of action potentials, therefore preserving energy. 2. Overview of the literature When taking into account the number of nerve cells in the mammalian nervous system and the number of their connections, one must question whether their communication is always effective. In fact, not all action potentials evoke neurotransmitter release and not all instances vesicle releases evoke action potentials (AP) in the postsynaptic cell. The rate of successful spike transmission varies between 0.1 and 0.9 (Quo, Li, 2012). Also, the rate of synaptic transmission and neurotransmitter concentration in the synapse following a release event have been shown to decrease over time during high frequency stimulation. There are reports to suggest that these phenomena are not simply "failures" or results of the overburdening of neural networks. In fact, synaptic failure and differences in neural firing might serve to enhance encoding of stimuli and transmission of information. As an addition, these phenomena help to lower energy consumption and heat production. The mechanisms giving rise to synaptic failure and the potential benefits it could bring about are discussed in this article. 3

4 It appears that electrical conduction itsself is relatively constant. Instead, information is lost where chemical transmission meets the electrical. In the neorcortex, experimental evidence indicates that axonal conduction is, essentially, information lossless. But there are 3 information- loosing transformations. Firstly, there is quantal failure. An impulse that has faithfully travelled down the axon can fail to evoke the release of a maximum number of neurotransmitter molecules in that synapse, otherwise known as a quantum (Levy, Baxter, 2002). For example, the hippocampal and neocortical excitatory synapses are able to transmit at most ~10 4 neurotransmitter molecules. However, the probability of evoking the release of a quantum is reported to be 0.25 to 0.5 (Thompson, 2000). Secondly, information can be lost due to quantal amplitude variation. Thirdly, information is approximated as a result of dendrosomatic summation. The three aforementioned transformations are depicted on figure 1. Figure 1 The three levels of information approximation for a single neuron that has 3 inputs and one output. The presynaptic axonal inputs to the postynaptic neuron is a vector of binary values X = [X1, X2,..., Xn]. Each input Xi is subject to quantal failures, the result of which is denoted by ϕ(xi). When this expression is scaled by the quantal amplitude,qi, the output from one axon becomes ϕ(xi)qi. This is integrated in the postsynaptic neuron across all the corresponding inputs. The output of the spike generator (soma) is a binary variable, Z, which is transmitted down the axon as Z'. As axonal conduction is nearly lossless, I(Z; Z') ~H(Z) (the amount of computational information transmitted in the axon roughly equals the Shannon entropy for the information encoded). There is a considerable amount of experimental data to support the hypothesis that synaptic failure reduces energy expenditure. Whereas AP creation in the cell body places a relatively low burden on the brain energy demand, ~47% of the total energy consumption is associated with AP creation in axons and ~34% with dendritic excitation. Embedded in those numbers are smaller energy costs attributable to, for example, recycling of neurotransmitter vesicles and repackaging, all of which can be avoided by quantal failure. Quantal failure also 4

5 enables to save energy on the cost of postsynaptic depolarization (Levy, Baxter, 2002) Since synaptic failure has been noted to be a significant determinant of neural transmission, attempts to quantify it have been made. For example, Levy and colleagues (2002) estimated the proportion of synaptic failures depends on the energy efficient maximum value of H(Z) f 1 4 H p*, and this statement does not depend on the number of inputs, n. For example, p* = 0.05 (the physiological optimal firing probability observed in the nonmotor neucortex and limbic cortex) implies f = 0.67 (fig 2). Quantal size itsself, however, leads to very little variations in failure rates. Figure 2 Optimal failure rate as a function of spike probability in one computational interval. The optimal failure rate decreases as the optimal firing probability (p*) increases. The vicinity of physiological p* ( for nonmotor neocortex and limbic cortex) predicts physiologically observed failure rates. Synaptic failure can be measured in biological systems indirectly by comparing the information encoded by different neurons on the same pathway (for example the visual pathway). For example Sincich and colleagues (2009) recorded inputs from single retinal ganglion cells (RGC) and outputs from connected lateral geniculate cells (LGC) and found the geniculate cells to modify the information in a way that enabled more information to be carried by each spike. In specific, average information rates increased from to bits/spike for the RGC and LGC, respectively. It was found that the LGC neurons exhibited a higher spike rate gain for certain stimulus features compared to RGCs (fig 3). Also, it was found that only those RGC spike trains that carried high information density (2.43 bits/spike) elicited a LGC spike, whereas low- density RGC spike trains had the opposite effect. These differences in spiking rates are surprising, as the mean 5

6 rate of RGC EPSPs (EPSPs/s) was found to be lower than LGN mean spike rates (Sincich, Horton, Sharpee, 2009). However, it shows that a reduction in the output rate can be made to an extent that preserves information transmission, possibily even enhancing it via selective activation for certain stimuli (Quo, Li, 2012). As in many other realms, quantity is not the same as quality. Figure 3 Population data comparing RGC and LGN spike rate gains for all filters (STA - substracted average, MID1, 2 - maximally informative dimensions 1 and 2). By picking out the stimulus features that explained a lot of the spiking activity in both RGC and LGC neurons, the vectors MID1 and MID2 were produced. Spike rate gains are defined as the average spiking rate resulting from stimuli with the same components along the relevant features. When both MID1 and MID2 filters were used, it was found that the same stimuli elicited more spiking in the LGCs. There are even studies to suggest that evoking synaptic failure might have a therapeutic value. For example, it has long been known that some of the symptoms of Parkinson's disease (such as tremor and bradykinesia) might be caused by pathological activation of the thalamus by the subthalamic nucleus (STN) (So, Kent, Grill, 2012). Rosenbaum and colleagues (2013) have shown by in vivo and in vitro recordings that deep brain stimulation (DBS) evokes synaptic failures in STN projections and reduces parkinsonian beta- oscillations and synchrony as a result. The model that they proposed imitated the findings of in vivo recordings in a precise manner (fig 4) and took into account the following phenomena (i) each stimulation pulse evokes an action potential with a probability that is decreased by each pulse, (ii) between pulses, the probability of successful action potential initation recovers over time, (iii) the time at which an action potential reaches the axon terminal is increased by each pulse and recovers exponentially in time and (iiii) during each pulse the amount of vesicles in the axon terminus decreases (Rosenbaum, Zimnik, Zheng, 2014). 6

7 A Normalized PSC amplitude In vitro recordings Computational model B Normalized FV amplitude Time since stimulation onset (s) Time since stimulation onset (s) C D FV latency (ms) Time since stimulation onset (s) Normalized FV amplitude Time since stimulation stopped (s) Figure 4 Synaptic and axonal failure during high frequency stimulation of STN. A,B amplitude of the mean post- synaptic currents (PSCs) and fiber volleys (FVs) in the SNc elicited by 130 Hz HFS in STN, plotted as a function of the time evolived since onset of stimulation. C Latency of the FV peak after each HFS pulse. D FV amplitude after HFS is replaced by slow 0.1 Hz stimulation, normalized by the final (recovered) amplitude. Blue error bars are from in vitro recordings in rodent SNc. Red curves are from simulations of the computational model. 3. The Model The details of the model we are planning to use can be found in the supplementary information of studies by Yeung and colleagues (2004) and Shouval and colleagues (2002) and will be implemented with help from Taivo Pungas (Yeung, Shouval, Blais et al., 2004; Shouval, Bear, Cooper, 2002). In brief, an Integrate- and- Fire model will be used to simulate the dynamics of the somatic membrane potential. The EPSP waveforms will take into account NMDAR Ca 2+ currents. The model was based on Taivo Pungas' bachelor thesis. Necessary changes to make the model suit our goals of research were made together with Ardi Tampuu and Raul Vicente. In essence, the model is an integrate and fire neuron. The original model was a neural network comprised of 100 excitatory neurons and 20 inhibitory neurons (the input neurons) connected to one output neuron. We used a network of 2 excitatory input neurons and 1 output neuron. The input generated was either (a) regular and uncorrelated, (b) Poissonian and 100% correlated, (c) Poissonian and 80% correlated and (d) totally uncorrelated. The input was generated in 1-7

8 second blocks for ease of implementation and the release of neurotransmitters caused by each presynaptic spike is assumed to last 1ms. The mean initial input rate of the input neurons was set to either 10Hz or 30Hz. The input rate was normalized to the synaptic failure probability: Re = Ri/(1- p), (1) where Re is the mean effective firing rate, Ri is the intial mean firing rate and p is the synaptic failure probability. This ensured that the amount of information provided to the postsynaptic neuron would stay relatively constant despite the increasing probability of synaptic failure (fig 5). There was no significant correlation between the probability of synaptic failure and the amount of spikes fired by the postsynaptic neuron (p = 0.7, r = 0.3). Figure 5 Relationship between synaptic failure probabilities and amount of postsynaptic spikes in trials of equal and unequal weights for the 2 inputs. The 2 excitatory inputs were connected to dendrite compartments in which the opening of glutamate- controlled ion channels was simulated. The resulting ion flow through the channels tends to drive Vpost towards the excitatory reversal potential, 0mV. This increases the probability of a postsynaptic neuron producing a spike. Each time the postsynaptic neuron fired a spike, reaching its spike potential 40mV, the membrane potential was again set to Vreset - 65mV - the resting membrane potential. Probabilities of failure ranging from 0.0 to 0.9 were studied in each experiment, in steps of 0.1. The probability of failure manifested itsself as a random removal of input spikes from the input trains generated. The probability of random spike removal increased in proportion with the probability of failure. Also, the two synapses were attributed either different (3 and 7) or equal (5 and 5) weights. The aim of this modification was to train a support vector machine (SVM) classifier to tell, at each trial, what set of weights were used. This serves to reflect the ability of the neuron to distinguish between its two inputs. 8

9 In several experiments, we use a Poissonian distribution to model spiketrains. In statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event. In our case, we used an average rate of neurons firing per second, to create a Poissonian distribution of all the firing rates over the simulation. Data analysis and implementation of the model was conducted in MATLAB, the source code for the conducted experiments is included as a separate file. 4. Aims (i) To see whether changing the membrane potential dynamics in response to a spike event in the postsynaptic neuron will change the amount of spikes fired. (ii) To see whether different probabilities of synaptic failure will affect the neuron s ability to distinguish one input from the other. (iii) To see how well the postsynaptic neuron distinguishes its inputs when input spike train types are altered. 5. Results Experiment 1 Classifier accuracy for fully regular input In this experiment the spike times of both of the pre- synaptic neurons were exactly the same. Once we introduced a failure rate, some spikes were randomly eliminated from both of the spiketrains independently. The SVM classifier was used to see whether the post- synaptic neuron was able to differentiate between the weights of the inputs. The results for different failure rates are showed in the graphs below (fig 6,7). 9

10 Figure 6. Normalised input 10Hz over 101 seconds As can be seen from the graph, the increase in failure rate also increases the accuracy of the classification. But if the failure rate is too high, the accuracy of the classifier starts to decrease. Highest accuracy is achieved with a 20-40% failure rate. With a higher input rate, the results become more heterogenous and overall accuracy decreases, as can be seen on figure 6,7. Figure 7. Normalised input of 30Hz, over 101 seconds 10

11 At 30Hz, the accuracy becomes more varied and lower, therefore no generalisations can be made, when using a higher input for the experiment. It should be noted that the accuracy of this classification is varied. In order to get results with an error rate of less than a few percent, longer simulations should be run and standard deviations are needed over several simulations, which would have been outside the scope of this project. It suffices to say that in the case of totally regular input, there is an optimal failure rate which increases the ability of the neuron to distinguish its channels of information. Experiment 2 Classifier accuracy for Poissonian and 100% correlated input trains In this experiment two Poissonian 100% correlated input trains were generated. Synaptic failure events in both inputs occurred simultaneously and cancelled out spikes in both spiketrains at the exact same time points. As can be expected, increasing the probability of synaptic failure does not affect the ability of the neuron to distinguish its inputs. Classifying accuracy undulates around chance precision at both 10 Hz and 30 Hz input frequency (fig 8, 9). Figure 8. Normalized input 10 Hz over 101 seconds 11

12 Figure 9 Normalized input 30 Hz over 101 seconds Experiment 3 Classifier accuracy for Poissonian and 80% correlated input In a way this experiment represents the reality in populations of neurons. For example, two neurons could be specific for the same stimuli, but encode it with some differences in spiking patterns. In other words, the neurons might not be synchronized. In this simulation two Poissonian spiking trains were produced that were 80% identical. Synaptic failure events cancelled out spikes in both spiketrains independently and therefore at different time points. In essence, synaptic failure in these inputs can be thought of as decorrelating the spiketrains. An input rate of 10Hz produced SVM prediction accuracy rates between 0.5 and 0.6 (fig 10). Changing the mean input rate to 30 Hz resulted in classifier accuracy rates between 0.6 and 0.9 (fig 11). Although mean errors were not compared in this study, it can be speculated that higher probabilities of failure result in increased classifier accuracies in partially correlated Poissonian spike trains. This can be explained as an increasing decorrelation between the (initially correlated) spike trains, which makes the inputs easier to distinguish. 12

13 Figure 10. Normalised input rate of 10Hz over 101 seconds Figure 11. Normalised input rate of 30Hz over 101 seconds 13

14 Experiment 4 Classifier accuracy for uncorrelated input In this experiment we tried to see, whether totally uncorrelated spikings would result in higher success rates. Common sense would say that if the inputs are uncorrelated, then failure rate would play a minimal role in influencing the amount of information a post- synaptic neuron receives. This was corroborated by the results. The results are portrayed in figure 12 and 13. Figure 12. Normalised input 10Hz over 101 seconds Figure 13. Normalised input of 30Hz over 101 seconds 14

15 As can be seen, it did not matter what the probability of failure was, all the accuracies were above 80%. The results at failure probability 10% can be ignored, because those can be attributed to the failure of the SVM classifier itself during training. As such, it does not represent the actual result. Experiment 5 Classifier accuracy for Poissonian and independent failure rate In this experiment we used Poissonian spiketrains that were initially fully correlated. Synaptic failure events, however, cancelled spike events independently in both spike trains and had a decorrelating effect (fig 14,15). Figure 14. Normalised input of 10Hz over 101 seconds As can be seen from the graph (fig 14), the accuracy of the classifier rises in proportion to the synaptic failure probability. At a 0% failure rate the two spiketrains were identical and there was no way for the classifier to differentiate between the weights of the input neurons. With a failure probability of 60% or more, the classification accuracy becomes close to maximum with both 10 Hz and 30 Hz input frequency (fig 14,15). 15

16 Figure 15. Normalized input of 30 Hz over 101 seconds 6. Concluding remarks It can be concluded that synaptic failure is a significant event in information processing. On the one hand, it serves to decorrelate nearly identical input spiketrains and therefore could sustain specificity of source information in the neuron model described above, and possibly, also in vivo. In fully decorrelated spiketrains synaptic failure does not alter the neuron s ability to distinguish its source of information and therefore does not enhance information transmission. Although no optimal probability of failure was pointed out in this study nor different accuracies compared statistically, this data might suggest that for each type of input type (except fully decorrelated spiketrains) there is an optimal failure probability between 0.1 and 0.8 that serves to enhance information processing and input discrimination. Future studies should address developing the model proposed above to contain (a) a bigger population of input neurons, (b) longer simulations to be able to gather more data and allocate more information to training and test sets, (c) different methods of classification, as the SVM classifier sometimes fails to adequately categorize the weights of the input neurons and, (d) different levels of correlation between Poissonian input spiketrains, and (e) experiments of plasticity, addressing the possibility of input- specific synaptic plasticity in the face of different probabilities of failure. 16

17 We would like to thank Ardi Tampuu, Raul Vicente and Taivo Pungas for their kind help and contributions to this work. References Levy, W.B., Baxter, R.A. (2002) Energy- efficient Neuronal Computation via Quantal Synaptic Failures. The Journal of Neuroscience, 22(11): Quo, D., Li, C. (2012) Population rate coding in recurrent neuronal networks with unreliable synapses. Cogn Neurodyn (6): Rosenbaum, R., Zimnik, A., Zheng, F, Turner, R.S., Alzheimer, C., Doiron, B & Rubin, J.E. (2014xonal and synaptic failure suppress the transfer of ring rate oscillations, synchony and information during high frquency deep brain stimlation. Neurobiology of Disease, (62): So, R.Q., Kent, A.R. & Grill, W.M. (2012) Relative contributions of local cell and passing fiver activation and silencing to changes in thalamic fidelity during deep brain stimulatino and lesioning: a computational modeling study. J Comput Neurosci, (32): Shouval, H.Z., Bear, M.F., Cooper, L.N. (2002) A unified model of NMDA receptor- dependent bidirectional synaptic plasticity. PNAS, 99(19), Sincich, L.C., Horton, J.C., Sharpee, O.T. (2009) Preserving Information in Neural Transmission. The Journal of Neuroscience, 29(19): Thomson A (2000) Facilitation, augmentation and potentiation at cen- tral synapses. Trends Neurosci 23: Yeung, L.C., Shouval, H.Z., Blais, B.S. & Cooper, L.N. (2004) Synaptic homeostasis and input selectivity follow from a calcium- dependent plastiity model. PNAS, 101(41),