Computational model of temporal processing in the auditory cortex

Transcription

1 ECOLE NORMALE SUPERIEURE Computational model of temporal processing in the auditory cortex by LEE Jong Hoon A thesis submitted in partial fulfillment for the degree of Research Master in Cognitive Sciences in the departement des Etudes Cognitives June 2017

2 Declaration of Originality I, LEE JONG HOON, declare that this thesis titled, Computational model of temporal processing in the auditory cortex and the work presented in it are my own. I confirm that: This work was done wholly while in candidature for a research degree at the Ecole Normale Superieure. Where I have consulted the published work of others, this is always clearly attributed. Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. I have acknowledged all main sources of help. Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself. Signed: Date: i

3 Declaration of Contribution I, LEE JONG HOON, declare that this thesis titled, omputational model of temporal processing in the auditory cortex and the work presented in it are my own. I confirm that: This work was done wholly while in candidature for a research degree at the Ecole Normale Superieure. Where I have consulted the published work of others, this is always clearly attributed. Identifying, Clarifying, and developing my specific research question was done in collaboration with my supervisor, Dr Bendor, who also gave me critical feedback on how I should approach the question and interpret obtained results. Although I have discussed the computational model with Dr Maneesh Sahani and Dr Peter Latham, the concept of the model and it s components was developped by Dr Bendor and myself. The electrophysiological recording data was collected by Dr Bendor in 2005, but the analysis of this data was performed by myself. The programming of the model and analysis of its results were done entirely by myself. Unless cited otherwise, the figures presented in this thesis were created by myself. Signed: Date: ii

4 Good data allows you to do decades of analyses and still find something new everytime. Samuel Solomon, Visual Neuroscience Lab, UCL

5 Acknowledgements I thank Daniel Pressnitzer of the Laboratoire de Systemes Perceptifs, ENS, my Master programme tutor, Yves Boubenec (Laboratoire de Systemes Perceptifs)and Srdjan Ostojic of the Group for Neural Theory, ENS, for helping me brainstorm ideas and possibilities for this project. Most of all, I thank Daniel Bendor of the Neural Encoding Laboratory, UCL, who was not only my project supervisor but also became my mentor during my first steps in the world academic research. It was a great privilege and pleasure to work with him and his team, who gave me a clearer idea of how I should approach fundamental research in neuroscience. I would also like to thank Ana, who supported me throughout this project and this academic year. Number of words : 9202 iv

6 Contents Declaration of Originality i Declaration of Contribution ii Acknowledgements iv List of Figures vii 1 Introduction Background Theory and Hypotheses Monotonic negative neurons The role of Synchronized neurons Study aims Results Synchronized monotonic neurons in A Limitations of the previous model Modelling short-term plasticity Results Non Synchronized monotonic neurons in A comparing Sync and nsync neurons Leaky Integrate-and-fire E-I balanced networks Results Discussion Summary Comparison with previous studies Model limitations Network parameters and stability Vector strength and spontaneous rate response to other stimuli Conclusion Methods Ethics statement v

7 Contents vi 4.2 Electrophysiological recordings and acoustic stimuli Computational model Single-unit model Short-term plasticity : Depression Network model and simulation Data analysis Classification of neurons A conductance input and membrane potential dynamics 28 B Pre-registration document 30 B.1 Background and rationale B.2 Key questions B.3 Methods B.3.1 Model B.3.2 Data B.3.3 Protocols B.3.4 Analysis B.4 Expected outcomes B.5 Distribution work Bibliography 34 References 34

8 List of Figures vii

9 Chapter 1 Introduction Processing temporal structure in acoustic stimuli is crucial for extracting information from complex sounds such as music, speech [1] [2], or conspecific vocalizations[3]: Information in such stimuli are contained not only in the nature of sound at a given time (place and frequency), but also in how the sound varies across time. Whereas the neural mechanisms of encoding place and frequency in the brain has been the main topic of research in auditory perception during the last few decades, the mechanisms of temporal processing is still not well known. One key element of temporal features in a sound is periodicity. Many of natural and biologically relevant sounds repeat quasi-periodically with a certain frequency. Although the nature of these stimuli are similar to each other, if the repetition rate of an acoustic event is between 10 and 45Hz, we distinguish a sequence of multiple events, or flutters. If the repetition rate is higher, then we no longer perceive discretised events but a fused sound (fusion). Although the auditory nerve can spike in synchrony to very high frequencies [4,5], the ability of a neuron to synchronize to fast repetition rates is lost as we move further upstream in the auditory system. Instead, repetition rates above the range of fusion is encoded by discharge rates of a separate sub-population of neurons that does not synchronize to repetitive acoustic stimuli. An analogue encoding scheme is found in the somatosensory system. In the primary somatosensory cortex (S1) vibrations in the flutter range are encoded by rapidly adapting neurons whereas those in the fusion range are encoded by pacinian neurons. In addition, previous studies in monkeys have found that stimuli in the flutter range evoked both periodic, stimulus-driven spikes (temporal coding) and variations in firing rate that increased monotonically with stimulus frequency (rate coding) in S1[6,7]. Furthermore, in areas upstream including the secondary somatosensory cortex (S2) only rate coding of stimulus frequency was observed. Other behavioral experiments[6] led Romo and his 1

10 Introduction 2 colleagues to conclude that rate coding, but not temporal coding, plays an important role to the decision making process during frequency discrimination tasks. Figure 1.1 (A.)Four responses of neurons to acoustic flutter. (B.) Cartoon explaining the model by Bendor(2015). The acoustic pulses (top) are converted into excitatory and inhibitory conductance (middle) which are used to generate input currents in an integrate-and-fire unit (bottom) 1.1 Background Different ways of encoding acoustic flutter The similarities between the two sensory systems in encoding repetitive stimuli led to the following question: Is flutter encoded in the auditory cortex as it is in the somatosensory cortex? In response to this question, Bendor and Wang(2007)[8] found that in awake marmosets, the repetition rate of an acoustic stimuli in the flutter range was encoded in the auditory cortex with both a temporal, synchronized code (Sync neurons) and a rate code (nsync neurons) that wasn t synchronized to stimuli timing. In both cases they found neurons that showed an increase (Monotonic positive) or a decrease (Monotonic negative) in average discharge rate for higher repetition rates. Response to an acoustic flutter was thus divided into four categories: Sync+, Sync-, nsync+, nsync- (figure1.a). Since, several attempts have been made to computationally model these responses to repetitive acoustic stimuli. Wehr and Zador(2003)[9] reported that an excitatory conductance closely followed by a stronger inhibitory input resulted in a spiking response

11 Introduction 3 with high temporal precision. Based on this concept, Bendor(2015)[10] developed a simple conductance-based integrate-and-fire model to simulate an auditory cortical neuron. As a result, Bendor was able to produce Sync+ neurons when excitation was followed by a strong inhibition (positive I-E delay). Gao and Wang(2016)[11] further developed the model by adding a simplified form of pre-synaptic depression, and by doing so was able to produce both nsync+ and nsync- responses. This was backed by their study of subthreshold activity in A1 neurons where they suggested that nsync neurons only received synchronized inputs at low repetition rates. Figure 1.2 Bendor and Wang 2007[8]. (A.)Cortical frequency map of one animal with the recording sites of synchronized (crosses) and unsynchronized (circles) neurons indicated. R, rostral; C, caudal; M, medial; L, lateral. (B.) A histogram showing the spatial distribution for these two neuron types. In this figure, Unsynchronized neurons correspond to nsync neurons in our study. We observe that Synchrony of neuron responses do not depend on characteristic frequency, but do seem to be distributed unequally in the auditory cortex, with more Sync neurons in A1 and more nsync neurons in Rostral fields. 1.2 Theory and Hypotheses Monotonic negative neurons Monotonic rate coding allows numerous variables to be encoded in the discharge rate, increasing the efficiency in which neurons store and relay information. However this high-dimension activity in a single neuron can also result in difficulties in extracting information from a single variable while excluding the others. The opponent coding of

12 Introduction 4 repetition rate of acoustic flutter using positive and negative discharge rate slopes could increase the accuracy of extracting this information by reducing positively correlated noise between neurons [12]. Both Bendor (2015)[10] and Gao and Wang(2016)[11] used the entire range of flutter and fusion to model neuron responses to repetitive acoustic events meaning that if the discharge rate slope of a nsync neuron in the fusion range was strongly positive or negative, the neuron could be classified as nsync+ or nsyncregardless of it s activity profile in the flutter range. However, if flutter and fusion are encoded by different subset of neurons [8,7], neural mechanisms producing both nsync+ and nsync- neurons uniquely in the flutter range should exist The role of Synchronized neurons In addition to this opponent coding problem, many other observations in real recordings have not been characterized in previous models, including the monotonicity of synchronized responses and the relationship between Sync and nsync neurons. Bendor and Wang (2007)[8] observed that the onset response latency in nsync neurons were significantly higher for nsync neurons than for Sync neurons. Furthermore, when studying the spatial distribution of these neurons in the primary auditory cortex (A1) and the Rostral fields, they found a higher proportion of Sync neurons in the A1 and a higher proportion of nsync neurons in the Rostral fields. Studies of membrane potential fluctuations during stimuli [11, 13] show that nsync neurons receive synchronized input in the flutter range. Could a sub-population of Sync neurons give rise to nsync neurons? Study aims In response to unsolved questions in previous studies, the aim of this master thesis is to provide a computational model that is able to emulate all four categories of responses to acoustic flutter, using model parameters that have been observed in sensory cortex neurons and an architecture that is biologically plausible. To do so we will (i.) Simulate Sync+ and Sync- neurons after analysing and emulating the biophysical mechanisms behind these different responses, and (ii.) explore whether inputs from Sync neurons can produce a nsync neuron. Simulations and data analysis will be done using MATLAB.

13 Chapter 2 Results 2.1 Synchronized monotonic neurons in A Limitations of the previous model In the previous model, Bendor(2015)[10] was able to reproduce synchronized monotonic positive(sync+) responses in the flutter range with a simple computational model based on biophysical mechanisms observed in real neurons (see methods). However, the model could not reproduce Sync- neurons with biologically plausible model parameters. Outside this parameter space some neurons could be classified as Sync-, but the discharge rate of these neurons were lower than the spontaneous discharge rate (figure 2.1), which was not the case in Sync- neurons in real data. Also, IE ratio (the strength of inhibition relative to excitation) was three fold larger than what was reported in intracellular recordings [9], and most likely not biologically plausible. Supposing that both Sync+ and Sync- neurons receive the same thalamic input, what neural mechanisms could give rise to these two opponent responses? Modelling short-term plasticity If at every acoustic event a neuron receives a positive input, the existence of synchronized monotonic positive neurons are not surprising. If the same number of spikes fire at each acoustic event, the more acoustic events there are in a given stimuli, the higher the average discharge rate will be. This is why the previous model could produce Sync+ neurons. Synchronized monotonic negative neurons, however, are counter intuitive because the discharge rate decreases for higher repetition rates (and thus for more acoustic events). 5

14 Results 6 Figure 2.1 (A.) classification of neuron type across two parameters (Excitatory input and Inhibitory input) with a fixed I-E delay of 5 ms. The black line indicates values for which the I/E ratio is 2. Under the black line are biologically plausible values. (B.) Raster plot (left), discharge rate (upper right) and vector strength (lower right) of model neuron with parameters: (E,I) = (2,10). The dotted line on the discharge rate plot indicates spontaneous discharge rate of the simulated neuron. (C.) model neuron with parameters: (E,I) = (4.5,8.5). One possible mechanism that could give rise to such activity is synaptic short-term plasticity, in particular, short term depression (STD). If there was adaptation, Recorded data would show a difference in firing rate amplitude between the start and the end of stimuli presentation. This difference would be larger for higher repetition rates, and a strong but short-term adaptation would be able to suppress the activity for high repetition rates while not affecting responses for low repetition rates. As predicted, the number of spikes in recorded data at each acoustic events showed a decrease between the start and the end of stimuli sets (figure2.2). Higher repetition rates showed a larger decrease than for lower repetition rates, the largest decrease seen at 48Hz whereas no decrease was observed at 8Hz (figure2.2c,d). In addition, the decrease in number of spikes was stronger in the early stages of stimuli presentation compared to the late stages. Moreover, depression seemed to be stronger for Sync- neurons than for Sync+ neurons (figure2.2c). These observations not only provided further support to include STD in the computational model, but also gave us clues on the mechanism behind Sync+ and Sync- neurons. The standard computational model for STD was first introduced by Tsodyk et al (1986) [14,15]. Pre-synaptic terminals of a synapse contains vesicles which in turn contain

15 Results 7 neurotransmitters. The number of vesicles charged with neurotransmitters compared to the number of depleted vesicles determine the probability of neurotransmitters release, or P rel. An action potential activating the pre-synaptic terminal will deplete a certain proportion (A D ) of available vesicles. If an pre-synaptic action potential reaches the terminal before all the vesicles have the time to recharge,( with a recovery time constant τ p ) the post synaptic unit will receive a smaller conductance. ( for a detailed explanation on the model, see methods). Figure 2.2 Number of spikes at each acoustic event. (A.) Sync+ neurons, (B.) Sync- neurons. (C.) The rate of adaptation of both Sync+ and Sync- neurons at 48Hz. The number of spikes per click is divided by the number of spikes in response to the first click of stimuli. (C.) The rate of adaptation of both Sync+ and Sync- neurons at 8Hz Results By varying the amplitude of depression A D for excitatory and inhibitory inputs, we were able to simulate both Sync+ and Sync- neurons in the flutter range. For Sync+ neurons, depression was stronger for inhibition than for excitation (figure2.3). The converse was true for Sync- neurons, where depression was stronger for excitation than inhibition (figure2.3). The range of time constant τ p was determined so that neurons would

16 Results 8 show no or very little depression for repetition rates under 8Hz, and thus corresponded approximately to the interval between two pulses at 8Hz. In this model as in the previous model, Excitation and inhibition determined the initial onset response, which did not seem to be affected by synaptic depression. Values were chosen so that the onset response was on average between 40 and 60 spikes per second. Figure 2.3 Comparison between real neuron example(a.) and simulated Sync+ neuron(b.).(top) raster plot for 10 repetitions for each repetition rate ranging from 8Hz to 48Hz. (middle) PSTH of both real and simulated Sync+ neurons. (bottom left) average discharge rate during stimuli presentation above spontaneous rate. (bottom right) Vector strength for both real and simulated neurons.

17 Results 9 Figure 2.4 Comparison between real neuron example(a.) and simulated Sync- neuron(b.).(top) raster plot for 10 repetitions for each repetition rate ranging from 8Hz to 48Hz. (middle) PSTH of both real and simulated Sync- neurons. (bottom left) average discharge rate during stimuli presentation above spontaneous rate. (bottom right) Vector strength for both real and simulated neurons. In order to understand the effects of synaptic depression on simulation responses, we explored the monotonicity of responses across parameter values used to model STD (figure2.5). We first calculated the probability to obtain monotonic positive(rho > 0.8, p value< 0.05) or negative(rho > -0.8, p value < 0.05) neurons across all values of A D for a give set of time constants { τ p E, τ p I }. In general, it was easier to obtain monotonic

18 Results 10 positive neurons with high τ p I and low τ p E, whereas low τ p I and high τ p E were needed to produce monotonic negative neurons. As we wanted to produce both types of responses with the same set of time constants, we chose the values { τ p E = 0.15, τ p I = 0.10 } for the next step of the analysis, and for all following simulations. Monotonicity for both model neurons were statistically significant (Sync+, Rho=0.91, p value <0.001)(Sync-, Rho= 0.85, p value =0.012). As expected, vector strengths of both neurons were significantly higher than 0.1 for all repetition rates. Figure 2.5 Probability of obtaining Sync+ neurons (A.) and Sync- neurons (B.) for a given set of recovery time constants { τ pe, τ pi }. Value of Rho (C.) and onset response amplitude (D.) at { τ pe = 0.15, τ pi = 0.10 } within the parameter space for Amplitude of depression(a D). 2.2 Non Synchronized monotonic neurons in A1 Traditionally, the relationship between the temporal pattern of an acoustic signal and neural firing has been the focus of studying neural encoding in the auditory system.

19 Results 11 neurons that represent acoustic events faithfully in time should, in theory, allow us to perceive temporal structure and irregularities in an acoustic stimuli. As we move upstream the auditory nervous system, however, neurons are less and less able to synchronize to stimuli with high repetition rates. In fact, non-synchronized rate-coding neurons were observed in A1 and in the Medial Geniculate Nucleus(MGB), but those found in the latter responded only in the fusion range, and most of these neurons showed a synchronized response in the flutter range. No non-synchronized neurons were found in the Inferior Colliculus (IC), which is downstream of the MGB [16]. Furthermore, around two-thirds of recorded neurons in the A1 were synchronized to flutter and onethird were non-synchronized, whereas in belt areas such as R and RT there were more nsync neurons. In the next part of the project, we aim to emulate these nsync neurons comparing Sync and nsync neurons In the original neuronal data, Bendor et al found several differences between synchronized and non-synchronized responses: Synchronized neurons showed much more variation in temporal dynamics (variations in firing activity throughout time) than Nonsynchronized neurons during stimulus, and peak response latencies to pure tones were significantly longer for nsync responses than for Sync responses.(figure 2.6) As mentioned in the introduction, nsync neurons received synchronized input, but showed a sustained irregular firing rate in response to repetitive stimuli. These properties led us to hypothetise that a stimulus with a certain repetition rate would trigger nsync neurons to produce a sustained output with an amplitude of response that correlated to the repetition rate of the input. The idea was that the nsync neurons would be in a stable state that would be activated by stimuli. One possible mechanism for this to be possible was by considering nsync neurons in a balanced Excitatory-Inhibitory recurrent network Leaky Integrate-and-fire E-I balanced networks Recent years have shown a surge in research in models of neuron networks, both in numerical simulations [17,18] and in analytical methods [19,20]. Population dynamics such as those seen in recurrent networks seem to provide clues to understand complex activities in the brain: clues that single neuron models alone cannot provide (see brunel 2013[21] for recent review). The advantage of Leaky integrate and fire (LIF) network models compared to neural mass models is that the former includes the dynamics of individual neurons, as well as that of the population as a whole. In our study, a sparsely connected, Excitatory-Inhibitory balanced network received feed-forward input

20 Results 12 Figure 2.6 Bendor and Wang 2007[8]. Sync and nsync responses are normalised with corresponding peak response amplitude. nsync responses rise to peak firing rate at stimulus onset significantly later than Sync responses. from synchronized neurons. We hypothesized that Sync+ neurons combined with the recurrent network would result in nsync+ neurons, and Sync- neurons would result in nsync- neurons. (See methods for details of the network) Results The recurrent network consisted of four parameters: strength of excitatory connections, strength of inhibitory connections, network connectivity and percentage of inhibitory neurons in the network. Although many theoretical studies have explored these variables, and physiological data exist for the range of plausible values for such variables, network dynamics for a given set of parameters also depend strongly on the total number of neurons. In other words, these four parameters need to be re-explored for each given size of the network population. In most studies, percentage of inhibitory neurons in the network is fixed to 20 percent[20,21,22,28], reflecting the number of inhibitory interneurons in relation to the number of excitatory pyramidal cells in a given area of the brain. networks of sparsely connected excitatory-inhibitory cells show a very rich behaviour depending on the values of the remaining three parameters. past studies have found synchronous oscillatory behaviour as well as asynchronous irregular firing states with stationary global activity [20,22]. In order to construct an Nsync neuron, the network must show an asynchronous irregular activity when given an input synchronized to repetitive stimuli.

21 Results 13 Figure 2.7 Exploring different parameters of the recurrent network. for different values of Excitatory synaptic strength (A.). Connectivity = 10%, inhibitory synaptic strength = 2.3nS. For different values of connectivity (B.) and (C.. Excitatory synaptic strength = 0.4nS, inhibitory synaptic strength = 2.3nS. In our study, a strongly connected network (more than 50 percent of the neurons are connected to one neuron) produces three different states: spontaneous explosion of firing rate, explosion of firing rate at stimulus input, or high synchrony to stimulus repetition rate. At a given acoustic pulse, a neuron not only fires in response to the input, but also immediately receive input from other neurons of the network. This results in a strong but transient firing activity (Data not shown). Too small connectivity will also result in transient responses synchronized to stimulus repetition rate. The values or recurrent connections for which the network reached an asynchronous irregular but stable state (without explosion at stimulus input) varied between different values for connectivity. As shown in figure 2.7, small increase in excitatory synaptic strength or in connectivity can result in strongly fluctuating and explosive firing activity. We chose parameters for which the network showed most stability when given Sync+ or Sync- input. With values for recurrent network parameters obtained from above, we connected either Sync+ neurons or Sync- neurons to excitatory neurons of the network(figure 2.8). A weak input from these neurons were sufficient to produce a population activity that resembled Nsync monotonic neurons. (Nsync+, Rho=0.87, p value = figure 2.9)(Nsync-, Rho= 0.81, p value =0.03 figure 2.10) When analysing individual neurons in the network, we found that there was a great diversity in responses. In the network receiving input from Sync+ neurons, around two thirds of the neuron population were classified as synchronized monotonic positive, whereas for neurons in the network receiving input from Sync- neurons, one third of the population were synchronized monotonic negative.

22 Results 14 Figure 2.8 Comparison between real neuron example(a.) and simulated Sync- neuron(b.).(top) raster plot for 10 repetitions for each repetition rate ranging from 8Hz to 48Hz. (middle) PSTH of both real and simulated Sync- neurons. (bottom left) average discharge rate during stimuli presentation above spontaneous rate. (bottom right) Vector strength for both real and simulated neurons. It is important to note that the current state of the network model is still subject to further exploration of network parameter dynamics and balance. However, these preliminary results show evidence that it is possible to obtain non-synchronized monotonic positive and negative responses from this recurrent network architecture.

23 Results 15 Figure 2.9 Comparison between real neuron example(a.) and simulated nsync+ neuron(b.).(top) raster plot for 10 repetitions for each repetition rate ranging from 8Hz to 48Hz. (middle) PSTH of both real and simulated nsync+ neurons. (bottom left) average discharge rate during stimuli presentation above spontaneous rate. (bottom right) Vector strength for both real and simulated neurons.

24 Results 16 Figure 2.10 architecture of recurrent network producing nsync+ (A) and nsync- (B) responses in excitatory neurons of the network. Sync neurons receive thalamic input at stimuli presentation, and shows either a Sync+ or Sync- response depending on short term depression. These Sync neurons give weak excitatory input to excitatory neurons in the recurrent network, resulting in corresponding nsync responses.

25 Chapter 3 Discussion 3.1 Summary In this study, we developed a computational model that is able to reproduce the four characteristic responses of auditory cortex neurons to acoustic pulse trains of different repetition rates, in the range of flutter perception, and in so, giving us an idea of cellular and population-level mechanisms underlying temporal coding schemes in the auditory cortex of awake marmosets. By integrating pre-synaptic short-term depression to the initial conductance-based integrate-and-fire model (Bendor 2015)[10] we obtained both synchronized monotonic positive and negative neurons. In the second stage of the project, we constructed an sparsely recurrently connected EI balanced network which, depending on the nature of input (Sync+ or Sync-) could produce either nonsynchronized monotonic positive or negative neurons without having to modify network parameters Comparison with previous studies Until recently, responses of the auditory cortex to time varying stimuli were studied mostly in anesthesized animals, where responses were dominated by firing patterns synchronized to stimuli [23]. non-synchronized firing in response to acoustic pulse trains were first found in awake marmosets[24], and later found in rats[13], cats[25], and ferrets[26]. Several years later multiple studies by Bendor and Wang[8,16] discovered positive and negative monotonic Sync and nsync neurons in awake marmosets using single-unit extracellular recordings. This difference between Sync and nsync neurons, combined with the fact that Sync neurons are mostly found in A1 whereas nsync neurons are mostly found in R and RT, could indicate that the cellular mechanisms behind 17

26 Discussion 18 these two types of neurons are different. Rabang and Bartlett(2011)[27] suggested a different method for generating temporal and rate coding using synaptic depression and facilitation: strong inputs with synaptic depression produced synchronized responses while weak inputs with facilitation generated non-synchronized responses. Our study supports the role of synaptic depression in creating synchronized neurons, but provide an alternative mechanism for nsync neurons. In another recent study, Gao and Wang (2016)[11] produced a computational model of the nsync- neuron by adding variablity in synaptic time constant and synaptic depression to excitation on top of the previous model by Bendor 2015[10]. with longer time constants and strong adaptation for excitatory input conductance, they were able to produce nsync- neurons as well as Sync+ and nsync+ neurons. Figure 3.1 Modelling nsync- neurons with longer synaptic time constant. Strong adaptation of excitatory input and long saturation time constant allows the model to produce nsync- neurons. (Gao and Wang 2016) However, their model raises some questions on biological plausibility. First, in their model of synaptic depression, the probability of pre-synaptic release is reduced to 0 at each acoustic pulse. This is not supported by literature [18,19] and could thus strongly affect the range of parameter values that are used to model depression.second, the study only changes the excitatory recovery time constant, with inhibition not affected by adaptation. Third, although there is variability in synaptic time constants for auditory cortex

27 Discussion 19 neurons, the range of values used in this study (as seen in figure 3.1) seems unrealistic. Last, and most importantly, Bendor and Wang 2007[8] believed that nsync neurons in the fusion range consisted an entirely different population of neurons to those in the flutter range. However, monotonicity in these model neurons were calculated across both flutter and fusion range. It is thus difficult to know if the said nsync monotonic positive or negative neurons show the same significant monotonicity in the flutter range. Our model reflect the temporal and anatomical differences between nsync and Sync neurons in the flutter range, and suggest that these differences rise from connectivity between neurons, and not from different biophysical parameters as suggested by previous models. In addition our model provides a clue to why nsync neurons are only found in awake animals: Anesthesized animals have shown strong lateral inhibition in the brain, which would weaken the recurrent connections and therefore prevent the emergence of nsync responses to stimuli. 3.2 Model limitations As mentioned in the results, studies of the network model is still in its preliminary stages, and much aspects are yet to be explored. The model does not explain all aspects of the data seen in awake marmosets, and although a computational model does not need emulate all the characteristics of neural data, we believe that our model can provide insight on a few other mechanisms that generate auditory cortex responses to acoustic pulses trains Network parameters and stability In the current state, network model parameters do not match biophysical values recorded from real neurons. reference values for inhibitory GABA and excitatory AMPA conductatnces for such recurrent networks have been reported in previous studies ( Cavallari et al 2014). In addition, the network is stable for a small range of parameter space. This could be due to the network architecture and artificial noise added to the membrane potential dynamics in the single-unit model (See methods). Another origin of network instability could be connections from a given neuron to itself. Previous studies have included such connections in a randomly connected recurrent network [29], but these studies were on how such recurrent connections store memory in the hippocampus. Such connectivity has been widely observed in the the Cornu Ammonis 3 (CA3) region of the hippocampus, but may not necessarily exist in the auditory cortex. Self connected neurons would transient bursts of activity whenever it is

28 Discussion 20 activated. Removing such connections on both excitatory and inhibitory neurons of our network could strongly increase network stability. Therefore, the next immediate step of the study would be to restructure the network to increase robustness within more biologically plausible parameters Vector strength and spontaneous rate When comparing the results between real and simulated Sync neurons, we observe a difference in the vector strength across repetition rates. Although vector strength is similar between the two neurons at 8Hz, VS decreases for higher repetition rates in real neurons, whereas it increases in simulated neurons. This raises a few questions about the biophysical mechanisms of Synchronized responses: Is low vector strength solely due to temporal jitter and noise of input? One other explanation could be connections from other neurons, whether they be feed-back connections from nsync neurons or lateral connections from other Sync neurons. Although in our model nsync neurons receive a feed-forward input from Sync neurons, Anatomical evidence shows that this may not be the case. nsync neurons are also found in A1, and Sync neurons in R and RT, even though in proportion there are more Sync neurons observed in A1 and more nsync neurons in R and RT. A feed-forward feed-back structure between A1 and R, where R have stronger recurrent connections than A1, could produce both Sync and nsync neurons in both areas, but with different proportions. Another difference between real and simulated neurons is the spontaneous rate in nsync responses. In the recurrent network, spontaneous activity is generated by both noise in the single-unit model and the recurrent connections. Noise in the single unit model is chosen so that a given neuron without input would produce a spontaneous rate of 5 spikes per second. This is globally within physiological observations. However, recurrent connections increase the spontaneous rate. A lower spontaneous activity could also further stabilise the network response to other stimuli Alongside Gaussian pulse trains, Bendor and Wang(2007)[8] also recorded responses of the same neurons to sinusoidal amplitude modulated (SAM) tones and to pure tones. In the current model, a Gaussian pulse is modelled as a single excitatory gaussian kernel followed by an inhibitory kernel. SAM tones have different spectral bandwidth and pulse duration depending on the modulation frequency, and cannot be represented accurately by our model. As for pure tone responses, our model represents the input as a net onset excitation followed by inhibition during stimulus presentation. Addition of parameters

29 Discussion 21 that account for these different types of stimuli could provide further improvements to the model. 3.3 Conclusion Despite these limitations of our current model, simulating how neurons integrate repetitive acoustic information using adaptation and recurrent connections opens up further possibilities to use this model in better understanding complex features of temporal processing. For example, recent studies have found that in the A1 as well as in higher belt areas, neurons encode not only the physical aspects of acoustic stimuli but also behavioural meaning [30]. If nsync neurons are responsible for encoding behavioural meaning, this difference in representation could be linked to the activation or suppression in the recurrent connections. Studies of single A1 neurons show that individual neurons encode multiple different features [31], making it difficult to extract individual information in complex high dimensional stimuli such as natural sounds and vocalisations. Another recent study showed that pitch perception in the auditory cortex could be modelled with a sparsely connected network[32], similar to our study. As such, connecting individual neurons in a population network could provide additional dimensionality to encoding and relaying auditory information.

30 Chapter 4 Methods 4.1 Ethics statement The electrophysiology data in this report comprised of previous published datasets [] collected at Johns Hopkins University (Laboratory of Xiaoqin Wang). All experimental procedures were approved by the Johns Hopkins University Animal Use and Care Committee and followed US National Institutes of Health guidelines 4.2 Electrophysiological recordings and acoustic stimuli Our electrophysiology data in this report comprised of previous published datasets [15,18,26]. For these datasets, the authors performed single-unit recordings with highimpedance tungsten micro- electrodes (25M Ω) in the auditory cortex of four awake, semi-restrained common marmosets (Callithrix jacchus). Action potentials were sorted on-line using a template-matching method (MSD, Alpha Omega Engineering). Experiments were conducted in a double-walled, soundproof chamber (Industrial Acoustic Co., Inc.) with 3-inch acoustic absorption foams covering each inner wall (Sonex, Illbruck, Inc.). Acoustic stimuli were generated digitally (MATLAB- custom software, Tucker Davis Technologies) and delivered by a free-field speaker located 1 meter in front of the animal. This physiological data was collected at Johns Hopkins University (Laboratory of Xiaoqin Wang). Recordings were made primarily for the three core fields of auditory cortex (177/210 neurons)- primary auditory cortex (AI), the Rostral field (R), and the Rostrotemporal field (RT), with the remaining neurons recorded from surrounding belt fields. For each single unit isolated, the best frequency (BF) and sound level threshold was first measured, using pure tone stimuli that were 200 ms in duration. We next generated a set of acoustic pulse trains, where each pulse was generated by windowing 22

31 Methods 23 a brief tone at the BF by a Gaussian envelope. Repetition rates ranged from 4Hz to 48Hz(in 4Hz steps) Acoustic pulse train stimuli were 500 ms in duration, and all intertrial in- tervals were at least 1 s long. Each stimulus was presented in a randomly shuffled order with other stimuli, and repeated at least five times for all neurons, and at least ten times for about 55% of neurons (115/210). Stimulus intensity levels for acoustic pulse trains were generally db above BF-tone thresholds for neurons with monotonic rate-level functions and at the preferred sound level for neurons with non-monotonic rate-level functions 4.3 Computational model In this section we will describe in detail the computational architecture used to simulate responses of auditory cortex neurons to acoustic pulse trains described above. The first paragraph of each subsection will give a general overview of underlying ideas in the choices of models that has been used in this study. Mathematical details can be skipped on first reading Single-unit model Much research has been conducted on biophysical mechanisms responsible for generating activity in individual neurons, and these provide the basis of constructing computational models. models of complex membrane dynamics such as Hodgkin-Huxley models, emulate individual activity of ion channels in response to input stimuli. However, for our current study, no research so far has recorded such precise activity in auditory cortex neurons in response to acoustic pulse trains. Such complexity is therefore unnecessary. Another model, the Leaky-Integrate and fire model, provides simpler computations by modelling input stimuli as a variation in either current or conductance, which in turn, modulates the membrane potential. These models do not explicitly include the biophysical mechanisms responsible for action potentials, and thus dramatically accelerate simulation time. In this model structure, an action potential occurs whenever the membrane potential of the model neuron reaches a threshold value V th. After the action potential,the potential is reset to a value E rest below the threshold potential, E rest < V th. The single unit model used in this study was based on the model published by Bendor[]. A conductance-based leaky integrate-and-fire model was simulated using MATLAB using the following equation, using parameters obtained from Wehr and Zador[]: V t+1 = dt C [g e(t)(v t E e ) + g i (t)(v t E i ) + g rest (t)(v t E rest )] + V t + σ s ω n t (4.1)

32 Methods 24 Each acoustic pulse was simulated as the summation of 10 excitatory and 10 inhibitory synaptic inputs [24], each temporally jittered (Gaussian distribution, σ = 1 ms). Each synaptic input was modeled as a time-varying conductance fit to an alpha function: α(t) = A(t)te t τs (4.2) When simulating neurons without short-term plasticity, A was determined by the excitatory or inhibitory input parameter and stayed constant throughout the simulation. This amplitude ranged between 0 to 6nS for excitatory inputs and 0 to 12nS for inhibitory inputs, as in Bendor (2015). A synaptic input delay was added to simulate the delay between peripheral auditory system and auditory cortex, and whereas in the previous study by Bendor [] the temporal delay between excitatory and inhibitory inputs (I-E delay) was a variable, in this study it was fixed. Fixed model parameters Membrane capacitance C 0.25nF Leak membrane conductance g rest 25nS Excitatory reversal potential E e 0mV Inhibitory reversal potential E i -85mV Alpha function time constant τ s 5ms Synaptic input delay I-E delay 10ms 5ms Simulation timestep t 0.1ms Scale of noise σ s 10 mvs 1 Gaussian noise ω n [-1:1] Short-term plasticity : Depression In order to introduce short-term plasticity in the model we regarded the probability of presynaptic release P rel as a dynamic variable depending on the input stimuli (acoustic pulse trains). In the absence of presynaptic activity, the release probability decays exponentially back to its initial value P 0 with the following equation: τ p dp rel dt = P 0 P rel (t) (4.3) Immediately after each stimuli input the release probability is reduced. P rel (t) f D P rel (t) (4.4)

33 Methods 25 A(t) = A(0) P rel (t) (4.5) where f D (0 < f D 1) controls the amount of depression. Modelling synaptic depression consisted thus of 4 parameters: the recovery time constants for both excitatory and inhibitory synapses (τ p E, τ p I) ranging from 50 to 200ms, and the depression factors f D E and f D I ranging from 0.5 to 1.0. P 0 in this model was equal to 1. These values were consistent with intra-cellular recordings in previous studies [Abott et al 1997], [David and Shamma 2013]. Figure 4.1 Cartoon explanation of the mechanism behind Short-term Depression. The probability of release at the time of each pulse determines the strength of subsequent excitatory and inhibitory post-synaptic potentials (EPSPs/IPSPs). Each click reduces the probability of release to f D P rel (t), after which it recovers back to 1 with an exponential decay Network model and simulation In order to study emergent population dynamics when neurons are connected in a network, we simulated a network of neurons modelled with the same mechanisms as above. The architecture of the network model used in this study was based on previous studies of conductance-based integrate-and-fire network models [Cessac et al 2008][Calvallari et al 2014]. In this model, the total sum of conductance received by a neuron is the linear sum of conductances evoked by presynaptic activity. the connectivity matrix W defined before the simulation indicates both the nature and the weight of a synapse connecting one neuron to the other, labelling what neurons are excitatory and what neurons are inhibitory in the network model. Both excitatory and inhibitory conductances of a neuron are given by the following equations:

34 Methods 26 g e,k (t) = g e,th (t) + g i,k (t) = g i,th (t) + N j=1,w j,k >1 N j=1,w j,k <1 W j,k δ(t t (n) j )α e (t t (n) j, A j (t)) (4.6) W j,k δ(t t (n) j )α i (t t (n) j, A j (t)) (4.7) where g,th(t) is the total conductance received from the stimuli. During pre-stimulus time period, the network finds balance between excitation and inhibition rises to a stable firing rate. At stimulus presentation, excitatory input is given from Sync neurons to excitatory neurons in the network, which activates the network into producing an asynchronous activity reflecting the amplitude of input, that should persist after stimulus presentation period. 4.4 Data analysis Classification of neurons Synchrony. Two tests were used to determine whether a neuron was Sync or NSync: Vector strength (VS) and rate response. Vector strength (VS) was calculated for each repetition rate from 8 to 48Hz with the following equation: V S = 1 N sin( 2πt(n) IP I )2 + cos( 2πt(n) IP I )2 (4.8) RS = 2 N V S 2 (4.9) where N is the number of spikes, t (n) is the time of nth and IP I the interpulse interval. If vector strength was significant (Rayleigh statistic RS > 13.8) and above 0.1 for three consecutive repetition rates, and if the rate response was also considered significant ( average discharge rate 2 s.d. above the mean spontaneous rate and an average of more than 1 spike per stimulus), then the neuron was considered Sync. If the rate response was significant but the neuron did not pass the synchrony criteria, it was considered Nsync. Monotonicity. The monotonicity of the discharge rate for a given repetition rate was determined by calculating the Spearman correlation coefficient (ρ) for stimuli spanning from 8 to 48Hz. If coefficient was larger than 0.8 and statistically significant (p-value > 0.05) the neuron was considered monotonic positive. If the coefficient was smaller than -0.8 and statistically significant, the neuron was considered monotonic negative.

35 Methods 27 Neurons satisfying neither of these criteria were considered non-monotonic. These three classification methods applied to both real and simulated neurons. In the real data, Bendor and Wang (2007) found 184 monotonic neurons adn 90 nonmonotonic neurons. 179 out of 184 monotonic neurons and 16 out of 90 non-monotonic neurons had statistically significant response slopes, on the basis of this analysis. PSTH Individual peri-stimulus time histograms (PSTHs) were calculated by convolving a Gaussian kernel (σ = 10ms) with a neuron spike train. The population PSTH was calculated as a mean of individual PSTHs.

36 Appendix A conductance input and membrane potential dynamics In this model, an acoustic pulse is modelled as a excitatory conductance kernel followed by an inhibitory conductance kernel of the same shape but different amplitude. When inhibition is stronger than excitation, membrane potential increases only during the time period when net excitation (the sum of excitation and inhibition) is positive. When the interval between two pulses (inter-pulse interval, or IPI) is longer than the width of the input kernel, the net excitation falls back to zero before increasing again with an excitatory input (see figure 1.1B). This would result in a synchronized response to stimulus repetition rate. However, if the IPI is too short, net excitation will remain negative, and in certain parameter conditions, the following excitatory input would not be enough to increase the net excitation above zero. This results in an onset followed by silence response, and is seen in the previous model (Bendor 2015) for high repetition rates. both monotonic synchronized positive and negative neurons showed a strong onset response followed by decrease in firing rate. This observation led us to think that there was short term plasticity in both excitatory and inhibitory input. However, the relationship between excitatory, inhibitory inputs and net excitation is not linear. Therefore, In order to better understand the mechanisms behind conductance input and membrane potential dynamics, we first studied the how net excitation evolved with adaptation, and how in was translated in to firing activity in the model. Both in the presence and absence of adaptation, the onset response depended almost uniquely on the amplitude of excitation, as long as excitation was weaker than inhibition (figure). Inhibition should therefore responsible to the responses following onset, and was crucial in understanding the difference between Sync+ and Sync- neurons. In the case of Sync+, net excitation must always be relatively high (similar scale of net excitation 28