Dopamine modulates firing rates and information transfer in
inhibitory and excitatory neurons of rat barrel cortex, but shows
no clear influence on neuronal parameters
Xenia Sterl
11597208
Supervisor
Fleur Zeldenrust
19th June 2020
AbstractDopamine plays an important role in sensory processing, modulating neuronal responses in sensory sys-tems. Activation of D1-like dopaminergic receptors (D1R) has been shown to facilitate action potentials and information transfer in fast-spiking interneurons, but a suppression of both in pyramidal neurons in the primary somatosensory cortex in rodents, also called barrel cortex. However, the exact mechanism via which dopamine exerts this influence remains unknown. The effect in interneurons is thought to happen through modulation of Kv3.1-channels in interneurons, a potassium channel that is responsible for the high firing rates observed in interneurons. To test this hypothesis and uncover any other neur-onal parameters that might be affected by dopamine, biophysical models for inhibitory interneurons as well as excitatory pyramidal neurons were developed in the neural simulator Brian and fitted to data of current-clamp recordings of neurons in the barrel cortex, made in the presence and absence of either D1-agonist, D2-agonist or dopamine. The differences in fitted parameters between the conditions with and without either D1-agonist, D2-agonist or dopamine were then statistically tested. Subsequently, the obtained data was analyzed using machine learning techniques. Moreover, the firing rates and mutual information in both the recorded and the simulated data were calculated and compared for both con-ditions. The results show that dopamine leads to an increase in firing rate and mutual information in interneurons and a slight decrease in pyramidal neurons, in the recorded as well as the simulated data. However, no significant effect on any of the fitted parameters or on the total parameter space has been discovered. This lack of evidence for an effect on the neuronal parameters could be due to very high heterogeneity among neurons. It has earlier been shown that neuronal parameters are subject to large a variability among neurons, which could lead to a possible effect of dopamine being lost when treating all neurons as belonging to the same group. Further research, in which neurons could for example be grouped into different subpopulations, is needed to further clarify the mechanisms via which dopamine influences sensory processing.
1
Introduction
Dopamine is one of the most important neurotransmitters in the mammalian brain. Although most com-monly known for its role in reward-based learning and disorders like Parkinson’s disease and schizophrenia, dopamine also plays an important role in sensory processing, modulating neuronal responses in sensory sys-tems (Gittelman et al., 2013). A good model for studying sensory processing is a subregion of the primary somatosensory cortex in rodents, called the barrel cortex. In the barrel cortex, sensory information coming from the whiskers is processed. The neural representation of the whiskers in the barrel cortex is somatotop-ically arranged, almost identical to the whisker layout on the rodent’s snout, not unlike the representation of fingers in the human somatosensory cortex (Petersen, 2007).
As shown by Calcini et al. (2019), dopamine controls sensory processing and neural representations of sens-ory information in the somatosenssens-ory cortex. In these experiments, D1-like dopaminergic receptors (D1R) in L2/3 of adult mouse barrel cortex were pharmacologically activated. Results showed that this activation led to a suppression of firing in cortical excitatory neurons, but a facilitation of action potential generation and information transfer in fast-spiking inhibitory neurons, due to a hyperpolarization of the spike-threshold. Moreover, the effects of D1R activation were observed on a behavioral level, which showed a faster integra-tion of sensory informaintegra-tion during tactile object localizaintegra-tion in freely behaving animals (Calcini et al., 2019). It is hypothesized that the observed effects of dopamine in interneurons are due to a modulation of the Kv3.1 channel. This potassium channel is unique to inhibitory interneurons and is thought to be responsible for their high firing rates (Martina et al., 1998; L.-Y. Wang et al., 1998). Additionally, these channels are able to control action potential duration, generally resulting in shorter action potentials (Fletterman, 2017). The deactivation rate of this channel is very high, at least 7-10 times faster than the deactivation rates of other known voltage-gated K+-channels, except for Kv1.7 (Coetzee et al., 1999). Moreover, it activates at
very high potentials, namely more than −10 mV (Hern´andez-Pineda et al., 1999), when an action potential has already started, generating a quickly recovering afterhyperpolarization. By increasing the rate of spike repolarization and shortening the duration of action potentials, Kv3.1 currents reduce the amount of N a+
channel inactivation during the action potential. In addition, the amount of recovery from the N a+
chan-nel inactivation following a spike is increased by the fast afterhyperpolarization produced by the current. Consequently, N a+ channels can fire action potentials again more quickly, without the refractory period or
spiking threshold increasing, which allows for the fast spikes observed in these neurons (Erisir et al., 1999; Rudy et al., 1999). It has been suggested that dopamine strengthens this effect, thus facilitating action potential generation and increasing the information transfer properties of inhibitory interneurons (Gruhn et al., 2005).
It remains unknown what the exact neuronal properties are that are affected by dopamine, and how this leads to the effects of dopamine observed in cell recordings. For example, studies about the influence of dopamine on N a+ channels in rat medial prefrontal cortex (mPFC) pyramidal neurons have yielded
contra-dictory results: while some suggest that this current is inhibited by dopamine (Geijo-Barrientos & Pastore, 1995), others have found the opposite effect (Yang & Seamans, 1996), and some have even found no mod-ulation at all (Maurice et al., 2001). Moreover, although effects of dopamine on K+ currents have been
found (Dong & White, 2003; Gorelova et al., 2002), little is known about the exact parameters of the ion channels that are affected by dopamine. Thus, this study will aim to determine what neuronal parameters are influenced by dopamine and how.
In addition, the question how dopamine influences the firing rate and information transfer in single neurons will be investigated. The information transfer can be calculated using the frozen noise method developed by Zeldenrust et al. (2017). In this method, a population of artificial presynaptic neurons generates input, based on the so-called ‘hidden state’: the absence or presence of the neurons’ preferred stimulus. This input is then presented to a neuron, of which the output spike train is measured. Subsequently, it is measured how well the hidden state can be constructed from this output, thus providing an estimate of the mutual information between the input and output (Zeldenrust et al., 2017). The expectation is that dopamine will lead to an increase of firing rate and mutual information in inhibitory neurons, with the opposite effect in
pyramidal neurons in the fitted models.
In order to achieve this, biophysical models for inhibitory interneurons as well as excitatory pyramidal neur-ons will be developed in the neural simulator Brian (Stimberg et al., 2019). Different parameters of these models will then be fitted using data of current-clamp recordings of neurons with and without either D1-agonist, D2-agonist or dopamine, obtained from an unpublished dataset similar to that of da Silva Lantyer et al. (2018). The fitted parameter values of the data with and without D1-agonist, D2-agonist and dopam-ine will be statistically compared, to determdopam-ine whether any of these parameters significantly changes in the presence of dopamine. Moreover, machine learning analyses will be carried out in an attempt to separate the two conditions based on all fitted parameters. Principal component analysis (PCA) and t-distributed Stochastic Neighbor Embedding (TSNE) will be used to visualize the high-dimensional data. Additionally, support vector machines (SVM) will be used to find the hyperplane in the parameter space that best separ-ates the dopamine and aCSF data. Finally, the firing rsepar-ates and information transfer of the neurons in the presence as well as the absence of dopamine will be calculated, of both the recorded and simulated data, in order to statistically test whether dopamine significantly influences the information transfer and firing rates. Note that this setup is different from the initial setup and goal of this study. An explanation of this initial goal can be found in section 5.2.
2
Materials & Methods
This section describes the procedures that were carried out for this research. First, the implemented models are discussed in section 2.1, which gives a general description of the theory behind the models as well as the specific models used for the interneurons (2.1.1) and the pyramidal neurons (2.1.2). Subsequently, the procedure that was carried out for fitting these models to the data is presented in section 2.2. Finally, section 2.3 will explain how the data was analyzed.
2.1
Model dynamics
The initial idea was to use a multicompartmental model as designed by Koenders (2018) (see also appendix section 5.2), but this proved to be too computationally expensive for fitting the parameters. Subsequently, the use of an integrate-and-fire model (Gerstner & Brette, 2009) was considered, but this type of model was too simple, making it impossible to fit the desired parameters. Thus, it was opted to choose models based on the descriptions of Hodgkin and Huxley (1952), for both the inhibitory and pyramidal neurons.
According to the model dynamics of Hodgkin & Huxley-models, the change in the membrane potential’s voltage is described by equation 1. In this equation, P
k
Ik(t) is the sum of charged components passing
through the membrane’s ion channels, I(t) is the current applied to the membrane, and Cmis the membrane
capacitance. dVm dt = −P k Ik(t) + I(t) Cm (1) Ii, the total current caused by ion i, is described by equation 2. gi is the maximum conductance of the ion,
miand hirespectively the activation and inactivation gating variables, pmiand phirespectively the number
of mi and hi gates in the channel (where phi is either 0 or 1, as not all channels have inactivation gates),
Vm the neuron’s membrane potential and Ei the ion’s reversal potential.
Ii(t) = gimpimih phi(V
m− Ei) (2)
Implementation of this equation results in the channel-specific currents for the leak, sodium, potassium and Kv3.1 potassium channels displayed in equations 3 - 6.
IN a= gN am3∞h(Vm− EN a) (4)
IK= gKm4K(Vm− EK) (5)
IKv3.1= gKv3.1m4Kv3.1(Vm− EK) (6)
The state of a certain gating variable x is described by equation 7, in which α is the opening rate and β the closing rate of the gate.
dx
dt = α(Vm)(1 − x) − β(Vm)x (7) The reversal potentials were set to default values, for both the inhibitory and excitatory neuron. EL was
set to −65 mV, EK to −90 mV and EN a to 50 mV.
2.1.1 Inhibitory interneuron
The dynamics of the inhibitory interneuron are based on the model described by X.-J. Wang and Buzs´aki (1996), with an added Kv3.1-channel. This model proved to give the best fit out of a few other models that were tested, of which an overview is provided in section 5.1, including the reason for exclusing each model. The model contains four types of ion channels: sodium, potassium, leak and Kv3.1.
Inactivating voltage-gated N a+ channel
The Wang-Buzs´aki model assumes that the activation variable m is fast and is thus substituted by its steady-state value (X.-J. Wang & Buzs´aki, 1996), as described by equation 8. This equation was rewritten as to include the half-activation voltage (V hm) and activation slope factor (km), as these could be possibly
influenced by dopamine. Equation 9 was obtained after first both V hm and km were fitted (see results
section 3.2). The kinetics of the inactivation variable h are described by equations 10-12. m∞= 1 1 + exp−(Vm−V hm) km (8) V hm= 3.223725km− 62.615488 (9) dh dt = 5(αh(1 − h) − βhh) (10) αh= 0.07 exp −(Vm+ 58) 20 (11) βh= 1 1 + exp(−0.1(Vm+ 28)) (12) Voltage-gated K+ channels
The activation variable n is described by equation 13, also according to the Wang-Buzs´aki model (X.-J. Wang & Buzs´aki, 1996). Equations 14 and 15 describe opening and closing rates αn and βn.
dn dt = 5(αn(1 − n) − βnn) (13) αn= −0.01(Vm+ 34) exp(−0.1(Vm+ 34)) − 1 (14) βn = 0.125 exp −(Vm+ 44) 80 (15)
Kv3.1 potassium channel
The Kv3.1 potassium current and activation variable nKv3.1 are described by equations 6 and 16. The
kinetics of the opening and closing variables αKv3.1and βKv3.1in equations 17 and 18 are based on the fits
made by Fletterman (2017). dnKv3.1 dt = αnKv3.1(1 − nKv3.1) − βnKv3.1nKv3.1 (16) αKv3.1= 1 exp(log(10)(−0.029Vm+ 1.9)) (17) βKv3.1= 1 exp(log(10)(0.021Vm+ 1.1)) (18)
2.1.2 Excitatory pyramidal neuron
The kinetics of the excitatory pyramidal neuron model are based on a standard model provided by Brian (Unknown, n.d.). An overview of other models that were tested can be found in section 5.1. The variable V T used in these equations was set to −63 mV by default.
Inactivating voltage-gated N a+ channel
The sodium channel activation variable for the excitatory neuron is also assumed to be at its steady-state value (equation 19). Like the inhibitory interneuron, Vm and km were included in the equation in order
to fit them. Moreover, the same was done for the inactivation variable, described by equation 21. This is because these parameters are important for the firing threshold and for adaptation, which is typical for pyramidal neurons and could be influenced by dopamine. Again, the relationship between V hm and km,
discribed by equation 20, was determined after first fitting both parameters. m∞= 1 1 + exp−(Vm−V hm) km (19) V hm= 3.583881km− 53.294451 (20) h∞= 1 1 + exp(Vm−V hh) kh (21) Voltage-gated K+ channels
Dynamics for the K+ channels are described by equations 22 - 24.
dn dt = αn(1 − n) − βnn (22) αn= 0.032(15 − Vm+ V T ) exp(15−Vm+V T 5 ) − 1 (23) βn= 0.5 exp 10 − Vm+ V T 40 (24)
2.2
Fitting procedure
The data that was used for fitting was obtained from an unpublished dataset (Department of Neuro-physiology, 2019), similar to that of da Silva Lantyer et al. (2018). This dataset contains recorded membrane potential traces from inhibitory as well as pyramidal neurons. Each neuron was measured in two conditions: either in artificial cerebrospinal fluid (aCSF), or in aCSF with either a D1-agonist, D2-agonist or dopamine added to it. For each neuron, the traces from both conditions were fitted.
Model fitting was done by using the brian2modelfitting package in Brian 2 (Stimberg et al., 2019). From this package, the functions TraceFitter and SpikeFitter were used. The TraceFitter fits recorded traces, in this case of the membrane potential. It takes the recorded trace, the input used to generate this trace, the model and the parameters to be fitted as input. From this, it returns values for the fitted parameters that best approximate the given trace, based on the given model. The SpikeFitter also generates the best fit for the required parameters, but takes the recorded spike times as input instead of the recorded trace, and in addition returns the fitted spike times.
Using the TraceFitter from this package, the parameters gL, gN a, gK, gKv3.1(only in the case of
interneur-ons), Cm, V hm, km, and, in the case of pyramidal neurons, V hh and kh were fitted. Initially, the values
for gL, gK and Cmwere obtained from this, as these are the parameters that are most important for the
neuron’s subthreshold characteristics. Subsequently, the other parameters, which are more important for the neuron’s spiking properties, were fitted once again using the SpikeFitter, which better approximates the spiking behavior than the TraceFitter. Although this worked well for the interneurons, it did not generate a good fit for the pyramidal neurons. However, it did work if only the values for gL and gK were obtained
from the TraceFitter, leaving Cmto be fitted by the SpikeFitter along with the other parameters. In order
to make the values of Cmof both the pyramidal and the inhibitory neurons more comparable to each other,
it was decided to also use this fitting method for the interneurons. The minimum and maximum values that were defined for the parameters to be fitted can be seen in Table 1.
Parameter Minimum Maximum gL 1 nS 100 nS gK 0.6 µS 60 µS gN a 2 µS 200 µS gKv3.1 0.6 mS 18 mS Cm 20 pF 400 pF V hm/V hh −60 mV 0 mV km/kh 0 mV 20 mV
Table 1: range for parameters to be fitted. Displayed are the minimum and maximum possible value for every parameter that was fitted.
For both the TraceFitter and the SpikeFitter, the Nevergrad optimizer was used, with differential evolution as optimization method. The metric used to measure the performance of the simulation in the TraceFitter was the mean square error. The SpikeFitter used the Gamma factor as metric, which measures the coin-cidence between spike times in the simulated and the target trace (Unknown, 2020), in which delta, the maximum tolerance for spikes to be considered coincident, was set to 2 ms. For both fitters, fitting was done over 20 rounds, drawing 20 samples in each round of fitting. In the SpikeFitter, a refractory period of 2 ms was defined, as well as a spiking threshold m > 0.5, were m is the activation variable of the N a+ channel
(see section 2.1).
Two different fitting procedures were carried out: one in which one fit was obtained for all different neurons, and one in which all neurons were fitted separately. This was done to compare the results of both procedures, as literature (Marder & Taylor, 2011) suggests that using one fit for all neurons is not always able to capture the behaviour of a neuron. Comparing both fitting methods, it was indeed seen that fitting all neurons
individually generated a much better fit than fitting all neurons together. Thus, it was decided to generate a fit for all neurons individually.
2.3
Data analysis
The obtained data was analyzed in a few different ways. First, the fitted parameters of the groups with and without dopamine were compared to each other. Second, it was attempted to separate the aCSF and dopamine distributions from each other using machine learning techniques. Lastly, the firing rates and mutual information of the traces in the conditions with and without dopamine were calculated and compared, for both the recorded and the simulated traces.
2.3.1 Analysis of fitted parameters
First of all, the fitted parameters of the neurons treated with either D1-agonist, D2-agonist or dopamine were compared to each other, to see whether these three groups were similar enough to be analyzed as one. This proved to be the case, as a Kruskal-Wallis test showed that there was no statistically significant difference between the three groups for any of the fitted parameter values (see section 3.1). Moreover, possible relationships between the different parameters were examined for all conditions. Subsequently, the fitted parameters of the aCSF and dopamine conditions were compared to each other for both interneurons and pyramidal neurons, in order to determine whether one of these parameters was affected by dopamine. For this, the data was first tested for the assumption of normality. If this assumption was met, a paired t-test was used; if not, a Wilcoxon sign-rank test. Additionally, the possible effect of dopamine on these parameters was further explored by examining, for each neuron, the difference in the parameters between the aCSF and dopamine conditions.
2.3.2 Machine learning
Machine learning techniques were used to determine whether the aCSF and dopamine distributions can be separated from each other, based on the fitted parameters. First, a principal component analysis was conducted, in order to reduce dimensionality and see whether the data was separable based on the first few principal components. Next, a t-distributed Stochastic Neighbor Embedding (TSNE) analysis was carried out, which is another tool for visualizing high-dimensional data. Lastly, support vector machines (SVMs) were used to determine how reliably the data can be classified as either aCSF or dopamine based on the fitted parameters. All analyses were done using the scikit-learn library (version 0.22) in Python 3 (Pedregosa et al., 2011).
2.3.3 Analysis of firing rate and mutual information
As a final analysis, the firing rates and the mutual information of the neurons in both conditions (aCSF and dopamine) were compared to each other. This was done for both the recorded and the fitted data, to check whether the difference observed in the recorded data was conserved in the fitted data. This data was then tested for statistically significant differences between aCSF and dopamine. First, a Shapiro-Wilk test was conducted to check the assumption of normal distribution. In case the data was normally distributed, a paired sample t-test was carried out; if the assumption failed, a Wilcoxon signed-rank test was used. The firing rates and mutual information were calculated in Matlab (version R2019b, 64 bits). All statistical tests were done using the stats package from the Python 3 library scipy (version 1.4.1).
3
Results
Figure 1 shows an example of the recorded and fitted output traces of an interneuron and a pyramidal neuron.
(a) (b)
Figure 1: Examples of recorded and corresponding simulated output traces. (a) Example of the recorded and simulated membrane potential during the first 3.5 seconds of recording for an interneuron. (b) Example of a pyramidal neuron.
3.1
Quality checks
Before the data was analyzed, a few checks were conducted to ensure the quality of the data. The first was a check to see whether the fitted parameters for the neurons treated with either D1-agonist, D2-agonist or dopamine were similar enough to combine the three datasets. For this, it was tested whether there was a statistical significant difference between the three classes for any of the parameters, using a Kruskal-Wallis test. It was opted to use non-parametrical testing because the sample sizes are relatively small, especially in the interneuron data. For the interneuron data (figure 2), the Kruskal-Wallis test showed that there was no statistical difference between any of the classes D1-agonist (Med, Q1, Q3: 5.32, 3.63, 27.76), D2-agonist (3.03, 2.16, 33.79), or dopamine (5.16, 4.13, 19.04) for the fitted values of parameter gK (H (2)=0.24;
p=0.89), which was also the case for the parameters gN a (D1: 89.32, 89.21, 126.25; D2: 163.38, 129.23,
182.34; Dop: 69.51, 49.68, 110.72) (H (2)=4.56; p=0.10), km (D1: 4.85, 3.98, 4.96; D2: 8.06, 3.72, 11.09;
Dop: 8.61, 3.64, 13.25) (H (2)=1.25; p=0.54), and gK3(D1: 13.66, 9.09, 15.03; D2: 9.38, 5.90, 11.27; Dop:
9.12, 6.00, 14.57) (H (2)=0.33; p=0.85). For the pyramidal neuron data (figure 3), the fitted values of the three classes also did not differ significantly for gK (D1: 25.78, 3.30, 51.26; D2: 16.83, 4.54, 49.99; Dop:
9.04, 3.48, 49.90) (H (2)=0.59; p=0.74), gN a (D1: 139.80, 92.47, 160.69; D2: 148.21, 91.54, 171.51; Dop:
124.21, 51.44, 177.17) (H (2)=0.52; p=0.77), km (D1: 4.95, 3.07, 6.86; D2: 3.45, 2.80, 5.68; Dop: 2.94,
2.61, 5.26) (H (2)=2.92; p=0.23), kh (D1: 6.37, 3.12, 11.12; D2: 5.83, 2.12, 10.37; Dop: 4.01, 2.96, 9.13)
(H (2)=1.20; p=0.55), or V hh (D1: −27.91, −41.85, −15.76; D2: −31.20, −41.06, −15.29; Dop: −36.98,
−48.80, −25.66) (H (2)=1.81; p=0.41). There was also no significant difference across the conditions for the parameters Cmand gL, for both the interneuron and pyramidal neuron data. The exact results can be
found in appendix section 5.4.
As none of the conducted tests showed a statistical significance, no correction for multiple comparisons was used. Based on these results, the three conditions were treated as one in all following analyses. This led to a dataset containing data of 72 pyramidal and 25 inhibitory neurons.
Second, the distributions of the metric, which was one minus the Gamma factor, were plotted for all conditions. This gives an indication of the quality of the fit: a low Gamma factor indicates a low coincidence between spike times in the simulated and the target trace. Thus, neurons with a relatively low Gamma factor were eliminated (figure 4). The same was done for the firing rates: neurons with a firing rate that was very different from the other neurons, which could be the result of wrong classification during the experiments, were removed from the dataset (figure 5). If a neuron did not meet the requirements in one condition, its data was deleted from the other condition as well to ensure that the same neurons were used in the aCSF as in the dopamine condition. After these checks were carried out, a total of 54 pyramidal and 19 inhibitory neurons remained.
Figure 2: Individual point plots of the fitted parameter values across the different conditions of the interneuron data. Shown are the fitted values for the neuronal parameters gK, gN a, km, kh, and
V hh for the dopamine, D1-agonist, and D2-agonist conditions.
Figure 3: Individual point plots of the fitted parameter values across the different conditions of the pyramidal neuron data. Shown are the fitted values for the parameters gK, gN a, km, kh, and
(a) (b)
(c) (d)
Figure 4: Distributions of 1-Gamma factor per condition. Shown are the frequency distributions of 1-Gamma factor, a metric for the quality of the simulated output traces, for each condition. The red line indicates the value above which neurons were discarded, which in this case was 0.05 for all conditions. (a) Distribution for the aCSF interneuron condition. (b) Distribution for the dopamine interneuron condition. (c) Distribution for the aCSF pyramidal neuron condition. (d) Distribution for the dopamine pyramidal neuron condition.
3.2
Fitted parameters
In the initial round of fitting, the parameters gL, gK, Cm, gN a, gK, V hm and km were all fitted. In
addition, gKv3.1 was fitted for the interneurons and V hh and kh for the pyramidal neurons. After this
round, the relations between all parameters were plotted, to determine whether there were parameters that were strongly connected to each other. Upon visual inspection, this turned out to be the case for only V hm
and km, between which there is a strong linear relation, for both the inhibitory and the pyramidal neurons.
Based on this finding, a linear regression was done on this data, as to obtain the equation for the relation between V hmand km(see figure 6). This equation was then used for the fits of the final dataset, in which
V hm was expressed as a function of km and only km was fitted. Plots of the rest of the parameters can be
found in appendix section 5.3.
After the final round of fitting, in which thus only kmand not V hmwas fitted, the obtained parameter values
of the aCSF and dopamine conditions were compared to each other to see whether there were parameters that were influenced by dopamine (figure 7). First, the difference scores between the dopamine and aCSF conditions for each parameter were tested for the assumption of normality using a Shapiro-Wilk test. For the interneuron data, the difference scores for gK (W =0.97; p=0.80), gK3 (W =0.96; p=0.56), gN a (W =0.91;
p=0.08) and km were all normally distributed. For the pyramidal neuron data, the difference scores for
gN a(W =0.98; p=0.71), kh(W =0.98; p=0.73) and V hh(W =0.98; p=0.59) were also normally distributed;
(a) (b)
(c) (d)
(e) (f )
(g) (h)
Figure 5: Distributions of firing rates per condition. Shown are the frequency distributions of the firing rates in Hz per condition. Neurons with values above the red line were discarded from the dataset. (a) Distribution for the recorded aCSF interneuron data. (b) Distribution for the recorded dopamine interneuron data. (c) Distribution for the recorded aCSF pyramial neuron data. (d) Distribution for the recorded dopamine pyramidal neuron data. (e) Distribution for the simulated aCSF interneuron data. (f) Distribution for the simulated dopamine interneuron condition. (g) Distribution for the simulated aCSF pyramidal neuron data. (h) Distribution for the simulated dopamine pyramidal neuron condition.
(a) (b)
Figure 6: Linear regression of the relation between V hm and km for the interneuron and
pyramidal neuron data. Shown are the orginal data points and the fitted regression line for the values of V hmand km obtained in the first round of model fitting. (a) Linear regression of the interneuron data
(R2= 0.914). (b) Linear regression of the pyramidal neuron data (R2= 0.826).
consistent in testing and use a Wilcoxon sign-rank test in all conditions, as some failed the assumption of normal distribution. This showed that for the interneuron data, there was no significant difference between the fitted values of gK3 in the aCSF (Med, Q1, Q3: 6.43, 3.96, 12.26) and dopamine (7.58, 4.61, 14.57)
conditions (z =0.48; p=0.63). This was also the case for gK (aCSF: 9.55, 3.36, 33.28; dopamine: 5.32, 2.93,
19.04) (z =−1.01; p=0.31), gN a (aCSF: 89.37, 40.79, 109.53; dopamine: 89.10, 49.68, 112.43) (z =−0.12;
p=0.90) and km (aCSF: 5.47, 2.78, 6.43; dopamine: 5.08, 3.42, 9.43) (z =0.93; p=0.35). For the pyramidal
neuron data, no significant difference was found for gK (aCSF: 15.86, 5.42, 51.79; dopamine: 13.22, 3.79,
50.36) (z =−0.51; p=0.61), gN a (aCSF: 129.03, 77.97, 158.98; dopamine: 142.18, 82.36, 170.50) (z =0.66;
p=0.51), km(aCSF: 3.20, 2.40, 5.31; dopamine: 3.39, 2.68, 5.26) (z =−0.15; p=0.88), kh(aCSF: 8.11, 4.76,
12.19; dopamine: 4.27, 2.50, 10.26) (z =−1.95; p=0.05), or V hh(aCSF: −25.36, −43.02, −16.80; dopamine:
−32.00, −43.01, −16.73) (z =−0.43; p=0.66). Of the parameters Cm and gL, there was only a significant
difference between the dopamine and aCSF conditions of gL of the pyramidal neuron data. As this was
the only significant difference, which was probably due to some big outliers in the data (see figure 17 in appendix section 5.5), the Bonferroni correction for multiple comparisons was not used. The exact results of the analyses on Cm and gL can be found in appendix section 5.5.
In order to better determine a possible effect of dopamine on the level of individual neurons, the difference between the dopamine and aCSF conditions per neuron was plotted, to see whether there was a certain direction in which the parameter values changed. However, this also showed no clear effect of dopamine on any parameter. Figures 8 and 9 show the results for gN a, gK, km, gK3, kh, and V hh. The results for Cm
and gL can be found in appendix section 5.5.
3.3
Machine learning
As the aforementioned comparisons of the fitted parameters failed to show a clear effect of dopamine on one or more parameters, it was explored whether the dopamine and aCSF distributions in the highdimensional parameter space were separable by using machine learning techniques. Using these techniques, it is possible to analyze all parameters together, and thus also possible relationships between them, instead of analyzing all parameters separately.
3.3.1 PCA
First, a principal component analysis (PCA) was conducted, to see whether the two populations could be grouped based on their principal components. For the interneuron data, the explained variance ratio of the first two principal components together was almost 1 (0.74 and 0.26 for the first two components respectively) (figure 10a), so the analysis was done using the first two principal components. The same was the case for the pyramidal neuron data, where the first two principal components togehter had a variance
ratio of 0.97 (0.88 and 0.08 for the first two principal components respectively) (figure 10b). Figures 10c and 10d show the first two principal components of respectively the interneuron and pyramidal neuron data.
Figure 7: Boxplots of the fitted parameter values. Shown are the median and interquartile ranges of the fitted values of gN a, gK, km, gK3, kh and V hh per type of neuron (interneuron or pyramidal) and
condition (aCSF or dopamine).
Figure 8: Bar graphs of the differences between the fitted parameter values in the aCSF and dopamine conditions per parameter for the interneurons. Each bar represents the fitted parameter value in the dopamine condition minus that in the aCSF condition for one neuron. Shown are the differences for the parameters gN a, gK, km, gK3.
Figure 9: Bar graphs of the differences between the fitted parameter values in the aCSF and dopamine conditions per parameter for the pyramidal neurons. Each bar represents the fitted parameter value in the dopamine condition minus that in the aCSF condition for one neuron. Shown are the differences for the parameters gN a, gK, km, kh and V hh.
3.3.2 TSNE
Another attempt to separate the two populations from each other was made, making use of t-distributed Stochastic Neighbor Embedding (TSNE), another tool to visualize high-dimensional data (Maaten & Hinton, 2008). The TSNE was carried out using 1000 iterations. The results on the first two eigenvectors of the interneuron and pyramidal neuron data are displayed in figure 11.
3.3.3 SVM
Finally, support vector machines (SVM) were used, to investigate how well the data could be classified into dopamine and aCSF based on the fitted parameters. Of the obtained data, 70% was used as training set, and 30% as test set. The standard kernel function, namely radial basis function (rbf), was used. The mean and standard deviation of the accuracy, precision and recall scores of five runs run for the interneuron and pyramidal neuron data are displayed in table 2.
The accuracy score reflects the total fraction of samples that have been labeled correctly. The precision score is defined as the number of true positives (in this case, ‘positive’ meaning labeled as belonging to the aCSF data and ‘negative’ to the dopamine data) divided by the total number of predicted positives. On the other hand, the recall score is the number of true positives divided by the total number of actual positives. None of these scores ever rise above chance level, meaning that the algorithm is unable to reliably group the samples as belonging to either the aCSF or the dopamine condition.
(a) (b)
(c) (d)
Figure 10: Principal component analysis of fitted parameters. The PCA was conducted on all fitted parameter values for both the interneurons and pyramidal neurons. (a) Explained variance ratio per principal component of the first three principal components of the interneuron data. (b) Explained variance ratio per principal component of the first three principal components of the pyramidal neuron data. (c) The first two principal components of the interneuron data. Each dot represents one neuron in either the aCSF or dopamine condition. (d) First two principal components of the pyramidal neuron data.
(a) (b)
Figure 11: TSNE of fitted parameter values of interneuron and pyramidal neuron data. Shown are the first two eigenvectors of a TSNE on all fitted parameter values per neuron. Each dot represents one neuron in either the dopamine or aCSF condition. (a) TSNE of interneuron data. (b) TSNE of pyramidal neuron data.
Accuracy Precision Recall Interneuron 0.38 ± 0.08 0.19 ± 0.23 0.33 ± 0.41 Pyramidal neuron 0.48 ± 0.05 0.36 ± 0.26 0.42 ± 0.22
Table 2: Mean ± standard deviation of accuracy, precision and recall scores of the SVM analysis on the 15
3.4
Firing rate and mutual information
A final analysis that was conducted, was a comparison of the firing rate and mutual information in the dopamine and aCSF conditions. This was done for the recorded as well as the simulated traces, to see whether a possible effect found in the recorded traces was conserved in the model traces.
3.4.1 Firing rate
The neuron’s firing rates were computed by calculating the number of spikes in its output trace and dividing this by the total recording time. For calculation of the number of spikes, the spiking threshold was set to 0 mV. The resulting data is displayed in figure 12.
For statistical analysis of the firing rate, the data was first tested on the assumption of normal distribution, using the Shapiro-Wilk test. The differences between the firing rates in the dopamine and aCSF conditions of the recorded (W =0.94; p=0.25) and simulated interneuron firing rates (W =0.95; p=0.36) were normally distributed, whereas the difference scores of the recorded pyramidal (W =0.91; p<0.001) and simulated pyramidal firing rates (W =0.88; p<0.001) were not. Despite the normal distribution, it was decided to use a non-parametric test, namely the Wilcoxon sign-rank test, on the interneuron data as well. The difference between the interneuron’s recorded firing rates in the dopamine (Med, Q1, Q3: 3.81, 2.86, 5.32) and aCSF (3.35, 2.40, 4.23) was statistically significant (z =2.86; p=0.0043), just like the difference between the dopamine (3.93, 2.99, 5.94) and aCSF (3.62, 2.54, 4.30) conditions of the simulated interneuron data (z =2.94; p=0.0033). For the pyramidal neurons, the difference between the recorded dopamine (0.56, 0.27, 1.26) and aCSF (0.76, 0.39, 1.26) firing rates was also significant (z =−2.56; p=0.01), whereas the firing rates in the simulated dopamine (0.66, 0.28, 1.61) and aCSF (1.11, 0.47, 1.83) conditions did not differ significantly (z =−1.75; p=0.08).
Figure 12: Boxplots of the firing rates. Shown are median and interquartile ranges of the firing rates of the interneurons and pyramidal neurons, for the recorded as well as the simulated data, in both the dopamine and aCSF conditions. An asterisk indicates a statistically significant difference between two groups.
3.4.2 Mutual information
The mutual information (MI) was calculated using the frozen-noise method developed by Zeldenrust et al. (2017). The resulting data is displayed in figure 13.
The differences between the dopamine and aCSF conditions were also first tested for the assumption of normality before being tested for statistical differences. The difference scores of the recorded (W =0.94; p=0.25) and simulated (W =0.95; p=0.36) interneuron MI were normally distributed, but this was not the case for the recorded (W =0.91; p<0.001) and simulated (W =0.88; p<0.001) pyramidal neuron MI difference scores. Following the same reasoning as for the firing rate data, all data was analyzed using the Wilcoxon sign-rank test. This showed that the MI in the recorded dopamine (0.09, 0.07, 0.11) and aCSF (0.07, 0.06, 0.09) conditions were significantly different (z =2.62; p=0.009). However, this was not the case
for the simulated MI of the interneurons in the dopamine (0.07, 0.06, 0.10) and aCSF (0.08, 0.06, 0.09) conditions (z =1.37; p=0.17). For the pyramidal neuron data, the recorded dopamine (0.05, 0.02, 0.08) and aCSF (0.07, 0.04, 0.09) conditions differed significantly (z =−3.06; p=0.002), although the dopamine (0.05, 0.02, 0.09) and aCSF (0.06, 0.03, 0.09) conditions in the simulated data did not (z =−0.56; p=0.57).
Figure 13: Boxplots of the mutual information. Shown are the median and interquartile ranges of the mutual information between the input and ouput of the interneurons and pyramidal neurons, for the recorded as well as the simulated data, in both the dopamine and aCSF conditions. An asterisk indicates a statistically significant difference between two groups.
4
Discussion
This study investigated the effects of dopamine on interneurons and pyramidal neurons in rodent’s somato-sensory cortex. Specifically, it was investigated whether dopamine influences certain neuronal parameters, and if so, in what way. In addition, the effect of dopamine on the neuron’s firing rates and mutual inform-ation between input and output were explored. The analyses on the firing rates and mutual informinform-ation show that dopamine leads to an increase of firing rates and mutual information in the recorded as well as the simulated interneurons. However, no clear effect of dopamine on the investigated parameters was found, neither on individual parameters nor in the total parameter space.
The outcomes from the statistical tests conducted on the firing rates and mutual information of the recorded neurons support the hypotheses that dopamine leads to an increase in firing rates and mutual information in interneurons, but a decrease in pyramidal neurons. However, although the data from this study shows a clear effect on the firing rates and mutual information in interneurons, the effect on pyramidal neurons remains debatable. The results of the recorded data showed a significant difference between the dopamine and aCSF conditions for the firing rates as well as the mutual information, both decreased in the presence of dopamine. However, looking at the data itself, in figures 12 and 13, the difference between both conditions seems to be very small. Moreover, the effect found in the recorded pyramidal neuron data was not reflected in the simulated data, although this was the case for the interneuron data. In addition, the test results on the pyramidal neuron data might not be very reliable, as the distribution of firing rates of the pyramidal neurons is very skewed (figure 5), whereas the Wilcoxon sign-rank test assumes that no skew is present in the data (Whitlock & Schluter, 2015). Thus, it is very questionable whether the significant difference that was found in the recorded pyramidal neuron data actually reflects an effect of dopamine.
On the contrary, the hypothesis that the effect of dopamine on interneurons could be due to modulation of the Kv3.1 channel is not supported by the findings of this study, as the obtained data shows no clear difference in Kv3.1 channel conductance between the aCSF and dopamine conditions. Moreover, none of the other investigated parameters seem to clearly change in the presence of dopamine, and attempts to reliably separate the aCSF and dopamine distributions from each other based on the fitted parameters using machine learning techniques also failed. Thus, no clear evidence for an effect of dopamine on the
investigated parameters has been found. However, this does not discard the possibility that dopamine does affect these parameters in some way. It could be that dopamine influences certain interactions between the parameters in ways that have simply not been found with the used techniques. Furthermore, it is very plausible that an effect of dopamine on the parameters can not be found when viewing all neurons together, as belonging to the same population. In reality, neurons are highly heterogeneous, their parameter values and properties being subject to high variability, as demonstrated by Marder and Taylor (2011). Moreover, it has been repeatedly demonstrated that multiple sets of parameters can result in the same, or at least similar, behaviors (Marder & Taylor, 2011). For example, it is not unlikely that two neurons with a highly different number of Kv3.1 channels are modulated by dopamine in different ways, that still elicit similar behavior. This is supported by the fact that the fitted parameters of individual neurons do show a difference between the aCSF and dopamine conditions; this change just does not happen with a consistent direction and magnitude for all neurons. Thus, the effect that dopamine has on certain parameters is possibly very ambiguous, explaining why no uniform effect can be found in the investigated data. A more clear effect might arise if the recorded neurons were to be grouped into different subpopulations, e.g. based on their firing rates, and looking for an effect of dopamine within these subpopulations. Likewise, Marder and Taylor (2011) suggest that it could be beneficial to construct a population of models to capture the behavior of the population, rather than a single model that tries to capture the behavior of a single neuron.
Besides grouping the neurons into subpopulations based on their properties, the effects of D1 receptor agonists, D2 receptor agonists and dopamine could also be studied separately. In this study, all three conditions were grouped together, as no significant difference in parameter values was detected. However, previous research does suggest that their influence can be different. For example, Dong and White (2003) showed that a slowly inactivating K+conductance in pyramidal neurons of the rat medial prefrontal cortex (mPFC) is decreased by D1R activation, but not by D2R activation. Similarly, research by Gorelova et al. (2002) demonstrated that dopamine-induced membrane depolarization of fast-spiking interneurons in the rat mPFC could be mimicked by D1/D5 agonists, but not by D2 agonists. Thus, perhaps the effects of different dopamine receptor types on the studied parameters are also unambiguous, and can only be de-termined when treating the different receptor agonists as separate conditions.
It could also be that dopamine exerts its influence, or part of it, through mechanisms that have not been taken into account in this study. A possible mechanism could be modulation of the hyperpolarization-activated current Ih, an inward current activated by hyperpolarization from the resting potential. Ih ion
channels are formed by hyperpolarization-activated, cyclic nucleotide modulated subunits. It has been shown that Ih plays an important role in modulating action potential generation in somatosensory neurons
(Momin et al., 2008). Furthermore, Ih is enhanced by dopamine in layer I interneurons of the neocortex in
rats, due to a depolarizing shift in the Ih activation curve, resulting in a depolarization of the interneurons
(Wu & Hablitz, 2005). It is, however, unknown whether this current also plays a role in layer 2/3 of the barrel cortex. Perhaps including the current in the neuron model could shine more light on this.
In addition, the models that were used in this study to describe the behaviors of the interneurons and pyramidal neurons might not have been ideal. An indication that the used models are unable to capture everything that determines the neuron’s behaviors, is the fact that the aCSF and dopamine conditions are significantly different when it comes to the mutual information in both the recorded interneurons and pyramidal neurons, but that this effect is not conserved in the simulated data. The same is the case for the pyramidal neuron’s firing rates. However, looking at figure 13 shows that the data itself is actually very similar for the recorded and simulated traces, so it is questionable how relevant this difference in statistical significance actually is.
Additionally, the procedure of fitting, where part of the parameters where fitted in the TraceFitter and part in the SpikeFitter (for more information, see section 2.2) that was used might also have been suboptimal. Although the spikes were in general fitted excellently, the quality of the subtreshold trace was relatively poor (see for example figure 1). When more parameters were fitted in the SpikeFitter, this quality improved, but the quality of the simulated spikes decreased. As ensuring a good fit of the spikes was crucial for this study, it was opted to use the method with which this was optimal, thereby worsening the subthreshold trace quality. It is unknown whether this really affected the resulting parameter fits, but it does show an
important limitation of the model. Thus, in order to yield more representative results, it could be worth-while to implement a better model or fitting method.
In conclusion, dopamine affects the firing rates and information transfer of interneurons, while having the opposite effect on pyramidal neurons in the rat barrel cortex. However, a clear effect of dopamine on the investigated neuronal parameters has not yet been found. This could be due to very high heterogeneity among neurons. Further research could focus on subgroups of neurons or on populations of neurons as a whole, to further uncover the ways in which dopamine functions.
References
Calcini, N., Yan, X., Bijlsma, A., Zhang, Y., da Silva Lantyer, A., Kole, K., Zeldenrust, F. & Celikel, T. (2019). Chapter 5: Cell-type specific control of stimulus-evoked responses by dopamine. In Prin-ciples of intracellular information transfer in the somatosensory cortex (pp. 157–190). Radboud University.
Coetzee, W. A., Amarillo, Y., Chiu, J., Chow, A., Lau, D., McCormack, T., Morena, H., Nadal, M. S., Ozaita, A., Pountney, D., Saganich, M., Miera, E. V.-S. & Rudy, B. (1999). Molecular Diversity of K+ Channels. Annals of the New York Academy of Sciences, 868 (1), 233–255. https://doi.org/10. 1111/j.1749-6632.1999.tb11293.x
Cruz, A. V., Mallet, N., Magill, P. J., Brown, P. & Averbeck, B. B. (2011). Effects of dopamine depletion on information flow between the subthalamic nucleus and external globus pallidus. Journal of Neurophysiology, 106 (4), 2012–2023. https://doi.org/10.1152/jn.00094.2011
da Silva Lantyer, A., Calcini, N., Bijlsma, A., Kole, K., Emmelkamp, M., Peeters, M., Scheenen, W. J. J., Zeldenrust, F. & Celikel, T. (2018). A databank for intracellular electrophysiological mapping of the adult somatosensory cortex. GigaScience, 7 (12). https://doi.org/10.1093/gigascience/giy147 Department of Neurophysiology. (2019). Unpublished dataset. Donders Institute, Nijmegen.
Dong, Y. & White, F. J. (2003). Dopamine d1-class receptors selectively modulate a slowly inactivating potassium current in rat medial prefrontal cortex pyramidal neurons. Journal of Neuroscience, 23 (7), 2686–2695.
Erisir, A., Lau, D., Rudy, B. & Leonard, C. S. (1999). Function of Specific K + Channels in Sustained High-Frequency Firing of Fast-Spiking Neocortical Interneurons. Journal of Neurophysiology, 82 (5), 2476–2489. https://doi.org/10.1152/jn.1999.82.5.2476
Fletterman, C. (2017). Kv3.1 channels can control action potential duration while only minimally affecting the spiking threshold: A modelling study. (Master’s thesis). University of Amsterdam. Amsterdam, NL.
Geijo-Barrientos, E. & Pastore, C. (1995). The effects of dopamine on the subthreshold electrophysiological responses of rat prefrontal cortex neurons in vitro. European Journal of Neuroscience, 7 (3), 358– 366.
Gerstner, W. & Brette, R. (2009). Adaptive exponential integrate-and-fire model. Scholarpedia, 4 (6), 8427. https://doi.org/10.4249/scholarpedia.8427
Gittelman, J. X., Perkel, D. J. & Portfors, C. V. (2013). Dopamine Modulates Auditory Responses in the Inferior Colliculus in a Heterogeneous Manner. Journal of the Association for Research in Otolaryngology, 14 (5), 719–729. https://doi.org/10.1007/s10162-013-0405-0
Gorelova, N., Seamans, J. K. & Yang, C. R. (2002). Mechanisms of dopamine activation of fast-spiking interneurons that exert inhibition in rat prefrontal cortex. Journal of neurophysiology, 88 (6), 3150– 3166.
Gruhn, M., Guckenheimer, J., Land, B. & Harris-Warrick, R. M. (2005). Dopamine Modulation of Two Delayed Rectifier Potassium Currents in a Small Neural Network. Journal of Neurophysiology, 94 (4), 2888–2900. https://doi.org/10.1152/jn.00434.2005
Hern´andez-Pineda, R., Chow, A., Amarillo, Y., Moreno, H., Saganich, M., de Miera, E. V.-S., Hern´ andez-Cruz, A. & Rudy, B. (1999). Kv3.1–Kv3.2 Channels Underlie a High-Voltage–Activating Component of the Delayed Rectifier K+ Current in Projecting Neurons From the Globus Pallidus. Journal of
Hodgkin, A. L. & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117 (4), 500–544. https://doi. org/10.1113/jphysiol.1952.sp004764
Koenders, E. (2018). Influence of axon initial segment morphology and location on space-clamp in voltage-clamp experiments. [Unpublished BSc thesis]. Amsterdam, NL.
Maaten, L. v. d. & Hinton, G. (2008). Visualizing data using t-sne. Journal of machine learning research, 9 (Nov), 2579–2605.
Marder, E. & Taylor, A. L. (2011). Multiple models to capture the variability in biological neurons and networks. Nature Neuroscience, 14 (2), 133–138. https://doi.org/10.1038/nn.2735
Martina, M., Schultz, J. H., Ehmke, H., Monyer, H. & Jonas, P. (1998). Functional and Molecular Differences between Voltage-Gated K + Channels of Fast-Spiking Interneurons and Pyramidal Neurons of
Rat Hippocampus. The Journal of Neuroscience, 18 (20), 8111–8125. https : / / doi . org / 10 . 1523 / JNEUROSCI.18-20-08111.1998
Maurice, N., Tkatch, T., Meisler, M., Sprunger, L. K. & Surmeier, D. J. (2001). D1/d5 dopamine receptor activation differentially modulates rapidly inactivating and persistent sodium currents in prefrontal cortex pyramidal neurons. Journal of Neuroscience, 21 (7), 2268–2277.
Momin, A., Cadiou, H., Mason, A. & McNaughton, P. A. (2008). Role of the hyperpolarization-activated current ih in somatosensory neurons. The Journal of physiology, 586 (24), 5911–5929.
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M. & Duchesnay, E. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12, 2825–2830.
Petersen, C. C. (2007). The Functional Organization of the Barrel Cortex. Neuron, 56 (2), 339–355. https: //doi.org/10.1016/j.neuron.2007.09.017
Rudy, B., Chow, A., Lau, D., Amarillo, Y., Ozaita, A., Saganich, M., Moreno, H., Nadal, M. S., Hernandez-Pineda, R., Hernandez-Cruz, A., Erisir, A., Leonard, C. & Miera, E. V.-S. (1999). Contributions of Kv3 Channels to Neuronal Excitability. Annals of the New York Academy of Sciences, 868 (1 MOLECULAR AND), 304–343. https://doi.org/10.1111/j.1749-6632.1999.tb11295.x
Stimberg, M., Brette, R. & Goodman, D. F. (2019). Brian 2, an intuitive and efficient neural simulator. eLife, 8, e47314. https://doi.org/10.7554/eLife.47314
Unknown. (n.d.). Tutorial: Tracefitter. https://brian2modelfitting.readthedocs.io/en/stable/introduction/ tutorial hh.html
Unknown. (2020). Brian2modelfitting Release 0.3. https://readthedocs.org/projects/brian2modelfitting/ downloads/pdf/latest/
Verhezen, S. (2019). The effect of inhibition on the information transfer of simulated pyramidal l2/3 mouse barrel cortex neurons. [Unpublished BSc thesis]. Amsterdam, NL.
Wang, L.-Y., Gan, L., Forsythe, I. D. & Kaczmarek, L. K. (1998). Contribution of the Kv3.1 potassium channel to high-frequency firing in mouse auditory neurones. The Journal of Physiology, 509 (1), 183–194. https://doi.org/10.1111/j.1469-7793.1998.183bo.x
Wang, X.-J. & Buzs´aki, G. (1996). Gamma Oscillation by Synaptic Inhibition in a Hippocampal Interneur-onal Network Model. The Journal of Neuroscience, 16 (20), 6402–6413. https://doi.org/10.1523/ JNEUROSCI.16-20-06402.1996
Whitlock, M. C. & Schluter, D. (2015). Chapter 13: Handling violations of assumptions. In The analysis of biological data (2nd ed., p. 387). New York, Macmillan education.
Wu, J. & Hablitz, J. J. (2005). Cooperative activation of d1 and d2 dopamine receptors enhances a hyperpolarization-activated inward current in layer i interneurons. Journal of Neuroscience, 25 (27), 6322–6328.
Yang, C. R. & Seamans, J. K. (1996). Dopamine d1 receptor actions in layers v-vi rat prefrontal cortex neurons in vitro: Modulation of dendritic-somatic signal integration. Journal of Neuroscience, 16 (5), 1922–1935.
Zeldenrust, F., de Knecht, S., Wadman, W. J., Den`eve, S. & Gutkin, B. (2017). Estimating the Inform-ation Extracted by a Single Spiking Neuron from a Continuous Input Time Series. Frontiers in Computational Neuroscience, 11, 49. https://doi.org/10.3389/fncom.2017.00049
5
Appendix
5.1
Model choice
Before the final model choice was made, namely the Wang-Buzs´aki model (X.-J. Wang & Buzs´aki, 1996) with added Kv3.1 channels for the interneurons and a Brian standard model (Unknown, n.d.) for the pyramidal neurons, a few other models were considered for fitting the data. Table 3 provides an overview of these models, the type of neuron they were considered for and the reason they were not used in the end.
Model Type of neuron Reason for not using
Adaptive exponential integrate-and fire model (Gerstner & Brette, 2009)
Interneuron, pyramidal Spikes were not fitted Brian standard model
(Un-known, n.d.) Interneuron
Fitted trace was too slow for ac-tual trace
Brian standard model with ad-ded Kv3.1 channels (Unknown, n.d.)
Interneuron, pyramidal
Fitted trace was too slow for ac-tual trace; spikes not fitted for pyramidal neuron
Table 3: overview of different models that were tested for fitting the data. Displayed are the model name and reference, the type of neuron for which this model was tested and the reason it was not used.
5.2
Initial setup
Initially, the goal of this study was to determine the influence of dopamine on the information transfer in microcircuits. This section provides the background information and experimental setup for this procedure. The experiments conducted by Calcini et al. (2019), as well as other research (Cruz et al., 2011), show that dopamine influences the information transfer of neurons. However, it remains unknown what the exact effect is of dopamine on the excitability of single neurons as well as on the information transfer in a microcircuit consisting of an excitatory pyramidal neuron and an inhibitory interneuron. Therefore, the aim of this study is to determine the effects of dopamine on both the single-neuron excitability and the information transfer in microcircuits. It is hypothesized that dopamine will lead to an increase in excitability and information transfer of interneurons, as this is what experimental data shows.
In order to achieve this, existing biophysical models of single excitatory and inhibitory neurons (Koenders, 2018) and microcircuits (Verhezen, 2019), made in the neural simulator Brian (Stimberg et al., 2019), will be used. First, an attempt will be made to reproduce the observed effects of dopamine on the excitability and information transfer properties of interneurons, by modulating the Kv3.1 channel in the interneuron model developed by Koenders (2018). Next, the effect of dopamine on excitability and information transfer in microcircuits will be simulated in the model by Verhezen (2019), which uses the frozen-noise information method (Zeldenrust et al., 2017) to calculate the information transfer in the microcircuit.
However, this original idea was not carried out. Instead, it was decided to use another model than that of Koenders (2018), as this model is very extensive with a long axon, which is not necessary for modelling the influence of dopamine. Thus, the search for a new, good model began, which proved to be a very time-consuming affair. Moreover, the data obtained from the fitting procedures proved to be interesting enough to analyze it using advanced machine learning techniques. As time would not allow for both the machine learning analysis and simulating the effect of dopamine in microcircuits, a decision between the two had to be made. It was then decided to carry on with the machine learning analysis, as this was more feasible regarding the time left for the research.
5.3
Relationships between parameters
Figures 14 and 15 show the relationships between respectively all fitted interneuron and pyramidal neuron parameters.
Figure 14: Scatter plots of the fitted interneuron parameters. Shown are the relationships between all fitted interneuron parameters in both the aCSF and dopamine condition.
5.4
Additional plots and analyses of dopamine conditions
Figure 16 shows the plots of the fitted values of Cm and gL for the conditions D1-agonist, D2-agonist and
dopamine in interneurons and pyramidal neurons. No statistically significant difference between any of the three classes was found for the interneuron data of both Cm(D1: 189.37, 154.81, 227.40; D2: 288.03, 196.94,
307.77; Dop: 259.72, 141.03, 327.10) (H (2)=0.58; p=0.75) and gL (D1: 5.59, 5.06, 11.68; D2: 7.01, 6.12,
9.97; Dop: 11.51, 7.89, 12.21) (H (2)=1.78; p=0.41). The same was true for the pyramidal neuron data of Cm (D1: 254.46, 107.59, 335.56; D2: 113.86, 65.08, 219.88; Dop: 120.81, 85.96, 264.75) (H (2)=5.44;
p=0.07) and gL(D1: 10.69, 8.91, 12.11; D2: 9.53, 6.81, 16.80; Dop: 7.20, 4.64, 12.69) (H (2)=4.74; p=0.09).
5.5
Analyses and plots of fitted parameters C
mand g
LFigure 17 shows the fitted values of Cmand gLper condition. In the interneuron data, no difference between
the aCSF (220.72, 157.30, 289.16) and dopamine (228.10, 118.08, 308.12) conditions was found (z =−0.24; p=0.81) for the fitted parameter values of Cm. The same was true for the fitted values of gL (aCSF: 8.85,
6.28, 10.61; dopamine: 9.92, 6.41, 12.21) (z =1.25; p=0.21). In the pyramidal neuron data, there was no difference between aCSF (156.11, 106.88, 215.41) and dopamine (130.51, 82.80, 252.43) for Cm(z =−0.004;
p=0.997), but there was a significant difference between aCSF (7.59, 5.70, 11.88) and dopamine (9.29, 7.04, 14.16) for gL(z =2.85; p=0.004). However, as the pyramidal neuron data for gL contains some big outliers,
rather than to an actual effect of dopamine on the fitted parameter values.
Figure 15: Scatter plots of the fitted pyramidal neuron parameters. Shown are the relationships between all fitted pyramidal neuron parameters in both the aCSF and dopamine condition.
(a) (b)
(c) (d)
Figure 16: Individual point plots of the fitted values for Cm and gL across the different
conditions of the interneuron and pyramidal neuron data. (a) and (b) The fitted values for the interneuron data. (b) and (d) The fitted values for the pyramidal neuron data.
Figure 17: Fitted values for Cm and gL. Shown are the median and interquartile ranges of the fitted
values of the dopamine and aCSF conditions in both interneurons and pyramidal neurons. Asterisks indicate statistically significant differences between two groups.
(a)
(b)
Figure 18: Bar graphs of the differences in fitted values between the aCSF and dopamine conditions of Cm and gL per neuron. Each bar represents the fitted parameter value of the dopamine
condition minus the aCSF condition for one neuron.(a) Differences for the interneuron data. (b) Differences for the pyramidal neuron data.
