EVALUACIÓN DEL PROCESO MERRILL CROWE DE TUCAR
4.1. PROCESO MERRILL CROWE
Simulation studies have suggested that heterogeneity within neuronal populations is a necessary feature for biologically relevant network models (Maex and De Schutter 2003; Chelaru and Dragoi 2008), and including empirically determined variance and covariance of the relevant parameters is a prerequisite of this. Investigating the
strongest (ρ > 0.75) correlations in our dataset revealed some trivial relationships, such as that between the capacitance and input conductance, both of which are largely determined by membrane surface area and the spatial density of channel expression. There were two strong non-trivial relationships in the dataset, both of which were consequences of effects common to the Ih current. The first was
between the spike-initiation current and input conductance (Figure 5.5D), which suggests that the distance to spike-onset threshold in neocortical pyramidal cells is not adjusted to compensate for cell size; the distance to spike-onset threshold is primarily determined by the resting potential, of which Ih current is a strong
determinant, rather than the absolute spike-onset threshold value. The second was between the distance to spike-onset threshold and sag percentage (Figure 5.5F), which is effectively a correlation between the resting potential and sag strength, both of which correlate with Ih current (Mominet al. 2008; Bielet al. 2009).
Finally, the primary outcome of this chapter was to provide a tool to aid the ex- ploration of heterogeneity in network models of neocortical microcircuits. The novel algorithm presented here for generating artificial datasets adheres to the experimen- tally determined marginal distributions and covariance structure of parameter space (Figure 5.7). Coupling this work with other studies quantifying synaptic connectivity and network topology will allow models to be constructed in which the within-class heterogeneities and layered structure of the neocortex are conserved. Such models will greatly contribute to our understanding of how network architecture affects how cortical microcircuits process information.
Chapter 6
Threshold Variability in
Thick-tufted Layer 5 Pyramidal
Cells
6.1
Introduction
Action potentials are triggered once a neuron has received sufficient synaptic input to be depolarised above threshold. However, this threshold is dynamic (Azouz and Gray 2000, 2003; de Polavieja 2005) and strongly correlated with the recent voltage history (Azouz and Gray 2000, 2003; Higgs and Spain 2011) and time since the last spike (Badel et al.2008a,b). In Chapter 4 I showed that, in neocortical pyramidal cells, the spike-onset threshold can jump by approximately 15 mV after an action potential and subsequently decays back to its baseline value over a period of tens of milliseconds (Figure 4.7B). Furthermore, the threshold has been shown to ac- cumulate as a result of increased recent spiking activity in pyramidal cells of the rodent hippocampus (Henze and Buzs´aki 2001) and electrosensory lateral line lobe of the weakly electric fish (Chacron et al.2007), and modelling studies have shown that a spike-triggered jump and subsequent threshold decay leads to experimentally observed computational properties, such as negative inter-spike interval (ISI) corre- lations (Chacronet al. 2001, 2003) and spike-frequency adaptation (Chacron et al.
2003). The simple monoexponential decay has also been extended to include mul- tiple time scales (Kobayashi et al. 2009) and voltage dependence (Yamauchi et al.
2011), allowing the capture of more complicated firing patterns such as intrinsic bursting, chattering, and post-inhibitory rebound spiking.
In this chapter I investigate post-spike threshold dynamics focussing on the re- sponse of neocortical thick-tufted layer 5 pyramidal cells (TL5). I look at three ex- tensions to the standard EIF model that attempt to capture experimentally observed post-spike threshold dynamics and compare their ability to mimic the response of TL5 pyramidal cells using the performance metrics introduced in Chapter 4. The first is the rEIF model introduced by Badel et al.(2008a), which well captures the response of pyramidal cells across the neocortex (Chapter 4). Although this model performs well it makes no attempt to capture the threshold accumulation seen in experiments (Henze and Buzs´aki 2001; Chacron et al. 2007). To address this, I quantify the degree to which spike threshold accumulates as a function of the pre- ceding inter-spike interval using experimental data. I use this to extend the rEIF model, leading to the Accumulating Threshold rEIF (ATrEIF) model. The third model is the Two-variable EIF (2vEIF) model, suggested by Badel et al. (2008b) due to its experimental relevance combined with its mathematical tractability. This is a two variable system consisting of the standard EIF model voltage dynamics coupled with the same refractory spike-onset threshold dynamics of the rEIF model. I compare the performance of the four models in replicating the response of the cell to novel stimuli not used for model fitting. I make two key findings: the addition of a non-renewal process accumulating threshold did not significantly improve the rEIF model; and the 2vEIF model performs worse than the rEIF and ETrEIF model, indicating the importance of the inclusion of a dynamic resting potential and mem- brane time constant, but performs significantly better than the standard EIF model with only a small increase in mathematical complexity.
50 mV 1 sec 6.2Hz 11.6Hz 14.8Hz 18.7Hz -55 -50 -45 -40 -35 -30 VT (mV) -50 -40 -30 VT (mV) 400mV/ms2 10mV 1ms VT
A
B
C
D
0 50 100 -50 -40 -30 VT (mV) Post-spike Time (ms) 1 nAFigure 6.1: Quantification of spike-initiation threshold of a thick-tufted layer 5 pyramidal cell during naturalistic stimuli. AResponses of a thick-tufted layer 5 pyramidal cell (top) to four distinct naturalistic current injections (bottom), firing at 6-19Hz. BSecond derivative threshold method used to determine spike-initiation thresholdVTfor each spike (black: V, red: d2V /dt2). C Main: Histogram of VT across four distinct recordings of naturalistic stimulation (2047 spikes). Black histogram is of all spikes, red histogram is burst spikes only, which were defined as those where the membrane potential after the preceding spike did not fall below the baseline threshold value, determined by fitting the pre-spike dynamic
I-V curve, before spiking again Inset: Histogram of VT with burst spikes removed (1603
spikes). This distribution fit to a skew-normal distribution with location parameter ξ =
−50.4 mV, scale parameterω= 4.44 mV, and shape parameterα= 4.05. DSpike-initiation threshold plotted against time since the last spike (points) including normal (grey) and burst (red) spikes, with a mono-exponential fit (line).
6.2
Results
The dynamicI-V method measures the average spike-onset threshold response dur- ing a naturalistic stimuli (Chapter 4). However, for a more detailed quantification I measured the threshold for individual spikes from a series of naturalistic stimuli at a range of firing rates (Figure 6.1A). To do this I use the second derivative method, which measures the peak in the voltage second derivative corresponding to the ‘kink’ in somatic voltage at spike-initiation (Figure 6.1B, Sekerli et al. 2004).
A histogram of spike-initiation threshold values displayed a bi-modal distribution with the right hand peak consisting mainly of burst spikes (Figure 6.1C main), which occur frequently in TL5 cells (Connors et al. 1982; Montoro et al. 1988; Chagnac- Amitaiet al.1990; Connors and Gutnick 1990). Removing burst spikes gives a skew- normal distribution skewed towards more depolarised threshold values (Figure 6.1C
0 1 2 3 -5
0 5 10
No. Spikes in Preceding 50 ms
Normalised Threshol d 0 1 2 3 -5 0 5 10
No. Spikes in Preceding 50 ms
Normalised Threshol
d
A
B
Figure 6.2: Variability in spike-initiation threshold due to an increasing number of spikes in the preceding 50 ms for thick-tufted layer 5 pyramidal cellsAincluding (9821 spikes from 6 cells) andBexcluding (8915 spikes from 6 cells) burst spikes. The normalised spike-initiation threshold was calculated fromVTnorm= (VT−VTbaseline)/σVT, whereVTbaseline andσVT are the mean and standard deviation of the threshold measured for those spikes with no spikes in the preceding 50ms, respectively. Bars denote statistical significance (p <0.014).
inset). The spike-initiation threshold depends on the time since the last spike, displaying a post-spike jump followed by a mono-exponential decay (Figure 6.1D) of the form
VT=VT0+VT1e−t/τT, (6.1)
wheretis the time since the last spike,VT0the baseline threshold,VT1the post-spike
jump, and τT the decay time constant, which is of the same form measured from
neocortical pyramidal cells using the dynamic I-V method (Chapter 4, Badel et al.
2008a,b).
To investigate how the spike-initiation threshold is affected by multiple spikes I measured its value for each spike and binned the results by the number of spikes in the preceding 50 ms. One spike in the preceding 50 ms gave a large increase in spike-initiation threshold; however, the relative threshold decreased again with an additional preceding spike. Three spikes in the preceding 50 ms was not significantly different from two spikes (Figure 6.2A). This appeared counter intuitive as one would expect the threshold to increase monotonically with the number of preceding spikes. This non-monotonic behaviour can be explained by the presence of burst spikes, which have a significantly higher threshold than non-burst spikes (Figure 6.1C) skewing the distribution. Removing burst spikes from the dataset led to a monotonic
increase (Figure 6.2B).