Figures and data in Visualization of currents in neural models with similar behavior and different conductance densities

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15 figures, 1 table and 1 additional file

Figures

Figure 1

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Landscape optimization can be used to find models with specific sets of features.

(A) Example model bursting neuron. The activity is described by the burst frequency and the burst duration in units of the period (duty cycle). The spikes detection threshold (red line) is used to determine the spike times. The ISI threshold (cyan) is used to determine which spikes are bursts starts (bs) and bursts ends (be). The slow wave threshold (blue line) is used to ensure that slow wave activity is separated from spiking activity. (B) Example model spiking neuron. We use thresholds as before to measure the frequency and the duty cycle of the cell. The additional slow wave thresholds (purple) are used to control the waveform during spike repolarization.

https://doi.org/10.7554/eLife.42722.003

Figure 2

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Currentscape of a model bursting neuron.

A simple visualization of the dynamics of ionic currents in conductance-based model neurons. (A) Membrane potential of a periodic burster. (B) Percent contribution of each current type to the total inward and outward currents displayed as pie charts and bars at times $T_{1}$ and $T_{2}$ (C) Percent contribution of each current to the total outward and inward currents at each time stamp. The black filled curves on the top and bottom indicate total inward outward currents respectively on a logarithmic scale. The color curves show the time evolution of each current as a percentage of the total current at that time. For example, at $t = T_{1}$ the total outward current is $\approx 2.5 n A$ and the orange shows a large contribution of $K C a$ . At $t = T_{2}$ the total outward current has increased to $\approx 4 n A$ and the $K C a$ current is contributing less to the total.

https://doi.org/10.7554/eLife.42722.004

Figure 3 with 1 supplement

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Membrane potential $V$ distributions.

(A) Distribution of membrane potential $V$ values. The total number of samples is $N = 2.2 \times 10^{6}$ . Y-axis scale is logarithmic. The area of the dark shaded region can be used to estimate of the probability that the activity is sampled between $- 50 m V$ and $- 40 m V$ , and the area of the light shaded region is proportional to the probability that $V (t)$ is sampled between $- 30 m V$ and $20 m V$ . The area of the dark region is $20$ times larger than the light region. (B) The same distribution in (A) represented as a graded bar. (C) Distribution of $V$ as a function of $V$ and $g N a$ , and waveforms for several $g N a$ values.The symbols indicate features of the waveforms and their correspondence to the ridges of the distribution of $V$ . (D) Waveforms under two conditions and their correspondence to the ridges of the distribution of $V$ . The ridges were enhanced by computing the derivative of the distribution along the $V$ direction.

https://doi.org/10.7554/eLife.42722.005

Figure 3—figure supplement 1

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Probability distributions of membrane potential.

(A) The black trace corresponds to the membrane potential $V (t)$ during a spike within a burst (total time $5.4 m s e c$ ). The y-axis is split into four equally sized bins (in colors) that span the full range of V values ( $m i n (V) \approx - 60 m V$ and $m a x (V) \approx 28 m V$ ). The probability that $V (t)$ is observed in a given bin at a *random* instant is proportional to the total time $V (t)$ spends at that bin. This is indicated in colors by the preimage of each bin. (B) The total time spent in each bin can be interpreted as a coarse-grained probability distribution of $V (t)$ . (C) (top) Membrane potential $V$ , more bins and their pre-images. (bottom) Probability distribution of $V$ . (D) Idem for $50$ bins. Note that the probability distribution of $V (t)$ displays sharp peaks for values of $V$ where local maxima (or minima) in time occur. This effect is more noticeable as the number of bins is increased.

https://doi.org/10.7554/eLife.42722.006

Figure 4

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Currentscapes of model bursting neurons.

(top) Maximal conductances of all model bursters. (bottom) The panels show the membrane potential of the cell and the percent contribution of each current over two cycles.

https://doi.org/10.7554/eLife.42722.007

Figure 5

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Response to current injections and interspike-intervals (ISI) distributions of model (a).

(A) (top) Control traces (no current injected $0 n A$ ), regular bursting ( $0.8 n A$ ), irregular bursting $1.95 n A$ . (B) (top) Fast regular bursting ( $f_{b} \approx 6 H z$ ), quadruplets ( $3.45 n A$ ), doublets ( $3.75 n A$ ) and singlets ( $4.5 n A$ ) (tonic spiking). (C) ISI distributions over a range of injected current.

https://doi.org/10.7554/eLife.42722.008

Figure 6

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ISI distributions of the six model bursting neurons over a range of injected current.

The panels show all ISI values of each model burster over a range on injected currents (vertical axis is logarithmic). All bursters transition into tonic spiking regimes for injected currents larger than $5 n A$ and the details of the transitions are different across models.

https://doi.org/10.7554/eLife.42722.009

Figure 7

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Effects of decreasing maximal conductances: inward currents.

The figure shows the membrane potential $V$ of all model cells as the maximal conductance $g_{i}$ of each current is gradually decreased from $100 %$ to $0 %$ . Each panel shows $11$ traces with a duration of 3 s. Dashed lines are placed at $0 m V$ and $- 50 m V$ . The shading indicates values of maximal conductance for which the activity the models differs the most.

https://doi.org/10.7554/eLife.42722.010

Figure 8

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Effects of decreasing maximal conductances: outward currents.

The figure shows the membrane potential $V$ of all model cells as the maximal conductance $g_{i}$ of each current is gradually decreased from $100 %$ to $0 %$ . Each panel shows $11$ traces with a duration of 3 s. Dashed lines are placed at $0 m V$ and $- 50 m V$ . The shading indicates values of maximal conductance for which the activity the models differs the most.

https://doi.org/10.7554/eLife.42722.011

Figure 9

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Decreasing $C a T$ in model (f).

The figure shows the traces and the currentscapes of model (f) as $C a T$ is gradually decreased. Top panels show $1$ second of data, center panels show $0.1$ seconds and the bottom panels show $2$ seconds (see full traces in Figure 8).

https://doi.org/10.7554/eLife.42722.012

Figure 10

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Complete removal of one current: inward currents.

The figure shows the traces and currentscapes for all bursters when one current is completely removed.

https://doi.org/10.7554/eLife.42722.013

Figure 11

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Complete removal of one current: outward currents.

The figure shows the traces and currentscapes for all bursters when one current is completely removed.

https://doi.org/10.7554/eLife.42722.014

Figure 12

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Changes in waveform as currents are gradually removed.

Inward currents. The figure shows the ridges of the probability distribution of $V (t)$ as a function of $V$ and each maximal conductance $p (V, g_{i})$ . The ridges of the probability distributions appear as curves and correspond to values of $V$ where the system spends more time, such as extrema. The panels show how different features of the waveform such as total amplitude, and the amplitude of each spike, change as each current is gradually decreased.

https://doi.org/10.7554/eLife.42722.015

Figure 13

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Changes in waveform as currents are gradually removed.

Outward and leak currents. The figure shows the ridges of the probability distribution of $V (t)$ as a function of $V$ and each maximal conductance $p (V, g_{i})$ . See Figure 12.

https://doi.org/10.7554/eLife.42722.016

Figure 14 with 1 supplement

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Changes in waveform of current shares as one current is gradually decreased.

The panels show the probability distribution of the share of each current $\hat{C_{i}} (t)$ for model (f) as $C a T$ is decreased (see Figure 14—figure supplement 1).

https://doi.org/10.7554/eLife.42722.017

Figure 14—figure supplement 1

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Probability distributions of currents shares.

The Figure shows the relationship between the currentscapes and the distributions of current shares. (A) Distribution of $A$ current share to the total outward current for $1001$ values of $g C a T$ between $0 %$ and $100 %$ . (B) Share of $A$ current as a time series. The $A$ current contributes with more than $50 %$ of the outward current for most of the time. At $70 % g C a T$ the cell spikes tonically and the $A$ contributes $50 %$ of the outward current most of the time. The symbols indicate features in the waveform that are mapped to ridges in the distribution. (C) Currentscapes. (D) Idem (B) but for $K C a$ . Notice the share of $K C a$ decreasing as $g C a T \to 0$ . (E) Distribution of $K C a$ current share to the total outward current for $1001$ values of $g C a T$ between $0 %$ and $100 %$ .

https://doi.org/10.7554/eLife.42722.018

Figure 15

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Changes in waveform of current shares as each current is gradually decreased.

The panels show the probability distribution of the share of each current $\hat{C_{i}} (t)$ for model (c) as each current is decreased.

https://doi.org/10.7554/eLife.42722.019

Tables

Table 1

Parameters used in this study and error value.

https://doi.org/10.7554/eLife.42722.020

	gNa	gCaT	gCaS	gA	gKCa	gKd	gH	gL	$τ_{C a}$	$E (g)$
model (a)	1076.392	6.4056	10.048	8.0384	17.584	124.0928	0.11304	0.17584	653.5	0.051
model (b)	1165.568	6.6568	9.5456	54.5104	16.328	110.7792	0.0628	0.10676	813.88	0.053
model (c)	1228.368	7.0336	11.0528	117.5616	16.328	111.2816	0.13816	0.10676	605.98	0.027
model (d)	1203.248	6.6568	10.5504	59.5344	16.328	111.4072	0.0	0.10676	653.5	0.471
model (e)	1210.784	8.164	6.28	113.04	12.56	118.4408	0.1256	0.0314	393.13	0.109
model (f)	1245.952	7.7872	6.7824	84.6544	12.56	113.9192	0.02512	0.0	174.34	0.047
model (Figure 2)	1228.368	7.0336	11.0528	117.5616	16.328	110.7792	0.13816	0.10048	605.98	0.007
model (Figure 3)	895.528	3.8936	16.5792	116.4312	21.352	115.6776	0.0	0.08792	828.73	0.058

Additional files

Transparent reporting form: https://doi.org/10.7554/eLife.42722.021
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Leandro M Alonso
Eve Marder

(2019)

Visualization of currents in neural models with similar behavior and different conductance densities

eLife 8:e42722.

https://doi.org/10.7554/eLife.42722

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Landscape optimization can be used to find models with specific sets of features.

Currentscape of a model bursting neuron.

Membrane potential V distributions.

Probability distributions of membrane potential.

Currentscapes of model bursting neurons.

Response to current injections and interspike-intervals (ISI) distributions of model (a).

ISI distributions of the six model bursting neurons over a range of injected current.

Effects of decreasing maximal conductances: inward currents.

Effects of decreasing maximal conductances: outward currents.

Decreasing CaT in model (f).

Complete removal of one current: inward currents.

Complete removal of one current: outward currents.

Changes in waveform as currents are gradually removed.

Changes in waveform as currents are gradually removed.

Changes in waveform of current shares as one current is gradually decreased.

Probability distributions of currents shares.

Changes in waveform of current shares as each current is gradually decreased.

Parameters used in this study and error value.

Transparent reporting form

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

Membrane potential $V$ distributions.

Decreasing $C a T$ in model (f).