Single-cell temporal dynamics
Michael Barkasi
August 19, 2026 (v1.1)
tutorial_membrane_temporal_dynamics.Rmd
Introduction
Single-cell network
Let’s set up the R environment by clearing the workspace, setting a random-number generator seed, and loading the DACx package.
# Clear the R workspace to start fresh
rm(list = ls())
# Set seed for reproducibility
set.seed(12345)
# Load DACx package
library(DACx, quietly = TRUE) Next, we create a new network object with the new.network function.
nonspiking_cell <- new.network()Set up cell
The parameters defining cell types in DACx are mostly biophysically interpretable and can be set with, or tested against, experimental data.
Parameters for transmitter type
- Valence: 1 for excitatory cells, -1 for inhibitory cells. Code variable: valence.
Temporal modulation parameters
The temporal modulation term T controlling the responsiveness (size) of \partial v/\partial t is determined by an exponential decay function with parameters:
- Temporal modulation bias: The baseline value b of T, in ms. Code variable: temporal_modulation_bias.
- Temporal modulation time constant: The time constant \tau of the exponential decay in T, in ms. Code variable: temporal_modulation_timeconstant.
- Temporal modulation amplitude: The amplitude A of the exponential decay in T, in ms. Code variable: temporal_modulation_amplitude. A value >0 induces bursting behavior, while a value of zero induces tonic (rhythmic) firing.
Development note: The values of these parameters are 1/0.0001 times the intended values in ms, due to debugging.
Intercell transmission parameters
- Transmission velocity: The speed of the action potential between neurons, in microns/ms. Code variable: transmission_velocity.
- Spine density: The proportion (a value between 0 and 1) of dendrite nodes expected to be spines. Code variable: spine_density.
- Axon target: The kind of nodes onto which the cell’s axons can synapse. Possible values include “spine”, “dendrite_shaft”, “soma”, and “axon_shaft”. Code variable axon_target.
Membrane parameters
- Potential bound: The maximum absolute value v_\mathrm{bound} of potential difference in electrical charge between the inside and outside of the cell, in mV. Code variable v_bound. Theoretically, we assume this is the absolute value of the rest voltage, plus a little bit. What matters is that -v_\mathrm{bound} \leq v \leq v_\mathrm{bound} for all possible membrane potentials v. For example, 75mV is a reasonable value.
- Metabolic energy derivative bound: Bound \partial I_\mathrm{influx} on the absolute value of the derivative \partial\mathcal{H}/\partial v of metabolic energy \mathcal{H} with respect to potential v, such that \partial I_\mathrm{influx} \geq |\partial\mathcal{H}/\partial v|, in mA. Code variable: dHdv_bound. Theoretically, we assume that this value is approximately the change in current when v crosses the spike threshold, which we assume is approximately the spike current. In practice, we add 5%.
- Spike current: The current of the action potential, i.e., the total current crossing the membrane over the entire area of the cell during a spike, in mA. Code variable: I_spike. As a starting point, we assume this is 10^{-3}mA, i.e., one mico amp.
- Spike potential: The value v_\mathrm{spike} of an action potential, in mV. Code variable: spike_potential. The default is 35mV.
- Resting potential: The potential difference v_\mathrm{rest} in electrical charge between the inside and outside of the cell at rest, in mV. Code variable: resting_potential. The default is -70mV.
- Threshold: The potential difference v_\mathrm{threshold} in electrical charge between the inside and outside of the cell at which an action potential is triggered, in mV. Code variable: threshold. The default is -55mV.
Parameters for process size and structure
- Axon branch count: An integer value giving the expected number of nodes per branch in the axon arbor. Code variable: axon_branch_count.
- Dendrite branch count: Same as axon branch count, but for dendrites. Code variable: dendrite_branch_count.
- Branch independence: The expected proportion (a value between 0 and 1) of branches which connect directly to the soma, with 1 meaning all branches connect directly to the soma and zero meaning that all branches connect to the soma from a single segment. Code variable: branch_independence.
- Branch spread: Scaled value between 0 and 1 controlling the tendency of arbor branches to repel away from the soma with 1 meaning a straight line away from the soma and 0 meaning no bias with respect to soma position. Code variable: branch_spread.
Apical dendrite parameters
- Apical target layer: Character string giving the name of the layer to which apical dendrite is expected to grow, if any; if none, “none”. Intended for modeling the circuit topology of pyramidal neurons. Code variable: apical_target_layer.
# The formula is: = v_traces.col(t - 1) + (STD_W.array() * dvdt.array() / tau.array()).matrix();
# So, the temporal modulation factor T is really STD_W/tau, where tau is a fast-response adaptation (e.g., for bursting) dependent on only time since last spike, and STD_W is a mesoscale adaptation ("short-term depression") dependent on some back-looking window of spikes.
# T(t) models ion channel kinetics (from ChatGPT): "T(t) is analogous to an effective membrane time-scale or effective membrane resistance in that it modulates the rate of voltage evolution without altering the underlying energy landscape."
modify.cell.type(
"neuron",
"subthreshold only",
v_bound = 2.0,
g_leak = 1.5, # nS, Slow leak for demonstration purposes
v_threshold = 1000 # Something large, to suppress spiking
)
nonspiking_cell <- set.network.structure(
nonspiking_cell,
neuron_types = c("subthreshold only"),
neurons_per_node = 1
)BGT simulations
This gives us the number of rows needed in our stimulus current matrix. For the number of columns, we need to know the number of time steps required:
stim_time_ms <- 1000
dt <- 1e-3
n_steps <- stim_time_ms/dt
cat("Number of time steps in the simulation:", n_steps)## Number of time steps in the simulation: 1e+06Now, suppose we want our simulation to involve a 20ms input current to just the spiny stellates, starting at 10ms. We can compute the initial and final time steps of this current, plus a mask for the spiny stellates, as follows:
A final question is how much current to apply. For this simulation, we’ll use a constant current of 100 pico amp (100\times 10^{-9}mA) to the spiny stellates during the stimulus period. It might be natural to leave the input current at zero outside of the stimulus period, but there is endogenous background activity even without exogenous input to the network. So, we’ll specify a baseline input current of 10 pico amps (10\times 10^{-9}mA) to all neurons throughout the entire stimulation period:
stim_magnitude <- 100
no_stim <- matrix(0, nrow = 1, ncol = n_steps)With the stimulus current matrix in hand, we can run the simulation:
nonspiking_cell_results <- run.BGT(
nonspiking_cell,
no_stim,
dt,
v_initial = 0.0
)
plot.network.traces(nonspiking_cell, I_stim = no_stim, plot_rates = FALSE)
integrating_cell <- new.network()
modify.cell.type(
"neuron",
"leaky integrator",
# Membrane kinetics
tau_fast = 1.0, # ms
tau_slow = 60.0, # ms
tau_Vs = 100.0, # ms/spike
dCdr = 0.01, # concentration/spike
dVdr = 0.05, # concentration/spike
max_spike_rate = 0.1, # spikes/ms
g_leak = 1.0, # nS
# Intercell transmission
spike_velocity = 500, # micons/ms, = 0.5 m/s
spine_density = 0.0,
axon_target = "dendrite_shaft",
# Spiking
I_spike = 1e3, # pA
dHdv_bound = 1.05,
v_spike = 35, # mV
tau_spike = 1.0, # ms
v_threshold = -55, # mV
v_eq = list ( # mV
"spiny stellate" = 0.0, # Excitatory, so drives postsynaptic cell membrane v up
"PV" = -80.0), # Inhibitory, so drives postsynaptic cell membrane v down
# Membrane characteristics
v_rest = -70, # mV
v_bound = 1.15,
g_syn = list( # nS
"spiny stellate" = 0.1,
"PV" = 0.1),
tau_syn = list( # ms
"spiny stellate" = 2.0, # Excitatory glutamate channels close quickly
"PV" = 6.0), # Inhibitory GABA channels stay open longer
# Neurite structure
axon_branch_count = 20,
dendrite_branch_count = 20,
branch_independence = 0.75,
branch_spread = 0.75,
apical_target_layer = "none"
)
integrating_cell <- set.network.structure(
integrating_cell,
neuron_types = c("leaky integrator"),
neurons_per_node = 1
)
# Set stimulus start and length
stim_length_ms <- 5
stim_start_ms <- seq(from = 50, to = 950, by = 100)
# Find start and end steps of the input stimulus current
stim_length <- stim_length_ms / dt
stim_start <- stim_start_ms / dt
stim_end <- stim_start + stim_length - 1
short_stims <- no_stim
for (i in seq_along(stim_start)) {
short_stims[, stim_start[i]:stim_end[i]] <- stim_magnitude
}
integrating_cell_results <- run.BGT(
integrating_cell,
short_stims,
dt,
v_initial = -70
)
plot.network.traces(integrating_cell, I_stim = short_stims, plot_rates = FALSE)
bursting_cell <- new.network()
modify.cell.type(
"leaky integrator",
"bursting cell",
dCdr = 0.09, # up from 0.01, to induce bursting
)
bursting_cell <- set.network.structure(
bursting_cell,
neuron_types = c("bursting cell"),
neurons_per_node = 1
)
# Set stimulus start and length
stim_length_ms <- 100
stim_start_ms <- seq(from = 100, to = 750, by = 200)
# Find start and end steps of the input stimulus current
stim_length <- stim_length_ms / dt
stim_start <- stim_start_ms / dt
stim_end <- stim_start + stim_length - 1
long_stims <- no_stim
for (i in seq_along(stim_start)) {
long_stims[, stim_start[i]:stim_end[i]] <- stim_magnitude
}
bursting_cell_results <- run.BGT(
bursting_cell,
long_stims,
dt,
v_initial = -70
)
plot.network.traces(bursting_cell, I_stim = long_stims, plot_rates = FALSE)
integrating_cell_results <- run.BGT(
integrating_cell,
long_stims,
dt,
v_initial = -70
)
plot.network.traces(integrating_cell, I_stim = long_stims, plot_rates = FALSE)
# Set stimulus start and length
stim_length_ms <- 800
stim_start_ms <- 100
# Find start and end steps of the input stimulus current
stim_length <- stim_length_ms / dt
stim_start <- stim_start_ms / dt
stim_end <- stim_start + stim_length - 1
continuous_stim <- no_stim
for (i in seq_along(stim_start)) {
continuous_stim[, stim_start[i]:stim_end[i]] <- stim_magnitude
}
network_both <- new.network()
network_both <- set.network.structure(
network_both,
neuron_types = c("bursting cell", "leaky integrator"),
neurons_per_node = 1
)
no_stim2 <- matrix(0, nrow = 2, ncol = n_steps)
continuous_stim2 <- no_stim2
for (i in seq_along(stim_start)) {
continuous_stim2[, stim_start[i]:stim_end[i]] <- stim_magnitude
}
network_both_long <- run.BGT(
network_both,
continuous_stim2,
dt,
v_initial = -70
)
plot.network.traces(
network_both,
I_stim = continuous_stim2,
plot_rates = TRUE,
window_size = 0.1,
return_plot = TRUE
)## Warning: Removed 49998 rows containing missing values or values outside the scale range (`geom_line()`).
## Removed 49998 rows containing missing values or values outside the scale range (`geom_line()`).
modify.cell.type(
"leaky integrator",
"slow recovery",
tau_Vs = 500.0 # up from 100.0
)
modify.cell.type(
"leaky integrator",
"slow drain",
dVdr = 0.01 # down from 0.05
)
network_both <- new.network()
network_both <- set.network.structure(
network_both,
neuron_types = c("leaky integrator", "slow recovery", "slow drain"),
neurons_per_node = 1
)
# Set stimulus start and length
stim_length_ms <- 1200
stim_start_ms <- 100
# Find start and end steps of the input stimulus current
stim_length <- stim_length_ms / dt
stim_start <- stim_start_ms / dt
stim_end <- stim_start + stim_length - 1
no_stim2 <- matrix(0, nrow = 3, ncol = stim_end + (100/dt))
continuous_stim2 <- no_stim2
recover_start_ms <- c(200, 500)
recover_length_ms <- c(100, 500)
recover_start <- recover_start_ms / dt
recover_length <- recover_length_ms / dt
recover_end <- recover_start + recover_length - 1
for (i in seq_along(stim_start)) {
continuous_stim2[, stim_start[i]:stim_end[i]] <- stim_magnitude
}
for (i in seq_along(recover_start)) {
continuous_stim2[, recover_start[i]:recover_end[i]] <- 0
}
network_both_long <- run.BGT(
network_both,
continuous_stim2,
dt,
v_initial = -70
)
plt <- plot.network.traces(network_both, I_stim = continuous_stim2, plot_rates = TRUE, window_size = 0.05, return_plot = TRUE)
plt <- plt & ggplot2::theme(
plot.title = ggplot2::element_text(hjust = 0.5, size = 14),
axis.title.y = ggplot2::element_text(size = 10),
axis.text.y = ggplot2::element_text(size = 8)
)
for (p in c(1:3)) {
plt[[p]][[1]] <- plt[[p]][[1]] + ggplot2::coord_cartesian(ylim = c(0, 120)) +
ggplot2::geom_hline(
yintercept = 75,
color = "red",
linetype = "dashed"
)
}Temporal modulation
The final step in GT models (including BGT models) is to divide the rate of change for membrane potential \partial v/\partial t by a temporal modulation term T, such that: v(t+1) = v(t) + \frac{\left.\frac{\partial v}{\partial t}\right|_{t+1}}{T} This term T is given by the following exponential decay model: T = b + A\exp\left(-\frac{x}{\tau}\right) where b is the temporal modulation bias, A is the temporal modulation amplitude, and \tau is the temporal modulation time constant. The traditional input x is filled by B, a “burst” step counter. The step counter B is merely a numerical device in the simulation to carry T repeatedly across the exponential decay via the input x. When T<b, B resets to zero (and thus T jumps again to a high number), resetting the exponential decay.
When the amplitude A is zero, the exponential decay has no effect and all that’s relevant is the bias b. When A>0, the effect is to increase T at the start of the step counter, thereby shrinking the effect of \partial v/\partial t. This shrinkage follows the exponential decay of T, so that there is little chance in v (i.e., small \partial v/\partial t) at the start of the step counter, but the possibility for large changes in v at the end of the step counter. Thus, when at the end of the step counter, neurons are prone to many spikes as their membrane potential rapidly changes, creating a bursting effect.
##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(ggplot2)
# Parameters matching DACx.cpp BGT simulation
theta_low <- 0.1
theta_high <- 0.9
theta_n <- theta_low^4 # places Hill midpoint at Ca = theta_high
tau_slow <- 60 # ms, Ca2+ decay time constant
dCdr_eff <- 0.05 # Ca2+ influx per unit tau_slow_effect
dt_plot <- 0.1 # ms, step size for this illustrative simulation
# Analytical curves: tau_slow_effect vs Ca2+ for each Schmitt trigger state
Ca_seq <- seq(0, 1, by = 0.001)
df_phase <- bind_rows(
tibble(Ca = Ca_seq,
tau = (1 - Ca_seq)^4 / ((1 - Ca_seq)^4 + theta_n),
phase = "Active (slow_current = 1)"),
tibble(Ca = Ca_seq,
tau = 0,
phase = "Inter-burst (slow_current = 0)")
)
# Simplified Ca2+ dynamics simulation
n_sim <- 60000L
Ca_sim <- numeric(n_sim)
tau_sim <- numeric(n_sim)
sc_sim <- logical(n_sim)
Ca_sim[1] <- 0
sc_sim[1] <- TRUE
for (t in 2:n_sim) {
sc <- sc_sim[t - 1]
Ca <- Ca_sim[t - 1]
Ca_n <- (as.numeric(sc) - Ca)^4
tau_se <- as.numeric(sc) * Ca_n / (Ca_n + theta_n)
tau_sim[t - 1] <- tau_se
Ca_new <- Ca + (dCdr_eff * tau_se - Ca / tau_slow) * dt_plot
Ca_sim[t] <- max(0, Ca_new)
if ( sc && Ca_new >= theta_high) sc_sim[t] <- FALSE
else if (!sc && Ca_new <= theta_low) sc_sim[t] <- TRUE
else sc_sim[t] <- sc
}
Ca_n_last <- (as.numeric(sc_sim[n_sim]) - Ca_sim[n_sim])^4
tau_sim[n_sim] <- as.numeric(sc_sim[n_sim]) * Ca_n_last / (Ca_n_last + theta_n)
t_ms_sim <- (seq_len(n_sim) - 1) * dt_plot
# Select a representative window with ~6 burst cycles (after transient settles)
win_start <- 500
win_end <- 1500
idx <- which(t_ms_sim >= win_start & t_ms_sim <= win_end)
df_ts <- tibble(t = t_ms_sim[idx], Ca = Ca_sim[idx],
tau = tau_sim[idx], sc = sc_sim[idx])
# Identify inter-burst intervals for shading
runs <- rle(df_ts$sc)
grp_end <- cumsum(runs$lengths)
grp_start <- c(1, grp_end[-length(grp_end)] + 1)
shade_df <- tibble(sc = runs$values,
t_min = df_ts$t[grp_start],
t_max = df_ts$t[grp_end]) |>
filter(!sc)
# Panel A: Phase portrait (analytical)
p_phase3 <- ggplot() +
geom_line(data = df_phase, aes(x = Ca, y = tau, color = phase), linewidth = 1.1) +
geom_vline(xintercept = theta_low, linetype = "dashed", color = "gray40", linewidth = 0.6) +
geom_vline(xintercept = theta_high, linetype = "dashed", color = "gray40", linewidth = 0.6) +
annotate("segment", x=0.18, xend=0.55, y=0.95, yend=0.75,
arrow=arrow(length=unit(0.2,"cm"), type="closed"), color="#2166ac", linewidth=0.8) +
annotate("segment", x=0.87, xend=0.87, y=0.30, yend=0.04,
arrow=arrow(length=unit(0.2,"cm"), type="closed"), color="gray30", linewidth=0.8) +
annotate("segment", x=0.73, xend=0.18, y=0, yend=0,
arrow=arrow(length=unit(0.2,"cm"), type="closed"), color="#d6604d", linewidth=0.8) +
annotate("segment", x=0.1, xend=0.1, y=0.02, yend=0.90,
arrow=arrow(length=unit(0.2,"cm"), type="closed"), color="gray30", linewidth=0.8) +
annotate("text", x=0.34, y=0.87, label="Ca accumulates\n(burst fires)", size=3.0, color="#2166ac", hjust=0) +
annotate("text", x=0.64, y=0.16, label="trigger\nOFF", size=3.0, color="gray30", hjust=0.5) +
annotate("text", x=0.44, y=0.07, label="Ca decays (silent)", size=3.0, color="#d6604d", hjust=0.5) +
annotate("text", x=0.13, y=0.48, label="trigger\nON", size=3.0, color="gray30", hjust=0) +
annotate("text", x=theta_low, y=0.22, label="theta_low", size=2.9, color="gray35", hjust=-0.05, fontface="italic") +
annotate("text", x=theta_high, y=0.22, label="theta_high", size=2.9, color="gray35", hjust= 1.05, fontface="italic") +
scale_color_manual(
values = c("Active (slow_current = 1)" = "#2166ac",
"Inter-burst (slow_current = 0)" = "#d6604d"),
labels = c("Active phase", "Inter-burst phase")
) +
scale_x_continuous(limits = c(0, 1), expand = c(0.02, 0)) +
scale_y_continuous(limits = c(0, 1.0), expand = c(0.01, 0.01)) +
labs(title = "A Phase portrait",
x = "Ca2+ (normalized)", y = "tau_slow", color = NULL) +
theme_bw(base_size = 11) +
theme(legend.position = c(0.98, 0.98),
legend.justification = c(1, 1),
legend.background = element_rect(fill = "white", color = "gray80"),
legend.text = element_text(size = 9),
plot.title = element_text(face = "bold", size = 11))
# Panel B: Ca2+ over time
p_ca3 <- ggplot(df_ts, aes(x = t, y = Ca)) +
geom_rect(data = shade_df,
aes(xmin = t_min, xmax = t_max, ymin = -Inf, ymax = Inf),
inherit.aes = FALSE, fill = "#fee0d2", alpha = 0.7) +
geom_hline(yintercept = theta_low, linetype = "dashed", color = "gray50", linewidth = 0.6) +
geom_hline(yintercept = theta_high, linetype = "dashed", color = "gray50", linewidth = 0.6) +
geom_line(color = "#2166ac", linewidth = 0.8) +
annotate("text", x=win_start+5, y=theta_low +0.06, label="theta_low", size=2.9, color="gray40", hjust=0, fontface="italic") +
annotate("text", x=win_start+5, y=theta_high-0.07, label="theta_high", size=2.9, color="gray40", hjust=0, fontface="italic") +
labs(title = "B Ca2+ over time", x = NULL, y = "Ca2+") +
theme_bw(base_size = 11) +
theme(plot.title = element_text(face = "bold", size = 11),
axis.text.x = element_blank(),
axis.ticks.x = element_blank())
# Panel C: tau_slow over time
p_tau3 <- ggplot(df_ts, aes(x = t, y = tau)) +
geom_rect(data = shade_df,
aes(xmin = t_min, xmax = t_max, ymin = -Inf, ymax = Inf),
inherit.aes = FALSE, fill = "#fee0d2", alpha = 0.7) +
geom_line(color = "#d6604d", linewidth = 0.8) +
annotate("text", x=1050, y=0.55,
label="inter-burst\n(slow_current = 0,\ntau_slow = 0)",
size=2.8, color="gray45", hjust=0.5) +
labs(title = "C Temporal modulation (tau_slow) over time",
x = "Time (ms)", y = "tau_slow") +
theme_bw(base_size = 11) +
theme(plot.title = element_text(face = "bold", size = 11))
# Combine panels
p_phase3 + (p_ca3 / p_tau3) +
plot_layout(widths = c(1, 1.5)) +
plot_annotation(
title = "Bursting via Ca2+-gated Schmitt trigger and Hill-function temporal modulation",
caption = paste("Shaded = inter-burst periods. Dashed lines = Schmitt trigger thresholds",
"(theta_low = 0.1, theta_high = 0.9)."),
theme = theme(plot.title = element_text(size = 11, face = "bold"),
plot.caption = element_text(size = 9, color = "gray40"))
)
p_phase3
Normalized spike cost in the lead-up to a spike
The quantity normalized_spike_cost (DACx.cpp, line 2514)
is the energetic heart of the BGT spike-generation mechanism. It is
defined as
\text{nsc}(t) = \frac{\overbrace{\partial\mathcal{H}_{\max} \cdot v(t)}^{\text{spike initiation power}} - \overbrace{\left.\frac{\partial\mathcal{H}}{\partial v}\right|_t \cdot v_{\text{bound}}}^{\text{rest maintenance power}}}{\underbrace{\partial\mathcal{H}_{\max} \cdot v_{\text{bound}}}_{\text{max initiation power from rest}} - \underbrace{\left.\frac{\partial\mathcal{H}}{\partial v}\right|_t \cdot v(t)}_{\text{maintenance power at current } v}}
where \partial\mathcal{H}/\partial v captures the net current balance at the membrane (synaptic + leak + stimulus + any ongoing spike current) and \partial\mathcal{H}_{\max} is its bound. The quantity nsc \in [-1, 1], where \text{nsc} = -1 corresponds to maximum hyperpolarization and \text{nsc} = 1 to maximum depolarization or maximum inward current.
nsc as an attractor. The raw rate of change of membrane potential is set as \partial v/\partial t = v_{\text{bound}} \cdot \text{nsc} - v, making v_{\text{bound}} \cdot \text{nsc} an attractor voltage toward which the membrane is continuously pulled. The temporal modulation term T (line 2526) then scales this raw \partial v/\partial t by T \cdot \Delta t, controlling the rate of movement toward the attractor independently of the attractor’s position. This cleanly separates the energetic direction of membrane dynamics (determined by nsc) from the kinetic rate of those dynamics (determined by T via spike history and calcium).
Energetic interpretation. The sign of nsc reflects a metabolic cost comparison: \text{nsc} < 0 means spike initiation is energetically cheaper than maintaining the current subthreshold state — the cell is continuously being pulled toward a spike. Under physiological depolarizing input this holds throughout the charging phase, with nsc rising (becoming less negative) as the membrane approaches threshold. The voltage threshold itself plays a secondary role: it only determines when the spike current I_\text{spike} enters the \partial\mathcal{H}/\partial v calculation, sharply increasing the outward current and collapsing nsc post-spike. Spiking in this model is therefore not a threshold-crossing rule but the outcome of continuous energetic accounting: the membrane moves toward the spike because that is the lower-energy trajectory.
The block below runs a leaky integrator cell (same parameters as the
tutorial) with a constant 100 pA input, reconstructs
normalized_spike_cost from the voltage trace, and plots it
alongside the membrane potential in the lead-up to the first spike.
library(DACx)
library(ggplot2)
library(patchwork)
# ── 1. Build a leaky integrator network (tutorial parameters) ──────────────────
nsc_cell <- new.network()
modify.cell.type(
"neuron", "leaky integrator",
tau_fast = 1.0, # ms
tau_slow = 60.0, # ms
tau_Vs = 100.0, # ms/spike
dCdr = 0.01, # concentration/spike
dVdr = 0.05, # concentration/spike
max_spike_rate = 0.1, # spikes/ms
g_leak = 1.0, # nS
spike_velocity = 500, # microns/ms
spine_density = 0.0,
axon_target = "dendrite_shaft",
I_spike = 1e3, # pA
dHdv_bound = 1.05,
v_spike = 35, # mV
tau_spike = 1.0, # ms
v_threshold = -55, # mV
v_eq = list("spiny stellate" = 0.0, "PV" = -80.0),
v_rest = -70, # mV
v_bound = 1.15,
g_syn = list("spiny stellate" = 0.1, "PV" = 0.1),
tau_syn = list("spiny stellate" = 2.0, "PV" = 6.0),
axon_branch_count = 20,
dendrite_branch_count = 20,
branch_independence = 0.75,
branch_spread = 0.75,
apical_target_layer = "none"
)
nsc_cell <- set.network.structure(
nsc_cell,
neuron_types = c("leaky integrator"),
neurons_per_node = 1
)
# ── 2. Stimulus: 100 pA constant input starting at 10 ms ──────────────────────
dt_nsc <- 1e-3 # ms
sim_ms <- 25 # ms (captures first spike)
n_steps <- sim_ms / dt_nsc
I_nsc <- matrix(0, nrow = 1, ncol = n_steps)
I_nsc[, round(10 / dt_nsc):n_steps] <- 100 # pA
# ── 3. Run BGT simulation ──────────────────────────────────────────────────────
run.BGT(nsc_cell, I_nsc, dt_nsc, v_initial = -70)## $v_traces
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62] [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74] [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86] [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98] [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107] [,108] [,109] [,110] [,111] [,112] [,113] [,114] [,115] [,116] [,117] [,118] [,119] [,120] [,121] [,122] [,123] [,124] [,125] [,126] [,127] [,128] [,129] [,130] [,131] [,132] [,133] [,134] [,135] [,136] [,137] [,138] [,139] [,140] [,141] [,142] [,143] [,144] [,145] [,146] [,147] [,148] [,149] [,150] [,151] [,152] [,153] [,154] [,155] [,156] [,157] [,158] [,159] [,160] [,161] [,162] [,163] [,164] [,165] [,166] [,167] [,168] [,169] [,170] [,171] [,172] [,173] [,174] [,175] [,176] [,177] [,178] [,179] [,180] [,181] [,182] [,183] [,184] [,185] [,186] [,187] [,188] [,189] [,190] [,191] [,192] [,193] [,194] [,195] [,196] [,197] [,198] [,199] [,200] [,201] [,202] [,203] [,204] [,205] [,206] [,207] [,208] [,209] [,210] [,211] [,212] [,213] [,214] [,215] [,216] [,217] [,218] [,219] [,220] [,221] [,222] [,223] [,224] [,225] [,226] [,227] [,228] [,229] [,230] [,231] [,232] [,233] [,234] [,235] [,236] [,237] [,238] [,239] [,240] [,241] [,242] [,243] [,244] [,245] [,246] [,247] [,248] [,249] [,250] [,251] [,252] [,253] [,254] [,255] [,256] [,257] [,258] [,259] [,260] [,261] [,262] [,263] [,264] [,265] [,266] [,267] [,268] [,269] [,270] [,271] [,272] [,273] [,274] [,275] [,276] [,277] [,278] [,279] [,280] [,281] [,282] [,283] [,284] [,285] [,286] [,287] [,288] [,289] [,290] [,291] [,292] [,293] [,294] [,295] [,296] [,297] [,298] [,299] [,300] [,301] [,302] [,303] [,304] [,305] [,306] [,307] [,308] [,309] [,310] [,311] [,312] [,313] [,314] [,315] [,316] [,317] [,318] [,319] [,320] [,321] [,322] [,323] [,324] [,325] [,326] [,327] [,328] [,329] [,330] [,331] [,332] [,333] [,334] [,335] [,336] [,337] [,338] [,339] [,340] [,341] [,342] [,343] [,344] [,345] [,346] [,347] [,348] [,349] [,350] [,351] [,352] [,353] [,354] [,355] [,356] [,357] [,358] [,359] [,360] [,361] [,362] [,363] [,364] [,365] [,366] [,367] [,368] [,369] [,370] [,371] [,372] [,373] [,374] [,375] [,376] [,377] [,378] [,379] [,380] [,381] [,382] [,383] [,384] [,385] [,386] [,387] [,388] [,389] [,390] [,391] [,392] [,393] [,394] [,395] [,396] [,397] [,398] [,399] [,400] [,401] [,402] [,403] [,404] [,405] [,406] [,407] [,408] [,409] [,410] [,411] [,412] [,413] [,414] [,415] [,416] [,417] [,418] [,419] [,420] [,421] [,422] [,423] [,424] [,425] [,426] [,427] [,428] [,429] [,430] [,431] [,432] [,433] [,434] [,435] [,436] [,437] [,438] [,439] [,440] [,441] [,442] [,443] [,444] [,445] [,446] [,447] [,448] [,449] [,450] [,451] [,452] [,453] [,454] [,455] [,456] [,457] [,458] [,459] [,460] [,461] [,462] [,463] [,464] [,465] [,466] [,467] [,468] [,469] [,470] [,471] [,472] [,473] [,474] [,475] [,476] [,477] [,478] [,479] [,480] [,481] [,482] [,483] [,484] [,485] [,486] [,487] [,488] [,489] [,490] [,491] [,492] [,493] [,494] [,495] [,496] [,497] [,498] [,499] [,500] [,501] [,502] [,503] [,504] [,505] [,506] [,507] [,508] [,509] [,510] [,511] [,512] [,513] [,514] [,515] [,516] [,517] [,518] [,519] [,520] [,521] [,522] [,523] [,524] [,525] [,526] [,527] [,528] [,529] [,530] [,531] [,532] [,533] [,534] [,535] [,536] [,537] [,538] [,539] [,540] [,541] [,542] [,543] [,544] [,545] [,546] [,547] [,548] [,549] [,550] [,551] [,552] [,553] [,554] [,555] [,556] [,557] [,558] [,559] [,560] [,561] [,562] [,563] [,564] [,565] [,566] [,567] [,568] [,569] [,570] [,571] [,572] [,573] [,574] [,575] [,576] [,577] [,578] [,579] [,580] [,581] [,582] [,583] [,584] [,585] [,586] [,587] [,588] [,589] [,590] [,591] [,592] [,593] [,594] [,595] [,596] [,597] [,598] [,599] [,600] [,601] [,602] [,603] [,604] [,605] [,606] [,607] [,608] [,609] [,610] [,611] [,612] [,613] [,614] [,615] [,616] [,617] [,618] [,619] [,620] [,621] [,622] [,623] [,624] [,625] [,626] [,627] [,628] [,629] [,630] [,631] [,632] [,633] [,634] [,635] [,636] [,637] [,638] [,639] [,640] [,641] [,642] [,643] [,644] [,645] [,646] [,647] [,648] [,649] [,650] [,651] [,652] [,653] [,654] [,655] [,656] [,657] [,658] [,659] [,660] [,661] [,662] [,663] [,664] [,665] [,666] [,667] [,668] [,669] [,670] [,671] [,672] [,673] [,674] [,675] [,676] [,677] [,678] [,679] [,680] [,681] [,682] [,683] [,684] [,685] [,686] [,687] [,688] [,689] [,690] [,691] [,692] [,693] [,694] [,695] [,696] [,697] [,698] [,699] [,700] [,701] [,702] [,703] [,704] [,705] [,706] [,707] [,708] [,709] [,710] [,711] [,712] [,713] [,714] [,715] [,716] [,717] [,718] [,719] [,720] [,721] [,722] [,723] [,724] [,725] [,726] [,727] [,728] [,729] [,730] [,731] [,732] [,733] [,734] [,735] [,736] [,737] [,738] [,739] [,740] [,741] [,742] [,743] [,744] [,745] [,746] [,747] [,748] [,749] [,750] [,751] [,752] [,753] [,754] [,755] [,756] [,757] [,758] [,759] [,760] [,761] [,762] [,763] [,764] [,765] [,766] [,767] [,768] [,769] [,770] [,771] [,772] [,773] [,774] [,775] [,776] [,777] [,778] [,779] [,780] [,781] [,782] [,783] [,784] [,785] [,786] [,787] [,788] [,789] [,790] [,791] [,792] [,793] [,794] [,795] [,796] [,797] [,798] [,799] [,800] [,801] [,802] [,803] [,804] [,805] [,806] [,807] [,808] [,809] [,810] [,811] [,812] [,813] [,814] [,815] [,816] [,817] [,818] [,819] [,820] [,821] [,822] [,823] [,824] [,825] [,826] [,827] [,828] [,829] [,830] [,831] [,832] [,833] [,834] [,835] [,836] [,837] [,838] [,839] [,840] [,841] [,842] [,843] [,844] [,845] [,846] [,847] [,848] [,849] [,850] [,851] [,852] [,853] [,854] [,855] [,856] [,857] [,858] [,859] [,860] [,861] [,862] [,863] [,864] [,865] [,866] [,867] [,868] [,869] [,870] [,871] [,872] [,873] [,874] [,875] [,876] [,877] [,878] [,879] [,880] [,881] [,882] [,883] [,884] [,885] [,886] [,887] [,888] [,889] [,890] [,891] [,892] [,893] [,894] [,895] [,896] [,897] [,898] [,899] [,900] [,901] [,902] [,903] [,904] [,905] [,906] [,907] [,908] [,909] [,910] [,911] [,912] [,913] [,914] [,915] [,916] [,917] [,918] [,919] [,920] [,921] [,922] [,923] [,924] [,925] [,926] [,927] [,928] [,929] [,930] [,931] [,932] [,933] [,934] [,935] [,936] [,937] [,938] [,939] [,940] [,941] [,942] [,943] [,944] [,945] [,946] [,947] [,948] [,949] [,950] [,951] [,952] [,953] [,954] [,955] [,956] [,957] [,958] [,959] [,960] [,961] [,962] [,963] [,964] [,965] [,966] [,967] [,968] [,969] [,970] [,971] [,972] [,973] [,974] [,975] [,976] [,977] [,978] [,979] [,980] [,981] [,982] [,983] [,984] [,985] [,986] [,987] [,988] [,989] [,990] [,991] [,992] [,993] [,994] [,995] [,996] [,997] [,998] [,999] [,1000] [,1001] [,1002] [,1003] [,1004] [,1005] [,1006] [,1007] [,1008] [,1009] [,1010] [,1011] [,1012] [,1013] [,1014] [,1015] [,1016] [,1017] [,1018] [,1019] [,1020] [,1021] [,1022] [,1023] [,1024] [,1025] [,1026] [,1027] [,1028] [,1029] [,1030] [,1031] [,1032] [,1033] [,1034] [,1035] [,1036] [,1037] [,1038] [,1039] [,1040] [,1041] [,1042] [,1043] [,1044] [,1045] [,1046] [,1047] [,1048] [,1049] [,1050] [,1051] [,1052] [,1053] [,1054] [,1055] [,1056] [,1057] [,1058] [,1059] [,1060] [,1061] [,1062] [,1063] [,1064] [,1065] [,1066] [,1067] [,1068] [,1069] [,1070] [,1071] [,1072] [,1073] [,1074] [,1075] [,1076] [,1077] [,1078] [,1079] [,1080] [,1081] [,1082] [,1083] [,1084] [,1085] [,1086] [,1087] [,1088] [,1089] [,1090] [,1091] [,1092] [,1093] [,1094] [,1095] [,1096] [,1097] [,1098] [,1099] [,1100] [,1101] [,1102] [,1103] [,1104] [,1105] [,1106] [,1107] [,1108] [,1109] [,1110] [,1111] [,1112] [,1113] [,1114] [,1115] [,1116] [,1117] [,1118] [,1119] [,1120] [,1121] [,1122] [,1123] [,1124] [,1125] [,1126] [,1127] [,1128] [,1129] [,1130] [,1131] [,1132] [,1133] [,1134] [,1135] [,1136] [,1137] [,1138] [,1139] [,1140] [,1141] [,1142] [,1143] [,1144] [,1145] [,1146] [,1147] [,1148] [,1149] [,1150] [,1151] [,1152] [,1153] [,1154] [,1155] [,1156] [,1157] [,1158] [,1159] [,1160] [,1161] [,1162] [,1163] [,1164] [,1165] [,1166] [,1167] [,1168] [,1169] [,1170] [,1171] [,1172] [,1173] [,1174] [,1175] [,1176] [,1177] [,1178] [,1179] [,1180] [,1181] [,1182] [,1183] [,1184] [,1185] [,1186] [,1187] [,1188] [,1189] [,1190] [,1191] [,1192] [,1193] [,1194] [,1195] [,1196] [,1197] [,1198] [,1199] [,1200] [,1201] [,1202] [,1203] [,1204] [,1205] [,1206] [,1207] [,1208] [,1209] [,1210] [,1211] [,1212] [,1213] [,1214] [,1215] [,1216] [,1217] [,1218] [,1219] [,1220] [,1221] [,1222] [,1223] [,1224] [,1225] [,1226] [,1227] [,1228] [,1229] [,1230] [,1231] [,1232] [,1233] [,1234] [,1235] [,1236] [,1237] [,1238] [,1239] [,1240] [,1241] [,1242] [,1243] [,1244] [,1245] [,1246] [,1247] [,1248] [,1249] [,1250] [,1251] [,1252] [,1253] [,1254] [,1255] [,1256] [,1257] [,1258] [,1259] [,1260] [,1261] [,1262] [,1263] [,1264] [,1265] [,1266] [,1267] [,1268] [,1269] [,1270] [,1271] [,1272] [,1273] [,1274] [,1275] [,1276] [,1277] [,1278] [,1279] [,1280] [,1281] [,1282] [,1283] [,1284] [,1285] [,1286] [,1287] [,1288] [,1289] [,1290] [,1291] [,1292] [,1293] [,1294] [,1295] [,1296] [,1297] [,1298] [,1299] [,1300] [,1301] [,1302] [,1303] [,1304] [,1305] [,1306] [,1307] [,1308] [,1309] [,1310] [,1311] [,1312] [,1313] [,1314] [,1315] [,1316] [,1317] [,1318] [,1319] [,1320] [,1321] [,1322] [,1323] [,1324] [,1325] [,1326] [,1327] [,1328] [,1329] [,1330] [,1331] [,1332] [,1333] [,1334] [,1335] [,1336] [,1337] [,1338] [,1339] [,1340] [,1341] [,1342] [,1343] [,1344] [,1345] [,1346] [,1347] [,1348] [,1349] [,1350] [,1351] [,1352] [,1353] [,1354] [,1355] [,1356] [,1357] [,1358] [,1359] [,1360] [,1361] [,1362] [,1363] [,1364] [,1365] [,1366] [,1367] [,1368] [,1369] [,1370] [,1371] [,1372] [,1373] [,1374] [,1375] [,1376] [,1377] [,1378] [,1379] [,1380] [,1381] [,1382] [,1383] [,1384] [,1385] [,1386] [,1387]
## [1,] -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 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-70
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[,3761] [,3762] [,3763] [,3764] [,3765] [,3766] [,3767] [,3768] [,3769] [,3770] [,3771] [,3772] [,3773] [,3774] [,3775] [,3776] [,3777] [,3778] [,3779] [,3780] [,3781] [,3782] [,3783] [,3784] [,3785] [,3786] [,3787] [,3788] [,3789] [,3790] [,3791] [,3792] [,3793] [,3794] [,3795] [,3796] [,3797] [,3798] [,3799] [,3800] [,3801] [,3802] [,3803] [,3804] [,3805] [,3806] [,3807] [,3808] [,3809] [,3810] [,3811] [,3812] [,3813] [,3814] [,3815] [,3816] [,3817] [,3818] [,3819] [,3820] [,3821] [,3822] [,3823] [,3824] [,3825] [,3826] [,3827] [,3828] [,3829] [,3830] [,3831] [,3832] [,3833] [,3834] [,3835] [,3836] [,3837] [,3838] [,3839] [,3840] [,3841] [,3842] [,3843] [,3844] [,3845] [,3846] [,3847] [,3848] [,3849] [,3850] [,3851] [,3852] [,3853] [,3854] [,3855] [,3856] [,3857] [,3858] [,3859] [,3860] [,3861] [,3862] [,3863] [,3864] [,3865] [,3866] [,3867] [,3868] [,3869] [,3870] [,3871] [,3872] [,3873] [,3874] [,3875] [,3876] [,3877] [,3878] [,3879] [,3880] [,3881] [,3882] [,3883] [,3884] [,3885]
## [1,] -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 -70 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-70
## [,3886] [,3887] [,3888] [,3889] [,3890] [,3891] [,3892] [,3893] [,3894] [,3895] [,3896] [,3897] [,3898] [,3899] [,3900] [,3901] [,3902] [,3903] [,3904] [,3905] [,3906] [,3907] [,3908] [,3909] [,3910] [,3911] [,3912] [,3913] [,3914] [,3915] [,3916] [,3917] [,3918] [,3919] [,3920] [,3921] [,3922] [,3923] [,3924] [,3925] [,3926] [,3927] [,3928] [,3929] [,3930] [,3931] [,3932] [,3933] [,3934] [,3935] [,3936] [,3937] [,3938] [,3939] [,3940] [,3941] [,3942] [,3943] [,3944] [,3945] [,3946] [,3947] [,3948] [,3949] [,3950] [,3951] [,3952] [,3953] [,3954] [,3955] [,3956] [,3957] [,3958] [,3959] [,3960] [,3961] [,3962] [,3963] [,3964] [,3965] [,3966] [,3967] [,3968] [,3969] [,3970] [,3971] [,3972] [,3973] [,3974] [,3975] [,3976] [,3977] [,3978] [,3979] [,3980] [,3981] [,3982] [,3983] [,3984] [,3985] [,3986] [,3987] [,3988] [,3989] [,3990] [,3991] [,3992] [,3993] [,3994] [,3995] [,3996] [,3997] [,3998] [,3999] [,4000] [,4001] [,4002] [,4003] [,4004] [,4005] [,4006] [,4007] [,4008] [,4009] 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-70
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-70
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##
## $spike_counts
## [1] 1
v_nsc <- as.numeric(nsc_cell$fetch_sim_results()$v_traces[1, ])
# ── 4. Reconstruct normalized_spike_cost from v_traces ────────────────────────
# Cell parameters (actual values, after internal scaling)
v_rest_p <- -70 # mV
v_thr_p <- -55 # mV
I_spike_p <- 1e3 # pA
g_leak_p <- 1.0 # nS
v_bound_p <- 1.15 * abs(v_rest_p) # mV (= 80.5)
dHdv_bnd_p <- 1.05 * I_spike_p # pA (= 1050)
n_nsc <- length(v_nsc)
nsc <- rep(NA_real_, n_nsc)
for (t in 2:n_nsc) {
# Sub-threshold voltage and spike flag at the previous step
# (v_traces stores v_sub + spike_height*spike, so clamp at threshold to recover v_sub)
v_sub_prev <- min(v_nsc[t - 1], v_thr_p)
is_spk <- v_nsc[t - 1] > v_thr_p
i_stim_t <- I_nsc[1, t - 1]
# dHdv: net current (outward-positive convention), bounded above by dHdv_bound
dHdv <- min(
-i_stim_t + g_leak_p * (v_sub_prev - v_rest_p) + as.numeric(is_spk) * I_spike_p,
dHdv_bnd_p - .Machine$double.eps
)
# Spike cost and its maximum (DACx.cpp lines 2506–2514)
spike_cost <- dHdv_bnd_p * v_sub_prev - dHdv * v_bound_p
max_spike_cost <- dHdv_bnd_p * v_bound_p - dHdv * v_sub_prev
nsc[t] <- spike_cost / max_spike_cost
}
# ── 5. Build tidy data frame and focus on stimulus onset → just past spike ────
t_ms_nsc <- seq_len(n_nsc) * dt_nsc
first_spk <- which(v_nsc > v_thr_p)[1]
win_start <- round(9 / dt_nsc)
win_end <- min(first_spk + round(1.5 / dt_nsc), n_nsc)
df_nsc <- data.frame(
t = t_ms_nsc[win_start:win_end],
v = v_nsc[win_start:win_end],
nsc = nsc[win_start:win_end]
)
spike_t <- t_ms_nsc[first_spk]
# ── 6. Plot ───────────────────────────────────────────────────────────────────
p_v_nsc <- ggplot(df_nsc, aes(x = t, y = v)) +
geom_vline(xintercept = spike_t, linetype = "dotted", color = "gray60", linewidth = 0.6) +
geom_hline(yintercept = v_thr_p, linetype = "dashed", color = "gray50", linewidth = 0.6) +
geom_line(color = "#2166ac", linewidth = 0.8) +
annotate("text", x = 10.3, y = v_thr_p + 1.5, label = "threshold (−55 mV)",
size = 3, hjust = 0, color = "gray40", fontface = "italic") +
annotate("text", x = spike_t + 0.15, y = 10, label = "spike",
size = 3, hjust = 0, color = "gray40", fontface = "italic") +
scale_x_continuous(expand = c(0.01, 0)) +
labs(title = "A Membrane potential", x = NULL, y = "Membrane potential (mV)") +
theme_bw(base_size = 11) +
theme(plot.title = element_text(face = "bold", size = 11))
p_nsc <- ggplot(df_nsc, aes(x = t, y = nsc)) +
geom_vline(xintercept = spike_t, linetype = "dotted", color = "gray60", linewidth = 0.6) +
geom_vline(xintercept = 10, linetype = "dashed", color = "gray50", linewidth = 0.6) +
geom_hline(yintercept = 0, linetype = "dashed", color = "gray50", linewidth = 0.6) +
geom_line(color = "#d6604d", linewidth = 0.8) +
annotate("text", x = 10.3, y = -0.73, label = "stim on (100 pA)",
size = 3, hjust = 0, color = "gray40", fontface = "italic") +
annotate("text", x = spike_t + 0.15, y = -0.70, label = "spike",
size = 3, hjust = 0, color = "gray40", fontface = "italic") +
scale_x_continuous(expand = c(0.01, 0)) +
labs(title = "B Normalized spike cost", x = "Time (ms)", y = "normalized_spike_cost") +
theme_bw(base_size = 11) +
theme(plot.title = element_text(face = "bold", size = 11))
p_v_nsc / p_nsc +
plot_annotation(
title = "Normalized spike cost in the lead-up to a spike",
subtitle = paste0(
"Leaky integrator cell, 100 pA input from t = 10 ms. ",
"nsc rises from \u2248\u22120.87 at rest to \u2248\u22120.64 at threshold."
),
theme = theme(
plot.title = element_text(size = 12, face = "bold"),
plot.subtitle = element_text(size = 9, color = "gray40")
)
)