§ DATASETS AND SIMULATIONS

§.§ Data sources

Table <ref> contains a complete list
of all experimental data sources for both original and unified

Channel     Gate         Data      N [1]
C [2]     Unified

$I_\text{Na}$     activation, $m$     $m_\infty$    Fig. 2 [3]

$\tau_m$    Fig. 3C [4]

inactivation$^\ast$, $\{h,j\}$     $\{h,j\}_\infty$    Fig. 7 [3]

$\tau_{\{h,j\}}$ (inact.)    Fig. 5B [3]

$\tau_{\{h,j\}}$ (recov.)    Fig. 9 [3]

2*$I_\text{CaL}$     2*activation, $d$
2*$d_\infty$     Fig. 5C [5]$^a$     2*$^a$     2*$^b$     2*$^b$

Fig. 2B [6]$^b$

$\tau_{d}$     Pg. H233 [6]

inactivation$^\dagger$, $f$     $f_\infty$     Fig. 2B [6]

2*$\tau_f$ (inact.)     Fig.
3B [6]$^a$
2*$^a$     2*$^b$

Fig. 4B [7]$^b$

$\tau_f$ (recov.)     Pg. H230 [6]

2*$I_\text{to}$     2*activation, $r$
2*$r_\infty$     Fig. 3A [8]$^a$
2*$^a$     2*$^b$     2*$^b$

Fig. 2A [9]$^b$

$\tau_r$ (act.)     Fig.
5D [2]$^\ddagger$

$\tau_r$ (deact.)     Fig.
5D [2]$^\ddagger$

2*inactivation, $s$     2*$s_\infty$
Fig. 3C [10]$^a$     2*$^a$     2*$^b$     2*$^b$

Fig. 2C [9]$^b$

2*$\tau_s$ (inact.)     Fig.
4C [1]$^{a,\ddagger}$     2*$^a$    2*$^b$    2*$^b$

5D [2]$^{b,\ddagger}$

2*$\tau_s$ (recov.)     Fig.
4C [1]$^{a,\ddagger}$    2*$^a$    2*$^b$    2*$^b$

5D [2]$^{b,\ddagger}$

$I_\text{Kur}$$^\ast$     activation, $a$     $a_\infty$     Fig.
8E [9]

$\tau_a$ (act.)     Fig. 8F [9]

$\tau_a$ (deact.)     Fig. 5B [2]$^\ddagger$

2*inactivation, $i$     2*$i_\infty$
Fig. 3C [10]$^{a,\S}$     2*$^a$    2*$^b$    2*$^a$

Fig. 7A [9]$^{b,\S}$

2*$\tau_i$ (inact.)     Fig.
4D [1]$^{a,\ddagger}$     2*$^a$     2*$^b$     2*$^a$

Fig. 5B [2]$^{b,\ddagger}$

$\tau_i$ (recov.)     Fig. 4D [1]$^\ddagger$

Summary of patch clamp experimental datasets used in modelling papers
in human atrial myocytes for each channel studied. Ticks and crosses are used
to indicate which datasets are included in the original model calibration and
which compose the unified dataset.
$^\ast$There are some differences in the terminology used in each model. The N model refers to the inactivation gates of $I_\text{Na}$ as $h_1$
and $h_2$, and the $I_\text{Kur}$ channel as $I_\text{sus}$.
$^\dagger$The L-type calcium current has a calcium-dependent inactivation process
which is not calibrated in this experiment (discussed further in results).
$^\ddagger$In some cases it was not clear from the modelling paper where the
comparison data plotted were obtained from. In these cases, the data points from the modelling paper
itself are used and a protocol assumed based on the experimental paper cited.
$^\S$In some cases it was not explicit which figure among a number of
possibilities within a cited data source was used; the choice was inferred from the modelling paper.

§.§ Temperature adjustment

The N model was created to simulate a human atrial action potential at
306.15K (33$^\circ C$), whereas the C model was created to simulate
at 310K ($\sim$37$^\circ C$). Time constant measurements of rise and decay rates are temperature-dependent, and thus it was important
to account for this during the calibration.
During ABC, time constant measurements from the experimental
sources were adjusted to the temperature of the model being
calibrated using a Q10 factor from an experimental source.
The Q10 factors used are: $I_\text{Na}$: 2.79 [11];
$I_\text{CaL}$: 1.7 (activation), 1.3 (inactivation), both calculated from
values in [6]; $I_{\{\text{to},\text{Kur}\}}$:
2.2 [9]. In the original publication for
the C model, $I_\text{to}$ and
$I_\text{Kur}$ were fitted at room temperature (295.15K) and then
adjusted by the authors to the model temperature (310K) by
dividing time constants by a factor of 3 [2].
To maintain consistency, we also calibrate the C model at
room temperature rather than make any adjustment to the experimental
data. The time constants for this channel are adjusted before
being used to simulate a full action potential.
The S model was always calibrated by adjusting experimental data
to 310K.
Figure <ref> shows the temperature-adjusted
datasets for all experiments across channel models.

Unified datasets for each channel model showing adjustments to experimental calibrating data at each model
temperature. The adjustment is made using a Q10
factor as indicated in the text. A $I_\text{Na}$. B
$I_\text{CaL}$. C $I_\text{to}$. D $I_\text{Kur}$.

When comparing channel models on the same figure throughout this work,
their time constants are adjusted for the same temperature of
310K. For full action potential simulations, the N and C model time
constants are kept at their model temperature, and only the S
model time constant adjusted from 310K to 306.15K when it is added to the N model.

§.§ Voltage-clamp protocols and summary statistic functions

Throughout this section, the lettering in the headers refers to the figure
describing voltage protocols for the channel.
All curve fitting for finding time constants was carried out using the
scipy.optimize Python library.

§.§.§ $I_\mathrm{Na}$

All experiments by Sakakibara et al. [3]
used equal extracellular and pipette solution sodium concentration of
$5\mathrm{mM}$ at a temperature of $290\mathrm{K}$ ($17^\circ C$). The time
constant of activation experiment from Schneider et
al. [4] used sodium
concentration of $120\mathrm{mM}$ in the extracellular solution and
$70\mathrm{mM}$ in the pipette solution, and the experiment was conducted at
$297\mathrm{K}$ ($24^\circ C$).

A: Steady-state activation
(p.538 [3]).  The standard protocol to
measure steady-state activation of the channel holds the membrane at a
sub-threshold potential of $-140\mathrm{mV}$ and then steps the channel to a
series of voltage steps between $-100\mathrm{mV}$ and $20\mathrm{mV}$, with
intervals of $10\mathrm{mV}$. The steps last for $1\mathrm{s}$ and there are
$10\mathrm{s}$ between each step.

The degree of steady-state activation is measured by recording the peak current
during the voltage step (normalised to cell capacitance). The conductance is
calculated by dividing the peak current by the forcing term, usually assumed to
be the potential difference to the Nernst potential of the primary ion carrier,
$g = \frac{I}{V-E_\mathrm{X}}$. In the computational protocols, we directly
measure the conductance of the channel to bypass this calculation. To plot
the activation curve, the conductance is plotted against the voltage step normalised
to its maximum value in any voltage step.

B: Time constant of activation
(p.85 [4]). The time constant constant of
inactivation is measured by fitting an equation to the current trace from a
standard steady-state activation protocol as described in the previous protocol. In this
case, the holding potential is $-135\mathrm{mV}$ and the steps are from
$-65\mathrm{mV}$ and $15\mathrm{mV}$ in steps of $10\mathrm{mV}$. The time at
holding potential between each step was not given and so assumed to be
$10\mathrm{s}$ (more than enough for the $I_\mathrm{Na}$ channel to return to
steady-state) and each test pulse lasted for $12\mathrm{ms}$.

The activation time constant was measured by fitting the entire current trace
at a pulse to the equation $I_\mathrm{Na} =
(p.87 [4]). In this equation, $t$ is the time in $\mathrm{ms}$,
$I_\mathrm{Na,max}$ is the peak of the current trace, $\tau_\mathrm{m}$ is the
activation time constant and $\tau_\mathrm{h}$ is the inactivation time

C: Steady-state inactivation
(p.541 [3]). The protocol used to measure
steady-state inactivation is often also referred to as an availability
protocol. The membrane is held at a holding potential of $-140\mathrm{mV}$ for
$10\mathrm{s}$, then stepped to a conditioning potential for $1\mathrm{s}$ to
activate and inactivate the channel. The membrane potential is returned to the
holding potential for $2\mathrm{ms}$ before stepping to a test
pulse at $-20\mathrm{mV}$ for $30\mathrm{ms}$. A series of different
conditioning pulses between $-140\mathrm{mV}$ and $-40\mathrm{mV}$ in steps of
$10\mathrm{mV}$ is used to test the amount of inactivation of the channel at different

The steady-state inactivation is measured by recording the peak current during
the test pulse, normalised to the current in a test pulse when no conditioning step
is applied (usually the maximum current amplitude). In the virtual voltage
clamp experiment, we measure conductance directly in this step (which is
equivalent as the forcing is the same during each test pulse and eliminated
during the normalisation).

D: Fast/slow inactivation time constant
(p.539 [3]). The protocol to determine
inactivation time constants is a simple steptrain of test pulses from a holding
potential of $-140\mathrm{mV}$ for $10\mathrm{s}$ to a series of
$100\mathrm{ms}$ test pulses to voltages from $-50\mathrm{mV}$ to
$-20\mathrm{mV}$ in steps of $10\mathrm{mV}$.

The fast and slow inactivation constants are determined by fitting the
decay part of the current trace (after the peak current) to the
(p.538 [3]) where
$A$ are amplitude variables, $t$ is the time and $\tau_\mathrm{f}$ and
$\tau_\mathrm{s}$ are the fast and slow time constants of inactivation

E: Fast/slow recovery time constant
(p.538 [3]). The time constants of recovery
from inactivation were determined using a double pulse protocol. The first
pulse is a conditioning pulse for $1000\mathrm{ms}$ to $-20\mathrm{mV}$
followed by a recovery period to a holding potential between $-140\mathrm{mV}$
and $-90\mathrm{mV}$ in steps of $10\mathrm{mV}$, of varying length between $2-1000\mathrm{ms}$
(this was not specified and we assumed a series of $t_\mathrm{r} = 2^i$
where $i=1,2...10$). The recovery period is followed by a test pulse identical
to the conditioning pulse. We assumed $10\mathrm{s}$ at holding potential between each pair
of pulses.

The recovery time constant is measured through a series of processing steps.
Firstly, the peak current in the test pulse is normalised to the peak current
in the preceding conditioning pulse to give a measurement of proportion of the
channel recovery for each recovery time period. This recovery measure is plotted against the recovery time
period and the resulting curve is fit to a double exponential equation $r =
A_0-A_1e^{-t_\mathrm{r}/\tau_\mathrm{r(f)}}-A_2e^{-t_\mathrm{r}/\tau_\mathrm{r(s)}}$ where $r$ is
the proportion of recovery, $A$ are amplitude parameters, $t$ is the recovery
time period and $\tau_\mathrm{r(f)}$ and $\tau_\mathrm{r(s)}$ are the fast and
slow recovery time constants respectively. These values are calculated for each
holding potential.

Voltage steps and current response (from C model) of
$I_\mathrm{Na}$ protocols. A: steady-state activation,
B: time constant of activation, C: steady-state inactivation, D: fast and slow time
constants of inactivation, E: fast and slow time constants of recovery from
inactivation. The recovery protocol is repeated at multiple holding
potentials (only one shown). See text for details of how the current traces are processed
into summary statistics.

§.§.§ $I_\mathrm{CaL}$

Experiments by Mewes and Ravens [5] were carried out at
room temperature (assumed by authors to be $295\mathrm{K}$) and external solution with calcium
concentration of $1.8\mathrm{mM}$. Those by Li and Nattel [6]
were conducted at $309\mathrm{K}$ with $2.0\mathrm{mM}$ external calcium
concentration.  Experiments by Sun et al. [7] were
completed at room temperature (assumed by authors to be $296\mathrm{K}$) and
external calcium concentration of $1\mathrm{mM}$. It is difficult to estimate
the level of intracellular calcium concentration during these experiments due
to the mechanisms of the intracellular calcium stores and buffering. In our
virtual voltage clamp experiments, the level of the intracellular calcium was
kept constant at the resting value from the published N and C models
(72.5nM and 101.3nM respectively) and, for the S model, set to the same
value as the C model (101.3nM).

A, B: Steady-state activation (p.1309 [5],
p.H228 [6]). In Mewes and Ravens [5],
steady-state activation was assessed using a conventional steptrain protocol
from a holding potential of $-40\mathrm{mV}$ to $450\mathrm{ms}$ steps between
$-35\mathrm{mV}$ to $15\mathrm{mV}$ in intervals of $5\mathrm{mV}$, with
$10\mathrm{s}$ between each pulse.  In Li and
Nattel [6], the activation curve was generated from the
IV curve dataset which used a similar step train protocol. This time the
holding potential was $-80\mathrm{mV}$ and the $300\mathrm{ms}$ test pulses
ranged from $-80\mathrm{mV}$ to $20\mathrm{mV}$ in steps of $10\mathrm{mV}$.
Both activation curves were generated as
described in $I_\mathrm{Na}$ steady-state activation.

B: Activation time constant (p.H233 [6]). The
single activation time constant value was determined from the current trace
evoked during the $10\mathrm{mV}$ test pulse in the activation protocol
from [6]. The activation time constant was estimated by
fitting the upstroke of the normalised current trace to
$I_\mathrm{CaL}=1-Ae^{-t/\tau_\mathrm{a}}$ where $A$ is an amplitude parameter,
$t$ is the time and $\tau_\mathrm{a}$ is the activation time constant.

C: Steady-state voltage-dependent inactivation
(p.H229 [6]). The voltage-dependent steady-state
inactivation was assessed using a standard availability protocol.
Conditioning pulses to a series of voltages between $-80\mathrm{mV}$ and
$50\mathrm{mV}$ in steps of $10\mathrm{mV}$ were followed immediately by a test
pulse to $10\mathrm{mV}$ for $300\mathrm{ms}$.
In [6], there are three datasets using different length
of conditioning pulses of either $150\mathrm{ms}$, $300\mathrm{ms}$ or
$1000\mathrm{ms}$. We use the $1000\mathrm{ms}$ prepulse dataset as this was
used for calibration in both modelling papers. The inactivation curve was
calculated as in $I_\mathrm{Na}$ steady-state inactivation.

D, E: Fast/slow voltage-dependent inactivation time constant
(p.H229-H230 [6], p.H1628 [7]).
Fast and slow inactivation time constants were calculated by fitting a
biexponential equation to the decay portion of the current trace during test
pulses from a holding potential.  In [6], three different
holding potentials were used and we use the same as the modelling papers:
$-80\mathrm{mV}$. Test pulses lasted $300\mathrm{ms}$ to steps between
$-10\mathrm{mV}$ and $30\mathrm{mV}$ in intervals of $10\mathrm{mV}$ (we assume
$10\mathrm{s}$ between pulses).  In [7], the holding
potential was $-80\mathrm{mV}$, test pulses had duration $1000\mathrm{ms}$ with
the same levels as above, and were preceded by a $500\mathrm{ms}$ pulse to
$-40\mathrm{mV}$. In both cases, time constants of inactivation were calculated
by fitting the decay portion of the current trace during the test pulses to
$I_\mathrm{CaL}=A_0+A_fe^{-t/\tau_\mathrm{f}}+A_se^{-t/\tau_\mathrm{s}}$ were
$A$ are amplitude parameters, $t$ is the time and $\tau_\mathrm{f}$ and
$\tau_\mathrm{s}$ are the fast and slow time constants respectively.

F: Fast/slow voltage-dependent recovery time constant
(p.H229-H230 [6]). Recovery time constants were assessed
with a two-pulse protocol as in $I_\mathrm{Na}$ recovery experiments.  In this
case, the holding potentials were $-80\mathrm{mV}$, $-60\mathrm{mV}$ and
$-40\mathrm{mV}$ with conditioning and test pulses both to $10\mathrm{mV}$ for
$300\mathrm{ms}$. Recovery periods were generated from $t_\mathrm{r}=2^i$
where $i=1,2,...,11$ based on the range of data points in Fig
4B [6]. The data was processed as in $I_\text{Na}$
recovery experiments with the exception that a single exponential function was
used to fit the $-80\mathrm{mV}$ recovery curve to give a single (slow)
recovery time constant.

Voltage steps and current response (from N model) of
$I_\mathrm{CaL}$ protocols. A: steady-state
activation [5], B: steady-state and time constant
of activation [6],
C:steady-state inactivation [6], D: fast and slow time
constants of inactivation [6], E: fast and slow time
constants of inactivation [7], F: fast and slow time constants of recovery from
inactivation [6]. The recovery protocol is repeated at multiple holding
potentials (only one shown). See text for details of how the current traces are processed
into summary statistics.

§.§.§ $I_\mathrm{to}$

Experiments by Shibata et al. [8] and Wang et
al. [9] were conducted at room temperature (assumed to
be $295\mathrm{K}$). Firek and Giles [10] used temperature of
$306\mathrm{K}$ ($33^\circ C$). Shibata et al. used an extracellular and
pipette potassium concentration of $4.5\mathrm{mM}$ and $150\mathrm{mM}$
respectively, Wang et al. used $5.4\mathrm{mM}$ and $130\mathrm{mM}$ and Firek
et al. used $5.4\mathrm{mM}$ and $140\mathrm{mM}$.

Some data for $I_\mathrm{to}$ was extracted directly from the N and C modelling
papers [1, 2] as the source of
the comparison experimental data plotted was not clear from the text. In these
cases, conditions were assumed to be the same as the lab which produced the
model.  Thus, conditions for the assumed experimental data from Nygren et
al. [1] was set to the same conditions as Firek and
Giles [10] above, and data from Courtemanche et
al. [2] was assumed to have been
collected at the conditions in Wang et
al. [9].

A, B: Steady-state activation (p.
H1776 [8], p.1065 [9]). In
Shibata et al. [8], steady-state activation was
determined by holding at a potential of $-60\mathrm{mV}$ for $20\mathrm{s}$,
then depolarising for $15\mathrm{ms}$ to a step between $-30\mathrm{mV}$ to
$80\mathrm{mV}$, and finally stepping to $-40\mathrm{mV}$ for $100\mathrm{ms}$.
The activation curve was generated by recording the peak current amplitude in
the final step (the `tail' current). Wang et al. [9] used a standard
steady-state activation protocol with a holding potential of $-80\mathrm{mV}$
to a series of test potentials between $-40\mathrm{mV}$ and $50\mathrm{mV}$ and
measured the peak current during the $1000\mathrm{ms}$ depolarising step
(before processing as above for $I_\mathrm{Na}$).

C: Activation time constant (p.H305 [2]).
Activation time constant data corresponding to that plotted in the modelling
paper could not be found in the cited experimental
source [9]. A simple steptrain protocol as described
in [9] was assumed with a holding potential of
$-50\mathrm{mV}$ and $100\mathrm{ms}$ test pulses. The activaton time course of
$I_\mathrm{to}$ was fitted to a single exponential equation:
$I_\mathrm{to}=A_0-Ae^{-t/\tau_\mathrm{a}}$ where $A$ parameters are
amplitudes, $t$ is the time course and $\tau_\mathrm{a}$ is the activation time

D: Deactivation time constant (p.H305 [2]).
The deactivation time constant data source is also uncertain and it is assumed
to use a similar protocol as in Fig. 9A in Wang et
al. [9]. This protocol holds the membrane potential at
$-50\mathrm{mV}$ for $20\mathrm{s}$ before applying a $10\mathrm{ms}$
conditioning pulse to $50\mathrm{mV}$. This is followed by a test pulse to
elicit a tail current, which is fit to a single exponential (same as the
activation time constant above) to determine the deactivation time constant.

E, F: Steady-state inactivation (p.34 [10],
p.1065 [9]). In Firek and Giles, a standard steady-state
availability protocol was applied as described in more detail in
$I_\mathrm{Na}$ steady-state inactivation. The holding potential is
$-80\mathrm{mV}$, followed by a $400\mathrm{ms}$ conditioning pulse to levels
between $-80\mathrm{mV}$ and $16\mathrm{mV}$, and finally a $400\mathrm{ms}$
test pulse to $0\mathrm{mV}$ to activate the outward current. Wang et
al. [9] similarly uses a standard availability protocol
with the same holding potential followed by $1000\mathrm{ms}$ conditioning
pulse to a range of voltages between $-90\mathrm{mV}$ and $30\mathrm{mV}$
followed by a $1000\mathrm{ms}$ test pulse to $60\mathrm{mV}$. Output was
processed into summary statistics as described in $I_\mathrm{Na}$ steady-state

G, H: Inactivation time constant (p.66 [1],
p.H305 [2]). It was not clear in either N or C model
where experimental comparison data of time constants of inactivation for $I_\mathrm{to}$ were obtained
from. Consequently, simple protocols were assumed based on single-pulse
protocols in experimental papers originating from the same labs.
For [1], a single pulse protocol from a holding
potential of $-80\mathrm{mV}$ to $400\mathrm{ms}$ test pulses between $0\mathrm{mV}$ and
$40\mathrm{mV}$ was applied and the decay phase of the current trace fit to a
single exponential equation as above for activation time constants.
For [2], a similar protocol was assumed based
on [9] with a holding potential of $-50\mathrm{mV}$ and
$100\mathrm{ms}$ test pulses to between $-40\mathrm{mV}$ and $50\mathrm{mV}$.

I, J: Recovery time constant (p.66 [1],
p.H305 [2]). Similarly to the inactivation time
constant data, it was unclear where the recovery data was obtained from for
both N and C models. For the N model, we assume the recovery protocol
in [8] was used. This is a standard two-pulse
recovery protocol with holding potentials of $-100\mathrm{mV}$,
$-80\mathrm{mV}$ and $-60\mathrm{mv}$ and $100\mathrm{ms}$ test pulses to
$20\mathrm{mV}$. For the C model, we assume the protocol
in [9] was used with holding potential between
$-60\mathrm{mV}$ and $40\mathrm{mV}$ and $200\mathrm{ms}$ test pulses to

Voltage steps and current response (from N model) of
all $I_\mathrm{to}$ protocols. From left to right: A: steady-state
activation [8], B: steady-state
activation [9], C: activation time
constants [2], D: deactivation time
constants [2],
E: steady-state inactivation [10], F: steady-state
inactivation [9], G: time
constant of inactivation [1], H: time constant of
inactivation [2], I: time constant of recovery from
inactivation [1], J: time constant of recovery
from inactivation [2]. The recovery protocols
are repeated at multiple holding
potentials (only one shown for each). See text for details of how the current traces are processed
into summary statistics.

§.§.§ $I_\mathrm{Kur}$

Experiments by Wang et al. [9] and Firek and
Giles [10] use the same conditions
stated above for $I_\mathrm{to}$. As before, in some cases it was unclear where
the comparison data in the modelling papers was obtained from. Details are
given in the following sections.

A: Steady-state activation, activation time constant (p.1069 [9]).
$I_\mathrm{Kur}$ was measured from a holding potential of $-50\mathrm{mV}$ followed by a
$1\mathrm{s}$ prepulse to $50\mathrm{mV}$ (experimentally used to inactivate
the $I_\mathrm{to}$ current which would otherwise interfere with isolating
$I_\mathrm{Kur}$). The potential is returned to $-50\mathrm{mV}$ for
$20\mathrm{ms}$ before being stepped to a range of $100\mathrm{ms}$ test pulses between
$-40\mathrm{mV}$ to $50\mathrm{mV}$ each followed by a repolarising pulse to $-10\mathrm{mV}$.
$I_\mathrm{Kur}$ was measured as the peak current in the final repolarising
pulse and the activation curve determined as previously described for $I_\mathrm{Na}$
steady-state activation. The activation time constants were determined by fitting the time course of
$I_\mathrm{Kur}$ trace during the test pulses to a single exponential function
as described above.

B: Deactivation time constant (p.305 [2]).
As it was not clear where the data points were obtained from, the protocol from
Fig. 9 in [9] was assumed to have been used. This is the
same protocol as described in deactivation time constant for $I_\mathrm{to}$.

C, D: Steady-state inactivation (p.34 [10],
p.1068 [9]). For Firek and
Giles [10], the protocol was the same as the steady-state
inactivation protocol described for steady-state inactivation of
$I_\mathrm{to}$ with an increase of the length of the conditioning pulse from
$400\mathrm{ms}$ to $2500\mathrm{ms}$. $I_\mathrm{Kur}$ was measured as the
steady-state current at the end of the test pulse. In Wang et
al. [9], steady-state inactivation is measured from the
steady-state current at the end of a $2000\mathrm{ms}$ test pulse to
$40\mathrm{mV}$ after a $1000\mathrm{ms}$ conditioning pulse from a range of
voltages. The holding potential was $-60\mathrm{mV}$.

E, F: Inactivation time constant (p.66 [1],
p.H305 [2]). It was unclear where the experimental
data points from the N model paper came from. We assume they are generated from
the protocol used in [10] from the same lab. This protocol
is a simple $400\mathrm{ms}$ step to a range of potentials from a holding potential of
$-80\mathrm{mV}$. In [10], the current decay is fit to a
double exponential equation in order to separate $I_\mathrm{to}$ and
$I_\mathrm{Kur}$ decay rates. As in the virtual voltage clamp there is only
$I_\mathrm{Kur}$, we fit the current decay to a single exponential.

Similary for the C model, we assume a similar protocol as
in [9] was used. This is a simple $2000\mathrm{ms}$ step
to a range of test potentials from a holding potential of $-50\mathrm{mV}$. The
decay portion of the current trace is fit to a single exponential function as

G: Recovery time constant (p.66 [1]). As
previously for $I_\mathrm{to}$, we assume that the recovery protocol
from [8] was used to determine a recovery time
constant for $I_\mathrm{Kur}$. The protocol is as described for $I_\mathrm{to}$
recovery time constant.

Voltage steps and current response (from N model) of
all $I_\mathrm{Kur}$ protocols. A: steady-state
activation and activation time constant [9],
B: deactivation time constants [2],
C: steady-state inactivation [10], D: steady-state
inactivation [9], E: time
constant of inactivation [1], F: time constant of
inactivation [2], G: time constant of recovery from
inactivation [1]. See text for details of
how the current traces are processed into summary statistics.

§ APPROXIMATE BAYESIAN COMPUTATION

Formally, ABC approximates the true parameter posterior distribution
$P(\boldsymbol{\lambda}|\boldsymbol{D})$ by
where $\boldsymbol{D}$ are the experimental data, $\rho$ is the chosen distance
function, $\boldsymbol{\hat{D}}$ is the model summary statistics and $\epsilon$
is the threshold value.  We use the Toni ABC sampler based on sequential Monte Carlo to infer our
parameter posterior distributions [12]. In this
sampler, the ABC process above is repeated through a number of iterations with
reducing $\epsilon$. A population of parameter samples, referred to as
`particles', are propagated through each iteration and represent a discrete
surrogate to the continuous posterior distribution.

At each iteration of the
algorithm, the previous population of particles are perturbed slightly, by a
multivariate Gaussian kernel, and used as the prior distribution for the
current iteration. $\epsilon$ is reduced over iterations and chosen as the
median distance of samples from the previous
iteration. The particle population number is
set according to the number of parameters being constrained in the experiment
by considering the size of the parameter sampling hyperspace and assuming at
least two particles in each dimension. A limit of 10000 particles is enforced
due to computational demands. The algorithm terminates when less than 1% of
parameter samples are accepted in a given iteration indicating the algorithm is
struggling to improve on the current optimum. This criterion is chosen over
termination at an absolute value of the distance metric termination used in
other studies due to differences in number of model parameters and availability
of data between experiments.

To compare our model summary statistics to
the experimental data (which include error measurements at each point),
we use a weighted Euclidean distance function

\begin{align}
\begin{split}
\rho(\boldsymbol{\hat{D}}, \boldsymbol{D})
&=\left[\sum_{i=0}^M \left( \frac{\hat{D}_i - D_i}{w_i} \right)^2
\right]^{1/2},\\
w_i &= \text{max}\left(\sigma_i,\delta\right) n_{\text{exp}|i},
\end{split}
\end{align}

where $w_i$ are the weights for each data point, $\sigma_i$ is the standard
deviation associated with the error at each data point, $\delta$ is a
regularisation factor applied when weights are close to zero, and $n_{\text{exp}|i}$
is the number of data points within the experiment. In this
work $\delta$ was set to 0.05. Once generated, the weights
are also mean-normalised to improve convergence of the ABC
algorithm. The choice of distance
function reduces the weighting of data points based on the magnitude of
experimental uncertainty. This allows us to use information of which
experimental data points we are relatively more confident about during the
model calibration, propagating some of the experimental uncertainties
through to this stage in the model development [13].
In some cases for $I_\text{to}$ and $I_\text{Kur}$,
it was not clear in the modelling paper where the data were obtained. In these
cases, the points displayed in the figure from the modelling paper were
digitised and 10% standard deviation error assumed (based on the error of
similar measurements given in [9]).

Additionally, we account for the fact that we are simultaneously calibrating
to multiple datasets by weighting according to the number of data points in a
specific experiment. This provides balance between the different types of
channel behaviour, rather than favouring an experiment with a greater number of data
points. Each dataset is normalised to the maximum value in that experiment to avoid
preference towards datasets with measurements at a larger scale in the ABC loss

A uniform prior distribution is used for each model parameter in the first
iteration. The width of this prior is set to be sufficiently wide to cover the
range of physiological possibilities. After convergence, the parameter
posterior distributions are inspected and, if observed to be restricted by the
lower or upper limit of the prior, the calibration is re-started with a wider
prior. For the S model, prior ranges are set as in [14].

§ ADDITIONAL RESULTS

§.§ Gating functions for calibrations to original and unified datasets

A-D Steady-state and time constant functions for each channel of the
N model using original calibration dataset and unified dataset. Blue
refers to original dataset and orange to unified dataset.
Data displayed as median line with shading representing
89% HDPI of 100 samples from the parameter posterior distribution.

A-D Steady-state and time constant functions for each channel of the
C model using original calibration dataset and unified dataset. Blue
refers to original dataset and orange to unified dataset.
Data displayed as median line with shading representing
89% HDPI of 100 samples from the parameter posterior distribution.
Note for $I_\text{Na}$ and
$I_\text{to}$ the original and unified dataset are the same.

§.§ $I_\mathrm{CaL}$

A Number of gating parameters in equations for
each $I_\text{CaL}$ model, separated into activation (dark)
and inactivation (light).
B Example traces from each model generated from the last
step of a train of 100 steps from -80 mV to -10 mV for 200 ms at a rate of
1 Hz using 100 samples from the parameter posterior distributions. Higher detail of the activation portion
of the trace is shown in
the inset plot.
Output is summarised as median line with shading
representing 89% HDPI.
Dashed lines indicate
the response of the published N and C models.
C Boxplot comparing runtime of the simulation to
generate each trace in B for each model.

§.§ $I_\mathrm{to}$

A Steady-state and time constant functions for
$I_\text{to}$ model. Plotted as median line
with shading indicated 89% HDPI from 100 samples
from the parameter posterior distribution. Dashed lines indicate the published values.
B Example traces from each model
generated from the last step of a pulse train of 100 steps from -50 mV to -10 mV
for 100 ms at a rate of 1 Hz using samples in A.
Higher detail of activation portion of trace is shown in inset.
Dashed lines indicate
the published N and C models. The boxplot below compares runtime of the simulations to generate the above traces for each model.

§.§ $I_\mathrm{Kur}$

A Results of calibrating each $I_\text{Kur}$ model to the
unified dataset.
Model output is plotted as median with shading
representing 89% HDPI generated from 100 samples from
parameter posterior distributions.
B Example traces from each model
generated from the last step of a pulse train of 100 steps from -50 mV to -10 mV
for 1000 ms at a rate of 0.1 Hz using samples from A.
Dashed lines indicate
the original N and C models.
Higher detail of activation portion of trace is shown in inset plot.
Boxplot compares runtime of simulations to generate
the traces above for each model.
C Steady-state and time
constant functions for each gate generated from samples in A displayed as median lines with shading showing 89% HDPI.
Dashed lines indicate original N and C models.
D Number of gating parameters (top-left).
Dark and light shading correspond to activation gate
and inactivation gate parameters respectively.
Goodness of fit assessed by converged residuals
from ABC (top-right). RSD of parameter posteriors (bottom).
Mann-Whitney U-test used to test significance.

§.§ Goodness-of-fit residuals

Min-max normalised residuals by experiment and model. Experiment ID follows order of appearance in main
figure for that channel.

§.§ Action potential response

Comparison of action potential morphology and major ion currents
underlying the action potential in published N and C models of the human atrial
cardiomyocyte. Inset graphs show more detail of the shaded time portion
in the main graphs. Action potentials were stimulated by 100s of pacing at a basic cycle length of 1 s using a stimulus current of 40
pA/pF for 1 ms. The plot shows the final pulse from the
pulse train protocol.

Action potential, major currents and intracellular
calcium concentrations for A: N model and B: C model. Traces
using published parameters are represented with dashed lines.
Samples from the full cell model with $I_\mathrm{CaL}$
replaced by the unified recalibrated parameterisation are displayed as a median line with 89% high density
posterior intervals. The orange plot highlights the channel
that is recalibrated using the parameter posterior distribution
from ABC. All other model parameters are unchanged from
published values.

Action potential, major currents and intracellular
calcium concentrations for A: N model and B: C model, with
the S form of $I_\mathrm{CaL}$ replacing the original form. Traces
using published parameters are represented with dashed lines.
Samples from the full cell model with $I_\mathrm{CaL}$
replaced by the unified recalibrated parameterisation are displayed as a median line with 89% high density
posterior intervals. The orange plot highlights the channel
that is replaced with the standardised model and using the parameter posterior distribution
from ABC. All other model parameters are unchanged from
published values.

Action potential, major currents and intracellular
calcium concentrations for A: N model and B: C model. Traces
using published parameters are represented with dashed lines.
Samples from the full cell model with $I_\mathrm{to}$
replaced by the unified recalibrated parameterisation are displayed as a median line with 89% high density
posterior intervals.. The orange plot highlights the channel
that is recalibrated using the parameter posterior distribution
from ABC. All other model parameters are unchanged from
published values.

Action potential, major currents and intracellular
calcium concentrations for A: N model and B: C model, , with
the S form of $I_\mathrm{to}$ replacing the original form. Traces
using published parameters are represented with dashed lines.
Samples from the full cell model with $I_\mathrm{to}$
replaced by the unified recalibrated parameterisation are displayed as a median line with 89% high density
posterior intervals. The orange plot highlights the channel
that is replaced with the standardised model and using the parameter posterior distribution
from ABC. All other model parameters are unchanged from
published values.

Action potential, major currents and intracellular
calcium concentrations for A: N model and B: C model. Traces
using published parameters are represented with dashed lines.
Samples from the full cell model with $I_\mathrm{Kur}$
replaced by the unified recalibrated parameterisation are displayed as a median line with 89% high density
posterior intervals. The orange plot highlights the channel
that is recalibrated using the parameter posterior distribution
from ABC. All other model parameters are unchanged from
published values.

Action potential, major currents and intracellular
calcium concentrations for A: N model and B: C model, , with
the S form of $I_\mathrm{Kur}$ replacing the original form. Traces
using published parameters are represented with dashed lines.
Samples from the full cell model with $I_\mathrm{Kur}$
replaced by the unified recalibrated parameterisation are displayed as a median line with 89% high density
posterior intervals. The orange plot highlights the channel
that is replaced with the standardised model and using the parameter posterior distribution
from ABC. All other model parameters are unchanged from
published values.

Model     Measure (units)     Published     $I_\mathrm{CaL}$ (89% HDPI)     $I_\mathrm{to}$ (89% HDPI)     $I_\mathrm{Kur}$ (89% HDPI)
N     RP (mV)             -74.1        -73.7 (-76.3, -17.5)            -72.7 (-72.7, -72.5)           -62.2 (-63.0, -61.4)

AMP (mV)            114.3         113.4 (39.0, 115.8)              113.4 (113.1, 113.6)           95.0 (94.2, 95.8)

APD90 (ms)          223.2         217.5 (16, 295)                   271 (266, 280)                 298 (295, 302)
C     RP (mV)             -81.2         -81.7 (-81.8, -81.6)            -81.3 (-81.4, -81.2)           -81.6 (-81.8, -80.9)

AMP (mV)            110.9         112.5 (112.3, 112.9)              109.4 (107.5, 110.9)           111.2 (109.8, 111.8)

APD90 (ms)          288.5         211 (189, 246)                   257 (247, 266)                 237.5 (190, 304)
N+S     RP (mV)             -74.1        -76.3 (-76.7, -70.3)            -73.2 (-73.2, -73.1)           -62.2 (-66.1, -58.0)

AMP (mV)            114.3         118.6 (106.1, 120.3)              110.8 (110.6, 111.0)           93.9 (88.2, 98.8)

APD90 (ms)          223.2         172.5 (131, 233)                   248 (245, 249)                 286 (283, 293)
C+S     RP (mV)             -81.2         -81.5 (-82.0, -27.1)            -81.2 (-81.2, -81.2)           -81.9 (-82.0, -81.8)

AMP (mV)            110.9         111.7 (39.4, 112.9)              109.2 (109.1, 109.3)           107.6 (106.4, 108.9)

APD90 (ms)          288.5         192 (35, $\infty$)                   267 (264, 270)                 179.5 (150, 206)

Effect on full AP of using parameter posterior distributions
to calibrate channel models. Measurements taken are
resting potential (RP), action potential amplitude (AMP) and
action potential duration to 90% repolarisation (APD90).
N: Nygren model, C: Courtemanche model, +S: represents the
indicated channel was replaced with the standardised form
in the full AP model.

§ MODEL EQUATIONS AND NUMERICAL RESULTS

§.§ $I_\mathrm{Na}$

\[
\begin{aligned}
I_{\mathrm{Na}}&=P_{\mathrm{Na}} m^{3}\left(\mathbf{s_1} h_{1}+(1-\mathbf{s_1}) h_{2}\right)\left[\mathrm{Na}^{+}\right]_{\mathrm{c}} \mathrm{V} \frac{\mathrm{F}^{2}}{\mathrm{RT}} \frac{e^{\left(\mathrm{V}-\mathrm{E}_\mathrm{Na}\right) \mathrm{F} / \mathrm{RT}}-1.0}{e^{\mathrm{VF} / \mathrm{RT}}-1.0}\\
\frac{\mathrm{d}m}{\mathrm{dt}}&=\frac{\widebar{m}-m}{\tau_{m}},\qquad
\frac{\mathrm{d}h_1}{\mathrm{dt}}=\frac{\widebar{h}-h_1}{\tau_{h_1}},\qquad
\frac{\mathrm{d}h_2}{\mathrm{dt}}=\frac{\widebar{h}-h_2}{\tau_{h_2}}\\
\widebar{m} &= \frac{1.0}{1.0+e^{-(\mathrm{V}+\mathbf{r_1})/\mathbf{r_2}}},\qquad
\tau_m = 1000(\mathbf{r_3} e^{-((\mathrm{V}+\mathbf{r_4})/\mathbf{r_5})^2} + \mathbf{r_6})\\
%r_1&=27.12, r_2=8.21, r_3=4.2\mathrm{e}{-5}, r_4=25.57, r_5=28.8,
\widebar{h} &= \frac{1.0}{1.0+e^{(\mathrm{V}+\mathbf{q_1})/\mathbf{q_2}}}\\
\tau_{h_1} &= 1000\left(\frac{\mathbf{q_3}}{1.0+e^{(\mathrm{V}+\mathbf{q_4})/\mathbf{q_5}}}+\mathbf{q_6}\right),\qquad
\tau_{h_2} = 1000\left(\frac{\mathbf{q_7}}{1.0+e^{(\mathrm{V}+\mathbf{q_4})/\mathbf{q_5}}}+\mathbf{q_8}\right)\\
%q_1&=63.6, q_2=5.3, q_3=0.03, q_4=35.1, q_5=3.2,
%q_6=3\mathrm{e}{-4}, q_7=0.12, q_8=3\mathrm{e}{-3}\\
\end{aligned}
\]

Gating kinetics in Nygren model of $I_\text{Na}$ channel
current(see Table 6 in [1]). Time constants are multiplied by 1000 to convert from $s$ to

3cOriginal                        3cUnified
1c89% HDPI
1c89% HDPI
r1       27.12          $\mathcal{U}$(0, 100)    52.25         (50.93, 53.52)             -1.795            42.83         (33.91, 55.13)             -0.7966

r2       8.21           $\mathcal{U}$(0, 20)     10.69         (9.769, 11.64)             -1.256            13.19         (7.761, 19.94)             -0.5127

r3$^\ast$       4.2e-05        $\mathcal{U}$(-6, -3)     2.097e-05     (1.009e-06, 0.000325)      -0.749            1.371e-05     (1.002e-06, 0.0002247)     -0.7856

r4       25.57          $\mathcal{U}$(0, 100)    57.99         (22.82, 99.97)             -0.3404           56.79         (16.97, 99.79)             -0.293

r5       28.8           $\mathcal{U}$(0, 20)     9.979         (0.2856, 17.75)            -0.2282           8.932         (0.03437, 17.49)           -0.1981

r6$^\ast$       2.4e-05        $\mathcal{U}$(-6, -3)     2.191e-05     (1.001e-06, 0.0005717)     -0.7021           9.662e-05     (5.195e-05, 0.0001536)     -1.43

q1       63.6               $\mathcal{U}$(0, 200)     95.57         (95.11, 96.11)             -2.465            93.94         (88.3, 99.55)              -1.4

q2       5.3                $\mathcal{U}$(0, 20)     6.5           (6.085, 6.841)             -1.432            8.182         (1.222, 13.13)             -0.3487

q3$^\ast$       0.03               $\mathcal{U}$(-3, 0)     0.09214       (0.001002, 0.4502)         -0.1696           0.004096      (0.002543, 0.02547)        -0.7312

q4       35.1               $\mathcal{U}$(0, 100)     34.98         (0.1474, 147.7)            -0.02249          53.57         (48.79, 57.53)             -1.263

q5       3.2                $\mathcal{U}$(0, 20)     12.76         (4.548, 19.99)             -0.361            10.61         (7.184, 13.18)             -0.7463

q6$^\ast$       0.0003             $\mathcal{U}$(-5, -2)     0.0002548     (1.002e-05, 0.004472)      -0.6137           0.0002403     (1.006e-05, 0.001556)      -0.7811

q7$^\ast$       0.12               $\mathcal{U}$(-3, 0)    0.07443       (0.001005, 0.3999)         -0.1983           0.02022       (0.002551, 0.02706)        -0.6835

q8$^\ast$       0.003              $\mathcal{U}$(-4, -1)    0.002224      (0.0001001, 0.04665)       -0.4589           0.0005268     (0.0001001, 0.00171)       -0.9219

s1       0.9                $\mathcal{U}$(0, 1)     0.5015        (0.08985, 0.9754)          -0.2317           0.4717        (0.1367, 0.8259)           -0.334

Summary of results for parameters of Nygren $I_\text{Na}$ model using original and unified dataset.
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space based on the scale of their published values and are presented in linear space. The prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

\[
\begin{aligned}
I_{\mathrm{Na}}&=g_\text{Na}m^3 h j (\mathrm{V}-\mathrm{E}_\mathrm{Na})\\
\frac{\mathrm{d}\phi}{\mathrm{dt}}&=\frac{\phi_\infty-\phi}{\tau_\phi},\qquad\text{ for } \phi=m, h, j\\
\tau_\phi &= \left(\alpha_\phi + \beta_\phi\right)^{-1},\qquad \phi_\infty=\alpha_\phi\tau_\phi,\qquad\text{ for } \phi=m, h, j\\
\alpha_{m}&=\left\{\begin{array}{l}{\mathbf{a_{m,2}} \frac{\mathrm{V}-\mathbf{a_{m,1}}}{1-e^{-\mathbf{a_{m,3}}(\mathrm{V}-\mathbf{a_{m,1}})}}} \\{\mathbf{a_{m,4}}, \text { if } \mathrm{V}=\mathbf{a_{m,1}}}\end{array}\right.,\qquad
\beta_{m}=\mathbf{b_{m,1}}e^{-\mathrm{V}/\mathbf{b_{m,2}}}\\
\alpha_{h}&=\left\{\begin{array}{l}{\mathbf{a_{h,1}} e^{(\mathrm{V}+\mathbf{a_{h,3}})/-\mathbf{a_{h,2}}}} \\
{a_{h,5},\qquad \text { if } \mathrm{V}\geq\mathbf{c_{h,1}}}
\end{array}\right.,\qquad
a_{h,5}=\mathbf{a_{h,1}} e^{(\mathbf{c_{h,1}}+\mathbf{a_{h,3}})/-\mathbf{a_{h,2}}}\\
\beta_{h}&=\left\{\begin{array}{ll}
{\mathbf{b_{h,4}} e^{\mathbf{b_{h,5}} \mathrm{V}}+\mathbf{b_{h,6}} e^{\mathbf{b_{h,7}} \mathrm{V}}} \\
{\left(b_{h,1}\left[1.0+e^{(V+\mathbf{b_{h,2}})/-\mathbf{b_{h,3}}}\right]\right)^{-1},} & {\text { if } V \geq\mathbf{c_{h,1}}}
\end{array}\right.\\
b_{h,1} &= \left(\mathbf{b_{h,4}}e^{\mathbf{b_{h,5}}\mathbf{c_{h,1}}} + \mathbf{b_{h,6}} e^{\mathbf{b_{h,7}}\mathbf{c_{h,1}}}\right)^{-1} \left(1.0+e^{(\mathbf{c_{h,1}}+\mathbf{b_{h,2}})/-\mathbf{b_{h,3}}}\right)^{-1}\\
\alpha_{j}&=\left\{\begin{array}{l}
[\left.-\mathbf{a_{j,1}} e^{\mathbf{a_{j,2}} \mathrm{V}}-\mathbf{a_{j,3}} e^{-\mathbf{a_{j,4}} \mathrm{V}}\right] \frac{\mathrm{V}+a_{j,5}}{1.0+e^{\mathbf{a_{j,6}}(\mathrm{V}+\mathbf{a_{j,7}})}} \\
{0, \quad \text { if } V \geq\mathbf{c_{j,1}}}
\end{array}\right.,\qquad
a_{j,5} = -\mathbf{c_{j,1}}\\
\beta_{j}&=\left\{\begin{array}{l}
{\mathbf{b_{j,5}} \frac{e^{-\mathbf{b_{j,6}} \mathrm{V}}}{1+e^{-\mathbf{b_{j,7}}(\mathrm{V}+\mathbf{b_{j,8}})}}} \\
{ b_{j,1}\frac{e^{-b_{j,2}\mathrm{V}}}{1+e^{-\mathbf{b_{j,3}}(\mathrm{V}+\mathbf{b_{j,4}})}}, \quad \text { if } V \geq\mathbf{c_{j,1}}}
\end{array}\right.,\qquad\\
b_{j,1}&= \mathbf{b_{j,5}} \frac{e^{\mathbf{-b_{j,6}} \mathbf{c_{j,1}}}}{1 + e^{\mathbf{-b_{j,7}} (\mathbf{c_{j,1}} + \mathbf{b_{j,8}})}} \left[\frac{e^{-b2_j \mathbf{c_{j,1}}}}{(1 + e^{-\mathbf{b_{j,3}} (\mathbf{c_{j,1}} + \mathbf{b_{j,4}})}}\right]^{-1},\qquad
\end{aligned}
\]

Gating kinetics in Courtemanche model of $I_\text{Na}$ channel
current (see Appendix in [2]). Values of $a_{h,5}$, $b_{h,1}$, $a_{j,5}$ and $b_{j,1}$ are set to
enforce continuity in piecewise functions.
$b_{j,2}$ is set to zero to reduce dimensionality of the calibration
problem as the published parameter was effectively zero ($2.535\times 10^{-7}$).

1c89% HDPI
$a1_m$     -47.13        $\mathcal{U}(-100, 0)$     -75.97        (-79.77, -73.65)          -1.586

$a2_m$     0.32          $\mathcal{U}(0, 1)$     0.2639        (0.2476, 0.2741)          -1.476

$a3_m$     0.1           $\mathcal{U}(0, 1)$     0.3355        (0.1947, 0.7643)          -0.2765

$a4_m$     3.2           $\mathcal{U}(0, 10)$     4.895         (1.699, 9.998)            -0.2421

$b1_m$     0.08          $\mathcal{U}(0, 10)$     1.263         (1.225, 1.322)            -1.64

$b2_m$     11.0          $\mathcal{U}(0, 100)$     23.21         (22.48, 23.74)            -1.774
$a1_h^\ast$     0.135         $\mathcal{U}(-2, 1)$     0.3845        (0.01157, 3.35)           0.269

$a2_h$     6.8           $\mathcal{U}(0, 50)$     15.48         (14.49, 15.99)            -1.465

$a3_h$     80.0          $\mathcal{U}(0, 200)$     122.2         (67.51, 155.4)            -0.6085

$b2_h$     10.66         $\mathcal{U}(0, 100)$     18.35         (5.525, 31.86)            -0.3218

$b3_h$     11.1          $\mathcal{U}(0, 50)$     16.73         (12.42, 21.47)            -0.7582

$b4_h^\ast$     3.56          $\mathcal{U}(-1, 2)$     15.11         (14.51, 15.79)            -1.999

$b5_h^\ast$     0.079         $\mathcal{U}(-3, 0)$     0.05808       (0.05716, 0.05887)        -2.492

$b6_h^\ast$     310000.0      $\mathcal{U}(3, 6)$     21500.0       (1002.0, 321300.0)        -0.6777

$b7_h^\ast$     0.35          $\mathcal{U}(-2, 1)$     1.327         (0.2776, 6.324)           0.4741

$c1_h$     -40.0         $\mathcal{U}(-100, 0)$     -37.27        (-45.94, -32.91)          -0.8902
$a1_j^\ast$     127100.0      $\mathcal{U}(3, 7)$     123700.0      (1180.0, 4778000.0)       -0.6361

$a2_j^\ast$     0.2444        $\mathcal{U}(-2, 2)$     5.144         (0.1528, 50.75)           0.02476

$a3_j^\ast$     3.474e-05     $\mathcal{U}(-5, -1)$     0.0003798     (1.015e-05, 0.001191)     -0.7783

$a4_j^\ast$     0.04391       $\mathcal{U}(-4, 0)$     0.003784      (0.0001, 0.02896)         -0.5131

$a6_j$     0.311         $\mathcal{U}(0, 1)$     0.4461        (0.01244, 0.8846)         -0.2087

$a7_j$     79.23         $\mathcal{U}(0, 100)$     41.53         (4.671, 91.36)            -0.1966

$b3_j$     0.1           $\mathcal{U}(0, 1)$     0.4481        (0.001746, 0.8611)        -0.1977

$b4_j$     32.0          $\mathcal{U}(0, 100)$     67.64         (21.51, 99.97)            -0.3641

$b5_j$     0.1212        $\mathcal{U}(0, 1)$     0.3552        (0.04405, 0.7968)         -0.1691

$b6_j^\ast$     0.01052       $\mathcal{U}(-4, 0)$     0.001531      (0.0001004, 0.01829)      -0.5618

$b7_j$     0.1378        $\mathcal{U}(0, 1)$     0.2679        (0.0008117, 0.7773)       -0.09422

$b8_j$     40.14         $\mathcal{U}(0, 100)$     72.38         (31.39, 99.94)            -0.4359

$c1_j$     -40.0         $\mathcal{U}(-100, 0)$     -33.07        (-74.3, -0.5147)          -0.179

Summary of results for parameters of Courtemanche $I_\text{Na}$
model using original/unified (equivalent) dataset.
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space based on the scale of their published values and are presented in linear space. The prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

1c89% HDPI
$p_1^\ast$      $\mathcal{U}$(1, 5)     5134.0       (1620.0, 9786.0)         -1.241

$p_2$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.2)     0.126        (0.1048, 0.1524)         -0.9488

$p_3^\ast$     $\mathcal{U}$(-3, 1)    3.374        (0.5586, 6.144)          -0.2008

$p_4$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)    0.0234       (0.002225, 0.04426)      -0.2237

$p_5^\ast$     $\mathcal{U}$(-1, 3)    6.091        (5.572, 6.662)           -1.495

$p_6$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.2)    0.0441       (0.04209, 0.04601)       -1.523

$p_7^\ast$     $\mathcal{U}$(-4, 0)    0.005353     (0.004147, 0.006667)     -1.496

$p_8$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.2)    0.04053      (0.03871, 0.04302)       -1.44

$A^\ast$       $\mathcal{U}$(0, 1)    4.195        (4.049, 4.314)           -1.869

Summary of results for parameters of standardised $I_\text{Na}$
model using unified dataset. $^\ast$Parameters were searched in $\mathrm{log}_{10}$ space and are presented in linear space. The prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

§.§ $I_\mathrm{CaL}$

\[
\begin{aligned}
I_{\mathrm{CaL}}&=\bar{g}_{\mathrm{Ca}, \mathrm{L}} d_{\mathrm{L}}\left[f_{\mathrm{Ca}} f_{\mathrm{L}_{1}}+\left(1-f_{\mathrm{Ca}}\right) f_{\mathrm{L}_{2}}\right]\left(\mathrm{V}-\mathrm{E}_{\mathrm{Ca}, \mathrm{app}}\right)\\
\frac{\mathrm{d}d_{\mathrm{L}}}{\mathrm{dt}}&=\frac{\widebar{d_{\mathrm{L}}}-d_\mathrm{L}}{\tau_{d_{\mathrm{L}}}},\qquad
\frac{\mathrm{d}f_{\mathrm{L}_{1}}}{\mathrm{dt}}=\frac{\widebar{f_{\mathrm{L}}}-f_{\mathrm{L}_{1}}}{\tau_{f_{\mathrm{L}_{1}}}},\qquad
\frac{\mathrm{d}f_{\mathrm{L}_{2}}}{\mathrm{dt}}=\frac{\widebar{f_{\mathrm{L}}}-f_{\mathrm{L}_{2}}}{\tau_{f_{\mathrm{L}_{2}}}}\\
\widebar{d_{\mathrm{L}}}&=\frac{1.0}{1.0+e^{(\mathrm{V}+\mathbf{p_1}) /-\mathbf{p_2}}},\qquad
\tau_{d_{\mathrm{L}}}= 1000\left(\mathbf{p_3} e^{-((\mathrm{V}+\mathbf{p_4}) / \mathbf{p_5})^{2}}+\mathbf{p_6}\right)\\
\widebar{f_{\mathrm{L}}}&=\frac{1.0}{1.0+e^{(\mathrm{V}+\mathbf{q_1}) / \mathbf{q_2}}}\\
\tau_{f_{\mathrm{L}_{1}}}&=1000\left(\mathbf{q_3} e^{-((\mathrm{V}+\mathbf{q_4}) / \mathbf{q_5})^{2}}+\mathbf{q_6}\right),\qquad
\tau_{f_{\mathrm{L}_{2}}}=1000\left(\mathbf{r_1} e^{-((\mathrm{V}+\mathbf{r_2}) / \mathbf{r_3})^{2}}+\mathbf{r_4}\right)\\
\end{aligned}
\]

Gating kinetics in Nygren model of $I_\text{CaL}$ channel
current (see Table 7 in [1]). Time constants are multiplied by 1000 to convert from $s$ to

3cOriginal                        3cUnified
1c89% HDPI
1c89% HDPI
p1       9.0         $\mathcal{U}$(-100, 100)     2.684        (2.529, 2.906)           -1.29             9.317         (5.103, 10.51)             -0.5683

p2       5.8         $\mathcal{U}$(0, 50)     5.055        (5.022, 5.083)           -2.416            7.378         (6.679, 8.916)             -0.9407

p3$^\ast$       0.0027      $\mathcal{U}$(-7, 3)    0.1048       (0.096, 0.1063)          -1.869            0.001129      (1e-07, 0.02533)           -0.2353

p4       35.0        $\mathcal{U}$(-100, 100)    -11.51       (-11.6, -11.36)          -2.151            -39.18        (-99.98, 74.02)            0.4508

p5       30.0        $\mathcal{U}$(0, 50)    18.58        (18.39, 18.86)           -2.078            28.21         (6.568, 49.05)             -0.2817

p6$^\ast$       0.002       $\mathcal{U}$(-7, 3)    0.00996      (0.009237, 0.0108)       -1.919            0.0009303     (1.027e-07, 0.0009643)     -0.5757
q1       27.4        $\mathcal{U}$(0, 100)    32.02        (21.21, 47.51)           -0.5415           32.02         (21.21, 47.51)             -0.5415

q2       7.1         $\mathcal{U}$(0, 50)    8.06         (1.553, 18.14)           -0.2068           8.06          (1.553, 18.14)             -0.2068

q3$^\ast$       0.161       $\mathcal{U}$(-7, 3)    0.04208      (1.103e-07, 0.7733)      -0.002009         0.04208       (1.103e-07, 0.7733)        -0.002009

q4       40.0        $\mathcal{U}$(0, 100)    59.81        (29.52, 99.4)            -0.3934           59.81         (29.52, 99.4)              -0.3934

q5       14.4        $\mathcal{U}$(0, 50)    25.73        (2.594, 43.97)           -0.2737           25.73         (2.594, 43.97)             -0.2737

q6$^\ast$       0.01        $\mathcal{U}$(-7, 3)    0.007372     (0.002444, 0.05932)      -0.5916           0.007372      (0.002444, 0.05932)        -0.5916

r1$^\ast$       1.332       $\mathcal{U}$(-7, 3)    0.05255      (1.14e-07, 2.713)        0.05333           0.05255       (1.14e-07, 2.713)          0.05333

r2       40.0        $\mathcal{U}$(0, 100)    45.95        (13.92, 96.56)           -0.2224           45.95         (13.92, 96.56)             -0.2224

r3       14.2        $\mathcal{U}$(0, 100)    46.89        (0.5929, 88.34)          -0.1519           46.89         (0.5929, 88.34)            -0.1519

r4$^\ast$       0.0626      $\mathcal{U}$(-7, 3)    0.01455      (1.051e-07, 0.05889)     -0.2101           0.01455       (1.051e-07, 0.05889)       -0.2101

Summary of results for parameters of Nygren $I_\text{CaL}$ model. Only activation parameters ($p$) recalibrated to unified dataset.
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space based
on the scale of their published values and are presented in linear space. The
prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

\[
\begin{aligned}
I_{\mathrm{CaL}}&=g_{\mathrm{Ca}, \mathrm{L}} d f f_{\mathrm{Ca}} (\mathrm{V}-\mathrm{E}_\mathrm{Ca,app})\\
\frac{\mathrm{d}d}{\mathrm{dt}}&=\frac{\widebar{d}-d}{\tau_{d}},\qquad
\frac{\mathrm{d}f}{\mathrm{dt}}=\frac{\widebar{f}-f}{\tau_{f}}\\
\widebar{d}&=\frac{1.0}{1.0+e^{(\mathrm{V}+\mathbf{p_4})/-\mathbf{p_5}}},\qquad
\tau_{d}=\frac{1-e^{(\mathrm{V}+\mathbf{p_1})/-\mathbf{p_2}}}{\mathbf{p_3}(\mathrm{V}+\mathbf{p_1})\left[1+e^{(\mathrm{V}+\mathbf{p_1})/-\mathbf{p_2}}\right]}\\
\widebar{f}&=\frac{1.0}{1.0+e^{(\mathrm{V}+\mathbf{q_6})/\mathbf{q_7}}},\qquad
\tau_{f}=\mathbf{q_1}\left[\mathbf{q_2} e^{-\mathbf{q_3}^{2}(\mathrm{V}+\mathbf{q_4})^{2}}+\mathbf{q_5}\right]^{-1}
\end{aligned}
\]

Gating kinetics in Courtemanche model of $I_\text{CaL}$ channel
current (see Appendix in [2]).

3cOriginal                        3cUnified
1c89% HDPI
1c89% HDPI
p1       10.0         $\mathcal{U}$(-100, 100)     -63.91        (-90.59, -30.08)           -0.5153           -38.24      (-99.15, 54.23)       0.2831

p2       6.24         $\mathcal{U}$(0, 50)    9.655         (1.853, 18.57)             -0.2793           19.17       (0.1832, 43.09)       -0.1334

p3$^\ast$       0.035        $\mathcal{U}$(-7, 3)    2.072e-07     (1.559e-07, 0.0001709)     -0.6749           0.02479     (0.01392, 0.0721)     -0.7863

p4       10.0         $\mathcal{U}$(-100, 100)    19.07         (6.624, 20.71)             -0.5022           10.44       (10.05, 10.71)        -1.66

p5       8.0          $\mathcal{U}$(0, 50)    6.078         (5.647, 7.053)             -1.029            7.447       (7.267, 7.638)        -1.754
q1$^\ast$       9.0          $\mathcal{U}$(0, 3)    57.97         (1.072, 435.5)             -0.372            5.315       (1.004, 19.81)        -0.2447

q2$^\ast$       0.0197       $\mathcal{U}$(-2, 3)    0.2487        (0.01006, 3.008)           0.2592            1.825       (0.1754, 6.422)       0.3113

q3$^\ast$       0.0337       $\mathcal{U}$(-4, 0)    0.01259       (0.0001002, 0.1925)        -0.3061           0.1147      (0.08051, 0.1534)     -1.006

q4       10.0         $\mathcal{U}$(-100, 100)    -11.13        (-71.3, 88.69)             0.8784            1.305       (-1.347, 4.125)       0.07887

q5$^\ast$       0.02         $\mathcal{U}$(-4, 0)    0.02488       (0.0001023, 0.4122)        -0.1906           0.1955      (0.03626, 0.6931)     -0.2331

q6       28.0         $\mathcal{U}$(-100, 100)    27.82         (25.28, 30.52)             -1.177            33.32       (25.89, 40.27)        -0.8614

q7       6.9          $\mathcal{U}$(0, 50)    6.879         (5.583, 8.993)             -0.8052           10.95       (7.257, 13.98)        -0.704

Summary of results of parameters of Courtemanche $I_\text{CaL}$
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space based
on the scale of their published values and are presented in linear space. The
prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

1c89% HDPI
$p_1^\ast$      $\mathcal{U}$(-7, 3)     0.5513      (1.02e-07, 1.073)        0.1053

$p_2$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)     0.01878     (1.245e-05, 0.05856)     -0.07143

$p_3^\ast$     $\mathcal{U}$(-7, 3)     0.375       (0.0056, 1.575)          0.07778

$p_4$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)     0.09998     (0.02278, 0.2473)        -0.1811

$p_5^\ast$     $\mathcal{U}$(-7, 3)     0.06489     (0.04241, 0.2347)        -0.6597

$p_6$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)     0.04437     (0.03053, 0.06118)       -0.6387

$p_7^\ast$     $\mathcal{U}$(-7, 3)     0.02056     (0.01379, 0.02842)       -1.205

$p_8$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)     0.02449     (0.01303, 0.03353)       -0.5575

$A^\ast$      $\mathcal{U}$(0, 3)        4.497       (3.235, 13.56)           -0.5354

Summary of results of parameters of standardised $I_\text{CaL}$
model using unified dataset.
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space and are presented in linear space. The prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

§.§ $I_\mathrm{to}$

\[
\begin{aligned}
I_{\mathrm{to}}&=\bar{g}_\mathrm{t} rs\left(\mathrm{V}-\mathrm{E}_{\mathrm{K}}\right)\\
\frac{\mathrm{d}r}{\mathrm{dt}}&=\frac{\widebar{r}-r}{\tau_{r}},\qquad
\frac{\mathrm{d}s}{\mathrm{dt}}=\frac{\widebar{s}-s}{\tau_{s}}\\
\widebar{r}&=\frac{1.0}{1.0+e^{(\mathrm{V}-\mathbf{p_1}) /-\mathbf{p_2}}},\qquad
\tau_{r}= 1000\left(\mathbf{p_3} e^{-(\mathrm{V} / \mathbf{p_4})^{2}}+\mathbf{p_5}\right)\\
\widebar{s}&=\frac{1.0}{1.0+e^{(\mathrm{V}+\mathbf{q_1}) / \mathbf{q_2}}},\qquad
\tau_{s}=1000\left(\mathbf{q_3} e^{-((\mathrm{V}+\mathbf{q_4}) / \mathbf{q_5})^{2}}+\mathbf{q_6}\right)
\end{aligned}
\]

Gating kinetics in Nygren model of $I_\text{to}$ channel
current (see Table 8 in [1]). Time constants are multiplied by 1000 to convert from $s$ to

3cOriginal             3cUnified
1c89% HDPI
1c89% HDPI

p1            1.0          $\mathcal{U}$(-100, 100)     3.25          (0.3302, 6.375)            -0.234      -0.577       (-7.205, 2.269)          0.4008

p2            11.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    10.32         (7.678, 12.61)             -0.8453     2.197        (1.381, 2.753)           -0.6039

p3$^\ast$            0.0035       $\mathcal{U}$(-7, 0)    4.613e-06     (1.013e-07, 0.0001495)     -0.6929     0.008113     (0.007376, 0.008801)     -1.931

p4            30.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    22.81         (0.2115, 43.89)            -0.2055     43.54        (40.81, 46.05)           -1.426

p5$^\ast$            0.0015       $\mathcal{U}$(-7, 0)    0.002083      (1.005e-07, 0.004469)      -0.4898     0.001244     (0.00109, 0.00137)       -1.973

q1            40.5         $\mathcal{U}$(-100, 100)    54.85         (21.94, 90.84)             -0.4189     28.97        (27.85, 30.79)           -1.473

q2            11.5         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    15.86         (5.989, 22.65)             -0.4416     1.161        (0.3452, 1.969)          -0.3639

q3$^\ast$            0.4812       $\mathcal{U}$(-5, 1)    0.3981        (0.3359, 0.5484)           -0.6558     0.09093      (0.08613, 0.09628)       -1.829

q4            52.45        $\mathcal{U}$(-100, 100)    57.94         (49.6, 63.12)              -1.104      38.16        (37.65, 38.63)           -2.083

q5            14.97        $\mathcal{U}$(1$\mathrm{e}$-7, 50)    12.1          (9.079, 16.57)             -0.7154     16.87        (16.17, 17.58)           -1.577

q6$^\ast$            0.01414      $\mathcal{U}$(-7, 0)    0.01171       (0.009782, 0.01371)        -1.577      0.008563     (0.008114, 0.008981)     -2.178

Summary of results for parameters of Nygren $I_\text{to}$ model.
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space based
on the scale of their published values and are presented in linear space. The
prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

\[
\begin{aligned}
I_{\mathrm{to}}&=g_\mathrm{to} o_\mathrm{a}^3 o_\mathrm{i}\left(\mathrm{V}-\mathrm{E}_{\mathrm{K}}\right)\\
\frac{\mathrm{d}\phi}{\mathrm{dt}}&=\frac{\phi_\infty-\phi}{\tau_\phi},\qquad\text{ for } \phi=o_\mathrm{a}, o_\mathrm{i}\\
\tau_\phi &= \left(\alpha_\phi + \beta_\phi\right)^{-1},\qquad \text{ for } \phi=o_\mathrm{a}, o_\mathrm{i}\\
\alpha_{o(\mathrm{a})}=\frac{\mathbf{p_3}}{e^{(\mathrm{V}+\mathbf{p_4})/-\mathbf{p_5}} + e^{(\mathrm{V}+\mathbf{p_6})/-\mathbf{p_7}}},\qquad
\beta_{o(\mathrm{a})}=\frac{\mathbf{p_3}}{\mathbf{p_8} + e^{(\mathrm{V}+\mathbf{p_9})/\mathbf{p_10}}}\\
\alpha_{o(\mathrm{i})}=\frac{1.0}{\mathbf{q_3} + e^{(\mathrm{V}+\mathbf{q_4})/\mathbf{q_5}}},\qquad
\beta_{o(\mathrm{i})}=\frac{1.0}{\mathbf{q_6} + e^{(\mathrm{V}+\mathbf{q_7})/-\mathbf{q_8}}}\\
\end{aligned}
\]

Gating kinetics in Courtemanche model of $I_\text{to}$ channel
current (see Appendix in [2]).

1c89% HDPI
p1       20.47        $\mathcal{U}$(-100, 100)     16.34       (7.558, 24.01)        -0.5041

p2       17.54        $\mathcal{U}$(1$\mathrm{e}$-7, 50)    19.03       (14.78, 23.36)        -0.8263

p3$^\ast$       0.65         $\mathcal{U}$(-3, 2)    0.06738     (0.002023, 0.259)     -0.3748

p4       10.0         $\mathcal{U}$(-100, 100)    28.32       (-0.545, 81.34)       -0.1259

p5       8.5          $\mathcal{U}$(1$\mathrm{e}$-7, 50)    12.98       (0.01876, 41.94)      -0.09246

p6       -30.0        $\mathcal{U}$(-100, 100)    23.19       (4.345, 94.19)        -0.07312

p7       59.0         $\mathcal{U}$(1$\mathrm{e}$-7, 100)    10.41       (0.008675, 37.07)     -0.05074

p8$^\ast$       2.5          $\mathcal{U}$(-3, 2)    0.1598      (0.001051, 2.304)     0.04982

p9       82.0         $\mathcal{U}$(-100, 100)    62.09       (-8.713, 99.55)       -0.08063

p10      17.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    41.35       (21.91, 49.99)        -0.5362
q1       43.1         $\mathcal{U}$(-100, 100)    33.51       (30.65, 35.14)        -1.353

q2       5.3          $\mathcal{U}$(1$\mathrm{e}$-7, 50)    6.981       (5.946, 8.025)        -0.8174

q3$^\ast$       18.53        $\mathcal{U}$(-1, 4)    3.668       (0.1006, 14.48)       0.1733

q4       113.7        $\mathcal{U}$(0, 200)    125.8       (114.5, 135.2)        -1.178

q5       10.95        $\mathcal{U}$(1$\mathrm{e}$-7, 50)    15.42       (13.43, 17.26)        -0.9771

q6$^\ast$       35.56        $\mathcal{U}$(-1, 4)    37.67       (36.17, 41.82)        -1.898

q7       1.26         $\mathcal{U}$(-100, 100)    31.78       (27.76, 36.86)        -0.7325

q8       7.44         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    0.6272      (0.003919, 1.28)      0.1188

Summary of results for parameters of Courtemanche $I_\text{to}$ model. Original and unified datasets are equivalent.
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space based
on the scale of their published values and are presented in linear space. The
prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

1c89% HDPI
$p_1^\ast$     $\mathcal{U}$(-7, 3)     0.00556       (0.005179, 0.006032)      -1.904

$p_2$    $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)     0.07096        (0.06763, 0.07326)        -1.586

$p_3^\ast$     $\mathcal{U}$(-7, 3)    0.1906        (0.1817, 0.1991)          -1.774

$p_4$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)    0.02528       (0.02459, 0.0261)         -1.724

$p_5^\ast$     $\mathcal{U}$(-7, 3)    0.1066        (0.1019, 0.1129)          -1.83

$p_6$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)    0.05923       (0.05696, 0.06139)        -1.57

$p_7^\ast$     $\mathcal{U}$(-7, 3)    0.0002949     (0.0002315, 0.000421)     -1.665

$p_8$     $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)    0.08746       (0.08027, 0.08944)        -1.478

Summary of results for parameters of standardised $I_\text{to}$
model using unified dataset.
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space and are presented in linear space. The prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

§.§ $I_\mathrm{Kur}$

\[
\begin{aligned}
I_{\mathrm{sus}}&=\bar{g}_\mathrm{sus} r_\text{sus}s_\text{sus}\left(\mathrm{V}-\mathrm{E}_{\mathrm{K}}\right)\\
\frac{\mathrm{d}r_\text{sus}}{\mathrm{dt}}&=\frac{\widebar{r_\text{sus}}-r_\text{sus}}{\tau_{r_\text{sus}}},\qquad
\frac{\mathrm{d}s_\text{sus}}{\mathrm{dt}}=\frac{\widebar{s_\text{sus}}-s_\text{sus}}{\tau_{s_\text{sus}}}\\
\widebar{r_\text{sus}}&=\frac{1.0}{1.0+e^{(\mathrm{V}+\mathbf{p_1}) /-\mathbf{p_2}}},\qquad
\tau_{r_\text{sus}} = 1000\left(\frac{\mathbf{p_3}}{1.0+e^{(\mathrm{V}+\mathbf{p_4})/\mathbf{p_5}}}+\mathbf{p_6}\right)\\
\widebar{s_\text{sus}}&=\frac{1.0-\mathbf{q_3}}{1.0+e^{(\mathrm{V}+\mathbf{q_1}) / \mathbf{q_2}}}+\mathbf{q_3},\qquad
\tau_{s_\text{sus}} = 1000\left(\frac{\mathbf{q_4}}{1.0+e^{(\mathrm{V}+\mathbf{q_5})/\mathbf{q_6}}}+\mathbf{q_7}\right)
\end{aligned}
\]

Gating kinetics in Nygren model of $I_\text{sus}$ ($I_\text{Kur}$) channel
current (see Table 8 in [1]). Time constants are multiplied by 1000 to convert from $s$ to

3cOriginal                           3cUnified
1c89% HDPI
1c89% HDPI
p1       4.3          $\mathcal{U}$(-100, 100)     1.895         (1.821, 1.946)             -1.68             2.031         (1.996, 2.056)             -2.028

p2       8.0          $\mathcal{U}$(1$\mathrm{e}$-7, 50)    4.54          (4.487, 4.564)             -2.226            4.305         (4.295, 4.325)             -2.61

p3$^\ast$       0.009        $\mathcal{U}$(-5, 0)    0.004119      (0.004024, 0.004169)       -2.667            0.002799      (0.002775, 0.002824)       -3.017

p4       5.0          $\mathcal{U}$(-100, 100)    -13.6         (-14.2, -13.1)             -1.582            -19.02        (-19.31, -18.77)           -2.056

p5       12.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    7.566         (7.169, 7.953)             -1.496            5.109         (4.959, 5.271)             -1.709

p6$^\ast$       0.0005       $\mathcal{U}$(-6, -1)    0.0007858     (0.0007327, 0.0008531)     -2.147            0.0008455     (0.0008235, 0.0008719)     -2.58
q1       20.0         $\mathcal{U}$(-100, 100)    21.14         (8.065, 51.78)             -0.1842      21.14         (8.065, 51.78)             -0.1842

q2       10.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    12.96         (0.8947, 27.71)            -0.2282      12.96         (0.8947, 27.71)            -0.2282

q3       0.6          $\mathcal{U}$(0, 1)    0.121         (0.0001271, 0.268)         -0.1557      0.121         (0.0001271, 0.268)         -0.1557

q4$^\ast$       0.047        $\mathcal{U}$(-4, 1)    0.06416       (0.01542, 0.133)           -0.6109      0.06416       (0.01542, 0.133)           -0.6109

q5       60.0         $\mathcal{U}$(-100, 100)    43.27         (-52.21, 99.65)            0.2045       43.27         (-52.21, 99.65)            0.2045

q6       10.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    27.02         (1.936, 45.79)             -0.238       27.02         (1.936, 45.79)             -0.238

q7$^\ast$       0.3          $\mathcal{U}$(-3, 2)    0.286         (0.2161, 0.3196)           -0.221       0.286         (0.2161, 0.3196)           -0.221

Summary of results for parameters of Nygren $I_\text{Kur}$ model. Only activation parameters ($p$) were recalibrated to unified dataset.
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space based on the scale of their published values and are presented in linear space. The prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

\[
\begin{aligned}
I_{\mathrm{Kur}}&=g_\mathrm{Kur}\left(1.0+\frac{\mathbf{r_1}}{1.0+e^{(V+\mathbf{r_2})/-\mathbf{r_3}}}\right) u_\mathrm{a}^3 u_\mathrm{i}\left(\mathrm{V}-\mathrm{E}_{\mathrm{K}}\right)\\
\frac{\mathrm{d}u_\mathrm{a}}{\mathrm{dt}}&=\frac{u_{\mathrm{a}(\infty)}-u_\mathrm{a}}{\tau_{u(\mathrm{a})}},\qquad
\frac{\mathrm{d}u_\mathrm{i}}{\mathrm{dt}}=\frac{u_{\mathrm{i}(\infty)}-u_\mathrm{i}}{\tau_{u(\mathrm{i})}}\\
\alpha_{u(\mathrm{a})}=\frac{\mathbf{p_3}}{e^{(\mathrm{V}+\mathbf{p_4})/-\mathbf{p_5}} + e^{(\mathrm{V}+\mathbf{p_6})/-\mathbf{p_7}}},\qquad
\beta_{u(\mathrm{a})}=\frac{\mathbf{p_3}}{\mathbf{p_8} + e^{(\mathrm{V}+\mathbf{p_9})/\mathbf{p_10}}}\\
\alpha_{u(\mathrm{i})}=\frac{1.0}{\mathbf{q_3} + e^{(\mathrm{V}+\mathbf{q_4})/-\mathbf{q_5}}},\qquad
\beta_{u(\mathrm{i})}=e^{(\mathrm{V}+\mathbf{q_6})/\mathbf{q_7}}\\
\tau_\phi &= \left(\alpha_\phi + \beta_\phi\right)^{-1},\qquad \text{ for } \phi=u_\mathrm{a}, u_\mathrm{i}
\end{aligned}
\]

Gating kinetics in Courtemanche model of $I_\text{Kur}$ channel
current (see Appendix in [2]).

3cOriginal                     3cUnified
1c89% HDPI
1c89% HDPI
p1       30.3         $\mathcal{U}$(-100, 100)     22.15       (20.09, 24.22)         -1.213            22.15       (20.09, 24.22)         -1.213

p2       9.6          $\mathcal{U}$(1$\mathrm{e}$-7, 50)    17.41       (13.63, 21.67)         -0.8446           17.41       (13.63, 21.67)         -0.8446

p3$^\ast$       0.65         $\mathcal{U}$(-3, 2)    0.04404     (0.00102, 0.1094)      -0.4886           0.04404     (0.00102, 0.1094)      -0.4886

p4       10.0         $\mathcal{U}$(-100, 100)    32.29       (-4.553, 88.19)        -0.1005           32.29       (-4.553, 88.19)        -0.1005

p5       8.5          $\mathcal{U}$(1$\mathrm{e}$-7, 50)    16.13       (3.228, 37.54)         -0.2495           16.13       (3.228, 37.54)         -0.2495

p6       -30.0        $\mathcal{U}$(-100, 100)    32.82       (-2.739, 87.54)        -0.1255           32.82       (-2.739, 87.54)        -0.1255

p7       59.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    16.26       (1.388, 32.48)         -0.2607           16.26       (1.388, 32.48)         -0.2607

p8$^\ast$       2.5          $\mathcal{U}$(-3, 2)    0.06393     (0.001001, 0.5319)     -0.1877           0.06393     (0.001001, 0.5319)     -0.1877

p9       82.0         $\mathcal{U}$(-100, 100)    47.77       (-22.92, 99.54)        0.04513           47.77       (-22.92, 99.54)        0.04513

p10      17.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    41.82       (29.25, 49.78)         -0.6841           41.82       (29.25, 49.78)         -0.6841

r1$^\ast$       10.0         $\mathcal{U}$(0, 2)    8.721       (1.004, 61.18)         -0.2278           8.721       (1.004, 61.18)         -0.2278

r2       -15.0        $\mathcal{U}$(-100, 100)    -6.353      (-84.56, 87.51)        1.22              -6.353      (-84.56, 87.51)        1.22

r3       13.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    25.3        (0.04052, 44.01)       -0.231            25.3        (0.04052, 44.01)       -0.231
q1       -99.45       $\mathcal{U}$(-200, 200)    -69.32      (-144.5, -0.2399)      -0.1766           54.84       (54.83, 54.85)         -3.809

q2       27.48        $\mathcal{U}$(1$\mathrm{e}$-7, 50)    34.61       (15.72, 49.44)         -0.4477           39.95       (39.94, 39.96)         -3.968

q3$^\ast$       21.0         $\mathcal{U}$(-1, 4)    1941.0      (0.1185, 5866.0)       -0.319            674.0       (674.0, 674.0)         -5.458

q4       -185.0       $\mathcal{U}$(-200, 200)    -118.8      (-199.4, -34.61)       -0.2815           74.15       (72.39, 81.09)         -1.373

q5       28.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    26.47       (0.6525, 43.54)        -0.2649           3.708       (2.084, 4.118)         -0.6464

q6       -158.0       $\mathcal{U}$(-200, 0)    -172.1      (-199.5, -133.3)       -0.8272           -151.0      (-199.9, -95.79)       -0.6078

q7       16.0         $\mathcal{U}$(1$\mathrm{e}$-7, 50)    23.66       (14.8, 28.97)          -0.5748           1.984       (0.03531, 4.561)       -0.1569

Summary of results for parameters of Courtemanche $I_\text{Kur}$. Only inactivation parameters ($q$) were recalibrated to unified dataset.
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space based on the scale of their published values and are presented in linear space. The prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

1c89% HDPI
$p_1^\ast$     $\mathcal{U}$(-7, 3)     0.0558        (0.0433, 0.06443)          -1.367

$p_2$    $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)    0.1464        (0.1281, 0.1683)           -1.043

$p_3^\ast$    $\mathcal{U}$(-7, 3)    0.1188        (0.1096, 0.1279)           -1.634

$p_4$    $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)    0.02021       (0.01904, 0.02213)         -1.306

$p_5^\ast$    $\mathcal{U}$(-7, 3)    0.004436      (0.004311, 0.004566)       -2.485

$p_6$    $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)    0.001568      (0.001221, 0.001863)       -0.8671

$p_7^\ast$    $\mathcal{U}$(-7, 3)    1.424e-07     (1.005e-07, 3.607e-07)     -1.417

$p_8$    $\mathcal{U}$(1$\mathrm{e}$-7, 0.4)    0.02784       (0.02351, 0.03098)         -1.079

Summary of results for parameters of standardised $I_\text{Kur}$
model using unified dataset.
$^\ast$Parameters were searched in $\mathrm{log}_{10}$ space and are presented in linear space. The prior for these parameters is still in the original $\mathrm{log}_{10}$ space.

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