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PLoS One
PLoS One
plos
PLOS ONE
1932-6203
Public Library of Science San Francisco, CA USA

PONE-D-24-14388
10.1371/journal.pone.0308809
Research Article
A biophysical minimal model to investigate age-related changes in CA1 pyramidal cell electrical activity
A biophysical minimal model to investigate age-related changes in CA1 pyramidal cell electrical activity
https://orcid.org/0000-0002-9430-5221
McKiernan Erin C. Conceptualization Formal analysis Investigation Methodology Software Validation Visualization Writing – original draft Writing – review & editing 1 *
https://orcid.org/0000-0001-8224-9077
Herrera-Valdez Marco A. Conceptualization Formal analysis Investigation Methodology Software Validation Visualization Writing – original draft Writing – review & editing 2 *
https://orcid.org/0000-0001-8422-8536
Marrone Diano F. Conceptualization Funding acquisition Project administration Supervision Writing – review & editing 3 4
1 Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México, CDMX, México
2 Laboratorio de Dinámica, Biofísica y Fisiología de Sistemas, Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México, CDMX, México
3 Department of Psychology, Wilfrid Laurier University, Waterloo, ON, Canada
4 McKnight Brain Institute, University of Arizona, Tucson, AZ, United States of America
Garcia-Ojalvo Jordi Editor
Universitat Pompeu Fabra, SPAIN
Competing Interests: The authors have declared that no competing interests exist.

* E-mail: emckiernan@ciencias.unam.mx (ECM); marcoh@ciencias.unam.mx (MAHV)
2024
4 9 2024
19 9 e030880911 4 2024
30 7 2024
© 2024 McKiernan et al
2024
McKiernan et al
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Aging is a physiological process that is still poorly understood, especially with respect to effects on the brain. There are open questions about aging that are difficult to answer with an experimental approach. Underlying challenges include the difficulty of recording in vivo single cell and network activity simultaneously with submillisecond resolution, and brain compensatory mechanisms triggered by genetic, pharmacologic, or behavioral manipulations. Mathematical modeling can help address some of these questions by allowing us to fix parameters that cannot be controlled experimentally and investigate neural activity under different conditions. We present a biophysical minimal model of CA1 pyramidal cells (PCs) based on general expressions for transmembrane ion transport derived from thermodynamical principles. The model allows directly varying the contribution of ion channels by changing their number. By analyzing the dynamics of the model, we find parameter ranges that reproduce the variability in electrical activity seen in PCs. In addition, increasing the L-type Ca2+ channel expression in the model reproduces age-related changes in electrical activity that are qualitatively and quantitatively similar to those observed in PCs from aged animals. We also make predictions about age-related changes in PC bursting activity that, to our knowledge, have not been reported previously. We conclude that the model’s biophysical nature, flexibility, and computational simplicity make it a potentially powerful complement to experimental studies of aging.

http://dx.doi.org/10.13039/501100000038 Natural Sciences and Engineering Research Council of Canada https://orcid.org/0000-0001-8422-8536
Marrone Diano F. Ontario Mental Health Foundation https://orcid.org/0000-0001-8422-8536
Marrone Diano F. DGAPA-UNAM-PAPIIT IA209817 https://orcid.org/0000-0002-9430-5221
McKiernan Erin C. DGAPA-UNAM-PAPIIT IA208618 & IN228820 https://orcid.org/0000-0001-8224-9077
Herrera-Valdez Marco A. DGAPA-UNAM-PAPIME PE114919 https://orcid.org/0000-0001-8224-9077
Herrera-Valdez Marco A. This work was supported by grants from the Natural Sciences and Engineering Research Council of Canada, as well as the Ontario Mental Health Foundation, awarded to DFM. This work was also supported by DGAPA-UNAM-PAPIIT IA209817 awarded to ECM; and by DGAPA-UNAM-PAPIIT IA208618 & IN228820, and DGAPA-UNAM-PAPIME PE114919 awarded to MAH-V. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Data AvailabilityResources generated by this study (code, figures, and manuscript files) are available via GitHub (github.com/emckiernan/agingCA1) and archived via Zenodo (doi.org/10.5281/zenodo.6788229). To facilitate reuse, resources are shared under open licenses (see the license file in our GitHub repository). To promote reproducibility, Python code is embedded in a Jupyter notebook that explains the code, how to use it, and how to generate the figures herein, plus additional ones.
Data Availability

Resources generated by this study (code, figures, and manuscript files) are available via GitHub (github.com/emckiernan/agingCA1) and archived via Zenodo (doi.org/10.5281/zenodo.6788229). To facilitate reuse, resources are shared under open licenses (see the license file in our GitHub repository). To promote reproducibility, Python code is embedded in a Jupyter notebook that explains the code, how to use it, and how to generate the figures herein, plus additional ones.
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pmcIntroduction

As we age, our brains undergo many changes [1, 2], but we understand relatively little about these and their effects on neural function. What does normal neurophysiological aging look like and what are the various stages? How does the electrical activity of neurons change and what are the biophysics underlying those changes? How do aging neurons respond to input from other cells? Answering these questions is not just fundamental to understanding aging as a neurophysiological process, but also to understanding how this process may be altered in age-related disorders of clinical importance such as Alzheimer’s [3] and Parkinson’s [4] disease.

Many aging studies have focused on the hippocampus, an area of the brain involved in learning, memory formation, and spatial processing [1, 2]. Aged rats [5–7] and humans [8] show impaired learning of hippocampal-dependent spatial tasks. Long-term potentiation (LTP), a proposed physiological substrate of memory formation, has been investigated in the hippocampus and its induction and maintenance shown to be impaired in aged rats [9, 10]. A short-term form of plasticity, frequency potentiation/facilitation (FP/FF), is also impaired in hippocampal pyramidal cells (PCs) from aged rats and correlates with learning deficits [11].

Plasticity changes and behavioral impairments may result in part from altered Ca2+ signaling in aged neurons [1, 2]. Compared to CA1 PCs from young animals, PCs from aged animals show larger and longer post-burst afterhyperpolarizations (AHPs) [12–14]. AHPs are mediated by Ca2+-dependent K+ currents, which can act like brakes on the electrical activity of CA1 PCs [15, 16]. As a result, PCs show increased spike frequency adaptation and fire fewer action potentials (APs) in response to acute stimuli or during bursting activity [17–19]. Larger AHPs are associated with increased intracellular Ca2+, mediated in part by Ca2+ entry via L-type channels [14, 18, 20, 21]. Aged animals show increases in L-type channel expression and/or channel density at the plasma membrane [22–25]. Animals with higher Ca2+ channel density perform poorly in spatial tasks [23], while blockers of L-type channels can restore learning and plasticity in older animals [26, 27].

It is not well understood how changes in ion channel gene expression and hippocampal PC excitability may affect neuron responsiveness and microcircuit output. In part, this is due to challenges inherent in performing the needed experiments. Single PCs are difficult to access in intact animals where hippocampal microcircuit function is preserved. It is also difficult to tease apart the influence of the many different neurophysiological factors that change during aging. Mathematical modeling provides a means to understand more about the effects of aging on hippocampal cellular excitability by controlling factors we cannot control experimentally.

Our previous work shows that mathematical expressions for different passive and active ion transport mechanisms can be derived from first principles of thermodynamics [28, 29] using a common functional form [30]. This results in a realistic representation of ionic flow across the membrane, and allows the model to reproduce phenomena such as rectification of ion currents seen in recordings. We present a model that reproduces the diversity of firing patterns in CA1 PC recordings, including adaptive firing, stimulus-induced bursting, and spontaneous bursting [31]. In addition, we reproduce several electrophysiological characteristics of aging by varying the expression of Ca2+ channels in the model, and make predictions about bursting activity in aged CA1 PCs, which to our knowledge has not been reported. We believe this model is ideal to further study the effects of various biophysical changes in CA1 PCs during aging, as well as potentially forming the basis for biophysical, yet computationally inexpensive, network models.

Materials and methods

Model

To simulate the electrical activity of CA1 PCs, we used an extended version of a two-dimensional, biophysical model previously developed and characterized by two of the present authors [28–30]. The present model differs from our previous formulations in that it includes Ca2+dynamics, i.e. it is three-dimensional, allowing for additional behaviors like bursting [32]. In addition, it is specially tuned by incorporating specific channel variants and corresponding experimental data from hippocampal PCs, as described below. The equations for the ionic currents are derived from first principles of thermodynamics. Previous modeling studies have shown that to reproduce firing behaviors such as spike frequency adaptation and bursting, the minimum number of variables is three [32, 33]. In particular, Ca2+ dynamics are important for producing adaptation and burst firing in CA1 PCs (for review see [31]). The model dynamics are therefore described by three ordinary differential equations for the time-dependent changes in the transmembrane potential (v, in mV), the proportion of open K+ channels (w in [0, 1]), and the intracellular Ca2+ concentration (c, in μM), respectively [30]. Based on a well-known relationship between voltage-dependent activation of delayed rectifier K+ channels and inactivation of Na+ channels, w also represents the proportion of inactivated Na+ channels [34, 35].

It is assumed that the membrane potential changes due to currents produced by ions transported across the membrane. We take into account currents mediated by a voltage-gated inactivating Na+ channel (INaT), voltage-gated L-type Ca2+ channel (ICaL), voltage- and Ca2+-gated K+ channels (IDK and ISK, respectively), and a Na+/K+-ATPase (INaK). We also incorporate a forcing term (IF), which can be used to stimulate the model PC and is explained in more detail below. The time-dependent change in membrane potential can be written as Cm∂tv=IF-INaT(v,w)-ICaL(v,c)-IDK(v,w)-ISK(v,c)-INaK(v). (1)

with ∂t representing the instantaneous change with respect to time. Cm (pF) is a constant representing the change in the density of charge around the membrane with respect to voltage, typically referred to as membrane capacitance in models based on electrical circuits [36]. Based on recordings from rat CA1 PCs, it is assumed that Cm = 25 pF [37].

All the currents in Eq (1) are modeled using the same generic functional form, a product Ix=axGxφx, (2)

x ∈ {NaT, CaL, DK, SK, NaK}, where ax is a whole-cell current amplitude (pA), Gx is a gating term (between 0 and 1), and φx is an adimensional term describing the driving force for the transmembrane flux (Table 1). The terms ax = sxNx, x ∈ {NaT, CaL, DK, SK, NaK} are whole-cell current amplitudes with sx (pA) representing the current flowing through a single channel (or pump), and Nx representing the number of membrane proteins mediating the current (e.g. number of K+ channels). Of interest, sx is ∼1 pA for most voltage-gated channels [38], and is ∼5–10 pA for SK channels [39].

10.1371/journal.pone.0308809.t001 Table 1 Transport mechanisms included in the model.

Transport mechanism	Current	Amplitude (a)	Gating (G)	Flux φ	
Transient Na+ channels	INaT(v, w)	a Na	Sm(v)(1 − w)	φNa(v)	
L-type Ca2+ channels	ICaL(v, c)	a Ca	Sn(v)	φCa(v)	
Delayed rectifier K+ channels	IDK(v, w)	a DK	w	φK(v)	
SK Ca2+-dependent K+ channels	ISK(v, c)	a SK	HSK(c)	φK(v)	
Na+/K+ pumps	INaK(v)	a NaK	1	φNaK(v)	
All ion fluxes are given by a product of the form Ix = axGxφx, where ax, Gx, and φx represent, respectively, the amplitude (normalized by membrane capacitance), gating, and driving force terms for the flux. GNaK = 1 represents saturation of the Na+/K+ pumps. Note that inactivation of Na+ channels is also represented by w [34, 35], so the proportion of non-inactivated Na+ channels is 1 − w.

Assuming that none of the currents in the model exhibit rectification [30], which agrees with recordings of the included currents, the adimensional component of the transmembrane flux can be simplified and written as φx(v)=2ηxsinh(ηxv-vx2vT), (3)

where ηx represents the number of charges transported across the membrane in a single transport event, and vx is the reversal potential for the current, x ∈ {NaT, CaL, DK, SK, NaK}. For channels, vx is the Nernst potential for the ion [30]. Of note, ηx = 1 for x ∈ {DK, SK, NaK} and ηNaT = −1 [30], which gives φx(v)=2sinh(v-vx2vT), (4)

for x ∈ {NaT, DK, SK, NaK}. For Ca2+ channels, the total charge transported by one ion crossing the membrane from the extracelular space is ηCaL = −2, so φCa(v)=4sinh(v-vCavT). (5)

The driving force for flux is assumed to be the same for DK and SK channels. Therefore, the label K is used for both fluxes from here on. The thermal potential vT = kT/q (mV), where k is Boltzmann’s constant (mJ/oK), T is the absolute temperature (oK), and q is the elementary charge (Coulombs). The Boltzmann constant can be thought of as a scaling factor between macroscopic (thermodynamic temperature) and microscopic (thermal energy) physics [40]. The reversal potentials for the different currents depend on the Nernst potentials for each ion, as given by vx=vTzxln([x]o[x]i),x∈{Na,Ca,K} (6)

where zx is the ion valence and [x]o and [x]i are the ion concentrations outside and inside the cell, respectively. The reversal potential for the Na+/K+-ATPase is given by vNaK = vATP + 3vNa − 2vK [30]. The Nernst potentials for Na+ and K+ are assumed to be constant, but vCa varies because the intracellular Ca2+ concentration is a state variable in the model.

Gating

The auxiliary functions describing voltage-dependent activation are given by Sj(v)=exp(gjv-vjvT)1+exp(gjv-vjvT),j∈{m,n,w}, (7)

where gj controls the steepness of the activation curve for Na+ (m), Ca2+ (n), or DK (w) channels, and vj represents the half-activation voltage for those channels. The function Rw(v)=rw[exp(bwgwv-vwvT)+exp((bw-1)gwv-vwvT)], (8)

describes the voltage-dependence of the rate of activation of the DK channels. The parameters rw and bw represent the recovery rate and the asymmetry in the gating relative to voltage that biases the time constant for the gating process, respectively.

The dynamics for the proportion of activated DK channels, w, are assumed to be logistic, ∂tw=w(Sw(v)-w)Rw(v), (9)

which yields better fits and is more consistent with the dynamics of activation in channel populations recorded in voltage-clamp experiments (e.g., see the activation curves in [41–43]).

The gating of the SK channel is not voltage-dependent, but instead depends on intracellular Ca2+ binding. Its activation is modeled using a Hill equation that depends on the intracellular concentration of Ca2+, as used to fit data from channel recordings [44]: HSK(c)=c2c2+cSK2, (10)

where cSK represents the half-activation Ca2+ concentration for the SK channels, with a reported value of 0.74 μM (740 nM) [39, 44].

For the dynamics of intracellular Ca2+, we assume recovery toward a steady state c∞ at a rate rc, with increments caused by the Ca2+ current ICa [35], ∂tc=rc(c∞-c)-k˜cICaL(v,c). (11)

The term k˜c in Eq (11) is a conversion factor (μM/pCoul) that accounts for the effect of Ca2+ flux across the membrane on the intracellular Ca2+ concentration.

The term IF represents a stimulus forcing the membrane; that is, current from an electrode (IStim), or time-dependent fluctuations from the local field potential (LFP). LFP activity is simulated by replacing the term IF with a time-dependent, Ornstein-Uhlenbeck (OU) process with amplitude aF(t) (pA). The mean is represented by μF (pA) (drift term) [45] given by [46] aF(t+δ)=aF(t)(1-δτF)+[μFδ+η(t)dStimδ], (12)

where δ is a small time step, τF is a relaxation time, and η(t) is an independent white noise process with zero-mean and unit standard deviation. In our simulations, the mean is set close to the rheobase for the model PCs (∼50 pA). The process has a variance σF2=dFδ/2 (pA), which means dF can be approximated if an estimation of the variance of the current aF is available [47, 48].

Change of variables to obtain numerical solutions

To simplify the numerics, we change variables u=v/vT, (13)

and adjust all voltages accordingly as ul=vl/vT,l∈{NaT,CaL,K,NaK,m,n,w}. (14)

The new equation for the normalized voltage is ∂tu=∂tvvT. (15)

To simplify the notation and reduce the number of operations during the numerical integration, we also reparametrize the amplitudes as Al=2al|ηl|vTCm, (16)

for l ∈ {NaT, CaL, K, NaK}, in units of 1/ms. Similarly, the activation functions for the Na+, Ca2+, and DK currents can also be rewritten respectively as f∞(u)={1+exp[gf(uf-u)]}-1,f∈{m,n,w}. (17)

The result is a new equation of the form ∂tu=JF-ANaT(1-w)m∞(u)φNa(u)-ACaLn∞(u)φCa(u,c)-(ADKw+ASKHSK(c))φK(u)-ANaKφNaK(u). (18)

The term JF (1/ms) is the input current IF (pA) divided by vTCm. After the change in variables and the normalization of the current amplitudes, Eq (11) changes to ∂tc=rc(c∞-c)-kcACaLn∞(u)φCa(u,c), (19)

where kc=k˜cvTCm.

Parameters

The currents were modeled to fit as closely as possible the biophysical properties of those carried by channel variants expressed in mammalian neurons, and specifically CA1 PCs, where data are available. The DK current is based on that mediated by Kv2.1 channels, the predominant channel underlying the delayed rectifier current in rat hippocampal neurons [49]. The L-type Ca2+ current is based on that carried by Cav1.2 (class C) channels, the predominant L-type channel isoform expressed in rat brain [50]. Additional details about the parameters can be found in Table 2.

10.1371/journal.pone.0308809.t002 Table 2 Constants and parameters.

parameter	description	value	units	reference	
k	Boltzmann’s constant	1.381e−20	mJ/K	physical constant [38]	
q	elementary charge	1.602e−19	C	physical constant [38]	
T	absolute temperature	273.15 + 37	K	adjusted to mammalian body temperature of 37°C [38]	
a NaT	amplitude of transient Na+ current	1000–2300	pA	set to produce currents of ∼2–7 nA, in range recorded in CA1 PCs from rats [53] and guinea pigs [54]	
a CaL	amplitude of L-type Ca2+ current	25 or 50	pA	set to produce currents of ∼2–3 nA or ∼5–6 nA as recorded in young and aged CA1 PCs, respectively [20]	
a DK	amplitude of delayed rectifier K+ current	6000–8000	pA	set to produce currents of ∼6–9 nA, in range recorded from HEK cells expressing rat Kv2.1 and IK in hippocampal neurons [55]	
a SK	amplitude of Ca2+-dependent K+ current	300–1600	pA	set to produce currents of ∼100–800 pA, depending on Ca2+ concentration, as recorded in SK-transfected cells [56]	
a NaK	amplitude of Na+/K+-ATPase current	10–23	pA	set to produce currents of ∼70–190 pA, similar to but on high end of range recorded in hippocampal PCs [57]	
η x	charge moved across the membrane in a single transport event x ∈ {NaK, DK, SK}	1	–	1 net positive charge moving outward [30]	
η NaT	charge transported across the membrane by NaT channels	-1	–	1 net positive charge moving inward [30]	
η CaL	charge transported across the membrane by Ca channels	-2	–	2 net positive charges moving inward [30]	
v Na	Nernst potential for Na+	60	mV	in range reported for mammalian cells [58]	
[Ca]o	extracellular Ca2+ concentration (intracellular varies)	1.5	mM	in range reported for mammalian neural tissue [59]	
v Ca	Nernst potential for Ca2+	variable; baseline ∼128	mV	in range reported for mammalian cells [58]; varies since intracellular Ca2+ concentration is a model variable	
v K	Nernst potential for K+	-89	mV	in range reported for mammalian cells [58]	
v ATP	Nernst potential for ATP	-420	mV	value used in model of mammalian heart cells and based on fit to data [60]	
v NaK	Nernst potential for Na+/K+-ATPase	-62	mV	calculated based on the Nernst potentials for ATP, Na+, and K+, and a 3:2 stoichiometry, respectively [61]; vNaK = 3vNa − 2vK − vATP	
r w	rate of activation of delayed rectifier K+ current	1.0–1.8	ms	fit so that the duration of the action potential is approximately 2 ms [62]	
s w	asymmetry of time constant of delayed rectifier K+ current	0.3	-	based on fit; if higher (0.5–0.7) APs are the wrong shape and do not ride on sufficient plateau potential compared to recordings	
v m	half-activation potential of Na+ current	-19	mV	in range reported for transient Na+ channels in CA1 PCs [63, 64]	
v n	half-activation potential of Ca2+ current	3	mV	in range recorded for high-voltage activated Ca2+ currents in rat CA1 PCs [65]; see also recordings from oocytes [66] or HEK cells [67] expressing Cav1.2 channels	
v w	half-activation potential of delayed rectifier K+ current	-1	mV	in range reported for rat Kv2.1 channels expressed in COS-1 cells [49]	
c SK	half-activation Ca2+ concentration for SK current	7.4e−4	mM	based on recordings from oocytes expressing rat SK channel variant [44]	
g m	activation slope of Na+ current	5.0	-	in range reported for Na+ current in mouse [68] and rat [69] CA1 neurons	
g n	activation slope of Ca2+ current	5.0	-	in range reported for Cav1.2 expressed in HEK cells [70]	
g w	activation slope of delayed rectifier K+ current	3.8	-	fit to data from rat brain delayed rectifier channels [71]	
c ∞	minimum intracellular Ca2+ concentration	1e−4	mM	equivalent to 100 nM, approximate resting intracellular Ca2+ concentration in rat CA1 PCs [17, 72, 73]	
r c	intracellular Ca2+ removal rate constant	1e−3 to 5e−3	ms−1	adjusted to produce Ca2+ dynamics as recorded in rat CA1 PCs [72]	
k c	conversion factor to calculate effect of Ca2+ current on intracellular Ca2+ concentration	3e−6 to 6e−6	mM	adjusted to produce Ca2+ dynamics as recorded in rat CA1 PCs [72]	

Wherever possible, model parameters were taken from studies in rodent (mice and rat) hippocampal CA1 PCs. If data were not available, we obtained parameters from other types of mammalian cell, or from studies of mammalian ion channels in expression systems like Xenopus oocyte. Physical constants and other parameters we would not expect to vary, such as the intra- and extracellular concentrations of ions or the cellular capacitance, were fixed. Biophysical properties of the ion channels, such as their half-activation voltages, were also fixed. The parameters we varied were primarily those corresponding to maximum current amplitudes, which can change acutely due to modulation or channel phosphorylation [51, 52], or chronically due to changes in ion channel expression that occur with age [22, 24].

By exploring the model through parameter variations, we were able to find parameter sets that produced different firing patterns, such as adaptive firing, conditional bursting, and spontaneous bursting. The rationale behind finding parameters for qualitatively different firing patterns that emerge in a three-dimensional model similar to this one was established by Av-Ron and colleagues [32]. For example, they show that one way to observe transitions between adaptive firing and bursting is to vary the ratio of DK to Ca2+-dependent K+channels. Therefore, in our study, we began by setting the model parameters within the base physiological range given by experimental recordings in PCs, and then took into consideration the different ratios of select parameters and their effects. Once we defined these different restricted parameter ranges, we then tuned semi-manually, i.e. using Python for loops to quickly run through a series of parameter values using knowledge of how increases or decreases in specific parameters should change the firing of cells (e.g., a larger SK current leads to greater inhibition of firing, lower firing frequencies, etc.). The specific PC firing patterns are described in more detail in the Results section, but the respective parameter sets are included in Table 3 for ease of comparison.

10.1371/journal.pone.0308809.t003 Table 3 Parameters used to produce different firing patterns in young PC.

parameter	adaptive firing	conditional bursting	spontaneous bursting	
aNaT (ANaT)	1000 (2.99)	1300 (3.89)	2300 (6.88)	
aCaL (ACaL)	25 (0.15)	25 (0.15)	25 (0.15)	
aDK (AKD)	8000 (23.95)	6000 (17.96)	7000 (20.95)	
aSK (ASK)	1400 (4.19)	1600 (4.79)	300 (0.90)	
aNaK (ANaK)	10.0 (0.03)	13 (0.04)	23 (0.07)	
r w	1.0	1.8	1.1	
r c	1e−3	5e−3	5e−3	
k c	3e−6	6e−6	6e−6	
Original amplitudes (ax) are in pA. Reparametrized amplitudes (Ax) in parentheses are calculated by 2*axvTCm for x ∈ {NaT, DK, SK, NaK} and 4*aCaLvTCm for Ca2+ channels. For all calculations, vTCm = 668.171 mV pF.

Simulations

All code was written in Python 3.7.4 and run on MacBook Pro laptops with 2.9 GHz Intel Core i5 processors. Simulations were performed using functions from the Python library NumPy [74]. Figures were produced with the Python library Matplotlib [75]. OU processes were simulated using the pyprocess package [76].

Resource availability

Resources generated by this study (code, figures, and manuscript files) are available via GitHub (github.com/emckiernan/agingCA1) and archived via Zenodo (doi.org/10.5281/zenodo.6788229). To facilitate reuse, resources are shared under open licenses (see the license file in our GitHub repository). To promote reproducibility, Python code is embedded in a Jupyter notebook [77] that explains the code, how to use it, and how to generate all figures, including those in the Supporting Information.

Study design

While aged cells display a number of biophysical changes, we focused on their Ca2+ channel expression. Aged CA1 PCs show an increase in the number of functional transmembrane L-type Ca2+ channels [22–24]. In particular, CA1 PCs from aged rats have increased expression of Cav1.2 at the plasma membrane [25]. With these results in mind, we decided to simulate one aspect of aging by changing the number of Cav1.2 channels in our model membrane. We asked the question, is a change in Cav1.2 expression sufficient to reproduce the various changes in excitability, such as increased spike frequency adaptation, observed experimentally in aged CA1 PCs? In addition, CA1 PCs are known to burst [31], but we are not aware of studies comparing their bursting patterns in young versus aged animals. Therefore, we used our model to also investigate the effects of altered Cav1.2 channel expression on bursting activity. In all the following simulations, once the models have been tuned to a specific firing pattern, young and aged model PCs (hereafter referred to as yPC and aPC, respectively) are identical with respect to every parameter except the maximum amplitude of their L-type Ca2+ current, which is set to produce currents of ∼2–3 nA or ∼5–6 nA to match the magnitude of currents seen in recordings of CA1 PCs from young and aged animals, respectively [20].

Results

CA1 PCs display diverse firing patterns, ranging from repetitive adaptive spiking to stimulus-induced or spontaneous bursting (for review see [31]). Thus, to represent these cells, our model must reproduce this diversity, as well as age-related effects on firing reported in the literature.

Modeling age-related changes in spike frequency adaptation

Many CA1 PCs respond to square-pulse current injection by firing several early spikes followed by adaptation which slows the frequency of firing [17, 18, 78]. To generate this firing pattern, we set the ionic currents to be the same amplitude range as observed in recordings of young adult CA1 PCs, with amplitudes for the Na+ and Ca2+ currents at ∼2–3 nA, the DK current approximately double the inward cationic currents, and the SK current at ∼400–700 pA, depending on the intracellular Ca2+ concentration (see Tables 2 and 3). This balance of ionic currents successfully generates adaptive firing similar to recordings (Fig 1A and S2 Fig).

10.1371/journal.pone.0308809.g001 Fig 1 Adaptive firing in model PCs.

(A.) Adaptive firing in the yPC (solid black traces) versus aPC (dashed red traces) in response to a 800 ms 150 pA square-pulse stimulation shown in (E.). Corresponding Ca2+ currents, intracellular Ca2+ concentration, and SK currents are shown in (B.), (C.), and (D.), respectively. Parameters for yPC: aNaT = 1000, aCaL = 25, aDK = 8000, aSK = 1400, rw = 1.0, rc = 1e−3, and kc = 3e−6. All parameters for aPC the same except aCaL = 50. Parameter units, and additional parameters kept constant for all simulations, are in Table 2.

Studies show that adaptation is more pronounced in aged than young animal cells, leading to a shorter initial period of fast spiking, followed by fewer spikes or complete cessation of firing [17–19, 79]. To compare the young (yPC) and aged (aPC) model cells, all parameters were fixed except for the maximum amplitude of the L-type Ca2+ current, which was set to produce currents of ∼2–3 nA (young) or ∼5–6 nA (aged), based on recordings [20]. This difference in the Ca2+ current causes the rate of firing in the first ∼100 ms (early firing) to decrease from 60 Hz in the yPC to 40 Hz in the aPC (Fig 1A and S4A Fig). Firing for the remaining stimulation time (late firing) is also affected, decreasing from ∼6 Hz to ∼3 Hz in the yPC versus aPC, respectively (Fig 1A and S4B Fig). The effect and frequencies are similar to those seen in recordings of CA1 PCs in young and old rabbits [18].

Examining the Ca2+ and SK dynamics during the response reveals the mechanisms underlying the stronger adaptation in the aPC (Fig 1B–1D). The first two spikes occur nearly simultaneously in the two model cells. However, the larger increase in intracellular Ca2+ in the aPC induces a larger SK current, which in turn slows the cell’s firing. The aPC falls behind the yPC by the third spike, and then slows its firing further as the response continues.

Modeling age-related changes in AHPs

AHP generation has been studied in CA1 PCs [80], particularly in the context of aging [17, 18, 79, 81]. To induce AHPs, we kept the same parameters as in the previous simulations. We then stimulated model PCs with a 100 ms square pulse of sufficient amplitude to generate a burst of 4 APs (Fig 2). The AHPs produced under these conditions in the yPC have a peak amplitude of 3–4 mV (S5 Fig inset), similar to recordings [14, 81]. The aPC required 35 pA more current than the yPC to fire the same number of spikes (Fig 2E). However, the aPC fires earlier than the yPC due to its increased Ca2+ current (Fig 2A inset). The aPC generates an AHP 1–2 mV larger than seen in the yPC (Fig 2B), similar to the difference observed in recordings between young and aged cells [14, 17, 18]. In the model, this larger AHP is due to an increased accumulation of Ca2+ in the aPC, which in turn produces a larger SK current (Fig 2C and 2D, respectively).

10.1371/journal.pone.0308809.g002 Fig 2 AHPs in model PCs.

(A.) Responses of the yPC (solid black traces) and aPC (dashed red traces) to 100 ms pulse. Voltage zoom in (B.) shows AHPs in detail. Corresponding Ca2+ concentrations and SK currents are shown in (C.), and (D.), respectively. Parameters same as in Fig 1, except for the current stimulation duration and amplitude. Current amplitude adjusted to the minimum required (within 1 pA) to produce 4 spikes in each cell, i.e. 106 pA in yPC and 141 pA in aPC, as shown in (E.).

Modeling age-related changes in burst firing

Bursting in response to stimulation

Some CA1 PCs fire bursts instead of trains of spikes [82], especially in certain developmental periods [83]. Burst firing can be generated in the model with several different parameter combinations. For the following simulations, we modified several of the current amplitudes and select kinetics, all within physiological limits (see Table 3). Under this parameter regime, model PCs are silent at rest but burst if stimulated (Fig 3 and S6 Fig).

10.1371/journal.pone.0308809.g003 Fig 3 Stimulated bursting in model PCs.

Bursting in the yPC (solid black traces) and aPC (dashed red traces) models in response to 800 ms current injections of 50–170 pA, as indicated in panels (A.)-(E.). Parameters for the yPC: aNaT = 1300, aCaL = 25, aDK = 6000, aSK = 1600, rw = 1.8, rc = 5e−3, kc = 6e−6. All parameters for the aPC the same except aCaL = 50.

To explore the effects of aging on bursting, we fixed all parameters except for the maximum Ca2+ current amplitude, as previously. We then stimulated the two model PCs with a series of square-pulse current injections of increasing amplitudes (50–170 pA) to compare their responses. Again, the larger Ca2+ current in the aPC causes it to fire either sooner or nearly simultaneously with the yPC shortly after stimulus onset in all simulations (S8 Fig). However, the relative timing of the PCs’ firing after the first burst depends on the stimulus amplitude (Fig 3).

At lower stimulation amplitudes (50 and 80 pA; Fig 3A and 3B), the aPC continues to burst sooner or nearly simultaneously, but always fires fewer spikes per burst than the yPC (2 versus 3, respectively). As the stimulation amplitude increases (110 pA; Fig 3C), the two PCs again fire nearly simultaneously at the onset. However, because the aPC fires fewer spikes per burst, it is able to recover sooner and burst before the yPC for four cycles. It is only towards the end of the stimulus that the larger AHP in the aPC eventually brings it into sync again with the yPC. Finally, at the highest stimulation amplitudes (140 and 170 pA; Fig 3D and 3E), both PCs show stronger adaptation, but the yPC maintains something akin to bursting, while the aPC ‘devolves’ to a pattern more like tonic spiking. Depending on what is considered the relevant electrical event—the single spike or the burst—the aPC shows an increased number of events relative to the yPC (13 spikes versus 8 burst-like events, respectively), but the normal bursting pattern is lost.

Spontaneous bursting

A small percentage of CA1 PCs fire bursts in the absence of stimulation [84]. To generate this pattern, we again modifed several of the current amplitudes and select kinetics, all within physiological limits (see Table 3). Under this parameter regime, the yPC fires spontaneous bursts at a frequency of ∼1 Hz with 3 spikes per burst (Fig 4C and S9 Fig), similar to recordings [85].

10.1371/journal.pone.0308809.g004 Fig 4 Spontaneous bursting in model PCs.

Comparison of spontaneous electrical activity in the yPC (solid black traces) and aPC (dashed red traces) for different levels of DK current amplitude. aDK decreasing from 8000 to 6000 pA (8 to 6 nA) in steps of 500 pA, as indicated in (A.)-(E.). Parameters: aNaT = 2300, aCaL = 25, aDK = 7000, aSK = 300, rw = 1.1, rc = 5e−2, kc = 6e−6, IF = 0.0. All parameters for aPC the same except aCaL = 50.

Increasing the Ca2+ current, as previously, changed the spontaneous firing pattern (Fig 4). Additional interesting effects can be seen if we vary the DK current amplitude within the range previously used for simulations, 6000–8000 pA (6–8 nA). At the highest DK amplitude, the yPC bursts spontaneously but with only 2 spikes per burst (Fig 4A). The aPC, however, does not burst but spikes tonically at a frequency of ∼2 Hz. When the DK amplitude is reduced (7.5 nA), the yPC continues to burst, now with 3 spikes per burst, while the aPC still spikes tonically (Fig 4B).

Reducing the DK amplitude further (7 nA or 6.5 nA; Fig 4C or 4D), causes both PCs to burst spontaneously, though the aPC always fires fewer spikes per burst. One can use our Jupyter notebook to explore further, and see that while the Ca2+ current is larger for the aPC, the maximum accumulation of intracellular Ca2+ is either similar or higher in the yPC due to its additional spiking (S11 Fig). This causes a similar or larger SK current in the yPC, and results in a slower burst frequency.

Finally, reducing the DK amplitude to the lowest level (6.0 nA; Fig 4E) removes more of the ‘brake’ on the yPC and causes it to spike at high frequency and then quickly block depolarize. The aPC, on the other hand, retains the spontaneous bursting pattern, now with more spikes per burst.

Responses to local field potential forcing

Square-pulse stimulation is useful for examining the timing of PC responses, but is not a physiologically realistic stimulus. Instead, to simulate local field potential (LFP) forcing onto CA1 PCs, we use an Ornstein-Uhlenbeck (OU) stochastic process [47, 48], as in Eq 12. First, we reset the model with the parameters needed to produce adaptive firing. In the yPC, LFP forcing produces repetitive, irregular firing at a frequency of ∼3 Hz on average (Fig 5A), which is similar to recordings of spontaneous firing in CA1 PCs [86], particularly in response to certain types of activity in the surrounding electrical field [87, 88].

10.1371/journal.pone.0308809.g005 Fig 5 LFP-induced firing in model PCs.

Responses of the yPC (solid black traces) and aPC (dashed red traces) to the same LFP forcing while in adaptive firing mode. (A.) yPC response, (B.) aPC response, and (C.) overlap of the two traces. Parameters for the yPC and aPC are the same as in Fig 1. LFP parameters: μF = 50.0 pA, σF = 25.0 pA, τF = 1/2.0 for both model PCs.

In response to the exact same LFP forcing applied to the yPC, the aPC with increased Ca2+ current shows a similar irregular firing pattern, but slower frequency of ∼2 Hz (Fig 5B; compare overlap in C). The simulation also shows several time points when the two cells fire almost simultaneously, and then the yPC fires again while the aPC does not. This apparent ‘spike failure’ has been seen in recordings of PCs from aged animals [13].

Next, we set the parameters to produce conditional bursting, as previously. The exact bursting pattern will vary depending on the stochastic OU process. However, under these conditions, LFP forcing in the yPC typically produces irregular burst firing at a frequency of ∼5Hz (i.e. theta frequency), with 2–4 spikes per burst (Fig 6A). This firing pattern is similar to spontaneous activity recorded in a subset of CA1 PCs known as phasic theta-ON cells, which preferentially burst during theta activity recorded from the surrounding field [87, 89]. Increased Ca2+ current in the aPC changes the firing pattern (Fig 6B). In response to LFP forcing, the aPC still fires irregular bursts, but with fewer spikes per burst (usually 3 max) and a higher occurrence of 2-spike bursts than seen in the yPC. In addition, the aPC fires single APs amidst the bursts, which occurs less frequently in the yPC under this parameter regime. Also, the timing of the bursts in the aPC can change relative to the yPC (see overlap in Fig 6C).

10.1371/journal.pone.0308809.g006 Fig 6 LFP-induced bursting in model PCs.

Responses of the conditionally bursting yPC (solid black traces) and aPC (dashed red traces) models to the same LFP forcing. (A.) yPC response, (B.) aPC response, and (C.) overlap of the two traces. Parameters for the yPC and aPC are the same as in Fig 3. LFP parameters the same as in Fig 5 except σF = 20.0 pA.

Discussion

Cellular heterogeneity

Our three-dimensional, single-compartment model derived from first principles of thermodynamics can reproduce the diversity of firing patterns recorded in CA1 PCs. Moving between the different patterns was achieved primarily by changes to the relative expression of ion channels in the model. We did not systematically explore the full parameter space, but future work could include bifurcation analysis to determine boundaries for each firing pattern. The flexibility of the model could be useful for researchers to study the effects of PC heterogeneity on network function. Geiller and colleagues [90] write, “Until very recently, hippocampus models and theories were built on a view of homogenous population of principal cells” (pg. 6). However, there is heterogeneity in CA1 PCs, especially during different development stages (for review, see [31]). Lee and colleagues [91] write, “how the heterogeneous PCs integrate into the CA1 circuit remains unknown” (pg. 1129).

Experimentally, it is difficult to quantify how many PCs in a given network are displaying a specific firing pattern, and even harder, if not impossible, to manipulate these percentages. Furthermore, cells can transition between firing patterns [92], meaning percentages might fluctuate. With our minimal model, however, we could build small networks with different balances of adapting versus bursting PCs, and explore how this affects network output. This might help researchers understand the extent of ‘acceptable’ heterogeneity within hippocampal circuits, or how sensitive these networks are to changes in the overall balance of cells displaying different firing patterns. Such insights will be relevant to neurophysiological aging, as these balances can change over a lifespan [83], and also to age-related brain disorders such as Alzheimer’s in which altered cell firing could disrupt the balance [93]. We could also model the progression of aging in the network by varying the percentage of PCs which have altered Ca2+ channel density, or implement a whole spectrum of channel expression across the simulated network. Studies like these may bring researchers closer to understanding the different stages of neurophysiological, or even pathophysiological, aging by allowing one to systematically vary biophysical parameters over a continuous range and identify points at which the system undergoes clear transitions in behavior.

Aging and Ca2+ channel expression

Our model can also reproduce changes in electrical activity seen in aged CA1 PCs, including larger AHPs [12–14] and increased adaptation [17–19], by increasing the L-type Ca2+ current amplitude to a level similar to that found in recordings. The L-type channel was modeled after the Cav1.2 isoform based on work showing this is the primary contributor in rodent brain, responsible for ∼70–80% of the L-type current [50, 94]. mRNA expression of Cacnac1C (the gene encoding Cav1.2) is increased in aged mice and rats [22, 95]. Increases in plasma membrane expression [25] and phosphorylation [96] of Cav1.2 channels have also been seen in aged rats. In addition, changes in Cacna1c/Cav1.2 expression are correlated with memory impairments [95, 97].

However, CA1 PCs also express the Cav1.3 isoform [98], which is responsible for ∼20% of the total L-type current [50, 94]. Studies have found both increased mRNA [22] and protein [24] expression of Cav1.3 in aged rats, and this increased expression is correlated with memory impairment [99]. Knockout studies in mice indicate that it is this isoform, and not Cav1.2, which contributes to slow AHP generation [100], possibly via activation of co-localized SK channels [98]. While experimental studies have been complicated by a lack of pharmacological agents which can isolate currents carried by the different isoforms, it would be relatively simple with our model to study the contributions of these two channels. The primary difference between the two is a shift in the activation curve of the Cav1.3 channel to more hyperpolarized values, relative to Cav1.2 [66]. Changing the parameter vj in Eq 7 would allow us to represent the different isoforms and explore how changes in the expression of each during aging might affect PC activity.

There are many cellular changes apart from Ca2+ channel expression that occur during aging and could contribute to altered activity in PCs. Studies have implicated Ca2+ release from intracellular stores as an important contributor, particularly to larger AHPs in aged animals (for reviews see [101, 102]). We did not explore the role of intracellular Ca2+ stores in this study, nor many of the other cellular changes that surely contribute to the multifactorial process of aging. It is not our intention to suggest Ca2+ channel expression is the only factor altering the activity of PCs in aged animals. Nevertheless, we do demonstrate that an increase in L-type Ca2+ channels is sufficient to reproduce many of the changes in PC firing seen during aging. These results agree with a previous modeling study, which also found that an increase in L-type Ca2+ conductance was sufficient to produce changes in adaptation and AHPs similar to those seen in aged CA1 PCs [103]. However, their model was mathematically complex, with 183 compartments and more than a dozen ionic currents—very different from the single-compartment, minimal model we present here. In addition, their study looked only at adaptation and AHPs, while our study goes further to investigate conditional bursting, spontaneous bursting, and responses to LFP stimulation.

Aging and excitability

Our simulations do show changes in the electrical activity of aged PCs, but do these changes represent decreased excitability? This question relates more broadly to how we think about excitability—the term is rarely clearly defined or used in a standardized way. In some studies, excitability is used to refer to a change in the firing rate of a cell over the course of an injected current pulse, claiming that PCs with stronger adaptation are less excitable [18]. In our simulations under the adaptive firing parameter regime, the aPC did have stronger adaptation and fired fewer times during the stimulation period than the yPC. However, under some circumstances, this stronger adaptation occurred only after the aPC initially fired faster than the yPC (see for example Fig 2 inset). Should we consider this decreased excitability?

If what concerns us with excitability is the activity of the cell over a given time period, then the results under the bursting parameter regimes are even less clear. The aPC always fired fewer APs per burst than the yPC, indicating something akin to stronger adaptation. However, if the ‘event’ we are considering is instead the burst, there are conditions under which the aPC fired a greater number of bursts in a given time period than the yPC. How should we interpret these results with respect to excitability? To our knowledge, there are very few experimental studies to date that have compared burst firing in young versus aged animal CA1 PCs, perhaps because of the relatively low percentage of cells with this firing pattern in certain developmental periods [83]. The only study of which we are aware compared spontaneous burst firing in young versus aged animal PCs during rest and exploratory behavior [104]. Unfortunately, there are several factors that make it difficult to compare our results with theirs. First, their recordings were extracellular. As such, no bursts from individual PCs are shown in the paper to compare to our simulations, which reproduce intracellular firing. Furthermore, the study focused on interspike intervals (ISIs), rather than the overall bursting pattern (e.g. number of bursts in a given period), which was our focus. Interestingly, Smith and colleagues [104] found that while ISIs were more left-skewed in aged animals when burst firing was recorded at rest, they found no difference between the age groups during behavior, suggesting that compensatory mechanisms work differently during behavior to adjust for changes in cellular excitability. Such compensatory mechanisms could be explored using our model, for example by adding simulated cholinergic input.

There are studies comparing bursting activity in young and aged animals in other areas of the brain. For example, Sagheddu and colleagues recorded from dopaminergic and GABAergic cells in the ventral tegmental area (VTA), and showed that both the percentage of spikes organized into bursts and the rate of bursting was lower in cognitively impaired aged rats [105]. In particular, their finding that the firing patterns of these cells in aged animals change from bursting to more single spiking (i.e. the percentage decrease) is consistent with some of our simulations.

Other researchers use the term excitability to describe how easy it is to get a cell to fire in response to stimulation, referring to “propensity” [106] or “readiness” [107]. In this context, excitability could be measured by the rheobase, or minimum current which generates firing in a neuron, as done in some studies of aging in CA1 [108]. However, ‘propensity’ or ‘readiness’ could also be interpreted as how quickly a cell fires after stimulus onset. In the AHP simulations, we saw that the aPC required additional current to fire the same number of spikes as for the yPC. On the other hand, the aPC often fired sooner than the yPC. These effects were a result of the increased Ca2+ current in aged cells—the larger Ca2+ current depolarized the cells faster and caused them to fire sooner, but it also caused the SK current to be larger and consequently slowed firing. It is as if the aPCs were initially more excitable, but then ‘burned out’ more quickly than the yPCs.

Overall, we believe our results highlight the importance of moving away from vague terms like ‘excitability’ in favor of precise language that describes the effect of interest (e.g., PCs spiked faster, spiked sooner, etc.). We hope that, in a broader sense, our study will encourage neuroscientists, and particularly aging researchers, to reevaluate how they think and write about excitability.

Supporting information

S1 Fig Plots of model functions.

(A.) Forward (αw) and backward (βw) rate functions, and the time constant (τw), of activation of DK channels in the model. (B.) Steady-state activation curves for DK (w∞), Na+(m∞), and L-type Ca2+(n∞) channels. (C.) Full expressions and plots for each ion current in the model.

(TIF)

S2 Fig Adaptive firing in yPC.

(A.) Voltage response of the young model PC (yPC) in response to a 800 ms 150 pA square-pulse stimulation seen in (B.).

(TIF)

S3 Fig APs and currents underlying adaptive firing in yPC.

(A.) Two action potentials (APs) from the response seen in S2 Fig. (B.) Voltage- and Ca2+-gated currents in the models as indicated in the legend, and their amplitudes and dynamics during the APs. Note that the Na+-K+pump current is not plotted due to its small amplitude.

(TIF)

S4 Fig Early and late adaptive firing in model PCs.

Further examination of the responses seen in Fig 1. (A.) Voltage responses of the yPC and aPC in the first ∼100 ms of the square-pulse stimulation (6 vs. 4 spikes). (B.) Voltage responses of the yPC and aPC in the last ∼700 ms of the square-pulse stimulation (4 vs. 2 spikes).

(TIF)

S5 Fig AHP in yPC.

(A.) Voltage response to a 100 ms square-pulse current injection of sufficient amplitude to elicit 4 APs in the yPC. Inset shows the amplitude and duration of the resulting afterhyperpolarization (AHP). (B.) Current pulse.

(TIF)

S6 Fig Conditional bursting in yPC.

(A.) Bursting in the yPC in response to a 800 ms 100 pA square-pulse current injection seen in (B.).

(TIF)

S7 Fig APs and currents underlying conditional burst firing in yPC.

(A.) Three APs from the response seen in S5 Fig. (B.) Voltage- and Ca2+-gated currents in the models as indicated in the legend, and their amplitudes and dynamics during the APs. Note that the Na+-K+pump current is not plotted due to its small amplitude.

(TIF)

S8 Fig Conditional bursting in yPC and aPC compared at a single stimulation amplitude.

A. Bursting in the yPC (solid black traces) versus aPC (dashed red traces) in response to a 800 ms 100 pA square-pulse stimulation seen in (E.). Corresponding Ca2+ currents, intracellular Ca2+ concentration, and SK currents are shown in (B.), (C.), and (D.), respectively.

(TIF)

S9 Fig Spontaneous bursting in yPC.

(A.) Changes in membrane potential (i.e. spontaneous bursting) in the absence of current stimulation (B.).

(TIF)

S10 Fig APs and currents underlying spontaneous burst firing in yPC.

(A.) Three APs from the response seen in S8 Fig. (B.) Voltage- and Ca2+-gated currents in the models as indicated in the legend, and their amplitudes and dynamics during the APs. Note that the Na+-K+pump current is not plotted due to its small amplitude.

(TIF)

S11 Fig Spontaneous bursting compared in yPC and aPC at single DK current amplitude.

A. Bursting in the yPC (solid black traces) versus aPC (dashed red traces) in the absence of stimulation (E.). Corresponding Ca2+ currents, intracellular Ca2+ concentration, and SK currents are shown in (B.), (C.), and (D.), respectively.

(TIF)

We thank reviewers whose suggestions helped us to improve this manuscript.

10.1371/journal.pone.0308809.r001
Decision Letter 0
Garcia-Ojalvo Jordi Academic Editor
© 2024 Jordi Garcia-Ojalvo
2024
Jordi Garcia-Ojalvo
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version0
9 Jun 2024

PONE-D-24-14388A biophysical minimal model to investigate age-related changes in CA1 pyramidal cell electrical activityPLOS ONE

Dear Dr. McKiernan,

Thank you for submitting your manuscript to PLOS ONE. I apologize for the delay in reaching a decision. We managed to secure the opinion of one reviewer, who has assessed your manuscript very positively; their report is attached below. I would be happy to accept the paper for publication after it has been revised to address the points raised by the reviewer.

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 [This work was supported by grants from the Natural Sciences and Engineering Research Council of Canada, as well as the Ontario Mental Health Foundation, awarded to DFM. This work was also supported by DGAPA-UNAM-PAPIIT IA209817 awarded to ECM; and by DGAPA-UNAM-PAPIIT IA208618 & IN228820, and DGAPA-UNAM-PAPIME PE114919 awarded to MAH-V.].  

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

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3. Have the authors made all data underlying the findings in their manuscript fully available?

Reviewer #1: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

Reviewer #1: Yes

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5. Review Comments to the Author

Reviewer #1: The model presented in this study is impressive, particularly given its simplicity: with just three variables (though many constants), with only one parameter to reproduce the age-related differences. It effectively reproduces the differences between young and old CA1 pyramidal cells in the hippocampus, such as adaptive firing, stimulus-induced bursting, and spontaneous bursting. I thoroughly enjoyed reading it and congratulate the authors on their impressive results, along with the well-done Jupyter notebook that complements the paper excellently. I encourage the authors to continue their work by exploring bifurcation analysis and conducting a more robust exploration of the model's parameter limitations compared to experimental values.

I hope my comments can help to improve this paper.

Major comments:

1) Abstract: The problem is well-introduced, and the rationale for the study is clear. However, please add some statements at the end about the conclusions of your research and its relevance to the field (what's the novelty?).

2) In the introduction you pose some questions [3-8] that are not fully answered by the paper. 2.1) I'd consider revisiting this questions in the discussion together with a mention on how this work could help in the field of AD or Parkinson's, or other age-related pathologies. 2.2) Can this be used to model the impairment of plastic mechanisms?

3) Methods [46-56]: Clarify better what distinguishes this model from the one previously developed.

4) Methods Section 2.1: Please provide a brief explanation of what I_{F} and I_{CaL} are when explaining Equation 1.

5) Clarification on s_x and N_x: The values of s_x are unclear for non-voltage-gated channels (NaT adn DK?), together with the values of N_x. Can you consider adding this information to the Table 1? Is there supporting literature from the values you choose?

6) Consider adding the figures of the Jupyter notebook in an Appendix/Supporting Material, so that it is easier to reference. They will help understanding the model functions and variables, contributions of I_x to V...

7) Recent paper of potential interest to add to the paper (bursting patterns aged vs. young, line 168-169): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10926450/ also consider mentioning it in the intro/discussion.

8) General comments to the figures: 8.1 There are no captions (?); 8.2 Please add the legend (yPC, aPC) + see next comment

9) Figure 1 (and methods 3.1).

9.1 (top panel) Not clear how do you compute the frequency (e.g., 60Hz vs. 40Hz). I think I’d be helpful to have in the figure a visual separation between the two segments you are referring to (first 100ms + the rest), plus a bar plot (for example) that shows quantitatively the differences between young and aged PCs.

9.2 Also, If you don’t want to include the figures in the notebook, at least add in the plot when the square pulse finishes and ends and with which amplitude.

9.3 Again, I’d add the rest of the figures (which are relevant in my opinion) in the appendix (at least).

9.4 Rephrase the text 197-201 so that it is easier to understand which panel you are referring to.

9.5 All above (9.1-9.3) also applies to the other figures (when applicable)!!

10) Parameter tuning: In the methods (and/or results), explain how parameters are tuned to find each firing pattern (I understand it is not only based on literature). Clarify which parameters are changed for each plot.

11) Figure 2, Bottom Panel: Indicate whether the graph shows saturation or continuous increase. If not changing the plot, mention in the caption that this is not a saturation effect.

12) Figures 5 and 6: Consider merging these figures as they contain overlapping information. Clearly indicate which parameters are changed between plots and the reasons for those changes.

Minor comments:

31 means → a means

46 CA1 in blue?

There is a problem with the references to the figures, and It was very hard to guess which figure you might be referring to.

Remove paragraph space between 290-291.

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10.1371/journal.pone.0308809.r002
Author response to Decision Letter 0
Submission Version1
23 Jul 2024

We have detailed our responses to all formatting requests from the editor in our cover letter, and all the suggestions from the reviewer in our response to reviewers document included in our uploaded files. All changes can be seen in the tracked changes version of our manuscript.

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10.1371/journal.pone.0308809.r003
Decision Letter 1
Garcia-Ojalvo Jordi Academic Editor
© 2024 Jordi Garcia-Ojalvo
2024
Jordi Garcia-Ojalvo
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version1
31 Jul 2024

A biophysical minimal model to investigate age-related changes in CA1 pyramidal cell electrical activity

PONE-D-24-14388R1

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10.1371/journal.pone.0308809.r004
Acceptance letter
Garcia-Ojalvo Jordi Academic Editor
© 2024 Jordi Garcia-Ojalvo
2024
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https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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