A Computational Framework for Myelin as a Regulator of Temporal Integration, Neuronal Excitability, and Synaptic Plasticity

ABSTRACT

Myelin regulates neural signaling not only by enabling fast conduction but also by dynamically tuning axonal conduction velocity (CV) and thereby shaping spike timing. While activity‐dependent myelination is thought to optimize neural communication, how changes in myelin translate into altered single‐cell dynamics and plasticity remains unclear. Using a computational modeling approach, we show that disruptions of axonal CV reorganize presynaptic input correlations, leading to systematic changes in postsynaptic excitability, excitation–inhibition balance, and spike‐timing‐dependent plasticity. By spanning CV regimes associated with healthy myelination, demyelination, and excessive myelination, our simulations illustrate how both deficient and excessive CV could induce maladaptive neuronal dynamics. The incorporation of firing‐rate homeostasis into our models further suggests distinct neuronal dynamic consequences for acute versus chronic myelin disruption. Ultimately, these results suggest that axonal CV may serve as a key mechanistic link between myelin plasticity and neural computation, offering a principled framework to interpret the functional consequences of myelin dysregulation in health and disease.

• Computational models illustrate how myelinating glia may shape the temporal integration of spikes upon a common postsynaptic target.

• Models show consequences for synaptic plasticity, neuronal excitability, and the fidelity of neural signals.

1. Introduction

Myelin wraps around axonal membranes and plays a fundamental role in neural signaling. By enabling saltatory conduction—which dramatically increases conduction velocity (CV)—myelin can adjust for variability in length and caliber between different axons (Salami et al. 2003; Seidl 2014; Swadlow et al. 1978; Swadlow and Waxman 2012). Moreover, myelin production by oligodendrocytes (OLs) is modulated by neuronal activity (Gibson et al. 2014; Mount and Monje 2017; Osso and Hughes 2024). This phenomenon (termed activity‐dependent myelination (ADM)) is thought to optimize neural communication by adjusting the CV of action potentials propagating along axons (Seidl 2014; Mount and Monje 2017; Bechler et al. 2015; Fields 2015; Fields and Bukalo 2020; Noori et al. 2020; Talidou et al. 2022; Arancibia‐Cárcamo et al. 2017). Variability in the arrival time of multiple action potentials is generally detrimental to network operations (Salami et al. 2003; Seidl 2014; Noori et al. 2020; Talidou et al. 2022; Pajevic et al. 2014). The modulation of axonal CV by ADM can normalize conduction delays and is thought to promote the coincident, synchronous arrival of presynaptic action potentials at target neurons (Salami et al. 2003; Seidl 2014; Swadlow et al. 1978; Swadlow and Waxman 2012; Fields 2015; Noori et al. 2020; Talidou et al. 2022; Almeida and Lyons 2017; Ford et al. 2015; Chacron 2022; Pajevic et al. 2023).

Little is known as to the effect of structural changes in myelin on the dynamics of individual cells and populations of neurons (Fields 2015; Fields and Bukalo 2020; Noori et al. 2020; Talidou et al. 2022; Bells et al. 2017, 2019), particularly how postsynaptic excitability and synaptic plasticity are influenced by changes in axonal CV. One way to quantify the impact of myelin changes on the dynamics of an individual neuron is to examine how axonal CV influences correlations in its presynaptic inputs. Presynaptic input correlations reflect the degree of synchrony in the timing of afferent action potentials: if spikes reach the postsynaptic cell simultaneously or with a consistent temporal relationship, these spike trains are more correlated (Lefebvre et al. 2025; Izhikevich 2006). Such correlations can emerge naturally due to recurrent circuit connectivity, oscillatory synchrony, common afferent inputs (e.g., sensory stimuli) or endogenous fluctuations in firing rate (Doiron et al. 2016; De La Rocha et al. 2007). Irrespective of their origin, modulations of axonal CV by myelin play an important role in shaping such correlations, with important consequences for neural communication (Seidl 2014; Osso and Hughes 2024; Ford et al. 2015; Pajevic et al. 2023; Lefebvre et al. 2025; Izhikevich 2006) and temporal integration (Jamann et al. 2025).

To characterize the consequences of changes in myelin on single cell dynamics, it is necessary to examine how presynaptic correlations change over a range of axonal CVs that are produced across healthy and pathological states. In the healthy brain, the tuning of presynaptic correlations by myelin plays an important functional role: regulating neural signaling, postsynaptic excitability and fostering synaptic plasticity (Salami et al. 2003; Seidl 2014; Mount and Monje 2017; Osso and Hughes 2024; Fields 2015; Arancibia‐Cárcamo et al. 2017; Almeida and Lyons 2017; Ford et al. 2015; Bacmeister et al. 2020; Caporale and Dan 2008; Ahmadian and Miller 2021). However, in demyelinating diseases, reduced myelination suppresses correlations, impacting temporal integration and causing maladaptive shifts in cellular excitability (Wang and Thompson 2008; Hamada and Kole 2015; Gasselin et al. 2015; Sutor et al. 2000; Madden et al. 2021; Bacmeister et al. 2022; Kuba et al. 2010; Bostock and Sears 1978; Felts et al. 1997; Grubb and Burrone 2010). Moreover, by limiting a network's capacity to tune its CVs, demyelination may impede the normalization of axonal conduction delays (Talidou et al. 2022; Chacron 2022) such that spike‐timing‐dependent plasticity (STDP) is compromised (Izhikevich 2006; Caporale and Dan 2008; Steadman et al. 2020; Madadi Asl et al. 2018a; Madadi Asl et al. 2018b). Conversely, excessive, abnormally increased myelination may reduce spike timing dispersion, amplifying presynaptic correlations and postsynaptic firing rates (Talidou et al. 2022) with potential pathological consequences (Gibson et al. 2014; Mount and Monje 2017; Knowles, Xu, et al. 2022; Kung et al. 2023).

Collectively, these observations suggest that by modulating presynaptic correlations, myelin‐induced changes in CV can entail either healthy or maladaptive effects at the level of individual neurons. These changes are, however, difficult to interpret, given that changes in myelination and neural activity are processes unfolding over vastly different timescales: neural activity operates in milliseconds to seconds, whereas myelination develops over hours to days (Salami et al. 2003; Mount and Monje 2017; Almeida and Lyons 2017; Brette 2009). Over such longer timescales, cellular compensatory mechanisms, such as firing rate homeostasis (FRH) play an important role (Yang and Prescott 2023; Hengen et al. 2013; Benda and Herz 2003; Peron and Gabbiani 2009; Benda 2021). FRH refers to the engagement of one or more activity‐dependent control mechanisms by which neurons adapt their excitability to normalize their spontaneous activity (Hamada and Kole 2015; Gasselin et al. 2015; Yang and Prescott 2023; Hengen et al. 2013), such as cell‐specific regulation of ion channel expression (Yang and Prescott 2023; O'Leary et al. 2014; Goaillard and Marder 2021; Drion et al. 2015; Alonso et al. 2023). Notably, this form of adaptation is invoked when neurons become persistently exposed to an abnormal magnitude of stimuli (Debanne et al. 2019; Campanac et al. 2013) (i.e., persistent exposure to higher or lower magnitudes of stimuli than were experienced previously). Indeed, such changes could be modulated by myelin's aforementioned effects on presynaptic correlations (Salami et al. 2003; Noori et al. 2020; Talidou et al. 2022; Almeida and Lyons 2017; Pajevic et al. 2023).

Previous studies lend support to a mechanistic framework where, by re‐organizing presynaptic correlations, myelin‐induced changes in CV (e.g., resulting from healthy ADM, or from a deficiency or excess in myelin) directly shape the dynamics of neural circuits and networks (Talidou et al. 2022; Bells et al. 2017; Lefebvre et al. 2025; Jamann et al. 2025). The current study extends this framework to model the effects of axonal myelination on neural dynamics at the cellular level. Specifically, our models explore how perturbations in axonal myelination—operationalized as changes in axonal CV (Salami et al. 2003; Arancibia‐Cárcamo et al. 2017; Almeida and Lyons 2017; Ford et al. 2015; Dutta et al. 2018; Freeman et al. 2015; Etxeberria et al. 2016)—may influence a host of neuron‐level dynamics, including temporal integration, neuronal excitability, and synaptic plasticity. Appreciating the relevance of both increases and decreases in myelination for healthy and pathological brain states alike (Bacmeister et al. 2022; Knowles, Xu, et al. 2022; Kung et al. 2023; Rahmanzadeh et al. 2021; Gibson et al. 2018; Knowles, Batra, et al. 2022), our models explore these neuron‐level consequences for both directions of change in myelination.

Our findings suggest that many processes witnessed at the neuronal level (Wang and Thompson 2008; Hamada and Kole 2015; Gasselin et al. 2015; Sutor et al. 2000; Madden et al. 2021; Bacmeister et al. 2022) may emerge naturally from the capacity of axonal CV to influence presynaptic correlations. Specifically, our modeling suggests that axonal CV can invoke both acute and chronic changes in neuronal activity, excitability, excitation‐inhibition (E/I) balance, and the faithful transmission of upstream patterns of activity (i.e., signal fidelity). Moreover, our results offer a possible mechanistic pathway linking changes in myelination to the modulation of spike timing‐dependent plasticity (STDP). Taken together, our simulations highlight a myriad of potential dynamical signatures of myelin plasticity at the cellular scale, with plausible implications for myelin plasticity's involvement across healthy and pathological brain states.

2. Materials and Methods

2.1. Model

We considered a sparsely connected network of Poisson neurons, set in the fluctuation‐driven regime (Talidou et al. 2022; Lefebvre et al. 2025), and relaxed some of its assumptions. In this regime, each neuron is subjected to $K$ convergent presynaptic inputs from a population of $N$ either excitatory or inhibitory cells. Assuming exponential response with the time constant ${\mathrm{\tau }}_m$, the postsynaptic membrane potential (PSP) $v$ of a given postsynaptic cell may be described by the following nondimensionalized stochastic differential equation (Talidou et al. 2022; Gerstner and Kistler 2002; Kriener et al. 2009),

$${\mathrm{\tau }}_m\frac{d}{\mathit{dt}}v=-v+{\sum }_{j=1}^K{w}_j{\mathrm{\eta }}_j\left(t-{\mathrm{\tau }}_j\right)$$ (1)

where $w_j$ are synaptic weights, $p$ is a connection probability (assumed to be identical for both excitatory and inhibitory afferents), and $K=\mathit{pN}$ the effective number of presynaptic neurons synapsing to the postsynaptic neuron. The total number of presynaptic inputs $K$ in Equation (1) can further be divided into excitatory (i.e., $K^E=p{N}^E$) and inhibitory (i.e., $K^I=p{N}^I$) inputs, so that $K^E+K^I=K=\mathit{pN}$ (i.e., superscripts represent whether neurons are either excitatory ($E$) or inhibitory (I)). The terms ${\mathrm{\eta }}_j\left(t\right)={\int }_0^{t}k\left(s\right)X_j\left(s\right)\mathit{ds}$ correspond to postsynaptic impulse response functions with kernel $k\left(s\right)$ over a presynaptic spike train $X_j\left(s\right)$. For simplicity, synaptic transmission is assumed to be instantaneous, such that $k\left(s\right)=D\left(s\right)$, where $D$ stands for the Dirac delta function.

The postsynaptic firing rate $r$ may be computed using the response function $f$, here defined by the sigmoid

$$r=f\left(v\right)=\frac{r_{\mathit{max}}}{2}\left(1+\mathrm{erf}\left[\beta \left(v-h\right)\right]\right)$$ (2)

where $\beta$ corresponds to the response gain and $h$ is the excitability threshold (i.e., analogous to the threshold of depolarization) of the postsynaptic cell. The response function $f$ corresponds to the instantaneous firing probability associated with the membrane potential $v_i$ in Equation (1). Increased probability translates to increased firing rate, whose maximum is here set to $r_{\mathit{max}}=$ 100 Hz. The resulting nonhomogeneous presynaptic Poisson spike trains $X_j$ in Equation (1) with respective presynaptic firing rates $r_j=f\left(v_j\right)$ are represented by the sum of impulses

$$X_j\left(t\right)={\sum }_{t_j}D\left(t-t_j\right)$$ (3)

where $t_j$ represent spike times at the axon initial segments, and $D$ stands for the Dirac delta function. Parameter definitions and values are summarized in Table 1.

TABLE 1.

Summary of model parameters, symbols and variables.

Parameters	Values	Units	Description
$v$	s.d.	a.u.	Membrane potential
${\tau }_m$	10	ms	Membrane time constant
${\tau }_{\text{adapt}}$	$10^3$	ms	FRH time constant
$h$	2	a.u.	Excitability threshold
$h_{\mathrm{ref}}$	2.35	a.u.	Reference threshold value (CV = 1 m/s)
$r_o$	Varies	Hz	Presynaptic firing rate
$r_{\mathrm{sp}}$	5	Hz	Target postsynaptic firing rate
$\beta$	20	a.u.	Neuronal response gain
$p$	s.d.	a.u.	Connection probability
$\mathrm{\tau }$	s.d.	ms	Axonal conduction delay
$c$	s.d.	m/s	Axonal conduction velocity (CV; unspecific)
$c^E$	s.d.	m/s	CV of excitatory afferent axons
$c^I$	s.d.	m/s	CV of inhibitory afferent axons
$K$	s.d.	—	Number of presynaptic cells/inputs (unspecific)
$K^E$	s.d.	—	Number of presynaptic excitatory cells/inputs
$K^I$	s.d.	—	Number of presynaptic inhibitory cells/inputs
$\mathrm{\Sigma }$	s.d.	—	Correlation matrix
${\rho }_{\mathrm{pre}}$, ${\rho }_{\mathrm{pre},\mathit{jk}}$	s.d.	—	Presynaptic spike train correlation coefficient
$k$	2	—	Scale parameter
$\mathrm{\theta }$	4	—	Shape parameter
$\mathrm{ϵ}$	1	${\mathrm{ms}}^{-1}$	STDP learning rate
$w_o$	0.2	a.u.	Baseline synaptic weight
$w_{\mathit{max}}$	0.4	a.u.	Upper bound on synaptic weights

Note: Detailed information is provided in figure captions as well as in source codes. s.d. = simulation‐dependent (see individual figure captions); a.u. = arbitrary units.

Equation (1) describes the membrane potential dynamics of an arbitrary postsynaptic neuron, allowing one to quantify how axonal CV shapes the statistics of its presynaptic inputs and, in turn, the response of the postsynaptic cell. This perspective has been widely adopted to extract analytically tractable and mechanistically interpretable descriptions of recurrent spiking networks (Gerstner and Kistler 2002; Amit and Brunel 1997; Roxin et al. 2011; Kempter et al. 1998; Ostojic et al. 2009). For this to hold, we assume that network connectivity is sparse and spatially uniform, such that each neuron is exposed to the same presynaptic input statistics (Lefebvre et al. 2025; Amit and Brunel 1997; Kempter et al. 1998; Ostojic et al. 2009). Under sparse connectivity, the probability of shared presynaptic inputs vanishes, and presynaptic neurons may be assumed to fire stochastically (Kempter et al. 1998; Derrida et al. 1987; Kree and Zippelius 1991). This further implies that the PSP probability density function $\mathrm{\varphi }\left(v\right)$ is identical across neurons, that is, $\mathrm{\varphi }\left(v_j\right)=\mathrm{\varphi }\left(v_k\right)$ for all $j,k$.

Motivated by these considerations, the dynamics of the membrane potential in Equation (1) depend only on the properties of convergent presynaptic inputs, greatly simplifying both the subsequent analysis and its interpretation. This framework builds upon our prior theoretical investigations into the impact of CV disruption on the dynamics of recurrent spiking neural networks (Talidou et al. 2022), with particular emphasis on regimes exhibiting correlated activity (Lefebvre et al. 2025). Those studies suggest that the impact of changes in myelin on neural activity can be characterized by quantifying how axonal CV shapes the statistics of presynaptic inputs received by individual cells. Indeed, this framework has proved effective for describing the dynamics of a variety of neural networks (Gerstner and Kistler 2002; Amit and Brunel 1997; Roxin et al. 2011; Renart et al. 2007).

2.2. Modeling Myelin, CV and Axonal Lengths

Myelin is known to shape neural activity in various ways (Osso and Hughes 2024; Dutta et al. 2018). In our analysis, we use a phenomenological approach in which the influence of myelin along an axon is modeled through its effect on the mean axonal CV measured across the axon. Axonal CV encompasses the effects of multiple biophysical and physiological factors, such as the axon caliber, the net contribution of myelin quantified by the g‐ratio, length of myelin sheaths, node placement and elongation (Gibson et al. 2014; Mount and Monje 2017; Fields 2015; Auer et al. 2018). In the present study, axon caliber is assumed to remain constant. Consequently, changes in mean axonal CV arise from alterations in myelin microstructure and should be interpreted as reflecting the aggregate effects of changes in g‐ratio, internode length, and nodal organization. These determinants are not modeled explicitly but are instead represented by a single effective parameter: the mean axonal CV. This approximation has successfully been used before to model ADM (Noori et al. 2020; Talidou et al. 2022), representing a trade‐off between physiological relevance and mathematical tractability. Consequently, presynaptic inputs in Equation (1) are subjected to time delays ${\mathrm{\tau }}_j$ which depend on axonal CV, $c$, and lengths $l_j$, that is, ${\mathrm{\tau }}_j=l_j/c$.

We modeled the effect of myelin over presynaptic afferent axons by comparing different physiologically relevant values of CV (Noori et al. 2020; Talidou et al. 2022). To ground our explorations, we focused on CVs reported experimentally in cortical and callosal myelinated fibers of mice, rabbits and cats (Swadlow and Waxman 2012; Ferraina et al. 2002). Using these empirical findings, we determined a physiologically relevant range of CVs spanning 0.3–4 m/s for our analysis. We considered CVs below that range (i.e., $c$ < 0.3 m/s) to reflect deficiency in myelination, while CVs above that range (i.e., $c$ > 4.0 m/s) to reflect excessive myelination.

Axonal lengths $l_j$, representing the distance traveled by action potentials along the presynaptic axon were sampled from a probability distribution whose statistics match those found experimentally: these were drawn from a gamma distribution ranging from 0 to ~30 mm, spanning the range of myelinated axonal fibers across many mammalian species and systems (i.e., callosal, cortico‐cortical, and cortico‐subcortical) (Swadlow and Waxman 2012; Ferraina et al. 2002). Specifically, the lengths $l_j$ have been sampled from a gamma distribution $\mathrm{\pi }\left(\mathrm{l}\right)=\mathrm{\Gamma }\left(\mathrm{l};\left[\alpha ,{\kappa }_l\right]\right)$ with scale parameter $\alpha$ and shape parameter $\mathrm{\kappa }$. The probability distribution of conduction delays follows directly from that choice and also follows a Gamma distribution given by $\mathrm{\pi }\left(\mathrm{\tau }\right)=\mathrm{\Gamma }\left(\mathrm{\tau };\left[\alpha ,{\kappa }_{\tau }\right]\right)$, where ${\mathrm{\kappa }}_{\mathrm{\tau }}={\mathrm{\kappa }}_{\mathrm{l}}/c$. We have here chosen the shape parameter $\alpha$ = 2 and varied the scale parameter ${\mathrm{\kappa }}_l$ to fit the physiological range of axonal lengths observed experimentally (i.e., Figure 1D; see Section 3).

FIGURE 1.

(A) Schematic of the influence of presynaptic conduction delays on postsynaptic activity. Presynaptic neurons (gray triangles) relay spikes to a postsynaptic cell (black circle). Differences in presynaptic axonal lengths (gray lines) and levels of myelination (overlaid black circles and rectangles, portraying myelinating oligodendrocytes) both shape presynaptic conduction delays, directly influencing temporal integration of spikes at the postsynaptic cell and, in turn, postsynaptic activity. Gray arcs denote synapses. (B) Sigmoidal response function of the postsynaptic cell, as outlined in Equation (2) (see Methods). Across all models, the instantaneous probability of a postsynaptic spike follows a sigmoidal relationship with postsynaptic membrane potential. (C) The inverse relationship between axonal CV and conduction delays, plotted over axonal lengths ($l$) of 5, 10, and 20 mm. As CV increases, conduction delays decrease to become more homogeneous across different axonal lengths. (D) Gamma distribution of presynaptic axonal lengths, common to all simulations performed.

2.3. Statistics of Postsynaptic Membrane Potential

Presynaptic spike trains $X_j$ in Equation (1) are a priori assumed to be correlated with pairwise correlation ${\rho }_{\mathrm{pre},\mathit{jk}}$. These correlations are thought to result from recurrent circuit connectivity (Talidou et al. 2022; Doiron et al. 2016), emergent synchrony and/or common afferent inputs (e.g., sensory), and their impact on neural activity relies heavily on axonal CV. Owing to the choice of synaptic kernel $k\left(s\right)$ above, the first moment (i.e., $\mu$) of the postsynaptic membrane potential (PSP) is easily computed, that is,

$$\mu \equiv ⟨v⟩={\sum }_{j=1}^N{w}_j{r}_j$$ (4)

since $⟨{\mathrm{\eta }}_j⟩=r_j$ and assuming independence between synaptic weights ($w_j$) and presynaptic firing rates (i.e., $r_j$). The average $⟨·⟩$ is here taken with respect to time (i.e., $⟨v⟩={\int }_{T}v\mathrm{\varphi }\left(v\right)\mathit{dv}$), where $\mathrm{\varphi }\left(v\right)$ corresponds to the PSP probability density function, assumed to be identical for all neurons in the network.

For balanced excitatory (i.e., $w_j=w_o>0$) and inhibitory (i.e., $w_j=-\left|w_o\right|<0$) synapses and identical presynaptic firing rates (i.e., $r_j=r_o$) the mean PSP simplifies further to

$$\mathrm{\mu }=p{N}^E{w}_o{r}_o-p{N}^I{w}_o{r}_o=\left(K^E-K^I\right)w_o{r}_o$$ (5)

which is zero when $K^E=K^I$. As can be seen in Equation (5), the PSP mean $\mathrm{\mu }$ does not depend on correlations in presynaptic inputs (i.e., ${\rho }_{\mathrm{pre},\mathit{jk}}$) or on axonal CV. These quantities impact the postsynaptic response through the second moment of the PSP, conditional on synaptic coupling and the distribution spike arrival times. The second moment of $v$ in Equation (1) may be expressed as (Gerstner and Kistler 2002)

$$⟨v^2⟩={\sum }_{j,k}^K{w}_j{w}_k{\int }_{-\infty }^t{\int }_{-\infty }^t\mathit{dsd}{s}^{\prime }{e}^{-\left(2t-s-s^{\prime }\right)}⟨X_j\left(s-{\mathrm{\tau }}_j\right)X_k\left(s^{\prime }-{\mathrm{\tau }}_k\right)⟩$$ (6)

To simplify the expression above, we first note that the covariance between two correlated spike trains with presynaptic pairwise correlation matrix $\mathrm{\Sigma }$ may be written as (Gerstner and Kistler 2002; Kriener et al. 2009),

$$⟨X_j\left(t_1\right)X_k\left(t_2\right)⟩={\mathrm{\rho }}_{\mathrm{pre},\mathit{jk}}\sqrt{r_j{r}_k}D\left(t_1-t_2\right)+r_j{r}_k$$ (7)

where ${\rho }_{\mathrm{pre},\mathit{jk}}={\left[\mathrm{\Sigma }\right]}_{j,k}$. Using this expression, one may perform the integral in Equation (6) to compute the variance ${\sigma }^2=⟨v^2⟩-{\mu }^2$ for the PSP in Equation (1), obtaining

$${\mathrm{\sigma }}^2=\frac{1}{2}{\sum }_{j,k}^K{w}_j{w}_k{\mathrm{\rho }}_{\mathrm{pre},\mathit{jk}}\sqrt{r_j{r}_k}{e}^{-\left|{\mathrm{\Delta }}_{\mathit{jk}}\right|}$$ (8)

with ${\mathrm{\Delta }}_{\mathit{jk}}={\mathrm{\tau }}_j-{\mathrm{\tau }}_k$ being the difference in conduction delay from the presynaptic neuron $j$ and $k$ towards the postsynaptic cell. As such, in absence of presynaptic correlation (i.e., ${\rho }_{\mathrm{pre},\mathit{jk}}=0$) or time delay (i.e., $c\to \infty$), Equation (8) reduces to the well‐known expression $⟨v^2⟩=\frac{1}{2}{\sum }_j^K{w}_j^2{r}_j$, which scales like $\mathcal{O}\left(K\right)$ as expected from the diffusion limit approximation (Gerstner and Kistler 2002; Capocelli and Ricciardi 1971; Lánskỳ 1984). In this case, there is no dependence on axonal CV. However, whenever ${\rho }_{\mathrm{pre},\mathit{jk}}\ne 0$, the variance scales with the square of the number of presynaptic inputs, that is, $\mathcal{O}\left(K^2\right)$ and further depends on CV. We note that Equation (8) is general and may be used for both excitatory and inhibitory presynaptic inputs. Equation (8) may be further simplified by introducing the effective pairwise correlation ${\rho }_{\mathrm{pre},\mathit{jk}}^{\mathrm{eff}}={\rho }_{\mathrm{pre},\mathit{jk}}{e}^{-{\mathrm{\Delta }}_{\mathit{jk}}}$ which takes axonal lengths and CV into account. These effective pairwise correlations are elements of the effective correlation matrix ${\mathrm{\Sigma }}^{\mathrm{eff}}$, that is, ${\left[{\mathrm{\Sigma }}^{\mathrm{eff}}\right]}_{j,k}={\rho }_{\mathrm{pre},\mathit{jk}}^{\mathrm{eff}}$. Using these, one may express the PSP variance as

$${\mathrm{\sigma }}^2=\frac{1}{2}{w}_o^2{r}_o{\sum }_{j,k}^K{\mathrm{\rho }}_{\mathrm{pre},\mathit{jk}}^{\mathrm{eff}}$$ (9)

where we have assumed balanced excitatory (i.e., $w_{j,k}=w_o>0$) and inhibitory (i.e., $w_{j,k}=-\left|w_o\right|<0$) synaptic weights and the same firing rate for all presynaptic spike trains (i.e., $r_{j,k}=r_o$). As an illustrative example, if one assumed that the CV (i.e., $c$) is the same for all axons, the delay dispersion between axons of lengths $l_j$ and $l_k$ becomes

$${\mathrm{\Delta }}_{\mathit{jk}}={\mathrm{\tau }}_j-{\mathrm{\tau }}_k=\frac{l_j}{c}\mathit{-}\frac{l_k}{c}=\frac{1}{c}\left(l_j\mathit{-}{l}_k\right)$$ (10)

which vanishes whenever $c\to \infty$ (i.e., $e^{-\left|{\mathrm{\Delta }}_{\mathit{jk}}\right|}\to 1$) or diverges whenever $c\to 0$ (i.e., $e^{-\left|{\mathrm{\Delta }}_{\mathit{jk}}\right|}\to 0$). Hence, the PSP variance ${\sigma }^2$ in Equation (9) scales with conduction velocity: the faster the CV, the higher the variance of the PSP (see Figure 5B).

FIGURE 5.

Excitatory and inhibitory CVs tune neural excitability and E/I balance. (A) Populations of excitatory (gray triangles) and inhibitory presynaptic cells (blue circles) with different axonal CVs, projecting to a common postsynaptic cell (black circle). The axonal CV of excitatory and inhibitory afferent axons (associated with red and blue myelinating OLs, respectively) can be varied independently. Gray arcs represent individual synapses. The bottom panel illustrates how discrepancies between excitatory and inhibitory CVs amplify postsynaptic potential (PSP) variance (red line: $c^E$ = 5.0 m/s, $c^I$ = 0.25 m/s; blue line: $c^E$ = 0.25 m/s, $c^I$ = 5.0 m/s), whereas similar CVs decrease PSP variance (black line: $c^E$ = $c^I$ = 5.0 m/s). (B) Mean PSP ($\mu$; top) as a function of the difference between excitatory and inhibitory CVs (i.e., $\mathrm{\Delta }c=c^E-c^I$ ) at different values of stimulation amplitude ($\mathit{\delta r}$ = [−50, 0, +50] Hz) (top). No change in mean PSP is seen, irrespective of CV or stimulus amplitudes. However, the PSP variance (${\sigma }^2$; bottom) scales with both $\mathrm{\Delta }c$ and stimulus amplitude. Both $c^E$ and $c^I$ were varied independently between 0.1 and 5 m/s. Numerical simulations (gray dots) are plotted alongside theoretical predictions (black lines). (C) Effective E/I ratio computed with EPSP and IPSPs variances, as a function of excitatory and inhibitory CVs. Balance is achieved (i.e., $E/I\approx 1$) whenever $c^E\approx c^I$ along the diagonal. (D) Associated changes in excitability threshold (i.e., $h$, in the chronic phase with FRH). Differences between excitatory and inhibitory CVs drive hypoexcitability (i.e., larger values for the excitability threshold). (E) Effect of excitatory and inhibitory CV on the postsynaptic excitability profile. Differences between excitatory and inhibitory CVs increase the postsynaptic spontaneous firing rate in the acute phase (i.e., no FRH) (top; $c^I$ = 1 m/s, $c^E$ = 0.25 m/s, blue line; 1 m/s, black line; 2.5 m/s, red line), but decrease it in the chronic phase (i.e., with FRH; bottom). (F) Cross‐correlation between pre‐ and postsynaptic spike trains ${\rho }_{\mathrm{pre}-\text{post}}$ as a function of the difference between excitatory and inhibitory CVs (i.e., $\mathrm{\Delta }c=c^E-c^I$). The cross‐correlation was computed and averaged over the presynaptic excitatory population across independent epochs of $T$ = 20 s at different stimulus amplitudes ($\mathrm{\delta }r$ = [−50, −25, 0, +25, and +50] Hz), with no noticeable difference in cross‐correlation across conditions (dots and error bars reflect the mean ± SD). Increasing the inhibitory CV invariably suppresses ${\rho }_{\mathrm{pre}-\text{post}}$, while the opposite occurs when excitatory CV is increased. Parameters are $\beta$ = 20, $w_o$ = 0.2, $h_{\mathrm{ref}}$= 2.35, $r_o$ = 80 Hz, $k$ = 2, ${\theta }_l$ = 4, $r_{\mathrm{sp}}$ = 5 Hz, $K^E$ = 50, $K^I$ = 50, ${\rho }_{\mathrm{pre},\mathit{jk}}$ = ${\rho }_{\mathrm{pre}}$ = 0.2. Parameters have a.u. unless otherwise specified.

2.4. Postsynaptic Excitability

The PSP $v$ in Equation (1) can be assumed to admit a normally distributed probability density function $\varphi \left(v\right)$ with mean $\mu$ and variance ${\sigma }^2$, so that the average postsynaptic firing rate resulting from a (non‐synaptic) input $I$ becomes (Lefebvre et al. 2025; Hutt et al. 2023)

$$\begin{array}{c}⟨r⟩=⟨f\left(v+I\right)⟩\approx {\int }_{-\infty }^{\infty }f\left(v+I\right)\mathrm{\varphi }\left(v\right)\mathit{dv}\hfill \\ =\frac{r_{\max }}{2}\left(1+\mathrm{erf}\left(\frac{\beta \left(\mu \mathit{+}I\mathit{-}h\right)}{\sqrt{2{\beta }^2{\sigma }^2+1}}\right)\right)\equiv F\left(I,\mu ;{\sigma }^2\right)\hfill \end{array}$$ (11)

The function $F$ above corresponds to the average excitability profile of the postsynaptic neuron associated with an input $I$, given an excitability threshold parameter $h$ and PSP statistics (i.e., $\mu$, ${\sigma }^2$) determined previously. We note that $F\left(0;\mu ,{\sigma }^2\right)$ corresponds to the mean firing rate of the postsynaptic neuron in absence of stimulation (i.e., $I$ = 0). Equation (11) was used alongside Equation (8) to confirm the alignment between numerical simulations and analytics. The effects of changes in axonal CV on Equations (11) (and by extension on Equations (5) and (9)) are plotted in Figures 3, 4, 5.

FIGURE 3.

Changes in axonal CV engage firing rate homeostasis. (A) Changes in CV influence postsynaptic firing rate and trigger firing rate homeostasis (FRH), modulating the excitability threshold ($h$) of the postsynaptic cell. Shaded lines correspond to independent trials, and bold lines correspond to theoretical predictions. Acute changes in CV (*left gray shaded box) cause either a sudden increase ($c$ = 5.0 m/s, red solid line) or decrease ($c$ = 0.25 m/s, blue solid line) in firing rate compared to the reference CV ($c$ = 1.0 m/s, black solid line). Associated changes in the excitability threshold (bottom; $c$ = 0.25 m/s, blue line; $c$ = 5.0 m/s, red line) due to FRH normalizes firing rates, making them similar to each other in the chronic phase (**right gray shaded box). (B) Postsynaptic firing rate as a function of CV and presynaptic spike train correlations (${\rho }_{\mathrm{pre}}$). Acute changes in CV significantly influence postsynaptic firing rates (left). After FRH in the chronic phase, postsynaptic firing rates homogenize (right), irrespective of presynaptic spike train correlations. Dots and error bars reflecting the mean ± SD for numerical results obtained over five independent trials of duration $T$ = 5 s are shown alongside analytical calculations (black lines). (C) Postsynaptic membrane potential (PSP) fluctuations resulting from correlated presynaptic inputs for various CVs ($c$ = 0.25 m/s, blue solid line; $c$ = 1.0 m/s, black solid line; and $c$ = 5.0 m/s, red solid line). Increases in axonal CV amplify the variance but not the mean of the PSP. The horizontal dashed lines correspond to the value of the excitability threshold (i.e., $h$) resulting from FRH. (D) Excitability of a postsynaptic neuron over different values of axonal CV ($c$ = 0.25 m/s, blue dots/line; $c$ = 1.0 m/s, black dots/line; $c$ = 5.0 m/s, red dots/line). Numerical results (dots) obtained over 10 independent trials of duration $T$ = 5 s are shown alongside analytical calculations (lines). In the acute phase (top), excitability generally increases with CV, whereas in the chronic phase (bottom), the opposite occurs. Parameters are $\beta$ = 20, $w_o$ = 0.2, $r_o$ = 80 Hz, $r_{\mathrm{sp}}$ = 5 Hz, ${\tau }_{\text{adapt}}$ = 10³ ms, $h_{\mathrm{ref}}$= 2.35, ${\rho }_{\mathrm{pre},\mathit{jk}}$ = ${\rho }_{\mathrm{pre}}$ = 0.2, $k$ = 2, $\theta$ = 4, $K^E$ = 100, $K^I$ = 0. Parameters have a.u. unless otherwise specified.

FIGURE 4.

Impact of axonal CV on presynaptic correlations and signal fidelity. (A) Axonal CV modulates pairwise correlations between presynaptic spike trains. The extent to which correlated presynaptic activity (${\rho }_{\mathrm{pre},\mathit{jk}}$) between two presynaptic neurons $j$ and $k$ (gray triangles) remains correlated upon delivery to the postsynaptic cell (${\rho }_{\mathrm{pre},\mathit{jk}}^{\mathrm{eff}}$) scales inversely with the difference in their conduction delays $(\mid {\tau }_k-{\tau }_j\mid )$. Similar delays preserve presynaptic correlations, whereas discrepant delays dampen them. (B) Effective correlation matrix ${\mathrm{\Sigma }}^{\mathrm{eff}}$ between presynaptic spike trains with uniform pairwise correlations ${\rho }_{\mathit{jk}}$ = ${\rho }_{\mathrm{pre}}$ = 0.2. To compute these correlations, gamma‐distributed axonal lengths (see Section 2) and a uniform CV of $c$ = 0.25 m/s (left), $c$ = 1.0 m/s (middle), or $c$ = 5.0 m/s (right) were used. The presynaptic neuron index represents each individual presynaptic neuron, ranked by its axonal length. At higher CVs, presynaptic correlations are increasingly preserved, regardless of axonal length, owing to a greater homogenization of conduction delays. (C) Excitability threshold $h$ as a function of axonal CV and presynaptic correlation (${\rho }_{\mathrm{pre}}$) resulting from FRH. (D) Cross‐correlation (${\rho }_{\mathrm{pre}-\text{post}}$) between a given presynaptic cell and the postsynaptic neuron as a function of stimulation amplitude (i.e., $\mathit{\delta r}$, expressed in Hz) and CV in the acute phase (i.e., no FRH) computed numerically over independent epochs of $T$ = 60 s. The cross‐correlation was computed with respect to a presynaptic (excitatory) neuron and averaged across the (excitatory) presynaptic population. The dashed line traces the maximum cross‐correlation across each of the three CVs. (E) Same as panel (D) in the chronic phase (i.e., with FRH). Other parameters are $\beta$ = 20, $w_o$ = 0.2, $h_{\mathrm{ref}}$= 2.35, $r_o$ = 80 Hz, $k$ = 2, ${\theta }_l$ = 4, $r_{\mathrm{sp}}$ = 5 Hz, $K^E$ = 100, $K^I$ = 0. In panels (B–E), ${\rho }_{\mathrm{pre},\mathit{jk}}$ = ${\rho }_{\mathrm{pre}}$ = 0.2. Parameters have a.u. unless otherwise specified.

2.5. Firing Rate Homeostasis

To include cellular compensatory effects into consideration in our model, we introduced firing rate homeostasis (FRH) (Yang and Prescott 2023; Hengen et al. 2013; Benda and Herz 2003; Peron and Gabbiani 2009; Benda 2021), which may be modeled by making the threshold (i.e., $h$) (Kobayashi et al. 2009; Mejias and Torres 2011) in Equation (2) adapt against variations of the firing rate. In our model, the threshold parameter $h$ obeys the following adaptation law

$${\tau }_{\text{adapt}}\frac{d}{\mathit{dt}}h=-h+G\left(\mu ,{\sigma }^2\right)$$ (12)

where $G\left(\mu ,{\sigma }^2\right)=\mu -\frac{\sqrt{1+2{\beta }^2{\sigma }^2}}{\beta }{\mathrm{erf}}^{-1}\left(2r_{\mathrm{sp}}/r_{\mathit{max}}-1\right)$ is simply the inverse of Equation (11) above for $I=0$. Note that here ${\mathrm{erf}}^{-1}$ refers to the inverse error function. By construction, the asymptotic value of the parameter $h$ in Equation (12) above maintains the spontaneous firing rate of the postsynaptic neuron at a given target set point $⟨r⟩=r_{\mathrm{sp}}$ (see Table 1). The parameter ${\tau }_{\text{adapt}}$ corresponds to the FRH time constant, considered to be slow compared with the membrane time constant of the postsynaptic neuron (i.e., ${\tau }_{\text{adapt}}\gg {\tau }_m$; see Table 1).

To quantify changes in excitability across different values of axonal CV, we have considered a reference threshold value $h_{\mathrm{ref}}$ associated with a CV of 1 m/s. This value was determined by evaluating the dynamics of Equation (1) for parameters listed in each figure (i.e., see Table 1 and figure captions), and corresponds to the asymptotic value (i.e., fixed point) of Equation (12) for $c$ = 1 m/s: $h_{\mathrm{ref}}=G\left(\mu ,{\sigma }_o^2\right)$, where the mean $\mathrm{\mu }$ and variance ${\sigma }_o^2$ are given by Equation (5) and Equation (9) for $c$ = 1 m/s, respectively. For simulations involving different CVs, this reference value for the threshold (i.e., $h_{\mathrm{ref}}$) was used as the initial condition in Equation (12), that is $h\left(0\right)=h_{\mathrm{ref}}$.

In our simulations, we have considered the effect of perturbations in CV over two distinct phases: (i) the acute phase, reflecting postsynaptic dynamics in response to CV changes before FRH is invoked (i.e., while the excitability threshold remains at a reference value $h=h\left(0\right)=h_{\mathrm{ref}}$); and (ii) the chronic phase, reflecting postsynaptic dynamics after FRH has stabilized, corresponding to the asymptotic value (i.e., fixed point) of Equation (12), that is, $h=G\left(\mu ,{\sigma }^2\right)$, where $\mu$ and ${\sigma }^2$ are computed for different CV and parameter values in each figure. For the benefit of accelerating simulations, the timescale ${\tau }_{\text{adapt}}$ was set to a higher value compared to what is observed experimentally. However, this does not impact the asymptotic value of Equation (12).

2.6. Cross‐Correlation and Signal Fidelity

The fidelity of neural signals between pre‐ and postsynaptic neurons may be quantified by computing the cross‐correlation ${\rho }_{\mathrm{pre}-\text{post}}$ between a given presynaptic spike train $X_j$ for a presynaptic neuron of index $j$ in Equation (1), and the postsynaptic spike train, which we here define as Y (Kempter et al. 1998). This correlation measures the extent to which a presynaptic spike train $X_j$ is represented in the response of a postsynaptic neuron. The covariance between pre‐ and postsynaptic spike trains is obtained by considering both the presynaptic spiking probability $P\left(X_j\right)$ and the conditional probability of a postsynaptic spike train $P\left(Y|X_j\right)$ given such a presynaptic spike train, that is

$$⟨X_{j}Y⟩=\int \int X_j\mathit{YP}\left(X_j\right)P\left(Y|X_j\right)d{X}_j\mathit{dY}$$ (13)

The above general expression can be computed by considering the average firing probability of the postsynaptic neuron conditioned on a PSP perturbation $\delta$, caused by one or many presynaptic spike(s). Mathematically, this can be expressed as (Kempter et al. 1998)

$$⟨X_{j}Y⟩\approx \frac{1}{T}{\int }_T{X}_j\left(s\right)F\left(\mathrm{\delta }\left(s\right)\right)\mathit{ds}$$ (14)

where $F$ is the average postsynaptic firing rate in Equation (11). The above expression reduces to

$$\frac{1}{T}{\sum }_{t_j}F\left(\mathrm{\delta }\left(t_j\right);\mathrm{\mu },{\mathrm{\sigma }}^2\right)=r_{j}F\left(\mathrm{\delta }\left(t_j\right);\mu ,{\sigma }^2\right)$$ (15)

where $r_j$ is the firing rate of the presynaptic spike train $X_j$ with spike timing $t_j$. In purely excitatory networks (i.e., $K=K^E,w_j=w_o>0$), instantaneous perturbations in PSP resulting from presynaptic spike trains with uniform presynaptic pairwise correlation (i.e., ${\rho }_{\mathrm{pre},\mathit{jk}}={\rho }_{\mathrm{pre}}$) can be written as (Gerstner and Kistler 2002; Kempter et al. 1998)

$$\begin{array}{c}\delta \left(s\right)=\left\{\begin{array}{c}\left(w_o+\left(K-1\right)w_o{\rho }_{\mathrm{pre}}S\right)e^{\left(t_j-s\right)},s>t_j\hfill \\ 0,\text{otherwise}.\hfill \end{array}\right.\hfill \end{array}$$ (16)

where $S={\mathbb{E}}_{\left(j,k\right)}\left[e^{-\left|{\mathrm{\Delta }}_{j}k\right|}\right]$ is the mean coincidence factor of presynaptic inputs averaged over all presynaptic neuron pairs, and ${\mathrm{\Delta }}_{\mathit{jk}}={\tau }_j-{\tau }_k$ is the conduction delay dispersion. These allow us to write the average pairwise zero‐lag covariance in purely excitatory networks

$$⟨X_{j}Y⟩\approx r_{o}F\left(\left(w_o+\left(K-1\right)w_o{\rho }_{\mathrm{pre}}S\right),\mu ;{\sigma }^2\right)$$ (17)

where we have assumed identical presynaptic firing rates (i.e., $r_j=r_o$). This expression allows us to appreciate the effect of correlated input and axonal CV on the fidelity of neuronal signals. If there is no presynaptic input correlation (i.e., ${\rho }_{\mathrm{pre}}=0$), postsynaptic firing probability increases only by an amount $w_o$ due to presynaptic spikes. However, whenever ${\rho }_{\mathrm{pre}}\ne 0$, the covariance between pre‐ and postsynaptic activity increases with the coincidence factor $S$, which scales with axonal CV. Indeed, $S\to 1$ whenever $c\to \infty$, and conversely, $S\to 0$ whenever $c\to 0$. Faster CV promotes presynaptic spike coincidence, thereby amplifying the covariance between pre‐ and postsynaptic spike trains.

Cross‐correlation follows directly:

$$\begin{array}{c}{\rho }_{\mathrm{pre}-\text{post}}=\frac{\left(r_{o}F\right(w_o+\left(K-1\right)w_o{\mathrm{\rho }}_{\mathrm{pre}}S;\mu ,{\sigma }^2)-r_{o}F(0;\mu ,{\sigma }^2))}{\sqrt{r_{o}F(0;\mu ,{\sigma }^2)}}\hfill \end{array}$$ (18)

where we assumed that $\mathrm{Var}\left[X\right]=r_o$ and $\mathrm{Var}\left[Y\right]=F\left(0;\mu ,{\sigma }^2\right)$ as expected for Poisson spike trains. Equation (18) was used to validate numerical simulations in Figure 4D,E as well as Figure 5F. In the case of statistical independence between presynaptic and postsynaptic spike trains, one obtains ${\mathrm{\rho }}_{\mathrm{pre}-\text{post}}=0$, as expected.

2.7. Extension to Excitatory and Inhibitory Presynaptic Inputs

Whenever both excitatory ($K^E$) and inhibitory ($K^I$) presynaptic inputs are present, it becomes convenient to separate the PSP $v$ in Equation (1) as the sum of both excitatory and inhibitory contributions

$$v=v^E+v^I$$ (19)

where $v^E$ and $v^I$ correspond to the excitatory (EPSP) and inhibitory postsynaptic potentials (IPSP), respectively. For balanced excitatory (i.e., $w_j=w_o>0$) and inhibitory (i.e., $w_j=-\left|w_o\right|<0$) synapses, identical presynaptic firing rates (i.e., $r_j=r_o$) and uniform pairwise presynaptic correlations ${\rho }_{\mathrm{pre},\mathit{jk}}={\rho }_{\mathrm{pre}}$, the EPSPs and IPSPs components in Equation (19) have the respective means

$${\mu }^E=⟨v^E⟩=K^E{w}_o{r}_o$$

$${\mu }^I=⟨v^I⟩=-K^I{w}_o{r}_o$$ (20)

and variances

$${\left({\sigma }^E\right)}^2=\frac{1}{2}{w}_o^2{r}_o{\rho }_{\mathrm{pre}}{\sum }_{j,k\in K^E}{e}^{-\left|{\mathrm{\Delta }}_{\mathit{jk}}^E\right|}$$

$${\left({\sigma }^I\right)}^2=\frac{1}{2}{w}_o^2{r}_o{\mathrm{\rho }}_{\mathrm{pre}}{\sum }_{j,k\in K^I}{e}^{-\left|{\mathrm{\Delta }}_{\mathit{jk}}^I\right|}$$ (21)

Here, the time delay dispersion terms are given by ${\mathrm{\Delta }}_{\mathit{jk}}^E=\frac{1}{c^E}\left(l_j^E-l_k^E\right)$ and ${\mathrm{\Delta }}_{\mathit{jk}}^I=\frac{1}{c^I}\left(l_j^I-l_k^I\right)$, where we have introduced the CV of both excitatory (i.e., $c^E$) and inhibitory (i.e., $c^I$) afferent axons. This allows us to vary the axonal CV of excitatory and inhibitory afferents independently. It is worth noting that the separation performed in Equations ((19), (20), (21)) preserves the overall PSP statistics in Equation (5) and (8). Indeed, one has $\mu ={\mu }^E+{\mu }^I$ and

$${\sigma }^2={\left({\sigma }^E\right)}^2+{\left({\sigma }^I\right)}^2-2\mathrm{Cov}\left(v^E,v^I\right)$$ (22)

where $\mathrm{Cov}\left(v^E,v^I\right)=1/2w_o^2{r}_o{\rho }_{\mathrm{pre}}\sum _{j\in K^E,k\in K^I}{e}^{-\left|{\mathrm{\Delta }}_{\mathit{jk}}^{E,I}\right|}$ corresponds to the covariance between the EPSP and IPSP. Postsynaptic mean firing rates as a function of $c^E$ and $c^I$ may hence be calculated directly from Equation (11), as shown in Figure 5E.

2.8. Signal Fidelity

The fidelity of neural signals can be quantified using the cross‐correlation ${\rho }_{\mathrm{pre}-\text{post}}$, now expressed as a function of the CV of either excitatory or inhibitory axons. Indeed, setting $K=K^E+K^I$, assuming balanced excitatory (i.e., $w_j=w_o>0$) and inhibitory (i.e., $w_j=-\left|w_o\right|<0$) synaptic coupling, one may rewrite Equation (16) as

$$\begin{array}{c}\delta \left(s\right)=\left\{\begin{array}{c}\left(w_o+\left(K^E-1\right)w_o{\rho }_{\mathrm{pre}}{\mathrm{S}}^E+K^i{w}_o{\rho }_{\mathrm{pre}}{\mathrm{S}}^I\right)e^{\left(t_j-s\right)},s>t_j\hfill \\ 0,\text{otherwise}.\hfill \end{array}\right.\hfill \end{array}$$ (23)

while for a presynaptic inhibitory cell, one obtains instead

$$\begin{array}{c}\delta \left(s\right)=\left\{\begin{array}{c}\left(-w_o+K^E{w}_o{\rho }_{\mathrm{pre}}{\mathrm{S}}^E+\left(K^I-1\right)w_o{\rho }_{\mathrm{pre}}{\mathrm{S}}^I\right)e^{\left(t_j-s\right)},s>t_j\hfill \\ 0,\text{otherwise}.\hfill \end{array}\right.\hfill \end{array}$$ (24)

Here, ${\mathrm{S}}^E={\mathbb{E}}_{\left(j,k\right)\in K^E}\left[e^{-\left|{\mathrm{\Delta }}_{\mathit{jk}}^E\right|}\right]$ and ${\mathrm{S}}^I={\mathbb{E}}_{\left(j,k\right)\in K^I}\left[e^{-\left|{\mathrm{\Delta }}_{\mathit{jk}}^I\right|}\right]$ corresponds to the mean coincidence factor taken among excitatory and inhibitory presynaptic populations, respectively.

2.9. Axonal CV and Excitation‐Inhibition Balance

It is possible to quantify the effect of axonal CVs on excitation–inhibition balance by using the statistics of EPSPs and IPSPs computed previously. By convention, this is usually done by computing the E/I ratio, which may be calculated as the ratio of the mean EPSP and IPSP as per Equation (20),

$$\frac{E}{I}=\left|\frac{{\mu }^E}{{\mu }^I}\right|$$ (25)

To emphasize the influence of axonal CV, one may consider the balanced state, in which the mean PSP is zero: mean excitatory presynaptic inputs are perfectly canceled by inhibitory inputs, setting postsynaptic responses into a fluctuation‐driven regime for which $E/I\approx 1$ (Ahmadian and Miller 2021; Renart et al. 2007; Baker et al. 2019). For simplicity, we here enforced this balance by choosing the same number of excitatory and inhibitory presynaptic neurons (i.e., $K^E=K^I$) as well as identical synaptic weights for both excitatory (i.e., $w_j=w_o>0$) and inhibitory (i.e., $w_j=-\left|w_o\right|<0$) synapses. In this case, $E/I=1$ whenever presynaptic neurons possess the same firing rate $r_o$.

By construction, Equation (25) does not capture the potential influence of axonal CVs, relying purely on the mean EPSP and IPSP and yielding $E/I=1$. One may alternatively consider the following ratio,

$$\frac{E}{I}=\frac{{\left({\sigma }^E\right)}^2}{{\left({\sigma }^I\right)}^2}$$ (26)

where the ratio is now computed using EPSP and IPSP variances instead (see Equation (21)). According to the assumptions listed above, the E/I ratio simplifies to:

$$\frac{E}{I}=\frac{{\sum }_{j,k\in K^E}{e}^{-\left|{\mathrm{\Delta }}_{\mathit{jk}}^E\right|}}{{\sum }_{j,k\in K^I}{e}^{-\left|{\mathrm{\Delta }}_{\mathit{jk}}^I\right|}}$$ (27)

The expression above is dependent only on the statistics of axonal lengths and CVs of excitatory and inhibitory afferent axons. If axon lengths are assumed to be similar between these different groups of presynaptic cells (e.g., by being sampled from the same distribution, for instance), Equation (27) suggests that the E/I ratio depends on how much excitatory and inhibitory CVs differ from one another. This prompted us to consider the quantity $\mathrm{\Delta }c=c^E-c^I$, defined as the difference between excitatory and inhibitory CV. Using this metric, for the same axonal length distributions, excitation‐inhibition balance (i.e., E/I $\approx 1$) is achieved whenever $\mathrm{\Delta }c\approx 0$ (i.e., whenever the excitatory and inhibitory CVs are equal to each other). However, if excitatory and inhibitory CVs differ, the E/I ratio may flip towards excitation (i.e., E/I > 1, $\mathrm{\Delta }c$>0) or inhibition (i.e., E/I < 1, $\mathrm{\Delta }c$<0). Equation (27) was computed numerically to generate Figure 5C.

2.10. Linking Axonal CV With Spike‐Timing‐Dependent Plasticity (STDP)

Changes in a synaptic weight $w_j$ resulting from Hebbian spike‐timing‐dependent plasticity (STDP) (Bi and Poo 1998) may be modeled through the use of the following expression

$$d{w}_j\left({\mathrm{\Delta }}_j\right)=\text{Signum}\left({\mathrm{\Delta }}_j\right)e^{-\left|{\mathrm{\Delta }}_j\right|}$$ (28)

where $d{w}_j=w_j\left(t+\mathit{dt}\right)-w_j\left(t\right)$ and ${\mathrm{\Delta }}_j=t_{\text{post}}-t_{\mathrm{pre}}^j$ represents the time difference between the postsynaptic and $j$th presynaptic neuron's spike timing computed at the synaptic terminal. It is possible to recast Equation (28) to include the effect of axonal CV. Let us assume that an action potential was generated by the presynaptic neuron $j$ at time $t$. One may hence express the presynaptic spike timing as $t_{\mathrm{pre}}^j=t+\tau$, where ${\mathrm{\tau }}_{\mathrm{j}}=l_j/c$ represents the conduction delay for the action potential to traverse along the axon and reach the synaptic terminal. Setting $t=0$, Equation (28) becomes

$$d{w}_j\left(c\right)=\text{Signum}\left(t_{\text{post}}-l_j/c\right)e^{-\left|t_{\text{post}}-\frac{l_j}{c}\right|}$$ (29)

which depends on the postsynaptic spike timing $t_{\text{post}}$, the axonal length $l_j$ and the CV $c$. Equation (29) illustrates how axonal CV may act as a driver of synaptic pruning. Indeed, changes in CV trigger the potentiation or depression of the synapse through adjustments of the presynaptic spike arrival time with respect to postsynaptic spike timing $t_{\text{post}}$. If $l_j/c<t_{\text{post}}$, synaptic potentiation will occur, while $l_j/c>t_{\mathit{\text{post}}}$ will induce depression.

2.11. STDP Simulations

For the purpose of the example illustrated in Figure 6B, STDP was considered at the level of a single excitatory synapse between a presynaptic neuron (i.e., $\mathit{pre}$) and postsynaptic neuron (i.e., $\mathit{\text{post}}$). Both neurons were assumed to display Poisson spike trains, with an instantaneous probability of spiking corresponding to an expected firing rate of $r_o$ = 80 Hz. Changes in synaptic weight—resulting from the dynamics of Equation (28)—were compiled across 100 trials for each combination of (i) CVs ranging from 0.6 to 1.4 m/s, and (ii) cross‐correlations between the pre‐ and postsynaptic spike trains (i.e., ${\rho }_{\mathrm{pre}-\text{post}}$) ranging from 0 (i.e., independent spike trains) to 1 (i.e., identical spike trains). The reference CV was set to 1 m/s. As per Equation (29), it was assumed that if both neurons shared identical spike trains, then at the reference CV, all presynaptic spikes would reach the postsynaptic terminal at the same time as the postsynaptic spike is generated, entailing no change in synaptic weight. Increases in CV would thus cause presynaptic spikes to advance, while decreases in CV would instead cause delay. It should be noted that when ${\rho }_{\mathrm{pre}-\text{post}}$ = 0, pre‐ and postsynaptic neurons share no spikes, yielding zero net change in synaptic weight as expected by STDP. It should also be noted that pre‐ and postsynaptic spiking were made independent of each other: that is, delivery of presynaptic spikes to the postsynaptic neuron was never taken into consideration in calculating the postsynaptic firing rate, nor were postsynaptic spikes assumed to have any effect on presynaptic firing.

FIGURE 6.

Axonal CV drives synaptic pruning through STDP. (A) Illustration of how changes in axonal CV may engage STDP to drive synaptic pruning. If a presynaptic spike reaches the postsynaptic cell at the moment that the postsynaptic cell spikes, then no change in synaptic weight is observed. However, if CV is decreased (e.g., under a deficiency in myelination), the resulting spike timing difference ($\mathrm{\Delta }$>0) yields depression. Conversely, if CV is increased (e.g., under excessive myelination), the spike timing difference ($\mathrm{\Delta }$<0) promotes potentiation instead. Colored arcs of different sizes represent changes in the efficacy of individual synapses. (B) Average synaptic weight change between two exemplar Poisson neurons (i.e., one presynaptic and one postsynaptic neuron) as a function of correlation between the pre‐ and postsynaptic spike trains (${\rho }_{\mathrm{pre}-\text{post}}$) and CV. Decreased CV yields depression (blue), whereas increased CV yields potentiation (red). The magnitude of both potentiation and depression scales with ${\rho }_{\mathrm{pre}-\text{post}}$. Shifts in CV reflect deviations from the reference CV (1 m/s), at which the synaptic weight does not change. Pre‐ and postsynaptic firing rates were set to $r_o$ = 80 Hz, and axonal length was set to $l$ = 20 mm. (C) Evolution of synaptic weights over time, following changes in CV. Presynaptic inputs are partitioned into four excitatory presynaptic populations synapsing with a common postsynaptic cell. The CV of axons from population 1 (upper left triangle) is increased to $c$ = 10 m/s, while that of the other three populations is kept at $c_0$ = 0.1 m/s. Consequently, synapses for population 1 are potentiated ($w_1$, red), while those of the other populations are depressed ($w_{2-4}$, blue). The final distribution of synaptic weights in each case is plotted to the right (red: $w_1$; blue: $w_{2-4}$). Presynaptic spike train correlations were kept at ${\rho }_{\mathrm{pre}}$ = 0.5. Each presynaptic population consists of 25 excitatory neurons. (D) Impact of presynaptic correlation ${\rho }_{\mathrm{pre}}$ and CV on synaptic weights from population 1 (i.e., $w_1$). (E) Impact of presynaptic correlation ${\rho }_{\mathrm{pre}}$ and CV on synaptic weights from populations 2–4 (i.e., $w_{2-4}$). In all panels, FRH was removed and the excitability threshold parameter was set to a fixed value of $h$ = 2. Other parameters are $N$ = 100, $\beta$ = 20, $w_o$ = 0.2, $w_{\mathit{max}}$ = 0.4, $r_o$ = 100 Hz, $k$ = 2, $\theta$ = 4. Parameters have a.u. unless otherwise specified.

For the purpose of Figures 6C–E and 7B–D, where synaptic weights between different pairs of pre‐ and postsynaptic neurons in Equation (1) are considered, STDP over synaptic weight $w_j$ was instead implemented by integrating numerically the following differential equation

$$\frac{d}{\mathit{dt}}{w}_j=\mathrm{ϵ}{w}_j\left(w_j-w_{\mathit{max}}\right)\text{Signum}\left({\mathrm{\Delta }}_j\right)e^{-\left|{\mathrm{\Delta }}_j\right|}$$ (30)

where $\mathrm{ϵ}$ stands for the learning rate and the term $w_j\left(w_j-w_{\mathit{max}}\right)$ has been added to bound the change of the synaptic weights between 0 and $w_{\mathit{max}}$.

FIGURE 7.

Impact of axonal CV on synaptic plasticity with excitatory and inhibitory presynaptic inputs. (A) Two excitatory populations (triangles 1 and 2) and two inhibitory populations (circles 3 and 4) synapse with a common postsynaptic neuron. CV is increased only along axons originating from populations 1 (excitatory, $c^E$, red) and 3 (inhibitory, $c^I$, blue), while remaining constant (1 m/s) for populations 2 and 4. Each population consists of 25 neurons, with their synapses (i.e., $w_{1-4}$) subjected to STDP. Black arcs represent individual synapses. (B–D) show average synaptic weight changes for presynaptic populations 1 ($w_1$), 3 ($w_3$), or 2 and 4 ($w_{2,4}$), respectively, following changes in the (excitatory) CV of population 1 and/or the (inhibitory) CV of population 3. In all panels, FRH was removed and the excitability threshold parameter was set to a fixed value of $h$ = 2. Parameters are $N$ = 100, $\beta$ = 20, $w_o$ = 0.2, $w_{\mathit{max}}$ = 0.4, $r_o$ = 100 Hz, $k$ = 2, $\theta$ = 4, ${\rho }_{\mathit{pre}}$ = 0.5. Parameters have a.u. unless otherwise specified.

3. Results

3.1. Modeling Activity‐Dependent Myelination

To investigate how changes in myelin might influence the dynamics of individual cells, we adapted a theoretical framework previously developed to study the dynamics of networks of myelinated neurons (Talidou et al. 2022; Lefebvre et al. 2025), operationalizing changes in axonal myelination as changes in axonal CV. Specifically, our model quantified how changes in axonal CV across populations of presynaptic neurons can (i) modulate the temporal integration of inputs received by a commonly‐targeted postsynaptic neuron, and (ii) how this modulation of temporal integration can in turn shape postsynaptic dynamics. Our model considered a purely feedforward network (i.e., no feedback from the postsynaptic neuron to influence presynaptic dynamics), with a single postsynaptic neuron subjected to convergent presynaptic inputs (Figure 1A). Adopting this circuit framework enabled us to isolate the influence of CV on presynaptic correlations and postsynaptic dynamics without the confounds of postsynaptic feedback.

In our model, each presynaptic input corresponds to a spike train with a given firing rate, traversing towards the postsynaptic neuron along axons of various lengths and degrees of myelination. Moreover, these inputs are assumed to be correlated with one another (i.e., spike trains from different presynaptic neurons have a similar temporal structure; see Section 2). Casting our network as a sparsely connected set of Poisson neurons in the fluctuation‐driven regime (Talidou et al. 2022; Lefebvre et al. 2025), the response of the postsynaptic neuron (Figure 1B) can be described as a sigmoidal function of (i) the rate and correlation structure of its presynaptic inputs, and (ii) the CV of its afferent axons (see Section 2).

To set axonal lengths in the model, we sampled values from a probability distribution whose statistics accord with those reported experimentally (Swadlow and Waxman 2012; Ferraina et al. 2002; Shimono and Hatano 2018). Specifically, axonal lengths were drawn from a gamma distribution ranging from 0 to ~30 mm (Figure 1C), thus spanning the distribution profile of myelinated axonal fibers observed across many mammalian species and systems (Swadlow and Waxman 2012; Arancibia‐Cárcamo et al. 2017; Ferraina et al. 2002; Shimono and Hatano 2018). In experiments considering both excitatory and inhibitory presynaptic populations, we assumed that the distributions of axonal lengths for both populations were equal. Though inhibitory and excitatory axons are known to exhibit various distinct anatomical features (Micheva et al. 2018; Basu et al. 2023; Call and Bergles 2021; Yang et al. 2020), we nonetheless treated their distributions of lengths as equal so as to better isolate the effects of axonal CV on neuronal dynamics, free of any confounds imposed by differences in axonal length. These assumptions thus entail that our model encompasses both local and long‐range projections.

Together, axonal CV and length determines the conduction delay (i.e., $\tau$) experienced by a presynaptic spike train: that is, the time it takes for action potentials to (i) travel from the axon initial segment of the presynaptic neuron to its axon terminal, (ii) induce neurotransmitter release and finally (iii) elicit a postsynaptic potential. These delays are computed by evaluating the ratio of the axonal length (i.e., $l$) over the CV (i.e., $c$, expressed in m/s), so that $\tau =l/c$ (Figure 1D). As can be seen in Figure 2B, whenever CV increases, conduction delays not only become shorter but also more homogeneous: the use of the gamma distribution to sample axonal lengths (see above) implies that both the mean and variance of the conduction delay distribution decrease whenever CV is increased (see Section 2) (Noori et al. 2020; Talidou et al. 2022; Lefebvre et al. 2025).

FIGURE 2.

Distinct modulation of postsynaptic activity across different CVs. (A) Excitatory presynaptic neurons (gray triangles) transmit spikes to a common postsynaptic cell (black circle) via axons of various lengths (gray lines) and levels of myelination (circles and rectangles, portraying myelinating oligodendrocytes). Postsynaptic activity was modeled across deficient (left; blue), reference (middle; black), and excessive (right; red) levels of myelination, all reflected in distinct CVs. Gray arcs denote synapses. (B) Axonal conduction delay distributions with associated gamma‐distributed probability density function for $c$ = 0.25 m/s (blue solid line), $c$ = 1.0 m/s (black solid line) and $c$ = 5.0 m/s (red solid line). (C) Exemplar responses of the postsynaptic neuron at fixed CVs ($c$ = 0.25 m/s, blue line; $c$ = 1.0 m/s, black line; $c$ = 5.0 m/s, red line). Instantaneous firing rates are plotted above the associated postsynaptic spike trains in each case. (D) Comparison of the postsynaptic firing rate distribution between $c$ = 1.0 m/s (black line) and $c$ = 5.0 m/s (red line; top‐left panel), and between $c$ = 1.0 m/s (black line) and $c$ = 0.25 m/s (blue line; bottom‐left panel). These were computed over independent trials of duration $T$ = 50 s. Insets shows firing rate means (top‐right panel) and variances (bottom‐right panel) for each CV. Error bars indicate ± SD across trials. (E) Excitability profile of the postsynaptic neuron for different CVs ($c$ = 0.25 m/s, blue line; $c$ = 1.0 m/s, black line; $c$ = 5.0 m/s, red line). Error bars indicate ± SD across 10 trials of $T$ = 800 ms duration. Parameters are $\beta$ = 20, $w_o$ = 0.2, $r_o$ = 80 Hz, $r_{\mathrm{sp}}$ = 5 Hz, $h_{\mathrm{ref}}$= 2.35, ${\rho }_{\mathrm{pre},\mathit{jk}}$ = ${\rho }_{\mathrm{pre}}$ = 0.2, $k$ = 2, $\theta$ = 4, $K^E$ = 100, $K^I$ = 0. Parameters have a.u. unless otherwise specified.

Lastly, to take single cell compensatory effects into consideration in our model, we incorporated firing rate homeostasis (FRH) through an adaptive depolarization threshold parameter (i.e., rheobase, $h$) (Benda and Herz 2003; Peron and Gabbiani 2009; Benda 2021; Kobayashi et al. 2009; Mejias and Torres 2011), whose values change in an activity‐dependent manner. In our model, FRH normalizes the spontaneous firing rate of the postsynaptic neuron in response to changes in CV along its afferent axons (see Section 2).

3.2. Axonal CV Modulates Temporal Integration

To assess the effects of perturbations in CV on temporal integration at the postsynaptic cell, we examined a range of CVs observed across healthy and pathological states (see Section 2). A CV of 1 m/s, which is consistently observed across a range of systems and species in healthy adult animals (Swadlow and Waxman 2012; Fields 2015; Arancibia‐Cárcamo et al. 2017; Ferraina et al. 2002; Shimono and Hatano 2018; Swadlow 1990; Silverstein et al. 2020), was chosen as a reference point (Figure 2A). As CVs in multiple mammalian species typically span 0.3–4 m/s (Swadlow and Waxman 2012; Fields 2015; Arancibia‐Cárcamo et al. 2017; Ferraina et al. 2002; Shimono and Hatano 2018; Swadlow 1990; Silverstein et al. 2020; Mancini et al. 2021), we considered CVs below this range (i.e., CV < 0.3 m/s) to reflect a deficiency in myelination, and CVs above it (i.e., CV > 4.0 m/s) to reflect excessive myelination (Figure 2A). Corresponding conduction delay distributions for each of these three conditions are illustrated in Figure 2B. Note that these CV ranges can easily be modified without qualitatively impacting our findings.

We started by considering purely excitatory synaptic inputs, in which we quantified the response of a given postsynaptic cell to correlated presynaptic spike trains transmitted at different CVs (Figure 2C). Keeping both the firing rate (i.e., $r_0$; Table 1) and correlation (i.e., ${\rho }_{\mathrm{pre}}$; Table 1) of the presynaptic spike trains constant, we analyzed the response statistics of the postsynaptic cell after prolonged exposure to these spike trains (i.e., once FRH stabilized). Note that in later experiments we varied presynaptic firing rates and correlations, in addition to considering inhibitory inputs (see below).

As shown in Figure 2C, changes in axonal CVs have important repercussions for temporal integration and, consequently, for postsynaptic activity. Despite displaying nearly identical spontaneous firing rates—as is expected due to FRH normalizing the amount of spontaneous neuronal activity (Hamada and Kole 2015; Gasselin et al. 2015; Yang and Prescott 2023; Hengen et al. 2013) through adaptation mechanisms such as modified ion channel expression (Yang and Prescott 2023; O'Leary et al. 2014; Goaillard and Marder 2021; Drion et al. 2015; Alonso et al. 2023)—decreasing CVs across all axons from the reference value of 1.0–0.25 m/s was found to trigger noticeably more volatile fluctuations in firing rate (i.e., relatively extended periods of quiescence followed by bursts of spikes), thus revealing that perturbations in axonal CV can significantly reshape postsynaptic spiking patterns, all the while exerting a relatively negligible effect on the average firing rate. Indeed, this observation was formally substantiated by comparing the firing rate probability density functions resulting from deficient, excessive and reference CVs (Figure 2D). While these firing rate distributions display the same mean value (i.e., due to FRH normalizing firing rates by adapting postsynaptic excitability), their variance differs significantly: Increasing CVs above the reference value (i.e., excessive myelination) decreases the firing rate variance of the postsynaptic cell, while decreasing CVs (i.e., deficiency in myelination) does the opposite.

The above results are suggestive of changes in postsynaptic excitability—that is, the propensity for postsynaptic spiking upon the invocation of excitatory postsynaptic potentials. To confirm this hypothesis, we simulated the application of external direct current stimulation to the postsynaptic neuron to quantify its excitability (i.e., how postsynaptic firing rate scales with the stimulation amplitude). We quantified the firing rate of the postsynaptic neuron as this input was increased. As can be seen in Figure 2E, perturbation of CV induces a significant change in the excitability profile of the postsynaptic cell. Excitability was found to decrease with CV: slower CV induces a non‐linear, hyperexcitable postsynaptic response, while faster CV does the opposite and yields more linear, hypoexcitable behavior. Indeed, these modeling findings accord with experimental observations (Madden et al. 2021; Bacmeister et al. 2022).

3.3. Axonal CV Modulates Postsynaptic Firing Threshold

While the postsynaptic membrane time constant $\left({\tau }_m\right)$ defines the postsynaptic neuron's propensity to integrate presynaptic inputs over relatively short timescales (i.e., on the order of 10 ms), the timescale over which FRH normalizes postsynaptic excitability $\left({\tau }_{\mathrm{adapt}}\right)$ is much longer (i.e., on the order of seconds for our simulations; see Section 2). This raises the possibility that the effects of CV changes on postsynaptic dynamics may vary over time following an initial CV perturbation. Accordingly, we set to investigate this possibility by examining the response of the postsynaptic cell over two distinct phases: (i) the acute phase, reflecting the immediate, albeit transient effect of sudden changes in CV on postsynaptic dynamics before any FRH takes place; and (ii) the chronic phase, reflecting the effect of long lasting changes in CV, where the contribution of FRH on neural activity has stabilized (see Section 2).

As shown in Figure 3A, the acute phase is characterized by a monotonic positive relationship between changes in CV and the postsynaptic firing rate: increases in CV amplify the postsynaptic firing rate, whereas decreases in CV suppress it. This occurs because increases in CV homogenize presynaptic conduction delays, supporting the synchronous arrival of presynaptic spikes at the postsynaptic cell (i.e., temporal integration of spikes to drive postsynaptic activity). Conversely, no such relationship exists in the chronic phase, as the recruitment of FRH gradually normalizes the postsynaptic firing rate across different values of CV through adaptive changes to the postsynaptic excitability threshold ($h$): that is, FRH increases the threshold under higher CVs and decreases it under lower CVs, thus countering the effects of either CV on postsynaptic activity as observed in the acute phase.

Appreciating that our findings for the acute phase emerge as a direct consequence of the effects of CV on temporal integration, we next sought to evaluate the extent to which another core parameter of our model with direct consequences for temporal integration—namely, presynaptic spike train correlations (i.e., ${\rho }_{\mathrm{pre}}$, reflecting the degree of similarity between different presynaptic spike trains)—may influence how CV modulates postsynaptic activity under the acute versus chronic phase. As shown in Figure 3B, an increase in CV and/or presynaptic spike train correlations amplifies postsynaptic firing rates in the acute phase, due to an enhanced propensity for the temporal integration of presynaptic spikes. However, this dependence once again vanishes in the chronic phase as a consequence of FRH normalizing postsynaptic excitability. Thus, our findings regarding the effects of CV on postsynaptic activity under the acute versus chronic phase are qualitatively robust across different presynaptic correlations.

The CV‐dependent modulation of PSP variance during the acute phase may be regarded as a form of gain control (Swadlow et al. 1978; Swadlow and Waxman 2012; Talidou et al. 2022) and is illustrated in (Figure 3C): sudden increases in axonal CV homogenize conduction delays, increasing the temporal integration of presynaptic spikes at the postsynaptic cell, thus maintaining it in a more depolarized state. By contrast, decreases in axonal CV diversify conduction delays, hampering the temporal integration of presynaptic spikes, thus maintaining the postsynaptic cell in a more hyperpolarized state. Over longer timescales, however, our simulations suggest that FRH compensates for this effect by shifting the excitability threshold in a CV‐dependent manner.

To further characterize the compensatory effects of FRH on CV‐induced shifts in postsynaptic excitability, in Figure 3D we show our analytic computations for the postsynaptic excitability profile in both the acute and chronic phases (see Section 2.5). Our analyses reveal that CV‐induced changes in postsynaptic excitability differ between the acute and chronic phases: in the acute phase, increases in CV generally support hyper‐excitability; by contrast, in the chronic phase, increases in CV generally support hypo‐excitability. These results align with previous experimental observations (e.g., neuronal hyperexcitability in mice with myelin deficiencies (Sutor et al. 2000)) and suggest a core role of FRH in adapting cellular excitability profiles to disruptions in axonal CV.

3.4. Axonal CV Modulates Correlations in Presynaptic Activity

The above results show that axonal CV can tune the timing of presynaptic inputs to modulate postsynaptic activity and excitability over time by engaging FRH. We hypothesized that this occurs because changes in conduction delays are well‐known to alter presynaptic spike train correlations (Izhikevich 2006; Nirenberg and Latham 2003), with important consequences for postsynaptic activity.

As illustrated in Figure 4A, correlations between simultaneously generated presynaptic spike trains can be preserved throughout transmission to the postsynaptic cell by similar conduction delays or, on the contrary, be dampened by discrepant conduction delays. Indeed, this owes to the simple fact that presynaptic spikes emitted simultaneously will also reach the postsynaptic cell simultaneously provided they experience equivalent conduction delays. We here use ${\rho }_{\mathrm{pre},\mathrm{jk}}$ to denote the correlation between two presynaptic spike trains $j$ and $k$ at the time of their generation, and ${\rho }_{\mathrm{pre},\mathrm{jk}}^{\mathrm{eff}}$ to denote their correlation upon arrival at the postsynaptic cell (i.e., the effective presynaptic correlation). Notably, it can be shown that ${\rho }_{\mathrm{pre},\mathrm{jk}}^{\mathrm{eff}}$ decays exponentially as conduction delay differences—and thus, by proxy, CV differences—between spike trains $j$ and $k$ increase (i.e., ${\rho }_{\mathrm{pre},\mathrm{jk}}^{\mathrm{eff}}={\rho }_{\mathrm{pre},\mathrm{jk}}{\mathrm{e}}^{-\mid {\mathrm{\Delta }}_{\mathrm{jk}}\mid }$, where ${\mathrm{\Delta }}_{\mathrm{jk}}={\tau }_k-{\tau }_j$ is the difference between conduction delays; see Section 2, and (Lefebvre and Clappison 2024)).

To specifically assess how CV impacts presynaptic correlations in our model, we computed the matrix of all pairwise effective presynaptic correlations (i.e., ${\mathrm{\Sigma }}^{\mathrm{eff}}$, containing the ${\rho }_{\mathrm{pre}}^{\mathrm{eff}}$ value between each pair of presynaptic neurons) across the same range of CVs as in Figure 2. We show these matrices in Figure 4B, where it can be seen that increasing CV amplifies presynaptic correlations. When axonal CVs are low, presynaptic spike trains are temporally dispersed, thus reducing presynaptic correlations. In contrast, when axonal CVs are high, conduction delays are normalized such that presynaptic spike trains become temporally aligned, thus increasing presynaptic correlations. Note that this trend is most prominent for spike trains transiting axons of similar lengths (i.e., positioned along the diagonal in Figure 4B) (Izhikevich 2006).

Because of FRH, the modulation of presynaptic correlations by axonal CV has important consequences for the excitability of the postsynaptic neuron (cf. Figure 3). We confirmed this by computing the excitability threshold (i.e., $h$) resulting from a chronic change in axonal CV, while varying presynaptic spike train correlations (assumed to be equal between any pair of spike trains; i.e., ${\rho }_{\mathrm{pre},\mathit{jk}}={\rho }_{\mathrm{pre}}$). Our analysis reveals that the excitability threshold scales with both CV and presynaptic correlations (Figure 4C): as both increased CV and increased presynaptic correlations support temporal integration at the postsynaptic cell, both changes effectively subject the postsynaptic cell to an increased excitatory drive, which FRH compensates for by raising the excitability threshold. Indeed, this accords with our previous findings plotted in Figure 3D.

Our finding that CV can alter correlations between presynaptic spike trains raises the possibility that it may be similarly capable of altering correlations between pre‐ and postsynaptic spike trains. The replication of presynaptic spike patterns in postsynaptic spiking, a concept we refer to here as signal fidelity, can be quantified using the cross‐correlation between pre‐ and postsynaptic spike trains (i.e., ${\rho }_{\mathrm{pre}-\text{post}}$). Higher cross‐correlations indicate a greater replication of presynaptic spike patterns in the postsynaptic response (i.e., higher signal fidelity). In Figure 4D, we show how signal fidelity relates to CV and stimulation amplitude (i.e., presynaptic firing rates) in the acute phase. In Figure 4E, we show the same simulations in the chronic phase. In both phases, signal fidelity increases with axonal CV, regardless of stimulus amplitude: that is, increases in CV broadly support the postsynaptic neuron's propensity to replicate presynaptic spike patterns. Signal fidelity is, however, also dependent on stimulation amplitudes: extremely low amplitudes fail to achieve sufficient temporal integration to elicit postsynaptic spiking, while extremely high amplitudes cause the postsynaptic neuron to spike continuously. Both extreme scenarios compromise the postsynaptic neuron's capacity to replicate presynaptic spike patterns and, in turn, hamper signal fidelity. Additionally, it may be noted that in the acute phase (Figure 4D), signal fidelity peaks at higher stimulus amplitudes as CV decreases, whereas no such trend exists in the chronic phase (Figure 4E). The acute phase trend emerges due to lower CVs reducing temporal integration, thus necessitating greater stimulation amplitudes for presynaptic spike patterns to be replicated by the postsynaptic cell. By contrast, in the chronic phase, FRH adapts the postsynaptic excitability threshold (cf. Figure 3) to counteract any changes away from the reference stimulation amplitude (i.e., increased excitability for below‐reference amplitudes; decreased excitability for above‐reference amplitudes), such that the greatest signal fidelity is achieved at approximately the reference amplitude. Altogether, these simulations suggest that CV not only unifies the temporal characteristics of presynaptic inputs with each other, but also with their invoked postsynaptic outputs.

3.5. CV Alterations Affect the Balance of Excitation vs. Inhibition

Our model hitherto considered only excitatory afferents. However, in vivo, neurons can receive both excitatory and inhibitory inputs. We thus set out to explore how independent perturbations in the axonal CVs of excitatory and inhibitory presynaptic cells may affect postsynaptic activity. We quantified the effects of these perturbations by considering their consequences for the excitation‐inhibition (E/I) balance (Okun and Lampl 2009; Sadeh and Clopath 2021) of the postsynaptic cell, operationalized as the ratio of excitatory versus inhibitory postsynaptic potential (PSP) variance. This operationalization of E/I balance is motivated by our analytical arguments (see Section 2) showing that, for equal axonal lengths between excitatory and inhibitory presynaptic cells, excitatory and inhibitory PSP variance is roughly equal (i.e., E/I $\approx 1$) when CVs between both presynaptic populations are equal, but can shift towards excitation (i.e., E/I > 1) or inhibition (i.e., E/I < 1) when CVs differ between the two populations.

We simulated perturbations in the CVs of afferent axons for each subtype (i.e., excitatory CV $c^E$; inhibitory CV $c^I$) independently (Figure 5A), motivated by the finding that changes in myelination can be highly specific to cell types (Micheva et al. 2018; Basu et al. 2023; Call and Bergles 2021; Yang et al. 2020). Spike trains of both excitatory and inhibitory presynaptic populations were also assumed to be correlated with each other (i.e., ${\rho }_{\mathrm{pre}}$) (Renart et al. 2007; Renart et al. 2010), and synaptic weights for both classes of input (excitatory or inhibitory) were chosen to be equal: both assumptions were implemented to maintain E/I balance at baseline (i.e., the mean synaptic input to a given postsynaptic cell is always zero) (Okun and Lampl 2009; Renart et al. 2010). In this same vein, the distribution of axonal lengths and range of CVs were also assumed to be equal between both populations.

We first examined how variations in excitatory and inhibitory CVs impact PSPs. As can be seen in Figure 5B, the mean PSP remains zero irrespective of the CV of excitatory or inhibitory axons. This was expected from the choice of setting excitatory and inhibitory synaptic weights equal to each other. PSP variance, however, scales with the difference in axonal CV between excitatory and inhibitory afferent axons (i.e., $\mathrm{\Delta }c$). Equal CVs between excitatory and inhibitory populations (i.e., $\mathrm{\Delta }c\approx 0$) decreases PSP variance by promoting the coincident arrival of excitatory and inhibitory inputs and, in turn, the mutual cancellation of their respective PSPs. Conversely, discrepancies between excitatory and inhibitory CVs (i.e., $\mathrm{\Delta }c\ne 0$) amplify PSP variance by promoting the asynchronous arrival of excitatory and inhibitory inputs, reducing their propensity to mutually cancel. We further found that this effect scales with different magnitudes of presynaptic stimulation (i.e., relatively higher or lower firing rates in the presynaptic populations), with greater magnitudes of presynaptic stimulation amplifying the effects of discrepant excitatory and inhibitory CVs on PSP variance, all the while leaving the mean PSP unchanged at zero (Figure 5B). These results indicate that discrepant changes in excitatory and inhibitory CVs may perturb E/I balance (Okun and Lampl 2009; Renart et al. 2010) independently of synaptic weights.

We further quantified this effect by computing the E/I ratio as a function of axonal CV. If we were to measure E/I ratio using the mean excitatory and inhibitory PSPs (i.e., the ratio between the mean EPSPs and mean IPSPs), we would find a state of apparently perfect balance (i.e., E/I = 1), since the mean PSP is always zero (Figure 5B). However, as such a metric would effectively mask consequential PSP fluctuations, we instead opted to use the variance of the EPSPs and IPSPs to compute the E/I ratio (see Section 2). Using this alternative metric, as shown in Figure 5C, E/I balance is achieved if excitatory and inhibitory afferent axons share similar CVs, but tilts in favor of excitation (i.e., E/I > 1) when excitatory CVs are greater than inhibitory CVs, or in favor of inhibition (i.e., E/I < 1) when inhibitory CVs are greater.

We next sought to explore how CV‐induced disruptions in E/I balance may influence postsynaptic excitability. In Figure 5D, we computed the excitability threshold (i.e., $h$) in the chronic phase across different excitatory and inhibitory CVs. The excitability threshold decreases as the E/I ratio becomes more balanced, indicating that postsynaptic excitability increases when excitatory and inhibitory CVs are similar and, in turn, PSP variance is small (cf. Figure 5B). This effect can also be appreciated by quantifying the intensity of postsynaptic responses to additional, external direct current stimulation when excitatory and inhibitory CVs are similar versus discrepant. In Figure 5E, we simulate said stimulation in both the acute and chronic phase. In the acute phase (i.e., before FRH), the intensity of postsynaptic responses is broadly similar regardless of whether excitatory and inhibitory CVs are discrepant or similar. This reflects the mean PSP being roughly equal (i.e., zero) across the three conditions, such that the propensity for postsynaptic spiking in response to external stimulation across the three conditions is, also, roughly equal. By contrast, in the chronic phase (i.e., after FRH), the intensity of postsynaptic responses varies as a function of discrepancies between excitatory and inhibitory CVs, with discrepant CVs (i.e., E/I imbalance) promoting hypoexcitability.

These results suggest that CV perturbations of excitatory and/or inhibitory axons may cause shifts in E/I balance: a finding which has also been reported experimentally (Benamer et al. 2020). To examine the consequences of CV‐induced shifts to E/I balance further, we considered how these shifts may influence signal fidelity. As with our previous simulations, we computed the cross‐correlation between pre‐ and postsynaptic spike trains (i.e., ${\rho }_{\mathrm{pre}-\text{post}}$) while varying the CV of excitatory and inhibitory inputs, across different presynaptic firing rates. As shown in Figure 5F, increasing the CVs of excitatory axons relative to those of inhibitory axons (i.e., $\mathrm{\Delta }c>0$) increases signal fidelity, as the inhibitory inputs become too temporally dispersed to counteract the increased correlations in excitatory spike trains: the excitatory inputs can thus temporally integrate to evoke a postsynaptic response and, in turn, support signal fidelity. However, if the excitatory CV increases further, the postsynaptic neuron can be brought towards saturation, hampering signal fidelity. Conversely, increasing the CVs of inhibitory axons relative to those of excitatory axons (i.e., $\mathrm{\Delta }c<0$) suppresses firing, thus hampering signal fidelity. Similar CVs (i.e., $\mathrm{\Delta }c\approx 0$) increase the coincidence of excitatory and inhibitory inputs, effectively decorrelating the presynaptic spike trains such that postsynaptic activity is only invoked by the uncorrelated components of the inputs. Additionally, signal fidelity was found to be invariant with respect to presynaptic firing rate, in contrast with the purely excitatory case (cf. Figure 4D,E). This follows from presynaptic firing rate having no bearing on the amount of mutual cancellation between excitatory and inhibitory inputs, which represents the core driver of postsynaptic activity in these simulations. All together, these simulations suggest that perturbations in CV of excitatory and/or inhibitory axons have the potential of causing shifts in E/I balance (Benamer et al. 2020), influencing postsynaptic response intensity and signal fidelity.

3.6. CV Variations Are Reflected in Synaptic Plasticity

Changes in axonal CV may also modulate synaptic plasticity, notably through the effects of altered conduction delays on spike timing‐dependent plasticity (STDP) (Izhikevich 2006; Madadi Asl et al. 2018a; Madadi Asl et al. 2018b; Bi and Poo 1998). In STDP, changes in synaptic strength depend on the relative timing of presynaptic and postsynaptic spikes (i.e., $\mathrm{\Delta }t=t_{\mathit{pre}}-t_{\mathit{\text{post}}}$), with synaptic potentiation typically occurring when presynaptic spikes precede postsynaptic spikes, and synaptic depression occurring when the opposite is true. Because conduction delays directly shape spike timing, changes in myelination (i.e., axonal CV) may influence STDP and, ultimately, synaptic connectivity. As illustrated in Figure 6A, according to standard (i.e., Hebbian) STDP rules (Izhikevich 2006; Gerstner and Kistler 2002; Kempter et al. 1998; Bi and Poo 1998), if pre‐ and postsynaptic spikes are coincident, no net change in synaptic weight usually occurs. However, if CV is decreased (e.g., by demyelination), associated increases in conduction delays may induce synaptic depression. Conversely, if CVs are increased (e.g., by increased myelination), associated decreases in conduction delays may induce synaptic potentiation. This is further illustrated in Figure 6B, where the mean synaptic weight change between a single presynaptic and postsynaptic neuron is plotted as a function of axonal CV and the cross‐correlation between the two neurons' respective spike trains. A Hebbian STDP profile (see Section 2) can be observed as axonal CV varies above and below the reference CV (i.e., $c$ = 1 m/s). This effect further scales with the magnitude of cross‐correlation between the pre‐ and postsynaptic spike trains: increasing the cross‐correlation decreases the absolute magnitude of spike timing differences between the pre‐ and postsynaptic cells, thus intensifying either form of STDP (i.e., potentiation or depression). Notably, our simulation also reveals an asymmetry in synaptic weight changes for increases versus decreases in CV: the range of CV increases supporting potentiation is wider than the range of CV decreases supporting depression. Indeed, this asymmetry owes to the non‐linear relationship between CV and conduction delay (i.e., $\tau =l/c$), which entails that decreases in CV invoke larger changes in conduction delays than do equivalent increases in CV and, in turn, more quickly yield conduction delays too large to invoke synaptic weight changes.

We further sought to investigate the interplay between CV and STDP in the presence of more complex synaptic inputs, originating from distinct groups of presynaptic cells. Since synaptic modifications generally occur at faster timescales than changes in CV, we assumed the effect of FRH to be negligible and fixed the excitability threshold to a set value (see Section 2). As illustrated in Figure 6C, we partitioned our presynaptic population into four groups of equal size, each providing correlated excitatory inputs along axons of different CVs to a common postsynaptic cell. The CV of axons from one of these populations (i.e., population 1; inset of Figure 6C) was increased, while axonal CV remained constant for all other populations (i.e., populations 2–4; inset of Figure 6C). All synapses were subjected to the same Hebbian STDP rule (Gerstner and Kistler 2002; Kempter et al. 1998), and set to the same initial synaptic weight value (i.e., $w_o=0.2$; see Section 2). Our simulations revealed that synapses from the presynaptic population with higher axonal CV (i.e., population 1) were mainly potentiated, while those from the other populations (i.e., with comparatively lower axonal CVs; populations 2–4) were depressed. This results from the amplification of correlated spiking between the presynaptic population with increased axonal CV and the postsynaptic cell: increasing CVs for a specific presynaptic population promotes the coincident delivery of that population's spikes to the postsynaptic cell, thus allowing that population to drive postsynaptic spiking rather than the slower, more temporally dispersed spikes of the lower‐CV presynaptic populations. The resultant propensity for postsynaptic spikes to consistently follow after those of the higher‐CV presynaptic population consequently promotes synaptic potentiation with that population, in accordance with Hebbian STDP rules (Izhikevich 2006; Gerstner and Kistler 2002; Kempter et al. 1998; Bi and Poo 1998).

We next generalized these results over various presynaptic spike train correlations and CVs. Specifically, we simulated CV variations for a single presynaptic population (i.e., population 1) while keeping the CVs of the other presynaptic populations (i.e., populations 2–4) constant, all across different levels of presynaptic spike train correlations. In each case, we measured the resulting percentage change in average synaptic weight for each presynaptic population. As can be seen in Figure 6D, over the range of axonal CVs and presynaptic correlations considered, a population's synaptic weights are mainly potentiated by increases in CV relative to other populations, except in cases of low to zero presynaptic correlations, for which axonal CV has no impact (i.e., as previously shown in Figure 3B). In contrast, synaptic weights for presynaptic populations with relatively lower CVs are predominantly depressed (Figure 6E). Together, these simulations suggest that changes in CV can selectively strengthen or weaken connectivity with specific presynaptic populations, thus indicating yet another dimension through which CV may serve as a gain modulator for presynaptic inputs.

As previously illustrated in Figure 5, axonal CV has the potential to disrupt E/I balance. To explore whether this may have consequences for synaptic plasticity, we recast our synaptic plasticity models to include distinct excitatory and inhibitory presynaptic populations. As illustrated in Figure 7A, we considered two excitatory presynaptic populations (i.e., populations 1 and 2) and two inhibitory presynaptic populations (i.e., populations 3 and 4). For each population type (i.e., excitatory or inhibitory), one population's CV was varied while the other population's CV was held constant (i.e., CVs for populations 1 and 3 were varied independently, while CVs for populations 2 and 4 were kept constant).

As shown in Figure 7B, as an excitatory population's CV (i.e., $c^E$) becomes increasingly discrepant from an inhibitory population's CV (i.e., $c^I$), synaptic weights for said excitatory population are potentiated. By contrast, similar CVs between the two populations (i.e., $c^E\approx c^I$) do not yield notable changes in synaptic weights for the excitatory population. This owes to discrepant excitatory/inhibitory CVs diminishing the probability of excitatory and inhibitory inputs arriving simultaneously, which in turn increases the probability that the excitatory inputs will drive postsynaptic spiking and, ultimately, synaptic potentiation with the excitatory population (i.e., as potentiation occurs when presynaptic spikes are delivered shortly before postsynaptic spikes). A different profile of synaptic weight changes emerges for CV variations in the inhibitory population, as illustrated in Figure 7C. As an inhibitory population's CV becomes increasingly discrepant from an excitatory population's CV, synaptic weights with said inhibitory population are increasingly depressed. This again owes to discrepant excitatory/inhibitory CVs supporting the excitatory population's propensity to induce postsynaptic spiking: spike events which are not consistently preceded by spikes from the inhibitory population, thus supporting synaptic depression with the inhibitory population.

A third, final profile of distinct synaptic weight changes is illustrated in Figure 7D for the presynaptic populations which do not experience CV changes (i.e., populations 2 and 4). These two populations' synaptic weights change as a consequence of CV variation in the presynaptic populations that do experience CV changes (i.e., in populations 1 and 2). Specifically, these two populations generally experience synaptic depression when excitatory CVs exceed inhibitory CVs in the other two populations, but are relatively more likely to experience synaptic potentiation when the opposite is true. This suggests that changes in excitatory and inhibitory CVs can entail opposite effects on synaptic plasticity for other presynaptic populations, even if those other presynaptic populations do not themselves experience any change in CV. Collectively, these simulations suggest distinct consequences for synaptic plasticity following CV changes in excitatory versus inhibitory presynaptic populations: discrepant excitatory/inhibitory CVs promote the potentiation of excitatory presynaptic populations and the depression of inhibitory presynaptic populations, each with consequences for the synaptic weights of other presynaptic populations—the nature of which depend on the form of the CV discrepancy (i.e., whether greater excitatory or inhibitory CVs).

4. Discussion

Changes in axonal myelination directly influence axonal CV and, by extension, the timing with which a neuron's spikes are delivered to its postsynaptic target (Salami et al. 2003; Seidl 2014; Swadlow et al. 1978; Swadlow and Waxman 2012). However, exactly how this might impact the dynamics of individual neurons has so far remained unclear. Our modeling suggests that changes in myelination may entail a core consequence of shaping temporal integration: that is, by virtue of modulating axonal conduction delays, changes in myelination can influence the probability that spikes from separate presynaptic cells arrive in close temporal proximity at a common postsynaptic cell. As summarized in Figure 8, our modeling further predicts that this core effect on temporal integration could entail consequences for the postsynaptic cell's excitability, its capacity to faithfully relay upstream signals (i.e., signal fidelity), its excitation‐inhibition balance, and its synaptic connectivity.

FIGURE 8.

Summary of the impact of axonal myelination on neuronal dynamics. Diagram showing how changes in myelination, operationalized as axonal conduction velocity (CV), may affect presynaptic correlations, synaptic plasticity, excitation‐inhibition (E‐I) balance, excitability, and signal fidelity in postsynaptic neurons, ultimately reshaping their response to incoming signals.

By shaping the temporal proximity with which spikes from separate presynaptic cells reach a common postsynaptic cell, axonal myelination may in turn shape the probability that said spikes temporally integrate to yield postsynaptic spiking. In the case of purely excitatory presynaptic cells, our simulations suggest that increases in axonal myelination should acutely predispose the postsynaptic cell to engage in increased activity, but that this effect is gradually reconciled as FRH renders the postsynaptic cell less excitable. These simulations also suggest that increases in myelination can increase signal fidelity, as correlated spike patterns between presynaptic cells will be more inclined to remain correlated through delivery to the postsynaptic cell and, in turn, temporally integrate to yield similar patterns of postsynaptic spiking. Furthermore, our modeling predicts that increases in myelination among excitatory presynaptic cells may shape synaptic connectivity with the postsynaptic cell. Specifically, increased myelination with a specific population of excitatory presynaptic cells could promote the coincident arrival of that population's spikes and, in turn, the probability that said spikes temporally integrate to yield a postsynaptic spike, thus supporting a presynaptic‐postsynaptic spike sequentiality which can be conducive to synaptic potentiation (Izhikevich 2006; Gerstner and Kistler 2002; Kempter et al. 1998; Bi and Poo 1998). It is worth underscoring that the inverse of all the above is predicted by decreases in myelination among excitatory presynaptic populations, namely: acutely reduced postsynaptic activity gradually followed by increased postsynaptic excitability; decreased signal fidelity; and synaptic depression. Altogether, this suggests a framework wherein myelination can effectively tune postsynaptic ‘selectivity’ to specific presynaptic populations—that is, the propensity for certain presynaptic populations to play a dominant role in shaping postsynaptic responses.

The addition of inhibitory presynaptic populations to our models adds a layer of nuance to the above predictions. Specifically, our models suggest that discrepant axonal CVs between excitatory and inhibitory presynaptic cells generally support the aforementioned predicted changes in postsynaptic dynamics, whereas similar axonal CVs leave postsynaptic dynamics largely unaffected. Indeed, this follows from similar axonal CVs in our model supporting similar conduction delays between excitatory and inhibitory presynaptic populations, which in turn increases the probability that the two types of input effectively cancel out upon delivery to the postsynaptic cell, thus yielding no substantial change in postsynaptic dynamics. Caution should, however, be taken in extrapolating these inferences to levels of myelination in excitatory versus inhibitory populations. Though our simulations assumed comparable axonal morphologies between excitatory and inhibitory presynaptic populations (i.e., similar lengths and diameters), these features can differ appreciably in reality (Micheva et al. 2018; Basu et al. 2023; Call and Bergles 2021; Yang et al. 2020), entailing that similar levels of myelination across the two cell types may not necessarily yield similar distributions of conduction delays. As such, a more appropriate inference with respect to myelination is that in so far as the myelination of excitatory presynaptic cells should support conduction delay distributions discrepant from those of inhibitory presynaptic cells, our models suggest that this should support the array of consequences for postsynaptic dynamics outlined above. Equivalently, it may be inferred that should myelination across the two types of cells instead support similar conduction delays, our models suggest that this should largely negate the predicted consequences for postsynaptic dynamics.

We and others have previously explored the role of myelin plasticity on brain oscillatory dynamics and associated brain functions (Noori et al. 2020; Pajevic et al. 2014, 2023; Bells et al. 2017, 2019; Lefebvre et al. 2025; Steadman et al. 2020). A common finding across these investigations has been that myelin plasticity can profoundly shape the propensity for neural circuits and networks to exhibit synchronous activity (Noori et al. 2020; Pajevic et al. 2014, 2023; Bells et al. 2017, 2019; Lefebvre et al. 2025; Steadman et al. 2020), with increased myelination often being associated with greater neural synchrony (Noori et al. 2020; Talidou et al. 2022; Bells et al. 2017, 2019; Steadman et al. 2020). Our modeling here suggests that this relationship may persist down to the cellular level, specifically through our findings that increased myelination may support signal fidelity and synaptic potentiation.

Myelination has been shown to change under a range of conditions including development, aging, learning and disease (Gibson et al. 2018; Knowles, Batra, et al. 2022). Experimental work in rodents has shown that induced disruptions in myelin can impair learning and memory (Steadman et al. 2020; Pan et al. 2020), while observational work in humans has suggested a causal link between white matter microstructure and cognitive processing (Bells et al. 2017, 2019; Kohama et al. 2012). While these relationships could quite well be due to the role of myelin in brain‐wide oscillatory dynamics (Fields 2015; Noori et al. 2020; Pajevic et al. 2014, 2023; Bells et al. 2017, 2019), our present findings suggest that neuron‐level consequences for excitability, signal reliability, excitation–inhibition balance, and/or synaptic plasticity could also contribute. Excessive myelination has been associated with epilepsy (Knowles, Xu, et al. 2022; Kung et al. 2023; Goldsberry et al. 2011; Duprez et al. 1998), while myelin damage is a hallmark of multiple sclerosis (Dobson and Giovannoni 2019). Our modeling predicts that increased myelination could, under specific circumstances, render neurons more likely to propagate upstream signals and become more strongly connected with the presynaptic cells from which they receive these signals. Whether these effects might be pushed to an extreme to support seizure propagation in certain forms of epilepsy (Knowles, Xu, et al. 2022; Kung et al. 2023) remains speculative, though the prospect presents a testable hypothesis for future research. Similarly, the extent to which myelin damage in conditions such as multiple sclerosis might compromise neuron‐level excitability, signal reliability, excitation–inhibition balance, and/or synaptic plasticity to impair neural communication also represents a prospective avenue for future research indicated by our present findings.

It is lastly worth emphasizing that our models are not without limitations. Firstly, to draw inferences from our findings as to how changes in myelination might reshape neuronal dynamics, one must assume that any such changes are reflected in altered axonal CV: changes in myelination that result in conduction failure (e.g., through a decrease in ion channel density) or otherwise impinge on the functionality of an axon's nodes of Ranvier are beyond the scope of our model. Our model also considered a relatively high range of pre‐ and postsynaptic firing rates (30–100 Hz). Though physiologically plausible, particularly in relation to sensory neurons (de Ruyter van Steveninck et al. 1997), it may be noted that our results remain qualitatively the same if lower firing rates are considered, provided that the number of presynaptic neurons is increased. Indeed, this follows from modeling postsynaptic dynamics as a function of the sum of inputs received at a given moment, which itself depends both on the total number of presynaptic neurons and their firing rate (see Section 2). We also note that while our models considered how axonal CV may shape the weights of pre‐existing synapses, they did not consider how axonal CV may influence synaptogenesis or synaptic pruning—nor how any such effects could in turn shape the structure and function of neuronal circuits. Finally, our assumptions of homogeneous synaptic delays and axonal diameters, as well as our neglect of space as a variable in the summation of PSPs are all noteworthy potential limitations of our models. Altogether, while our work accounted for manifold temporal aspects of the relationship between myelination and neuronal dynamics, future work affording similar attention to spatial aspects of these same processes has the potential to contribute to a more holistic framework.

In conclusion, we have presented a novel paradigm for the manipulation of neuronal dynamics by myelin plasticity through its effect on axonal CV. As changes in myelination present across manifold brain states, from healthy to pathological, our modeling raises the possibility that myelin changes in any number of these states could entail direct consequences for neuronal dynamics: a prospect whose validity we hope may be formally assessed in future investigations ex silico.

Author Contributions

J.L. designed the research; D.O., A.P. and J.L. performed research; D.O., A.P., D.T. and J.L. performed simulations; D.O., A.P. and J.L. analyzed data; D.O., A.P., N.Z.A.D, J.K.K., P.W.F., D.M. and J.L. wrote the manuscript.

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (RGPIN‐2026‐04461) and Canadian Institutes of Health Research (PJT‐156164).

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.