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Current Opinion in

Neurobiology

Computational roles of intrinsic synaptic dynamics
Genki Shimizu1,2, Kensuke Yoshida1,2, Haruo Kasai3,4 andTaro Toyoizumi1,2
Abstract

Conventional theories assume that long-term information
storage in the brain is implemented by modifying synaptic efficacy. Recent experimental findings challenge this view bydemonstrating that dendritic spine sizes, or their corresponding
synaptic weights, are highly volatile even in the absence ofneural activity. Here, we review previous computational works
on the roles of these intrinsic synaptic dynamics. We firstpresent the possibility for neuronal networks to sustain stableperformance in their presence, and we then hypothesize that
intrinsic dynamics could be more than mere noise to withstand,but they may improve information processing in the brain.
Addresses
1
Laboratory for Neural Computation and Adaptation, RIKEN Center for
Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan2
Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-8656, Japan
3
Laboratory of Structural Physiology, Center for Disease Biology andIntegrative Medicine, Faculty of Medicine, The University of Tokyo,
Tokyo, Japan
4
International Research Center for Neurointelligence (WPI-IRCN),UTIAS, The University of Tokyo, Bunkyo-ku, Tokyo, Japan
Corresponding author: Toyoizumi, Taro (taro.toyoizumi@riken.jp)

Current Opinion in Neurobiology 2021, 70:34–42
This review comes from a themed issue on Computational
Neuroscience
Edited by Julijana Gjorgjieva and Ila Fiete
For a complete overview see the Issue and the Editorial

https://doi.org/10.1016/j.conb.2021.06.002
0959-4388/© 2021 The Author(s). Published by Elsevier Ltd. This is an
open access article under the CC BY license (http://creativecommons.
org/licenses/by/4.0/).

Introduction
Learning is a major area of research in both neuroscienceand machine learning. Synaptic plasticity, changes insynaptic weight depending on the activity of neurons, is an
essential mechanism for learning and memory in the brain[1]. One of the prevailing properties of synaptic plasticity
is characterized by Hebb’s rule [2,3], in which synaptic
weights change as per the correlation between presynaptic
Current Opinion in Neurobiology 2021, 70:34–42

and postsynaptic neuronal activities. Hebbian plasticity,
including long-term potentiation and depression [1] andvariants such as spike-timing-dependent plasticity(STDP) [4,5], has been proposed to contribute to efficient information processing in the brain. Furthermore,
being originally inspired by operations of neurons in thebrain, artificial neural networks (ANNs) have been
investigated as a promising subject in machine learning.
Synaptic weights are trained in ANNs by an algorithm toachieve optimal performance (e.g. by the error backpropagation rule [6]). Although there are differences in
the learning rules used in the brain and ANNs [7], theimportance of changing the synaptic weight is established.
The postsynaptic counterpart of the synapse that receives a signal from the presynaptic neuron is called thedendritic spine, a small protrusion from a neuron’s dendritic shaft (Figure 1A) [8,9]. Previous experimental results showed that the spine volume of a synapse is closely
correlated with its weight [10e13], and synaptic plasticity protocols such as long-term potentiation anddepression [14e17] and STDP [18,19] induce spine
enlargement or shrinkage. Several in vivo studies havedemonstrated that behavioral learning involves change inspine volumes and numbers [20e22] and that the selective shrinkage of the spines potentiated during
training causes memory erasure [23]. These experiments
give strong evidence that spines play a fundamental rolein both learning and memory via Hebbian plasticity.
However, many studies have reported that spines arehighly volatile (Figure 1B) [24,25]. About 40% of thespines in the hippocampus are replaced within 4 days
[26], and more than 50% of the spines in the auditory
cortex are replaced within two weeks [27]. The volume
of existing spines also exhibits substantial variability[28]. Although this variability can partly be explained by
the effect of neuronal activities, spine volumes change
significantly in an activity-independent manner as well.
Several studies reported that spine sizes [29*] or postsynaptic density molecules [30] fluctuate even under
the condition where neuronal activities were inhibited
pharmacologically. Spine formation and elimination
under the suppression of neuronal activities were also
observed in in vivo studies [31*]. Surprisingly, one study
reported that more than half of the changes of individual
spines are estimated to occur independently of theneuronal activities by analyzing the size correlation ofwww.sciencedirect.com

Computational roles of intrinsic synaptic dynamics Shimizu et al.

Figure 1

Memory could be stable despite synaptic
fluctuations
Previous studies have proposed different theoreticalperspectives on how memory could be stable despite
intrinsic synaptic dynamics. We begin this section by
discussing the possibility that memory might be stored
in synapses that are little affected by intrinsic dynamics.
We then focus on the paradigms in which neuralcomputation primarily relies on the network architecture rather than individual synaptic weights. Finally, we
discuss that the effect of intrinsic dynamics could
partially be canceled by extrinsic synaptic dynamics.
These perspectives are not mutually exclusive but cancooperate toward stability in the presence of volatility.

abExtrinsic dynamics

Intrinsic dynamics might be harmless

Intrinsic dynamics

Current Opinion in Neurobiology

A schematic image of dendritic spines and spine fluctuations. (a) Presynaptic neurons transmit information to postsynaptic neurons throughsynapses. The postsynaptic sites of excitatory synapses mostly form
dendritic spines, small protrusions on dendritic shafts. Synaptic weights
are nearly in proportion to spine volumes, and potentiation/depression ofsynapses are associated with enlargement/shrinkage of dendritic spines.
(b) The spine size is regulated by two factors: extrinsic dynamics (activitydependent plasticity) that reflects neuronal activities and intrinsic dynamics (fluctuation) that is independent of neuronal activities. Note that forlarger spines, intrinsic dynamics are dominant, whereas smaller spines
are rather subject to extrinsic dynamics.

spines between the same presynaptic and postsynaptic
neurons [32]. Note that, in contrast to the intrinsic
dynamics, we call synaptic changes due to activitydependent synaptic plasticity extrinsic synaptic dynamics hereafter.
The existence of intrinsic synaptic dynamics raises two
important questions. First, how is memory retained in
the presence of intrinsic dynamics? Although manystudies have attributed memory to synaptic weight,
some recent works have suggested stability of memory
under spine fluctuations. Second, do intrinsic dynamics
provide benefits for information processing in thebrain? Generally, fluctuations can play an importantrole in biological processing such as selecting a suitablegene expression attractor with noise [33] and allowing
molecular motors to transport cargoes robustly
exploiting thermal Brownian components [34]. In thebrain, recent theoretical and experimental studies on
intrinsic spine dynamics further suggest their benefits
for statistical inference, stable memory, and explorationin reinforcement learning. We address these questions
by reviewing several studies on intrinsic spine
dynamics.
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35

If intrinsic dynamics do not affect synapses that essentially store memory, the stability of memory is not surprising. For example, dendritic spines are more stable inthe cortex than in the hippocampus [26,27]; within thesame area, the lifetime of spines becomes longer with
their size, age, or morphological and functional maturation [27,35]. Thus, long-term memory might be maintained via those relatively long-lasting synapses.
Computational models which predict the stability of
only a subset of synapses for memory storage support
this idea [36e38**]. For example, Mongillo et al. [38**]
showed that rewiring of excitatory connections hadmuch less influence on memory compared with rewiringof inhibitory connections in the balanced spiking neuralnetwork model of the cortical circuit (Figure 2A). Theirresult arises from the condition that, under the balanced
regime, the firing rates of the inhibitory neurons arehigher and more diverse than the excitatory counterpart,and thus, an inhibitory synapse has a greater influenceon neural activity than an excitatory synapse on average.
Another line of works focuses on the prevalence ofmultisynaptic connection [39]. Although traces of
extrinsic dynamics naturally correlate among synapses
between the same pair of neurons, intrinsic dynamics
are independent of each other. Thus creating multiple
synaptic contacts could partly cancel the perturbation
caused by intrinsic dynamics [40e42*].
Is it connectome that matters?

Another perspective emphasizes the importance offinding a suitable structure of network connectivity
rather than optimizing each synaptic weight parameter. If
intrinsic dynamics preserve this structure, fluctuation inweights could be insignificant. In the field of neuroscience, connectome studies aim to draw a comprehensive‘wiring diagram’ of the brain [43]. It has been reported
that various features of network architectures, both local
and global, might be well preserved among individuals or
species [44] and that abnormal connectivity is linked to
psychiatric disorders [45]. This reproducibility of theCurrent Opinion in Neurobiology 2021, 70:34–42

36 Computational Neuroscience

Figure 2

a

c

Δ

=

Δ +

ΔBt

b

Current Opinion in Neurobiology

Examples of various computational perspectives on intrinsic dynamics. (a) Information might be mainly stored in the subset of neurons and synapses, andmodifying the rest could be harmless. In the schema, memory is stored in the neurons and synapses in the right population (blue). As a result, rewiring
synaptic connections in the right population impairs memory, whereas rewiring in the left (orange) does not. For example, in the case of computationalmodeling work by Mongillo et al. [38**], rewiring excitatory synapses did not hinder memory recall, whereas rewiring inhibitory synapses did. Note thatthey used a balanced cortical network model with the average firing rate higher and more diverse in inhibitory neurons, and also they assumed that cell
assemblies were formed via anti-Hebbian plasticity of inhibitory synapses as well as Hebbian plasticity of excitatory neurons. (b) It is widely accepted thatthe brain represents and manipulates uncertainty in various ways. The framework proposed by Kappel et al. [66,67**] suggests that a combination of
extrinsic and intrinsic dynamics could work as sampling dynamics from the target distribution of possible network connectivity. (c) The skewed and heavytailed distribution of synaptic weights naturally arises from modeling synaptic dynamics as a stochastic process. If we use Brownian motion to describe
the randomness of synaptic dynamics, fluctuations with an average change mðw Þ and a standard deviation sðw Þ can be described by a stochastic differential equation dw ¼ mðw Þdt + sðw ÞdBt (where Bt represents standard Brownian motion). The drifting term mðw Þ and diffusion term sðw Þ were
measured in various conditions, with which the stationary distributions of synaptic weights could be obtained. Orange: control condition [29*,86*]. Blue:silenced condition [29*]. Green: Fmr1 knockout (KO) condition, which is a mouse model for autism spectrum disorder (ASD) [86*]. The distributions have acommon skewed and heavy-tailed shape in all conditions. The smaller spines observed in the Fmr1 KO model are explained by the enhanced spine
turnover (larger sðw Þ). Note that the plots are schematic illustrations that approximate but do not exactly replicate original fittings.

connectome hints that the network structure might playa major role in neural computation, separately from individual synaptic weights.
In accordance with this idea, recent works have shown invarious settings that neural networks with appropriately
designated architectures for specific tasks can performreasonably even with random initialization. For example,
two well-known building blocks in ANNs, convolutional
neural network (for visual image [46]) and long shortterm memory (for processing time-series data [47]), arecapable of effective image processing [48,49] and timeseries prediction [50], respectively, with random assignment of synaptic weights. Inspired by these results, Gaierand Ha [51] proposed a generic algorithm to search forarchitectures that could perform well over a wide range of
weights. Their algorithm is a variant of evolutionary
computing for topology search, starting from simple
initial status and evolving network architectures incrementally based on their average performance over a set ofdifferent weight parameters. Another example where
Current Opinion in Neurobiology 2021, 70:34–42

individual synaptic weights are insignificant for neuralcomputation is found in the study by Dubreuil et al.
[52*]. This work demonstrated that low-rank structuresin recurrent networks can be essential for task performance, where resampling the network connectivity while
keeping the underlying structures led to a comparable
performance. Altogether, these works raise the possibility
that fluctuations in synaptic weights can be mitigated aslong as the qualitative characteristic of network connectivity is preserved.
Intrinsic dynamics might be continually corrected by
extrinsic dynamics

We conclude this section by mentioning that memory
could be maintained via continual correction by extrinsic
dynamics [53e55*]. This possibility has long been
examined in theoretical settings (e.g. Ref. [56]), andrecent modeling works inspect it in more true-to-lifesituations, showing that cell assembly (an ensemble ofneurons whose coherent activity represents memory)[54*] or neural representation [55*] is maintained if
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Computational roles of intrinsic synaptic dynamics Shimizu et al.

activity-dependent plasticity counteracts synaptic
changes induced by intrinsic dynamics. Although thetheories in the previous sections assume that a part ofneural circuit components evades intrinsic dynamics,
this paradigm can apply to the situation where intrinsic
dynamics affect every synapse.

Intrinsic dynamics could contribute to brain
functionIn the previous section, we reviewed work supporting theidea that (some) synaptic fluctuations may be harmless
under certain conditions. An implicit assumption behindthem is that spontaneous fluctuations are undesirable
noises, which in principle lead to deterioration of theperformance. Considering the significant magnitude of
intrinsic dynamics [32,57], however, one could suspect
an opposite case where intrinsic dynamics are more
beneficial than harmful. In the following, we review thispossibility for representing probabilistic information,
maintaining memory, or acquiring new information.
Statistical inference via synaptic stochasticity

One possible role of intrinsic dynamics is regarding
probabilistic computation in the brain. As we all know,
life is full of uncertainty: the external world is innately
irregular, and available information on the environment isalways imperfect and noisy. It is natural, then, to supposethat the brain can efficiently represent and manipulate
stochasticity, and many experiments have indeed verified
that the brain conducts probabilistic inference at the near
Bayesian-optimal level [58]. There are several proposals
on how probabilistic computation is implemented in thebrain [59,60], and the sampling hypothesis, which statesthat a ‘snapshot’ of a neural circuit is a draw from theencoded distribution [61], is drawing attention among
them. Although many works focus on the sampling ofneural activities (e.g. stochastic firing of neurons [62] orvariability of membrane potentials [63e65*]), the brain
might also perform sampling of circuit configuration via
intrinsic dynamics (Figure 2B). Two sampling paradigms
differ in timescales (one is from milliseconds to seconds,
the other is from hours to days), and the brain might use
both in a complementary manner. In the following, we
introduce several examples.
In a series of works by Kappel et al. [66,67**], theymodeled synaptic dynamics as a variant of Langevinsampler [68], which asymptotically represents the posterior distribution. These dynamics allowed synaptic
parameters, although changing continuously and stochastically, to remain mostly within a high-dimensional
region of high posterior probability (in the setting of
unsupervised learning [66]) or large expected reward (inthe setting of reinforcement learning [67**]), leading tohigh computational performance in the presence ofongoing synaptic dynamics. The derived synaptic updatewww.sciencedirect.com

37

algorithm reproduced a (reward-modulated) STDP
plasticity rule [69,70] as well as showing good generalization ability and robustness to perturbation because of
its Langevin dynamics.
Another recent work by Teramae [71**] integrated two
different timescales of sampling in the synapse andneuron. It generalized Boltzmann machine [72] learningwith additional weight sampling and proposed thatfluctuations of both neural activity and synaptic weights
arose as a result of the Gibbs sampling [73]. The derived
algorithm reproduced several nontrivial experimental
findings such as the power-law coding of the cortex [74]at the neural activity level and was consistent with the
STDP rule at the synaptic level.
Homeostatic effect of intrinsic dynamics

Recent findings, both experimental and theoretical,
have been revealing that intrinsic dynamics could
contribute to homeostasis of the neuronal network in
two distinct manners, stability of cell assembly and therobust shape of synaptic weight distribution. Although
Hebbian plasticity can successfully explain the formation of cell assembly via learning, maintaining themduring spontaneous activity has been remaining a challenging problem for conventional learning rules. In arecurrent network, formed assemblies tend to become
unstable in additive Hebbian plasticity models becauseof positive feedback effect [75,76] and degenerative in
multiplicative Hebbian plasticity models [77]. Several
works have introduced different mechanisms for stabilization [78] such as inhibitory plasticity [75], homeostatic plasticity [79], heterosynaptic plasticity [76], or
embedding memory in a synaptic component that is notaltered by spontaneous activity [80*], but these models
often yield synaptic weight distributions which are far
different from experimental observation.
Many experimental works have consistently reported thatthe distribution of synaptic weights (or the corresponding
dendritic spine volumes) has a unimodal, heavy-tailed,and skewed shape (for review, see Refs. [81e83]; notethat the tail of the distribution is cut off at the upperbounds of spine size [~1 mm3]). This stereotypical shapeseems almost universally preserved, even in the extreme
conditions where neuronal networks developed in theabsence of synaptic transmission [84,85], spiking activity[29*,57], or expression of key molecules for physiologicalneuronal development [86*e88]. It has been suggested
that the characteristic shape could play various computational roles, such as efficient information transmission[89,90], enriched repertoires of activity patterns [91], andcriticality in the brain [92*]. Thus, finding a model ofsynaptic dynamics which is consistent with this distribution of synaptic weights is necessary for an accurate
description of the neural circuit.

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38 Computational Neuroscience

A synaptic plasticity model with intrinsic dynamics
might be an answer for this challenge. First, the intrinsic
dynamics model explains the robustness of weight distribution in the following way. As per experimental
observation [29*], the dynamics of synaptic weight are
well described with the Langevin equation dw ¼
mðwÞdt þ sðwÞdBt (where Bt represents standard
Brownian motion). The drift term mðwÞdt and diffusion
term sðwÞdBt represent, respectively, extrinsic dynamics(activity-dependent plasticity) and intrinsic dynamics(activity-independent fluctuation). The stable distribution that is computed from the measurement of mðwÞand sðwÞ reproduced the actual distribution of synaptic
weights in both physiological [28,29*,57] and pathological conditions [86*] (Figure 2C). The analysis of the
diffusion process yields that skewness and a heavy tailappear robustly for a wide range of activity-dependent
plasticity terms, as long as the magnitude of intrinsic
dynamics, sðwÞ; is approximately proportional to synaptic weight [9,29*].
Several modeling works have also consistently demonstrated that the combination of intrinsic and extrinsic
dynamics can lead to stable maintenance of memory[54*,55*,93**]. In particular, a work by Humble et al.
[93**] hinted that intrinsic dynamics are more thannoise to be continually corrected by extrinsic dynamics.
In their settings where memory is represented as cell
assemblies in a recurrent network and synaptic changes
are driven by STDP and intrinsic dynamics, intrinsic
dynamics alleviate the positive feedback effect of STDP
by preventing unnecessary synapses from growing.
Further analysis has revealed that an appropriate combination of STDP and intrinsic dynamics could introduce bistability in a group of synaptic weights [9]. The
combination created a separation point between large
and small synapses to minimize their interconversion,
separating strong intra-assembly and weak noneintraassembly synapses while roughly confining the synaptic
weight distribution to a stereotypical shape (Figure 3A).
Although the influence of having cell assemblies on theweight distribution looks small in the standard linear
plot, it is magnified and forms a secondary peak in thesemilogarithmic plot (Figure 3B), which was experimentally detected only recently by the advancement ofserial section electron microscopy (ssEM) [42*,94].
These findings are reminiscent of older theory on binarysynaptic states [95], which exhibited high performancein ANNs [96], suggesting that the brain might use two‘representative’ synaptic weights. An additional important property of the above-mentioned model is that
individual synapses do not take independent binary
statesdrather, most intra-assembly synapses take thestrong state, and most noneintra-assembly synapses
take the weak state.

Current Opinion in Neurobiology 2021, 70:34–42

Exploration via intrinsic dynamics?

Another underexplored potential of intrinsic synaptic
dynamics is to enhance exploration. Because theexplorationeexploitation trade-off is a key concept in
reinforcement learning, engineeringly many algorithms
have been proposed to ensure the exploration of theagent. Among them, adding random (and reward- or
environment-independent) noise to the policy parameters is simple to implement and has exhibited impressive performance in various settings [97e99]. The
advantage of perturbations for enhanced exploration has
also been studied in neuronal models, but these studies
sought the origin of perturbation for the exterior of thelearning network [100], stochasticity of presynaptic
vesicle release [101], or intrinsic excitability of neurons
Figure 3abCurrent Opinion in Neurobiology

Normal and semilogarithmic plots of spine sizes and their multistability.
The data are from Figure 3E of the study by Humble et al. [93**], in which
synaptic weight w is proportional to spine size. (a) A standard plot ofsynaptic weight distribution f ðw Þ. Even after stable memory formation wasachieved by the cell assemblies, the model yielded the monotonously
decaying stationary distributions for synaptic weights. (b) A semilogarithmic plot of synaptic weight distribution. Following the coordinatew 1
transformation, the distribution is given by jd log
dw j f ðw Þ ¼ wf ðw Þ. It
displayed an additional peak at large synaptic weight if cell assemblies
are embedded. This was because the semilogarithmic plot magnified thenearly invisible difference in (a) for the distributions with and without cell
assemblies. Note that the major peak around log w ¼  3:0, which isabsent in f ðw Þ, was produced by the coordinate transformation.

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Computational roles of intrinsic synaptic dynamics Shimizu et al.

[102,103]. Although direct evidence remains elusive,
synaptic fluctuations might be a novel mechanism toimplement trial-and-error exploration of better neuronal
networks.
A link to another dynamics in the brain:
representational drift

So far we have mainly discussed brain dynamics at thesynaptic level. However, other dynamic features of information processing in the brain are drawing attention
as well. In particular, several experimental works havedemonstrated that neuronal representation, whichrefers to the neural activity specifically related to eachmemory, is continuously drifting over time (for reviewsof the relevant literature, see Refs. [104,105]). The drift
seems ubiquitous across many brain areas including the
hippocampus, sensory cortex, and motor cortex, evenwhen the animal shows no apparent change in its
behavior. The cause and role of representational drift
largely remain unknown. Some modeling works haveproposed the framework in which extrinsic synaptic
dynamics change neural codes to be consistent with thelearning criterion and intrinsic dynamics add isotropic
random changes, thereby the representation drifts in the‘neutral’ dimensions of the learning criterion[67**,106**]. For example, the network model of thestudy by Kappel et al. [67**] was driven by both
intrinsic dynamics and the gradient of expected reward.
As a result, although the action and rewards were almost
identical over trials after learning completion, the neuralrepresentation encoding such action was continuously
drifting. Experimental evidence to support this idea is
not sufficient at present, but the combination of
intrinsic and extrinsic synaptic dynamics might be
crucial for the brain to be both adaptive and flexible.

Conclusion
In this work, we reviewed recent developments, basedon both experimental and modeling tasks, on thecomputational roles of intrinsic synaptic dynamics.
Although conventional rules of neural plasticity attempt
to describe synaptic weight changes based on neuralactivities, here, we propose that the widespread presence of activity-independent synaptic fluctuations warrants the investigation of intrinsic dynamics tocharacterize the changes. In some previous works, it isassumed (although often only implicitly) that intrinsic
dynamics do not compromise network performance.
Different insights from neuroscience and machinelearning, however, raise the possibility that brain dynamics not only are constantly affected by intrinsic dynamics but also could benefit from their presence.
Future theoretical and experimental studies might give
us an understanding of why our brain evolutionarily has
chosen to develop neural networks based on intrinsicallydynamical components.

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39

Conflict of interest statement
Nothing declared.

Acknowledgements
The authors thank M. Baltieri for proofreading the manuscript and K.
Ichikawa for helpful discussions. The study was supported by RIKEN
Center for Brain Science, Brain/MINDS from AMED under Grant no.
JP21dm0207001 (T.T.), KAKENHI Grant-in-aid JP18H05432 (T.T.),
20H05685 (H.K.), and JP21J10564 (K.Y.) from JSPS, RIKEN JuniorResearch Associate Program (K.Y.), Masason Foundation (K.Y.), WPI from
MEXT (H.K.), CREST JPMJCR1652 (H.K.) from JST, and SRPBS
JP20dm0107120 (H.K.) from AMED.

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