REVIEWS
Spine dynamics in the brain, mental
disorders and artificial neural networks
Haruo Kasai 1,2 ✉, Noam E. Ziv
and Taro Toyoizumi 4,5, Hitoshi Okazaki1,2, Sho Yagishita1,2

3

Abstract | In the brain, most synapses are formed on minute protrusions known as dendritic spines.
Unlike their artificial intelligence counterparts, spines are not merely tuneable memory elements:
they also embody algorithms that implement the brain’s ability to learn from experience andcope with new challenges. Importantly, they exhibit structural dynamics that depend on activity,
excitatory input and inhibitory input (synaptic plasticity or ‘extrinsic’ dynamics) and dynamics
independent of activity (‘intrinsic’ dynamics), both of which are subject to neuromodulatory
influences and reinforcers such as dopamine. Here we succinctly review extrinsic and intrinsic
dynamics, compare these with parallels in machine learning where they exist, describe theimportance of intrinsic dynamics for memory management and adaptation, and speculate on
how disruption of extrinsic and intrinsic dynamics may give rise to mental disorders. Throughout,
we also highlight algorithmic features of spine dynamics that may be relevant to future artificial
intelligence developments.

1
Laboratory of Structural
Physiology, Center for
Disease Biology andIntegrative Medicine, Facultyof Medicine, The University ofTokyo, Tokyo, Japan.
2International ResearchCenter for Neurointelligence(WPI-​IRCN), UTIAS,The University of Tokyo,
Bunkyo-​ku, Tokyo, Japan.
3
Technion Faculty of
Medicine and Network
Biology Research Labs,
Technion City, Haifa, Israel.
4
Laboratory for NeuralComputation and Adaptation,
RIKEN Center for Brain
Science, Saitama, Japan.
5
Department of Mathematical
Informatics, Graduate Schoolof Information Science andTechnology, The Universityof Tokyo, Tokyo, Japan.

✉e-​mail:hkasai@m.u-​tokyo.ac.jp
https://doi.org/10.1038/
s41583-021-00467-3

The major sites of synaptic change in the mammalianbrain are dendritic spines (Fig. 1a), small protrusions that
extend laterally from dendrites and that are the postsynaptic sites of most excitatory glutamatergic synapses1–3.
The spine is characterized by a bulbous head with a volume between 0.005 and 1 μm3, shaped by actin-​based
scaffolds. The spine head contains a postsynaptic density(PSD) that anchors glutamate receptors and other signalling molecules to the postsynaptic membrane. The
PSD, in turn, is juxtaposed across the synapse with apresynaptic axonal bouton. The spine head is connectedto the dendritic shaft by a narrow neck with a diameter of 0.1–0.5 μm and a length of 0.1–2.5 μm. There are
estimated to be 100 trillion spines in the human cortex,
vastly outnumbering the 175 billion synapses in the largest deep neural networks in current-​use artificial intelligence (AI)4,5. Thousands of dendritic spines decorate thedendrites of major neuron types in the brain, reachingdensities of one to ten spines per micrometre and constituting 70% of synapses in the cortex. Dendritic spines aredensest in principal (projection) neurons of vertebrates,
but can be found in insects6,7 and even in nematodes8.
Spines are not fixed structures: new spines form
while others are eliminated, and spines grow larger andsmaller and change shape. Some of these dynamics are
directly linked to major forms of synaptic plasticity
such as long-​term potentiation (LTP) and long-​term
depression (LTD) of functional connectivity. Althoughsuch changes have been reported in many synapses9,10,
it is only at the spine synapses that synapse-​specific andNature Reviews | Neuroscience
0123456789();:weight changes lasting a day or so have been directly
demonstrated. These dynamics, as well as many additional functional and structural properties of spines, aremediated by hundreds of gene products found at theseminute synaptic specializations, subtle variations ofwhich affect mental function. It follows that dendritic
spines are involved in virtually all mental functions andin many mental disorders.
Recent progress in machine learning and AI is largely
based on artificial neural networks (ANNs), whosearchitectures were inspired by, and share similarities
with, those of the brain. ANNs are composed of feedforward or recurrently connected ‘neurons’, in whichthe ‘synapses’ connecting the neurons have tuneable
weights (strengths). Typically, these weights are set during a training phase in which errors (differences between
the actual output and the desired output) are propagatedfrom the output backward throughout the network (via‘backpropagation’). Although it is not clear whether thishighly effective procedure is used in the brain, it has beensuggested that it might be in some form11. Regardless,the synapse is a central, common denominator of ANNsand brains, the seat of fundamental mental functions
in humans and animals. Although ANNs are radicallysimplified variants of their biological counterparts,
lessons learned in this field might provide importantframeworks for understanding brain function12.
Reinforcement learning (RL) is another biologicallyinspired machine learning field. In RL, agents exploring interactive environments learn action models that

Reviewsa2 μm

Spine enlargement

Repetitive glutamate uncagingb

Spine shrinkage and pruning

Repetitive glutamate uncaging+ GABA (tonic or uncaged)cStress-ﬁbre-like structure

Enlargement

P

Glutamate

NMDAR

Actionpotential

VDCC↑↑ [Ca2+]i

CaMKIIPAK

LIMKShrinkageP
CoﬁlinPSD
Enlargement

P
SSH

Shrinkage
Glutamate
Actionpotential

Dynamic
F-actin
Shrinkage

NMDAR
VDCC

StableF-actin↑ [Ca2+]i

Calcineurin

SSH

CoﬁlinShrinkage

GABA

Coﬁlind

Focal adhesion complex
Stress ﬁbre
F-actinP

ARP2/3
P Coﬁlin
14-3-3ξ LIMK
Myosin II
P SSH
RHOA
FAK

CulturedneuronStress ﬁbre
Focal adhesion
complex

10 μm

5 nm

Integrin
Extracellularmatrixmaximize cumulative rewards. In recent years, RL has
been combined with ANN-​based deep learning, giving
rise to the field of deep RL. Here too, insights gained
might offer new frameworks and hypotheses for understanding brain function13. Although AI has surpassed
human performance in well-​defined tasks5, current
AI falls short in realistic, complex situations in whichhuman (and often animal) intelligence excels. Notably,
unlike in AI, the goals and algorithms underlying
information processing in the brain are not explicitly
designed. Instead, they are embedded in the physical implementations of neural circuits and synapses(‘nature’) and in the way these circuits and synapses are
tuned through interactions with the environment (‘nurture’). It is thus likely that much of the algorithmic richness embedded in synapses and neural circuits remains
to be discovered14.
Here we attempt to provide a concise review of spine
dynamics, their relationships with explicit and implicit
brain ‘algorithms’, how these dynamics relate to key
mental functions and certain mental dis­orders, andhow these insights might further inform neuro-inspired
AI. We first consider extrinsic dynamics — forms ofspine enlargement and shrinkage that are dependent on
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Reviews◀ Fig. 1 | enlargement and shrinkage of dendritic spines. a | Two-​photon-​induced

glutamate uncaging can be used to selectively stimulate long-​term potentiation (LTP)
at a single synapse (in the absence of Mg2+ or spike timing-​dependent plasticity). This
leads to enlargement and LTP of the stimulated synapse but not of nearby synapses.
b | Two-​photon-​induced glutamate uncaging at a single spine in the presence of GABA
(tonic or uncaged during a short time window) can be used to target a spine for shrinkage
or elimination. However, shrinkage is not confined to the targeted spine and can ‘spread’
along the dendrite to affect neighbouring spines. c | Signalling cascades for spine
enlargement and shrinkage. Large increases in intracellular Ca2+ concentration ([Ca2+]i)
activate Ca2+/calmodulin-​dependent kinase II (CaMKII) (within about 1 second)39,70,
resulting in the activation of a serine/threonine-​protein kinase, PAK, and the phosphorylation of many proteins, including LIM-​domain kinase (LIMK), slingshot (SSH) and cofilin,
which are responsible for the stable enlargement of filamentous actin (F-​actin) networks,
and are constituents of stress fibres (red shaded area). By contrast, moderate increases
in intracellular Ca2+ concentration selectively activate calcineurin (in about 1 second)70
but not CaMKII, leading to the dephosphorylation of SSH and cofilin. The encircled ‘P’denotes protein phosphorylation. A lateral spread of cofilin induces shrinkage of neighbouring spines. In addition to the global increases in intracellular Ca2+ concentration,
Ca2+ nanodomains beneath the cytosolic mass of synaptic NMDA receptors (NMDARs)
are necessary for synaptic plasticity37,58. The involvement of a small, representative subset
of molecules in spine remodelling is more fully described in the main text. d | Stress fibres
and adhesion complexes in a cell (left). The right-​hand schematic shows stress fibres andadhesion complexes whose molecular composition is similar to that of the enlarged, stable
F-​actin networks at the spine base. Many of the proteins activated or phosphorylated by
CaMKII are components of stress fibres in cultured cells. SSH bundles F-​actin, to which
RHOA, phosphorylated LIMK, phosphorylated cofilin, myosin II, actin-​related protein
2/3 complex (ARP2/3) and drebrin (not shown) bind. Protein 14-3-3ζ binds with these
phosphoproteins. The fibres are anchored to the extracellular matrix via focal adhesion
molecules, such as FAK and integrins. This supramolecular complex is referred to as a
stress fibre and connects the extracellular matrix and the cytosol. Many of these proteins
are requisite for LTP. PSD, postsynaptic density; VDCC, voltage-​dependent calcium channel.

excitatory (and inhibitory) input or neuromodulation —and then consider intrinsic dynamics — activityindependent changes in spine sizes and numbers thatare also amenable to neuromodulation. The cooperative
actions of both extrinsic and intrinsic dynamics may
enable functions that are still missing in contemporary
AI, such as self-​management of memory systems, deep
adaptability and creativity. Moreover, a full appreciation of these dynamics is key to understanding brain
dysfunction and psychiatric disorders. We apologize for not being able to cite all relevant literature or
cover additional frameworks and molecular mechanisms owing to space limitations. For further reading
on dendritic spines, we refer readers to several otherreviews15–21.

Spike timing-​dependent
plasticity(STDP). Adjustments ofconnection strengths basedon the relative timing of theoutput of a particular neuron
and input spikes.

Spine enlargement
Studying the function of single spines requires theability to selectively stimulate specific spines (Fig. 1a,b).
Commonly used optogenetic methods are not suitable as they stimulate multiple targeted axons. Electro­
physiological stimulation is even less specific as it excites
multiple presynaptic fibre types, including glutamatergic(excitatory), GABAergic (inhibitory) and neuromodulatory fibres, creating complications addressed in later
sections. By contrast, two-​photon glutamate uncaging
releases glutamate within a femtolitre volume and thus isparticularly suited for stimulating spine synapses along
dendritic shafts22. Such glutamate uncaging has demonstrated the tight correlation between the spine-​head
size and the functional expression of fast AMPA-​type
glutamate receptors (AMPARs), a major determinant

Nature Reviews | Neuroscience
0123456789();:of synaptic weight22,23. The results agree with electron
microscopy studies showing that the spine-​head sizes
are proportional to PSD area24 and AMPAR contents25,26,
while a recent study reported a direct correlation
between synaptic strength and ultrastructure27. Thesefindings imply that structural alterations are inevitably
associated with functional modifications. Moreover,given their nature, structural alterations are probably
the most likely means for implementing long-​lasting
functional modifications. These structure–function relationships also obviate painstaking and error-​prone estimates of postsynaptic glutamate sensitivity (or functional
AMPAR expression).
Dendritic spines have been demonstrated to undergo
rapid enlargement within approximately 1 minute ofrepetitive glutamate uncaging28 (Fig. 1a) or glutamate
uncaging repeatedly followed by postsynaptic spikes29–31 toinduce spike timing-​dependent plasticity (STDP)32,33. These
protocols result in effective opening of Ca2+-​permeable
NMDA-​type glutamate receptors (NMDARs) and large
increases in intracellular Ca2+ concentration. Importantly,
spine enlargement induced by such protocols is associated with increased glutamate sensitivity28,32–34. Thus,
spine enlargement presumptively constitutes the structural basis of LTP in spine synapses10,28. Consistent withmany LTP studies, spine enlargement requires activationof Ca2+/calmodulin-​dependent kinase II (CaMKII)35–39
and small GTPases40,41, which through activation andphosphorylation of many proteins (partly listed inFig. 1c) lead to the polymerization of filamentous actin(F-​actin)16,18,42–45 (Fig. 1c).
Confinement of spine enlargement. Uncaging studies
indicate that spine enlargement and LTP are confined tostimulated spines, as neighbouring spines did not show
enlargement or shrinkage (neither LTP nor LTD)28,32,33,37(Fig. 1a). This enables independent modification of synapses, similar to weight modification in ANNs. The ability to confine changes to single synapses is not trivial,
given that hundreds of molecular species are involved inspine enlargement, and many of these have been shownto diffuse from spines to dendrites and among nearby
spines44,46–49. Indeed, spine shrinkage readily spreads,
as discussed below (Fig. 1b). Moreover, LTP leads to theselective activation of several key molecules, including
CaMKII and small GTPases37,40,41,48,50 (Fig. 1c). The degree
to which these molecules spread is determined by theirdiffusion and inactivation rates, which for some key
molecules (for example, CaMKII and CDC42) effectively
confine their activation to within approximately 1 μm of
stimulated spines. For others, such as RAS, RHOA and
RAC1, the situation is less clear, as confinement of spine
enlargement is not well explained by their diffusion andinactivation rates18.
An alternative explanation for the confinement ofspine enlargement relates to the presence of higher-​ordermolecular assemblies within spines, in particular thedense F-​actin networks that define and regulate spine
morphology. As actin networks are primary targets ofmany LTP-​activated molecules, it is plausible that theirsteric properties and polymerization–depolymerization
dynamics confine the activities of LTP-activatedReviews
Filopodia
Thin transient protrusions thatact as ‘feelers’ that allow cells
to probe their surrounding
environment. Can occasionallygive rise to dendritic spines.

Integrins
Transmembrane moleculesthat facilitate cell–cell andcell–extracellular matrix
adhesion by connecting stressfibres and other intracellularactin structures to theextracellular matrix.

Metaplasticity
The plasticity of synaptic
plasticity.

Nanodomains
The cytosolic domains
within about 10 nm of theopen pore of Ca2+ channels or
NMDA receptors where Ca2+
concentrations can readily
exceed 10 μM.

Shunting inhibition
A predominant form of
GABAergic inhibition that
depends on increases in
the membrane conductancebut not necessarily on
hyperpolarization.

molecules in space and time. Spine actin networks sharemany similarities with other actin-​based structures, suchas stress fibres, lamellipodia and filopodia, that shapeand underlie motility in non-​neuronal (and neuronal)
cells51–53. Furthermore, integrins have also been shown
to be involved in LTP54 (Fig. 1d). Strikingly, many proteins that regulate spine enlargement (such as RAC1,
CDC42 and RHOA) also regulate actin dynamics andactin-​based cell motility in other settings on timescalesof minutes51–57 (Fig. 1c,d).
One key molecule in this respect is cofilin. Cofilinbinds F-​actin and severs F-​actin polymers when cofilin isdephosphorylated. Conversely, phosphorylation of cofilin suppresses its binding and F-​actin-​severing activity(Fig. 1c), consequently allowing spine enlargement48,58.
Although phosphorylated cofilin (p-​cofilin) is highly
diffusive in dendrites, p-​cofilin generated during spine
enlargement is observed to be trapped selectively instimulated spines48, indicating that p-​cofilin is boundto higher-​order molecular complexes (Fig. 1d). In support of this view, during spine enlargement, F-​actin can
rapidly (within approximately 1 minute) form a stablegel (the enlargement pool of F-​actin)44, which occasionally (in about 20% of enlarged spines) flows out en
bloc into the dendritic shaft, followed by the reversal ofspine growth44, resulting in only transient enlargement.
Conversely, if the F-​actin gel remains in the spine head,enlargement is long-​lasting, possibly because the gelclears space in the spine head, facilitating PSD growthand consolidation over the course of about 1 hour33,59.
Thus, the rapid, independent and long-​term modifiability of synaptic specializations relies on ubiquitous cellular mechanisms used by most living cells for shaping andrapidly modifying their structures (Fig. 1d).
Confined spine enlargement can last at least
3–6 hours in vitro, and a fraction of newly generated orenlarged spines can last more than 2 months in vivo20,60.
Spine enlargement can be efficiently induced in mostsmall spines (more than 90%), although the extent ofenlargement is highly variable among spines, even inyoung hippocampal in vitro preparations28,33,61. The
variability is more prominent in the adult cortex, where
spine enlargement occurred in only 20% of small spines
even though similar uncaging protocols were used62. Aninteresting possibility is that this heterogenic amenability to enlargement is a manifestation of the ‘cascade
model’ of synaptic metaplasticity63 in which each synapse exhibits a cascade of states with different levels ofplasticity, connected by metaplastic transitions, thereby
preventing overwriting of synaptic memory traces tomake memory long-​lasting. Regardless, in vivo experimental evidence points to the importance of corticalspine enlargement in motor memory, as selective optical‘undoing’ of the enlargement of approximately 400,000
spines in the motor cortex associated with learning a
specific motor task selectively erased learning acquired
for that motor task64.

Spine shrinkage and pruning
Prolonged, low-​frequency stimulation of specific spines
can lead to their shrinkage and pruning48,58,65,66. Here we
discuss how and why such shrinkage spreads to otherspines along the dendrite, the roles of inhibitory signalling in this shrinkage and implications of these extrinsic
dynamics.
Spreading of spine shrinkage and pruning. Unlike spine
enlargement, spine shrinkage and pruning can spreadto neighbouring spines, as far as 15 µm from the stimulated spine58 (Fig. 1b). This is consistent with many studies
reporting the spread of LTD31,62,67–69 and spine pruning66
when an input fibre bundle is stimulated at a low frequency. Notably, neighbouring spines that are stimulatedwith a protocol that induces spine enlargement are ‘protected’ against the spine shrinkage that may otherwise
spread from neighbouring synapses58.
Spine shrinkage depends on Ca 2+ flux through
NMDARs (influx through dendritic voltage-​g atedchannels is not sufficient), which leads to moderateincreases in intracellular Ca2+ concentrations sufficientto activate the Ca2+-​dependent phosphatase calcineurin, but not CaMKII70 (Fig. 1c). Activation of calcineurin
depends on Ca2+ nanodomains underneath the cytosolic
openings of NMDARs58, as is the case with CaMKII inspine enlargement37 for synaptic specificity. Calcineurinis thought to dephosphorylate p-​cofilin, and by doingso, it activates the latter’s F-​actin-​severing ability (Fig. 1c),
resulting in spine shrinkage48,58,71,72 (Fig. 1b). By diffusing
to neighbouring spines, dephosphorylated cofilin acts asa spreading shrinkage factor48 shown to be necessary58,71
and sufficient for spine shrinkage48. Spreading of spine
shrinkage has been observed in the visual cortex of adultmice62, although it seems to be less common and more
confined than spreading in hippocampal slices fromyoung rats48,58. Notably, a form of spine shrinkage that
depends on NMDARs, but not on ion flux through thesereceptors73, occurs in young but not adult animals74.
Whereas spine enlargement typically occurs within
1 minute28,37,59,62 (Fig. 1b), spine shrinkage occurs onmuch longer timescales (for example, over 10–60 minutes)58,62,66,68. This difference probably reflects the rapid
dynamics of actin polymerization involved in initial spine enlargement43,44 as compared with the slow
dismantling of PSD scaffolds75.
Roles of inhibition in spine shrinkage and pruning. When
postsynaptic spikes precede presynaptic stimulation,
stimulated synapses will often undergo LTD29,31(Fig. 1b).
As mentioned earlier, this depends on Ca 2+ influx
through NMDARs that elevate intracellular Ca2+ concentration to moderate levels only9,31 (Fig. 1c). Precisely
timed activation of postsynaptic GABA type A receptors(GABAARs) could serve to restrict intracellular Ca2+ concentration elevations to such levels by shunting inhibition.
Indeed, feedforward (and feedback) GABAergic neuron
activity driven by glutamatergic fibre stimulation has
been shown to be necessary for LTD induction69. In
support of this finding, glutamate uncaging-​mediatedspine stimulation paired with postsynaptic stimulationinduced spine shrinkage only when increases in spine
intracellular Ca2+ concentration were dampened by
GABAergic inhibition (or intracellular calcium chelation)58 (Fig. 1c). By contrast, when intracellular Ca2+
concentration increases were not suppressed, CaMKII
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Reviews
was activated and competed with calcineurin, and theshrinkage was abated58 (Fig. 1c). Thus, spine growth andshrinkage are determined by spine intracellular Ca2+levels (Fig. 1c), and inhibitory neurons play a key role indetermining these levels.
Extrinsic dynamics versus weight adjustments in ANNs.
Extrinsic dynamics share similarities with synaptic
weight adjustments in ANNs, but also differ from thesesubstantially. In ANNs, weight adjustments are basedon comparisons between computed network output
and desired network output; errors at the output level
are then ‘backpropagated’ and used to adjust synaptic
weights in the entire network. Purely local rules, suchas simple Hebbian learning, can enhance features in the
input9,10,31,76 but cannot be used to solve a general taskthat requires information (feedback in some form) as
to the manner by which local synaptic changes affectnetwork output and ultimately behaviour. This observation indicates that purely local rules might not suffice
to explain the role of extrinsic dynamics in behaviourallearning. Indeed, global error signals might play criticalroles (see the section entitled Reinforcement learning)11.
Alternatively, backpropagation might occur indirectly through feedback connections and circuit-​level
organization11,77,78.
Other important differences between extrinsic dyna­
mics in the brain and ANN synaptic weight adjustments
also exist. ‘Synapses’ in ANNs can have positive or negative weights, whereas spine synapses are predominantly
excitatory, hinting at the importance of inhibitory
synapses79. Furthermore, extrinsic dynamics are asymmetric: spine growth is rapid and spatially confined,
whereas shrinkage is slow, is non-​local and can lead topruning. Rapid, confined spine enlargement could help
diversify downstream circuits (see the section entitled
Reinforcement learning), whereas non-​local pruning(as a form of heterosynaptic plasticity) may help to remove
inactive synapses, which synapse-​specific plasticity nor
backpropagation enables11. These differences may be
instrumental for circuit rewiring during critical periodsin the course of development 80, and in the ANN
domain for finding sparsely connected subnetworks(see the section entitled Pruning and rewiring)81.
Critical periods
Periods during developmentin which a particular skill or
characteristic is believed tobe most readily acquired.

Operant conditioning
A form of learning that uses
rewards and punishments
for enforcing behaviour.
Sometimes called‘instrumental conditioning’.

Eligibility trace
A temporary record of theoccurrence of an event whichmarks the memory parameters
associated with the event
as eligible for undergoinglearning changes.

Reinforcement learning
RL is a machine learning approach in which agents
explore interactive environments, receive feedback(reward) in response to selected actions and learn action
models for maximizing cumulative rewards. RL82 wasinspired by concepts developed in behavioural experiments, in particular operant conditioning83. A key concept
adopted in RL is the eligibility trace, with which agents(such as robots) involved in producing behaviours are
sensitive to feedback for the effective detection of contingencies between actions and rewards for a certain period.
Such learned associations are later used to predict rewards
and estimate the reward prediction errors (RPEs),
the differences between expected and actual rewards.
Substantial experimental work suggests that RPE signals might be encoded in the brain by the firing of midbrain dopaminergic neurons84–86 that densely innervate

Nature Reviews | Neuroscience
0123456789();:the striatum. In particular, these neurons innervate thenucleus accumbens (NAc; Fig. 2a) in the ventral striatum, which is considered to be a major ‘reward centre’
involved in classical conditioning and addiction86–88.
Dendrites of NAc spiny projection neurons (SPNs;
also called ‘medium spiny neurons’) are decorated withspines that receive inputs from both glutamatergic anddopaminergic fibres (Fig. 2a). Dopamine activities are
mediated by dopamine receptors, members of a family of ~400 non-​olfactory G-​protein-​coupled receptors(GPCRs) expressed in the brain and that also mediate activities of many additional, crucially importantneuromodulators89. D1-​like family receptors (D1Rs)
and D2Rs stimulate and inhibit adenylate cyclases (ACs),thus increasing and decreasing levels of intracellularcyclic AMP (cAMP), respectively. Compounds that elevate dopamine concentrations can cause drug addiction,owing to excessive D1R activation88.
D1Rs and the eligibility trace. What might be the biological substrate of the eligibility trace? Although various mechanisms have been explored theoretically (forexample, see ref.90), experimental validation has proved
difficult, mainly because methods based on electricalstimulation inevitably recruit both glutamatergic anddopaminergic fibres91. This difficulty was solved by useof two-​photon glutamate uncaging to selectively stimulate individual spines, and optogenetics to independently
stimulate dopaminergic fibres34. In these experiments,
performed in D1R-​expressing SPNs in mice NAc slice
preparations, STDP protocols and timed dopaminergic
stimulation were used to assess the effects of dopaminergic input on spine enlargement (Fig. 2b). Dopamine
was found to promote spine enlargement only when
its release was triggered within a narrow time window(0.3–2 seconds) after the onset of glutamatergic input(Fig. 2c,d), which tracked the temporal profiles of intracellular cAMP levels. These results are interpreted toindicate that increases in intracellular Ca2+ concentration
associated with STDP prime Ca2+-​dependent AC (AC1),such that D1R-​induced activation of stimulatory G proteins at the delayed reward time efficiently triggers cAMPsyn­t hesis 92,93 (Fig. 2e) . Increases in intracellularcAMP con­centration lead to CaMKII disinhibition (viaprotein kinase A (PKA)), and thus repetitive conditioning summates to induce measurable spine enlargements
within about 1 minute34,93, according to the molecularcascade shown in Fig. 2e. Moreover, similar time windows
were also observed to determine the effects of noradrenaline on spine size 94, suggesting that these timing
dependences may reflect the kinetics of conformationalchanges of AC95. Importantly, the timing of the dopamine
sensitivity of spines (Fig. 2d) is similar to the minimum
behavioural time window needed for reward conditioning measured in behavioural experiments96. Thus, thetemporal features of the eligibility trace are embeddedin the molecular cascades within spine synapses (Fig. 2e).
D2Rs and psychosis. D2Rs are a second class of dopamine receptors of particular relevance to psychiatry, as
they are the major targets of drugs used to treat psychosis (including symptoms such as delusions andReviewsaTwo-photon uncaging

Glutamatergic
ﬁbre

Optogenetics

ChR2+
dopaminergic
ﬁbre

457 nm
720 nm

457 nmGlutamate

ChR2

Two-photon
excitation focus
D1R-expressing SPN or
D2R-expressing SPN

720 nmbc
Glu + 3APs

Δt = +10 ms

Time (min)Before

1 µm
Time (s)01

× 15 trains

2

3

4

5

2

3

4

5

Time (s)****50 min1–175

ΔVH (%)

0

10 Hz × 10

Dopaminergic
ﬁbre (ChR2)
30 Hz × 10

10 Hz × 10

100 Hz × 3

Glu + 3APsd

Dopaminergic
ﬁbre (ChR2)
30 Hz × 10,
Delay +1 s

50
25
0

w/o DA–1

0

1

DA delay (s)eHebbian plasticity
Glutamate

NMDAR

Actionpotential

VDCC[Ca2+]iSensorimotor
signal

CaMKII

Enlargement

e(t)
PP1

Reinforcement plasticity
Reinforcement
stimuli

Dopamine
burst

Modulator

Gs-coupled receptor(e.g. A2AR)

Punishment
stimuli

Dopamine
dip

D1R

Gs

AC1

cAMP

Gi,o

PDE

PKA

DARPP32

AC > PDE

RGS
D2R
The timing generatorfg

Dichotomous regulation

Sensorimotor
signals
Dopamine
burst or dip

Striatal SPNs
Direct or
indirect path
Behavioural

D2R

D1R

1.0

2.0

D1N

ΔV (%)

50

D2N

GPi

GPe
GPi

Positive
reinforcement

Negative
reinforcement

0
0.0

0.2

0.5

[Dopamine] (μM)

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Reviews◀ Fig. 2 | reinforcement plasticity of dendritic spines in D1 and D2 neurons.

a–d | Two-​photon-​mediated uncaging of glutamate combined with optogenetic stimulationof dopaminergic inputs to spiny projection neurons (SPNs) expressing dopamine
1 receptors (D1Rs) leads to spine enlargement only if the dopaminergic stimulation is
performed 0.3–2 seconds after the onset of glutamatergic spike timing-​dependent(STDP) stimulation. This time window can be considered the lifespan of the synaptic
eligibility trace. e | The signalling cascades for the modulation of spine enlargementby dopamine. Adenylate cyclase 1 (AC1) in the grey shaded region dictates the timecourse of the eligibility trace (e(t)). Sensory stimuli (for classical conditioning) or motor
command activity (for operant learning) are translated into elevations of intracellular
Ca2+ concentration ([Ca2+]i), which prime AC1 for subsequent activation by dopamine
signalling. f | The optogenetically driven bursting and pausing (blue) of dopaminergic
axons following STDP stimulation (red) of D1R-​expressing SPNs and D2R-​expressing
SPNs for the control of behaviours. D1R-​expressing SPNs project mainly to the globus
pallidus interna (GPi), whereas D2R-​expressing SPNs project indirectly to the GPi via theglobus pallidus externa (GPe) and the subthalamic nucleus. All neurons in the direct andindirect pathways are inhibitory. g | Dichotomous regulation of spine enlargement at
50 minutes after induction by dopamine concentrations surrounding D1R-​expressing
SPNs and D2R-​expressing SPNs. **Statistically significant. A2AR, adenosine A2A receptor;
AP, action potential; CAMKII, Ca2+/calmodulin-​dependent kinase II; cAMP, cyclic AMP;
ChR2, channelrhodopsin 2; D1N, D1 neuron; D2N, D2 neuron; DA, dopamine; DARPP32,
protein phosphatase 1 regulatory subunit 1B; Glu, glutamate; NMDAR, NMDA receptor;
PDE, phosphodiesterase; PKA, protein kinase A; PP1, protein phosphatase 1; RGS,
regulator of G protein signalling; VDCC, voltage-​dependent calcium channel; w/o,
without. Parts a–d are adapted with permission from ref.34, AAAS. Part g is adaptedfrom ref.103, Springer Nature Limited.

Salience
The quality of being
particularly noticeable
or important.

hallucinations) in disorders such as schizophrenia, forexample. Psychotic symptoms have been hypothesized toresult from aberrant attribution of salience (the ‘saliencemisattribution hypothesis’)97,98. How dopamine causessalience misattribution, however, is largely unknown.
Several findings provide important pieces to thispuzzle. First, as mentioned already, D2Rs inhibit AC(Fig. 2e). Second, dopaminergic neurons typically firetonically at approximately 5 Hz and, following rewardomission or punishment, cease firing for brief periods(0.4–2 seconds), resulting in transient ‘dips’ in extracellular dopamine levels84,86,99,100. Such dips would be
expected to be detected by D2Rs and lead to transient
increases in intracellular cAMP concentration. Third,
about half of SPNs selectively express D1Rs, whereas
the others express D2Rs87,101,102. These SPN populations
belong to the direct and indirect basal ganglia pathways,
which are used in positive and negative control of cortical activities (and behaviour), respectively (Fig. 2f). These
three observations have led to the suggestion that the
dopamine dip associated with reward omission (or punishment) suppresses behaviours due to D2R-​expressing
SPN-​mediated negative reinforcement. Indeed, recent
experiments, using two-​photon uncaging and optogenetics, showed that D2Rs detect dopamine dips as
short as 0.4 seconds, which are followed by PKA and
CaMKII-​dependent spine enlargement in D2R-​SPNs103(Fig. 2e–g) . These findings are further supported byin vivo measurements of dopaminergic neuron activity,
extracellular dopamine levels and PKA activity in SPNs
during learning104 as well as a systems biology analyses of D2R signalling93. Collectively, they suggest that
dopamine has dichotomous effects on D1R-​expressing
SPNs and D2R-​expressing SPNs (Fig. 2g) such that they
store memories of reward and reward omission (or punishment), respectively, through cell type-​specific spine
enlargement.

Nature Reviews | Neuroscience
0123456789();:Reward conditioning via D1R-​expressing SPNs exhibits an unexpectedly high degree of generalization103,105.
Intriguingly, dopamine-​dip detection by D2R-​expressing
SPNs seems to be particularly important for discrimination learning; that is, the ability to discriminate between
similar conditioning stimuli103. Thus, D2R-​expressing
SPNs sculpt conditioning, tuning it to specific stimuli103.
Consequently, impairment of discrimination learning
might result in overgeneralized conditioning, giving
rise to salience misattribution and misplaced emotional
reactions. The dopamine generalization–discrimination
hypothesis described here103 naturally explains how salience can be misattributed and subsequently trigger psychotic symptoms97,98. Indeed, repetitive amphetamine
treatment — which typically induces psychosis in humans
and mice — impairs discrimination learning, whereas D2R
antagonists can mitigate these impairments103. Collectively,
these ideas and findings provide a physiological framework for understanding psychosis and antipsychotics,
with the discrimination task representing a rational
behavioural diagnostic for evaluating psychosis andpotential treatments in both humans and animal models.
Neuromodulator-​gated learning. Traditional RL typically involves a single RPE and a single target system.
However, if traces engraved by reward and reward omission or punishment are stored separately, the possibility
arises that they might also be activated differentially, inparticular in different brain states shaped by neuromodulatory influences89. This multiplexing of multivariate
storage103 and complex readout modes might underlie
the rich landscape of emotional influences characteristic of mammals89,106. The advantages of multivariate
reward signals were demonstrated in dichotomous RL
machines, which were able to flexibly modulate risk preference of the agent107,108. Intriguingly, disturbances thatcaused noisy generalization and impaired discrimination
led to aberrant behaviour108.
The coding of RPE by dopamine seems to apply only
to part of the NAc and only in certain contexts103. Even
though the same eligibility and dichotomous mechanisms
probably hold in the dorsal striatum, dopamine may code
internal, more subjective signals other than explicit sensory signals for reward and punishment109,110. In addition,
GPCR agonists other than dopamine may work on othertimescales, with their operation acting as a three-​factor
learning rule77,111, in which change in synaptic weight is
described by a product of a presynaptic factor, a postsynaptic factor and an additional third factor, such asa GPCR agonist. The three-​factor learning framework
may provide versatile bases for neuromodulator-​gatedlearning in the brain and AI. Notably, more than one
third of the 400 non-​olfactory GPCRs are targets ofauthority-​approved drugs, and a better understandingof neuromodulator-​gated learning, in general, will be key
to advancing psychiatry and neuroscience-​inspired AI.

Intrinsic dynamics
So far we have described major features of extrinsic
dendritic spine dynamics — that is, spine enlargement and shrinkage driven by activity, synaptic input
and neuromodulation — and highlighted parallels andReviews
a

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differences between these and modifications to synaptic
weights implemented in ANNs. Dendritic spines, however, unlike synaptic weights in ANNs, also change spontaneously, in manners independent of activity61,112,113.
The definition of activity independence is somewhat
nebulous and differs subtly among studies. Here we referto intrinsic spine dynamics as forms of remodelling not
driven directly by evoked synaptic transmission at thespines in question. Within this framework, however,characteristics of intrinsic dynamics are still amenable
to the influences of global features such as background
activity levels or neuromodulatory tone. Althoughthese intrinsic dynamics (Fig. 3a–d) are in all likelihood associated with corresponding changes in synaptic strength114, they were, until quite recently, mostly
unheeded. We therefore describe these dyna­mics insome detail, and then consider their implications for the

management of memory systems and their contributions
to ‘heuristic’ algorithms.
Presence of intrinsic spine dynamics. Multiple studies
have shown that blocking synaptic transmission andnetwork activity only moderately suppresses the extent
of spine-​size fluctuations61,115,116. Similarly, rates of spine
formation and elimination are only weakly affected
when activity is fully suppressed in vivo117. Indeed,
a complete gamut of dendritic spine sizes and shapes
is observed even when networks develop in the complete absence of synaptic transmission118,119. Moreover,although blockade of key molecules that underlie extrinsic dynamics results in severe behavioural deficits120,121,
only subtle changes in spine-​size distributions areobserved122,123. The nearly universal shape of spine-​size
distributions — unimodal, skewed and heavy-​tailed124,125
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Reviews◀ Fig. 3 | intrinsic dynamics and rewiring of dendritic spines. a | Transitions of spines

among the three categories. Nascent spines without stable presynaptic partners arereferred to here as ‘filopodia’ (F). Spines with small (S) or large (L) heads are connected
to presynaptic partners. They may carry working memory and long-​term memory,
respectively (see the main text). Note that transition from F to S might involve a switch
in the spines’ presynaptic partner, further limiting the lifetime of specific connections60,61.
b | Spontaneous fluctuations of spine-​head sizes over a 2-​hour period. Spine-​size
fluctuations are proportionally greater in larger spines. Over these short timescales,
sizes fluctuate around their mean values due to filamentous actin (F-​actin) dynamics.
c,d | Spontaneous fluctuations over days in the presence of an NMDA receptor inhibitor,
APV, for initially small spines (c) and large ones (d). Most small spines stay in the same
category, whereas some become bigger or are eliminated. Large spines show proportionallylarge fluctuations. e | Rewiring of synaptic connections during spine pruning and generation,
which occurs for 1–2% of spines per day even in the absence of spiking activity, as
compared with 1–8% in active networks60,117,210. f | Semilogarithmic plot of spine-​size
distributions fz with the logarithm of synaptic weight z = log w. Most spines are small(black, S), but an additional large peak (grey, L) can be seen in certain preparations or in
the artificial neural network simulation141 only after learning that results in the formationof cell assemblies. We use the natural logarithm, and z = –4 corresponds to w = 0.018 μm3.
The L peak (at z = –1.4) in the semilogarithmic plot is introduced by the coordinatetransformation from w to z182,193,194,211. By the same token, the occurrence of the smallest
spines and spine genesis or pruning (transition between S and F) may seem to occur
less frequently than they actually do (see Boxes 1–3). Part b adapted from ref.28, Springer
Nature Limited. Parts c,d adapted with permission from ref.61, Society for Neuroscience.
(Boxes 1–3) — emerges even in networks that neverexperienced any activity whatsoever 61,116. Intrinsic
spine-​size fluctuations account for more than 50% of
the size changes that individual spines undergo in active
networks115,126 and occur independently of neighbouring
spine dynamics61.

Drift
The averaged change of aparameter in a certain period.
In the general case, thedrift, μ(w), is dependent on
the current value of theparameter w.

Diffusion
The standard deviation ofa parameter in a certain
period. In the generalcase, the diffusion, σ(w), isdependent on the current
value of the parameter w.

Mechanisms of intrinsic dynamics. Intrinsic dynamics have at least two components. The first is a rapid
component (Fig. 3b) mediated mainly by continuous
reorganization of the actin scaffold28,127 that does notstrongly affect PSD size but does seem to drive spine‘morphing’ and glutamate receptor dynamics over timescales of minutes75,128. The second component involveschanges in PSD sizes over timescales of many hours75
and encompasses the entire range of spine sizes115,129(Fig. 3c,d). The latter dynamics seem to be driven by
the continuous binding, unbinding and interchange of
PSD molecules116,130 (over a typical timescale of several
hours)47,75 and their metabolic turnover (over a timescale of many days131). These dynamics also depend on
the extracellular matrix15,117 and interactions with motile
microglia and astrocytes132. Comparable molecular
dynamics probably drive size fluctuations in presynaptic specializations75, as well as postsynaptic specializations of GABAergic synapses133. Thus, it would seem that
intrinsic dynamics are inevitable by-​products of ongoingbiological processes.
Quantification of intrinsic dynamics and weight distributions. Despite this complexity, multiple studies
demonstrate that measurement of a single parameter —spine size — provides a good approximation of intrinsic
dynamics, quantitative explanations of underlying phenomena and insights concerning their consequences.
Moreover, these studies show that size dynamics can be
captured surprisingly well by very low parametric processes that are essentially stochastic61,116,129,134,135. Details
differ somewhat among studies, but they can be generally

Nature Reviews | Neuroscience
0123456789();:characterized as stochastic processes that have drift anddiffusion terms (Box 3 figure parts a–c). Importantly,

these models account quite accurately for the experimentally observed stationary, unimodal, skewed andheavy-​tailed distributions of synaptic sizes (Box 3 figure
part d), which peak at values lower than the population
mean (Box 3). This skewed shape can be attributed to theobservation that the diffusion term (which describes
the magnitude of size fluctuations) scales with synaptic
size61,134 (Box 3 figure part b; Fig. 3c,d).
More quantitatively, the standard deviation of sizefluctuations σ(w) is approximately proportional to themomentary synaptic weight, w, or more precisely tospine surface or PSD area116,135. Thus, relatively large
spines occasionally make large excursions in size suchthat they grow even larger (Fig. 3d) , whereas small
spines make smaller excursions, and consequently tend
to change less and accumulate (Box 3 figure part d).
This dependence of size fluctuations on momentary
size might be related to multiplicative synaptic change
rules134 or to continuous, noisy multiplicative downscaling of synaptic sizes129. At a more detailed level, it might
be explained by the dependence of molecular dynamics on surface area135 or the cooperative binding andunbinding kinetics of synaptic molecules130.
The presence of a fixed point (FP) in the driftcom­p onent of the aforementioned stochastic processes has important implications. First, it implies
that newly formed spines, which tend to be particularly small114,115,136,137 (that is, smaller than the FP; Box 3
figure part c), will tend to grow larger. Second, it implies
that synapses with sizes greater than the fixed point
will tend to become smaller. Both tendencies are dueto the negative slope of the drift component (Box 3
figure part c) in the absence116 and presence of ongoing activity61,115,116,129,134,135,138,139. Consequently, synaptic
weight distributions are confined (in a quasi-​lognormalmanner; Box 3) to mostly below about 1 μm3, regardlessof the details of the drift term. Thus, intrinsic dynamics can serve to normalize synaptic weights61,116,135,140,141.
Notably, most cerebellar Purkinje cell spines are relatively large24, suggesting that FP is large in Purkinje cells,
while it is set to lower values in other neurons, possibly
for reasons described later.
The stochastic models of size fluctuations describedabove also account for the rate of spine elimination
observed in experiments61,116, which can be calculated
by counting changes in the number of spines that hit
the detection threshold volume (for example, 0.02 μm3;
Fig. 3a) over a measurement interval61,135,141. Indeed, thelife expectancy of small spines has been consistently
reported to be shorter than that of large spines61,137,142–144.
In this sense, small spines are less persistent than large
spines simply because the former are closer to thepruning boundary115,116.
Rewiring via dendritic filopodia. The elimination of(small) spines is continually matched by the formationof new (small) spines (Fig. 3e), at typical rates of a few
percent per day in the cortex20,145 and about 10% in the
hippocampus61,144,146. Although these rates are affec­
ted by many forms of learning and external stimuli

Reviews(for example, see refs60,64,117,147–150), spine formation andelimination continue at surprisingly high rates evenwhen action potentials and Ca2+ entry to neurons areblocked117,137, suggesting that spine formation is mediated in part by intrinsic dynamics. New formations
include dendritic filopodia and transient spines, (relatively) short-​lived protrusions that extend and retractfrom dendrites, forming ephemeral contacts with nearby
axons. A fraction of these formations occasionally evolve
into bona fide synaptic connections within hours todays, facilitated by learning-​associated stabilization andenlargement20,148,151–153. Filopodia and transient spines
define overlapping ‘capture volumes’ around dendritic
shafts 154,155 within which dendrites can potentiallyestablish connections with three or four nearby axons
within approximately 6 μm (refs156–158). This mode ofsynapse formation undoubtedly contains an importantBit
A binary digit. The smallest
unit of measurement used
to quantify computer data.

Box 1 | Dendritic spines in schizophrenia
schizophrenia is characterized by positive symptoms (such as delusions andhallucinations), negative symptoms (such as anhedonia and lack of motivation) andcognitive symptoms19,212. analysis of many mice lacking or harbouring mutations in genes
implicated in schizophrenia has revealed that synaptic plasticity is often impaired212.
impairments in long-​term potentiation may account for working memory deficits
and therefore represent a possible underlying mechanism of schizophrenia cognitive
symptoms212,213. Notably, spine loss reported in individuals with schizophrenia seems toapply mainly to small spines173,174, in contrast to observations in individuals with autism
spectrum disorder (Box 2). the same tendency was found in mice harbouring mutations
detected in people with schizophrenia123,214, for example, in calcineurin B (Cnb)-​knockout(KO) mice (see the figure)123, which also show impairments in long-​term depression
and working memory215. these observations suggest that small spines may have key
roles in working memory, which may be impaired by defective spine enlargement or
reductions in small-​spine numbers (see the figure). if so, the functional outcome of suchmutations is probably severer than implied by the subtle effects on size distributions(in common with autism spectrum disorder models).
Both positive and negative symptoms of schizophrenia may reflect impairments insensitivity to dopamine: positive symptoms (also called ‘psychotic symptoms’) may result
from a disrupted ability to detect dopamine dips (see the main text), which is extremely
sensitive to either increases in baseline dopamine concentrations or genetic mutations
affecting spine enlargement212, either of which can prevent discrimination learning.
impairments to spine enlargement may further contribute to the negative symptomsof schizophrenia by impairing reward-​based learning via striatal dopamine 1 receptor-​
expressing spiny projection neurons216. thus, both positive and negative symptoms
might be attributable to the dichotomous regulation of spine enlargement by dopamine(Fig. 2f,g). **statistically significant. wt, wild type. Figure reproduced with permission
from ref.123, elsevier.
50

KO

WT

Cnb-KO**

Frequency (%)

40

30

20

10

0

0.0

0.5

1.0

Area (μm2)

1.5random, exploratory component and thus a route foractivity-​independent ‘rewiring’ of neuronal circuitry(Fig. 3e). Note, however, that spinogenesis might also
occur in a targeted fashion towards neurotransmittersor neurotrypsin secreted by active axons159,160.
The formation of filopodia and spines is also regu­
lated by broadly acting biological signals related tophysiological and pathological processes. For example, spine genesis and pruning are affected by corticosteroid and sex steroid hormones161–164, linking
stress, circadian rhythms and reproductive cycles,
among other factors, to spine dynamics. Likewise, theanaesthetic ketamine has been shown to drive spine
genesis, possibly explaining its slow-​onset, long-​term
antidepressant effects in the mouse prefrontal cortex165.
Intrinsic spine dynamics are also affected by multiple
neuromodulators, including canonical ones such asacetylcholine166. Moreover, mounting evidence points tothe importance of spine generation in conferring resilience to Alzheimer disease167. Collectively, these findings highlight the importance of intrinsic and extrinsic
dynamics to network rewiring (Fig. 3a,e), and, in turn,its importance for brain function, and potentially for
novel ANN algorithms (see the section entitled Pruning
and rewiring).

Spine dynamics and memory management
Humans can recall an enormous number of events that
occurred in the preceding few days — places we visited,people we met and much of what was said. Such memories are essential for executive functions in daily life.
Eventually, however, most of these memories are lost,and only a small fraction persists beyond a few days.
Memories that do persist, however, tend to be retained
for longer periods, such that forgetting is characterized
by an ever-​decreasing rate of memory decay168, as originally observed more than a century ago169. To date, theroles of intrinsic spine dynamics in memory management and decay have rarely been considered. In the following sections, we point to potential ties between these
phenomena.
Storage of new and working memories in small spines.
Extensive evidence indicates a central role of small
spines in the storage of new memories 2,170. First,
small spines most frequently show rapid spine enlargement following glutamate uncaging28,33,62, natural61 andsynchronous activity115. Even after their enlargement(by as much as 50%)32,33,62, they tend to remain relatively small (Fig. 1a). The precise timing of the onset ofenlargement is difficult to measure, but can be less than
10 seconds from uncaging28. Second, as evident from theskewed shape of spine-​size distributions (Box 3), mostdendritic spines are small with potentially huge storage
capacity. Small spines could account for about 10 TB ofmemory if we attribute one bit to one spine, because 80%of 100 trillion spines are small (Fig. 3f). Thus, intrinsic
dynamics, by giving rise to these skewed distributions(Box 3), produce extensive capacity for new memory storage. Third, because small spines are close to the pruningboundary, their life expectancies are short, congruent
with the short lifetimes of most new memories168.
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Reviews
Box 2 | Dendritic spines in autism spectrum disorderindividuals with autism spectrum disorder (asD) show early-​onset abnormalities incommunication and behaviour and often exhibit epileptic brain activity19,217. although thecauses of asD remain a topic of intense research, a common co-​morbidity is intellectual
disability. early studies reported particularly small spine sizes (spine dysgenesis) in thebrains of individuals with various intellectual disabilities172. in Fmr1-​knockout mice,a model of fragile X syndrome, which is often associated with asD, spine dysgenesis isoften less obvious (see the figure)135. By contrast, rates of spine turnover (genesis andpruning) are strikingly increased (twofold to threefold higher) compared with thosein control animals117,171,218–220. these increases in spine-​turnover rates are not affectedby blockade of spikes and NMDa receptors in a fragile X syndrome mouse model117,
suggesting that they reflect exaggerated intrinsic spine dynamics. the fluctuations weredirectly measured in Fmr1-​knockout mice, and the amplitudes were larger, in line withhigher turnover rates and the smaller spine sizes135. this demonstrates that even subtle
changes in spine-​size distributions might reflect severe impairments in the selectionof synapses.
Consistently, proteins crucial for spine structure and function, such as neuroligins,
sHaNK proteins (sH3 and multiple ankyrin repeat domains proteins; also known as
prosaPs), fragile X mental retardation protein (FMrP), methyl-​CpG-​binding protein 2(MeCP2) and cell adhesion molecules are implicated in asD19, in line with the idea that
asD might stem in part from impaired synaptic tenacity221. the shorter lifetimes of spines
would be expected to give rise to slower acquisition of long-​term memory141,222 and thismay manifest itself as spine dysgenesis. Moreover, a compensatory increase in synaptic
connections involved in memory functions may contribute to the epilepsy141 often foundin individuals with asD217. thus, schizophrenia (Box 1) and asD may be ascribed topreferential impairments in extrinsic and intrinsic synaptic dynamics, respectively223(Fig. 3a).
it is worth emphasizing that mental disorders are not discrete entities, and are better
thought of as a spectrum224. in particular, owing to diagnostic criteria, many different
early-​onset communication disorders are often classified as asD, irrespective of thecause. For example, symptoms related to mutations in plasticity-​related molecules suchas synaptic ras GtPase-​activating proteins225 and Ca2+/calmodulin-​dependent kinaseiiγ226 are diagnosed as asD because of their early onset. KO, knockout; wt, wild type.
Figure adapted from ref.135, CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/).

KO

Probability density

8

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Fmr1 KO

4

0

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Working memories
Information stored in anaccessible state for use incomplex mental tasks.

Further evidence for this reasoning can be found in
the observation that a shift towards small spine sizesin Shank1-​knockout mice (an animal model of autism
spectrum disorder) is associated with enhanced acquisition of working memories and new memories171. Strikingly,
in these same animals, long-​term memory preservation was impaired, in line with the predicted effects ofreductions in the levels of SHANK1 (SH3 and multiple
ankyrin repeat domains protein 1), a PSD molecule,on intrinsic spine dynamics and synaptic tenacity116.
Indeed, small spines are prevalent in individuals with
autism spectrum disorders172 (Box 2). By contrast, thenumbers of small spines are reduced in individuals with

Nature Reviews | Neuroscience
0123456789();:schizophrenia173,174, in aged rhesus monkeys175 and in
calcineurin B-​knockout mice123 (Box 1), all of which tend
to exhibit deficits in working memory.
Memory persistence via multisynaptic connections.
Intrinsic dynamics may seem to challenge the stability of spine-​based memory encoding79,113. Their functional consequences, however, might be dampened
by connections formed of multiple synapses113. Morequantitatively, if a connection is based on N synapses,
each with a weight of w and variance of σ2, and giventhat the intrinsic fluctuations of individual synapses in
the connection are uncorrelated61, the total connection
variance will be Nσ2w2, as compared with N2σ2w2 for asingle synapse with the weight Nw (Box 3 figure part b).
In this sense, compound connections that are based on
multiple (weak) synapses are stabler than connections
based on single strong synapses. Moreover, the stability
conferred by such compound connections might extend
beyond connection strength to connection persistence,as suggested recently176,177. Compound synapses (involving two to six synapses) are commonly found amongconnected cortical neurons178, seem to occur more than
expected by chance179 and, given spine-​size distributions, are likely to be composed primarily of multiple
small spines. As might be expected, synapse remodellingwithin compound connections is partially correlated126
as are synaptic sizes within such connections126,179–183.
Notably, new spines formed following task learning
are frequently added to existing connections between
neurons136,149,184,185.
The advantage of multiple synapses might also
apply for synapses from different presynaptic neurons whose activities are correlated177. Along this line,
recent studies186,187 reported the enrichment of synapses
receiving inputs from co-​active neurons, and the functional predominance of synapse multitude over synapse
strength, indicating that populations of co-​active synapses might be both very large and functionally important. Thus, N in the aforementioned description might
be huge as well. Indirect support may also be found in an
estimate of spine numbers affected by motor task learning, which are, as mentioned earlier, in the hundreds ofthousands in the motor cortex alone64.
Memory persistence through reliance on large spines.
Large spines, owing to their remoteness from the pruning boundary, are likely to be more persistent. Moreover,it has been speculated that such spines, the heavy tail ofspine-​size distributions, are particularly important for
network function188–190 (but see ref.187). For example, thestrongest 25% of connections are responsible for 75% ofcortical ocular dominance191. This idea faces two challenges, however. First, owing to the positive-​feedback
nature of Hebbian-​like synaptic plasticity, ongoing network activity would lead to runaway activity due to thesynaptic strengthening it entails and, consequently, to a
non-​physiological excess of large synapses192. Second, as
intrinsic dynamics scale with synaptic size, the largest
and most functionally important synapses would also be
expected to fluctuate the most. Both challenges might
be partially resolved by intrinsic dynamics, however.

Reviews
Box 3 | stochastic models of dendritic spines
assuming synaptic weight, w, fluctuates from w(t) tow(t + Δt), the fluctuation can be approximated by thenormal distribution with a mean (μ) and a standard
deviation (sD; σ) (see the figure, part a). the generalcase, in which the mean and sDs are functions of w
(rather than constants), gives rise to a stochastic
differential equation (sDe)227:aw(t + Δt)

w(t)

w
μ

dw = μ(w )dt + σ (w )dBt ,

σ

f(w)
(μm3)

μ(w)
(μm3 day–1)σ(w)(μm3 day–0.5)

Δw = μ(w)Δt + σ(w)ΔBt
where Bt is Brownian motion, μ(w)dt is the drift termand σ(w)dBt is the diffusion term. Note that both μ andGeometric OUP
KestenLognormal
σ depend on w (see the figure, parts b,c).
b
the dynamics of spines determine the stationary
0.3
weight distributions, f(w) (see the figure, part d). thisdependency was explored independently by three0.2
groups (colour coded in figure parts b–d): dark blue61,
light blue116,129 and red134. as can be seen in parts b,c ofthe figure, all studies point to the conclusions below.
0.1
First, the sD, σ(w), is approximately proportional to the
OUP
spine size, yielding a multiplicative noise term (σwdBt)
0.0(part b of the figure), which gives rise to skewed and
0.0
0.2
0.4
0.6
0.8
1.0
stationary weight distributions (part d of the figure).
c
By way of contrast, if this term is constant (as in anBlack–Scholes
0.10
Ornstein–Uhlenbeck process (OuP) in part b of the
figure), the stationary distribution is normal and not
0.05
skewed (not shown). second, the drift term, μ(w), has a
0.4
0.6
0.8
1.0
0.00
negative slope, crossing the w axis at FP (part c of the
0.2
figure), which would be a stable fixed point in the–0.05
absence of the diffusion term. Because of this drift term,–0.01
the peak of the distribution is shifted from 0 to theFPpositive weight of about 0.1 μm3, although not exactly at–0.15
FP. a very similar picture emerges when the dynamics
are modelled as a Kesten process, in which size changesd5
are given by a drift term (as in part c of the figure, light
blue line) with a stochastic slope and offset129 (also4described by an sDe as below)116. when the slope is3
negative, spine distributions are closer to lognormal(quasi-​lognormal) distributions than to power-​law
2
distributions (the latter having heavier tails; not shown),
1
and spine sizes are constrained to mostly below about
1 μm3 (part d of the figure). if the drift term instead
0
0.0
0.2
0.4
0.6
0.8
1.0
has a positive slope (part c of the figure, grey line), thew (μm3)Black–Scholes model (used for modelling stock prices
in financial markets, for example) emerges, predicting a
power-​law stationary distribution (not shown)227. all these distributions are heavy-​tailed; that is, they decay more slowly
than do exponential distributions. the three lines in parts b–d of the figure are based on theories from refs61,116,134. in partsb,c of the figure, the theories have been expressed in the standard sDe formalism shown below for comparison. theparameters of the equations have been modified to emphasize similarities of the resulting stationary distributions in part dof the figure. the relevant equations are shown below:
Geometric OuP (dark blue): dw = −(0.1w −0.02)dt +(0.2w +0.01)dBt .
Kesten (light blue): dw = −(0.06w −0.011)dt + 0.059w 2+0.0005 dBt .
Lognormal (red): dw = −(0.11w +0.08w log w )dt +0.29w dBt .

Brownian motion
Random movement of
microscopic particles
suspended in liquids resulting
from the effect of moleculesof the surrounding medium.

Ornstein–Uhlenbeck
process
A type of stochastic process
whose stationary distribution
is normal (Gaussian).

Black–Scholes model
The most popular stochastic
differential equation in financial
economics to estimate thechanging value of an option
over time.

Figure adapted with permission from ref.116, society for Neuroscience.

First, as explained earlier, intrinsic dynamics confine
synaptic size distributions, effectively normalizing themand preventing runaway plasticity116,140,141. Moreover,the normalization process can adjust these distributions
according to global features such as overall activity levels or neuromodulatory tone113,115,116,129,139. This normalization process is effective only if extrinsic and intrinsic
dynamics accumulate over time to a similar magnitude,irrespective of the kinetics of their elementary processes.
Second, under certain assumptions, combined intrinsic

and extrinsic dynamics can create a separation point
between large and small synapses that minimizes theirinterconversion141. In this model, this division is predicted
to manifest itself as a secondary peak in spine-​size distributions, particularly in semilogarithmic plots193 (Fig. 3f), as
supported by several studies of synapse ultrastructure182,194.
These findings hint that the brain might effectively use
two ‘representative’ spine sizes, echoing older suggestions
regarding binary synaptic states195 and the utility of binarysynapses in high-​performance ANNs196.
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Synapses and learning algorithms
The preceding sections indicate that intrinsic dynamics
effectively give rise to a ‘self-​managing’ memory system.
Synapses, however, are not merely memory elements
or tuneable parameters that change neural network
function: they also embody the ‘learning algorithms’
that drive the tuning, the processes that implement thebrain’s ability to learn from experience and handle newchallenges. Extrinsic dynamics, which can be described
as Hebbian learning, RL and three-​factor learning,
clearly constitute learning algorithms. Here we argue
that intrinsic dynamics also give rise to important ‘heuristic’ learning algorithms that might confer organisms
and possibly ANNs as well with significant adaptive
properties.

Gradient descent
An optimization algorithm
for finding a local minimumof a differentiable function.

Overfitting
The fitting that corresponds
too closely to a particular setof data, and may therefore failto fit additional data or predict
future observations reliably.

Search space
The space of all feasible
solutions, among which thedesired solution resides.

Bayesian network inference
Use of a Bayesian network to
estimate the probability thata hypothesis is true basedon evidence.

Initialization
The assignment of initialvalues to parameters, such as
synaptic weights in the context
of artificial neural networks.

Synaptic weight noise. The importance of synaptic weight‘noise’ in the context of ANN training is well established,
as explained below. ANNs are typically trained by minimizing a loss function that quantifies their performance.
Specifically, in each training step, a change is calculated
for each synapse such that in the next step the overallloss (effectively, the difference between the actual result
and the desired result) will be lessened and performance
will be increased. Consequently, with each step, synaptic
weights move ‘downhill’ along the loss function gradient. In the stochastic gradient descent method197, the loss
function is evaluated using a subset of training samples.
Consequently, synaptic weight changes do not strictly
follow the gradient (which would be computed using
all samples) but fluctuate according to the (randomly
chosen) subset. The fluctuations improve learning by
allowing synaptic weights to escape ‘saddles’ of the loss
function in which learning slows down owing to shallow
gradients198. The fluctuations also alleviate overfitting byregularizing networks (that is, imposing more-​generalsolutions by focusing on global features of the loss function)199. Moreover, multiplicative weight noise (typicalof intrinsic dynamics; Box 3 figure part b) might further
improve learning and generalization by narrowing thesynaptic weight search space200. Weight noise might also
provide a means to prepare for and cope with unforeseenchallenges. For example, spine-​size fluctuations might
be used to sample synaptic weights from the posterior
distribution (that is, the probability distribution of synaptic weights to reproduce observed sensory inputs) for
Bayesian network inference201. Intrinsic dynamics can be
combined with RL to obtain a distribution of changes insynaptic weights proportional to the expected reward202.
More generally, by driving random weight changes andrewiring, intrinsic dynamics might produce new solutions
where none existed before, giving rise to the elusive feature
known as ‘creativity’. Thus viewed, creativity may be considered an emergent feature of trial-​and-​error rewiring —a brain-​specific instantiation of the ubiquitous biologicalprinciple of diversification and selection115.
Continuous network initialization. Intrinsic dynamics
mediate the continuous production of small spines andstochastic resetting of their sizes. This continual introduction of randomly weighted synapses into ‘trained’
networks might be viewed as a form of continual

Nature Reviews | Neuroscience
0123456789();:initialization. In this regard, biological networks differ

greatly from ANNs, which are initialized once and thentrained. This interleaving of initialization and training in
the brain might be viewed as a necessary adaptation toa non-​stationary world. How this might be done selectively, without impairing previously acquired knowledge
or causing catastrophic forgetting203 is currently an open
question (for example, see refs204,205).
Pruning and rewiring. Densely connected ANNs, firstinitialized and then trained, were recently shown tocontain sparsely connected subnetworks comprisingless than 10% of the original numbers of connections,referred to as ‘winning ticket’ (WTk) networks. These
WTk subnetworks can be trained faster, perform andgeneralize better and are more robust to noise than theirparent networks81,206,207. The biological principles of synaptic generation and rewiring can also be used in discovering such WTk networks206,207. WTk networks might
be represented in biological networks that show spine
formation within overlapping ‘capture volumes’ (seeearlier)154,155 during development, as well as spreadingof spine shrinking (also described earlier) — processes
that might find their way into AI as well.
Notably, human brains harness 100 trillion spines,
a number generally maintained by balanced spine genesis
and pruning. By contrast, contemporary AI networks
contain up to 175 billion connections 4 and alreadyrequire efforts to radically reduce these numbers to lessthan 10%81,206,207. As hardware limitations for AI are mitigated in the future, ANNs will also scale up and may
adapt sparse information coding using spikes as in thebrain208,209 for energy efficiency. In such large and distributed networks, pruning can be of central importance.
Consequently, using pruning and rewiring for discovering suitable sparse subnetworks within combinatoriallyhuge possibilities will become of paramount importance,as they seem to be in the brain.

Conclusions
Evidently, dendritic spine dynamics are not merely
passive manifestations of memory embedding processes: they are complex biological processes that giverise to implicit algorithms at cellular and system levels.
Impairments in these processes can result in psychiatric symptoms, such as psychosis, impaired learning andpossibly complex syndromes such as autism spectrum
disorder. Synaptic dynamics — such as non-​local pruning, regulation by inhibitory neurons, dichotomous andmultivariate RL, management of memory systems
and heuristic algorithms — might also inspire newmachine learning algorithms. Our understanding ofthese dynamics and the algorithms they might giverise to is still primordial and crude, and obtaining a
principled understanding is a challenge for the years
ahead. Hopefully, such understanding will provide
insights into our deep adaptability and creativity, enable future neuro-​inspired AI that is more flexible andadaptable, and lay down the necessary groundwork forunderstanding mental disorders in physiological terms.
Published online xx xx xxxx

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Acknowledgements
The authors thank D. Soudry, N. Brenner, R. Meir, O. Barak,Y. Loewenstein, S. Rumpel, S. Ishii and S. Koike for helpful
discussions. This work was supported by Grants-​in-​A id(20H05685 and 26221001 to H.K., JP18H05432 toT.T. and 19K16249, 16H06395, 16H06396 461 and
16K21720 to S.Y.) from the Japan Society for the Promotionof Science; the World Premier International Research Center
Initiative from the Japan Ministry of Education, Culture,
Sports, Science and Technology (MEXT); Core Research for
Evolutional Science and Technology (JPMJCR1652 to H.K.)
from the Japan Science and Technology Agency; the Strategic
Research Program for Brain Sciences (JP20dm0107120 toH.K.); Brain Mapping by Integrated Neurotechnologies for
Disease Studies (Brain/MINDS) (21dm0207069h0001 to
S.Y. and JP21dm0207001 to TT) from the Japan Agency for
Medical Research and Development; and the Israel Science
Foundation (1470/18) and the State of Lower-​Saxony and theVolkswagen Foundation (N.E.Z).

Author contributions
All authors researched data for the article, contributed substantially to discussions concerning its contents and reviewed
and/or edited the manuscript before submission. H.K.,
N.E.Z. and T.T. wrote the article.

Competing interests
The authors declare no competing interests.

Peer review information
Nature Reviews Neuroscience thanks A. Kirkwood and theother, anonymous, reviewer(s) for their contribution to
the peer review of this work.

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