HTT gene encoding the huntingtin protein (Htt). Mutated Htt (mHtt) easily aggregates, thereby inducing ER stress that in turn leads to neuronal injury and apoptosis. Therefore, both the inhibition of mHtt aggregate formation and the acceleration of mHtt degradation represent attractive strategies to delay HD progression, and even for HD treatment. Here, we describe the mechanism underlying mHtt degradation by the ubiquitin–proteasome system (UPS), which has been shown to play a more important role than the autophagy–lysosomal pathway. In particular, we focus on E3 ligase proteins involved in the UPS and detail their structure–function relationships. In this framework, we discuss the possible exploitation of PROteolysis TArgeting Chimeras (PROTACs) for HD therapy. PROTACs are heterobifunctional small molecules that comprise two different ligands joined by an appropriate linker; one of the ligands is specific for a selected E3 ubiquitin ligase, the other ligand is able to recruit a target protein of interest, in this case mHtt. As a consequence of PROTAC binding, mHtt and the E3 ubiquitin ligase can be brought to a relative position that allows mHtt to be ubiquitinated and, ultimately, allows a reduction in the amount of mHtt in the cell.Huntington Disease (HD) is a dominant, lethal neurodegenerative disorder caused by the abnormal expansion (>35 copies) of a CAG triplet located in exon 1 of the  Huntington disease (HD) is an autosomal, dominant, lethal neurodegenerative disorder affecting between 0.42 and 17.2 per 100,000 individuals around the world  HD resulHTT gene, which encodes for the huntingtin (Htt) protein. The HTT gene contains a repeat of 6–35 CAG triplets in exon 1, which is translated into a polyglutamine (polyQ) stretch in the Htt N-terminal region. The HD patients’ gene contains ≥36 CAG triplets, encoding for a mutated Htt (mHtt) with an expanded polyQ region [Primary symptoms generally occur in adults  and gradually progress, leading to the deterioration of patients’ health, and finally death, after 10–20 years. Although several clinical trials are ongoing, there is no cure for HD at present. HD is caused by a mutation in the Q region . mHtt isQ region ,9.CAG stretches that are longer than 60 repeats in the Htt gene are associated with Juvenile-onset Huntington Disease (JoHD). This is a rare HD variant that accounts for about 4–10% of all cases, typically defined based on the appearance of symptoms at age 20 years or younger .Since both soluble and aggregated mHtt are well known to induce ER (Endoplasmic Reticulum) stress, leading to neuronal injury and apoptosis , both thHere, we describe the mechanism of mHtt ubiquitination, with particular emphasis on the structure–function relationships in E3 ligases involved in the process. Finally, we discuss how knowledge of these relationships can be exploited to develop PROteolysis TArgeting Chimeras (PROTACs), which may be used to develop innovative drugs able to increase mHtt clearance in HD patients.The UPS comprises ubiquitin (Ub), proteasome, and three classes of enzymes, and plays key roles in various essential biological processes, such as cell cycle progression, signal transduction, maintenance of genome integrity, and tumorigenesis .UPS activity consists of two main processes: (1) covalent attachment of multiple Ub molecules to the target protein; and (2) degradation of the resulting covalent target protein–Ub complex by the 26S proteasome complex . The firOnce monoubiquitination has occurred, the Ub moiety can be ubiquitinated again at one of the seven lysine sidechains  or at the free main-chain amine group of the N-terminal methionine residue (M1) , thus exPolyubiquitin linkages are classified as: (i) homotypic, if Ub molecules are bound to a single lysine position of the substrate; (ii) heterotypic, in case Ub molecules are bound at different lysine positions of the substrate; (iii) branched, when ubiquitination takes place at two or more sites on a single Ub molecule . Ub exerMonoubiquitination contributes to several processes, including DNA repair, control of transcription, metabolism, and apoptosis .The role of homotypic chains depends on the position of the lysine residue involved in the linkage. K48 Ub, wherein a Ub chain is covalently bonded to the ε-amino group of the lysine at position 48 of the preceding Ub molecule, is the most abundant linkage type in homotypic polyubiquitin chains and represents the canonical signal for proteasomal degradation . K11 Ub The heterotypic, branched K48 and K11 are associated with proteasomal degradation of several cell-cycle regulators, including cyclin B1 and securin, thereby promoting mitotic exit.Currently, the functions of other Ub linkages are beginning to emerge.There are only two human E1s , with a total estimated number of over 600 E3 ligase genes, representing ~3% of the human genome [E3  in complex with UBCH7 E2 illustrates several notable features of the RING domain [The RING-type E3 ligases contain a ZnG domain . In partThe cullin RING ligase (CRL) superfamily comprises multi-subunit RING domain-containing proteins. One of the members of this superfamily is the SCF complex, consisting of S-phase kinase associated protein 1 (SKP1), cullin and F-box protein, and the anaphase promoting complex/cyclosome (APC/C) .The U-box-type E3 ligases contain a domain of 70 amino acids that is conserved in proteins from yeast to humans and has been identified in yeast for the first time (Ufd2). Ufd2, the prototype U-box protein, is a Ub chain assembly factor (E4) that cooperates with one E1, one E2, and one E3 enzyme to catalyze the conjugation of a Ub chain to substrates. Mammalian U-box proteins, in conjunction with E1 and E2, are also able to polyubiquitylate proteins, facilitating the transfer of Ub from E2 to the target in the absence of HECT-type or RING-type E3 ligases. For this reason, they can be considered to be a third family of E3s .Deubiquitinating enzymes (DUBs) remove Ub molecules thanks to their Ub C-terminal hydrolytic activity. The human genome encodes ∼100 DUBs, which are divided into six families: Ub-specific proteases (USPs); Ub C-terminal hydrolases (UCHs); ovarian tumor proteases (OTUs); Machado–Joseph domain-containing proteases (MJDs); JAB1/MPN/MOV34 family (JAMMs); and motif interacting with Ub-containing novel DUB (MINDY) family. All enzymes belonging to these families, with the exception of the JAMM zinc metalloproteases, are cysteine proteases .The 26S proteasome is the major proteolytic machine in eukaryotic cells. It is responsible for protein degradation in both cytosol and nucleus. It degrades target proteins that have been covalently modified by ubiquitination. Ub molecules attached to lysine side chains are removed at the proteasome prior to substrate degradation . The proThe high selectivity and control of protein degradation are guaranteed by the specific Ub labelling of protein substrates and by the architecture of the 26S proteasome holoenzyme. The proteasome is formed by a barrel-shaped 20S core particle, which contains the proteolytic active sites, and a 19S regulatory particle, which caps one or both ends of the core particle. Ubiquitinated substrates are recognized by Ub receptors RPN1, RPN10, and RPN13. To access the proteolytic sites, protein substrates have to penetrate narrow axial pores, which cannot be reached by folded or even largely unfolded polypeptides. The regulatory particle controls the opening of pores and favors substrate translocation into the degradation chamber. Substrate globular domains are mechanically unfolded by a ring-like heterohexameric adenosine triphosphatase (ATPase) motor. This consists of six distinct subunits (RPT1–RPT6) from the ‘ATPases associated with diverse cellular activities’ (AAA+) family and regulates the engagement, the RPN11-catalysed deubiquitination, and the degradation of substrates in an ATP-dependent manner through a mechanism that is still partially unknown ,46.In HD patients, the polyQ region located after the first seventeen N-terminal Htt residues is expanded beyond a threshold of 36 glutamine residues (mHtt) .A distinctive feature of HD is the progressive death of striatal projection neurons (SPNs), which are GABAergic output neurons representing >90% of striatal cells. SPNs are divided into two groups, depending on whether they belong to the direct (DP) or indirect (IP) pathway . Both SPN sub-types receive extensive glutamatergic inputs from cortex and thalamus, and dopaminergic inputs from the ventral tegmental area and substantia nigra pars compacta .Within neurons, mHtt molecules form toxic aggregates with a rate proportional to the length of the polyQ expansion. mHtt co-aggregates with a number of different proteins, which decreases their concentration in the cell. Several studies demonstrate that polyQ expansion in mHtt results in a toxic gain-of-function phenotype. Other studies, which include gene knockouts and knockdowns, demonstrate that polyQ expansion in mHtt can also have loss-of-function effects. The role of wild-type Htt should therefore be taken into account in the development of a potential therapy, as well as that of mHtt .The structure of Htt in complex with HAP40 has been recently solved by cryo-EM at 4 Å resolution . ConversThe cryo-EM structure revealed that Htt is formed by three domains: N-terminal domain and C-terminal domain, both of which contain multiple HEAT repeats, joined to a bridge domain .The N-terminal domain  forms a typical α-solenoid, comprising 21 HEAT repeats arranged as a one-and-a-half turn, right-handed superhelix. The N-HEAT was predicted to contain two membrane binding regions: the 1–17 N-terminal tail (not visible in the structure), which was predicted to form an amphipathic helix , and a lThe C-HEAT (a.a. 2092–3098) comprises 12 HEAT repeats that form an elliptical ring of ~80 × 30 Å.The N-HEAT and C-HEAT are joined by the bridge domain. This contains six tandem α-helical repeats, of which repeats three, four and six are Armadillo-like. The repeat region is flanked by five non-repeat helices and a flexible C-terminus (a.a. 2062–2092), which is unresolved.The lack of interactions between the N-HEAT and C-HEAT domains explains the flexibility of the Htt structure in the absence of interactors. HAP40 binds to a large cleft between these two domains. Within the complex, Htt and HAP40 share large interfaces that comprise mostly hydrophobic interactions. Interestingly, bioinformatic analyses has provided evidence of the evolutionary conservation of these interfaces in all Htt-encoding animal species .Recently, the structure of wild-type Htt in complex with HAP40 has been compared with other mHtt–HAP40 complexes differing in the length of the polyQ repeat, namely, 46QHtt–HAP40  and 128QHtt–HAP40 (128 being an extremely high polyQ length). Quite surprisingly, both crosslinking mass spectrometry and cryo-EM experiments revealed no major structural differences among the different complexes, indicating that the polyQ insertion does not alter the Htt fold .Htt function has not yet been fully elucidated, but Htt has been proposed to be involved in cellular processes such as mitotic spindle orientation, autophagy, and vesicle transport ,53,54,55Htt is crucial for energetic metabolism not only in the brain  but alsoRecent studies carried out using mouse embryonic stem cell demonstrated that Htt is necessary for mitochondrial structure and function from the earliest stages of embryogenesis, providing a molecular explanation for the early embryonic lethality of Htt knockdown .SPN death in HD has mostly been ascribed to toxic ‘gain-of-function’ by mHtt. However, evidence of Htt ‘loss-of-function’ contribution is also available. Indeed, wild-type Htt has been shown to be neuroprotective and, therefore, able to shield neurons against mHtt toxicity . AdditioHtt is a protein with high ubiquitination potential. It contains 124 lysine residues, many of which are placed on the protein surface, as shown by cryo-EM structural analysis, and may in principle be ubiquitinated or linked to other Ub-like (Ubl) proteins, such as SUMO .Ubiquitination and/or SUMOylation has been demonstrated for the 30 Htt lysine residues reported in Ubiquitination has been linked to reduced mHtt toxicity, most likely due to increased mHtt clearance by the proteasome . ConversAs described above, the presence of seven lysine residues allows Ub to transmit different signals on target proteins. Therefore, Htt polyubiquitination can take place with different mechanisms, which have not yet been completely understood. Two among the 40 E2 enzymes present in the human genome have been demonstrated to interact with Htt: UBE2W, which is known to target the N-termini of disordered proteins such as Tau, RBPB8, and ATXN3, as well as mHtt ; and UBEA variety of E3 Ub ligases have been shown to act on polyQ-containing proteins such as mHtt, thereby determining a reduction in mHtt cellular levels, aggregation, and cellular toxicity. Some of these E3 Ub ligases are able to directly polyubiquitinate Htt via K48 of Htt-linked ubiquitin, allowing its clearance by the UPS. These include UBE3A/E6AP ,81, CHIPHD has been associated with global changes in the UPS, such as the accumulation of K48- K63- and K11-linked polyUb chains, and the inhibition of proteasome activity by mHtt has been proposed to contribute to neurotoxicity, although the molecular basis of this process is not clear. The autophagic pathway has been involved in Htt aggregate clearance, and autophagy upregulation has been shown to reduce polyQ expansion toxicity in HD mouse models .Only a few DUBs have been reported to deubiquitinate Htt. ATXN3, which contains a polyQ region itself, and USP19 are the only DUBs known to target Htt besides proteasome-associated DUBs ,91.UBE2K, also known as the Ub-conjugating enzyme E2-25K, was reported to be expressed in all areas of the brain, with higher levels in the striatum and frontal cortex, which are among the most affected areas in HD patients . UBE2K iUBE2W (Ub-conjugating enzyme 2W) is the only E2 enzyme known to be involved in the ubiquitination of substrates at their N-termini, likely preferring substrates with disordered N-termini such as mHtt. This conjugating enzyme can function with various Ub ligases, including the C-terminus of Hsc-70-interacting protein (CHIP) .In cells, mHtt exists in at least three distinct states: soluble monomers; soluble oligomers; and insoluble aggregates. Soluble oligomers have been demonstrated to be more toxic than monomers and insoluble aggregates .In studies conducted on immortalized cells, primary neurons, and a HD knock-in mouse model, UBE2W deficiency resulted in a reduced formation of mHtt oligomers and an increased formation of soluble mHtt monomers and neuron survival. The reason for this behavior is still unknown, but the most accredited hypothesis is that mHtt ubiquitination increases protein aggregation and/or impedes other post-translational modifications such as SUMOylation, which takes place on the same mHtt lysine residues as ubiquitination .UBE3A, also known as E6AP, is a HECT-type E3 ligase. The crystal structure of UBE3A catalytic HECT domain was solved both in the apo form  and in complex with the UBCH7 conjugating enzyme fragment comprising residues 495 to 852  A. The HEUBE3A plays a critical role in Htt ubiquitination. This role is modulated by UBE3A levels of expression, which decreases with age. UBE3A associates with mHtt in the striatum of a HD knock-in mouse model. Co-immunoprecipitation assays in HEK293 cells transfected with several N-terminal Htt fragments showed that UBE3A binds higher amounts of mHtt than wild-type Htt, and, in particular, it binds the shortest mHtt fragment N67-150Q . UBE3A expression levels decrease with aging and may be further downregulated by the presence of mHtt. As a result, the decrease in UBE3A expression levels occurring in the aged HD knock-in mouse model causes an impairment of the mHtt degradation process that takes place via K48 ubiquitination. Conversely, K63-ubiquitinated mHtt and mHtt fragment levels increase and lead to the formation of aggregates that give rise to the K63 immunoreactive signal in the striatum. On the other hand, when HEK293 cells transfected with N-terminal mHtt fragments  are transfected with UBE3A as well, the level of these short mHtt fragments decreases, indicating that they are degraded via UPS .All together, these data indicate that UBE3A increases the levels of mHtt and mHtt fragment ubiquitinated via K48 and degraded via UPS; with aging, UBE3A levels in the cell decrease and, as a consequence, the aggregates of mHtt increase.The C-terminus of Hsc70-interacting protein (CHIP) is a U-box E3 ligase whose N-terminal tetratricopeptide repeat (TPR) regions bind HSP70, HSC70, and HSP90 chaperones and potentially target any chaperone-bound protein for degradation . CHIP isHrd1 is an endoplasmic reticulum (ER), membrane-spanning, RING finger, E3 ubiquitin ligase whose catalytic domain faces the cytosol and can ubiquitinate misfolded proteins therein. Hrd1 levels were found to be increased in cells overexpressing the 588-residue N-terminal fragment of Htt containing an expanded (138 residues) polyQ region (HttN). HttN was stabilized by Hrd1 expression silencing by RNA interference, whereas Hrd1 forced expression enhanced the degradation of HttN. Hrd1 was demonstrated to interact with and ubiquitinate HttN, recruit HttN to the ER, and co-localize with juxtanuclear aggregates of HttN in cells. Hrd1 interacts with HttN fragments comprising polyQ region of different length, with a preference for longer polyQ regions, and targets pathogenic HttN for degradation and protects cells against HttN-induced cell death .Parkin (PK) is a RING-between-RING E3 ligase that possesses both a canonical RING domain and a catalytic cysteine that is characteristic of HECT E3 ligases. For this reason, it is also termed as a ‘RING/HECT hybrid’ .PK promotes proteasomal degradation of abnormal proteins. The effect of partial PK suppression on HD phenotype was investigated by studying the behavior and brain histology and biochemistry of wild-type, R6/1 (mice with mHtt containing about 115 CAG repeats), R6/1/PK+/−, and PK+/− mice. PK partial suppression did not cause additional neural loss either in striatal regions or other parts of the brain, indicating that the lower expression of PK is partially compensated by other protection mechanisms. However, R6/1/PK+/− mice have a higher level of apoptotic cells in hippocampus and striatum with respect to the R6/1 mouse, as well as a higher Bax/Bcl2 ratio. This increment in apoptotic cells results in an exacerbation of motor and behavioral deficits in R6/1 mouse models .The Skp, Cullin, F-box-containing (SCF) complex is an E3 Ub ligase . The X-rHECT domain- and ankyrin repeat-containing E3 Ub protein ligase 1 (HACE1), known to play a protective role against stress-induced tumorigenesis in mice, also play a role in antioxidative stress response and, as a consequence, in neurodegeneration.HACE1 KO mice exhibit increased oxidative stress in the brain and a reduced expression of NQO1, a marker of antioxidative stress response, and of the NRF2 (nuclear factor-erythroid 2-related factor 2) transcription factor. Thus, the consequences of HACE1 deficiency are similar to those measured in the absence of NRF2, indicating that HACE1 positively regulates the NRF2-mediated antioxidative stress response and has a fundamental role in maintaining redox homeostasis in brain tissue. In particular, HACE1 levels are decreased in mHtt-expressing STHdhQ111 cells, which correlates with the diminished activity of NRF2 and the increased oxidative stress. On the other hand, ectopic HACE1 expression in STHdhQ111 cells increases NRF2 activity, thereby providing protection against mHtt-induced redox imbalance and hypersensitivity to oxidative stress. Increasing HACE1 expression may therefore represent a strategy to counteract the consequences of HD and, possibly, other neurodegenerative diseases on redox metabolism .NEDD4-like E3 Ub protein ligase  is a 922-residue HECT E3 ligase that promotes the ubiquitination and internalization of various plasma membrane channels, such as ENaC, SCN2A/Nav1.2, SCN3A/Nav1.3, SCN5A/Nav1.5, SCN9A/Nav1.7, SCN10A/Nav1.8, KCNA3/Kv1.3, KCNH2, EAAT1, KCNQ2/Kv7.2, KCNQ3/Kv7.3, or CLC5 ,101. TheTumor Necrosis Factor Receptor-Associated Factor 6 (TRAF6) is a 522 residue protein structurally belonging to the RING-type E3 ligase family. It has an important role in the receptor-mediated activation of various signaling pathways in response to cytokines and bacterial products. TRAF6 also possesses E3 Ub ligase activity that results in Lys-63-linked polyubiquitination of target proteins ,103.Among these, TRAF6 mediates the polyubiquitination of proteins involved in immune signal activation via K63, such as inhibitor of nuclear factor kappa-B kinase subunit gamma (IKBKG), interleukin-1 receptor-associated kinase 1 (IRAK1), AKT1, and AKT2, thereby modulating the immune and inflammation responses . TRAF6 wProteolysis targeting chimeras (PROTACs) are heterobifunctional small molecules composed of two active moieties joined to each other via an appropriate linker; one of the moieties binds a target protein of interest (POI), the other binds an E3 Ub ligase . PROTACspVHL is a subunit of the E3 Ub ligase CUL2–RBX1–ElonginB–ElonginC–VHL (CRL2VHL) complex. pVHL is responsible for the recognition and binding of hypoxia-inducible factor-1α (HIF1-α factor), which controls a series of biological processes, such as ROS production, angiogenesis, and cancer metastasis. Upon pVHL binding, the HIF1-α factor is ubiquitinated for proteasomal degradation. The crystal structure of the pVHL–ElonginB–ElonginC complex, bound to the C-terminal oxygen-dependent degradation (CODD) motif of HIF1α, has allowed the pVHL structural features required to bind a specific hydroxyl proline residue present on CODD to be identified ,110,111.Cereblon (CRBN) forms an E3 Ub ligase complex with damaged DNA binding protein 1 (DDB1), Cullin-4A (CUL4A), and Regulator of Cullins 1 (ROC1) . CRBN isIAP family members are characterized by the presence of three baculovirus IAP repeat (BIR) domains at the N-termini, and they act as apoptosis inhibitors. Some of these proteins, such as cellular inhibitor of apoptosis-1 (cIAP1) and X-linked inhibitor of apoptosis protein (XIAP), contain a RING domain and are able to function as E3 ligases. It was reported that methyl bestatin binds to the BIR3 domain of cIAP1, thereby inducing self-ubiquitination and degradation. PROTACs made of bestatin, all-trans retinoic acid (ATRA), and a polyethylene glycol (PEG) linker were found to successfully induce the degradation of cellular retinoic acid binding protein-2 (CRABP2) and have been called SNIPERs (Specific and Nongenetic Inhibitor of Apoptosis Protein (IAP)-Dependent Protein Erasers) ,120. OneOther recent works have expanded the toolbox for PROTACs, such as the Kelch-like ECH-associated protein-1 (KEAP1), which is able to form a complex with Cullin-3 (CUL3) E3 ligase, to bind and induce the ubiquitination and degradation of Nrf2 . Both peAnother protein which acts as an atypical substrate-specific component of CUL4B-based E3 complex is the arylhydrocarbon receptor (AhR) transcription factor. Ohhoka and coworkers synthesized PROTACs able to bind AhR, thereby inducing the AhR-dependent degradation of CRABP-1 and CRABP-2 via the ubiquitin–proteasome pathway . Other gThe discovery of novel PROTAC protein degraders is one of the most promising approaches for neurologic diseases, which have been historically difficult to treat. This is partly due to the difficulty of crossing the blood–brain barrier and delivering therapeutic molecules to the brain, and to the fact that many of the targets within the central nervous system (CNS) are considered to be ‘undruggable’. Arvinas and other companies are developing PROTAC protein degraders as potential therapeutics for neurodegenerative diseases.PROTACs have important advantages with respect to other therapies, including: the ability to cross the blood–brain barrier (BBB), which is a substantial challenge for monoclonal antibodies and genomic therapies; the ability to enter cells of the CNS, which may allow pathogenic proteins to be degraded inside the cell; iterative  activity by which a single PROTAC molecule can induce the degradation of hundreds of copies of disease-causing proteins; potential for oral dosing unlike other therapies that may require intrathecal or intravenous (IV) administration.One of the ideas that has been explored for HD therapy consists of the elimination of mHtt through the UPS by increasing mHtt polyubiquitination via K48 . For thiThe use of molecules that interact with both mHtt and the proteins of the autophagy-lysosomal pathway (which is outside of the scope of the present review but is worth mentioning in this context) is another possible strategy for degrading mHtt. Compounds interacting with both polyQ stretches and the autophagosome protein microtubule-associated protein 1A/1B light chain 3 (LC3) have been discovered by high-throughput screening (HTS). Four of these compounds, i.e., AN1, AN2, 10O5, and 8F20, were found to be able to lower the level of both mHtt and ataxin-3 by targeting them to the autophagosomes .The polyubiquitination of proteins is a pathway that controls protein expression and degradation. Polyubiquitination involves the side chains of the seven Ub lysine residues and the free main-chain of the N-terminal methionine residue and can be either homotypic or heterotypic. The specific type of polyubiquitination determines the fate of the target protein.Monoubiquitinated mHtt can be polyubiquitinated via either K48 or one of the other Ub lysine residues . The polyubiquitination of mHtt and its fragments via K48 ensures their clearance through the proteasome complex, whereas polyubiquitination via K63 promotes aggregate formation.Several E3 ligases that are involved in the polyubiquitination of Htt and Htt fragments via K48, promoting their degradation via proteosome, have been identified and described in this review . In particular, UBE3A expression decreases with age in both healthy mice and the R6/2 mouse model, and the diminished expression of UBE3A in neurons is strongly related to aging and to the worsening of the HD phenotype.Conversely, WWP1 and TRAF6 E3 ligases, which polyubiquitinate mHtt via K63 of mHtt-linked ubiquitin, are overexpressed in R6/2 mice. As a consequence, the UPS system becomes highly unbalanced upon aging, with uncontrolled increase in polyubiquitinated mHtt, which remains free in the cells .All current strategies to cure HD by decreasing mHtt concentration are based on antisense oligonucleotides (ASOs), which target mRNA of both mHtt and Htt, or mHtt alone, in cells. Different ASO-based drugs have entered clinical trials, and some of them have already failed in phase III  or in phase II clinical trials . The reasons underlying these failures have not yet been disclosed. However, all these therapies require drug delivery by lumbar punctures to be administered at least every two months.www.rcsb.org).Due to their effectiveness and the relative facility and velocity of implementation, strategies aimed at modulating mHtt metabolism by selectively enhancing mHtt ubiquitination by PROTACs appear to be advantageous for HD therapy. Among the targets that can be exploited to design lead compounds aimed at decreasing soluble mHtt concentration, UBE3A appears to be particularly promising because it is the E3 ligase that normally polyubiquitinates Htt via K48 and has a key role in the control of mHtt concentration in the cell. The development of PROTACs targeting both UBE3A and mHtt is particularly attractive due to the possibility to rationally design effective ligands of both proteins based on the three-dimensional structures of UBE3A catalytic domain and wild-type Htt available from the Protein Data Bank (


During development, biological neural networks produce more synapses and neurons than needed. Many of these synapses and neurons are later removed in a process known as neural pruning. Why networks should initially be over-populated, and the processes that determine which synapses and neurons are ultimately pruned, remains unclear. We study the mechanisms and significance of neural pruning in model neural networks. In a deep Boltzmann machine model of sensory encoding, we find that (1) synaptic pruning is necessary to learn efficient network architectures that retain computationally-relevant connections, (2) pruning by synaptic weight alone does not optimize network size and (3) pruning based on a locally-available measure of importance based on Fisher information allows the network to identify structurally important vs. unimportant connections and neurons. This locally-available measure of importance has a biological interpretation in terms of the correlations between presynaptic and postsynaptic neurons, and implies an efficient activity-driven pruning rule. Overall, we show how local activity-dependent synaptic pruning can solve the global problem of optimizing a network architecture. We relate these findings to biology as follows: (I) Synaptic over-production is necessary for activity-dependent connectivity optimization. (II) In networks that have more neurons than needed, cells compete for activity, and only the most important and selective neurons are retained. (III) Cells may also be pruned due to a loss of synapses on their axons. This occurs when the information they convey is not relevant to the target population. Biological neural networks need to be efficient and compact, as synapses and neurons require space to store and energy to operate and maintain. This favors an optimized network topology that minimizes redundant neurons and connections. Large numbers of extra neurons and synapses are produced during development, and later removed as the brain matures. A key question to understand this process is how neurons determine which synapses are important. We used statistical models of neural networks to simulate developmental pruning. We show that neurons in such networks can use locally available information to measure the importance of their synapses in a biologically plausible way. We demonstrate that this pruning rule, which is motivated by information theoretic considerations, retains network topologies that can efficiently encode sensory inputs. In contrast, pruning at random, or based on synaptic weights alone, was less able to identify redundant neurons. The number of neurons and synapses initially formed during brain development far exceeds those in the mature brain . Up to hWhat characterizes the cells and synapses that survive as opposed to the ones that die? A key factor for survival is neuronal activity. Initially, spontaneous activity is thought to drive survival. The refinement of cortical circuits then relies increasingly on sensory-driven and thus experience-dependent neuronal activity . NeuronsHere, we explore several local and biologically plausible rules for iteratively pruning unimportant synapses and units from artificial neural network models. Many models of neural pruning simply remove small synaptic weights –22. HoweInformation-theoretic approaches to network reduction provide a principled starting point. For example, the Optimal Brain Surgeon algorithm  estimateEstimates of parameter importance based on Fisher Information (FI) have recently been used to overcome catastrophic forgetting in artificial neural networks . In contSimilar to neuronal sensory systems, RBMs extract and encode the latent statistical causes of their inputs. They consist of two layers of stochastic binary units, resembling the spiking of neurons. The visible units correspond to sensory input, while the hidden units encode a latent representation of this data. By adjusting their hidden representations to maximize the likelihood of the data , RBMs leWe organize the results as follows: we first introduce our estimates of synaptic importance based on locally-available activity statistics. We then discuss the overall network curvature and demonstrate that important synapses center on overall highly informative neurons. Based on these observations, we introduce local pruning rules to iteratively remove synapses and neurons from RBMs and DBMs that were trained on image patches from two different data sets. We evaluate the fit of the pruned models across different pruning criteria by assessing their generative and encoding performance. Finally, we discuss the biological plausibility of our activity-dependent pruning rules by comparing them to alternative rules used in our own and related work and provide implications of our findings.vi stands for visible unit i, hj stands for hidden unit j and wij for the bidirectional weight connecting them. Lower energy corresponds to higher probability of the respective model state. We work with Bernoulli RBMs, and all neurons are binary: vi and hj are either firing (1) or silent (0). The biases ϕ = {W, bv, bh}.The goal of this work is to derive and use a local pruning rule to reduce network size and identify a relevant network topology in restricted and deep Boltzmann machines. By ‘relevant network topology’ we mean a topology optimized for computational needs that includes only neurons and synapses that are relevant for the task at hand. In our experiments this task is the encoding of visual stimuli in hidden representations of RBMs and DBMs. RBMs are energy-based models whose energy function is given by:Pv,h is the probability of jointly observing visible pattern v and hidden state h. The FIM locally approximates the Kullback-Leibler divergence between the model distribution under the current parameter set ϕ, and the model distribution when a pair of parameters ϕi and ϕj is slightly perturbed.The Hessian of the objective function of a model gives information about the importance of parameters, and can be used for pruning , 25. It Pv,h. In the case of the RBM, the Fisher information for two weights wij and wkl takes the form:wij = wkl). It captures the effect on the error when we modify a single weight. For the FI of the weights, A crucial advantage of the FIM is that its values are closely connected to the distribution of activity and can be estimated by sampling from the distribution In a first line of experiments, we inspected the curvature of the energy landscape of overcomplete models that had more latent units than needed to encode the visible stimuli. We started by fitting overcomplete RBMs to circular, binarized patches of images of natural scenes see  using th0) is larger than the second largest eigenvalue by an order of magnitude . This low-rank structure implies that the FIM can be approximated by a rank-1 outer product of its leading eigenvector, u. This, in turn, implies that the diagonal entries  were associated with specific units see . This suOverall, these empirical investigations reveal that there are only few important units, and that important weights align with them. This confirms that parameter importance as revealed by the FIM contains meaningful information for pruning, and predicts that synaptic pruning will eventually lead to the removal of whole neurons that lack relevant afferent or efferent connections.We now present our results of applying the local estimate of Fisher information as a criterion to prune RBMs. We compare this estimate to removing poorly specified, unimportant weights according to different pruning criteria and random pruning. We also test a pruning criterion based on the full FIM to confirm that the diagonal approximation closely tracks importance. For this, we assess importance as the magnitude assigned to each weight in the leading eigenvector of the FIM.vihj〉. We refer to this as the “variance” estimate of the FIM diagonal. However, neurons need not track this coincident firing explicitly. Activity-driven correlations influence synaptic weights and vice versa. As a result, the statistical quantities relevant to pruning are tied to the synaptic weights themselves. This opens up a broader range of possible biological implementations of the rules we explore here. It also highlights that apparent correlations between synaptic weights and pruning in vivo could arise from a FI-based pruning strategy. In Materials and Methods: Heuristic estimate of Fisher Information we derive a mean-field approximation of the pre-post correlations that depends only on the synaptic weight and the average firing rates of the presynaptic and postsynaptic neurons:nv = 13 visible units, nh = 70 hidden units, and nw = nv × nh = 910 weights. We then iteratively deleted half of the weights with lowest estimated importance, while monitoring model fit.For our synaptic pruning experiments, we ranked weights according to their importance assessed by one of the aforementioned local estimates, or by the first eigenvector of the FIM. The unpruned full model initially had We assessed the fit of a given model based on its generative performance, i.e. how well the generated patterns in the visible layer match the patterns available in the training data. Following the approach by Reichert et al. , we use most important weights (‘Anti-FI’ pruning) served as reference criteria for pruning. We also added a control case of neuron pruning: instead of pruning random connections, whole units were randomly taken out of the network. Unconnected hidden units were removed from the model. Absolute weight magnitude, random weight pruning, and removal of the Excessive pruning degraded generative performance. Regardless of the pruning criterion, the distributions of generated patterns vs. the training data generally diverged immediately after pruning . HoweverFor “random weight” and “Anti-FI” pruning, the distributions of generated patterns diverged from the training data and could only be partially rescued by retraining see . This isWe conjectured that the FI-based rules allowed local synaptic dynamics to identify and remove unimportant neurons. To confirm this, we ran a simulation which removed a random subset of neurons. This showed a large divergence between the distribution of training patterns and generated patterns immediately after pruning, but performance could be restored by re-training . This conh after each of the three pruning iterations, averaged across ten simulations. Although the number of remaining weights nw was matched across pruning criteria, different numbers of units were disconnected through repeated weight pruning. Fisher information typically concentrated on few hidden units , were completely removed. Thus, the total number of deleted weights may be larger than specified by the importance measure as a secondary effect. The removal of such “dead-end” units is also the reason for the high variability of the number of remaining weights for the Anti FI pruned models  was particularly harmful: classification performance deteriorated after the first pruning event, and eventually remained below chance even with retraining. This suggests that Anti-FI pruning causes a loss of topologically relevant neurons. The visualization of the pixels corresponding to the remaining units in the final visible layers h1 is less sparse from the beginning, as the receptive fields pre-structure the network and the number of hidden units in this layer equals the number of visible units (average activity in h1 in the first pruning iteration ranged between 0.37–0.43 as opposed to 0.0006–0.018 in h2). Initial activity in h2 is sparse and as a consequence FI pruning quickly identifies all units with low (covariant) activity: their weights are pruned and the unimportant units are removed from the model. This also allows a faster reduction of model size: to reach a comparable total number of weights, only six pruning iterations were necessary for our FI estimates, but ten iterations for the random weight and weight magnitude pruning.The encoding also remained useful for classification. When weights were pruned according to our heuristic estimate of Fisher information, the performance of the classifier only fell below baseline after the number of weights was reduced by more than one order of magnitude. Models pruned according to the variance FI estimate dipped in their performance after the third iteration of pruning. Arguably, the optimal model size was already reached after the first pruning iteration. We hypothesize that an increase of the average activation of hidden units may indicate the arrival at the optimal model size and thus be a signal to stop pruning . Such a topological optimization within multiple layers cannot be achieved by random unit removal. In this control case, where we pruned a comparable number of weights by randomly deleting hidden units, too many units were removed from h1 for the encoding to remain useful for classification.FI pruning topologically optimizes the model: more weights (and units) are removed in h2 see , while iRandom weight pruning and pruning by absolute weight magnitude failed to reduce the model size in terms of neuron number: Neither pruning criterion led to any of the hidden units becoming disconnected. In the visible layer, a maximum of one pixel became disconnected in each case see . PruningTaken together, these results show that the pruning criterion matters in deeper networks. The network performance can recover through retraining if activity-dependent pruning is used (FI and weight-magnitude pruning), but is permanently damaged by random or Anti-FI pruning. Furthermore, FI-pruning produces the most efficient network topology and selectively retains the most important neurons, unlike simpler strategies such as pruning by weight magnitude.Previous studies explored deep Boltzmann machines as a generative model of hallucinations, for example those seen in Charles Bonnet Syndrome . In thisEvaluation).Inspired by these results, we asked whether pruned networks retain a meaningful description of the latent structure in their inputs. We assessed this by measuring the generative performance of the networks over the course of pruning. To quantify generative performance, we asked a classifier trained on the raw digits to categorize samples and predict probabilities of them belonging to each digit class. These were summarized as digit-wise quality scores and diversity scores for the generated patterns  in these networks are not biologically plausible, they implement minimization of variational free energy as an unsupervised learning objective. This is a plausible first principle for learning in neural circuits, in particular in sensory systems where limited bandwidth requires efficient coding , 54. RecIn biology, pruning and learning occur simultaneously. To emulate this, we retrained networks for ten epochs after each batch of pruning. This batched form of sensory-driven plasticity allowed the networks to recover from a performance drop observed immediately after pruning. In biology, numerous types of homeostatic plasticity could compensate for the loss of cells and synapses without error-driven retraining . SynaptiModel networks can provide insight into neurological disorders. For example, Reichert et al.  use deepStatistical theories view hallucinations as errors in internal predictive models , 61. HalThis suggests a speculative connection to schizophrenia, for which hallucinations and altered cognition are core symptoms. Schizophrenia also involves pathological neural pruning , 11–13. Apart from neurological disorders, understanding pruning is important for understanding learning and cognitive flexibility. In all of our experiments, the sensory encoding task was fixed. Overzealous optimization to a fixed distribution could impair flexibility, a phenomenon that might relate to developmental critical periods and neurological disorders . In biolOverall, we have shown that local activity-dependent synaptic pruning can solve the global problem of optimizing a network architecture. In contrast to pruning rules based on synaptic weights, our information-based procedure readily identified redundant neurons and led to more efficient and compact networks. The pruning strategy we outline uses quantities locally available to each synapse, and is biologically plausible. The artificial neural networks explored here are abstract. If analogous processes operate in biology, then a similar pruning procedure could optimize metabolic cost by eliminating redundant neurons. An important future direction is to analyze these pruning rules in conjunction with synapse formation, which has been hypothesized to provide an additional mechanism for functional optimization of network topologies .We used two different datasets of visual image patches to train and evaluate our models. For Figs For Figs n binary units (neurons) that are organized in two layers: a visible layer v that directly corresponds to a given input vector and a hidden (or latent) layer h which contains an encoding of the input data. Each visible layer neuron vi has undirected weighted connections (synapses) to each hidden neuron hj and vice versa, but neurons within a layer are not connected to each other  by maximizing the first term in v, and minimizing the second term. From the restricted connectivity it follows that the probability of a unit being in the on-state is conditionally independent from the states of units of the same layer, given a configuration of the other layer:The training objective is to adjust the parameters patterns . Lowerinp(hj|v)), the model metaphorically dreams about p(vi|h) in the negative or sleep phase. Specifically, the visible layer is initialized to a random state and the layers are updated iteratively following alternating Gibbs sampling for k → ∞ times. The goal is for the final sample to originate from the equilibrium distribution of the model. k-step contrastive divergence , where p(vi) corresponds to the fraction of training instances where pixel i was in the on-state. No mini-batches were used, updates were applied after each training instance. RBMs were trained for 2 epochs, with a decaying learning rate from 0.1 to 0.01 and momentum of 0.9. Weights were not regularized to encourage a sloppy pattern in parameter sensitivities as is characteristic for biological networks  A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).Important additional instructions are given below your reviewer comments.Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.Sincerely,Blake A RichardsAssociate EditorPLOS Computational BiologyLyle GrahamDeputy EditorPLOS Computational Biology***********************Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: The paper investigates the pruning of connections with low Fisher Information in restricted and deep Boltzmann machines. This approach is compared with pruning based on a locally computable proxy of Fisher information, the maximum Fisher information, and the synaptic weight, as well as random pruning.As the most interesting property, the authors demonstrate that the low FI approach typically removes all connections to a hidden neuron, such that the synapse pruning can also implement neuron pruning. At the same time, the pruned networks retain high encoding/classification and generative performance. The methods the authors use to demonstrate their finding are sound and appropriate. However, I am missing error estimates or a validation by multiple trials.Moreover, although the topic of pruning is a very interesting and relevant topic both in biological and artificial neural networks, I think the findings and writing of the paper are more on the artificial intelligence than on the biological networks side , which should be changed to be suitable for publication in this journal.Major points:Errors:It seems as if all the results stem from single network instances and there are no error estimates reported. As the pruning and RBM training heavily depend on the initial network, I think it would be good to compare results over multiple initialization.Link to biology:The bidirectional weights and their training within RBMs are not exactly biological. Thus, it is unclear whether the advantage FI provides over weight-dependent pruning will still hold in biologically more realistic settings. Moreover, if the biological realistic implementation of an information based learning rule is in the focus, it should be highlighted and discussed better in the results instead of being hidden in the methods/appendix.Neuron removal:Throughout the paper, the authors often stress the fact that FI-based approaches prune connections such that whole neurons can be removed. I feel like there is a proper control missing for this to demonstrate the superiority of the FI approach. I would propose to introduce a pruning strategy which removes whole neurons (either randomly or by minimum sum of incoming weights). In that way, there would be a control case with similar neuron number to compare with.Minor points:all Figures: Colors of Random and weight-dependent pruning were not so well discernible for me.p.2 l.81: it should be b^h in the parameter-set instead of h^h. Also, I would move the sentence about the Bernoulli RBM after the description of the activities, which are the binary quantitiesp.3 l.87 I would move the discussion of diagonality after the example FI (Eqs.2/3), because i think these examples would make it easier to understand that non-local information is needed for the full FIp.3 l.95 I am not completely sure what is meant by redundant here. Is each parameter redundant for the network or are they redundant (covariant or so) w.r.t. each other? Pleas clarify.Fig 1C/D: the labels h and v were a bit confusing. Shouldn't it be b^v and b^h?Fig 2: It is hard to see a strong effect in the pattern distributions. Is there a way to make this clearer? Possibly show ratios?Also the demonstrated changes in distributions will strongly depend on the size of the model and initial overparametrizationp.7 l 210 The explanation on generative performance is a bit distracting here. I would suggest moving it to the respective section.p.7 l 223 The reason for calculating the percentile is unclear. Are these the pruned synapses? Please clarify! Also, making more clear that these are the 10% of the weights with the lowest FI, would make sense.p.7 l.227 The reading flow here was a bit unsteady. Possibly move the statement of the before-pruning accuracy to line 210, where they are introduced.p.7 l. 236 Isn't this a consequence of your FI-estimator being zero for many more units than the weight such that you remove more connections. I think the plot 3b is a fair way to compare the pruning strategies. If you want to compare, let the weight-pruning run longer.Fig. 3C: Plotting over n_wh does not add much here. I would plot over the iteration number for comparability.Fig. 4D: Why invert the x-axis?p.9 l.311 *Anti-FIp.9 l.300 Typo "versus"l. 353 There is a lot of experimental and theoretical work on connectivity overshoot, e.g. by Arjen van Oojen and Jaap van Pelt (based on activity dependent rewiring). Also spine turnover  has been demonstrated to be much higher during maturation. Would this be the direction this is aiming at? What would be the functional use of a "critical phase"?Reviewer #2: A salient feature of neural development is pruning: the number of neurons and connections first grows, but at some point both decrease. It is not known why this happens, or which connections and neurons are pruned. The authors address the latter question, and propose that weights that have the smallest effects on activity, as measured by the Fisher information, are preferentially pruned; and if all connections from or to a neuron are pruned, the neuron is pruned as well.I'm not an expert, but this is, I believe, a novel and interesting hypothesis, and will make a nice contribution to the field. My comments are almost exclusively about presentation -- there were a lot of places I simply got lost. That didn't really detract from the big picture, but it would be nice if things were clarified.1. Sloppiness is mentioned in the abstract, and not again until methods. It would make sense to me to either drop it in the abstract or mention it in the main text.2. I personally would drop initials, and spell out RBM, DBM, FIM and FI. Or at least spell out the first three. I'm not sure why anybody uses initials; in my view authors should be allowed to use at most one. There's actually a reason for that: people rarely read papers beginning to end, and it's very annoying to have to hunt through a paper to look for the meaning of initials.3. Given the definition of the energy, I believe Eq. 2 is wrong: the derivative should be with respect to the partition function, not the energy. If so, that should be corrected.4. I don't think P_v,h was ever defined.5. l 95-6: "When F_ij tends towards zero, the two parameters phi_i and phi_j are redundant." I can't for the life of me even guess what that means. It should be explained. Or dropped; I don't think it was ever used.6. l 99-100: "The resulting entries of the FIM depend on coincident firing of pre- and postsynaptic neurons and are arguably locally available." How can something that depends on two presynaptic and two postsynaptic neurons be locally available?7. I could not figure out what's in fig. 1c and d. This should be explained much more clearly.8. l 115-7: "The correspondence between parameter importance estimated from the first eigenvector and from the diagonal supports our use of Optimal Brain Damage for larger models, when computing the full FIM was no longer feasible." Couldn't make sense of this. It doesn't help that Optimal Brain Damage was (I believe) never explained.9. l 117-22:. "Strikingly, the important weights typically aligned with few hidden units and their biases. This structure of the FIM suggests a separation into important hidden units and unimportant ones. It follows that FI motivated pruning likely leads to entire units becoming disconnected, which would allow their removal from the network. This would correspond to neuron apoptosis after excessive synaptic pruning." The second two sentences make sense. But the first two don't, and so it's not clear how the second follow from the first.10. l 131-3: "For a pruning criterion based on the full FIM, we used the weight-specific entries of its first eigenvector as a direct indicator of weight importance." Couldn't make sense of this.11. After Eq. 4, I think it's important to write down the expression for Fisher information (Eq. 19) that was actually used, written in a human-readable form. As far as I can tell, Eq. 19 can be written<v_i h_j=""> = <v_i><h_j>/[<v_i> + (1-<v_i>)exp(-w_ij (1-<h_j>))].Algebra mistakes are possible, but I believe the correct expression looks something like this. And it's kind of easy to make sense of: besides the dependence on v_i and h_j, it's an approximately sigmoidal function of the weights. So it would be nice to include it.12. l 160: "Generally, excessive pruning was detrimental to generative performance" It seems that it's only for the orange line (Heuristic FI?) that pruning was detrimental to generative performance.13. Fig. 2 caption: "For all pruning strategies except Anti-FI pruning the model retains the ability to match the distribution of the training data (dashed lines) after retraining, indicating good generative performance." As far as I can tell, Anti-FI matched the true distribution in all but one panel.14. l 186-8: "In sum, for all pruning strategies , the network could recover from the loss of weights and units through retraining". It looks to me like Anti-FI recovers as well.15. mnist is 28x28. why scale to 20x20? The reason for this should probably be explained.16. Fig. 3B: why did random and [w] stop at 10^5?17. fig. 4: probability may not be the best measure -- it's possible in principle that probability deteriorates but performance stays high. I think it would be good to report both performance and probability.And again, why stop at 10^5 for random and [w], and even higher for Anti-FI?18. l 350-3: "A recent study of the effects of perturbing the input during different time points of training in neural networks suggests that a critical learning period may be visible in a plateau of the FIM trace [45]." I couldn't make sense of this.</h_j></v_i></v_i></h_j></v_i></v_i>**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Computational Biologydata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: Yes**********what does this mean?). 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If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #2: YesFigure Files:https://pacev2.apexcovantage.com. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, Data Requirements:http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: Reproducibility:https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocolsTo enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at  29 Jun 2021Attachmentrebuttal_letter1_ploscomp.pdfSubmitted filename: Click here for additional data file. 19 Aug 2021Dear Dr. Hennig,Thank you very much for submitting your manuscript "The Information Theory of Developmental Pruning: Optimizing Global Network Architecture Using Local Synaptic Rules" for consideration at PLOS Computational Biology. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.Please be sure to address the remaining smaller comments from the reviewers. If you feel that the additional analyses proposed by reviewer 1 are outside the scope of this particular paper (which the reviewer recognised they may be), please just state this clearly in your response to reviewers and consider adding commentary in the discussion in this direction.Please prepare and submit your revised manuscript within 30 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email.When you are ready to resubmit, please upload the following:[1] A letter containing a detailed list of your responses to all review comments, and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).Important additional instructions are given below your reviewer comments.Thank you again for your submission to our journal. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.Sincerely,Blake A RichardsAssociate EditorPLOS Computational BiologyLyle GrahamDeputy EditorPLOS Computational Biology***********************ploscompbiol@plos.org immediately:A link appears below if there are any accompanying review attachments. If you believe any reviews to be missing, please contact [LINK]Please be sure to address the remaining smaller comments from the reviewers. If you feel that the additional analyses proposed by reviewer 1 are outside the scope of this particular paper (which the reviewer recognised they may be), please just clarify and consider adding commentary in the discussion in this direction.Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: The authors put great effort into improving the paper and addressed most of my concerns. I only have a few remaining issues (and suggestions) before I recommend publication:Concerning 1.4: Random unit pruning:(a) "... in the one-layer RBM all visible units are connected to all hidden units.When a hidden unit is removed here, the activity and Fisher information can completely re-arrange with re-training". As the unit pruning seems to be the main advantage of the FI-approach, I think this control case should also be included for the single layer RBM. The above intuition can the be discussed and demonstrated in Fig 2C: One would see a large divergence before but not after retraining.(b) From what I see in Figure 3, the random unit pruning is not really fair with respect to the units in hidden layer 1, as it removes an order of mangitude more neurons in that layer. To really demonstrate that FI-pruning leads to a better network structure more quickly, I propose to adapt this and remove less neurons in h1 to arrive at a comparable structurel.134/l.333f Could you provide more motivation why it is easier to track firing rates and weights instead of correlation and weights. Biologically, Ca or CaMKII are thought to be local proxies of correlated activity, but I am not aware of molecular signals tracking especially the presynaptic rate.l.165 I guess here you need to discuss the results a bit deeper, as otherwise panel 2C would have been sufficient to make the point. Specifically, I noticed that the generative performance only seems to be poor for seldom patterns whereas the performance for abundant patterns seem to match . Is this really so bad for neural system? From an information theoretic viewpoint, they are surely the most informative patterns. However, as these unmatched patterns are rare, the error introduced by them may be negligible.l.372 The statement seems a bit bold. Maybe use "activity-dependent pruning that aims to identify uninformative neurons"Suggestions to improve readability:- In my opinion, it would make sense to move the introduction of the RBMs (l.23-33) to the end of the introduction (after l.55)- l.70 Maybe one could also mention the relation between energy and pattern probability in equation 1.- l.101 I would mention how the models were fitted here .- l.101 It is not immediately clear what is meant by "parameter-wise" (first mention). I would stick to the terms full and diagonal or at least specify what is meant in this sentence. Moreover, I think it is may be less confusing to discuss the results in the order they are presented in the figure and move the Also, an activity dependent form is only available from Equation 3 or 4, right?- l.141 It is not immediately clear why the FI introduced before is "variance" based. Maybe the term could be introduced together with the method and the motivation of "variance" could be explained.- l.150 I think it should be shortly motivated what the generative performance means/relates to in the neuronal/biological system, to give a better intuition what the FI-approach actually preserves.Finally, I would have another suggestion:Another advantage of the FI-dependent pruning over other methods may be the fact that it could be used to determine when pruning should be stopped. At the moment this is not the case as the lowest-FI quantile of synapses is always removed. If, instead, only synapses below an FI-threshold would be removed, pruning would naturally stop if all synapses have high FI. Such a convergence would remove the necessity to select a suitable number of pruning iterations for the model and prevent the performance loss of the FI-based models after massive pruning in Fig 3. Assuming that pruning stops after all synapses have high FI, one would get one "optimal" pruned model (instead of one per pruning iteration). Determining these optimal models for different input statistic would also allow predictions on the number of surviving synapses and neurons as well as weight distributions (for example comparing the networks after training with a 5-class MNIST subset and the full dataset). Varying the input statistics and getting different resulting models would greatly underline the point that FI-pruning actually selects input-related "optimal" model architectures and not just "smaller" models whose size is determined by the number of iterations. Moreover, such an analysis would provide more insight into the relation between the encoding of the Boltzmann machine and optimal pruned models, which, I guess, was a goal of this line of research.The differences in the resulting optimal networks could, in turn, be compared with existing data on network complexity/ neuron and spine densities in animals reared in different environments . This would make a nice connection to biology and provide actually testable pre/postdictions .I am aware that this additional analysis may be work-intensive and beyond the scope of this paper. However, I think it may greatly improve the manuscript or at least provide an interesting direction for future research.Reviewer #2: The paper is _much_ improved, and I'm happy with it. Only two comments:1. in Eq. 10, I believe the weights should have superscripts.2. I would suggest moving A1 and A2 to Methods. I suspected the more mathematically inclined will be interested. I certainly was, since I got it wrong the first time around. ;) This is, though, completely up to the authors.**********Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: YesReviewer #2: Yes**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool, Data Requirements:http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: Reproducibility:https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocolsTo enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at References:Review your reference list to ensure that it is complete and correct. 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Neurotrophic factors (NTFs) are essential for cell growth, survival, synaptic plasticity, and maintenance of specific neuronal population in the central nervous system. Multiple studies have demonstrated that alterations in the levels and activities of NTFs are related to the pathology and symptoms of neurodegenerative disorders, such as Parkinson’s disease (PD), Alzheimer’s disease (AD), and Huntington’s disease. Hence, the key molecule that can regulate the expression of NTFs is an important target for gene therapy coupling adeno-associated virus vector (AAV) gene. We have previously reported that the Ras homolog protein enriched in brain (Rheb)–mammalian target of rapamycin complex 1 (mTORC1) axis plays a vital role in preventing neuronal death in the brain of AD and PD patients. AAV transduction using a constitutively active form of Rheb exerts a neuroprotective effect through the upregulation of NTFs, thereby promoting the neurotrophic interaction between astrocytes and neurons in AD conditions. These findings suggest the role of Rheb as an important regulator of the regulatory system of NTFs to treat neurodegenerative diseases. In this review, we present an overview of the role of Rheb in neurodegenerative diseases and summarize the therapeutic potential of AAV serotype 1 (AAV1)-Rheb(S16H) transduction in the treatment of neurodegenerative disorders, focusing on diseases, such as AD and PD. Neurodegenerative diseases are debilitating disorders characterized by the gradual loss of anatomically or physiologically related function or structure of the central nervous system and include various diseases with different pathological patterns and clinical manifestations, such as Alzheimer’s disease (AD), Huntington’s disease (HD), Parkinson’s disease (PD), and amyotrophic lateral sclerosis (ALS) ,2,3. TheRas homolog protein enriched in brain (Rheb) is a member of the Ras superfamily, which consists of Rheb1 and Rheb2 . Rheb1 aThese findings suggest that Rheb involvement in neurodegenerative diseases and its important role in the production of various NTFs can be considered as one of the potential therapeutic targets for neurodegenerative diseases. This review provides insights into the involvement of the Rheb/mTORC1 signaling pathway in neurodegenerative diseases and the neuroprotective effects of Rheb as a potential therapeutic target, focusing on AD and PD.Despite the several in-depth studies that have been conducted over previous decades on neurodegenerative diseases, these disorders remain poorly understood. Most neurodegenerative diseases, such as AD ,45,46,47AD is a progressive psychiatric and neurodegenerative disease of unknown etiology. The clinical features of AD are a progressive decline in cognitive and memory processes and often difficulties with language ,80,81. TloxP/Cre  systems showed no significant differences in the number of TH-positive neurons, motor function, or metabolite levels of dopamine. In addition, it has been reported that overproduction of GDNF in the α-synuclein model does not prevent the aggregation of α-synuclein in the SN, loss of dopamine neurons by α-synuclein, or motor dysfunction [F-dopa uptake measured by positron emission tomography (PET). In addition, it was confirmed that TH-immunopositive nerve fibers were increased in the postmortem brain tissue study of a patient who had received unilateral infusion for 48 months [PD is a neurodegenerative disorder characterized by resting tremors, loss of postural reflexes, muscle rigidity, and bradykinesia, accompanied by festinating gait, cognitive decline, and postural malformations ,93. PD ifunction ,72. Impofunction . Howeverfunction . Anotherfunction . Trials function . In a mufunction . Patient8 months . In othe8 months ,113. Int8 months . After s8 months . In anot8 months ,117. TheVarious NTFs have been investigated in animal models for the treatment of other neurodegenerative diseases. ALS, the most common form of motor neuron disease, is a fatal adult-onset neurodegenerative disease that results in progressive and preferential degeneration and death of both the upper motor neurons of the motor cortex and the alpha lower motor neurons of the brain stem and spinal cord ,119. SevSome NTFs such as BDNF, CNTF, and GDNF are promising candidates for future treatment as they affect the glial activation status and have a beneficial effect on the outcomes of neurodegenerative diseases. Exogenous BDNF treatment has been found to prevent the apoptotic cell death of astrocytes and neurons induced by neurotoxin 3-nitropropionic acid in culture conditions. BDNF treatment also regulates glutamate transporter expression and inflammatory responses in astrocytes. This observation suggests that the BDNF-induced beneficial function of astrocytes has therapeutic potential against neurodegenerative diseases . AnotherTaken together, evidence suggests that the absence of neurotrophic support contributes significantly to neurodegeneration and that NTFs have emerged as a promising therapeutic strategy for neurodegenerative diseases . HoweverRheb is inactivated in the form of guanosine diphosphate-bound Rheb by a tuberous sclerosis complex (TSC) complex consisting of TSC1 (hamartin), TSC2 (tuberin), and TBC1D7 that act as guanosine triphosphatase (GTP)-activating proteins (GAT) . InsulinInterestingly, in this context, our own recent studies have shown that a higher constitutive level of Rheb(S16H), a constitutively active mutant protein transduced using AAV serotype 1 (AAV1), can protect hippocampal neurons in the adult brain against neurotoxic conditions through neurotrophic interactions between neurons and astrocytes ,41,151. In PD conditions, the role of mTOR remains controversial as it could exert either neuroprotective ,160 or nOverall, the evidence reported to date suggests that Rheb–mTOR signaling is associated with neuronal loss that occurs in different neurodegenerative diseases and could therefore be a potential therapeutic target for a wide range of such disorders.As described earlier, the Rheb–mTOR signaling pathway is a key regulator of diverse mechanisms involved in the survival and regeneration of neurons. Accordingly, several studies have identified Rheb mutations that cause this protein to become constitutively active ,151. Our+)-induced neurotoxicity in nigrostriatal striatal dopaminergic projections [Similarly, in our other previous studies, we found that the expression of neuronal Rheb(S16H) protects dopaminergic neurons through the upregulation of NTF expression in the substantia nigra in a neurotoxin-induced PD model. AAV1-hRheb(S16H) transduction of dopamine neurons protects against 6-OHDA-induced neurodegeneration and induces neuroprotective effect, including the abilities to both preserve and restore the dopaminergic axonal projections, through mTORC1 signaling ,150 Othejections . In addijections . Neurotojections ,181. Ourjections   transduction was found to induce a persistent increment in the expression levels of TrkB and CNTFRα within activated astrocytes and hippocampal neurons, respectively . We alsoAlthough a cure for neurodegenerative diseases has yet to be developed, there are several symptomatic treatments. Remarkably however, all these diseases will eventually progress. Our previous studies have clarified that the transduction of hippocampal neurons by Rheb(S16H) transduction stimulates NTF production, thereby strengthening the neuroprotective system and reducing neurodegeneration in the hippocampus and dopaminergic systems of the adult brain. Therefore, although further research is necessary to determine the clinical applicability of AAV1-Rheb(S16H) transduction to treat neurodegenerative diseases, this approach may be a useful strategy to protect neurons in the lesioned brain, and it may have beneficial effects in patients with neurological disorders, such as AD and PD.