how deacetylases influences ligand binding: an overvie2015 drug dis… · of a computational method...

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REVIEWS Drug Discovery Today � Volume 20, Number 6 � June 2015

How the flexibility of human histonedeacetylases influences ligandbinding: an overviewNathalie Deschamps, Claudia Avello Simoes-Pires, Pierre-Alain Carrupt andAlessandra Nurisso

School of Pharmaceutical Sciences, University of Geneva, University of Lausanne, Quai Ernest Ansermet, 30, CH-1211 Geneva 4, Switzerland

Over the past decade, human histone deacetylases (HDACs) have become interesting as therapeutic

targets because of the benefits that their modulation might provide in aging-related disorders. Recently,

studies using crystallography and computational chemistry have provided information on the structure

and conformational changes related to HDAC-mediated recognition events. Through the description of

the key mass and one-off movements observed in metal-dependent HDACs, here we highlight the impact

of flexibility on drug-binding affinity and specificity. The collected information will be useful for not

only a better understanding of the biological functions of HDACs, but also the conception of new

selective binders.

IntroductionProtein flexibility is a property that regulates how certain biologi-

cal effects are exerted in nature [1,2]. In fact, proteins are found to

exist in solution in a dynamic equilibrium of energetically similar

conformations [3]. Distinct ligands, such as protein-binding part-

ners, physiological compounds, or drug candidates, are hypothe-

sized to modify this structural energy landscape through

interactions with a limited number of protein conformations.

Conformational selection increases the proportion of specific

conformers in the total protein population, leading to an increase

in the interaction phenomena that are the basis of biological

processes [3]. This recently developed mechanistic model over-

comes the old but still popular lock-and-key and induced-fit

models [4]. X-ray crystallography, nuclear magnetic resonance

(NMR) and molecular modeling strategies, such as molecular

dynamics (MD) simulations, have already revealed possible

conformer-dependent binding scenarios for several proteins, dem-

onstrating an intimate connection between protein flexibility,

complex formation and biological activity [5–7]. Flexibility related

to histone deacetylases (HDACs), a family of 18 enzymes known

for their ability to catalyze the removal of acetyl moieties from the

lysine residues of histones and other substrates, was first detected

Corresponding author: Nurisso, A. ([email protected])

736 www.drugdiscoverytoday.com

10 years ago [8,9]. Since then, information from crystallography

coupled with computational studies has been exploited for not

only linking structural information to observed biological func-

tions (mechanistic purposes), but also developing HDAC isoform-

selective modulators (drug design purposes). The latter is currently

needed to investigate the roles of individual HDAC isoforms in

biological pathways as well as for producing efficient drugs with

fewer adverse effects compared with the pan-HDAC inhibitors

currently on the market as anticancer therapies [10–12]. To the

best of our knowledge, the dynamic aspects of HDAC isoforms that

are the basis of catalytic and protein/protein interaction phenom-

ena have not been previously reviewed. Here, we investigate what

is known about HDAC flexibility and how this information can be

exploited for the conception of novel potent and selective HDAC

modulators.

A brief focus on HDACsHDACs have become interesting as therapeutic targets because of

the benefits that their modulation might provide in the impairment

of the acetylation status found in many diseases, including aging-

related disorders [13]. The modulation of gene expression by

HDACs via chromatin modification was first highlighted as a po-

tential anticancer target. HDAC catalytic inhibition can promote

transcriptional reprogramming, which can be associated with the

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therapeutic success of inhibitors in cancer therapy that has resulted

in positive clinical trials [14]. Moreover, we and others recently

reviewed the outcomes of a specific type of HDAC modulation in

neurodegenerative conditions [15,16]. However, there are still

unknowns regarding the mechanisms of HDAC modulation, which

are dependent upon isoform specificity, tissue and cell particula-

rities, such as the diversity of available partner proteins and cellular

signaling pathways [17,18].

The HDAC family is clustered into five evolutionarily classes

based on phylogenetic features: HDAC1–3 and 8 (class I); HDAC4,

5, 7 and 9 (class IIa); HDAC6 and 10 (class IIb); sirtuins SIRT1–7

(class III); and HDAC11 (class IV). Class I, IIa/b and IV enzymes

require a divalent zinc ion for catalysis, whereas sirtuins are NAD+-

dependent enzymes. The latter, which are structurally different

from the other classes, are not discussed here [19,20]. Class I

HDACs are almost exclusively nuclear, often operating through

multiprotein complexes, and are mainly responsible for histone

deacetylation. By contrast, class II enzymes either shuttle between

the nucleus and cytoplasm or are primarily cytoplasmic [21–25].

They are able to deacetylate nonhistone proteins and can be found

in complex with several protein partners [26–29]. Comparable to

class I isoforms, HDAC11, being the sole member of class IV, is also

found in the nucleus [30]. From a structural point of view, all

HDAC enzymes share an approximately 11-A tube-like catalytic

channel, which accommodates a zinc ion that is responsible for

their deacetylase activity. With a few exceptions, the residues

lining this active pocket in the catalytic domain are widely con-

served among different isoforms, making the design of selective

inhibitors and/or modulators challenging [8,9,31–37]. Among

class I HDACs, a 14-A tunnel located perpendicular to the 11-A

channel bottom is also conserved. This water-filled pocket, also

called the internal cavity or foot pocket, has been suggested to be

the egression route for the acetate product and is potentially an

additional target area for selective structure-based inhibitor design

[31,32,36,38,39]. This channel has also been observed in HDAC4;

however, it differs from class I HDACs in terms of its size and

residue composition [34,40]. Many authors agree that the 11-A

channel rim is the best place to find exploitable structural differ-

ences for the rational design of selective inhibitors or modulators.

For this reason, most of the HDAC inhibitors that have been

reported to date obey a common ‘cap–linker–chelator’ pharmaco-

phore model, where the cap moiety is designed to explore selec-

tively the isoform channel rim, whereas the linker mimics the

lysine side chains of substrates [41,42].

MD: a powerful tool for detecting the plasticity ofHDAC proteinsTo date, 29 crystallographic structures of human zinc-dependent

HDACs have been deposited in the Protein Data Bank (PDB; http://

www.wwpdb.org/). These structural data are a precious resource

for the design of new compounds using structure-based techni-

ques. Nevertheless, because crystals are a collection of photos

representing particular conformational states of proteins, they

lack information concerning their dynamic continuity in a sol-

vated environment. This limitation, together with the expensive

and extensive work required to collect crystals, has led to the

development of a computational method called MD simulation,

which is able to predict protein fluctuations as a function of time

in a dynamic solvated environment. This technique is based on

Newtonian physics and offers important insights regarding the

protein motions that are the basis of ligand recognition and

allosteric phenomena [43]. Moreover, the recent efforts that have

been made to decrease computational time, through the develop-

ment of MD algorithms supporting Graphics Processing Units

(GPU), are having a strong impact on the use of this computational

strategy in routine drug design projects [44]. To gain insights into

the conformational dynamics of HDACs, complementary infor-

mation from crystallography and MD were taken into account and

summarized.

Class I HDAC1–2 and 8: dynamics of catalytic site mightbe linked to ligand propertiesDynamic transitions between different conformational states are

well-known phenomena in enzymology. Such motions are con-

sidered intrinsic enzymatic properties, but they can also be a

consequence of external perturbations, such as ligand or protein

binding [45].

The reported motions of class I HDACs are in line with the latter

concept. Enzymes of this class are mostly nuclear and are studied

as relevant targets against cancer and central nervous system (CNS)

diseases [10,13]. Among them, HDAC8 is the most documented in

terms of crystallographic data and, to date, two main conforma-

tional changes have been observed: mass movements, which

involve entire regions of the proteins, and one-off movements,

which are associated with conformational variations in single

amino acid side chains. By investigating the superimposition of

co-crystals and apo-forms, several studies have shown that the

active pocket of HDAC8 can convert from a wide-open state (also

called the open state, which displays a single wide-open pocket

[46]) into a sub-open state, which displays two cavities (one deep

tunnel adjacent to the 11 A channel), and then into a unique

cavity (the 11 A channel), which is the closed conformational state

(Fig. 1) [8,46,47]. These dynamic transitions have all been reported

or hypothesized to be in equilibrium and to be a consequence of

ligand (substrate or inhibitor) binding, ligand release, or product

egression through the protein structure [46–48]. Two loops have

been identified as primarily responsible for such induced-fit

motions: the L1 loop, which comprises seven residues from

Ser30 to Lys36, and the L2 loop, which comprises residues from

Pro91 to Thr105. L1 is capable of moving outward from the

catalytic site to widen the cavity opening or inward to occlude

any adjacent cavities and create the closed conformational state,

in which only the 11 A tube-like cavity is accessible [8,49]. L2 is

organized in complexes but not in the apo-form [8,46,48]. The

architecture of the catalytic site and the channel rim of HDAC8

adapt to accommodate ligands according to their size, shape and

chemical properties; a large and hydrophobic cap group (such as

for CRA-A) would preferably bury into a deep hydrophobic groove

(i.e. the open state) to reduce solvent exposure, whereas a small

and rather hydrophilic cap group (such as SAHA) would rather stay

freely exposed at the protein surface (i.e. binding to the HDAC8

closed state) (Fig. 1) [8,46]. Punctual residues have an important

role in HDAC8 cavity plasticity. For example, Tyr306 forms the

end of the 11 A channel wall and is involved in ligand recognition,

and Phe152 (which is found on the 11 A channel rim next to

Tyr306) can either be packed against the Lys33 side chain from the

www.drugdiscoverytoday.com 737

http://www.wwpdb.org/

http://www.wwpdb.org/


(a)

Zn ZnZn

L1

L2

THR105

LYS33

PHE152

PHE152

LYS33

PRO91

Zn

Zn

(b) (c)

(d)

Drug Discovery Today

FIGURE 1

Transition between histone deacetylase 8 (HDAC8) conformations: wide-open (a) [Protein Data Bank (PDB) code 1VKG], sub-open (b) (PDB code 1T64) and closed(c) (PDB code 1T69) conformational states. Molecular surfaces are drawn 5.5 A around the co-crystallized ligands using a lipophilicity color code from magenta to

green for hydrophilic and hydrophobic areas, respectively. In (a), a unique wide pocket is clearly visible, whereas in (b), two pockets are present, separated by a

hydrophobic wall. In (c), only the 11-A channel remains. The zinc ion is indicated as a blue sphere. (d) The mass and punctual movements of HDAC8 in L1 and L2

loops. The HDAC8 sub-open (PDB code 1T64) and closed (PDB code 2V5X) states are superimposed to highlight the mass movements of both the L1 and L2 loopsand the punctual motions of the residues. L1 loop, Lys33 and Phe152 motions are shown either in pink or light blue, depending on whether they belong to the

sub-open or the closed conformational state, respectively. The zinc ion (light-blue sphere) and its chelating triad are shown as reference points. The L2 loop (from

Pro91 to Thr105) is shown either in violet or in dark blue, depending on whether it belongs to the sub-open (loop only) or the closed (short pseudo helix)

conformation, respectively. Images were generated with MOE 2012.10.

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L1 loop, occluding the second pocket of the HDAC8 sub-open

conformation, or be rotated away from Lys33 in a position ap-

proximately 6 A away to create the open state conformation of

HDAC8 (Fig. 1) [8,39,47,50,51]. One-off movements also charac-

terize Trp141, which is located at the bottom of the HDAC8

catalytic pocket and is part of a gate-keeping system that controls

access to the 14 A channel [47,50,52] (Table 1). The 14-A channel,

which has an entrance that is governed by other gatekeepers (Table

1), is part of the inner machinery of the enzyme. Interestingly, it

has been suggested to be a possible egression route for both acetate

product and ligands [38,52–54].

In the cases of HDAC1 and 2, several egression routes and

gatekeepers have been hypothesized to be important in the design

of selective compounds. An aromatic wall formed by face-to-face

Phe150/Phe155 and Phe205/210 residues lines the 11-A channel


entrance of HDAC1 and 2, respectively. These residues seem to be

involved in both ligand stabilization, such as for N-(2-aminophe-

nyl)benzamide, through favorable hydrophobic contacts, and

product release [55]. Moreover, the 14-A channel exit is mediated

in HDAC1 and 2 by a transient zip-on zip-off mechanism via the

tilting of a Tyr residue toward a Phe residue (Table 1) [55]. Another

transient subchannel, which is unique to HDAC1, also allows

ligand egression through the two gatekeepers Met30 and

Tyr303, and to the best of our knowledge, to date, this is one of

the few differences between the HDAC1 and 2 isoforms [55].

MD simulation studies, in contradiction with each other, aimed

to provide information about the plasticity of all of the HDAC1–2

catalytic channels. In some studies, no significant flexibility was

expected with respect to HDAC8 because of their longer L1 loop

(HDAC8 is two amino acids shorter) [8,32,47,49]; however, several


TABLE 1

Areas of flexibility detected in class I HDACs

Isoform Region(s) and/or residue(s) involved Structural consequences Refs

Mass motions

HDAC1 Loops surrounding active site (Tyr201–Lys220)

and terminal regions

Opening and closing of 11 A channel; 14 A channel;

subchannel involved in the acetate release (unique

to HDAC1); ligand accommodation

[31,32,51,55]

HDAC2 Loops surrounding active site (Val190–Ala210)and terminal regions

HDAC3 Loop L1 (Ala19–Pro25); Helix 6 (Gln78–Asn88) HDAC3–DAD–IP4 complex stabilization: catalytic

activity allowed

[35,51,52]

HDAC8 L1 or B loop (Ser30–Lys36) Opening and closing of 11 A channel; 14 A channelSer39 phosphorylation might inactivate HDAC8

through L1 conformational changes

[8,32,38,39,46–54,63,64]L2 or A loop (Glu85–Glu106)

Loops lining catalytic site (Val204–Gln223;Gly272–Met274)

Ligand accommodation

One-off motions

HDAC1 Phe205 Accommodation of ligands with large cap group [31,32,51,55]

Met30, Tyr303 Opening of subchannel unique to HDAC1Tyr22, Tyr24 and Phe109 Closing of 14 A channel

Phe150 Ligand-release mechanisms through enlargement

of zinc-binding area

HDAC2 Tyr27, Tyr29 and Phe144 Closing of 14 A channelPhe155 Ligand-release mechanism through enlargement of

zinc-binding area

HDAC3 Tyr107 and Leu133 Avoiding accommodation of ligands with bulky

zinc-binding groups

[35,51,52]

Tyr298 Assuming an inward orientation when HDAC3–

DAD–IP4 complex is formed; substrate recognition

HDAC8 Phe152 and Tyr306 Interconversion between wide-open, sub-open, or

closed state of catalytic site; ligand accommodationand release

[8,32,38,39,46–54,63,64]

Tyr111, Trp141 and Tyr154

Leu31, Arg37, Tyr111, Trp141, Gly139, Gly303

and Gly305

Closing of 14 A channel

Tyr18, Tyr20 and His42 Regulation of second adjacent pocket exit


authors have confirmed the high flexibility of the channels by

using root mean square deviation (RMSD) analyses of simulations

in line with the high temperature factors reported for L1 in the

homologous histone deacetylase-like protein (HDLP from Aquifex

aeolicus) crystal [31,55]. Such motions have yet to be confirmed by

new X-ray structures.

In summary, isoforms 1, 2 and 8 of the class I HDACs show a

different flexibility profile that is intimately linked to ligand

properties (polarity, size and shape of each moiety). This should

be taken into account as a key factor in the rational design of

HDAC-selective catalytic inhibitors.

Class I HDAC3: the dynamics of the catalytic site may bedependent on allosteric mechanismsThe dynamics of HDAC3 differs from the isoforms described above

in terms of its 11-A channel, which is flexible in an unbound state.

However, HDAC3 appears to assume a more rigid catalytic archi-

tecture when recruited into the co-repressor complex NCoR/

SMRT, which is necessary for biologically functional HDAC3

[35,37,51,52]. This recruitment is dependent on the interaction

between SMRT and HDAC3 through the binding of inositol tetra-

phosphate, IP4, which works as a liaison molecule between the two

proteins. This interaction occurs in a region adjacent to the

catalytic channel rim of HDAC3 (Table 1) and allows the protein

to be catalytically active [35]. An allosteric mechanism regulating

HDAC3/NCoR/SMRT complex formation has been suggested

[51,53]. Thus, the design of compounds that are able to target

the apo-form to prevent complex formation would be an interest-

ing approach for probing the biological functions of HDAC3.

Jiggling and wiggling of an additional zinc-bindingmodule influences the catalytic activity of class IIaHDACsThe work carried out by Bottomley and co-workers provided in-

depth structural detail about class IIa HDACs and was the first to

describe the crystallographic structure of HDAC4 [34]. According

to that study, the core of the protein exhibits a layered a–b–a-fold,

with a central parallel b sheet of eight b strands and a catalytic zinc

ion, showing an overall similarity to HDAC isoform 8 (Ca RMSD

2.2 A) [34]. HDAC4, together with all the members of class IIa

HDACs, is also characterized by an additional zinc-binding motif

in the vicinity of the catalytic site. This module seems to have key

roles in both substrate recognition and complex association

[33,34,40]. Characterized by two protein segments held together

by a tetra-coordinated structural zinc ion (Table 2), the structural

zinc-binding subdomain is able to adopt an open or a closed

conformational state, which consequently affects the catalytic

pocket size and shape [33,34]. Upon ligand binding, the protein

structure is able to adopt (or not) the open conformation depend-

ing on the properties of the ligand [33,34,40]. In the open state, the

additional zinc-binding motif moves 10–20 A away from the active

site (Fig. 2). In this conformational state, the 14-A channel is not



TABLE 2

Areas of flexibility detected in class II and IV HDACs

Isoform Region(s) and/or residue(s) involved Structural consequences Refs

Mass motions

HDAC4 Loops a1–a2 (His665–Glu680) Opening and closing of second zinc-binding

subdomain

[34,40]

Loops a6–a7–b3–b4 (Leu733–His766) Closed state: switch in zinc-chelating residues (fromHis665 and His678 to Cys669 and His675)

Open state: switch in zinc-chelating residues (from

His675 and Cys669 to His665 and His678), with this

position locked by Cys669–Cys700 disulfide bondsHDAC10 Loops lining active site channel (Glu302–Tyr305) Ligand accommodation [63,64]

HDAC11 Loops lining active site channel (Ser301–Tyr304) Ligand accommodation [63,64]

One-off motions

HDAC4/7 His976/His843 HDAC4/7 deacetylase activity stimulation (?) [33,34,40,42]HDAC6 Arg1155 and Tyr1156 Opening or closing of ubiquitin-binding groove [61]

HDAC10 Glu302–Tyr305 11 A channel plasticity [63,64]

HDAC11 Phe141 11 A channel plasticity [63,64]Ser301–Tyr304 and Phe141

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formed. By contrast, when the closed state is promoted, the zinc-

binding subdomain is packed toward the active site, opening the

14 A channel, and exposing a groove that some studies have sug-

gested to be the area that mediates the formation of multiprotein

complexes, such as the HDAC4/7–HDAC3�N-CoR assembly [33,34,

56,57]. Interestingly, a zinc-coordination switch coordinates with

Catalytic Zn

(a) (b)

(d)

Catalytic Zn

D = 2.7 Å

TYR1156

ARG1155

ARG1155TYR1156

D = 6.6 Å

FIGURE 2

Transition between the open and closed conformational states of histone deacet

subdomain (His665–Arg681; Leu733–His766). As a reference point, the catalytic zinc

and its corresponding surface is colored in pink. This conformation is obtained when[Protein Data Bank (PDB) code 2VQJ]. (b) Both open (pink) and closed (dark blue) sta

arrangement. (c) The zinc-binding subdomain is closed and packed toward the c

conformation is obtained when HDAC4 is complexed to a carboxamide derivative

conformations of the HDAC6 ubiquitin-binding domain. The open (PDB code 3C5superimposed to highlight Tyr1156 and Arg1155 one-off movements. A main view o

involved residues. Tyr1156 and Arg1155 are shown as sticks, either in pink or in

conformation, respectively. Images generated with MOE 2012.10.


these motions, highlighting the high dynamism of such systems

(Table 2). The debate regarding whether class II HDACs are bona fide

deacetylases is still open. Notably, in these HDACs, a His replaces the

catalytic Tyr that is found in class I HDACs, and this replacement

decreases the deacetylase activity of class II HDACs (Table 2)

[33,34,42,58]. Flexibility related to such a His residue might have

(c)

Catalytic Zn

ZnZn

Zn

Drug Discovery Today

ylase 4 (HDAC4). The molecular surface is drawn around the zinc-binding

ion is shown as a light-blue sphere. (a) The zinc-binding subdomain is open,

HDAC4 is complexed to a thiophene derivative, shown as pink balls and stickstes are superimposed to highlight the significant differences in terms of spatial

atalytic site, and its corresponding surface is colored in dark blue. This

, shown as blue balls and sticks (PDB code 4CBY). (d) The open and closed

K) and closed (PDB code 3PHD) states of the ubiquitin-binding domain aref the domain is provided to locate both zinc ions (light-blue spheres) and the

light blue depending on whether they belong to the open or the closed



a fundamental role in deacetylase activity, but this hypothesis still

needs to be proven through additional biological and structural

studies.

Ideally, the design of a selective compound that is able to interfere

with the closed conformation of HDACs would inhibit not only the

deacetylase activity, but also all the downstream pathways regulated

by these enzymes, providing insights into related biological func-

tions. Nevertheless, the ligand properties that regulate such confor-

mational changes are still unclear (i.e. not all catalytic inhibitors are

able to promote an open conformation, which is the case for TSA in

HDAC8) [8,33,40,48]. For example, although they have the same

zinc-binding group (hydroxamic acid), several inhibitors might or

might not promote the open state of HDAC4 or 7; for example, an

achiral ligand {N-hydroxy-5[(3-phenyl-5,6-dihydroimidazo[1,2-

a]pyrazin-7(8H)-yl)carbonyl]thiophene-2-carboxamide} was co-

crystallized within the open conformation of HDAC4, whereas

several chiral ligands or more flexible ligands {(1R,2R,3R)-2-[4-(5-

fluoranylpyrimidin-2-yl)phenyl]-N-oxidanyl-3phenyl-cyclopro-

pane-1-carboxamide; (1R,2R,3R)-2-[4-(1,3-oxazol-5-yl)phenyl]-N-

oxidanyl-3-phenyl-cyclopropane-1-carboxamide; TSA and SAHA,

respectively} were crystallized in complex with HDAC4 and 7 in

their closed states [33,40]. Even if no structural data about HDAC5

and 9 are available, it seems reasonable to think that the conserved

zinc-binding motif present in all HDAC class IIa isoforms assume

similar dynamic behaviors. The identification of regions that are

significant for selectivity within class IIa remains an open research

area.

Two dynamic gatekeepers control the interactionbetween class IIb HDAC6 and ubiquitinDo flexible mechanisms exist within class IIb HDACs? That is, does

compound and/or protein binding impact the class IIb HDAC

conformational state? HDAC6 is the most studied isoform of this

class because of its involvement in CNS disorders [16], and it

displays two catalytic domains and a ubiquitin (Ub)-binding

domain (also called a zinc finger) that is unique among HDACs

[59–61]. The latter has been crystallized alone and in complex with

its physiological ligand, showing significant conformational

changes upon Ub binding, mainly because of the flexible behavior

of the Arg1155 and Tyr1156 side chains (Fig. 2 and Table 2) [61].

Although nothing is known about the full 3D architecture of

HDAC6, a direct impact of Ub binding on HDAC6 catalytic activity

has been hypothesized [62]. A structural arrangement might be the

cause of this regulatory mechanism.

What about the remaining isoforms?To date, few structural and biological data have been reported for

the HDAC10 and 11 isoforms. Information concerning flexibility

has been obtained by coupling homology modeling and MD

simulation studies [63,64]. A flexible trend of the 11-A channel

has been reported for these isoforms, but such reports should be

assessed with caution (Table 2).

Concluding remarksHDACs are enzymes that are currently considered to be major

targets for the development of drugs against aging-related dis-

eases. The importance of HDACs is also the reason for the large

body of literature on these enzymes, even at the structural level.

To date, this is the first review to summarize the dynamic aspects

of HDAC isoforms and their importance in catalysis and complex

assembly. In agreement with [46], understanding the different

enzymatic conformations is essential in drug design and should

be taken into account in the conception of novel selective HDAC

modulators. Here, we highlighted structural elements that could

be targeted for the conception of new specific HDAC isoform

binders. We also suggested the design of isoform-specific molec-

ular probes that are able to stabilize one specific conformation,

thus modulating the related downstream pathway. The issue

addressed here is important because the subject concerns not

only HDACs, but also many other proteins [65]. The resolution of

novel crystallographic structures combined with computational

studies together with the collection of new biological data are still

necessary to understand fully the structural and biological mech-

anisms of HDACs.

AcknowledgementsThe authors thank Ernst & Lucie Schmidheiny and Pierre Mercier

foundations for financial support. A.N. is also grateful to the

‘Boursiere d’Excellence’ programme of the University of Geneva

(Switzerland).

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