Mathieu Schwartz
email: mathieu.schwartz@inrae.fr

Jade Moreno

Nicolas Poirier

Francis Canon

Fabrice Neiers

Understanding the in-mouth release of aroma sulfur compounds from food precursors and the role of microbial C-S lyases

Keywords: flavor, volatile sulfur compounds, oral microbiota, enzymes

. Protein sequence analysis of C-S lyases in the oral anarobe Fusobacterium nucleatum was carried out and led to the identification of several putative targets. The C-S lyase FnaPatB1 from F. nucleatum animalis, showed high activity with a range of aroma precursors. FnaPatB1 metabolizes cysteine derivatives within a unique active site environment that enables the formation of flavor sulfur compounds. As sulfur compounds can be associated with food aversion especially at high concentration, we have designed an in vitro assay, based on the recombinant enzyme, to identify inhibitors of the C-S lyase activity. Among a food compounds library, we identified several compounds able to reduce the C-S lyase activity of FnaPatB1 in vitro. Future prospects will rely on the study of this oral microbiota metabolism and strategies to control it using both in vitro and ex vivo approaches.


R Ohayon

VIBRATIONS OF FLUID-STRUCTURE COUPLED SYSTEMS

h ;,i-proposed t.o invest.igate alternati\"e symmet. ric formulat.ions valid for static and modal analysis based either on the representation oft-he liquid by a pressure field and a displacement potential field, either on the representation of the structure by a displacement field and a reaction .force (or acceleration) field.

INTRODUCTION

Transient and modal analysis of fluid-st.ructure problems have been the subject of many investigations [l). For such problems. the choice of field \1uiables for the \"8.riational statements is of prime importance. The description of the fluid, in the compressible case, by a stres-1!-(pressure) scalar \lUia.ble p, or by a displacement potential y> introducf'l! non symmetric mat.rices after a finite element discret.ization, we refer t.o t,he pioneering work of [32, 33, 34J followed then by [2, 7, 12, 22, 28, 29]. An attempt to symmetrize the non symmetric matrix syst.em by using matrix manipulation algebra, has been im,estigat. ed in [START_REF] Daniel | finite <• lr nu n.t ffu1d-str11dun rigu, l'a h, r prohl, m[END_REF][START_REF] Ller | Simpltfi td a1,Cal y . , rs of lrn f.ar ftu1d-. ,lr1,Dr/r!r; 111tr1•[END_REF]. In this respect, let, us also mention the BJ1a.lysis of [9, 10] based 011 matrix scaling concepts.

Another idea lies in the utilization of the velocity potential inst.ea.cl of the displacement pot,entia.l or instead of t.he pressure. The result.ing symmetric matrix system invokes a complex jw term, if.,; denotes the circular frequency [START_REF] Ever | � ymmctrzral 1w trntrnl . fonnulatrnn fo r . ff 1 1ul-. ,t!'lld11rc intaaclions[END_REF]. The corresponding formulation ha.� been improved in [27] in order to take into account the st.a.tic case. The analysis leads to a numerical procedure which involves a special purpose eigem-alue solver.

In reference [START_REF] Morand | fnt•tsftg1,@trn11 of l'a1'iatzonal[END_REF] and in the subsequent references [START_REF] Morand | 2bstr11 ct urt rarratio11al 1,Bnal y s1. , fo r thr n brations of cott.p le.d ff oid-. ,truct 11re .,y. 'lt,-m[END_REF]25], a three-field symmetric variat.ional formulation has been introduced using p and ;p a.s fluid unknowns, while t.he displacement field u is used to describe t.he stn1ct.11re. The formulat, ion involves coupling p -'f and u -,.p terms in the mass matrix. Its utilization in nuclear engineering problems is described in [3]. A complete re-investigation of this formulation in order to get rid of the "spurious zero-frequency fluid modes" generally encountered, is the subject of reference [START_REF] Morand | Fi 1,=itf. dt mriit mrthod applz i1,Ã to thr pnd1r tio1[END_REF]. Some at.tempt. in order to eliminat.e those spurious modes has also been analyzed in {11).

Let us also recall that a descript.ion of the fluid t.hrough a displll("ement \-ariable. introduces difficulties related to t . he appropriate discret.ization of the 1rrot1,4tionality ,•ottlfitton I. or t. hP fluid. A rlii;pl1,Ucement fonm1l1,Vtion hn" h1,Õen preseute1,Ø in an appendix uf [START_REF] Morand | fnt•tsftg1,@trn11 of l'a1'iatzonal[END_REF], the currespondin!!; finit"' 1,3le111i>11I a. na. lysii-j., prei:;ented in [13j. ln references (23, 26J, a three-field ( 11; p, 1,Ô) variational r;ymmetri<' for mulation haM been int. roduced. It involvl:'s ,�oupling terms in the stiffness ma trix. Applications. with . aıffe.reu.t. interpolation functions for p and ,;• <:an be found in reference [START_REF] Sandberg | A symm.drir finite dtme11l tlemrnt fo rm ula ti"n for acousti,: fs11id-str11clun interodio11 a)/(tl y sis[END_REF].

Two three-field ( "• R; p) aud ( u, R; ,-,) 8ymmPtric formulations, havf' been introduced in referen.-:es [24, 26). Bot. h inrnlve an additional unknown in the st. ructure, namely t. be d_vnamic react.ion force R or the aA,celera. t.ion •,. \.\'e t.hen obt.ain either a "mass-coupling" matrix Pigenv11 lue system, eithn a "stiffness-coupling" matrix s�•stO?m, Th• ose formulations have bet>n used through particular modal synthesis procedures in [6] and [START_REF] Fî | pnnc1plo a11 d modal methods in flit id-, qtru.ctm•e interaction problt: m. q[END_REF]. Finally, let. us ment. ion t.he introduct-ion of sloshing simple model in [25,[START_REF] Kehr-Candille | Elasto-aco1,1$f1c v1brat1on. � of' a strucf l trr contai1ii11g a ga. s[END_REF].

A complet. e modal interaction scheme talcing into a r c01mt. both comprer;s ibility and gravit.y effects is a.naJyzed in [17] . .'.\lodal synt. hesis procedurP. haw already been im,estigated for elai,toacoustic vibrations using strnd ural modes in [START_REF] Morand | fnt•tsftg1,@trn11 of l'a1'iatzonal[END_REF], and hydroelatltic incomprei.sible modes in [START_REF] Morand | 2bstr11 ct urt rarratio11al 1,Bnal y s1. , fo r thr n brations of cott.p le.d ff oid-. ,truct 11re .,y. 'lt,-m[END_REF], to g ethf'T with arous.tie modes as Rit. z vPct.ors, in order t.o study the vibrat.ions of a structure con taining a. ga.s [START_REF] Morand | fnt•tsftg1,@trn11 of l'a1'iatzonal[END_REF] or a. compressible liquiJ with a free surface while neglectiug g ravity effects [START_REF] Morand | 2bstr11 ct urt rarratio11al 1,Bnal y s1. , fo r thr n brations of cott.p le.d ff oid-. ,truct 11re .,y. 'lt,-m[END_REF]. Fluid-structure interface damping effects may be found iu

(1 5].
The subject of the ptesen1. paper is t. o reinvestigate somP of the pr,,.,•iou.i formulations in order t.o take into a<•count static cases. This meam; that the formulat.ions should not contain. in t,he modal situations. non ph _v -,ical zpro eigenvalues.

The variat. ional methodology is based on a direct ut.ili1,Äation oft. he lm�al equat. ions of the c�upled syst. em. Let. us mention a. n asrmptotit• mathema. ticaJ approach to coupled problems in [START_REF] Sanche | t 0[END_REF].

In a first. step, we shall recall the basic local equations of the coupled system [START_REF] Morand | Fi 1,=itf. dt mriit mrthod applz i1,Ã to thr pnd1r tio1[END_REF].

In a second step, we shall extend thP three-field ( 11; p, • ;) symmetric ,-ariat. iona. 1 formulat. ion. of lltiffness-coupling type, whid1 has hPen estahlisht>d for a compressible liquid with a 1,Å�ro pressure fsee smface condition [23,[START_REF] Nicolas-Vnllierme | Fl1,Gid-. �ir11 durr intcror/101,H fo r bo u nded and infinite medium vibratio11 proble m[END_REF], to the caQ of a structure completely filled with a compressible gas. We shall show t. ha. t the static case can he PaNily handled.

Finally. in a third step, we shall investiga. te. for a. partially damped struct. ure cont.aining either a compressible gas, either 1,5. com pr,.. ,ssi hie liqn id with a free-surface (neglecting gravity effects), a three-fidd symmetric variational formulation of "ma1,è'!-.-:ouplin g " type [24] extended in or1,×er lo take into a1,Ócouut static caOes. -�p + >.po �,:; = 0 tJp 8, p

--+>.po -=0

Bn tin

In

( 1) ( 2 )
(3) (4)

(!;) ( 6) ( i) ( 8)
( 9 1

The system (�), ( 9) is equivale-nt t.o ( l). The ne-w loc:il hounrla. met.hfţ f5J as follows:

\Ve multiply ( 8) by a ( reg11lar) tPSt function hp E I : , and WP 11:-te I hP Green fomuila to take into account the boundary cond ition j 9).

We multiply equation (2) by a ( regul:u) test funrtion ,\ ; E 1• ., and WP use the Green fprmula to take into account ( : n.

At la8t, we multiply E>qHation (S) by a (r,.g11liu) tP.st fo rwtion , � 11 <:: l� and we use t.he Green fqrmula to t11.ke into an�ount the houudary ,•onditions (4) and (6).

14, ; V ., .afít t_;, arf'--admissihle-<'la�-of r�11 lnr function" \WN hen obtain the frllowing vatiational fsrmn lat ion.

The symmetric vaiiational ftrmulation

Find (Ii; JJ and :.;) E 1;, xi � �: i• ,, and .\ � 0 sudi that: After a finite element discretizat ion. and using u. p and :.; as the vector of nodal \'alues of the continuum fields. we oblu.in the followiufÄ mat rix eq uatiou: The �q,iat,ion ( 10) t.hen lwcomes: One ran e1L. c;il y see that . t. he on ly ZPro-fr eq nency movemPnt.s are t-h"' six physical rigid hod�• motions ztR : IL = UR [START_REF] Morand | Fi 1,=itf. dt mriit mrthod applz i1,à to thr pnd1r tio1[END_REF] for wich . WP have: [START_REF] Morand | fnt•tsftg1,@trn11 of l'a1'iatzonal[END_REF] TherPfore. frn thosf' movements, WP obt.ain as f'Xpect.ed: [START_REF] Morand | 2bstr11 ct urt rarratio11al 1,Bnal y s1. , fo r thr n brations of cott.p le.d ff oid-. ,truct 11re .,y. 'lt,-m[END_REF] This pr<wes t ha. t the static r11se ra. n be Pasily handled .

From a pract ical point of view. it is only necessary to use the stiifopss mat rix of ( 14 ,l and t.o impofŪe t.o all p-nodal values t.o be equal . This is a way t.o overcome the diftc11lt.y concerning the non standa.rcl finit.e element discret.izat.ion of t.he &econd bilinear form of ( 17 ) .

2.5 Tbe "con d ensed" ( u , ,? ) symmetric variatio11al formu l at i on p can be eliminated f r om equation [START_REF] Fî | pnnc1plo a11 d modal methods in flit id-, qtru.ctm•e interaction problt: m. q[END_REF] . leading to a two-field symmet.l;c sliffne,;s-cou pling formulation .

2.6 A fonr-field ( u, : p ., P, :; ) formulation • In orrler t.o exhibit t. he const ant. ( over the domain fl ) so-calle..-1 pneumatic pre,sirn re 1'• [START_REF] Morand | fnt•tsftg1,@trn11 of l'a1'iatzonal[END_REF] . it. l"o uld be eonveuient. t.o recasi. the formulation ( 10) -( 14) through the following change of repre�ntation: with: and fl = p, + p

Pu C 2 i P• = -\'olffZ ) � u . . n. 1 P=O ( 21 ) ( 22 ) ( 23 )
For sake of brevity , we do not enter int-0 the det.a. ils of such modified formulat.ion wich will be discuSSf!d elsewhere.

(C, ,; P ) SYMMETR1C FORMULATION ( MASS-COUPLING )

Tbe local boundary valne equations

Referring to reference [ 24, 26 ) , introduciug a new unknown variable for lht:> �tructure enables us t,o obtain t.wo t-hree-fi.eld symmetric formulations involving respect ively p or 'r-" for the fluid (resp. mass-or stiftitess-coupling). (25)

(26) (2i) ( 21<) (29) (30)
( 3 1) [START_REF] Zienkiewicz | iewton R.E., Co upled vibratio11s of 11 struct 11. 1•t s• 11 b moyul in a. comp 1•e�. ,iblc fluid[END_REF] if W<" ignorP tht> f>fjllations {:!0)-( 32 24)-( 29), onf' mrn,t add [START_REF] Zieukiewicz | Co 11. pled prohle ms 1111.d th.fir numtriw. l . w lu ti011[END_REF] in order to eliminate the constant zero-frequency mode (p = con6tant) . \Vith this respect, it is conwuient to reea�t the syst<'lll (24)-( 29) by introducing t. wo new \•a riables p_ , and I' instead p, namely tho1:-e defined by ( 21), ( 22 The lol--al equation (3r(,l fŨ <i then re<"asted as follows:

(44)

The lornl equations which lead to a rnriational formulati,m implying th., unknowns (u. •; ; P., . P) are then [START_REF] Zienkiewicz | The Finite Element ::\fothod[END_REF], (:13), 1:Hi ). (3,J. (31JJ, (-W) , (4:l) and ( 4-t) .

The variable P ( and the corr,•,-,pondin g test fn 1w t io11 /, P) must -;ati,;fr tfūe constramt: Rema. rk 3

For sake of bre\•ity, we do not enl er l11�re into the detailed analysis of (45 ) . In ( 46), for damped struct ure . . 011t nm dt m inot. ,, anrl it c::in he shown that the rf'Sult.ing three-fidd formulation ( �: p, , P) 1. , symmrtr1c and is valid for t. he static ca.se .

Remark -!

�n the case of a free surface r. one must Sf't. t. lw followin� P<JUation (rc•f erenc� [START_REF] Morand | Fi 1,=itf. dt mriit mrthod applz i1,Ã to thr pnd1r tio1[END_REF] ). p = O Ir (47 ) It ita P.tt!"Y •to•l'lee that this case does not require the ,:onst,rnint [START_REF] Zieukiewicz | Co 11. pled prohle ms 1111.d th.fir numtriw. l . w lu ti011[END_REF]. Conse qu""ntly, I he rn. riable p, doPs not. appear.

CONCLUSIO N

\Ve have int rod11ced iwo alternative formulations va. lid for the :otatic ca .. e, which mean dutl, the only zero-freqtiency modei; are the physical six ri�id Lody strnct.urnl mot ions.

The numPri,•al 11. pplic-11 tions of s1wh fo rmu lations depends on the gPomet, ry of the fluid-stru l't ure syMem. For instaJ1,•e. for a. partiall)' damped structure of shell t�• pe which contains a hugt' amount of compr�sible fluid , the formulation whirh introduces an addit ional vari11.hle for the st.rnctnre is of interest .

  1. LOCAL EQUATIO NS OF THE BOUNDARY VA LUE PROBLEM 1.1 Notation s n, I resp. n) r " "• � structure { resp. fluid ) domain at equilibrium (bo rizout.ali eq uilibrium free surfac.e unit normal (external to the fluid boundary) unit 11 om1al (extE":-nal to the structure boundary ) fluid/st.rncture contact surface maS8 densit.y of t,he st ructure (resp. of t. he fluid ) µ, I reSJJ. /10) Ujj ("I strei;s tenwr considered M a function of the displacement u according to the following definition: u;j = Oij 1o1�1t1( u) :;1 = ½ (u 1,,1 + 11 1.k ) strain t.ensor "ii 1-1 elastic coefficients ,\ = :... ,� square of t. he circular frequency c VPlnc:ity nf sound in t. he comprPssible fluid TbP E"< fllll t iono, of tl1E" bmmdary eigE"nvaluE" problem are [18]: Remark l -\'i.1 + .\ po v;,; = 0 p + Po c 2 �:;. � = 0 iJ . .; 1/n. = u.n U;j ( u I n/ = p ll; u,;,;(u) +. \p, fl; = 0 U,j(U)flj ° = 0 /( ;,;) = 0, lnt.erpr.,tat.ion of t. hP above equations In Euler t><IUation of the inviscid compressible irrotat ionnal fluid . (2) "con8tiluti\•e law" of the linear fluid. (3) (kinE"mat kal) ,�ontact rondition. 1_4) force equilibrium condition at fluid-structure interface. (f >) (linear) dynamic equat.ion for a.n elast.ic st.ructme. ( 6) free boun<la.ry t�ondit-ion on the struct.ure. (,) uniqueness condit. ion for .p (defiued through an additi\"e constant). 2. (F; P, .,;) SYMMETRIC FO RM ULATION (STIFFNESS-COUPLING) 2.1 The local boundary value equations Let uis recast. the equat.ion (1) as follows:

  Let us set ,\= 0 in the furmulation (10)-(13). Tht> equat.ion j 12'! show, that p i� constant over the domain fl:p = p.

( 15 )

 15 Therefvre, the equation (II_ ) giv"" thP va!11P. of thfÅ con,;;taut pr,.,;;,;;11rP tif'ld ].' . • as a fwnction of the normal displacenwnt 11.ri of �: Pu <' 2 j p, = --\, 1 " 11 .fĬ '0 (H) �

  \ pl)U.TI n,, !T;j\U) 11; ' = p11; t'.Ti j , J (") +>.p, u; = 0 t'.Tj j (II) 11 j • = fJ I. I = fJ

  ), onP. must, 11.cid thP following eon straiut eqnation in order t.o obtain p = 0 in the A= 0 case: i� ohtain1cd by integrating PO) o,n S) and by taking int.o account (:lll. lf WP. consiciPr only the sy,-tem dPfined by (

  ) and (23). The local Pq11 a1 ions thPn arP as follows: . \ ,\ �P +--:-P+--:;-p, = O c 2 1'.• DP -::;--= ,\ pr,u.n (111 /Jo C � 1 1 v, +\ . l•r.• u.n=O, P=O o l i:_I i::; n lT; j ( tt ) 11 ; • = P n i + p • n, lT; j , 5 ( 11 ) + >..p, u; order to obt ain n symmPtri,• variational formulat ion, we shall use as prt>viously [24. 26] , a new stru ctural variable, namely t.he dynamic react.ion force: 141) or the w;celerahon: "; = ,\ II

3. 2

 2 The ''condensed'' symmetric variational formulation ( •: p ., P) The variational formulation corresponding to ( 11 . •1 : p., P) can be est ab lished by using st andard test function procedure. One obtains:-[ '\ P. VI! P + ,\ ;• po u . n t, P ln �. \ 1 f' /' .\ 1 p


Sophie Sacquin-Mora
email: sacquin@ibpc.fr

Coarse-grain simulations on NMR conformational ensembles highlight functional residues in proteins

Keywords: NMR conformational ensembles, proteins mechanics, coarse-grain simulations, elastic network model, protein gating residues

Dynamics are a key feature of protein function, and this is especially true of gating residues, which occupy cavity or tunnel lining positions in the protein structure, and will reversibly switch between open and closed conformations in order to control the diffusion of small molecules within a protein's internal matrix. Earlier work on globins and hydrogenases have shown that these gating residues can be detected using a multiscale scheme combining all atom classic molecular dynamics simulations and coarse grain calculations of the resulting conformational ensemble mechanical properties. Here we show that the structural variations observed in the conformational ensembles produced by NMR spectroscopy experiments are sufficient to induce noticeable mechanical changes in a protein, which in turn can be used to identify residues important for function and forming a mechanical nucleus in the protein core. This new approach, which combines experimental data and rapid coarse-grain calculations and no longer needs to resort to time-consuming all-atom simulations, was successfully applied to five different protein families.

! 2

Introduction

Far from being static, rigid objects, proteins are highly flexible molecules, and understanding this flexibility is essential for understanding protein function [START_REF] Micheletti | Comparing proteins by their internal dynamics: exploring structure-function relationships beyond static structural alignments[END_REF][START_REF] Orozco | A theoretical view of protein dynamics[END_REF].

Interestingly, protein conformational diversity and dynamics do not always involve large-scale protein motions, and function can arise from small structural changes [START_REF] Monzon | Conformational diversity analysis reveals three functional mechanisms in proteins[END_REF]. In their work investigating the conformational changes between the apo and ligand-bound state in 60 enzymes, Gutteridge and Thornton showed that over 90% of the studied proteins presented root mean square deviations (RMSDs) below 2 Å [START_REF] Gutteridge | Conformational changes observed in enzyme crystal structures upon substrate binding[END_REF]. These small conformational variations are nonetheless sufficient to support enzymatic activity, and inversely, slightly disrupting a protein's structure can greatly affect its biological function [START_REF] Mesecar | Orbital steering in the catalytic power of enzymes: small structural changes with large catalytic consequences[END_REF][START_REF] Koshland | Conformational changes: how small is big enough?[END_REF]. As a consequence, current de novo protein design strategies do not only involve the production of a particular fold, but also need to take into account protein dynamics, if one wants to achieve a specific function [START_REF] Boehr | Engineered control of enzyme structural dynamics and function[END_REF][START_REF] Johansson | Structural heterogeneity and dynamics in protein evolution and design[END_REF][START_REF] Maria-Solano | Role of conformational dynamics in the evolution of novel enzyme function[END_REF].

Molecular gates represent a particular class of dynamic structures that play an important role in protein activity. They can be defined as a system, involving individual residues, loops or secondary structure elements, that can reversibly switch between open and closed conformations, and that control the passage of small molecules into and out of the protein structure [START_REF] Zhou | The gates of ion channels and enzymes[END_REF][START_REF] Gora | Gates of enzymes[END_REF]. Gating residues, lining internal channels connecting a buried active site to the surface, or two distant active sites within a single protein, are a common feature in the protein world, with more than 60% of the enzymes in the Catalytic Site Atlas [START_REF] Furnham | The Catalytic Site Atlas 2.0: cataloging catalytic sites and residues identified in enzymes[END_REF] presenting channels at least 15 Å long [START_REF] Pravda | Anatomy of enzyme channels[END_REF], and as shown by the 70 examples discussed in a review by Gora et al. [START_REF] Gora | Gates of enzymes[END_REF]. The dynamic properties of these tunnel lining residues play a key role in controlling catalytic efficiency and enzymes substrate specificity [START_REF] Kingsley | Substrate tunnels in enzymes: structure-function relationships and computational methodology[END_REF][START_REF] Kaushik | Impact of the access tunnel engineering on catalysis is strictly ligand-specific[END_REF], and they can be seen as a new category of ! 3 functional residues, that take a part in regulating biological processes without being directly involved in the catalytic reaction. As a consequence they have attracted growing interest among the drug design community over the recent years [START_REF] Marques | Enzyme Tunnels and Gates As Relevant Targets in Drug Design[END_REF].

From a theoretical point of view, numerous tools are nowadays available for investigating protein dynamics [START_REF] Kingsley | Substrate tunnels in enzymes: structure-function relationships and computational methodology[END_REF][START_REF] Maximova | Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics[END_REF]. Classic all-atom Molecular Dynamics (MD) simulations represent a common strategy, sometimes combined with experimental approaches [START_REF] Narayanan | Applications of NMR and computational methodologies to study protein dynamics[END_REF][START_REF] Debiec | Integrating NMR, SAXS, and Atomistic Simulations: Structure and Dynamics of a Two-Domain Protein[END_REF], which can however be computationally costly when working on large systems or modeling events taking place on a long time-scale [START_REF] Seyler | Sampling large conformational transitions: adenylate kinase as a testing ground[END_REF]. Another option is to use coarse-grain models, that combine simplified protein representations and energy functions [START_REF] Poma | Combining the MARTINI and Structure-Based Coarse-Grained Approaches for the Molecular Dynamics Studies of Conformational Transitions in Proteins[END_REF][START_REF] Tiwari | Conservation of intrinsic dynamics in proteins-what have computational models taught us?[END_REF][START_REF] Zheng | A survey of coarse-grained methods for modeling protein conformational transitions[END_REF]. Elastic Network Models (ENM) [START_REF] Tirion | Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis[END_REF][START_REF] Bahar | Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential[END_REF] in particular have led to many results regarding protein mechanics and dynamics [START_REF] Hinsen | Analysis of domain motions in large proteins[END_REF][START_REF] Atilgan | Anisotropy of fluctuation dynamics of proteins with an elastic network model[END_REF][START_REF] Tama | Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and elastic network theory[END_REF][START_REF] Yang | Close correspondence between the motions from principal component analysis of multiple HIV-1 protease structures and elastic network modes[END_REF][START_REF] Yang | Protein elastic network models and the ranges of cooperativity[END_REF].

In that perspective, we initially developed the ProPHet (Probing Protein Heterogeneity) program, which models proteins as an elastic network, to investigate protein mechanical properties on the residue level [START_REF] Sacquin-Mora | Investigating the local flexibility of functional residues in hemoproteins[END_REF]. The rigidity profiles produced by ProPHet then turned out to be a remarkable tool for linking a protein structure to its dynamic properties and its function, showing how small conformational changes within a protein could induce large, non trivial, mechanical effects and in turn impact its activity [START_REF] Sacquin-Mora | Probing the flexibility of the bacterial reaction center: the wild-type protein is more rigid than two site-specific mutants[END_REF][START_REF] Sacquin-Mora | Motions and mechanics: investigating conformational transitions in multidomain proteins with coarse-grain simulations[END_REF][START_REF] Sacquin-Mora | Bridging Enzymatic Structure Function via Mechanics: A Coarse-Grain Approach[END_REF]. In earlier sudies on globins [START_REF] Bocahut | Frontier residues lining globin internal cavities present specific mechanical properties[END_REF] and [NiFe]-hydrogenases [START_REF] Oteri | Multiscale simulations give insight into the hydrogen in and out pathways of [NiFe]-hydrogenases from Aquifex aeolicus and Desulfovibrio fructosovorans[END_REF], we also showed that the mechanical variations (calculated with ProPHET) observed in the conformational ensemble produced by classical equilibrium MD simulations can be used to identify a mechanical nucleus (MN) in the protein, which is a cluster formed by cavity lining residues occupying conserved positions along the protein sequence. In both cases, MN residues appear to be gating residues, oscillating between rigid and ! 4 flexible states along the MD trajectory and controlling ligand migration in the vicinity of the active site.

Since its initial developments a few decades ago, NMR spectroscopy has turned out to be a powerful tool for exploring the structure and dynamics of proteins in solution [START_REF] Narayanan | Applications of NMR and computational methodologies to study protein dynamics[END_REF][START_REF] Wider | NMR spectroscopy of large molecules and multimolecular assemblies in solution[END_REF][START_REF] Kay | New Views of Functionally Dynamic Proteins by Solution NMR Spectroscopy[END_REF][START_REF] Jiang | NMR Studies of Large Proteins[END_REF]. In particular, proteic entries in the Protein Data Bank [START_REF] Berman | The Protein Data Bank[END_REF] (PDB) produced by solution NMR often provide a conformational ensemble containing between 10 and 30 structural models instead of a single structure. In this work, we used these conformational ensembles to investigate the mechanical properties in five globular protein families using CG simulations performed by ProPHet. The conformational variations in the experimental NMR ensembles are sufficient to induce large mechanical changes between models from a single PDB entry. Combined with sequence alignements, the coarse-grain calculations based on the NMR structural models permit us to identify MN residues in the proteins without resorting to computationally costly all-atom MD simulations, thus highlighting potential mutational targets in a drug-design perspective.

Material and Methods

NMR conformational ensembles:

We searched the PDB for proteins where NMR conformational ensembles, comprising a minimum of ten models, are available for at least three different species. This led to the selection of 19 PDB entries belonging to five protein families with various folds listed in table 1: Globins, dihydrofolate reductase (DHFR), cyclophilin A (CPA), peptidyl-tRNA hydrolase (PTH), and parvulin.

Each NMR ensemble comprises between 10 and 40 models, and the most representative ones (between 2 and 7 models) were selected using the OLDERADO webserver, http:// www.ebi.ac.uk/pdbe/nmr/olderado/ [START_REF] Kelley | OLDERADO: on-line database of ensemble representatives and domains. On Line Database of Ensemble Representatives And DOmains[END_REF]. If the NMR structure was not listed online, we used the Ensemble cluster tool, which employs the same method as OLDERADO [START_REF] Kelley | An automated approach for clustering an ensemble of NMR-derived protein structures into conformationally related subfamilies[END_REF], in the UCSF-Chimera program, https://www.cgl.ucsf.edu/chimera/ [START_REF] Pettersen | UCSF Chimera--a visualization system for exploratory research and analysis[END_REF], to determine the most representative models. Both the ChannelsDB database, https:// webchemdev.ncbr.muni.cz/ChannelsDB/index.html [START_REF] Pravda | ChannelsDB: database of biomacromolecular tunnels and pores[END_REF], and the CASTP webserver, http://sts.bioe.uic.edu/castp/index.html?2r7g [START_REF] Tian | CASTp 3.0: computed atlas of surface topography of proteins[END_REF], were used to identify tunnel and cavity lining residues within all these protein structures.

Coarse-grain Simulation: Coarse-grain Brownian Dynamics (BD) simulations were performed using the ProPHet program, http://bioserv.rpbs.univ-paris-diderot.fr/services/ ProPHet/ [START_REF] Sacquin-Mora | Motions and mechanics: investigating conformational transitions in multidomain proteins with coarse-grain simulations[END_REF][START_REF] Sacquin-Mora | Bridging Enzymatic Structure Function via Mechanics: A Coarse-Grain Approach[END_REF][START_REF] Sacquin-Mora | Mechanical variations in proteins with large-scale motions highlight the formation of structural locks[END_REF], on all the representative models listed in table 1. Diverging from most common CG models, where each residue is described by a single pseudo-atom [START_REF] Tozzini | Coarse-grained models for proteins[END_REF], ProPHet uses a more detailed model enabling different residues to be distinguished, in which the amino acids are represented by one pseudo-atom located at the C𝛼 position, and either one or two (for larger residues) pseudo-atoms replacing the side-chain (with the exception of Gly) [START_REF] Zacharias | Protein-protein docking with a reduced protein model accounting for side-chain flexibility[END_REF]. Interactions between the pseudo-atoms are treated according to the standard Elastic Network Model (ENM) [START_REF] Tozzini | Coarse-grained models for proteins[END_REF], that is, pseudoatoms closer than the cutoff parameter, Rc = 9 Å, are joined by Gaussian springs that all have identical spring constants of 𝛾 = 0.42 N m -1 (0.6 kcal mol -1 Å -2 ). The springs are taken to be relaxed for the starting conformation of the protein, i. e. its crystallographic structure. Mechanical properties are obtained from 200,000 BD steps at 300 K. The simulations are analyzed in terms of the fluctuations of the mean distance between each pseudo-atom belonging to a given amino acid and the pseudo-atoms belonging to the remaining protein residues. The inverse of these fluctuations yields an ! 7 effective force constant ki that describes the ease of moving a pseudo-atom i with respect to the overall protein structure:

where 〈〉 denotes an average taken over the whole simulation and di=〈dij〉j* is the average distance from particle i to the other particles j in the protein (the sum over j* implies the exclusion of the pseudo-atoms belonging to the same residue as i). The distances between the C𝛼 pseudo-atom of residue k and the C𝛼 pseudo-atoms of the adjacent residues k-1 and k+1 are excluded, since the corresponding distances are virtually constant. The force constant for each residue k in the protein is the average of the force constants for all its constituent pseudo-atoms i. We will use the term rigidity profile to describe the ordered set of force constants for all the residues in a given protein. Note that, following earlier studies which showed how prosthetic groups, such as hemes, or small ligands had little influence on calculated force constants [START_REF] Sacquin-Mora | Investigating the local flexibility of functional residues in hemoproteins[END_REF][START_REF] Sacquin-Mora | Locating the active sites of enzymes using mechanical properties[END_REF], we chose not to include these in the protein representations. This enables us to study the proteins intrinsic mechanical properties independently of the nature and position of any bound ligand.

Following a procedure developed during earlier work on globins [START_REF] Bocahut | Frontier residues lining globin internal cavities present specific mechanical properties[END_REF] and hydrogenases [START_REF] Oteri | Multiscale simulations give insight into the hydrogen in and out pathways of [NiFe]-hydrogenases from Aquifex aeolicus and Desulfovibrio fructosovorans[END_REF], we compared the rigidity profiles obtained for the selected representatives models.

The models extracted from the NMR conformational ensembles do not present important structural variations, with Cα rmsds between two models from the same PDB entry being always inferior to 3Å (except for the structure of parvulin domain from S. aureus, 2jzv, which presents both a flexible N-terminal tail and a flexible loop).

However, these small structural changes are nonetheless sufficient to induce noticeable

! 8 € k i = 3k B T d i -d i ( ) 2
variations in the mechanical properties of a limited number of residues. We made a systematic pairwise comparison of all the rigidity profiles produced for the representative models from a single PDB entry and, for each residue in the protein, kept the maximum value that could be observed for its force constant variation. We then use the resulting max(|Δk|) profiles to determine mechanically sensitive (MS) residues, i. e.

residues presenting the largest force constant variations between two structural models.

MS residues are defined as residues whose maximum force constant variation satisfies the following criterion:

with ⟨|Δk|max⟩ being the average value of the maximum force constant variation over the whole protein sequence and σ(|Δk|max) its variance. This procedure leads to the selection of roughly 5-10% of the residues for each one of the NMR structures that are listed in Table 1.

Sequence alignments: Sequences from pdb entries belonging to the same protein family were aligned using the online MUSCLE tool, https://www.ebi.ac.uk/Tools/msa/ muscle/ [START_REF] Edgar | MUSCLE: multiple sequence alignment with high accuracy and high throughput[END_REF], with the default parameters. Despite the important mechanical similarity that can be observed in the rigidity profiles within a single protein family, the corresponding sequences display relatively low identities ranging from 15% to 82% (see table 1). Mechanically sensitive residues that were identified using the protocol described in the previous section are highlighted in bold and color along the protein sequences in Figure 3a and all throughout the electronic supplementary material.

! 9 | k| max (i) h| k| max i + 1.5 (| k| max ) 50

Results

Globins

Four NMR structures were selected in the PDB for the globin family: Myoglobin (Mgb) from P. catodon (PDB entry 1myf), truncated hemoglobin (Tr. Hb) from S. sp. PCC 6803 (1mwb), and the α and β chains from human hemoglobin, Hb (2m6z). The force constant profiles for the main representative model of each protein are shown in Figure 1. Similar to what has been observed in previous studies [START_REF] Bocahut | Frontier residues lining globin internal cavities present specific mechanical properties[END_REF][START_REF] Sacquin-Mora | Mechanical variations in proteins with large-scale motions highlight the formation of structural locks[END_REF], the analogous aspects of the profiles reflect the common globin fold, with α-helices appearing as grouped rigidity peaks along the protein sequence. The max(Δk) profiles resulting from the systematic pairwise comparison of the force constants calculated for different representative models for a given NMR conformational ensemble are shown in Figure 2 and residues with max(Δk) values above the threshold given in the Material and Methods section (indicated by the red horizontal line) are defined as mechanically sensitive residues, since their mechanical properties are the most impacted by the small conformational variations observed between the NMR models. The MS residue positions are highlighted in red on the multiple sequence alignement shown in Figure 3a and we can see that most of these positions are common to one or more globins. Four positions in particular, that are framed and highlighted in bold green in Figure 3a, E11, E15, G8 and G12 (using the standard numbering for globins that indicates the residue position along helices E and G) correspond to MS residues in three chains out of four.

We can see from Figure 3b that these residues form a central cluster right at the heart of the globin fold, with their side chain tightly interacting, and they all correspond to tunnel or pocket lining residues. These four positions also exactly concurs with the mechanical nucleus of globins which was determined in our earlier work using a similar properties for all four MN residues have also been shown to be particularly sensitive to pressure changes in high-pressure crystallography [START_REF] Colloc'h | Determinants of neuroglobin plasticity highlighted by joint coarse-grained simulations and high pressure crystallography[END_REF].

Dihydrofolate reductase

Four NMR conformational ensembles were found in the PDB for dihydrolate reductases (DHFR) from H. sapiens (1yho), L. casei (2l28), B. anthracis (2kgk), and H. volcanii (2ith). The combination of coarse-grain mechanical calculations and multiple sequence alignement leads to the identification, when keeping only MS residues that are present Force constant variation in at least 3 out of 4 sequences (see the alignment in Figure SI-1), of a six-residues mechanical nucleus comprising Cys6, Ile7, Val8, Val115, Gly116 and Try121 (using the human sequence numbering) shown in Figure 4. All residues from the mechanical nucleus are listed as tunnel lining or cavity lining in ChannelsDB or CASTP and lie on the interface between the subdomains defined in ref. [START_REF] Sawaya | Loop and subdomain movements in the mechanism of Escherichia coli dihydrofolate reductase: crystallographic evidence[END_REF]. A search in the experimental literature shows residues 6-8 belong to the protein initial β-strand, that contains residues critical for ligand and cofactor binding [START_REF] Kovalevskaya | Solution structure of human dihydrofolate reductase in its complex with trimethoprim and NADPH[END_REF][START_REF] Beierlein | The solution structure of Bacillus anthracis dihydrofolate reductase yields insight into the analysis of structure-activity relationships for novel inhibitors[END_REF], Phe96 from the BaDHFR (corresponding to Val115 in the human DHFR) is also involved in ligand biding [START_REF] Beierlein | The solution structure of Bacillus anthracis dihydrofolate reductase yields insight into the analysis of structure-activity relationships for novel inhibitors[END_REF] and so is Ile94, its equivalent in the E. coli DHFR variant [START_REF] Bhabha | A dynamic knockout reveals that conformational fluctuations influence the chemical step of enzyme catalysis[END_REF]. Interestingly, the F98Y mutation in DHFR from S. aureus (which corresponds to a mutation of Tyr121 in human DHFR) is responsible for an important loss in TMP affinity, due to Tyr98 forming a hydrogen bond with Leu5 (Ile7 in human), thus preventing it from binding the TMP ligand [START_REF] Frey | Crystal structures of wild-type and mutant methicillin-resistant Staphylococcus aureus dihydrofolate reductase reveal an alternate conformation of NADPH that may be linked to trimethoprim resistance[END_REF]. The same mutation has also been investigated in DHFR from M. tuberculosis, with the Y100F mutant displaying low affinity for classical DHFR inhibitors [START_REF] Dias | Mycobacterium tuberculosis dihydrofolate reductase reveals two conformational states and a possible low affinity mechanism to antifolate drugs[END_REF].

! 13

Cyclophilin A

Coarse-grain calculations were made on three NMR conformational ensembles for cyclophilin A from H.sapiens (1oca), G. kaustophilus (2mvz) and E. coli (1clh). The consensus mechanical nucleus is formed by six residues (Phe36, Gly65, Leu98, Phe112, Phe113 and Phe129, using the human sequence numbering) that correspond to MS positions in at least 2 out of the 3 sequences (see Figure SI-1 for the alignment) and is shown in Figure 5. The ChannelsDB entry for 3rdd, which corresponds to a crystallographic structure for human CPA, indicates that Phe113 is a tunnel lining ! 14 residues, and CASTP calculations identify all the MS residues in the E. coli CPA as cavity lining residues. From the experimental literature, we find that the ligand binding pocket in human CPA comprises residues Gly65, Leu98, Phe112 and Phe113, and Phe36, Phe112 and Phe129 belong to the protein aromatic core [START_REF] Ottiger | The NMR solution conformation of unligated human cyclophilin A[END_REF]. In a study using NMR relaxation experiments [START_REF] Eisenmesser | Intrinsic dynamics of an enzyme underlies catalysis[END_REF], Eisenmesser et al. showed how the protein motions play an essential part in its catalytic activity, and this catalytic activity is severely diminished for the F113W mutant. In addition, the large variations in rigidity observed for Leu98, Ser99 and Phe113 in human CPA concur with the fact that these residues display the largest differences in NMR chemical shifts between the enzyme's major and minor conformers. A mutational study on Ser99 (which lies outside of the catalytic site), designed to stabilized the previously hidden minor conformation, causes a large decrease in the catalytic rate [START_REF] Fraser | Hidden alternative structures of proline isomerase essential for catalysis[END_REF]. In the E. coli CPA, residues Ile88, Phe103 and Phe125 belong to the protein hydrophobic core, but are not directly involved in its isomerase activity [START_REF] Clubb | Three-dimensional solution structure of Escherichia coli periplasmic cyclophilin[END_REF]. Interestingly, MS residues Ala91 and Phe103 are located on both extremities of the B5-B6 surface loop, which overlooks the active site. As a consequence, mechanical variations in these two residues are likely to impact the loop conformational variability, and therefore the ligand's access to the catalytic site. A similar effect is also observed in the CPA from G. kaustophilus, with residues Gly57, Met87 and Phe101 lying on the edge of active site loops [START_REF] Holliday | Structure and Dynamics of GeoCyp: A Thermophilic Cyclophilin with a Novel Substrate Binding Mechanism That Functions Efficiently at Low Temperatures[END_REF].

! 15

Peptidyl-tRNA hydrolase

Three NMR conformational ensembles were found in the PDB for peptidyl-tRNA hydrolase (Pth) from M. tuberculosis (2jrc), M. smegmatis (2lgj) and V. cholerae (2mjl), which lead to the identification of a five-residues mechanical nucleus formed by Gly11, Ala26, Gly27, Ala95 and His96 (using the V. cholerae sequence numbering) shown in which controls the entrance to the substrate binding cleft [START_REF] Singh | Crystal structure of peptidyl-tRNA hydrolase from a Gram-positive bacterium, Streptococcus pyogenes at 2.19 A resolution shows the closed structure of the substrate-binding cleft[END_REF][START_REF] Zhang | Crystal structure of Staphylococcus aureus peptidyl-tRNA hydrolase at a 2.25 A resolution[END_REF][START_REF] Kabra | Unraveling the stereochemical and dynamic aspects of the catalytic site of bacterial peptidyl-tRNA hydrolase[END_REF], and has to move away to permit ligand binding in the enzyme's active site, which means that a perturbation of their mechanical properties is likely to disrupt the protein catalytic activity. In addition, NMR studies on the E. coli Pth show that Ala 26, Gly27 and Ala95 are affected by RNA binding to Pth, despite their central position in the protein core [START_REF] Giorgi | RNA-binding site of Escherichia coli peptidyl-tRNA hydrolase[END_REF], due to the interplay between the tRNA binding region and the peptide binding channel [START_REF] Pulavarti | Solution structure and dynamics of peptidyl-tRNA hydrolase from Mycobacterium tuberculosis H37Rv[END_REF]. Ala95 also forms van der Waals contacts with docked substrates in the V. cholerae Pth [START_REF] Kabra | Unraveling the stereochemical and dynamic aspects of the catalytic site of bacterial peptidyl-tRNA hydrolase[END_REF].

Parvulin

Five NMR conformational ensembles were found in the PDB for human parvulin (1nmw), and variants from E. coli (1jns), A. thaliana (1j6y), C. symbiosum (2rqs) and S. aureus (2jzv), thus leading to the identification of a four-residues mechanical nucleus formed by His59, Ile60, Il158 and Ile159 (using human sequence numbering) shown in Figure 7 (see Figure SI-1 for the sequence alignment). In parvulin from E. Coli, all the mechanical nucleus residues are listed as tunnel binding by ChannelsDB and cavity lining by CasTP (see table1). Structural studies on human parvulin highlight the functional importance of the two conserved histidines His59, His157 and Ile159, which are located in the enzyme's active center [START_REF] Ranganathan | Structural and functional analysis of the mitotic rotamase Pin1 suggests substrate recognition is phosphorylation dependent[END_REF][START_REF] Bayer | Structural analysis of the mitotic regulator hPin1 in solution: insights into domain architecture and substrate binding[END_REF][START_REF] Bailey | The dual histidine motif in the active site of Pin1 has a structural rather than catalytic role[END_REF]. Interestingly, later mutational studies on the His59/His157 pair showed that theses residues are not directly involved in the parvulin isomerase activity, but more likely contribute to the enzyme's stability [START_REF] Bailey | The dual histidine motif in the active site of Pin1 has a structural rather than catalytic role[END_REF].

His8 in E. coli parvulin, and His14 from the C. symbiosum parvulin (which both correspond to His59 in human parvulin) are located in the protein hydrophobic core and belong to the putative binding pocket [START_REF] Kuhlewein | Solution structure of Escherichia coli Par10: The prototypic member of the Parvulin family of peptidyl-prolyl cis/trans isomerases[END_REF][START_REF] Jaremko | Structure and dynamics of the first archaeal parvulin reveal a new functionally important loop in parvulin-type prolyl isomerases[END_REF], in parvulin from A. thaliana, His12 displays no chemical shift after binding of the peptide ligand, thus suggesting that this ! 18 residue is not directly involved in the catalytic cycle [START_REF] Landrieu | Solution structure of the single-domain prolyl cis/trans isomerase PIN1At from Arabidopsis thaliana[END_REF]. The NMR conformational ensemble obtained for S. aureus parvulin highlights the structural variability of the catalytic histidines (His 146 and His239), and the protein hydrophobic core also comprises residue Ile137, Ile240 and Ile241 [START_REF] Heikkinen | Solution structure of the parvulin-type PPIase domain of Staphylococcus aureus PrsA--implications for the catalytic mechanism of parvulins[END_REF]. A later study combining Molecular Dynamics Simulation and experimentally available S 2 order parameter for three parvulins suggests that the conserved histidines play a key role in the modulation of the enzyme's internal dynamics [START_REF] Czajlik | Fine-tuning the extent and dynamics of binding cleft opening as a potential general regulatory mechanism in parvulin-type peptidyl prolyl isomerases[END_REF].

! 19

Discussion and Conclusion

As shown in earlier work on globins and hydrogenases, protein mechanical properties are a dynamic feature [START_REF] Bocahut | Frontier residues lining globin internal cavities present specific mechanical properties[END_REF][START_REF] Oteri | Multiscale simulations give insight into the hydrogen in and out pathways of [NiFe]-hydrogenases from Aquifex aeolicus and Desulfovibrio fructosovorans[END_REF]. Due to the robustness of the Elastic Network Model approach [START_REF] Lopez-Blanco | New generation of elastic network models[END_REF], a protein's rigidity profile remains qualitatively the same along time, with its main peaks associated with a given set of residues (that are often likely to be catalytic residues). However, it will also present noticeable variations from one equilibrium structure to the other for another limited number of residues (termed as mechanically sensitive, MS, residues), even though the conformational variations between these structures remains negligible. We have shown previously that one could use conformational ensembles produced by classic all-atom Molecular Dynamics trajectories to identify MS residues in a protein, and repeating this approach on several homologous proteins will lead to the definition of a mechanical nucleus for this protein family, i. e. a set of conserved positions along the protein sequence that are occupied by MS residues. In the present work, we use protein conformational ensembles obtained by NMR spectroscopy for five distinct protein families, and show that the structural sampling from these ensembles is sufficient to identify a mechanical nucleus comprising between 3 and 6 residues in each group. In the case of globins, this mechanical nucleus concurs perfectly with the globin MN determined using trajectories from MD simulations. Its four constitutive residues have been highlighted as playing a key role in substrate diffusion in the protein matrix in numerous experimental approaches. The MN residues identified in the four other protein families also appear to be excellent candidates for playing a part in protein function as gating residues. Most of them are tunnel or cavity lining residues (underlined residues in Table 1), and for each ! 20 protein family, experimental evidence, from point mutation studies or evolutionary data, supports the hypothesis that, while not being directly involved in the chemical reaction taking place in the protein active site, the MN residues are nonetheless important for protein function. In particular, by modulating the shape and size of the cavities and tunnels leading to the protein active site, MN residues can impact an enzyme's substrate selectivity and catalytic efficiency. Therefore, they represent an interesting target for the fine tuning of protein function.

Conformational ensembles built from crystallographic structures can bring a lot of information regarding protein dynamics [START_REF] Phillips | Describing protein conformational ensembles: beyond static snapshots[END_REF][START_REF] Fraser | Accessing protein conformational ensembles using room-temperature X-ray crystallography[END_REF][START_REF] Sankar | Comparisons of Protein Dynamics from Experimental Structure Ensembles, Molecular Dynamics Ensembles, and Coarse-Grained Elastic Network Models[END_REF]. In order to see wether these could also be used with this approach, we performed mechanical calculations and a pairwise comparison of the rigidity profiles on crystallographic structures of DHFR from three variants, using the PDB IDs listed in [START_REF] Sankar | Distributions of experimental protein structures on coarse-grained free energy landscapes[END_REF]: DHFR from B. anthraci : chain A from 4alb, 4ale, 4elf, 4elg, 4elh (5 structures), human DHFR, chains A and B from 2w3a, 2w3b and 2w3m (6 structures), DHFR from E. coli, chain a from 1rx1, 1rx2, 1rx3, 1rx4, 1rx5, 1rx6, 1rx7, 1rx8, 1rx9 (9 structures). The resulting force constant variation profiles lead to the same mechanical nucleus as when using NMR ensembles, except for Ty121 (using the human sequence numbering), which is no longer a mechanically sensitive residues for any of the three species (see Figure SI-2). This loss in the mechanical nucleus definition is not negligible, since this position has been shown to be functionally important for DHFR from S. aureus and M. tuberculosis [START_REF] Frey | Crystal structures of wild-type and mutant methicillin-resistant Staphylococcus aureus dihydrofolate reductase reveal an alternate conformation of NADPH that may be linked to trimethoprim resistance[END_REF][START_REF] Dias | Mycobacterium tuberculosis dihydrofolate reductase reveals two conformational states and a possible low affinity mechanism to antifolate drugs[END_REF].

Another issue with ensembles of crystallographic structures is the choice of representative structures which will be used for mechanical calculations (ideally one should retain around 4-6 models to limit the computational cost of the approach). In the dataset listed in Ref. [START_REF] Sankar | Distributions of experimental protein structures on coarse-grained free energy landscapes[END_REF], at least 45 structures are retained for each protein. However, ! 21 selecting structures that are to mechanically too close can lead to a poor discrimination of mechanically sensitive residues, resulting in a poorly defined mechanical nucleus.

As an example, we performed mechanical calculations on 10 crystallographic structures from human cyclophilin A (PDB 5noq 5nor 5nos 5not 5nou 5nov 5now 5nox 5noy 5noz). The pairwise comparison of all ten rigidity profiles leads to the same selection of mechanically sensitive residues as when using the NMR conformational ensemble (see the lower black line in Figure SI-3a). However, if one selects structures that are too close from a mechanical point of view (namely 5noq, 5nor, 5nou and 5nov), the residues force constant variations are always below 10 kcal mol -1 Å -2 , thus making the selection of mechanically sensitive residues more difficult (see the red line in Figure Altogether, it seems that our methode can also use crystallographic structures. But this will request more work from a potential user, since one has to build an ensemble from several PDB structures, instead of using a single NMR ensemble, and be careful that the mechanical properties of the selected structures vary sufficiently in order to clearly define the mechanically sensitive residues.

Finally, our use of NMR structural ensembles and coarse-grain calculations provides us with a simple and efficient tool for identifying key spots in the protein structure, where ! 22 point mutations could help modulate the protein enzymatic activity or specificity. While the current study has been limited to small proteins, comprising less than 200 residues, recent progress in NMR spectroscopy on large systems [START_REF] Jiang | NMR Studies of Large Proteins[END_REF] should ensure that experimental conformational ensembles for larger proteins will be accessible in the near future.

Acknowledgments

Figure 1 :

 1 Figure 1: Rigidity profiles (in kcal.mol -1 .Å -2 ) of the first NMR representative model for the four globin chains under study. (a) Mgb, (b) Tr. Hb, (c) αHb, (d) βHb.

Figure 2 :

 2 Figure 2: Maximum variation (in kcal.mol -1 .Å -2 ) of the force constant observed upon pairwise comparison of the NMR representative models. (a) Mgb, (b) Tr. Hb, (c) αHb, (d) βHb. The red horizontal line indicates the threshold value used (following the criterion given in the Material and Methods section) for the selection of mechanically sensitive residues listed in table 1.

Figure 3 :

 3 Figure 3: (a) Multiple sequence alignment for the globin structures; mechanically sensitive residues are shown in bold red, and residues belonging to the mechanical nucleus are framed and highlighted in bold green. (b) Cartoon representation of myoglobin with the heme group shown in black and the mechanical nucleus residues as green van der Waals spheres. Figure 3a and Figures 4-7 were prepared using Visual Molecular Dynamics 78 .

Figure 4 :

 4 Figure 4: (a) Upper black line, rigidity profile of the first NMR representative model of human DHFR. Lower black line, maximum variation of the force constant observed upon pairwise comparison of the NMR representative models for human DHFR, the

Figure 5 :

 5 Figure 5: (a) Upper black line, rigidity profile of the first NMR representative model of human CPA. Lower black line, maximum variation of the force constant observed upon pairwise comparison of the NMR representative models for human CPA, the red horizontal line indicates the threshold value used for the selection of mechanically sensitive residues listed in table 1. (b) Cartoon representation of human CPA with the mechanical nucleus residues as green van der Waals spheres.

Figure 6 ,

 6 Figure 6, with MN residue occupying MS positions in at least 2 out of the 3 sequences

Figure 6 :

 6 Figure 6: (a) Upper black line, rigidity profile of the first NMR representative model of Pth from V. cholerae. Lower black line, maximum variation of the force constant observed upon pairwise comparison of the NMR representative models for Pth from V. cholerae, the red horizontal line indicates the threshold value used for the selection of mechanically sensitive residues listed in table 1. (b) Cartoon representation of Pth from V. cholerae with the mechanical nucleus residues as green van der Waals spheres and the catalytic residues (at the entrance of the peptide binding cleft) as red van der Waals spheres.

Figure 7 :

 7 Figure 7: (a) Upper black line, rigidity profile of the first NMR representative model of human parvulin. Lower black line, maximum variation of the force constant observed upon pairwise comparison of the NMR representative models for human parvulin, the red horizontal line indicates the threshold value used for the selection of mechanically sensitive residues listed in table 1. (b) Cartoon representation of human parvulin with the mechanical nucleus residues as green van der Waals spheres.

  SI-3a), a situation that was never observed for any of the 19 NMR ensembles used in this work. Moreover, in the case of structures with low rmsds (below 2.5 Å), the rmsd and the maximum force constant variation between two structures are not correlated, as can be seen on Figure SI-3b and FigureSI-4b. Which means that selecting structures on the basis of their rmsd is no guarantee that they will be sufficiently different from a mechanical point of view.

:

  This work was supported by the "Initiative d'Excellence" program from the French State (Grant "DYNAMO", ANR-11-LABX-0011-01). Supporting Material: The multiple sequence alignments for the 5 protein families under study are available as supporting information. ------STLYEKLGGTTAVDL------AVDKFYERVLQDDRIKHFFADVDM-------A 41 1MYF: -VLSEGEWQLVLHVWAKVEADVAGHGQDILIRLFKSHPETLEKFDRFKHLKTEAEMKASE 59 2M6Z:A -VLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHF-DLSH-----GSA 53 2M6Z:B VHLTPEEKSAVTALWGKVNVD--EVGGEALGRLLVVYPWTQRFFESFGDLSTPDAVMGNP 58 1MWB: KQRAHQKAFLTYAFGGTDKYDGRYMREAHKELVENHG----LNGEHFDAVAEDLLATLKE 97 1MYF: DLKKHGVTVLTALGAILKKKG--HHEAELKPLAQSHATKHKIPIKYLEFISEAIIHVLHS 117 2M6ZA QVKGHGKKVADALTNAVAHVD--DMPNALSALSDLHAHKLRVDPVNFKLLSHCLLVTLAA 111 2M6ZB KVKAHGKKVLGAFSDGLAHLD--NLKGTFATLSELHCDKLHVDPENFRLLGNVLVCVLAH 116 1MWB: MGVPEDLIAEV-AAVAGAPAHKRDVLNQ---------124 1MYF: -RHPGDFGADAQGAMNKALELFRKDIAAKYKELGYQG 153 2M6Z:A -HLPAEFTPAVHASLDKFLASVSTVLTSKYR------141 2M6Z:B -HFGKEFTPPVQAAYQKVVAGVANALAHKYH------146

! 5 Table 1 :

 51 List of the NMR structural ensembles used in this work. In the last column, cavity or tunnel lining residues are underlined and mechanical nucleus residues are highlighted in bold red.

			MS residues		Val17, Ile28, Ala53, Met55, Leu69, Leu72, Glu83,	Leu104, Ile107
	Maximum Cα RMSD	between two	representative models	(in Å)	2.10
	Representative NMR	models (starting with the	most representative one)	2,5,1,6,8
		Residues	number	153
		number of	NMR models	12
		PDB NMR	structures	1myf
			Protein name		Globins

, Ile111, Leu135 Sequences identity range : 15-45 %

	Val62
	2.35
	16,2,13,15,18
	141
	20
	2m6z-A

, Leu66, Phe98, Leu101, Ser102, Leu105, Val132 MN with 3MS positions/4

	Trp15, Ala27, Gly64, Val67, Phe71, Asn102, Leu106,	Gly107, Leu110, Val134	Ser2, Phe21, Val25, His46,
	1.60	2.65
	16,2,13,15,18	17,15,19
	146	123
	20	20
	2m6z-B	1mwb

Phe50, Ala54, Val87, His117 Dihydrofolate Reductase

	Phe3, Leu4, Trp5, Phe30, Gln33, Thr34, Val95,	Ala97, Gly98
	2.00
	1,6,22,23,25
	162
	25
	2l28

, Phe103 Sequences identity range : 23-38 %

	Phe5
	2.40
	1, 7, 5, 6, 9, 12
	162
	15
	2kgk

, Met6, Val7, Asn19, Leu21, Phe96, Gly97, Tyr102 MN with 3MS positions/4

	Ser5, Val6, Ala7, Glu20, Val99, Ile100, Gly101	Cys6, Ile7, Val8, Trp113, Ile114, Val115, Gly116,	Tyr121	Phe31
	1.52	0.90	1.80
	7,9,12,20	3,6,10,13,19,21,24	5,7,8,14,15
	162	186	146
	20	25	20
	2ith	1yho	2mvz
				Cyclophilin A

, Gly57, Met87, Phe101, Ile103, Phe118 Sequences identity range : 34-41 %

	Phe8, Leu24, Asn35, Phe36, Ser40, Phe 53, Gly65,	Leu98, Ser99, Met100, Phe112
	0.74
	6,18
	165
	20
	1oca

, Phe113, Ile114 MN with 2MS positions/3

	Leu18, Phe32, Gln56, Gly57, Gly59, Ile88, Ala91,	Gln102, Phe103, Phe104, Phe125, Gly126	Gly9, Leu24
	2.30	2.13
	1,2,8,9	10, 8, 7, 6, 9
	166	191
	12	10
	1clh	2lgj
			Peptidyl-tRNA hydrolase

, Gly25, Val92, Ile93, His94 Sequences identity range : 39-82 %

	Gly25, Ile93	Leu9, Val10, Gly11, Ala13, Ala26, Gly27,Val30,	Met93, Ala95, His96, Leu136, Leu138	His8, Ile9, Gly46, Phe61, Val64,
	1.62	1.34	1.64
	5, 26, 29	6, 4, 2	15, 12, 11, 16, 3
	191	197	92
	40	10	18
	2jrc	2mjl	1jns
		MN with 2MS positions/3	Parvulin

Ile85, Ile86 Sequences identity range : 31-55 %

	His59, Leu60, Leu61, Cys113,
	1.52
	7, 3, 4, 10
	114
	10
	1nmw

Ile158, Ile159 MN with 4MS positions/5

	His12, Ile13, Leu14, Ser68, Ser72, Asp105, His114,	Ile115	Cys12, His14, Phe36, Leu56, Phe59, Phe68, Val92,	Ile93	His146
	2.60	2.91	3.27
	19, 18	3, 20, 8, 19	6, 11, 12
	120	97	111
	20	20	25
	1j6y	2rqs	2jzv

, Ile147, His239, Ile240, Ile241 1