Probing micro-solvation in numbers : The case of neutral dipeptides in water.

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1 ELETRONI SUPPLEMENTARY INFORMATION Probing micro-solvtion in numbers : The cse of neutrl dipeptides in wter. Pnteleimon G Tkis, Konstntinos D. Ppvsileiou, b Louks D. Peristers, c Vsilios S. Melisss* b nd Anstssios N. Trognis* Deprtment of Biologicl Applictions nd Technology, Biophysics Lbortory, University of Ionnin, GR-45 0 Ionnin, Greece, b Deprtment of hemistry, University of Ionnin, GR-45 0 Ionnin, Greece c Scienomics Srl, 7 squre Edourd VII, Pris, Frnce *Authors to whom correspondence should be ddressed: Vsilios S. Melisss: E-mil: melisss@chem.uth.gr, Tel.: , Fx: nd Anstssios N. Trognis: E-mil: trogni@cc.uoi.gr, Tel.: , Fx:

2 Index Pges Further detils for eqns (2) nd (5)... S2 The cse of internl motion (Lipri nd Szbo)... S3 From eqns (5) nd (6) to the clcultion of the weighted correltion times... S5 Full expression of eqn ()... S6 The mesured relxtion times (T ) for 3 α nd 3 β nuclei t three mgnetic fields... S7 Tble S.... S7 Tble S2.... S8 omprison between relxtion rtes for 3 α nd 3 β nuclei... S9 Tble S3... S9 Tble S4.... S0 Tble S5.... S Fig. S.... S2 Dipeptides correltion times ( τ ) from 3 α nd 3 β relxtion dt... S3 Tble S6.... S3 Dipeptides correltion times ( τ ) from 3 α nd 3 β relxtion dt vs. their M W... S5 Tble S7.... S5 Tble S8.... S5 Fig. S2.... S6 Alnine Dipeptide Fully optimized structure by DFT... S7 Fig. S3.... S7 H-bonds interction energies (E int ) clcultion... S8 Tble S9.... S8 Fig. S4.... S9 Alnine Dipeptide/0 H 2 Os complex... S20 Fig. S5.... S20 Supplementry References... S2 Geometricl detils nd energetics of fully optimized AD/(H 2 O) n (n=0, 7-9) supermolecules... S22 AD/(H 2 O) 0 (Fig. S3)... S22 AD/(H 2 O) 7 (Fig. 4)... S24 AD/(H 2 O) 8 (Fig. 4b)... S26 AD/(H 2 O) 9 (Fig. 4c)... S28 S

3 Further detils for eqns (2) nd (5) As it ws mentioned, sclr contribution is insignificnt to T determintion nd it cn be clculted by the following eqution: T, i N, sc since J coupling constnt nd T, N i JNT i 3 N 2 N 2, N 2 T 2 2, N, (S) relxtion time of the nitrogen toms re known. J coupling constnt is pproximtely equl to 30 Hz, wheres T vlues, N i re determined by the width t the hlf height (Δν /2 ) of the 4 N-NMR pek. Our previous studies, concerning mino cids nd cetyl-mino cids 2 mino nd imino groups hydrtion, respectively, indicted tht T 2 vlues for mino cids lie between, N 36 to 08 Hz nd for cetyl-mino cids between 70 to 495 Hz. Nevertheless, the sclr contribution to T relxtion is very smll (< 0.0 %) nd the overll estimted error in the clcultion of the relxtion times rtio [eqn (5)] is less thn 0-6 %, if no subtrction of the sclr contribution tkes plce. In fct, none of the terms in eqn (2) cn be clculted precisely, minly due to the vrition in distnce r between i-crbon nd i- or j-protons for ll studied molecules nd it cnnot be defined ccurtely. 2 N However, X-ry diffrction mesurements showed tht the men proton-crbon (-H) distnce is pproximtely ~. Å. 3 Moreover, our reserch group clculted by the mens of DFT nd MP2 theoreticl clcultions 2 the bove distnce for vrious mino cids nd dipeptides resulting in Å. This smll vrition in proton-crbon distnce contributes quite significntly (6 % devition) to the clcultion. onsequently, the ccurte determintion of the correltion time,, demnds either the knowledge of the exct proton-crbon distnces or n independent of them novel method for clcultion. S2

4 The cse of internl motion (Lipri nd Szbo) According to Lipri nd Szbo, 4 in the cse of internl motion the spectrl density is given by the expression: 2 S S Ji( ), where S is generlized order prmeter, which is the mesure of motion s sptil restriction degree nd τ equls to: e, (S2) (S3) where e is n effective correltion time, which is mesure of the internl motion s rte. Thus, the longitudinl relxtion time (T ), described by eqn (), will be the sum of two terms. Nmely, one term will be chrcterized by the correltion time,, nd multiplied by the fctor S 2, while the other term will be chrcterized by the correltion time e e nd multiplied by the fctor S 2 : T, i 2 2,, e S f S f, e where f, is the second term in eqn (). (S4) onsidering the bove, someone could wonder if eqn (5) still permits the ccurte clcultion of. The error of using eqn (5) s is (without tking into considertion the effect of the internl motion), cn be clculted by expnding eqn (5), fter the inclusion of eqn (S4) in it, in Mclurin series (since e is expected to be very smll, nmely few ps) round e 0 s. Inclusion of eqn (S4) to eqn (5) leds to: S3

5 f,,, 2 e S H H 2 S e e e 2 e H e H 2 2 e e e S H H 2 S e e 2 e e H e H 2 2 e e e (S5) Expnsion of the bove eqution in Mclurin series results in: where n,,,,,, 2 e 2 2 f n, f,0,0, n! f e (S6) n f n is the n-th derivtive of eqution f. The term,, 2,0 f represents the T rtio t two different mgnetic fields when no internl motion is tken into considertion [nmed eqn (5)] therefore, the term n f,, 2,0 error of the pproximtion. n represents the n! e Assuming tht S 0.8, since slower motion domintes in relxtion processes 0 (ccording to Lipri S vlue is expected to be lmost one), 0 s, 0 s, re the proton nd crbon resonnces t nd MHz nd 2 re the resonnces t nd MHz respectively, the clculted error is %. As result, the estimted error in eqn (5) is much less thn 0. %, proving tht eqn (5) n still leds to the ccurte clcultion of the correltion time,. e S4

6 From eqns (5) nd (6) to the clcultion of the weighted correltion times The inclusion of eqn () to eqns (5) nd (6) results in two equtions whose expnsion in Mclurin series until the 3 rd term leds to: nd T, Oi, H H H 2H T, Oi, 2 (S7) T, Oi, T, Oi, H H 2 2H 2H P P P P P P 2 2 b, b b, b, b, (S8) Furthermore, tking into considertion tht the st terms of eqn (S7) nd eqn (S8) re equl, led to their 2 nd terms equlity nd 2 nd degree polynomil whose solution round results in the weighted verge clcultion of the correltion times through eqn (S9): P P P P P P (S9) 2 2 b, b b, b, b, S5

7 Full expression of eqn () T, Oi, T, Oi, 2 f,, M 2 W 3 6 P c MW H cmw cmw H cmw 3 6 Pb cmw 8Nw H cmw 8Nw cmw 8Nw H cmw 8Nw 3 6 P c M cm cm cm W H W 2 W 2 2H W P cm 3 6 8N b W w 2 cm N cm N cm N H W w 2 W w 2 2H W w S6

8 The mesured relxtion times (T ) for 3 α nd 3 β nuclei t three mgnetic fields Tble S. The 3 α nuclei mesured T vlues (t 298 K) of ech dipeptide t three mgnetic fields (± indictes the StdDev with n = 20). Dipeptides (-NH 2 -OOH) M W ph = MHz 400 MHz 250 MHz T (s) for 3 α Al Gly ± ± ± ± ± ± 0.02 Gly Al ± ± ± ± ± ± Αl Al ± ± ± ± ± ± Gly Ser ± ± ± ± ± ± Gly Leu ± ± ± ± ± ± Vl Ser ± ± ± ± ± ± Vl Thr ± ± ± ± ± ± 0.08 Thr Leu ± ± ± ± ± ± 0.08 Al Phe ± ± ± ± ± ± 0.06 Phe Al ± ± ± ± ± ± 0.04 Vl Met ± ± ± ± ± ± 0.09 Tyr Al ± ± ± ± ± ± 0.0 Met Leu ± ± ± ± ± ± 0.06 Phe Vl ± ± ± ± ± ± 0.07 α M W is the moleculr weight of dipeptides zwitterionic form. S7

9 Tble S2. The 3 β nuclei mesured T vlues (t 298 K) of ech dipeptide t three mgnetic fields (± indictes the StdDev with n = 20). Dipeptides (-NH 2 -OOH) M W ph = MHz 400 MHz 250 MHz T (s) for 3 β Al Gly ± // ± 0.00 // ± 0.00 // Gly Al 46.4 // ± // ± 0.02 // ± 0.00 Αl Al ± ± ± ± ± ± 0.00 Gly Ser 62.4 // ± 0.06 // ± 0.05 // ± 0.03 Gly Leu // ± 0.04 // ± 0.0 // ± 0.04 Vl Ser ± ± ± ± ± ± 0.04 Vl Thr ± ± ± ± ± ± 0.08 Thr Leu ± ± ± ± ± ± 0.0 Al Phe ± ± ± ± ± ± 0.0 Phe Al ± ± ± ± ± ± Vl Met ± ± ± ± ± ± 0.0 Tyr Al ± ± ± ± ± ± 0.0 Met Leu ± ± ± ± ± ± 0.0 Phe Vl ± ± ± ± ± ± 0.06 α M W is the moleculr weight of dipeptides zwitterionic form. S8

10 omprison between relxtion rtes for 3 α nd 3 β nuclei The relxtion rte of 3 nucleus is equl to / T, where N is the number of the ttched protons to the crbon. The following Tbles S3-S5 describe the corresponding relxtion rtes of 3 α nd 3 β nuclei nd their differences T T / / for ech studied dipeptide s component t three mgnetic fields: 3 3 Tble S3. The 3 α nd 3 β nuclei mesured relxtion rtes / T t 500 MHz (± indictes the StdDev with n = 20). Dipeptides (-NH 2 -OOH) M W S9 vlues (t 298 K) of ech dipeptide ph = MHz (s - ) for 3 α / T (s - ) for 3 β / T / T / T b 3 3 Al Gly ± ± ± // // Gly Al ± ± 0.03 // ± // Αl Al ± ± ± ± Gly Ser ± ± 0.02 // ± 0.05 // Gly Leu ± ± // ± // Vl Ser ± ± ± ± Vl Thr ± ± ± ± Thr Leu ± ± ± ± Al Phe ± ± ± ± Phe Al ± ± ± ± Vl Met ± ± ± ± Tyr Al ± ± ± ± Met Leu ± ± ± ± Phe Vl ± ± ± ± α M W is the moleculr weight of dipeptides zwitterionic form. b / T / T correspond to ech dipeptide s component. vlues 3 3 (s - )

11 Tble S4. The 3 α nd 3 β nuclei mesured relxtion rtes / T t 400 MHz (± indictes the StdDev with n = 20). Dipeptides (-NH 2 -OOH) M W vlues (t 298 K) of ech dipeptide ph = MHz (s - ) for 3 α / T (s - ) for 3 β / T / T / T b 3 3 Al Gly ± ± ± 0.0 // // Gly Al ± ± 0.04 // 0.68 ± 0.04 // Αl Al ± ± ± ± Gly Ser ± ± 0.06 // 0.70 ± 0.05 // Gly Leu ± ± // 0.92 ± 0.08 // Vl Ser ± ± ± ± Vl Thr ± ± ± ± Thr Leu ± ± ± ± Al Phe ± ± ± ± Phe Al ± ± ± ± Vl Met ± ± ± ± Tyr Al ± ± ± ± Met Leu ± ± ± ± Phe Vl ± ± ± ± α M W is the moleculr weight of dipeptides zwitterionic form. b / T / T correspond to ech dipeptide s component. 3 3 (s - ) vlues S0

12 Tble S5. The 3 α nd 3 β nuclei mesured relxtion rtes / T t 250 MHz (± indictes the StdDev with n = 20). vlues (t 298 K) of ech dipeptide Dipeptides (-NH 2 -OOH) M W ph = MHz (s - ) for 3 α / T (s - ) for 3 β / T / T / T b 3 3 (s - ) Al Gly ± ± ± 0.02 // // Gly Al ± ± // 0.64 ± 0.0 // Αl Al ± ± ± ± Gly Ser ± ± 0.07 // ± 0.03 // Gly Leu ± ± // ± // Vl Ser ± ± ± ± Vl Thr ± ± ± ± Thr Leu ± ± ± ± Al Phe ± ± ± ± Phe Al ± ± ± ± Vl Met ± ± ± ± Tyr Al ± ± ± ± Met Leu ± ± ± ± Phe Vl ± ± ± ± α M W is the moleculr weight of dipeptides zwitterionic form. b / T / T correspond to ech dipeptide s component. vlues 3 3 Obviously, 3 relxtion rtes depend on the mgnetic field [eqn ()], however their differences, nmely in our cse / T / T coincidence for both 3 α nd 3 β nuclei. S, for the three mgnetic 3 3 fields, re independent of the mgnetic field. Therefore, s indicted in Fig. S (see below), lmost ll / T / T vlues lie between the 3 3 [2 (StdDev)] = round their men vlue, 5 demonstrting / T vlues

13 Fig. S. omprison between T T α nd 3 β nuclei relxtion rtes. Since, the / / vlues for the three mgnetic fields re independent of the mgnetic field, they re plotted vs. dipeptides M W. Almost ll vlues (except of 7, n = 72) lie between the clculted ± (2 StdDev) round their men vlue T 3 T s. Obviously, / 3 T 3 nd / T 3 / / coincide. vlues S2

14 Dipeptides correltion times ( τ ) from 3 α nd 3 β relxtion dt Tble S6. The clculted vlues from 3 α nd 3 β T vlues of ech dipeptide by eqn (5). Dipeptides (-NH 2 -OOH) M W α 3 α b (s) S3 3 β b (s) Al-Gly ± ± 0.07 Al-Gly ± ± Al-Gly ± ± 0.03 Al-Gly ± 0.07 Al-Gly ± 0.08 Al-Gly ± Gly-Al ± Gly-Al ± Gly-Al ± Gly-Al ± ± Gly-Al ± ± Gly-Al ± ± 0.34 Al-Al ± ± Al-Al ± ± 0.03 Al-Al ± ± 0.74 Al-Al ± ± 0.06 Al-Al ± ± Al-Al ± ± Gly-Ser ± Gly-Ser ± Gly-Ser ± Gly-Ser ± ± Gly-Ser ± ± 0.02 Gly-Ser ± ± Gly-Leu ± Gly-Leu ± 0.07 Gly-Leu ± Gly-Leu ± ± Gly-Leu ± ± 0.07 Gly-Leu ± ± Vl-Ser ± ± Vl-Ser ± ± 0.00 Vl-Ser ± ± 0.02 Vl-Ser ± ± 0.0 Vl-Ser ± ± Vl-Ser ± ± 0.04 Vl-Thr ± ± Vl-Thr ± ± Vl-Thr ± ± Vl-Thr ± ± 0.09 Vl-Thr ± ± 0.00

15 Vl-Thr ± ± Thr-Leu ± ± Thr-Leu ± ± Thr-Leu ± ± Thr-Leu ± ± Thr-Leu ± ± Thr-Leu ± ± 0.42 Al-Phe ± ± Al-Phe ± ± Al-Phe ± ± 0.54 Al-Phe ± ± 0.79 Al-Phe ± ± Al-Phe ± ± Phe-Al ± ± 0.0 Phe-Al ± ± Phe-Al ± ± Phe-Al ± ± 0.0 Phe-Al ± ± Phe-Al ± ± Vl-Met ± ± Vl-Met ± ± 0.06 Vl-Met ± ± Vl-Met ± ± 0.00 Vl-Met ± ± 0.09 Vl-Met ± ± Tyr-Al ± ± 0.30 Tyr-Al ± ± 0.40 Tyr-Al ± ± 0.64 Tyr-Al ± ± Tyr-Al ± ± 0.04 Tyr-Al ± ± 0.8 Met-Leu ± ± Met-Leu ± ± Met-Leu ± ± 0.08 Met-Leu ± ± 0.65 Met-Leu ± ± Met-Leu ± ± Phe-Vl ± ± 0.07 Phe-Vl ± ± 0.03 Phe-Vl ± ± Phe-Vl ± ± 0.02 Phe-Vl ± ± Phe-Vl ± ± α M W is the moleculr weight of dipeptides zwitterionic form. b The correltion times ( ) re multiplied by 0 0. They were clculted by eqn (5) for three mgnetic fields s follows: 400 MHz / 500 MHz, 250 MHz / 500 MHz nd 250 MHz / 400 MHz, corresponding to ech dipeptide s component (in bold for ech cse) 3 α nd 3 β nuclei, respectively. S4

16 Dipeptides correltion times ( τ ) from 3 α nd 3 β relxtion dt vs. their M W st order dt fitting Tble S7. Sttistics for lest-squres liner ( st degree polynomil) regression nlysis of dipeptides correltion times ( ) from 3 α nd 3 β T vlues vs. their M W (see Fig. ). α 0 α R 2 S.S. 3 α (Fig. ) Dipeptides (ph = 6.0) ± ± β (Fig. b) Dipeptides (ph = 6.0) ± ± nd order dt fitting Tble S8. Sttistics for lest-squres nonliner (2 nd degree polynomil) regression nlysis of dipeptides correltion times ( ) from 3 α nd 3 β T vlues vs. their M W (see below Fig. S2). α 0 α α 2 R 2 S.S. 3 α (Fig. S2) Dipeptides (ph = 6.0).730 ± ± ± β (Fig. S2b) Dipeptides (ph = 6.0).0070 ± ± ± S5

17 Fig. S2. Sttistics for lest-squres nonliner regression (2 nd degree polynomil) nlysis of dipeptides correltion times ( ) from 3 α nd 3 β T vlues. () The correltion times derived from 3 α Τ relxtion dt vs dipeptides M W. (b) The correltion times,, derived from 3 β Τ relxtion dt vs dipeptides M W. S6

18 Alnine Dipeptide Fully optimized structure by DFT Fig. S3. The fully optimized neutrl ph structure of lnine dipeptide in queous solution. The unconstrint optimiztion performed t the X3LYP/cc-pVTZ level of theory using the IEF-PM model for bulk wter nd chrcterized by vibrtionl nlysis t the sme level of theory, resulting in the most stble AD structure. Geometricl detils nd energetics of the bove fully optimized structure re reported t the end of ESI. S7

19 H-bonds interction energies (E int ) clcultion The H-bond interction energy is the energy of interction of ll the seprted molecules in the solvted complexes nd it cn be clculted through the following eqution: E E E E, (S0) int where E is the energy of the AD/H 2 Os supermolecule, nd E nd E re the single-point energies of monomers A (energy clcultion of the AD structure t the sme intermoleculr configurtion s in the fully optimized supermolecule in the bsence of the H-bonded H 2 Os cluster counterprt) nd B (energy clcultion of the H-bonded H 2 Os cluster structure t the sme intermoleculr configurtion s in the fully optimized supermolecule in the bsence of the AD counterprt), respectively. int Nmely, comprison between the interction energies E for the AD/(H 2 Os) n (n = 7-9) supermolecules indictes the most fvorbly stbilized complex. All energy clcultions performed t the X3LYP/cc-PVTZ level of theory nd the IEF-PM model ws pplied to mimic queous solution. The following Supplementry Tble S9 collects the electronic nd interction energies for the hydrted AD/(H 2 Os) n (n = 7-9) nd Supplementry Fig. S4 presents their interction energies evolution. Tble S9. Totl energy, E tot, (in Hrtree) nd interction energy, E int, (in kcl mol - ) for the hydrted AD/(H 2 Os) n (n = 7 9) supermolecules clculted t X3LYP/cc-PVTZ level of theory, pplying the IEF-PM model for bulk wter. AD/7 H 2 Os AD/8 H 2 Os AD/9 H 2 Os -E tot E int S8

20 Fig. S4. omprison between E int for the three AD/H 2 Os supermolecules. The AD/8 H 2 Os supermolecule exhibits the highest interction energy mong the ones studied, implying its extr stbiliztion nd providing further support to our spectroscopic results. S9

21 Alnine Dipeptide/0 H 2 Os complex Fig. S5. DFT clcultions of lnine dipeptide/0 H 2 Os supermolecule. DFT clcultions demonstrted tht the tenth H 2 O (w 0 ) directly intercts either with () α or (b) H 3 of AD. Both H-bond lengths vry between Å. omprison between these H-bond lengths nd those of ll other bound H 2 Os with the polr sides of AD (<.9 Å) indictes the wekness of the w 0 H-bonds, s expected from similr studies, 6,7 implying their insignificnt contribution to the AD vlues. S20

22 Supplementry References. A. N. Trognis,. Tsnktsidis, nd I. P. Gerothnssis, J. Mgn. Reson. Ser. B, 2003, 64, P. G. Tkis, V. S. Melisss, nd A. N. Trognis, New J. hem., 202, 36, A. A. Al-Krghouli, F. E. ole, M. S. Lehmnn,. F. Miskell, J. J. Verbist, nd T. F. Koetzle, J. hem. Phys., 975, 63, G. Lipri nd A. Szbo, J. Am. hem. Soc., 982, 04, G. Tsifoulis, V. Exrchou, P. P. Tziov, E. Birktri, I. P. Gerothnssis, nd A. N. Trognis, Anl. Bionl. hem., 20, 399, M. P. Bhte, J.. Woodrd, nd M. A. Meht, J. Am. hem. Soc., 2009, 3, B. Yogeswri, R. Knkrju, S. Boopthi, nd P. Kolndivel, J. Mol. Grphics Modell., 202, 35, 20. S2

23 Geometricl detils nd energetics of fully optimized AD/(H 2 O) n (n=0, 7-9) supermolecules (hrge = 0) 23 Atoms E = Hrtrees AD/(H 2 O) 0 (Fig. S3) X Y Z N H O H H N H H H H H O O S22

24 H H H H S23

25 (hrge = 0) 44 Atoms E = Hrtrees AD/(H 2 O) 7 (Fig. 4) X Y Z N H O H H H O H H O H H O H N H H S24

26 H H H O O O H H O H H O H H O H H H H H H S25

27 (hrge = 0) 47 Atoms E = Hrtrees AD/(H 2 O) 8 (Fig. 4b) X Y Z N H O H H H O H H O H H O H N H H S26

28 H H H O O O H H O H H O H H O H H H H H H O H H S27

29 (hrge = 0) 50 Atoms E = Hrtrees AD/(H 2 O) 9 (Fig. 4c) X Y Z N H O H H H O H H O H H O H N H H S28

30 H H H O O O H H O H H O H H O H H H H H H O H H S29

31 O H H S30