J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1857-1864 Photoinduced Electron Transfer in a-Helical Poly(L4ysine) carrying RandomIy Dist r ibu ted Donor-Acce pto r Pa irs A Kinetic and Conformational Statistics Investigation Basilio Pispisa* and Mariano Venanzi Dipartimento di Scienze e Tecnologie Chimiche, Universita ' di Roma ' Tor Vergata ', 00133 Roma, Italy Antonio Palleschi Dipartimento di Chimica, Universita' di Roma 'La Sapienza ', 00185 Roma, Italy The photophysics of protoporphyrin IX (P) and 1-naphthylacetic acid (N), covalently bound to &-amino groups of poly(L-lysine) (PL) in a [PI : [N] molar ratio of 0.25, were investigated as a function of pH. Differential circular dichroism spectra and polarized fluorescence data on PNPL and blank samples (NPL and PPL) suggest that the amide bond in the chromophore linkages slows down the internal rotation of the aliphatic side-chains of the polypeptide. The conformational mobility of these linkages is further reduced by varying the pH from 7 to 11, the a-helical conformation of the backbone chain making the whole structure stiffer.Steady-state fluorescence, transient-absorption spectra and time-decay measurements indicate that quenching of excited naphthalene chiefly results from interconversion to the triplet state when the polymeric matrix is in a random coil conforma- tion (pH ca. 7) and from intramolecular electron transfer, P -+ 'N*, when it is in an a-helical conformation (pH ca. 11).The kinetic law of these processes, based on a two-state model for the polypeptide matrix, is presented.The specific rate constant of the photoinduced electron transfer is 3.1 x lo7 s-' (25"C),in very good agreement with that obtained from the lifetimes of naphthalene fluorescence in a-helical PNPL and NPL (pH ll),i.e. 2.7 x lo7 s-' . PNPL solutions exhibit very little exciplex fluorescence, whatever the pH, suggesting a relatively large average separation distance between the chromophores, in agreement with the results of a conformational statistics analysis on the fully ordered PNPL. The probability distribution of centre-to-centre distances between the chromophores, as obtained by adopting a rotational isomeric state model of the probe linkages, allowed us to reproduce the experimental fluorescence decay curves and estimate the parameters governing the electron- transfer process . Photoinduced intramolecular electron transfer in biomimetic systems is a subject of considerable interest because of its implications in several fields, such as photochemistry, polymer chemistry, biology and biotechnology.'v2 Among the different materials used, synthetic polypeptides carrying cova- lently bound fluorophores are well suited for obtaining basic information on this type of process because they are both structurally simple and well defined.3 Direct contact between donor (D) and acceptor (A) species is generally believed to be a requirement for charge separa- ti~n,~and several experiments support the idea that a through-bond interaction between D and A is more effective than a through-space intera~tion.~ It has been recently shown, however, that electron transfer in a-helical polypeptides carrying covalently bound PA pairs chiefly occurs by the latter mechani~m,~ the semirigid helical conformation being excluded to take part in the process, at least in the nanose- cond timescale.We have recently reported the photophysics of proto-porphyrin IX (P) and 1-naphthylacetic acid (N), covalently and randomly attached to &-amino groups of poly(L-lysine), showing that the conformational equilibria in solution of PNPL system affect the excited-state processes of the bound chromophore~.~ We now present the results of the calculations on the dis- tribution of the interchromophoric distances in the or-helical PNPL.For the sake of comparison with computed values, we also summarize here some of the experimental material pre- viously reported, together with new results on the solution properties of PNPL and on the quenching process of excited naphthalene. The probability distribution of centre-to-centre distances between the N and P molecules in the fully ordered PNPL was evaluated by a conformational statistics analysis, making use of a rotational isomeric state model of the chromophore linkages. We were thus able to reproduce the fluorescence decay curves and to get a reliable estimate of the parameters governing the electron transfer process, P --* IN*, that occurs only when PNPL attains an a-helical conforma- tion.Experimental Materials The following abbreviations are used throughout the text. Protoporphyrin IX : P ; naphthyl chromophore : N ; poly(L-lysine): PL; poly(L-lysine) carrying both N and P groups: PNPL; poly(L-lysine) carrying P or N group only: PPL or NPL, respectively. PNPL, PPL and NPL samples, which have the chromo- phores bound to &-amino group of the side-chains of poly(L- lysine), were prepared using analytical-grade reagents. A typical procedure was as follows. To a water/DMF (24:76, v:v) mixture at O"C, containing 1.13 x monomol of poly(L-1ysineeHBr) (Sigma), 1.13 x mol of 1-naphthylacetic acid (Aldrich), 3.39 x mol of N(Et), (C. Erba) and 1.13 x lop4mol of protoporphyrin IX (Aldrich), 3.39 x mol of l-ethyl-3-(3'-dimethylaminopropyl)car-bodiimine hydrochloride (Nova biochem) were added.After stirring for 2 h at 0°C and standing at room temperature for about 18 h, the mixture was lyophilized and then dissolved in 50 ml of water. The solid residue was filtered and the solution dialysed against 0.01 mol dm-3 HC1, using pre-treated dialy- sis tubes (A. Thomas Co., Philadelphia). After freeze-drying, PNPL was obtained, with a yield of 75%. Blanks were pre- pared following the same procedure, and the yields were 38% (PPL) and 62% (NPL). The amount of bound P and N molecules was determined by both 'H NMR and absorption measurements, the agree- ment being better than 10%. The naphthalene content is 8.7% in NPL and 5.2% (w) in PNPL, while the porphyrin content is 4.1% in PPL and 4.2% (w) in PNPL, the molar ratio between the chromophores in PNPL being thus [PI :[N] = 0.25.Elemental analyses were in good agreement with these results. Found: C% 47.25, 46.65 and 45.86; N% 15.04, 15.83 and 15.26; H% 7.48, 7.71 and 7.33 for NPL, PPL and PNPL, respectively. Calculate: C% 48.21, 45.13 and 47.83; N% 15.86, 16.78 and 16.10; H% 7.79, 7.89 and 7*26for (C,8N202H,0XC60N2H12 * HC1)10 9 (C40N604H44) (C60N2H12 HC1)77 and (C18N202H20)4(C40N604H44)(C60N2H12HC1)68, respectively. -Porphyrin molecules were linked to &-amino groups of poly(L-lysine) by only one pendant carboxylic group, the ratio of the NMR signals between the porphyrin B-protons (6 x 3.2)7 and the 6-protons of the substituted side-chains of the polypeptide (6 x 2.6) being around 1 : 2.The major portion of the solid residue of the syntheses (see above) is, instead, formed by poly(L-lysine) chains cross-linked by both carboxylic groups of porphyrin. Bis-Tris Propane? (pH = 6.5-9) and Caps$ (9.5-11) buffers (Sigma) were employed in a concentration of 0.01 mol dm-3. All measurements were carried out on freshly prepared solu- tions, using doubly distilled water. Methods All fluorescence experiments were carried out in quartz cells, using solutions that were bubbled for about 20 min with ultrapure nitrogen. Steady-state fluorescence spectra were performed on a Hitachi MPF-2D fluorimeter and fluores- cence anisotropy measurements were performed on a SPC Fluorolog-SPEX apparatus, equipped with Glan-Thomson polarising prisms.Time-decay measurements were carried out using an excimer pumped dye laser, frequency doubled on a KDP crystal to produce 5 ns pulses of a few tens of mJ, tuned at 285 nm. The emisssion was focussed on a double mono- chromator tuned at 340 nm, with a resolution of 2 nm. The output of a 56DUVP photomultiplier was fed into a Tektro- nix R7912 AD digitizer (bandpass 400 MHz). The decay curves were fitted by a non-linear least-squares analysis to exponential functions by an iterative deconvolution method, using a conventional PC. Time-resolved emission spectra were obtained by the same apparatus, using a boxcar inte- grator with a time window of 5 ns. Transient absorption spectra were carried out by a flash- photolysis set-up, the pulsed excitation (308 nm) being achieved by a Xe/HCl excimer laser (Lambda Physik EMG 50E).The pulse width was about 15 ns, the laser energy <10 mJ per pulse, and the delay time <1 ns.The light (150 W Xe lamp) was examined through a Baird-Tatlock monochro- mator, a Hamamatsu R928 photomultiplier and then cap- tured by a Tektronix DSA602 transient digitizer. 'H NMR spectra were recorded on a Bruker AM 400 instrument operating at 400.135 MHz. The spectral width used was 14 ppm and a residual water resonance of 4.77 ppm was assumed for chemical shift calibration. Absorption spectra were recorded on a Jasco 7850 appar-atus, and circular dichroism (CD) measurements were carried out on a Jasco 5-600 instrument with appropriate quartz cells. The other apparatus has already been rep~rted.~,~ t Bis-Tris Propane is 1,3-bis[tris(hydroxymethyl)methylamino] propane.$ Caps is 3-(cycIohexylamino)-l-propanesulfonicacid. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Results and Discussion Differential Circular Dichroism and Polarized Fluorescence Spectra Circular dichroism spectra of both blanks (NPL and PPL) and PNPL show that in all cases the coil-to-a-helical tran- sition in the poly(L-lysine) matrix is shifted towards lower PH.~@)This shift is greater than 0.5 pH units in the case of PNPL, indicating a remarkable efficiency of the bulky, apolar N and P groups in increasing the stability of the a-helical structure in aqueous solution.Although the chromophores are bound to the main chain by a rather long spacer, i.e. [-(CH,),-NH-CO-CH,-naphthalene] or [-(CH,),-NH-CO-(CH,),-porphyrin ring], they experience a rotational mobility which is more hindered than that of polymer-free molecules, probably due to the amide bond in the substituted side-chains and intramolecular hydrophobic interactions between the probes. Fig. 1 illus- trates the differential circular dichroism (DCD) spectra of NPL and PNPL against PL at pH = 11.1, i.e. under condi- tions where the samples are in a-helical conformation. Naph- thalene exhibits extrinsic CD bands in the 'Bb and 'Cb absorption region (220-190 nm),3(a)79 despite the fact that it is bound far away from the chiral C" atom.This is a strong indication of hindered conformational mobility of the side- chains carrying N, which is enhanced by the presence of P molecules in the chain, because the rotational strength is defi- nitely larger in PNPL than in NPL. The lack of exciton split- ting suggests, however, that naphthyl groups are not regularly arranged around the ordered polymeric matrix. Exciton state in aromatic poly(a-aminoacid)s is normally achieved only when the chromophores are bound to the chiral atom in the backbone chain by the shortest possible linkage^.^'") By contrast, at pH 7, DCD spectra show only a weak (negative) background rotation below 200 nm, as one would expect owing to the flexibility of the disordered chains. The results of polarized fluorescence measurements on N (Aex = 280, Aem = 337 nm) and P (Aex = 503, A,, = 625 nm) in NPL, PPL and PNPL samples are fully consistent with the aforementioned data.Table 1 lists the relative variation of the anisotropy coefficient r, according to eqn. (l), where subscript h and c denote a-helical and coil states. On inspection of Table 1, it appears that the conforma- tional mobility of the probe linkages decreases on going from pH 7 to 11, the a-helical conformation of the backbone chain r 180 200 220 240 260 A/n m Fig. 1 Differential circular dichroism (DCD) spectra of (a) NPL and (b) PNPL against PL at pH 11.1 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Relative variation of fluorescence anisotropy coefficients N P sample ,pb ,p.c NPL 1.3 - PPL - 0.8 PNPL 4.9 2.0 a K = (ih-rc)/i, and r = [(I,,-ZJ(Zll331 nm; ' A,, = 503, A,, = 625 nm.+ 2ZJ; * A,, = 280, A,, = stiffening the whole structure. Furthermore, the observation that the fluorescence anisotropy coeficient of PNPL is larger than that of NPL or PPL indicates that the internal rotation of the probes in the former sample is more hindered than in the latter ones, i.e. that intramolecular interactions between N and P molecules are more effective than those between the same type of chromophores in the blanks. Steady-state and Time-resolved Fluorescence Steady-state fluorescence spectra show that exciplex emission (ca.420 nm) is minor, as illustrated in Fig.2, where the emis- sion spectra of PNPL at the two extreme conditions of pH 7 and 11 are reported. The spectra consist mostly of monomer fluorescence, with both the peak position and intensity of the exciplex being almost insensitive to pH (Fig. 2, insert). The results of time-resolved emission spectra by laser excitation at 285 nm (not shown) are consistent with this finding in that a broad emission peak at around 420 nm, characterized by a fast rise time (7'x 6 ns) and a strictly monoexponential time decay of 60 ns, was observed within the whole range of pH explored. The rate constant of exciplex formation was evaluated by eqn. (2),where @NpL = 0.25, @)pNpL = 0.1g4 and zo = 35 ns, the former being the quantum yields of N in the blank (NPL) and in PNPL at pH 7, and the latter the excited-state lifetime of naphthalene in NPL at the same pH.[The value of @NpL is quite similar to that of the free molecule (0.23),4*1'(b) indicat-ing the absence of photophysical interactions between the chromophore and backbone chain.] From the results, k, = 9.0 x lo6 s-', i.e. the rate of exci- plex formation is more than one order of magnitude slower than the timescale of local side-chain fluctuations, as deter- mined by 13C NMR relaxation measurements on the CBof X 20 .-0 $0 1859 Table 2 Fluorescence quantum yields of N and P chromophores at different pH values" A,, = 340 nm A,, = 625 nm PH %I? @)rNPL WPPLb %NPL 7.0 1 1 1 1 9.0 0.96 0.77 0.96 0.74 10.0 0.88 0.45 0.96 0.50 11.0 0.83 0.39 0.89 0.35 a They are normalized to the quantum yield at pH 7; A,, = 280 nm.Blank samples. helical poly(y-benzyl-L-glutamate).lo According to the afore- mentioned DCD and polarized fluorescence data, this is very likely because the P and N groups in the polypeptide chain experience a rather rigid arrangement. Where the fluorescence quantum yields of P and N in PPL, NPL and PNPL solutions, measured at 625 and 340 nm, respectively, are normalized to those at pH 7, the values of a',reported in Table 2, are obtained. The main inference to be drawn from this Table is that the quantum yields of both P and N in the blanks (WppLand WNpL)decrease by less than 20% on going from pH 7 to 11, while those in PNPL (WpNP,j lowers by more than 60% within the same range of pH.It appears, therefore, that quenching of N* by P effectively occurs as the amount of ordered polypeptide matrix increases, a process that cannot be ascribed to a Forster-type N* -+P energy transfer,l' otherwise increasing quantum yields of P emission would have been observed.12 Consistent- ly, the excitation spectra of P (Aern = 625 nm) do not exhibit any variation under pH changes, within the whole wave-length region explored (240-340 nm). We next investigated the time-resolved fluorescence as a function of pH. Fig. 3 shows typical decay curves of excited naphthalene in PNPL solutions at pH 7.7 and 10.8. No sig-nificant change was observed on varying sample concentra- tions within two orders of magnitude (10-5-10-3 mol dm- 3), which rules out the occurrence of interchain effects. The curves are described by a three-component exponen- tial decay, i.e. (z) = xiaizi (i = 1 to The first 3).3(')94(b)*'3 component is very short (d2 ns), partially overlapping the laser profile.The resolution time of our apparatus is, in fact comparable to early events, thus resulting in an inaccurate detection of the initial fluorescence decay following laser pulse. While deconvolution techniques can be, in principle, employed to successfully recover lifetime components 2-3 '5 0.4 c. .-!I 300 340 380 420 460 500 I A/nm 0 50 100 150 200 Fig. 2 Steady-state fluorescence spectra (Aex = 285 nm) of PNPL at time/ns pH (a) 7.0 and (b) 11.0.The insert shows the exciplex emission at the Fig.3 Time decay of naphthalene fluorescence in PNPL (Ae,,, = 340 same pH values. nm) at (a)pH 7.7 and (b)10.8. Curve (c)is the laser profile. 1860 35 30 v)F 25 c, 20 15 PH Fig. 4 Variation of the middle component of naphthalene time decay, z2 0, and of a-helical fraction of poly(L-lysine) in PNPL, fh (---), as a function of pH. +,70 (NPL). times shorter than the excitation pulse length,14 in our case an unavoidable scattering contamination, probably due to the polymeric nature of the samples, gives rise to a severe distortion of the first few tenths of channels of the decay profile. As a result, the very first part of the time decay curve cannot be fully analysed.However, the (7) values are insensi- tive to this effect because the other lifetime components refer to kinetic processes that take place on a much slower time- scale. The long-time component (z3= 60 ns) is pH-independent and reminiscent of the decay behaviour of exciplex emission, as observed by time-resolved emission spectra (see above). The middle component, z,, is the only one that varies with pH, thus appearing to be sensitive to the interchromophoric distances and hence to the structural fea- tures of the polypeptide. This is shown in Fig. 4,where the 2-helical fraction in the polymeric matrix (fh) is also reported. It was obtained by the conventional expression bobs = CAEh fh + (1 -fh)AcC], where the differential molar absorption coefficients, A&, measured at 222 nm, are as follows: AE~= -9.3 and AE~0.8 dm3 mol- ' cm-'for the helical and coil = form of PNPL, respectively.The same sigmoidal trend of z2 us. pH was observed by lowering the temperature from 25 to 8°C. By contrast, the time decay of N* in NPL, zo, remains nearly constant when the pH is increased, as shown in Fig. 4. Comparison between the relative quenching eficiencies of steady-state (Q$pL/QNpL) and time-resolved ((z)/zo) fluores-cence is good, within experimental errors, at all values of pH investigated. This result, illustrated in Fig. 5, suggests that a fast quenching process or (strong) ground-state interactions are absent. [@:ApL is the overall quantum yield, as given by 0.6' ' ' ' ' ' ' ' ' ' ' 7 a 9 10 11 12 PH Fig.5 Relative quenching efficiencies, from (a) time-resolved (z)/zo and (b) steady-state @p&/DNPLmeasurements, as a function of pH J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 @FApL= QE + QpNpL, where QE = QNpL -a,,,, = 0.06 (PH 7) is the quantum yield of the exciplex. Note the good agree- ment between k,, as obtained by eqn. (2), and k, = @&' = 0.06/6 x low9= 1 x lo7 s-', z' being the characteristic time of exciplex formation]. The time decay of P in PNPL (z" = 20 ns; Lex = 285, Lem = 625 nm) is insensitive to pH changes, while the quantum yield at 625 nm definitely decreases as pH increases. Since the quantum yield of P in the blank (PPL) is only slightly affected by pH (Table 2), one may safely conclude that the protoporphyrin ground state is involved in the quen- ching process of excited naphthalene.This, in turn, suggests that or-helical PNPL experiences a P -,N* electron-transfer process, an hypothesis confirmed by the results of transient absorption spectra, as shown below. Transient Absorption Spectra Transient absorption spectra of the PNPL solution at pH 6.8 [Fig. 6(a)] exhibit the characteristic triplet-triplet (T-T) absorption of protoporphyrin at around 430 nm and the bleaching of the Soret band at 400 nm.' 5(u) Instead, at pH 11 the T-T absorption is absent while there is a new band at ca. 460 nm [Fig. 6(b)]. Since the same spectra of bound naphthyl or protoporphyryl chromophore alone show the T-T absorp- tion,15 whatever the pH (not reported), one may conclude that interconversion to the triplet state is an effcient process, except for PNPL at high pH values where the quenching of N* by P predominates.Transient kinetics following laser flash excitation of PNPL at pH 11 suggest that the absorption at 460 nm is due to a long-lived species, with a slow decay (T',~ = 5.5 p).This finding is reminiscent of that found in flash-photolysis studies on functionalized, water-soluble porphyrins, where the absorption at 450-460 nm was assigned to a charged porphy- rin moiety, i.e. P*+.'6*1 In addition, kinetic experiments by oxygen saturation following laser excitation of PNPL solu-tions show that at pH 7 the second-order rate constant for bleaching the 430 nm absorption is 3 x lo9 dm3 mol-' s-', a value which agrees quite well with those reported for triplet quenching by 0, .15(')-16 Instead, at pH 11 the rate constant I I qd -0.2 0.05 I "' I -0.05 1 300 400 500 600 700 l/nm Fig.6 Transient absorption spectra of PNPL solutions at pH (a) 6.8 and (b) 11.0 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 for bleaching the 460 nm band is one order of magnitude smaller, i.e. 3 x lo8dm3 mol-' s-'.'' To summarize, besides minor exciplex formation that occurs regardless of the polypeptide conformation, quenching of excited naphthalene in PNPL takes place by two competi- tive, pH-dependent mechanisms. One is interconversion to the triplet state, with rate constant k,, and the other intra- molecular electron transfer from the porphyrin ground state to the singlet excited state of N (AGO FZ -0.6 eV"), with rate constant k,.The former process predominates at pH ca. 7 while the latter at pH ca. 11. A similar competition between triplet and (singlet) charge-separated states has been recently reported for a tetraphenyl-porphyrin-quinone system.20 Kinetics Interconversion to the triplet state and exciplex formation account for quenching of N* when PNPL is randomly coiled. However, as pH increases PNPL experiences an intramolecu- lar electron transfer, that eventually becomes the predomi- nant process. The role of the ordered polymer thus appears to be rather subtle: the rigidity of the structure allows the N and P groups to be sufficiently accessible so that the quen- ching can occur while maintaining sufficient separation to prevent the immediate charge recombination reaction.The aforementioned quenching pathways of N* in PNPL, under the extreme conditions of coil (c) and a-helix (h) state, are summarized in Scheme 1 while the kinetic law of these processes, based on the two-state model for the polymeric matrix [eqn. (3)], is given by eqn. (4),on the assumption that light excitation does not perturb the equilibrium conditions of the coil-to-a-helix transition, i.e. k&, = k,*/k,*. [The a-helical fraction is then given byf, = k,/(kd + k,)]. L(N-P)~-kd (N-p)h (3) kw In eqn. (3), (N-P)c(h)denotes PNPL in the ground state and k, and k, the specific rates for the forward and reverse reac- tion, while in eqn.(4),[A,*(h,]= [N*-P],,,,, where [A,*ch,] is the population of A* in the coil or helical state, respectively, and the subscripts of the specific rate constants refer to the processes illustrated in Scheme 1. \b107 k*, /.ixl (N*-P)E 3( N*-P), Scheme 1 Since (A*) = (A,*) + (A:), one can also write: where kobs (=(z)-') is given by eqn. (6a)or (6b),depending on which step is rate-determining.4(b)*21When the fastest process is the equilibrium A,*+A,*, and hence (A*) = [(k,/kd) (A:) + (A:)] because the coil and helical substates are in equilibrium at each pH, one gets eqn. (64, otherwise, i.e. when electron transfer is faster than any other process and hence one may safely assume that (A:) x 0, eqn.(6b). By plotting (/cobs -k, -kE) as a function Offh, within the pH range 7-11, a straight line is obtained, in full agreement with eqn. (64. This is shown in Fig. 7. From the least-squares analysis of the data, the intercept is k, = (1.2 & 0.3) x lo7 s-', in fairly good agreement with the rate constant for radi- ationless population of triplet states of aromatic molecules," and the slope (k, -kJ = (1.9 f0.3) x lo7 s-l (25°C). The specific rate constant for charge separation is then k, = (3.1 & 0.5) x lo7 s-', which compares very well with the electron transfer rate constant estimated from the lifetimes of N in PNPL and NPL at pH 11, i.e.(z; -z; ') = 2.7 x lo7 s-at 25 and 1.8 x lo7 s-' at 8°C.The activation energy is thus 4.0 kcal rno1-l and the activation entropy around -13 cal mo1-' deg-'. According to the foregoing results, 'gating' effects in the reaction investigated can be ruled out,21 i.e. k, 4 k:. This implies that k, represents the actual specific rate of the intra- molecular electron transfer, in agreement with the kinetic theory of helix-coil transition in polypeptides,22 for which the initial rate constant for helix growth in a helix region at the ends of a chain is of the order of 10" s-1,22,23although it drops to a range of 107-1010 s-' 24-26 at midpoint tran- sition (fh = 0.5) because the elementary step of growth of a helix is a diffusion-controlled proce~s.~~.~~ Finally, the (N--P+) -,ground-state rate constant, evalu- ated by the decay kinetics of the radical species absorbing at 460 nm (see above), is k, z 1.4 x lo5 s-'.The larger rate constant of (singlet) charge separation over charge recombi- nation probably reflects the inverted character of the highly exergonic charge-recombination step, as opposed to the normal character of the charge-separation process,2o in agreement with Marcus A ,-A0& 0 , ,-A' 0 0 I' , 0 0.25 0.50 0.75 1.oo ftl Fig. 7 (kobs-k, -kE) as a function of the a-helical fraction in PNPL, according to eqn. (64. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Conformational Statistics The problem of the flexibility of the probes linkages and the random distribution of the chromophores in the polymer chain was then addressed. If a wide distribution of lifetimes results, comprising all decay values, it is reasonable to expect that each lifetime component changes as pH varies. In fact, this is not the case.Only the middle component, z2, is seen to decrease from about 30 to 18 ns on going from pH 7 to 11, while both the longer component, z3, and the shorter one are unperturbed. This finding suggests that each lifetime rep- resents a different decay process, distinctly separated from the others, an idea consistent with the observation that the varia- tion of z2 within pH 7-11 is too large compared with that found in NPL (ca. 4 ns) to be solely ascribed to the confor- mational transition.To check the foregoing hypothesis and evaluate to what extent the distribution of fluorescence lifetimes may affect the kinetic model based on a multiexponential discrete deconvol- ution, we have undertaken a conformational statistical analysis on the a-helical PNPL, using the method described in the Appendix for evaluating the interprobe distances dis- tribution function, P(R).The fluorescence decay intensity was then calculated by eqn. (7), where (k, + k, + kf) are the rate constants of eqn. (64 for the casef, = 1, as that under exami- nation. The hypothesis, here is that (i) electron transfer does not depend on the number of bonds between N and P groups, otherwise it would have been also measured in the random coil sample. Instead, it depends exponentially on the separation distance of the reactants, eqn.(8),27-31where /? is a parameter associated with the attenuation length of the wave functi~n,~~*~~*~~ R, = 3 A is the van der Waals contact and k, is the specific rate when R = R,. (ii) Besides exciplex formation which occurs with rate constant kE, the donor P group does not introduce any additional quenching mechanism of naphthalene fluorescence other than electron transfer, P -+ IN*. (iii) The natural fluorescence decay of the bound naphthyl molecules is monoexponential, occurring with rate constant k,. P(R)[exp -(k, + k, -k kE)t] dR (7) Regardless of the functional form of P(R), the integration of eqn. (7) can be approximated to a sum taken over all R values from zero to the maximum interchromophoric dis- tance, R,,,, when the whole integration range, 0 to R,,,, is divided into N equivalent subintervals of increment SR = R,,,/N, i.e.32 ~(t)= I, 1 P(R)[exp -(k, + kf + kE)t]6R (9) c In our case, N z 700, corresponding to SR = 0.1 A.There-fore, after excitation of naphthalene in the a-helical PNPL by a &pulse radiation, the emission intensity for the fraction P(R)SR of macromolecular chains, which have an interprobe distance between R and R + 6R, decreases according to eqn. (9). However, the laser profile needs also to be considered because the excitation pulse is not extremely short-lived. Therefore, the fluorescence decay I(t) must be deconvoluted to the excitation profile L(t’-t) at time t’, according to eqn. (lo),where K is a scaling factor.Itheor(t’) K 1P(R)GR Yt’ -t)[exp -(k, + kf + kE)t] dt= r (10) 120 r 100 t A A -a-.-c c 3 r 40 0 50 100 150 200 ti me/ns 20 I 1 , I 0 50 100 150 200 time,’ns Fig. 8 Comparison between calculated [eqn. (lo)] and experimental fluorescence decay curves of ordered PNPL (pH 11). The weighted residuals are shown in the insert. From the result, the plot of Fig. 8 is obtained, where the experimental decay curve of PNPL at pH 11 is compared to the theoretical one, eqn. (lo), that makes use of the following parameters: k, = (6.9 ~t0.7) x lo6 s-I, kE = (9.0 2 0.9) x lo6 s-’,and R, = 3 A, while P(R)is given by eqn. (A2) in the Appendix. The agreement between the two curves is satis- factory.Moreover, if comparison is made between three experimental decay curves, within pH 10.6-11.0, and those calculated by eqn. (10) using the aforementioned parameters, one obtains /? = 1.0 f0.1 A-’ and k, = (9.2 f0.2) x 10l2 s-’. These values compare very well with those reported for electron transfer in proteins where a non-adiabatic long-range process is thought to occur.3c~27-31 (kf) = 1 P(RPRkf(R) (1 1)5 Finally, the average electron transfer rate constant, evalu- ated by eqn. (ll), is close to that experimentally determined, i.e. (4.0 f0.4)x lo7 s-’. This finding clearly indicates that the kinetic data are well described by a narrow distribution of interprobe distances, as that implicitly assumed in the multiexponential decay analysis of the model used.According to Fig. 9, where the functions kf(R), eqn. (8), and P(R), eqn. (A2), are reported, the average interchromophoric distance for which the electron transfer has the highest probability of occurring is ca. 12 A, which corresponds approximately to three helical turns. This is also approximately the centre-to- 1.2r (b) -6x10-’ n wQ 0.8i -I \(a)I/ \ I ... I 0.4 tt h s ot -0 CL 0 10 20 30 40 50 60 RIA Fig. 9 (a) Probability distribution of interchromophoric distances, P(R), for the case in which the contacts between non-bonded atoms shorter than 2.5 A were discarded for steric reasons; (b) distance dependence of the electron transfer rate constant, reported as k,/k,; (c) resulting function, as given by eqn.(11). The figure 2 x lo7 is a scaling factor, and the area under this curve gives the ratio (k,)/k, . J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 centre distance of other donor-acceptor pairs covalently bound to a-helical polypeptides, exhibiting both an electron transfer rate constant (ca. 5 x lo7 s-'; 20°C) and an elec- tronic driving force (-0.4 eV) of the same order of magnitude as that of P-N in PNPL.3(') This result can be taken as a further indication of a through-space mechanism, otherwise the rate constant would have been much larger in both ca~es.~(').~ Conclusion Three major conclusions are drawn from the present study. First, the relaxation time for the coilea-helix transition in PNPL is <20 ns.Secondly, electron transfer occurs only within a rigid frame, i.e. when the a-helical conformation of the backbone chain stiffens the whole structure. This also implies that the process takes place primarily by a through- space (or through-solvent) mechanism. Thirdly, the proposed treatment of fluorescence data is effective in reproducing the experimental decay curves of randomly distributed pairs in the a-helical PNPL. It makes use of the rate constants of the exciplex model for the kinetics, and of a rotational isomeric state model of the chromophore linkages for the distribution function of the donor-acceptor distances. We thank Prof. M. DAlagni for preparing the samples, and Drs. F. Elisei, P.Morales and L. Nencini for collaboration in transient-absorption and fluorescence-decay measurements. This work was supported in part by the National Research Council (CNR) and in part by MURST (Rome). Appendix To evaluate the distribution of interchromophoric distances, we began by considering PNPL as formed by macro-molecular units of 272 residues, carrying randomly distrib- H-N h-H@+, 10 x ;?a- C ,'C L XC T o=c Xll II 0 aT-H C=O Fig. A1 Molecular representation of a poly(1ysine) chain carrying protoporphyrin IX (P) and naphthyl (N) chromophores covalently bound to the &-amino groups. The features of the ensemble examined are such that each chain contains 272 L-IYS residues in a-helical con- formation ($ = -57', Y = -47', o = 180°), with 4 P and 16 N molecules (see text).The intramolecular centre-to-centre distance for a given conformation m of the side-chains carrying P and N, and a given configuration i, is denoted as R(m, i) = IR(m, i). The angles of internal rotation are indicated as za(6 = 1-17). Hydrogen atoms are omitted for clarity. 1863 Table A1 Relative energies and statistical weights of the rotational isomeric states of the donor and acceptor chromophore linkages" bond rotational rotat. isomeric energy angleb state' (En,jsId (stat. wt.),,, jse +60 0 1XlO XI -60 0 1 180 0 1 +60 0.5 exp(-OS/RT)XI 1 x2 -60 0.5 exp( -0.5JRT) 180 0 1 +60 0.5 exp( -0.5JRT) x12 x3 -60 0.5 exp(-OS/RT) 180 0 1 +60 0.5 exp(-OS/RT)XI 3 x4 -60 0.5 exp( -0.5/RT) 180 0 1 x14 x5 +60 0 1 -60 0 1 180 0 1 180 0 1x15 x6 x16 XI +60 0 1 -60 0 1 180 0 1 -Xa +60 0.5 exp(-0.5JR T) -60 0.5 exp( -OS/RT) 180 0 1 x17 x9 +90 0 1 -90 0 1 ~ ~~ The value of both relative energies, Ers,js (kcal mol-I), and sta- tistical weights of the rotational isomeric states are based on confor- mational analysis data of compounds containing similar structural elements.35 Dihedral angles, as illustrated in Fig.Al. 'The defini- tion of the angles conforms to IUB-IUPAC recommendations. Relative energy in kcal mol-'. The statistical weight is given by exp(- E,,JRT) or exp(- EjJRT). uted protoporphyrin IX and naphthalene probes, i.e. 4 P and 16 N, in agreement with both the experimentally determined stoichiometry and the average degree of polymerization of the sample used.We then define a configuration i as a polymer unit in which the relative position of the side-chains carrying N and P chromophores is fixed, each configuration being thus characterized by a given value of Ap-N. The fre- quency of the occurrence of configuration i,S,, is given by the ratio of li over 1 = cili,where li is the number of times that the event occurs, and the probability of the relative distances between the C" atom carrying the naphthyl moiety and that carrying the porphyrin moiety (AP-J by pi = lim (li/r) for 1 + a.This probability was calculated by the expression I(A)k+ -(A)k I < where the subscripts refer to the kth and (k + 1)th iterative process, each process taking into account a number of units lo5 larger than the preceding one.We next evaluated the probability distribution of the centre-to-centre distances between the chromophores bound to a-helical poly(L-lysine), making use of the geometrical parameters shown in Fig. Al, where the intramolecular dis- tance for a given conformation m, when the configuration is i, is written as R(m, i) = IR(m, i) I, while each bond in P chromophore linkage, denoted in the following as j, is num- bered from 1 to 9, and each bond in the N chromophore linkage, denoted as r, from 10 to 17. We adopted a rotational isomeric state for the probe linkages, in which rotation around each single bond is restricted to a few, highly populated low-energy isomeric states.The actual distribution of conformations is thus assumed to be well represented with this restriction. Table A1 lists the isomeric states, relative energies and statistical weights for the donor and acceptor linkages in the polypep- tide.35 By discarding both the conformations g+g- and g-g+ for the aliphatic portion of lysine side-chain, owing to their very low probability, and the conformations in which the centre of the chromophore is <7 8, from the helical axis, owing to steric hindrances, the total number of conformers of the probe linkages is ztot= 802,256, i.e. 1,508 for P and 532 for N linkage. Owing to this large number of side-chain confor- mations, each configuration i is coupled with a distribution of interchromophoric distances, whose probabilities are given by eqn.(Al), z1 (stat. wt.), P(R),= Zto11 (stat. wt.), (A1) m= 1 where z is the number of conformers having a given value of (R),, and (stat. wt.), = n,(stat. wt.),, nj(stat. wt.)j,.. The pro- ducts are taken over all bonds r and j of N and P chromo-phore linkages, respectively, while (stat. wt.),, and (stat. wt.)js, are the statistical weight assigned to bond r when populating the s state, and to bond j when populating the s’ state, respec- tively (Table A 1). The interprobe distance distribution func- tion, P(R), can be then written as eqn. (A2), and is illustrated in Fig. 9(a) for the case in which the contacts between non- bonded atoms shorter than 2.5 8, were discarded for steric reasons.References F. C. De Schryver, N. Boens and J. Put, Adv. Photochem., 1977, 10,359; G.L. Closs and J. R. 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