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J. Phys. Chem. B 2009, 113, 2284–2292
Effect of Time on the Rate of Long Range Polymer Segmental Intramolecular Encounters Mark Ingratta and Jean Duhamel* Institute for Polymer Research, Department of Chemistry, UniVersity of Waterloo, 200 UniVersity AVenue West, Waterloo, ON N2L 3G1, Canada ReceiVed: September 17, 2008; ReVised Manuscript ReceiVed: December 14, 2008
The kinetics of encounters between the pyrene pendants randomly attached along a polystyrene chain (PyPS) were monitored with a fluorescence blob model (FBM) as an external quencher was added to the solution to decrease the lifetime of the excited pyrene. The fluorescence decays acquired with the Py-PS samples yielded a measure of the volume Vblob probed by an excited pyrene during its lifetime in the form of Noblob, the number of monomers found within Vblob, and koblob, which is inversely proportional to Vblob. Both Noblob and koblob-1 were found to increase with increasing probing time as the excited pyrene was allowed to probe a larger Vblob volume. The rate constant for pyrene-pyrene encounters was obtained from the product 〈kblobNblob〉. 〈kblobNblob〉 was found to decrease with increasing probing time, in agreement with scaling arguments suggesting that, as the probing time increases, the excited pyrene probes a larger Vblob where the local concentration of ground-state pyrenes in the polymer coil, [Py]loc, is smaller. koblob, which is inversely proportional to Vblob, was found to scale as NoblobR, where R equaled -1.5 and -1.2 in DMF and THF, respectively. The R exponents found for the Py-PS samples are in the same range as those found for other polymers exhibiting a random polymer coil conformation in solution and were much smaller than those obtained with more compact structured R-helical polypeptides randomly labeled with pyrene. Master curves were also constructed that describe how koblob and the product 〈kblobNblob〉 scale as a function of solvent viscosity, probing time, and Noblob. These scaling laws illustrate the opposite effects that probing time and viscosity have on Noblob, Voblob, and the product 〈kblobNblob〉. Introduction A protein folding in solution represents a classic example where the inherent interplay that exists between time and distance during the intramolecular diffusion-controlled encounters of the amino acids of the polypeptide must be carefully tuned to avoid dire consequences.1-4 Proteins are polymers made of amino acids which are, in essence, associating units distributed along the chain whose encounters in solution are controlled by long range polymer chain dynamics (LRPCD). Two possible paths resulting from the encounters between three selected units of a given polypeptide are depicted in Scheme 1. Encounters between monomers A and B in Scheme 1 induce the formation of a cluster of amino acids, which acts as a folding initiation site from which the nascent secondary structures of the protein will form, leading through the folding process to the proper fully functional structure of the protein.1-4 However, if LRPCD enables monomer A to encounter monomer C before it encounters monomer B, the wrong folding initiation site might be generated, initiating the wrong folding pathway, and resulting in a misfolded nonfunctional or, even worse, misfunctioning protein.1 Public awareness that misfolded proteins are cause for a number of fatal human diseases such as bovine spongiform encephalopathy (BSE),5 Creuzfeld-Jakob disease (CJD),5 or amyotrophic lateral sclerosis (ALS)6 has contributed to the sustained effort aimed at better understanding the process of protein folding1-4 in general and LRPCD in particular.7-19 In homogeneous solution, the dynamics of encounters between two reactants A and B where B is present in large excess can be described by the probability, Pr(A-B,t), that at a given time t, the reactants A and B have reacted. The expression of Pr(A-B,t) is given in eq 1 where k is the rate constant that * To Whom correspondence should be addressed:
describes the diffusional encounters between reactants A and B, and [B] is the concentration of reactant B present in excess. For diffusion-controlled encounters, k depends on T/η where T is the absolute temperature in K and η is the solvent viscosity.
Pr(A-B,t) ) 1 - exp(-k[B]t)
(1)
LRPCD are probed in a similar fashion by monitoring the diffusion-controlled encounters between two reactants A and B covalently attached onto a polymer and diffusing inside the polymer coil. The product k[B] that describes the rate at which A and B encounter is used to determine Pr(A-B,t) according to eq 1.20-22 Because A-B encounters are diffusion-controlled, k depends on T/η. However, a major difference with the case of reactions in homogeneous solution is that [B] represents the local concentration of B, [B]loc, inside the polymer coil surrounding A. As it turns out, [B]loc is not expected to remain constant throughout the polymer coil but rather decreases with increasing distance separating A and B. The decrease in [B]loc with increasing time is a consequence of how the density of polymer segments varies inside the polymer coil. As time elapses, the volume probed by the species A and B diffusing inside the polymer coil increases, and [B]loc depends on the number of B molecules that can be found in that volume, which will be referred to hereafter as a blob of volume Vblob. Different procedures have been considered to covalently attach the reactants A and B onto a polymer, but the most favored ones consist of attaching the reactants either at the ends of a monodisperse chain7-44 or at random locations along the chain.45-55 Regardless of the mode of attachment, polymer physics predicts that Vblob scales as the number of monomers encompassed in a blob, namely Nblob, to the power of 3ν where
10.1021/jp8082858 CCC: $40.75 2009 American Chemical Society Published on Web 02/05/2009
Polymer Segmental Intramolecular Encounters SCHEME 1
ν equals 0.5 or 0.6 if the polymer is dissolved in a mediocre (Θ) or good solvent, respectively.56 Consequently, [B]loc scales as either 1/Vblob ) Nblob-3ν if a single B is attached at the other end of the chain or xNblob/Vblob ) xNblob1-3ν if a molar fraction x of B molecules has been randomly attached along the chain. As time elapses, Vblob increases and so does Nblob, resulting, in turn, in a decrease of [B]loc with Nblob-3ν or Nblob1-3ν whether B is attached at the other end of the chain or at random locations along the chain, respectively. Because -3ν is more negative than 1 - 3ν, the decrease in [B]loc with increasing time is expected to be more pronounced for end-labeled polymers than for randomly labeled polymers. To the best of our knowledge, no experiments have ever been attempted to probe such trends. Yet a study of how the product k[B]loc varies with time when two reactants A and B are attached onto a chain would provide valuable information on how time affects the rate of segmental encounters, with important implications for, in particular, the understanding of the early steps of the folding of a polypeptide. The present study reports on how a measure of k[B]loc as a function of time was obtained by monitoring the fluorescence signal emitted by a series of polystyrenes randomly labeled with the chromophore pyrene (Py-PS). Several reasons laid behind the selection of Py-PS for these experiments. Pyrene was chosen for its ability to form an excimer from the diffusion-controlled encounter between an excited pyrene and a ground-state pyrene.57 In other words, shining the Py-PS solution with UV light results in the excitation of some pyrenes that, in Scheme 1, would play the part of reactant A, whereas the remaining ground-state pyrenes would act as reactant B. The rate at which excimer is formed provides a measure of the rate at which reactants A (Py*) and B (Py) encounter. It can be determined from the global analysis of the monomer and excimer fluorescence decays acquired with a timeresolved fluorometer. In these fluorescence experiments, Vblob represents the volume probed by an excited pyrene while it remains excited.45 The size of Vblob depends on the lifetime of pyrene, which can be adjusted by the addition to the solution of an external quencher such as nitromethane58 that quenches the excited pyrene via an electron transfer mechanism.59 Addition of more quencher to the solution results in a shorter lifetime for the excited pyrene that probes a smaller Vblob. Polymers randomly labeled with pyrene were selected over endlabeled polymers due to the momentous gain in excimer formation associated with their use60 and the weaker dependence of [B]loc with time expected from scaling considerations (cf. earlier discussion). Last, but not least, recent studies have showed that the analysis of the monomer and excimer fluorescence decays of polymers randomly labeled with pyrene such as Py-PS with a fluorescence blob model (FBM) provides a direct measure of the product k[B]loc.60
J. Phys. Chem. B, Vol. 113, No. 8, 2009 2285 TABLE 1: Pyrene Contents, x, in mol % and λPy in µmol g-1, Molecular Weights and PDI of the Py-PS Samplesa
a The samples with 5.2 and 6.9 mol % pyrene (marked with asterisks) were only used in DMF and THF, respectively, due to the small amount of polymer synthesized.
Experimental Section Materials. Distilled in glass N, N-dimethylformamide (DMF) and tetrahydrofuran (THF) purchased from Caledon Laboratories (Georgetown, ON) were used as received. Synthesis of Pyrene-Labeled Polystyrene. An earlier publication has reported the synthesis and characterization of the poly(styrene-co-1-pyrenemethylacrylamide) (Py-PS).61 Table 1 lists the pyrene content expressed in mol % of pyrene labeled monomer (x) or µmol of pyrene per gram of polymer (λPy), the number-average molecular weights, the polydispersity indices and the chemical structure of the Py-PS samples. Steady-State Fluorescence Measurements. A PTI fluorometer was used to acquire all fluorescence spectra with the right angle geometry. All solutions with an optical density of approximately 0.1 were degassed for 30 min under a gentle flow of N2 to remove oxygen. Special care was taken with the samples in the more volatile THF solution to ensure that no solvent evaporated during the degassing procedure. The emission spectrum of the degassed solutions was collected from 350 to 600 nm with an excitation wavelength set at 344 nm. The fluorescence intensity of the monomer (IM) and excimer (IE) was integrated from 372 to 378 and 500 to 530 nm, respectively. Time-Resolved Fluorescence Measurements. The timeresolved fluorescence measurements were conducted on polymer solutions that had been prepared in the same manner as for the steady-state fluorescence experiments. The solutions were excited at 340 nm with an IBH 340 nm LED, and the emission was collected at 375 and 510 nm for the monomer and excimer, respectively. The lamp and decay profiles used 1024 channels and had 20 000 counts at the peak maximum. The instrument response function was determined by applying the MIMIC method62 to the reference decays obtained with PPO [2,5diphenyloxazole] in cyclohexanol (τ ) 1.42 ns) and BBOT [2,5bis(tert-butyl-2-benzoxazolyl)thiopene] in ethanol (τ ) 1.47 ns) for the monomer and excimer decays, respectively. Analysis of the Fluorescence Decays. Global analysis of the monomer and excimer decays was conducted with eqs 2 and 3, respectively.63
[( ]
* [Py*](t) ) [Pydiff ](t)0) exp - A2 +
)
1 tτM
A3(1 - exp(-A4t)) + [Py*free](t)0) exp(-t/τM) (2)
2286 J. Phys. Chem. B, Vol. 113, No. 8, 2009
[E*] )
* -[Pydiff ](t)0)e-A3
((
exp -
Ingratta and Duhamel
∞
Ai3 A2 + iA4 × i! 1 1 i)0 + A2 + iA4 τM τE0
SCHEME 2
∑
))
(
1 * ](t)0)e-A3 + A2 + iA4 t + [E0*](t)0) + [Pydiff τM
∞
)
Ai3 A2 + iA4 e-t/τE0 + [D*]0e-t/τD (3) i! 1 1 i)0 + A2 + iA4 τM τE0
∑
Equations 2 and 3 use the parameters A2, A3, and A4 which are described in eq 4. Numerous examples can be found in the literature where eqs 2-4 have been used to study polymer dynamics in solution.45
A2〈n〉
kblobke[blob] kblob2 A3 ) 〈n〉 kblob + ke[blob] (kblob + ke[blob])2 A4 ) kblob + ke[blob]
(4)
Equations 2-4 were derived by assuming that some of the excimer is formed through diffusive encounters between an * , and a ground-state pyrene. The behavior excited pyrene, Pydiff * of the Pydiff monomers are described in the monomer decays by the first exponential in eq 2. The second exponential in eq 2 accounts for the fraction of pyrene groups that are isolated * . Analysis of the fluorescence and cannot form excimer, Pyfree decays of a low pyrene content Py-PS sample (
