Physical Gelation of Polypeptide–Polyelectrolyte–Polypeptide (ABA

Article pubs.acs.org/Macromolecules

Physical Gelation of Polypeptide−Polyelectrolyte−Polypeptide (ABA) Copolymer in Solution Ran Zhang,† Xiaozheng Duan,† Tongfei Shi,*,† Hongfei Li,† Lijia An,† and Qingrong Huang‡ †

State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China ‡ Food Science Department, Rutgers University, 65 Dudley Rd., New Brunswick, New Jersey 08901, United States ABSTRACT: The gelation behavior of polypeptide−polyelectrolyte−polypeptide in solution is investigated by Monte Carlo techniques. It is found that different hydrogen bonding styles, parallel and antiparallel, provide a major influence on the sol− gel transition and the chain conformation. The antiparallel hydrogen bonding style favors the bridge conformation, while loop conformation has less structural limitation with parallel bonding. However, in the parallel style, polyelectrolyte blocks are aligned in the same side of β-sheets, which induces more steric constrains and the electrostatic repulsion. Consequently, compared with the parallel bonding style, the sol−gel transition of antiparallel style occurs at lower hydrogen bonding energy and the dihedral angle θ of antiparallel β-sheets is a little higher. The increase of charging fraction of polyelectrolyte blocks prompts the sol−gel transition of both bonding styles but causes an impact on the number of hydrogen bond and the dihedral angle, indicating a decrease in the structure integrity. mutual restraint to the formation of β-sheet structures, which might prohibit the 1-D elongation3,11 of sheets; (c) the most important one is that the difference between a parallel and antiparallel hydrogen bonding style might cause discrepancy in their gelation behavior, which is rarely reported in the literature. Moreover, the charging fraction of the peptide block can be controlled by tuning pH values, according to the content of basic and acidic amino acid monomers, which, too, incurs an influence on the assembling structures.13 Here, the above-mentioned features are combined in the triblock copolymer: polypeptide−polyelectrolyte−polypeptide, where the sequences of peptide blocks are designed to have Nterminals or C-terminals at both chain ends, facilitating the forming β-sheet structures. Using the Monte Carlo simulation technique, we investigated the sol−gel transition properties of the polymer solution and found that the gelation behavior diverged when the peptide blocks were aligned in the parallel and antiparallel direction, respectively: (i) Chain conformation investigation used to analyze the gelation behavior of telechelic polyelectrolytes23 was adopted to characterize the behavior of the polymer. The cross-linking (and consequently gel formation) structure of polymer chains could be well represented by certain types of chain conformations, which are observed with different probabilities depending on the preferential β-sheet assembly style (parallel vs antiparallel): the bridge conformation was more favorable in the antiparallel

1. INTRODUCTION Novel bioactive and smart materials acquired by incorporating peptide blocks into copolymers have received intensive attention.1,2 Besides the convenience of peptide resources, from either nature or synthesis, they possess the ability to form stable conformation and association structure with precise control.1 The idea of adopting the self-assembled structure formed by peptide blocks as the cross-linking points of a physical gel recently was carried out by a few research groups.3−9 One feature of this kind of gel is that the noncovalent bonding between peptide monomers renders the formation of physical gel network, which is able to switch its properties according to conditions like pH, salt, temperature, or solvent property.1 The other feature is that the cross-links are the ordered secondary structures as helical and β-sheet structures formed with these peptide strands, especially the βsheet structure can be parallel or antiparallel style according to the species and sequence of peptides.10−15 As a typical associating polymer,16,17 the triblock polymer has its functional blocks, usually hydrophobic polymer blocks,17−22 assigned at the two ends of the middle chain backbone. When the peptide blocks are considered in this configuration to replace the hydrophobic blocks, some comparisons can be made with the hydrophobic associating polymers: (a) the association driving force includes not only the hydrophobicity originated from the selective solvent quality, but also the hydrogen bonding interaction between the hydrogen donor N−H and the acceptor CO group,11 which is the fundamental elements in the amino acids; (b) the assignment of peptide blocks at both ends of the chain might induce a © 2012 American Chemical Society

Received: April 1, 2012 Revised: June 14, 2012 Published: July 27, 2012 6201

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method is simplified and used in our Monte Carlo simulation. For the saturation of hydrogen bonding, each peptide monomer is allowed to form two bonds. The first condition under which the hydrogen bonding is allowed is when two peptide monomers are within the distance of 1.5σ. Then, an activation energy of the first hydrogen bond is defined as

bonding style and the loop conformation in the parallel style. (ii) We found that small-sized sheet structure, instead of the elongated β-sheets, acted as the cross-linking points of gel networks, and the discrepancies in gelation behavior resided in the different steric hindrance and assembly features of the two hydrogen-bonding styles. (iii) We also found that the increase in charging fraction of polyelectrolyte block would render the sol−gel transition to a much lower concentration range, however, at the cost of the integrity of β-sheet structures. This work was inspired by de la Cruz’s research on peptides.11,24,25 The model design and simulation details are depicted in section 2. In section 3 we present the simulation results and relevant discussions. The conclusion is drawn in the section 4.

Ua = εβ cos(ϑij)

where εβ is the energy of hydrogen bonding and ϑij is the angle between bonding monomers,11 with cos(ϑij) = (Δri⃗ ·Δrj⃗ )/ (ΔriΔrj), Δri⃗ = ri⃗ +1 − ri⃗ −1. Monomers i and j are from different peptide blocks, and Δri⃗ is the vector defined by the adjacent neighbors of monomer i (see Figure 1a).

2. MODELS AND SIMULATION DETAILS The triblock copolymer we use here is a polyelectrolyte chain with both ends modified by short polypeptide blocks, represented by a coarse-grained freely jointed chain model. The whole chain has a structure A6B18A6 and contains 30 monomers, with A standing for the peptide monomers at both ends and B the polyelectrolyte monomers. Each monomer possesses a diameter of 1σ with σ the unit length. The adjacent monomers have a fixed bond length of 1.4σ. Polyelectrolyte monomers are monovalent and carrying negative charges; their counterions, positively charged, are also explicitly considered with the same diameter in our simulation. We uniformly charge/discharge the middle polyelectrolyte blocks every n (n = 1, 2, 3, ...) monomers and acquire polyelectrolyte block charging fraction f from 100% to 0. The charged polyelectrolyte monomers and counterions equal in numbers to maintain the charge neutrality. Solvent molecules are implicitly treated as a dielectric background, providing a good solvent condition for the copolymer chain. Consequently, a repulsive LJ potential in the short range describes the interaction between monomers: ⎛ σrep ⎞12 ⎟ Urep = 4εrep⎜ ⎝ r ⎠

Figure 1. (a) Schematic representation of β-sheet styles (taken from Figure 2 of ref 11). (b) Antiparallel and parallel β-pleated sheets.

(2.1)

With this definition, the direction of hydrogen bonding is controlled so that the peptide block is aligned in the same direction, resulting in paralleled structures, or the opposite directions with Δri⃗ = ri⃗ −1 − ri⃗ +1 and Δrj⃗ = rj⃗ +1 − rj⃗ −1, resulting in antiparalleled structures (here the ranking of peptide monomers are counted from the ends to the center of the chain). A schematic picture showing these structures can be found in Figure 1b. Since we have fixed bond length along the polymer chain, the modified FENE potential between bonded peptide monomers is not cited here. Owing to the configuration of each amino acid, when the second hydrogen bond of the same peptide monomer (i for instance) is formed, the third peptide monomer k must be laid along the direction of the peptides i and j, and the structure of β-sheet requires the angle between the two hydrogen bonds ij and ik to be obtuse (see Figure 1a). Therefore, the activation energy of the second hydrogen bond is defined as

The long-range interactions between charged monomers and counterions are computed by Ewald summation in Monte Carlo simulation:23 N

N

Uelec = λBkBT ∑ ∑ i

qiqj

j>i

rij

(2.2)

where the coefficient εrep is 0.5kBT, λB defined as the distance at which two unit charges have the interaction energy kBT and has the expression λB = e2/(4πε0εrkBT). Here λB is fixed at 0.5σ. Compared with the flexible polyelectrolyte, the short polypeptide block has a stiff backbone, controlled by a rigidity potential: Urigid = gi(1 + cos θ )2

(2.4)

(2.3)

where cos θ = ((ri⃗ +1 − ri⃗ )·(ri⃗ −1 − and gi is the rigidity constant, gi/kBT = 100; r0 is the bond length. The peptide model is more complicated since the peptides are capable of forming hydrogen bonding between peptide units,3,26−28 and the simulation of hydrogen bonding is very time-consuming. Among the studies approaching to hydrogen bonding interaction, de la Cruz et al. came up with a brilliant solution to the hydrogen bonding problem.11 Here, this ri⃗ ))/r02,

Ua = εβ cos(ϑij) cos(ϕi)

(2.5)

where ϕi is the angle between the two hydrogen bonds and cos(ϕi) = (Δrk⃗ i·Δri⃗ j)/(ΔrkiΔrij). The peptide monomers are designed without electrostatic interactions for simplicity. At last, the probability of forming/breaking of a hydrogen bond is controlled by11 6202

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Macromolecules pform =

pbreak =

Article

g (Ua, ij) 1 + g (Ua, ij) 1 1 + g (Ua, ij)

(2.6)

(2.7)

where g(Ua,ij) = exp(−Ua,ij/kBT), Ua,ij (according to eq 2.4 or 2.5) being the activation energy of peptide monomers i and j. The Monte Carlo simulation is performed in the NVT (constant particle numbers, constant volume and temperature) ensemble according to the Metropolis algorithm, in a cubic cell (L = 48σ) with periodic boundary conditions in 3 dimensions. Hydrogen bonding potential εβ varies from 0 to 6 kBT, and up to 150 chains are used to achieve the highest concentration. Counterions move with a displacement of at most 5σ in one MC trial. To relax the chains, we use several algorithms such as pivot, crankshaft, kink-jump, and translation.23 Here a MC step means an MC trial of all the particles (monomers and counterions) in average. The simulation starts with random distributions of polymer chains and counterions. After 3 × 105 athermic MC steps the system is followed by 106 normal MC steps to achieve equilibration. A production run contains another 2 × 105 MC steps to calculate the averages of properties. After the athermic moves, an extra MC trial is carried out before each MC trial of monomers to judge the breaking or forming of hydrogen bonding between peptide monomers according to eqs 2.6 and 2.7. Up to 10 samples of different starting positions are performed to achieve the average at each condition. Methods like percolation29,30 and conformation investigation23,31,32 could be applied to this system. Four basic types of chain conformation, free, loop, dangling, and bridge, are defined according to the hydrogen bonding of their polypeptide blocks;23 i.e., no hydrogen bonds formed on peptide blocks of a free chain; a loop chain has its two peptide blocks bonded in the same β-sheet; a dangling chain has only one of its peptide blocks bonded with other chains and two ends of a bridge chain bond to different β-sheets. The proportion of each type of chain in the system is an important property in describing the cross-linking structure. Two chains are considered to form a cluster when hydrogen bonding connects their peptide blocks, and cluster size distribution function W(M) is calculated by N(M)/[N(1) + N(2) + ... + N(N)], where N(M) is the number of cluster at size M. As for the percolation definition, if the cluster is large enough to build a channel with its bridge chains across two boundaries along any of the dimensions, the system is considered to be percolated. To investigate the structure of formed β-sheets, the number of hydrogen bonds and the dihedral angle θ of saturated peptide monomers (which is the average of angle ϕi introduced in the model section) in the βpleated sheets are also calculated. During the production steps, the above-mentioned properties are calculated and finally averaged.

Figure 2. Dependence of percolation probability on hydrogen bond potential εβ.

Figure 3. (a) Fraction of formed hydrogen bonds Nt over its theoretical maximum Nmax at different εβ, f h‑bond (εβ) = Nt/Nmax, is shown in different squares for parallel and antiparallel styles; the fraction of hydrogen bonds contributing to the saturated peptide monomers (in circles) is also plotted. (b) The averaged dihedral angle θ of saturated peptide monomers in the β-pleated sheets.

concentration: the peptide monomers form β-sheet-like structures, which act as the cross-linking points to form a 3D network, while the polyelectrolyte blocks play a role in the gel as bridges connecting different β-sheet structures.3 The way βsheet structures contribute to the gel structure to some degree resembles the spherical hydrophobic aggregation core of a micelle,23,33,34 but it rather takes a 2D planar configuration. In Figure 2, the physical gelation process is described by the developing of percolation probability P(εβ) with the increase of εβ. The charging fraction for the polyelectrolyte block is set at 1/ 3, and the concentration ϕ = 0.0325. As defined in the models, εβ controls the breaking and forming of hydrogen bonding. P(εβ) is zero when εβ/kBT < 1, suggesting the forming of hydrogen bond is unfavorable and the system is in the sol state. With increasing εβ, an increasing of P(εβ) means the system enters the sol−gel transition field. The probability of forming of a hydrogen bond in eq 2.6 is increasing and P(εβ) increases, indicating effective aggregation between different peptide blocks (due to the rigidity of the polypeptide, hydrogen bond between monomers of the same peptide block is avoided).

3. RESULTS AND DISCUSSION Comparison between Gelation Behavior under Parallel and Antiparallel Cross-Linking. The gelation behavior of polypeptide−polyelectrolyte−polypeptide triblock copolymer is investigated in this section. Because of the hydrogen bonding and repulsive electrostatic interaction between the middle polyelectrolyte block, the polymer exhibits an association behavior at appropriate hydrogen bonding energy and 6203

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Figure 4. Simulation snapshots of association structures formed by hydrogen bonds of β-sheet. (a) and (c) are parallel β-sheets; (b) and (d) are antiparallel β-sheets. εβ/kBT = 1 for (a) and (b); εβ/kBT = 5 for (c) and (d).

Figure 6. Schematic representation of chain association in β-sheet styles: (a, c) parallel β-pleated sheet; (b, d, e) antiparallel β-pleated sheet. (c) contains the only form of loop in parallel β-pleated sheet, and (d, e) illustrate the two different forms of loop in antiparallel βpleated sheet.

in maintaining the planar structure of β-sheets, and its contribution reaches about 20% of Nmax when the system enters the gel state at εβ/kBT > 4. It is observed that when εβ/ kBT > 5, f h‑bond(εβ) exhibits a decrease with further increase of εβ. This is mainly due to the quenching of strong hydrogen bonding interaction, which causes a significant thermal barrier to the formation of β-sheets. Similarly, the aggregation of peptide monomers was found developing into amorphous structures if the hydrogen bonding interaction energy is too high.11

Figure 5. Dependence of fraction of chain f(εβ) on hydrogen bond potential εβ for different hydrogen bonding style. Some of the chains in loop conformation in (b) exist in a circling round manner as Figure 6e exhibits, denoted by loop′.

In the corresponding εβ range (1 < εβ/kBT < 4), f h‑bond(εβ) for formed hydrogen bonds and those contributing to the saturated peptide monomers in Figure 3a show a significant rising with εβ. f h‑bond(εβ) for Nt reaches nearly 55% of the Nmax when εβ/kBT > 4. The saturated peptide monomers play a role 6204

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Figure 7. Simulation snapshot of β-sheet structures. (a), (c), and (e) are parallel β-sheets; (b), (d), and (f) are antiparallel. εβ/kBT = 1 for (a) and (b), εβ/kBT = 3 for (c) and (d), εβ/kBT = 5 for (e) and (f).

transition field at lower εβ, f h‑bond(εβ) of the antiparallel style is higher than the parallel style when 1 < εβ/kBT < 4, and the antiparallel style clearly possesses a higher θ. However, a further increasing of εβ induces that f h‑bond(εβ) of the antiparallel style decreases faster than the parallel style, probably due to the more significant influence of mutual restraint with εβ. The reason for these differences could be attributed to the way how hydrogen bond is formed. The configuration difference of between parallel and antiparallel style could lead to the variation of conformation of chains during the gelation process. In Figure 5, the fraction of different chain types f(εβ) is plotted against εβ. The developing trends of chain conformations under parallel and antiparallel hydrogen bonding styles resemble each other but vary in quantity. With the increasing of εβ, f free(εβ) keeps decreasing and reaches zero when εβ/kBT > 3 for both the parallel and antiparallel styles. Dangling chain could be viewed as the transition intermediate

A simulation snapshot of the association structure is shown in Figure 4a−d. At εβ/kBT = 1, the chains are rather homogeneously distributed in the simulation box, without significant hydrogen bonding between peptide blocks. The small-sized β-sheets instead of elongated ones can be captured when εβ/kBT = 5, with polyelectrolyte blocks bridging different β-sheets. In experimental studies, such small-sized β-sheets were also witnessed during the forming of reversible thermal gels.3 Here, such structures are found as cross-linking points in the gel network. The dihedral angel θ of saturated bonds increases with εβ (see Figure 3b), indicating that the β-sheet structure is forming. The criterion of the forming of β-sheet is set at θ0 = 150°. After θ0 is reached, the increasing of θ is much slower. Moreover, the direction of peptide monomers aligned (parallel and antiparallel) apparently has an influence on the gelation behavior of this copolymer: the antiparallel style clearly enters the sol−gel 6205

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the antiparallel style and 0.6 for the other. This tendency maintains with further increase of εβ. Two stages could be identified in the development of bridge conformation with εβ. Before εβ/kBT = 3, f bridge(εβ) shows a significant increase speed, corresponding to the forming of β-sheet structure; then the increase becomes much slower. While for the loop chains, f loop(εβ) develops into a higher value with εβ for the parallel style. A schematic representation of chain association in β-sheet styles (see Figure 6) might help in understanding these differences in chain conformations. The increase of bridge chains favors the forming and strengthening of gel network,22,35−37 and there are some features in the forming of bridge and loop conformation in the β-sheet structure: (1) Compared with the parallel bonding style in Figure 6a, the antiparallel style in Figure 6b clearly favors the distribution of polyelectrolyte blocks from alternating directions, which avoids steric hindrance and electrostatic repulsion; this is also responsible for the higher θ and f h‑bond(εβ) in Figure 3. (2) Two ends from the same chain can form the loop conformation without the assistance of other peptides as Figure 6c shows. (3) While for the antiparallel style two situations exist: one is with the help of another peptide block (see Figure 6d); the other is also a single chain behavior as in (2), but with two peptide blocks circling around as Figure 6e exhibits, which is also considered in Figure 5b as loop′ with a crossed triangle symbol. Additionally, compared with the parallel style, the alternating distribution of polyelectrolyte blocks of the antiparallel β-sheet creates a larger distance between these blocks, resulting in the antiparallel β-sheet forming under less steric hindrance and smaller electrostatic repulsion, which together with the investigation of chain conformation interprets the difference in sol−gel transition in Figure 2. In Figure 7, the snapshots of β-sheet structure with increasing εβ are exhibited. When εβ/kBT = 1 (see Figure 7a,b), the peptide monomers present an amorphous aggregation structure; the rudiment β-sheet structure is formed when εβ/kBT = 3 in Figure 7c,d and keeps growing with increasing εβ; the β-sheets exhibited in Figure 7e,f actually act as cross-linking points connecting the gel structure. With the growing and completing of β-sheet structures, different β-sheets will aggregate together by bridge chains and form clusters of different sizes. The corresponding distributions of clusters MW(M) according to their sizes are presented in Figure 8. M is the association number of chains in the cluster, while W(M) describes the number-average percentage of cluster with association number M. When εβ/kBT < 2, clusters are mainly composed of single β-sheet structures formed by several chains, with a narrow distribution; with increasing εβ, the clusters develop into bigger sizes: for the parallel style, big clusters appear at εβ/kBT = 4, and their sizes exceed 100 with a comparatively wide distribution; for the antiparallel style, the corresponding phenomena occurs at εβ/kBT = 3, due to the three reasons mentioned above. For both bonding styles, clusters with much bigger sizes appear with a narrower distribution and percolate the system when εβ increases further, which again appears first for the antiparallel style. Influence of Coulombic Interaction. A charging fraction of 1/3 is applied for the polyelectrolyte block in the above investigation. The increased electrostatic repulsion will cause more steric hindrance to the alignment of peptide blocks, which undoubtedly influences the integrity of the β-sheet structures as well as their role of cross-linking points; while in the aspect of chain conformation, the increased electrostatic repulsion favors

Figure 8. Dependence of size distribution of clusters on εβ for parallel and antiparallel bonding styles.

Figure 9. Dependence of percolation probability on concentration at different charging fraction f B: (a) f B = 1/3, (b) f B = 1. The hydrogen bond potential εβ = 4kBT.

between free and loop/bridge chains,23 but fdangling(εβ) shows no turning points in Figure 5. fdangling(εβ) does not show significant decreasing with εβ until εβ/kBT > 2 and approaches zero when εβ/kBT > 5. The major difference exists in the fractions of loop and bridge conformations. By the antiparallel bonding, f bridge(εβ) develops into a higher value with εβ than the parallel style. When εβ/kBT = 3, for instance, f bridge(εβ) approaches 0.75 for 6206

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Figure 10. Dependence of the fraction of chain type on ϕ at different f B.

Figure 11. Influence of f B on (a) the total number of hydrogen bond (squares) and the number of hydrogen bond of which the saturation value is 2 (circles) and on (b) the dihedral angle θ of saturated hydrogen bond in the β-pleated sheets.

kBT = 4 the hydrogen bonding is strong enough, leaving in the system only few percent of free and dangling chains. For the parallel bonding style, loop conformation is highly favored at lower concentration, causing a loop conformation taking over 90% of the chains. With the increase of ϕ, f bridge(ϕ) is increasing and f loop(ϕ) decreasing. f bridge(ϕ) exceeds f loop(ϕ) in the sol−gel transition field, and after ϕ = 0.022 f bridge(ϕ) and f loop(ϕ) exhibit much slower changes. For the antiparallel style, bridge conformation is more preferred than the loop. At ϕ = 0.002, f bridge(ϕ) only reaches 0.3 and f loop(ϕ) over 0.6; f bridge(ϕ) increases at a faster speed and exceeds f loop(ϕ) at lower ϕ than in the parallel style. When entering the gel state, f bridge(ϕ) keeps growing and approaches over 0.8 with increasing ϕ, while f loop(ϕ) decreases to a much smaller value under 0.2. Variability of pH and sequences of peptide block provides a major influence on the forming of β-sheet structure.13 Here, for simplicity, the electrostatic interaction originated from pH−

the forming of bridge chains, which promotes the developing and strengthening of gel structure.22,36,37 A comparative study is implemented for different charging fractions of the polyeletrolyte block in the following content. The hydrogen bonding energy is set at εβ/kBT = 4 to meet the condition of βsheets forming, and the concentration is considered as a variable. Figure 9 presents the percolation probability P(ϕ) as a function of concentration ϕ at different charging fraction f B = 1/3 and 1. When f B = 1/3, the system provides a sol−gel transition field from about ϕ = 0.011 to ϕ = 0.027 for the parallel bonding style, while for the antiparallel style the sol−gel transition occurs at a much lower range of concentration (0.002 < ϕ < 0.018), indicating the structural influence of β-sheet caused by parallel/antiparallel hydrogen bonding. The conformation changing with ϕ in Figure 10a,b interprets the different sol−gel transition fields at a microscale level. At εβ/ 6207

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pKa38,39 balance is introduced as fixed charges on the middle flexible block. An increase of f B from 1/3 to 1 brings more electrostatic repulsion to the chains, resulting in significant changes in gelation behavior (see Figure 9b). The increase of f B enables a much lower sol−gel transition field of the system, for both the parallel and antiparallel bonding styles. This can be attributed to the unfavorable loop conformation and increased bridge conformation with the expanding of chain. In Figure 10c, f loop(ϕ) and f bridge(ϕ) change with the same trend as in Figure 10a but at a much faster speed with ϕ. Compared with Figure 10a, a lower f loop(ϕ) of about 0.1 and a higher f bridge(ϕ) above 0.8 are captured when entering the gel state. A small percent of free conformation appears at ϕ = 0.002 and decreases to zero with ϕ. The dangling conformation shows a maximum of 0.2 in the sol−gel transition field owing to their role as intermediates in the gelation process. Similar behavior also happens for the antiparallel style: f bridge(ϕ) approaches 0.9 and f loop(ϕ) about 0.1 when entering the gel state. Figure 11a,b depicts that the total number of hydrogen bonds Nt and the saturated peptide monomers experience a decrease when f B increases from 1/3 to 1, especially for the parallel β-sheets. The alignment of peptide blocks in the same direction renders the charged polyelectrolytes to pile up on one side of the β-sheet, which is more likely to be influenced with increased electrostatic repulsion than the antiparallel β-sheets. These decreases in number of hydrogen bonds and the dihedral angle θ of β-sheets might indicate drawbacks in mechanical properties. When f B = 1/3, the value of θ is not sensitive to the variation of concentration, fluctuating in the range from 150° to 155°. While f B increases to 1, for the parallel β-sheets, a significant drop of θ to about 134° occurs at ϕ = 0.002 due to the reason mentioned above, suggesting the integrity of β-sheet structure is influenced.

bond.46 Therefore, dramatically diverged rheological behavior of these two different gel materials may be anticipated in consideration of the above-mentioned physical nature of parallel and antiparallel β-sheets, and materials containing both the parallel and antiparallel β-sheets could add up their complexity. Further research could focus on the corresponding experimental verification or the application of relevant materials in biofunctional fields.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel +86-431-85262309; Fax +86-43185262969. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Special Funds for National Basic Research Program of China (2009CB930100), the National Natural Science Foundation of China (51028301, 21174146) Programs, and the Fund for Creative Research Groups (50921062).

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REFERENCES

(1) Marsden, H. R.; Kros, A. Macromol. Biosci. 2009, 9 (10), 939− 951. (2) Cui, H.; Webber, M. J.; Stupp, S. I. Biopolymers 2010, 94 (1), 1− 18. (3) Kim, E. H.; Joo, M. K.; Bahk, K. H.; Park, M. H.; Chi, B.; Lee, Y. M.; Jeong, B. Biomacromolecules 2009, 10 (9), 2476−2481. (4) Veerman, C.; Rajagopal, K.; Palla, C. S.; Pochan, D. J.; Schneider, J. P.; Furst, E. M. Macromolecules 2006, 39 (19), 6608−6614. (5) Niece, K. L.; Czeisler, C.; Sahni, V.; Tysseling-Mattiace, V.; Pashuck, E. T.; Kessler, J. A.; Stupp, S. I. Biomaterials 2008, 29 (34), 4501−4509. (6) Larsen, T. H.; Branco, M. C.; Rajagopal, K.; Schneider, J. P.; Furst, E. M. Macromolecules 2009, 42 (21), 8443−8450. (7) Jang, W. D.; Aida, T. Macromolecules 2003, 36 (22), 8461−8469. (8) Carrick, L. M.; Aggeli, A.; Boden, N.; Fisher, J.; Ingham, E.; Waigh, T. A. Tetrahedron 2007, 63 (31), 7457−7467. (9) Anderson, J. M.; Andukuri, A.; Lim, D. J.; Jun, H.-W. ACS Nano 2009, 3 (11), 3447−3454. (10) Aggeli, A.; Bell, M.; Boden, N.; Carrick, L. M.; Strong, A. E. Angew. Chem., Int. Ed. 2003, 42 (45), 5603−5606. (11) Velichko, Y. S.; Stupp, S. I.; de la Cruz, M. O. J. Phys. Chem. B 2008, 112 (8), 2326−2334. (12) Lefevre, T.; Subirade, M. Biopolymers 2000, 54 (7), 578−586. (13) Aggeli, A.; Bell, M.; Carrick, L. M.; Fishwick, C. W. G.; Harding, R.; Mawer, P. J.; Radford, S. E.; Strong, A. E.; Boden, N. J. Am. Chem. Soc. 2003, 125 (32), 9619−9628. (14) Diez-Pascual, A. M.; Wong, J. E. J. Colloid Interface Sci. 2010, 347 (1), 79−89. (15) Radu-Wu, L. C.; Yang, J.; Wu, K.; Kopecek, J. Biomacromolecules 2009, 10 (8), 2319−2327. (16) Hoy, R. S.; Fredrickson, G. H. J. Chem. Phys. 2009, 131 (22), 224902. (17) Zhang, H.; Xu, K.; Cao, X.; Liu, P.; Zhu, L.; Chen, M. Petrochem. Technol. 2006, 35 (7), 695−700. (18) Kimerling, A. S.; Rochefort, W. E.; Bhatia, S. R. Ind. Eng. Chem. Res. 2006, 45 (21), 6885−6889. (19) Vasilevskaya, V. V.; Potemkin, I. I.; Khokhlov, A. R. Langmuir 1999, 15 (23), 7918−7924. (20) Bossard, F.; Aubry, T.; Gotzamanis, G.; Tsitsilianis, C. Soft Matter 2006, 2 (6), 510−516. (21) Potemkin, II; Vasilevskaya, V. V.; Khokhlov, A. R. J. Chem. Phys. 1999, 111 (6), 2809−2817.

4. CONCLUSION Because of the complexity of protein folding and its enigmatic assembly behavior in life,40,41 the combining of peptide segments into polymers and then further applying of them as useful biofunctional nanomaterials claim sufficient experimental preparation and necessary theoretical directions. In this paper, the illustration of the assembly details between parallel and antiparallel β-sheets in gel forming by means of computer simulation has provided better understanding of the fundamental knowledge in the conception and design of experimental studies. Conformation analysis was also used in this hybrid material study and successfully connected the chemical structure of the copolymers with their gelation behavior. The results reveal that the introduction of peptide blocks brings novel properties for the gelation material, especially for the antiparallel cross-linking gels. Similar to the telechelic polyelectrolytes,21−23,42 which possess novel mechanical properties such as a yield stress and several shear-thinning regimes.22,43−45 It could be predicted that the peptide− polyelectrolyte copolymer gels with small β-sheets structures as cross-links also provide similar properties. However, according to the research on mechanical properties of βsheets,46−48 both the type (parallel and antiparallel) of β-sheets and the direction of force application could influence their mechanical properties.49−51 Depending on the orientations of force vector and peptide strands, a “tear” model or a “shear” model could be used to describe the mechanical behavior of a single β-sheet structure, which indicates a breaking force from 1 to almost n times of that needed to rupture one hydrogen 6208

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Macromolecules

Article

(22) Tsitsilianis, C.; Katsampas, I.; Sfika, V. Macromolecules 2000, 33, 9054−9059. (23) Zhang, R.; Shi, T. F.; An, L. J.; Sun, Z. Y.; Tong, Z. J. Phys. Chem. B 2010, 114 (10), 3449−3456. (24) Greenfield, M. A.; Hoffman, J. R.; Olvera de la Cruz, M.; Stupp, S. I. Langmuir 2010, 26 (5), 3641−3647. (25) Solis, F. J.; Stupp, S. I.; de la Cruz, M. O. J. Chem. Phys. 2005, 122 (5), 054905. (26) Cui, H.; Pashuck, E. T.; Velichko, Y. S.; Weigand, S. J.; Cheetham, A. G.; Newcomb, C. J.; Stupp, S. I. Science 2010, 327 (5965), 555−559. (27) Toksoz, S.; Guler, M. O. Nano Today 2009, 4 (6), 458−469. (28) Xun, W.; Wu, D.-Q.; Li, Z.-Y.; Wang, H.-Y.; Huang, F.-W.; Cheng, S.-X.; Zhang, X.-Z.; Zhuo, R.-X. Macromol. Biosci. 2009, 9 (12), 1219−1226. (29) Stauffer, D.; Aharony, A. Introduction to Percolation Theory; Taylor & Francis: London, 1992. (30) Lipson, J. E. G.; Milner, S. T. Eur. Phys. J. B 2009, 72, 133−137. (31) Tanaka, F. J. Non-Cryst. Solids 2002, 307, 688−697. (32) Li, Y.; Shi, T.; Sun, Z.; An, L.; Huang, Q. J. Phys. Chem. B 2006, 110 (51), 26424−26429. (33) Bedrov, D.; Smith, G. D.; Yoon, J. Langmuir 2007, 23 (24), 12032−12041. (34) Uhlik, F.; Limpouchova, Z.; Matejicek, P.; Prochazka, K.; Tuzar, Z.; Webber, S. E. Macromolecules 2002, 35 (25), 9497−9505. (35) Katsampas, I.; Tsitsilianis, C. Macromolecules 2005, 38 (4), 1307−1314. (36) Tsitsilianis, C.; Iliopoulos, I. Macromolecules 2002, 35 (9), 3662−3667. (37) Esquenet, C.; Terech, P.; Boue, F.; Buhler, E. Langmuir 2004, 20 (9), 3583−3592. (38) Longo, G. S.; Olvera de la Cruz, M.; Szleifer, I. Macromolecules 2011, 44 (1), 147−158. (39) Cheng, H.; de la Cruz, M. O. Macromolecules 2006, 39, 1961− 1970. (40) Alberts, B. Cell 1998, 92, 291−294. (41) Robinson, C. V.; Sali, A.; Baumeister, W. Nature 2007, 450, 973−982. (42) de la Cruz, M. O.; Ermoshkin, A. V.; Carignano, M. A.; Szleifer, I. Soft Matter 2009, 5 (3), 629. (43) Tsitsilianis, C.; Iliopoulos, I.; Ducouret, G. Macromolecules 2000, 33, 2936−2943. (44) Katsampas, I.; Tsitsilianis, C. Macromolecules 2005, 38, 1307− 1314. (45) Stavrouli, N.; Aubry, T.; Tsitsilianis, C. Polymer 2008, 49, 1249− 1256. (46) Brockwell, D. J.; Paci, E.; Zinober, R. C.; Beddard, G. S.; Olmsted, P. D.; Smith, D. A.; Perham, R. N.; Radford, S. E. Nat. Struct. Biol. 2003, 10 (9), 731−737. (47) Keten, S.; Buehler, M. J. Nano Lett. 2008, 8 (2), 743−748. (48) Sun, J. K.; Doig, A. J. J. Phys. Chem. B 2000, 104, 1826−1836. (49) Carrion-Vazquez, M.; Oberhauser, A. F.; Fisher, T. E.; Marszalek, P. M.; Li, H.; Fernandez, J. M. Prog. Biophys. Mol. Biol. 2000, 74, 63−91. (50) Lu, H.; Schulten, K. Proteins 1999, 35, 453−463. (51) Rohs, R.; Etchebest, C.; Lavery, R. Biophys. J. 1999, 76, 2760− 2768.

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