Stefan Tsonchev et al- Phase Diagram for Assembly of Biologically-Active Peptide Amphiphiles

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Phase Diagram for Assembly of Biologically-Active Peptide Amphiphiles ² Stefan Tsonchev,* ,‡,| Krista L. Niece, ‡,§ George C. Schatz, Mark A. Ratner, and Samuel I. Stupp ‡,§ Department of Chemistry and Center for Nanofabrication and Molecular Self-Assembly, and Department of Materials Science and Engineering, and Feinberg School of Medicine, Northwestern UniVersity, EVanston, Illinois 60208, and Department of Chemistry, Northeastern Illinois UniVersity, Chicago, Illinois 60625 ReceiVed: August 5, 2007 We construct a phase diagram for self-assembling biologically active peptide amphiphiles. The structure and stability of the assemblies are studied as a function of pH and salinity of the solution. The general features of the phase diagram are predicted based on theoretical modeling of the self-assembly process, as well as experimental data, and further experiments are performed to verify and ascertain the boundary locations of the diagram. Depending on solution conditions, the amphiphiles can form cylindrical or spherical micelles, intermediate structures between these, or may not assemble at all. We also demonstrate that changing conditions may result in phase transitions among these structures. This type of phase diagram could be useful in the design of certain supramolecular nanostructures by providing information on the necessary conditions to form them. 1. Introduction Peptide amphiphiles comprise a new class of self-assem- bling molecules 1-4 that form materials with nanoscale structure intended for biological applications such as regen- erative medicine. We have recently reported on peptide amphiphiles that under favorable conditions self-assemble from aqueous solutions into cylindrical nanostructures, which subsequently bundle to form networks and, therefore, macro- scopic gels. 1,2 The amphiphilic molecules are designed in such a way that after self-assembly the biologically active functional groups appear on or near the surface of the nanostructures, where they are accessible to the external environment for cell signaling. Changing the conditions under which self-assembly takes place has a dramatic impact on the final shape and properties of the resulting supramolecular nanostructure. The structure does not form if certain conditions are not met. Therefore, it is of crucial importance to determine the most favorable conditions and most efficient means for the formation of a given targeted structure. Also, in many cases the intention is to synthesize molecules that will self-assemble under physiological conditions, and therefore, one must be able to control the self-assembly process within a narrow range of parameters. There has been a large number of studies in molecular self-assembly modeling 5-13 as well as experimental work in this area. 14-35 We have investigated the properties of a partic- ular peptide amphiphile belonging to the general class of self-assembling materials discussed here, intended for use in regenerative medicine. 1,36-39 It was shown that at pH 3 1,40 this amphiphile assembles into cylindrical nanofibers that can bundle to form a gel. The gel can in turn be used as a matrix for cell proliferation. Our analysis determined that the cylindrical shape of the structures is the result of strong directional electrostatic interactions between large dipoles in the headgroups of the amphiphilic molecules under the conditions of the experiment, as well as formation of a - sheet due to hydrogen bonding between the peptide seg- ments of the molecules. 37-39 During these studies it became clear that changing the conditions of the experiment would lead to different charges in the headgroups and hence to very different interactions between the amphiphiles. And indeed, it was observed for negatively charged PA molecule 1,40 that the cylindrical fibers did not form, or they disas- sembled, when the pH of the solution was above the 2-4 range. Since these amphiphiles are intended for physiological applications, it would be desirable for self-assembly to occur at physiological pH. It is, therefore, advantageous to manipulate the shape and stability of the assembly by varying environmental conditions, and in particular, to be able to induce self-assembly at a pH 7. These considerations suggested the current investigation into how the process of self-assembly is affected by changing environmental parameters. Our goal in this work is to build a pH/salinity phase diagram for the peptide amphiphile reported in ref 1 using both modeling and experi- mental characterization. In section 2, we present some theoretical considerations, that determine the general shape of the phase diagram. Section 3 shows results from Monte Carlo and molecular dynamics simulations, intended to verify the theoretical predictions and to give an idea about the stability of the self-assembled structures in the different regions of the diagram. In section 4, we provide results from experiments that were performed to verify the theoretical predictions and to provide a quantitative determi- nation of the two-phase lines in the diagram. Section 5 contains the discussion of results and conclusions. ² Part of the “James T. (Casey) Hynes Festschrift”. * To whom correspondence should be addressed. E-mail address: [email protected]. Department of Chemistry and Center for Nanofabrication and Molecular Self-Assembly, Northwestern University. § Department of Materials Science and Engineering, and Feinberg School of Medicine, Northwestern University. | Northeastern Illinois University. 441 J. Phys. Chem. B 2008, 112, 441-447 10.1021/jp076273z CCC: $40.75 © 2008 American Chemical Society Published on Web 12/19/2007

Transcript of Stefan Tsonchev et al- Phase Diagram for Assembly of Biologically-Active Peptide Amphiphiles

Page 1: Stefan Tsonchev et al- Phase Diagram for Assembly of Biologically-Active Peptide Amphiphiles

Phase Diagram for Assembly of Biologically-Active Peptide Amphiphiles†

Stefan Tsonchev,*,‡,| Krista L. Niece,‡,§ George C. Schatz,‡ Mark A. Ratner, ‡ andSamuel I. Stupp‡,§

Department of Chemistry and Center for Nanofabrication and Molecular Self-Assembly, and Department ofMaterials Science and Engineering, and Feinberg School of Medicine, Northwestern UniVersity, EVanston,Illinois 60208, and Department of Chemistry, Northeastern Illinois UniVersity, Chicago, Illinois 60625

ReceiVed: August 5, 2007

We construct a phase diagram for self-assembling biologically active peptide amphiphiles. The structure andstability of the assemblies are studied as a function of pH and salinity of the solution. The general featuresof the phase diagram are predicted based on theoretical modeling of the self-assembly process, as well asexperimental data, and further experiments are performed to verify and ascertain the boundary locations ofthe diagram. Depending on solution conditions, the amphiphiles can form cylindrical or spherical micelles,intermediate structures between these, or may not assemble at all. We also demonstrate that changing conditionsmay result in phase transitions among these structures. This type of phase diagram could be useful in thedesign of certain supramolecular nanostructures by providing information on the necessary conditions toform them.

1. Introduction

Peptide amphiphiles comprise a new class of self-assem-bling molecules1-4 that form materials with nanoscalestructure intended for biological applications such as regen-erative medicine. We have recently reported on peptideamphiphiles that under favorable conditions self-assemblefrom aqueous solutions into cylindrical nanostructures, whichsubsequently bundle to form networks and, therefore, macro-scopic gels.1,2 The amphiphilic molecules are designed in sucha way that after self-assembly the biologically active functionalgroups appear on or near the surface of the nanostructures,where they are accessible to the external environment for cellsignaling.

Changing the conditions under which self-assembly takesplace has a dramatic impact on the final shape and propertiesof the resulting supramolecular nanostructure. The structure doesnot form if certain conditions are not met. Therefore, it is ofcrucial importance to determine the most favorable conditionsand most efficient means for the formation of a given targetedstructure. Also, in many cases the intention is to synthesizemolecules that will self-assemble under physiological conditions,and therefore, one must be able to control the self-assemblyprocess within a narrow range of parameters.

There has been a large number of studies in molecularself-assembly modeling5-13 as well as experimental work inthis area.14-35 We have investigated the properties of a partic-ular peptide amphiphile belonging to the general class ofself-assembling materials discussed here, intended for use inregenerative medicine.1,36-39 It was shown that at pH≈ 31,40

this amphiphile assembles into cylindrical nanofibers that canbundle to form a gel. The gel can in turn be used as amatrix for cell proliferation. Our analysis determined that thecylindrical shape of the structures is the result of strongdirectional electrostatic interactions between large dipolesin the headgroups of the amphiphilic molecules under theconditions of the experiment, as well as formation of aâ-sheet due to hydrogen bonding between the peptide seg-ments of the molecules.37-39 During these studies it becameclear that changing the conditions of the experiment wouldlead to different charges in the headgroups and hence tovery different interactions between the amphiphiles. Andindeed, it was observed for negatively charged PA molecule1,40

that the cylindrical fibers did not form, or they disas-sembled, when the pH of the solution was above the 2-4range.

Since these amphiphiles are intended for physiologicalapplications, it would be desirable for self-assembly to occurat physiological pH. It is, therefore, advantageous to manipulatethe shape and stability of the assembly by varying environmentalconditions, and in particular, to be able to induce self-assemblyat a pH ≈ 7. These considerations suggested the currentinvestigation into how the process of self-assembly is affectedby changing environmental parameters. Our goal in this workis to build a pH/salinity phase diagram for the peptideamphiphile reported in ref 1 using both modeling and experi-mental characterization.

In section 2, we present some theoretical considerations, thatdetermine the general shape of the phase diagram. Section 3shows results from Monte Carlo and molecular dynamicssimulations, intended to verify the theoretical predictions andto give an idea about the stability of the self-assembled structuresin the different regions of the diagram. In section 4, we provideresults from experiments that were performed to verify thetheoretical predictions and to provide a quantitative determi-nation of the two-phase lines in the diagram. Section 5 containsthe discussion of results and conclusions.

† Part of the “James T. (Casey) Hynes Festschrift”.* To whom correspondence should be addressed. E-mail address:

[email protected].‡ Department of Chemistry and Center for Nanofabrication and Molecular

Self-Assembly, Northwestern University.§ Department of Materials Science and Engineering, and Feinberg School

of Medicine, Northwestern University.| Northeastern Illinois University.

441J. Phys. Chem. B2008,112,441-447

10.1021/jp076273z CCC: $40.75 © 2008 American Chemical SocietyPublished on Web 12/19/2007

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2. Theoretical Considerations

In our earlier work,37 we concluded that at pH values between2 and 4 the peptide amphiphile shown in Figure 1 becomes azwitterion possessing a large dipole in its hydrophilic headgroup,perpendicular to the backbone of the molecule. We explainedthe cylindrical shape of its self-assemblies as a result ofdirectional electrostatic interactions between the dipoles in theheadgroups. A simple scheme, shown in Figure 2, where theinteracting molecules are modeled in a coarse-grained manneras “lolly pops”, or chains of beads, explains the competitionbetween the electrostatic and hydrophobic interactions. In thisqualitative model, the dipoles could be also considered asincluding the hydrogen bonds between the molecules, as thesealso result from electrostatic interactions and have a well-defineddirection.

The hydrophobic interaction between the “lolly pops” by itselfwould lead to the formation of a spherical micelle36 and ismodeled by an interaction potential of the form41

whereγ is a surface tension constant which is treated as a freeparameter used to calibrate the equation, so that it gives theproper hydrophobic energy per particle in the hydrophobic coreof the final assembly. In modeling the molecule in Figure 1, avalue ofγ of 0.7787 in units ofkT at 298 K is appropriate.Dis the distance between the tails of the lolly pops, which isdetermined in the following way. It is taken as the minimumaverage distance between two points on the lolly pop tail. Thefirst point is the center of the smallest sphere in the tail, andthe second is located on the lolly pop axis at 0.44 length units

from the tip. After determiningD in this way, it is shortenedby the distances between each lolly pop axis and its surface, tomeasure the actual distance between the lolly pop surfaces. Themeasure of the range of the hydrophobic interaction,λ, typicallyvaries between 1-2 nm; here we have takenλ to be 2 nm.

The electrostatic interaction between each pair of charges isgiven by

whereq1 andq2 are the two interacting charges separated by adistancer, ε0 is the dielectric permittivity of free space,ε is thedielectric constant of the solution, taken as 78.5, andκ is theDebye length.

The considerations which led to the explanation of thecylindrical structure are based on the higher stability of theparallel formation of lolly pops, assuming that the salt concen-tration in the solution is low, as in the actual experiment.However, it is clear that increased salt concentration would leadto screening of the charges, producing a weaker interactionbetween them. Generally speaking, at some point, the electro-statics would no longer dominate the hydrophobic forces, andthe structure in the right of Figure 2 would be more stable. Thus,we could try to estimate when the electrostatic interaction wouldbe offset by the hydrophobic stabilization. Naively, one couldthink that by using eqs 1 and 2 one could easily construct atranscendental equation forκ from which to estimate the saltconcentration necessary to make the process to the right inFigure 2 preferable. However, the salt concentration calculatedin this way is very high, a few molar, and therefore, thisapproach cannot be used, since eq 2 assumes the Debye-Huckeltheory, which is valid for much lower concentrations, on theorder of 10-2 M. Hence, we have relied on experiment todetermine the level of screening necessary to induce a possiblephase transition between the cylindrical and spherical structuresin this pH range.

On the basis of the pKa values of the component amino acids,we expect that, at a pH lower than 2, the amphiphile moleculeswould possess a charge of+1 each, due to the positive chargeon the guanidino group of the arginine. In this case, assumingfor simplicity that the charges are located at the centers of thelargest spheres of the hydrophilic headgroups, it is easy tocalculate the electrostatic repulsion for two particles at contactas shown in Figure 3. Forκ f ∞ (infinite dilution), theelectrostatic repulsion without the hydrogen bonding amountsto about 0.5 kT at 298 K, whereas the hydrophobic attractionbetween the particles stabilizes the system by-0.78 kT,compared to the reference state of the two particles infinitelyfar apart. The total stabilization of about-0.28 kT would notbe enough to keep the particles together against their thermalmotion if it were not for the hydrogen bonding between them.

Figure 1. Chemical structure of the self-assembling peptide amphiphile studied in this work.

Figure 2. Model of interactions between the peptide amphiphiles forthe pH range 2-4. The parallel arrangement of the molecules ispreferable for low salt concentration due to the more favorableelectrostatic interactions between the (red) headgroups.37 In the caseof very strong screening, the structure on the right is expected to becomemore stable. The opposite charges on the finite dipoles in the hydrophilicheadgroups are shown in black and white.

Eh ) -γe-D/λ (1)

Eel )q1q2e

-r/κ

4πε0εr(2)

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This was found in our earlier work39 to be about 2.7 H-bondsper particle, which is more than 10 kT. Hence, we would expectthe particles to stay together in a cylindrical assembly until apH of about or below 0, when protonation of the backboneamide oxygens in the cysteines would destroy the intermolecularhydrogen bonding and the structures would disassemble, as hasbeen observed in the experiments.40 At this pH, increasing thesalt concentration in the solution to a sufficiently high valuewould screen the charges and allow the particles to assembleinto spheres, since the hydrogen bonding, which favors theformation of cylindrical structures, would be absent. In the nextsection, we will demonstrate this point with Monte Carlosimulations.

Increasing the pH above 4 to about 7 could lead to a totalcharge of-3 in the hydrophilic headgroups due to the negativecharges in the phosphate and carboxylic groups and the positivecharge on the arginine. When the pH reaches about 9, the thiolgroups in the cysteines, whose pKa’s are approximately 9, couldalso acquire a negative charge, bringing the net charge possiblyup to as high as-7. After the pH exceeds about 12.5, thearginine would be neutralized and the total charge could becomeas high as-9. Thus, from the titration points (pKa’s) of thecomponent amino acids (see the marked inflection points inFigure 7), we could infer transition lines of a phase diagramand predict possible phase transitions along the pH coordinate.For negligible salt concentration, in the pH range 4-9, the

electrostatic repulsion is calculated to be between 2.0 and 4.0kT ,which would overcome the hydrophobic attraction betweenthe tails; however, the hydrogen bonding is still expected to bestronger, so we would expect mainly cylindrical nanostructuresin this range, albeit not so stable as the ones observed for thepH range 2-4. Relatively low salt concentration should beenough to stabilize the cylindrical structures and allow them toform the fibers necessary for the gel formation. This is thetargeted range around neutral pH for the envisioned physiologi-cal applications of these amphiphiles.

For pH > 9 and no added salt, a simple calculation showsthat the electrostatic repulsion drastically increases up to about18 kT and cannot be compensated by the hydrophobic interac-tion and the hydrogen bonding in theâ-sheet. Using eq 2 topredict the salt concentration needed to screen the electrostaticrepulsion to the level of these attractive interactions is inad-equate, since the obtained salt concentrations are far above the10-2 M limit of the Debye-Huckel theory. Here, once again,we will rely on experiment to find the transition lines along thesalinity coordinate of the diagram, where the screening of thecharges is strong enough to allow the formation of the cylindricalnanostructures. We will also perform force field moleculardynamics simulations on the system in the pH range 9-12.5 atzero added salt and in 5 M NaCl solution, to demonstrate thestability of the structure at these concentrations and to illustratethe screening effect of the ions.

3. Phase Transitions Predicted from ComputerSimulations

3.1. Monte Carlo Simulations in the Limit pH f 0. Wewill use the approach developed in our earlier work37 to performMonte Carlo simulations on a system consisting of a largenumber of amphiphiles modeled as lolly pops with a charge of+1 at the centers of their hydrophilic headgroups, which wouldbe the charge of the amphiphiles in the limit pHf 0, andhydrophobically interacting tails.

We start the simulations by placingN particles in a cubicbox of lengthL ) 30.0, in relative units for which the distancebetween the center of the largest sphere and the tip of eachlolly pop is unity. The particles are distributed at random, exceptfor a fraction which are put in the center of the box, close toeach other, to serve potentially as a nucleation kernel for themicelle that might be formed. The particles interact accordingto eqs 1 and 2 as explained earlier and are moved one at a time.The motion is somewhat biased along the length of the particleto speed up the simulation in the case when a micelle is formed.

Figure 3. At pH f 0, the two particles (now charged) would staytogether in a spherical formation, provided the salt concentration inthe solution is high enough to screen the electrostatic repulsion betweenthe charges. The charges are shown as black dots in the centers of thelargest spheres of the hydrophilic headgroups.

Figure 4. Left panel shows a sample of an equilibrium configurationof a system of 194 particles with a charge of+1 each in a solution of0.016 M monovalent salt concentration. In a solution of 0.023 Mmonovalent salt concentration, the particles assemble into a sphericalmicelle, shown on the right. The structure is dynamic in nature, withparticles constantly leaving and entering it, while preserving its overallspherical shape.

Figure 5. When the pH is lowered from 3 to about 0 while eliminatingthe charges in the headgroups or making them all positive and screened,the system starts as a cylinder, which collapses into a spherical micelleafter an equilibration period. The initial cylindrical configuration isshown on the left, and a sample snapshot of the equilibrium sphericalconfiguration is shown on the right.

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To investigate the dependence of the resulting structure onsalinity, we have variedκ, corresponding to different saltconcentrations. Atκ ) 24 Å, corresponding to a 0.016 Mmonovalent salt solution, we observe no assembly of particles.Instead, after an equilibration period, the initial kernel falls apartand the particles scatter in the box and remain in such a stateindefinitely, as can be seen from the left panel of Figure 4.However, reducingκ to 20 Å, which is equivalent to increasingthe salt concentration to about 0.023 M, has a dramatic effect

on the system. As a result of the stronger screening, now thehydrophobic interaction prevails and keeps the particles together.After an initial equilibration period, the kernel grows to includealmost all of the particles, which form a dynamical sphericalmicelle, as shown in the right panel of Figure 4.

The limit pH f 0 was achieved experimentally by placingthe self-assembled peptide amphiphile nanofibers in HClvapor,40 and in the above simulations, we have only taken intoaccount the charges on the amphiphiles and the dissolved salt,

Figure 6. Equilibrium structure at pH) 3 and zero salt concentration is used as a starting configuration for the simulations at pH) 11 and shownin the left panel. The P atoms are shown in red, the S atoms are in green, the C atoms of the guanidino group of the arginine are in blue, and therest of the atoms are in gray. The dipoles near the surface, determined by the negatively charged phosphate (red) and positively charged guanidinogroup of the arginine (blue), and the hydrogen bonds between the cysteines, which are outlined by the green S atoms and form aâ-sheet in thelower part of the headgroups, contribute to the order along one of the periodic axes, which is identified as the cylindrical axis of the fullnanostructure.38,39 In the central panel is shown a sample of the resulting structure after several nanoseconds of molecular dynamics simulations atpH ) 11 with no added salt. The destruction of both the dipole-dipole and hydrogen-bonding order is clearly visible. In this structure the head andtail regions of some of the peptide amphiphiles have gotten mixed together, while in the structures shown in the other panels heads interact withheads, and tails with tails. In the right panel we show the structure resulting from the simulations at pH) 11 when an additional 94 Na+ and Cl-

ions are added to the system, approximately a 5 M solution. In this case the original pH 3 structure remains intact due to the screening effect ofthe added salt. In all panels the Na+ and Cl- ions, hydrogen atoms, and water molecules are not shown, for simplicity.

Figure 7. pH/salinity phase diagram of the self-assembling peptide amphiphiles. The experimental verification points (derived from a combinationof visual examination, rheology, TEM) are shown with the figures containing the letters g, i, s, and n, as explained above. Under the diagram, wehave shown the titration curve of the amphiphile, where the titration inflection points corresponding to the transition lines of the diagram areshown. The inset shows the dependence of the damping factorG′′/G′ on pH, with G′′/G′ < 0.2 corresponding to a gel. This provides us with aquantitative picture of the degree of gelation, which is correlated with the length and stability of the fibers.

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whose concentrations are reasonably small so that the Debye-Huckel approach used here is valid. However, it is clear thatthe calculations are only qualitatively useful, and in a truesolution of pHf 0, there would be a much higher concentrationof charged species, which would invalidate the Debye-Huckelapproach. The simulations predict that a phase transition betweenno assembly and a spherical micelle would occur if the saltconcentration is increased past about 0.02 M for pHf 0.Consequently, we would expect that another phase transition,between a cylindrical and a spherical micelle, would be observedat a salt concentration higher than 0.02 M when lowering thepH from the range 2-4 to near 0. This can be demonstrated byanother Monte Carlo simulation which starts from a cylindricalmicelle, with the charges in the headgroups of the amphiphilesswitched to positive and screened, or eliminated for simplicity,as shown in the left panel of Figure 5. It is observed that afteran initial period of equilibration the cylindrical micelle collapsesinto a spherical one and then remains in that state indefinitely.Figure 5 shows the initial state and a snapshot sample of thefinal configuration. Unlike this transition, the micelle remainsin the cylindrical configuration indefinitely if the conditions arenot changed, i.e., pH) 3.37

3.2. Molecular Dynamics Simulations in the pH Range9-12.5.In this pH range, the amphiphiles are highly charged.Here, as well as in the cases of high salinity, the Debye-Huckel theory is inadequate due to the high concentration ofcharged species in solution. Therefore, for these cases we haveused the MM3 force field to perform all-atom moleculardynamics simulations,42 implemented in theTinker package,43

as explained earlier.39 These simulations were run within thecanonical ensemble using the Berendsen algorithm,44 and thehydrogen atoms were constrained at their ideal bond distanceusing therattle algorithm.45 As before, we have performed thesimulations in 2D periodic boundary conditions, starting fromthe equilibrium structure obtained by us earlier for pH) 3,39

which was taken as the initial configuration for a moleculardynamics simulation at pH) 11. For this purpose, we removedthe hydrogens from the four thiols of the cysteines of eachmolecule, as well as from the carboxylic groups, and thecorresponding sulfur and oxygen atoms were charged accord-ingly. To balance the charges, we added 96 Na+ ions in theelementary cell. Also, we have used explicit solvent, adding450 water molecules above the surface of the assembly. Thiswas enough to form at least three layers and ensure properscreening of the charges, after an equilibration periodduring which the water molecules “soaked” the hydrophilicheadgroups.

First, we performed simulations on the system with no addedsalt for several nanoseconds. The initial assembly and a sampleof the resulting structure from these simulations are shown inFigure 6, in the left and central panels, respectively. It is obviousfrom Figure 6 that when no salt is added to the solution theelectrostatic repulsion between the charged thiols and carboxylicgroups destroys theâ-sheet of the self-assembly, as well as theordering of the dipoles in the headgroups. Therefore, at pH)11 and with no added salt in the solution to screen theelectrostatic repulsion, we expect that the amphiphiles wouldnot assemble. On the other hand, if we add enough Na+ andCl- ions, to make up about 5 M solution (in this case 94 ionseach), the screening due to these ions is enough to prevent themicelle from disassembling, and the regularity of theâ-sheetand dipolar ordering in the headgroups is largely retained, ascan be inferred from the right panel of Figure 6. Thus, it isclear that, even at much higher than physiological pH, the

amphiphiles would still assemble if enough salt is added in thesolution to reduce their electrostatic repulsion.

4. Experimental Methods

4.1. General Information. Synthesis of the peptide am-phiphile (PA) in Figure 1 was performed as described previ-ously.1 All other reagents were purchased from Aldrich Chemi-cal Co. (Milwaukee, WI) unless otherwise stated and used asreceived. Synthesis was confirmed by mass spectrometry and1H NMR. Purity was estimated at 85% using analytical HPLC.The PA was dissolved in slightly basic water containing 40molar equiv of dithiothreitol to reduce any disulfide bonds, thenaliquoted, lyophilized, and stored desiccated at-20 °C untilneeded.

4.2. pH Titration. PA was dissolved at 0.1% by weight inMillipore water and sufficient potassium hydroxide to bring thepH to 12.87 as determined by a Mettler-Toledo Delta 320 pHmeter. Basicity was confirmed independently by pH paper.Dilute hydrochloric acid (HCl) was added in aliquots and theresulting pH recorded after stabilization. Approximate pKa’swere determined by plotting pH versus HCl added and identify-ing the corresponding inflection points.

4.3. Oscillating Rheometry.PA was dissolved at 1% byweight in Millipore water and mixed with various quantities ofHCl on the stage of a Paar Physica Modular Compact Rheometer(MCR) 300. A 25 mm parallel plate configuration was used.After 10 min, storage (G′) and loss (G′′) moduli were measuredat 3% strain in a frequency sweep from 100 to 0.1 Hz. Theseparameters were as determined previously.23 The pH of thesolution or gel was measured after the frequency sweep usingpH paper. 4.22 Hz was chosen from the middle of the linearviscoelastic region of the sweep, and data at that frequency wereused to determine the damping factor (G′′/G′). For pH 5, 3.16Hz was used instead, as the linear region ended at this frequency.At pH 6.5, no gelation occurred as gauged by the ratio of storageand loss moduli, and the damping factor was always greaterthan one. All data are the average of two runs.

4.4. Transmission Electron Microscopy.PA was dissolvedat 1% by weight in Millipore water and then diluted 10× inaqueous solutions of various pH and sodium chloride (NaCl)salt concentration. The pH was measured and recorded afterthis dilution using pH paper. Visual observations with regardto gelation were noted at this point as well. After 1 h, 0.1 Niodine solution was added in 100µL aliquots until the solutionremained brown. This was done to oxidize the thiol groups andcovalently capture the solution structure. After several hours,samples containing salt at concentrations higher than 1 M weredialyzed against water at the same pH as the PA solution. Afterhours to days, TEM samples were prepared by drop-casting 10µL of this PA solution onto Quantifoil 1.2/2.3 carbon-coatedcopper grids. The residue was wicked off after 1 min and thegrid rinsed once with distilled water before drying. Sampleswere stained using 2% phosphotungstic acid in water and viewedon an HF8100 Hitachi TEM.

5. Discussion and Conclusions

From theoretical considerations and calculations as well asexperimental results presented above, we have been able to builda semiquantitative pH/salinity phase diagram for the self-assembling peptide amphiphile studied here (shown in Figure7). The phase transitions along the pH axis are determined bythe equivalence points of the amphiphile, as confirmed by itstitration curve shown in the figure. The transition lines alongthe salinity axis are determined by theory and experiment, and

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their agreement is evident in cases where a comparison has beenpossible. It should be pointed out that the actual transition linesare smeared and there is a continuous transition between thedifferent phases, as has been indicated by the transition regions,where an intermediate state exists, with short fibers that areunable to form a gel. The difference between the variousstructures existing in the different regions of the phase diagramcan be seen from the TEM pictures shown in Figure 8, wherewe see gel-forming fibers at low pH and low salinity, contrastedto the disassembled state of the highly charged amphiphiles athigh pH and relatively low salinity.

An important part of the phase diagram, from a practicalperspective, is the region around pH) 7 because it applies tophysiological conditions. Here we see the advantage of havinga phase diagram for such a system, by recognizing that it cansuggest obvious means for self-assembling the amphiphiles ina physiological environment. Namely, increasing the salinityof the environment to below 1 M at pH ≈ 7, allows for self-assembly and gelation, which would be necessary for theformation of a gel matrix for in vivo applications.

We have used theoretical and experimental tools to derive apH/salinity phase digram of self-assembling peptide amphiphilesintended initially for use in regenerative medicine. The diagramshows the regions in which the amphiphiles would assembleinto fibers, forming a gel that could be used as a matrix forcells. The gradual phase transitions between cylindrical fibersand spherical micelles, or a disassembled state, are also shown.We have shown how theory and experiment can be combinedin systematic studies of a complex self-assembly process, toproduce a phase diagram describing how shape and stability ofa self-assembled nanostructure depend on environmental condi-tions.

Acknowledgment. This paper is in honor of Casey Hynes-brilliant chemist, gifted teacher, visionary scientist and warmfriend. This research was supported by grants from DoE (GrantNo. DE-FG0200RT45810/A006), DoD/MURI (Grant No.F49620-00-1-0283), NIH (Grant No. SR01EB003806-02), NSF-MRSEC (Grant No. DMR 0520513), and NSF (Grant No. CHE-0550497). The authors also thank Professor Wes Burghardt atNorthwestern University for access to the rheometer used inthese experiments. The TEM work was performed in the EPICfacility of NUANCE Center at Northwestern University. NU-ANCE Center is supported by NSF-NSEC, NSF-MRSEC, KeckFoundation, the State of Illinois, and Northwestern University.

Supporting Information Available: 1H NMR of PA, HPLCtrace, and full rheology data. This material is available free ofcharge via the Internet at http://pubs.acs.org.

References and Notes

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Figure 8. TEM pictures of the self-assembling amphiphiles. On the left are shown fibers bundled together and forming a gelatinous structure atpH ) 0.5 and zero salinity. The right panel shows the disassembled system at pH) 13.0 in a 0.9 M salt solution, where no structure is seen.

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