Role of molecular charge and hydrophilicityin regulating the kinetics of crystal growthS. Elhadj*†, J. J. De Yoreo‡, J. R. Hoyer‡§, and P. M. Dove*†
*Department of Geosciences, Virginia Tech, Blacksburg, VA 24061; ‡Department of Chemistry and Materials Science, Lawrence Livermore NationalLaboratory, P.O. Box 808, Livermore, CA 94551; and §Department of Pediatrics, University of Pennsylvania School of Medicine andChildren’s Hospital of Philadelphia, Philadelphia, PA 19104
Edited by Joanna Aizenberg, Lucent, Murray Hill, NJ, and accepted by the Editorial Board November 1, 2006 (received for review July 9, 2006)
The composition of biologic molecules isolated from biomineralssuggests that control of mineral growth is linked to biochemicalfeatures. Here, we define a systematic relationship between theability of biomolecules in solution to promote the growth of calcite(CaCO3) and their net negative molecular charge and hydrophilic-ity. The degree of enhancement depends on peptide composition,but not on peptide sequence. Data analysis shows that this rateenhancement arises from an increase in the kinetic coefficient. Weinterpret the mechanism of growth enhancement to be a catalyticprocess whereby biomolecules reduce the magnitude of the dif-fusive barrier, Ek, by perturbations that displace water molecules.The result is a decrease in the energy barrier for attachment ofsolutes to the solid phase. This previously unrecognized relation-ship also rationalizes recently reported data showing accelerationof calcite growth rates over rates measured in the pure system bynanomolar levels of abalone nacre proteins. These findings showthat the growth-modifying properties of small model peptides maybe scaled up to analyze mineralization processes that are mediatedby more complex proteins. We suggest that enhancement of calcitegrowth may now be estimated a priori from the composition ofpeptide sequences and the calculated values of hydrophilicity andnet molecular charge. This insight may contribute to an improvedunderstanding of diverse systems of biomineralization and designof new synthetic growth modulators.
biomineral � calcite � proteins
Organisms are able to achieve rapid rates of mineralizationwhile also selectively inhibiting or completely blocking the
growth of biomineral faces. However, the mechanisms that allowfor such a fine degree of control are poorly understood. Somecalcifiers use the formation of amorphous precursors (1–3),whereas others appear to use classical crystal growth processes(4, 5). The widely accepted view of the latter mechanism is thatmacromolecular modifiers in solution are capable of directinggrowth morphology, but have only neutral or inhibitory effectson growth rate. Recently, this dogma was challenged by showingthat low nanomolar levels of proteins isolated from abalonenacre actually increased rates of calcite growth by as much as5-fold by accelerating the kinetics of molecular step propagationacross mineral surfaces (6, 7).
Additional support for this perspective was provided by atomicforce microscopy (AFM) studies of the dependence of growth onlevels of linear peptides containing one to six aspartic acids (8).That study focused on inhibition occurring at high peptideconcentrations and the role of water in the interactions of thesepeptides with steps during growth. However, further examina-tion of that data also shows that lower concentrations of all ofthese molecules accelerated growth by small amounts that scaledwith chain length (8). Because low levels of both peptides andproteins accelerate calcite growth rates, we now postulate thatthe degree of rate enhancement might be proportional to specificphysicochemical variables such as molecular size or net charge.
A probable relationship between the chemical features ofbiomolecules and crystal growth control is supported by many
observations showing that proteins isolated from sites of biomin-eralization in tissues are unusually enriched in highly acidicamino acids, notably aspartic acid and also glutamic acid (9–13).The Asp-rich motifs have been postulated to function by pref-erentially binding to cations such as Ca2� (14) during thecontrolled formation of minerals such as calcite (12). Underphysiological conditions, the carboxyl groups of aspartic acid arenegatively charged and are believed to engage in electrostaticinteractions with Ca2� ions at the nascent crystal surface (15).Moreover, the charge and stereochemistry of exposed aminoacid side chains are known to mediate specific interactions withcalcite steps and surfaces (16, 17). However, although favoredinteractions and morphological consequences have been dem-onstrated, the mechanistic and kinetic roles of these moleculesin modifying growth, particularly through growth acceleration,are less well understood.
In the present investigation, we sought to better define therelationship between chemical structure and the regulation ofcalcite growth by examining the effects of low concentrations ofAsp-dipeptides and linear aspartic acid-rich peptides (18) thatare intermediate in size when compared with the very smallpeptides (8) and proteins (6, 7) known to accelerate calcitegrowth. We use the results of these studies to show that there isa link between the net molecular charge and hydrophilicity ofbiomolecules and the acceleration of calcite growth.
ResultsThe dependence of molecular step speed on peptide concentrationwas measured by using in situ AFM to image growth on the (104)face of calcite in solutions at a fixed supersaturation, �, of 0.92 (Fig.1). The supersaturation is defined as � � ln(aCa��aCO3�/Ksp),where a denotes the species activity, and Ksp denotes the equilib-rium solubility constant at 25°C. From previous measurements inour group, calcite step velocity dependence on �, v(�), remainslinear up to a � of at least 1.2 in a pure system, although somenonlinearity exists for � � 0.3 (19). Low concentrations of alldipeptides induced increases in step velocities above those observedin peptide-free control experiments and the larger Asp-rich 27-merpeptides induced much larger increases in step velocities (Fig. 2).However, at higher concentrations, step acceleration was reversedwith step speeds decreasing rapidly to zero, an inhibitory effectdiscussed by Elhadj et al. (8).
The step acceleration portions of growth curves were furtheranalyzed to evaluate the relative effects of low concentrations of
Author contributions: S.E. and P.M.D. designed research; S.E. performed research; J.R.H.contributed new reagents/analytic tools; S.E., J.J.D.Y., and P.M.D. analyzed data; and S.E.,J.J.D.Y., J.R.H., and P.M.D. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS direct submission. J.A. is a guest editor invited by the Editorial Board.
11 peptides on growth velocity. The effect on growth rateobserved with each peptide may be expressed as a step velocityratio, v/v0, where v0 is the step speed for the pure system, and vis the step speed in the presence of peptides. For purposes ofanalysis, we used the experimental data from Fig. 2 and the datafrom refs. 6 and 7 to calculate the rate enhancement at anarbitrary concentration of 0.1 �M, (v/v0)0.1�M, by linear inter-polation. Table 1 shows that 0.1-�M levels of the peptidescontaining as many as six aspartic acids enhanced growth by0.5–15% over the control velocity. The v/v0 values at 0.1 �M forlarger synthetic linear 27-mer peptides, (Asp3–Gly)6–Asp3 and(Asp3–Ser)6–Asp3, showed much greater increases in step ve-locity of 64% and 44%, respectively.
To relate these findings for synthetic peptides to effects ofnative proteins, we also calculated interpolated values for(v/v0)0.1�M from the data obtained in the studies of Fu et al. (6)and Kim et al. (7). It should be noted that step velocity data inthese studies were obtained at slightly different supersaturationand ionic strength conditions (6, 7). The most potent additivewas AP8-�, an 8-kDa, highly acidic protein extracted from themineralized tissue of abalone (10). At the 0.1-�M level of thisprotein the acceleration was 150%, a value 10-fold more than forAsp-6, the most potent of the very small peptides (Table 1).
DiscussionTable 1 shows that the rate-enhancing ability of these biomol-ecules is related to their overall acidity. This finding suggests twopossible correlations, one with biomolecule charge and the otherwith hydrophilicity, the latter being a measure of the extent of
solvation around biomolecules in an aqueous solvent. First, weconsider the correlation with molecular charge. Fig. 3 shows thatln[(v/v0)0.1�M] scales approximately linearly with net negativecharge for the entire series of compounds from a single Aspresidue to synthetic polypeptides to full native proteins. The datafor AP7-N, the only hydrophobic peptide overall, deviates fromthe latter trend, suggesting that ln[(v/v0)0.1�M] may also correlatewith increasing hydrophobicity.
To understand the potential mechanism of enhancement, thefactors that control step speed must be considered. At the drivingforce used in this study, the dependence of step speed on calciumactivity exhibits linear kinetics (20). That is,
v � ��a � ae� , [1]
where a and ae are the actual and equilibrium solute activitiesand � is a constant known as the kinetic coefficient (20). Dataon v(�) in the presence of a fixed concentration (10�4 M) ofAsp-1 impurity shows that v(�) is near-linear to linear (21),especially in the range of 0.20 � � � 1.07 (r2 � 0.99) [seesupporting information (SI) Fig. 5]. For the other impuritiesused in this study we assume that v(�) remains linear, especiallyconsidering the very low concentrations (10�4 M) that apply to
a
b
c
d
Fig. 1. Representative in situ AFM images (5.6 2.8 �m) illustrate thesteady-state morphology of calcite growth hillock. (a) In the absence ofgrowth modifiers, the hillock structure exhibits the c-glide plane axis ofsymmetry and four step directions of the symmetrically equivalent obtuse andacute steps. (b and c) In the presence of increasing concentrations of Asp–Hisstep edges become roughened. (d) Illustration shows how the orientation ofthe carbonate groups with respect to the (104) surface gives rise to thedirection-specific differences in the step edge structure of the obtuse andacute step risers.
a
b
Fig. 2. Experimental measurements of step propagation rate along theobtuse direction versus peptide concentration for dipeptides and 27-merpeptides (a) and aspartates of increasing molecular size (b). Normalizedpropagation rates are shown as step velocity in the presence of peptideimpurities, v, over the step velocity without impurities, v0. Note that, whenplotted on linear-log scale diagram (which here spans six orders of magni-tude), the apparent trends shown do not fully reflect the relative magnitudeof the slopes between peptides.
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the regime of growth acceleration (Fig. 2). Thus, the assumptionthat v(�) is linear will produce negligible error in the evaluationof v or � from Eq. 1.
In the present case, because the ratio of calcium to carbonateactivities is fixed at unity in the bulk solution, a and ae can be
replaced by the activities of Ca2�. For v/v0 to exceed unity Eq.1 shows that either ae must decrease or � must increase. But ata supersaturation of 0.92, the value of ae is already 2.5 times lessthan a. Even if ae were decreased to zero, the increase in a � aecould not exceed 1.3 times and thus would be insufficient toaccount for the observed enhancement of �1.6 times measuredhere for (Asp3–Gly)6–Asp3 and as much as five times reportedfor AP8-� protein (6). Moreover, because acidic peptides formcomplexes with Ca2�, the value of ae is more likely to shift toeven higher values. From this analysis we conclude that thevelocity enhancement is, in fact, because of an increase in � andthe enhancement v/v0, is approximately given by �/�0.
The magnitude of � is controlled by two primary factors, thefirst is the density of kink sites along the step nk and the secondis the net probability of attachment to a site, which we write asexp(�Ek/kT), where Ek is an effective barrier to attachment ata kink. In other words, � � nk exp(�Ek/kT). In the regime oflinear kinetics, the kink density is constant (22), althoughchanges in kink density from step impurities cannot be excluded.For the purposes of this analysis, kink density is assumed to beindependent of �. This assumption is equivalent to that alreadymade above on the linearity of v(�) in systems with impuritiesbecause v(�) would become nonlinear if nk depended on � (Eq.1). Moreover, for calcite in this regime the step is likely to berough, i.e., the kink site density has its maximum value andimpurities can only decrease this value by blocking active kinksites (23). This kink blocking effect is suggested at higherconcentrations by the drop in v/v0 (Fig. 2). Thus, in the regimeof acceleration, ln(v/v0) � �E, where �E is the differencebetween Ek in the pure and peptide-bearing systems. Thisanalysis, although crude, leads us to hypothesize that enhance-ment is a catalytic process in which the barrier to reaction isreduced in the presence of the peptides.
Because rates of step propagation depend on the uptake ofcalcium and carbonate ionic units into kink sites at step edges,the relationship in Fig. 3 suggests that the physical basis for themeasured rate enhancements must be related to electrostaticinteractions between impurities and growth sites. Asp-rich im-purities are well known to have preferential interactions withstep edges rather than terraces (8, 17), which hints at possiblescenarios for increasing step velocity. First, the presence of thecharged peptides at the steps could increase the local potentialgradient and, therefore, the electrostatic force for the cations to
Table 1. Physical properties and the normalized step acceleration, (v�v0)0.1�M of obtuse stepsfor the peptides and proteins shown in Figs. 3 and 4
Summary gives data obtained in present study and from previous investigations.
αβ
µ
Fig. 3. Logarithm of step velocity enhancement, (v/v0)0.1�M, versus calculatedpeptide net charge. The normalized step enhancements are reported as thestep velocity interpolated at a 0.1-�M biomolecule concentration relative tothe control (Table 1). Comparisons to Fig. 2 show the growth rate enhance-ments are directly proportional to the initial slope of the experimental data(see Materials and Methods). Values of net charge represent the ionizationstate of the peptides at the experimental pH of 8.5 and were calculated basedon the pKa of functional groups on the individual amino acids of the peptides(Table 1). Legend is color-coded according to synthetic 27-mer peptides,biomineral-associated whole proteins, and synthetic 30-mers of the activeportion of the nacre-specific protein sequences.
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either incorporate into existing kink sites or attach to the stepedges and create new kink sites, thereby increasing step speeds.Whatever the specific processes involved in growth enhancementare, they must involve electrostatic interactions (Fig. 3) thatconstitute a primary driver in these impurity-induced growthrate enhancements.
The above picture ignores the fact that CaCO3 grows byaddition of two distinct species. This consideration raises analternative explanation based on the conventional assumptionthat the desolvation of Ca2� is the rate-limiting step duringCaCO3 formation (24). Because negatively charged peptides cancomplex with cations at the steps (14), the local Ca2� and CO3
2�
stoichiometry may be shifted toward Ca2�-rich, even underconstant saturation, to produce an increase in step velocity (25).
Although the relationship in Fig. 3 indicates that chargedimpurities may interfere with the electrostatic interactions be-tween growth units and the kink site environment, a closerinspection suggests that differences in biomolecule charge alonecannot fully explain the results. For example, whereas Asp–Leuand Asp–His have the same net charge, the latter induces agreater step enhancement (Table 1). Likewise, an explanationbased solely on differences of molecular weight (Table 1) islikewise unsatisfactory; Asp-1, single amino acid, causes greaterenhancement than larger dipeptides such as Asp–Leu, andAsp–Gly (also compare, for ex., a dimer, Asp-2, that produces agreater enhancement effect than AP7-N, a 30-mer with a muchlarger molecular weight). Moreover, these three molecules havethe same net charge. The spread in the data in Fig. 3 make it clearthat, in addition to molecular charge and size, other factors mustplay a role in growth enhancement.
Our previous studies of Asp–calcite interactions show that atthe low concentrations causing growth enhancement, Asp-1, aswell as polyaspartates, have weak electrostatic interactions withthe surface that affect the solvation of the step edge environ-ment. The result is a biomolecule-specific effect on the kineticsof step propagation (8), which suggests the roles of desolvationbarriers to incorporating growth units within kink sites may beimportant. Thus, by modulating kinetic barriers to dehydrationof solvated growth units, changes in growth rates may arise. Totest this idea, for each peptide and protein we calculated themolecular hydrophilicity by using the residues index from Hoppand Woods (26) as described in Materials and Methods. Hydro-philicity is a property that describes the effects of biomoleculeson water-mediated interactions. During crystallization of thesolutes, part of the entropic and enthalpic components of thefree energy change reflects the water structuring at molecularinterfaces and beyond, as water accommodates the solutes, theforming crystal, and the biomolecules (27). These hydrophilicinteractions thus depend on how water molecules interact withthe amino acid moieties of the peptides via ionic, hydrogen,polar, and van der Waals bonds, but also depend on ‘‘hydro-phobic surface patches’’ on parts of the peptides that presentunfavorable water interactions, such as from neutral or nonpolarresidues, and thus restrict water–water binding and structuring(28). Therefore, in essence, we are using hydrophilicity as a proxyfor estimating the extent of water restructuring around each typeof molecule in the system and, also, at the step edges.
Fig. 4 shows that increasing positive values of molecularhydrophilicity correlate well with step propagation rates. Apossible explanation for this effect comes from recent experi-mental studies of step dynamics during growth from solutions(29). There it was concluded that the rate-limiting step duringcrystallization was desolvation of the solute, where the barrier todesolvation was that associated with bulk diffusion limited by therestructuring of water. Specifically, the diffusion barrier toattachment was attributed to ‘‘ . . . repulsive potentials due towater structuring at hydrophobic and hydrophilic surfacepatches . . . ’’ (29). The same diffusion-limited kinetics and po-
tential energy barriers were also shown to control incorporationof small inorganic molecules into solids such as CaCO3 crystals(29). Therefore, from measurements of activation energies ofstep incorporation of small inorganic solutes, the crossing of anenergy barrier is required for the solute-to-solid phase transfor-mation during crystallization, including that of calcite (29), forwhich the barrier was experimentally determined to be 33kJ/mol (0.34 eV per molecule) (19).
Moreover, these water-dependent interactions can have signifi-cant range (30, 31), consistent with our finding that very limitedamounts of peptides produce significant velocity enhancements(Fig. 2). Based on an assumption that the concentration near thesurface is the same as the average in the bulk solution, the addedturnover rate of Ca2� and CO3
2� at the accelerated steps must beon the order of 103 to 104 per peptide per second. However, toeffectively describe the magnitude of the impact of biomolecules onthe solutes, it is more accurate to consider the distribution ofbiomolecules between the surface and the bulk solution becausegrowth is controlled locally at the crystal surface (32). A Langmuir-type adsorption isotherm best predicts this distribution between thebulk solution and the surface fractional coverage of impurities (8,33, 34). Nevertheless, the relatively low amounts of biomoleculesneeded to affect growth rates likely reflect the much larger sizes ofthe biomolecules compared with the solute ions and thus thebiomolecules greater ability to perturb the solvation environment ofthe solute ions compared with smaller impurities (35). Theseenhancements are thus expected to scale with the concentration Ci
of biomolecules [i.e., �(Ci)], in the growth solution up until the pointof onset of inhibition as is indeed experimentally observed (Fig. 2).
µ
αβ
Fig. 4. Logarithm of normalized step enhancement velocity, (v/v0)0.1�M,versus calculated peptide hydrophilicity. The normalized step enhancementsare reported as the step velocity interpolated at a 0.1-�M biomolecule con-centration relative to the control. Peptide hydrophilicity is calculated based onthe Hopp and Woods hydrophilicity scale (26) of the constituents amino acids(see Materials and Methods). Legend is color-coded according to the samescheme used in Fig. 3. Step accelerations and hydrophilicity values are re-ported in Table 1.
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The above relations suggest that the measured rate enhance-ments, as described by an increase in �, stem in part from areduction in the heights of diffusive barriers, Ek, through localperturbation in the structuring of water. The amount, �E, by whichbiomolecules need to reduce Ek to produce the measured enhance-ments in v are then estimated from �E � kTln(v/v0)0.1�M. For1.005 � (v/v0)0.1�M � 2.53 (Table 1), �E ranges from 0.00013 to0.024 eV compared with Ek � 0.34 eV for the formation of calcite(19). Thus reductions in the total energy barrier �8% are requiredto account for the measured enhancements. The exact relationshipbetween the local water restructuring and how biomolecules alterthe energy pathway during crystallization remains unknown. How-ever, the observed correlation in Figs. 3 and 4 suggests that thisvariation in diffusive barrier height, and, therefore, of the reactionrates for the formation of calcite, may be determined a priori, andin large part, by knowledge of the peptides’ constituent amino acidsfrom which the hydrophilicity and net charge values were calcu-lated. In the case of growth enhancement, we propose that thepeptides ability to perturb local water structuring is such that thebarrier for attachment of the growth unit to the solid during phasetransition is reduced. In other words, we propose that the releaseof water molecules around the solutes during incorporation in thesolid is facilitated by the influence of biomolecules on waterstructure. Recent molecular dynamics simulations suggest that anincrease in the structuring of water at the molecular interface canproduce a reduction in the rate of desolvation (36, 37). Therefore,because cations are much more firmly associated with the sur-rounding water molecules and their desolvation is rate limiting (24),the perturbation of the structured water shell should involve that ofCa2� ions in particular. This physical model is consistent with recentfindings that ions on highly charged surfaces are partially dehy-drated (38). In addition, accumulation of Na� counterions onApoferritin proteins was shown to influence the magnitude of theintermolecular hydration forces (39). Thus, simple inorganic cat-ions also have the ability to disrupt the surrounding water structure,and the degree of this entropic effect has been shown to promotedevelopment of negative charges on silica surfaces (40). Moreover,it was recently found that the step kinetics on calcium oxalatemonohydrate could be enhanced by the addition of small amounts(10–25 nM) of Tamm-Horsfall protein (M. Weaver, S. R. Qiu,J.J.D.Y., J.R.H., and W. H. Casey, unpublished data). Increasingthe protein concentration to 75 nM, i.e., toward normal levels inurine, causes the step speed to drop, a pattern of modulation similarto that in the present studies of calcite. These observations suggestthe possibility that the hydrophilicity of organic or inorganic solutescan regulate the degree of growth enhancement, in a variety ofmineral systems.
Although hydrophilicity is strongly related to the ionic charge viahydrogen bond interactions with polar water molecules duringsolvation, it does not entirely depend on charge. Uncharged moi-eties within residues also contribute to reductions or increases in theoverall hydrophilicity of a biomolecule. The degree to which they doso depends on a number of factors, such as their polarity and/or thehydrophobic character of their alkyl or phenyl groups. Thus, ingeneral, the extent of velocity enhancement is the result of somecombination of molecular factors, which include molecular size,charge, hydrophilicity, and secondary structure, which all canimpact the trends seen in Figs. 3 and 4. However, the correlationwith molecular size is clearly not as strong, and determining thedegree to which there is dependence on secondary structure willrequire further experiments that specifically control for this mo-lecular parameter. Nevertheless, hydrophilicity and its impliedimpact on the hydration layer at the growth interface appears to bean important determinant because it is well correlated with theobserved rate increases.
These findings suggest a key role for local biomolecule chem-istry as a microenvironmental control on rates of mineralformation. For example, because impurity contents in calcites
are sensitive to growth rate (19, 41), native biomolecules mayindirectly impact the compositional signatures of some biogeniccalcites that are currently used to interpret formation of paleo-environments. These findings also provide an avenue for de-signing the structural and chemical features of synthetic mole-cules that will allow modulation of growth rates with a degree ofcontrol that is currently expressed only in biogenic minerals.
Materials and MethodsCrystal Substrate and Solution Preparation. Natural calcite crystals(Chihuahua, Mexico) were cleaved to produce 0.2 0.2 0.05cm3 fresh (104) faces as substrates for calcite growth. Calcitesamples were used immediately upon cleaving after a briefcleaning with a nitrogen jet to remove any debris. Growthsolutions were prepared immediately before use from reagentgrade calcium chloride (CaCl2�H2O), sodium bicarbonate(NaHCO3), and sodium chloride (NaCl) dissolved in deionized(�18 M�) and filtered water (0.2 �m). The chemistry of thebaseline growth solution was carefully controlled with ionicstrength fixed at 0.11 M, pH 8.50, and a supersaturation of � �0.92. Supersaturation is defined as � � ln(aCa��aCO3�/Ksp),where a denotes the species activity calculated from Geochem-ist’s Workbench (Urbana, IL) for specified parameters (pH,ionic strength, and temperature), and Ksp denotes the equilib-rium solubility constant at 25°C. For all experiments, the aCa��/aCO3� 1.0. The dipeptides Asp–His, Asp–Leu, Asp–Glu, andAsp–Gly were obtained from Sigma-Aldrich (St Louis, MO).The (Asp3–Gly)6–Asp3 and(Asp3–Ser)6–Asp3 27-mers were syn-thesized as described (42, 43).
In Situ AFM. During calcite growth, we imaged the steady-statemorphology of atomic steps at constant supersaturation (� �0.92) for peptide concentrations from 0 to 0.10 M. Usingestablished methods, calcite was overgrown onto the surface ofa calcite seed crystal in an AFM flow-through cell (50 �l) thatcontinuously supplied the input solution at a rate of 30 ml/h viaa syringe pump. These flow conditions insured that calcitegrowth was reaction and not transport limited as demonstratedin previous studies (44). Measurements of step speeds wereconducted at room temperature with a Digital InstrumentsNanoscope III (Veeco, Santa Barbara, CA) operating in ContactMode. The AFM images were collected by using scan rates of5–20 Hz and a resolution of 512 512, while minimizingtip-surface force interactions during the flow-through of thegrowth solutions to minimize artifactual effects on step edgemorphology and measured velocities (20). Negative (acute) stepvelocities mirrored those obtained for positive (obtuse) steps,although, as in previous reports, the speeds remained lower andshowed greater variability for the acute steps (19, 41). The effectsof peptides on calcite growth were measured in situ by usingAFM measurements of the surface for a series of peptidesbearing solutions at a fixed supersaturation � of 0.92. Allpeptides were aspartate-based. The 27-mers were included togain data concerning effects of molecular size, whereas thedipeptides were included to gain data concerning molecularcharge for ‘‘hydrophobic’’ (Asp–Gly and Asp–Leu), ‘‘basic’’(Asp–His), and ‘‘acidic’’ (Asp–Glu) dipeptides. Step velocitymeasurements were conducted for both the positive and negativestep edge directions on growth hillocks that had equilibratedwith each type of growth solution (20).
Calculation of Step Velocity Enhancement, Peptide Net Charge, andHydrophilicity. The increased growth rates were determined bymeasuring the step propagation velocity in control solutions (� �0.92) and solutions containing low levels of the peptides at thesame driving force (� � 0.92). Step velocity enhancements oraccelerations, (v/v0)0.1�M, were calculated from step velocitymeasurements and determined for a common arbitrary concen-
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tration of 0.1 �M for all peptides. This normalization of the dataassumes the step velocity versus peptide concentration curvesare near-linear at lower peptide concentrations, thus the first twodata points on each curve were used to approximate the corre-sponding initial slope as �vi/�Ci (nm/s per �M, where v is thestep velocity, i represents a given peptide, and Ci is the peptideconcentration) that was used to interpolate the value of v at 0.1�M. The step velocity enhancements thus calculated provide ameasure of the acceleration of step speed caused by the presenceof the peptides in solution and allows comparison across peptidesand proteins on a common concentration basis. Because at lowpeptide concentrations there is a weak dependence of stepvelocity enhancement on peptide concentration, any nonlinear-ity in this region would not cause significant errors in thedetermination of step acceleration, (v/v0)0.1�M. Each of the stepaccelerations reported represent the average over three to sixmeasurements of step velocities from a given growth spiral. Thestandard deviations of the measurements are equal to or lessthan the size of the data points.
Net peptide charge was calculated based on knowledge of thepeptide sequence, pKa values (45) of (i) the individual residuesand (ii) the peptide end groups N and C terminus. Using the wellknown Henderson–Hasselbach equation (46) at the fixed exper-imental pH 8.5, the extent of protonation, i.e., the chargeassociated with individual amino acids, could be calculated andtheir contribution to the net peptide charge summed over theentire peptide sequence. By this approach the net charge is anapproximation that does not take into account, for example, thepeptide 3D structure, and the effects of the local environment onpKa. However, this approximation enables simple determinationof the relative magnitude of the peptide’s net charge.
The peptide hydrophilicity was calculated based on an empir-ical hydrophilicity scale for individual amino acids modified by
Hopp and Woods (26), and derived by Levitt (47) and Nozakiand Tanford (48). This hydrophilicity scale was derived fromamino acid solubility data in aqueous, mixed, and nonaqueoussolvents to determine the free energy change (using the Van’tHoff equation), �G (kJ/mol), during the amino acids transferfrom an aqueous to a nonaqueous phase (47, 48). The hydro-philicity for a given peptide was calculated as the sum of eachindividual amino acid hydrophilicity value making up the aminoacid sequence of the peptide. Hydrophilicity values can be bothpositive for hydrophilic amino acids and negative for hydropho-bic amino acids. Calculating hydrophilicity in this way is arbitraryand does not represent an absolute value of the peptides’hydrophilicity but, rather, is designed to predict the relativehydrophilicity of the peptides. It does not take into account,among other things, the secondary structure of the peptide thatcan reduce solvent exposure of hydrophobic amino acids. How-ever, this type of approach, which simply uses a linear combi-nation of the amino acids’ hydrophilicity, was successfully usedto predict antigenic sites within sequences of a broad range ofantibodies and is thus mostly functional and empirical (26).Other hydrophobicity scales were used for comparison (49–53)and yielded qualitatively similar results, although not as linear aswith the Hopp and Woods scaling (26).
We thank Alex Chernov, Peter Vekilov, and the anonymous reviewer forhelpful comments. The U.S. Department of Energy, Division of Chem-ical Sciences, Geosciences and Biosciences Contract DE-FG02–00ER15112 and National Science Foundation Chemical OceanographyProgram OCE-0526670 provided funding for this project to VirginiaTech. This work was performed under the auspices of the U.S. Depart-ment of Energy by the University of California, Lawrence LivermoreNational Laboratory, under Contract W-7405-Eng-48, and NationalInstitutes of Health Grants DK61673 and DK33501.
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