Hydrates and Solid-State Reactivity:A Survey of b-Lactam Antibiotics

MAGALI B. HICKEY, MATTHEW L. PETERSON, ERIC S. MANAS, JUAN ALVAREZ, FREDRIK HAEFFNER, ORN ALMARSSON

TransForm Pharmaceuticals, Inc., 29 Hartwell Avenue, Lexington, Massachusetts 02421

Received 8 September 2006; revised 24 October 2006; accepted 2 November 2006

Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.20919

ABSTRACT: Crystalline hydrates of hydrolytically susceptible pharmaceuticals arecommonly encountered, and are particularly prevalent in the b-lactam class ofantibiotics. In order to rationalize how the apparent chemical incompatibility betweenwater and b-lactams is reduced through crystallization, a review of the publishedliterature and available structural information on the solid state stability was under-taken. A search in the CSD yielded a total of 32 crystal structures of water-containingb-lactamswhichwere examined and classified in terms of hydrogen-bonded networks. Inmost cases the waters of hydration in the single crystal structures were found to fulfillstructural roles and were not sufficiently close in proximity to react with the b-lactamring. Published data for the solid-state of several hydrates were also considered. Ingeneral, the stability data indicate high thermal stability for the crystalline hydrates.Moreover, even whenwatermolecules are in appropriate proximity and orientation withrespect to the b-lactammoiety for a reaction to occur, the crystalline solids remain stable.The use of the crystal structure information along with computational modelingsuggests that a combination of proximal relationships, steric and mechanistic argu-ments can explain the observed solid-state stability of crystalline b-lactam hydrates.� 2007Wiley-Liss, Inc. and theAmericanPharmacists Association JPharmSci 96:1090–1099, 2007

Keywords: hydrates; crystallinity; b-lactam; antibiotic; chemical stability;solid-state; hydrolysis; amorphous

INTRODUCTION

Pharmaceutical hydrates are an important classof pharmaceutical materials which have beenwidely studied in terms of physico-chemicalattributes, including thermal stability, dissolu-tion and bioavailability.1 Several reviews havebeen written exploring the interactions of thewater molecules in crystalline hydrates withother water molecules in the crystal as well asinteractions with the active pharmaceuticalingredient (API).2,3 The contributions of the late

David Grant in this area were of seminalimportance, culminating in his efforts to under-stand functional properties of hydrate–anhydratesystems and the relationships with molecular-level structure.1,4

b-Lactam antibiotics are a broad class of anti-biotics used in the treatment of bacterial infectionscaused by susceptible organisms, including grampositive and gram negative bacteria.5 Thisclass of antibiotics includes penicillin derivatives,cephalosporins, monobactams, and carbapenems.Compounds containing the b-lactam core areknown to react and degrade both in aqueoussolutions and in the solid-state with one of themajor routes of degradation being hydrolysis of theb-lactam ring.6,7 The solid-state stability of thesematerials depends heavily on the crystallinity ofthe compounds and the conditions under which

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This article contains supplementary material, available atwww.interscience.wiley.com/jpages/0022-3549/suppmat.

Correspondence to: Magali B. Hickey (Telephone: þ1-781-674-7833; Fax: 1-781-863-6519; E-mail: MHickey1@tpius.jnj.com)

Journal of Pharmaceutical Sciences, Vol. 96, 1090–1099 (2007)� 2007 Wiley-Liss, Inc. and the American Pharmacists Association

they are stored.8–10 However, the data in theliterature suggest that even hydrates of b-lactams,where water is a putative reactant in degradation,can be remarkably stable in the solid-state andprovide the opportunity to make products withroom-temperature stability of years.8

In order to better understand how watermolecules interact with the b-lactam ring in thesolid-state, a search in the Cambridge StructuralDatabase (CSD) was carried out to identifyhydrates of b-lactams. The purpose of the studywas to evaluate the crystal structures of thehydrates in order to gain insight into the struc-ture/stability relationships. We sought to answerthree basic questions: (1) How are the watermolecules positioned and oriented in crystallineb-lactam structures? (2) Are there cases where thewater molecules are in a particular orientation,given a set of criteria for alignment, to react withthe b-lactam ring? (3) If the water molecules areoriented to react with the electrophilic center inthe b-lactam ring, are there factors that caninhibit reactivity? What follows is the structuralanalysis, classification, computational evaluationand comparison of the solid-state stability forseveral hydrates of b-lactams.

EXPERIMENTAL SECTION

Cambridge Structural Database (CSD) Search

A search of the CSD using (ConQuest v. 1.8; CSDv. 5.27; May 2006 update) was conducted, identi-fying 80 structures containing both the b-lactamcore and water. This search was narrowed downto 32 structures by excluding those that didnot have full 3D coordinates of structures thatcontained heavy atoms, as well as organicsalts, organic solvates, and clathrates. The struc-tures were inspected using Mercury (V. 1.4).REFCODES of all structures are listed in thesupplementary materials section.

Meropenem Degradation Analysis

Data from Reference [10] was digitized usingUnScanIt software (Silk Scientific, Inc., V5.0,Orem, UT). The data were imported to Kaleida-graph 3.5.1 (Synergy Software) for plotting andfurther analysis. The time courses of loss of theactive were fit using the following equation:

% remaining ¼ % initial � ð1�D0 � t1=2Þ ð1Þ

where t is time in days and D0 is a parameter thatis characteristic of the rate in the non-lineardegradation time course of a particular sample.11

Initial rate was also estimated using data forthe first 1% of conversion, which for thefast degrading samples gives relatively lineardegradation profiles.

Modeling

Molecular mechanics calculations were carriedout using the OPLS2005 forcefield, as imple-mented in Macromodel (Macromodel 9.1; Schro-dinger, LLC, Portland, OR). Conformationalstrain imposed by the crystal for the ring-openintermediate (after the b-lactam ring is attackedby water) was evaluated by minimization in thepresence of the remainder of the crystal (trun-cated after three replicates of the unit cell in alldirections and held rigid), as well as minimizationand conformational analysis in solution. Bulkaqueous solvation was taken into account using aGeneralized Born/Surface Area (GB/SA) model.In order to examine the energy landscape ofthe ring-open portion of the molecule whilemaintaining crystal contacts for the remainingportion, calculations were performed holding theatomic coordinates for this latter portion fixedor constrained. Structures were minimized toconvergence within a 0.05 kJ/A-mol gradienttolerance using the Polak–Ribier ConjugateGradient algorithm. Conformational analysiswas performed using the Systematic Pseudo-Monte Carlo (SPMC) and Monte Carlo MultipleMinimum (MCMM) search functionalities ofMacromodel, with a maximum of 10000 searchsteps (convergence for the Monte Carlo simula-tion generally occurred at 1000 steps).

RESULTS AND DISCUSSION

Crystalline b-lactam compounds are generallystable materials, despite the fact that manyof them are hydrates. Both water and theb-lactam, which are necessary for hydrolysisto occur, are present in the b-lactam hydratecrystal lattice. Table 1 is a compilation of b-lactamantibiotics that have been or are currentlymarketed. Based on information in the Physi-cian’s Desk Reference (PDR),12 this search indi-cates that approximately 45% exist as crystallinehydrates.13

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Although the PDR does not exhaustively coverevery b-lactam in use, the data are suggestiveof the prevalence of stable hydrates in marketedb-lactams. Crystallinity appears to be a feature ofall but two of the products, Spectracef (a cepha-losporin) and Invanz (a carbapenem).12

In order to evaluate the structure/propertyrelationships of b-lactam hydrates in the solidstate, three main questions require consideration:(1) How are the water molecules positioned andoriented in crystalline b-lactamstructures? (2) Arethere cases where the water molecules are in aparticular orientation, given a set of criteria foralignment, to react with the b-lactam ring? (3) Ifthe water molecules are oriented to react with theelectrophilic center in the b-lactam ring, are therefactors that can inhibit reactivity?

Solid-State Stability Dependence on Crystallinity

One example of the impact of crystallinity onstability of a b-lactam hydrate is provided by thesolid-state stability of meropenem (MERREM1),a trihydrate of a carbapenem antibiotic. In astudy of solid-state degradation at elevated

temperatures, the stability of meropenem wasfound to be largely dependent on its degree ofcrystallinity.10 An increase in amorphous contenthas a profound effect on the rate and extent ofdegradation of the solid, as shown in Figure 1.Meropenem trihydrate exhibits a roughly 300-foldimprovement in stability compared to a samplecontaining 80% amorphous content, as shown inTable 2. The stability enhancement, calculatedusing the ratio of initial rates (%/day), is aconservative estimate, since it is conceivable thatthe origin of the degradation of the intacttrihydrate is due to a defect population ratherthan intrinsic reactivity within the contiguouscrystal lattice itself.14 While the dependenceof the %/day rate is not a linear function of%trihydrate, the D0 parameter calculated from anonlinear fit of the data (Eq. 1) increases in aroughly proportional manner with decreasing%trihydrate content. This is indicative of acollection of reactive populations that satisfy a‘‘square root of time’’ dependence of the degrada-tion rate. Since it is the initial rate of degradationthat a compound exhibits which is most impor-tant, one can conclude that crystallinity improves

Table 1. Survey of b-Lactam Antibiotics from the Physician’s Desk Reference (PDR)

Compound Name Product1 Class Salt Hydrate Crystalline

Ceftazidime FORTAZ Cephalosporin Pyridinium(inner salt)

5 Yes

Cefpodoxime proxetil VANTIN Cephalosporin — — N/ACefaclor CECLOR Cephalosporin — 1 YesCefepime HCl MAXIPIME Cephalosporin HCl 1 YesCefdinir OMNICEF Cephalosporin — 1* YesCefditoren pivoxil SPECTRACEF Cephalosporin — — NoCefazolin sodium ANCEF Cephalosporin Na — YesAmpicillin

sodium/sulbactamsodium

UNASYN Cephalosporin Na N/A N/A

Cefuroxime ZINACEF Cephalosporin Na — YesCeftibuten dihydrate CEDAX Cephalosporin — 2 YesCefuroxime axetil CEFTIN Cephalosporin — — NoCefproxil CEFXIL Cephalosporin — 1 YesCefotaxime sodium CLAFORAN Cephalosporin Na N/A N/ACefoxitin sodium MEFOXIN Cephalosporin Na — YesAztreonam AZACTAM Monobactam — — YesClavulanate potassium/

ticarcillin sodiumTIMENTIN Penicillin K/Na — N/A

Ampicllin trihydrate N/A Penicillin — 3 YesPiperacillin/tazobactam ZOSYN Penicillin Na — N/AAmoxicillin AMOXIL Penicillin — 3 YesImipenem monohydrate PRIMAXIN Carbapenem — 1 YesErtapenem sodium INVANZ Carbapenem Na — NoMeropenem trihydrate MERREM Carbapenem — 3 Yes

*Anhydrate used in product; hydrate recently disclosed.13

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stability by more than two orders of magnituderelative to the amorphousmaterial of meropenem.The level of improvement will be a function of thespecific compound in question, but similar obser-vations were reported by Pikal and co-workers forcephalosporins.6,7

The solid-state stability of a series of penicillinderivatives has been reported.15 Determination ofactivation free energy of solid-state decompositionat a series of temperatures was carried out,and values obtained at 1008C and 1008C/75%RH allowed for comparison of the stability ofanhydrous and hydrated forms of several crystal-line penicillin antibiotics. The analysis of theDGat

1008C for ampicillin and amoxicillin is shown inFigure 2. The data in Figure 2 indicate thatfor ampicillin, stability is comparable for thetrihydrate as well as the crystalline sodium saltwith DG values of approximately 120 kJ/mol. Inthe case of amoxicillin, the trihydrate appears tobe more stable at elevated temperature andhumidity, whereas the anhydrous form is morestable under dry conditions, which is likely due todehydration of the trihydrate at 1008C.

The examples described herein clearly suggestthat hydrates of b-lactams can be remarkablystable chemically in the solid-state, on par withanhydrate counterparts. Instability in the hydratecan be attributed to the physical loss of crystallinewater, which may result in an increase of amor-phous material, making the material significantlymore susceptible to degradation in the solid stateeven under ostensibly dry conditions.16

Cambridge Structural Database (CSD) Survey

A search in the CSD produced 32 crystal struc-tures of b-lactam hydrates, following eliminationof data sets lacking 3D coordinates as well asexclusion of organic salts, solvates and clathrates.The water environments were described accord-ing to the interactions outlined by Gillon et al.2

Close inspection of the water environments of b-lactam hydrates reveals that water moleculesoccur in 3 hydrogen bonding environments,as shown in Figure 3. Six out of 32 structuresshowed water molecules in environment A, wherewater acts as a donor forming two hydrogenbonds. Environments B and C are represented in13 structures each, with water acting as both adonor and acceptor.

Table 2. Stability Parameters for Meropenem as aFunction of Hydration State at 408C*

% ofTrihydrate

D0 FromFita

Initial Rate(%/Day)b

RelativeReactivityc

100d 0.00076 0.011 1.063 0.016 0.73 6520 0.029 3.4 3� 102

*Derived from fitting of data from Reference [11].aSee Eq. (1).bEstimated from the data in Figure 1, (�1% degradation).cRatio of initial rate relative to the rate deduced for ‘100% of

trihydrate.’dValue for meropenem trihydrate, assuming a negligible

amorphous state.

Figure 1. Time courses ofmeropenem degradation at408C for three different hydration states (data adaptedfrom Reference [11]). The thick dashed lines representnon-linear least-squares fits of the respective data setsto Eq. (1).

Figure 2. DG (kJ/mol) values for the hydrated andanhydrous forms of ampicillin and amoxicillin at 1008C,ambient RH and 1008C, 75% RH. Data adapted fromReference [15].

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One example of a structure displaying environ-ment A is a Penicillin V derivative (refcode:TICPEA),17 where the water molecules bridgetwo molecules of the penicillin through S––O���Hand C––O���H hydrogen bonds, as shown inFigure 4. Themajority of the remaining structurescontained water molecules which were hydrogenbonded to one another as well as the drug. InREFCODE OBIVUQ,18 two molecules of a mono-bactam derivative are bridged by the watermolecule with C––O���H bonds. The water alsohydrogen bonds to neighboring water moleculesthrough O�H���O bonds, as shown in Figure 5.The crystal structure of amoxicillin trihydrate(REFCODE AMOXCT10)19 is an example wherewater molecules exhibit environment C, with themajority of the water molecules held through aseries of C––O���H and O�H���O, as illustrated inFigure 6. The analysis of the water environments

in the structures of b-lactams in the CSD indicatesthat the crystalline materials fall into the threemost common water environments described byGillon et al.2 These observations confirm thatb-lactam hydrates are consistent with previouslycategorized arrangements of water molecules inthe solid state. In 26 of the 32 structures, thewatermolecules adopt donor and acceptor roles simulta-neously and as such are tied up in a manner thatdoes not support the possibility of nucleophillicattack.

Criteria for the reactivity of organic materialsin the solid-state is a subject that has beenextensively studied and reviewed.20 In organicsolid-state reactions, it has been proposed that thereacting molecules must be in close proximity inorder to allow the reaction to proceed. According tothe topochemical postulate, which was first intro-duced by Kohlschutter21 a ‘‘reaction in the solidstate occurs with a minimum amount of atomic ormolecular movement.’’ Based on this set of criteriaSchmidt and Cohen came up with some require-ments of a reaction cavity where molecules are

Figure 3. Most common water environmentsobserved in b-lactam hydrates. A: Environment wherewater is a donor forming two hydrogen bonds. B,C:Environments where water serves as both donor andacceptor. In (C), the electron pairs of the water oxygenare fully engaged in hydrogen-bonding and cannot beconsidered nucleophilic in this context.

Figure 4. Hydrogen bonding of awatermoleculewith2 molecules of a penicillin V derivative REFCODE(TICPEA), illustrating the water in environment A.None-polar hydrogen atoms are excluded for clarity.

Figure 5. Hydrogen bonding of awatermoleculewithtwo molecules of a monobactam derivative and aneighboring water molecule, illustrating the water inenvironment B. REFCODE (OBIVUQ). Non-polarhydrogen atoms are excluded for clarity.

Figure 6. Hydrogen bonding of awatermoleculewithamoxicillin trihydrate and neighboring water mole-cules, illustrating the water in environment C.REFCODE (AMOXCT01). Nonpolar hydrogen atomsare excluded for clarity.

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held together by their nearest neighbors in rigid3Dcavities.22Once a reactionbegins, the geometrychangeswithin the cavity. If the reaction results inminimal geometric changes within the reactantcavity then these are ‘‘topochemically’’ allowed.Criteria for nuclephilic attack on carbonyl systemshave also been suggested by Lipscomb et al.23 andBurgi et al.24 In the systems studied, one of therequirements is for the nucleophile, or the pair ofelectrons on the nucleophile, to be in closeproximity to the electrophilic center, typically�3 A. The approach of the nucleophile or anglewith respect to the plane of the carbonyl isdependent on the distance above and has beendescribed as needing to be within a ‘‘reactionfunnel’’23 in order for reactivity to occur. Morerecently, Bruice and co-workers have publishedseveral papers on the parameters required forintramoleculargeminaldialkyl substitution, refer-red to as the near-attack conformation (NAC).25

TheNACmustmeet two important criteria, whichare that (1) the distance of the nucleophile fromthe electrophilic center must be�3.2 A and (2) thenucleophile must be within a cone of 308 withthe axis being 158 off of the normal of the reactiveplane.

In order to initiate the search for structures ofb-lactam hydrates which may meet the require-ments for reactivity in the solid state, the followingwas considered. First, the hydrogen atoms on thewater molecules in many of the structures werenot resolved, therefore criteria for the approach orangle of the water molecules with respect to theb-lactam carbonyl were not strictly followed.Second, the distances of the water molecules(oxygen atom) to the b-lactam carbonyl carbonwere analyzed and distances that were within thesum of the van der Waals radii of oxygen andcarbon (�3.2 A) were considered.

From the data available in the CSD it wasfound that there are 20 distances within 3–4 A,16 distances between 4–5 A and the majority ofdistances being >5 A. The distances that arewithin 4 A of the b-lactam ring are shown inFigure 7. The analysis indicates that only onestructure, cefadroxil monohydrate, has a watermolecule that satisfies the geometric criteriaestablished for nucleophilic attack to occur in thecrystal. Thevastmajority of thewatermolecules instructures of b-lactam hydrates are too far fromthe reactive center.26 Therefore, they are expectedto be stable to reactivity with water fromthe crystal under ambient conditions. Ampicillintrihydrate,27 shown in Figure 8, was found to be

more stable at room temperature, degrading�10%over 3 years, compared to the crystalline sodiumsalt, which loses the same amount in 1.25 years.28

The water molecules are proximal to the C––O butlie in or near the plane defined by the ring.

In cefadroxil monohydrate (REFCODE JOS-WAP)29 the distance from the water oxygen atomto the b-lactam carbonyl was found to be 3.2 A, asshown in Figure 9. Although this structure meetsthe basic criteria for reactivity, the material hasbeen found to be stable in the solid-state.30

Cefadroxil monohydrate has an interesting his-tory at the interface between chemistry andpatents with the discovery of a second hydratedform (cefadroxil trihydrate) being central to a

Figure 7. Overlay of b-lactam ring in 32 structuresfrom the CSD with all water molecules within 4A fromthe lactam ring.

Figure 8. Packing diagram of ampicillin trihydrate,viewed along the c-axis, indicating the shortest dis-tances from the water oxygen atoms to the b-lactamcarbonyl. Nonpolar hydrogen atoms are excluded forclarity.

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patent dispute.31 The trihydrate has less stabilitydata in the public domain relative to the mono-hydrate, but it is clear that both are sufficientlychemically robust to meet the requirements formaking stable pharmaceutical products. Thestability of the monohydrate leads back to thequestion posed at the beginning of the section: Ifthe water molecules are aligned properly, whatprevents them from reacting in the solid state?

Structural Basis for Stability ofCefadroxil Monohydrate

If one considers the Arrhenius rate law,k ¼ Ae�DEA=RT, there are two basic ways tomodulate the rate constant: via the Arrheniusprefactor A (which includes effects such asrelative orientation of reactants, and steric hin-drance of the initial approach), or the activationenergy DEA. As shown in Figure 10, the relativeenergies of the products, reactants, and transitionstate will determine both the reaction energy(DErxn), as well as the forward and reverseactivation energy barriers.

As discussed above, for most b-lactam crystal-line hydrates the water molecules are so far fromthe b-lactam ring that the Arrhenius prefactor islikely to be extremely small, leading to a very slowreaction rate. However, for cefadroxil monohy-drate, the prefactor is probablymuch larger, due tothe positioning of the water molecule with respect

to the lactam carbonyl. This raises the question ofwhy no apparent catalytic effect on hydrolysis isobserved in the solid state. In what follows, weconsider several arguments based on activationenergy, providing explanations for the stability ofcefadroxilmonohydratewith respect tohydrolysis.

Figure 11 depicts the b-lactam neutral hydro-lysis mechanism.32 The reaction begins the attackbywater of the b-lactam ring (A) to form a reactantcomplex (B), followed by cleavage of the amidebond and proton transfer to the b-lactam nitrogento generate the open-ring product (D). Conversionfrom (B) to (D) can occur either via a singletransition state (concerted) or through a tetrahe-dral second transition state (C) in a step-wisemanner. The mechanism is slightly different foralkaline hydrolysis (attack by OH� rather thanH2O).

Although the exact pathway for hydrolysisremains unclear, there are various effects thatcould potentiate the progression of the reaction.The most obvious perhaps is the ability of interac-tions within the crystal to increase the nucleophi-licity of the water molecule, or to stabilize thepolarization of the amide carbonyl during thereaction, in a fashion analogous to the oxyanion

Figure 9. Illustration of cefadroxilmonohydratewithwater molecules in close proximity to the b-lactamcarbonyl.

Figure 10. Schematic of the energy landscape for achemical reaction.

Figure 11. Schematic of b-lactam neutral hydrolysis(Adapted from Reference [32]).

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hole of b-lactamases. Inspection of interactionswithin the cefadroxil monohydrate crystal sug-gests either of these reaction-enhancementmechanisms are somewhat unlikely in the solidstate.

On the other hand, the crystalline environmentmay provide protection from ancillary waters thatcould lower the free energy of the transition state.Calculations reported by Pitarch et al.32 at theMP2/6-31G* level of theory suggest that anancillary water molecule can lower the activationbarrier of the rate-limiting step for hydrolysis byapproximately 6–13 kcal/mol (depending on themechanism), although there is almost no effectat the Hartree-Fock level of theory. However,application of a continuum dielectric model torepresent bulk solvent was shown to oppose thiseffect. If one considers the resulting change inbarrier height for the fully solvated b-lactam(e.g., high dielectric environment with access toancillarywatermolecules) relative to a crystalline-like environment (low dielectric, without ancillarywaters), the barrier is only lowered by about 1.6–3 kcal/mol in the solvated environment. Althoughthe exact effect on barrier height may varydepending on the level of theory, basis set, andenvironment (e.g., specific interactions in thecrystal), it is clear that the physical barrier toancillary waters provided by the rest of the crystalmay be an important factor in the stability ofcefadroxil monohydrate.

Another factor affecting stability is likely to bethe low degree of conformational flexibility in thecrystal. Studies on the b-lactamase enzyme haveshown that catalysis is accompanied by significantconformational changes in the substrate,33 whichof course can readily occur in a solvent exposedprotein active site. However, the environmentinside of a smallmolecule crystal is quite different.As shown inFigure 12a, localmolecularmechanicsminimization of the open-ringproduct of cefadroxil(post-hydrolysis) followed by superposition onthe cefadroxil monohydrate crystal structureindicates that several atoms would lie outside ofthe molecular surface formed by the rest of thecrystal, indicating steric clashes. Furthermore,localminimization in the presence of the rest of thecrystal leads to a molecular geometry (shown inFig. 12b) that is greater in energy by approxi-mately 24.6 kcal/mol, relative to the global mini-mum in bulk aqueous solvent.34 Thus, assumingminimal relaxation of the reaction cavity, theenergy of the productwould be significantly higherthan if themoleculewere free to relax in solution or

in some other less constrained environment.Although the steric constraints may also raisethe transition state energy to some degree, it is notlikely to be increase asmuch as that of the product.This would effectively lower the activation barrierfor the reverse reaction (see Fig. 10). Therefore, ifthe b-lactam ring openingwere to occur within thecrystal, the energy of the product would be so highrelative to that of the transition state (perhaps

Figure 12. a: ring-open product following hydrolysisof cefadroxil (carbons gray), locally minimized in solu-tion and superimposed on the cefadroxil monohydratestructure. For the purposes of this figure, atoms on theleft hand side of the molecule were held fixed in order toemphasize differences in the ring-open portion of themolecule. Arrows indicate atoms extending outside ofthe molecular surface formed by other molecules in thecrystal. b: Ring-open product minimized in the presenceof the rest of the crystal (held rigid). Hydrogenshave been omitted from (a) and (b) for the sake of clarity.

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even greater) that the nitrogen could attack theacid and re-form the b-lactam.

CONCLUSION

The above findings are consistent withgeneral observations that the rate of hydrolysisdecreases rapidly with time when sealed samplesof b-lactam crystalline hydrates are studied,suggesting that the majority of the hydrolysisoccurs at the surface of the crystal where thereare fewer steric constrains, and access to watermolecules (reactive and ancillary) is greater. Aftera relatively short period of time, the reactionmost likely becomes diffusion-limited, since anywater molecules outside of the solid must diffusethrough a product-layer in order to facilitatefurther hydrolysis. We point out that moleculesin amorphous solids may also have greateraccessibility to multiple waters, in addition togreater conformational flexibility. This is consis-tent with the observation that amorphoussolids are more susceptible to hydrolysis asrelative humidity is increased. It is also importantto distinguish hydrolysis or decomposition ofthe b-lactam in the solid state, which often occursunder elevated temperatures or humidity, andtrue solid state hydrolysis. If decomposition isinduced by heating or humidity (external source)and the reaction occurs close to the melt as isoften the case, then it is difficult to prove thatthe reaction is really taking place in the solidstate.35

Crystalline hydrates of other electrophilicdrugs besides b-lactams have also been studied.The cases of neotame and aspartame illustrate asimilar principle to the one discussed in this paper.The methyl esters are relatively stable in the solidstate unless they are rendered amorphous.36 It isfair to say that b-lactams are among the mostelectrophilic drugs with the lowest barriers to ringopening due to their inherent ring strain. Yet,many important and successful antibiotics havebeen made in the last half century with long-termshelf stability, using crystallinity as the savinggrace in pharmaceutical product design.

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14. Discussion, of the effect of defect density on thedegradation of crystalline b-lactams and theirhydrates can not be supported by publishedliterature and is beyond the scope of the currentwork.

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26. While individual water molecules may be some-what mobile in the crystal lattice, the vibrationalmobility is likely small, as represented by the aniso-tropic displacement parameters. An illustration of2 structures drawn with ellipsoids at 99% prob-ability are shown in the supplementary material.However, as crystalline hydrates are desiccatedand collapse into amorphous phases water mole-cules will become more mobile. For references see:

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34. We point out that the reactant molecule is alsostrained relative to its global minimum in solution,but to a much lesser extent (�5.2 kcal/mol).

35. For another example see: (a) Carstensen JT,Attarchi F, Hou XP. 1985. Decomposition of aspirinin the solid state in the presence of limited amountsof moisture. J Pharm Sci 74:741–745. (b) CarstensenJT, Attarchi F. 1988. Decomposition of aspirin inthe solid state in the presence of limited amounts ofmoisture. III: Effect of temperature and a possiblemechanism. J Pharm Sci 77:318–321. (c) Byrn SR,Xu W, Newman AW. 2001. Chemical reactivity insolid-state pharmaceuticals: formulation implica-tions. Adv Drug Deliv Rev 48:115–136.

36. (a) Leung SS, Padden BE, Munson EJ, Grant DJ.1998. Hydration and dehydration behavior ofaspartame hemihydrate. J Pharm Sci 87:508–513.(b) Dong Z, Salsbury JS, Zhou D, Munson EJ,Schroeder SA, Prakash I, Vyazovkin S, Wight CA,Grant DJ. 2002. Dehydration kinetics of neotamemonohydrate. J Pharm Sci 91:1423–1431.

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