Crystallization Kinetics of Cephalexin Monohydrate in the Presence of

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Crystallization kinetics of cephalexin monohydrate in the presence of cephalexin precursors Matthew A. McDonald, Grant D Marshall, Andreas S Bommarius, Martha A. Grover, and Ronald W. Rousseau Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.9b00429 • Publication Date (Web): 22 Jul 2019 Downloaded from pubs.acs.org on July 23, 2019

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Crystal Growth & Design

Crystallization kinetics of cephalexin monohydrate in the presence of cephalexin precursors Matthew A. McDonald, Grant D. Marshall, Andreas S. Bommarius, Martha A. Grover, Ronald W. Rousseau*

*School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta GA, 30332

The solubility and crystallization kinetics of cephalexin monohydrate, an important β-lactam antibiotic, are reported for the first time for an aqueous solution. The nucleation and growth kinetics are determined with online process analytical technologies (PAT) and offline image analysis to support implementation of a continuous process. Effects of two co-solutes, 7-aminodesacetoxycephalosporanic acid (7-ADCA) and phenylglycine methyl ester (PGME), on nucleation and growth are examined. These co-solutes are precursors in the enzymatic synthesis of cephalexin.

ACS Paragon Plus Environment

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Primary nucleation of cephalexin was unaffected by the co-solutes, but 7-ADCA, even in small quantities ( 1 Well Mixed

0

0

200

400

600

Stir rate,

(rpm)


28

800

1000

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Figure 9. A mixing diagram for the crystallizer geometry used to determine cephalexin crystallization kinetics. Experiments marked with an open circle (○) were well mixed and were used to fit the kinetic model. Experiments marked with a cross (×) showed poor mixing and experiments marked with a plus (+) showed significant foaming.

In Figure 9, the boundary between the poorly mixed (orange) and well mixed (yellow) regions was linearly regressed with the cross (×) points; the boundary compares favorably with the theoretical boundary based on transition to turbulent flow as determined by the measured (solid red line) and extrapolated (dashed red line) Reynolds Number, Re, defined in equation 15.

 D2 Re  

(15)

At suspension densities as low as 1.5%, crystallization in a quiescent vessel led to a “sherbet-like” slurry that would not flow under force of gravity. Similar non-flowability is observed in the non-mixed regions in low-rpm experiments. The non-flowability can be explained through the lens of yield stress; below a critical mixing intensity the slurry behaves as a solid, however above a certain stress the material yields and flows as a


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slurry. Formation of dead zones is a function of both rpm and solids concentration. Dead zones, where the stress due to mixing is below the yield stress, may be expected when the Reynolds number indicates predominately laminar flow (Re < 3,000);38 however, the red line in Figure 8 shows the observed sherbet behavior occurred at Reynolds numbers greater than 3,000. The density used in equation 15 was calculated with the known solids fraction, using a measured liquid density of 1.005 g/mL for a saturated solution at pH 4.5 and a solid density of 1.403 g/mL. The viscosity was measured with a capillary viscometer, which was not practical for solids fraction greater than 1%. Measuring the viscosity of suspensions is difficult; the measured viscosity is an estimate useful for qualitative interpretation of the mixing results. A linear relation between solids fraction and viscosity was measured (supplemental Figure S8) and used to construct the solid portion of the red line in Figure 9 and then extrapolated to higher solids fractions (dashed red line). Dead zones were accompanied by a decrease in the observed rate of desupersaturation, and experiments showing poor mixing behavior were excluded from the parameter fitting routine.


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The boundary of the foaming (blue) region is the convex hull of the experiments that generated foam, with the zero suspension density point being determined with the Froude number, Fr. The foam generated at high stirrer speeds consisted of air bubbles and entrained mother liquor stabilized by the needle-shaped crystals.

Engineered

needle-shaped particles have been used to stabilize surfactant foams,39 and the presence of the crystals in the cephalexin system is critical to the foam stability. Foaming was only observed once crystallization began, and foam accumulated and did not collapse when mixing ceased; FBRM results showed a reduction in counts of nearly 30% which qualitatively indicated a significant amount of solids was sequestered in the foam (supplemental Figure S9). The Froude number indicates formation of aerating surface vortices when Fr is of order unity; in Figure 9, Fr = 1 is indicated at ω = 930, however the real transition is less well-defined than the abrupt change at ω = 930. Fr, defined in Equation 16 (where gr is the acceleration due to gravity), predicted significant aeration at greater than 900 rpm, however Figure 9 shows significant foaming occurred at stir rates as low as 650 rpm (blue region). Foam forming experiments were also


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excluded in the parameter fitting routine, leaving a narrow window in which to operate (yellow region in Figure 9).

Fr  

D 2 gr

(16)

Equation 7 assumes a power law relationship between stirring energy input ε and secondary nucleation rate, B, hence the need to examine a range of stirring rpm. Within the narrow range of well-mixed ω there was no obvious correlation between ε (as calculated with Equation 14) and B. Therefore, the stir power input exponent, p, was set to zero to avoid overfitting the limited data. All further experiments were conducted at 400 rpm for consistency. With p = 0 and no co-solute present, the secondary nucleation rate and growth rate were simultaneously fit (see the next section for discussion of growth rate). The secondary nucleation prefactor, kB, had a value 2.98 × 105 min-1 L-1 (95% C.I: 1.01 × 105 4.95 × 105). The secondary nucleation exponent, b, had a fit value of 0.99, which was not statistically different from b = 1. Since there is a theoretical justification for b to be unity,36 b was set to 1 and a confidence interval was not calculated. The suspension


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density exponent, m, was found to be 0.46 (0.30 0.62). A value of m < 1 suggests secondary nuclei form from crystal-impeller collisions, but not all crystals breed nuclei upon impeller impact; perhaps only crystals of a certain size breed secondary nuclei in such events. Since secondary nucleation is defined in terms of the growth rate (see Equation 7), the effect of co-solutes on secondary nucleation was mathematically captured by the effect of co-solutes on growth rate, which are discussed in the next section. That the growth rate equation completely captured the co-solute dependence may indicate that secondary nucleation occurs by attrition of larger crystals,40 however these data are too sparse to exclude other, less pronounced, effects of co-solutes on secondary nucleation, e.g. surface nucleation.41 In any case, the functional dependence of secondary nucleation and growth on supersaturation is empirical and appears to be the same. In Figure 10 (left), the CSD is shown for pure cephalexin, with PGME (30 mM) as co-solute, and with 7-ADCA (30 mM) as co-solute. A Kolmogorov-Smirnov test (which is agnostic to the underlying distribution) failed to reject the null hypothesis that the


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measured CSD for pure cephalexin and measured CSD for PGME co-solute sampled different underlying distributions at the 95% confidence level. However, as is apparent from the yellow bars at long crystal lengths in Figure 10 (left), a Kolmogorov-Smirnov test rejected the null hypothesis (at the 95% confidence level) that the pure CSD and 7ADCA co-solute CSD came from the same distribution. This result was repeated in several data sets. When fitting the experiments with 7-ADCA co-solute, the value of m (the suspension density exponent in Equation 7) was consistently at the high end of the confidence interval determined for pure cephalexin monohydrate (0.30 0.62). Simulated experiments in silico showed that larger values of m result in wider spread CSDs. It is possible that the presence of 7-ADCA increased the sensitivity of secondary nucleation to the suspension density (i.e. increased m), however, there was no statistically significant difference between the values of m determined from fitting pure experiments and co-solute containing experiments.

Therefore, it was concluded that co-solutes did

not have a substantial impact on the kinetics of secondary nucleation (beyond the proportionality between B and G established in Equation 7), especially when compared to the impact of co-solutes on the kinetics of crystal growth.


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Cephalexin supersaturation

0.4

Normalized frequency

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


No co-solute 30 mM PGME 30 mM 7-ADCA

0.3 0.2 0.1 0

0

20

40

60

80

100

120

No co-solute 30 mM PGME 30 mM 7-ADCA

2.50

2.00

1.50

1.00

0

Crystal Length ( m)

20

40

60

80

Time (minutes)

Figure 10. Left, the final CSD of cephalexin monohydrate without co-solute (blue), with 30 mM PGME co-solute (red), and 30 mM 7-ADCA co-solute (yellow). Right, the desupersaturation of cephalexin without co-solute (blue circle), with 30 mM PGME cosolute (red diamond), and 30 mM 7-ADCA co-solute (yellow square).

Growth kinetics The different co-solutes had different impacts on crystal growth. Having determined that the co-solute impact on nucleation was negligible compared to the impact on growth (these two phenomena were determined simultaneously while fitting crystallization experiments with the PBM), the decrease in desupersaturation rate observed in the presence of co-solutes, particularly 7-ADCA, was the result of growth inhibition by the co-solutes. Two models of growth inhibition were considered, a


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competitive model based on co-solute and solute competing for surface adsorption sites,42, 43 and a step-pinning model based on adsorbed co-solutes impeding advancing growth steps.44 Both models captured the decreased rate of desupersaturation, however only the step-pinning model accounts for the observed incomplete desupersaturation seen in the presence of co-solutes. In Figure 10 (right) the cephalexin supersaturation stopped decreasing at long times in the presence of PGME (red diamonds) or 7-ADCA (yellow squares), a behavior captured by the step pinning model of growth.

kG  S  Scr  S  1 g 1 S  Scr G 0 S  Scr 

(17)

In the step-pinning mechanism of crystal growth inhibition, a modified growth rate, defined in Equation 17, is used when the supersaturation is above a critical supersaturation, Scr, and zero growth rate is used when the supersaturation is below

Scr.

The

critical

supersaturation

prevents

the

solution

from

completely

desupersaturating. Figure 11 shows how the critical supersaturation increased as the concentration of each co-solute increased.


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1.4

Critical supersaturation, Scr

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


7-ADCA

1.3

PGME

1.2 1.1 1 0

20

40

60

80

100

120

Co-solute concentration (mM) Figure 11. The critical supersaturation, Scr, as a function of co-solute concentration. The lines are best fits of Equation 18. The error bars are 95% confidence intervals.

The Langmuir adsorption isotherm was used to fit the dependence of the critical supersaturation on co-solute concentration because the step-pinning mechanism is based on co-solutes adsorbing onto the growing surface. The critical supersaturation depends on the energy required to create new cephalexin monohydrate surface, γ, the area of the growth unit, a, the average spacing between adsorption sites, l, the Langmuir equilibrium coefficient, K, and the concentration of co-solute, ccs according to Equation 18. Using the value of γ calculated from primary nucleation and the fit of Scr in


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Figure 11, the ratio a l evaluated to approximately 1 (fit value of 1.15) for 7-ADCA and 0.5 (fit value of 0.61) for PGME, suggesting that 7-ADCA adsorption sites and cephalexin monohydrate growth units are equally spaced but PGME adsorption sites are spaced over every two growth units. 7-ADCA, containing both an acid and an amine group may be able to form hydrogen bonds with the cephalexin monohydrate crystal in two locations, while PGME, containing only an amine group, may only form a hydrogen bond with the growing crystal in one location. However this interpretation is not definite as there is substantial uncertainty surrounding the values of a l , especially for PGME where the fit to Equation 18 is poor (see Figure 11). PGME and 7-ADCA may also preferentially adsorb onto different crystal faces.

Scr 

 aKccs

kTl 1  Kccs 

1

(18)

The needle-like morphology causes a small crystal surface area (the faces on the ends) to account for the majority of desupersaturation. At high supersaturation, the strong adsorption of 7-ADCA onto the fast growing faces suggests the possibility that 7ADCA would be incorporated into the cephalexin monohydrate crystal; PGME on the


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other hand would not be expected to incorporate into the crystal to the same extent. PXRD did not show any peak shifts in the pattern for cephalexin crystallized with the 7ADCA co-solute, indicating the 7-ADCA and cephalexin are not crystallizing together (as a co-crystal) in a distinct crystal lattice. HPLC showed that crystals produced with 7ADCA co-solute contained 7-ADCA in proportion with the amount of initial 7-ADCA, even after washing with cold water (see supplemental Figure S10). However the amount of 7-ADCA was always less than 0.2% by weight of the final product after washing, indicating washed crystals were of pharmaceutical quality. PGME was not detected in washed crystals produced with PGME co-solute. Discussion of continuous manufacturing All aspects of the design of an end-to-end CM process for cephalexin need to consider the crystallization kinetics of cephalexin monohydrate. The rate of primary nucleation is slow, even at considerable supersaturation, therefore the process should rely on secondary nucleation, either by recycling product crystals or using a well-mixed crystallizer. Secondary nucleation did not depend on the mixing intensity within the range of mixing intensities that were feasible for the studied crystallizer geometry.


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However, the stir rate was important because cephalexin monohydrate suspensions have a propensity to form poorly mixed “sherbets” with insufficient agitation and difficultto-handle foams with excess agitation. In the enzymatic synthesis of cephalexin, one of the parameters than can be used to optimize the process is the reactant concentration ratio of PGME and 7-ADCA.7 This work suggests that, from the viewpoint of crystallization, it is best to run the reaction lean in 7-ADCA. Complete consumption of 7-ADCA in the reaction will lead to lower crystal growth inhibition, rendering more of the cephalexin recoverable (by crystallization) in a shorter time. A 7-ADCA lean process is further supported by the finding that 7-ADCA is more likely than PGME to incorporate into the cephalexin monohydrate crystal, albeit at part per thousand concentrations, and that 7-ADCA is more valuable than PGME. Conclusion The crystallization kinetics of cephalexin monohydrate are reported for the first time in an aqueous environment, summarized in Table 2, and the effect of co-solutes that would be found in the enzymatic synthesis of cephalexin were investigated. The


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solubility was determined over a range of pH values (4 to 8) and at two temperatures (5.0 °C and 25.0 °C), crystallization kinetics were explored only at 25.0 °C. Primary nucleation of cephalexin monohydrate occurred slowly, even at high supersaturation (S > 2), and was not impacted by the presence of PGME or 7-ADCA co-solutes. The secondary nucleation of cephalexin birthed many more crystals than primary nucleation (see Supplemental Figure S11) and depended on the growth rate and suspension density, but did not appear to depend on the mixing power in the regime accessible in this crystallizer geometry. At low mixing intensity the needle-shaped crystals were prone to forming dead zones while at high mixing intensities the needle-shaped crystals stabilized the formation of difficult-to-handle foam. Table 2. Kinetic parameters for the crystallization of cephalexin monohydrate with 95% confidence interval. Confidence interval values marked “ns” indicate parameters that were not significantly different from a theoretically justified value, therefore they have been fixed at the theoretically predicted value. Parameter name

symbol [units]

Primary nucleation prefactor kJ [min-1 L-1]

Value

Lower bound Upper bound

2.54

1.39


41

9.00


Primary nucleation

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Bo

1.79

1.28

2.88

kB [min-1 L-1]

2.98 ×

1.01 × 105

4.95 × 105

exponential Secondary nucleation prefactor

105

b

1.0

ns

ns

m

0.46

0.30

0.62

Mixing power exponent

p

0

ns

ns

Growth prefactor

kG [μm min-1]

6.52

5.16

7.43

growth exponent

g

2.0

ns

ns

Secondary nucleation exponent Suspension density exponent

The crystal growth rate was inhibited by both co-solutes, though 7-ADCA was a more potent inhibitor. 7-ADCA inhibited cephalexin crystal growth by adsorbing onto the growing faces and impeding the advancement of growth steps. These results in aggregate all suggest that an end-to-end CM process for cephalexin would be most efficient in a 7-ADCA-lean configuration. Acknowledgements The authors thank Dr. Giovanni Maria Maggioni for his discussions on nucleation kinetics. We thank the Specialty Separations Center at Georgia Institute of Technology for supporting this project. We gratefully acknowledge funding and insight provided by


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the US FDA under Grant U01FD006484-01. M.A. McDonald also acknowledges support from the NSF I/UCRC Center for Pharmaceutical Development (CPD) (Grant 1540017).


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[38] Sinnott, R. K. (1993) CHAPTER 10 - Equipment Selection, Specification and Design, In Coulson and Richardson's Chemical Engineering (Second Edition) (Sinnott, R. K., Ed.), pp 352-438, Pergamon, Amsterdam. [39] Alargova, R. G., Warhadpande, D. S., Paunov, V. N., and Velev, O. D. (2004) Foam superstabilization by polymer microrods, Langmuir 20, 10371-10374. [40] Garside, J., Rusli, I., and Larson, M. A. (1979) Origin and size distribution of secondary nuclei, AIChE Journal 25, 57-64. [41] Tai, C. Y., Wu, J.-F., and Rousseau, R. W. (1992) Interfacial supersaturation, secondary nucleation, and crystal growth, Journal of Crystal Growth 116, 294306. [42] Kubota, N., and Mullin, J. (1995) A kinetic model for crystal growth from aqueous solution in the presence of impurity, Journal of Crystal Growth 152, 203-208. [43] Albon, N., and Dunning, W. (1962) Growth of sucrose crystals: determination of edge energy from the effect of added impurity on rate of step advance, Acta

Crystallographica 15, 474-476. [44] Parker, R. L. (1970) Crystal Growth Mechanisms: Energetics, Kinetics, and Transport, In Solid State Physics (Ehrenreich, H., Seitz, F., and Turnbull, D., Eds.), pp 151-299, Academic Press.


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Page 48 of 49

Page 49 of 49

For Table of Contents Use Only Crystallization kinetics of cephalexin monohydrate in the presence of cephalexin precursors Matthew McDonald, Grant Marshall, Andreas Bommarius, Martha Grover, Ronald

1.4 7-ADCA

1.3 1.2 PGME

1.1 1 0

50

100

Co-solute concentration (mM)

Normalized frequency

Rousseau Critical supersaturation, S cr

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Pure PGME 7-ADCA

0.04 0.03 0.02 0.01 0

0

50

100

Crystal Length ( m)

150

The co-solutes 7-ADCA and PGME inhibit growth and secondary nucleation of cephalexin crystals below a critical supersaturation, Scr. 7-ADCA is a more potent inhibitor than PGME. Image analysis used to construct size distributions show 7-ADCA resulting in larger average crystal size while PGME does not affect crystal size.

The supporting material document contains information regarding: in-situ IR spectroscopy, simulated crystallization observed with FBRM, offline image analysis, bootstrapping for construction of confidence intervals, details of mixing failure modes, purity analysis, and details of nucleation.


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Crystallization Kinetics of Cephalexin Monohydrate in the Presence of

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