Estimating Thermodynamic Stability Relationship of Polymorphs of

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Estimating Thermodynamic Stability Relationship of Polymorphs of Sofosbuvir Ming-Hui Qi, Ming-Huang Hong, Yan Liu, En-Fu Wang, Fuzheng Ren, and GuoBin Ren Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.5b01038 • Publication Date (Web): 24 Aug 2015 Downloaded from http://pubs.acs.org on August 25, 2015

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Crystal Growth & Design

Estimating Thermodynamic Stability Relationship of Polymorphs of Sofosbuvir Ming-Hui Qi,† Ming-Huang Hong,† Yan Liu, En-Fu Wang. Fu-Zheng Ren and Guo-Bin Ren* Laboratory of Pharmaceutical Crystal Engineering & Technology, School of Pharmacy, East China University of Science and Technology, Shanghai 200237, P. R. China

ABSTRACT: The polymorphism of sofosbuvir has been investigated. Three polymorphs have been identified and characterized by X-ray powder diffraction (XRPD) and thermal analysis. Form A and Form B was determined as enantiotropic system according to the Heat of Fusion Rule. The melting data and isobaric heat capacities of both polymorph have been determined calorimetrically, and the solubility data of each polymorph in water at different temperatures have been determined. With these data, the transition temperature (Ttr) was then estimated using solubility extrapolation method, heat of transition (∆Htr) method, melting data method and configurational free energy (Gc) phase diagram method. The values of Ttr was found to be 93.29 o

C, 90.59 oC and 108.37 oC for the first three method, respectively. In the Gc phase diagram

method case, Ttr was found to be 109.25 oC when eq 19 was used, compared to 109.28 oC when eq 20 was used.

INTRODUCTION

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Polymorphism is defined as the ability of a compound to exist in several solid crystalline phases, which have different arrangements and/or conformations of molecules in the solid state.1 Increasing numbers of polymorphs have been recorded over the past decades proving the growing interest in polymorphism in pharmaceutical industry, because of different polymorphs have different properties and solubility. Process parameters such as solvents, temperature, ultrasound, supersaturation, and even storage conditions, can greatly affect the appearance of polymorphs or induce polymorphism.2,3 Polymorphs fall into two types, i.e., enantiotropic system or monotropic system. Polymorphs that are enantiotropic have Ttr, at which, their Gibbs free energy are equal, below the melting temperature (Tm) of the lowest melting polymorph, and the relative stability between two polymorphs changes before and after Ttr. In contrast, polymorphs that are monotropic have their Tt beyond Tm of the polymorphs and one form is always more stable than another across the temperature range.4,5 Therefore, evaluating the thermodynamic stability relationships of polymorphs and estimating in the case of enantiotropic polymorphic pairs is very important for drug development, as a more stable form should be chosen on the basis of the thermodynamic stability. Sofosbuvir6,7 (Sovaldi®; formerly GS-7977; Gilead Sciences, USA) is a novel anti-HCV agent that has demonstrated impressively high SVR rates that have never been seen before in HCVinfected patients. It is a nucleotide analogue inhibitor of the HCV NS5B polymerase that was approved by the United States Food and Drug Administration on 6 December 2013 for the treatment of chronic HCV infection in patients with genotypes 1, 2, 3 or 4, including those with hepatocellular carcinoma meeting Milan criteria (awaiting liver transplantation) and those with HCV/HIV-1 coinfection. There are a number of reports available in the literature on the synthesis8, pharmacology and pharmacokinetics/pharmacodynamics9 or clinical studies10 of


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sofosbuvir. However, the thermodynamic relationship of polymorphs of sofosbuvir has not been reported until now. In this work, we determine the thermodynamic relationship of polymorphs of sofosbuvir, as well as estimate the Ttr of a polymorphic pair which are defined as enantiotropic system on the basis of four methods: solubility extrapolation method, ∆Htr method, melting data method and Gc phase diagram method. It was found that sofosbuvir exists in six polymorphic forms (Forms 1-6), out of which Forms 4 and 5 are solvates, Forms 2 and 3 are very unstable that can easily transform to Form 1 on isolation, while Form 1 will be transformed into Form 6 (refer to as Form A in the context for the purpose of convenient description) as an anhydrous solid when suspends in water 5-50 mg/mL at ambient temperature over a few hours.11 Recently, we found a new crystal form of sofosbuvir named Form B via High-throughput screening technique, Form B will also be transformed into Form A via solution-mediated phase transformation (SMPT). THEORETICAL SECTION Solubility Extrapolation Method. The solubility of a crystal, as a function of the temperature follows van’t Hoff equation12: ln =

Δ 1 1 − (1)

where X is the ideal molar solubility, R is the ideal gas constant, ∆Hf is the heat of fusion, Tm is the onset melting temperature, and T is any temperature. Provided ∆Hf is assumed to be independent of T in a narrow temperature range, therefore, the ln X versus 1/T plot is linear. At the transition temperature, the Gibbs free energies or solubility of two polymorphs are equal. Ttr is then estimated by extrapolating the solubility curves to the intersection point.


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∆Htr Method.13 According to eq 1, at a temperature of T0, the solubility of an enantiotropic polymorphic pair Form A and Form B can be written as below: ln , =

Δ,, 1 1 − (2) ,

ln , =

Δ,, 1 1 − (3) ,

Subtracting eq 3 from eq 2, obtains: ln , − ln , = −

Δ, Δ,, Δ,, + − (4) , ,

where ∆Htr,T0 is the heat of transition at T0 corresponding to the difference in the heat of fusion (∆Hf,A,T0 − ∆Hf,B,T0). In the same manner, at Ttr: ln , ! − ln , ! = −

Δ, ! Δ,, ! Δ,, ! + − = 0 (5) , ,

Provided ∆Hf is assumed to be independent of T in a narrow temperature range, the values of

∆Htr,T0 and ∆Htr,Ttr can be regarded as equal, therefore, subtraction of eq 5 from eq 4 yields: ln , − ln , = −

Δ 1 1 − (6)

Thus, Ttr can be calculated from ∆Htr and solubility at a given temperature T0: )*

&ln , − ln , ' 1 = % + ( Δ

(7)


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Melting Data Method. Yu14 proposed a method to determine the Ttr of a pair of enantiotropic polymorphs. The transition enthalpy (∆Htr,Tm,A) and transition entropy (∆Str,Tm,A) from the lower melting polymorph (Form A) to the higher melting polymorph (Form B) at Tm,A can be computed by the following equations: Δ,,,- = Δ, − Δ, + .

,,4

,,-

Δ6,,,- =

&/0,1 − /0, '23 (8)

,,4 &/ Δ, Δ, 0,1 − /0, ' − +. 23 (9) 3 , , ,,-

where Cp,B and Cp,L are the heat capacities of Form B and the supercooled liquid, respectively.

∆Hf,A and ∆Hf,B, Tm,A and Tm,B are the heat of fusion and melting temperature of Form A and the Form B, respectively. (Cp,L – Cp,B) is assumed constant as the range of the integration (Tm,A to Tm,B) is normally not too large (typically < 20 K). From eqs 8, 9 and ∆G = ∆H – T∆S, obtains: Δ8,,,- = Δ,

, , − 1 + &/0,1 − /0, ' % , − , − , ln ( (10) , ,

where ∆Gtr,Tm,A is the transition free energy from Form A to Form B at Tm,A. Since the value of

∆Gtr,A is determined mainly by the first term in eq 10, it can be obtained that d∆G/dT = -∆S. If ∆G is approximately liner in a temperature range, its value at an arbitrary temperature T below Tm,A can be obtained by: Δ8 = Δ8,,,- − Δ6,,,- & − , ' (11) At Ttr, ∆G equals zero, which gives:


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=

Δ,,,Δ6,,,-

=

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Δ, − Δ, + &/0,1 − /0, '& , − , ' (12) Δ, Δ, , − + &/0,1 − /0, ' ln , , ,

Gc Phase Diagram Method. Configurational terms of the amorphous form and crystalline form, namely, enthalpy (Hc), entropy (Sc), and free energy (Gc) were calculated using the following equations15: ,

9 = Δ − . /0:;

Estimating Thermodynamic Stability Relationship of Polymorphs of

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