Liver X receptor modulators

1. A method of treating a subject with disease or disorder selected from common acne, comedones, polymorphs, rosacea, nodulocystic acne, acne conglobate, senile acne, secondary acne, solar acne, medicinal acne, occupational acne, ichthyosis, ichthyosiform conditions, Darier's disease, palmoplantar keratoderma, leukoplakia, leukoplakiform conditions, cutaneous or mucous lichen, cutaneous psoriasis, mucous psoriasis, ungual psoriasis, psoriatic rheumatism, cutaneous atopy, respiratory atopy, gingival hypertrophy, common warts, flat warts, epidermodysplasia verruciformis, oral or florid papillomatoses, T lymphoma, cutaneous T-cell lymphoma, basocellular epithelioma, spinocellular epithelioma, precancerous skin lesions, keratoacanthomas, immune bullous immune diseases, collagen diseases, scleroderma, keratosis, sebaceous function disorders, cicatrization disorders, stretch marks, pigmentation disorders, hyperpigmentation, melasma, hypopigmentation, vitiligo, and alopecia, comprising administering to the subject an effective amount of a compound represented by the following structural formula:

or a pharmaceutically acceptable salt thereof, wherein:

X is N or CR c ;

R 1 is alkyl or —NR a R b ;

R 2 is H; halogen; —CN; —NRC(O)R; —C(O)OR; —C(O)NR a R b ; monocyclic heteroaromatic optionally substituted with one or more groups selected from alkyl, —CN, —NRC(O)R, —C(O)OR, —C(O)NR a R b and halogen; monocyclic non—aromatic heterocycle optionally substituted with one or more groups selected from alkyl, halogen, —CN and ═O; or alkyl optionally substituted by one or more groups selected from halogen, hydroxy, alkoxy, —NR a R b , —NRC(O)R, —NRC(O)O(alkyl), —NRC(O)N(R) 2 , —C(O)OR, thiol, alkylthiol, nitro, —CN, ═O, —OC(O)H, —OC(O)(alkyl), —OC(O)O(alkyl), —OC(O)N(R) 2 and —C(O)NR a R b ;

R 3 is alkyl, haloalkyl, hydroxyalkyl, alkoxyalkyl, cycloalkyl, monocyclic non-aromatic heterocycle, monocyclic heteroaromatic or phenyl, wherein the phenyl, monocyclic non-aromatic heterocycle, and monocyclic heteroaromatic group represented by R 3 are optionally substituted with one or more groups selected from alkyl, halogen, haloalkyl, alkoxy, haloalkoxy, nitro and —CN;

R 4 is halogen, —CN, —OR, —SR, —N(R) 2 , —C(O)R, —C(O)OR, —OC(O)O(alkyl), —C(O)O(haloalkyl), —OC(O)R, —C(O)N(R) 2 , —OC(O)N(R) 2 , —NRC(O)R, —NRC(O)O(alkyl), —S(O)R, —SO 2 R, —SO 2 N(R) 2 , —NRS(O)R, —NRSO 2 R, —NRC(O)N(R) 2 , —NRSO 2 N(R) 2 , haloalkyl, haloalkoxy, cycloalkoxy, cycloalkyl, monocyclic non—aromatic heterocycle, monocyclic heteroaromatic or alkyl, wherein the monocyclic non—aromatic heterocycle, monocyclic heteroaromatic and alkyl group represented by R 4 are optionally substituted with one or more groups selected from —CN, —OR, —SR, —N(R) 2 , ═O, —C(O)R, —C(O)OR, —C(O)O(haloalkyl), —OC(O)R, —OC(O)O(alkyl), —C(O)N(R) 2 , —OC(O)N(R) 2 , —NRC(O)R, —NRC(O)O(alkyl), —S(O)R, —SO 2 R, —SO 2 N(R) 2 , —NRS(O)R, —NRSO 2 R, —NRC(O)N(R) 2 and —NRSO 2 N(R) 2 ;

Each R independently is H or alkyl;

R a and R b are independently H, alkyl or R a and R b can be taken together with the nitrogen to which they are attached to form a monocyclic non-aromatic heterocycle; and

R c is H, alkyl, or halogen.

2. The method of claim 1 , wherein:

R 3 is alkyl, haloalkyl, hydroxyalkyl, alkoxyalkyl, cycloalkyl or phenyl, wherein the phenyl represented by R 3 is optionally substituted with one or more groups selected from alkyl, halogen, haloalkyl, alkoxy, haloalkoxy, nitro and —CN;

R 4 is halogen, —CN, —OR, —SR, —N(R) 2 , —C(O)R, —C(O)OR, —OC(O)O(alkyl), —C(O)O(haloalkyl), —OC(O)R, —C(O)N(R) 2 , —OC(O)N(R) 2 , —NRC(O)R, —NRC(O)O(alkyl), —S(O)R, —SO 2 R, —SO 2 N(R) 2 , —NRS(O)R, —NRSO 2 R, —NRC(O)N(R) 2 , —NRSO 2 N(R) 2 , haloalkyl, haloalkoxy, cycloalkoxy, cycloalkyl or alkyl, wherein the alkyl group represented by R 4 is optionally substituted with one or more groups selected from —CN, —OR, —SR, —N(R) 2 , ═O, —C(O)R, —C(O)OR, —C(O)O(haloalkyl), —OC(O)R, —OC(O)O(alkyl), —C(O)N(R) 2 , —OC(O)N(R) 2 , —NRC(O)R, —NRC(O)O(alkyl), —S(O)R, —SO 2 R, —SO 2 N(R) 2 , —NRS(O)R, —NRSO 2 R, —NRC(O)N(R) 2 and —NRSO 2 N(R) 2 .

3. The method of claim 1 , wherein the compound is represented by the following structural formula:

or a pharmaceutically acceptable salt thereof.

4. The method of claim 1 , wherein the compound is represented by the following structural formula:

or a pharmaceutically acceptable salt thereof.

5. The method of claim 4 , wherein the compound is represented by the following structural formula:

or a pharmaceutically acceptable salt thereof.

6. The method of claim 1 , wherein the compound is represented by the following structural formula:

or a pharmaceutically acceptable salt thereof.

7. The method of claim 6 , wherein the compound is represented by the following structural formula:

or a pharmaceutically acceptable salt thereof.

8. The method of claim 7 , wherein:

R 1 is methyl or —NH 2 ;

R 2 is H or methyl, wherein the methyl group represented by R 2 is optionally substituted with one or more groups selected from halogen, hydroxy, alkoxy, —NR a R b , —NRC(O)R, —NRC(O)O(alkyl), —NRC(O)N(R) 2 , —C(O)OR, thiol, alkylthiol, nitro, —CN, ═O, —OC(O)H, —OC(O)(alkyl), —OC(O)O(alkyl), —C(O)NR a R b and —OC(O)N(R) 2 ;

R 3 is methyl, ethyl, propyl, isopropyl, tent-butyl, sec-butyl, iso-butyl, —CH 2 CF 3 , —CH(CH 2 F) 2 , —CH(CHF 2 ) 2 , —CH(CF 3 ) 2 , —CF(CH 3 ) 2 , —CF 3 , cyclopropyl, cyclobutyl, cyclopentyl cyclohexyl, —C(OH)(CH 3 ) 2 , —CH(OH)(CH 3 ), or phenyl, wherein the phenyl group represented by R 3 is optionally substituted with one or more groups selected from alkyl, halogen, haloalkyl, alkoxy, haloalkoxy, nitro and —CN; and R c , where present, is H.

9. The method of claim 8 , wherein R 2 is H or —CH 2 OH.

10. The method of claim 9 , wherein R 4 is halogen, hydroxy, alkyl, cycloalkyl, cycloalkoxy, alkoxy, haloalkoxy, haloalkyl, —N(R) 2 , —C(O)OH, —C(O)O(alkyl), —C(O)O(haloalkyl), —C(O)(alkyl), —C(O)N(R) 2 , —NRC(O)R, —SO 2 N(R) 2 , —OC(O)N(R) 2 , —CN, hydroxyalkyl or dihydroxyalkyl.

11. The method of claim 10 , wherein R 4 is methyl, ethyl, hydroxy, CF 3 , isopropyl, cyclopropyl, CH 2 OH, —CH(OH)(CH 2 )(OH), —C(OH)(CH 3 ) 2 , —CH(OH)(CH 3 ), —CH(OH)(CH 2 )(CH 3 ), —CH(OH)(CH 2 ) 2 (CH 3 ), —C(O)NH 2 , C(O)N(CH 3 ) 2 , —C(O)OH, —C(O)NH(CH 3 ), C(O)CH 3 , C(O)CH 2 CH 3 , C(O)O(CH 2 )(CH 3 ), —C(O)O (tert-butyl), —C(O)O(C)(CH 3 ) 2 (CF 3 ), —NHC(O)CH 3 , —OCHF 2 , —OCF 3 , —OCH 2 CH 3 , —OCH(CH 3 ) 2 or —OCH 3 .

12. The method of claim 11 , wherein R 4 is alkyl, haloalkyl, cycloalkyl, alkoxy, or haloalkoxy.

13. The method of claim 12 , wherein R 4 is methyl, halogenated methyl, cyclopropyl, —OCHF 2 or —OCH 3 .

14. The method of claim 1 , wherein the compound is represented by a structural formula selected from:

or a pharmaceutically acceptable salt of any of the foregoing.

15. A method of treating a subject with disease or disorder selected from common acne, comedones, polymorphs, rosacea, nodulocystic acne, acne conglobate, senile acne, secondary acne, solar acne, medicinal acne, occupational acne, ichthyosis, ichthyosiform conditions, Darier's disease, palmoplantar keratoderma, leukoplakia, leukoplakiform conditions, cutaneous or mucous lichen, cutaneous psoriasis, mucous psoriasis, ungual psoriasis, psoriatic rheumatism, cutaneous atopy, respiratory atopy, gingival hypertrophy, common warts, flat warts, epidermodysplasia verruciformis, oral or florid papillomatoses, T lymphoma, cutaneous T-cell lymphoma, basocellular epithelioma, spinocellular epithelioma, precancerous skin lesions, keratoacanthomas, immune bullous immune diseases, collagen diseases, scleroderma, keratosis, sebaceous function disorders, cicatrization disorders, stretch marks, pigmentation disorders, hyperpigmentation, melasma, hypopigmentation, vitiligo, and alopecia, comprising administering to the subject an effective amount of a compound of the formula:

or a pharmaceutically acceptable salt thereof.

16. The method of claim 15 , wherein the compound is of the formula:

or a pharmaceutically acceptable salt thereof.