US2008312228A1PendingUtilityA1

Pyrimidine compound and medical use thereof

Assignee: JAPAN TOBACCO INCPriority: Jun 11, 2004Filed: Mar 21, 2008Published: Dec 18, 2008
Est. expiryJun 11, 2024(expired)· nominal 20-yr term from priority
A61P 35/00C07C 2601/16C07D 239/545C07D 487/04C07D 239/62C07D 471/04A61K 31/519C07D 471/16C07C 275/30A61P 29/00C07D 239/553C07F 9/53C07C 275/50
64
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Claims

Abstract

The present invention relates to a pyrimidine compound or a pharmaceutically acceptable salt thereof represented by the following formula [I] wherein each symbol is as defined in the specification and a method of therapeutically or prophylactically treating an undesirable cell proliferation, comprising administering such a compound. The compound of the present invention has superior activity in suppressing undesirable cell proliferation, particularly, an antitumor activity, and is useful as an antitumor agent for the prophylaxis or treatment of cancer, rheumatism, and the like. In addition, the compound of the present invention can be a more effective antitumor agent when used in combination with other antitumor agents such as an alkylating agent or metabolism antagonist.

Claims

exact text as granted — not AI-modified
1 . A method of therapeutically or prophylactically treating an undesirable cell proliferation in a mammal comprising administering to the mammal a therapeutic or prophylactic amount of a compound represented by the following formula [I] or a pharmaceutically acceptable salt, hydrate, or solvate thereof: 
     
       
         
         
             
             
         
       
     
     wherein
 X 1  and X 2  are the same or different and each is a carbon atom or a nitrogen atom, a 
 
     
       
         
         
             
             
         
       
     
     moiety is 
     
       
         
         
             
             
         
       
       R 1 , R 2 , and R 6  are the same or different and each is 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, or 
 
     
     
       
         
         
             
             
         
       
       
         wherein m is 0 or an integer of 1 to 4, 
         ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, 
 
       
       R 3 , R 4 , and R 5  are the same or different and each is 
       a hydrogen atom, 
       a hydroxyl group, 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, 
 
       a C 3-12  carbon ring group or 
       a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, or 
 
       R 2  and R 3  are optionally linked to form a C 1-4  alkylene group, or R 4  and R 5  are optionally linked to form a C 1-4  alkylene group, 
       wherein group A is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-4  alkyl group, 
       5) —OR A1  wherein R A1  is a hydrogen atom or a C 1-4  alkyl group, 
       6) —SR A2  wherein R A2  is a hydrogen atom or a C 1-4  alkyl group, 
       7) —NR A3 R A4  wherein R A3  and R A4  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       8) —COOR A5  wherein R A5  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR A6 COR A7  wherein R A6  is a hydrogen atom or a C 1-4  alkyl group, R A7  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       10) —NR A8 COOR A9  wherein R A8  and R A9  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       11) a C 3-12  carbon ring group and 
       12) a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, 
 each of the C 1-4  alkyl groups of the above-mentioned 4), R A1 , R A2 , R A3 , R A4 , R A5 , R A6 , R A7 , R A8  and R A9  is optionally substituted by the same or different 1 to 3 substituents selected from the following group C, and 
 each of the C 3-12  carbon ring groups of the above-mentioned 11) and R A7 , and the heterocyclic groups of 12) and R A7  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C 
 
       group B is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-8  alkyl group, 
       5) a C 2-4  alkenyl group, 
       6) a C 2-4  alkynyl group, 
       7) —OR B1  wherein R B1  is a hydrogen atom or a C 1-4  alkyl group, 
       8) —SR B2  wherein R B2  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR B3 R B4  wherein R B3  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, and R B4  is a hydrogen atom or a C 1-4  alkyl group, 
       10) —NR B5 COR B6  wherein R B5  is a hydrogen atom or a C 1-4  alkyl group, and R B6  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       11) —NR B7 COOR B8  wherein R B7  and R B8  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       12) —NR B9 CONR B10 R B11  wherein R B9 , R B10  and R B11  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       13) —NR B12 CONR B13 OR B14  wherein R B12 , R B13  and R B14  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       14) —NR B15 SO 2 R B16  wherein R B15  is a hydrogen atom or a C 1-4  alkyl group, and R B16  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       15) —SO 2 —R B17  wherein R B17  is a C 1-4  alkyl group or a heterocyclic group, 
       16) —SO 2 NR B18 R B19  wherein R B18  and R B19  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       17) —P(═O)(R B20 )(R B21 ) wherein R B20  and R B21  are the same or different and each is a C 1-4  alkyl group, 
       18) —COOR B22  wherein R B22  is a hydrogen atom or a C 1-4  alkyl group, 
       19) —CONR B23 R B24  wherein R B23  and R B24  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       20) —NR B25 SO 2 NR B26 R B27  wherein R B25 , R B26  and R B27  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       21) —NR B28 SO 2 NR B29 CONR B30 R B31  wherein R B28 , R B29 , R B30  and R B31  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       22) a C 3-12  carbon ring group and 
       23) a heterocyclic group
 wherein each of the “C 1-8  alkyl group” of the above-mentioned 4), and the C 1-4  alkyl groups for R B1  to R B31  is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 each of the C 2-4  alkenyl group of 5) and the C 2-4  alkynyl group of 6) is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and 
 each of the C 3-12  carbon ring group of the above-mentioned 22), R B3 , R B6  and R B16 , and the heterocyclic group of the above-mentioned 23), R B3 , R B6 , R B16  and R B17  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C, and 
 
       group C is a group consisting of 
       1) a halogen atom, 
       2) a cyano group, 
       3) a C 1-4  alkyl group, 
       4) —OR C1  wherein R C1  is a hydrogen atom or a C 1-4  alkyl group, 
       5) —NR C2 R C3  wherein R C2  and R C3  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       6) —COOR C4  wherein R C4  is a hydrogen atom or a C 1-4  alkyl group and 
       7) an oxo group,
 whereupon the undesirable cell proliferation is treated. 
 
     
   
   
       2 . The method of  claim 1 , wherein the compound is represented by the following formula [I-1]: 
     
       
         
         
             
             
         
       
     
     wherein each symbol in the formula is as defined in  claim 1 . 
   
   
       3 . The method of  claim 1 , wherein the compound is represented by the following formula [I-2]: 
     
       
         
         
             
             
         
       
       wherein each symbol in the formula is as defined in  claim 1 . 
     
   
   
       4 . The method of  claim 1 , wherein the compound is represented by the following formula [I-3]: 
     
       
         
         
             
             
         
       
       wherein each symbol in the formula is as defined in  claim 1 . 
     
   
   
       5 . The method of  claim 1 , wherein R 1  is a C 1-6  alkyl group. 
   
   
       6 . The method of  claim 1 , wherein R 1  is 
     
       
         
         
             
             
         
       
       wherein m is 0, and ring Cy is a C 3-12  carbon ring group, 
       wherein the C 3-12  carbon ring group is optionally substituted by 1 to 5 substituents selected from group B of  claim 1 . 
     
   
   
       7 . The method of  claim 1 , wherein R 1  is a C 3-8  cycloalkyl group. 
   
   
       8 . The method of  claim 7 , wherein R 1  is a cyclopropyl group. 
   
   
       9 . The method of  claim 1 , wherein R 2  is 
     
       
         
         
             
             
         
       
       wherein m is 0, and ring Cy is a C 3-12  carbon ring group or a heterocyclic group, 
       wherein the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from group B of  claim 1 . 
     
   
   
       10 . The method of  claim 1 , wherein R 3  is a C 1-6  alkyl group. 
   
   
       11 . The method of  claim 1 , wherein R 4  is a hydrogen atom. 
   
   
       12 . The method of  claim 1 , wherein R 5  is a hydrogen atom. 
   
   
       13 . The method of  claim 1 , wherein R 6  is 
     
       
         
         
             
             
         
       
       wherein m is 0, and ring Cy is a C 3-12  carbon ring group or a heterocyclic group, 
       wherein the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from group B of  claim 1 . 
     
   
   
       14 . The method of  claim 1 , wherein the undesirable cell proliferation causes rheumatism. 
   
   
       15 . The method of  claim 1 , wherein the undesirable cell proliferation causes a tumor. 
   
   
       16 . A compound represented by the following formula [I′] or a pharmaceutically acceptable salt thereof: 
     
       
         
         
             
             
         
       
       wherein 
       X 1  and X 2  are the same or different and each is a carbon atom or a nitrogen atom, a 
     
     
       
         
         
             
             
         
       
     
     moiety is 
     
       
         
         
             
             
         
       
       R 1′ , R 2′  and R 6  are the same or different and each is 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group, 
       wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, or 
     
     
       
         
         
             
             
         
       
       m is an integer of 0 or 1 to 4, 
       ring Cy is a C 3-12  carbon ring group or a heterocyclic group 
       wherein the heterocyclic group is a saturated or unsaturated ring having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, 
       R 3 , R 4 , and R 5  are the same or different and each is 
       a hydrogen atom, 
       a hydroxyl group, 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, 
 
       a C 3-12  carbon ring group or 
       a heterocyclic group, 
       wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, or 
       R 4  and R 5  are optionally linked to form a C 1-4  alkylene group, 
       wherein group A is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-4  alkyl group, 
       5) —OR A1  wherein R A1  is a hydrogen atom or a C 1-4  alkyl group, 
       6) —SR A2  wherein R A2  is a hydrogen atom or a C 1-4  alkyl group, 
       7) —NR A3 R A4  wherein R A3  and R A4  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       8) —COOR A5  wherein R A5  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR A6 COR A7  wherein R A6  is a hydrogen atom or a C 1-4  alkyl group, R A7  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       10) —NR A8 COOR A9  wherein R A8  and R A9  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       11) a C 3-12  carbon ring group and 
       12) a heterocyclic group, 
       wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, 
       each of the C 1-4  alkyl groups of the above-mentioned 4), R A1 , R A2 , R A3 , R A4 , R A5 , R A6 , R A7 , R A8  and R A9  is optionally substituted by the same or different 1 to 3 substituents selected from the following group C, and 
       each of the C 3-12  carbon ring groups of the above-mentioned 11) and R A7 , and the heterocyclic groups of 12) and R A7  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C 
       group B is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-8  alkyl group, 
       5) a C 2-4  alkenyl group, 
       6) a C 2-4  alkynyl group, 
       7) —OR B1  wherein R B1  is a hydrogen atom or a C 1-4  alkyl group, 
       8) —SR B2  wherein R B2  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR B3 R B4  wherein R B3  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, and R B4  is a hydrogen atom or a C 1-4  alkyl group, 
       10) —NR B5 COR B6  wherein R B5  is a hydrogen atom or a C 1-4  alkyl group, and R B6  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       11) —NR B7 COOR B8  wherein R B7  and R B8  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       12) —NR B9 CONR B10 R B11  wherein R B9 , R B10  and R B11  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       13) —NR B12 CONR B13 OR B14  wherein R B12 , R B13  and R B14  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       14) —NR B15 SO 2 R B16  wherein R B15  is a hydrogen atom or a C 1-4  alkyl group, and R B16  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       15) —SO 2 —R B17  wherein R B17  is a C 1-4  alkyl group or a heterocyclic group, 
       16) —SO 2 NR B18 R B19  wherein R B18  and R B19  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       17) —P(═O)(R B20 )(R B21 ) wherein R B20  and R B21  are the same or different and each is a C 1-4  alkyl group, 
       18) —COOR B22  wherein R B22  is a hydrogen atom or a C 1-4  alkyl group, 
       19) —CONR B23 R B24  wherein R B23  and R B24  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       20) —NR B25 SO 2 NR B26 R B27  wherein R B25 , R B26  and R B27  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       21) —NR B28 SO 2 NR B29 CONR B30 R B31  wherein R B28 , R B29 , R B30  and R B31  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       22) a C 3-12  carbon ring group and 
       23) a heterocyclic group 
       wherein each of the “C 1-8  alkyl group” of the above-mentioned 4), and the C 1-4  alkyl groups for R B1  to R B31  is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A,
 each of the C 2-4  alkenyl group of 5) and the C 2-4  alkynyl group of 6) is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 
       the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and 
       each of the C 3-12  carbon ring group of the above-mentioned 22), R B3 , R B6  and R B16 , and the heterocyclic group of the above-mentioned 23), R B3 , R B6 , R B16  and R B17  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C, and 
       group C is a group consisting of 
       1) a halogen atom, 
       2) a cyano group, 
       3) a C 1-4  alkyl group, 
       4) —OR C1  wherein R C1  is a hydrogen atom or a C 1-4  alkyl group, 
       5) —NR C2 R C3  wherein R C2  and R C3  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       6) —COOR C4  wherein R C4  is a hydrogen atom or a C 1-4  alkyl group and 
       7) an oxo group, 
       provided that, when the 
     
     
       
         
         
             
             
         
       
       moiety is 
     
     
       
         
         
             
             
         
       
       then R 2′  is not a methyl group, and 
       when R 2′  is a phenyl group, then R 1′  is not a phenyl group. 
     
   
   
       17 . A pharmaceutical composition which comprises
 (a) a compound of  claim 16  or a pharmaceutically acceptable salt thereof, and   (b) a pharmaceutically acceptable carrier.   
   
   
       18 . A commercial package comprising
 (i) a pharmaceutical composition comprising   (a) a compound of the formula [I] of  claim 1  or a pharmaceutically acceptable salt thereof, and   (b) a pharmaceutically acceptable carrier and   (ii) a written matter associated therewith, wherein the written matter states that the pharmaceutical composition can or should be used for treating a disease caused by an undesirable cell proliferation.   
   
   
       19 . The commercial package of  claim 18 , wherein the disease is a tumor or rheumatism. 
   
   
       20 . A pharmaceutical composition comprising
 (a) a compound of the formula [I] of  claim 1  or a pharmaceutically acceptable salt thereof,   (b) at least one antitumor compound that is not a compound of the formula [I], and   (c) a pharmaceutically acceptable carrier.   
   
   
       21 . A kit comprising
 (i) a pharmaceutical composition comprising   (a) a compound of the formula [I] of  claim 1  or a pharmaceutically acceptable salt thereof, and   (b) a pharmaceutically acceptable carrier; and   (ii) a pharmaceutical composition comprising   (a) at least one antitumor agent that is not a compound of the formula [I], and   (b) a pharmaceutically acceptable carrier.   
   
   
       22 . A method of inhibiting MEK in a mammal comprising administering to the mammal an MEK inhibiting amount of a compound represented by the following formula [I] or a pharmaceutically acceptable salt, hydrate, or solvate thereof: 
     
       
         
         
             
             
         
       
     
     wherein
 X 1  and X 2  are the same or different and each is a carbon atom or a nitrogen atom, a 
 
     
       
         
         
             
             
         
       
     
     moiety is 
     
       
         
         
             
             
         
       
       R 1 , R 2 , and R 6  are the same or different and each is 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, or 
 
     
     
       
         
         
             
             
         
       
       
         wherein m is 0 or an integer of 1 to 4, 
         ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, 
 
       
       R 3 , R 4 , and R 5  are the same or different and each is 
       a hydrogen atom, 
       a hydroxyl group, 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6 alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, 
 
       a C 3-12  carbon ring group or 
       a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, or 
 
       R 2  and R 3  are optionally linked to form a C 1-4 alkylene group, or R 4  and R 5  are optionally linked to form a C 1-4 alkylene group, 
       wherein group A is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-4  alkyl group, 
       5) —OR A1  wherein R A1  is a hydrogen atom or a C 1-4  alkyl group, 
       6) —SR A2  wherein R A2  is a hydrogen atom or a C 1-4  alkyl group, 
       7) —NR A3 R A4  wherein R A3  and R A4  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       8) —COOR A5  wherein R A5  is a hydrogen atom or a C 1-4  alkyl group. 
       9) —NR A6 COR A7  wherein R A6  is a hydrogen atom or a C 1-4  alkyl group, R A7  is a C 1-4 alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       10) —NR A8 COOR A9  wherein R A8  and R A9  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       11) a C 3-12  carbon ring group and 
       12) a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, 
 each of the C 1-4  alkyl groups of the above-mentioned 4), R A1 , R A2 , R A3 , R A4 , R A5 , R A6 , R A7 , R A8  and R A9  is optionally substituted by the same or different 1 to 3 substituents selected from the following group C, and 
 each of the C 3-12  carbon ring groups of the above-mentioned 11) and R A7 , and the heterocyclic groups of 12) and R A7  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C 
 
       group B is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-8  alkyl group, 
       5) a C 2-4  alkenyl group, 
       6) a C 2-4  alkynyl group, 
       7) —OR B1  wherein R B1  is a hydrogen atom or a C 1-4  alkyl group, 
       8) —SR B2  wherein R B2  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR B3 R B4  wherein R B3  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, and R B4  is a hydrogen atom or a C 1-4  alkyl group, 
       10) —NR B5 COR B6  wherein R B5  is a hydrogen atom or a C 1-4  alkyl group, and R B6  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       11) —NR B7 COOR B8  wherein R B7  and R B8  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       12) —NR B9 CONR B10 R B11  wherein R B9 , R B10  and R B11  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       13) —NR B12 CONR B13 R B14  wherein R B12 , R B13  and R B14  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       14) —NR B15 SO 2 R B16  wherein R B15  is a hydrogen atom or a C 1-4  alkyl group, and R B16  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       15) —SO 2 —R B17  wherein R B17  is a C 1-4  alkyl group or a heterocyclic group, 
       16) —SO 2 NR B18 R B19  wherein R B18  and R B19  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       17) —P(═O)(R B20 )(R B21 ) wherein R B20  and R B21  are the same or different and each is a C 1-4  alkyl group, 
       18) —COOR B22  wherein R B22  is a hydrogen atom or a C 1-4  alkyl group, 
       19) —CONR B23 R B24  wherein R B23  and R B24  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       20) —NR B25 SO 2 NR B26 R B27  wherein R B25 , R B26  and R B27  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       21) —NR B28 SO 2 NR B29 CONR B30 R B31  wherein R B28 , R B29 , R B30  and R B31  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       22) a C 3-12  carbon ring group and 
       23) a heterocyclic group
 wherein each of the “C 1-8  alkyl group” of the above-mentioned 4), and the C 1-4 alkyl groups for R B1  to R B31  is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 each of the C 2-4  alkenyl group of 5) and the C 2-4  alkynyl group of 6) is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and 
 each of the C 3-12  carbon ring group of the above-mentioned 22), R B3 , R B6  and R B16 , and the heterocyclic group of the above-mentioned 23), R B3 , R B6 , R B16  and R B17  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C, and 
 
       group C is a group consisting of 
       1) a halogen atom, 
       2) a cyano group, 
       3) a C 1-4  alkyl group, 
       4) —OR C1  wherein R C1  is a hydrogen atom or a C 1-4  alkyl group, 
       5) —NR C2 R C3  wherein R C2  and R C3  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       6) —COOR C4  wherein R C4  is a hydrogen atom or a C 1-4  alkyl group and 
       7) an oxo group,
 whereupon MEK is inhibited. 
 
     
   
   
       23 . A method of inducing p15 protein in a mammal comprising administering to the mammal a p15 protein inducing amount of a compound represented by the following formula [I] or a pharmaceutically acceptable salt, hydrate, or solvate thereof: 
     
       
         
         
             
             
         
       
     
     wherein
 X 1  and X 2  are the same or different and each is a carbon atom or a nitrogen atom, a 
 
     
       
         
         
             
             
         
       
     
     moiety is 
     
       
         
         
             
             
         
       
       R 1 , R 2 , and R 6  are the same or different and each is 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group, are optionally substituted by 1 to 3 substituents selected from the following group A, or 
 
     
     
       
         
         
             
             
         
       
       
         wherein m is 0 or an integer of 1 to 4, 
         ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, 
 
       
       R 3 , R 4 , and R 5  are the same or different and each is 
       a hydrogen atom, 
       a hydroxyl group, 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, 
 
       a C 3-12  carbon ring group or 
       a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, or 
 
       R 2  and R 3  are optionally linked to form a C 1-4  alkylene group, or R 4  and R 5  are optionally linked to form a C 1-4  alkylene group, 
       wherein group A is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-4  alkyl group, 
       5) —OR A1  wherein R A1  is a hydrogen atom or a C 1-4  alkyl group, 
       6) —SR A2  wherein R A2  is a hydrogen atom or a C 1-4  alkyl group, 
       7) —NR A3 R A4  wherein R A3  and R A4  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       8) —COOR A5  wherein R A5  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR A6 COR A7  wherein R A6  is a hydrogen atom or a C 1-4  alkyl group, R A7  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       10) —NR A8 COOR A9  wherein R A8  and R A9  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       11) a C 3-12  carbon ring group and 
       12) a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, 
 each of the C 1-4  alkyl groups of the above-mentioned 4), R A1 , R A2 , R A3 , R A4 , R A5 , R A6 , R A7 , R A8  and R A9  is optionally substituted by the same or different 1 to 3 substituents selected from the following group C, and 
 each of the C 3-12  carbon ring groups of the above-mentioned 11) and R A7 , and the heterocyclic groups of 12) and R A7  is optionally substituted by the same or different 1 to substituents selected from the following group C 
 
       group B is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-8  alkyl group, 
       5) a C 2-4  alkenyl group, 
       6) a C 2-4  alkynyl group, 
       7) —OR B1  wherein R B1  is a hydrogen atom or a C 1-4  alkyl group, 
       8) —SR B2  wherein R B2  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR B5 R B4  wherein R B3  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, and R B4  is a hydrogen atom or a C 1-4  alkyl group, 
       10) —NR B5 COR B6  wherein R B5  is a hydrogen atom or a C 1-4  alkyl group, and R B6  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       11) —NR B7 COOR B8  wherein R B7  and R B8  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       12)-NR B9 CONR B10 R B11  wherein R B9 , R B10  and R B11  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       13) —NR B12 CONR B13 OR B14  wherein R B12 , R B13  and R B14  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       14) —NR B15 SO 2 R B16  wherein R B15  is a hydrogen atom or a C 1-4 alkyl group, and R B16  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       15) —SO 2 R B17  wherein R B17  is a C 1-4  alkyl group or a heterocyclic group, 
       16) —SO 2 NR B18 R B19  wherein R B18  and R B19  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       17) —P(═O)(R 20 )(R B21 ) wherein R B20  and R B21  are the same or different and each is a C 1-4  alkyl group, 
       18) —COOR B22  wherein R B22  is a hydrogen atom or a C 1-4  alkyl group, 
       19) —CONR B23 R B24  wherein R B23  and R B24  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       20) —NR B25 SO 2 NR B26 R B27  wherein R B25 , R B26  and R B27  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       21) —NR B28 SO 2 NR B29 CONR B30 R B31  wherein R B28 , R B29 , R B30  and R B31  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       22) a C 3-12  carbon ring group and 
       23) a heterocyclic group
 wherein each of the “C 1-8 alkyl group” of the above-mentioned 4), and the C 1-4  alkyl groups for R B1  to R B31  is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 each of the C 2-4  alkenyl group of 5) and the C 2-4  alkynyl group of 6) is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and 
 each of the C 3-12  carbon ring group of the above-mentioned 22), R B3 , R B6  and R B16 , and the heterocyclic group of the above-mentioned 23), R B3 , R B6 , R B16  and R B17  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C, and 
 
       group C is a group consisting of 
       1) a halogen atom, 
       2) a cyano group, 
       3) a C 1-4  alkyl group, 
       4) —OR C1  wherein R C1  is a hydrogen atom or a C 1-4  alkyl group, 
       5) —NR C2 R C3  wherein R C2  and R C3  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       6) —COOR C4  wherein R C4  is a hydrogen atom or a C 1-4  alkyl group and 
       7) an oxo group,
 whereupon p15 protein is induced. 
 
     
   
   
       24 . A method of regulating cell cycle in a mammal comprising administering to the mammal a cell cycle regulating amount of a compound of the represented by the following formula [I] or a pharmaceutically acceptable salt, hydrate, or solvate thereof: 
     
       
         
         
             
             
         
       
     
     wherein
 X 1  and X 2  are the same or different and each is a carbon atom or a nitrogen atom, a 
 
     
       
         
         
             
             
         
       
     
     moiety is 
     
       
         
         
             
             
         
       
       R 1 , R 2 , and R 6  are the same or different and each is 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, or 
 
     
     
       
         
         
             
             
         
       
       
         wherein m is 0 or an integer of 1 to 4, 
         ring Cy is a C 3-12  carbon ring group or a heterocyclic group, 
         wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, 
       
       R 3 , R 4 , and R 5  are the same or different and each is 
       a hydrogen atom, 
       a hydroxyl group, 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, 
 
       a C 3-12  carbon ring group or 
       a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, or 
 
       R 2  and R 3  are optionally linked to form a C 1-4 alkylene group, or R 4  and R 5  are optionally linked to form a C 1-4  alkylene group, 
       wherein group A is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-4  alkyl group, 
       5) —OR A1  wherein R A1  is a hydrogen atom or a C 1-4  alkyl group, 
       6) —SR A2  wherein R A2  is a hydrogen atom or a C 1-4  alkyl group, 
       7) —NR A3 R A4  wherein R A3  and R A4  are the same or different and each is a hydrogen atom or a C 1-4 alkyl group, 
       8) —COOR A5  wherein R A5  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR A6 COR A7  wherein R A6  is a hydrogen atom or a C 1-4  alkyl group, R A7  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       10) —NR A8 COOR A9  wherein R A8  and R A9  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       11) a C 3-12  carbon ring group and 
       12) a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, 
 each of the C 1-4 alkyl groups of the above-mentioned 4), R A1 , R A2 , R A3 , R A4 , R A5 , R A6 , R A7 , R A8  and R A9  is optionally substituted by the same or different 1 to 3 substituents selected from the following group C, and 
 each of the C 3-12  carbon ring groups of the above-mentioned 11) and R A7 , and the heterocyclic groups of 12) and R A7  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C 
 
       group B is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-8  alkyl group, 
       5) a C 2-4  alkenyl group, 
       6) a C 2-4  alkynyl group, 
       7) —OR B1  wherein R B1  is a hydrogen atom or a C 1-4  alkyl group, 
       8) —SR B2  wherein R B2  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR B3 R B4  wherein R B3  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, and R B4  is a hydrogen atom or a C 1-4  alkyl group, 
       10) —NR B5 COR B6  wherein R B5  is a hydrogen atom or a C 1-4  alkyl group, and R B6  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       11) —NR B7 COOR B8  wherein R B7  and R B8  are the same or different and each is a hydrogen atom or a CA alkyl group, 
       12) —NR B9 CONR B10 R B11  wherein R B9 , R B10  and R B11  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       13) —NR 12 CONR B13 OR B14  wherein R B12 , R B13  and R B14  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       14) —NR B15 SO 2 R B16  wherein R B15  is a hydrogen atom or a C 1-4  alkyl group, and R B16  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       15) —SO 2 —R B17  wherein R B17  is a C 1-4  alkyl group or a heterocyclic group, 
       16) —SO 2 NR B18 R B19  wherein R B18  and R B19  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       17) —P(═O)(R B20 )(R B21 ) wherein R B20  and R B21  are the same or different and each is a C 1-4  alkyl group, 
       18) —COOR B22  wherein R B22  is a hydrogen atom or a C 1-4  alkyl group, 
       19) —CONR B23 R B24  wherein R B23  and R B24  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       20) —NR B25 SO 2 NR B26 R B27  wherein R B25 , R B26  and R B27  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       21) —NR B28 SO 2 NR B29 CONR B30 R B31  wherein R B28 , R B29 , R B30  and R B31  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       22) a C 3-12  carbon ring group and 
       23) a heterocyclic group
 wherein each of the “C 1-8  alkyl group” of the above-mentioned 4), and the C 1-4 alkyl groups for R B1  to R B31  is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned grout A, 
 each of the C 2-4  alkenyl group of 5) and the C 2-4  alkynyl group of 6) is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and 
 each of the C 3-12  carbon ring group of the above-mentioned 22), R B3 , R B6  and R B16 , and the heterocyclic group of the above-mentioned 23), R B3 , R B6 , R B16  and R B17  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C, and 
 
       group C is a group consisting of 
       1) a halogen atom, 
       2) a cyano group, 
       3) a C 1-4  alkyl group, 
       4) —OR C1  wherein R C1  is a hydrogen atom or a C 1-4  alkyl group, 
       5) —NR C2 R C3  wherein R C2  and R C3  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group 
       6) —COOR C4  wherein R C4  is a hydrogen atom or a C 1-4  alkyl group and 
       7) an oxo group,
 whereupon the cell cycle is regulated. 
 
     
   
   
       25 . A compound represented by the following formula or a pharmaceutically acceptable salt, hydrate, or solvate thereof: 
     
       
         
         
             
             
         
       
     
     wherein
 X 1  and X 2  are the same or different and each is a carbon atom or a nitrogen atom, a 
 
     
       
         
         
             
             
         
       
     
     moiety is 
     
       
         
         
             
             
         
       
       R 1  and R 6  are the same or different and each is 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, or 
 
     
     
       
         
         
             
             
         
       
       
         wherein m is 0 or an integer of 1 to 4, 
         ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, 
 
       
       R 2  is 
       a C 2-6  alkenyl group,
 wherein the C 2-6  alkenyl group is optionally substituted by 1 to 3 substituents selected from the following group A, or 
 
     
     
       
         
         
             
             
         
       
       
         wherein m is 0 or an integer of 1 to 4, 
         ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, 
 
       
       R 3 , R 4 , and R 5  are the same or different and each is 
       a hydrogen atom, 
       a hydroxyl group, 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, 
 
       a C 3-12  carbon ring group or 
       a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, or 
 
       R 2  and R 3  are optionally linked to form a C 1-4  alkylene group, or R 4  and R 5  are optionally linked to form a C 1-4  alkylene group, 
       wherein group A is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-4  alkyl group, 
       5) —OR A1  wherein R A1  is a hydrogen atom or a C 1-4  alkyl group, 
       6) —SR A2  wherein R A2  is a hydrogen atom or a C 1-4  alkyl group, 
       7) —NR A3 R A4  wherein R A3  and R A4  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       8) —COOR A5  wherein R A5  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR A6 COR A7  wherein R A6  is a hydrogen atom or a C 1-4  alkyl group, R A7  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       10) —NR A8 COOR A9  wherein R A8  and R A9  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       11) a C 3-12  carbon ring group and 
       12) a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, 
 each of the C 1-4  alkyl groups of the above-mentioned 4), R A1 , R A2 , R A3 , R A4 , R A5 , R A6 , R A7 , R A8  and R A9  is optionally substituted by the same or different 1 to 3 substituents selected from the following group C, and 
 each of the C 3-12  carbon ring groups of the above-mentioned 11) and R A7 , and the heterocyclic groups of 12) and R A7  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C 
 
       group B is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-8  alkyl group, 
       5) a C 2-4  alkenyl group, 
       6) a C 2-4  alkynyl group, 
       7) —OR B1  wherein R B1  is a hydrogen atom or a C 1-4  alkyl group, 
       8) —SR B2  wherein R B2  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR B3 R B4  wherein R B3  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, and R B4  is a hydrogen atom or a C 1-4  alkyl group, 
       10) —NR B5 COR B6  wherein R B5  is a hydrogen atom or a C 1-4  alkyl group, and R B6  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       11) —NR B7 COOR B8  wherein R B7  and R B8  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       12) —NR B9 CONR B10 R B11  wherein R B9 , R B10  and R B11  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       13) —NR B12 CONR B13 OR B14  wherein R B12 , R B13  and R B14  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       14) —NR B15 SO 2 R B16  wherein R B15  is a hydrogen atom or a C 1-4  alkyl group, and R B16  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       15) —SO 2 —R B17  wherein R B17  is a C 1-4  alkyl group or a heterocyclic group, 
       16) —SO 2 NR B18 R B19  wherein R B18  and R B19  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       17) —P(═O)(R B20 )(R B21 ) wherein R B20  and R B21  are the same or different and each is a C 1-4  alkyl group, 
       18) —COOR B22  wherein R B22  is a hydrogen atom or a C 1-4  alkyl group, 
       19) —CONR B23 R B24  wherein R B23  and R B24  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       20) —NR B25 SO 2 NR B26 R B27  wherein R B25 , R B26  and R B27  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       21) —NR B28 SO 2 NR B29 CONR B30 R B31  wherein R B28 , R B29 , R B30  and R B31  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       22) a C 3-12  carbon ring group and 
       23) a heterocyclic group
 wherein each of the “C 1-8  alkyl group” of the above-mentioned 4), and the C 1-4  alkyl groups for R B1  to R B31  is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 each of the C 2-4  alkenyl group of 5) and the C 2-4  alkynyl group of 6) is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and 
 each of the C 3-12  carbon ring group of the above-mentioned 22), R B3 , R B6  and R B16 , and the heterocyclic group of the above-mentioned 23), R B3 , R B6 , R B16  and R B17  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C, and 
 
       group C is a group consisting of 
       1) a halogen atom, 
       2) a cyano group, 
       3) a C 1-4  alkyl group, 
       4) —OR C1  wherein R C1  is a hydrogen atom or a C 1-4  alkyl group, 
       5) —NR C2 R C3  wherein R C2  and R C3  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       6) —COOR C4  wherein R C4  is a hydrogen atom or a C 1-4  alkyl group and 
       7) an oxo group,
 provided that when R 2  is a phenyl group, then R 1  is not a phenyl group, and 
 wherein the compound has at least one hydroxyl group that is substituted by a moiety selected from the group consisting of —CO-alkyl, —CO 2 -alkyl, —CONH-alkyl, —CO-alkenyl, —CO 2 -alkenyl, —CONH-alkenyl, —CO-aryl, —CO 2 -aryl, —CONH-aryl, —CO-heterocycle, —CO 2 -heterocycle, —CONH-heterocycle, and —PO 3 H 2 , wherein the alkyl, alkenyl, aryl, and heterocycle groups are optionally substituted by a halogen atom, alkyl group, hydroxyl group, alkoxy group, carboxy group, amino group, amino acid residue, —PO 3 H 2 , —SO 3 H, —OPO 3 H 2 , or —OSO 3 H. 
 
     
   
   
       26 . The compound of  claim 25 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the compound is represented by the following formula: 
     
       
         
         
             
             
         
       
     
   
   
       27 . The compound of  claim 25 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group,
 wherein the C 3-12  carbon ring group is optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       28 . The compound of  claim 26 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group,
 wherein the C 3-12  carbon ring group is optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       29 . The compound of  claim 27 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is a C 3-8  cycloalkyl group. 
   
   
       30 . The compound of  claim 28 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is a C 3-8  cycloalkyl group. 
   
   
       31 . The compound of  claim 29 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is a cyclopropyl group. 
   
   
       32 . The compound of  claim 30 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is a cyclopropyl group. 
   
   
       33 . The compound of  claim 25 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 2  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       34 . The compound of  claim 26 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 2  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       35 . The compound of  claim 25 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 3  is a C 1-6  alkyl group. 
   
   
       36 . The compound of  claim 26 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 3  is a C 1-6  alkyl group. 
   
   
       37 . The compound of  claim 25 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 5  is a hydrogen atom. 
   
   
       38 . The compound of  claim 26 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 5  is a hydrogen atom. 
   
   
       39 . The compound of  claim 25 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 6  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       40 . The compound of  claim 26 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 6  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       41 . The compound of  claim 25 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R A1  is a hydrogen atom. 
   
   
       42 . The compound of  claim 41 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the compound is 
     
       
         
         
             
             
         
       
     
   
   
       43 . The compound of  claim 41 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the compound is 
     
       
         
         
             
             
         
       
     
   
   
       44 . The compound of  claim 41 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the compound is 
     
       
         
         
             
             
         
       
     
   
   
       45 . The compound of  claim 41 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the compound is 
     
       
         
         
             
             
         
       
     
   
   
       46 . The compound of any of  claims 25 - 45 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the at least one hydroxyl group of the compound is substituted by a group selected from the group consisting of acetyl, propionyl, isobutyryl, pivaloyl, palmitoyl, benzoyl, 4-methylbenzoyl, dimethylcarbamoyl, dimethylaminomethylcarbonyl, sulfo, alanyl, and fumaryl. 
   
   
       47 . The compound of any one of  claims 25 - 45 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the at least one hydroxyl group of the compound is substituted by sodium salt of 3-carboxybenzoyl or sodium salt of 2-carboxyethylcarbonyl group. 
   
   
       48 . A compound represented by the following formula or a pharmaceutically acceptable salt, hydrate, or solvate thereof: 
     
       
         
         
             
             
         
       
     
     wherein
 X 1  and X 2  are the same or different and each is a carbon atom or a nitrogen atom, a 
 
     
       
         
         
             
             
         
       
     
     moiety is 
     
       
         
         
             
             
         
       
       R 1  and R 6  are the same or different and each is 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, or 
 
     
     
       
         
         
             
             
         
       
       
         wherein m is 0 or an integer of 1 to 4, 
         ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, 
 
       
       R 2  is 
       a C 2-6  alkenyl group,
 wherein the C 2-6  alkenyl group is optionally substituted by 1 to 3 substituents selected from the following group A, or 
 
     
     
       
         
         
             
             
         
       
       
         wherein m is 0 or an integer of 1 to 4, 
         ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, 
 
       
       R 3 , R 4 , and R 5  are the same or different and each is 
       a hydrogen atom, 
       a hydroxyl group, 
       a C 1-6  alkyl group, 
       a C 2-6  alkenyl group,
 wherein the C 1-6  alkyl group and the C 2-6  alkenyl group are optionally substituted by 1 to 3 substituents selected from the following group A, 
 
       a C 3-12  carbon ring group or 
       a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from the following group B, or 
 
       R 2  and R 3  are optionally linked to form a C 1-4  alkylene group, or R 4  and R 5  are optionally linked to form a C 1-4  alkylene group, 
       wherein group A is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-4  alkyl group, 
       5) —OR A1  wherein R A1  is a hydrogen atom or a C 1-4  alkyl group, 
       6) —SR A2  wherein R A2  is a hydrogen atom or a C 1-4  alkyl group, 
       7) —NR A3 R A4  wherein R A3  and R A4  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       8) —COOR A5  wherein R A5  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR A6 COR A7  wherein R A6  is a hydrogen atom or a C 1-4  alkyl group, R A7  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       10) —NR A8 COOR A9  wherein R A8  and R A9  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       11) a C 3-12  carbon ring group and 
       12) a heterocyclic group,
 wherein the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, 
 each of the C 1-4  alkyl groups of the above-mentioned 4), R A1 , R A2 , R A3 , R A4 , R A5 , R A6 , R A7 , R A8  and R A9  is optionally substituted by the same or different 1 to 3 substituents selected from the following group C, and 
 each of the C 3-12  carbon ring groups of the above-mentioned 11) and R A7 , and the heterocyclic groups of 12) and R A7  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C 
 
       group B is a group consisting of 
       1) a halogen atom, 
       2) a nitro group, 
       3) a cyano group, 
       4) a C 1-8  alkyl group, 
       5) a C 2-4  alkenyl group, 
       6) a C 2-4  alkynyl group, 
       7) —OR B1  wherein R B1  is a hydrogen atom or a C 1-4  alkyl group, 
       8) —SR B2  wherein R B2  is a hydrogen atom or a C 1-4  alkyl group, 
       9) —NR B3 R B4  wherein R B3  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, and R B4  is a hydrogen atom or a C 1-4  alkyl group, 
       10) —NR B5 COR B6  wherein R B5  is a hydrogen atom or a C 1-4  alkyl group, and R B6  is a hydrogen atom, a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       11) —NR B7 COOR B8  wherein R B7  and R B8  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       12) —NR B9 CONR B10 R B11  wherein R B9 , R B10  and R B11  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       13) —NR B12 CONR B13 R B14  wherein R B12 , R B13  and R B14  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       14) —NR B15 SO 2 R B16  wherein R B15  is a hydrogen atom or a C 1-4  alkyl group, and R B16  is a C 1-4  alkyl group, a C 3-12  carbon ring group or a heterocyclic group, 
       15) —SO 2 —R B17  wherein R B17  is a C 1-4  alkyl group or a heterocyclic group, 
       16) —SO 2 NR B18 R B19  wherein R B18  and R B19  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       17) —P(═O)(R B20 )(R B21 ) wherein R B20  and R B21  are the same or different and each is a C 1-4  alkyl group, 
       18) —COOR B22  wherein R B22  is a hydrogen atom or a C 1-4  alkyl group, 
       19) —CONR B23 R B24  wherein R B23  and R B24  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       20) —NR B25 SO 2 NR B26 R B27  wherein R B25 , R B26  and R B27  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       21) —NR B28 SO 2 NR B29 CONR B30 R B31  wherein R B28 , R B29 , R B30  and R B31  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       22) a C 3-12  carbon ring group and 
       23) a heterocyclic group
 wherein each of the “C 1-8  alkyl group” of the above-mentioned 4), and the C 1-4  alkyl groups for R B1  to R B31  is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 each of the C 2-4  alkenyl group of 5) and the C 2-4  alkynyl group of 6) is optionally substituted by the same or different 1 to 3 substituents selected from the above-mentioned group A, 
 the heterocyclic group is a saturated or unsaturated ring group having, besides carbon atom, 1 to 4 hetero atoms selected from an oxygen atom, a nitrogen atom and a sulfur atom, and 
 each of the C 3-12  carbon ring group of the above-mentioned 22), R B3 , R B6  and R B16 , and the heterocyclic group of the above-mentioned 23), R B3 , R B6 , R B16  and R B17  is optionally substituted by the same or different 1 to 5 substituents selected from the following group C, and 
 
       group C is a group consisting of 
       1) a halogen atom, 
       2) a cyano group, 
       3) a C 1-4  alkyl group, 
       4) —OR C1  wherein R C1  is a hydrogen atom or a C 1-4  alkyl group, 
       5) —NR C2 R C3  wherein R C2  and R C3  are the same or different and each is a hydrogen atom or a C 1-4  alkyl group, 
       6) —COOR C4  wherein R C4  is a hydrogen atom or a C 1-4  alkyl group and 
       7) an oxo group,
 provided that when R 2  is a phenyl group, then R 1  is not a phenyl group, and 
 wherein the compound has at least one —NH 2  group that is substituted by a moiety selected from the group consisting of —CO-alkyl, —CO 2 -alkyl, —CO-alkenyl, —CO 2 -alkenyl, —CO 2 -aryl, —CO-aryl, —CO-heterocycle, —CO 2 -heterocycle, and —PO 3 H 2 , wherein the alkyl, alkenyl, aryl, and heterocycle groups are optionally substituted by a halogen atom, alkyl group, hydroxyl group, alkoxy group, carboxy group, amino group, amino acid residue, —PO 3 H 2 , —SO 3 H, —OPO 3 H 2 , or —OSO 3 H. 
 
     
   
   
       49 . The compound of  claim 48 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the compound is represented by the following formula: 
     
       
         
         
             
             
         
       
     
   
   
       50 . The compound of  claim 48 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is a C 1-6  alkyl group. 
   
   
       51 . The compound of  claim 49 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is a C 1-6  alkyl group. 
   
   
       52 . The compound of  claim 48 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group,
 wherein the C 3-12  carbon ring group is optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       53 . The compound of  claim 49 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group,
 wherein the C 3-12  carbon ring group is optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       54 . The compound of  claim 52 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is a C 3-8  cycloalkyl group. 
   
   
       55 . The compound of  claim 53 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is a C 3-8  cycloalkyl group. 
   
   
       56 . The compound of  claim 54 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is a cyclopropyl group. 
   
   
       57 . The compound of  claim 55 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 1  is a cyclopropyl group. 
   
   
       58 . The compound of  claim 48 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 2  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       59 . The compound of  claim 49 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 2  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       60 . The compound of  claim 48 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 3  is a C 1-6  alkyl group. 
   
   
       61 . The compound of  claim 49 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 3  is a C 1-6  alkyl group. 
   
   
       62 . The compound of  claim 48 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 5  is a hydrogen atom. 
   
   
       63 . The compound of  claim 49 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 5  is a hydrogen atom. 
   
   
       64 . The compound of  claim 48 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 6  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       65 . The compound of  claim 49 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R 6  is 
     
       
         
         
             
             
         
       
     
     wherein m is 0, and ring Cy is a C 3-12  carbon ring group or a heterocyclic group,
 wherein the C 3-12  carbon ring group and the heterocyclic group are optionally substituted by 1 to 5 substituents selected from group B. 
 
   
   
       66 . The compound of  claim 48 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein R B18  and R B19  are hydrogen. 
   
   
       67 . The compound of  claim 66 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the compound is 
     
       
         
         
             
             
         
       
     
   
   
       68 . The compound of  claim 66 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the compound is 
     
       
         
         
             
             
         
       
     
   
   
       69 . The compound of  claim 66 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the compound is 
     
       
         
         
             
             
         
       
     
   
   
       70 . The compound of any one of  claims 48 - 69 , or a pharmaceutically acceptable salt, hydrate, or solvate thereof, wherein the at least one —NH 2  group of the compound is substituted by a moiety selected from the group consisting of tert-butyl, docosanoyl, pivaloylmethyloxy, alanyl, hexylcarbamoyl, pentylcarbamoyl, 3-methylthio-1-(acetylamino)propylcarbonyl, 1-sulfo-1-(3-ethoxy-4-hydroxyphenyl)methyl, (5-methyl-2-oxo-1,3-dioxol-4-yl)methyl, (5-methyl-2-oxo-1,3-dioxol-4-yl)methoxycarbonyl, tetrahydrofuranyl, and pyrrolidylmethyl. 
   
   
       71 . A pharmaceutical composition comprising
 (a) a compound of  claim 25  or  48  or a pharmaceutically acceptable salt, hydrate, or solvate thereof, and   (b) a pharmaceutically acceptable carrier.   
   
   
       72 . A method of therapeutically or prophylactically treating an undesirable cell proliferation in a mammal comprising administering to the mammal a therapeutic or prophylactic amount of a compound of  claim 25  or  48  or a pharmaceutically acceptable salt, hydrate, or solvate thereof, whereupon the undesirable cell proliferation is treated. 
   
   
       73 . A method of inhibiting MEK in a mammal comprising administering to the mammal an MEK inhibiting amount of a compound of  claim 25  or  48  or a pharmaceutically acceptable salt, hydrate, or solvate thereof, whereupon MEK is inhibited. 
   
   
       74 . A method of inducing p15 protein in a mammal comprising administering to the mammal a p15 protein inducing amount of a compound of  claim 25  or  48  or a pharmaceutically acceptable salt, hydrate, or solvate thereof, whereupon p15 protein is induced. 
   
   
       75 . A method of regulating cell cycle in a mammal comprising administering to the mammal a cell cycle regulating amount of a compound of  claim 25  or  48  or a pharmaceutically acceptable salt, hydrate, or solvate thereof, whereupon the cell cycle is regulated. 
   
   
       76 . A compound which is N-{3-[3-cyclopropyl-5-(4-ethynyl-2-fluorophenylamino)-6,8-dimethyl-2,4,7-trioxo-3,4,6,7-tetrahydro-2H-pyrido[4,3-d]pyrimidin-1-yl]phenyl}acetamide, or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
   
   
       77 . The compound of  claim 76 , wherein the compound is an acetic acid solvate thereof. 
   
   
       78 . A compound which is N-{3-[5-(2-fluoro-4-iodophenylamino)-3,6,8-trimethyl-2,4,7-trioxo-3,4,6,7-tetrahydro-2H-pyrido[4,3-d]pyrimidin-1-yl]phenyl}methanesulfonamide, or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
   
   
       79 . The compound of  claim 78 , wherein the compound is a sodium salt thereof. 
   
   
       80 . A compound which is N-{3-[3-cyclopropyl-5-(2-fluoro-4-iodophenylamino)-6,8-dimethyl-2,4,7-trioxo-3,4,6,7-tetrahydro-2H-pyrido[4,3-d]pyrimidin-1-yl]phenyl}methanesulfonamide, or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
   
   
       81 . A compound having the structural formula 
     
       
         
         
             
             
         
       
       or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
     
   
   
       82 . A compound having the structural formula 
     
       
         
         
             
             
         
       
       or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
     
   
   
       83 . A compound having the structural formula 
     
       
         
         
             
             
         
       
       or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
     
   
   
       84 . A compound having the structural formula 
     
       
         
         
             
             
         
       
       or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
     
   
   
       85 . A compound having the structural formula 
     
       
         
         
             
             
         
       
       or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
     
   
   
       86 . A compound having the structural formula 
     
       
         
         
             
             
         
       
       or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
     
   
   
       87 . A compound having the structural formula 
     
       
         
         
             
             
         
       
       or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
     
   
   
       88 . A compound having the structural formula 
     
       
         
         
             
             
         
       
       or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
     
   
   
       89 . A compound having the structural formula 
     
       
         
         
             
             
         
       
       or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
     
   
   
       90 . A compound having the structural formula 
     
       
         
         
             
             
         
       
       or a pharmaceutically acceptable salt, hydrate, or solvate thereof. 
     
   
   
       91 . A pharmaceutical composition comprising
 (a) a compound of any one of  claims 76 ,  78 , and  80 - 90  or a pharmaceutically acceptable salt, hydrate, or solvate thereof, and   (b) a pharmaceutically acceptable carrier.

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