Biphenyl derivatives

1. A method of antagonizing a muscarinic receptor or agonizing a β 2 adrenergic receptor in a biological system or sample, the method comprising:

(a) contacting a biological system or sample having a muscarinic receptor or a β 2 adrenergic receptor with a muscarinic receptor-antagonizing or a β 2 adrenergic receptor-agonizing amount of a compound of formula I:

wherein

a is 0 or an integer of from 1 to 3;

each R 1 is independently selected from (1-4C)alkyl, (2-4C)alkenyl, (2-4C)alkynyl, (3-6C)cycloalkyl, cyano, halo, —OR 1a , —C(O)R 1b , —SR 1c , —S(O)R 1d , —S(O) 2 R 1e and —NR 1f R 1g ;

each of R 1a , R 1b , R 1c , R 1d , R 1e , R 1f and R 1g is independently hydrogen, (1-4C)alkyl or phenyl-(1-4C)alkyl;

b is 0 or an integer of from 1 to 3;

each R 2 is independently selected from (1-4C)alkyl, (2-4C)alkenyl, (2-4C)alkynyl, (3-6C)cycloalkyl, cyano, halo, —OR 2a , —C(O)OR 2b , —SR 2c , —S(O)R 2d , —S(O) 2 R 2e and —NR 2f R 2g ;

each of R 2a , R 2b , R 2c , R 2d , R 2e , R 2f and R 2g is indedpendently hydrogen, (1-4C)alkyl or phenyl-(1-4C)alkyl;

W is attached to the 3- or 4-position with respect to the nitrogen atom in the piperidine ring and represents O;

c is 0 or an integer of from 1 to 4;

each R 3 is independently selected from (1-4C)alkyl, (2-4C)alkenyl, (2-4C)alkynyl, (3-6C)cycloalkyl, cyano, halo, —OR 3a , —C(O)OR 3b , —SR 3c , —S(O)R 3d , —S(O) 2 R 3e and —NR 3f R 3g ; or two R 3 groups are joined to form (1-3C)alkylene, (2-3C)alkenylene or oxiran-2,3-diyl;

each of R 3a , R 3b , R 3c , R 3d , R 3e , R 3f and R 3g is independently hydrogen or (1-4C)alkyl;

R 4 is a divalent group of the formula:

—(R 4a ) d -(A 1 ) e -(R 4b ) f -Q-(R 4c ) g -(A 2 ) h -(R 4d ) i —

wherein

d, e, f, g, h and i are each independently selected from 0 and 1;

R 4a , R 4b , R 4c and R 4d are each independently selected from (1-10C)alkylene, (2-10C)alkenylene and (2-10C)alkynylene, wherein each alkylene, alkenylene or alkynylene group is unsubstituted or substituted with from 1 to 5 substituents independently selected from (1-4C)alkyl, fluoro, hydroxy, phenyl and phenyl-(1-4C)alkyl;

A 1 and A 2 are each independently selected from (3-7C)cycloalkylene, (6-10C)arylene, —O-(6-10C)arylene, (6-10C)arylene-O—, (2-9C)heteroarylene, —O-(2-9C)heteroarylene, (2-9C)heteroarylene-O— and (3-6C)heterocyclene, wherein each cycloalkylene is unsubstituted or substituted with from 1 to 4 substituents selected independently from (1-4C)alkyl, and each arylene, heteroarylene or heterocyclene group is unsubstituted or substituted with from 1 to 4 substituents independently selected from halo, (1-4C)alkyl, (1-4C)alkoxy, —S-(1-4C)alkyl, —S(O)-(1-4C)alkyl, —S(O) 2 -(1-4C)alkyl, —C(O)O(1-4C)alkyl, carboxy, cyano, hydroxy, nitro, trifluoromethyl and trifluoromethoxy;

Q is selected from a bond, —O—, —C(O)O—, —OC(O)—, —S—, —S(O)—, —S(O) 2 —, —N(Q a )C(O)—, —C(O)N(Q b )-, —N(Q c )S(O) 2 —, —S(O) 2 N(Q d )-, —N(Q e )C(O)N(Q f )-, —N(Q g )S(O) 2 N(Q h )-, —OC(O)N(Q i )-, —N(Q j )C(O)O— and —N(Q k );

Q a , Q b , Q c , Q d , Q e , Q f , Q g , Q h , Q i , Q j and Q k are each independently selected from hydrogen, (1-6C)alkyl, A 3 and (1-4C)alkylene-A 4 , wherein the alkyl group is unsubstituted or substituted with from 1 to 3 substituents independently selected from fluoro, hydroxy and (1-4C)alkoxy; or together with the nitrogen atom and the group R 4b or R 4c to which they are attached, form a 4-6 membered azacycloalkylene group;

A 3 and A 4 are each independently selected from (3-6C)cycloalkyl, (6-10C)aryl, (2-9C)heteroaryl and (3-6C)heterocyclyl, wherein each cycloalkyl is unsubstituted or substituted with from 1 to 4 substituents selected independently from (1-4C)alkyl and each aryl, heteroaryl or heterocyclyl group is unsubstituted or substituted with from 1 to 4 substituents independently selected from halo, (1-4C)alkyl and (1-4C)alkoxy;

provided that R 4 contains from 4 to 16 contiguous atoms in the shortest chain between the two nitrogen atoms to which R 4 is attached;

R 5 represents hydrogen or (1-4C)alkyl;

R 6 is —NR 6a CR 6b (O) and R 7 is hydrogen; or R 6 and R 7 together form —NR 7a C(O)—CR 7b ═CR 7c —;

each of R 6a , and R 6b is hydrogen; and

each of R 7a , R 7b , and R 7c is hydrogen;

or a pharmaceutically acceptable salt or stereoisomer thereof.

2. The method of claim 1 , wherein the biological system or sample is a cell or cellular extract.

3. The method of claim 1 , wherein the biological system or sample is a plasma membrane or tissue sample.

4. The method of claim 1 , wherein the biological system or sample is a mammal.

5. The method of claim 1 , wherein the mammal is a mouse, rat, guinea pig, rabbit, dog or pig.

6. The method of claim 1 , wherein R 4 in the compound of formula I is (4-10C)alkylene.

7. The method of claim 1 , wherein the compound of formula I used in the method at a concentration in the range from about 0.1 nanomolar to about 100 nanomolar.