BIARYL SUBSTITUTED DIAZABICYCLOALKANE DERIVATIVES

1 . A compound of formula (I)

or a pharmaceutically acceptable salt or prodrug thereof, wherein

R 1 is selected from group consisting of hydrogen, alkyl, cyclic alkyl, haloalkyl, aryl, and heteroaryl;

a and c are each independently selected from 0, 1, 2; b and d are each independently selected from 1, 2, or 3; provided that when both b and d are 1, a and c can not be 1 simultaneously;

Ar 1 is selected from 5- or 6-membered aromatic group of formula:

wherein

A 1 , A 2 , A 3 and A 4 are each —N— or —CR a ;

X 1 , X 3 , X 4 are independently selected from group consisting of —CR a , —NR a , —O—, and —S—;

X 2 is —C— or —N—, provided that when X 2 is —C—, at least one of X 1 , X 3 , X 4 is other than —C—;

R a is selected from group consisting of hydrogen, alkyl, cyclic alkyl, haloalkyl, aryl, heteroaryl, halogen, —CO 2 R 1 , —COR 1 , —CONR 1 , —OR 1 , and —NR 1 ;

Ar 2 is a fused bicyclic aromatic group of formula

wherein

B 1 , B 2 , B 3 , B 4 , B 5 , B 6 are each independently —N— or —CR 3 —;

Y is selected from group consisting of —NR d —, —O— and —S—;

R a is selected from group consisting of hydrogen, alkyl, cyclic alkyl, haloalkyl, aryl, heteroaryl, halogen, —CO 2 R 1 , —COR 1 , —CONR 1 , —OR 1 , and —NR 1 ; and

R d is selected from group consisting of hydrogen, alkyl, and cyclic alkyl.

2 . The compound of claim 1 , wherein the fused diazabicycloalkane moiety is selected from the group consisting of

3 . The compound of claim 1 , wherein Ar 1 is selected from the group consisting of midazolyl, isoxazolyl, isothiazolyl, furyl, oxazolyl, 1,2,4-oxadiazolyl, 1,3,4-oxadiazolyl, phenyl, pyrazolyl, pyridinyl, pyrimidinyl, pyridazinyl, pyrazinyl, thiophenyl, thiazolyl, 1,2,4-thiadiazolyl, and 1,3,4-thiadiazolyl.

4 . The compound of claim 3 , wherein Ar 1 is selected from the group consisting of pyridazinyl, pyridinyl, thiazolyl, 1,3,4-thiadiazolyl, and 1,3,4-oxadiazolyl, wherein Ar 1 is substituted with 0, 1, or 2 substitutents selected from alkoxy, alkyl, cyano, haloalkyl, hydroxy, halogen and NR 1 .

5 . The compound of claim 1 , wherein Ar 2 is selected from the group consisting of benzofuranyl, benzo[d]imidazolyl, benzo[d]isoxazolyl, benzo[d]isothiazolyl, benzo[d]oxazolyl, benzo[d]thiazolyl, benzo[b]thiophenyl, furo[3,2-b]pyridinyl, furo[3,2-c]pyridinyl, imidazo[4,5-b]pyridinyl, imidazo[4,5-c]pyridine, indolyl, indazolyl, isoxazolo[4,5-b]pyridinyl, isoxazolo[4,5-c]pyridinyl, isoxazolo[5,4-b]pyridinyl, isoxazolo[5,4-c]pyridinyl, isothiazolo[4,5-c]pyridinyl, isothiazolo[4,5-c]pyridinyl, isothiazolo[5,4-b]pyridinyl, isothiazolo[5,4-c]pyridinyl, oxazolo[4,5-b]pyridinyl, oxazolo[4,5-c]pyridinyl, oxazolo[5,4-b]pyridinyl, oxazolo[5,4-c]pyridinyl, pyrazolo[3,4-b]pyridinyl, pyrazolo[3,4-c]pyridinyl, pyrazolo[4,3-b]pyridinyl, pyrazolo[4,3-c]pyridinyl, pyrrolo[2,3-b]pyridinyl, pyrrolo[2,3-c]pyridinyl, pyrrolo[3,2-b]pyridinyl, pyrrolo[3,2-c]pyridinyl, thiazolo[4,5-b]pyridinyl, thiazolo[4,5-c]pyridinyl, thiazolo[5,4-b]pyridinyl, thiazolo[5,4-c]pyridinyl, thieno[2,3-b]pyridinyl, thieno[2,3-c]pyridinyl, thieno[3,2-b]pyridinyl, and thieno[3,2-c]pyridinyl.

6 . The compound of claim 2 , wherein the fused diazabicycloalkane moiety is

7 . The compound of claim 3 , wherein Ar 1 is selected from the group consisting of

wherein

R 2 , R 3 and R 4 are independently selected from the group consisting of alkoxy, alkyl, cyano, haloalkyl, hydroxy, halogen and NR 1 .

8 . The compound of claim 4 , wherein Ar 2 is selected from the group consisting of

wherein

R u and R V are each independently selected from the group consisting of alkoxy, alkyl, cyano, haloalkyl, hydroxy, halogen and NR 1 ; and

m and n are each independently selected from the group consisting of 0, 1 and 2.

9 . The compound of claim 1 , wherein the compound is one selected from the group consisting of

5-{5-[(1S,5S)-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

5-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

4-{5-[(1S,5S)-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

4-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

6-{5-[(1S,5S)-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

6-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

5-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-2-(trifluoromethyl)-1H-indole;

(1S,5S)-3-(5-(benzofuran-5-yl)pyridin-3-yl)-6-methyl-3,6-diazabicyclo[3.2.0]heptane;

5-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indazole;

(1S,5S)-3-[5-(benzo[b]thiophen-5-yl)pyridin-3-yl]-3,6-diazabicyclo[3.2.0]heptane;

(1S,5S)-3-[5-(benzo[b]thiophen-5-yl)pyridin-3-yl]-3,6-diazabicyclo[3.2.0.]heptane;

7-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

5-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-benzo[d]imidazole;

3-methyl-5-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

3-{5-[(1S,5S)-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-9H-carbazole;

5-{5-[(1S,5S)-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-3-methyl-1H-indole;

3-(5-((1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl)pyridin-3-yl)-9H-carbazole;

7-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-pyrrolo[2,3-c]pyridine;

5-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-pyrrolo[2,3-b]pyridine;

3-{5-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1-(phenylsulfonyl)-1H-indole;

3-(5-((1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl)pyridin-3-yl)-1H-indole;

4-{6-[(1S,5S)-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyrazin-2-yl}-1H-indole;

4-{6-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyrazin-2-yl}-1H-indole;

5-{6-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyrazin-2-yl}-1H-indole;

6-{6-[(1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyrazin-2-yl}-1H-indole;

5-(6-((1S,5S)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl)pyrazin-2-yl)-2-(trifluoromethyl)-1H-indole

5-{5-[(1R,5R)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

4-{5-[(1R,5R)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

6-{5-[(1R,5R)-6-methyl-3,6-diazabicyclo[3.2.0]heptan-3-yl]pyridin-3-yl}-1H-indole;

5-{5-[(1R,5S)-3,6-diazabicyclo[3.2.0]heptan-6-yl]pyridin-3-yl}-1H-indole;

5-{5-[(1R,5S)-3-methyl-3,6-diazabicyclo[3.2.0]heptan-6-yl]pyridin-3-yl}-1H-indole;

6-{5-[(1R,5S)-3,6-diazabicyclo[3.2.0]heptan-6-yl]pyridin-3-yl}-1H-indole;

6-{5-[(1R,5S)-3-methyl-3,6-diazabicyclo[3.2.0]heptan-6-yl]pyridin-3-yl}-1H-indole;

4-(5-((1R,5S)-3-methyl-3,6-diazabicyclo[3.2.0]heptan-6-yl)pyridin-3-yl)-1H-indole;

6-{5-[(3aS,6aS)-5-methylhexahydropyrrolo[3,4-b]pyrrol-1(2H)-yl]pyridin-3-yl}-1H-indole; and

5-{5-[(3aS,6aS)-5-methylhexahydropyrrolo[3,4-b]pyrrol-1(2H)-yl]pyridin-3-yl}-1H-indole.

10 . A pharmaceutical composition comprising a therapeutically effective amount of a compound of claim 1 and a pharmaceutically acceptable carrier.

11 . A method of selectively modulating an α7 nicotinic acetylcholine receptors, α4β2 nicotinic acetylcholine receptors, or both α7 and α4β2 nicotinic acetylcholine receptors in a mammal comprising administering an effective amount of a compound of claim 1 .

12 . The method of claim 11 , wherein the compound is an agonist of at least one α7 or α4β2 nicotinic acetylcholine receptor.

13 . A method of treating an α7 and α4β2 nicotinic acetylcholine receptor-mediated condition or disorder of a subject comprising administering a compound of claim 1 to the subject.

14 . The method of claim 13 , wherein the α7 and α4β2 nicotinic acetylcholine receptor-mediated condition or disorder is selected from the group consisting of attention deficit disorder, attention deficit hyperactivity disorder, Alzheimer's disease, mild cognitive impairment, senile dementia, AIDS dementia, Pick's Disease, dementia associated with Lewy bodies, dementia associated with Down's syndrome, amyotrophic lateral sclerosis, Huntington's disease, diminished CNS function associated with traumatic brain injury, acute pain, post-surgical pain, chronic pain, inflammation, inflammatory pain, neuropathic pain, infertility, need for new blood vessel growth associated with wound healing, need for new blood vessel growth associated with vascularization of skin grafts, and lack of circulation, rheumatoid arthritis, Crohn's disease, ulcerative colitis, inflammatory bowel disease, organ transplant rejection, acute immune disease associated with organ transplantation, chronic immune disease associated with organ transplantation, septic shock, toxic shock syndrome, sepsis syndrome, depression, rheumatoid spondylitis, and substance abuse.

15 . The method according to claim 14 , wherein the α7 and α4β2 nicotinic acetylcholine receptor-mediated condition or disorder is an α7 nicotinic acetylcholine receptor-mediated condition or disorder, and is selected from the group consisting of a cognitive disorder, neurodegeneration, and schizophrenia.

16 . The method according to claim 15 , wherein the compound is an agonist of at least one α7 nicotinic acetylcholine receptor, and wherein the method further comprises administering an atypical antipsychotic.

17 . The method of claim 16 , wherein the atypical antipsychotic is at least one selected from the group consisting of clozapine, risperidone, olanzapine, quietapine, ziprasidone, zotepine, and iloperidone.

18 . The method of claim 11 , further comprising administering a compound of claim 1 with a second composition to treat a cognitive disorder.

19 . The method of claim 18 , wherein the cognitive disorder is attention deficit disorder, and the second composition comprises at least one compound selected from the group consisting of dextroamphetamine, levoamphetamine, dextrothreomethylphenidate, levothreomethylphenidate, amantadine, amineptine, benzphetamine, bupropion, clonidine, modafinil, pemoline, selegiline, and milnacipran.

20 . The method of claim 18 , wherein the cognitive disorder is Alzheimer's disease, and the second composition comprises at least one selected from the group consisting of an acetylcholinesterase inhibitor, a NMDA antagonist, vitamin C, and vitamin E.