Substituted hydroxyethylamine aspartyl protease inhibitors

• US 20050239790A1
• Filed: 03/09/2005
• Published: 10/27/2005
• Est. Priority Date: 03/09/2004
• Status: Abandoned Application

• Current Assignee: Elan Pharmaceuticals Incorporated (Perrigo Company PLC)
• Original Assignee: Elan Pharmaceuticals Incorporated (Perrigo Company PLC)
• Inventors: Neitz, R. Jeffrey, Maillard, Michel, Jagodzinska, Barbara, Tucker, John, John, Varghese, Shah, Neerav, Brogley, Louis, Tung, Jay S.
• Application Number:
  US11/075,294
• Publication Number:
  US 20050239790A1
• Time in Patent Office: Days
• US Class Current: 514/252.100
• CPC Class Codes: A61P 25/02 for peripheral neuropathies
• CPC Class Codes: A61P 25/28 for treating neurodegenerative disorders of the central nervous system, e.g. nootropic agents, cognition enhancers, drugs for treating Alzheimer's disease or other forms of dementia
• CPC Class Codes: A61P 29/00 Non-central analgesic, antipyretic or antiinflammatory agents, e.g. antirheumatic agents; Non-steroidal antiinflammatory drugs [NSAID]
• CPC Class Codes: A61P 31/00 Antiinfectives, i.e. antibiotics, antiseptics, chemotherapeutics
• CPC Class Codes: A61P 43/00 Drugs for specific purposes, not provided for in groups A61P1/00-A61P41/00
• CPC Class Codes: C07C 211/40 containing only non-condensed rings
• CPC Class Codes: C07C 215/44 bound to carbon atoms of the same ring or condensed ring system
• CPC Class Codes: C07C 215/70 with rings other than six-membered aromatic rings being part of the carbon skeleton
• CPC Class Codes: C07C 237/20 the carbon skeleton containing six-membered aromatic rings
• CPC Class Codes: C07C 2601/14 The ring being saturated
• CPC Class Codes: C07C 2602/10 the other ring being six-membered, e.g. tetraline
• CPC Class Codes: C07D 233/64 with substituted hydrocarbon radicals attached to ring carbon atoms, e.g. histidine
• CPC Class Codes: C07D 257/04 Five-membered rings
• CPC Class Codes: C07D 263/32 with only hydrogen atoms, hydrocarbon or substituted hydrocarbon radicals, directly attached to ring carbon atoms
• CPC Class Codes: C07D 285/08 1,2,4-Thiadiazoles; Hydrogenated 1,2,4-thiadiazoles
• CPC Class Codes: C07D 285/135 Nitrogen atoms
• CPC Class Codes: C07D 333/20 by nitrogen atoms nitro, nitroso radicals C07D333/12
• CPC Class Codes: C07D 333/24 Radicals substituted by carbon atoms having three bonds to hetero atoms with at the most one bond to halogen, e.g. ester or nitrile radicals
• CPC Class Codes: C07D 401/12 linked by a chain containing hetero atoms as chain links
• CPC Class Codes: C07D 403/12 linked by a chain containing hetero atoms as chain links
• CPC Class Codes: C07D 405/12 : linked by a chain containing hetero atoms as chain links
• CPC Class Codes: C07D 413/06 : linked by a carbon chain containing only aliphatic carbon atoms
• CPC Class Codes: C07D 417/12 : linked by a chain containing hetero atoms as chain links

Abstract

The invention relates to novel compounds and also to methods of treating at least one disease, disorder, or condition associated with amyloidosis using such compounds. Amyloidosis refers to a collection of diseases, disorders, and conditions associated with abnormal deposition of A-beta protein.

Claims

1. A compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein

R₁ is

wherein

n is 0 or 1;

q is 0 or 1;

r is 0, 1, or 2;

K is selected from

—

(CR_3aR_3b)—

,

—

O—

,

—

SO₂—

,

—

C(O)—

, and

—

CH(NR₅₅R₆₀)—

;

R₅₅ and R₆₀ are each independently selected from hydrogen and alkyl;

R_3a and R_3b are independently selected from

-hydrogen,

-halogen,

—

O-alkyl, and

-alkyl optionally substituted with at least one group selected from halogen, —

CN, —

CF₃, and —

OH;

W is selected from —

(CH₂)_1-4—

, —

O—

, —

S(O)_0-2—

, —

N(R₅₅)—

, and —

C(O)—

;

E is a bond or alkyl;

A is selected from

-aryl optionally substituted with at least one group independently selected from R₅₀,

-cycloalkyl optionally substituted with at least one group independently selected from R₅₀,

-heteroaryl optionally substituted with at least one group independently selected from R₅₀, and

-heterocycle optionally substituted with at least one group independently selected from R₅₀, wherein at least one atom of the heterocycle is optionally replaced with —

C(O)— and

—

S(O)_0-2—

;

wherein at least one heteroatom of the heteroaryl or heterocycle is optionally substituted with a group independently selected from —

(CO)_0-1R₂₁₅, —

(CO)_0-1R₂₂₀, —

S(O)_0-2R₂₀₀, and —

N(R₂₀₀)—

S(O)_0-2R₂₀₀;

wherein

if n, q, and r are zero, or

if n is zero, and q and r are not equal, and E is a bond, then aryl, cycloalkyl, heterocycle, and heteroaryl are not optionally substituted with R₅₀, but are substituted with at least one group independently selected from R_50a, wherein when aryl, cycloalkyl, heterocycle, and heteroaryl are substituted with at least one R_50a, then aryl, cycloalkyl, heterocycle, and heteroaryl are optionally substituted with at least one group independently selected from R₅₀;

R₅₀ is independently selected from

—

OH,

—

OCF₃,

—

NO₂,

—

CN,

—

N(R)CO(R′

)R,

—

CO₂—

R,

—

NH—

CO₂—

R,

—

O-(alkyl)-CO₂H,

—

NRR′

,

—

SR,

—

CH₂OH,

—

C(O)-alkyl,

—

C(O)NRR′

,

—

SO₂NRR′

,

—

S(O)_1-2alkyl,

-alkyl optionally substituted with at least one group independently selected from —

CF₃, -halogen, —

O-alkyl, —

OCF₃, —

NRR′

, —

OH, and —

CN,

-cycloalkyl optionally substituted with at least one group independently selected from —

CF₃, -halogen, —

O-alkyl, —

OCF₃, —

NRR′

, —

OH, and —

CN,

-halogen,

—

O-alkyl optionally substituted with at least one group independently selected from —

CF₃, -halogen, —

O-alkyl, —

OCF₃, —

NRR′

, —

OH, and —

CN,

—

O-benzyl optionally substituted with at least one substituent independently selected from —

H, —

OH, -halogen, and -alkyl,

—

O—

(CH₂)_0-2—

O—

(CH₂)_1-2—

O-alkyl, and

—

(CH₂)_0-2—

O—

(CH₂)_1-2—

OH;

R and R′

are each independently selected from hydrogen, alkyl, —

(CH₂)_0-2-aryl and —

(CH₂)_0-2-cycloalkyl, wherein each aryl or cycloalkyl is optionally substituted with at least one group independently selected from halogen, hydroxy, alkyl, O-alkyl, amino, monoalkylamino, and dialkylamino;

R_50a is independently selected from

—

N(R)CO(R′

)R,

—

CO₂—

R,

—

NH—

CO₂—

R,

—

O-(alkyl)-CO₂H,

—

NR₂₅R′

,

—

SR₂₅,

—

C(O)—

R₂₅,

—

C(O)NRR′

,

—

SO₂NRR′

,

—

S(O)_1-2R₂₅,

—

(C₃-C₁₀)alkyl optionally substituted with at least one group independently selected from —

CF₃, -halogen, —

O-alkyl, —

OCF₃, —

NH₂, —

OH, and —

CN,

—

O—

(C₂-C₁₀)alkyl, and

—

(CH₂)_0-2—

O—

(CH₂)_1-2—

OH;

R₂₅ is selected from C₂-C₁₀ alkyl, —

(CH₂)_0-2-aryl and —

(CH₂)_0-2-cycloalkyl, wherein each aryl or cycloalkyl is optionally substituted with at least one group independently selected from halogen, hydroxy, alkyl, O-alkyl, amino, monoalkylamino, and dialkylamino;

L is '"'"'selected from a bond, —

C(O)—

, —

S(O)_1-2—

, —

O—

, —

C(R₁₁₀)(R₁₁₂)O—

, —

OC(R₁₁₀)(R₁₁₂)—

, —

N(R₁₁₀)—

, —

C(O)N(R₁₁₀)—

, —

N(R₁₁₀)C(O)—

, —

C(R₁₁₀)(R′

)—

, —

C(OH)R₁₁₀—

, —

SO₂NR₁₁₀—

, —

N(R₁₁₀)SO₂—

, —

N(R₁₁₀)C(O)N(R₁₁₂)—

, —

N(R₁₁₀)CSN(R₁₁₂)—

, —

OCO₂—

, —

NCO₂—

, and —

OC(O)N(R₁₁₀)—

;

R₁₁₀ and R₁₁₂ are each independently selected from

-hydrogen and

-alkyl optionally substituted with at least one group independently selected from —

OH, —

O-alkyl, and -halogen;

G is selected from

-alkyl optionally substituted with at least one group independently selected from —

CO₂H, —

CO₂(alkyl), —

O-alkyl, —

OH, —

NRR′

, -alkyl, -haloalkyl, -alkyl-O-alkyl, aryl optionally substituted with at least one group independently selected from R₅₀, and heteroaryl optionally substituted with at least one group independently selected from R₅₀;

—

(CH₂)_0-3-cycloalkyl wherein cycloalkyl is optionally substituted with at least one group independently selected from —

CO₂H, —

CO₂-(alkyl), —

O-alkyl, OH, NH₂, haloalkyl, alkyl, -alkyl-O-alkyl, mono(alkyl)amino, di(alkyl) amino, aryl optionally substituted with at least one group independently selected from R₅₀, and heteroaryl optionally substituted with at least one group independently selected from R₅₀;

—

(CRR)_0-4-aryl wherein aryl is optionally substituted with at least one group independently selected from R₅₀,

—

(CH₂)_0-4-heteroaryl wherein the heteroaryl is optionally substituted with at least one group independently selected from R₅₀,

—

(CH₂)_0-4-heterocycle, wherein the heterocycle is optionally substituted with at least one group independently selected from R₅₀, and

—

C(R₁₀)(R₁₂)—

C(O)—

NH—

R₁₄;

R₁₀ and R₁₂ are each independently selected from

—

H,

-alkyl,

-(alkyl)_0-1-aryl,

-(alkyl)_0-1-heteroaryl,

-(alkyl)_0-1-heterocycle,

-aryl,

-heteroaryl,

-heterocycle,

—

(CH₂)_1-4—

OH,

—

(CH₂)_1-4-Z-(CH₂)_1-4-aryl, and

—

(CH₂)_1-4-Z-(CH₂)_1-4-heteroaryl,

wherein the heterocycle, aryl, and heteroaryl groups included in R₁₀ and R₁₂ are optionally substituted with at least one group independently selected from R₅₀;

Z is selected from —

O—

, —

S—

, and —

NR₁₆—

;

R₁₄ is;

—

H,

—

C₁-C₆ alkyl,

-aryl,

-heteroaryl,

-heterocycle,

-(alkyl)-aryl,

-(alkyl)-heteroaryl,

-(alkyl)-, and

—

(CH₂)_0-2—

O—

(CH₂)_0-2—

OH;

wherein the heterocycle, aryl, and heteroaryl groups included in R₁₄ are optionally substituted with at least one group independently selected from R₅₀;

R₁₆ is selected from hydrogen and alkyl;

R₂ is selected from

—

H,

—

OH,

—

O-alkyl (optionally substituted with at least one group independently selected from R₂₀₀),

—

O-aryl (optionally substituted with at least one group independently selected from R₂₀₀),

-alkyl, optionally substituted with at least one group independently selected from R₂₀₀,

—

NH-alkyl, optionally substituted with at least one group independently selected from R₂₀₀;

-heterocycloalkyl, (wherein at least one carbon is optionally replaced with a group independently selected from —

(CR₂₄₅R₂₅₀)—

, —

O—

, —

C(O)—

, —

C(O)C(O)—

, —

N(R₂₀₀)_0-1—

, and —

S(O)_0-2—

, and wherein the heterocycloalkyl is optionally substituted with at least one group independently selected from R₂₀₀);

—

NH-heterocycloalkyl, wherein at least one carbon is optionally replaced with a group independently selected from —

(CR₂₄₅R₂₅₀)—

, —

O—

, —

C(O)—

, —

C(O)C(O)—

, —

N(R₂₀₀)_0-1—

, and —

S(O)_0-2—

, and wherein the heterocycloalkyl is optionally substituted with at least one group independently selected from R₂₀₀,

—

C(O)—

N(R₃₁₅)(R₃₂₀),

wherein R₃₁₅ and R₃₂₀ are each independently selected from H, alkyl, and phenyl,

—

O—

C(O)—

N(R₃₁₅)(R₃₂₀),

—

NH—

R₄₀₀,

—

R₄₀₀,

—

NH—

R₅₀₀,

—

R₅₀₀,

—

NH—

R₆₀₀,

—

R₆₀₀, and

—

NH—

R₇₀₀;

R₄₀₀ is

wherein R₄₀₅ is selected from —

H, —

N(R₅₁₅)₂ and O-alkyl;

R₅₀₀ is a heteroaryl selected from III(a) and III(b)

wherein

M₁ and M₄ are independently selected from

—

C(R₅₀₅)—

,

—

N—

,

—

N(R₅₁₅)—

,

—

S—

, and

—

O—

;

M₂ and M₃ are independently selected from

—

C(R₅₁₀)—

,

—

N(R₅₂₀)_0-1—

,

—

S—

, and

—

O—

;

M₅ is selected from —

C— and

—

N—

;

R₅₀₅ is independently selected from

—

H,

-alkyl,

-halogen,

—

NO₂,

—

CN,

—

R₂₀₀, and

-phenyl;

R₅₁₀ is independently selected from

—

H,

-alkyl,

-halogen,

-amino,

—

CF₃,

—

R₂₀₀, and

-phenyl;

R₅₁₅ is independently selected from

—

H,

-alkyl, and

-phenyl;

R₅₂₀ is independently selected from

—

H,

-alkyl,

—

(CH₂)_0-2-phenyl, and

—

C(Ph)₃;

R₆₀₀ is a monocyclic, bicyclic, or tricyclic heteroaryl ring system of 6, 7, 8, 9, 10, 11, 12, 13, or 14 atoms, optionally substituted with at least one group independently selected from R₆₀₅;

R₆₀₅ is selected from -hydrogen, -halogen, -alkyl, -phenyl, alkyl-O—

C(O)—

, -nitro, —

CN, -amino, —

NR₂₂₀R₂₂₅, -thioalkyl, —

CF₃, —

OH, —

O-alkyl, and -heterocycloalkyl;

R₇₀₀ is aryl optionally substituted with at least one R₂₀₅;

R_C is selected from

—

(CH₂)_0-3-cycloalkyl wherein the cycloalkyl is optionally substituted with at least one group independently selected from —

R₂₀₅ and —

CO₂-(alkyl);

-alkyl optionally substituted with at least one group selected from R₂₀₅;

—

(CR₂₄₅R₂₅₀)_0-4—

R_X, wherein at least one —

(CR₂₄₅R₂₅₀)—

is optionally replaced with a group independently selected from —

O—

, —

N(R₂₁₅)—

, —

C(O)_1-2—

, —

C(O)N(R₂₁₅)— and

—

S(O)_0-2—

),

-formulae (IVa), (IVb), (IVc), (IVd), (IVe), (IVf), and (IVg);

R_X is selected from

-hydrogen,

-aryl,

-heteroaryl,

-cycloalkyl,

-heterocycloalkyl, and

—

R_Xa—

R_Xb, wherein R_Xa and R_Xb are independently selected from aryl, heteroaryl, cycloalkyl, and heterocycloalkyl;

wherein each aryl or heteroaryl group attached directly or indirectly to —

(CR₂₄₅R₂₅₀)_0-4—

is optionally substituted with at least one group independently selected from R₂₀₀;

wherein each cycloalkyl or heterocycloalkyl group attached directly or indirectly to —

(CR₂₄₅R₂₅₀)_0-4—

is optionally substituted with at least one group independently selected from R₂₁₀ and —

(CR₂₄₅R₂₅₀)_0-4—

R₂₀₀;

wherein at least one atom of the heteroaryl or heterocycloalkyl group attached directly or indirectly to —

(CR₂₄₅R₂₅₀)_0-4—

is independently optionally replaced with a group selected from —

O—

, —

C(O)—

, —

N(R₂₁₅)_0-1—

, and —

S(O)_0-2—

;

wherein at least one heteroatom of the heteroaryl or heterocycloalkyl group attached directly or indirectly to —

(CR₂₄₅R₂₅₀)_0-4—

is independently optionally substituted with a group selected from

—

(CO)_0-1R₂₁₅,

—

(CO)_0-1R₂₂₀,

—

S(O)_0-2R₂₀₀, and

—

N(R₂₀₀)—

S(O)_0-2R₂₀₀;

R₂₄₅ and R₂₅₀ at each occurrence are independently selected from

—

H,

—

(CH₂)_0-4C(O)—

OH,

—

(CH₂)_0-4C(O)—

O-alkyl,

—

(CH₂)_0-4C(O)-alkyl,

-alkyl,

-hydroxyalkyl,

—

O-alkyl,

—

O-haloalkyl,

—

(CH₂)_0-4-cycloalkyl,

—

(CH₂)_0-4-aryl,

—

(CH₂)_0-4-heteroaryl, and

—

(CH₂)_0-4-heterocycloalkyl;

or

R₂₄₅ and R₂₅₀ are taken together with the carbon to which they are attached to form a monocyclic or bicyclic ring system of 3, 4, 5, 6, 7, 8, 9, or 10 carbon atoms,

wherein at least one bond in the monocyclic or bicyclic ring system is optionally a double bond,

wherein the bicyclic ring system is optionally a fused or spiro ring system,

wherein at least one carbon atom in the monocyclic or bicyclic ring system is optionally replaced by a group independently selected from

—

O—

,

—

C(O)—

,

—

S(O)_0-2—

,

—

C(═

N—

R₂₅₅)—

,

—

N—

,

—

NR₂₂₀—

,

—

N((CO)_0-1R₂₀₀)—

, and

—

N(SO₂R₂₀₀)—

;

 

wherein the aryl, heteroaryl and heterocycloalkyl groups included in R₂₄₅ and R₂₅₀ are optionally substituted with at least one group independently selected from -halogen, -alkyl, —

N(R₂₂₀)(R₂₂₅), —

CN, and —

OH;

wherein the monocyclic and bicyclic groups included in R₂₄₅ and R₂₅₀ are optionally substituted with at least one group independently selected from -halogen, —

(CH₂)_0-2—

OH, —

O-alkyl, -alkyl, —

(CH₂)_0-2—

S-alkyl, —

CF₃, aryl, —

N(R₂₂₀)(R₂₂₅), —

CN, —

(CH₂)_0-2—

NH₂, —

(CH₂)_0-2—

NH(alkyl), —

NHOH, —

NH—

O-alkyl, —

N(alkyl)(alkyl), —

NH-heteroaryl, —

NH—

C(O)-alkyl, and —

NHS(O₂)-alkyl;

formula (IVa) is

wherein Q₁ is selected from (—

CH₂—

)_0-1, —

CH(R₂₀₀)—

, —

C(R₂₀₀)₂—

, and —

C(O)—

;

Q₂ and Q₃ each are independently selected from (—

CH₂—

)_0-1, —

CH(R₂₀₀)—

, —

(R₂₀₀)₂—

, —

O—

, —

C(O)—

, —

S—

, —

S(O)₂—

, —

NH—

, and —

N(R₇)—

;

Q₄ is selected from a bond, (—

CH₂—

)_0-1, —

CH(R₂₀₀)—

, —

C(R₂₀₀)₂—

, —

O—

, —

C(O)—

, —

S—

, —

S(O)₂—

, —

NH—

, and —

N(R₇)—

;

P₁, P₂, P₃, and P₄ each are independently selected from —

CH—

, —

C(R₂₀₀)—

, and —

N—

;

formula (IVb) is

wherein R₄ is selected from —

H and -alkyl, and

P₁, P₂, P₃, and P₄ at each occurrence are independently selected from —

CH—

, —

C(R₂₀₀)—

, and —

N—

;

formula (IVc) is

wherein R₄ is selected from H and alkyl, and

P₁, P₂, P₃ and P₄ at each occurrence are independently selected from —

CH—

, —

CR₂₀₀—

, and —

N—

;

formula (IVd) is

wherein m is 0, 1, 2, 3, 4, 5, or 6;

Y′

is selected from —

H, —

CN, —

OH, —

O-alkyl, —

CO₂H, —

C(O)OR₂₁₅, -amino, -aryl, and -heteroaryl; and

P₁ and P₂ at each occurrence are independently selected from —

CH—

, —

C(R₂₀₀)—

, and —

N—

,

or P₁ and P₂ are optionally taken together to form a monocyclic or bicyclic ring system of 3, 4, 5, 6, 7, 8, 9, or 10 carbon atoms,

P₃ and P₄;

at each occurrence are independently selected from —

CH—

, —

C(R₂₀₀)—

, and —

N—

,

or P₃ and P₄ are optionally taken together to form a monocyclic or bicyclic ring system of 3, 4, 5, 6, 7, 8, 9, or 10 carbon atoms,

P₅ at each occurrence is independently selected from —

CH—

, —

C(R₂₀₀)—

, and —

N—

,

wherein at least one bond in the monocyclic or bicyclic ring system included in P₁ and P₂ or P₃ and P₄ is optionally a double bond,

wherein the bicyclic ring system included in P₁ and P₂ or P₃ and P₄ is optionally a fused or spiro ring system,

wherein at least one carbon atom in the monocyclic or bicyclic ring system included in P₁ and P₂ or P₃ and P₄ is optionally replaced by a group independently selected from

—

O—

,

—

C(O)—

,

—

S(O)_0-2—

,

—

C(═

N—

R₂₅₅)—

,

—

N—

,

—

NR₂₂₀—

,

—

N((CO)_0-1R₂₀₀)—

, and

—

N(SO₂R₂₀₀)—

;

formula (IVe) is

wherein

U is selected from —

CH₂—

CR₁₀₀R₁₀₁—

, —

CH₂—

S—

, —

CH₂—

S(O)—

, —

CH₂—

S(O)₂—

, —

CH₂—

N(R₁₀₀)—

, —

CH₂—

C(O)—

, —

CH₂—

O—

, —

C(O)—

C(R₁₀₀)(R₁₀₁)—

, —

SO₂—

N(R₁₀₀)—

, —

C(O)—

N(R₅₅)—

, —

N(R₅₅)—

C(O)—

N(R₅₅)—

, —

O—

C(O)—

O—

, —

N(R₅₅)—

C(O)—

O—

, and —

C(O)—

O—

;

wherein R₁₀₀ and R₁₀₁ at each occurrence are independently selected from —

H, -alkyl, -aryl, —

C(O)-alkyl, —

(CO)_0-1R₂₁₅, —

(CO)_0-1R₂₂₀, and —

S(O)₂-alkyl;

formula (IVf) is

wherein the B ring is optionally substituted with at least one group independently selected from -alkyl, -halogen, —

OH, —

SH, —

CN, —

CF₃, —

O-alkyl, —

N(R₅)C(O)H, —

C(O)H, —

C(O)N(R₅)(R₆), —

NR₅R₆, R₂₈₀, R₂₈₅, -aryl, and -heteroaryl;

R₂₈₀ and R₂₈₅ and the carbon to which they are attached form a C₃-C₇ spirocycle which is optionally substituted with at least one group independently selected from -alkyl, —

O-alkyl, -halogen, —

CF₃, and —

CN;

wherein the A ring is aryl or heteroaryl, each optionally substituted with at least one group independently selected from R₂₉₀ and R₂₉₅;

R₂₉₀ and R₂₉₅ at each occurrence are independently selected from

-alkyl optionally substituted with at least one group selected from -alkyl, -halogen, —

OH, —

SH, —

CN, —

CF₃, —

O-alkyl, and —

NR₅R₆,

—

OH,

—

NO₂,

-halogen,

—

CO₂H,

—

CN,

—

(CH₂)_0-4—

C(O)—

NR₂₁R₂₂,

—

(CH₂)_0-4—

CO₂R₂₀,

—

(CH₂)_0-4—

SO₂—

NR₂, R₂₂,

—

(CH₂)_0-4—

S(O)-(alkyl),

—

(CH₂)_0-4—

S(O)₂-(alkyl),

—

(CH₂)_0-4—

S(O)₂-(cycloalkyl),

—

(CH₂)_0-4—

N(H or R₂₀)—

C(O)—

O—

R₂₀,

—

(CH₂)_0-4—

N(H or R₂₀)—

C(O)—

N(R₂₀)₂,

—

(CH₂)_0-4—

N—

C(S)—

N(R₂₀)₂,

—

(CH₂)_0-4—

N(H or R₂₀)—

CO—

R₂₁,

—

(CH₂)_0-4—

NR₂₁R₂₂,

—

(CH₂)_0-4—

R₁₁,

—

(CH₂)_0-4—

O—

C(O)-(alkyl),

—

(CH₂)_0-4—

O—

P(O)—

(OR₅)₂,

—

(CH₂)_0-4—

O—

C(O)—

N(R₂₀)₂,

—

(CH₂)_0-4—

O—

C(S)—

N(R₂₀)₂,

—

(CH₂)_0-4—

O—

(R₂₀)₂,

—

(CH₂)_0-4—

O—

(R₂₀)—

CO₂H,

—

(CH₂)_0-4—

S—

(R₂₀),

—

(CH₂)_0-4—

O-(alkyl optionally substituted with at least one halogen),

-cycloalkyl,

—

(CH₂)_0-4—

N(—

H or R₂₀)—

S(O)₂—

R₂₁, and

—

(CH₂)_0-4-cycloalkyl;

formula (IVg) is

wherein

a is 0 or 1;

b is 0 or 1;

S′

is selected from —

C(O)— and

—

CO₂—

;

T′

is —

(CH₂)_0-4—

;

U′

is —

(CR₂₄₅R₂₅₀)—

;

V′

is selected from -aryl- and -heteroaryl-;

W′

is selected from

-a bond,

-alkyl- optionally substituted with at least one group independently selected from R₂₀₅,

—

(CH₂)_0-4—

(CO)_0-1—

N(R₂₂₀)—

,

—

(CH₂)_0-4—

(CO)_0-1—

,

—

(CH₂)_0-4—

CO₂—

,

—

(CH₂)_0-4—

SO₂—

N(R₂₂₀)—

,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

CO₂—

,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

SO₂—

,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

C(O)—

N(R₂₁₅)—

,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

C(O)—

,

—

(CH₂)_0-4—

N(R₂₂₀)—

,

—

(CH₂)_0-4—

O—

, and

—

(CH₂)_0-4—

S—

;

X′

is selected from aryl and heteroaryl;

wherein each cycloalkyl included in formula (IVg) is optionally substituted with at least one group independently selected from R₂₀₅;

wherein each aryl or heteroaryl group included in formula (IVg) is optionally substituted with at least one group independently selected from R₂₀₀;

wherein at least one heteroatom of the heteroaryl group included in formula (IVg) is optionally substituted with a group selected from

—

(CO)_0-1R₂₁₅,

—

(CO)_0-1R₂₂₀, and

—

S(O)_0-2R₂₀₀;

R₁₁ at each occurrence is heterocycloalkyl

wherein at least one carbon of the heterocycloalkyl is optionally replaced with —

C(O)—

, —

S(O)—

, and —

S(O)₂—

,

wherein the heterocycloalkyl is optionally substituted with at least one group independently selected from -alkyl, —

O-alkyl, and -halogen;

R₁₇ at each occurrence is aryl optionally substituted with at least one group independently selected from

-alkyl optionally substituted with at least one group independently selected from alkyl, halogen, OH, SH, —

NR₅R₆, —

CN, —

CF₃, and —

O-alkyl,

-halogen,

—

O-alkyl optionally substituted with at least one group independently selected from halogen, —

NR₂₁R₂₂, —

OH, and —

CN,

-cycloalkyl optionally substituted with at least one group independently selected from halogen, OH, SH, —

CN, —

CF₃, —

O-alkyl, and —

NR₅R₆,

—

C(O)-(alkyl),

—

S(O)—

O—

NR₅R₆,

—

C(O)—

NR₅R₆, and

—

S(O)—

O-(alkyl);

R₁₈ at each occurrence is heteroaryl optionally substituted with at least one group independently selected from

-alkyl optionally substituted with at least one group independently selected from -alkyl, -halogen, —

OH, —

SH, —

CN, —

CF₃, —

O-alkyl, and —

NR₅R₆,

-halogen,

—

O-alkyl optionally substituted with at least one group independently selected from -halogen, —

NR₂₁R₂₂, —

OH, and —

CN,

-cycloalkyl optionally substituted with at least one group independently selected from -halogen, —

OH, —

SH, —

CN, CF₃, —

O-alkyl, and —

NR₅R₆,

—

C(O)-(alkyl),

—

S(O)₂—

NR₅R₆,

—

C(O)—

NR₅R₆, and

—

S(O)₂-(alkyl);

R₁₉ at each occurrence is heterocycloalkyl wherein at least one carbon is optionally replaced with —

C(O)—

, —

S(O)—

, and —

S(O)₂—

, wherein the heterocycloalkyl is optionally substituted with at least one group independently selected from

-alkyl optionally substituted with at least one group independently selected from alkyl, halogen, OH, SH, —

CN, —

CF₃, —

O-alkyl, and —

NR₅R₆,

-halogen,

—

O-alkyl optionally substituted with at least one group independently selected from halogen, OH, —

CN, and —

NR₂₁R₂₂,

-cycloalkyl optionally substituted with at least one group independently selected from halogen, OH, SH, —

CN, —

CF₃, —

O-alkyl, and —

NR₅R₆,

—

C(O)-(alkyl),

—

S(O)₂—

NR₅R₆,

—

C(O)—

NR₅R₆, and

—

S(O)₂-(alkyl);

R₂₀ is selected from alkyl, cycloalkyl, —

(CH₂)_0-2—

(R₁₇), and —

(CH₂)_0-2-(R₁₈);

R₂₁ and R₂₂ are each independently selected from

—

H,

-alkyl optionally substituted with at least one group independently selected from OH, amino, halogen, alkyl, cycloalkyl, -(alkyl)-(cycloalkyl), -alkyl-O-alkyl, —

R₁₇, and —

R₁₈,

—

(CH₂)_0-4—

C(O)-(alkyl),

—

(CH₂)_0-4—

C(O)-(cycloalkyl),

—

(CH₂)_0-4—

C(O)—

R₁₇,

—

(CH₂)_0-4—

C(O)—

R₁₈,

—

(CH₂)_0-4—

C(O)—

R₁₉, and

—

(CH₂)_0-4—

C(O)—

R₁₁;

R₂₀₀ at each occurrence is independently selected from

-alkyl optionally substituted with at least one group independently selected from R₂₀₅,

—

OH,

—

NO₂,

—

NH₂,

-halogen,

—

CN,

—

CF₃,

—

OCF₃,

—

(CH₂)_0-4—

C(O)H,

—

(CO)_0-1R₂₁₅,

—

(CO)_0-1R₂₂₀,

—

(CH₂)_0-4—

C(O)—

NR₂₂₀R₂₂₅,

—

(CH₂)_0-4—

(C(O))_0-1—

R₂₁₅,

—

(CH₂)_0-4—

(C(O))_0-1—

R₂₂₀,

—

(CH₂)_0-4—

C(O)-alkyl,

—

(CH₂)_0-4—

(C(O))_0-1-cycloalkyl,

—

(CH₂)_0-4—

(C(O))_0-1-heterocycloalkyl,

—

(CH₂)_0-4—

(C(O))_0-1-aryl,

—

(CH₂)_0-4—

(C(O))_0-1-heteroaryl,

—

(CH₂)_0-4—

C(O)—

O—

R₂₁₅,

—

(CH₂)_0-4—

S(O)₂—

NR₂₂₀R₂₂₅,

—

(CH₂)_0-4—

S(O)_0-2-alkyl,

—

(CH₂)_0-4—

S(O)_0-2-cycloalkyl,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

C(O)—

O—

R₂₁₅,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

S(O)—

O—

R₂₂₀,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

C(O)—

N(R₂₁₅)₂,

—

(CH₂)_0-4—

N(—

H or R₂₁₅)—

C(O)—

R₂₂₀,

—

(CH₂)_0-4—

NR₂₂₀R₂₂₅,

—

(CH₂)_0-4—

O—

C(O)-alkyl,

—

(CH₂)_0-4—

O—

(R₂₁₅),

—

(CH₂)_0-4—

S—

(R₂₁₅),

—

(CH₂)_0-4—

C(O)H,

—

(CH₂)_0-4—

O-(alkyl optionally substituted with at least one halogen), and

-adamantane,

wherein each aryl and heteroaryl group included within R₂₀₀ is optionally substituted with at least one group independently selected from

—

R₂₀₅,

—

R₂₁₀, and

-alkyl optionally substituted with at least one group independently selected from R₂₀₅ and R₂₁₀;

wherein each cycloalkyl or heterocycloalkyl group included within R₂₀₀ is optionally substituted with at least one group independently selected from

—

R₂₀₅,

—

R₂₁₀, and

-alkyl optionally substituted with at least one group independently selected from R₂₀₅ and R₂₁₀;

R₂₀₅ at each occurrence is independently selected from

-alkyl,

-heteroaryl,

-heterocycloalkyl,

-aryl,

—

O-haloalkyl,

—

(CH₂)_0-3-cycloalkyl,

-halogen,

—

(CH₂)_0-6—

OH,

—

O-phenyl,

—

OH,

—

SH,

—

(CH₂)_0-4—

C(O)CH₃,

—

(CH₂)_0-4—

C(O)H,

—

(CH₂)_0-4—

CO₂H,

—

(CH₂)_0-6—

CN,

—

(CH₂)_0-6—

C(O)—

NR₂₃₅R₂₄₀,

—

CF₃,

—

OCF₃,

—

C(O)₂-benzyl,

—

O-alkyl,

—

C(O)₂alkyl, and

—

NR₂₃₅R₂₄₀;

R₂₁₀ at each occurrence is independently selected from

—

OH,

—

CN,

—

(CH₂)_0-4—

C(O)H,

-alkyl wherein a carbon atom is optionally replaced with —

C(O)—

, and wherein a carbon atom is optionally substituted with at least one group independently selected from R₂₀₅,

—

S-alkyl,

-halogen,

—

O-alkyl,

—

O-haloalkyl,

—

NR₂₂₀R₂₂₅,

-cycloalkyl optionally substituted with at least one group independently selected from R₂₀₅,

—

C(O)-alkyl,

—

S(O)₂—

NR₂₃₅R₂₄₀,

—

C(O)—

NR₂₃₅R₂₄₀, and

—

S(O)₂-alkyl;

R₂₁₅ at each occurrence is independently selected from

-alkyl,

—

(CH₂)_0-2-aryl,

—

(CH₂)_0-2-cycloalkyl,

—

(CH₂)_0-2-heteroaryl, and

—

(CH₂)_0-2-heterocycloalkyl;

wherein the aryl groups included in R₂₁₅ are optionally substituted with at least one group independently selected from R₂₀₅ and R₂₁₀;

wherein the heterocycloalkyl and heteroaryl groups included in R₂₁₅ are optionally substituted with at least one group independently selected from R₂₁₀;

R₂₂₀ and R₂₂₅ at each occurrence are independently selected from

—

H,

—

OH,

-alkyl (wherein alkyl is optionally substituted with at least one group independently selected from R₂₀₅),

—

(CH₂)_0-4—

C(O)H,

—

(CH₂)_0-4—

C(O)CH₃,

-alkyl-OH,

—

(CH₂)_0-4—

CO₂alkyl (wherein alkyl is optionally substituted with at least one group independently selected from R₂₀₅),

-aminoalkyl,

—

S(O)₂-alkyl,

—

(CH₂)_0-4—

C(O)-alkyl, wherein alkyl is optionally substituted with at least one group independently selected from R₂₀₅,

—

(CH₂)_0-4—

C(O)—

NH₂,

—

(CH₂)_0-4—

C(O)—

NH(alkyl),

—

(CH₂)_0-4—

C(O)—

N(alkyl)(alkyl),

-haloalkyl,

—

(CH₂)_0-2-cycloalkyl,

-alkyl-O-alkyl,

—

O-alkyl,

-aryl,

-heteroaryl, and

-heterocycloalkyl,

wherein the aryl, heteroaryl, and heterocycloalkyl groups included in R₂₂₀ and R₂₂₅ are each optionally substituted with at least one group independently selected from R₂₇₀;

R₂₇₀ at each occurrence is independently selected from

—

R₂₀₅,

-alkyl optionally substituted with at least one group independently selected from R₂₀₅,

-phenyl,

-halogen,

—

O-alkyl,

—

O-haloalkyl,

—

NR₂₃₅R₂₄₀,

—

OH,

—

CN,

-cycloalkyl optionally substituted with at least one group independently selected from R₂₀₅,

—

C(O)-alkyl,

—

S(O)₂—

NR₂₃₅R₂₄₀,

—

CO—

NR₂₃₅R₂₄₀,

—

S(O)₂-alkyl, and

—

(CH₂)_0-4—

C(O)H;

R₂₃₅ and R₂₄₀ at each occurrence are independently selected from

—

H,

-alkyl,

—

C(O)-alkyl,

—

OH,

—

CF₃,

—

OCH₃,

—

NH—

CH₃,

—

N(CH₃)₂,

—

(CH₂)_0-4—

C(O)—

(H or alkyl),

—

SO₂-alkyl, and

-phenyl;

R₂₅₅ is selected from -hydrogen, —

OH, —

N(R₂₂₀)(R₂₂₅), and —

O-alkyl;

R₅ and R₆ are independently selected from —

H and -alkyl, or

R₅ and R₆, and the nitrogen to which they are attached, form a 5 or 6 membered heterocycloalkyl ring; and

R₇ is selected from

—

H,

-alkyl optionally substituted with at least one group independently selected from OH, amino, and halogen,

-cycloalkyl, and

-alkyl-O-alkyl.

2. The method according to claim 1, wherein R₁ is selected from 3-allyloxy-5-fluoro-benzyl, 3-benzyloxy-5-fluoro-benzyl, 3-propyl-thiophen-2-yl-methyl, 3,5-difluoro-2-propylamino-benzyl, 2-ethylamino-3,5-difluoro-benzyl, 2-hydroxy-5-methyl-benzamide, 3-fluoro-5-[2-(2-methoxy-ethoxy)-ethoxy]-benzyl, 3-fluoro-5-heptyloxy-benzyl, and 3-fluoro-5-hexyloxy-benzyl.

3. The method according to claim 1, wherein R_c is —

C(R₂₄₅)(R₂₅₀)—

R_x, wherein R₂₄₅ and R₂₅₀ are taken together with the carbon to which they are attached to form a monocyclic or bicyclic ring system of 3, 4, 5, 6, 7, 8, 9, or 10 carbon atoms, wherein at least one bond in the monocyclic or bicyclic ring system is optionally a double bond, wherein the bicyclic ring system is optionally a fused or spiro ring system, and wherein at least one atom within the monocylic or bicyclic ring system is optionally replaced by a group independently selected from

—

O—

,

—

C(O)—

,

—

S(O)_0-2—

,

—

C(═

N—

R₂₅₅)—

,

—

N—

,

—

NR₂₂₀—

,

—

N((CO)_0-1R₂₀₀)—

, and

—

N(SO₂R₂₀₀)—

; and

wherein the monocyclic or bicyclic groups included within R₂₄₅ and R₂₅₀ are optionally substituted with at least one group independently selected from halogen, —

(CH₂)_0-2—

OH, —

O-alkyl, alkyl, —

(CH₂)_0-2—

S-alkyl, —

CF₃, aryl, —

N(R₂₂₀)(R₂₂₅), —

CN, —

(CH₂)_0-2—

NH₂, —

(CH₂)_0-2—

NH(alkyl), —

NHOH, —

NH—

O-alkyl, —

N(alkyl)(alkyl), —

NH-heteroaryl, —

NH—

C(O)-alkyl, and —

NHS(O₂)-alkyl; and

wherein R_x, R₂₂₀, R₂₂₅, R₂₅₅, and R₂₀₀ are as defined in claim 1.

4. The compound according to claim 1, wherein R_c is selected from formulae (Va), (Vb), (Vc), and (Vd),

wherein,

A, B, and C are independently selected from

—

CH₂—

,

—

O—

,

—

C(O)—

,

—

S(O)_0-2—

,

—

N((CO)_0-1R₂₀₀)—

,

—

N(SO₂R₂₀₀)—

,

—

C(═

N—

R₂₅₅)—

, and

—

N(R₂₂₀)—

;

A′

at each occurrence is independently selected from —

CH₂— and

—

O—

;

wherein (Va), (Vb), (Vc), and (Vd) are each optionally substituted with at least one group independently selected from alkyl, —

O-alkyl, —

(CH₂)_0-2—

OH, —

(CH₂)_0-2—

S-alkyl, —

CF₃, —

CN, halogen, —

(CH₂)_0-2—

NH₂, —

(CH₂)_0-2—

NH(alkyl), —

NHOH, —

NH—

O-alkyl, —

N(alkyl)(alkyl), —

NH-heteroaryl, —

NH—

C(O)-alkyl, and —

NHS(O₂)-alkyl; and

R_x, R₂₂₀, R₂₅₅, and R₂₀₀ are as defined in claim 1.

5. The compound according to claim 1, wherein Rc is selected from formulae (IVa) and (IVb),

wherein at least one carbon of the heterocycloalkyl of formula (VIa) and the cycloalkyl of formula (VIb) is optionally replaced with a group independently selected from —

O—

, —

SO₂—

, and —

C(O)—

, wherein at least one carbon of the heterocycloalkyl or cycloalkyl is optionally substituted with at least one group independently selected from R₂₀₅, R₂₄₅, and R₂₅₀, wherein R₁₀₀, R₂₀₀ R₂₀₅, R₂₄₅, and R₂₅₀ are as defined in claim 1.

6. The compound according to claim 1, wherein R_c is selected from 6-isobutyl-1,1-dioxo-1λ

⁶-thiochroman-4-yl, 6-Isopropyl-2,2-dioxo-2λ

⁶-isothiochroman-4-yl, 6-ethyl-2,2-dioxo-2λ

⁶-isothiochroman-4-yl, 7-ethyl-1,2,3,4-tetrahydro-naphthalen-1-yl, and 1-(3-tert-Butyl-phenyl)-cyclohexyl, and 3-methoxy-benzyl.

7. The compound according to claim 1, wherein R₂ is selected from hydrogen, 3-Bromo-[1,2,4]thiadiazol-5-ylamino, [1,2,4]thiadiazol-5-ylamino, 4-Chloro-[1,2,5]thiadiazol-3-ylamino, [1,2,5]thiadiazol-3-ylamino, thiazol-2-ylamino, 5-Bromo-[1,3,4]thiadiazol-2-ylamino, [1,3,4]thiadiazol-2-ylamino, 5-Amino-[1,3,4]thiadiazol-2-ylamino, 2-Bromo-thiazol-5-ylamino, thiazol-5-ylamino, 5-trifluoromethyl-[1,3,4]thiadiazol-2-ylamino, 5-trifluoromethyl-[1,3,4]oxadiazol-2-ylamino, 5-Amino-[1,3,4]oxadiazol-2-ylamino, 1-trityl-1H-[1,2,4]triazol-3-ylamino, 1H-[1,2,4]triazol-3-ylamino, oxazol-2-ylamino, 5-Bromo-2-trityl-2H-[1,2,3]triazol-4-ylamino, 2-trityl-2H-[1,2,3]triazol-4-ylamino, 5-Bromo-2H-[1,2,3]triazol-4-ylamino, 2H-[1,2,3]triazol-4-ylamino, thiophen-2-ylamino, 3-methyl-5-nitro-3H-imidazol-4-ylamino, 4-Cyano-5-phenyl-isothiazol-3-ylamino, 4-phenyl-[1,2,5]thiadiazol-3-ylamino, 3,4-dioxo-cyclobut-1-enylamino, 2-methoxy-3,4-dioxo-cyclobut-1-enylamino, and 2-methylamino-3,4-dioxo-cyclobut-1-enylamino.

8. The compound according to claim 2, wherein R_X is selected from 3-(1,1-dimethyl-propyl)-phenyl, 3-(1-ethyl-propyl)-phenyl, 3-(1H-pyrrol-2-yl)-phenyl, 3-(1-hydroxy-1-methyl-ethyl)-phenyl, 3-(1-methyl-1H-imidazol-2-yl)-phenyl, 3-(1-methyl-cyclopropyl)-phenyl, 3-(2,2-dimethyl-propyl)-phenyl, 3-(2,5-dihydro-1H-pyrrol-2-yl)-phenyl, 3-(2-Chloro-thiophen-3-yl)-phenyl, 3-(2-Cyano-thiophen-3-yl)-phenyl, 3-(2-fluoro-benzyl)-phenyl, 3-(3,5-dimethyl-3H-pyrazol-4-yl)-phenyl, 3-(3,6-dimethyl-pyrazin-2-yl)-phenyl, 3-(3-Cyano-pyrazin-2-yl)-phenyl, 3-(3-formyl-fu ran-2-yl)-phenyl, 3-(3H-[1,2,3]triazol-4-yl)-phenyl, 3-(3H-imidazol-4-yl)-phenyl, 3-(3-methyl-butyl)-phenyl, 3-(3-methyl-pyridin-2-yl)-phenyl, 3-(3-methyl-thiophen-2-yl)-phenyl, 3-(4-Cyano-pyridin-2-yl)-phenyl, 3-(4-fluoro-benzyl)-phenyl, 3-(4H-[1,2,4]triazol-3-yl)-phenyl, 3-(4-methyl-thiophen-2-yl)-phenyl, 3-(5-Acetyl-thiophen-2-yl)-phenyl, 3-(5-Acetyl-thiophen-3-yl)-phenyl, 3-(5-formyl-thiophen-2-yl)-phenyl, 3-(5-oxo-pyrrolidin-2-yl)-phenyl, 3-(6-methyl-pyridazin-3-yl)-phenyl, 3-(6-methyl-pyridin-2-yl)-phenyl, 3-(Cyano-dimethyl-methyl)-phenyl, 3-[1-(2-tert-Butyl-pyrimidin-4-yl)-cyclohexylamino, 3-[1,2,3]triazol-1-yl-phenyl, 3-[1,2,4]oxadiazol-3-yl-phenyl, 3-[1,2,4]oxadiazol-5-yl-phenyl, 3-[1,2,4]thiadiazol-3-yl-phenyl, 3-[1,2,4]thiadiazol-5-yl-phenyl, 3-[1,2,4]triazol-4-yl-phenyl, 3-Acetyl-5-tert-butyl-phenyl, 3′

-Acetylamino-biphenyl-3-yl, 3-Adamantan-2-yl-phenyl, 3-Bromo-[1,2,4]thiadiazol-5-yl)-phenyl, 3-Bromo-5-tert-butyl-phenyl, 3-Cyano-phenyl, 3-Cyclobutyl-phenyl, 3-Cyclopentyl-phenyl, 3-Cyclopropyl-phenyl, 3-ethyl-phenyl, 3-ethynyl-phenyl, 3-fluoro-5-(2-hydroxy-1,1-dimethyl-ethyl)-phenyl, 3-fu ran-3-yl-phenyl, 3-imidazol-1-yl-phenyl, 3-isobutyl-phenyl, 3-isopropyl-phenyl, 3-isoxazol-3-yl-phenyl, 3-isoxazol-4-yl-phenyl, 3-isoxazol-5-yl-phenyl, 3-pent-4-enyl-phenyl, 3-pentyl-phenyl, 3-Phenyl-propionic acid ethyl ester, 3-pyrazin-2-yl-phenyl, 3-pyridin-2-yl-phenyl, 3-pyrrolidin-2-yl-phenyl, 3-sec-Butyl-phenyl, 3-tert-Butyl-4-chloro-phenyl, 3-tert-Butyl-4-cyano-phenyl, 3-tert-Butyl-4-ethyl-phenyl, 3-tert-Butyl-4-methyl-phenyl, 3-tert-Butyl-4-trifluoromethyl-phenyl, 3-tert-Butyl-5-chloro-phenyl, 3-tert-Butyl-5-cyano-phenyl, 3-tert-Butyl-5-ethyl-phenyl, 3-tert-Butyl-5-fluoro-phenyl, 3-tert-Butyl-5-methyl-phenyl, 3-tert-Butyl-5-trifluoromethyl-phenyl, 3-tert-Butyl-phenyl, 3-thiazol-2-yl-phenyl, 3-thiazol-4-yl-phenyl, 3-thiophen-3-yl-phenyl, 3-trifluoromethyl-phenyl, 4-Acetyl-3-tert-butyl-phenyl, 4-tert-Butyl-pyridin-2-yl, 4-tert-Butyl-pyrimidin-2-yl, 5-tert-Butyl-pyridazin-3-yl, 6-tert-Butyl-pyridazin-4-yl, and 6-tert-Butyl-pyrimidin-4-yl.

11. The method according to claim 9, wherein R_c is —

C(R₂₄₅)(R₂₅₀)—

R_x, wherein R₂₄₅ and R₂₅₀ are taken together with the carbon to which they are attached to form a monocyclic or bicyclic ring system of 3, 4, 5, 6, 7, 8, 9, or 10 carbon atoms, wherein at least one bond in the monocyclic or bicyclic ring system is optionally a double bond, wherein the bicyclic ring system is optionally a fused or spiro ring system, and wherein at least one atom within the monocylic or bicyclic ring system is optionally replaced by a group independently selected from

—

O—

,

—

C(O)—

,

—

S(O)_0-2—

,

—

C(═

N—

R₂₅₅)—

,

—

N—

,

—

NR₂₂₀—

,

—

N((CO)_0-1R₂₀₀)—

, and

—

N(SO₂R₂₀₀)—

; and

wherein the monocyclic or bicyclic groups included within R₂₄₅ and R₂₅₀ are optionally substituted with at least one group independently selected from halogen, —

(CH₂)_0-2—

OH, —

O-alkyl, alkyl, —

(CH₂)_0-2—

S-alkyl, —

CF₃, aryl, —

N(R₂₂₀)(R₂₂₅), —

CN, —

(CH₂)_0-2—

NH₂, —

(CH₂)_0-2—

NH(alkyl), —

NHOH, —

NH—

O-alkyl, —

N(alkyl)(alkyl), —

NH-heteroaryl, —

NH—

C(O)-alkyl, and —

NHS(O₂)-alkyl; and

wherein R_x, R₂₂₀, R₂₂₅, R₂₅₅, and R₂₀₀ are as defined in claim 1.

12. The method according to claim 9, wherein R_c is selected from formulae (Va), (Vb), (Vc), and (Vd),

wherein,

A, B, and C are independently selected from

—

CH₂—

,

—

O—

,

—

C(O)—

,

—

S(O)_0-2—

,

—

N((CO)_0-1R₂₀₀)—

, —

N(SO₂R₂₀₀)—

,

—

C(═

N—

R₂₅₅)—

, and

—

N(R₂₂₀)—

;

A′

at each occurrence is independently selected from —

CH₂— and

—

O—

;

wherein (Va), (Vb), (Vc), and (Vd) are each optionally substituted with at least one group independently selected from alkyl, —

O-alkyl, —

(CH₂)_0-2—

OH, —

(CH₂)_0-2—

S-alkyl, —

CF₃, —

CN, halogen, —

(CH₂)_0-2—

NH₂, —

(CH₂)_0-2—

NH(alkyl), —

NHOH, —

NH—

O-alkyl, —

N(alkyl)(alkyl), —

NH-heteroaryl, —

NH—

C(O)-alkyl, and —

NHS(O₂)-alkyl; and

R_x, R₂₂₀, R₂₅₅, and R₂₀₀ are as defined in claim 1.

13. The method according to claim 9, wherein Rc is selected from formulae (IVa) and (IVb),

wherein at least one carbon of the heterocycloalkyl of formula (VIa) and the cycloalkyl of formula (VIb) is optionally replaced with a group independently selected from —

O—

, —

SO₂—

, and —

C(O)—

, wherein at least one carbon of the heterocycloalkyl or cycloalkyl is optionally substituted with at least one group independently selected from R₂₀₅, R₂₄₅, and R₂₅₀, wherein R₁₀₀, R₂₀₀ R₂₀₅, R₂₄₅, and R₂₅₀ are as defined in claim 1.

21. A method of preventing or treating at least one condition associated with amyloidosis, comprising:

administering to a host a composition comprising a therapeutically effective amount of at least one beta-secretase inhibitor of formula (I),

or pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined in claim 1.

22. A method of preventing or treating at least one condition associated with amyloidosis, comprising:

administering to a host a composition comprising a therapeutically effective amount of at least one beta-secretase inhibitor of formula (I),

further comprising a composition including beta-secretase complexed with at least one compound of formula (I), or pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined in claim 1.

23. A method of preventing or treating the onset of dementia comprising:

administering to a patient a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof to the patient, wherein R₁, R₂, and R_C are defined as in claim 1.

24. A method of preventing or treating at least one condition associated with amyloidosis by administering to a host an effective amount of at least one compound of formula (I):

or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

25. A method of preventing or treating Alzheimer'"'"'s disease by administering to a host an effective amount of at least one compound having the following structure:

or a stereoisomer, or pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

26. A method of preventing or treating dementia by administering to a host an effective amount of at least one compound having the following structure:

or a stereoisomer, or pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

27. A method of inhibiting beta-secretase activity in a cell, the method comprising the step of administering to the cell an effective amount of at least one compound of formula (I) or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

28. A method of inhibiting beta-secretase activity in a host, the method comprising the step of administering to the host an effective amount of at least one compound of formula (I) or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

29. The method according to claim 28, wherein the host is a human.

30. A method of affecting beta-secretase-mediated cleavage of amyloid precursor protein in a patient, comprising administering a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

31. A method of inhibiting cleavage of amyloid precursor protein at a site between Met596 and Asp597 (numbered for the APP-695 amino acid isotype), or at a corresponding site of an isotype or mutant thereof, comprising:

administering a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

32. A method of inhibiting cleavage of amyloid precursor protein or mutant thereof at a site between amino acids, comprising:

administering a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1, wherein the site between amino acids corresponds to

between Met652 and Asp653 (numbered for the APP-751 isotype);

between Met671 and Asp672 (numbered for the APP-770 isotype);

between Leu596 and Asp597 of the APP-695 Swedish Mutation;

between Leu652 and Asp653 of the APP-751 Swedish Mutation;

or between Leu671 and Asp672 of the APP-770 Swedish Mutation.

33. A method of inhibiting production of A-beta, comprising:

administering to a patient a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

34. A method of preventing or treating deposition of A-beta, comprising:

administering a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

35. A method of preventing, delaying, halting, or reversing a disease characterized by A-beta deposits or plaques, comprising:

administering a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

36. The method according to claim 35, wherein the A-beta deposits or plaques are in a human brain.

37. A method of preventing, delaying, halting, or reversing a condition associated with a pathological form of A-beta in a host comprising:

administering to a patient in need thereof an effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1.

38. A method of inhibiting the activity of at least one aspartyl protease in a patient in need thereof, comprising:

administering a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1, to the patient.

39. The method according to claim 38 wherein the at least one aspartyl protease is beta-secretase.

40. A method of interacting an inhibitor with beta-secretase, comprising:

administering to a patient in need thereof a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1, wherein the at least one compound interacts with at least one of the following beta-secretase subsites;

S1, S1′

, and S2′

.

41. A method of treating a condition in a patient, comprising:

administering a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt, derivative or biologically active metabolite thereof, to the patient, wherein R₁, R₂, and R_C are defined as in claim 1.

42. The method according to claim 41, wherein the condition is selected from Alzheimer'"'"'s disease, Down'"'"'s syndrome or Trisomy 21 (including mild cognitive impairment (MCI) Down'"'"'s syndrome), hereditary cerebral hemorrhage with amyloidosis of the Dutch type, chronic inflammation due to amyloidosis, prion diseases (including Creutzfeldt-Jakob disease, Gerstmann-Straussler syndrome, kuru scrapie, and animal scrapie), Familial Amyloidotic Polyneuropathy, cerebral amyloid angiopathy, other degenerative dementias, dementia associated with Parkinson'"'"'s disease, dementia associated with progressive supranuclear palsy and dementia associated with cortical basal degeneration, diffuse Lewy body type of Alzheimer'"'"'s disease, and frontotemporal dementias with parkinsonism (FTDP).

43. The method according to claim 41, wherein the condition is Alzheimer'"'"'s disease.

44. The method according to claim 41, wherein the condition is dementia.

45. A method of prescribing a medication for preventing, delaying, halting, or reversing at least one disorder, condition or disease associated with amyloidosis comprising:

identifying in a patient symptoms associated with at least one disorder, condition or disease associated with amyloidosis; and

prescribing at least one dosage form of at least one compound of formula (I),

or a pharmaceutically acceptable salt, derivative or biologically active metabolite thereof, to the patient, wherein R₁, R₂, and R_C are defined as in claim 1.

46. An article of manufacture, comprising:

(a) at least one dosage form of at least one compound of formula (I),

or pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1;

(b) a package insert providing that a dosage form comprising a compound of formula (I) should be administered to a patient in need of therapy for disorders, conditions or diseases associated with amyloidosis; and

(c) at least one container in which at least one dosage form of at least one compound of formula (I) is stored.

47. A packaged pharmaceutical composition for treating at least one condition related to amyloidosis, comprising:

(a) a container which holds an effective amount of at least one compound of formula (I), or a pharmaceutically acceptable salt thereof, as defined in claim 1;

and

(b) instructions for using the pharmaceutical composition.

48. An article of manufacture, comprising:

(a) a therapeutically effective amount of at least one compound of formula (I)

or pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1;

(b) a package insert providing an oral dosage form should be administered to a patient in need of therapy for disorders, conditions or diseases associated with amyloidosis; and

(c) at least one container comprising;

at least one oral dosage form of at least one compound of formula (I).

49. An article of manufacture, comprising:

(a) at least one oral dosage form of at least one compound of formula (I)

or pharmaceutically acceptable salt thereof, wherein R₁, R₂, and R_C are defined as in claim 1;

in a dosage amount ranging from about 2 mg to about 1000 mg;

associated with

(b) a package insert providing that an oral dosage form comprising;

a compound of formula (I) in a dosage amount ranging from about 2 mg to about 1000 mg should be administered to a patient in need of therapy for disorders, conditions or diseases associated with amyloidosis; and

(c) at least one container in which at least one oral dosage form of at least one compound of formula (I) in a dosage amount ranging from about 2 mg to about 1000 mg is stored.

50. An article of manufacture, comprising:

(a) at least one oral dosage form of at least one compound of formula (I)

wherein R₁, R₂, and R_C are defined as in claim 1, in a dosage amount ranging from about 2 mg to about 1000 mg in combination with

(b) at least one therapeutically active agent;

associated with

(c) a package insert providing that an oral dosage form comprising;

a compound of formula (I) in a dosage amount ranging from about 2 mg to about 1000 mg in combination with at least one therapeutically active agent should be administered to a patient in need of therapy for disorders, conditions or diseases associated with amyloidosis; and

(d) at least one container in which at least one dosage form of at least one compound of formula (I) in a dosage amount ranging from about 2 mg to about 1000 mg in combination with a therapeutically active agent is stored.

51. The article of manufacture according to claim 50 wherein the therapeutically active agent is selected from an antioxidant, an anti-inflammatory, a gamma-secretase inhibitor, a neurotrophic agent, an acetyl cholinesterase inhibitor, a statin, an A-beta, and an anti-A-beta antibody.

52. An article of manufacture, comprising:

(a) at least one parenteral dosage form of at least one compound of formula (I)

wherein R₁, R₂, and R_C are defined as in claim 1, in a dosage amount ranging from about 0.2 mg/mL to about 50 mg/mL;

associated with

(b) a package insert providing that a parenteral dosage form comprising;

a compound of formula (I) in a dosage amount ranging from about 0.2 mg/mL to about 50 mg/mL should be administered to a patient in need of therapy for disorders, conditions or diseases associated with amyloidosis; and

(c) at least one container in which at least one parenteral dosage form of at least one compound of formula (I) in a dosage amount ranging from about 0.2 mg/mL to about 50 mg/mL is stored.

53. An article of manufacture comprising:

(a) a medicament comprising;

an effective amount of at least one compound of formula (I)

wherein R₁, R₂, and R_C are defined as in claim 1, in combination with active and/or inactive pharmaceutical agents;

(b) a package insert providing that an effective amount of at least one compound of formula (I) should be administered to a patient in need of therapy for disorders, conditions or diseases associated with amyloidosis; and

(c) a container in which a medicament comprising;

an effective amount of at least one compound of formula (I) in combination with active and/or inactive pharmaceutical agents is stored.

54. A kit comprising:

(a) at least one dosage form of at least one compound according to claim 1;

and

(b) at least one container in which at least one dosage form of at least one compound according to claim 1 is stored.

55. A kit according to claim 54, further comprising a package insert:

a) containing information of the dosage amount and duration of exposure of a dosage form containing at least one compound of formula (I) as defined in claim 1, and

b) providing that the dosage form should be administered to a patient in need of therapy for disorders, conditions or diseases associated with amyloidosis.

56. The kit according to claim 55 further comprising:

at least one therapeutically active agent.

57. The kit according to claim 56 wherein the therapeutically active agent is selected from an antioxidant, an anti-inflammatory, a gamma-secretase inhibitor, a neurotrophic agent, an acetyl cholinesterase inhibitor, a statin, an A-beta, and an anti-A-beta antibody.

58. A method of producing A-beta-secretase complex comprising:

exposing beta-secretase to a compound of formula (I) as defined in claim 1, or a pharmaceutically acceptable salt thereof, in a reaction mixture under conditions suitable for the production of the complex.

59. A manufacture of a medicament for preventing, delaying, halting, or reversing Alzheimer'"'"'s disease, comprising:

adding an effective amount of at least one compound of formula (I) as defined in claim 1, to a pharmaceutically acceptable carrier.

9. A method of preventing or treating at least one condition which benefits from inhibition of at least one aspartyl-protease, comprising:

administering to a host a composition comprising a therapeutically effective amount of at least one compound of formula (I),

or a pharmaceutically acceptable salt thereof, wherein

R₁ is

wherein

n is 0 or 1;

q is 0 or 1;

r is 0, 1, or 2;

K is selected from

—

(CR_3aR_3b)—

,

—

O—

,

—

SO₂—

,

—

C(O)—

, and

—

CH(NR₅₅R₆₀)—

;

R₅₅ and R₆₀ are each independently selected from hydrogen and alkyl;

R_3a and R_3b are independently selected from

-hydrogen,

-halogen,

—

O-alkyl, and

-alkyl optionally substituted with at least one group selected from halogen, —

CN, —

CF₃, and —

OH;

W is selected from —

(CH₂)_1-4—

, —

O—

, —

S(O)_0-2—

, —

N(R₅₅)—

, and —

C(O)—

;

E is a bond or alkyl;

A is selected from

-aryl optionally substituted with at least one group independently selected from R₅₀,

-cycloalkyl optionally substituted with at least one group independently selected from R₅₀,

-heteroaryl optionally substituted with at least one group independently selected from R₅₀, and

-heterocycle optionally substituted with at least one group independently selected from R₅₀, wherein at least one atom of the heterocycle is optionally replaced with —

C(O)— and

—

S(O)_0-2—

;

wherein at least one heteroatom of the heteroaryl or heterocycle is optionally substituted with a group independently selected from —

(CO)_0-1R₂₁₅, —

(CO)_0-1R₂₂₀, —

S(O)_0-2R₂₀₀, and —

N(R₂₀₀)—

S(O)_0-2R₂₀₀;

wherein

if n, q, and r are zero, or

if n is zero, and q and r are not equal, and E is a bond, then aryl, cycloalkyl, heterocycle, and heteroaryl are not optionally substituted with R₅₀, but are substituted with at least one group independently selected from R_50a, wherein when aryl, cycloalkyl, heterocycle, and heteroaryl are substituted with at least one R_50a, then aryl, cycloalkyl, heterocycle, and heteroaryl are optionally substituted with at least one group independently selected from R₅₀;

R₅₀ is independently selected from

—

OH,

—

OCF₃,

—

NO₂,

—

CN,

—

N(R)CO(R′

)R,

—

CO₂—

R,

—

NH—

CO₂—

R,

—

O-(alkyl)-CO₂H,

—

NRR′

,

—

SR,

—

CH₂OH,

—

C(O)-alkyl,

—

C(O)NRR′

,

—

SO₂NRR′

,

—

S(O)_1-2alkyl,

-alkyl optionally substituted with at least one group independently selected from —

CF₃, -halogen, —

O-alkyl, —

OCF₃, —

NRR′

, —

OH, and —

CN,

-cycloalkyl optionally substituted with at least one group independently selected from —

CF₃, -halogen, —

O-alkyl, —

OCF₃, —

NRR′

, —

OH, and —

CN,

-halogen,

—

O-alkyl optionally substituted with at least one group independently selected from —

CF₃, -halogen, —

O-alkyl, —

OCF₃, —

NRR′

, —

OH, and —

CN,

—

O-benzyl optionally substituted with at least one substituent independently selected from —

H, —

OH, -halogen, and -alkyl,

—

O—

(CH₂)_0-2—

O—

(CH₂)_1-2—

O-alkyl, and

—

(CH₂)_0-2—

O—

(CH₂)_1-2—

OH;

R and R′

are each independently selected from hydrogen, alkyl, —

(CH₂)_0-2-aryl and —

(CH₂)_0-2-cycloalkyl, wherein each aryl or cycloalkyl is optionally substituted with at least one group independently selected from halogen, hydroxy, alkyl, O-alkyl, amino, monoalkylamino, and dialkylamino;

R_50a is independently selected from

—

N(R)CO(R′

)R,

—

CO₂—

R,

—

NH—

CO₂—

R,

—

O-(alkyl)-CO₂H,

—

NR₂₅R′

,

—

SR₂₅,

—

C(O)—

R₂₅,

—

C(O)NRR′

,

—

SO₂NRR′

,

—

S(O)_1-2R₂₅,

—

(C₃-C₁₀)alkyl optionally substituted with at least one group independently selected from —

CF₃, -halogen, —

O-alkyl, —

OCF₃, —

NH₂, —

OH, and —

CN,

—

O—

(C₂-C₁₀)alkyl, and

—

(CH₂)_0-2—

O—

(CH₂)_1-2—

OH;

R₂₅ is selected from C₂-C₁₀ alkyl, —

(CH₂)_0-2-aryl and —

(CH₂)_0-2-cycloalkyl, wherein each aryl or cycloalkyl is optionally substituted with at least one group independently selected from halogen, hydroxy, alkyl, O-alkyl, amino, monoalkylamino, and dialkylamino;

L is selected from a bond, —

C(O)—

, —

S(O)_1-2—

, —

O—

, —

C(R₁₁₀)(R₁₁₂)O—

, —

OC(R₁₁₀)(R₁₁₂)—

, —

N(R₁₁₀)—

, —

C(O)N(R₁₁₀)—

, —

N(R₁₁₀)C(O)—

, —

C(R₁₁₀)(R′

)—

, —

C(OH)R₁₁₀—

, —

SO₂NR₁₁₀—

, —

N(R₁₁₀)SO₂—

, —

N(R₁₁₀)C(O)N(R₁₁₂)—

, —

N(R₁₁₀)CSN(R₁₁₂)—

, —

OCO₂—

, —

NCO₂—

, and —

OC(O)N(R₁₁₀)—

;

R₁₁₀ and R₁₁₂ are each independently selected from

-hydrogen and

-alkyl optionally substituted with at least one group independently selected from —

OH, —

O-alkyl, and -halogen;

G is selected from

-alkyl optionally substituted with at least one group independently selected from —

CO₂H, —

CO₂(alkyl), —

O-alkyl, —

OH, —

NRR′

, -alkyl, -haloalkyl, -alkyl-O-alkyl, aryl optionally substituted with at least one group independently selected from R₅₀, and heteroaryl optionally substituted with at least one group independently selected from R₅₀;

—

(CH₂)_0-3-cycloalkyl wherein cycloalkyl is optionally substituted with at least one group independently selected from —

CO₂H, —

CO₂-(alkyl), —

O-alkyl, OH, NH₂, haloalkyl, alkyl, -alkyl-O-alkyl, mono(alkyl)amino, di(alkyl) amino, aryl optionally substituted with at least one group independently selected from R₅₀, and heteroaryl optionally substituted with at least one group independently selected from R₅₀;

—

(CRR)_0-4-aryl wherein aryl is optionally substituted with at least one group independently selected from R₅₀,

—

(CH₂)_0-4-heteroaryl wherein the heteroaryl is optionally substituted with at least one group independently selected from R₅₀,

—

(CH₂)_0-4-heterocycle, wherein the heterocycle is optionally substituted with at least one group independently selected from R₅₀, and

—

C(R₁₀)(R₁₂)—

C(O)—

NH—

R₁₄;

R₁₀ and R₁₂ are each independently selected from

—

H,

-alkyl,

-(alkyl)_0-1-aryl,

-(alkyl)_0-1-heteroaryl,

-(alkyl)_0-1-heterocycle,

-aryl,

-heteroaryl,

-heterocycle,

—

(CH₂)_1-4—

OH,

—

(CH₂)_1-4-Z-(CH₂)_1-4-aryl, and

—

(CH₂)_1-4-Z-(CH₂)_1-4-heteroaryl,

wherein the heterocycle, aryl, and heteroaryl groups included in R₁₀ and R₁₂ are optionally substituted with at least one group independently selected from R₅₀;

Z is selected from —

O—

, —

S—

, and —

NR₁₆—

;

R₁₄ is;

—

H,

—

C₁-C₆ alkyl,

-aryl,

-heteroaryl,

-heterocycle,

-(alkyl)-aryl,

-(alkyl)-heteroaryl,

-(alkyl)-, and

—

(CH₂)_0-2—

O—

(CH₂)_0-2—

OH;

wherein the heterocycle, aryl, and heteroaryl groups included in R₁₄ are optionally substituted with at least one group independently selected from R₅₀;

R₁₆ is selected from hydrogen and alkyl;

R₂ is selected from

—

H,

—

OH,

—

O-alkyl (optionally substituted with at least one group independently selected from R₂₀₀),

—

O-aryl (optionally substituted with at least one group independently selected from R₂₀₀),

-alkyl, optionally substituted with at least one group independently selected from R₂₀₀,

—

NH-alkyl, optionally substituted with at least one group independently selected from R₂₀₀;

-heterocycloalkyl, (wherein at least one carbon is optionally replaced with a group independently selected from —

(CR₂₄₅R₂₅₀)—

, —

O—

, —

C(O)—

, —

C(O)C(O)—

, —

N(R₂₀₀)_0-1—

, and —

S(O)_0-2—

, and wherein the heterocycloalkyl is optionally substituted with at least one group independently selected from R₂₀₀);

—

NH-heterocycloalkyl, wherein at least one carbon is optionally replaced with a group independently selected from —

(CR₂₄₅R₂₅₀)—

, —

O—

, —

C(O)—

, —

C(O)C(O)—

, —

N(R₂₀₀)_0-1—

, and —

S(O)_0-2—

, and wherein the heterocycloalkyl is optionally substituted with at least one group independently selected from R₂₀₀,

—

C(O)—

N(R₃₁₅)(R₃₂₀),

wherein R₃₁₅ and R₃₂₀ are each independently selected from H, alkyl, and phenyl,

—

O—

C(O)—

N(R₃₁₅)(R₃₂₀),

—

NH—

R₄₀₀,

—

R₄₀₀,

—

NH—

R₅₀₀,

—

R₅₀₀,

—

NH—

R₆₀₀,

—

R₆₀₀, and

—

NH—

R₇₀₀;

R₄₀₀ is

wherein R₄₀₅ is selected from —

H, —

N(R₅₁₅)₂ and O-alkyl;

R₅₀₀ is a heteroaryl selected from III(a) and III(b)

wherein

M₁ and M₄ are independently selected from

—

C(R₅₀₅)—

,

—

N—

,

—

N(R₅₁₅)—

,

—

S—

, and

—

O—

;

M₂ and M₃ are independently selected from

—

C(R₅₁₀)—

,

—

N(R₅₂₀)_0-1—

,

—

S—

, and

—

O—

;

M₅ is selected from —

C— and

—

N—

;

R₅₀₅ is independently selected from

—

H,

-alkyl,

-halogen,

—

NO₂,

—

CN,

—

R₂₀₀, and

-phenyl;

R₅₁₀ is independently selected from

—

H,

-alkyl,

-halogen,

-amino,

—

CF₃,

—

R₂₀₀, and

-phenyl;

R₅₁₅ is independently selected from

—

H,

-alkyl, and

-phenyl;

R₅₂₀ is independently selected from

—

H,

-alkyl,

—

(CH₂)_0-2-phenyl, and

—

C(Ph)₃;

R₆₀₀ is a monocyclic, bicyclic, or tricyclic heteroaryl ring system of 6, 7, 8, 9, 10, 11, 12, 13, or 14 atoms, optionally substituted with at least one group independently selected from R₆₀₅;

R₆₀₅ is selected from -hydrogen, -halogen, -alkyl, -phenyl, alkyl-O—

C(O)—

, -nitro, —

CN, -amino, —

NR₂₂₀R₂₂₅, -thioalkyl, —

CF₃, —

OH, —

O-alkyl, and -heterocycloalkyl;

R₇₀₀ is aryl optionally substituted with at least one R₂₀₅;

R_C is selected from

—

(CH₂)_0-3-cycloalkyl wherein the cycloalkyl is optionally substituted with at least one group independently selected from —

R₂₀₅ and —

CO₂-(alkyl);

-alkyl optionally substituted with at least one group selected from R₂₀₅;

—

(CR₂₄₅R_250)0-4—

R_X, wherein at least one —

(CR₂₄₅R₂₅₀)—

is optionally replaced with a group independently selected from —

O—

, —

N(R₂₁₅)—

, —

C(O)_1-2—

, —

C(O)N(R₂₁₅)— and

—

S(O)_0-2—

),

-formulae (IVa), (IVb), (IVc), (IVd), (IVe), (IVf), and (IVg);

R_X is selected from

-hydrogen,

-aryl,

-heteroaryl,

-cycloalkyl,

-heterocycloalkyl, and

—

R_Xa-R_Xb, wherein R_Xa and R_Xb are independently selected from aryl, heteroaryl, cycloalkyl, and heterocycloalkyl;

wherein each aryl or heteroaryl group attached directly or indirectly to —

(CR₂₄₅R₂₅₀)_0-4—

is optionally substituted with at least one group independently selected from R₂₀₀;

wherein each cycloalkyl or heterocycloalkyl group attached directly or indirectly to —

(CR₂₄₅R₂₅₀)_0-4—

is optionally substituted with at least one group independently selected from R₂₁₀ and —

(CR₂₄₅R₂₅₀)_0-4—

R₂₀₀;

wherein at least one atom of the heteroaryl or heterocycloalkyl group attached directly or indirectly to —

(CR₂₄₅R_250)0-1—

is independently optionally replaced with a group selected from —

O—

, —

C(O)—

, —

N(R₂₁₅)_0-1—

, and —

S(O)_0-2—

;

wherein at least one heteroatom of the heteroaryl or heterocycloalkyl group attached directly or indirectly to —

(CR₂₄₅R₂₅₀)_0-4—

is independently optionally substituted with a group selected from

—

(CO)_0-1R₂₁₅,

—

(CO)_0-1R₂₂₀,

—

S(O)_0-2R₂₀₀, and

—

N(R₂₀₀)—

S(O)_0-2R₂₀₀;

R₂₄₅ and R₂₅₀ at each occurrence are independently selected from

—

H,

—

(CH₂)_0-4C(O)—

OH,

—

(CH₂)_0-4C(O)—

O-alkyl,

—

(CH₂)_0-4C(O)-alkyl,

-alkyl,

-hydroxyalkyl,

—

O-alkyl,

—

O-haloalkyl,

—

(CH₂)_0-4-cycloalkyl,

—

(CH₂)_0-4-aryl,

—

(CH₂)_0-4-heteroaryl, and

—

(CH₂)_0-4-heterocycloalkyl;

or

R₂₄₅ and R₂₅₀ are taken together with the carbon to which they are attached to form a monocyclic or bicyclic ring system of 3, 4, 5, 6, 7, 8, 9, or 10 carbon atoms,

wherein at least one bond in the monocyclic or bicyclic ring system is optionally a double bond,

wherein the bicyclic ring system is optionally a fused or spiro ring system,

wherein at least one carbon atom in the monocyclic or bicyclic ring system is optionally replaced by a group independently selected from

—

O—

,

—

C(O)—

,

—

S(O)_0-2—

,

—

C(═

N—

R₂₅₅)—

,

—

N—

,

—

NR₂₂₀—

,

—

N((CO)_0-1R₂₀₀)—

, and

—

N(SO₂R₂₀₀)—

;

wherein the aryl, heteroaryl and heterocycloalkyl groups included in R₂₄₅ and R₂₅₀ are optionally substituted with at least one group independently selected from -halogen, -alkyl, —

N(R₂₂₀)(R₂₂₅), —

CN, and —

OH;

wherein the monocyclic and bicyclic groups included in R₂₄₅ and R₂₅₀ are optionally substituted with at least one group independently selected from -halogen, —

(CH₂)_0-2—

OH, —

O-alkyl, -alkyl, —

(CH₂)_0-2—

S-alkyl, —

CF₃, aryl, —

N(R₂₂₀)(R₂₂₅), —

CN, —

(CH₂)_0-2—

NH₂, —

(CH₂)_0-2—

NH(alkyl), —

NHOH, —

NH—

O-alkyl, —

N(alkyl)(alkyl), —

NH-heteroaryl, —

NH—

C(O)-alkyl, and —

NHS(O₂)-alkyl;

formula (IVa) is

wherein Q₁ is selected from (—

CH₂—

)_0-1, —

CH(R₂₀₀)—

, —

C(R₂₀₀)₂—

, and —

C(O)—

;

Q₂ and Q₃ each are independently selected from (—

CH₂—

)_0-1, —

CH(R₂₀₀)—

, —

(R₂₀₀)₂—

, —

O—

, —

C(O)—

, —

S—

, —

S(O)₂—

, —

NH—

, and —

N(R₇)—

;

Q₄ is selected from a bond, (—

CH₂—

)_0-1, —

CH(R₂₀₀)—

, —

C(R₂₀₀)₂—

, —

O—

, —

C(O)—

, —

S—

, —

S(O)₂—

, —

NH—

, and —

N(R₇)—

;

P₁, P₂, P₃, and P₄ each are independently selected from —

CH—

, —

C(R₂₀₀)—

, and —

N—

;

formula (IVb) is

wherein R₄ is selected from —

H and -alkyl, and

P₁, P₂, P₃, and P₄ at each occurrence are independently selected from —

CH—

, —

C(R₂₀₀)—

, and —

N—

;

formula (IVc) is

wherein R₄ is selected from H and alkyl, and

P₁, P₂, P₃ and P₄ at each occurrence are independently selected from —

CH—

, —

CR₂₀₀—

, and —

N—

;

formula (IVd) is

wherein m is 0, 1, 2, 3, 4, 5, or 6;

Y′

is selected from —

H, —

CN, —

OH, —

O-alkyl, —

CO₂H, —

C(O)OR₂₁₅, -amino, -aryl, and -heteroaryl; and

P₁ and P₂ at each occurrence are independently selected from —

CH—

, —

C(R₂₀₀)—

, and —

N—

,

or P₁ and P₂ are optionally taken together to form a monocyclic or bicyclic ring system of 3, 4, 5, 6, 7, 8, 9, or 10 carbon atoms,

P₃ and P₄ at each occurrence are independently selected from —

CH—

, —

C(R₂₀₀)—

, and —

N—

,

or P₃ and P₄ are optionally taken together to form a monocyclic or bicyclic ring system of 3, 4, 5, 6, 7, 8, 9, or 10 carbon atoms,

P₅ at each occurrence is independently selected from —

CH—

, —

C(R₂₀₀)—

, and —

N—

,

wherein at least one bond in the monocyclic or bicyclic ring system included in P₁ and P₂ or P₃ and P₄ is optionally a double bond,

wherein the bicyclic ring system included in P₁ and P₂ or P₃ and P₄ is optionally a fused or spiro ring system,

wherein at least one carbon atom in the monocyclic or bicyclic ring system included in P₁ and P₂ or P₃ and P₄ is optionally replaced by a group independently selected from

—

O—

,

—

C(O)—

,

—

S(O)_0-2—

,

—

C(═

N—

R₂₅₅)—

,

—

N—

,

—

NR₂₂₀—

,

—

N((CO)_0-1R₂₀₀)—

, and

—

N(SO₂R₂₀₀)—

;

formula (IVe) is

wherein

U is selected from —

CH₂—

CR₁₀₀R₁₀₁—

, —

CH₂—

S—

, —

CH₂—

S(O)—

, —

CH₂—

S(O)₂—

, —

CH₂—

N(R₁₀₀)—

, —

CH₂—

C(O)—

, —

CH₂—

O—

, —

C(O)—

C(R₁₀₀)(R₁₀₁)—

, —

SO₂—

N(R₁₀₀)—

, —

C(O)—

N(R₅₅)—

, —

N(R₅₅)—

C(O)—

N(R₅₅)—

, —

O—

C(O)—

O—

, —

N(R₅₅)—

C(O)—

O—

, and —

C(O)—

O—

;

wherein R₁₀₀ and R₁₀₀ at each occurrence are independently selected from —

H, -alkyl, -aryl, —

C(O)-alkyl, —

(CO)_0-1R₂₁₅, —

(CO)_0-1R₂₂₀, and —

S(O)₂-alkyl;

formula (IVf) is

wherein the B ring is optionally substituted with at least one group independently selected from -alkyl, -halogen, —

OH, —

SH, —

CN, —

CF₃, —

O-alkyl, —

N(R₅)C(O)H, —

C(O)H, —

C(O)N(R₅)(R₆), —

NR₅R₆, R₂₈₀, R₂₈₅, -aryl, and -heteroaryl;

R₂₈₀ and R₂₈₅ and the carbon to which they are attached form a C₃-C₇ spirocycle which is optionally substituted with at least one group independently selected from -alkyl, —

O-alkyl, -halogen, —

CF₃, and —

CN;

wherein the A ring is aryl or heteroaryl, each optionally substituted with at least one group independently selected from R₂₉₀ and R₂₉₅;

R₂₉₀ and R₂₉₅ at each occurrence are independently selected from

-alkyl optionally substituted with at least one group selected from -alkyl, -halogen, —

OH, —

SH, —

CN, —

CF₃, —

O-alkyl, and —

NR₅R₆,

—

OH,

—

NO₂,

-halogen,

—

CO₂H,

—

CN,

—

(CH₂)_0-4—

C(O)—

NR₂₁R₂₂,

—

(CH₂)_0-4—

CO₂R₂₀,

—

(CH₂)_0-4—

SO₂—

NR₂₁R₂₂,

—

(CH₂)_0-4—

S(O)-(alkyl),

—

(CH₂)_0-4—

S(O)₂-(alkyl),

—

(CH₂)_0-4—

S(O)₂-(cycloalkyl),

—

(CH₂)_0-4—

N(H or R₂₀)—

C(O)—

O—

R₂₀,

—

(CH₂)_0-4—

N(H or R₂₀)—

C(O)—

N(R₂₀)₂,

—

(CH₂)_0-4—

N—

C(S)—

N(R₂₀)₂,

—

(CH₂)_0-4—

N(H or R₂₀)—

CO—

R₂₁,

—

(CH₂)_0-4—

NR₂₁R₂₂,

—

(CH₂)_0-4—

R₁₁,

—

(CH₂)_0-4—

O—

C(O)-(alkyl),

—

(CH₂)_0-4—

O—

P(O)—

(OR₅)₂,

—

(CH₂)_0-4—

O—

C(O)—

N(R₂₀)₂,

—

(CH₂)_0-4—

O—

C(S)—

N(R₂₀)₂,

—

(CH₂)_0-4—

O—

(R₂₀)₂,

—

(CH₂)_0-4—

O—

(R₂₀)—

CO₂H,

—

(CH₂)_0-4—

S—

(R₂₀),

—

(CH₂)_0-4—

O-(alkyl optionally substituted with at least one halogen),

-cycloalkyl,

—

(CH₂)_0-4—

N(—

H or R₂₀)—

S(O)₂—

R₂₁, and

—

(CH₂)_0-4-cycloalkyl;

formula (IVg) is

wherein

a is 0 or 1;

b is 0 or 1;

S′

is selected from —

C(O)— and

—

CO₂—

;

T′

is —

(CH₂)_0-4—

;

U′

is —

(CR₂₄₅R₂₅₀)—

;

V′

is selected from -aryl- and -heteroaryl-;

W′

is selected from

-a bond,

-alkyl- optionally substituted with at least one group independently selected from R₂₀₅,

—

(CH₂)_0-4—

(C)_0-1—

N(R₂₂₀)

—

(CH₂)_0-4—

(CO)_0-1—

,

—

(CH₂)_0-4—

CO₂—

,

—

(CH₂)_0-4—

SO₂—

N(R₂₂₀)—

,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

CO₂—

,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

SO₂—

,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

C(O)—

N(R₂₁₅)—

,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

C(O)—

,

—

(CH₂)_0-4—

N(R₂₂₀)—

,

—

(CH₂)_0-4—

O—

, and

—

(CH₂)_0-4—

S—

;

X′

is selected from aryl and heteroaryl;

wherein each cycloalkyl included in formula (IVg) is optionally substituted with at least one group independently selected from R₂₀₅;

wherein each aryl or heteroaryl group included in formula (IVg) is optionally substituted with at least one group independently selected from R₂₀₀;

wherein at least one heteroatom of the heteroaryl group included in formula (IVg) is optionally substituted with a group selected from

—

(CO)_0-1R₂₁₅,

—

(CO)_0-1R₂₂₀, and

—

S(O)_0-2R₂₀₀;

R₁₁ at each occurrence is heterocycloalkyl

wherein at least one carbon of the heterocycloalkyl is optionally replaced with —

C(O)—

, —

S(O)—

, and —

S(O)₂—

,

wherein the heterocycloalkyl is optionally substituted with at least one group independently selected from -alkyl, —

O-alkyl, and -halogen;

R₁₇ at each occurrence is aryl optionally substituted with at least one group independently selected from

-alkyl optionally substituted with at least one group independently selected from alkyl, halogen, OH, SH, —

NR₅R₆, —

CN, —

CF₃, and —

O-alkyl,

-halogen,

—

O-alkyl optionally substituted with at least one group independently selected from halogen, —

NR₂₁R₂₂, —

OH, and —

CN,

-cycloalkyl optionally substituted with at least one group independently selected from halogen, OH, SH, —

CN, —

CF₃, —

O-alkyl, and —

NR₅R₆,

—

C(O)-(alkyl),

—

S(O)—

O—

NR₅R₆,

—

C(O)—

NR₅R₆, and

—

S(O)—

O-(alkyl);

R₁₈ at each occurrence is heteroaryl optionally substituted with at least one group independently selected from

-alkyl optionally substituted with at least one group independently selected from -alkyl, -halogen, —

OH, —

SH, —

CN, —

CF₃, —

O-alkyl, and —

NR₅R₆,

-halogen,

—

O-alkyl optionally substituted with at least one group independently selected from -halogen, —

NR₂₁R₂₂, —

OH, and —

CN,

-cycloalkyl optionally substituted with at least one group independently selected from -halogen, —

OH, —

SH, —

CN, CF₃, —

O-alkyl, and —

NR₅R₆,

—

C(O)-(alkyl),

—

S(O)₂—

NR₅R₆,

—

C(O)—

NR₅R₆, and

—

S(O)₂-(alkyl);

R₁₉ at each occurrence is heterocycloalkyl wherein at least one carbon is optionally replaced with —

C(O)—

, —

S(O)—

, and —

S(O)₂—

, wherein the heterocycloalkyl is optionally substituted with at least one group independently selected from

-alkyl optionally substituted with at least one group independently selected from alkyl, halogen, OH, SH, —

CN, —

CF₃, —

O-alkyl, and —

NR₅R₆,

-halogen,

—

O-alkyl optionally substituted with at least one group independently selected from halogen, OH, —

CN, and —

NR₂₁R₂₂,

-cycloalkyl optionally substituted with at least one group independently selected from halogen, OH, SH, —

CN, —

CF₃, —

O-alkyl, and —

NR₅R₆,

—

C(O)-(alkyl),

—

S(O)₂—

NR₅R₆,

—

C(O)—

NR₅R₆, and

—

S(O)₂-(alkyl);

R₂₀ is selected from alkyl, cycloalkyl, —

(CH₂)_0-2—

(R₁₇), and —

(CH₂)_0-2—

(R₁₈);

R₂₁ and R₂₂ are each independently selected from

—

H,

-alkyl optionally substituted with at least one group independently selected from OH, amino, halogen, alkyl, cycloalkyl, -(alkyl)-(cycloalkyl), -alkyl-O-alkyl, —

R₁₇, and —

R₁₈,

—

(CH₂)_0-4—

C(O)-(alkyl),

—

(CH₂)_0-4—

C(O)-(cycloalkyl),

—

(CH₂)_0-4—

C(O)—

R₁₇,

—

(CH₂)_0-4—

C(O)—

R₁₈,

—

(CH₂)_0-4—

C(O)—

R₁₉, and

—

(CH₂)_0-4—

C(O)—

R₁₁;

R₂₀₀ at each occurrence is independently selected from

-alkyl optionally substituted with at least one group independently selected from R₂₀₅,

—

OH,

—

NO₂,

—

NH₂,

-halogen,

—

CN,

—

CF₃,

—

OCF₃,

—

(CH₂)_0-4—

C(O)H,

—

(CO)_0-1R₂₁₅,

—

(CO)_0-1R₂₂₀,

—

(CH₂)_0-4—

C(O)—

NR₂₂₀R₂₂₅,

—

(CH₂)_0-4—

(C(O))_0-1—

R₂₁₅,

—

(CH₂)_0-4—

(C(O))_0-1—

R₂₂₀,

—

(CH₂)_0-4—

C(O)-alkyl,

—

(CH₂)_0-4—

(C(O))_0-1-cycloalkyl,

—

(CH₂)_0-4—

(C(O))_0-1-heterocycloalkyl,

—

(CH₂)_0-4—

(C(O))_0-1-aryl,

—

(CH₂)_0-4—

(C(O))_0-1-heteroaryl,

—

(CH₂)_0-4—

C(O)—

O—

R₂₁₅,

—

(CH₂)_0-4—

S(O)₂—

NR₂₂₀R₂₂₅,

—

(CH₂)_0-4—

S(O)_0-2-alkyl,

—

(CH₂)_0-4—

S(O)_0-2-cycloalkyl,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

C(O)—

O—

R₂₁₅,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

S(O)—

O—

R₂₂₀,

—

(CH₂)_0-4—

N(H or R₂₁₅)—

C(O)—

N(R₂₁₅)₂,

—

(CH₂)_0-4—

N(—

H or R₂₁₅)—

C(O)—

R₂₂₀,

—

(CH₂)_0-4—

NR₂₂₀R₂₂₅,

—

(CH₂)_0-4—

O—

C(O)-alkyl,

—

(CH₂)_0-4—

O—

(R₂₁₅),

—

(CH₂)_0-4—

S—

(R₂₁₅),

—

(CH₂)_0-4—

C(O)H,

—

(CH₂)_0-4—

O-(alkyl optionally substituted with at least one halogen), and

-adamantane,

wherein each aryl and heteroaryl group included within R₂₀₀ is optionally substituted with at least one group independently selected from

—

R₂₀₅,

—

R₂₁₀, and

-alkyl optionally substituted with at least one group independently selected from R₂₀₅ and R₂₁₀;

wherein each cycloalkyl or heterocycloalkyl group included within R₂₀₀ is optionally substituted with at least one group independently selected from

—

R₂₀₅,

—

R₂₁₀, and

-alkyl optionally substituted with at least one group independently selected from R₂₀₅ and R₂₁₀;

R₂₀₅ at each occurrence is independently selected from

-alkyl,

-heteroaryl,

-heterocycloalkyl,

-aryl,

—

O-haloalkyl,

—

(CH₂)_0-3-cycloalkyl,

-halogen,

—

(CH₂)_0-6—

OH,

—

O-phenyl,

—

OH,

—

SH,

—

(CH₂)_0-4—

C(O)CH₃,

—

(CH₂)_0-4—

C(O)H,

—

(CH₂)_0-4—

CO₂H,

—

(CH₂)_0-6—

CN,

—

(CH₂)_0-6—

C(O)—

NR₂₃₅R₂₄₀,

—

CF₃,

—

OCF₃,

—

C(O)₂-benzyl,

—

O-alkyl,

—

C(O)₂alkyl, and

—

NR₂₃₅R₂₄₀;

R₂₁₀ at each occurrence is independently selected from

—

OH,

—

CN,

—

(CH₂)_0-4—

C(O)H,

-alkyl wherein a carbon atom is optionally replaced with —

C(O)—

, and wherein a carbon atom is optionally substituted with at least one group independently selected from R₂₀₅,

—

S-alkyl,

-halogen,

—

O-alkyl,

—

O-haloalkyl,

—

NR₂₂₀R₂₂₅,

-cycloalkyl optionally substituted with at least one group independently selected from R₂₀₅,

—

C(O)-alkyl,

—

S(O)₂—

NR₂₃₅R₂₄₀,

—

C(O)—

NR₂₃₅R₂₄₀, and

—

S(O)₂-alkyl;

R₂₁₅ at each occurrence is independently selected from

-alkyl,

—

(CH₂)_0-2-aryl,

—

(CH₂)_0-2-cycloalkyl,

—

(CH₂)_0-2-heteroaryl, and

—

(CH₂)_0-2-heterocycloalkyl;

wherein the aryl groups included in R₂₁₅ are optionally substituted with at least one group independently selected from R₂₀₅ and R₂₁₀;

wherein the heterocycloalkyl and heteroaryl groups included in R₂₁₅ are optionally substituted with at least one group independently selected from R₂₁₀;

R₂₂₀ and R₂₂₅ at each occurrence are independently selected from

—

H,

—

OH,

-alkyl,

—

(CH₂)_0-4—

C(O)H,

—

(CH₂)_0-4—

C(O)CH₃,

-alkyl-OH,

—

(CH₂)_0-4—

CO₂alkyl (wherein alkyl is optionally substituted with at least one group independently selected from R₂₀₅),

-aminoalkyl,

—

S(O)₂-alkyl,

—

(CH₂)_0-4—

C(O)-alkyl, wherein alkyl is optionally substituted with at least one group independently selected from R₂₀₅,

—

(CH₂)_0-4—

C(O)—

NH₂,

—

(CH₂)_0-4—

C(O)—

NH(alkyl),

—

(CH₂)_0-4—

C(O)—

N(alkyl)(alkyl),

-haloalkyl,

—

(CH₂)_0-2-cycloalkyl,

-alkyl-O-alkyl,

—

O-alkyl,

-aryl,

-heteroaryl, and

-heterocycloalkyl,

wherein the aryl, heteroaryl, and heterocycloalkyl groups included in R₂₂₀ and R₂₂₅ are each optionally substituted with at least one group independently selected from R₂₇₀;

R₂₇₀ at each occurrence is independently selected from

—

R₂₀₅,

-alkyl optionally substituted with at least one group independently selected from R₂₀₅,

-phenyl,

-halogen,

—

O-alkyl,

—

O-haloalkyl,

—

NR₂₃₅R₂₄₀,

—

OH,

—

CN,

-cycloalkyl optionally substituted with at least one group independently selected from R₂₀₅,

—

C(O)-alkyl,

—

S(O)₂—

NR₂₃₅R₂₄₀,

—

CO—

NR₂₃₅R₂₄₀,

—

S(O)₂-alkyl, and

—

(CH₂)_0-4—

C(O)H;

R₂₃₅ and R₂₄₀ at each occurrence are independently selected from

—

H,

-alkyl,

—

C(O)-alkyl,

—

OH,

—

CF₃,

—

OCH₃,

—

NH—

CH₃,

—

N(CH₃)₂,

—

(CH₂)_0-4—

C(O)—

(H or alkyl),

—

SO₂-alkyl, and

-phenyl;

R₂₅₅ is selected from -hydrogen, —

OH, —

N(R₂₂₀)(R₂₂₅), and —

O-alkyl;

R₅ and R₆ are independently selected from —

H and -alkyl, or

R₅ and R₆, and the nitrogen to which they are attached, form a 5 or 6 membered heterocycloalkyl ring; and

R₇ is selected from

—

H,

-alkyl optionally substituted with at least one group independently selected from OH, amino, and halogen,

-cycloalkyl, and

-alkyl-O-alkyl.

10. The method according to claim 9, wherein R₁ is selected from 3-allyloxy-5-fluoro-benzyl, 3-benzyloxy-5-fluoro-benzyl, 3-propyl-thiophen-2-yl-methyl, 3,5-difluoro-2-propylamino-benzyl, 2-ethylamino-3,5-difluoro-benzyl, 2-hydroxy-5-methyl-benzamide, 3-fluoro-5-[2-(2-methoxy-ethoxy)-ethoxy]-benzyl, 3-fluoro-5-heptyloxy-benzyl, and 3-fluoro-5-hexyloxy-benzyl.

14. The method according to claim 9, wherein R_c is selected from 6-isobutyl-1,1-dioxo-1λ

⁶-thiochroman-4-yl, 6-Isopropyl-2,2-dioxo-2λ

⁶-isothiochroman-4-yl, 6-ethyl-2,2-dioxo-2λ

⁶-isothiochroman-4-yl, 7-ethyl-1,2,3,4-tetrahydro-naphthalen-1-yl, and 1-(3-tert-Butyl-phenyl)-cyclohexyl, and 3-methoxy-benzyl.

15. The method according to claim 9, wherein R₂ is selected from hydrogen, 3-Bromo-[1,2,4]thiadiazol-5-ylamino, [1,2,4]thiadiazol-5-ylamino, 4-Chloro-[1,2,5]thiadiazol-3-ylamino, [1,2,5]thiadiazol-3-ylamino, thiazol-2-ylamino, 5-Bromo-[1,3,4]thiadiazol-2-ylamino, [1,3,4]thiadiazol-2-ylamino, 5-Amino-[1,3,4]thiadiazol-2-ylamino, 2-Bromo-thiazol-5-ylamino, thiazol-5-ylamino, 5-trifluoromethyl-[1,3,4]thiadiazol-2-ylamino, 5-trifluoromethyl-[1,3,4]oxadiazol-2-ylamino, 5-Amino-[1,3,4]oxadiazol-2-ylamino, 1-trityl-1H-[1,2,4]triazol-3-ylamino, 1H-[1,2,4]triazol-3-ylamino, oxazol-2-ylamino, 5-Bromo-2-trityl-2H-[1,2,3]triazol-4-ylamino, 2-trityl-2H-[1,2,3]triazol-4-ylamino, 5-Bromo-2H-[1,2,3]triazol-4-ylamino, 2H-[1,2,3]triazol-4-ylamino, thiophen-2-ylamino, 3-methyl-5-nitro-3H-imidazol-4-ylamino, 4-Cyano-5-phenyl-isothiazol-3-ylamino, 4-phenyl-[1,2,5]thiadiazol-3-ylamino, 3,4-dioxo-cyclobut-1-enylamino, 2-methoxy-3,4-dioxo-cyclobut-1-enylamino, and 2-methylamino-3,4-dioxo-cyclobut-1-enylamino.

16. The method according to claim 9, wherein R_x is selected from 3-(1,1-dimethyl-propyl)-phenyl, 3-(1-ethyl-propyl)-phenyl, 3-(1H-pyrrol-2-yl)-phenyl, 3-(1-hydroxy-1-methyl-ethyl)-phenyl, 3-(1-methyl-1H-imidazol-2-yl)-phenyl, 3-(1-methyl-cyclopropyl)-phenyl, 3-(2,2-dimethyl-propyl)-phenyl, 3-(2,5-dihydro-1H-pyrrol-2-yl)-phenyl, 3-(2-Chloro-thiophen-3-yl)-phenyl, 3-(2-Cyano-thiophen-3-yl)-phenyl, 3-(2-fluoro-benzyl)-phenyl, 3-(3,5-dimethyl-3H-pyrazol-4-yl)-phenyl, 3-(3,6-dimethyl-pyrazin-2-yl)-phenyl, 3-(3-Cyano-pyrazin-2-yl)-phenyl, 3-(3-formyl-furan-2-yl)-phenyl, 3-(3H-[1,2,3]triazol-4-yl)-phenyl, 3-(3H-imidazol-4-yl)-phenyl, 3-(3-methyl-butyl)-phenyl, 3-(3-methyl-pyridin-2-yl)-phenyl, 3-(3-methyl-thiophen-2-yl)-phenyl, 3-(4-Cyano-pyridin-2-yl)-phenyl, 3-(4-fluoro-benzyl)-phenyl, 3-(4H-[1,2,4]triazol-3-yl)-phenyl, 3-(4-methyl-thiophen-2-yl)-phenyl, 3-(5-Acetyl-thiophen-2-yl)-phenyl, 3-(5-Acetyl-thiophen-3-yl)-phenyl, 3-(5-formyl-thiophen-2-yl)-phenyl, 3-(5-oxo-pyrrolidin-2-yl)-phenyl, 3-(6-methyl-pyridazin-3-yl)-phenyl, 3-(6-methyl-pyridin-2-yl)-phenyl, 3-(Cyano-dimethyl-methyl)-phenyl, 3-[1-(2-tert-Butyl-pyrimidin-4-yl)-cyclohexylamino, 3-[1,2,3]triazol-1-yl-phenyl, 3-[1,2,4]oxadiazol-3-yl-phenyl, 3-[1,2,4]oxadiazol-5-yl-phenyl, 3-[1,2,4]thiadiazol-3-yl-phenyl, 3-[1,2,4]thiadiazol-5-yl-phenyl, 3-[1,2,4]triazol-4-yl-phenyl, 3-Acetyl-5-tert-butyl-phenyl, 3′

-Acetylamino-biphenyl-3-yl, 3-Adamantan-2-yl-phenyl, 3-Bromo-[1,2,4]thiadiazol-5-yl)-phenyl, 3-Bromo-5-tert-butyl-phenyl, 3-Cyano-phenyl, 3-Cyclobutyl-phenyl, 3-Cyclopentyl-phenyl, 3-Cyclopropyl-phenyl, 3-ethyl-phenyl, 3-ethynyl-phenyl, 3-fluoro-5-(2-hydroxy-1,1-dimethyl-ethyl)-phenyl, 3-furan-3-yl-phenyl, 3-imidazol-1-yl-phenyl, 3-isobutyl-phenyl, 3-isopropyl-phenyl, 3-isoxazol-3-yl-phenyl, 3-isoxazol-4-yl-phenyl, 3-isoxazol-5-yl-phenyl, 3-pent-4-enyl-phenyl, 3-pentyl-phenyl, 3-Phenyl-propionic acid ethyl ester, 3-pyrazin-2-yl-phenyl, 3-pyridin-2-yl-phenyl, 3-pyrrolidin-2-yl-phenyl, 3-sec-Butyl-phenyl, 3-tert-Butyl-4-chloro-phenyl, 3-tert-Butyl-4-cyano-phenyl, 3-tert-Butyl-4-ethyl-phenyl, 3-tert-Butyl-4-methyl-phenyl, 3-tert-Butyl-4-trifluoromethyl-phenyl, 3-tert-Butyl-5-chloro-phenyl, 3-tert-Butyl-5-cyano-phenyl, 3-tert-Butyl-5-ethyl-phenyl, 3-tert-Butyl-5-fluoro-phenyl, 3-tert-Butyl-5-methyl-phenyl, 3-tert-Butyl-5-trifluoromethyl-phenyl, 3-tert-Butyl-phenyl, 3-thiazol-2-yl-phenyl, 3-thiazol-4-yl-phenyl, 3-thiophen-3-yl-phenyl, 3-trifluoromethyl-phenyl, 4-Acetyl-3-tert-butyl-phenyl, 4-tert-Butyl-pyridin-2-yl, 4-tert-Butyl-pyrimidin-2-yl, 5-tert-Butyl-pyridazin-3-yl, 6-tert-Butyl-pyridazin-4-yl, and 6-tert-Butyl-pyrimidin-4-yl.

17. The method according to claim 9, wherein at least one compound of formula (I) is administered in combination with a pharmaceutically acceptable carrier or diluent.

18. The method according to claim 9, wherein the condition is selected from Alzheimer'"'"'s disease, Down'"'"'s syndrome or Trisomy 21, hereditary cerebral hemorrhage with amyloidosis of the Dutch type, chronic inflammation due to amyloidosis, prion diseases, Familial Amyloidotic Polyneuropathy, cerebral amyloid angiopathy, other degenerative dementias, dementia associated with Parkinson'"'"'s disease, dementia associated with progressive supranuclear palsy and dementia associated with cortical basal degeneration, diffuse Lewy body type of Alzheimer'"'"'s disease, and frontotemporal dementias with parkinsonism.

19. The method according to claim 9, wherein the condition is Alzheimer'"'"'s disease.

20. The method according to claim 9, wherein the condition is dementia.