1461151924-3c9013ad-6aa5-4117-9e9e-bc1d7a72ab47

1. A compound represented by the following structural formula:
or pharmaceutically acceptable salts, solvates or hydrates thereof, wherein:
Y is C\u2550O, S(O), or S(O)2;
X1, X2, and X3 are each independently N or CR, provided that at least one of X1, X2, or
X3 is CR;
R, for each occurrence, and R1 are each independently H, an aliphatic group, haloalkyl, aryl, arylalkyl, alkoxy, cycloalkoxy, haloalkoxy, aryloxy, arylalkoxy, alkylthio, halo, nitro, cyano, sulonamido, sulfone, sulfoxide, hydroxy, NR11CO2R12, C(O)N(R11)2, C(O)R12, CO2R12, OC(O)N(R11)2, OC(O)R12, N(R11)2, or NR11C(O)R12; wherein R11, for each occurrence is, independently, H or an aliphatic group, and R12 is an aliphatic group;
R6 is H, an aliphatic carbonyl group, or an aliphatic ester;
Ar1 is a substituted or unsubstituted group selected from pyridyl, N-oxido pyridyl, pyrimidinyl, and pyrazinyl; and
Ar2 is a substituted or unsubstituted aryl group or a substituted or unsubstituted heteroaryl group.
2. The compound of claim 1, wherein Ar1 is a substituted or unsubstituted group selected from pyrid-4-yl, N-oxido pyrid-4-yl, pyrimidinyl, and pyrazinyl.
3. The compound of claim 2, wherein R1 is H, R6 is H, and Y is C\u2550O, and the compound is represented by one of the following structural formulae:
wherein X4 is N or N+\u2014O\u2212;
ring A is unsubstituted or is substituted with one or more independent occurrences of aliphatic, haloalkyl, aryl, arylalkyl, alkoxy, cycloalkoxy, haloalkoxy, aryloxy, arylalkoxy, alkylthio, halo, nitro, cyano, sulonamido, sulfone, sulfoxide, hydroxy, NR11CO2R12, C(O)N(R11)2, C(O)R12, CO2R12, OC(O)N(R11)2, OC(O)R12, N(R11)2, or NR11C(O)R12; wherein R11, for each occurrence is, independently, H or an aliphatic group, and R12 is an aliphatic group;
ring B is substituted or unsubstituted; and
Ar2 is a substituted or unsubstituted aryl or a substituted or unsubstituted heteroaryl group.
4. The compound of claim 3, wherein Ar2 is a substituted or unsubstituted group selected from phenyl, naphthyl, thienyl, and thianaphthenyl.
5. The compound of claim 3, wherein Ar2 is a substituted or unsubstituted group selected from phenyl and pyridyl.
6. The compound of claim 3, wherein Ar2 is a substituted or unsubstituted group selected from phenyl and thienyl.
7. The compound of claim 3, wherein Ar2 is unsubstituted or is substituted with one or more substituents selected from substituted aliphatic, unsubstituted aliphatic, aryl, arylalkyl, substituted alkoxy, unsubstituted alkoxy, aryloxy, arylalkoxy, alkylthio, halo, nitro, cyano, S(O)-(aliphatic), S(O)2-(aliphatic), NR11S(O)2-(aliphatic), C(O)N(R11)2, C(O)R12, N(R11)2, NR11C(O)2R12, and NR11C(O)R12, wherein R11 for each occurrence is independently H or an aliphatic group, and R12 is an aliphatic group.
8. The compound of claim 3, wherein Ar2 is unsubstituted or is substituted with one or more substituents selected from aliphatic, alkoxy, and haloalkoxy.
9. The compound of claim 3, wherein one or both rings A and B are unsubstituted or are independently substituted with a substituent selected from halo, aliphatic, alkoxy, and haloalkyl.
10. The compound of claim 3, wherein ring A is substituted para to the sulfonamide group with an electron withdrawing substituent selected from halo, haloalkyl, nitro, cyano, sulfonamide, sulfone, and sulfoxide.
11. The compound of claim 3, wherein the compound is represented by the following structural formula:
wherein X4 is N or N+\u2014O\u2212;
ring A is unsubstituted or is substituted with one or more independent occurrences of aliphatic, haloalkyl, aryl, arylalkyl, alkoxy, cycloalkoxy, haloalkoxy, aryloxy, arylalkoxy, alkylthio, halo, nitro, cyano, sulonamido, sulfone, sulfoxide, hydroxy, NR11CO2R12, C(O)N(R11)2, C(O)R12, CO2R12, OC(O)N(R11)2, OC(O)R12, N(R11)2, or NR11C(O)R12; wherein R11, for each occurrence is, independently, H or an aliphatic group, and R12 is an aliphatic group;
ring B is substituted or unsubstituted; and
Ar2 is a substituted or unsubstituted aryl or a substituted or unsubstituted heteroaryl group.
12. The compound of claim 11, wherein Ar2 is a substituted or unsubstituted group selected from phenyl, naphthyl, thienyl, and thianaphthenyl.
13. The compound of claim 11, wherein Ar2 is a substituted or unsubstituted group selected from phenyl and pyridyl.
14. The compound of claim 11, wherein Ar2 is a substituted or unsubstituted group selected from phenyl and thienyl.
15. The compound of claim 11, wherein Ar2 is a substituted or unsubstituted phenyl ring and the compound is represented by the following structural formula
16. The compound of claim 15, wherein ring A is substituted by R8 and the compound is represented by the following structural formula:
wherein R8 is H, halo, haloalkyl, nitro, cyano, sulfonamide, sulfone, or sulfoxide.
17. The compound of claim 16, wherein the compound is represented by the following structural formula:
wherein
R8 is H, halo, haloalkyl, nitro, cyano, sulfonamide, sulfone, or sulfoxide;
m and n are each, independently, 0 or an integer from 1 to 3;
each R9 is, independently, aliphatic, haloalkyl, aryl, arylalkyl, alkoxy, cycloalkoxy, haloalkoxy, aryloxy, arylalkoxy, alkylthio, halo, nitro, cyano, hydroxy, NR11CO2R12, C(O)N(R11)2, C(O)R12, CO2R12, OC(O)N(R11)2, OC(O)R12, N(R11)2, or NR11C(O)R12; or two adjacent R9 groups taken together with the atoms to which they are attached form a fused, saturated, unsaturated or partially unsaturated 5 to 7 membered ring having 0, 1, or 2 heteroatoms selected from N, O, and S;
wherein each R11 is, independently, H or an aliphatic group; and R12 is an aliphatic group; and

each R10 is, independently, halo, aliphatic group, alkoxy, or haloalkyl; or two adjacent R10 groups taken together with the atoms to which they are attached form a fused, saturated, unsaturated or partially unsaturated 5 to 7 membered ring having 0, 1 or 2 heteroatoms selected from N, O, and S.
18. The compound of claim 17, wherein:
R8 is halo, nitro, alkylcarbonyl, or trihaloalkyl; and
n is 1 and R9 is para to the sulfonamide substituent and is an aliphatic, alkoxy, or haloalkoxy group.
19. The compound of claim 18, wherein R8 is Cl, Br, or NO2.
20. A pharmaceutical composition, comprising a pharmaceutically acceptable carrier and the compound of claim 1.
21. A pharmaceutical composition, comprising a pharmaceutically acceptable carrier and the compound of claim 17.
22. A method of inhibiting a CCR9 receptor function in a subject in need thereof, comprising the step of administering to the subject an effective amount of a compound of claim 1.
23. A method of inhibiting a CCR9 receptor function in a subject in need thereof, comprising the step of administering to the subject an effective amount of a compound of claim 17.
24. A method of treating an inflammatory disease or condition in a subject in need thereof, comprising administering to the subject an effective amount of a compound of claim 1.
25. A method of treating an inflammatory disease or condition in a subject in need thereof, comprising administering to the subject an effective amount of a compound of claim 17.
26. The method of claim 24, wherein the inflammatory disease or condition is an inflammatory bowel disease (IBD).
27. The method of claim 24, wherein the inflammatory bowel disease is E ulcerative colitis, Crohn’s disease, ileitis, Celiac disease, nontropical Sprue, enteritis, enteropathy associated with seronegative arthropathies, microscopic or collagenous colitis, eosinophilic gastroenteritis, or pouchtis resulting after proctocolectomy, or ileoanal anastomosis.
28. The method of claim 24, wherein the inflammatory disease or condition is Crohn’s disease or colitis.
29. The method of claim 24, wherein the inflammatory disease or condition is Celiac’s disease.
30. A method of treating a disease or condition in a subject in need thereof, wherein the disease or condition is an inflammatory disease or condition, an allergic disease or condition, an autoimmune disease or condition, or graft rejection, comprising administering to the subject an effective amount of a compound of claim 1.
31. The method of claim 30, wherein the disease or condition is inflammatory bowel disease, mastitis, vaginitis, cholecystitis, cholangitis or pericholangitis, chronic bronchitis, chronic sinusitis, systemic anaphylaxis or hypersensitivity responses, drug allergies, insect sting allergies, psoriasis, inflammatory dermatoses, vasculitis, spondyloarthropathies, scleroderma, respiratory allergic diseases, arthritis, multiple sclerosis, systemic lupus erythematosus, myasthenia gravis, juvenile onset diabetes, glomerulonephritis and other nephritides, autoimmune thyroiditis, Behcet’s disease, allograft rejection, graft-versus-host disease, atherosclerosis, restenosis, or myositis.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1. An apparatus for generating differential signals, the apparatus comprising:
a first operational amplifier receiving a first signal;
a second operational amplifier receiving a second signal;
a first transistor, the first transistor including a first gate, a first terminal, and a second terminal;
a second transistor, the second transistor including a second gate, a third terminal, and a fourth terminal;
a first resistor coupled to the first terminal and the third terminal;
a second resistor coupled to the second terminal and the fourth terminal;
a first current supplier coupled to the first terminal;
a second current supplier coupled to the second terminal;
a third current supplier coupled to the third terminal;
a fourth current supplier coupled to the fourth terminal;
wherein:
the gate of the first transistor is coupled to the first operational amplifier;
the gate of the second transistor is coupled to the second operational amplifier;
the second terminal is configured to output a third signal;
the fourth terminal is configured to output a fourth signal;
a first difference between the fourth signal and the third signal is substantially proportional to a second difference between the first signal and the second signal.
2. The apparatus of claim 1 wherein:
the first signal corresponds to one input signal;
the second signal corresponds to another input signal.
3. The apparatus of claim 1 wherein:
the first signal corresponds to one input signal;
the second signal is biased to a predetermined voltage level.
4. The apparatus of claim 1, and further comprising a common-mode feedback device, the common-mode feedback device being configured to receive at least the third signal and the fourth signal and to adjust the second current supplier and the fourth current supplier.
5. The apparatus of claim 4 wherein a sum of the third signal and the fourth signal is substantially equal to two times of a common-mode voltage.
6. The apparatus of claim 1 wherein the first transistor and the second transistor are the same.
7. The apparatus of claim 1 wherein the first transistor is an NMOS transistor, and the second transistor is another NMOS transistor.
8. The apparatus of claim 1 wherein the first current supplier and the third current supplier are the same.
9. The apparatus of claim 1 wherein the second current supplier and the fourth current supplier are the same.
10. The apparatus of claim 1 wherein the first operational amplifier and the second operational amplifier are the same.
11. The apparatus of claim 1 wherein the first resistor and the second resistor are the same.
12. The apparatus of claim 11 wherein the first difference between the fourth signal and the third signal is substantially the same as the second difference between the first signal and the second signal.
13. The apparatus of claim 1 wherein the first operational amplifier receives a fifth signal from the first terminal, and the second operational amplifier receives a sixth signal from the second terminal.
14. The apparatus of claim 1 wherein the first terminal is one selected from a group consisting of a first source and a first drain, and the second terminal is the other one selected from a group consisting of the first source and the first drain.
15. The apparatus of claim 1 wherein the third terminal is one selected from a group consisting of a second source and a second drain, and the fourth terminal is the other one selected from a group consisting of the second source and the second drain.
16. An apparatus for generating differential signals, the apparatus comprising:
a first operational amplifier receiving a first signal;
a second operational amplifier receiving a second signal;
a first transistor, the first transistor including a first gate, a first terminal, and a second terminal;
a second transistor, the second transistor including a second gate, a third terminal, and a fourth terminal;
a first resistor coupled to the first terminal and the third terminal;
a second resistor coupled to the second terminal and the fourth terminal;
a first current supplier coupled to the first terminal;
a second current supplier coupled to the second terminal;
a third current supplier coupled to the third terminal;
a fourth current supplier coupled to the fourth terminal;
a common-mode feedback device;
wherein:
the gate of the first transistor is coupled to the first operational amplifier;
the gate of the second transistor is coupled to the second operational amplifier;
the second terminal is configured to output a third signal;
the fourth terminal is configured to output a fourth signal;
the common-mode feedback device is configured to receive at least the third signal and the fourth signal;
the common-mode feedback device is configured to adjust the second current supplier and the fourth current supplier;
a first difference between the fourth signal and the third signal is substantially proportional to a second difference between the first signal and the second signal.
17. The apparatus of claim 16 wherein:
the first signal corresponds to one input signal;
the second signal corresponds to another input signal.
18. The apparatus of claim 16 wherein:
the first signal corresponds to one input signal;
the second signal is biased to a predetermined voltage level.
19. The apparatus of claim 16 wherein a sum of the third signal and the fourth signal is substantially equal to two times of the predetermined voltage level.
20. The apparatus of claim 16 wherein the common-mode feedback device is biased to a predetermined voltage level.
21. The apparatus of claim 16 wherein a sum of the third signal and the fourth signal is substantially equal to two times of a common-mode voltage.
22. A method for generating differential signals, the method comprising:
receiving a first signal and a second signal;
generating a third signal and a fourth signal, the third signal being substantially equal to the first signal, the fourth signal being substantially equal to the second signal;
converting a first voltage difference between the third signal and the fourth signal to a first current;
generating a second current, the second current being substantially the same as the first current in magnitude;
converting the second current to a second voltage difference between a fifth signal and a sixth signal;
wherein the first voltage difference is proportional to the second voltage difference.
23. The method of claim 22, and further comprising:
determining a common-mode voltage for the fifth signal and the sixth signal;
wherein a sum of the fifth signal and the sixth signal is substantially equal to the common-mode voltage.