Inhibitors of e1 activating enzymes

Abstract

This invention relates to compounds that inhibit E1 activating enzymes, pharmaceutical compositions comprising the compounds, and methods of using the compounds. The compounds are useful for treating disorders, particularly cell proliferation disorders, including cancers, inflammatory and neurodegenerative disorders; and inflammation associated with infection and cachexia.

1 . (canceled) 
     
     
         2 . A compound of formula (I-A): 
       
         
           
           
               
               
           
         
       
       or a pharmaceutically acceptable salt thereof, wherein:
 stereochemical configurations depicted at asterisked positions indicate relative stereochemistry; 
 Ring A is selected from the group consisting of: 
 
       
         
           
           
               
               
           
         
          wherein one ring nitrogen atom in Ring A optionally is oxidized; 
         X is —CH 2 —, —CHF—, —CF 2 —, —NH—, or —O—; 
         Y is —O— or —S—; 
         R a  is selected from the group consisting of hydrogen, fluoro, —CN, —N 3 , —OR 5 , —N(R 4 ) 2 , —NR 4 CO 2 R 6 , —NR 4 C(O)R 5 , —C(O)N(R 4 ) 2 , —C(O)R 5 , —OC(O)N(R 4 ) 2 , —OC(O)R 5 , —OCO 2 R 6 , or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); or R a  and R c  together form a bond; 
         R b  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
         R c  is selected from the group consisting of hydrogen, fluoro, —CN, —N 3 , —OW, —N(R 4 ) 2 , —NR 4 CO 2 R 6 , —NR 4 C(O)R 5 , —C(O)N(R 4 ) 2 , —C(O)R 5 , —OC(O)N(R 4 ) 2 , —OC(O)R 5 , —OCO 2 R 6 , or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); or R a  and R c  together form a bond; 
         R d  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
         R e  is hydrogen, or C 1-4  aliphatic; or R e , taken together with one R f  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         R e′  is hydrogen or C 1-4  aliphatic; 
         each R f  is independently hydrogen, fluoro, C 1-4  aliphatic, or C 1-4  fluoroaliphatic, provided that if X is —O— or —NH—, then R f  is not fluoro; or two R f  taken together form ═O; or two R f , taken together with the carbon atom to which they are attached, form a 3- to 6-membered carbocyclic ring; or one R f , taken together with R e  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         R g  is hydrogen, halo, —NO 2 , —CN, —C(R 6 )═C(R 6 ) 2 , —C≡C—R 5 , —OR 5 , —SR 6 , —S(O)R 6 , —SO 2 R 6 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 2 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 6 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 6 , —OCO 2 R 6 , —OC(O)N(R 4 ) 2 , —C(O)R 5 , —CO 2 R 6 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 5 , —C(O)N(R 4 )C(═NR 4 )N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 5 , —C(═NR 4 )—N(R 4 ) 2 , —C(═NR 4 )—OR 5 , —N(R 4 )—N(R 4 ) 2 , —N(R 4 )—OR 5 , —C(═NR 4 )—N(R 4 )—OR 6 , —C(R 6 )═N—OR 5 , or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl; 
         each R h  independently is hydrogen, halo, —CN—, —N(R 4 ) 2 , —SR 6 , or an optionally substituted C 1-4  aliphatic group; 
         R i  is hydrogen, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted aliphatic, aryl, or heteroaryl group; 
         R k  is hydrogen, halo, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted C 1-4  aliphatic group; 
         R m  is hydrogen, fluoro, —N(R 4 ) 2 , or an optionally substituted C 1-4  aliphatic group; and 
         R n  is hydrogen, fluoro, or an optionally substituted C 1-4  aliphatic group; or 
         R m  and R n  together form ═O or ═C(R 5 ) 2 ; 
         each R 4  independently is hydrogen or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl group; or two R 4  on the same nitrogen atom, taken together with the nitrogen atom, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; 
         R 4x  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted; 
         R 4y  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted, or an optionally substituted 5- or 6-membered aryl, heteroaryl, or heterocyclyl ring; or 
         R 4x  and R 4y , taken together with the nitrogen atom to which they are attached, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; and 
         each R 5  independently is hydrogen or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl group; 
         each R 5x  independently is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or an optionally substituted C 6-10  aryl or C 6-10  ar(C 1-4 )alkyl; 
         each R 6  independently is an optionally substituted aliphatic, aryl, or heteroaryl group; and 
         m is 1, 2, or 3. 
       
     
     
         3 . The compound of  claim 2 , wherein:
 R g  is hydrogen, C 1-6  aliphatic, C 1-6  fluoroaliphatic, halo, —R 1g , —R 2g , -T 1 -R 1g , -V 1 -T 1 -R 1g , and -V 1 -T 1 -R 2g ;   T 1  is a C 1-6  alkylene chain substituted with 0-2 independently selected R 3a  or R 3b , wherein the alkylene chain optionally is interrupted by —C(R 5 )═C(R 5 )—, —C≡C—, —O—, —S—, —S(O)—, —S(O) 2 —, —SO 2 N(R 4 )—, —N(R 4 )—, —N(R 4 )C(O)—, —NR 4 C(O)N(R 4 )—, —N(R 4 )C(═NR 4 )—N(R 4 )—, —N(R 4 )—C(═NR 4 )—, —N(R 4 )CO 2 —, —N(R 4 )SO 2 —, —N(R 4 )SO 2 N(R 4 )—, —OC(O)—, —OC(O)N(R 4 )—, —C(O)—, —CO 2 —, —C(O)N(R 4 )—, —C(═NR 4 )—N(R 4 )—, —C(NR 4 )═N(R 4 )—, —C(═NR 4 )—O—, or —C(R 6 )═N—O—, and wherein T 1  or a portion thereof optionally forms part of a 3-7 membered ring;   V 1  is —C(R 5 )═C(R 5 )—, —O—, —S—, —S(O)—, —S(O) 2 —, —SO 2 N(R 4 )—, —N(R 4 )—, —N(R 4 )C(O)—, —NR 4 C(O)N(R 4 )—, —N(R 4 )C(═NR 4 )—N(R 4 )—, —N(R 4 )C(═NR 4 )—, —N(R 4 )CO 2 —, —N(R 4 )SO 2 —, —N(R 4 )SO 2 N(R 4 )—, —OC(O)—, —OC(O)N(R 4 )—, —C(O)—, —CO 2 —, —C(O)N(R 4 )—, —C(O)N(R 4 )—O—, —C(O)N(R 4 )C(═NR 4 )—N(R 4 )—, —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)—, —C(═NR 4 )—N(R 4 )—, —C(NR 4 )═N(R 4 )—, —C(═NR 4 )—O—, or —C(R 6 )═N—O—;   each R 1g  independently is an optionally substituted aryl, heteroaryl, heterocyclyl, or cycloaliphatic ring;   each R 29  independently is —NO 2 , —CN, —C(R 5 )═C(R 5 ) 2 , —C≡C—R 5 —OR 5 , —SR 6 , —S(O)R 6 , —SO 2 R 6 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 2 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 6 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 5 , —OCO 2 R 6 , —OC(O)N(R 4 ) 2 , —C(O)R 5 , —CO 2 R 5 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 5 , —C(O)N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 5 , —C(═NR 4 )—N(R 4 ) 2 , —C(═NR 4 )—OR 5 , —N(R 4 )—N(R 4 ) 2 , —N(R 4 )—OR 5 , —C(═NR 4 )—N(R 4 )—OR 5 , or —C(R 6 )═N—OR 3 ;   each R 3a  independently is selected from the group consisting of —F, —OH, —O(C 1-4  alkyl), —CN, —N(R 4 ) 2 , —C(O)(C 1-4  alkyl), —CO 2 H, —OCO 2 (C 1-4  alkyl), —C(O)NH 2 , and —C(O)NH(C 1-4  alkyl);   each R 3b  independently is a C 1-3  aliphatic optionally substituted with R 3a  or R 7 , or two substituents R 3b  on the same carbon atom, taken together with the carbon atom to which they are attached, form a 3- to 6-membered cycloaliphatic ring; and   each R 7  independently is an optionally substituted aryl or heteroaryl ring.   
     
     
         4 . The compound of  claim 2 , characterized by one or more of the following features:
 (a) X is —O—;   (b) Y is —O—;   (c) R a  is —OH;   (d) R b  and R d  are each independently hydrogen, fluoro, or C 1-4  aliphatic;   (e) R c  is hydrogen, fluoro, or —OR 5 ;   (f) R e  and R e′  are each hydrogen;   (g) each R f  is hydrogen;   (h) each R h  is hydrogen;   (i) R j  is hydrogen or C 1-4  aliphatic;   (j) R k  is hydrogen, halo, or C 1-4  aliphatic;   (k) m is 1; and   (l) stereochemical configurations depicted at asterisked positions indicate absolute stereochemistry.   
     
     
         5 . The compound of  claim 4 , characterized by formula (III): 
       
         
           
           
               
               
           
         
         or a pharmaceutically acceptable salt thereof, wherein Q is ═N— or ═C(R k )—. 
       
     
     
         6 . The compound of  claim 5 , wherein:
 R g  is -V 1 -T 1 -R 1g , -V 1 -R 1g , -T 1 -R 1g , -T 1 -V 1 -R 1g ;   V 1  is —C(R 5 )═C(R 5 ), —O—, —S—, or —N(R 4 )—;   T 1  is a C 1-4  alkylene chain optionally substituted with one or two groups independently selected from fluoro or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 6x , —N(R 4x )(R 4y ), —CO 2 R 5x , and —C(O)N(R 4x )(R 4y ); and   R 1g  is an optionally substituted mono- or bicyclic aryl, heteroaryl, heterocyclyl, or cycloaliphatic group.   
     
     
         7 . The compound of  claim 6 , characterized by formula (V): 
       
         
           
           
               
               
           
         
       
       or a pharmaceutically acceptable salt thereof, wherein:
 V 1  is —N(R 8 )—, —O—, or —S—; 
 R 8  is hydrogen or C 1-4  aliphatic; 
 T 1  is a C 1-4  alkylene chain optionally substituted with one or two groups independently selected from fluoro or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , and —C(O)N(R 4x )(R 4y ); and 
 Ring C is a 3- to 8-membered heterocyclyl or cycloaliphatic ring, or a 5- or 6-membered aryl or heteroaryl ring, any of which rings is substituted with 0-2 R o  and 0-2 R 8o ;
 each R o  independently is halo, —NO 2 , —CN, —C(R 5 )═C(R 5 ) 2 , —C≡C—R 5 , —SR 6 , —S(O)R 6 , —SO 2 R 6 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 2 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 6 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 5 , —OCO 2 R 6 , —OC(O)N(R 4 ) 2 , —C(O)R 5 , —CO 2 R 6 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 5 , —C(O)N(R 4 )C(═NR 4 )—N(R) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 5 , —C(═NR 4 )—N(R 4 ) 2 , —C(═NR 4 )—OR 5 , —C(═NR 4 )—N(R 4 )—OR 5 , —C(R 6 )═N—OR 6 , or an optionally substituted aliphatic, or an optionally substituted aryl, heterocyclyl, or heteroaryl group; or two R o  on the same saturated ring carbon atom, taken together with the carbon atom, form an optionally substituted 3- to 8-membered spirocyclic cycloaliphatic or heterocyclyl ring; or two adjacent R o , taken together with the intervening ring atoms, form an optionally substituted fused 4- to 8-membered aromatic or non-aromatic ring having 0-3 ring heteroatoms selected from the group consisting of O, N, and S; 
 
 each R 8o  independently is selected from the group consisting of C 1-4  aliphatic, C 1-4  fluoroaliphatic, halo, —OR 5x , —N(R 4x )(R 4y ), or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); 
 R 4x  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted; 
 R 4y  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted, or an optionally substituted 5- or 6-membered aryl, heteroaryl, or heterocyclyl ring; or 
 R 4x  and R 4y , taken together with the nitrogen atom to which they are attached, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; and each R 5x  independently is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or an optionally substituted C 6-10  aryl or C 6-10  ar(C 1-4 )alkyl. 
 
     
     
         8 . The compound of  claim 7 , wherein:
 T 1  is a C 1-2  alkylene chain optionally substituted with one or two groups independently selected from fluoro or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , and —C(O)N(R 4x )(R 4y ); and   Ring C is a C 3-6  cycloaliphatic, phenyl, oxazolyl, or isoxazolyl ring, any of which is substituted with 0-2 R 8o  and optionally is fused to an optionally substituted benzene, dioxolane, or dioxane ring.   
     
     
         9 . The compound of  claim 5 , characterized by formula (VI): 
       
         
           
           
               
               
           
         
       
       or a pharmaceutically acceptable salt thereof, wherein:
 T 1  is a C 1-4  alkylene chain optionally substituted with one or two groups independently selected from fluoro or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , and —C(O)N(R 4x )(R 4y ); and 
 Ring C is a 3- to 8-membered heterocyclyl or cycloaliphatic ring, or a 5- or 6-membered aryl or heteroaryl ring, any of which rings is substituted with 0-2 R o  and 0-2 R 8o ; 
 each R o  independently is halo, —NO 2 , —CN, —C(R 5 )═C(R 5 ) 2 , —OR 5 , —SR 6 , —S(O)R 6 , —SO 2 R 6 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 2 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 6 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 5 , —OCO 2 R 6 , —OC(O)N(R 4 ) 2 , —C(O)R 5 , —CO 2 R 5 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 5 , —C(O)N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 5 , —C(═NR 4 )—N(R 4 ) 2 , —C(═NR 4 )—OR 5 , —C(═NR 4 )—N(R 4 )—OR 5 , —C(R 8 )═N—OR 5 , or an optionally substituted aliphatic, or an optionally substituted aryl, heterocyclyl, or heteroaryl group; or two R o  on the same saturated ring carbon atom, taken together with the carbon atom, form an optionally substituted 3- to 8-membered spirocyclic cycloaliphatic or heterocyclyl ring; or two adjacent R o , taken together with the intervening ring atoms, form an optionally substituted fused 4- to 8-membered aromatic or non-aromatic ring having 0-3 ring heteroatoms selected from the group consisting of O, N, and S; 
 each R 8o  independently is selected from the group consisting of C 1-4  aliphatic, C 1-4  fluoroaliphatic, halo, —OR 5x , —N(R 4x )(R 4y ), or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); 
 R 4x  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted; 
 R 4y  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted, or an optionally substituted 5- or 6-membered aryl, heteroaryl, or heterocyclyl ring; or 
 R 4x  and R 4y , taken together with the nitrogen atom to which they are attached, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; and each R 5x  independently is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or an optionally substituted C 6-10  aryl or C 6-10  ar(C 1-4 )alkyl. 
 
     
     
         10 . The compound of  claim 9 , wherein:
 T 1  is a C 1-2  alkylene chain optionally substituted with one or two groups independently selected from fluoro or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , and —C(O)N(R 4x )(R 4y ); and   Ring C is phenyl, which is substituted with 0-2 R 8o  and optionally is fused to an optionally substituted benzene, dioxolane, or dioxane ring.   
     
     
         11 . The compound of  claim 5 , characterized by formula (VII): 
       
         
           
           
               
               
           
         
       
       or a pharmaceutically acceptable salt thereof, wherein:
 V 2  is —N(R 8 )—, —O—, or —S—; 
 R 8  is hydrogen or C 1-4  aliphatic; and 
 Ring D is an optionally substituted mono-, bi-, or tricyclic ring system. 
 
     
     
         12 . The compound of  claim 11 , wherein Ring D is selected from the group consisting of furanyl, thienyl, pyrrolyl, oxazolyl, thiazolyl, imidazolyl, pyrazolyl, isoxazolyl, isothiazolyl, oxadiazolyl, triazolyl, thiadiazolyl, phenyl, naphthyl, pyranyl, pyridyl, pyridazinyl, pyrimidinyl, pyrazinyl, triazinyl, indolizinyl, indolyl, isoindolyl, indazolyl, benzimidazolyl, benzthiazolyl, benzothienyl, benzofuranyl, purinyl, quinolyl, isoquinolyl, cinnolinyl, phthalazinyl, quinazolinyl, quinoxalinyl, naphthyridinyl, pteridinyl, tetrahydrofuranyl, tetrahydrothienyl, pyrrolidinyl, pyrrolidonyl, piperidinyl, pyrrolinyl, tetrahydroquinolinyl, tetrahydroisoquinolinyl, decahydroquinolinyl, oxazolidinyl, piperazinyl, dioxanyl, dioxolanyl, diazepinyl, oxazepinyl, thiazepinyl, morpholinyl, quinuclidinyl, tetrahydroquinolinyl, tetrahydroisoquinolinyl, indanyl, phenanthridinyl, tetrahydronaphthyl, indolinyl, benzodioxanyl, benzodioxolyl, chromanyl, cyclopropyl, cyclobutyl, cyclopentyl, cyclopentenyl, cyclohexyl, cyclohexenyl, cycloheptyl, cycloheptenyl, cyclooctyl, cyclooctenyl, cyclooctadienyl, bicycloheptanyl and bicyclooctanyl. 
     
     
         13 . The compound of  claim 12 , wherein:
 each substitutable saturated ring carbon atom in Ring D is unsubstituted or substituted with ═O, ═S, ═C(R 5 ) 2 , ═N—N(R 4 ) 2 , ═N—OR 6 , ═N—NHC(O)R 5 , ═N—NHCO 2 R 6 , ═N—NHSO 2 R 6 , ═N—R 5  or —R p ;   each substitutable unsaturated ring carbon atom in Ring D is unsubstituted or substituted with —R p ;   each substitutable ring nitrogen atom in Ring D is unsubstituted or substituted with —R 9p ;   each R p  independently is halo, —NO 2 , —CN, —C(R 5 )═C(R 5 ) 2 , —C≡C—R 5 , —SR 6 , —S(O)R 6 , —SO 2 R 6 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 2 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 6 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 5 , —OCO 2 R 6 , —OC(O)N(R 4 ) 2 , —C(O)R 5 , —CO 2 R 6 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 6 , —C(O)N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 6 , —C(═NR 4 )—N(R 4 ) 2 , —C(═NR 4 )—OR 6 , —C(═NR 4 )—N(R 4 )—OR 5 , —C(R 6 )═N—OR 5 , or an optionally substituted aliphatic, or an optionally substituted aryl, heterocyclyl, or heteroaryl group; or two R p  on the same saturated carbon atom, taken together with the carbon atom to which they are attached, form an optionally substituted 3- to 6-membered spirocyclic cycloaliphatic ring; and   each R 9p  independently is —C(O)R 5 , —C(O)N(R 4 ) 2 , —CO 2 R 8 , —SO 2 R 8 , —SO 2 N(R 4 ) 2 , or a C 1-4  aliphatic optionally substituted with R 3  or R 7 .   
     
     
         14 . The compound of  claim 12 , wherein:
 each R p  independently is selected from the group consisting of halo, C 1-6  aliphatic, C 1-6  fluoroaliphatic, —R 1p , —R 2p , -T 2 -R 1p , and -T 2 -R 2p ; or two R p  on the same saturated carbon atom, taken together with the carbon atom to which they are attached, form an optionally substituted 3- to 6-membered spirocyclic cycloaliphatic ring;   T 2  is a C 1-6  alkylene chain optionally substituted with R 3a  or R 3b ;   each R 1p  independently is an optionally substituted aryl, heteroaryl, or heterocyclyl group; and   each R 2p  independently is —NO 2 , —CN, —C(R 5 )═C(R 5 ) 2 , —C≡C—R 5 , —OR 5 , —SR 6 , —S(O)R 6 , —SO 2 R 8 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 2 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 6 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 5 , —OCO 2 R 6 , —OC(O)N(R 4 ) 2 , —C(O)R 5 , —CO 2 R 5 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 5 , —C(O)N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 5 , —C(═NR 4 )—N(R 4 ) 2 , —C(═NR 4 )—OR 5 , —C(═NR 4 )—N(R 4 )—OR 5 , or —C(R 8 )═N—OR 5 .   
     
     
         15 . The compound of  claim 14 , wherein Ring D is an optionally substituted indanyl, tetrahydronaphthyl, or chromanyl. 
     
     
         16 . The compound of  claim 15 , wherein:
 V 1  is —N(R 8 )—;   Ring D is selected from the group consisting of:   
       
         
           
           
               
               
           
         
         each R p  independently is selected from the group consisting of halo, —OR 5x , —N(R 4x )(R 4y ), CO 2 R 5x , or —C(O)N(R 4x )(R 4y ), or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); 
         each R 8p  independently is selected from the group consisting of fluoro, —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ), or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ), provided that R 8p  is other than —OR 5x  or —N(R 4x )(R 4y ) when located at a position adjacent to a ring oxygen atom, and further provided that when two R 8p  are attached to the same carbon atom, one must be selected from the group consisting of fluoro, —CO 2 R 5x , —C(O)N(R 4x )(R 4y ), and C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); or two R 8  on the same carbon atom together form ═O or ═C(R 5x ) 2 ; or two R 8p  on the same carbon atom are taken together with the carbon atom to which they are attached to form a 3- to 6-membered spirocyclic ring; 
         s is 0, 1, 2, 3, or 4; 
         t is 0, 1, or 2. 
       
     
     
         17 . (canceled) 
     
     
         18 . (canceled) 
     
     
         19 . A compound of formula (IX): 
       
         
           
           
               
               
           
         
       
       wherein:
 depicted stereochemical configurations indicate absolute stereochemistry; 
 R b  is selected from the group consisting of fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
 R d  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
 R e  is hydrogen or C 1-4  aliphatic; or R e , taken together with one R f  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
 each R f  independently is hydrogen, fluoro, C 1-4  aliphatic, or C 1-4  fluoroaliphatic; or two R f , taken together with the carbon atom to which they are attached, form a 3- to 6-membered carbocyclic ring; or one R f  taken together with R e  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
 R aa  and R bb  are each independently hydrogen or a hydroxyl protecting group, or R aa  and R bb  together form a cyclic diol protecting group. 
 
     
     
         20 . The compound of  claim 19 , represented by the formula: 
       
         
           
           
               
               
           
         
       
     
     
         21 . A compound of formula (X): 
       
         
           
           
               
               
           
         
       
       wherein:
 depicted stereochemical configurations indicate absolute stereochemistry; 
 R b  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
 R d  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
 R e  is hydrogen or C 1-4  aliphatic; or R e , taken together with one R f  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
 each R f  independently is hydrogen, fluoro, C 1-4  aliphatic, or C 1-4  fluoroaliphatic; or two R f , taken together with the carbon atom to which they are attached, form a 3- to 6-membered carbocyclic ring; or one R f  taken together with R e  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
 R aa  is hydrogen or a hydroxyl protecting group; and 
 R bb  is hydrogen or a hydroxyl protecting group; or 
 R aa  and R bb  together form a cyclic diol protecting group. 
 
     
     
         22 . The compound of  claim 21 , characterized by formula (Xa): 
       
         
           
           
               
               
           
         
         wherein Ar is an optionally substituted aryl group. 
       
     
     
         23 . The compound of  claim 22 , selected from the group consisting of: 
       
         
           
           
               
               
           
         
       
     
     
         24 . A compound of formula (XI) or formula (XII): 
       
         
           
           
               
               
           
         
       
       wherein:
 depicted stereochemical configurations indicate absolute stereochemistry; 
 Ring A is selected from the group consisting of: 
 
       
         
           
           
               
               
           
         
          wherein one ring nitrogen atom in Ring A optionally is oxidized; 
         R b  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
         R d  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
         R e  is hydrogen or C 1-4  aliphatic; or R e , taken together with one R f  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         each R f  independently is hydrogen, fluoro, C 1-4  aliphatic, or C 1-4  fluoroaliphatic; or two R f , taken together with the carbon atom to which they are attached, form a 3- to 6-membered carbocyclic ring; or one R f  taken together with R e  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         R g  is hydrogen, halo, —NO 2 , —CN, —C(R 5 )═C(R 5 ) 2 , —C≡C—R 5 , —OR 5 , —SR 6 , —S(O)R 6 , —SO 2 R 6 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 2 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 6 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 5 , —OC(O)N(R 4 ) 2 , —C(O)R 5 , —CO 2 R 5 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 5 , —C(O)N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 5 , —C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )—N(R 4 ) 2 , —N(R 4 )—OR 5 , —C(═NR 4 )—N(R 4 )—OR 5 , —C(R 6 )═N—OR 5 , or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl; 
         each R h  independently is hydrogen, halo, —CN, —OH, —O—(C 1-4  aliphatic), —NH 2 , —NH—(C 1-4  aliphatic), —N(C 1-4  aliphatic) 2 , —SH, —S—(C 1-4  aliphatic), or an optionally substituted C 1-4  aliphatic group; 
         R j  is hydrogen, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted aliphatic, aryl, or heteroaryl group; 
         R k  is hydrogen, halo, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted C 1-4  aliphatic group; 
         R aa  is hydrogen or a hydroxyl protecting group; and 
         R bb  is hydrogen or a hydroxyl protecting group; 
         R cc  is hydrogen or a hydroxyl protecting group; or 
         R aa  and R bb  together form a cyclic diol protecting group; or 
         R aa  and R cc  together form a cyclic diol protecting group. 
       
     
     
         25 . The compound of  claim 24 , characterized by formula (XIa) or (XIIa) 
       
         
           
           
               
               
           
         
         wherein Ar is an optionally substituted aryl group. 
       
     
     
         26 . The compound of  claim 24 , selected from the group consisting of: 
       
         
           
           
               
               
           
         
         wherein Ar is an optionally substituted aryl group. 
       
     
     
         27 . The compound of  claim 24 , selected from the group consisting of: 
       
         
           
           
               
               
           
         
         wherein R aa  and R cc  are each independently a hydroxyl protecting group, or R aa  and R cc  together form a cyclic diol protecting group. 
       
     
     
         28 . The compound of  claim 24 , selected from the group consisting of: 
       
         
           
           
               
               
           
         
         wherein R aa  and R bb  are each independently a hydroxyl protecting group. 
       
     
     
         29 . A pharmaceutical composition, comprising a compound of formula (I-A): 
       
         
           
           
               
               
           
         
       
       or a pharmaceutically acceptable salt thereof, wherein:
 stereochemical configurations depicted at asterisked positions indicate relative stereochemistry; 
 Ring A is selected from the group consisting of: 
 
       
         
           
           
               
               
           
         
         wherein one ring nitrogen atom in Ring A optionally is oxidized; 
         X is —CH 2 —, —CHF—, —CF 2 —, —NH—, or —O—; 
         Y is —O— or —S—; 
         R a  is selected from the group consisting of hydrogen, fluoro, —CN, —N 3 , —OR 5 , —N(R 4 ) 2 , —NR 4 CO 2 R 6 , —NR 4 C(O)R 6 , —C(O)N(R 4 ) 2 , —C(O)R 5 , —OC(O)N(R 4 ) 2 , —OC(O)R 5 , —OCO 2 R 6 , or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 6x , —N(R 4x )(R 4y ), —CO 2 R 6x , or —C(O)N(R 4x )(R 4y ); or R a  and R c  together form a bond; 
         R b  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
         R c  is selected from the group consisting of hydrogen, fluoro, —CN, —N 3 , —OR 5 , —N(R 4 ) 2 , —NR 4 CO 2 R 6 , —NR 4 C(O)R 5 , —C(O)N(R 4 ) 2 , —C(O)R 5 , —OC(O)N(R 4 ) 2 , —OC(O)R 5 , —OCO 2 R 6 , or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR S ″, —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); or R a  and R c  together form a bond; 
         R d  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
         R e  is hydrogen, or C 1-4  aliphatic; or R e , taken together with one R f  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         R e′  is hydrogen or C 1-4  aliphatic; 
         each R f  is independently hydrogen, fluoro, C 1-4  aliphatic, or C 1-4  fluoroaliphatic, provided that if X is —O— or —NH—, then R f  is not fluoro; or two R f  taken together form ═O; or two R f , taken together with the carbon atom to which they are attached, form a 3- to 6-membered carbocyclic ring; or one R f , taken together with R e  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         R g  is hydrogen, halo, —NO 2 , —CN, —C(R 5 )═C(R 5 ) 2 , —C≡C—R 5 , —OR 5 , —SR 6 , —S(O)R 6 , —SO 2 R 6 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 2 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 6 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 6 , —OCO 2 R 6 , —OC(O)N(R 4 ) 2 , —C(O)R 5 , —CO 2 R 5 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 6 , —C(O)N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 5 , —C(═NR 4 )—N(R 4 ) 2 , —C(═NR 4 )—OR 5 , —N(R 4 )—N(R 4 ) 2 , —N(R 4 )—OR 5 , C(═NR 4 )—N(R 4 )—OR 5 , —C(R 6 )═N—OR 5 , or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl; 
         each R h  independently is hydrogen, halo, —CN—, —N(R 4 ) 2 , —SR 6 , or an optionally substituted C 1-4  aliphatic group; 
         R 1j  is hydrogen, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted aliphatic, aryl, or heteroaryl group; 
         R k  is hydrogen, halo, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted C 1-4  aliphatic group; 
         R m  is hydrogen, fluoro, —N(R 4 ) 2 , or an optionally substituted C 1-4  aliphatic group; and 
         R n  is hydrogen, fluoro, or an optionally substituted C 1-4  aliphatic group; or 
         R m  and R n  together form ═O or ═C(R 5 ) 2 ; 
         each R 4  independently is hydrogen or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl group; or two R 4  on the same nitrogen atom, taken together with the nitrogen atom, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; 
         R 4x  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted; 
         R 4y  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted, or an optionally substituted 5- or 6-membered aryl, heteroaryl, or heterocyclyl ring; or 
         R 4x  and R 4y , taken together with the nitrogen atom to which they are attached, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; and 
         each R 5  independently is hydrogen or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl group; 
         each R 5x  independently is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or an optionally substituted C 6-10  aryl or C 6-10  ar(C 1-4 )alkyl; 
         each R 6  independently is an optionally substituted aliphatic, aryl, or heteroaryl group; and 
         m is 1, 2, or 3; and 
         a pharmaceutically acceptable carrier. 
       
     
     
         30 . The pharmaceutical composition of  claim 29 , formulated for administration to a human patient. 
     
     
         31 . A method of decreasing an E1 enzyme activity in a sample, comprising contacting the sample with a compound of formula (I-A): 
       
         
           
           
               
               
           
         
       
       or a pharmaceutically acceptable salt thereof, wherein:
 stereochemical configurations depicted at asterisked positions indicate relative stereochemistry; 
 Ring A is selected from the group consisting of: 
 
       
         
           
           
               
               
           
         
          wherein one ring nitrogen atom in Ring A optionally is oxidized; 
         X is —CH 2 —, —CHF—, —CF 2 —, —NH—, or —O—; 
         Y is —O—, —S—, or —C(R m )(R n )—; 
         R a  is selected from the group consisting of hydrogen, fluoro, —CN, —N 3 , —OR 5 , —N(R 4 ) 2 , —NR 4 CO 2 R 6 , —NR 4 C(O)R 5 , —C(O)N(R 4 ) 2 , —C(O)R 5 , —OC(O)N(R 4 ) 2 , —OC(O)R 5 , —OCO 2 R 6 , or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); or R a  and R c  together form a bond; 
         R b  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
         R c  is selected from the group consisting of hydrogen, fluoro, —CN, —N 3 , —OR 5 , —N(R 4 ) 2 , —NR 4 CO 2 R 6 , —NR 4 C(O)R 5 , —C(O)N(R 4 ) 2 , —C(O)R 5 , —OC(O)N(R 4 ) 2 , —OC(O)R 5 , —OCO 2 R 6 , or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); or R a  and R c  together form a bond; 
         R d  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic, 
         R e  is hydrogen, or C 1-4  aliphatic; or R e , taken together with one R f  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         R e′  is hydrogen or C 1-4  aliphatic; 
         each R f  is independently hydrogen, fluoro, C 1-4  aliphatic, or C 1-4  fluoroaliphatic, provided that if X is —O— or —NH—, then R f  is not fluoro; or two R f  taken together form ═O; or two R f , taken together with the carbon atom to which they are attached, form a 3- to 6-membered carbocyclic ring; or one R f , taken together with R e  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         R g  is hydrogen, halo, —NO 2 , —CN, —C(R 5 )═C(R 5 ) 2 , —OR 5 , —SR 6 , —S(O)R 6 , —SO 2 R 6 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 7 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 6 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 5 , —OCO 2 R 6 , —OC(O)N(R 4 ) 2 , —C(O)R 5 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 5 , —C(O)N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 5 , —C(═NR 4 )—N(R 4 ) 2 , —C(═NR 4 )—OR 5 , —N(R 4 )—N(R 4 ) 2 , —N(R 4 )—OR 5 , —C(═NR 4 )—N(R 4 )—OR 5 , —C(R 6 )═N—OR 5 , or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl; 
         each R h  independently is hydrogen, halo, —CN—, —OR 5 , —N(R 4 ) 2 , —SR 6 , or an optionally substituted C 1-4  aliphatic group; 
         R j  is hydrogen, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted aliphatic, aryl, or heteroaryl group; 
         R k  is hydrogen, halo, —OR 5 , —SR 6 , —N(R 4 ) 7 , or an optionally substituted C 1-4  aliphatic group; 
         R m  is hydrogen, fluoro, —N(R 4 ) 2 , or an optionally substituted C 1-4  aliphatic group; and 
         R n  is hydrogen, fluoro, or an optionally substituted C 1-4  aliphatic group; or 
         R m  and R n  together form ═O or ═C(R 5 ) 2 ; 
         each R 4  independently is hydrogen or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl group; or two R 4  on the same nitrogen atom, taken together with the nitrogen atom, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; 
         R 4x  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted; 
         R 4y  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted, or an optionally substituted 5- or 6-membered aryl, heteroaryl, or heterocyclyl ring; or 
         R 4x  and R 4y , taken together with the nitrogen atom to which they are attached, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; and 
         each R 5  independently is hydrogen or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl group; 
         each R 5x  independently is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or an optionally substituted C 6-10  aryl or C 6-10  ar(C 1-4 )alkyl; 
         each R 6  independently is an optionally substituted aliphatic, aryl, or heteroaryl group; and 
         m is 1, 2, or 3. 
       
     
     
         32 . The method of  claim 31 , wherein the E1 enzyme is selected from the group consisting of NAE, UAE, and SAE. 
     
     
         33 . The method of  claim 31 , wherein the E1 enzyme is NAE. 
     
     
         34 . A method for treating cancer in a patient in need thereof, comprising administering to the patient a compound of formula (I-A): 
       
         
           
           
               
               
           
         
       
       or a pharmaceutically acceptable salt thereof, wherein:
 stereochemical configurations depicted at asterisked positions indicate relative stereochemistry; 
 Ring A is selected from the group consisting of: 
 
       
         
           
           
               
               
           
         
          wherein one ring nitrogen atom in Ring A optionally is oxidized; 
         X is —CH 2 —, —CHF—, —CF 2 —, —NH—, or —O—; 
         Y is —O—, —S—, or —C(R m )(R n )—; 
         R a  is selected from the group consisting of hydrogen, fluoro, —CN, —N 3 , —OR 5 , —N(R 4 ) 2 , —NR 4 CO 2 R 6 , —NR 4 C(O)R 5 , —C(O)N(R 4 ) 2 , —C(O)R 5 , —OC(O)N(R 4 ) 2 , —OC(O)R 5 , —OCO 2 R 6 , or a C 1-4  aliphatic or C 1-4 -fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); or R a  and R c  together form a bond, 
         R b  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
         R c  is selected from the group consisting of hydrogen, fluoro, —CN, —N 3 , —OR 5 , —N(R 4 ) 2 , —NR 4 CO 2 R 6 , —NR 4 C(O)R 5 , —C(O)N(R 4 ) 2 , —C(O)R 5 , —OC(O)N(R 4 ) 2 , —OC(O)R 5 , —OCO 2 R 6 , or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); or R a  and R c  together form a bond; 
         R d  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic; 
         R e  is hydrogen, or C 1-4  aliphatic; or R e , taken together with one R f  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring 
         R e′  is hydrogen or C 1-4  aliphatic; 
         each R f  is independently hydrogen, fluoro, C 1-4  aliphatic, or C 1-4  fluoroaliphatic, provided that if X is —O— or —NH—, then R f  is not fluoro; or two R f  taken together form ═O; or two R f , taken together with the carbon atom to which they are attached, form a 3- to 6-membered carbocyclic ring; or one R f , taken together with R e  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         R g  is hydrogen, halo, —NO 2 , —CN, —C(R 5 )═C(R 5 ) 2 , —C≡C—R 5 , —OR 5 , —SR 6 , —S(O)R 6 , —SO 2 R 6 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 2 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 6 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 5 , —OCO 2 R 6 , —OC(O)N(R 4 ) 2 , —C(O)R 5 , —CO 2 R 5 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 5 , —C(O)N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 5 , —C(═NR 4 )—N(R 4 ) 2 , —C(═NR 4 )—OR 5 , —N(R 4 )—N(R 4 ) 2 , —N(R 4 )—OR 5 , —C(═NR 4 )—N(R 4 )—OR 5 , —C(R 6 )═N—OR 5 , or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl; 
         each R h  independently is hydrogen, halo, —CN—, —OR 5 , —N(R 4 ) 2 , —SR 6 , or an optionally substituted C 1-4  aliphatic group; 
         R j  is hydrogen, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted aliphatic, aryl, or heteroaryl group; 
         R k  is hydrogen, halo, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted C 1-4  aliphatic group; 
         R m  is hydrogen, fluoro, —N(R 4 ) 2 , or an optionally substituted C 1-4  aliphatic group; and 
         R n  is hydrogen, fluoro, or an optionally substituted C 1-4  aliphatic group; or 
         R m  and R n  together form ═O or ═C(R 5 ) 2 ; 
         each R 4  independently is hydrogen or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl group; or two R 4  on the same nitrogen atom, taken together with the nitrogen atom, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; 
         R 4x  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted; 
         R 4y  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted, or an optionally substituted 5- or 6-membered aryl, heteroaryl, or heterocyclyl ring; or 
         R 4x  and R 4y , taken together with the nitrogen atom to which they are attached, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; and 
         each R 5  independently is hydrogen or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl group; 
         each R 5x  independently is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or an optionally substituted C 6-10  aryl or C 6-10  ar(C 1-4 )alkyl; 
         each R 6  independently is an optionally substituted aliphatic, aryl, or heteroaryl group; and 
         m is 1, 2, or 3. 
       
     
     
         35 . The method of  claim 34 , wherein the cancer is lung cancer, colorectal cancer, ovarian cancer, or a hematological cancer. 
     
     
         36 . A method for treating an immune response disorder or vascular cell proliferation disorder in a patient in need thereof, comprising administering to the patient a compound of formula (I-A): 
       
         
           
           
               
               
           
         
       
       or a pharmaceutically acceptable salt thereof, wherein:
 stereochemical configurations depicted at asterisked positions indicate relative stereochemistry; 
 Ring A is selected from the group consisting of: 
 
       
         
           
           
               
               
           
         
          wherein one ring nitrogen atom in Ring A optionally is oxidized; 
         X is —CH 2 —, —CHF—, —CF 2 —, —NH—, or —O—: 
         Y is —O—, —S—, or —C(R m )(R n )—; 
         R a  is selected from the group consisting of hydrogen, fluoro, —CN, —N 3 , —OR 5 , —N(R 4 ) 2 , —NR 4 CO 2 R 6 , —NR 4 C(O)R 5 , —C(O)N(R 4 ) 2 , —C(O)R 5 , —OC(O)N(R 4 ) 2 , —OC(O)R 5 , —OCO 2 R 6 , or a C 1-4  aliphatic or fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); or R a  and R c  together form a bond; 
         R b  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic. 
         R c  is selected from the group consisting of hydrogen, fluoro, —CN, —N 3 , —OR 5 , —N(R 4 ) 2 , —NR 4 CO 2 R 6 , —NR 4 C(O)R 5 , —C(O)N(R 4 ) 2 , —C(O)R 5 , —OC(O)N(R 4 ) 2 , —OC(O)R 5 , —OCO 2 R 6 , or a C 1-4  aliphatic or C 1-4  fluoroaliphatic optionally substituted with one or two substituents independently selected from the group consisting of —OR 5x , —N(R 4x )(R 4y ), —CO 2 R 5x , or —C(O)N(R 4x )(R 4y ); or R a  and R c  together form a bond; 
         R d  is selected from the group consisting of hydrogen, fluoro, C 1-4  aliphatic, and C 1-4  fluoroaliphatic. 
         R e  is hydrogen, or C 1-4  aliphatic; or R e , taken together with one R f  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         R e′  is hydrogen or C 1-4  aliphatic; 
         each R f  is independently hydrogen, fluoro, C 1-4  aliphatic, or C 1-4  fluoroaliphatic, provided that if X is —O— or —NH—, then R f  is not fluoro; or two R f  taken together form ═O; or two R f , taken together with the carbon atom to which they are attached, form a 3- to 6-membered carbocyclic ring; or one R f  taken together with R e  and the intervening carbon atoms, forms a 3- to 6-membered spirocyclic ring; 
         R g  is hydrogen, halo, —NO 2 , —CN, —C(R 5 )═C(R 5 ) 2 , —C≡C—R 5 , —OR 5 , —SR 6 , —S(O)R 6 , —SO 2 R 6 , —SO 2 N(R 4 ) 2 , —N(R 4 ) 2 , —NR 4 C(O)R 5 , —NR 4 C(O)N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—R 6 , —NR 4 CO 2 R 5 , —N(R 4 )SO 2 R 6 , —N(R 4 )SO 2 N(R 4 ) 2 , —O—C(O)R 6 , —OCO 2 R 6 , —OC(O)N(R 4 ) 2 , —C(O)R 6 , —CO 2 R 6 , —C(O)N(R 4 ) 2 , —C(O)N(R 4 )—OR 6 , —C(O)N(R 4 )C(═NR 4 )—N(R 4 ) 2 , —N(R 4 )C(═NR 4 )—N(R 4 )—C(O)R 6 , —C(═NR 4 )—N(R 4 ) 2 , —C(═NR 4 )—OR 5 , —N(R 4 )—N(R 4 ) 2 , —N(R 4 )—OR 5 , —C(═NR 4 )—N(R 4 )—OR 5 , —C(R 6 )═N—OR 5  or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl, 
         each R h  independently is hydrogen, halo, —CN—, —N(R 4 ) 2 , —SR 6 , or an optionally substituted C 1-4  aliphatic group; 
         R j  is hydrogen, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted aliphatic, aryl, or heteroaryl group, 
         R k  is hydrogen, halo, —OR 5 , —SR 6 , —N(R 4 ) 2 , or an optionally substituted C 1-4  aliphatic group; 
         R m  is hydrogen, fluoro, —N(R 4 ) 2 , or an optionally substituted C 1-4  aliphatic group; and 
         R n  is hydrogen, fluoro, or an optionally substituted C 1-4  aliphatic group; or 
         R m  and R n  together form ═O or ═C(R 5 ) 2    
         each R 4  independently is hydrogen or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl group; or two R 4  on the same nitrogen atom, taken together with the nitrogen atom form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; 
         R 4x  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted; 
         R 4y  is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, C 6-10  ar(C 1-4 )alkyl, the aryl portion of which may be optionally substituted, or an optionally substituted 5- or 6-membered aryl, heteroaryl, or heterocyclyl ring; or 
         R 4x  and R 4y , taken together with the nitrogen atom to which they are attached, form an optionally substituted 4- to 8-membered heterocyclyl ring having, in addition to the nitrogen atom, 0-2 ring heteroatoms independently selected from N, O, and S; and 
         each R 5  independently is hydrogen or an optionally substituted aliphatic, aryl, heteroaryl, or heterocyclyl group; 
         each R 5x  independently is hydrogen, C 1-4  alkyl, C 1-4  fluoroalkyl, or an optionally substituted C 6-10  aryl or C 6-10  ar(C 1-4 )alkyl; 
         each R 6  independently is an optionally substituted aliphatic, aryl, or heteroaryl group; and 
         m is 1, 2, or 3.