Biodegradable lipids for the delivery of active agents

[0001] This application claims the benefit of U.S. Patent Application No. 61/351,146, filed Jun. 3, 2010, and U.S. Patent Application No. 61/489,197, filed May 23, 2011, each of which is incorporated by reference in its entirety.

[0002] The present invention relates to biodegradable lipids and to their use for the delivery of active agents such as nucleic acids.

[0003] Therapeutic nucleic acids include, e.g., small interfering RNA (siRNA), micro RNA (miRNA), antisense oligonucleotides, ribozymes, plasmids, immune stimulating nucleic acids, antisense, antagomir, antimir, microRNA mimic, supermir, U1 adaptor, and aptamer. These nucleic acids act via a variety of mechanisms. In the case of siRNA or miRNA, these nucleic acids can down-regulate intracellular levels of specific proteins through a process termed RNA interference (RNAi). Following introduction of siRNA or miRNA into the cell cytoplasm, these double-stranded RNA constructs can bind to a protein termed RISC. The sense strand of the siRNA or miRNA is displaced from the RISC complex providing a template within RISC that can recognize and bind mRNA with a complementary sequence to that of the bound siRNA or miRNA. Having bound the complementary mRNA the RISC complex cleaves the mRNA and releases the cleaved strands. RNAi can provide down-regulation of specific proteins by targeting specific destruction of the corresponding mRNA that encodes for protein synthesis.

[0004] The therapeutic applications of RNAi are extremely broad, since siRNA and miRNA constructs can be synthesized with any nucleotide sequence directed against a target protein. To date, siRNA constructs have shown the ability to specifically down-regulate target proteins in both in vitro and in vivo models. In addition, siRNA constructs are currently being evaluated in clinical studies.

[0005] However, two problems currently faced by siRNA or miRNA constructs are, first, their susceptibility to nuclease digestion in plasma and, second, their limited ability to gain access to the intracellular compartment where they can bind RISC when administered systemically as the free siRNA or miRNA. These double-stranded constructs can be stabilized by incorporation of chemically modified nucleotide linkers within the molecule, for example, phosphothioate groups. However, these chemical modifications provide only limited protection from nuclease digestion and may decrease the activity of the construct. Intracellular delivery of siRNA or miRNA can be facilitated by use of carrier systems such as polymers, cationic liposomes or by chemical modification of the construct, for example by the covalent attachment of cholesterol molecules. However, improved delivery systems are required to increase the potency of siRNA and miRNA molecules and reduce or eliminate the requirement for chemical modification.

[0006] Antisense oligonucleotides and ribozymes can also inhibit mRNA translation into protein. In the case of antisense constructs, these single stranded deoxynucleic acids have a complementary sequence to that of the target protein mRNA and can bind to the mRNA by Watson-Crick base pairing. This binding either prevents translation of the target mRNA and/or triggers RNase H degradation of the mRNA transcripts. Consequently, antisense oligonucleotides have tremendous potential for specificity of action (i.e., down-regulation of a specific disease-related protein). To date, these compounds have shown promise in several in vitro and in vivo models, including models of inflammatory disease, cancer, and HIV (reviewed in Agrawal, Trends in Biotech. 14:376-387 (1996)). Antisense can also affect cellular activity by hybridizing specifically with chromosomal DNA. Advanced human clinical assessments of several antisense drugs are currently underway. Targets for these drugs include the bcl2 and apolipoprotein B genes and mRNA products.

[0007] Immune-stimulating nucleic acids include deoxyribonucleic acids and ribonucleic acids. In the case of deoxyribonucleic acids, certain sequences or motifs have been shown to illicit immune stimulation in mammals. These sequences or motifs include the CpG motif, pyrimidine-rich sequences and palindromic sequences. It is believed that the CpG motif in deoxyribonucleic acids is specifically recognized by an endosomal receptor, toll-like receptor 9 (TLR-9), which then triggers both the innate and acquired immune stimulation pathway. Certain immune stimulating ribonucleic acid sequences have also been reported. It is believed that these RNA sequences trigger immune activation by binding to toll-like receptors 6 and 7 (TLR-6 and TLR-7). In addition, double-stranded RNA is also reported to be immune stimulating and is believe to activate via binding to TLR-3.

[0008] One well known problem with the use of therapeutic nucleic acids relates to the stability of the phosphodiester internucleotide linkage and the susceptibility of this linker to nucleases. The presence of exonucleases and endonucleases in serum results in the rapid digestion of nucleic acids possessing phosphodiester linkers and, hence, therapeutic nucleic acids can have very short half-lives in the presence of serum or within cells. (Zelphati, O., et al., Antisense. Res. Dev. 3:323-338 (1993); and Thierry, A. R., et al., pp 147-161 in Gene Regulation: Biology of Antisense RNA and DNA (Eds. Erickson, R P and Izant, J G; Raven Press, NY (1992)). Therapeutic nucleic acid being currently being developed do not employ the basic phosphodiester chemistry found in natural nucleic acids, because of these and other known problems.

[0009] This problem has been partially overcome by chemical modifications that reduce serum or intracellular degradation. Modifications have been tested at the internucleotide phosphodiester bridge (e.g., using phosphorothioate, methylphosphonate or phosphoramidate linkages), at the nucleotide base (e.g., 5-propynyl-pyrimidines), or at the sugar (e.g., 2′-modified sugars) (Uhlmann E., et al. Antisense: Chemical Modifications. Encyclopedia of Cancer, Vol. X., pp 64-81 Academic Press Inc. (1997)). Others have attempted to improve stability using 2′-5′ sugar linkages (see, e.g., U.S. Pat. No. 5,532,130). Other changes have been attempted. However, none of these solutions have proven entirely satisfactory, and in vivo free therapeutic nucleic acids still have only limited efficacy.

[0010] In addition, as noted above relating to siRNA and miRNA, problems remain with the limited ability of therapeutic nucleic acids to cross cellular membranes (see, Vlassov, et al., Biochim. Biophys. Acta 1197:95-1082 (1994)) and in the problems associated with systemic toxicity, such as complement-mediated anaphylaxis, altered coagulatory properties, and cytopenia (Galbraith, et al., Antisense Nucl. Acid Drug Des. 4:201-206 (1994)).

[0011] To attempt to improve efficacy, investigators have also employed lipid-based carrier systems to deliver chemically modified or unmodified therapeutic nucleic acids. In Zelphati, O and Szoka, F. C., J. Contr. Rel. 41:99-119 (1996), the authors refer to the use of anionic (conventional) liposomes, pH sensitive liposomes, immunoliposomes, fusogenic liposomes, and cationic lipid/antisense aggregates. Similarly siRNA has been administered systemically in cationic liposomes, and these nucleic acid-lipid particles have been reported to provide improved down-regulation of target proteins in mammals including non-human primates (Zimmermann et al., Nature 441: 111-114 (2006)).

[0012] In spite of this progress, there remains a need in the art for improved lipid-therapeutic nucleic acid compositions that are suitable for general therapeutic use. Preferably, these compositions would encapsulate nucleic acids with high-efficiency, have high drug:lipid ratios, protect the encapsulated nucleic acid from degradation and clearance in serum, be suitable for systemic delivery, and provide intracellular delivery of the encapsulated nucleic acid. In addition, these lipid-nucleic acid particles should be well-tolerated and provide an adequate therapeutic index, such that patient treatment at an effective dose of the nucleic acid is not associated with significant toxicity and/or risk to the patient. Compositions, methods of making the compositions, and methods of using the compositions to introduce nucleic acids into cells, including for the treatment of diseases are provided.

[0013] The present invention relates to a cationic lipid having one or more biodegradable groups located in the mid- or distal section of a lipidic moiety (e.g., a hydrophobic chain) of the cationic lipid. These cationic lipids may be incorporated into a lipid particle for delivering an active agent, such as a nucleic acid (e.g., an siRNA). The incorporation of the biodegradable group(s) into the cationic lipid results in faster metabolism and removal of the cationic lipid from the body following delivery of the active agent to a target area. As a result, these cationic lipids have substantially lower toxicity than similar cationic lipids without the biodegradable groups.

[0014] In one embodiment, the cationic lipid is a compound of the formula:

[0015]
or a salt thereof (e.g., a pharmaceutically acceptable salt thereof),
wherein

[0016] R′ is absent, hydrogen, or alkyl (e.g., C₁-C₄ alkyl);

[0017] with respect to R¹ and R²,

• • [0018] (i) R¹ and R² are each, independently, optionally substituted alkyl, alkenyl, alkynyl, cycloalkyl, cycloalkylalkyl, or heterocycle;
  • [0019] (ii) R¹ and R², together with the nitrogen atom to which they are attached, form an optionally substituted heterocylic ring; or
  • [0020] (iii) one of R¹ and R² is optionally substituted alkyl, alkenyl, alkynyl, cycloalkyl, cycloalkylalkyl, or heterocycle, and the other forms a 4-10 member heterocyclic ring or heteroaryl (e.g., a 6-member ring) with (a) the adjacent nitrogen atom and (b) the (R)_a group adjacent to the nitrogen atom;

[0021] each occurrence of R is, independently, —(CR³R⁴)—;

[0022] each occurrence of R³ and R⁴ are, independently H, OH, alkyl, alkoxy, —NH₂, alkylamino, or dialkylamino (in one preferred embodiment, each occurrence of R³ and R⁴ are, independently H or C₁-C₄ alkyl);

[0023] or R³ and R⁴, together with the carbon atom to which they are directly attached, form a cycloalkyl group, wherein no more than three R groups in each chain attached to the carbon C* are cycloalkyl (e.g., cyclopropyl);

[0024] the dashed line to Q is absent or a bond;

[0025] when the dashed line to Q is absent then Q is absent or is —O—, —NH—, —S—, —C(O)O—, —OC(O)—, —C(O)N(R⁴)—, —N(R⁵)C(O), —S—S—, —OC(O)O—, —O—N═C(R⁵)—, —C(R⁵)═N—O—, —OC(O)N(R⁵)—, —N(R⁵)C(O)N(R⁵)—, —N(R⁵)C(O)O—, —C(O)S—, —C(S)O— or —C(R⁵)═N—O—C(O)—; or

[0026] when the dashed line to Q is a bond then (i) b is 0 and (ii) Q and the tertiary carbon adjacent to it (C*) form a substituted or unsubstituted, mono- or bi-cyclic heterocyclic group having from 5 to 10 ring atoms (e.g., the heteroatoms in the heterocyclic group are selected from O and S, preferably O);

[0027] Q¹ and Q² are each, independently, absent, —O—, —S—, —OC(O)—, —C(O)O—, —SC(O)—, —C(O)S—, —OC(S)—, —C(S)O—, —S—S—, —C(O)(NR⁵)—, —N(R⁵)C(O)—, —C(S)(NR⁵)—, —N(R⁵)C(O)—, —N(R⁵)C(O)N(R⁵)—, or —OC(O)O—;

[0028] Q³ and Q⁴ are each, independently, H, —(CR³R⁴)—, aryl, or a cholesterol moiety;

[0029] each occurrence of A¹, A², A³ and A⁴ is, independently, —(CR⁵R⁵—CR⁵═CR⁵)—;

[0030] each occurrence of R⁵ is, independently, H or alkyl;

[0031] M¹ and M² are each, independently, a biodegradable group (e.g., —OC(O)—, —C(O)O—, —SC(O)—, —C(O)S—, —OC(S)—, —C(S)O—, —S—S—, —C(R⁵)═N—, —N═C(R⁵)—, —C(R⁵)═N—O—, —O—N═C(R⁵)—, —C(O)(NR⁵)—, —N(R⁵)C(O)—, —C(S)(NR⁵)—, —N(R⁵)C(O)—, —N(R⁵)C(O)N(R⁵)—, —OC(O)O—, —OSi(R⁵)₂O—, —C(O)(CR³R⁴)C(O)O—, or —OC(O)(CR³R⁴)C(O)—);

[0032] Z is absent, alkylene or —O—P(O)(OH)—O—;

[0033] each ------ attached to Z is an optional bond, such that when Z is absent, Q³ and Q⁴ are not directly covalently bound together;

[0034] a is 1, 2, 3, 4, 5 or 6;

[0035] b is 0, 1, 2, or 3;

[0036] c, d, e, f, i, j, m, n, q and r are each, independently, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10;

[0037] g and h are each, independently, 0, 1 or 2;

[0038] k and l are each, independently, 0 or 1, where at least one of k and l is 1; and

[0039] o and p are each, independently, 0, 1 or 2,

wherein

• • [0040] (i) the compound does not contain the following moiety:

[0041]

• • [0042] wherein ---- is an optional bond; and

[0043] (ii) Q³ and Q⁴ are each, independently, separated from the tertiary carbon atom marked with an asterisk (*) by a chain of 8 or more atoms (e.g., 12 or 14 or more atoms).

[0044] In one embodiment, (i) R¹ and R² are each, independently, optionally substituted alkyl, alkenyl, alkynyl, cycloalkyl, cycloalkylalkyl, or heterocycle; or (ii) R¹ and R², together with the nitrogen atom to which they are attached, form an optionally substituted heterocylic ring.

[0045] In a preferred embodiment of the compound of formula (I),

• • [0046] (a) when Q¹ is a biodegradable group (e.g., —C(O)O—), then c is at least 4;
  • [0047] (b) when Q² is a biodegradable group, then d is at least 4; and
  • [0048] (c) Q³ and Q⁴ are each, independently, separated from the tertiary carbon atom marked with an asterisk (*) by a chain of 10 or more atoms (e.g., 12 or 14 or more atoms).

[0049] In another preferred embodiment, a carbon atom alpha or beta to a biodegradable group (e.g., —C(O)O—) in formula (I) may be substituted with one or two alkyl groups (e.g., one C₁-C₄ alkyl group, such as a —CH₃ substituent, or two C₁-C₄ alkyl groups, such as two —CH₃ substituents) or have a spirocyclic group (e.g., a C₃-C₅ cycloalkyl such as a C₃ cycloalkyl). For example, a carbon atom alpha or beta to a biodegradable group can be independently selected from

[0050]
(where n is 4-6).

[0051] In one embodiment, the M¹ or M² group and neighboring variable(s) form the group:

[0052]

[0053] (where n is 4-6).

[0054] Yet another embodiment is a cationic lipid of the formula

[0055]
or a salt thereof (e.g., a pharmaceutically acceptable salt thereof), wherein

[0056] R¹, R², R, a, and b are as defined with respect to formula (I);

[0057] Q is absent or is —O—, —NH—, —S—, —C(O)O—, —OC(O)—, —C(O)N(R⁴)—, —N(R⁵)C(O), —S—S—, —OC(O)O—, —O—N═C(R⁵)—, —C(R⁵)═N—O—, —OC(O)N(R⁵)—, —N(R⁵)C(O)N(R⁵)—, —N(R⁵)C(O)O—, —C(O)S—, —C(S)O— or —C(R⁵)═N—O—C(O)—;

[0058] R′ is absent, hydrogen, or alkyl (e.g., C₁-C₄ alkyl); and

[0059] each of R⁹ and R¹⁰ are independently C₁₂-C₂₄ alkyl (e.g., C₁₂-C₂₀ alkyl), C₁₂-C₂₄ alkenyl (e.g., C₁₂-C₂₀ alkenyl), or C₁₂-C₂₄ alkoxy (e.g., C₁₂-C₂₀ alkoxy) having one or more biodegradable groups; each biodegradable group independently interrupts the C₁₂-C₂₄ alkyl, alkenyl, or alkoxy group or is substituted at the terminus of the C₁₂-C₂₄ alkyl, alkenyl, or alkoxy group,

wherein

[0060] (i) the compound does not contain the following moiety:

[0061]
wherein ---- is an optional bond; and

[0062] (ii) the terminus of R⁹ and R¹⁰ is separated from the tertiary carbon atom marked with an asterisk (*) by a chain of 8 or more atoms (e.g., 12 or 14 or more atoms).

[0063] In another embodiment, the cationic lipid is a compound of the formula:

[0064]

[0065] or a salt thereof (e.g., a pharmaceutically acceptable salt thereof), wherein

[0066] R′ is absent, hydrogen, or alkyl (e.g., C₁-C₄ alkyl);

[0067] R¹ and R² are each, independently, optionally substituted C₁-C₄ alkyl, C₂-C₄ alkenyl, C₂-C₄ alkynyl, C₃-C₆ cycloalkyl, (C₃-C₆ cycloalkyl)C₁-C₄ alkyl, or a monocyclic heterocycle; or

[0068] R¹ and R², together with the nitrogen atom to which they are attached, form an optionally substituted 5- or 6-membered heterocylic ring (e.g., a C₅ or C₆ heterocyclic ring);

[0069] each occurrence of R is, independently, —(CR³R⁴)—;

[0070] each occurrence of R³ and R⁴ are, independently H, OH, alkyl, alkoxy, —NH₂, alkylamino, or dialkylamino (in one preferred embodiment, each occurrence of R³ and R⁴ are, independently H or C₁-C₄ alkyl);

[0071] or R³ and R⁴, together with the carbon atom to which they are directly attached, form a C₃-C₆ cycloalkyl group, wherein no more than three R groups in each chain attached to the carbon C* are cycloalkyl (e.g., cyclopropyl);

[0072] the dashed line to Q is absent or a bond;

[0073] when the dashed line to Q is absent, Q is absent or is —O—, —NH—, —S—, —C(O)O—, —OC(O)—, —C(O)N(R⁴)—, —N(R⁵)C(O), —S—S—, —OC(O)O—, —O—N═C(R⁵)—, —C(R⁵)═N—O—, —OC(O)N(R⁵)—, —N(R⁵)C(O)N(R⁵)—, —N(R⁵)C(O)O—, —C(O)S—, —C(S)O— or —C(R⁵)═N—O—C(O)—; or

[0074] when the dashed line to Q is a bond, b is 0 and Q and the tertiary carbon adjacent to it (C*) form a substituted or unsubstituted, mono- or bi-cyclic heterocyclic group having from 5 to 10 ring atoms (e.g., the heteroatoms in the heterocyclic group are selected from O and S, preferably O);

[0075] Q³ and Q⁴ are each, independently, H, —(CR³R⁴)—, aryl, or a cholesterol moiety;

[0076] each occurrence of A¹, A², A³ and A⁴ is, independently, —(CR⁵R⁵—CR⁵═CR⁵)—;

[0077] each occurrence of R⁵ is, independently, H or alkyl;

[0078] M¹ and M² are each, independently, —C(O)—O—, —OC(O)—, —C(R⁵)═N—, —C(R⁵)═N—O—, —O—C(O)O—, —C(O)N(R⁵)—, —C(O)S—, —C(S)O—, —OSi(R⁵)₂O—, —C(O)(CR³R⁴)C(O)O—, or —OC(O)(CR³R⁴)C(O)—;

[0079] Z is absent, alkylene or —O—P(O)(OH)—O—;

[0080] each ------ attached to Z is an optional bond, such that when Z is absent, Q³ and Q⁴ are not directly covalently bound together;

[0081] a is 1, 2, 3, 4, 5 or 6;

[0082] b is 0, 1, 2, or 3;

[0083] d, e, i, j, m, n, q and r are each, independently, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10;

[0084] g and h are each, independently, 0, 1 or 2;

[0085] the sum of d+3h is at least 4, and the sum of e+3g is at least 4;

[0086] k and l are each, independently, 0 or 1, where at least one of k and l is 1; and

[0087] o and p are each, independently, 0, 1 or 2,

[0088] wherein Q³ and Q⁴ are each, independently, separated from the tertiary carbon atom marked with an asterisk (*) by a chain of 8 or more atoms (e.g., 12 or 14 or more atoms).

[0089] In one embodiment, R′ in formula (IA-2) is absent or hydrogen. In one embodiment, R′ in formula (IA-2) is absent or alkyl (e.g., methyl).

[0090] In one embodiment, R¹ and R² in formula (IA-2) are each, independently, C₁-C₄ alkyl (e.g., methyl or ethyl).

[0091] In one embodiment, each occurrence of R in formula (IA-2) is, independently, —CH₂— or —CH(CH₃)—.

[0092] In one embodiment, Q³ and Q⁴ in formula (IA-2) are each, independently, H, aryl, or a cholesterol moiety.

[0093] In one embodiment, each occurrence of A¹, A², A³ and A⁴ in formula (IA-2) is, independently, —(CH₂—CH═CH)—;

[0094] In one embodiment, M¹ and M² in formula (IA-2) are each —C(O)—O—.

[0095] In one embodiment of the compound of formula (IA-2), Z is absent and each ------ is absent (i.e., Q³ and Q⁴ are not directly covalently bound together).

[0096] In one embodiment, the sum of e+3g+i+m+3o+q in formula (IA-2) is from about 8 to about 20. In another embodiment, the sum of e+3g+i+m+3o+q in formula (IA-2) is from about 12 to about 20.

[0097] In one embodiment, the sum of d+3h+j+n+3p+r in formula (IA-2) is from about 8 to about 20. In another embodiment, the sum of d+3h+j+n+3p+r in formula (IA-2) is from about 12 to about 20.

[0098] In another embodiment, the cationic lipid is a compound of the formula

[0099]
wherein

[0100] R¹, R², R, a, b, M¹, and M² are as defined with respect to formula (I);

[0101] Q is absent or is —O—, —NH—, —S—, —C(O)O—, —OC(O)—, —C(O)N(R⁴)—, —N(R⁵)C(O), —S—S—, —OC(O)O—, —O—N═C(R⁵)—, —C(R⁵)═N—O—, —OC(O)N(R⁵)—, —N(R⁵)C(O)N(R⁵)—, —N(R⁵)C(O)O—, —C(O)S—, —C(S)O— or —C(R⁵)═N—O—C(O)—;

[0102] R′ is absent, hydrogen, or alkyl (e.g., C₁-C₄ alkyl);

[0103] each of R⁹ and R¹⁰ are independently alkylene, or alkenylene; and

[0104] each of R¹¹ and R¹² are independently alkyl or alkenyl, optionally terminated by COOR¹³ where each R¹³ is independently alkyl (e.g., C₁-C₄ alkyl such as methyl or ethyl);

[0105] R⁹, M¹, and R¹¹ are together at least 8 carbons atoms in length (e.g., 12 or 14 carbon atoms or longer); and

[0106] R¹⁰, M², m and R¹² are together at least 8 carbons atoms in length (e.g., 12 or 14 carbon atoms or longer).

[0107] In a preferred embodiment of the compound of formula (IB), R⁹ and R¹⁰ are each independently C₄-C₁₂ alkylene or C₄-C₁₂ alkenylene, M¹ and M² are —C(O)O—, and R¹¹ and R¹² are C₄-C₁₂ alkylene or C₄-C₁₂ alkenylene. In one embodiment, R⁹, M¹, and R¹¹ are together at 12 to 24 carbons atoms in length. In another embodiment, R⁹, M¹, and R¹¹ are together at 14 to 18 carbons atoms in length. In one embodiment, R¹⁰, M², and R¹² are together at 12 to 24 carbons atoms in length. In another embodiment, R¹⁰, M², and R¹² are together at 14 to 18 carbons atoms in length.

[0108] The R′R¹R²N—(R)_a-Q-(R)_b— group can be any of the head groups described herein, including those shown in Table 1 below, and salts thereof. In one preferred embodiment, R′R¹R²N—(R)_a-Q-(R)_b— is (CH₃)₂N—(CH₂)₃—C(O)O—, (CH₃)₂N—(CH₂)₂—NH—C(O)O—, (CH₃)₂N—(CH₂)₂—OC(O)—NH—, or (CH₃)₂N—(CH₂)₃—C(CH₃)═N—O—.

[0109] In yet another embodiment, the cationic lipid is a compound of the formula

[0110]
wherein

[0111] R¹, R², R, a, and b are as defined with respect to formula (I);

[0112] Q is absent or is —O—, —NH—, —S—, —C(O)O—, —OC(O)—, —C(O)N(R⁴)—, —N(R⁵)C(O), —S—S—, —OC(O)O—, —O—N═C(R⁵)—, —C(R⁵)═N—O—, —OC(O)N(R⁵)—, —N(R⁵)C(O)N(R⁵)—, —N(R⁵)C(O)O—, —C(O)S—, —C(S)O— or —C(R⁵)═N—O—C(O)—; R′ is absent, hydrogen, or alkyl (e.g., C₁-C₄ alkyl);

[0113] each of R⁹ and R¹⁰ are independently C₁₂-C₂₄ alkyl or alkenyl substituted at its terminus with a biodegradable group, such as —COOR¹³ where each R¹³ is independently alkyl (preferably C₁-C₄ alkyl such as methyl or ethyl).

[0114] In a preferred embodiment of the compound of formula (IC), R⁹ and R¹⁰ are each independently C₁₄-C₁₈ alkylene or C₁₄-C₁₈ alkenylene. In another preferred embodiment, the biodegradable group is —COOR¹³ where R¹³ is C₁-C₄ alkyl (such as methyl or ethyl).

[0115] The R′R¹R²N—(R)_a-Q-(R)_b— group can be any of the head groups described herein, including those shown in Table 1 below. In one preferred embodiment, R′R¹R²N—(R)_a-Q-(R)_b— is (CH₃)₂N—(CH₂)₃—C(O)O—, (CH₃)₂N—(CH₂)₂—NH—C(O)O—, (CH₃)₂N—(CH₂)₂—OC(O)—NH—, or (CH₃)₂N—(CH₂)₃—C(CH₃)═N—O—.

[0116] Yet another embodiment are intermediates of the formula:

[0117]
or a salt thereof (e.g., a pharmaceutically acceptable salt thereof),
wherein

[0118] R′ is absent, hydrogen, or alkyl (e.g., C₁-C₄ alkyl);

[0119] R¹ and R² are each, independently, optionally substituted alkyl, alkenyl, alkynyl, cycloalkyl, cycloalkylalkyl, or heterocycle; or

[0120] R¹ and R², together with the nitrogen atom to which they are attached, form an optionally substituted heterocylic ring;

[0121] each occurrence of R is, independently, —(CR³R⁴)—;

[0122] each occurrence of R³ and R⁴ are, independently H, OH, alkyl, alkoxy, —NH₂, alkylamino, or dialkylamino (in one preferred embodiment, each occurrence of R³ and R⁴ are, independently H or alkyl);

[0123] or R³ and R⁴, together with the carbon atom to which they are directly attached, form a cycloalkyl group, wherein no more than three R groups in each chain attached to the carbon C* are cycloalkyl (e.g., cyclopropyl);

[0124] the dashed line to Q is absent or a bond;

[0125] when the dashed line to Q is absent, Q is absent or is —O—, —NH—, —S—, —C(O)O—, —OC(O)—, —C(O)N(R⁴)—, —N(R⁵)C(O), —S—S—, —OC(O)O—, —O—N═C(R⁵)—, —C(R⁵)═N—O—, —OC(O)N(R⁵)—, —N(R⁵)C(O)N(R⁵)—, —N(R⁵)C(O)O—, —C(O)S—, —C(S)O— or —C(R⁵)═N—O—C(O)—; or

[0126] when the dashed line to Q is a bond, b is 0 and Q and the tertiary carbon adjacent to it (C*) form a substituted or unsubstituted, mono- or bi-cyclic heterocyclic group having from 5 to 10 ring atoms (e.g., the heteroatoms in the heterocyclic group are selected from O and S, preferably O);

[0127] Q¹ and Q² are each, independently, absent, —O—, —S—, —OC(O)—, —C(O)O—, —SC(O)—, —C(O)S—, —OC(S)—, —C(S)O—, —S—S—, —C(O)(NR⁵)—, —N(R⁵)C(O)—, —C(S)(NR⁵)—, —N(R⁵)C(O)—, —N(R⁵)C(O)N(R⁵)—, or —OC(O)O—;

[0128] Q³ and Q⁴ are each, independently, H, —(CR³R⁴)—, aryl, —OH, or a cholesterol moiety;

[0129] each occurrence of A¹, A², A³ and A⁴ is, independently, —(CR⁵R⁵—CR⁵═CR⁵)—;

[0130] each occurrence of R⁵ is, independently, H or alkyl;

[0131] M¹ and M² are each, independently, a biodegradable group (e.g., —OC(O)—, —C(O)O—, —SC(O)—, —C(O)S—, —OC(S)—, —C(S)O—, —S—S—, —C(R⁵)═N—, —N═C(R⁵)—, —C(R⁵)═N—O—, —O—N═C(R⁵)—, —C(O)(NR⁵)—, —N(R⁵)C(O)—, —C(S)(NR⁵)—, —N(R⁵)C(O)—, —N(R⁵)C(O)N(R⁵)—, —OC(O)O—, —OSi(R⁵)₂O—, —C(O)(CR³R⁴)C(O)O—, or —OC(O)(CR³R⁴)C(O)—);

[0132] Z is absent, alkylene or —O—P(O)(OH)—O—;

[0133] each ------ attached to Z is an optional bond, such that when Z is absent, Q³ and Q⁴ are not directly covalently bound together;

[0134] a is 1, 2, 3, 4, 5 or 6;

[0135] b is 0, 1, 2, or 3;

[0136] c, d, e, f, i, j, m, n, q and r are each, independently, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10;

[0137] g and h are each, independently, 0, 1 or 2;

[0138] k and l are each, independently, 0 or 1;

[0139] o and p are each, independently, 0, 1 or 2,

wherein

• • [0140] (i) the compound does not contain the following moiety:

[0141]

• • [0142] wherein ---- is an optional bond; and
  • [0143] (ii) Q³ and Q⁴ are each, independently, separated from the tertiary carbon atom marked with an asterisk (*) by a chain of 8 or more atoms (e.g., 12 or 14 or more atoms).

[0144] In yet a further embodiment, the cationic lipid is a compound of formula IE:

[0145]
or a salt thereof (e.g., a pharmaceutically acceptable salt thereof),
wherein

[0146] R¹ is a C₁₀ to C₃₀ group having the formula -L^1a-(CR^1aR^1b)_α-[L^1b-(CR^1aR^1b)_β]_γ-L^1c-R^1c, where L^1a is a bond, —CR^1aR^1b—, —O—, —CO—, —NR^1d—, —S—, or a combination thereof;

[0147] each R^1a and each R^1b, independently, is H; halo; hydroxy; cyano; C₁-C₆ alkyl optionally substituted by halo, hydroxy, or alkoxy; C₃-C₈ cycloalkyl optionally substituted by halo, hydroxy, or alkoxy; —OR^1c; —NR^1cR^1d; aryl; heteroaryl; or heterocyclyl;

[0148] each L^1b, independently, is a bond, —(CR^1aR^1b)_1-2—, —O—, —CO—, —NR^1d—, —S—,

[0149]
or a combination thereof; or can have the formula

[0150]
where j, k, and l are each independently 0, 1, 2, or 3, provided that the sum of j, k and l is at least 1 and no greater than 8; and R^1f and R^1g are each independently R^1b, or adjacent R^1f and R^1g, taken together, are optionally a bond;
or can have the formula

[0151]
where j and k are each independently 0, 1, 2, 3, or 4 provided that the sum of j and k is at least 1; and R^1f and R^1g are each independently R^1b, or adjacent R^1f and R^1g, taken together, are optionally a bond;
or can have the formula

[0152]
where —Ar— is a 6 to 14 membered arylene group optionally substituted by zero to six independent R^1a groups;
or can have the formula

[0153]
where -Het- is a 3 to 14 membered heterocyclylene or heteroarylene group optionally substituted by zero to six independent R^1a groups;

[0154] L^1c is —(CR^1aR^1b)_1-2—, —O—, —CO—, —NR^1d—, —S—,

[0155]
or a combination thereof;

[0156] R^1c is H; halo; hydroxy; cyano; C₁-C₆ alkyl optionally substituted by halo, hydroxy, alkoxy, or aryl; C₃-C₈ cycloalkyl optionally substituted by halo, hydroxy, alkoxy, or aryl; aryl; heteroaryl; or heterocyclyl; or R^1c has the formula:

[0157]

[0158] R^1d is H; halo; hydroxy; cyano; C₁-C₆ alkyl optionally substituted by halo, hydroxy, or alkoxy; C₃-C₈ cycloalkyl optionally substituted by halo, hydroxy, or alkoxy; aryl; heteroaryl; or heterocyclyl;

[0159] α is 0-6, inclusive;

[0160] each β, independently, is 0-6, inclusive;

[0161] γ is 0-6, inclusive;

[0162] R² is a C₁₀ to C₃₀ group having the formula -L^2a-(CR^2aR^2b)_δ-[L^2b-(CR^2aR^2b)_ε]_ζ-L^2c-R^2c, where L^2a is a bond, —CR^2aR^2b, —O—, —CO—, —NR^2d—, —S—, or a combination thereof;

[0163] each R^2a and each R^2b, independently, can be H; halo; hydroxy; cyano; C₁-C₆ alkyl optionally substituted by halo, hydroxy, or alkoxy; C₃-C₈ cycloalkyl optionally substituted by halo, hydroxy, or alkoxy; —OR^2c; —NR^2cR^2d; aryl; heteroaryl; or heterocyclyl;

[0164] each L^2b, independently, can be a bond, —(CR^2aR^2b)_1-2—, —O—, —CO—, —NR^2d—, —S—,

[0165]
or a combination thereof;
or can have the formula

[0166]
where j, k, and l are each independently 0, 1, 2, or 3, provided that the sum of j, k and l is at least 1 and no greater than 8; and R^2f and R^2g are each independently R^2b, or adjacent R^2f and R^2g, taken together, are optionally a bond;
or can have the formula

[0167]
where j and k are each independently 0, 1, 2, 3, or 4 provided that the sum of j and k is at least 1; and R^2f and R^2g are each independently R^2b, or adjacent R^2f and R^2g, taken together, are optionally a bond;
or can have the formula:

[0168]
wherein —Ar— is a 6 to 14 membered arylene group optionally substituted by zero to six independent R^2a groups;
or can have the formula:

[0169]
where -Het- is a 3 to 14 membered heterocyclylene or heteroarylene group optionally substituted by zero to six independent R^2a groups;

[0170] L^2c is —(CR^2aR^2b)_1-2—, —O—, —CO—, —NR^2d—, —S—,

[0171]
or a combination thereof;

[0172] R^2c is H; halo; hydroxy; cyano; C₁-C₆ alkyl optionally substituted by halo, hydroxy, alkoxy or aryl; C₃-C₈ cycloalkyl optionally substituted by halo, hydroxy, alkoxy or aryl; aryl; heteroaryl; or heterocyclyl; or R^2c has the formula:

[0173]

[0174] R^2d is H; halo; hydroxy; cyano; C₁-C₆ alkyl optionally substituted by halo, hydroxy, or alkoxy; C₃-C₈ cycloalkyl optionally substituted by halo, hydroxy, or alkoxy; aryl; heteroaryl; or heterocyclyl;

[0175] δ is 0-6, inclusive;

[0176] each ε, independently, is 0-6, inclusive;

[0177] ζ is 0-6, inclusive;

[0178] L₁ is C(R^a), —(CR⁵R⁶)_xC(R^a)—, or P(Q₂);

[0179] R^a is H, alkyl, alkoxy, —OH, —N(Q)Q, or —SQ;

[0180] L₂ is —(CR⁵R⁶)_x—, —C(O)—(CR⁵R⁶)_x—, —(CR⁵R⁶)_x—C(O)—, —(CR⁵R⁶)_x—CR⁵═CR⁵—(CR⁵R⁶)_y—, —C(O)—(CR⁵R⁶)_x—CR⁵═CR⁵—(CR⁵R⁶)_y—, —(CR⁵R⁶)_x—CR⁵═CR⁵—(CR⁵R⁶)_y—C(O)—, —O—, —S—, —N(Q)-, —C(O)O—, —OC(O)—, —C(O)—, —N(Q)C(O)—, —C(O)N(Q)-, —N(Q)C(O)O—, —OC(O)N(Q)-, S(O), —N(Q)S(O)₂N(Q)-, —S(O)₂—, —N(Q)S(O)₂—, —SS—, —O—N═, —C(O)—N(Q)-N═, —N(Q)-N═, —N(Q)-O—, —C(O)S—, arylene, heteroarylene, cyclalkylene, or heterocyclylene;

[0181] each x, independently, can be 0-6, inclusive;

[0182] each y, independently, can be 0-6, inclusive;

[0183] R³ is of the formula:

[0184]

[0185] Y₁ is alkyl, cycloalkyl, aryl, aralkyl, or alkynyl, wherein Y₁ is optionally substituted by 0 to 6 independent R_n;

[0186] Y₂ is alkyl, cycloalkyl, aryl, aralkyl, or alkynyl, wherein Y₂ is optionally substituted by 0 to 6 independent R_n;

[0187] Y₃ is absent, or if present, is alkyl, cycloalkyl, aryl, aralkyl, or alkynyl, wherein Y₃ is optionally substituted by 0 to 6 independent R_n;

[0188] Y₄ is absent, or if present, is alkyl, cycloalkyl, aryl, aralkyl, or alkynyl, wherein Y₄ is optionally substituted by 0 to 6 independent R_n;

[0189] or any two of Y₁, Y₂, and Y₃ are taken together with the N atom to which they are attached to form a 3- to 8-member heterocycle optionally substituted by 0 to 6 independent R_n;

[0190] or Y₁, Y₂, and Y₃ are all be taken together with the N atom to which they are attached to form a bicyclic 5- to 12-member heterocycle optionally substituted by 0 to 6 independent R_n;

[0191] each independently, can be H, halo, cyano, hydroxy, amino, alkyl, alkoxy, cycloalkyl, aryl, heteroaryl, or heterocyclyl;

[0192] L₃ is a bond, —N(Q)-, —O—, —S—, —(CR₇R₈)_a—, —C(O)—, or a combination of any two of these;

[0193] L₄ cis a bond, —N(Q)-, —O—, —S—, —(CR₇R₈)_a—, —C(O)—, or a combination of any two of these;

[0194] L₅ is a bond, —N(Q)-, —O—, —S—, —(CR₇R₈)_a—, —C(O)—, or a combination of any two of these; each occurrence of R₇ and R₈ is, independently, H, halo, cyano, hydroxy, amino, alkyl, alkoxy, cycloalkyl, aryl, heteroaryl, or heterocyclyl;

[0195] or two R₇ groups on adjacent carbon atoms can be taken together to form a double bond between their respective carbon atoms;

[0196] or two R₇ groups on adjacent carbon atoms and two R₈ groups on the same adjacent carbon atoms can be taken together to form a triple bond between their respective carbon atoms;

[0197] or, an R₇ or R₈ substituent from any of L₃, L₄, or L₅ can be optionally taken with an R₇ or R₈ substituent from any of L₃, L₄, or L₅ to form a 3- to 8-member cycloalkyl, heterocyclyl, aryl, or heteroaryl group;

[0198] or any one of Y₁, Y₂, or Y₃, can be optionally taken together with an R₇ or R₈ group from any of L₃, L₄, and L₅, and atoms to which they are attached, to form a 3- to 8-member heterocyclyl group;

[0199] each a, independently, can be 0, 1, 2, or 3;

[0200] each occurrence of R₅ and R₆ can be, independently, H, halo, cyano, hydroxy, amino, alkyl, alkoxy, cycloalkyl, aryl, heteroaryl, or heterocyclyl;

[0201] each Q, independently, is H, alkyl, acyl, cycloalkyl, alkenyl, alkynyl, aryl, heteroaryl or heterocyclyl; and

[0202] Each Q₂, independently, is O, S, N(Q)Q, alkyl or alkoxy.

[0203] In some embodiments, L₁ can be —C(R₅R₆)_xC(R_a)—; or L₁ can be —CH₂—C(R_a)—. L₂ can be —C(O)O—, —OC(O)—, —N(Q)C(O)—, —C(O)N(Q)-, —N(Q)C(O)O—, —OC(O)N(Q)-, —SS—, —O—N═, or ═N—O—. L₂ can be —C(O)O—, —OC(O)—, —SS—, or ═N—O—.

[0204] In some embodiments, -L^1a-(CR^1aR^1b) can be —(CH₂)₈—. -L^2a-(CR^2aR^2b)_δ— can be —(CH₂)₈—. L^1b-(CR^1aR^1b)_β can be CH₂CH₂CH₂, CH═CH—CH₂, or

[0205]
and β is 1, 2, or 3. L^2b-(CR^2aR^2b)_ε can be CH₂CH₂CH₂, CH═CH—CH₂, or

[0206]
and ε is 1, 2, or 3.

[0207] In one embodiment of the compound of formula IE, at least one L^1a, L^1b, L^1c, L^2a, L^2b, or L^2c present in the compound is a biodegradable group, such as ester —C(O)O—, —OC(O)—, disulfide (—S—S—), —C(R⁵)═N—, —O—C(O)O—, —C(O)N(R⁵), —N(R⁵)C(O)—, —N(R⁵)C(O)N(R⁵)—, —C(O)S—, —SC(O)—, —C(O)(CR^1aR^1b)C(O)O—, or —OC(O)(CR^1aR^1b)C(O)—. In another embodiment of the compound of formula IE, at least one L^1a, L^1b, and L^1c present in the compound is a biodegradable group and at one L^2a, L^2b, L^2c present in the compound is a biodegradable group (such as those mentioned above). In yet another embodiment of the compound of formula IE, α in R¹ is at least 4, δ in R² is at least 4, at least one L^1a, L_1b, and L^1c present in the compound is a biodegradable group and at one L^2a, L^2b, L^2c present in the compound is a biodegradable group (such as those mentioned above). In another embodiment, the carbon chain in R¹ and/or R² is saturated. In yet another embodiment, the carbon chain in R¹ and/or R² contains one or two double bonds.

[0208] In yet another embodiment, the cationic lipid is a compound selected from compounds of formulas II-XXIII:

[0209]
and salts thereof (e.g., pharmaceutically acceptable salts thereof),
wherein

[0210] m, n, o and p are each, individually, 1-25, with the proviso that:

• • [0211] (i) in Formulas (II), (IV), (VI) and (VII), m and p are both 4 or greater;
  • [0212] (ii) in Formulas (VIII), (X), (XII), (XIV), (XVI), (XVIII), (XXI) and (XXIII), m is 4 or greater; and
  • [0213] (iii) in Formulas (VIII), (IX), (XII) and (XIII), p is 8 or greater (e.g., 12 or 14 or greater).

[0214] In another embodiment, the present invention relates to a cationic lipid or a salt thereof having:

[0215] (i) a central carbon atom,

[0216] (ii) a nitrogen containing head group directly bound to the central carbon atom, and

[0217] (iii) two hydrophobic tails directly bound to the central carbon atom, each hydrophobic tail comprising a C₈ or greater aliphatic group (preferably a C₁₄ or greater aliphatic group) attached to the central carbon atom, where one or both of the aliphatic group(s) (a) is interrupted by a biodegradable group such that there is a chain of at least four carbon atoms between the biodegradable group and the central carbon atom, or (b) includes a biodegradable group at the terminal end of the hydrophobic tail. For instance, the biodegradable group is selected from —OC(O)—, —C(O)O—, —SC(O)—, —C(O)S—, —OC(S)—, —C(S)O—, —S—S—, —C(O)(NR⁵)—, —N(R⁵)C(O)—, —C(S)(NR⁵)—, —N(R⁵)C(O)—, —N(R⁵)C(O)N(R⁵)—, and —OC(O)O—.

[0218] Yet another embodiment is a lipid particle that includes a cationic lipid of the present invention. In one embodiment, the lipid particle includes a compound of any of formulas II-XXIII as described herein. In another embodiment, the lipid particle includes a compound of formula I as described herein. In another embodiment, the lipid particle includes a compound of formula IA-1, IA-2, IB, IC, ID or IE as described herein.

[0219] In a preferred embodiment, the lipid particle includes a neutral lipid, a lipid capable of reducing aggregation, a cationic lipid, and optionally, a sterol (e.g., cholesterol). Suitable neutral lipids include, but are not limited to, distearoylphosphatidylcholine (DSPC), dipalmitoylphosphatidylcholine (DPPC), POPC, DOPE, and SM. Suitable lipids capable of reducing aggregation include, but are not limited to, a PEG lipid, such as PEG-DMA, PEG-DMG, or a combination thereof.

[0220] The lipid particle may further include an active agent (e.g., a therapeutic agent). The active agent can be a nucleic acid such as a plasmid, an immunostimulatory oligonucleotide, an siRNA, an antisense oligonucleotide, a microRNA, an antagomir, an aptamer, or a ribozyme.

[0221] In another embodiment, the lipid particle includes a cationic lipid of the present invention, a neutral lipid and a sterol. The lipid particle may further include an active agent, such as a nucleic acid.

[0222] Yet another embodiment of the invention is a pharmaceutical composition which includes a lipid particle of the present invention and a pharmaceutically acceptable carrier.

[0223] Yet another embodiment is a method of delivering a nucleic acid molecule in a subject comprising administering to the subject a lipid particle comprising the nucleic acid molecule and a cationic lipid (or a salt thereof), the cationic lipid having

[0224] (i) a central carbon atom,

[0225] (ii) an nitrogen containing head group directly bound to the central carbon atom, and

[0226] (iii) two hydrophobic tails directly bound to the central carbon atom, each hydrophobic tail comprising a C₈ or greater aliphatic group (preferably a C₁₄ or greater aliphatic group) attached to the central carbon atom, where one or both of the aliphatic group(s) (a) is interrupted by a biodegradable group such that there is a chain of at least four carbon atoms between the biodegradable group and the central carbon atom, or (b) includes a biodegradable group at the terminal end of the hydrophobic tail.

[0227] In one embodiment, the cationic lipid remains intact until delivery of the nucleic acid molecule after which cleavage of the hydrophobic tail occurs in vivo.

[0228] Yet another aspect is a method of modulating the expression of a target gene in a cell by providing to the cell a lipid particle of the present invention. The active agent can be a nucleic acid selected from a plasmid, an immunostimulatory oligonucleotide, an siRNA, an antisense oligonucleotide, a microRNA, an antagomir, an aptamer, and a ribozyme.

[0229] Yet another aspect is a method of treating a disease or disorder characterized by the overexpression of a polypeptide in a subject by providing to the subject a pharmaceutical composition of the present invention, wherein the active agent is a nucleic acid selected from an siRNA, a microRNA, and an antisense oligonucleotide, and wherein the siRNA, microRNA, or antisense oligonucleotide includes a polynucleotide that specifically binds to a polynucleotide that encodes the polypeptide, or a complement thereof.

[0230] Yet another aspect is a method of treating a disease or disorder characterized by underexpression of a polypeptide in a subject by providing to the subject a pharmaceutical composition of the present invention, wherein the active agent is a plasmid that encodes the polypeptide or a functional variant or fragment thereof.

[0231] Yet another aspect is a method of inducing an immune response in a subject by providing to the subject a pharmaceutical composition wherein the active agent is an immunostimulatory oligonucleotide.

[0232] Yet another aspect is a transfection agent that includes the composition or lipid particles described above, where the composition or lipid particles include a nucleic acid. The agent, when contacted with cells, can efficiently deliver nucleic acids to the cells. Yet another aspect is a method of delivering a nucleic acid to the interior of a cell, by obtaining or forming a composition or lipid particles described above, and contacting the composition or lipid particles with a cell.

[0233] Other features and aspects will be apparent from the description and the claims.

[0238] In one aspect, the present invention relates to a lipid particle that includes a neutral lipid, a lipid capable of reducing aggregation, a cationic lipid, and optionally a sterol. In certain embodiments, the lipid particle further includes an active agent (e.g., a therapeutic agent). Various exemplary embodiments of these lipids, lipid particles and compositions comprising the same, and their use to deliver therapeutic agents and modulate gene and protein expression are described in further detail below.

The Cationic Lipid

[0239] In one embodiment, the cationic lipid is a compound of formula I-XXIII. In another embodiment, the cationic lipid is a compound of one of formulas II-XXIII. In one embodiment, the cationic lipid is a compound of formula I. In another embodiment, the cationic lipid is a compound of formula IA-1, IA-2, IB, IC or ID. The following disclosure represents various embodiments of a compound of Formula I.

[0240] In one embodiment, M¹ and M² are each, independently:

[0241] —OC(O)—, —C(O)O—, —SC(O)—, —C(O)S—, —OC(S)—, —C(S)O—, —S—S—, —C(R⁵)═N—, —N═C(R⁵)—, —C(R⁵)═N—O—, —O—N═C(R⁵)—, —C(O)(NR⁵)—, —N(R⁵)C(O)—, —C(S)(NR⁵)—, —N(R⁵)C(O)—, —N(R⁵)C(O)N(R⁵)—, —OC(O)O—, —OSi(R⁵)₂O—, —C(O)(CR³R⁴)C(O)O—, or —OC(O)(CR³R⁴)C(O)—.

[0242] In another embodiment, M¹ and M² are each, independently:

[0243] —OC(O)—, —C(O)—O—, —C(R⁵)═N—, —N═C(R⁵)—, —C(R⁵)═N—O—, —O—N═C(R⁵)—, —O—C(O)O—, —C(O)N(R⁵)—, —N(R⁵)C(O)—, —C(O)S—, —SC(O)—, —C(S)O—, —OC(S)—, —OSi(R⁵)₂O—, —C(O)(CR³R⁴)C(O)O—, or —OC(O)(CR³R⁴)C(O)—.

[0244] In yet another embodiment, M¹ and M² are each, independently:

[0245] —C(O)—O—, —OC(O)—, —C(R⁵)═N—, —C(R⁵)═N—O—, —O—C(O)O—, —C(O)N(R⁵)—, —C(O)S—, —C(S)O—, —OSi(R⁵)₂O—, —C(O)(CR³R⁴)C(O)O—, or —OC(O)(CR³R⁴)C(O)—.

[0246] In another embodiment, M¹ and M² are each —C(O)O—.

[0247] In one embodiment, R¹ and R² are each, individually, optionally substituted alkyl, cycloalkyl, cycloalkylalkyl, or heterocycle. In one embodiment, R¹ is alkyl and R² is alkyl, cycloalkyl or cycloalkylalkyl. In one embodiment, R¹ and R² are each, individually, alkyl (e.g., C₁-C₄ alkyl, such as methyl, ethyl, or isopropyl). In one embodiment, R¹ and R² are both methyl. In another embodiment, R¹ and R², together with the nitrogen atom to which they are attached, form an optionally substituted heterocylic ring (e.g., N-methylpiperazinyl). In another embodiment, one of R¹ and R² is

[0248]
(e.g., R¹ is one of the two aforementioned groups and R² is hydrogen).

[0249] In one embodiment, R′ is hydrogen or alkyl. In another embodiment, R′ is hydrogen or methyl. In one embodiment, R′ is absent. In one embodiment, R′ is absent or methyl.

[0250] For compounds in which R′ is not absent, the nitrogen atom to which R′ is attached carries a positive charge, and the compound also contains a negatively charged counter ion. The counterion can be any anion, such as an organic or inorganic anion. Suitable examples of anions include, but are not limited to, tosylate, methanesulfonate, acetate, citrate, malonate, tartarate, succinate, benzoate, ascorbate, α-ketoglutarate, α-glycerophosphate, halide (e.g., chloride), sulfate, nitrate, bicarbonate, and carbonate. In one embodiment, the counterion is a halide (e.g., Cl).

[0251] In one embodiment each R is, independently, —(CR³R⁴)—, wherein R³ and R⁴ are each, independently, H or alkyl (e.g., C₁-C₄ alkyl). For example, in one embodiment each R is, independently, —(CHR⁴)—, wherein each R⁴ is, independently H or alkyl (e.g., C₁-C₄ alkyl). In another embodiment, each R is, independently, —CH₂—, —C(CH₃)₂— or —CH(iPr)— (where iPr is isopropyl). In another embodiment, each R is —CH₂—.

[0252] In another embodiment R⁵ is, in each case, hydrogen or methyl. For example, R⁵ can be, in each case, hydrogen.

[0253] In one embodiment, Q is absent, —C(O)O—, —OC(O)—, —C(O)N(R⁴)—, —N(R⁵)C(O)—, —S—S—, —OC(O)O—, —C(R⁵)═N—O—, —OC(O)N(R⁵)—, —N(R⁵)C(O)N(R⁵)—, —N(R⁵)C(O)O—, —C(O)S—, —C(S)O— or —C(R⁵)═N—O—C(O)—. In one embodiment, Q is —C(O)O—.

[0254] In one embodiment, Q¹ and Q² are each, independently, absent or —O—. For example, in one embodiment, Q¹ and Q² are each absent. In another embodiment, Q¹ and Q² are each —O—.

[0255] In one embodiment, the dashed line to Q is absent, b is 0 and R′R¹R²N—(R)_a-Q- and the tertiary carbon adjacent to it (C*) form the following group:

[0256]
where n is 1 to 4 (e.g., n is 2).

[0257] In one embodiment, the dashed line to Q is absent, b is 0 and R′R¹R²N—(R)_a-Q- and the tertiary carbon adjacent to it form the following group:

[0258]
where n is 1 to 4 (e.g., n is 2), and R¹, R², R, a, and b are as defined with respect to formula (I). In one embodiment, a is 3.

[0259] In one embodiment, the dashed line to Q is absent, b is 0 and R′R¹R²N—(R)_a-Q- and the tertiary carbon adjacent to it form the following group:

[0260]
where n is 1 to 4 (e.g., n is 2), and R¹, R², R, a, and b are as defined with respect to formula (I). In one embodiment, a is 0. For example, the group can be:

[0261]

[0262] In one embodiment, b is 0. In another embodiment, a is 2, 3, or 4 and b is 0. For example, in one embodiment, a is 3 and b is 0. In another embodiment, a is 3, b is 0, and Q is —C(O)O—.

[0263] In one embodiment, the compound of formula (I) is of subformula:

[0264]

[0265] Formula (IF) wherein R, R′, R¹, R², A¹, A², A³, A⁴, Q¹, Q², Q³, Q⁴, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q and r are as defined in any of the embodiments disclosed herein.

[0266] In additional embodiments of the compound of formula (IF), one or more of the following applies:

[0267] (i) Q¹ and Q² are absent;

[0268] (ii) M¹ and M² are both —C(O)O—;

[0269] (iii) g and h are both 1;

[0270] (iv) g and h are both 0;

[0271] (v) c and e total 7;

[0272] (vi) d and f total 7;

[0273] (vii) c, e, and i total 7;

[0274] (viii) d, f and j total 7;

[0275] (ix) i and j are each 7;

[0276] (x) k and l are both 1;

[0277] (xi) m and n are both 0;

[0278] (xii) m and q total 1 or m and q total 2;

[0279] (xiii) m and l total 6;

[0280] (xiv) r and n total 6;

[0281] (xv) p and o are both 0;

[0282] (xvi) n and r total 2 or n and r total 1; and

[0283] (xvii) Q³ is H.

[0284] In certain embodiments, the biodegradable group present in the cationic lipid is selected from an ester (e.g., —C(O)O— or —OC(O)—), disulfide (—S—S—), oxime (e.g., —C(H)═N—O— or —O—N═C(H)—), —C(O)—O—, —OC(O)—, —C(R⁵)═N—, —N═C(R⁵)—, —C(R⁵)═N—O—, —O—N═C(R⁵)—, —O—C(O)O—, —C(O)N(R⁵), —N(R⁵)C(O)—, —C(S)(NR⁵)—, (NR⁵)C(S)—, —N(R⁵)C(O)N(R⁵)—, —C(O)S—, —SC(O)—, —C(S)O—, —OC(S)—, —OSi(R⁵)₂O—, —C(O)(CR³R⁴)C(O)O—, or —OC(O)(CR³R⁴)C(O)—.

[0285] In one embodiment, the aliphatic group in one or both of the hydrophobic tails of the cationic lipid includes at least one carbon-carbon double bond.

[0286] A suitable cholesterol moiety for the cationic lipids of the present invention (including compounds of formulas (I), IA-2, ID, IE and IF) has the formula:

[0287]

[0288] Additional embodiments include a cationic lipid having a head group, one or more hydrophobic tails, and a linker between the head group and the one or more tails. The head group can include an amine; for example an amine having a desired pK_a. The pK_a can be influenced by the structure of the lipid, particularly the nature of head group; e.g., the presence, absence, and location of functional groups such as anionic functional groups, hydrogen bond donor functional groups, hydrogen bond acceptor groups, hydrophobic groups (e.g., aliphatic groups), hydrophilic groups (e.g., hydroxyl or methoxy), or aryl groups. The head group amine can be a cationic amine; a primary, secondary, or tertiary amine; the head group can include one amine group (monoamine), two amine groups (diamine), three amine groups (triamine), or a larger number of amine groups, as in an oligoamine or polyamine. The head group can include a functional group that is less strongly basic than an amine, such as, for example, an imidazole, a pyridine, or a guanidinium group. The head group can be zwitterionic. Other head groups are suitable as well.

[0289] The one or more hydrophobic tails can include two hydrophobic chains, which may be the same or different. The tails can be aliphatic, for example, they can be composed of carbon and hydrogen, either saturated or unsaturated but without aromatic rings. The tails can be fatty acid tails. Some such groups include octanyl, nonanyl, decyl, lauryl, myristyl, palmityl, stearyl, α-linoleyl, stearidonyl, linoleyl, γ-linolenyl, arachadonyl, and oleyl. Other hydrophobic tails are suitable as well.

[0290] The linker can include, for example, a glyceride linker, an acyclic glyceride analog linker, or a cyclic linker (including a spiro linker, a bicyclic linker, and a polycyclic linker). The linker can include functional groups such as an ether, an ester, a phosphate, a phosphonate, a phosphorothioate, a sulfonate, a disulfide, an acetal, a ketal, an imine, a hydrazone, or an oxime. Other linkers and functional groups are suitable as well.

[0291] In one embodiment, the cationic lipid is a racemic mixture. In another embodiment, the cationic lipid is enriched in one diastereomer, e.g. the cationic lipid has at least 95%, at least 90%, at least 80% or at least 70% diastereomeric excess. In yet another embodiment, the cationic lipid is enriched in one enantiomer, e.g. the lipid has at least 95%, at least 90%, at least 80% or at least 70% enantiomer excess. In yet another embodiment, the cationic lipid is chirally pure, e.g. is a single optical isomer. In yet another embodiment, the cationic lipid is enriched for one optical isomer.

[0292] Where a double bond is present (e.g., a carbon-carbon double bond or carbon-nitrogen double bond), there can be isomerism in the configuration about the double bond (i.e. cis/trans or E/Z isomerism). Where the configuration of a double bond is illustrated in a chemical structure, it is understood that the corresponding isomer can also be present. The amount of isomer present can vary, depending on the relative stabilities of the isomers and the energy required to convert between the isomers. Accordingly, some double bonds are, for practical purposes, present in only a single configuration, whereas others (e.g., where the relative stabilities are similar and the energy of conversion low) may be present as inseparable equilibrium mixture of configurations.

[0293] In some cases, a double-bonded unsaturation can be replaced by a cyclic unsaturation. The cyclic unsaturation can be a cycloaliphatic unsaturation, e.g., a cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl, or cyclooctyl group. In some cases, the cyclic group can be a polycyclic group, e.g., a bicyclic group or tricyclic group. A bicyclic group can be bridged, fused, or have a spiro structure.

[0294] In some cases, a double bond moiety can be replaced by a cyclopropyl moiety, e.g.,

[0295]
can be replaced by

[0296]
For example, the moiety shown below has two carbon-carbon double bonds, each of which can independently be replaced by a cyclic moiety, e.g., a cyclopropyl moiety. Thus, substitutes for:

[0297]
can include:

[0298]

[0299] For further example, substitutes for

[0300]
include:

[0301]

[0302] For further example, substitutes for

[0303]
include:

[0304]

[0305] For further example, substitutes for

[0306]
include:

[0307]

[0308] The cationic lipid includes one or more biodegradable groups. The biodegradable group(s) include one or more bonds that may undergo bond breaking reactions in a biological environment, e.g., in an organism, organ, tissue, cell, or organelle. Functional groups that contain a biodegradable bond include, for example, esters, dithiols, and oximes. Biodegradation can be a factor that influences the clearance of the compound from the body when administered to a subject. Biodegradation can be measured in a cell based assay, where a formulation including a cationic lipid is exposed to cells, and samples are taken at various time points. The lipid fractions can be extracted from the cells and separated and analyzed by LC-MS. From the LC-MS data, rates of biodegradation (e.g., as t_1/2 values) can be measured.

[0309] For example, the compound

[0310]
includes an ester linkage in each aliphatic chain, which can undergo hydrolysis in a biological environment, for example, when exposed to, e.g., a lipase or an esterase. The structure of the compound, of course, influences the rate at which the compound undergoes biodegradation. Thus, a related compound such as

[0311]
would be expected to exhibit a different rate of biodegradation. Greater effects on that rate would be expected from changes in the structure of the compound at the site of hydrolysis. One modification that can influence the rate of hydrolysis, and thereby influence the rate of biodegradation and clearance from a subject's body, is to make the leaving group of the hydrolysis reaction have a primary, rather than secondary, alcohol.

[0312] For example, without wishing to be bound by theory, Compounds 1 and 2 shown above may be metabolized as shown in FIG. 2.

[0313] In one embodiment, a cationic lipid of any of the embodiments described herein has an in vivo half life (t_1/2) (e.g., in the liver, spleen or plasma) of less than about 3 hours, such as less than about 2.5 hours, less than about 2 hours, less than about 1.5 hours, less than about 1 hour, less than about 0.5 hour or less than about 0.25 hours.

[0314] In another embodiment, a cationic lipid of any of the embodiments described herein containing a biodegradable group or groups has an in vivo half life (t_1/2) (e.g., in the liver, spleen or plasma) of less than about 10% (e.g., less than about 7.5%, less than about 5%, less than about 2.5%) of that for the same cationic lipid without the biodegradable group or groups.

[0315] Some cationic lipids can be conveniently represented as a hydrophobic group combined with a headgroup. By way of example, the compound:

[0316]
can be thought of as a combination of a headgroup and a hydrophobic group as follows:

[0317]

[0318] Thus, some suitable head groups include those depicted in Table 1:

[0319]

TABLE 1

[0320] Some suitable hydrophobic tail groups include those depicted in Table 2:

[0321]

TABLE 2

[0322] In another aspect, the present invention relates to a method of preparing a compound of any of formulas I-XXIII. Suitable exemplary synthetic methods are illustrated in Schemes A-G below. The variables in the schemes below are the same as those variables at the same position in formulas I-XXIII above.

[0323]

[0324] The lipid chain length and linker length in Scheme A can be varied. Additionally, the R group in the ester functionality and substituents on the nitrogen atom can be derivatized.

[0325]

[0326] As shown in Scheme B, copper-mediated coupling affords a di-yne containing lipid chain with terminal functional groups R, which can be reduced to generate di-ene containing lipid chains. The length of the linker and lipid chain can be varied, and the functional substituent groups (R, R₁, R₂) can be derivatized.

[0327]
where Rx is alkyl, substituted alkyl, alkenyl, substituted alkenyl, alkynyl, substituted alkynyl, aryl, or substituted aryl, and HEAD Group is defined in Table 1.

[0328] The HEAD Group in Scheme C can be any head group disclosed herein (see, e.g., Table 1).

[0329]

[0330]

[0331]

[0332]

[0333] Examples of cationic lipids of the present invention include those shown in Tables 3-13 below, and salts thereof (including pharmaceutically acceptable salts thereof).

[0334]

TABLE 3

[0335]

TABLE 4

[0336]

TABLE 5
m	n	p	q
1	12	1	12
2	11	2	11
3	10	3	10
4	9	4	9
5	8	5	8
6	7	6	7
7	6	7	6
8	5	8	5
9	4	9	4
10	3	10	3
11	2	11	2
12	1	12	1
1	12	2	11
2	11	3	10
3	10	4	9
4	9	5	8
5	8	6	7
6	7	7	6
7	6	8	5
8	5	9	4
9	4	10	3
10	3	11	2
11	2	12	1
12	1	1	12
1	12	3	10
2	11	4	9
3	10	5	8
4	9	6	7
5	8	7	6
6	7	8	5
7	6	9	4
8	5	10	3
9	4	11	2
10	3	12	1
11	2	2	11
12	1	4	9
1	12	4	9
2	11	5	8
3	10	6	7
4	9	7	6
5	8	8	5
6	7	9	4
7	6	10	3
8	5	11	2
9	4	12	1
10	3	2	11
11	2	3	10
12	1	4	9
1	12	5	8
2	11	6	7
3	10	7	6
4	9	8	5
5	8	9	4
6	7	10	3
7	6	11	2
8	5	12	1
9	4	2	11
10	3	3	10
11	2	4	9
12	1	5	8
1	12	6	7
2	11	7	6
3	10	8	5
4	9	9	4
5	8	10	3
6	7	11	2
7	6	12	1
8	5	2	11
9	4	3	10
10	3	4	9
11	2	5	8
12	1	6	7
1	12	7	6
2	11	8	5
3	10	9	4
4	9	8	5
5	8	9	4
6	7	10	3
7	6	11	2
8	5	12	1
9	4	2	11
10	3	3	10
11	2	4	9
12	1	5	8
12	1	12	1
11	2	11	2
10	3	10	3
9	4	9	4
8	5	8	5
7	6	7	6
6	7	6	7
5	8	5	8
4	9	4	9
3	10	3	10
2	11	2	11
1	12	1	12
12	1	11	2
11	2	10	3
10	3	9	4
9	4	8	5
8	5	7	6
7	6	6	7
6	7	5	8
5	8	4	9
4	9	3	10
3	10	2	11
2	11	1	12
1	12	12	1
12	1	10	3
11	2	9	4
10	3	8	5
9	4	7	6
8	5	6	7
7	6	5	8
6	7	4	9
5	8	3	10
4	9	2	11
3	10	1	12
2	11	11	2
1	12	10	3
12	1	9	4
11	2	8	5
10	3	7	6
9	4	6	7
8	5	5	8
7	6	4	9
6	7	3	10
5	8	2	11
4	9	1	12
3	10	11	2
2	11	10	3
1	12	11	2
12	1	8	5
11	2	7	6
10	3	6	7
9	4	5	8
8	5	4	9
7	6	3	10
6	7	2	11
5	8	1	12
4	9	11	2
3	10	10	3
2	11	11	2
1	12	12	1
12	1	7	6
11	2	6	7
10	3	5	8
9	4	4	9
8	5	3	10
7	6	2	11
6	7	1	12
5	8	11	2
4	9	10	3
3	10	11	2
2	11	12	1
1	12	1	12
12	1	6	7
11	2	5	8
10	3	4	9
9	4	3	10
8	5	2	11
7	6	1	12
6	7	11	2
5	8	10	3
4	9	11	2
3	10	12	1
2	11	1	12
1	12	2	11

[0337]

TABLE 6
m	n	p	q
1	12	1	12
2	11	2	11
3	10	3	10
4	9	4	9
5	8	5	8
6	7	6	7
7	6	7	6
8	5	8	5
9	4	9	4
10	3	10	3
11	2	11	2
12	1	12	1
1	12	2	11
2	11	3	10
3	10	4	9
4	9	5	8
5	8	6	7
6	7	7	6
7	6	8	5
8	5	9	4
9	4	10	3
10	3	11	2
11	2	12	1
12	1	1	12
1	12	3	10
2	11	4	9
3	10	5	8
4	9	6	7
5	8	7	6
6	7	8	5
7	6	9	4
8	5	10	3
9	4	11	2
10	3	12	1
11	2	2	11
12	1	4	9
1	12	4	9
2	11	5	8
3	10	6	7
4	9	7	6
5	8	8	5
6	7	9	4
7	6	10	3
8	5	11	2
9	4	12	1
10	3	2	11
11	2	3	10
12	1	4	9
1	12	5	8
2	11	6	7
3	10	7	6
4	9	8	5
5	8	9	4
6	7	10	3
7	6	11	2
8	5	12	1
9	4	2	11
10	3	3	10
11	2	4	9
12	1	5	8
1	12	6	7
2	11	7	6
3	10	8	5
4	9	9	4
5	8	10	3
6	7	11	2
7	6	12	1
8	5	2	11
9	4	3	10
10	3	4	9
11	2	5	8
12	1	6	7
1	12	7	6
2	11	8	5
3	10	9	4
4	9	8	5
5	8	9	4
6	7	10	3
7	6	11	2
8	5	12	1
9	4	2	11
10	3	3	10
11	2	4	9
12	1	5	8
12	1	12	1
11	2	11	2
10	3	10	3
9	4	9	4
8	5	8	5
7	6	7	6
6	7	6	7
5	8	5	8
4	9	4	9
3	110	3	10
2	11	2	11
1	12	1	12
12	1	11	2
11	2	10	3
10	3	9	4
9	4	8	5
8	5	7	6
7	6	6	7
6	7	5	8
5	8	4	9
4	9	3	10
3	10	2	11
2	11	1	12
1	12	12	1
12	1	10	3
11	2	9	4
10	3	8	5
9	4	7	6
8	5	6	7
7	6	5	8
6	7	4	9
5	8	3	10
4	9	2	11
3	10	1	12
2	11	11	2
1	12	10	3
12	1	9	4
11	2	8	5
10	3	7	6
9	4	6	7
8	5	5	8
7	6	4	9
6	7	3	10
5	8	2	11
4	9	1	12
3	10	11	2
2	11	10	3
1	12	11	2
12	1	8	5
11	2	7	6
10	3	6	7
9	4	5	8
8	5	4	9
7	6	3	10
6	7	2	11
5	8	1	12
4	9	11	2
3	10	10	3
2	11	11	2
1	12	12	1
12	1	7	6
11	2	6	7
10	3	5	8
9	4	4	9
8	5	3	10
7	6	2	11
6	7	1	12
5	8	11	2
4	9	10	3
3	10	11	2
2	11	12	1
1	12	1	12
12	1	6	7
11	2	5	8
10	3	4	9
9	4	3	10
8	5	2	11
7	6	1	12
6	7	11	2
5	8	10	3
4	9	11	2
3	10	12	1
2	11	1	12
1	12	2	11

[0338]

TABLE 7
m	n	p	q
1	13	1	13
2	12	2	12
3	11	3	11
4	10	4	10
5	9	5	9
6	8	6	8
7	7	7	7
8	6	8	6
9	5	9	5
10	4	10	4
11	3	11	3
12	2	12	2
13	1	13	1
1	13	2	12
2	12	3	11
3	11	4	10
4	10	5	9
5	9	6	8
6	8	7	7
7	7	8	6
8	6	9	5
9	5	10	4
10	4	11	3
11	3	12	2
12	2	13	1
13	1	1	13
1	13	3	11
2	12	4	10
3	11	5	9
4	10	6	8
5	9	7	7
6	8	8	6
7	7	9	5
8	6	10	4
9	5	11	3
10	4	12	2
11	3	13	1
12	2	1	13
13	1	2	12
1	13	1	13
2	12	2	12
3	11	3	11
4	10	4	10
5	9	5	9
6	8	6	8
7	7	7	7
8	6	8	6
9	5	9	5
10	4	10	4
11	3	11	3
12	2	12	2
13	1	13	1
1	13	2	12
2	12	3	11
3	11	4	10
4	10	5	9
5	9	6	8
6	8	7	7
7	7	8	6
8	6	9	5
9	5	10	4
10	4	11	3
11	3	12	2
12	2	13	1
13	1	1	13
1	13	3	11
2	12	4	10
3	11	5	9
4	10	6	8
5	9	7	7
6	8	8	6
7	7	9	5
8	6	10	4
9	5	11	3
10	4	12	2
11	3	13	1
12	2	1	13
13	1	2	14

[0339]

TABLE 8
m	n	p
1	12	18
2	11	18
3	10	18
4	9	18
5	8	18
6	7	18
7	6	18
8	5	18
9	4	18
10	3	18
11	2	18
12	1	18
1	12	17
2	11	17
3	10	17
4	9	17
5	8	17
6	7	17
7	6	17
8	5	17
9	4	17
10	3	17
11	2	17
12	1	17
1	12	16
2	11	16
3	10	16
4	9	16
5	8	16
6	7	16
7	6	16
8	5	16
9	4	16
10	3	16
11	2	16
12	1	16
1	12	15
2	11	15
3	10	15
4	9	15
5	8	15
6	7	15
7	6	15
8	5	15
9	4	15
10	3	15
11	2	15
12	1	15
1	12	14
2	11	14
3	10	14
4	9	14
5	8	14
6	7	14
7	6	14
8	5	14
9	4	14
10	3	14
11	2	14
12	1	14
1	12	13
2	11	13
3	10	13
4	9	13
5	8	13
6	7	13
7	6	13
8	5	13
9	4	13
10	3	13
11	2	13
12	1	13
1	12	12
2	11	12
3	10	12
4	9	12
5	8	12
6	7	12
7	6	12
8	5	12
9	4	12
10	3	12
11	2	12
12	1	12
1	12	11
2	11	11
3	10	11
4	9	11
5	8	11
6	7	11
7	6	11
8	5	11
9	4	11
10	3	11
11	2	11
12	1	11
12	1	10
1	12	10
2	11	10
3	10	10
4	9	10
5	8	10
6	7	10
7	6	10
8	5	10
9	4	10
10	3	10
11	2	10
12	1	10
1	12	9
2	11	9
3	10	9
4	9	9
5	8	9
6	7	9
7	6	9
8	5	9
9	4	9
10	3	9
11	2	9
12	1	9
1	12	8
2	11	8
3	10	8
4	9	8
5	8	8
6	7	8
7	6	8
8	5	8
9	4	8
10	3	8
11	2	8
12	1	8
12	1	18
11	2	18
10	3	18
9	4	18
8	5	18
7	6	18
6	7	18
5	8	18
4	9	18
3	10	18
2	11	18
1	12	18
12	1	17
11	2	17
10	3	17
9	4	17
8	5	17
7	6	17
6	7	17
5	8	17
4	9	17
3	10	17
2	11	17
1	12	17
12	1	16
11	2	16
10	3	16
9	4	16
8	5	16
7	6	16
6	7	16
5	8	16
4	9	16
3	10	16
2	11	16
1	12	16
12	1	15
11	2	15
10	3	15
9	4	15
8	5	15
7	6	15
6	7	15
5	8	15
4	9	15
3	10	15
2	11	15
1	12	15
12	1	14
11	2	14
10	3	14
9	4	14
8	5	14
7	6	14
6	7	14
5	8	14
4	9	14
3	10	14
2	11	14
1	12	14
12	1	13
11	2	13
10	3	13
9	4	13
8	5	13
7	6	13
6	7	13
5	8	13
4	9	13
3	10	13
2	11	13
1	12	13
12	1	12
11	2	12
10	3	12
9	4	12
8	5	12
7	6	12
6	7	12
5	8	12
4	9	12
3	10	12
2	11	12
1	12	12
12	1	11
11	2	11
10	3	11
9	4	11
8	5	11
7	6	11
6	7	11
5	8	11
4	9	11
3	10	11
2	11	11
1	12	11
12	1	10
11	2	10
10	3	10
9	4	10
8	5	10
7	6	10
6	7	10
5	8	10
4	9	10
3	10	10
2	11	10
1	12	10
12	1	10
11	2	9
10	3	9
9	4	9
8	5	9
7	6	9
6	7	9
5	8	9
4	9	9
3	10	9
2	11	9
1	12	9
12	1	9
11	2	8
10	3	8
9	4	8
8	5	8
7	6	8
6	7	8
5	8	8
4	9	8
3	10	8
2	11	8
1	12	8
12	1	8

[0340]

TABLE 9
m	n	p	q
1	12	8	8
2	11	8	8
3	10	8	8
4	9	8	8
5	8	8	8
6	7	8	8
7	6	8	8
8	5	8	8
9	4	8	8
10	3	8	8
11	2	8	8
12	1	8	8
1	12	9	7
2	11	9	7
3	10	9	7
4	9	9	7
5	8	9	7
6	7	9	7
7	6	9	7
8	5	9	7
9	4	9	7
10	3	9	7
11	2	9	7
12	1	9	7
1	12	10	6
2	11	10	6
3	10	10	6
4	9	10	6
5	8	10	6
6	7	10	6
7	6	10	6
8	5	10	6
9	4	10	6
10	3	10	6
11	2	10	6
12	1	10	6
1	12	11	5
2	11	11	5
3	10	11	5
4	9	11	5
5	8	11	5
6	7	11	5
7	6	11	5
8	5	11	5
9	4	11	5
10	3	11	5
11	2	11	5
12	1	11	5
1	12	12	4
2	11	12	4
3	10	12	4
4	9	12	4
5	8	12	4
6	7	12	4
7	6	12	4
8	5	12	4
9	4	12	4
10	3	12	4
11	2	12	4
12	1	12	4
1	12	13	3
2	11	13	3
3	10	13	3
4	9	13	3
5	8	13	3
6	7	13	3
7	6	13	3
8	5	13	3
9	4	13	3
10	3	13	3
11	2	13	3
12	1	13	3
1	12	14	2
2	11	14	2
3	10	14	2
4	9	14	2
5	8	14	2
6	7	14	2
7	6	14	2
8	5	14	2
9	4	14	2
10	3	14	2
11	2	14	2
12	1	14	2
1	12	7	9
2	11	7	9
3	10	7	9
4	9	7	9
5	8	7	9
6	7	7	9
7	6	7	9
8	5	7	9
9	4	7	9
10	3	7	9
11	2	7	9
12	1	7	9
12	1	6	10
1	12	6	10
2	11	6	10
3	10	6	10
4	9	6	10
5	8	6	10
6	7	6	10
7	6	6	10
8	5	6	10
9	4	6	10
10	3	6	10
11	2	6	10
12	1	6	10
1	12	4	11
2	11	5	11
3	10	5	11
4	9	5	11
5	8	5	11
6	7	5	11
7	6	5	11
8	5	5	11
9	4	5	11
10	3	5	11
11	2	5	11
12	1	5	11
1	12	4	12
2	11	4	12
3	10	4	12
4	9	4	12
5	8	4	12
6	7	4	12
7	6	4	12
8	5	4	12
9	4	4	12
10	3	4	12
11	2	4	12
12	1	4	12
12	1	8	8
11	2	8	8
12	3	8	8
9	4	8	8
8	5	8	8
7	6	8	8
6	7	8	8
5	8	8	8
4	9	8	8
3	10	8	8
2	11	8	8
1	12	8	8
12	1	9	7
11	2	9	7
10	3	9	7
9	4	9	7
8	5	9	7
7	6	9	7
6	7	9	7
5	8	9	7
4	9	9	7
3	10	9	7
2	11	9	7
1	12	9	7
12	1	10	6
11	2	10	6
10	3	10	6
9	4	10	6
8	5	10	6
7	6	10	6
6	7	10	6
5	8	10	6
4	9	10	6
3	10	10	6
2	11	10	6
1	12	10	6
12	1	11	5
11	2	11	5
10	3	11	5
9	4	11	5
8	5	11	5
7	6	11	5
6	7	11	5
5	8	11	5
4	9	11	5
3	10	11	5
2	11	11	5
1	12	11	5
12	1	12	4
11	2	12	4
10	3	12	4
9	4	12	4
8	5	12	4
7	6	12	4
6	7	12	4
5	8	12	4
4	9	12	4
3	10	12	4
2	11	12	4
1	12	12	4
12	1	13	3
11	2	13	3
10	3	13	3
9	4	13	3
8	5	13	3
7	6	13	3
6	7	13	3
5	8	13	3
4	9	13	3
3	10	13	3
2	11	13	3
1	12	13	3
12	1	14	2
11	2	14	2
10	3	14	2
9	4	14	2
8	5	14	2
7	6	14	2
6	7	14	2
5	8	14	2
4	9	14	2
3	10	14	2
2	11	14	2
1	12	14	2
12	1	7	9
11	2	7	9
10	3	7	9
9	4	7	9
8	5	7	9
7	6	7	9
6	7	7	9
5	8	7	9
4	9	7	9
3	10	7	9
2	11	7	9
1	12	7	9
12	1	6	10
11	2	6	10
10	3	6	10
9	4	6	10
8	5	6	10
7	6	6	10
6	7	6	10
5	8	6	10
4	9	6	10
3	10	6	10
2	11	6	10
1	12	6	10
12	1	6	10
11	2	5	11
10	3	5	11
9	4	5	11
8	5	5	11
7	6	5	11
6	7	5	11
5	8	5	11
4	9	5	11
3	10	5	11
2	11	5	11
1	12	5	11
12	1	5	11
11	2	4	12
10	3	4	12
9	4	4	12
8	5	4	12
7	6	4	12
6	7	4	12
5	8	4	12
4	9	4	12
3	10	4	12
2	11	4	12
1	12	4	12
12	1	4	12

[0341]

TABLE 10
m	n	p
1	12	18
2	11	18
3	10	18
4	9	18
5	8	18
6	7	18
7	6	18
8	5	18
9	4	18
10	3	18
11	2	18
12	1	18
1	12	17
2	11	17
3	10	17
4	9	17
5	8	17
6	7	17
7	6	17
8	5	17
9	4	17
10	3	17
11	2	17
12	1	17
1	12	16
2	11	16
3	10	16
4	9	16
5	8	16
6	7	16
7	6	16
8	5	16
9	4	16
10	3	16
11	2	16
12	1	16
1	12	15
2	11	15
3	10	15
4	9	15
5	8	15
6	7	15
7	6	15
8	5	15
9	4	15
10	3	15
11	2	15
12	1	15
1	12	14
2	11	14
3	10	14
4	9	14
5	8	14
6	7	14
7	6	14
8	5	14
9	4	14
10	3	14
11	2	14
12	1	14
1	12	13
2	11	13
3	10	13
4	9	13
5	8	13
6	7	13
7	6	13
8	5	13
9	4	13
10	3	13
11	2	13
12	1	13
1	12	12
2	11	12
3	10	12
4	9	12
5	8	12
6	7	12
7	6	12
8	5	12
9	4	12
10	3	12
11	2	12
12	1	12
1	12	11
2	11	11
3	10	11
4	9	11
5	8	11
6	7	11
7	6	11
8	5	11
9	4	11
10	3	11
11	2	11
12	1	11
12	1	10
1	12	10
2	11	10
3	10	10
4	9	10
5	8	10
6	7	10
7	6	10
8	5	10
9	4	10
10	3	10
11	2	10
12	1	10
1	12	9
2	11	9
3	10	9
4	9	9
5	8	9
6	7	9
7	6	9
8	5	9
9	4	9
10	3	9
11	2	9
12	1	9
1	12	8
2	11	8
3	10	8
4	9	8
5	8	8
6	7	8
7	6	8
8	5	8
9	4	8
10	3	8
11	2	8
12	1	8
12	1	18
11	2	18
10	3	18
9	4	18
8	5	18
7	6	18
6	7	18
5	8	18
4	9	18
3	10	18
2	11	18
1	12	18
12	1	17
11	2	17
10	3	17
9	4	17
8	5	17
7	6	17
6	7	17
5	8	17
4	9	17
3	10	17
2	11	17
1	12	17
12	1	16
11	2	16
10	3	16
9	4	16
8	5	16
7	6	16
6	7	16
5	8	16
4	9	16
3	10	16
2	11	16
1	12	16
12	1	15
11	2	15
10	3	15
9	4	15
8	5	15
7	6	15
6	7	15
5	8	15
4	9	15
3	10	15
2	11	15
1	12	15
12	1	14
11	2	14
10	3	14
9	4	14
8	5	14
7	6	14
6	7	14
5	8	14
4	9	14
3	10	14
2	11	14
1	12	14
12	1	13
11	2	13
10	3	13
9	4	13
8	5	13
7	6	13
6	7	13
5	8	13
4	9	13
3	10	13
2	11	13
1	12	13
12	1	12
11	2	12
10	3	12
9	4	12
8	5	12
7	6	12
6	7	12
5	8	12
4	9	12
3	10	12
2	11	12
1	12	12
12	1	11
11	2	11
10	3	11
9	4	11
8	5	11
7	6	11
6	7	11
5	8	11
4	9	11
3	10	11
2	11	11
1	12	11
12	1	10
11	2	10
10	3	10
9	4	10
8	5	10
7	6	10
6	7	10
5	8	10
4	9	10
3	10	10
2	11	10
1	12	10
12	1	10
11	2	9
10	3	9
9	4	9
8	5	9
7	6	9
6	7	9
5	8	9
4	9	9
3	10	9
2	11	9
1	12	9
12	1	9
11	2	8
10	3	8
9	4	8
8	5	8
7	6	8
6	7	8
5	8	8
4	9	8
3	10	8
2	11	8
1	12	8
12	1	8