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2.12 Asymmetric Mukaiyama Aldol Reaction

DOI: 10.1055/sos-SD-202-00309

Liu, L.; Wang, D.; Li, C. -J.Science of Synthesis: Stereoselective Synthesis, (20112585.

General Introduction

The aldol reaction of carbonyl compounds with silyl enol ethers under Lewis acid or Lewis base catalysis has been recognized as one of the most important tools for the construction of new CC bonds in organic synthesis. It was discovered by Mukaiyama in the early 1970s and has been referred to as the Mukaiyama aldol reaction.[‌1‌,‌2‌] The use of a silyl enol ether, which is stable and isolable under the aldol reaction conditions, avoids undesired side reactions and favors the cross aldol reaction.[‌3‌] The starting silyl enol ether can be conveniently prepared regioselectively under either kinetically or thermodynamically controlled conditions. Aldehydes, ketones, esters, and thioesters can be converted into the silyl enol ethers, silyl ketene acetals, and silyl ketene thioacetals, respectively, which can subsequently undergo the Mukaiyama aldol reaction by acting as carbon nucleophiles. The molecular structures of typical silyl enol ethers are depicted in Scheme 1.

Meeeee 8 Meeeeee Meeee Meee Meeeee

Meee M- ee M-eeeee eeee eeeeee ee eeeeeeee eeeeeeeeeeeeeee, eee Meeeeeeee eeeee eeeeeeee eee eeee eee eee eeeeeeee eeeeeeeeeeeee eeeeeeeeeeeeee, eeeeeeee eeeeeee ee eeee eee eeeeeeee eee eee eeeeeeee eeeeeeeeeeeee (eee ee eeee) ee eee eeeee eeeeeeee (Meeeee 8). Mee eee/eeee eeeee ee eee eeeee eeeeeee ee eeeeeeee ee eee-eeeeeeee eeeeee eeeeeee ee eee eeeeeeee eeeeeeee, eee eeeee eeee eeeee (eeeeeeeee eee eeeeeeeeeeeee ee eee eeeeee eeee eee eeee ee eee eeeeeeeeeeee), ee eeee ee eee eeeeee ee eee eeeeeeee eeeee eeee.

Meeeeeeee eeeee eeeeeeeee eee eeeeeeeee eeeeeeeee ee Meeee eeeee. Mee eeeeeeee ee eeeeeeeee eee eee Meeeeeeee eeeeeeee eeee ee eeeeeeeeeeee eeeeeeeee ee eee-eeeee eeeeeee eeeeeeeeeeee ee eee eeeeeeeeeeeee ee eee eeeee eeee eeeee eeeeeeee, eee eeee e eeee eee eeeeeeeee eee eeeeeeee eee eeeeeeeee eee eeeeeeeeeeeee eeee-eeeee eeeeeee. Me eeeee ee Meeeee 8, eee eeeeeee ee eeeeeee eee-eeeeeee eee eeee eeeeeeeeee ee eeeeee eeeeeeeee eeeeeee eee eeeee eeeee ee eee eeeeeeee (M8) eee eee α-eeeee eeeee (M8) ee eee eeeee eeee eeeee ee eee eeeeeee eeeeeeeeee-eeeee eeeeee. Meeee ee eeeee eeee eeeeeeeeee-eeeee eeeeee ee eee ee eeeeeeeee eeee ee eeeee Meeee eeeee eee eeee, eee eeeeeeeeeee eeeeeee eee M8 eeeee eee eee Meeee eeee eeee ee eeeeeeee, eeee eeeeeeee eeeeeeeeee ee eeee-eeeeeee.[‌8‌]

Meeeee 8 Mee Meeeeeeee Meeee Meeeeeee eee Meeeeeeeee-Meeee Meeeee eee eee Meeeeeeee ee eeee- eee eee-Meeeeee[‌8‌]

Mee eeeeeeeeee Meeeeeeee eeeee eeeeeeee ee eee ee eee eeee eeeeeeee eeeee eee eeeeeeeeee eee MM eeeee ee eeeeeeeeeee eee eeeeeeee eeeeeeeeeeeeee ee eeeee eeeeee eeeeee eeeeeee. Me eeeee, eeeeeeeeeeeeeeeeee Meeeeeeee eeeee eeeeeeeee eeee eeeeeeeee eeeee eeeeee eeeeeeeee ee eeeeee eeeee eeee eeeeee ee eee eeeeeeee ee ee eeeeeee eeeeeeee eee eee 8,8- eee 8,8-eeeeeeeeee eeeeeeeee ee eee Meeeeeeee eeeee eeeeeeee eee eeee eeeeeeeeeeee ee eeeeee.[‌8‌,‌8‌] Meeeeeeee eeeeeeeeeeeeeeeeeeeeee [ee (8/8) ee ee 88:8] eeee eeee eeeeeeee ee eee eeeee eeeeeeeeeeeeeeeeee eeeee eeeeeee eeeeeeee Meeeeeeee eeeeeeeee eeee eeee-eeeeeeeeeee eeeeeeeee eeee-8 eee eeeee eeee eeeeee 8, eeeeeee eee eee-eeeeeeeeeee eeeeeeeee eee-8, eee eeeeeeeeeeeee eeeeeee eeeeeeeeeeee ee eee α- eee β-eeeeeeeeeeee eeeeeee eeeeeeeeeeee eeeeeeee ee eeeeeeee eeeeeeeeeeeeee ee eee eeeeeeee eeeeee [ee (8/8) ee ee 88:8] (Meeeee 8; eee eeeeeee eeeeeee eee Meeeeee 8.88.8.8). Mee eeeeeeeeeeeeeeeeee Meeeeeeee eeeee eeeeeeee ee e eeeee eeeeee eeeeee eeee ee eeeeeeeeeeeeeeee eeee eeee-eeeeeeeeeee eeeeeeeee eeeeeeee eeeeeeee ee eeeeeeeee eeeeeeeeeeeeee eeeee eeeeeee eee eeee eeee ee e eee eeee ee eee eeeeeeeeeeee ee eee M-eeee eeeeee ee eee eeeeeeeee eeeee, eeeee.[‌8‌]

Meeeee 8 Meeee Meee Meeeeeee Meeeeeeeeeeeeeeeee Meeeeeeee Meeee Meeeeeeee ee eeee- eee eee-Meeeeeeeeee Meeeeeeee[‌8‌]

Meeeeeeeeee 8

M8 M8 ee (8/8) Meeee (%) Mee
e-Me MMM 88:8 88 [‌8‌]
Me MMM 88:8 88 [‌8‌]
e-Me MMMMM 88:8 88 [‌8‌]
Me MMMMM 88:88 88 [‌8‌]

Meeeeeeeeee 8M

M8 M8 ee (8/8) Meeee (%) Mee
e-Me MMM 88:8 88 [‌8‌]
e-Me MMMMM 88:8 88 [‌8‌]

Me ee eeeeeee eeee eee eeeeeeee ee eeeee eeeeee eeeeee 8 eeee α-eeeee eeeeeeee 8 ee eee eeeeeeee ee eee(MM) eeeeeeee eeeee 8,8-eee-eeeee eeeeeee 8 eeeee eeeeeeeee-eeeeeee eeeeeeeeee (Meeeee 8),[‌8‌] eeeeeee eeeee eee eeee eeeeeeeeee eee eeeeeeee eeeeeeeeeeeeeeeeeeee ee eeeeeeee eeee α-eeeeeeeeeeeeee eeeeeeee 88 ee eeeeeee ee ee eeeeeeeeeeee eeee eeeee eeeeee eeeeee 88 ee eeee eeeee eeeeee 88 (Meeeee 8).[‌8‌] Me eee eeee ee eeeeeeeeeeee 88, eee eeeeeeeeee eeeee ee eee eeeeeeee eeeee eeeee e eee-eeeeeeeee eeeee eee 8,8-eeee eeeeeeeeeee.

Meeeee 8 Meeeeeeee Meeeeeeeee Meeeeeeeeeeeeee ee eee Meeeeeeee Meeee Meeeeeee[‌8‌]

Meeeee 8 Mee-Meeeeeeee Meeeeeeeee Meeeeeeeeeeeeee ee eee Meeeeeeee Meeee Meeeeeee[‌8‌]

Mee Meeee eeee eeeeeeee eeeeeeeeeeeeeeeeee Meeeeeeee eeeee eeeeeeee eee eeee eeeeeee ee e eeeeeeeee ee eeeeeeeeeeeee eeeeeeeeeeee ee eeee eee eeeeeeee eeeee (Meeeee 8; eee eeeeeee eeeeeee eee Meeeeee 8.88.8.8).[‌88‌] Meeeeee eeeeeeeeeeeee, eeee ee eeeeeee, eeeeee 88, eee eeeeeee 88 eeeeeeeeeeeee, eee ee eeeeeeeeeee ee eeee eeeeee eeee eeeeeeeeeeeeee eeeeee, eeee β-eeeeeee eeeeeeeee (e.e., 88) eee eeeee eeee eeeee eeeeeeeeeee (e.e., 88) eeeeee ee eeeeeeee eee eeeeeee eee Meeee eeee eeee.

Meeeee 8 Meeeeeeeeeeeeeee Meeeeeeeeeee Meeeeeeee eee e Meeeeeeeeeeeeeeeee Meeeeeeee Meeee Meeeeeee[‌88‌]

Meeeeeeeeee 8

M8 M8 M8 Meeee Meeeee ee (88/88) ee (%) Meeee (%) Mee
MMe MMMMM MMMMM 88 >88:8 88 88 [‌88‌]
M=M(MMMM)Me-Me MMMMM MMMMM 88 8:88 88 88 [‌88‌]
MMe MMMMM MMMMM 88 8:88 88 88 [‌88‌]
MMe MMMMM MMMMM 88 >88:8 88 88 [‌88‌]
MMe MMMMMM MMMMMM 88 >88:8 88 88 [‌88‌]
MMe Me MMMMMM 88 >88:8 88 88 [‌88‌]

Me 8888, ee eee eeeeeeee eeee eeeeeeeeeeeeeeeeee Meeeeeeee eeeee eeeeeeeee ee α-eeeeee-eeeeeeeeeee α,β-eeee- eee α,β-eee-eeeeeeeee 88 eeee eeeee eeee eeeee 88 eee ee eeeeeeeeeee eeeeeeeee ee eeeee eeeeeeeeeeeeeeeeee eeeee eeeeeee.[‌88‌] Mee eeeee eeeeeeee eeeee eee eeeeeeee eeee 8,8-eee-8,8-eeee (ee 88:8) eee 8,8-eee-8,8-eee eeeeeeeeeeeeee (ee 88:8), eeeeeeeeeeee (Meeeee 8).

Meeeee 8 Meeeeeeeeeeeeeeeee Meeeeeeee Meeee Meeeeeee ee α-Meeeee-Meeeeeeeeee Meeeeeeee[‌88‌]

Mee eeeee eeeeee eeeeee 88 eeeeeee eeee M-eeeeeeeeeeeeeee eee eeee eeee ee e eeeeee eeeee eeee eeeee ee eeeeeeeeeeeeeeeeee Meeeeeeee eeeee eeeeeeeee. Mee eeeeeeeeee ee eeeeee-eeee eeeeeeee, M8/M8 eeeeeeee eeeeeeeeeeeee ee eee eeeeee eeeeeeeee eeeee, eeeeeeeee eeeee ee eeeeeeee, eee eee eeeee ee eee eeeeeeee ee eee eeeeeeeeeeeeee eeeeeee ee eee eeeeeeee eeee eeee eeeeeeeee (Meeeee 8; eee eeee Meeeeee 8.88.8.8).[‌88‌,‌88‌]

Meeeee 8 Meeeeeeeeeeeeeeeee Meeeeeeee Meeeeeee ee e Meeeee Meeee Meee Meeee Meeeeee eeee ee M-Meeeeeeeeeeeeee Meeee[‌88‌]

Meeeeee eeeeeee ee eee eeeeeeeeeeeeeeeeee Meeeeeeee eeeee eeeeeeee ee eee eee ee eeeeee eeeee eeeeee eeeeee 88 eeeeeee eeee e eeeeee eeeeeeeeeeeeeeeeee. Mee eeeeeeeeeeeeeeeeeeee ee eeeeeeeee ee eee eeeee eeeeeeee 88/88 ee ee eeee ee 88:8 (Meeeee 8).[‌88‌]

Meeeee 8 Meeeeeeeeeeeeeeeee Meeeeeeee Meeeeeee ee e Meeeee Meeee Meee Meeee Meeeeee eeee e Meeeeeeeeeeeeeeeee[‌88‌]

Meeeeeeeeee 8

M8 ee (88/88) Meeee (%) Mee
Me 88:8 88 [‌88‌]
eMe 88:8 88 [‌88‌]

Meeeeeeeeeeeeeee Meeeeeeee eeeee eeeeeeeee eeeeeeee ee eeeeeeeeeeeeee eeeeee Meeee eeeee eeee eeee eeee eeeeeeee.[‌88‌‌88‌] Meeeeeeee ee e eeeeee eeeeeee eeee eee(MM) eee eee eeee eeeeee eee eee eeeeeeeeeeeeee eeeeeeeeeeeeeeee Meeeeeeee eeeee eeeeeeee. Me 8888, eee eeeee eeeeeee ee eeeeeeeee eeeeeeeeee eeeee eeeeeeeee ee e eeeee eeee eeeee eeee eeeeeeeee ee eeeee eeeeee eeeeeee eeeeeeeeeee eee(MM) eeeeeeeeeeeeeeeeeeeeeeeee ee e eeeeee eeeeeeee eee eeeeeeee.[‌88‌] Meeeeeeeeeee, eeeeeee eeeeeeeeeeeeee ee eeee eeeee eeeeeeeee eeee eeee eeeeeeee ee eeee eeeee eeeeeeee eeeeee.[‌8‌,‌88‌] Mee eeeeee Meeee eeee eeeeeeeee eeeeeeee eee eee eeeeeeeee eeeeeeeeee Meeeeeeee eeeee eeeeeeee eeeeeee eeeeee eeeee,[‌88‌‌88‌] eeeeeeee,[‌88‌‌88‌] eeeeeeeee,[‌88‌,‌88‌] eee,[‌88‌] eee eeeeee[‌88‌‌88‌] eeeeeeeee.

Meeee eee eeeeeeeee eee eeeeeeeeee Meeeeeeee eeeee eeeeeeeee, eee ee eee eeeeeeeee eeeeeeeeeeee eee eeee eee eee ee eeeeee eeeeeeee(MM) eeeeeeeee. Meeeeeee ee eeee eeee eee eeee eeeeeeee eeeeeeeeeeeee ee eeeeeee eeeeee[‌88‌‌88‌] eee eeeeeeeee eeeee ee 8,8-ee-8-eeeeeeee (MMMMM) eeeee eeeeeeee(MM) eeeeeeeee (8888) eeee eeee eeeeeee eeeeeeeeeeee ee eeeeee eeeeeeeee eeeeeeeee (Meeeee 88; eee eeee Meeeeee 8.88.8.8).

Meeeee 88 Meeeee MMMMM-Meeee Meeeeeee(MM) Meeeeeeee eee Meeeeeeeeeeeeeee Meeeeeeee Meeee Meeeeeeee[‌88‌‌88‌]

Meeeeeeeeee 88

M M8 M8 Meeeeeee ee (%) Meeee (%) Mee
M Me MM8MMe 88 88 88 [‌88‌]
M Me MM=MMMe 88 88 8888 [‌88‌]
M Me Me 88 88 8888 [‌88‌]
M e-Me Me 88 88 88 [‌88‌]

Meee eeeeeeee ee eeeeee eeee eeeeeeeeeee ee eee Meeeeeeee eeeee eeeeeeee eeee eeee eeee. M eeeeeeeeeee eeeeeee eee eeee eeeeeeee eeee eee eee ee eeeeeeeee eeeeeeee 88 (Meeeee 88; eee eeee Meeeeee 8.88.8.8).[‌88‌] Me eeee eeeeeeee, eeee-eeeee eeeeeee eeee eeee eeeeeeee eeee eeee M- eee M-eeeeeeee, e eeeeee eeee ee eeeeeeeeee ee eee eeeeeeeee ee ee eeeeeee eeeeeeeeee eeeee eeeeee eee eeeee eeeeeeee. Mee eee eeeeeeeee(MM)-eeeeeeeee eeeeeeeeee eeeee eeeeeeee, eee eee ee e eeeeeee eeeeeee eeeee ee eeeeeeeee eeee ee eeeeeeeeee eee eeeeeeeee eeeee.

Meeeee 88 Meeeeeeee(MM)-Meeeeeeee Meeeeeeeee Meeeeeeee Meeee Meeeeeee[‌88‌]

Meeeeeeeeee 88

M8 ee (eee/eeee) ee (%) Meeee (%) Mee
Me 8:88 88 88 [‌88‌]
8-MeMM8M8 8:88 88 88 [‌88‌]
8-MeM8M8 8:88 88 88 [‌88‌]
MM=MMMe 88:88 88 88 [‌88‌]
MM=MMMe 88:88 88 88 [‌88‌]
(MM8)8Me 88:88 88 88 [‌88‌]

Me eee eeee eeeeeeee[‌88‌] eeee eee(MM) eeeeeeeee ee 8,8-eeeeeeeeeeeeeeeee[(8M)-8-eeeeee-8,8-eeeeeeeeeeeeee] (88) eee 8,8-eee[(8M)-8-eeeeee-8,8-eeeeeeeeeeeee-8-ee]eeeeeeee (88) eeeeeeeeeee eeeeeeee eee eeeeeeee ee eeeee eeeeee eeeeeeeeee 88 eeee eeeeee eeeeeeee ee eeee eeeeeeeeeeeeeeeeee eee eeee eeee eeee eeeeeeeeeeeeeeeeeeee, eee eeee eeeeeeee eeeeeeeeeeeeee ee eee eeeee eeeeeeeee eeeeee eeeeeee. Meeeeeeeeeeee, eee eee eeee eeeeeeee eee eee ee e eeeeee(MM) eeeeeee ee 8,8-eeeeeeeeeeeeeeeee[(8M)-8-eeee-eeeee-8,8-eeeeeeeeeeeeee] (88) ee eeeeeeee eeeeeeee eee eeeeeeeeeeeeeeeeeeee, eeee eeee eeee eeeeeeeeeeeeeeeeee (Meeeee 88; eee eeee Meeeeee 8.88.8.8).

Meeeee 88 Mee(MM)- eee Meeeee(MM)-Meeeeeeee Meeeeeeeee Meeeeeeee Meeee Meeeeeeee[‌88‌]

Meeeeeeeeee 88

M Meeeee Meeeee ee (eee/eeee) ee (%) Meeeee (%) Mee
Me 88 (8M)-eeee 8:88 88 88 [‌88‌]
Me 88 (8M)-eeee 8:88 88 e.e. [‌88‌]
Me 88 (8M)-eee 88:8 88 e.e. [‌88‌]

e e.e.=eee eeeeeeee.

Meeee ee eee eeeeeee ee eeeeee eee eee eeeeee eeeeeeeee,[‌88‌‌88‌] eeeeeeee(MMM) eee(eeeeeeeeeeeeee) eeeeeeeee eeee eeee eeeeeeeee ee eeeeee Meeee eeeee eee eee eeeeeeeee eeeeeeeeee Meeeeeeee eeeee eeeeeeee (Meeeee 88; eee eeee Meeeeee 8.88.8.8).[‌88‌] Me eee eeeeeeee(MMM) 8,8-eee[(8M)-8-eeee-eeeee-8,8-eeeeeeeeeeeee-8-ee]eeeeeeee eeeeeee 88 eeeeeeeee eeeee eeeeeeeee ee eeeee eeeeeeeeee, eeeeeeeee eeeeeeeeeeeeeeeeeeee (ee ee 88% ee) eee eee eeeeeeeeeeeeeeeeeeeeee (ee ee 88:8) eee eeeeeeee. Mee eeeeeeee(MMM) eeeeeeeee, ee eeeeee ee e eeeeee eeeeee eeeeeeee eeeeee, eeeee ee eeee eeeeee Meeee eeee eeeeeeeee eeee eeeeee(MM), eeee(MM), ee eee(MM) eeeeeeeee. Meeeee, eee eeeeeeee eeeeeeeee eeeeeee eeeeeeeee eeeeeeee ee eee eeeeeeeee eeeee eee eee ee eeeeeeee ee eeeeeee ee eee ee 8eee%. Meeeeeeeeee, eee eeeeeee-eeeeeeeee eeeeee eee(eeeeeeeeeeeeee) eeeeee 88 eee ee eeee ee eeeeeeeeeeeee eeeeee-eeeeeeeee eeeeeeeeee Meeeeeeee eeeee eeeeeeeee ee eeeeeee eee eeeee eeeeeeee ee eeee eeeee (88%) eee eeee eeee eeeeeeeeeeeeeeeeee (88% ee).[‌88‌]

Meeeee 88 M Meeeeeee(MMM) Mee(eeeeeeeeeeeeee) Meeeeee eee e Meeeeee-Meeeeeeee Mee(eeeeeeeeeeeeee) Meee eee Meeeeeeeee Meeeeeeee Meeee Meeeeeeee[‌88‌,‌88‌]

Me eee eeeee eeee, eeeeeee eeeee ee eee eeeeeeeee eeeeeee eee eeeeeeee eeeeeee ee eee eeeeeeeeeeeeee eeeeeee ee eee eeeeeeeeee eeeee eeeeeeee.[‌88‌] Mee eeeeeeeee eeeeee ee eeee eeeeeeee ee eeee eeeeeeee eeeeeeee eeeeeee eeeeeee ee eee eeee eeeee- ee eeeeeeeeeeeeee eeeee eeeeeeee ee eee eeeeeeee eeeeee eeeeee eeee eeeeeeeeeeee eeeeeeeeee ee eee eeeeee eeeeeeee (eeee M ee eeee M, Meeeee 88). Meeeeeeeeeee, eee eeeeeee-eeeeeeeee eeeeeee eeeee eeeeeee eeeeee ee eeeeeeeeee. Me eeee eeeeeee, eeeeeee eeeeeee eeeeeeeeee eeeeee eeee eee eee ee e eeeee eeeee eeeeeee eeee eeee eeeee ee ee eeeeeeeee eee eeeeeeeee eeeeeeee eeeeeeee, eeeeeeee, eee eeeeeeeeeeeeeeeeee.[‌88‌,‌88‌,‌88‌]

Meeeee 88 Mee Meeeeeee ee eee Meeeeeeee Meeeeeeeee Meeeeeeee Meeee Meeeeeee[‌88‌,‌88‌,‌88‌]

Meeeeeeeeeeee eeeeee eeeee eeeeeeeee, eeeeeee eeeeeeeee eeee eeee eeeeeeee eeeeeee ee e eeeeeee eeeee ee eeeeeeeeeeeeeeee eeeeeeeee eee Meeeeeeee eeeee eeeeeeeee. Me eeeeeeeeeeee eeeeeeeeee eeeeeeeeee, Meeee eeee eeeeeeeeeeeeeee eee Meøeeeee eeee eeeeeeeeeeeeeee eeee eeeeeeee eeeeeee eeeeee ee eeeeee eeeeee eeeeeeeee, eeeeeeeee eee Meeeeeeee eeeee eeeeeeee.

Meee Meeee eeee eeeeeeeee eeeeeeeeee Meeeeeeee eeeee eeeeeeeee eee eeeeeeee ee eee eeeeeeeeee ee eee eeeeeeeeeeeee eeeeeeeee ee eee eeeeeeee. Me eeeeeeee ee eeeeee Meeee eeeee, e eeeeeeeeeeee eeeeeeeee eeeeeeee eeeee ee eee eeeeeeeeee ee eee eeeeeeeeeeee eeeeeeeee eee e Meeee eeee eee eeee eeeeeeeeeeee eeeeeeeeeeee.[‌88‌] Meeee eeeeeeeee eeeeeeeeee, eeeeeeeeeeeee eeeeeee eeeeeeeeeeeeee eeee eeeeee 88,[‌88‌] eeeee eee eeeeee eeeeeeee eeeeee eee eeeeee eeeeeeeeeeeeeee eeeeeeeeee eeeee eeeeeeeee, eeeeeee eeeeeeee ee eeeeeeeee ee eee eeeeeeee ee eeeeee eeeeeeeeeeeee (M,M)-88. Mee eee-eeeeeee eee-88 eee eee eeeeeeeeeee eeeeeee eeeeeeee eeee M-eeeeeeee, eeeee M-eeeeeeeeee eeeeeeee eeee eeee ee eee eeee-eeeeeee eeee-88 (Meeeee 88).[‌88‌] Me ee eeeeeeeeee eeee ee eee eeeeeee ee eee eeeeeeee eee M-eeeeeee eeeeeee eeeeee eee eee-eeeeee.

M eeeeeeeeeeeeeee eeeeeeeeee eeeeeee eee eeee eeeeeeeee ee ee eeeeeeeeeee eee eee eeeeeeeeeeeeeeeee. Meee eeeeeeeeeeeeee eeeeeeee eeeee eeee eeeeeeeee, eee eeeeee ee eee eeeee eeeeeeeeeeeee eeeee eeeeeeeeee ee eee eeeeeee ee eeee e eeeeeeee eeeee eeee eeeee eeeeeeeeeeee 88 (Meeeee 88), eeeee eeeeeeeeeeee eeeee ee eee eeeeeeeeeeeee eeeeeeee ee eeeeee eeeeeeeeeeee.[‌88‌]

Meeeee 88 Meeeeeeeee Meeeeeeee Meeee Meeeeeee Meeeeeeee ee e Meeeee Meeeeeeeeeeee[‌88‌] eee Meeeeeee Meeeeeeeee Meeeee ee Meeee Meee Meeeeeee Meeeeeeeee Meeeeeeee Meeeeeee[‌88‌]

Meeeeeeeeee 88

Meeeeee Meeeeeee M8 M8 ee (eee/eeee) ee (%) Meeee (%) Mee
M Me (MM8)8Me 88:8 88 88 [‌88‌]
M Me (MM8)8Me 8:88 88 88 [‌88‌]
M Me Me 88:8 88 88 [‌88‌]
M Me Me 8:88 88 88 [‌88‌]
M MM=MMMe Me 88:8 88 88 [‌88‌]
M MM=MMMe Me 8:88 88 88 [‌88‌]
M (MM8)8Me Me 88:8 8 88 [‌88‌]
M (MM8)8Me Me 8:88 88 88 [‌88‌]

Me eee eeeee ee eeeeeeeeeeeeee ee Meeee eeee eeeeeeeee, e eeeeeee eee eee eeeeeeeeee ee eee eeee Meeee eeee eeeeeee eeeeeeeeeeeee ee e eeeeeeee Meeee eeeee eeeeeeeeeeeee eee eeee eeeeeeeee.[‌88‌,‌88‌] Meeeeee ee eee eeeeeeeeeeeee eeeeeeeee eee MeMe eeeee, eeeeeee ee eeeeeeeeee ee e eeeeeeee eee eeeeeeeee ee e eeeeeeeeeeeee eeeeee, eeeeeeeeeeeeeeee eeeeeeeeeeeeee eeeeee 88 (Meeeee 88). Mee eeeeeeeee eeeeee eee eeeeeeeeee ee e eeee Meeee eeee ee Meeee eeee eee eeee eeeeeee ee eee eeeeeeeeee eeeee eeeeeeee ee eeeee eeeeee eeeeeee eeee eeeeeeeee ee eeee β-eeeeeeeeeeeeeeeeeee ee eeee eeeeee eeee eeee eeeeeeeee- eee eeeeeeeeeeeeeeeeeeee. Meeeeeee eeeeeee ee eee ee 8eee% eee ee eeeeeeee eeeeeee eee eeeeeeeeeee ee e eeee eeeeeeee eeee.

Meøeeeee eeee eeeeeeeeeeeeeee eee eeeeee e eeeeeeee eeee ee eeeeeeeeee eeeeeeeee. Me eeeeeeeee eee M8-eeeeeeeee eeeeeeeeee eeeeeeeeeee 88 ee e eeeeee Meøeeeee eeee eeeeeeee, e eeeeee eeeeeeeee eee eeeeeeeeeeeeeeee Meeeeeeee eeeee eeeeeeee eee eeee eeeeeeeeeee eeee ee eeeeeeeeee eeeeeeeeeeee-eeeeeeee eeeeeeeee (MMMM) eeeeeeee (Meeeee 88; eee eeee Meeeeee 8.88.8.8).[‌88‌] Mee Meøeeeee eeee eeeeeeeee eeeeeeee eeeeeeee e eeeeeeee ee e eeeeeee eeeeeeee ee eee Meeee eeee eeeeeeeee eeeeeeeeeeeeeeee eeeee eeeeeeee, eeeee ee eeeeeeeeee ee eee-eeeeeeeeeeeeeeee eeeeeeeeee eeeeeeeee eeeeeeee ee eee eeeeeee eeeeeee eeeeee (M88Me+; eee Meeeee 88).

Meeeee 88 Meeeeeeeee Meeeeeeee Meeeeeee Meeeeeeee ee e Meeeee Meeeeeeeeeeee[‌88‌]

Meeeeeeeeee 88

M8 M8 M8 ee Meeee (%) Mee
8-eeeeeeee Me Me 88:8 88 [‌88‌]
8,8-(MeM)8M8M8 Me Me 88:8 88 [‌88‌]
8-eeeeeeee M eMe 88:8 88 [‌88‌]
Me M eMe 88:88 88 [‌88‌]
M(Me)=MMMe M eMe 88:8 88 [‌88‌]

Mee eeeeeeeeee Meeeeeeee eeeee eeeeeeee eee ee eeeeeeeeeee eeeeeeeee ee eee eeeeee eeeee-eeeeeeee eeeeeee eeeeeeeeee eeeeeeee eeeeeeee 88 ee e eeeeee eeeeeeeeeeeeee ee eeee eeee-eeeee eeeeeee 88 ee eeee eeeeeeeeeeeeeeeeeeee (Meeeee 88).[‌88‌] Mee eeeeeeeeee eeeeeeee eeeeeeeee eee ee eeeeeeeee ee eeee eeee eee eeeeeeeeeeeee eeeeeeee eeeeeeee eeeeeeee ee eeeeeeeee eeee eeeeeeeeeeee eeeeeeeee eeeeeeeee eeeeeeee (MM8M8M) ee eeeeeeeeeeeeeee eee eeeeeeee eeee ee eee eeeeeeeee Meeeeeeee eeeee eeeeeeee ee eeeee eeee eeeee 88 eeee eeeeeeeee.

Meeeee 88 Meeeeeeeee Meeeeeeee Meeeeeee Meeeeeeee ee e Meeeee Meeee-Meeeeeee Meeeeee[‌88‌]

Meeeeeeeeee 88

M8 ee ee (%) Meeee (%) Mee
Me 88:88 88 88 [‌88‌]
8-eeeeeeee 88:8 88 88 [‌88‌]
8-eeeeeeeeeee 88:8 88 88 [‌88‌]

Mee eeeeeee ee eeeeeeeeeeeeeee eeeeeeee ee eeeee eeeeeeee ee eeeeeee eee eeee eeeeeeee eeeeeee e eeeeee Meeee eeee eeeeeeeee Meeeeeeee eeeee eeeeeeee ee eee eeeeee eeeeeeee eeeeeeeeeeeeee eeee eeeee 88 ee eeeeee eeeeeee eeee eeeeee eeeeeee (e.e., eeeeeeeeeeee) ee eee eeeeeeee ee e eeeeeeeee eeeeee ee eeeeee eee-M-eeeee 88. Mee eeeeeeeee eeeeeee eee eeeee eeeeeee (e.e., 88) ee eeeeeeeee eeeeee eeee eeeeeeeeeeee eeeeeeee eeeeeee eeee eeee eee eeeeeeee eeeeeee ee eeeeeeee eee eeeeeeeee eee eeeeee-eeeeeeeeee eeeeeee (Meeeee 88).[‌88‌]

Meeeee 88 Meeeeeeeee Meeeeeeee Meeeeeee ee e Meeeee Meeeee Meeeeeeee ee e Meeeee Mee-M-eeeee[‌88‌]

Meeeeeee eee ee eeeeeee ee eee eeeeeeeeeeee ee eeeeeeeeee eeeeeee eeeeeee e eeeeeeeeee eeeeee.[‌88‌] Me eee Meeeeeeee eeeee eeeeeeee, eee eeeeeeeeeee eeeee eeeeeee eeeeeeeeeeee eee ee eeeeeeee ee M-eeeeeeeee eeeeeeeeee, eeeeeeeeeeeeeeee eeeeeee ee γ-eeeee eeeeeeee (Meeeee 88). Mee eeeeeeeeee Meeeeeeee eeeee eeeeeee eee eeeeeeeeeee eeeeeeeeee eee δ-eeeeeee-β-eeee eeeeee eee β,δ-eeee eeeeee, eeeee eeee eeee eeeeeee ee eee eeeeeeeee ee eeeeeeee eeeeeee eeeeeeee.[‌88‌‌88‌]

Meeeee 88 Meeeeeeeeeeeeeee ee eee Meeeeeeeee Meeeeeeee-Meee Meeee Meeeeeee[‌88‌]

Mee eeee eeeeeeeeee eeeeeeeeee Meeeeeeee eeeee eeeeeeeee, eee eeeeee eeeeeeee ee e eeeeee Meeee eeee, eeeee eeeee ee eee eeeeeeee eee eeeeeeeeeeee ee eee eeeeeeeee eeeee ee eeeeeeeee eeeeeeeeeeeee eeeeeeeeee. Mee eeeee eeeeeeeee eeeeeeee eeeeee eeee ee eee eeeeeeeeee eeeeeeeeee eeeee eeeeeeee eee e eeeeee(MM) eeeeeeee/8,8-eee(ee-8-eeeeeeeeeeeeee)-8,8-ee-8-eeeeeeee (MeeMMMMM, 88) eeeeeeee, eeeeeeeee ee 8888 (Meeeee 88).[‌88‌] Meee eeeeee eee eeeeeeeeeeeeeeeeeeee eeee eeee eeeeeeee eee eeeeeeee, eeeeeeeeeeeeee, eee eeeeee-eeeeeeeeee eeeeeeeee ee eee eeeeeeee ee eee eeeeeeeee-eeeeeee eeeeee 88. Mee eeeeeeee eee eeee eeeeeeee ee eeeeeee eee e eeeeeeeee ee eeeee eee eeeeee(MM) eeeeeeee eeeeeeee eeeeee eeee eee eeeee eeeeee eeeee ee eeeeeeee e eeeeee eeeeee eeeeeeeee ee eee eeeeee eeeeeee ee eee eeeeeeeeee MM eeee-eeeeeeeee eeee.

Meeeee 88 Meeeeeeeee Meeeeeeee-Meee Meeee Meeeeeee Meeeeeeee ee Meeeee MeeMMMMM/Meeeee(MM)[‌88‌]

Meeeeeeeeee 88

M8 ee (%) Meeee (%) Mee
Me 88 88 [‌88‌]
8-eeeeeeee 88 88 [‌88‌]
8-eeeee 88 88 [‌88‌]
8-eeeeeee 88 88 [‌88‌]
8-MeMM8M8 88 88 [‌88‌]

Meeeee(MM) 8,8-eee[(8M)-8-eeeeee-8,8-eeeeeeeeeeeee-8-ee]eeeeeeee (Me-eeeee) eeeeeeee 88 eee eeee eeee eeeeeeee ee eeeeeeee eee eeeeeeee ee α-eeeeeeeeee-eeeeeeeeeee eeeeeeee 88 eeee eeeeeeeeeeee-eeeeeee eeee eeeeeeeeee 88 (Meeeee 88). Meeeeeeee eeee eee eeeeeeeeeee eeeeeeeeee, eee eeee eeeeeeee Meeeʼe eeeee 88[‌88‌] eeeee eeeee eeeeeeee eeeeeeee (8.8eee%), eee eeeee-eeeee eeeeeeeee (8.8eeee, eeee ee ee 88.8eeee, ee eeeeeeee eeeeeeee, ee 8.8eeee eee eee eeeeee eeeeeeeee) eee ee eeeeeee eee (Meeeee 88; eee eeee Meeeeee 8.88.8.8).[‌88‌]

Meeeee 88 Meeeeeeeee Meeeeeeee-Meee Meeee Meeeeeee Meeeeeeee ee e Meeeee Meeeee(MM)Me-eeeee Meeeeee[‌88‌]

Mee eeeeeeeeeee ee Meeee eeee eeeeeeeeee ee Meeee eeee eeeeeeeee ee eee eeeee eeeeeeee eee eeee eeeeeeee ee eee eeeeeeeeee Meeeeeeee eeeee eeeeeeee. Mee eeeeeeee ee eeeee eeeeeeeeee eeeeeee eeee α,β-eeeeeeeeeee eeeeee ee α,β-eeeeeeeeeee eeeeee ee eeeeeeeee eee ee eeeeeeeee ee e eeeeee eeeeeeeeeeeeeeee eeeeeeee ee eeeeeeeeeee eeee eeeeeee eeeeeeeeeeeee eee eee ee eeee eeeeeeeee ee e eeeeeeee eeeeee eeeeeeeeee eee, eeeeeee ee eee eeeee eeeeee eeee eeee eeeee- eee eeeeeeeeeeeeeeeeeeee.[‌88‌]

Meeeeee eee eeeeeeeeeeeeeeeee ee eee Meeeeeeee eeeee eeeeeeee eeeeee eeee eee Meeee eeeee eeeeeeee, eeeee eeeee eeeeeeeee eeeeeee eeeeee eeeeeeeee eeeeeee ee eeeeeeeeeeeeeee eee eeeeeeeeee MM eeee-eeeeeeeee eee eeee eeee eeeeeee ee eee eeeee eeeeeeeee ee eeeeeee eeeeeeee. Mee eeeeeeee, eee eeeee eeeeeeeee ee eeeeeeeeeee (88), e eeeeeee eeeeeeeee eeeeeeeeee, eee eeee eeeeeeee eeeeeeeeeee eee M88 eeeeeeeeeeee eee ee eeeeeeeeee Meeeeeeee eeeee eeeeeeee eeeeeeeee eeeeee eeeeeeee eeeeeee 88[‌88‌] (Meeeee 88).[‌88‌]

Meeeee 88 Meeeeeeee ee Meeeeeeeeee[‌88‌]

Mee eeeeeeeeee Meeeeeeee eeeee eeeeeeee eeeeeeeee ee eeeeee eeeeeee eeeeee 88 eeee eee(MM) eeeeeeeee [Me(MMe)8 eee MeM] eee eeee eeeeeee ee eeeeeee eee eee eeee eeeeeeeee ee eeeeeeeeeeeee M (88) ee eeeeeeeee eeeeeee- eee eeeeeeeeeeeeeeeeeeeeee. Meeeeeeeeee ee eee eee eeeeeeeee 88 eee 88 eee eeeeeeeeee eeeee eeee eee ee eee eeeee eeeeeeeee ee eeeeeeeeeeeee M (88) (Meeeee 88).[‌88‌]

Meeeee 88 Meeeeeeee ee Meeeeeeeeeeee M[‌88‌]

Meeeeee eeeeeee ee eee eeeee eeeeeeeee ee e eeeeeee eeeeeee, eeeeeeeeeeeeee M (88), ee eeeee eee eeeeee-eeeeeeeee eeeeeeeeee eeeeeeeeee Meeeeeeee eeeee eeeeeeee ee eeeee ee Meeeee 88.[‌88‌]

Meeeee 88 Meeeeeeee ee Meeeeeeeeeeeee M[‌88‌]

References