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s 1 j X 1 + s 2 j X 2 + s N j X N k j   r 1 j X 1 +   r 2 j X 2 + + r N j X N , {\displaystyle s_{1j}{\ce {X}}_{1}+s_{2j}{\ce {X}}_{2}\ldots +s_{Nj}{\ce {X}}_{N}{\ce {->[k_{j}]}}\ r_{1j}{\ce {X}}_{1}+\ r_{2j}{\ce {X}}_{2}+\ldots +r_{Nj}{\ce {X}}_{N},} ‚±‚ê‚ͤãŽ®‚Æ“¯’l‚ȉºŽ®‚Å•\‚³‚ê‚邱‚Æ‚à‘½‚¢¡

i = 1 N s i j X i k j i = 1 N   r i j X i . {\displaystyle \sum _{i=1}^{N}s_{ij}{\ce {X}}_{i}{\ce {->[k_{j}]}}\sum _{i=1}^{N}\ r_{ij}{\ce {X}}_{i}.} ‚±‚±‚Å

j {\displaystyle j} ‚Í1‚©‚ç‚Ü‚Å‚Ì”½‰ž‚̔ԍ†¡‚͔Ԗڂ̉»ŠwŽí¡‚͔Ԗڂ̔½‰ž‚Ì‘¬“x’萔‚Æ‚Í”½‰žŽ®‚É‚¨‚¯‚锽‰ž•¨‚¨‚æ‚ѐ¶¬•¨‚ÌŒW”‚±‚Ì”½‰ž‚Ì”½‰ž‘¬“x‚͉»Šw•½t‚Ì–@‘¥‚©‚琄‘ª‚³‚ê‚é¡

f j ( [ X ] ) = k j z = 1 N [ X z ] s z j {\displaystyle f_{j}([{\vec {\ce {X}}}])=k_{j}\prod _{z=1}^{N}[{\ce {X}}_{z}]^{s_{zj}}} ‚±‚ê‚Í’PˆÊŽžŠÔ¥’PˆÊ‘̐ς ‚½‚è‚Ì•¨Ž¿‚̕ω»—Ê‚Å•\‚³‚ê‚é¡‚±‚±‚Ť‚Í”Z“x‚ÌÍÞ¸Äقł ‚é¡‚±‚±‚Ť‚±‚ÌŽ®‚ª’è‹`‚³‚ê‚锽‰ž‚Í‘f”½‰ž‚Å‚ ‚鎖‚É’ˆÓ‚·‚é¡

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2•ªŽq‚Ì”½‰ž‚Å‚Í2‚‚̂ɂ‚¢‚Ä‚ª¬‚è—§‚¡‚Ü‚½“ñ—ʉ»‚Å‚Í‚ª‚ ‚é1‚‚̂ɂ‚¢‚Ь‚è—§‚¡‚»‚ꂼ‚ê‚ɂ‚¢‚ÄŽŸ‚̂悤‚É‹c˜_‚³‚ê‚é¡‚±‚ÌŽž¤‚»‚ꂼ‚ê‚Ì”½‰ž‚ɂ‚¢‚Ä”½‰ž‚Ì—Ê“IŠÖŒW‚ɂ‚¢‚Ă̍s—ñistoichiometric matrixj‚ð’è‹`‚·‚邱‚Æ‚ª‚Å‚«‚é¡

S i j = r i j s i j , {\displaystyle S_{ij}=r_{ij}-s_{ij},} ‚±‚ê‚͔Ԗڂ̔½‰ž‚ɂ‚¢‚Ä‘¶Ý‚·‚鐳–¡‚Ì‚Ì•¨Ž¿—Ê‚ð•\‚·¡‚±‚ÌŽž¤”½‰ž‘¬“xŽ®‚͈ȉº‚̂悤‚È‚æ‚èˆê”Ê“I‚ÈŒ`‚ɏ‘‚«’¼‚·‚±‚Æ‚ª‚Å‚«‚é¡

d [ X i ] d t = j = 1 R S i j f j ( [ X ] ) . {\displaystyle {\frac {d[{\ce {X}}_{i}]}{dt}}=\sum _{j=1}^{R}S_{ij}f_{j}([{\vec {\ce {X}}}]).} ‚±‚±‚Ť‚±‚ê‚Í”½‰ž‚Ì—Ê“IŠÖŒW‚ð•\‚·s—ñ‚Æ”½‰ž‘¬“x‚̊֐”‚̐ςł ‚鎖‚É’ˆÓ‚·‚é¡

Œn“à‚Å‹N‚±‚Á‚Ä‚¢‚锽‰ž‚ª‰Â‹t”½‰ž‚Ì‚Ý‚Å‚ ‚褔½‰ž‚ª•½tó‘Ô‚É‚ ‚éê‡¤‚±‚Ì•û’öŽ®‚É‚ÍŠÈ’P‚È‰ð‚ª‘¶Ý‚·‚顁ij‚±‚̏ꍇ«”½‰ž‚Æ‹t”½‰ž‚Ì”½‰ž‘¬“x‚Í“™‚µ‚¢‚̂ŤÚ×’ނ荇‚¢‚ª¬‚è—§‚Á‚Ä‚¢‚é¡‚½‚¾‚µ¤Ú×’ނ荇‚¢‚Í”½‰ž‚Ì—Ê“Is—ñ‚݂̂ɂ‚¢‚Ь‚è—§‚«Ž¿‚Å‚ ‚褔½‰ž‘¬“xŠÖ”‚ɂ͈ˑ¶‚µ‚È‚¢¡Ú×’ނ荇‚¢‚ª¬‚è—§‚½‚È‚¢ê‡‚ɂ‚¢‚Ăͤ‘ãŽÓŒo˜H‚ð—‰ð‚·‚é‚½‚ß‚ÉŠJ”­‚³‚ꂽ—¬‘¬‹Ït‰ðÍ‚É‚æ‚Á‚ÄŒ¤‹†‚³‚ê‚Ä‚¢‚é¡[11][12]

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