Según la teoría general de la acción enzimática, de Michaelis-Menten, la enzima (E) se combina en primer lugar de forma reversible con su sustrato formando un complejo enzima-sustrato (ES) en un paso reversible relativamente rápido. El complejo ES se descompone seguidamente en un segundo paso más lento dando la enzima libre y el producto (P) de la reacción:
Podemos definir la velocidad de la reacción como:
Consideración 1:
En condiciones de velocidad inicial![\left [ P \right ]_{t=0}=0](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tPiYowOstyJ8nohqQ1iVYc5yMJ5r-D9HEp2fagJRjvrR4BdQcKtjukbSzY_j45xKL7scbKIqf4JchLbgHife7xjcyxrQT5bDTDICjgbaJ72KD0P7xbJ8H7H_k5v7wOokKUnIKDiPuMkuSbzIB0DDGL0ZNwPzFIyh4wwDESj576aY9MjqvG29Q=s0-d)
y![\left [ S \right ]_{t=x}> > > \left [ P \right ]_{t=x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vDnIhbUyTuho7m8PLCOozNtnlHr6ws33fXFgSYxZLCXDGAXa9dV3LEQnf-0X4isSLIbXxIpvXMoB8BkPrdHpNuQD9pkH0jthcCuC4MOl2ZHIQKWyQ5Iz3TbQKFTL34yeAD0nYIum9AmoJvPLC4ua5DcKcis1ZavZeXbRCW64DH4A2W_e5F1d14S9MjOzBqGjMkNBhuHfkQYWqb5RXezvYtnnCb19gVIkH0RUZTq1sqF9UO3xGI5Cimz7vlDXgdzSZvCwpZF-qP9vWSvSGk0RUGuafAnzHOiEfIrwn3tOg=s0-d)
se puede despreciar la reacción inversa.
![\Rightarrow v_{0}=k_{2}\cdot \left [ ES \right ]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uVsj37vpgHIsbmTgsLrwJRa7qWwYjwD-YOoveDpwmXm4y7WvIRBWXk6iY6miCQG0u5c2ASYH4N6CcyidloGNBelBz8GQ5gjwTzIpsIhPW6-zRHZFI800qWEOQcq8OBjn0Q7hQtME0ILdXVwRdVotmwkL-KT8SrhYOh7c2--cOt3H6fpjoUw0b3WZjfD-dgc5rTLki4m8F1DT2RNl_3rsqJDAsiiG39naEGmrqGKRfp=s0-d)
no se puede conocer!!!
Consideración 2:
![\left [ S \right ]> > > \left [ E \right ]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vpXPN69uVebZ0qSLySQp346fzlMyfhCUjUrKR1qbRZyf64d_bI3nRZi9pbn44O4M8UceMSEYPqCw99pzJQVpF4p_8q5insvmkDQBsmN7zVLSVpjXSAMOuEX0TmhjkycuzRzQL0I76X48iQZWBGDL1p2f80XKV5ATZF41wPOVPBacNlC3yy9SUKKk05JDclOtRv2SNRqAmgy9GIWV2IzHF9d4tjeoj-c5dU7ascqY81i2_DKYDHS8FrIUoTvIlW1ztbNt53I0CW-9Ry=s0-d)
Balance de masa:
es despreciable.
Cinética del estado estacionario:
![\frac{\mathrm{d} \left [ ES \right ]}{\mathrm{d} t}=-\frac{\mathrm{d} \left [ ES \right ]}{\mathrm{d} t}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_s3uw62nELr4-SpNbX8-SE3ayRdcSqHJ5DRD0aG7eTjBBoh_kt4osYRy3yjMgez2kkf4nq-YLDzwIi63S_kOFyhV84brpf5bu3bJBv9hA4jRiRwkurRIU6SwMPfKgU3gnMDQR6T2brA6mXz3Z5MKCDHxUQel7nJIyEBlsRm-WsL20AyBt4cZPPTimB-WOlFVowrOmdmI0FYpzUojJ43aT5uQefBiETqq676dKH55FZBnqsD6eh7drI3Ls1tp_m3VvPVa9axkptH0N10uuxtME3D0Ub9GDRemjuneEXuwsQyJPIMjfyb-Umd5Mixwbrzw8LQCtpDTb7RdoxIKeBS_3W0O1cEaWYEyuVcpdi-S0XJZq6VBvE7WjQi6QNsnLBa3dZ644K4xzhR3NzDZFIorOzcU-2MCg=s0-d)
o:
![\frac{\mathrm{d} \left [ ES \right ]}{\mathrm{d} t}=k_{1}\cdot \left [ E \right ]\cdot \left [ S \right ]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sv4TNKxpoWekjUvgdSJHzSWzKBDy3Yopy3D5U8MCr48OKop9zO7mUCCp2dTFhl-uLSDR_bqsFJ2eOH_N186L0kSM8QvrW5gMMx6YoZeRMNCQvFaG4r_V-pxdWL9_jP28Jnw5mkMf3M0bMR-JN87IRo60lvVQ8R9cf_NtGBkwEW5prefWooQlusab-zT64qFx9oIVc8qbIJ7KsbN-GB8wGYKy2djvqPz1UglSYMHU0ADXupyozxaz4W36ZWxDSBpi8hYndTKR5O9GoI068MvUK3O7McQW6nDMLncYSno8M4Gl2KgdF1tpTs6UTf2nhWnq-GeYEju0sDiGLjNJfSWMiIq3OKMWGxo4DAmUCvm4lWRFJ1x0YbMeeTcga9Kagxul0OX74YBVTpMdxm_U_x0tJaXAIbsAjUL7fs81NvD1EODxJnyVqsACg=s0-d)
![-\frac{\mathrm{d} \left [ ES \right ]}{\mathrm{d} t}=k_{-1}\cdot \left [ ES \right ]+k_{2}\cdot \left [ ES \right ]=\left [ ES \right ]\cdot \left ( k_{-1} +k_{2}\right )](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_s7rZcBAZFBaX9O0h6MRq3Cr9q8eY40EUIL3ext1-21mbFaeRrjMmCRHWjgz0RrMrganjA0sOIFHl6zYXq42uuP94mz4pATZV95OWn3wDhPn3owda2bqsAvXW_VZJE_yVogJHQQs2_x3OOLnGifX8Q80mbG0kDPhFcogWGtoGezsluR92fg_OywGCs2oPwNvTVPEul7RCpFOAlyTXUGN_uIvt4HN2XSgQ1QpDdcvlDwtsGokyUGp0q8neDKeLYhgahC0T4ZjkAGeHHpoFlFvqsHVB6jL2TqFluKKm_LnJxrzJIqZ3iDlyGV341n1pLsEyCBRx7YTP9cB2O5aYU3lvIAsOmx2QLwdkTYeC9eQYQJlzYnvOx4SzZS4Drp6_UFoexbl0uj_H5xVSm964_jEhEWgOByWJ8FDY0yPJHtyQZgK4U-7uRiTzI1fxevvqPpgIBS7vOhJxkBvjtufr4-GaL8RKZ1fW5G48s6_nUdjeoBHoimEZJMlPsbc9ZGQY9oDdnSzmIWjWrXldS4CbVzeiqR8uw3PmN9MF4bA9R7Dj2WQFyIuluK2Cxn6T0pTDmT6UBTxX7d6Az_xXkMGmBMX4t_OKxlDfSpH0_UdhbzJvHeZGTg6jRYQhJ0=s0-d)
Por balance de masa:
![\left [ ES \right ]=\frac{k_{1}\cdot \left [ E \right ]_{T}\cdot\left [ S \right ]}{k_{-1}+k_{2}+k_{1}\cdot \left [ S \right ]}=\frac{k_{1}\cdot \left [ E \right ]_{T}\cdot \left [ S \right ]}{k_{1}\cdot \left \{ \left ( \frac{k_{-1}+k_{2}}{k_{1}} \right ) +\left [ S \right ]\right \}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tUbnwPzMRa3d9Rq4qPs75XZVGXvY8YbZapqD83shBOkOZA3yISGP2o3_JXWTu3jp2-0oXjCJdN8ptKiQmVIvLrrfwPMqs7ha6qWDEFA6GegxK-mhdmNQW7qCaqspC_PVD3YuOPqdpeeLt2UNwLew-NhsKPYmjc6wUz_uYihOc31XSJx0G1eS3ZdCC1Ijgm61yeHNddb_dmwLlRpJIsiv3NA2wmroJ-Xjids9dzOdcnQwjrKgjDbHVmxRSX_8oJAYJcAlaK0feBUTien4-l0uKZNCh73Pr6G71pkM-EQ9u-Pmt13aqykWvWVN6CQfnXyaOS1qrBmTXU5alYONUWul6b1hlQdlHACkLXZNwOIwAWxN370wwVp8jktHao9d4EPkNnApSvJAWHFmZR4JlOVrEMf66uHL-zsG9ZiD-7cdzOlgOn38uwKH1I22hE852nj9C0TFo6UqyGybDnURoPnpDnMR03FwuaNUeFsO-MBm5LAg85giKZCHhFISRxJEY_KTn9cJ1SwG3HpvyrTTXJ388SWmw8Ny_U1gFT3-vgQgc4ZxnsMduGB6gndaUhdl6z3S6907yd-aEDsB-uKT8y0hL4K_Y62xTRQiCpRqSYcF622wDURqK809ki8hlcJoGqBj3fzEfmRAQYcuYaQQh5N_erQXXTvIvEVgpDjtobRpESyqn1zpixQIrTb-OyBtRVbTIER4talMZItZAmf15RbwPBcypSN4PzkAmZJzMDgHPnORsW_nYfLuse00snxhpSzxFRor0IbMm9kdN1cwGveL6t6s8Fmo6UiF6O9uA63l1QZeubfGvdvL9pxvkoFPblS_60N1RUx-YvJU5KAygyNaPvacBNS4uUxDM9lioIcIAhoWBUtHPB2bnd5ur3ibmxCTvc46mJBBybbX1i9URLdHROyTCq7h2XU4aFroOayRN7KYY-pfVd_JoisRbgXK86t0OTEqrAT6D-qahrQSa1Kstl70Pmj1wP5g1WvCHJNnwd-JeaOavHjrmSWbY=s0-d)
![\Rightarrow \left [ ES \right ]=\frac{\left [ E \right ]_{T}\cdot \left [ S \right ]}{\frac{k_{-1}+k_{2}}{k_{1}}+\left [ S \right ]}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_v3TNDz8a5vISScaInPlg16_GgA1CKw3uSgBNOJLU5kA4UI9_wXZ0aro3nKbUUJzxSXUjPHf4S3QJfu0XqCHvtNMk0rSKs4i1Rrx50tt_PdTo04t6E6k4T37CL8vPvkzVNOXXHHGrWWnqMKGSp17y8QpY5wn6VTPcuLSswqht4h5u1Lf5KnVC02BhMP_uqxcQmMvKpYZPjq7-nCUkyR5mKa4tVw98QJx8N-onE2boI0fNf3zcRdMKCiQoDnKMue8KLvhgxh1OSF31gBHPVvUbm2-EuYCxB9ITtugmv8QMLBqT8jMVVT3Tk9AqrWLvEyEspKdjRGXY3FsiUKR7ktqc-STygK3wAf2bhErqogvosPnDvIXCeti-0jyPaCZcAVVS6x94J-m9KvayKnsdilh4NiF2o_0lfArTpyXp25dNMkss-Zm8iIFmojUAsLZNiGNYBZIYDUTmgM2jM0Bsv5MxMMh2iILzFW39_IwiM0V7P4rGLVk7bvT2uYVLu4iF9wGTk=s0-d)
![\Rightarrow \left [ ES \right ]=\frac{\left [ E \right ]_{T}\cdot \left [ S \right ]}{K_{M}+\left [ S \right ]}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tBEyfZ1B4KsKXv1IWGxAnKDE_jXiXilBOYOfOUH7qKillgkh_Gpt0QFrN2AjjkDGjoFOW62KcPSvFJ9wePA01XgjB0kpObO7rV21K3kM9xEYCCbTW0LhTJkK_Ons8GTuLk7WsFVNj6BV3FRPvtRxbMabHYvEjGVXdxur8IqkQhe3JXeLSLwb9kZVgVzvuYzrDhkw6lviV0Sy3ksyfWTTN0pvN7ZEOXHNmv1m2YZLW5PBzVbpxEZMPIUf51KhhxfgFw20ALYX4n94PJa81MWfkgMhh2ImgD-g1WTVWxIetS6EU_vkXs2pzvoEhxw0uDhV1pFCm4-DOPDWDuDX9hRNV3MOCqS9QJE_aGa_JNd-cu41zgQaygCkpjhgR2e9HuU-62Fz6Ta203IRC4JoaQ-rYRmMYpCvuZSr7pAbYWMGpE7cPSD8nozbNu5Fohur0LJX06AuaNapsB994=s0-d)
De esta manera es posible calcular:
![v_{0}=k_{2}\cdot \left [ ES \right ]=\frac{k_{2}\cdot \left [ E \right ]_{T}\cdot \left [ S \right ]}{K_{M}+\left [ S \right ]}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vM3pW_utvHAw1T_XIN-_lsxbWPuWEdK1PWB49FeaJOnaTgNffGPwT4gwFKTfvzk1TKrmaztnUI_lJFQjDpHx2a_CFyIUlhG4fuyVFNaeEdln_wlqP0LJnVhkd4mBzSiy0PTvhvSc7J_nyQjQMEW1MulcOlKVAsLChB0DUyHHpGVajnZEfZZ97zhFlhPVI8gOWu6uPGH1OTLxpj50m0YwNEnzkhGOE9hgrSGSocNV0QQ5IzWUnRJ00eeJ3KhgBXXj1cCDtCr4VesZElEzjxs5zoTcaS0U23TGksJ4BOMB8RGkxs8_GN52v3ZbjIOth-kp-VaRN7tJExG9bxIju4FrtgIcIQXDNSRmhu4vZLi1LhddZGKhvLjOwtKy-AM0caQhySTLbM181ZgAneL61m6A-gwlWvvqk5RYFsCNr16po2Nzre4bx411jEaLOKhsMzIASDqrARhBeIFLkOss-gNz4gFd0yrfrbS2TnCD8mDrmZzh3KK8U3iym8mcEyfUY=s0-d)
entonces podemos definir![v_{m\acute{a}x}=k_{2}\cdot\left[E\right]_{T}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t5Ph2Rkkt6-r85MkiJDWEw9n-Oemt-Y2l5AmK2RMTNA8XKuqunKoXXP3Q8x07WH550e5dEd499U5h6IXFm390mSEk4AI3ERh3NWt8PCr9i3ocrS0JuqZYQfIigdZGxjVDUefMXX8OYfY5fqkBpvczTXYnoAd12LEVFnjI4eIHPSIiMSQb5f8kr32QU83Mkbg=s0-d)
Dando así la ecuación de Michaelis-Menten.
![v_{0}=\frac{v_{m\acute{a}x}\cdot\left[S\right]}{K_{M}+\left[S\right]}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uOGpImQRlXVVrRCmumCYMXsQF924113NIA5WeNRnY_JmAtNbdhuNG4jZazabTX2A72mSNn4-d4ReVFGJ6MTV-J8qhlh1iGl2mZkidN66xxgkRWdDpkIrMAOPXkZOIv6U0SBiB0ulwQ8GUDmKUtmfi3bQWQHnR6AkPzbU4vM3Bb65w2i9vyjUC5vVXL_uKegvBUCTXEEp-0uA389ve3zlyQ1iOFxqn_6WRmbmCIGccIYWh53vpnyP1Ajv4q=s0-d)
La ecuación de Michaelis-Menten es la ecuación de velocidad de una reacción catalizada enzimáticamente con un sustrato.
En condiciones de velocidad inicial
y
Consideración 2:
Balance de masa:
Cinética del estado estacionario:
o:
Por balance de masa:
Constante de Michaelis:
De esta manera es posible calcular:
Dado que la velocidad máxima se obtendrá cuando la enzima está saturada, es decir cuando [ES]=[E]T
entonces podemos definir
Dando así la ecuación de Michaelis-Menten.
La ecuación de Michaelis-Menten es la ecuación de velocidad de una reacción catalizada enzimáticamente con un sustrato.
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