Team:NTU Taida/M6
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Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate to , the concentration of a substrate S. Its formula is given by </p> | Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate to , the concentration of a substrate S. Its formula is given by </p> | ||
- | <center><img src=" | + | <center><img src="https://static.igem.org/mediawiki/2014/5/58/NTU_Taida_H14.jpg"> </p></center> |
Here, represents the maximum rate achieved by the system, at maximum (saturating) substrate concentrations. The Michaelis constant is the substrate concentration at which the reaction rate is half of .[11]Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions.</p> | Here, represents the maximum rate achieved by the system, at maximum (saturating) substrate concentrations. The Michaelis constant is the substrate concentration at which the reaction rate is half of .[11]Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions.</p> | ||
The mathematical model of the reaction [10] involves an enzyme E binding to a substrate S to form a complex ES, which in turn is converted into a product P and the enzyme. This may be represented schematically as </p> | The mathematical model of the reaction [10] involves an enzyme E binding to a substrate S to form a complex ES, which in turn is converted into a product P and the enzyme. This may be represented schematically as </p> | ||
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where , , and denote the rate constants,[12]and the double arrows between S and ES represent the fact that enzyme-substrate binding is a reversible process.</p> | where , , and denote the rate constants,[12]and the double arrows between S and ES represent the fact that enzyme-substrate binding is a reversible process.</p> | ||
Under certain assumptions – such as the enzyme concentration being much less than the substrate concentration – the rate of product formation is given by | Under certain assumptions – such as the enzyme concentration being much less than the substrate concentration – the rate of product formation is given by | ||
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The reaction rate increases with increasing substrate concentration , asymptotically approaching its maximum rate , attained when all enzyme is bound to substrate. It also follows that , where is the enzyme concentration. , the turnover number, is the maximum number of substrate molecules converted to product per enzyme molecule per second.</p> | The reaction rate increases with increasing substrate concentration , asymptotically approaching its maximum rate , attained when all enzyme is bound to substrate. It also follows that , where is the enzyme concentration. , the turnover number, is the maximum number of substrate molecules converted to product per enzyme molecule per second.</p> | ||
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Hill equation :</p> | Hill equation :</p> | ||
- | <center><img src=" | + | <center><img src="https://static.igem.org/mediawiki/2014/f/f2/NTU_Taida_H17.jpg"> </p></center> |
- | <img src=" | + | <img src="https://static.igem.org/mediawiki/2014/b/b3/NTU_Taida_H18.jpg"> - free (unbound) ligand concentration. |
- | <img src=" | + | <img src="https://static.igem.org/mediawiki/2014/c/ce/NTU_Taida_H19.jpg"> - Apparent dissociation constant derived from the law of mass action (equilibrium constant for dissociation). |
- | <img src=" | + | <img src="https://static.igem.org/mediawiki/2014/1/13/NTU_Taida_H20.jpg">- ligand concentration producing half occupation (ligand concentration occupying half of the binding sites). This is also the microscopic dissociation constant. In recent literature, this constant is sometimes referred to as <img src="https://static.igem.org/mediawiki/2014/3/31/NTU_Taida_H21.jpg"> . |
- | <img src=" | + | <img src="https://static.igem.org/mediawiki/2014/3/31/NTU_Taida_H22.jpg">- Hill coefficient, describing cooperativity (or possibly other biochemical properties, depending on the context in which the Hill equation is being used).</p> |
Taking the reciprocal of both sides, rearranging, inverting again, and then taking the logarithm on both sides of the equation leads to an alternative formulation of the Hill equation:</p> | Taking the reciprocal of both sides, rearranging, inverting again, and then taking the logarithm on both sides of the equation leads to an alternative formulation of the Hill equation:</p> | ||
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When appropriate, the value of the Hill coefficient describes the cooperativity of ligand binding in the following way :</p> | When appropriate, the value of the Hill coefficient describes the cooperativity of ligand binding in the following way :</p> | ||
- | ● <img src=" | + | ● <img src="https://static.igem.org/mediawiki/2014/4/49/NTU_Taida_H24.jpg"> - Positively cooperative binding: Once one ligand molecule is bound to the enzyme, its affinity for other ligand molecules increases.</p> |
- | ● <img src=" | + | ● <img src="https://static.igem.org/mediawiki/2014/3/34/NTU_Taida_H25.jpg"> - Negatively cooperative binding: Once one ligand molecule is bound to the enzyme, its affinity for other ligand molecules decreases.</p> |
- | ● <img src=" | + | ● <img src="https://static.igem.org/mediawiki/2014/a/ab/NTU_Taida_H26.jpg"> - Noncooperative binding: The affinity of the enzyme for a ligand molecule is not dependent on whether or not other ligand molecules are already bound. In this case, the Hill equation (as a relationship between the concentration of a compound adsorbing to binding sites and the fractional occupancy of the binding sites) is equivalent to the Langmuir equation.</p> |
molecule is not dependent on whether or not other ligand molecules are already bound. In this case, the Hill equation (as a relationship between the concentration of a compound adsorbing to binding sites and the fractional occupancy of the binding sites) is equivalent to the Langmuir equation.</p> | molecule is not dependent on whether or not other ligand molecules are already bound. In this case, the Hill equation (as a relationship between the concentration of a compound adsorbing to binding sites and the fractional occupancy of the binding sites) is equivalent to the Langmuir equation.</p> |
Latest revision as of 01:08, 18 October 2014