Predefined Kinetic Types
Generic  


This is the most simple kinetic type and the one that is assigned to any newly defined reaction by default. The rate of reaction is not sensitive to any chemical species and therefore is constant. This is also know as a zeroorder reaction or a pump. It has only one kinetic constant which has units of flux:




This is the plain, uncatalysed, kynetic type. In the irreversible case there is only one rate constant, the reversible case has two (one for the forward and one for the reverse directions):




This is the plain, uncatalysed, kynetic type. In the irreversible case there is only one rate constant, the reversible case has two (one for the forward and one for the reverse directions):


One Substrate/One Product  


This is the classical enzyme kinetic mechanism. One substrate is converted to one product (isomerisation), the process is irreversible and has two kinetic constants:




This is the reversible equivalent of the HenriMichaelisMenten type. It was first derived by Haldane and is also known as Haldane kinetics. The kinetic equation is:
So, when you assign values for the four kinetic constants you are setting the value of the equilibrium constant. Note that when you do scans of any of the four parameters and you do not want to change the equilibrium constant, you must adjust one other parameter for this purpose. You may want to use instead the equivalent Uni Uni type which uses the equilibrium constant explicitly in the equation. 



This is an enzyme catalysed kinetic type with one substrate and one product. It is the same as the Reversible MichaelisMenten type but makes use of the equilibrium constant explicitly in the kinetic equation. It is the reversible equivalent of the HenriMichaelisMenten type. The kinetic equation is:




This is an enzyme catalysed kinetic type with one substrate and one product. Unlike the Reversible MichaelisMenten or the Uni Uni types, this mechanism assumes that the free enzyme form that results from the release of P is not in the same form as the one that binds S. Some permeases follow this mechanism, and the isomerisation of the enzyme after releasing the product (the transported metabolite on the other side of the membrane) is thought to be a reorientation of the protein in the membrane. Note that if you assign this kinetic type to a permease reaction you must set the Keq parameter to 1 (as the substrate is the same molecule as the product). The kinetic equation is:




This is the classical "sigmoidal" enzyme kinetic mechanism. The reaction has one only substrate that binds cooperatively to the enzyme. If the Hill coefficient is greater than 1, the rate shows positive cooperativity (one molecule of S bound facilitates another molecule of S to bind to the enzyme)  the shape of the curve is a sigmoid; if the Hill coefficient is smaller than 1 then the rate shows negative cooperativity (one molecule of S bound makes the binding of another molecule of S to the enzyme harder)  the shape of the curve is a false (but similar to) hyperbola. The kinetic equation is:




This is the reversible equivalent of Hill kinetics. Both the substrate and the product bind cooperatively to the enzyme. If the Hill coefficient (h) is greater than 1, the rate shows positive cooperativity (one molecule of S bound facilitates another molecule of S to bind to the enzyme, the same with P)  the shape of the curve is a sigmoid; if the Hill coefficient is smaller than 1 then the rate shows negative cooperativity (one molecule of S bound makes the binding of another molecule of S to the enzyme harder, the same with P)  the shape of the curve is a false (but similar to) hyperbola. The equation, derived by Hofmeyr and CornishBowden (Comput. Appl. Biosci. 13, 377  385 (1997)) is:




This is Reversible Hill kinetics with 1 modifier. The modifier can be either a positive or negative modulator depending on the value of (positive for values larger than 1, negative for values smaller than 1; no effect if exactly 1). reflects the effect of the presence of S and P on the binding of M (the modifier). The equation, derived by Hofmeyr and CornishBowden (Comput. Appl. Biosci. 13, 377  385 (1997)), is:




This is Reversible Hill kinetics with 2 modifiers. The modifiers can be either positive or negative modulators depending on the values of and (positive for values larger than 1, negative for values smaller than 1; no effect if exactly 1). This type assumes that the two modifiers can bind at separate sites, with possible effects on each other (binding of one of them facilitating or not the binding of the other). The synergetic effects of the two modifiers depend on the parameter (if unity then they are independent; if zero they compete for the same binding site). and reflect the effect of the presence of S and P on the binding of Ma or Mb (the modifiers). The equation, derived by Hofmeyr and CornishBowden (Comput. Appl. Biosci. 13, 377  385 (1997)), is:




This enzyme kinetic type, available both for irreversible and reversible reactions, has one substrate and one product. Along with its normal effect of enhancing the rate of reaction, the substrate also acts as an inhibitor. Mechanistically this can be achieved if the enzyme contains a second (nonactive) binding site for the substrate. The inhibition constant is then the dissociation constant for this binding site. Note that at high substrate concentrations the rate decreases with increased substrate concentration which then acts as a negative feedforward effect (contrary to the normal positive feedforward of mass action). The equations reduce to the HenriMichaelisMenten or reversible MichaelisMenten equations in the limit as Ki approaches infinity. The kinetic equation for the irreversible case is:




The kinetic equation for the reversible case is:




This enzyme kinetic type, available only for irreversible reactions, has one substrate and one product. Along with the usual activesite, the enzyme has a another binding site for the substrate. When this site is occupied the enzyme becomes activated. Binding of the substrate to the two sites can occur in any order (random order mechanism). This kinetic type produces sigmoidal kinetics. The kinetic equation is:




This enzyme kinetic type, available both for irreversible and reversible reactions, has one substrate, one product and one modifier (inhibitor). The inhibitor is competitive with the substrate, i.e. its effect can be reversed by elevating the substrate concentration. Mechanistically, this can be achieved if the inhibitor binds reversibly to the substrate binding site, thus blocking it. The inhibitor has the effect of increasing the apparent Km. The equations reduce to the HenriMichaelisMenten or reversible MichaelisMenten equations in the limit as I approaches zero (or Ki approaches infinity). The kinetic equation for the irreversible case is:




The kinetic equation for the reversible case is:




This enzyme kinetic type, available both for irreversible and reversible reactions, has one substrate, one product and one modifier (inhibitor). The inhibitor is noncompetitive with the substrate, i.e. its effect is only to decrease the apparent limiting rate. Mechanistically, this can be achieved if the inhibitor and substrate bind the enzyme independently of each other. The inhibition cannot be totally overcome by elevating the substrate conc. and the effect is as if less enzyme was present. The equations reduce to the HenriMichaelisMenten or reversible MichaelisMenten equations in the limit as I approaches zero (or Ki approaches infinity). The kinetic equation for the irreversible case is:




The kinetic equation for the reversible case is:




This enzyme kinetic type, available both for irreversible and reversible reactions, has one substrate, one product and one modifier (inhibitor). The inhibitor is uncompetitive with the substrate, i.e. its effect is to decrease the apparent limiting rate and the Km by the same extent (thus it is a special case of mixed inhibition. Mechanistically, this can be achieved if the inhibitor can only bind to the enzyme after the substrate and the ternary complex ESI is unreactive. The inhibition is more severe at high substrate concentration. The equations reduce to the HenriMichaelisMenten or reversible MichaelisMenten equations in the limit as I approaches zero (or Ki approaches infinity). The kinetic equation for the irreversible case is:




The kinetic equation for the reversible case is:




This enzyme kinetic type, available both for irreversible and reversible reactions, has one substrate, one product and one modifier (inhibitor). The inhibitor modifies the rate through two effects: competitive and noncompetitive. Therefore both the apparent limiting rate and apparent Michaelis constant are affected by the presence of the inhibitor. Mechanistically, this can be achieved if the inhibitor is capable of binding both to the free enzyme and enzymesubstrate complex, the ternary complex enzymesubstrateinhibitor is not reactive. The equations reduce to the HenriMichaelisMenten or reversible MichaelisMenten equations in the limit as I approaches zero (or Kis and Kic approach infinity simultaneously). The kinetic equation for the irreversible case is:




The kinetic equation for the reversible case is:




This enzyme kinetic type, available both for irreversible and reversible reactions, has one substrate, one product and one modifier (activator). The activator enhances the rate of reaction by decreasing the apparent Michaelis constant. Mechanistically, this can be achieved if the enzyme needs to bind the activator before it can bind the substrate (essential activation); clearly, without activator the reaction does not take place. This kinetic type is the activation equivalent of competitive inhibition. The equations reduce to the HenriMichaelisMenten or reversible MichaelisMenten equations in the limit as A approaches infinity. The kinetic equation for the irreversible case is:
For reasons of performace and to avoid divisions by zero, the equation actually used in the program is:




The kinetic equation for the reversible case is:
For reasons of performace and to avoid divisions by zero, the equation actually used in the program is:




This enzyme kinetic type, available both for irreversible and reversible reactions, has one substrate, one product and one modifier (activator). The activator enhances the rate of reaction by increasing the apparent limiting rate Mechanistically, this can be achieved if the enzymesubstrate complex needs to bind the activator to be reactive (essential activation); clearly, without activator the reaction does not take place. This kinetic type is the activation equivalent of noncompetitive inhibition. The equations reduce to the HenriMichaelisMenten or reversible MichaelisMenten equations in the limit as A approaches infinity. The kinetic equation for the irreversible case is:
For reasons of performace and to avoid divisions by zero, the equation actually used in the program is:




The kinetic equation for the reversible case is:
For reasons of performace and to avoid divisions by zero, the equation actually used in the program is:




This enzyme kinetic type, available both for irreversible and reversible reactions, has one substrate, one product and one modifier (activator). The activator enhances the rate of reaction through two effects: specific and catalytic. Therefore the activator acts by increasing the apparent limiting rate and decreasing apparent Michaelis constant. Mechanistically, this can be achieved if the activator is capable of binding both to the free enzyme and enzymesubstrate complex, the substrate bind only the enzymeactivator complex and only the ternary complex enzymeactivatorsubstrate is reactive. The activator is essential for the reaction to proceed. The equations reduce to the HenriMichaelisMenten or reversible MichaelisMenten equations in the limit as A approaches infinity. The kinetic equation for the irreversible case is:
For reasons of performace and to avoid divisions by zero, the equation actually used in the program is:




The kinetic equation for the reversible case is:
For reasons of performace and to avoid divisions by zero, the equation actually used in the program is:




This enzyme kinetic type, available both for irreversible and reversible reactions, has one substrate, one product and one modifier. The effect of the modifier depends on the values of the kinetic connstants and it can act either as an inhibitor or activator (even as both depending on substrate concentration). Mechanistically, this can be achieved if the modifier can bind to all forms of the enzyme and if all enzymesubstrate complexes are reactive, the values of a and b. The equations reduce to the HenriMichaelisMenten or reversible MichaelisMenten equations in the limit as M approaches zero. The kinetic equation for the irreversible case is:




The kinetic equation for the reversible case is:




These two mechanisms have one inhibitor that reduces the rate of reaction with a Hill coefficient different from one.Two mechanisms are considered here: the MWC (irreversible) and an empirical one (reversible). Irreversible (MWC): this is based on the MonodWymanChangeaux model (Monod et al. (1965) J. Molec. Biol. 12, 88118). The enzyme is assumed to be a symetrical polymer of n monomers that exists in two forms, one active (R) and one inactive (T), that are in equilibrium. The inhibitor binds the inactive form and thus reduces the amount of the active one decreasing the rate. The effect of the inhibitor is also to change the shape of the curve of rate versus concentration of substrate. The equation for the rate of reaction is:




Reversible (empirical): this equation is based on the reversible MichaelisMenten with a competitive inhibitor, where in this case the inhibitor acts with a Hill coefficient not necessarily unity. This is an empirical equation and is maintained for compatibility with previous versions. You should probably use the Reversible Hill kinetics with 1 modifier. The equation for the rate of reaction is:


Multireactants  


This is an enzyme catalysed reaction with one substrate and two products. The products are released from the enzyme in ordered fashion: P first then Q. The kinetic equation is:




This is an enzyme catalysed reaction with two substrates and one product. The substrates bind to the enzyme in ordered fashion: A first then B. The kinetic equation is:




This is an enzyme catalysed reaction with two substrates and two products. The substrates bind to the enzyme in ordered fashion (A first, then B), and the products are released from the enzyme also in ordered fashion (P first, then Q). This is the mechanism followed by most NADH dehydrogenases. The kinetic equation is:




This is an enzyme catalysed reaction with two substrates and two products. The substrates and products bind to the enzyme in an alternate way: A binds first, then P is released, then B (the second substrate) binds and finally Q is released. This is the mechanism followed by most transaminases.The kinetic equation is:




This is an enzyme catalysed reaction with two substrates and one product. If the concentration of one substrate, known as the constant substrate, is held constant, while that of the other, known as the variable substrate, is varied, the rate is of the form of the MichaelisMenten equation in terms of the variable substrate. The kinetic equation is:
