Lecture # 3, 4 – Selecting a Catalyst (Non-Kinetic Parameters), Review of Enzyme Kinetics, Selectivity, pH and Temperature Effects

10.492 - Integrated Chemical Engineering (ICE) Topics: Biocatalysis MIT Chemical Engineering Department Instructor: Professor Kristala Prather Fall 2004 Lecture # 3, 4 – Selecting a Catalyst (Non-Kinetic Parameters), Review of Enzyme Kinetics, Selectivity, pH and Temperature Effects 1. Selecting an enzyme catalyst Now that we’ve discussed the various enzyme classes and talked a bit about specificity, the question becomes how do we determine if an enzyme is appropriate to use as our catalyst? For a given type of reaction, it’s not enough to know that we need a lipase or a protease from the hydrolase family, we need to identify one or two enzymes to carry forward for development. And even if we can narrow down the exact EC number, enzymes with the same function but from different sources will have different reaction characteristics against a particular substrate. For design purposes, we will need to know the kinetic parameters to size a reactor and set the process cycle time. But for the initial selection process, we can choose an enzyme based on non-kinetic characteristics. By looking at several candidate enzymes, we can screen to determine the best choice of enzyme to use. To set up our screen, we can put together a set of reactions that are identical except for the choice of catalyst. (Note that to be fair, the concentration of catalyst in each reaction should be the same.) We then fix the reaction time and at the end of this short batch cycle, we can take a sample and measure the concentrations of substrate and products. From these measurements, we can determine the following: (1.1) Conversion = X = S0 − S f S0 × 100% = ∑P i ( usu . R , S ) S0 × 100% (1.2) Yield Pi = Pi × 100% for each product, and if the products are chiral, S0 (1.3) EE ( R ) = R−S × 100% R+S We can look at the conversion to get a sense of the kinetics, since enzymes that “work” faster will have converted more substrate in this fixed unit of time. We look at the EE to get a sense of the enantioselectivity/specificity. Given these two parameters, how do you choose an enzyme to take forward? While the kinetics are important for an efficient process, these can often be optimized by adjusting the reaction conditions (eg, pH, temperature, co-solvents, etc.). Thus, we can use our basic engineering knowledge for optimization to get the fastest reaction. What is much more difficult to control is the Dr. Kristala L. Jones Prather, Copyright 2004. MIT Department of Chemical Engineering Lecture #3, p.2 selectivity. This is more likely to require a more complicated biological optimization rather than our standard physico-chemical based engineering optimization. So, all things being equal, we would like an enzyme to deliver the highest EE material possible, while also achieving “good” conversions in the initial phase. The goal of process development is to then make that good conversion better. 2. Michaelis-Menten kinetics As with standard chemical reactions, biocatalytic reactions also have characteristic kinetics and reaction rates based on the reaction equation. As a review, consider the most commonly followed reaction kinetics, Michaelis-Menten kinetics. Start with the following equation for the reaction: k1 k2 (1.1) E + S ⇔ E ⋅ S ⎯⎯→ E+P k-1 This equation assumes that the binding of substrate and enzyme is a reversible step, and that product release from the enzyme is essentially instantaneous (not kinetically limited). Stoichiometric rate equations can be written for the substrate, enzyme, enzyme-substrate complex and product species as follows: (1.2) v = (1.3) − d [ P] = k2 [E ⋅ S ] dt d [S ] = k1 [ E ][ S ] − k −1 [ E ⋅ S ] dt (1.4) d [E ] = −k1 [ E ][ S ] + k −1 [ E ⋅ S ] + k 2 [ E ][ P ] dt (1.5) d [E ⋅ S ] = k1 [ E ][ S ] − k −1 [ E ⋅ S ] − k 2 [ E ⋅ S ] dt Since the amount of enzyme present is small relative to the substrate concentration (that’s why it’s a catalyst!), we can assume that Equation (5) is ~ 0. This is the quasi-steady state approximate. Then rearrange this equation: (1.6) k1 [ E ][ S ] = ( k −1 + k 2 )[ E ⋅ S ] ⇒ [ E ⋅ S ] = k1 [ E ][ S ] ( k −1 + k 2 ) Now look at the mass balance for total (observable) enzyme – Lecture #3, p.3 (1.7) [ E 0 ] = [ E ] + [ E ⋅ S ] Note that we know the initial charge of enzyme, E0 Plugging back into Equation (6), we get the following expression: (1.8) [E ⋅ S ] = k1 k1 k1 ([E0 ] − [E ⋅ S ])[S ] = [E 0 ][S ] − [S ][E ⋅ S ] (k −1 + k 2 ) (k −1 + k 2 ) (k −1 + k 2 ) k1 [E0 ][S ] [E0 ][S ] (k −1 + k 2 ) = (1.9) [E ⋅ S ] = k1 (k −1 + k 2 ) + [S ] 1+ [S] k1 (k −1 + k 2 ) Finally, plug back into Equation (2) to obtain the following equation: (1.10) v= k [E ][S ] Vmax [S ] k 2 [E0 ][S ] = cat 0 = (k −1 + k 2 ) K + [S ] K M + [S ] M + [S ] k1 This is the classic Michaelis-Menten rate equation, where the first order rate constant, kcat is k2, Vmax is the product of this value and the enzyme concentration, and KM, the Michaelis constant is a mixture of the rate constants that describes the formation and dissociation of the enzyme-substrate complex. This gives a sense of the affinity of the enzyme for the substrate. Note that when [S]>>Km (small Km = high affinity), the reaction kinetics are first-order with respect to the enzyme concentration, and equal to the max rate Vmax. When [S]<