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The electric potential across cell membranes is of the order of 10 to 250 mV, which corresponds to a field intensity of 20 to 500 kV/cm. Under such a strong field, molecules will behave quite differently than they will under the zero field condition. Ion pairs will dissociate, dipoles will orient, molecules will be electronically and automatically polarized, equilibria between different conformers of a protein will be shifted, etc. [16,17]. There are two geometric situations under which these changes can take place. The first is where all molecules and ions freely diffuse. The second is when they are fixed relative to the field direction. The first situation is represented by a reaction in an homogeneous aqueous solution. The field effect on the rapidly tumbling molecule is generally small and has been discussed elsewhere [12,16,17]. Here we will focus on the second situation which is more relevant for dealing with effects of an electric field on a membrane protein. Let us start by considering a general enzyme catalytic reaction.
Cyclic process of enzyme catalysis
An enzyme catalytic process is a cyclic reaction because the enzyme is recycled at each turnover. A cyclic process will respond to a periodic driving force with which the enzyme can interact. As a result of this interaction, the enzyme will oscillate between its different conformational states. This phenomenon has been shown to have an implication in cellular membrane processes. To examine the cyclic behavior of an enzyme, we will consider the simple Michaelis-Menten mechanism (scheme 1 of Fig. 1). The enzyme bonds to the substrate to form an enzyme-substrate complex.
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{Fig. 1. Cyclic enzyme catalytic process. Many membrane processes mediated by receptors and enzymes exhibit kinetic characteristics similar to the {?-missing} of a Michaelis-Menten enzyme. Such an enzyme is susceptible to periodic perturbation. This paper considers how oscillating electric fields can interact with membrane ATPases and in so doing induce enzyme conformational oscillations, thus allowing utilization of the binding energy of ligands for catalyzing endergonic reactions. See text for details.}
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The product is then released and the initial enzyme state is regenerated when the complex dissociates. The driving force of this reaction is the negative free energy of the S to P conversion. In fact, with a non-reversible step at the product releasing step, the reaction is implied to proceed to the left even if the free energy has a positive sign. Enzyme recycling has a specific rate, given by the turnover rate of the Michaelis-Menten mechanism. Generally, most investigators agree that there is another state preceding the formation of the product, namely the enzyme-product complex, as shown in scheme 2. If the two reversible steps are much faster than the dissociation of the enzyme- product complex, the kinetics of scheme 2 will be indistinguishable from that of scheme 1, and scheme 2 is in essence a Michaelis-Menten mechanism. In the third scheme, we simply rewrite the second scheme in a more consistent manner. It becomes a cyclic mechanism. Again, the reaction is driven by the negative free energy of the S to P conversion, although the description of the process is inherently unidirectional since it is shown to proceed only in the clockwise direction. To be more precise, the enzyme state which favors the binding substrate must be different from the state which favors the binding of the product state. A distinction between E(1) and E(2) is necessary. The Michaelis-Menten mechanism of scheme 1 is now more generally written as scheme 4. However, scheme 4 has an inconsistency. We all accept that without an additional
