PENTAGON OSCILLATING ELECTRIC FIELDS (FREE ENERGY 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

PENTAGON OSCILLATING ELECTRIC FIELDS (FREE ENERGY 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

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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.} .

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

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free energy source an enzyme can only catalyze a reaction towards but not against the equilibrium. If the product dissociation step is thought irreversible, then whether the S to P conversion is energetically favorable or not, the reaction will proceed clockwise anyway. We know from our experience with hundreds of enzymes that this is not the case. The inconsistency can easily be be removed by writing a reversible product dissociation step. Now the reaction becomes scheme 5. Scheme 5 has been used to describe many membrane transport and energy transducing processes. The reaction of scheme 5 can proceed clockwise or counter-clockwise depending on the sign of the free energy of the S to P conversion, clockwise if (delta)G is negative and counter-clockwise if it is positive. More importantly, when a cell membrane is involved this scheme represents an efficient mechanism for energy and signal transductions as we shall see later; yet, the enzyme E is basically a Michaelis-Menten enzyme. An external energy source can be coupled to this scheme so that enzyme can catalyze a reaction against its chemical potential gradient. Scheme 5 has a characteristic frequency. Only an oscillating driving force the frequency of which matches this charateristic frequency will be effective in propelling the “catalytic wheel” of scheme 5, as will be discussed more explicitly in the following sections

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