In the laboratory the speed with which RNA polymerase acts can be varied by adjusting the concentrations of the reactants (as Judith Levin and Michael J. Chamberlin of the University of California at Berkeley have shown). As the concentrations are brought closer to equilibrium the enzyme works more slowly and dissipates less energy to copy a given section of DNA, because the ratio of forward to backward steps is smaller.
Although RNA polymerase merely copies information without processing it, it is relatively easy to imagine how a hypothetical chemical Turing machine might work. The tape is a single long backbone molecule to which two types of base, representing the binary 0 and 1, attach at periodic sites. A small additional molecule is attached to the 0 or 1 group at one site along the chain. The position of this additional molecule represents the position of the Turing machine's head. There are several different types of "head molecule," each type representing a different machine state.
The machine's transition rules are represented by enzymes. Each enzyme is capable of catalyzing one particular reaction. The way these enzymes work is best demonstrated by an example.
Suppose the head molecule is type A (indicating that the machine is in state A) and is attached to a 0 base. Also suppose the following transition rule applies: "When the head is in state A and reads a 0, change the 0 to a 1, change state to B and move to 'the right." A molecule of the enzyme representing this rule has a site that fits a type-A head molecule attached to a 1 base. It also has one site that fits a 0 base and one site that fits a B head [see illustration on opposite page).
To achieve the transition, the enzyme molecule first approaches the tape molecule at a location ‘just to the right of the base on which the A head resides. Then it detaches from the tape both the head molecule and the 0 base to which the head was attached, putting in their place a 1 base. Next it attaches a B head to the base that is to the right of the 1 base it has just added to the tape. At this point the transition is complete. The head's original site is changed from a 0 to a 1, the head molecule is now a type B, and it is attached to the base that is one notch to the right of the previous head position.
During the operation of a Brownian Turing machine the tape would have to be immersed in a solution containing many enzyme molecules, as well as extra O's, 1 's, A's and B's. To drive the reaction forward there would have to be some other reaction that cleaned the enzyme molecules of detached heads and bases. The concentrations of the reactants that clean the enzyme molecules represent the force that drives the Turing machine forward. Again we can expend as little energy as we wish simply by driving the machine forward very slowly.
The enzymatic Turing machine would not be error-free. Occasionally a reaction that is not catalyzed by any enzyme might occur; for example, a 0 base could spontaneously detach itself from the backbone molecule and a 1 base could be attached in its place. Similar errors do indeed occur during RNA synthesis.
In principle it would be possible to eliminate errors by building a Brownian Turing machine out of rigid, frictionless clockwork. The clockwork Turing machine involves less idealization than the billiard-ball computer but more than the enzymatic Turing machine. On the one hand, its parts need not be manufactured to perfect tolerances, as the billiard balls would have to be; the parts fit loosely together, and the machine can operate even in the presence of a large amount of thermal noise. Still, its parts must be perfectly rigid and free of static friction, properties not found in any macroscopic body.
Because the machine's parts fit together loosely, they are held in place not by friction but by grooves or notches in neighboring parts. Although each part of the machine is free to jiggle a little, like the pieces of a well-worn wood puzzle, the machine as a whole can only follow one "computational path." That is, the machine's parts interlock in such a way that at any time the machine can make only two kinds of large-scale motion: the motion corresponding to a forward computational step and that corresponding to a backward step.