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Computing Comes to Life

Brian Hayes

The Logic of Life

A digital technology usually starts with Boolean logic gates—devices that operate on signals with two possible values, such as true and false, 1 and 0. An and gate has two or more inputs and one output; the output is true only if all the inputs are true. An or gate is similar except that the output is true if any of the inputs are true. The simplest of all gates is the NOT gate, which takes a single input signal and produces the opposite value as output: true becomes false, and false becomes true.

In electronic circuits, a NOT gate can be made from a single transistor, wired so that a high voltage at the input produces a low voltage at the output, and vice versa. When the gate switches between its two states, it does so abruptly, like a snap-action light switch. It is this sudden, nonlinear response that gives digital devices their resistance to noise and error. Because a gate is either fully on or totally off, a signal can pass through a long chain of gates without degradation.

Are there any biochemical equivalents to transistor gates? As a matter of fact, yes: There are hundreds of candidates. Perhaps the most interesting among them are the mechanisms of genetic control, which switch genes on and off.

The archetypal example of genetic regulation in bacteria is the lac operon of E. coli, first studied in the 1950s by Jacques Monod and François Jacob. The operon is a set of genes and regulatory sequences involved in the metabolism of certain complex sugars, including lactose. The bacterium's preferred nutrient is the simpler sugar glucose, but when glucose is scarce, the cell can make do by living on lactose. The enzymes for digesting lactose are manufactured in quantity only when they are needed—specifically when lactose is present and glucose is absent.

As in the expression of any genes, synthesis of the lac enzymes is a two-stage process. First the DNA is transcribed into messenger RNA by the enzyme RNA polymerase; then the messenger RNA is translated into protein by ribosomes. The process is controlled at the transcription stage. Before the genes can be transcribed, RNA polymerase must bind to the DNA at a special site called a promoter, which is just "upstream" of the genes; then the polymerase must travel along one strand of the double helix, reading off the sequence of nucleotide bases and assembling a complementary strand of messenger RNA. One mechanism of control prevents transcription by physically blocking the progress of the RNA polymerase molecule. The blocking is done by the lac repressor protein, which binds to the DNA downstream of the promoter region and stands in the way of the polymerase.

When lactose enters the bacterial cell, the lac operon is released from this restraint. A metabolite of lactose binds to the lac repressor, changing the protein's shape and thereby causing it to loosen its grip on the DNA. As the repressor protein drifts away, the polymerase is free to march along the strand and transcribe the operon.

The repressor system is only half of the lac control strategy. Even in the presence of lactose, the lac enzymes are synthesized only in trace amounts if glucose is also available in the cell. The reason, it turns out, is that the lac promoter site is a feeble one, which does a poor job of attracting and holding RNA polymerase. To work effectively, the promoter requires an auxiliary molecule called an activator protein, which clamps onto the DNA and makes it more receptive. Glucose causes the activator to fall away from the DNA just as lactose causes the repressor to let go—but the ultimate effect is the opposite. Without the activator, the lac operon lies dormant.

All these tangled interactions of activators and repressors can be simplified by viewing the control elements of the operon as a logic gate. The inputs to the gate are the concentrations of lactose and glucose in the cell's environment. The output of the gate is the production rate of the three lac enzymes. The gate computes the logical function: (lactose AND (NOT glucose)).

Figure 2.Click to Enlarge ImageFigure 1.Click to Enlarge Image

A question remains: Do these biochemical control mechanisms exhibit the on-off, all-or-nothing character of digital circuits? Although the transition between states is never perfectly sharp, the digital approximation is often a good one. A factor that tends to steepen the response curve is the cooperative action of multiple subunits in the regulatory proteins. The lac repressor consists of four subunits, and the lac activator has two. Although the first subunit may be slow in binding to the DNA, subsequent units stick to one another as well as to the DNA, and so the binding goes faster. The net effect is to make the threshold for repression or activation sharper.

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