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Logical Operations and Computation by Molecular Machines

All molecular machines perform logical operations. For example, if one strand of DNA contains 5' TAC 3', then a complete and correct hybridization operation requires that the complementary strand contain 3' A $\cal{AND}$ T $\cal{AND}$ G 5'. Likewise the restriction enzyme EcoRI cuts DNA only with the pattern 5' G $\cal{AND}$ A $\cal{AND}$ A $\cal{AND}$ T $\cal{AND}$ T $\cal{AND}$ C 3'while other restriction enzymes will bind to only one DNA pattern $\cal{OR}$ another [Smith, 1979,Roberts, 1989], and the lac repressor protein will bind the operator only if it is $\cal{NOT}$ also binding an inducer [Watson et al., 1987]. Any logical function, including $\cal{OR}$, addition, and the other algebraic operations, can be constructed entirely from$\cal{AND}$ and $\cal{NOT}$ [Wait, 1967,Gersting, 1986,Schilling et al., 1989]. According to the channel capacity theorem [Shannon, 1949,Schneider, 1991] even operations performed by individual molecules can be precise and almost error free.

Bennett and Landauer [Bennett, 1987,Landauer, 1988] have proposed that it is not necessary to dissipate energy in order to perform computations. We can show that this is correct by using examples from molecular biology. For example, EcoRI effectively performs Boolean logic every time it binds to DNA. Since any computation can be reduced to Boolean operations, EcoRI will do arbitrarily large amounts of ``computation'' when it is non-specifically bound to a DNA that does not contain its binding sites. (The result of the computation in this case is FALSE since some of the bases do not match the required pattern.) However, EcoRI must dissipate energy in order to bind at GAATTC. Therefore each completed operation (``output'') performed by a molecular machine in the presence of thermal noise must be accompanied by a dissipation of energy, according to the Second Law of Thermodynamics, equation (15). That is, although computation does not have an energetic bound, output does. This distinction was recognized by Feynman [Feynman, 1987]. Recognizing that output costs at least ${\cal E}_{min}$ joules per bit while computation itself is energetically unlimited resolves a long standing dispute [Bennett, 1973,Bennett, 1982,Robinson, 1984,Porod et al., 1984,,Mayer et al., 1985,Hastings & Waner, 1985,Bennett, 1987,,Keyes, 1989].