1.4 Pertinent Molecular Properties

The trade-off principle asserts that systems with nonprogrammable structure-function relations are capable of implementing transforms that are too complex to embody in general-purpose (programmable) architectures. The physical dynamics of such systems, suitably interpreted, effectuates the computation. Conceivably many types of physical dynamics could be utilized in this manner. Macromolecules afford a particularly powerful combination of properties (see table 1.1).

Table 1.1: Computationally important properties of macromolecules
Property	Draws on	Confers

Folded shape	Long flexible chains, weak bonding, rotation around single bonds	Specificity, self-assembly
Conformational dynamics	Folded shape	Milieu sensitivity, allosteric control
Well-defined ground state	Individual molecules (not statistical ensembles)	Precisely duplicatable nonlinearity, specific shape
Brownian motion	Specific shape, low mass, heat bath	Cost-free search
High evolvability	Combinatorial variety, high dimensionality	Diverse repertoire of specialized functions
Specificity with speed	Defined shape, Brownian motion	Low dissipation pattern recognition
Supramolecular structure	Self-assembly, free energy minimization	Rich, extended 3-D architecture
Diverse specificities	Building block principle, heat bath, folded shape	Heterogeneous organization, dynamic complexity

The main property is folded shape. This requires long, nonconjugated polymers (because rotation around single bonds is necessary). Carbon, the atom of life, supports this requirement. Silicon, the only competitor for carbon in this respect, is rather inferior (Henderson 1913; Conrad 1994b).

The C-C bond energy is about the same as for bonds with H or O. The energy required to break the Si-Si bond is only about half as much as the energy required to break Si-H and Si-O bonds. The number of carbon-based structures that are possible is accordingly much greater than is possible with silicon (Sidgwick 1950; Edsall and Wyman 1958). The longer chains possible with carbon allow for a greater variety of folded shapes.

The well-known lock-key metaphor (Fischer 1894) for enzyme-substrate recognition is based on this fact of folded shape. Proteins must be big enough to have significant shape features (not true for individual atoms) but small enough to scan each other's shapes through diffusion (which we can refer to as Brownian search). The shape fitting is in reality dynamic; conformational motions are critical to the rate of complex formation and (in the case of catalysis) complex decomposition. The conformational motions are sensitive to a variety of milieu features (e.g., temperature, ions, control molecules). The prototype device that we will shortly turn to utilizes this context selectivity for signal pattern recognition.

As in all chemical reactions, thermal fluctuation (heat motion) is sine qua non. The term Brownian search, used above, is intended to suggest its computational significance. Recall the discussion of complexity: Complexity must either be provided in a program fed to a system from the outside or it must have self-organizing dynamics, therefore nonprogrammable structure-function relations. Protein folding and complex formation are prime examples. The heat bath is a potent source of complexity. The amino acid sequence draws on thermal fluctuations to explore itself in the folding process. The folded structure draws on thermal fluctuations to explore molecules with which it interacts in the complex formation process. In general, physical selforganization is based either on energy minimization or entropy maximization. The randomness of the heat bath is an essential ingredient in both cases. If entropy maximization is the controlling feature, the fluctuations allow the system to assume a greater number of structural forms. If energy minimization dominates, thermal energy must be given up to the heat bath in an irreversible way. From the point of view of algorithmic complexity theory, the complexity of a pattern or process increases as the size of the shortest program required to generate it increases—that is, as its description becomes less compressible. Of all phenomena considered in physics, perhaps the heat bath has the most incompressible description.

The combinatorial variety of carbon compounds is another powerful virtue. The number of possible amino acid or nucleotide sequences is hyperastronomically large. The important point is that the notion of a general-purpose system takes on a new guise. Conventional electronic machines are constructed from simple standard building blocks—for example, NAND gates. Biological systems, in contrast, are built from an extremely large variety of macromolecular species, each capable of performing a specific complex transform. Cells and organisms with different input-output behaviors arise through adaptive processes that modify the proteins in the repertoire or that express these proteins in different combinations.

The high evolvability of proteins is requisite for the efficacy of the adaptation process. Again, folding is the key feature, because it allows for structure-function malleability. As noted in section 1.3, there is an intimate connection between evolvability and complexity. If protein folding could be described by an extremely compressed program, therefore a simple process from the algorithmic complexity point of view, then the structure-function relations would approach programmability and would be fragile. Most mutations would be cataclysmic. Evolutionary considerations thus imply that folding and (chemical) complex formation are complex processes in the algorithmic sense. At the same time, the introduction of redundant amino acids in the sequence and the utilization of amino acids with high replaceability serve to buffer the effect of mutation on conformational features critical for function (Conrad and Volkenstein 1981).

Sometimes the argument is put forward that biological molecules are insufficiently reliable for computing. The opposite is actually the case. Single molecules have definite ground states, as opposed to the macroscopic switches from which conventional computers are built. The latter are built from statistical aggregates of particles and are therefore subject to erosion. The reliability issue is rather subtle, because it is clear that with solid-state components, it is possible to perform many repetitive operations and to do so rapidly. But if we want to build a reliable information processing system out of nonlinear base components, the capability for reproducing the nonlinearity in a highly precise manner is absolutely critical. This is infeasible with conventional electronic or other macroscopic components, simply because it is impossible to exactly duplicate a statistical aggregate of particles, let alone preserve their nonlinear characteristics on an operational time scale. The discrete amino acid sequences that determine the function of proteins can be precisely specified. This is sufficient, at least for a large class of sequences, to uniquely determine the folded shape and the set of available conformational states. The shape (or conformation), of course, changes when the protein interacts with its environment, but the existence of a ground state and, more generally, discrete energy levels confer precision that is unobtainable with macroscopic processing elements.