ARTICLES

ON DESIGN PRINCIPLES FOR A MOLECULAR

If the unique information-processing capabilities of enzymes could be adapted for , then evolvable, more efficient systems for such applications as pattern recognition and process control are in principle possible.

MICHAEL CONRAD

It is only recently that a serious interest in the possibil- systems, which are ultimately based on the conforma- ity of using carbon-based materials for computing has tional properties of protein enzymes, suggest this ap- developed in the scientific community. Formerly, indi- proach (see Figures l-3). Although elaborate conforma- viduals expressing an interest in exploring this possibil- tion is probably incompatible with good conductivity, it ity would have been advised to implement their com- allows for the lock-and-key type interactions that en- puting concepts in existing electronic technologies. In- able enzymes to recognize specific molecular objects by deed, to the best of my knowledge, no molecular com- exploring their shapes.’ Shape-based specificity is a puting device has so far been constructed or shown to form of tactile pattern recognition. Admittedly, en- be imminent. However, a convergence of developments zymes make for much slower switches than transistors in a number of fields, including polymer chemistry, (typically 0.1 millisecond, as compared to.a nanosec- various , the physics of computation, ond). To simulate the sensory and control functions and computer science, has changed the situation. Theo- they perform, however, would require an enormous retical arguments suggest that more efficient and adapt- number of switching processes in a digital computer. able modes of computing are possible, while emerging Designs that use functions of this sort as primitives- biotechnologies point to possibilities for implementa- predefined elements that are irreducible as far as the tion. Their common ground is molecular computing. computing power of the machine is concerned-can One immed:iate objective is to produce a von reasonably be expected to yield significant increases in Neumann-type computer in carbon, rather than silicon computational power for such tasks as pattern recogni- [3]. The assumption is that carbon chemistry may facil- tion and process control. In addition, enzymes have the itate the construction of smaller and faster devices. At- virtue of being adaptable switches, which makes them tention has therefore been focused on the possibilities amenable to tailoring for particular functions through for organic sw:itching devices and conducting polymers trial-and-error evolution. The evolution process pro- [21,41], and secondarily on the problems of contact ceeds by variation of the sequence of amino acids in and reliability. Certainly, work in this area is poten- the enzyme, followed by selection and propagation of tially important. Even so, it is likely that molecular the best-performing sequences (see Figure 4). computing will prove to be much more valuable out- However, these advantages can only be exploited at side the context of conventional von Neumann com- the expense of programmability, which is the major puters. Critically important computing needs such as feature of today’s computers. This idea can be stated in adaptive pattern recognition and process control may the form of a trade-off principle: A system cannot at the be refractory to simple decreases in size and increases same time be effectively programmable, amenable to evolu- in speed. Instead of suppressing the unique properties tion by variation and selection, and computationally effi- of carbon polymers, we should consider how to harness cient. The von Neumann computer opts for programma- them to fill these needs. bility. The trade-off theorem suggests that an alterna- The information-processing capabilities of biological ’ The argument is that the conformational flexibility of biopolymers is con- 0 1985 ACM OOOl-0782/135/0500-041%750 comitant to the lack of conjugation required for electronic conductivity [43].

464 Communications of the ACM May 1985 Volume 28 Number 5 Articles tive domain of computing is in principle possible, have access to the same computational resources at the where programmability is exchanged for efficiency and same time, is also possible, but, in general, only at the adaptability. Biological systems, as the products of evo- expense of effective programmability (for a discussion lution, must operate in this alternative domain. of parallelism and speedup, see [26]).

ESSENTIAL FEATURES OF VON NEUMANN The von Neumann computer also has fundamental COMPUTERS shortcomings: Let us first list some of the fundamental features of von 6. Inefficiency. Von Neumann computers make ineffi- Neumann computers. These features have become so cient use of available space, time, and energy resources. familiar that it is possible to forget how remarkable The vast majority of processors are dormant at any they really are [6]: given time. 1. Programming languages exist. It is a fact of experi- 7. Sensitivity. The sensitivity of programs to change ence that if we can conceive of an algorithm we can is a matter of common and usually unpleasant experi- always express it directly in any of a large number of ence. computer languages (e.g., ALGOL, LISP, Pascal). A basic feature of all such languages is that they are defined by The strengths of the von Neumann design (properties a finite, discrete base set of symbolic primitives. Were l-5) are all control properties. Intensive efforts are un- these symbols not finite in number, a user’s manual der way in computer science to retain these control could not be finite either. Were the symbols not dis- properties while removing the constraints on efficiency crete, it would be necessary to perform calculations to and adaptability [properties 6 and 7). The trade-off prin- ascertain what algorithm a program actually expresses. ciple suggests that the strengths of the von Neumann The psychological sense of directness conveyed by to- computer are inextricably linked to its limitations. day’s computer languages is derived from these proper- ties. THE TURING-CHURCH THESIS 2. Effective programmability. Once a program is writ- The capabilities computer scientists generally associate ten, it is always possible to effectively communicate it with the von Neumann computer are summed up in to an actual machine. From a user’s point of view, this the famous thesis of Turing and Church (a recent gen- communication process may be mediated by an inter- eral discussion can be found in [zJ]). One statement of preter, which can read and follow any particular pro- this thesis is any effectively computable function is com- gram, or by a compiler, which sets the state of the putable by a formal process involving simple operations on machine so as to execute the desired program. strings of symbols. A program is a rule that generates such a process. The classic Turing formalization of a 3. Structural programmability. Digital computers all computing process is illustrated in Figure 6. The Turing employ a small repertoire of simple switches (e.g., logic machine program can be rewritten in any general- gates and on-off devices). Each switch constitutes a purpose algorithmic language. These various formaliza- switching primitive. It is always possible to write a pro- tions all define the same class of functions-the partial gram in a language that directly maps the structure of recursive functions. To prove this, it is only necessary the machine and the state of each component [8, 141. to show that they are all equivalent up to the point of This property, structural programmability, is the basis for simulation, that is, up to the coding of strings of sym- all other forms of programmability in today’s com- bols into other strings of symbols. This equivalence puters. The network in Figure 5 illustrates the concept supports the Turing-Church thesis, although it does not of structural programmability. It shows how algorithms actually prove it. Indeed, proof is impossible, since the expressed in terms of the symbolic primitives of a claim is that an informal concept of computation is highly simplified programming language can be ex- equivalent to any of a large number of formal models of pressed directly in terms of the switching primitives of computation. Disproof, however, is possible if a con- the network. Of course, the diagram of the network is vincing counterexample can be found. Computer scien- also a language, and the “switching” primitives in it are tists generally accept Turing-Church because no such also symbolic primitives. However, they are symbolic counterexample has ever been discovered. primitives that can easily be realized as switches. The Turing-Church thesis is sometimes interpreted narrowly as encompassing only the processes of logic 4. Universality. Were there no limitations on time and space, the von Neumann computer could run any and mathematics. The strongest interpretation is that conceivable program. It is also universal in that, so far any physically realizable system or process must be effec- as is known, it can simulate any physically realizable tively computable. If a physically realizable system or process in nature (more on this in the next section). process were not effectively computable, it could be used as a new primitive of computation, thereby en- 5. Sequentiality. It is possible for the von Neumann larging the class of functions computable by systems in computer to execute a single elementary operation at a nature. For the purpose of this article, I accept this time. True parallelism, as where two or more programs strong form of the Turing-Church thesis, first because

May 1985 Volume 28 Number 5 Communications of the ACM 465 Articles

energy-dependent folding T-t,Y

The sequence of bases in DNA, which stores are pictured with dark springs, and weak bonds, which the information accumulated during the course of eV0k.b determine the folded structure, by light springs. Only tion, is translated to the sequence of amino acids in pro- some features of the enzyme’s folded shape are critical teins. The amlino-acid sequence is pictured schematically for its function. Here, the relative position of the triangles as a string of beads, each different type of bead stand- conveys the critical shape feature. Natural are ing for one tyjpa of . Weak interactions among built from 20 types of amino acids. A typical protein might the amino acilds cause this linear representation of in- comprise a folded string of 300 amino acids. The func- formation to spontaneously fold up, forming a thrae- tions performed by the protein are determined by its dimensional spatial structure. Strong or covalent bonds three-dimensional structure and dynamics.

FIGURE1. The Representation of Information in Proteins

B:‘~l substrate enzyme

A protein serves as an enzyme, or biological catalyst, if it the two molecules become significant. Shapedependent speeds the formation or severing of a particular covalent recognition is sometimes described as a “lock-key” mech- bond in a parhcular target molecule, called the substrate. anism; in reality, though, the dynamical properties of the In so doing, the protein switches the substrate from one enzyme also play a role. The enzyme may assume differ- state to another. Before switching can occur, the enzyme ent shapes, or states with different functional properties, must recognize the substrate-that is, distinguish it from as a result of interactions with control molecules, Fea- other, possibly quite similar molecules. Recognition is a tures of shape may serve a6 binding sites that allow the tactile phenomenon involving the complementary fit of en- enzyme to recognize and stick to specific molecular zyme and substrate shapes. The enzyme and substrate structures. Some proteins with purely structural functions explore one another by means of diffusional motion. use this type of lock-key interaction to self-assemble into When a close ‘fit occurs, short-range interactions between larger molecular structures.

FIGURE2. Proteins as Pattern-Recognizing Switches

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(a)

New proteins arise through variation mechanisms, such as mutation, which alter the amino-acid sequence. A sin- gle mutation of a crucial amino acid may disrupt the abil- ity of the protein to recognize and switch substrates. Other mutations produce only slight changes in shape and function. Diagram (a) shows how folding can serve to distribute the effects of mutation over the whole struc- ture. The mutated amino acid is represented by the large striped circle. The relative orientation of the triangles, which represent a feature of shape critical for function, is altered as compared to the unmutated protein illustrated in Figure 1. By distributing the effects of mutation, folding allows the critical shape feature (i.e., the orientation of the triangles) to change only slightly in a significant number of cases. The effects of mutation on this feature may be further buffered by redundancies: Redundancy in the number of types of amino acids allows for mutation to closer structural analogs, as represented by the some- what smaller striped circle in (b). Redundancy in the num- ber of amino acids increases the capacity of the protein to absorb the effects of mutation in features of shape that are not critical for function. This is illustrated by the par- tially restored alignment of the triangles in (c). Redundan- ties that buffer the effects of mutation lead to an enor- mous speedup of the evolution process.

FIGURE3. The EvolutionaryAdaptability of Proteins

May 1985 Volume 28 Number 5 Communications of the ACM 467 Articles

The “programmer” specifiesthe task and the criteria for success. EVolution proceeds by variation of the amino- acid sequences of the pioteins. Selection is based on how well each protein performs a desired task. In general this evalliation is based on the performance of the system in which the protein is acting, just as in nature it is based on how well the performs. Better-performing Systems are said to be more “fit.” Propagation of fit pro- teins is achieved by producing copies of them rather than of less fit proteins. Improvement is achieved by coupling the copy process to the variation process. In nature this is achieved by differential reproduction of , where reproduction is coupled to variation of genes. The artificial selection process pictured here differs in two ma- jor ways from evolutionary processes in nature. First, there is the fad that in nature many genes control the traits of organisms. Higher mechanisms of variation such as crossing over, recombination, and variations affecting the regulation of gene expression are important. As with simple mut&tions, however, these higher mechanisms re- quire the organizations on which they act to be capable of improvement through sequences of single variation events in order for them to make an effective contribution to the evolutionary process. The second major difference is that the task-definition and selection processes are artificial, that is, determined by a programmer, rather than consequences of ongoing interactions among organisms or between organisms and their environment. The evolu- tionary programmer specifies goals in terms of criteria of selection, whereas a digital-computer programmer speci- fies structures to achieve the desired goals.

and dynamical processes far removed from those con- jured up by the mechanisms present in a von Neumann computer. The von Neumann computer is a physical realization of a formal system executing simple opera- tions on strings of symbols. We say that such a com- puter simulates a dynamical system if states of the com- puter can be made to correspond to states of the dy- namical system at each point in time to an arbitrarily high degree of approximation. (We do not, however, require that every state of the machine correspond to a state of the dynamical system [IS].) According to Turing-Church, all physically realizable dynamics are equivalent to computation in that they can be simulated by a von Neumann computer under the idealization that space and time bounds can be ignored. If we could demonstrate that the dynamics of a particular physical system could not be so simulated, then we could use this system to solve problems effectively (i.e., by a defi- FIGURE4. The Evolutionary Learning Algorithm nite procedure) that would be unsolvable by a digital process. For example, we could solve the problem of generating the behavior of this particular dynamical what is of interest is the computational uses to which system. Either the Turing-Church thesis implies that physically realizable systems can be put, and second all physically realizable processes can be duplicated by because the thesis would be rather trivial if physically digital computers, or it fails to put any limits on what realizable systems existed that could violate it. real systems are effectively capable of doing. Of course, the simulation of a phenomenon-of a nu- THE EQUIVALENCE OF DYNAMICS clear explosion, for instance-is not the same thing as AND COMPUTATION the phenomenon itself. All simulations are abstract in Taken in this strong form, the Turing-Church thesis that they fail to capture some aspect of the simulated provides a link between formal models of computation system. This is the case whether the simulation is of

466 Communications oj the ACM May 1985 Volume 28 Number 5 Articles

lb)

For simplicity we consider a machine (technically a semi- automaton) with three inputs, xl, x2, and x3, and three states, ql, q2, and q3. The program is a sequence of triples of the form qixiqk. The primitives of the construc- tion are McCultoch-Pitts formal neurons (a). These fire if the sum of their inputs (inputs can be 0 or 1) equals or exceeds a threshold, which in thiscase is always 2. In the canonical network (b), state q, is coded by the firing of a formal neuron in column i, and input x1 by the firing of

FIGURE5. The Concept of StructuralProgrammability

one string process by another or of a continuous dy- be imagined that are not computable by simple opera- namical process by a string process, as in the example tions on strings of symbols-a map of all computer pro- of the nuclear explosion. The execution sequence of grams into the two categories, correct and incorrect, for the computer has the same ontological relationship to instance. Computing this map is equivalent to solving the real explosion as do the hydrodynamic equations the halting problem, which we know to be unsolvable that describe the explosion. The equations are a map by a Turing machine or any process equivalent to a from states to states that is meaningfully defined only Turing machine [16]. If an actual system could realize in terms of some method of computation. The explosion this map, it would constitute a new primitive that could and the machine that simulates it can be thought of as not be duplicated with any set of primitives formerly alternative means of computing this map. The real con- believed to define the class of computable functions. tent of the Turing-Church thesis, if it is correct, is that The proposed equivalence of dynamics and computa- any physically realizable map can also be realized by tion makes it clear that tying the concept of computing the execution sequence of a physical system performing to any single model of computation is arbitrary. Any formal operations on strings of symbols. Many maps can physically realizable process whatsoever can be admit-

May 1985 Volume 28 Number 5 Communications of the ACM Articles

in these ways, it could be argued that machines like the von Neumann computer, which are constrained to real. ize formal sets of rules, are limited in their ability to duplicate a crucial aspect of human intelligence. Such e limitation would not necessarily apply to systems like the molecular computer design here described, which are not so constrained. For ascertaining whether it is useful to enlarge the pantheon of computational primi- tives, however, it is sufficient to accept the Turing- Church thesis as formulated. The class of Turing com- putable functions is so much larger than the class of functions that could be computed by any finite system that it is the comparative performance within this class, The three components are a finite-state machine (A). a indeed within a rather minute subdivision of it, that is read-write head, and a tape that can be read, marked, or the issue of immediate concern. It is sufficient to show moved a square to the right or left. The inputs to A are that a molecular computer could perform some useful tape symbols, and the outputs either tape symbols or tasks that could only be performed by a present-day moves. The program of the luring machine oan Be ex- computer at an excessive cost in terms of computa- pressed as a set of quadruples of the form q,x,y&, tional resources. where 4, is tihe initial state, xj the symbol read on tple tape, yh the output symbol or move, and 9 the finat state. PROGRAMMABILITY VERSUS EVOLVABILITY Turing thought of A as an abstraction of a person per- The first part of the trade-off theorem states that pro- forming some symbolic process (e.g., an arithmetic pro- cess) on a notepad (i.e., the tape). The program.ex- grammability is a cost in terms of evolutionary adapta- presses the rule according to which the “states elf mind” bility. Recall (from Figure 5) that a system is structur- of A change. The finite-state device can always be real- ally programmable if it is possible to communicate algo- ized by a selt of McCuIIoch-Pitts formal neurcjns of the rithms to it by setting the states and connections of its type shown in Figure 5. physical primitives using a finite programmer’s manual. Consider two structurally programmable computers P FIGURE6. A Turing Machine and P’, which differ by a single structural feature (cor- responding to a single alteration according to the con- struction manual]. Given the same input, how different ted as a computational primitive. Our current prefer- will the processes executed by these two systems be? ence for simple switching processes can be attributed to This problem, which I call the unsolvable transformabil- our desire to exert prescriptive control over computa- ity problem, is unsolvable in just the sense and for just tion. Even if a dynamical process is effectively comput- the reason that the halting problem for Turing ma- able, the machine that incorporates this process as a chines is unsolvable [g]. primitive need not be effectively programmable. The Suppose, as the reductio hypothesis, that it is possible discrete, finite aspect of the primitives would be lost, to write a program U to solve the gradual transformabil- and with it the ability to communicate algorithms di- ity problem. This program could use any nontrivial rectly to the machine. [Analog computers are of course metric to measure the similarity of the two processes. an exception alf sorts. It is possible to use a precisely By a nontrivial metric, I mean any metric that does not defined system analogy to guide design. Admitting arbi- result in P and P’ being classified as similar indepen- trary physical processes as primitives of computation dent of what states they are in. Thus it is only neces- is generally incompatible with prescriptive design, sary to divide the state set of P and P’ into at least two however.) disjoint, nonempty subsets of states. Suppose that the We have observed that all simulations are abstract in criterion of similarity is that, given the same input, P’ that they only represent what they simulate. This raises gives a defined computation whenever P does. The the question, could this “abstractness” be a significant computation is defined if the machine running the pro- limitation? The philosopher Ludwig Wittgenstein ar- gram reaches a halt state. We are free to take as P any gued that the interpretation of a rule could never be an program that halts. For the reductio hypothesis to hold, intrinsic property of the rule itself [48]. For example, it is at least necessary that U go to a halt state and emit the interpretat:ion of the symbol ‘I+” is not inherent in as output “not similar” whenever P’ does not go to a that symbol. If we accept the idea that all essential halt state. Suppose that U is itself P’. Then U halts if it aspects of human intelligence can be duplicated by fol- does not halt, that is, answers “not similar” when it lowing formal rules expressed as computer programs does not answer “not similar.” Since this is clearly a- (i.e., by following algorithms), then we must maintain contradiction, the assumption that U is a possible ma- either that rules can carry their own interpretation or chine must be incorrect. that an interpretation can be an emergent property of a The unsolvability of the gradual transformability set of rules. If symbol interpretation cannot be achieved problem corresponds to the common experience that a

470 Communications of the ACM May 1985 Volume 28 Number 5 Articles

single change in a computer program (other than a pa- a point mutation-that is, by a single change in amino- rameter change) usually leads to major changes in the acid sequence [45] (See Figure 3). Portions of the en- execution sequence. Rarely does such a randomly al- zyme that are critical for function, like the active and tered system serve any useful function. Redundancies control sites, can be buffered from the effects of point can be introduced to confer fault tolerance, but in this mutation by functionally less significant portions of the case changes in function are actually prevented. Fragile molecule. “Programming” occurs at the level of the systems of this type are unsuited to evolution; variation amino-acid sequence, but structural programmability is and selection is efficient as a method of self-organiza- lost since shape and function emerge from this se- tion only if a useful P’ can always be produced from P quence through a continuous dynamical folding pro- by a single structural alteration. The probability of an cess. The intervention of this continuous dynamical improvement or of a step that can bring the system process increases the likelihood that single mutations closer to an improved form is then proportional to p, will lead to functionally acceptable forms of the en- the probability of a single change. If II simultaneous zyme, and is thus critically important for maintaining a changes are necessary, the probability of an improve- nonnegligible rate of evolution. As we have seen, this is ment is proportional to p”, a very small number for any because the evolutionary rate decreases sharply when reasonable choice of p even when n is 2 [5, 121. Large it depends on the simultaneous occurrence of two or values of p are never reasonable, since these always more structural variations. Assuming that it someday lead to the introduction of many undesirable changes, becomes possible to compute the shape and function of except in trivially small programs. proteins from primary structure, we might entertain This argument is the basis for the first part of the the idea of building a virtual machine with open-ended trade-off principle: that evolution is not compatible evolutionary capabilities using the von Neumann com- with structural programmability. This is not to say that puter as the base machine. The computational costs of evolutionary processes cannot be simulated on struc- simulating folding processes would, however, be pro- turally programmable computers. After all, according to hibitively high-much higher than the cost of simulat- Turing-Church, it must be possible to simulate evolu- ing features that would confer a moderate evolutionary tion, otherwise a physically realizable process would capability. exist in nature that is not effectively computable. Com- puter programs have in fact been written that success- PROGRAMMABILITY VERSUS EFFICIENCY fully use the evolutionary principle (e.g., Samuel’s We have seen that simulating evolution on structurally checkers program [JO], Bremermann’s optimization al- programmable computers is computationally expensive. gorithm [2], and evolutionary learning algorithms used In this section we show that structural programmability in simulations of structurally nonprogrammable sys- can be exchanged for computational power. To see why tems [25]). The key to all such programs is restricting this is so, let us consider the operation of a structurally evolutionary changes to parameters and parameterizing programmable computer at three levels. problems as much as possible. The logical extension of The network level. The efficiency with which the com- this strategy is to increase the degree of parameteriza- putational resources of a computer are utilized in- tion by simulating the types of dynamical features and creases as a greater fraction of processors in the system redundancies that facilitate the evolutionary process in is active at any given time. For effective programmabil- biological systems. Continuous dynamical features are ity, the system must be constrained to operate sequen- evolution facilitating since they make it possible to de- tially to ensure that unanticipated conflicts do not oc- fine a small perturbation in a way that would be impos- cur (for a discussion of problems in this area, see [18]). sible in a formal system. For instance, a structurally This means that most of the processors remain dormant stable developmental process can undergo a wide vari- at any given time. Of course, if a program is naturally ety of useful transformations in response to genetic decomposable into a number of independent parts, each change, while retaining coherent organization [38, 441. having approximately the same running time, the dor- Redundancies are evolution facilitating since they can mancy can be greatly reduced. The running time can buffer the effects of genetic change on features critical only be predicted in special cases, however, since pre- for function [ll]. To the extent that we are willing to dicting running times would be tantamount to deter- pay to simulate such evolution-facilitating features, we mining whether programs are defined and thus to solv- can build virtual machines having an effective evolu- ing the halting problem. tionary capability on top of von Neumann machines. The underlying program would remain fragile, how- The component level. For structural programmability, ever, and the cost of simulation would have to be the number of types of switching primitives used must weighed against the potential benefits. be finite, and each must have predefined switching ca- The simplest and most important illustration of a sys- pabilities. Consequently, these primitives cannot in tem structured for effective evolution is the protein en- general be adapted to the task at hand. As the number zyme [13]. The enzyme assumes its shape and function of types of components (primitives) increases, the num- through an energy-dependent folding process, which in ber of components required to implement any given a significant number of cases is only slightly altered by program typically decreases, since the functions per-

May 1985 Volume 28 Number 5 Communicationsof the ACM 471 Articles

formed by the added primitives would not need to be velopment of the system is not described by an analytic simulated by combinations of already existing primi- function (since the execution sequence of a formal tives. When our objective is to perform a highly selec- computation must in general be independent of any tive information-processing task with the smallest num- subsequence). They must also ensure that the system’s ber of components, an arbitrarily large repertoire of time development corresponds to a classically pictura- component types is obviously desirable. This is essen- ble execution sequence, that is, quantum mechanics tially the situation when the components are protein must be irrelevant to the system as a whole. In fact, all enzymes. Thlere are at least 20~” different amino-acid dynamical processes involving the system as a whole sequences that could be fabricated by biological sys- must be suppressed, in contrast to most systems in na- tems or by recombinant DNA techniques. Since the ture. Since the components must be in one of a number functional properties of each of these sequences arise of distinct states (corresponding, say, to 0 and l), the through an energy-dependent folding process, however, number of distinct quantum states available is a poten- they cannot be prescribed by a manageably small pro- tial limitation. Distinct quantum states contribute to the grammer’s manual. reliability of storage and switching, requirements that This inefficiency at the component level contributes do not apply to all physical systems. To achieve struc- to inefficiency at the network level. If components tural programmability, engineers must impose addi- could always evolve to specifically suit the task at tional enforcement constraints to ensure that only in- hand, networks could learn to use their resources in teractions that allow each component to realize its pre- parallel. If we are willing to do without effective pro- defined function can occur and that prevent the occur- grammability in order to use components in parallel, rence of all other interactions. The limit of n-fold paral- the only reason for working with a restricted set of lelism in today’s machines is a consequence of these component types is the practical one that fabricating enforcement constraints. new primitives out of silicon is expensive. This limit of These constraints are a contributing factor to physi- current technology is hardly relevant to biological sys- cal limitations on present-day computers. Communica- tems, however, which can always use their genetic ap- tion among components is limited by signal velocity paratus to generate and mass-produce new carbon poly- and ultimately by the velocity of light. Signal velocity is mers.* already becoming a limiting factor in some supercom- puters. Structural programmability generally requires The physical level. Structural programmability also special functions that could otherwise be performed by cuts into the computing potential allowed by the princi- a single specifically adapted component to be dupli- ples of physic:; [Z]. Recall that, according to Turing- cated by a combination of components, thus increasing Church, a structurally programmable physical realiza- the distance over which signals must be sent. Brownian tion of a formal computation process should be capable motion is also a physical limitation (on reliability), but of simulating any physical process when space and only to the extent that we desire computation to fulfill time are unlimited. Space and time resources are never preexisting specifications and if randomness is not one unlimited in the real world, however, and are in fact of these specifications. If randomness is desired, Brown- generally limited in different ways for the simulating ian motion can actually be viewed as extremely heavy system (the machine) and the simulated system (the computation. For example, an enzyme exploring a sub- physical process). A simulating system consisting of a strate utilizes Brownian motion for tactile pattern rec- set of particles constrained to execute formal computa- ognition. Exploration of this kind would be incompati- tions could never keep pace with a simulated system ble with the enforcement constraints required for struc- consisting of tlhe same number of particles; if the simu- tural programmability. lating system j.sstructurally programmable, it is even The most important physical limitation on today’s further constrained.3 computers is heat export. Like living systems, com- According to known force laws, n2 interactions could puters feed on high-grade energy and give off heat. conceivably contribute to the behavior of a system con- Transistors in present-day computers dissipate about sisting of n particles. The potential parallelism here 10" kT per step. Enzymatic reactions in biological sys- is at least n-fold greater than that obtainable by one tems typically dissipate lo-100 kT per step. This is an n-processor machine of conventional design. For the impressive difference, especially when we consider that system to exhibit formal computational behavior, con- enzymes perform a tactile pattern-recognition task that straints must be introduced to suppress a large fraction would involve many steps for a digital computer. Care- of the interactions (the importance of constraints, in ful examination reveals an even more remarkable fact particular nonholonomic constraints, is emphasized in about enzymatic computing: An enzyme actually per- [ST]). These constraints must ensure that the time de- forms its pattern-recognition task reversibly. At equilib- ‘The limitation on the number of primitives is not contradicted by micropro- rium each enzyme continues to recognize substrates grammable systems. These are properly thought of as general-purpose ma- chines comprising general-purpose components. not components specifically and to make or break covalent bonds. Energy dissipa- trimmed for a particular task. tion drives the reaction being catalyzed, rather than the ‘This physical view of computing has the paradoxical implication that the ultimate physical capabilities of nature must forever escape a constructive pattern-recognition activity of the enzyme. Driving the mathematical treatment. reaction forward is essential for coupling the pattern-

472 Communications of the ACM May 1985 Volume 28 Number 5 Articles

recognition activity of the enzyme to the control of increase by as much as a factor of 105-a dramatically macroscopic processes, but not for the pattern- significant improvement. It is clear, therefore, that recognition activity itself. boosting computational resources will not make an in- In recent years Bennett, Fredkin, and Landauer dent on the combinatorial explosion, but that it can be [I, SO] have produced a surprising result that connects very helpful for problems admitting an efficient solu- in an interesting way to this fact about enzymes. This tion. There is an important qualifier, however. In gen- result is that physical realizations of formal computa- eral, the increase in problem size is much less than 105. tion processes can in principle proceed with arbitrarily The extent to which this limit can be approached de- low dissipation when speed, reliability, and required pends on the efficiency with which computing re- memory space are not considerations. The construction sources can be coupled to a problem’s solution. In they used to demonstrate this is based on a thermo- structurally programmable computers, the efficiency of dynamically reversible . It is also possible to coupling is low, and an increase in computing power view this result in the light of the Turing-Church the- along conventional lines is not necessarily as valuable sis: A logically reversible Turing process that is compu- as we might at first assume. If most machine resources tation universal is in principle possible. It is only neces- are dormant at any given time, an enormous increase sary to record all the intermediate states on the mem- in parallelism will not be worth the cost. Systems that ory tape, record the answer, and then use the memory opt for efficiency and evolutionary adaptability would tape to recover all the initial information. If a thermo- be better suited to coupling increases in computational dynamically reversible realization of this logically re- resources to increases in problem size. versible Turing machine were demonstrably impossible Could analog processes or other dynamical processes even in the limit of idealization, it would be impossible counteract the combinatorial explosion? It is not possi- to use a digital process to simulate reversible processes ble to answer this question a priori, but it is possible to in nature without losing reversibility. If it were impos- focus the issue more precisely. Suppose a particular sible to duplicate a reversible process digitally without dynamical process could be used for solving a large embedding it in an irreversible process, then a weaken- exponential-time problem. Furthermore, suppose that ing of the strong interpretation of the Turing-Church this process could be simulated on a digital computer thesis would be necessary [7]. over a short interval of time. A constant factor speedup The Bennett-Fredkin-Landauer result shows that+ of the digital computer would then allow what is by there is no machine-independent thermodynamic limit hypothesis an exponential-time problem to be solved in to computing. Thermodynamic costs can be traded for polynomial time [15]. Thus if we assume that particular other costs that can be reckoned in terms of compo- dynamical processes can be harnessed for solving nents, reliability, and speed. If a machine is structurally exponential-time problems, we must also assume that programmable, these other costs are high, and hence these processes are refractory to digital simulation for the cost of adding more components or accepting less even the smallest time slices. speed and reliability in order to reduce the dissipation The existence of dynamically exotic processes capa- would soon outweigh the advantage to be gained. If the ble of solving exponential-time problems is of course a system foregoes structural programmability, the bal- logical possibility. The phenomenon of turbulence ance changes, since the amount that must be invested would conceivably fall into this category. The Turing- to obtain a given decrease in dissipation is less. This is Church thesis would not be contradicted by such pro- a probable explanation for the relatively low energy cessessince it does not matter, in terms of the thesis, dissipation found in biological computing. whether the number of resources used for the digital simulation grows exponentially. The potential value of EFFICIENCY VERSUS COMPLEXITY structurally nonprogrammable computers does not de- To properly appreciate the significance of this extra pend on this logical possibility, however. The value is efficiency, it is useful to distinguish between actually greatest for problems admitting efficient solu- polynomial-time and exponential-time problems [19]. A tions, for here the size of problems that are manageable task falls into the polynomial-time class if the number grows the most. Indeed it may be that the dramatically of resources required to solve it increases as a low- different capabilities of biological organisms and von order polynomial function of problem size (say as n*, Neumann machines are largely due to the fact that the where n is any reasonable measure of problem size). A former are capable of solving much larger problems in problem is in the exponential-time class if the re- the polynomial-time class. From the standpoint of con- sources required to solve it increase at least exponen- structing artificial computers out of new materials, tially with problem size, say as 2”. Problems involving the implication is clear: What is needed is not von this type of increase entail a combinatorial explosion. Neumann computers fabricated from alternative mate- In the explosive 2” case, a 10”-fold increase in re- rials, but new computer designs to address computing sources allows an additive increase in problem size of needs not efficiently met by von Neumann machines4 at most 33, a very modest return for a major invest- ‘Of course. there may be other reasons for building van Neumann machines ment. In the polynomial-time n* case, the same lOlo- out of alternative materials. such as the desirability of machines resistant to fold increase in resources allows the problem size to pulses of electromagnetic radiation.

May 1985 Volume 28 Number 5 Communicationsof the ACM 473 Articles

THE PRINCIIPLE OF DOUBLE DYNAMICS input output How could a structurally nonprogrammable system be pattern organized to perform useful functions? Undoubtedly many guiding principles could be used for design in this area. However, I will focus on one, the principle of chemical gradient double dynamics, which seems to be particularly promis- ing and which appears to play a role in biological infor- mation processing. Double dynamics would exploit the trade-off princi- ple and would be chemically implementable. As in con- ventional computing, we would need building-block modules to transform patterns of input signals into pat- terns of output signals. Since conventional computers operate on the programmability side of the trade-off principle, their building blocks perform this transfor- mation in a manner completely describable in terms of a finite user’s manual. In order to shift to the efficiency-adaptability side of the trade-off relation, transformation. should combine elements of continuity and gradual modifiability with decision making. l = immobilized biosensor Chemistry offers the tactile pattern-matching capabil- ity inherent in the conformation of proteins and other The input pattern is a nontactile pattern such as of optical carbon polymers. Such polymers can be gradually mod- or electrical signals. This pattern is transduced into a ified and, with enzymes at least, supply the element of chemical-concentration pattern that can be read out by decision making. However, enzymes respond to surface immobilized biosensors, that is, by enzymes linked to an properties such as the shapes of particular substrate output device. The output either controls a process or is molecules in their immediate environment. This tactile passed to a von Neumann computer. The chemical me- form of pattern recognition is unsuitable for the electri- dium provides the upper level of dynamics. The readout cal, optical, and mechanical signals that are most con- enzymes provide the lower level. The time required for the device to transduce an input pattern into an output veniently presented to a module. pattern could be much reduced if diffusion in a chemical Chemistry also offers various kinds of dynamics in- medium were replaced by a mechanical propagation of volving reaction and diffusion that could transduce signals in a network of structural proteins. nontactile signals into a form that enzymes can recog- nize. These dynamics supply the continuity required FIGURE7. A Double-Dynamics Device for generalization, as well as an element of gradual transformability if the dynamics are structurally stable. The studies of IPrigogine and his school [36] have suppose that the action of the enzymes on their sub- shown that, in the presence of suitable nonlinearities, strates in the reaction-diffusion layer is picked up spec- complex spatial and temporal patterns (known as dissi- troscopically. The action of the enzyme is thus a dis- pative structures) can be created in a chemical medium tinct, second level of dynamics that controls the output through the production of entropy, thereby providing a of the device. If it is sufficiently rich, the top level of dynamic structure-formation principle that comple- reaction-diffusion dynamics converts different input- ments the energy-based self-assembly principle utilized signal patterns into different chemical patterns. The de- by polymers possessing conformation. The advantage of vice is “programmed” through variation at the enzy- dissipative dynamics is that it can process patterns of matic level of dynamics and selection on the basis of signals into surface structures in the form of chemical the pattern-processing performance of the whole sys- gradients. tem. The variations may involve the spatial arrange- The device pictured in Figure 7 combines these two ment of the enzymes or modifications in their response powerful forms of pattern processing-enzymatic action to a given chemical milieu. As long as the top level of and dissipative structures-to implement the principle dynamics is not initial-condition sensitive, similar of double dynamics. The enzymes are immobilized on a input-signal patterns should often give rise to similar surface covered. by, say, a photochemically sensitive chemical patterns, thus conferring some power of gen- medium. The nonlinear, dissipative dynamics of this eralization on the system. medium serves to transduce spatial and temporal pat- The first potential use of such a device is as a pre- terns of input signals (e.g., photons) into a chemical processor-a kind of eye-for a conventional von concentration gradient. This is the first level of dynam- Neumann machine. The purpose would not be simply ics. The chemical concentrations are interpreted by the to transduce environmental stimuli, but to use the rich enzymes, each of which can be thought of as a biosen- dynamics of the diffusion layer and the intelligence of sor coupled to an output device. For concreteness we the enzyme to code environmental patterns into a form

474 Comtnunications of the ACM May 1985 Volume 28 Number 5 Articles simple enough to be managed by a structurally pro- module is much less powerful than it might be, but is grammable machine. still more powerful than classical formal neurons of the As a second step, we could directly couple the output McCulloch-Pitts type. These fire whenever the average to an effector organ-for instance, a robot arm. Deci- of their inputs exceeds a threshold, whereas our dy- sions about the type of motion the arm makes are con- namic modules would fire in response to particular in- trolled through the von Neumann machine, but fine put patterns (assuming that the reaction-diffusion dy- motion, in response to the particularities of the envi- namics are sufficiently rich and the enzymes suffi- ronmental situation, is controlled by the way the en- ciently sensitive). However, we know that any finite zymes interpret this situation as it is represented in the automaton can be simulated by networks of McCulloch- dissipative dynamics of the reaction-diffusion layer. Pitts neurons, even neurons as simple as the threshold- Figure 8 illustrates an expanded version of such an two elements in Figure 5. It follows that networks of adaptive pattern-recognition and process-control sys- more powerful enzymatic modules must be capable of tem. The figure shows a bank of double-dynamics mod- simulating any finite automaton. The simulation is po- ules, each individually controlling a different part (or tentially more efficient since it does not have to work degree of freedom) of a robot arm. Each module re- around predefined modules. Since each module is po- ceives the same environmental input and represents tentially unique, however, there can be no predefined this input in the same dissipative pattern. The enzymes construction manual. in each module are selected differently, though, so the This leads us to conclude that it is possible to build a timing and intensity of the outputs are different. Each computer that is computation universal but not struc- module can be thought of as an analog of the motor turally programmable (for the formal construction, see element it controls. This shifts the problem of coordi- [g]). Since networks of enzymatically driven modules nating the whole arm (in the context of a particular can simulate any finite automaton, it must be possible type of action) to the problem of evolving suitable ana- to use them to simulate an interpreter. Thus it would log modules. be possible to build a structurally nonprogrammable To ascertain the class of functions that a network of computer that is nevertheless effectively programmable such enzymatically driven modules is in principle ca- at an interpretive level. There is a model for such a pable of computing, we can suppose, for simplification, machine: People can read and follow rules despite the that a threshold property is introduced to reduce the fact that the human brain, as a product of evolution, possible outputs to one or zero. This can be done in a must be structurally nonprogrammable. variety of ways, but for present purposes it is sufficient Turing machines compute a much larger class of to divide the module up into small regions and to ig- functions than finite automatons. However, Turing ma- nore the enzymatic signal in any region if it is either chines with finite memory tapes-the realistic assump- above or below a prescribed strength. The resulting tion-can always be simulated by finite automatons.

input (digitized picture)

component 1 component 2 component 3 component 4

Each module receives the same input, but interprets it which it is an analog. The modules are versions of the differently to control that component of the robot arm for double-dynamics device shown in Figure 7.

FIGURE8. An Array of Double-Dynamics Devices

May 1985 Volume 28 Number 5 Communications of the ACM 475 Articles

Practically speaking, some sort of manipulable memory double-dynamics device illustrated in Figure 7. In both store is a great advantage. Modern digital computers cases it serves to transduce macroscopic signals [e.g., use an addressable memory, that is, a memory in which nerve impulses or light rays) to a microscopic form at each switch is located on a grid in a manner that allows the molecular level of organization and then back to a it to be accessed individually. Alternative structures macroscopic form. A major contribution to the comput- are possible in which patterns of activity of highly in- ing occurs at the molecular level of organization in the terconnected memory units play a role; this is probably device, where enzymes read the concentration gra- what happens in the nervous system. Memory storage dients. The great advantage from the standpoint of effi- would be greatly increased by such multiple utilization ciency is that this enormously reduces the heat produc- of components, although powerful pattern-processing tion that accompanies the computation. If the same capabilities would be needed to manipulate such a dis- amount of computation were performed at the macro- tributed memory structure [lo]. This is just the kind of scopic level of nerve impulses, dissipation would be- capability that could be provided by enzyme-driven come a significant limiting factor. This thermodynamic networks. consideration suggests that a major contribution to bio- logical computing occurs at the molecular level in the DOUBLE DYNAMICS IN NATURE neuron, just as it does in the hypothetical device. We have not been specific about the chemistry of man- The obvious analogy is that the reaction-diffusion dy- made double-dynamics devices since none has as yet namics at the level of cyclic is read out by been produced. Our group at Wayne State University kinases attached to gating proteins, just as the immobi- has conducted extensive simulation studies of devices lized enzymes in Figure 7 read out the concentration that utilize the double-dynamics principle, however, gradients in the device. The rich internal structure of and has developed evolutionary learning algorithms for the neuron also suggests other more powerful possibili- communicating desired performance to them [25-271. ties. Recent microinjection experiments indicate that The reactions used in these simulations occur in real the effect of CAMP may in some instances be mediated neurons and can therefore be specified with some de- by the cytoskeleton, a network of microtubules and mi- gree of confidence. crofilaments that support the membrane and run The reactions involve molecules called second mes- through the cell [23, 331. It is conceivable that the po- sengers, which serve as intracellular signal carriers. tential for highly parallel signal processing and vibra- Second messengers such as CAMP, calcium, and possi- tory behavior on the part of microtubules and other bly cGMP are now known to control nerve-impulse ac- cytoskeletal elements could play a significant role. In tivity in some neurons. Some of the key reactions of the this case second messengers would most plausibly serve CAMP control system are illustrated in Figure 9 [20]. to initialize or modulate these cytoskeletal dynamics in Presynaptic inputs activate receptors on the cell mem- a manner that reflects the pattern of input to the neu- brane that produce CAMP, which in turn acts on pro- ron. The interpretive function could be provided by a tein kinases. These kinases may activate gating pro- repertoire of readout molecules tuned to recognize sig- teins, which control the electrical activity of the mem- nificant patterns of cytoskeletal activity and capable of brane, or may act on other target proteins inside the initiating processes (such as the production of CAMP or neuron. If the neuron fires, calcium enters to activate cGMP) to modulate the firing of the neuron. Although the enzyme phosphodiesterase, which in turn resets the this is only speculation, it does serve to show that an neuron to its initial state by converting CAMP to the enormous amount of computation could be allocated to inactive mononucleotide. There are a number of other the most microscopic molecular levels of organization proteins in this system that also play a controlling role, in the double-dynamics framework. such as binding proteins that control messenger diffu- The molecular mechanisms of gene action and hered- sion rates and an enzyme (phosphoprotein phosphatase) ity constitute a well-understood biological information- that reverses the activation of protein kinase. It is possi- processing system whose organization is in some ways ble to experiment on this system by microinjecting parallel to that of a double-dynamics device. The DNA CAMP into neurons and studying the effects on nerve- sequence of genes is a structural code controlling an impulse activity. Liberman et al. [31, 32, 341 have re- organism’s phenotypic features under the interpretation ported an extensive series of such experiments, which of molecular decoding machinery (e.g., m-RNA, t-RNA). indicate that CAMP injected into large neurons of a That the phenotypic features are often suited to the snail’s central nervous system has a depolarizing effect, environment is due to the Darwinian mechanism of that is, increases the rate of neural firing. Other investi- evolution. By comparison, the upper level dynamics of gators have also reported effects, in some cases involv- a double-dynamics device [or of a neuron) can be ing increased :neural activity [28] and in others de- thought of as a dynamic code controlling the actions of creased activity (for a recent review, see [IT]). The the device (or organism) under the interpretation of kinds of control that second messengers exert on nerve- molecular readout machinery (e.g., enzymes and mo- impulse activity have not been definitively resolved, lecular resonators). These actions are often suited to the but the evidence that these molecules provide a two- environment as a consequence of evolution through way link between the nerve impulses and molecular variation and selection, though it is largely the readout processes inside neurons is consistently strong. enzymes that undergo evolutionary changes rather This two-way link also operates in the much simpler than the dynamic code. Readin mechanisms allow reg-

476 Communications of the ACM May 1985 Volume 28 Number 5 Articles

------/ \ / \ nerve / \ impulse / \ \ I/ receptor 1 \ \ I I % I transmitter L I I MICROSCOPIC I I I / / / \ memDrane 1 gatizprotein QJ J / \ N-e------_-- ,

nerve impulse MACROSCOPIC

,/ ~~lrb;~~fftingofapresynaptic neuron releases a transmitter neuron continues to fire, however, until the kinase is ~$W&r&nes with a receptor on the postsynaptic mem- deactivate$f by the-enzyme phosphoprotein phosphatase bran!%The recaptor activates the enzyme adenylate cy- (not shown). Many types ?f effector proteins, such as :’ -1 (aa&; which catalyzes the production of CAMP from ATP. prot6inq a$sOciatad v&h VM cytosketetoh, can be linked ~%$&P‘~iffusqs to another kxation on the membrane, ?o*kinaSqsand activated &CAMP, ‘I‘he time required for j,,‘: :.I&@ it ?otjvates a protein kinase, which in turn activates the neuron to-tran@uce the spatiotemporai pattern of ‘., ~‘Y&ins,,oalleU gating proteins, that control the flow of pul$& impinging on it toa frequency&x&d output would IV*ior& [email protected] membrane. If these ion channel proteins ti J%I$$ reduced if CAMP aNed by init@ing mechanical ,_I~~&$sWfi&3~tij, activ$xi, the neuron fires, causing cat- signal!! in tf& q%oskeleten,, The important feature to note I. &q&a?*) t&be released, and activates the’ enzyme in thi!!$&hem4 is the flow ‘Qf information from macro- $Ihpsphodiesterase. Aotivated phosphodiesterase causes ScoprCto incresjsingly rnicroshopic Ieve& (sensory input &I@@ t&be broken down to the inactive mononucfeoticie, -+ nerve impulses -* crzenticat rea0tiiMs -+ mdacular ~~Hfeot$u~lyresetting the neuron to its initial state. The everWand then back to macrosi$piq levels. ” FIGURE9. Key Reactions of the CAMPSystem of lntraneuronal Control

ulatory substances to alter the expression of DNA in membrane and cytoskeletal architecture in which it is response to the environment, just as second messengers embedded, requires for support all the metabolic and may effect changes in cytoskeletal dynamics. self-regulatory processes of an entire organism. Creat- ing such a self-enclosed support system artificially is THE IMPETUS FROM clearly infeasible. How then could we ever exploit the Enzyme-driven computing in biological systems de- efficiency-adaptability side of the trade-off relation? pends on intricate processes of self-organization and There are at least four conceivable approaches. The self-maintenance. The complex sequence of reactions first is working with virtual machines built on top of in the cyclic nucleotide system, not to mention the the von Neumann computer while consciously accept-

May 1985 Volume 28 Number 5 Communications of the ACM 477 Articles

ing the limitations imposed by the computational costs on whose further development molecular-computer de- of simulating Idynamics. The second is constructing sign is predicated. Aside from gene technology, these electronic devices to embody the desired dynamical include biosensor technology [46], static and dynamic principles to the greatest extent possible. Devices of this chemical dissipative structures, immobilized enzyme kind could be useful, but they would not enjoy the engineering [47], immunoglobulin tessellation tech- shape-based pattern-recognition capability that proteins niques [42] or other structure-formation techniques possess, nor is it likely that the same fineness of micro- based on the principle of self-assembly, and synthesis of scopic processing could be achieved. A third possibility artificial membranes with controllable electrical prop- is culturing existing organisms to perform a useful erties [39]. The simplest devices would be predicated information-p:rocessing function [22]. While it may be only on gene and enzymatic biosensor technologies, useful to pursue this possibility, it is generally true that and on reaction-diffusion dynamics. Although all of a system with a full evolutionary potential will pursue these technologies are in an early stage of development, its own goals, rather than the goals that we would at- the amount of effort now being expended on them for a tempt to impose on it. The fourth approach is concen- wide range of applications is enormous. Whether mo- trating on sim:ple enzyme-driven devices and, at least lecular computers can ever become practical depends initially, on tasks for which the lifetime of the device is on whether a simple device can be developed to fill a not a major consideration. Prior to the development of computing need critical enough to stimulate further de- recombinant DNA technology, enzyme-driven devices velopment. Novel designs like double dynamics should could only have been interesting as gedanken instru- have an advantage over conventional designs in this ments for the ‘development of brain models. With the respect, since they would not have to face competition advance of this technology, though, it should be feasi- from already mature technologies. ble to produce the required proteins in commercial Even if the technology comes into place, the evolu- quantities. tion of the dynamics and of the proteins suitable for a Table I presents a series of design stages relevant to given task will require time. Conceivably a point will molecular-computer development. The table is patently be reached at which a proliferation of devices suitable futuristic, but it does serve to enumerate technologies for a variety of special-purpose tasks will occur. We should point out that these devices will never compete TABL,EI. A Progressively Futuristic Design with humans at those tasks for which humans have Process for a Molecular-Computing Device been adapted by evolution. Technical problems aside, the time frame for such evolution would be beyond all practical limits. 1 Develop a bask5 module like the one illu&feU in Figure 2 (asimpte trfwducerorpr&&- : *_ cassing sen3e orgatl for a cOnv~r@rjatdigi- CONCLUDING REMARKS tal4x3mputer), . The adaptability-efficiency-programmability trade-off 2 Replace simple ctkemical,gractierite ljy Ml@S )_1. 8.. ties together a variety of information-processing phe- dynamics {e.g., symma&y-breakirrg @&pa- .. I’ . _’ . :/ _ nomena exhibited by both technical and biological sys- tive dynamic stwture$). tems. The technical problems that must be addressed in 3 Perfect and mas+produtie suitab~~bie&G~& ... order to exploit this trade-off with molecular and chemical mechanisms have an admittedly forbidding aspect. However, it is noteworthy that the required bio- logical technologies, especially the ability to produce specific proteins on a massive scale, are likely to de- velop and in time to significantly influence the chemi- cal industry, agriculture, and medicine. While it is hard to imagine that the development of a commercially via- ble molecular computer is imminent, it is equally diffi- cult tp imagine a future world in which computing remains aloof from the prevailing technical infrastruc- ture. There are two respects in which the trade-off princi- ple is of immediate interest [4]. First, gene technology is expanding the possibilities for biological design. If this technology is used as a means for prescriptive plan- ning of biological systems similar to the prescriptive control exerted over a von Neumann computer, the trade-off principle predicts that we will inevitably lose evolutionary adaptability. The second area of immediate concern is the use of the von Neumann computer or of any other structur-

478 Communications (of the ACM May 1985 Volume 28 Number 5 Arficles

AN EMERGINGCONSENSUS ON MOLECULARCOMPUTING? Michael Conrad proposes that the information-processing ca- Danny Hillis, a fgunding scientist at Thinking Machines pabilities of organic molecules could be used in computers in Corporation in Cambridge, Massachusetts, feels that a tech- place of digital switching primitives. So far, though, there is nological bridge between computing and biology must be no dear consensus as to the viability of this concept or the built before molecular devices can even ba attempted: ‘If best strategy for molecular computing. There have now been specific proteins-receptors or antibodies-could be built two international workshops on fabricating both inorganic from scratch, then a whole range of applications could be and biologically derived molecular circuitlike devices, as well opened up. In the meantime, though, there is no technologi- as a conference on chemically based computer design; cal foundation for bringing organic materials directly into Conrad’s paper is in fact based on his keynote address from computers.” that conference. In lieu of this, however, there are a number of approaches According to Kevin Ulmer. vice-president for advanced that might successfully combine computing and biology. Ac- technology at Genex Corporation. a major genetic engineer- cording to Ulmer, “If general solid-state bidogical sensors ing firm, however, “no one could legitimately claim to be could be developed that were sufficiently small, sensitive, working on a bk3ogically derived molecular electronic device stable, and specific, they could be useful in a number of right now. In fact, there is hardly any experimental work of ways. We could use such biosensors as the ‘noses’ and consequence being conducted even for nonbiological ap ‘taste buds’ of computers. This woufd complement the work proaches. ” currently being done in robotics to give computers a crude The development of molecularcomputing devices is cur- form of vision, a sense of touch, and an ability to manipulate rently limited both by materials science and analytical meth- objects.” Ulmer also suggests that the interesting electronic ods. As to the specific problem of adapting proteins, “it will and optical properties of some protein crystals could be uti- be necessary to develop a protein engineering technology for lized for electro-optical devices. altering the structure and function of proteins in a precise David Waltz, a senior scientist at Thinking Machines Cor- and predictable fashion before anything else can be done,” poration, lists four possible advantages that molecular- says Ulmer. computing devices might have if they can ever be developed: Ulmer believes that a likely first step would be to design Current computer technologies are essentially planar, and hybrid devices-solid-state biological sensors built from both are thus limited in overall density and use of three- conventional semiconductors and proteins. This would be dimensional space. much easier than working on the molecular processing level. ‘It’s the bulk electronic properties of biological materials that There are limits to miniaturization with current technolo we should ba looking at. Building individual switches based gies-wires cannot be made much smaller without becom- on molecules is simply beyond our present capabilities.” ing subject to destruction by stray wsmic radiation or Mark Stefik, a principal scientist in the Intelligent Systems semiconductor impurities. Molecular-computing devices, Laboratory at Xerox PARC, doubts that proteins could make besides being much smaller than anything we can make computers more adaptable: “Adaptability is an emergent with current technology, may even offer possibilities for property at much higher levels than enzymes in living sys- self-repair or self-regeneration. tems. The interesting information processes that underlie ev- Certain computations may, in fact, as Conrad suggests, be olution do not arise out of the properties of isolated mote- better suited to molecular devices. cules, but rather out of the structure and organization of Molecular devices may force us to explore the relation- living cells.” Furthermore, the “architecture” of biological sys- ships among programmability, adaptability, and efficiency, tems remains only partially understood. “There may be very and so lead to new theoretical insights on computation special possibilities for miniaturization in mdecular technol- and intelligence, and in the process to new computing ogy. But we’re a long way from understanding any viable engines that will be superior in certain ways to existing principles of operation at this point.” computers.

ally programmable computing system. According to the the relationships among adaptability, efficiency, and trade-off principle, these systems are inherently less programmability. Here the study of molecular- adaptable than biological systems and inherently less computer designs has immediate practical significance efficient for the performance of a wide variety of criti- for computer science independent of whether or not cal computing tasks. It cannot be doubted that the con- such designs can be concretized either in the near or trollable information-processing power of current com- distant future. puters is an enormously valuable new resource and that the current expansion of this form of computing Acknowledgments. This article is a written version of can have an enhancing effect on various aspects of hu- the keynote address delivered at the Conference on man activity. If the trade-off principle is correct, how- Chemically-Based Computer Design, sponsored by the ever, there are aspects of human intelligence that digi- National Science Foundation and the UCLA Crump In- tal computers will never be powerful enough to dupli- stitute for Medical Engineering, and held in October cate. The trade-off principle does not contradict the 1983. I am indebted to F. E. Yates, the chief organizer, claim of Turing and Church, but it clearly contradicts and to other participants for valuable comments that the expectations of many advocates of artificial intelli- enabled me to improve the presentation. The confer- gence. To productively incorporate computing into the ence proposal was based in part on the report “Bio- infrastructure of society, it is necessary to understand chips: A Feasibility Study,” prepared by myself,

May 1985 Volume 28 Number 5 Communications of the ACM 479 Articles

C. Friedlander, and K. Akingbehin, and supported by 27. Kirby, KC., and Conrad, M. The enzymatic neuron as a reaction- diffusion network of cvclic nucleotides. Bull. Mafh. Biol. 46. 5-6 National GenasSciences. Wayne State University fac- (1984), 765-783. . ulty participating in the study group also included 26. Kononenko, N.I., Kostyuk. P.G.. and Sherbatko. A.D. The effect of R. Kampfner and R. Rada (from the Computer Science intracellular CAMP injections on stationary membrane conductance and voltage- and time-dependent ionic currents in identified snail Department) and R. Arking, H. Burr, V. Hari, D. Njus, neurons. Brain Res. 268, 2 (June 1983). 321-338. A. Seigel, and A. Sodja (from the Biological Sciences 29. Kuck. D. The Structure of Computers and Computafions, vol. 1. John Wiley & Sons, New York, 1976. Department). J. Taylor facilitated the study and contrib- 30. Landauer. R. Uncertainty principle and minimal energy dissipation uted to it. I also acknowledge useful conversation with in the computer. Int. J. Theor. Phys. 21, 3-4 (Apr. 1982), 283-297. H. M. Hasting, and support from the Computer Science 31. Liberman. E.A.. Minina. S.V.. and Golubtsov, K.V. The study of the metabolic synapse. 1. Effect of intracellular microinjection of 3’,5’- Section of the National Science Foundation (Grant AMP. Biophysics 20, 3 (1975). 457-463. MCS-82-05423, Evolutionary Programming Techniques for 32. Liberman, E.A.. Minina. S.V.. and Shklovsky-Kordy. N.E. Neuron Adaptive Information Processing). membrane depolarization by 3’.5’-adenosine monophosphate and its possible role in neuron molecular cell computer (mcc) action. Biophysics 23, 2 (1978). 306-314. REFERENCES 33. Liberman, E.A., Minina. S.V., Shklovsky-Kordy, N.E., and Conrad, 1. Bennett, C.H. Logical reversibility of computation. JBM 1. Res. Dev. M. Change of mechanical parameters as a possible means for infor- 17.6(Nov.1973) 525-532. mation processing by the neuron. Biophysics 27, 5 (1962), 906-915. 2. Bremermann. H.J. Optimization through evolution and recombina- 34. Liberman. E.A.. Minina. S.V.. Shklovsky-Kordy, N.E., and Conrad, tion. In Se/J-Organizing Sys&ms, M.C. Yovits, G.T. Jacobi, and M. Microinjection of cyclic nucleotides provides evidence for a dif- G.D. Goldstein, Ilds. Spartan Books, Washington, DC, 1962. fusional mechanism of intraneuronal control. BioSystems 15, 2 pp. 93-106. (1982), 127-132. 3. Carter, F.L.. Ed. Molecular Elecfronic Devices. Marcel Dekker. New 35. Minsky, M. Computation: Finife and Jnfinife Machines. Prentice-Hall, York, 1982. Englewood Cliffs, N.J., 1967. 4. Conrad, M. Adaptability. Plenum Publishing Corp., New York, 1983, 36. Nicolis. G., and Prigogine, 1. Self-Organizafion in Nonequilibrium Sys- pp.234, 347-3'70. tems. Wiley-Interscience. New York, 1977. 5. Conrad, M. Evolution of the adaptive landscape. In Theoretical Ap- 37. Pattee. H.H. Physical problems of decision-making constraints. In proaches to Complex Systems, R. Heim and G. Palm, Eds. Springer- The Physical Principles of Neuronaf and Organismic Behavior. Verlag. New Y&k, 1978. M. Conrad and M. Magar. Eds. Gordon and Breach, Science Publish- 6. Conrad, M. Information processing in molecular systems. BioSystems ers, New York, 1973, pp. 217-225. 5, 1 (Aug. 197i’), l-14. 36. Poston, T.. and Stewart, I. Caksrrophe Theory and its Applications. 7. Conrad, M. Microscopic-macroscopic interface in biological informa- Pitman Publishing, Marshfield. Mass., 1978. tion processing. BioSystems 16. 3-4 (1984). 345-363. 39. Przybylski. A.T.. Statten. W.P.. Syren, R.M., and Fox, S.W. Mem- 8. Conrad, M. Molecular automata. In Physics and Mathematics of the brane, action, and oscillatory potentials in simulated protocells. Na- Neroous System, M. Conrad, W. Giittinger. and M. Dal Cin. Eds. lunuissenschaffen 69. 12 (Dec. 1982), 561-563. Springer-Verlag. New York, 1974, pp. 419-430. 40. Samuel, A.L. Some studies of machine learning using the game of 9. Conrad, M. Molecular information processing in the central nervous checkers. IBM]. Res. Dev. 3, 3 (July 19591, 211-229. system, part 1. In Physics and Mathemafics of fhe Nervous System. 41. Street, G.B.. and Clarke, T.C. Conducting polymers: A review of M. Conrad, W. Giittinger, and M. Dal Cin. Eds. Springer-Verlag, New recent work. IBM I. Res. Dev. 25, 1 (Jan. 1981). 51-57. York, 1974, pp. 82-107. 42. Uzgiris. E.E.. and Kornberg, R.D. Two-dimensional crystallization 10. Conrad, M. Molecular information structures in the brain. I. NPU- technique for imaging macromolecules, with application to antigen- rosci. Res. 2, 3 (1976). 233-254. antibody-complement complexes. Nature 301, 589613 (Jan. 1983). 11. Conrad, M. Mutation-absorption model of the enzyme. Bull. Math. 125-129. Biol. 41, 3 (1979). 367-405. 43. Volkenstein. M.V. Physics and Biology. Academic Press, New York, 12. Conrad, M. Natural selection and the evolution of neutralism. Bio- 1982. Systems 15, l(~l982). 63-65. 44. Waddington, C.H. The Strategy of Genes. George Allen and Unwin. 13. Conrad, M. The importance of molecular hierarchy in information London, 1957. processing. In Towards a Theorefical Biology. vol. 4, C.H. Waddington. 45. Wills, C. Production of yeast alcohol dehydrogenase isoenzymes by Ed. Edinburgh University Press, United Kingdom, 1972. pp. 222-228. selection. Natlrre 261. 5555 [May 1976). 26-29. 14. Conrad, M. The limits of biological simulation. 1. Theor. Biol. 45, 2 46. Wingard. L.B.. Jr. Immobilized enzyme electrodes for glucose deter- (June 1974). 585-590. mination for the artificial pancreas. Fed. Proc. 42, 2 (Feb. 1983). 15. Conrad, M.. and Rosenthal, A. Limits on the computing power of 271-272. biological systems. Bull. Math. Biol. 43, I (1980). 59-67. 47. Wingard. L.B.. Jr.. Berezin, I.V.. and Klysov. A.A., Eds. Enzyme Engi- 16. Davis, M. Computabilify and Unsolvability. McGraw-Hill, New York, neering. Plenum Publishing Corp., New York, 1980. 1958. 48. Wittgenstein, L. Philosophical Investigations. MacMillan & Co., Lon- 17. Drummond, G.I. Cyclic nucleotides in the nervous system. In Ad- don, 1953. vances in Cyclic Nucfeotide Research, vol. 15, P. Greengard and G.A. Robison. Eds. Raven Press, New York, 1983. pp. 373-494. 16. Enslow. P.H. h4ultiprocessor organization-A survey. Comput. Sure. CR Categories and Subject Descriptors: Cl.3 [Processor Architectures]: 9, 1 (Mar. 1977), 103-129. Other Architecture Styles--adaptable architectures; F.l.l [Computation 19. Garey, M.R.. and Johnson, D.S. Computers and Intractabilily. by Abstract Devices]: Models of Computation; L2.m [Artificial Intelli- W.H. Freeman and Co., San Francisco, Calif.. 1979. gence]: Miscellaneous 20. Greengard. P. Cyclic Nucleotides, Phosphorylated Proteins, and NPU- General Terms: Design, Theory ronal Function. Raven Press, New York, 1978. Additional Key Words and Phrases: biological information processing, 21. Gutmann. F., and Lyons, L.E. Organic Semiconductors. Part A. evolutionary programming. learning, modes of computation, molec- R.E. Krieger Publishing Co.. Melbourne, Fla., 1981. ular computers, pattern recognition, trade-offs among complexity 22. Haddon. R.. and Lamola, A. The organic computer: Can microchips measures be built by bacteria? The Sciences 23, 3 (May-June 1983), 40-45. 23. Hameroff, S.R , and Watt, R.C. Information processing in micro- Author’s Present Address: Michael Conrad, Dept. of Computer Science, tubules. j. Theor. Biol. 98.4 (Oct. 1982). 549-561. Wayne State University, Detroit, MI 48202. 24. Hofstadter. D. Gbdel, Escher, Bach: An Eternal Golden Braid. Vintage Books, New York. 1980. 25. Kampfner. R., and Conrad, M. Computational modeling of evolution- Permission to copy without fee all or part of this material is granted ary learning processes in the brain. Bull. Math. Biol. 45, 6 (1983). provided that the copies are not made or distributed for direct commer- 931-968. cial advantage, the ACM copyright notice and the title of the publication 26. Kampfner. R.. and Conrad, M. Sequential behavior and stability and its date appear, and notice is given that copying is by permission of properties of enzymatic neuron networks. Bull. Math. Biol. 45, 6 the Association for Computing Machinery. To copy otherwise. or to (19831, 969-980. republish, requires a fee and/or specific permission.

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