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Towards a biomolecular computer
BioSystems, 27 (1992) 219- 222
219
Elsevier Scientific Publishers Ireland Ltd.
Towards a biomolecular computer N.G. Rambidi International Research Institute for Management Sciences, Prospekt 60-1et Oktyabria 9, 117312 Moscow (Russia)
A new version of computing and information processing devices may result from major principles of information processing at molecular level. Non-discrete biomolecular computers based on these principles seems to be capable of solving problems of high computational complexity. One of the possible ways to implement these devices is based on biochemical non-linear dynamical systems. Means and ways to materialize biomolecular computers are discussed.
Keywords: Bimolecular computing; Non-discrete biomolecular information processing device; Problems of high computational complexity.
1. Introduction
The contemporary investigations in the field of molecular and biomolecular computing may be divided into three basic trends: • using organic materials for IC production based on the traditional circuit design and on existing planar technology; • discrete molecular computing based on digital device simulation, i.e. an attempt to replace the known silicon based primitives by molecules (or simple assemblies of molecules) which have the same silicon based primitives characteristics; • non-discrete biomolecular computing based on the main principles of information processing at the molecular level specific for simple biomolecular systems. The first trend is only the way to extend the choice of materials available in modern semiconductor device technology. It gives no opportunity to use any other physical mechanisms of information processing than those for conventional materials and devices. The second and the third ones are based on the qualitatively new approaches to design and conCorrespondence to: N.G. Rambidi, International Institute of Management Sciences, Prospekt 60-let Oktyabria, 9, 117312 Moscow, Russia.
struction of computing and information processing devices. Primitives that can be used for the implementation of molecular devices should basically differ from the semiconductor primitives. The digital silicon based IC elements are subminiature semiconductor devices, i.e. macrodevices. In the molecular circuits under investigation these primitives are supposed to be replaced by micro-objects such as molecules or small molecular assemblies. The properties of these primitives differ form the properties of silicon based ones to the same extent as quantum theory of solids differs from quantum mechanics of molecules. The discrete molecular primitives allow for the improvement of a number of information processing device characteristics as compared with similar characteristics of silicon based devices. At the same time, molecular primitives should have some qualitatively different properties other than those of the silicon based ones. The characteristics of molecular circuits that may be considered to be improved due to the use of the molecular primitives are: • higher degree of integration, although the estimated difference in integration between molecular and semiconductor based devices is not so large;
220
• considerably less switching energies; • enhanced stability of circuits with respect to radiation, especially while increasing the degree of integration. Among qualitatively new characteristics of molecular primitives should be named: • complete identity of characteristics of the molecular primitives, unlike the spread of characteristics of semiconductor based ones due to their technological failures; • shot noise free one-electron processes, that are typical of molecular objects; • specific molecular mechanisms of signal transfer allowing elaboration of more logically complicated primitives than the semiconductor based ones. At the same time the discrete computing devices constructed at the molecular level and using planar technology should suffer from the nightmare of interconnections while increasing the degree of integration. Besides, computational possibilities of the molecular devices should be the same as for semiconductor digital computers due to the likeness of their circuit design and architecture. The discrete molecular computer may solve problems of high computational complexity only with considerable restrictions as well as with semiconductor ones. Non-discrete biomolecular devices are characterized by the same advantages as the discrete ones, that is due to specific features of their constituent molecular units. But in this case the device structure qualitatively changes as compared with semiconductor based devices. The latter have rigid structural organization. At the same time, the biomolecular systems that implement information processes are characterized by a functionally flexible structure optimally adapted to the solution of a specific problem. That is why molecular processors seem to be used for solving problems of high computational complexity. Thus, development of the theory and means of implementing non-discrete biomolecular devices for calculations and information processing may be the most interesting and promising trend of molecular computing. It is hoped this trend may lead to a qualitatively new class of computing
and information processing devices, that wouldn't compete with future digital computers, but supplement them and considerably widen their possibilities.
II. General principle of information processing at the molecular level Over forty years Claude Shannon's information theory has been the paradigm in the field of information transmission and processing. This system of conceptions proved to be a highly successhtl description of the operational principles for information transmission devices, therefore its use was widespread. Recently, however, its connection with progress in the study of the information features of chemical, biological and other complicated dynamical objects this formal description appeared to be inadequate. Moreover, there arose recently the belief that information processing systems of complicated behavior should exist, which do not use the man-made principle of device complication to achieve a high behavioral complexity. One of the possible means of designing such systems is the use of the basic principles of information processing at the molecular level that are materialized in primitive biological (supramolecular) structures. These principles are: • giant parallelism of information processing; • dynamic processing mechanisms based on complicated non-linear processes; • high efficiency of information transformation; • considerable information complexity of initial (pseudo-elementary) operations; • ability for variation and evolution of molecular components of information processing devices including the ability for evolutionary learning. III. Design principles of biomolecular computers Given the information properties of non-linear dynamical biomolecular systems, one might picture some versions of the information processing devices that may be embodied practically.
221
For instance, a device of this type may be formed based on a system of parallel-operating pseudo-flat primitive elements, each of them (or several of them) corresponding to a certain level of information processing. A single primitive element should be a limited size fiat carrier (artificial biomembrane, polymer film, etc) that contains immobilized individual components of the biochemical system (enzymes, receptors and other biomacromolecules) used. Optimally, the carrier should be porous to provide transport of the reaction components through the device, i.e. energy supply. The interconnections between different levels may be of a chemical type, i.e. the products of reactions at some levels being substrates for reactions at the next level. A flat two-dimensional structure of elements allows parallel information input-output to be easily realized and parallel information processing to be carried out (for instance, input of information by projecting the light pattern onto the active layer that transforms the light signal into spatial distribution of the photochemical reaction product). i
An interesting possibility for implementation of biomolecular information processing devices is provided by the heterogeneous distributed biochemical systems that can be fabricated, for instance, using multibox compartmentalized supramolecular structures where the walls between compartments are permeable for molecular components (Fig. 1). They provide a rigid pre-assigned geometry of the system components and the possibility to arrange steady local control. Use within this study model was based on the oxidation reaction of uric acid which is catalyzed by the uricase enzyme: uric acid 02, H20 > allontoin uricase uricase The reaction can proceed in the membrane with the immobilized enzyme. In this system where the membrane separates two solutions with constant substrate and excess of cosubstrate concentrations and where the reaction is sustained by diffusion of substrate and cosubstrate from solution, the phenomenon of hysteresis was experimentally observed. Computer simulation of the dynamics in a single cell (one box) revealed that the system may have three steady states that can be conventionally termed as + 1, 0 and -1. Given the planar two-dimensional multibox system fabricated from uricase boxes and given a definite choice of model parameters, the dynamics of the system can be described by the equations: ~ = ~xi-
xi 3 -
yi;
Yk
I
p
I
Fig. 1. The simplified model of a biochemical multibox information processing device. S and P are flows of substrates and products.
where xi and yi are concentrations of substrate and co-substrate in the ith compartment; 6, % d are parameters of the model (the meaning of them is obvious). Computer simulation of the system dynamics has shown that the homogeneous state of the system determined by uniform distribution of substrate and co-substrate concentrations
222 whether an even or odd number of compartments separate the perturbed boxes the surface is either completely filled with the chess-board pattern or dislocations of O-type states will appear at the interfaces. Numerical investigations have demonstrated that the dynamic processes proceeding in the system under consideration can be used as the basis to perform various complicated logical operations such as image extraction from a noisy pattern, extraction of the figure contour, smoothing the contour of a complicated image, etc. Details of this investigation will be published in the near future (Gritsenko et al., 1992; Rambidi and Chernavskii, 1992; Rambidi et al., 1992). Fig. 2. Dissipative pattern formation in distributed multiboxdynamicalsystem.1, 2 and 3 correspond to the temporal evolutionof a one-dimensionalsystem.
appears to be unstable with respect to local perturbations, i.e. to the increase of the concentration of the substrate (co-substrate) at any point. In this case a dissipative pattern formation has been observed around the perturbation points (Fig. 2). The structure of the pattern resembles a chess-board picture where the compartments with + 1 and -1 states alternate. Depending on
References Gritsenko, O.V., Sidelnikov,D.I., Simonova,A.P., Rambidi, N.G. and Chernavskii, D.S., 1992, Towards a biomolecular computer. 3. Information processing features of distributed biochemicalsystems functioning in the mode of dissipative structures formation. J. Mol. Electron. 7, 155-166. Rambidi, N.G. and Chernavskii, D.S., 1992, Towards a biomolecular computer. 2. Information processing and computing devices based on biochemical non-linear dynamical systems. J. Mol. Electron. 7, 115-125. Rambidi, N.G., Chernavskii,D.S. and Sandier, Yu. M., 1992, Towards a biomolecularcomputer. 1. Ways, means, objective. J. Mol. Electron. 7, 105-114.
219
Elsevier Scientific Publishers Ireland Ltd.
Towards a biomolecular computer N.G. Rambidi International Research Institute for Management Sciences, Prospekt 60-1et Oktyabria 9, 117312 Moscow (Russia)
A new version of computing and information processing devices may result from major principles of information processing at molecular level. Non-discrete biomolecular computers based on these principles seems to be capable of solving problems of high computational complexity. One of the possible ways to implement these devices is based on biochemical non-linear dynamical systems. Means and ways to materialize biomolecular computers are discussed.
Keywords: Bimolecular computing; Non-discrete biomolecular information processing device; Problems of high computational complexity.
1. Introduction
The contemporary investigations in the field of molecular and biomolecular computing may be divided into three basic trends: • using organic materials for IC production based on the traditional circuit design and on existing planar technology; • discrete molecular computing based on digital device simulation, i.e. an attempt to replace the known silicon based primitives by molecules (or simple assemblies of molecules) which have the same silicon based primitives characteristics; • non-discrete biomolecular computing based on the main principles of information processing at the molecular level specific for simple biomolecular systems. The first trend is only the way to extend the choice of materials available in modern semiconductor device technology. It gives no opportunity to use any other physical mechanisms of information processing than those for conventional materials and devices. The second and the third ones are based on the qualitatively new approaches to design and conCorrespondence to: N.G. Rambidi, International Institute of Management Sciences, Prospekt 60-let Oktyabria, 9, 117312 Moscow, Russia.
struction of computing and information processing devices. Primitives that can be used for the implementation of molecular devices should basically differ from the semiconductor primitives. The digital silicon based IC elements are subminiature semiconductor devices, i.e. macrodevices. In the molecular circuits under investigation these primitives are supposed to be replaced by micro-objects such as molecules or small molecular assemblies. The properties of these primitives differ form the properties of silicon based ones to the same extent as quantum theory of solids differs from quantum mechanics of molecules. The discrete molecular primitives allow for the improvement of a number of information processing device characteristics as compared with similar characteristics of silicon based devices. At the same time, molecular primitives should have some qualitatively different properties other than those of the silicon based ones. The characteristics of molecular circuits that may be considered to be improved due to the use of the molecular primitives are: • higher degree of integration, although the estimated difference in integration between molecular and semiconductor based devices is not so large;
220
• considerably less switching energies; • enhanced stability of circuits with respect to radiation, especially while increasing the degree of integration. Among qualitatively new characteristics of molecular primitives should be named: • complete identity of characteristics of the molecular primitives, unlike the spread of characteristics of semiconductor based ones due to their technological failures; • shot noise free one-electron processes, that are typical of molecular objects; • specific molecular mechanisms of signal transfer allowing elaboration of more logically complicated primitives than the semiconductor based ones. At the same time the discrete computing devices constructed at the molecular level and using planar technology should suffer from the nightmare of interconnections while increasing the degree of integration. Besides, computational possibilities of the molecular devices should be the same as for semiconductor digital computers due to the likeness of their circuit design and architecture. The discrete molecular computer may solve problems of high computational complexity only with considerable restrictions as well as with semiconductor ones. Non-discrete biomolecular devices are characterized by the same advantages as the discrete ones, that is due to specific features of their constituent molecular units. But in this case the device structure qualitatively changes as compared with semiconductor based devices. The latter have rigid structural organization. At the same time, the biomolecular systems that implement information processes are characterized by a functionally flexible structure optimally adapted to the solution of a specific problem. That is why molecular processors seem to be used for solving problems of high computational complexity. Thus, development of the theory and means of implementing non-discrete biomolecular devices for calculations and information processing may be the most interesting and promising trend of molecular computing. It is hoped this trend may lead to a qualitatively new class of computing
and information processing devices, that wouldn't compete with future digital computers, but supplement them and considerably widen their possibilities.
II. General principle of information processing at the molecular level Over forty years Claude Shannon's information theory has been the paradigm in the field of information transmission and processing. This system of conceptions proved to be a highly successhtl description of the operational principles for information transmission devices, therefore its use was widespread. Recently, however, its connection with progress in the study of the information features of chemical, biological and other complicated dynamical objects this formal description appeared to be inadequate. Moreover, there arose recently the belief that information processing systems of complicated behavior should exist, which do not use the man-made principle of device complication to achieve a high behavioral complexity. One of the possible means of designing such systems is the use of the basic principles of information processing at the molecular level that are materialized in primitive biological (supramolecular) structures. These principles are: • giant parallelism of information processing; • dynamic processing mechanisms based on complicated non-linear processes; • high efficiency of information transformation; • considerable information complexity of initial (pseudo-elementary) operations; • ability for variation and evolution of molecular components of information processing devices including the ability for evolutionary learning. III. Design principles of biomolecular computers Given the information properties of non-linear dynamical biomolecular systems, one might picture some versions of the information processing devices that may be embodied practically.
221
For instance, a device of this type may be formed based on a system of parallel-operating pseudo-flat primitive elements, each of them (or several of them) corresponding to a certain level of information processing. A single primitive element should be a limited size fiat carrier (artificial biomembrane, polymer film, etc) that contains immobilized individual components of the biochemical system (enzymes, receptors and other biomacromolecules) used. Optimally, the carrier should be porous to provide transport of the reaction components through the device, i.e. energy supply. The interconnections between different levels may be of a chemical type, i.e. the products of reactions at some levels being substrates for reactions at the next level. A flat two-dimensional structure of elements allows parallel information input-output to be easily realized and parallel information processing to be carried out (for instance, input of information by projecting the light pattern onto the active layer that transforms the light signal into spatial distribution of the photochemical reaction product). i
An interesting possibility for implementation of biomolecular information processing devices is provided by the heterogeneous distributed biochemical systems that can be fabricated, for instance, using multibox compartmentalized supramolecular structures where the walls between compartments are permeable for molecular components (Fig. 1). They provide a rigid pre-assigned geometry of the system components and the possibility to arrange steady local control. Use within this study model was based on the oxidation reaction of uric acid which is catalyzed by the uricase enzyme: uric acid 02, H20 > allontoin uricase uricase The reaction can proceed in the membrane with the immobilized enzyme. In this system where the membrane separates two solutions with constant substrate and excess of cosubstrate concentrations and where the reaction is sustained by diffusion of substrate and cosubstrate from solution, the phenomenon of hysteresis was experimentally observed. Computer simulation of the dynamics in a single cell (one box) revealed that the system may have three steady states that can be conventionally termed as + 1, 0 and -1. Given the planar two-dimensional multibox system fabricated from uricase boxes and given a definite choice of model parameters, the dynamics of the system can be described by the equations: ~ = ~xi-
xi 3 -
yi;
Yk
I
p
I
Fig. 1. The simplified model of a biochemical multibox information processing device. S and P are flows of substrates and products.
where xi and yi are concentrations of substrate and co-substrate in the ith compartment; 6, % d are parameters of the model (the meaning of them is obvious). Computer simulation of the system dynamics has shown that the homogeneous state of the system determined by uniform distribution of substrate and co-substrate concentrations
222 whether an even or odd number of compartments separate the perturbed boxes the surface is either completely filled with the chess-board pattern or dislocations of O-type states will appear at the interfaces. Numerical investigations have demonstrated that the dynamic processes proceeding in the system under consideration can be used as the basis to perform various complicated logical operations such as image extraction from a noisy pattern, extraction of the figure contour, smoothing the contour of a complicated image, etc. Details of this investigation will be published in the near future (Gritsenko et al., 1992; Rambidi and Chernavskii, 1992; Rambidi et al., 1992). Fig. 2. Dissipative pattern formation in distributed multiboxdynamicalsystem.1, 2 and 3 correspond to the temporal evolutionof a one-dimensionalsystem.
appears to be unstable with respect to local perturbations, i.e. to the increase of the concentration of the substrate (co-substrate) at any point. In this case a dissipative pattern formation has been observed around the perturbation points (Fig. 2). The structure of the pattern resembles a chess-board picture where the compartments with + 1 and -1 states alternate. Depending on
References Gritsenko, O.V., Sidelnikov,D.I., Simonova,A.P., Rambidi, N.G. and Chernavskii, D.S., 1992, Towards a biomolecular computer. 3. Information processing features of distributed biochemicalsystems functioning in the mode of dissipative structures formation. J. Mol. Electron. 7, 155-166. Rambidi, N.G. and Chernavskii, D.S., 1992, Towards a biomolecular computer. 2. Information processing and computing devices based on biochemical non-linear dynamical systems. J. Mol. Electron. 7, 115-125. Rambidi, N.G., Chernavskii,D.S. and Sandier, Yu. M., 1992, Towards a biomolecularcomputer. 1. Ways, means, objective. J. Mol. Electron. 7, 105-114.