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Evolving hardware as model of enzyme evolution
BioSystems 61 (2001) 15 – 25 www.elsevier.com/locate/biosystems
Evolving hardware as model of enzyme evolution R. Lahoz-Beltra * Department of Applied Mathematics, Faculty of Biological Sciences, Complutense Uni6ersity of Madrid, Madrid 28040, Spain Received 28 February 2000; received in revised form 30 October 2000; accepted 15 February 2001
Abstract Organism growth and survival is based on thousands of enzymes organized in networks. The motivation to understand how a large number of enzymes evolved so fast inside cells may be relevant to explaining the origin and maintenance of life on Earth. This paper presents electronic circuits called ‘electronic enzymes’ that model the catalytic function performed by biological enzymes. Electronic enzymes are the hardware realization of enzymes defined as molecular automata with a finite number of internal conformational states and a set of Boolean operators modelling the active groups of the active site. One of the main features of electronic enzymes is the possibility of evolution finding the proper active site by means of a genetic algorithm yielding a metabolic ring or k-cycle that bears a resemblance to Krebs (k=7) or Calvin (k=4) cycles present in organisms. The simulations are consistent with those results obtained in vitro evolving enzymes based on polymerase chain reaction (PCR) as well as with the general view that suggests the main role of recombination during enzyme evolution. The proposed methodology shows how molecular automata with evolvable features that model enzymes or other processing molecules provide an experimental framework for simulation of the principles governing metabolic pathways evolution and self-organization. © 2001 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Enzyme evolution simulation; Electronic enzyme; Genetic algorithm; Evolvable molecular automata
1. Introduction Evolution of enzymes is one of the key features for explaining the origin and maintenance of life on Earth. Since life is a chemical process based on thousands of enzymes organized in networks, the following question arises: how such a large number of enzymes — over 1500 are known (Fersht, 1985) — evolved so fast on earth? At present * Tel.: +34-91-3944888; fax: +34-91-3945051. E-mail address: [email protected] (R. LahozBeltra).
several strategies have been proposed for in vitro evolution of enzymes. Such approaches are based on polymerase chain reaction (PCR) allowing in vitro homologous recombination or reassembly of two or more DNA segments with random or selected mutations. Before reassembly DNA segments are subjected to in vitro random mutagenesis by error-prone PCR, random nucleotide insertion or selection by previously directed mutations. For instance, one of these protocols known as DNA shuffling has been applied to the artificial evolution of beta-lactamase (Stemmer, 1994), fungal peroxidase (Cherry et al., 1999), para-
0303-2647/01/$ - see front matter © 2001 Elsevier Science Ireland Ltd. All rights reserved. PII: S0303-2647(01)00127-7
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Fig. 1. (a) Chromosome showing E1 and E4 genes; (b) single-point crossover (P1 and P2, parental or mating chromosomes; R1 and R2, offspring or recombinant chromosomes; crossover point, white arrow); and (c) flip-bit mutation (mutation position, white arrow).
nitrobenzyl (pB) esterase (Moore et al. 1997), as well as to the optimization and tailoring of industrial enzymes and peptides of special interest in biotechnology (Harayama, 1998). On the other hand, computer simulation experiments using genetic algorithms (Goldberg, 1989), i.e. search algorithms based on Darwinian natural selection (Fig. 1), have demonstrated a counterpart ap-
proach which could help to find new clues and insights about molecular evolution. It obviously follows from this that genetic algorithms could lead to relevant findings about enzyme evolution. The present work arose out of a previous one where we explored molecular self-assembly modelling Escherichia coli membrane construction, including the operation of ATP synthase as well as
R. Lahoz-Beltra / BioSystems 61 (2001) 15–25
the bacterial flagellar motor (Lahoz-Beltra, 1997). In the aforementioned paper a pending question was the possibility of defining molecular automata, including Turing machine capabilities within the automata modelling enzymes or other processing molecules. In agreement with Marijuan (1991) enzymes could be conceived as biological transistors, a possibility that has been explored to a very limited extent. Such a view is one of the main motivations of the present paper. Since in bacterium and eukaryotic organisms growing and surviving is sustained on the basis of a large number of metabolic reactions, in this paper we have simulated how electronic circuits modelling the catalytic function performed by biological enzymes and called ‘electronic enzymes’1 evolved, yielding to a metabolic ring or k-cycle that bears a resemblance to Krebs (k = 7) or Calvin (k = 4 in the simplified diagram of biochemistry textbooks, i.e. Elliot and Elliot, 1997) cycles present in organisms. In Section 2, we introduce the general features of the electronic enzyme model and its hardware realization, including several genetic algorithm protocols to evolve the active site of enzymes involved in the reactions that define a hypothetical metabolic ring. Section 3 presents the results of the computer simulation experiments described in Section 2. Finally, Section 4 discusses the possible impact of this work and its future directions.
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sented by an n-bit word c1j, c2j, …, cnm and a set of operations or instructions modelling the ‘active groups’ of the active site and given by o1j, o2j, …, onm Boolean operators: Em: (c1j, c2j, …, cnm, o1j, o2j, …, onm). Based on above definitions, an enzymatic reaction Sm + Em Pm: Em
s1j, s2j, …, snm p1j, p2j, …, pnm has been defined as the Boolean operations given by: p1j = s1j o1j c1j, p2j = s2j o2j c2j, …, pnm = snmonmcnm. For instance, let ‘1110’ be a substrate S1 (note that s11 = 1, s21 = 1, s31 = 1, s41 = 0) and E1 an enzyme defined as follows: c11 = 1, c21 = 0, c31 = 1, c41 = 0 with Boolean operators o11 = ‘AND’, o21 = ‘XOR’, o31 = ‘XOR’, o41 = ‘XOR’. In consequence, given the above definition the obtained product P1 of the enzymatic reaction will be equal to ‘1100’ since p11 = 1 AND 1 =1, p21 = 1 XOR 0= 1, p31 = 1 XOR 1 =0 and p41 = 0 XOR 0 =0. The hardware realization of such an automaton, thus the electronic enzyme (Fig. 2), is based on NAND integrated circuits where the input and gate interconnections result in Boolean operators, in this particular case ‘AND’ or ‘XOR’, resem-
2. Model description
2.1. Electronic enzyme modelling and hardware realization Let s1j, s2j, …, snm and p1j, p2j,..., pnm be the n-bit words (i=1, 2, …, n) whose values (i.e. 001 … 0, 011 … 1) represent the substrate Sm and product Pm, respectively of an m enzymatic reaction ( j=1, 2,..., m) performed by enzyme Em. An enzyme Em has been defined (Reviriego and Lahoz-Beltra, 1995) as an automaton with a finite number of internal ‘conformational’ states repre1
Spanish pending patent no. 200000174.
Fig. 2. Electronic enzyme realization (for explanation see text).
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bling the ‘active site’ of an enzyme. Operator (oim, i= 1, 2, …, n) two-way inputs are received from one of the switches whose final states 0/1 or off/on simulate the internal ‘conformational’ state (cim, i=1, 2, … , n) of the enzyme and from one of the LED diodes resembling the substrate (sim, i= 1, 2, …, n). Since in our simulation experiments n was set equal to 4, substrate values were implemented as a combination of 0/1 or off/on states on four LED diodes.
2.2. Chromosome coding of electronic enzymes In this model, we define a population of chromosomes (Fig. 1(a)) simulated as binary strings composed of 0’s and 1’s. In genetic algorithm terminology, genes were defined as substrings of eight binary digits of equal length. Each gene models the combining site within the active site where the substrate binds to one particular enzyme. At each gene, and from left to right, the first four 0/1 digits represent the internal or ‘conformational’ state of an enzyme whereas the other four 0/1 digits represent the ‘active groups’ involved in the reaction modeled as Boolean operators. In the present simulations genes are limited to ‘AND’ and ‘XOR’ operators coded as 1 and 0, respectively. Substrates were simulated as binary strings but with a length equal to four digits and enzymes were simulated as automata whose active site perform Boolean operations after it binds with substrate. Once ‘catalytic’ operations are finished, the output simulates the product Pm of the reaction that will be the substrate Sm + 1 for the next coupled enzymatic reaction. The initial conditions are substrate values which were arbitrarily set up as S1 =‘1110’, S2 = ‘1100’, S3 =‘1000’ and S4 = ‘0000’, relying on a genetic algorithm to search for the proper active site of each one of the four enzymes E1, E2, E3 and E4 involved in the reactions defining the following hypothetical 4-cycle: S1 + E1 P1 S2 + E2 P2 S3 + E3 P3 S4 + E4 P4
Note that in the above reactions P1, P2, P3 and P4 are S2, S3, S4 and S1 respectively. Since in the present experiments we need one gene with a length of eight binary digits per enzyme and the experiments were carried out with a series of four coupled enzymatic reactions, chromosomes were defined as linear arrays 32 binary digits long.
2.3. E6ol6ing a metabolic ring with a simple genetic algorithm The protocol SGA (Fig. 3(a)) is a conventional simple genetic algorithm (Goldberg, 1989) which evaluates a population of chromosomes before reproduction and once a new generation is obtained based on a single cycle of recombination and mutation. The current genetic algorithm uses one-point recombination, a population size of 400, a recombination probability of 0.95 and a mutation probability of 0.1. Starting with a random population of chromosomes reproduction, recombination and mutation were simulated, obtaining new generations of equal size.
2.3.1. Reproduction At each generation, the fitness f of each chromosome, thus the degree of achievement of the whole cycle composed of all the enzymes involved in the 4-cycle formation, was evaluated using the following fairly linear function:
m
n
f= h l - % % Hij(p*, ij si( j + 1)) , j=1 i=1
where l is the chromosome length, 32 in our simulations, and h denotes a coefficient which was set equal to 10. In order to obtain the value of f, the binary values on the chromosome were decoded or translated to the configuration of each one of the enzymes Em, thus to the off/on states of the switches simulating the internal ‘conformational’ state, and to the Boolean operators resembling the ‘active groups’ of their ‘active site’. Once an enzyme configuration was obtained enzymes were tested with their respective substrates (Sm, see substrate values at Section 2.2) and the reaction products returned (P *) m from each enzyme. In the fitness function, the similarity or matching between the obtained product p *ij from an enzy-
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Fig. 3. Genetic algorithm protocols. (a) SGA, (b) SDS, (c) Lamarck and (d) Wallace.
matic reaction and the expected product, thus the substrate si( j + 1) value of the next coupled reaction, was calculated using their Hamming distance. The Hamming distance, or Hij (p*, ij si( j + 1)), is the number of digit positions in which two binary words of the same length differ. Note that correct enzyme Em (m = 1, …, 4) active site finding occurs when the Hamming distance: 4
% Hij (p*, ij si( j + 1))= 0. i=1
Indeed, for 4
4
% % Hij (p*, ij si( j + 1)) = 0, j=1 i=1
a maximum value of f is reached and the search for enzymes defining the 4-cycle is completed. Therefore the fitness function captures the performance of the entire cycle instead of single enzymes. Immediately after chromosomes are evaluated, we select the mating pool of the next generation using the wheel parents selection al-
gorithm (Davis, 1991). This is a popular method for implementing reproduction, and thereby Darwinian selection, by spinning a roulette wheel that assigns to each chromosome a slot whose arc size is proportional to its fitness value.
2.3.2. Recombination Once a new generation of offspring chromosomes is obtained, a single point crossover proceeds with pairs of mates randomly selected. Whether or not we are going to perform crossover on a current pair of parent chromosomes is decided on the basis of a Bernoulli trial regarding recombination as having a given probability (recombination probability). Then a crossover point is randomly selected choosing a number from a uniform distribution. Obviously crossing over was only allowed at selected random crossing sites (8, 16 or 24) between genes. Finally, a single point crossover occurs when segments of two parent chromosomes are swapped (Fig. 1(b)) after a crossover point is selected.
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2.3.3. Mutation Mutation at a point was simulated by a ‘flip a bit’ method (Fig. 1(c)), thus changing at random digit positions from 1 to 0 or replacing 0 by 1. Once again whether or not to change a bit on a chromosome is decided on the basis of a Bernoulli trial, mutation being a success with a given probability (mutation probability). 2.4. Genetic algorithm protocols Simulation experiments based on SGA (Fig. 4(a)) revealed that a tailored genetic algorithm could perform properly. The goal of the following experiments was to find out how a different ar-
rangement of recombination and mutation operators performed in different protocols and thus to be able to select the best protocol for the final algorithm. Experiments were carried out using one-point recombination, a population size of 400, setting the recombination and mutation probabilities to 0.95 and 0.1, respectively. We have tried out three protocols (Fig. 3) which were called SDS (simulated DNA shuffling), Lamarck and Wallace (these names were arbitrarily chosen). The protocol SDS was inspired by protein in vitro evolution experiments (Fig. 3(b)). The protocol involves a cycle of mutation and recombination through 50 generations as emulation of error-prone PCR or random nucleotide insertion
Fig. 4. Performance graph obtained under different protocols. (a) SGA; (b) SDS; (c) Lamarck; and (d) Wallace.
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and DNA reassembly by homologous recombination followed by repeated cycles of recombination, one per generation, in absence of mutation. One of the two other protocols, Lamarck (Fig. 3(c)), consists of a first cycle during 100 generations with only recombination followed by alternate cycles of recombination in the absence of mutation and mutation with recombination. In Lamarck both cycles had an equal duration of 150 generations. Finally, Wallace (Fig. 3(d)) was defined as follows. A simulation experiment starts with a first cycle that includes only recombination for one hundred initial generations. In a second cycle mutation is introduced together with recombination until to reach 250 generation. The experiment concludes in a third cycle with recombination in absence of mutation.
3. Computer simulation results Computer simulation experiments were carried out using the substrate values described in Section 2.2 as well as the recombination and mutation probabilities referred in Section 2.3. In Fig. 4, we show the performance graph for each one of the experiments performed under different protocols. Performance was measured as the average fitness per generation as is usual in experiments based on genetic algorithms. In the SGA protocol, the scattered fitness values (Fig. 4(a)) suggest the uselessness of conventional genetic algorithms when they are naively applied to simulate molecular evolution. In contrast to SGA, under the Lamarck protocol (Fig. 4(c)) the population of chromosomes climbs, reaching after each cycle of mutation and recombination a high average fitness but below the optimum value. Indeed, SDS (Fig. 4(b)) as well as Wallace (Fig. 4(d)) are effectively the only protocols driving the population of chromosomes to a uniform population with a maximum average fitness of 320. The experiments were replicated four times, each time obtaining similar results. In the random number generator different seed values were tried but this had a little impact on the overall results. However, in some experiments and setting up a recombination probability equal to 0.25 we obtained isoenzymes. These were
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different forms in terms of their ‘amino acid’ sequence (for details see Price and Stevens, 1996) of an enzyme catalysing the same reaction. In such experiments two E2 isoenzymes, 00000100 and 11001011, were obtained in the population using the Wallace protocol. In Fig. 5, we show a representative 4-cycle composed of evolved hardware representing the appropriate electronic enzymes. Electronic enzyme configurations were obtained by decoding one of the chromosomes selected from a uniform population (all chromosomes are the same) evolved under the Wallace protocol with maximum average fitness. Our results indicate, therefore, that conventional genetic algorithms are not similar to Darwinian natural selection during molecular evolution. Furthermore, if the SGA protocol were applied to experiments of in vitro enzyme evolution then it could lead to DNA instability. Nevertheless, SGA are powerful design optimization tools when they are applied to inanimate or ‘lifeless objects’ like an aircraft (Bramlette and Bouchard, 1991), its engine turbines or simple cooling fans (Powell et al., 1989). Although SDS as well as Wallace make several simplifying assumptions and the simulation conditions are extreme — i.e. a 10% mutation rate in our experiments compared with a 0.5% (Hemmi et al., 1997) and lower (Louis and Rawlins, 1991) in experiments evolving digital circuits — both protocols could bear a closer resemblance to the role of Darwinian natural selection on molecular evolution than conventional genetic algorithms. Taken together, our results indicate that evolution of enzymes by mutation seems a most unlikely process in Nature since electronic enzyme performance was very sensitive to replacement of one binary digit by another, resulting in non-functional electronic enzymes except for those with neutral mutations. Note that Wallace is basically the same protocol as Lamarck except that in the former more than one cycle of mutation and recombination is carried out. In agreement with Schaffer and Eshelman (1991) it appears that as selection pressure leads to more converged and more fit populations, mutation tended to become more risky. Furthermore, the analysis of performance surfaces suggests a stronger role for muta-
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Fig. 5. Evolved hardware for a 4-cycle obtained using Wallace protocol. The snapshot shows electronic enzymes as well as the four substrates implemented as a combination of two states (switch on/switch off) on four LED diodes. (Top) Electronic enzyme configurations were obtained decoding the evolved chromosome sequence.
tion than has previously been admitted (Schaffer et al., 1989). Indeed, in the biological realm while normal enzymes are highly beneficial, mutated enzymes have been tied to numerous diseases (Ward et al., 1997). Our findings therefore support the view that recombination is the process that plays the key role in enzyme evolution as has
been proposed for eukaryotic organisms, where enzymes could have evolved by recombination of exons (Fersht, 1985; Price and Stevens, 1996). As a consequence, metabolic pathways could have evolved by the sequential addition of enzymes with the proper active site to previous enzymatic reactions (Clarke, 1981; Woese, 1987).
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4. Discussion The simulation results are consistent with the general picture of enzyme evolution as well as with the in vitro enzyme evolution results based on PCR. In consequence electronic enzymes sufficiently capture the role of the active site of real enzymes to justify the acceptance of model assumptions as is shown evolving a 4-cycle hardware realization of a metabolic ring. For instance, the simplistic definition of substrates and reaction products as binary strings as well as the assumption of Boolean operations as the underlying logic of an enzymatic reaction are basically the same theoretical principles used by Siatkowski and Carter (1988) when they applied the Spencer-Brown algebra to logical operations with chromophore moieties. The electronic enzyme proposed in this paper is the hardware realization or strong simulation of a particular kind of molecular automaton. Sipper et al. (1997) showed how certain features of living systems such as self-replication (e.g. Langton’s self-replicating loop), self-repair and growth (i.e. L-systems) can be implemented in integrated circuits. Of course, the realization of electronic enzymes is not more powerful than its underlying computer model. Moreover, actual biological enzymes have more complex functions than those expressed in the simple rules of the computer model. Other enzyme automata models could be adapted and used in our simulation experiments but our model (Reviriego and Lahoz-Beltra, 1995) makes hardware realization easier than others. For instance, Marijuan’s (1991) enzyme automaton is a probabilistic automaton with input and output that are trains of binary digits. The enzyme is ruled by a logical table which summarizes the variables and state transitions of the system. Bray (1995) assumed that enzymes are computational elements like McCulloch-Pitts neurons since the input/output relationship is typically either hyperbolic or sigmoidal, bearing a strong resemblance to the continuous activation functions used with artificial neural networks. The former model is basically the
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concept of an enzymatic neuron introduced by Kirby and Conrad (1986) but without the internal molecular dynamics involved during information processing and based on continuous firing functions instead of the Heaviside step function. Furthermore, our experiments could be carried out with real reconfigurable electronic circuits, that is, evolvable hardware such as Xilinx XC6216, a commercially available VLSI chip called FPGA (Oldfield and Dorf, 1995; Thompson et al., 1999) which can be changed based on genetic algorithms. However, with a few NAND chips, cable, and two-way switches as well as LED diodes and other affordable electronic devices it is possible to perform ‘home-made experiments’ and try out the plausibility of biological hypotheses. We propose that the ultimate realistic simulation of the dynamic activities exhibited inside cells could be achieved by developing a hardware realization of molecular automata like the CAM machine developed by Toffoli (1984) for cellular automata. This approach would be particularly useful if molecular automata were designed with evolvable features, for instance automata that support affinity changes between connected bond sites (Lahoz-Beltra, 1997, 1998) or electronic enzymes whose active sites take its fine shape during evolution, such as those introduced in the present paper. In the simulation experiments, genetic algorithms like the SDS protocol are able to find the proper active site of electronic enzymes. However in the biological realm PCR appears to be much less prone to evolve new molecular types in vitro than are 3SR and Qi replicase reactions (Bull and Pease, 1995). This is an important observation that substantiates the difficulties of explaining satisfactorily how a large number of enzymes evolved so fast on Earth. Once again the motivation of the present paper has been to understand the formal principles governing biological function namely, self-assembly (Lahoz-Beltra, 1997, 1998), computation (Lahoz-Beltra et al., 1993) and evolutionary signs of the essential principle ruling biological systems known as selforganization.
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Acknowledgements We thank to Carmen Lahoz Beltra for her comments on the manuscript and discussion about PCR as well as DNA shuffling. We are grateful to Deborah Conrad for helpful suggestions about manuscript style. This work was supported by Laboratorio de Bioinformatica, Universidad Complutense.
References Bramlette, M.F., Bouchard, E.E., 1991. Genetic algorithms in parametric design of aircraft. In: Davis, L. (Ed.), Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York, pp. 109–123. Bray, D., 1995. Protein molecules as computational elements in living cells. Nature 376, 307 –312. Bull, J.J., Pease, C.M., 1995. Why is the polymerase chain reaction resistant to in vitro evolution? J. Mol. Evol. 41, 1160 – 1164. Cherry, J.R., Lamsa, M.H., Schneider, P., Vind, J., Svendsen, A., Jones, A., Pedersen, A.H., 1999. Directed evolution of a fungal peroxidase. Nat. Biotechnol. 17, 379 – 384. Clarke, P.H., 1981. Enzyme in bacterial populations. In: Gutfreund, H. (Ed.), Biochemical Evolution. Cambridge University Press, Cambridge, pp. 116 –149. Davis, L. (Ed.), 1991. Handbook of Genetic Algorithms. Van Nostrand Reinhold. Elliot, W.H., Elliot, D.C., 1997. Biochemistry and Molecular Biology. Oxford University Press, London. Fersht, A., 1985. Enzyme Structure and Mechanism. W.H. Freeman, San Francisco, CA. Goldberg, D.E., 1989. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, MA. Harayama, S., 1998. Artificial evolution by DNA shuffling. Trends Biotechnol. 16, 76 –82. Hemmi, H., Mizoguchi, J., Shimohara, K., 1997. Evolving large scale digital circuits. In: Langton, C.G., Shimohara, K. (Eds.), Artificial Life V. Proceedings of the Fifth International Workshop on the Synthesis and Simulation of Living Systems. A Bradford Book. MIT Press, Cambridge, MA, pp. 213 –218. Kirby, K.G., Conrad, M., 1986. Intraneuronal dynamics as a substrate for evolutionary learning. In: Farmer, D., Lapedes, A., Packard, N., Wendroff, B. (Eds.), Evolution, Games and Learning: Models for Adaptation in Machines and Nature. Physica D 22, pp. 205 –215. Lahoz-Beltra, R., Hameroff, S.R., Dayhoff, J.E., 1993. Cytoskeletal logic: a model for molecular computation via Boolean operations in microtubules and microtubule-as-
sociated proteins. BioSystems 29, 1 – 23. Lahoz-Beltra, R., 1997. Molecular automata assembly: principles and simulation of bacterial membrane construction. BioSystems 44, 209 – 229. Lahoz-Beltra, R., 1998. Molecular automata modeling in structural biology. Adv. Struct. Biol. 5, 85 – 101. Louis, S.J., Rawlins, G.J.E., 1991. Designer genetic algorithms: genetic algorithms in structure design. In: Belew, R.K., Booker, L.B. (Eds.), Proceedings of the Fourth International Conference on Genetic Algorithms. Morgan Kaufmann, pp. 53 – 60. Marijuan, P.C., 1991. Enzymes and theoretical biology: sketch of an informational perspective of the cell. BioSystems 25, 259 – 273. Moore, J.C., Jin, H.M., Kuchner, O., Arnold, F.H., 1997. Strategies for the in vitro evolution of protein function: enzyme evolution by random recombination of improved sequences. J. Mol. Biol. 272, 336 – 347. Oldfield, J.V., Dorf. R.C., 1995. Field Programmable Gate Arrays: Reconfigurable Logic for Rapid Prototyping and Implementation of Digital Systems. Wiley, New York. Powell, D.J., Tong, S.S., Skolnick, M.M., 1989. EnGENEous domain independent, machine learning for design optimization. In: Spatz, B. (Ed.). Proceedings of the Third International Conference on Genetic Algorithms. Morgan Kaufmann, pp. 151 – 159. Price, N.C., Stevens, L., 1996. Fundamentals of Enzymology. Oxford University Press, London. Reviriego Eiros, M., Lahoz-Beltra, R., 1995. Enzymes, Turing machines and random origin of metabolic pathways. Third European Conference on Artificial Life, Granada, Spain. Schaffer, J.D., Caruana, R.A., Eshelman, L.J., Das, R., 1989. A study of control parameters affecting online performance of genetic algorithms for function optimization. In: Schaffer, J.D. (Ed.), Proceedings of the Third International Conference on Genetic Algorithms. Morgan Kaufmann, pp. 51 – 60. Schaffer, J.D., Eshelman, L.J., 1991. On crossover as an evolutionary viable strategy. In: Belew, R.K., Booker, L.B. (Eds.), Proceedings of the Fourth International Conference on Genetic Algorithms. Morgan Kaufmann, pp. 61 – 68. Siatkowski, R.E., Carter, F.L., 1988. The chemical elements of logic. In: Carter, F.L., Siatkowski, R.E., Wohltjen, H. (Eds.), Molecular Electronic Devices. Elsevier Science Publishers B.V., North-Holland, pp. 321 – 327. Sipper, M., Mange, D., Stauffer, A., 1997. Ontogenic hardware. BioSystems 44, 193-207. Stemmer, W.P., 1994. DNA shuffling by random fragmentation and reassembly: in vitro recombination for molecular evolution. Proc. Natl. Acad. Sci. USA 91, 10747 – 10751. Thompson, A., Layzell, P., Salem Zebulum, R., 1999. Explorations in design space: unconventional electronics design through artificial evolution. IEEE Trans. Evol. Comput. 3 (3), 167 – 196.
R. Lahoz-Beltra / BioSystems 61 (2001) 15–25 Toffoli, T., 1984. CAM: a high-performance cellular-automaton machine. Physica D 10, 195 –204. Ward, W., Alvarado, L., Rawlings, N.D., Engel, J.C., Franklin, C., McKerrow, J.H., 1997. A primitive enzyme
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Evolving hardware as model of enzyme evolution R. Lahoz-Beltra * Department of Applied Mathematics, Faculty of Biological Sciences, Complutense Uni6ersity of Madrid, Madrid 28040, Spain Received 28 February 2000; received in revised form 30 October 2000; accepted 15 February 2001
Abstract Organism growth and survival is based on thousands of enzymes organized in networks. The motivation to understand how a large number of enzymes evolved so fast inside cells may be relevant to explaining the origin and maintenance of life on Earth. This paper presents electronic circuits called ‘electronic enzymes’ that model the catalytic function performed by biological enzymes. Electronic enzymes are the hardware realization of enzymes defined as molecular automata with a finite number of internal conformational states and a set of Boolean operators modelling the active groups of the active site. One of the main features of electronic enzymes is the possibility of evolution finding the proper active site by means of a genetic algorithm yielding a metabolic ring or k-cycle that bears a resemblance to Krebs (k=7) or Calvin (k=4) cycles present in organisms. The simulations are consistent with those results obtained in vitro evolving enzymes based on polymerase chain reaction (PCR) as well as with the general view that suggests the main role of recombination during enzyme evolution. The proposed methodology shows how molecular automata with evolvable features that model enzymes or other processing molecules provide an experimental framework for simulation of the principles governing metabolic pathways evolution and self-organization. © 2001 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Enzyme evolution simulation; Electronic enzyme; Genetic algorithm; Evolvable molecular automata
1. Introduction Evolution of enzymes is one of the key features for explaining the origin and maintenance of life on Earth. Since life is a chemical process based on thousands of enzymes organized in networks, the following question arises: how such a large number of enzymes — over 1500 are known (Fersht, 1985) — evolved so fast on earth? At present * Tel.: +34-91-3944888; fax: +34-91-3945051. E-mail address: [email protected] (R. LahozBeltra).
several strategies have been proposed for in vitro evolution of enzymes. Such approaches are based on polymerase chain reaction (PCR) allowing in vitro homologous recombination or reassembly of two or more DNA segments with random or selected mutations. Before reassembly DNA segments are subjected to in vitro random mutagenesis by error-prone PCR, random nucleotide insertion or selection by previously directed mutations. For instance, one of these protocols known as DNA shuffling has been applied to the artificial evolution of beta-lactamase (Stemmer, 1994), fungal peroxidase (Cherry et al., 1999), para-
0303-2647/01/$ - see front matter © 2001 Elsevier Science Ireland Ltd. All rights reserved. PII: S0303-2647(01)00127-7
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Fig. 1. (a) Chromosome showing E1 and E4 genes; (b) single-point crossover (P1 and P2, parental or mating chromosomes; R1 and R2, offspring or recombinant chromosomes; crossover point, white arrow); and (c) flip-bit mutation (mutation position, white arrow).
nitrobenzyl (pB) esterase (Moore et al. 1997), as well as to the optimization and tailoring of industrial enzymes and peptides of special interest in biotechnology (Harayama, 1998). On the other hand, computer simulation experiments using genetic algorithms (Goldberg, 1989), i.e. search algorithms based on Darwinian natural selection (Fig. 1), have demonstrated a counterpart ap-
proach which could help to find new clues and insights about molecular evolution. It obviously follows from this that genetic algorithms could lead to relevant findings about enzyme evolution. The present work arose out of a previous one where we explored molecular self-assembly modelling Escherichia coli membrane construction, including the operation of ATP synthase as well as
R. Lahoz-Beltra / BioSystems 61 (2001) 15–25
the bacterial flagellar motor (Lahoz-Beltra, 1997). In the aforementioned paper a pending question was the possibility of defining molecular automata, including Turing machine capabilities within the automata modelling enzymes or other processing molecules. In agreement with Marijuan (1991) enzymes could be conceived as biological transistors, a possibility that has been explored to a very limited extent. Such a view is one of the main motivations of the present paper. Since in bacterium and eukaryotic organisms growing and surviving is sustained on the basis of a large number of metabolic reactions, in this paper we have simulated how electronic circuits modelling the catalytic function performed by biological enzymes and called ‘electronic enzymes’1 evolved, yielding to a metabolic ring or k-cycle that bears a resemblance to Krebs (k = 7) or Calvin (k = 4 in the simplified diagram of biochemistry textbooks, i.e. Elliot and Elliot, 1997) cycles present in organisms. In Section 2, we introduce the general features of the electronic enzyme model and its hardware realization, including several genetic algorithm protocols to evolve the active site of enzymes involved in the reactions that define a hypothetical metabolic ring. Section 3 presents the results of the computer simulation experiments described in Section 2. Finally, Section 4 discusses the possible impact of this work and its future directions.
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sented by an n-bit word c1j, c2j, …, cnm and a set of operations or instructions modelling the ‘active groups’ of the active site and given by o1j, o2j, …, onm Boolean operators: Em: (c1j, c2j, …, cnm, o1j, o2j, …, onm). Based on above definitions, an enzymatic reaction Sm + Em Pm: Em
s1j, s2j, …, snm p1j, p2j, …, pnm has been defined as the Boolean operations given by: p1j = s1j o1j c1j, p2j = s2j o2j c2j, …, pnm = snmonmcnm. For instance, let ‘1110’ be a substrate S1 (note that s11 = 1, s21 = 1, s31 = 1, s41 = 0) and E1 an enzyme defined as follows: c11 = 1, c21 = 0, c31 = 1, c41 = 0 with Boolean operators o11 = ‘AND’, o21 = ‘XOR’, o31 = ‘XOR’, o41 = ‘XOR’. In consequence, given the above definition the obtained product P1 of the enzymatic reaction will be equal to ‘1100’ since p11 = 1 AND 1 =1, p21 = 1 XOR 0= 1, p31 = 1 XOR 1 =0 and p41 = 0 XOR 0 =0. The hardware realization of such an automaton, thus the electronic enzyme (Fig. 2), is based on NAND integrated circuits where the input and gate interconnections result in Boolean operators, in this particular case ‘AND’ or ‘XOR’, resem-
2. Model description
2.1. Electronic enzyme modelling and hardware realization Let s1j, s2j, …, snm and p1j, p2j,..., pnm be the n-bit words (i=1, 2, …, n) whose values (i.e. 001 … 0, 011 … 1) represent the substrate Sm and product Pm, respectively of an m enzymatic reaction ( j=1, 2,..., m) performed by enzyme Em. An enzyme Em has been defined (Reviriego and Lahoz-Beltra, 1995) as an automaton with a finite number of internal ‘conformational’ states repre1
Spanish pending patent no. 200000174.
Fig. 2. Electronic enzyme realization (for explanation see text).
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bling the ‘active site’ of an enzyme. Operator (oim, i= 1, 2, …, n) two-way inputs are received from one of the switches whose final states 0/1 or off/on simulate the internal ‘conformational’ state (cim, i=1, 2, … , n) of the enzyme and from one of the LED diodes resembling the substrate (sim, i= 1, 2, …, n). Since in our simulation experiments n was set equal to 4, substrate values were implemented as a combination of 0/1 or off/on states on four LED diodes.
2.2. Chromosome coding of electronic enzymes In this model, we define a population of chromosomes (Fig. 1(a)) simulated as binary strings composed of 0’s and 1’s. In genetic algorithm terminology, genes were defined as substrings of eight binary digits of equal length. Each gene models the combining site within the active site where the substrate binds to one particular enzyme. At each gene, and from left to right, the first four 0/1 digits represent the internal or ‘conformational’ state of an enzyme whereas the other four 0/1 digits represent the ‘active groups’ involved in the reaction modeled as Boolean operators. In the present simulations genes are limited to ‘AND’ and ‘XOR’ operators coded as 1 and 0, respectively. Substrates were simulated as binary strings but with a length equal to four digits and enzymes were simulated as automata whose active site perform Boolean operations after it binds with substrate. Once ‘catalytic’ operations are finished, the output simulates the product Pm of the reaction that will be the substrate Sm + 1 for the next coupled enzymatic reaction. The initial conditions are substrate values which were arbitrarily set up as S1 =‘1110’, S2 = ‘1100’, S3 =‘1000’ and S4 = ‘0000’, relying on a genetic algorithm to search for the proper active site of each one of the four enzymes E1, E2, E3 and E4 involved in the reactions defining the following hypothetical 4-cycle: S1 + E1 P1 S2 + E2 P2 S3 + E3 P3 S4 + E4 P4
Note that in the above reactions P1, P2, P3 and P4 are S2, S3, S4 and S1 respectively. Since in the present experiments we need one gene with a length of eight binary digits per enzyme and the experiments were carried out with a series of four coupled enzymatic reactions, chromosomes were defined as linear arrays 32 binary digits long.
2.3. E6ol6ing a metabolic ring with a simple genetic algorithm The protocol SGA (Fig. 3(a)) is a conventional simple genetic algorithm (Goldberg, 1989) which evaluates a population of chromosomes before reproduction and once a new generation is obtained based on a single cycle of recombination and mutation. The current genetic algorithm uses one-point recombination, a population size of 400, a recombination probability of 0.95 and a mutation probability of 0.1. Starting with a random population of chromosomes reproduction, recombination and mutation were simulated, obtaining new generations of equal size.
2.3.1. Reproduction At each generation, the fitness f of each chromosome, thus the degree of achievement of the whole cycle composed of all the enzymes involved in the 4-cycle formation, was evaluated using the following fairly linear function:
m
n
f= h l - % % Hij(p*, ij si( j + 1)) , j=1 i=1
where l is the chromosome length, 32 in our simulations, and h denotes a coefficient which was set equal to 10. In order to obtain the value of f, the binary values on the chromosome were decoded or translated to the configuration of each one of the enzymes Em, thus to the off/on states of the switches simulating the internal ‘conformational’ state, and to the Boolean operators resembling the ‘active groups’ of their ‘active site’. Once an enzyme configuration was obtained enzymes were tested with their respective substrates (Sm, see substrate values at Section 2.2) and the reaction products returned (P *) m from each enzyme. In the fitness function, the similarity or matching between the obtained product p *ij from an enzy-
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Fig. 3. Genetic algorithm protocols. (a) SGA, (b) SDS, (c) Lamarck and (d) Wallace.
matic reaction and the expected product, thus the substrate si( j + 1) value of the next coupled reaction, was calculated using their Hamming distance. The Hamming distance, or Hij (p*, ij si( j + 1)), is the number of digit positions in which two binary words of the same length differ. Note that correct enzyme Em (m = 1, …, 4) active site finding occurs when the Hamming distance: 4
% Hij (p*, ij si( j + 1))= 0. i=1
Indeed, for 4
4
% % Hij (p*, ij si( j + 1)) = 0, j=1 i=1
a maximum value of f is reached and the search for enzymes defining the 4-cycle is completed. Therefore the fitness function captures the performance of the entire cycle instead of single enzymes. Immediately after chromosomes are evaluated, we select the mating pool of the next generation using the wheel parents selection al-
gorithm (Davis, 1991). This is a popular method for implementing reproduction, and thereby Darwinian selection, by spinning a roulette wheel that assigns to each chromosome a slot whose arc size is proportional to its fitness value.
2.3.2. Recombination Once a new generation of offspring chromosomes is obtained, a single point crossover proceeds with pairs of mates randomly selected. Whether or not we are going to perform crossover on a current pair of parent chromosomes is decided on the basis of a Bernoulli trial regarding recombination as having a given probability (recombination probability). Then a crossover point is randomly selected choosing a number from a uniform distribution. Obviously crossing over was only allowed at selected random crossing sites (8, 16 or 24) between genes. Finally, a single point crossover occurs when segments of two parent chromosomes are swapped (Fig. 1(b)) after a crossover point is selected.
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2.3.3. Mutation Mutation at a point was simulated by a ‘flip a bit’ method (Fig. 1(c)), thus changing at random digit positions from 1 to 0 or replacing 0 by 1. Once again whether or not to change a bit on a chromosome is decided on the basis of a Bernoulli trial, mutation being a success with a given probability (mutation probability). 2.4. Genetic algorithm protocols Simulation experiments based on SGA (Fig. 4(a)) revealed that a tailored genetic algorithm could perform properly. The goal of the following experiments was to find out how a different ar-
rangement of recombination and mutation operators performed in different protocols and thus to be able to select the best protocol for the final algorithm. Experiments were carried out using one-point recombination, a population size of 400, setting the recombination and mutation probabilities to 0.95 and 0.1, respectively. We have tried out three protocols (Fig. 3) which were called SDS (simulated DNA shuffling), Lamarck and Wallace (these names were arbitrarily chosen). The protocol SDS was inspired by protein in vitro evolution experiments (Fig. 3(b)). The protocol involves a cycle of mutation and recombination through 50 generations as emulation of error-prone PCR or random nucleotide insertion
Fig. 4. Performance graph obtained under different protocols. (a) SGA; (b) SDS; (c) Lamarck; and (d) Wallace.
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and DNA reassembly by homologous recombination followed by repeated cycles of recombination, one per generation, in absence of mutation. One of the two other protocols, Lamarck (Fig. 3(c)), consists of a first cycle during 100 generations with only recombination followed by alternate cycles of recombination in the absence of mutation and mutation with recombination. In Lamarck both cycles had an equal duration of 150 generations. Finally, Wallace (Fig. 3(d)) was defined as follows. A simulation experiment starts with a first cycle that includes only recombination for one hundred initial generations. In a second cycle mutation is introduced together with recombination until to reach 250 generation. The experiment concludes in a third cycle with recombination in absence of mutation.
3. Computer simulation results Computer simulation experiments were carried out using the substrate values described in Section 2.2 as well as the recombination and mutation probabilities referred in Section 2.3. In Fig. 4, we show the performance graph for each one of the experiments performed under different protocols. Performance was measured as the average fitness per generation as is usual in experiments based on genetic algorithms. In the SGA protocol, the scattered fitness values (Fig. 4(a)) suggest the uselessness of conventional genetic algorithms when they are naively applied to simulate molecular evolution. In contrast to SGA, under the Lamarck protocol (Fig. 4(c)) the population of chromosomes climbs, reaching after each cycle of mutation and recombination a high average fitness but below the optimum value. Indeed, SDS (Fig. 4(b)) as well as Wallace (Fig. 4(d)) are effectively the only protocols driving the population of chromosomes to a uniform population with a maximum average fitness of 320. The experiments were replicated four times, each time obtaining similar results. In the random number generator different seed values were tried but this had a little impact on the overall results. However, in some experiments and setting up a recombination probability equal to 0.25 we obtained isoenzymes. These were
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different forms in terms of their ‘amino acid’ sequence (for details see Price and Stevens, 1996) of an enzyme catalysing the same reaction. In such experiments two E2 isoenzymes, 00000100 and 11001011, were obtained in the population using the Wallace protocol. In Fig. 5, we show a representative 4-cycle composed of evolved hardware representing the appropriate electronic enzymes. Electronic enzyme configurations were obtained by decoding one of the chromosomes selected from a uniform population (all chromosomes are the same) evolved under the Wallace protocol with maximum average fitness. Our results indicate, therefore, that conventional genetic algorithms are not similar to Darwinian natural selection during molecular evolution. Furthermore, if the SGA protocol were applied to experiments of in vitro enzyme evolution then it could lead to DNA instability. Nevertheless, SGA are powerful design optimization tools when they are applied to inanimate or ‘lifeless objects’ like an aircraft (Bramlette and Bouchard, 1991), its engine turbines or simple cooling fans (Powell et al., 1989). Although SDS as well as Wallace make several simplifying assumptions and the simulation conditions are extreme — i.e. a 10% mutation rate in our experiments compared with a 0.5% (Hemmi et al., 1997) and lower (Louis and Rawlins, 1991) in experiments evolving digital circuits — both protocols could bear a closer resemblance to the role of Darwinian natural selection on molecular evolution than conventional genetic algorithms. Taken together, our results indicate that evolution of enzymes by mutation seems a most unlikely process in Nature since electronic enzyme performance was very sensitive to replacement of one binary digit by another, resulting in non-functional electronic enzymes except for those with neutral mutations. Note that Wallace is basically the same protocol as Lamarck except that in the former more than one cycle of mutation and recombination is carried out. In agreement with Schaffer and Eshelman (1991) it appears that as selection pressure leads to more converged and more fit populations, mutation tended to become more risky. Furthermore, the analysis of performance surfaces suggests a stronger role for muta-
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Fig. 5. Evolved hardware for a 4-cycle obtained using Wallace protocol. The snapshot shows electronic enzymes as well as the four substrates implemented as a combination of two states (switch on/switch off) on four LED diodes. (Top) Electronic enzyme configurations were obtained decoding the evolved chromosome sequence.
tion than has previously been admitted (Schaffer et al., 1989). Indeed, in the biological realm while normal enzymes are highly beneficial, mutated enzymes have been tied to numerous diseases (Ward et al., 1997). Our findings therefore support the view that recombination is the process that plays the key role in enzyme evolution as has
been proposed for eukaryotic organisms, where enzymes could have evolved by recombination of exons (Fersht, 1985; Price and Stevens, 1996). As a consequence, metabolic pathways could have evolved by the sequential addition of enzymes with the proper active site to previous enzymatic reactions (Clarke, 1981; Woese, 1987).
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4. Discussion The simulation results are consistent with the general picture of enzyme evolution as well as with the in vitro enzyme evolution results based on PCR. In consequence electronic enzymes sufficiently capture the role of the active site of real enzymes to justify the acceptance of model assumptions as is shown evolving a 4-cycle hardware realization of a metabolic ring. For instance, the simplistic definition of substrates and reaction products as binary strings as well as the assumption of Boolean operations as the underlying logic of an enzymatic reaction are basically the same theoretical principles used by Siatkowski and Carter (1988) when they applied the Spencer-Brown algebra to logical operations with chromophore moieties. The electronic enzyme proposed in this paper is the hardware realization or strong simulation of a particular kind of molecular automaton. Sipper et al. (1997) showed how certain features of living systems such as self-replication (e.g. Langton’s self-replicating loop), self-repair and growth (i.e. L-systems) can be implemented in integrated circuits. Of course, the realization of electronic enzymes is not more powerful than its underlying computer model. Moreover, actual biological enzymes have more complex functions than those expressed in the simple rules of the computer model. Other enzyme automata models could be adapted and used in our simulation experiments but our model (Reviriego and Lahoz-Beltra, 1995) makes hardware realization easier than others. For instance, Marijuan’s (1991) enzyme automaton is a probabilistic automaton with input and output that are trains of binary digits. The enzyme is ruled by a logical table which summarizes the variables and state transitions of the system. Bray (1995) assumed that enzymes are computational elements like McCulloch-Pitts neurons since the input/output relationship is typically either hyperbolic or sigmoidal, bearing a strong resemblance to the continuous activation functions used with artificial neural networks. The former model is basically the
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concept of an enzymatic neuron introduced by Kirby and Conrad (1986) but without the internal molecular dynamics involved during information processing and based on continuous firing functions instead of the Heaviside step function. Furthermore, our experiments could be carried out with real reconfigurable electronic circuits, that is, evolvable hardware such as Xilinx XC6216, a commercially available VLSI chip called FPGA (Oldfield and Dorf, 1995; Thompson et al., 1999) which can be changed based on genetic algorithms. However, with a few NAND chips, cable, and two-way switches as well as LED diodes and other affordable electronic devices it is possible to perform ‘home-made experiments’ and try out the plausibility of biological hypotheses. We propose that the ultimate realistic simulation of the dynamic activities exhibited inside cells could be achieved by developing a hardware realization of molecular automata like the CAM machine developed by Toffoli (1984) for cellular automata. This approach would be particularly useful if molecular automata were designed with evolvable features, for instance automata that support affinity changes between connected bond sites (Lahoz-Beltra, 1997, 1998) or electronic enzymes whose active sites take its fine shape during evolution, such as those introduced in the present paper. In the simulation experiments, genetic algorithms like the SDS protocol are able to find the proper active site of electronic enzymes. However in the biological realm PCR appears to be much less prone to evolve new molecular types in vitro than are 3SR and Qi replicase reactions (Bull and Pease, 1995). This is an important observation that substantiates the difficulties of explaining satisfactorily how a large number of enzymes evolved so fast on Earth. Once again the motivation of the present paper has been to understand the formal principles governing biological function namely, self-assembly (Lahoz-Beltra, 1997, 1998), computation (Lahoz-Beltra et al., 1993) and evolutionary signs of the essential principle ruling biological systems known as selforganization.
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Acknowledgements We thank to Carmen Lahoz Beltra for her comments on the manuscript and discussion about PCR as well as DNA shuffling. We are grateful to Deborah Conrad for helpful suggestions about manuscript style. This work was supported by Laboratorio de Bioinformatica, Universidad Complutense.
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