Exploration of RNA Editing and Design of Robust Genetic Algorithms

Transcription

1 Exploraton of RNA Edtng and Desgn of Robust Genetc Algorthms Chen-Feng Huang Modelng, Algorthms and Informatcs Group (CCS-3) Computer and Computatonal Scences Dvson Los Alamos Natonal Laboratory, MS B56 Los Alamos, NM 87545, USA Lus M. Rocha Modelng, Algorthms and Informatcs Group (CCS-3) Computer and Computatonal Scences Dvson Los Alamos Natonal Laboratory, MS B56 Los Alamos, NM 87545, USA Abstract -- Ths paper presents our computatonal methodology usng Genetc Algorthms (GA) for explorng the nature of RNA edtng. These models are constructed usng several genetc edtng characterstcs that are gleaned from the RNA edtng system as observed n several organsms. We have expanded the tradtonal Genetc Algorthm wth artfcal edtng mechansms as proposed by (Rocha, 1997). The ncorporaton of edtng mechansms provdes a means for artfcal agents wth genetc descrptons to gan greater phenotypc plastcty, whch may be envronmentally regulated. Our frst mplementatons of these deas have shed some lght nto the evolutonary mplcatons of RNA edtng. Based on these understandngs, we demonstrate how to select proper RNA edtors for desgnng more robust GAs, and the results wll show promsng applcatons to real-world problems. We expect that the framework proposed wll both facltate determnng the evolutonary role of RNA edtng n bology, and advance the current state of research n Genetc Algorthms. 1 Introducton The most famous RNA edtng system s that of the Afrcan Trypanosomes (Benne, 1993; Stuart, 1993). Its genetc materal was found to possess strange sequence features such as genes wthout translatonal ntaton and termnaton codons, frame shfted genes, etc. Furthermore, observaton of mrna s showed that many of them were sgnfcantly dfferent from the genetc materal from whch they had been transcrbed. These facts suggested that mrna s were edted post-transcrptonally. It was later recognzed that ths edtng was performed by gude RNA s (grna s) coded mostly by what was prevously thought of as non-functonal genetc materal (Sturn and Smpson, 1990). In ths partcular genetc system, grna s operate by nsertng, and sometmes deletng, urdnes. To apprecate the effect of ths edton let us consder Fgure 1. The frst example (Benne, 1993, p. 14) shows a massve urdne nserton (lowercase u s); the amno acd sequence that would be obtaned pror to any edton s shown on top of the base sequence, and the amno acd sequence obtaned after edton s shown n the gray box. The second example shows how, potentally, the nserton of a sngle urdne can change dramatcally the amno acd sequence obtaned; n ths case, a termnaton codon s ntroduced. It s mportant to retan that a mrna molecule can be more or less edted accordng to the concentratons of the edtng operators t encounters. Thus, several dfferent protens coded by the same gene may coexst n an organsm or even a cell, f all (or some) of the mrna s obtaned from the same gene, but edted dfferently, are meanngful to the translaton mechansm. Fgure 1. U-nserton n Trypanosomes RNA The role of RNA edtng n the development of more complex organsms has also been shown to be mportant. Lomel et al. (1994) dscovered that the extent of RNA edtng affectng a type of receptor channels responsble for the medaton of exctatory postsynaptc currents n the central nervous system, ncreases n rat bran development. As a consequence, the knetc aspects of these channels dffer accordng to the tme of ther creaton n the bran s developmental process. Another example s that the development of rats wthout a gene (ADAR1) known to be nvolved n RNA edtng, termnates mdterm (Wang et al., 000). Ths showed that RNA Edtng s more prevalent and mportant than prevously thought. RNA edtng processes have also been dentfed n mammalan brans (Smpson and Emerson, 1996), ncludng human brans (Mttaz et al., 1997). Although RNA edtng seems to play an essental role n the development of some genetc systems and more and more edtng mechansms have been dentfed, not much has been advanced to understand the potental evolutonary advantages, f any, that RNA edtng processes may have provded. To acqure nsghts for answerng ths queston, we need a systematc study on how RNA edtng works. Furthermore, a deeper understandng of the nature of RNA edtng can be

2 exploted to mprove evolutonary computaton tools and ther applcatons to complex, real-world problems. Ths paper reports some of our results towards these two goals. Introducng Edtng n Genetc Algorthms In scence and technology Genetc Algorthms (GA) (Holland, 1975) have been used as computatonal models of natural evolutonary systems and as adaptve algorthms for solvng optmzaton problems. Although GA are smplfed, dealzed models of evolutonary systems, ths approach has led to mportant dscoveres n both natural and artfcal systems. For nstance, Lndgren (1991) used GA to evolve terated prsoner s dlemma rules and modeled many processes observed n bologcal evoluton such as stass, punctuated equlbra, varyng speeds of evoluton, mass extnctons, symboss, and complexty ncrease. Snce GA, at the very least, are a good model of adaptve processes obtaned by varaton and selecton of genotypes n natural systems, n the present work we use them to explore the evolutonary mplcatons of edted genotypes, such as the RNA edtng system. Table 1 depcts the process of a smple genetc algorthm. Table 1. Mechansm of a smple GA 1. Randomly generate an ntal populaton of l n-bt agents, each defned by a genotype strng (chromosome) of symbols from a small alphabet.. Evaluate each agent s (phenotype) ftness. 3. Repeat untl l offsprng agents have been created. a. select a par of parent agents for matng; b. apply crossover operator to genotype strng; c. apply mutaton operator to genotype strng. 4. Replace the current populaton wth the new populaton. 5. Go to Step untl termnatng condton. GAs operate on an evolvng populaton of artfcal organsms, or agents. Each agent s comprsed of a genotype and a phenotype. Evoluton occurs by terated stochastc varaton of genotypes, and selecton of the best phenotypes n an envronment accordng to a ftness functon. In machne learnng, the phenotype s a canddate soluton to some optmzaton problem, whle the genotype s an encodng, or descrpton, of that soluton by means of a doman ndependent representaton, namely, bnary symbol strngs (or chromosomes). In tradtonal GAs, ths code between genotype and phenotype s a drect and unque mappng. In bologcal genetc systems, however, there exsts a multtude of processes, takng place between the transcrpton of a descrpton and ts expresson, responsble for the establshment of an uncertan relaton between genotype and phenotype. For nstance, t was shown that RNA edtng has the power to dramatcally alter gene expresson (Pollack, 1994, P. 78): cells wth dfferent mxes of (edtng mechansms) may edt a transcrpt from the same gene dfferently, thereby makng dfferent protens from the same opened gene. In other words, n a genetc system wth RNA edtng, before a gene s translated nto the space of protens t may be altered through nteractons wth other types of molecules, namely RNA edtors such as grna s. Based upon ths analogy, (Rocha, 1995; Rocha, 1997) proposed a new class of GAs that mplement a process of stochastc edton of the genotypes (chromosomes) of agents, pror to beng translated nto phenotypes (canddate solutons). The edtng process s mplemented by a set of edtors wth dfferent edtng functons, such as nserton or deleton of symbols n the orgnal chromosomes. Before chromosomes can be translated nto the space of solutons, they must pass through successve layers of edtors, present n dfferent concentratons. In each generaton, each chromosome has a certan probablty (gven by the concentratons) of encounterng an edtor n ts layer. If an edtor matches some subsequence of the chromosome when they encounter each other, the edtor s functon s appled and the chromosome s edted. The detaled mplementaton of the smplest GA wth Edton (GAE) s descrbed n the followng: The GAE model conssts of a famly of r m-bt strngs, denoted as ( E, 1 E,, E ), whch s used as the set of r edtors for the chromosomes of the agents n a GA populaton. The length of the edtor strngs s assumed much smaller than that of the chromosomes: m << n, usually an order of magntude. An edtor E s sad to match a substrng, of sze m, of a chromosome, S, at poston k f e = s k +, =1,,, m, 1 = k = n-m, where e and s denote the -th bt value of E and S, respectvely. For each edtor, there exsts an assocated edtng functon that specfes how a partcular edtor edts the chromosomes: when the edtor matches a porton of a chromosome, a number of bts are nserted nto or deleted from the chromosome. For nstance, f the edtng functon of edtor E s to add one randomly generated allele at s when k + m + 1 E matches S at poston k, then all alleles of S from poston k+m+1 to n-1 are shfted one poston to the rght (the allele at poston n s removed). Analogously, f the edtng functon of edtor E s to delete an allele, ths edtor wll nstead delete the allele at s when k + m + 1 E matches S at poston k. All the alleles after poston k+m+1 are shfted n the nverse drecton (one randomly generated allele s then assgned at poston n). Fnally, let the concentraton of the edtor famly be defned by ( v 1, v,, v ). Ths means that the r concentraton of edtor E s denoted as v, and the probablty that S encounters E s thus gven by v. Wth these settngs, the algorthm for the GA wth strng edtng s essentally the same as the regular GA, except that step n Table 1 s now more complcated and redefned as:

3 For each ndvdual n the GA populaton, apply each edtor E wth probablty v (.e., concentraton). If E matches the ndvdual s chromosome S, then edt S wth the edtng functon assocated wth E and evaluate the resultng ndvdual s ftness. respectvely; and populaton sze 40 over 00 generatons for 50 runs. A famly of 5 edtors s randomly generated, wth edtor length selected n the range of to 4 bts. Table 3 shows the correspondng parameters generated for these edtors. Table 3. Parameters of the fve RNA edtors 3 Propertes of Genotype Edtng 3.1 Improvement Rate and Buldng-Block Dynamcs How rapd s evolutonary change, and what determnes the rates, patterns, and causes of change, or lack thereof? Answers to these questons can tell us much about the evolutonary process. The study of evolutonary rate n the context of GA usually nvolves defnng a performance measure that embodes the dea of rate of mprovement, so that ts change over tme can be montored for nvestgaton. In many practcal problems, a tradtonal performance metrc s the best-so-far curve that plots the ftness of the best ndvdual that has been seen thus far by generaton n. To understand how Genotype Edtng works n the GAE model, we employ a testbed, the small Royal Road S1, whch s a mnature of the class of the Royal Road functons (Forrest and Mtchell, 1993). Table. Small royal road functon S1 Table llustrates the schematc of the small Royal Road functon S1. Ths functon nvolves a set of schemata S = ( s 1,..., s ) and the ftness of a bt strng 8 (chromosome) x s defned as F ( x) = c σ ( x), s S s where each c s a value assgned to the schema s as defned n the table; σ (x) s defned as 1 f x s an s nstance of s and 0 otherwse. In ths functon, the ftness of the global optmum strng (40 1 s) s 10*8 = 80. We select ths Royal Road functon as a testbed because t belongs to a class of buldng-block-based functons, n whch search advancements depend entrely on the dscovery and explotaton of buldng blocks. Ths serves as an dealzed testbed for observng how edtng mproves the GA s search power by tracng the orgn of each advance n performance. The GAE experments conducted n ths subsecton are based on a bnary tournament selecton, one-pont crossover and mutaton rates of 0.7 and 0.005, In Table 3, length, alleles and concentraton denote the length, alleles and concentraton of each edtor, respectvely; and functon denotes the correspondng edtng functon. For example, the edtng functon of edtor 1 s to delete 4 bts, meanng that ths edtor deletes 4 alleles at the postons followng the chromosome substrng that matches the edtor. The emprcal results are dsplayed n Fgure. One can see that the averaged best-so-far located by the GA wth edtors s 80 at the end of the experments, 1 ndcatng that the optmum has been found by the GA for all 50 runs. On the other hand, our detaled results show that n the case of the GA wthout edtors the optmum s located n 17 out of 50 runs, and the averaged best-so-far only reaches ftness of around 70 by 00 generatons. A mcroscopc nspecton shows that the search power of the regular GA s lmted by the effects of htchhkng: a well-known phenomenon that occurs when some newly dscovered allele (or sets of alleles) offers great ftness advantages. As that allele spreads quckly through the populaton, the closely lnked alleles (though they may make no contrbuton to the ftness) could propagate to the next generaton by htchhkng on that allele. The rapd occupancy of those non-relevant alleles thus greatly reduces exploraton of alternatves at those loc. They ether drown out other already-dscovered alleles that are advantageous, or leave no room for not-yet-dscovered benefcal alleles. In GA research, htchhkng has been dentfed as a maor problem that lmts mplct parallelsm by reducng the samplng frequency of varous buldng blocks (Forrest and Mcthell, 1993). We can trace htchhkng drectly by plottng the denstes (percentage of the populaton that are nstances) of the relevant schemata over tme to observe how edtng suppresses htchhkng. Fgure 3 s a typcal run that llustrates such densty dynamcs. One can see that the optmum has never been found n the GA wthout edtors, because s was never 3 dscovered. A closer nspecton shows that some 1 The value of the averaged best-so-far performance metrc s calculated by averagng the best-so-fars obtaned at each generaton for all 50 runs, where the vertcal bars overlayng the metrc curves represent the 95-percent confdence ntervals. Ths apples to all the expermental results obtaned n ths paper.

4 htchhkers, 11010, of s at the locaton of s ndeed 3 preclude the dscovery of s. However, n the GA wth 3 edtors, the edtors tend to edt the htchhkers by matchng subsequences of s and offer a larger lkelhood for the GA to dscover s. Ths demonstrates how the edtng 3 mechansm can mprove the GA s search performance by suppressng the effects of htchhkng. snce more edtors tend to ncur more edtng processes. Furthermore, n case of the GAE wth fve edtors, the most strkng dfference s that the correspondng edtng frequency declnes dramatcally as the GAE s populaton evolves, and tends to drop to zero at the end of the experments. Fgure. Averaged best-so-far performance Fgure 3. Buldng Block Dynamcs 3. Effects of Sze of the Famly of Edtors An mportant parameter that may play a key role n the GA s search power s the sze of the famly of edtors. To study the effects of ths factor we conduct experments usng two dfferent famles of two and ten edtors (the other parameters are generated as n the precedng subsecton), n comparson wth the famly of fve edtors studed prevously. Fgure 4.a dsplays the expermental results for 50 runs, n whch the GAE wth fve edtors outperforms the other two GAEs. (The optmum s found n all the 50 runs for the GAE wth fve edtors, but not n the other two GAEs.) Further results on edtng frequency -- the total number of tmes all edtors edted chromosomes n a generaton -- llustrated n Fgure 4.b show that, n the begnnng of the experments, the edtng frequency for the GAE wth two or fve edtors s substantally smaller than that of the GAE wth ten edtors. These results are qute ntutve, Fgure 4. Effects of sze of the edtor famly To further elucdate the effects of sze of the edtor famly, Fgure 5.a dsplays results of edtng frequency n a typcal run for each type of GAE. (The correspondng maxmal ftness located by the GAE wth two, fve, and ten edtors s 70, 80 and 50, respectvely.) One can notce that n the typcal GAE runs where the optmum s not found (.e., the cases for and 10 edtors), the edtng frequency does not sgnfcantly drop to zero near the end of the experments. It appears that these GAs populatons contnue utlzng the edtors to explore the search space. Ths s the reason that the correspondng populaton dversty dsplayed n Fgure 5.b s far from zero n the case of the GAE wth 10 edtors. For the GAE wth edtors, the best-so-far ftness located s close to the optmum -- the results n Fgure 5.a and 5.b show that the degree of edtng s then reduced and the populaton s not as dverse as that of the GAE wth 10 edtors. All ths ndcates that the system settles nto a dynamc equlbrum n whch the exploratory power of the edtng process s balanced by the explotatve pressure of selecton. For the case of the GA wth 5 edtors, the results dsplayed n Fgure 5, however, show that the GA s populaton dversty s lost and the edtng process ultmately comes to an end. Based on the effects of edtor length and concentraton, n the next two subsectons we wll present more results to support our observaton. To measure dversty at the -th locus of a GA strng, a smple btwse dversty metrc s defned as (Mahfoud, 1995): D = p, where p s the proporton of 1s at locus n the current generaton. Averagng the btwse dversty metrc over all loc offers a combned allelc dversty measure l for the populaton: D = ( D ) l. D has a value of 1 when =1 / the proporton of 1s at each locus s 0.5 and 0 when all of the loc are fxed to ether 0 or 1. Effectvely t measures how close the allele frequency s to a random populaton (1 beng closest).

5 Fgure 5 Edtng frequency and populaton dversty 3.3 Effects of Edtor Length Another mportant parameter that may also play a crtcal role s the length of edtors. To examne the effects of ths factor we conduct experments for another two GAEs where all the fve edtors are of bts or 10 bts. (All the other parameters are generated by the same way used n Secton 3.1.) Fgure 6.a llustrates the results for these GAEs, n whch the GAE of Secton 3.1 (denoted as Edtor length=...4 n the fgure) outperforms the other two GAEs. Our hypothess s that, as the length of edtors s too long, matchngs between edtors and subsequences of the GAE s chromosomes are rather unlkely, thereby nducng almost no edtng. On the contrary, f the length of edtors s too short, numerous matchngs may occur and the GAE s populaton wll undergo consderable edtng processes. Ths may result n serous dsruptve effect on ft ndvduals. In other words, the performance dscrepancy of the GAEs wth dfferent edtor length may agan depend on edtng frequency. The emprcal results for edtng frequency shown n Fgure 6.b confrm our expectaton. The edtng frequency for the GAE wth 10-bt edtors (nearly zero frequency over the whole course of the experments) s far smaller than that of the GAE wth -bt edtors. In ths case, the edtors make almost no contrbuton to the GAE s search power. Nonetheless, for the GAE wth -bt edtors, t s obvous that the GAE undergoes consderable edtng processes whch n turn dsrupt the already-dscovered ft ndvduals. As for the GAE used n Secton 3.1 (wth edtors of to 4 bts long), the results show that the GA s populaton undergoes moderate edtng processes n the begnnng of the evolutonary process, whch seems to facltate the GAE s exploraton of the search space. Therefore, proper length of the edtors s essental to acheve search benefts, and a benefcal edtng mechansm would requre moderate edtng frequency. 3.4 Effects of Edtor Concentraton As a further llustraton for the Royal Road testbed, we examne the effects of edtor concentraton on the GAE s search performance. Instead of varous concentratons of the edtors used n Secton 3.1, each edtor s now gven concentraton of 1, meanng that the probablty that the chromosomes encounter each edtor s 1. Fgure 7.a and 7.b dsplay the effects of concentraton and the correspondng edtng frequency. (Concentraton 1 and n the fgure denote the concentraton used n Secton 3.1 and ths subsecton, respectvely.) Snce the probablty of the chromosomes meetng wth edtors s now 1, the populaton would naturally undergo more edtons than n the GAE wth smaller edtor concentratons. These results agan ndcate that the performance dfference les n the number of the performed edtons. As the GA s populaton s consderably edted by the edtors, too much exploraton of the search space would then generate deleterous effects on performance advancement. Approprate edtor concentraton s thus essental for the GAE, snce a benefcal edton requres proper edtor s concentraton to nduce moderate edtng processes. Fgure 6. Effects of edtor length Fgure 7. Effects of edtor concentraton 3.5 Effects of Edtor Functon As the last llustraton, we examne the effects of edtor functon on the GAE s search performance. Instead of the edtor functons used n Secton 3.1, the functons of all the edtors are now desgnated to delete 10 bts, meanng that the chromosomes wll encounter massve gene deletons when they are matched by the edtors. Fgure 8.a and 8.b dsplay the effects of the edtor functons and the correspondng edtng frequency. (Functon 1 and n the fgure denote the edtor functons used n Secton 3.1 and ths subsecton, respectvely.) Snce the gene deleton frequency of the chromosomes s now ncreased, the GAE s populaton would naturally undergo more dsruptve processes than the GAE used n Secton These results ndcate that the performance dfference les n the degree of gene deleton n chromosomes. As the edtors remove consderabe genes of chromosome, 3 We have obtaned smlar results for massve gene nsertons (not shown n ths paper).

6 benefcal genes tend to be deleted, whch would n turn hamper the GAE s search. Approprate edtor functon s thus crucal for the GAE to gan subtstantal search progress. z ( t f ), whch s then plotted on Z-axs. There are clusters of spkes at two corners of the search space, and a hll that occupes most of the space. The magnfed vew on the rght sde of Fgure 8 shows a clearer vew of the heght and area of the hll. As can be seen, the heght of the hll s much lower than that of the spkes, but snce t occupes most of the search space, we expect that most of the populaton ndvduals would be attracted to the hlltop, whch then mpars the GA s search power. Ths problem has been recognzed n GA research as premature convergence. Fgure 8. Effects of edtor functon 4 Applcatons The study of Genotype Edtng has provded us wth nsghts nto how to choose edtor parameters for developng more robust GAs. Bascally, n order to faclate the GAE s search process, the gudelnes are: the sze of the edtor famly, the length and concentraton of the edtors need to be moderate so as to avod over or under-edtng processes; the edtor functon should be far from generatng massve deletons (or nsertons). Furthermore, the choce of the edtor parameters s not absolute, t depends on the problem at hand. In ths secton we apply these rules to select proper genotype edtors for the desgn of more robust GAEs, and test them on two real, non-buldng-block-based test functons: an optmal control problem and Mchalewcz s epstatc functon (Huang, 00). 4.1 An Optmal Control Test Problem Optmal Control problems often arse n many dfferent felds of engneerng and scences. Ths class of problems has been well studed from both theoretcal and computatonal perspectves. The models used to descrbe optmal control problems almost always nvolve more or less nonlnearty n nature. Ths often results n the exstence of multple local optma n the area of nterest. In ths subsecton we employ an artfcal optmal control problem desgned n (Huang, 00). The constrants of the artfcal optmal control problem are: The goal s to maxmze z t ) by searchng for two constant control varables, u and 1 u (-5 = u, 1 u = 5). A sketch of ths functon s dsplayed on the left sde of Fgure 8. The X and Y axes represent the ndex of sample ponts n parameters u and 1 u that are used to compute ( f Fgure 9. The optmal control problem Wth the results obtaned prevously, one may expect that the GAE can use edtors to facltate advance n search by edtng the populaton ndvduals that prematurely converge on the hll, n order to relocate these ndvduals nto hgher ftness spkes. Our man obectve n ths subsecton s to test f the GAE can provde advantages n search. In ths subsecton, each of the two varables s encoded by 30 bts, and thus each ndvdual s a bnary strng of length 60. We use a populaton sze 50, bnary tournament selecton, and crossover and mutaton rates of 0.7 and 0.005, respectvely. The experments are conducted for 100 runs, each run wth 00 generatons. For the famly of edtors, snce the strng length and populaton sze used s of the same order as those used n the last secton, we also use fve edtors, of length between 3 and 6, moderate concentraons, and moderate degree of nserton or deleton. These parameters are shown n Table 4. Table 4. Parameters of the fve edtors Fgure 10 dsplays the averaged best-so-far performance, whch shows that the genotype edton agan acheved an advantage n search. As we examne the detaled results, we see that for the case where edtors are absent the best-so-far located by the GA s only of 7.01 (the ftness at the hlltop) n nearly 60 out of 100 runs. However, the GAE explores more of the search space and extends the best-so-fars to hgher range. Ths tells us how these edtors mprove the GAE s search process.

7 Fgure 10. Averaged best-so-far performance All other GAE parameter values reman the same as those used n the prevous subsecton. Fgure 1 dsplays the correspondng averaged best-so-far performance, where one can see that the search performance of the GAE, wth the assstance of edtors, s mproved. 4. Epstatc Mchalewcz Functon In contrast to the relatvely smple ftness landscape of the optmal control problem, a much more complcated testbed, the modfed epstatc Mchalewcz functon (Huang, 00), s used: Fgure 1. Averaged best-so-far performance and m = 10, 0 = x = π for 1 = = N. A system s lttle (very) epstatc f the optmal allele for any locus depends on a small (large) number of alleles at other loc. The concept of epstass n nature corresponds to nonlnearty n the context of GA (Goldberg, 1989). A sketch of a two-dmensonal verson of ths functon s dsplayed n Fgure 11. Ths functon s a hghly multmodal, nonlnear and nonseparable testbed. Due to the complcated, nonlnear dependence among alleles, one can expect that ths problem presents consderable dffculty to the GA s search. Fgure 11. Modfed Mchalewcz functon In ths subsecton, we use fve varables (N = 5), each varable beng encoded by 10 bts. Thus each chromosome s a bnary strng of length 50. The parameters of the 5 edtors are: 5 Concluson and Future Work We have presented the framework of edtng usng Genetc Algorthms and tested several evolutonary scenaros. The prelmnary results obtaned have shed some lght nto Genotype Edtng: Edtng frequency plays a crtcal role n the evolutonary advantage provded by the edtors -- only a moderate degree of edtng processes would facltate organsms exploraton of the search space. Our results also ndcate that edtng frequency declnes dramatcally as the populaton dversty s lost, ndcatng that the edtng process ultmately comes to an end. If the edtng frequency does not substantally decrease, the system settles nto a dynamc equlbrum where the exploratory power of the edtng process s balanced by the explotatve pressure of selecton. We have also learned some rules for settng up edtors parameters to develop robust GAEs. The results obtaned on real testbeds show promsng applcatons to practcal problems -- n the context of GA the edtng mechansms demonstrate the capablty of substantally mprovng the soluton qualty n functon optmzatons and engneerng. Together wth the nsghts acqured prevously, n future work we am at conductng more bologcally realstc experments whch may lead us towards a better understandng of the advantages of RNA edtng n nature, and elaboratng the condtons under whch the edtng framework wll result n further mprovement n the GA s search performance, as well.

8 In ths paper we dscussed GAs wth edton solely wth constant parameters, such as fxed concentratons, of edtors and a stable envronment defned by a fxed ftness functon. Our prelmnary tests (not dscussed here), however, also show that constant concentratons of edtors may not grant the system any evolutonary advantage when the envronment changes. In order to smulate a genetc system n whch the lnkng of edtors concentratons wth envronmental states may be advantageous n tme-varyng envronments, (Rocha, 1995; Rocha, 1997) proposed a new type of GA known as Contextual Genetc Algorthms (CGA). In ths class of algorthms, the concentratons of edtors change wth the states of the envronment, thus ntroducng a control mechansm leadng to phenotypc plastcty and greater evolvablty. We have already constructed a prelmnary model that allows the relaton between envronmental states and edtors characterstcs (such as concentratons or strngs) to be adaptve. Bascally, we evolve the concentratons of edtors usng an addtonal GA, or allow (slower) mutaton of edtng strngs. Ths way, edtors co-evolve wth the populaton of edted agents n a dynamc envronment. Our prelmnary results on applyng ths co-evolvng CGA to a smple Royal Road testbed (Huang, 00) ndeed show that as the concentratons of edtors co-evolve wth edted agents to the envronmental demands, the CGA s search performance can be mproved wth respect to functon optmzaton. We expect that ths co-evolved lnkng of the parameters of edtors wth changes n envronments to be even more powerful n solvng dynamc, stochastc real-world problems. Our future work wll report on our contnued efforts to systematcally study and determne the condtons under whch CGA can provde artfcal agents an mproved adaptablty to dynamc envronments. Such a deeper understandng of CGA wll lead us to tackle our two ultmate goals: (1) develop novel evolutonary computaton tools for dealng wth dynamc real-world tasks, and () gan a greater understandng of the evolutonary value of RNA Edtng n Bology. Bblography Benne, R. (Ed.) (1993). RNA Edtng: The Alteraton of Proten Codng Sequences of RNA. Ells Horwood. Forrest, S. and Mtchell, M. (1993). Relatve Buldng Block Ftness and the Buldng Block Hypothess. Foundatons of Genetc Algorthms, pp Goldberg, D. E. (1989). Genetc Algorthms n Search, Optmzaton, and Machne Learnng. Readng, MA: Addson Wesley. Huang, C-F. (00). A Study of Mate Selecton n Genetc Algorthms. Doctoral dssertaton. Ann Arbor, MI: Unversty of Mchgan, Electrcal Engneerng and Computer Scence. Lndgren, K. (1991). Evolutonary Phenomena n Smple Dynamcs. In: Artfcal Lfe II. Langton et al. (Eds). Addson-wesley, pp Lomel, H. et al. (1994). Control of Knetc Propertes of AMPA Receptor Channels by RNA Edtng. Scence, 66: pp Mahfoud, S. W. (1995). Nchng Methods For Genetc Algorthms. Ph. D. thess, IllGAL Report No Urbana, IL: Unversty of Illnos at Urbana-Champagn. Mttaz, L., Antonaraks, S. E., Hguch, M. and Scott, H. S. (1997). Localzaton of a Novel Human RNA-edtng Deamnase (hred or ADARB) to Chromosome 10p15. Human Genetcs, 100: pp Pollack, R. (1994). Sgns of Lfe: The Language and Meanngs of DNA. Houghton Mffln. Rocha, Lus M. (1995). Contextual Genetc Algorthms: Evolvng Developmental Rules. Advances n Artfcal Lfe. Moran, J., Moreno, A., Merelo, J. J., and Chacon, P. (Eds.). Sprnger Verlag, pp Rocha, Lus M. (1997). Evdence Sets and Contextual Genetc Algorthms: Explorng Uncertanty, Context and Embodment n Cogntve and bologcal Systems. PhD. Dssertaton. State Unversty of New York at Bnghamton. Scence. Smpson, L. and Emerson, R. B. (1996). RNA Edtng. Annual Revew of Neuroscence, 19: pp Stuart, K. (1993). RNA Edtng n Mtochondra of Afrcan Trypanosomes. In: RNA Edtng : The Alteraton of Proten Codng Sequences of RNA. Benne, R. (Ed.). Ells Horwood Publshers. pp Sturn, N. R. and Smpson, L. (1990). Knetoplast DNA Mncrcles Encode Gude RNA s for Edtng of Cytochrome Oxdase Subunt III mrna. Cell, 61: pp Wang, Q., Khllan, J., Gadue, P., and Nshkura, K. (000). Requrement of the RNA Edtng Deamnase ADAR1 Gene for Embryonc Erythropoess. Scence, 90 (5497): pp Holland, J. H. (1975). Adaptaton n Natural and Artfcal Systems. Unversty of Mchgan Press.