Physical Model for the Evolution of the Genetic Code

Transcription

1 Physcal Model for the Evoluton of the Genetc Code Tatsuro Yamashta Osamu Narkyo Department of Physcs, Kyushu Unversty, Fukuoka 8-856, Japan Abstract We propose a physcal model to descrbe the mechansms of two major scenaros of the genetc code evoluton, the codon capture and ambguous ntermedate scenaros, n a consstent manner. We sketch the lowest dmensonal verson of our model, a mnmal model, by ntroducng a physcal quantty, codon level. On the bass of the herarchcal structure of the codon levels two scenaros are classfed nto two dfferent routes of the evolutonal process. In the case of the ambguous ntermedate scenaro we perform a smulaton mplemented cost selecton of amno acds and confrm a rapd transton of the code change. Such rapdness reduces uncomfortableness of the non-unque translaton of the code at ntermedate state that s the weakness of the scenaro. Keywords Genetc code evoluton Codon capture Ambguous ntermedate Physcal mechansm Cost selecton

2 Introducton The genetc code s the central element of every bologcal phenomenon. It was supposed to be frozen at frst, but t turned out to be evolvable after the dscovery of nonstandard code n mtochondra []. After that several scenaros for the evoluton of the genetc code [-3], namely the reassgnment of codons to amno acds, have been proposed. Among them the codon capture [,4] and ambguous ntermedate [5,6] scenaros are major ones. In the text-book argument [] the possblty of the latter scenaro was questoned. However, recent analyss [7] for observed codon reassgnments supports both scenaros accordng to the stuaton. The codon capture scenaro s supported by observed codon reassgnments from stop to an amno acd. On the other hand, the ambguous ntermedate scenaro s supported by observed codon reassgnments from one amno acd to another. Thus n ths paper by ntroducng a concept of codon level we try to construct a physcal model whch realzes both scenaros n a consstent manner. On the bass of our physcal model we can dscuss the mechansm of the genetc code evoluton. As far as we know, a study of the mechansm by physcal arguments has not been reported. Ths paper s organzed as follows. In Secton we summarze two scenaros and ntroduce our physcal model. Some smulaton results on the bass of our model are dscussed n Secton 3 focusng on the tme dependence of the genetc code evoluton. Our concluson s gven n Secton 4. Model - Codon Capture and Ambguous Intermedate Scenaros The abstract of the codon capture [,4] and ambguous ntermedate [5,6] scenaros are shown n Fg.. The codon reassgnments manly arse from alteratons n trna. Accordng to the poston of the trna alteraton, favored scenaro changes as shown n Fg.. The stuaton s summarzed [,3] as follows and we adopt ths summary as a bass of our model. If the alteraton occurs at the antcodon n trna, the codon reassgnment proceeds accordng as the codon capture scenaro. On the other hand, f the alteraton occurs at locatons other than the antcodon n trna, the codon reassgnment proceeds accordng to the ambguous ntermedate scenaro.

3 Fg. Two major scenaros of genetc code evoluton: codon capture and ambguous ntermedate scenaros. In the ntermedate state both codon and trna dsappear n codon capture scenaro but a codon s recognzed by two dfferent trnas n ambguous ntermedate scenaro.

4 Fg. Mutatons n trna. An alteraton at the antcodon n trna s the drvng force of the codon capture scenaro, whle the ambguous ntermedate scenaro s drven by that at locatons other than the antcodon. Another mportant bass of our model s the followng dscrmnaton [7] between two scenaros. The codon capture scenaro s supported by observed codon reassgnments from stop to an amno acd. On the other hand, the ambguous ntermedate scenaro s supported by observed codon reassgnments from one amno acd to another. On these two bases we ntroduce a concept of codon level and dscuss ts structure as a key ngredent to obtan a unfed framework for the codon capture and ambguous ntermedate scenaros. - Codon Level Here we model the affnty of trna for codon. The property of the target codon can be represented as a vector n a hgh-dmensonal coordnate space. The coordnates consttute of the nformaton of the propertes of the codon such as the form and the

5 physcal quanttes. For example, the charge or hydrophobcty dstrbuton of the codon s such a physcal quantty. Snce the purpose of ths paper s to sketch our scheme, we adopt a scalar, representng the property of the target codon, nstead of a vector, for smplcty. In the followng we call ths scalar the codon level. Ths smplfed model s a mnmal model to dscuss the mechansm of the genetc code evoluton. A smlar constructon [8] has been done n the study of mmunty and a shape space s employed to descrbe the process of recognton between antgens and antbodes. As the frst step the -dmensonal shape space has been thoroughly nvestgated there. On the above-mentoned two bases we can naturally assume a structure n the dstrbuton of the codon levels. The structure conssts of ntermttent scatter of clusters as shown n Fg. 3. The cluster corresponds to the famly box of four codons n the genetc code table. These codons n the same famly are often translated to the same amno acd by wobble base-parng between codons and antcodons. Such a wobble parng s consdered to result form two factors. One s the closeness of the codon levels n the cluster. The other s the spread of the range of the codon recognton of trna. Ths range s expressed as a secton n the coordnate axs along the codon level as shown n Fg. 3. If a substructure wth level gap exsts n the cluster, codons separated by the gap may be translated to dfferent amno acds.

6 Fg. 3 Codon level scheme. In general the levels of four codons, belongng to the same famly box of the genetc code table, form a cluster and clusters belongng to dfferent famles are separated by gaps n the level scheme. The range of the codon recognton of a trna s expressed as a secton along the codon level axs. Codon capture and ambguous ntermedate scenaros are understood as dfferent evolutonal routes. The former scenaro corresponds to the genetc code evoluton va nter-cluster route and the latter va ntra-cluster route. In our codon level scheme both codon capture and ambguous ntermedate scenaros are naturally understood as dfferent evolutonal route n the same coordnate space. The former scenaro corresponds to the genetc code evoluton va nter-cluster route and the latter va ntra-cluster route. Snce the change n the range of codon recognton of trna by an alteraton at antcodon s so large to exceed the level gap between codon clusters, the nter-cluster route arses from an alteraton at the antcodon n trna. On the other hand, the ntra-cluster route arses from an alteraton at locatons other than the antcodon n trna. The change n the range of codon recognton of trna by ths type

7 of alteraton s smaller than the level gap. Snce the needed coordnate space s smaller and the mechansm of the selecton among competng trnas can be mplemented explctly, we smulate the ambguous ntermedate scenaro n the next secton. 3 Smulaton Here we perform some smulatons on the bass of our codon level model focusng on the smallest part of the level scheme n whch we can realze the ambguous ntermedate scenaro. We pursue the tme dependence of the trna dstrbuton around two codon levels n a codon cluster. Our algorthm for the tme evoluton of trna s as follows. Step : We prepare the system consstng of two homogeneous groups of trnas. Step : We ntroduce mutatons nto trnas. Step : We elmnate ll-condtoned trnas wth too narrow or too wde range of codon recognton. Step 3: We replcate trnas accordng to the cost of the synthess of correspondng amno acds. Step 4: We dvde the system nto two, mmckng cell dvson, when the number of trnas reach a crtcal value. We repeat the procedure from Step to Step 4 sequentally. In the followng we descrbe the detal of the smulaton. Step : As the ntal condton for the smulaton, the -th generaton of the system, we prepare two homogeneous groups of trna, trna- and trna-. The ntal number of trnas of each group s N. The range of codon recognton for each trna, t, s gven as C W t C W for trna- and C W t C W for trna- where each trna s labeled by number. The codon level for codon- s C and the center of t for trna- s chosen as C. The codon level for codon- s C and the center of t for trna- s chosen as C. The values of the centers, C and C, are assumed to be determned by the antcodons n trnas and constants n the followng. The constant shft represents the possblty that trna- may be taken over by trna-. The wdths of the range, W and W, are constants at ntal stage so that the groups of trna- and trna- are homogeneous. Step : We ntroduce random mutaton nto randomly selected trna and gve new wdth of the range, w, of codon recognton. Such mutatons are assumed to occur at locatons other than the antcodons n trnas and change only wdths of the recognton range keepng the center values unchanged. If a mutaton occurs at the antcodon n

8 f(x) trna, the center value s drastcally changed and the recognton range s pushed out of the codon cluster now nvestgated. Such a mutaton correspondng to the codon capture scenaro s not consdered here. The rate of the mutaton,, s fxed as N / N where N s the number of selected trnas as mutants. In order to represent the varety of nucleotdes we use a weght functon f ( x) w [ ( L L x shown )] n Fg. 4 and mutate w nto w f ( x ) where x s a random number generated for each trna. Wth ths mutated wdth w new range of recognton, t, s gven as C w t C w for trna- and C w t C w for trna x Fg. 4 Weght functon f ( x) w [ ( L L x wth )] L. Step : We evaluate the effect of the mutaton by keepng only trnas satsfyng the condton W w W whch guarantees the ablty of codon recognton. The lower value mn mn max W represents a tolerance n order to functon n some fluctuatng envronment not explctly taken nto account n our present model. The upper value W guarantees a sngular nature of the recognton. The other trnas wth poor max recognton ablty are elmnated. Step 3: We replcate survvng trnas and expand the system. The rate of the replcaton s determned by the cost of the correspondng amno acd producton. Thus

9 n(trn A :codon) we explctly mplement the selecton among competng trnas. The amno acds transported by trna- and trna- are named aa- and aa-, respectvely. Snce we focus on the case where trna- s taken over by trna-, the rapdty, r, of the replcaton for aa- s set to be larger than that, r, for aa-. The orgnal trna for the replcaton s chosen randomly. Step 4: When the total number of trnas reach the crtcal value, 4N, we make new systems at the next generaton by dvdng the system nto two, each of whch conssts of randomly selected N trnas, and pursue one of the new systems afterward. The system of the g -th generaton results from g tmes dvsons. 9 8 n(tr N A -:codon-) n(tr N A -:codon-) 4 3 n(tr N A -:codon-) n(tr N A -:codon-) g Fg. 5 Codon assgnment transton for N 5, C 5, C,, W max 8, W mn.,. The number of trna s represented, for example, as n(trna-:codon-) whch s the number of trna- recognzng codon-. In the ntal state all codon- are recognzed by trna- and all codon- by trna-. In the fnal state all of codon- and codon- are recognzed by trna-, snce we have chosen as r r. 5. Here g represents the generaton defned by the number of cell dvson. / In Fg. 5 an example of the tme dependence of the codon recognton of trnas s shown. The trna wth hgher cost of amno acd producton, trna, s taken over by

10 g() - g() the other, trna. For savng the smulaton tme the mutaton rate s set to be hgh as. Once a trna whch recognzes both codons appears the takeover rapdly progresses rrespectve of the mutaton rate. The rate controls the startng tme of the takeover. The perod of the ambguous translaton s ndependent of the cost of amno acd producton f the costs for two amno acds dffer consderably as shown n Fg. 6. Snce slght dfference of the reactons leads to drastc change n the characterstc tme of amno acd producton, t s taken for granted that the costs dffer sgnfcantly when the takeover occurs. Thus the perod s about generatons and very short n comparson wth the tme scale of evoluton. Such rapdness of the takeover reduces uncomfortableness of the non-unque translaton of the code at ntermedate state that s the weakness of the ambguous ntermedate scenaro r /r Fg. 6 Transton tme as a functon of r / r for the smulaton n Fg. 5. At the generaton g (), n(trna-:codon-) frst exceeds 5 and at g (), t frst exceeds 95. The transton tme s estmated by g( ) g().

11 4 Concluson We have proposed a physcal model to dscuss the mechansm of the genetc code evoluton. In the framework of our smplfed model, a mnmal model, the codon capture and ambguous ntermedate scenaros are understood n a unfed manner. On the bass of the herarchcal structure of the codon levels two scenaros are classfed nto two dfferent routes of the evolutonal process. Our smulaton mplemented cost selecton of amno acds has demonstrated a rapd transton of the code change n the case of the ambguous ntermedate scenaro. Ths rapdness of the transton covers the drawback, the non-unque translaton of the code durng the transton, of the scenaro. It should be noted, however, that the cost s only one of the selecton pressures and we have to consder the selecton from more global pont of vew for the envronment of cells n future study. Snce the am of our paper s to llustrate the herarchcal structure of the coordnate space of trna, our model s too smple and abstract. Although we should employ more realstc model n order to descrbe bologcal phenomena, such elaboraton s left to future study. Another attempt [9] to unfy the codon capture and ambguous ntermedate scenaros has been reported. Such a probablstc approach does not reach the mechansm, whch s our man subject, of the genetc code evoluton. References [] Osawa S (995) Evoluton of the genetc code. Oxford Unversty Press, Oxford [] Knght RD, Freeland SJ, Landweber LF () Rewrng the keyboard: evolvablty of the genetc code. Nature Rev. Genet., [3] Knght RD, Landweber LF, Yarus M () How mtochondra redefne the code. J. Mol. Evol. 53, [4] Osawa S, Jukes TH (989) Codon reassgnment (codon capture) n evoluton. J. Mol. Evol. 8, 7-78 [5] Schultz DW, Yarus M (994) Transfer RNA mutaton and the malleablty of the genetc code. J. Mol. Bol. 35, [6] Schultz DW, Yarus M (996) On malleablty n the genetc code. J. Mol. Evol. 4, [7] Swre J, Judson OP, Burt A (5) Mtochondral Genetc Codes Evolve to Match

12 Amno Acd Requrements of Protens. J. Mol. Evol. 6, 8-39 [8] Perelson AS, Wesbuch G (997) Immunology for physcsts. Rev. Mod. Phys. 69, 9-67 [9] Sengupta S, Hggs PG (5) A Unfed Model of Codon Reassgnment n Alternatve Genetc Codes. Genetcs 7, 83-84