Genetically Structured Mathematical Modeling of trp Attenuator Mechanism

Transcription

1 Genetically Structure Mathematical Moeling of trp Attenuator Mechanism Boon Tong Koh, 1 Reginal B. H. Tan, 1 Mirana G. S. Yap 2 1 Department of Chemical Engineering, National University of Singapore, 10 Kent Rige Crescent, Singapore ; telephone: ; fax: Bioprocessing Technology Centre, National University of Singapore Receive 2 April 1997; accepte 10 October 1997 Abstract: A genetically structure mathematical moel of the trp attenuator in Escherichia coli base on known coupling mechanisms of the transcription of the trp leaer region an translation of the trp leaer peptie region is propose. The moel simulates, both qualitatively an quantitatively, the effects of tryptophan on the repression of clone gene proucts. It shows that repression by attenuation mechanism alone operates over a narrow trp concentration range of 1 to 5 µm compare with 1 to 100 µm for trp repressor mechanism. This implies that attenuation by transcription termination is not relaxe until tryptophan starvation is severe. Simulation results show that the attenuator starts to erepress when the repressor is about 40% represse, an becomes significantly erepresse only when the repressor repression ecrease to about 20%. Unlike the case of repressor-operator interaction, the operating range of tryptophan concentration in the attenuator mechanism is not sensitive to plasmi copy number John Wiley & Sons, Inc. Biotechnol Bioeng 58: , Keywors: genetically structure mathematical moel; trp operon; clone gene expression control INTRODUCTION Corresponence to: Reginal B. H. Tan The ability to regulate the expression of clone genes is an important factor in ensuring maximum prouctivity of valuable recombinant proteins in Escherichia coli. A typical process involves effectively repressing clone gene transcription uring cell growth an, subsequently, inucing the cells to maximize protein prouction (Lee et al., 1988; Seow et al., 1989). Such intracellular control can be achieve by expression systems built into the clone genes. A common example is the trp promoter which has been use to control the expression of a number of useful proteins such as human tumor necrosis factor (Seow et al., 1989) an human interferon- (Mizukami et al., 1986). The etaile mechanism of how the trp promoter controls the expression of the clone genes has been eluciate in recent years. This involves unerstaning the mechanism of the trp operon transcription, which is regulate by both repression an attenuation. Repression, locate at the promoter-operator site, regulates transcription initiation in response to changes in the intracellular level of free tryptophan (Koh an Yap, 1993; Yanofsky an Crawfor, 1987). Attenuation, locate ownstream of the promoter-operator site, regulates transcription termination in response to changes in the levels of charge an uncharge trna Trp (Elsenberg et al., 1980; Lee an Yanofsky, 1977; Oxener et al., 1979; Zurawski et al., 1978). The combine action of these two regulatory mechanisms allows expression of the operon to be varie over a 500-fol range; repression an attenuation account for about 80- an 6-fol variations, respectively (Bertran an Yanofsky, 1976; Yanofsky et al., 1984). In a previous article (Koh an Yap, 1993), a genetically structure mathematical moel of the trp repressor-operator interactions was evelope, which accounts for the operation of the trp operon uner repression control. The moel showe that the important parameters governing expression inclue tryptophan, inoleacrylic aci, aporepressor concentrations, an the plasmi copy number. The moel coul be use to optimize these parameters for effective repression an subsequent erepression of the clone gene. For example, our moel preicts that for high copy number plasmis, full repression is not possible in spite of high tryptophan levels in the meium, because of limiting aporepressor concentration in recombinant E. coli cells. This accounts for leaky expressions often reporte in literature (Kawai et al., 1986; Mizukami et al., 1986; Schroeckh et al., 1992; Siegel an Ryu, 1985). However, the above moel is not complete because it oes not account for the effect of attenuator control on protein expression. Attenuator control is known to influence expression levels. An increase in clone gene prouct has been observe when the attenuator is eliminate (Seow et al., 1989; Tacon et al., 1983). In aition, compare with the repressor mechanism, repression of the attenuator is achieve at much lower concentration (Yanofsky et al. 1984). In this article, a mathematical moel, which complements the previous one, is evelope base on present unerstaning of trp attenuation mechanisms. The moel seeks to preict the important parameters an the range of tryptophan levels that govern trp attenuation. It can be combine with the previous moel on trp repressor to fully escribe the regulation of the trp 1998 John Wiley & Sons, Inc. CCC /98/

2 repressor an attenuator mechanisms on clone gene repression. It also enables us to compare the ifferences in the regulation of trp repressor an attenuator mechanisms an increase our unerstaning of their biological functions. MODEL DESCRIPTION Attenuation in the trp operon is a ynamic process involving both transcription of the leaer region an translation of the trp leaer peptie (#27 71) locate within this leaer region (#1 140). This leaer transcript is capable of foling to form mutually exclusive seconary structures as shown in Figure 1. Formation of the {3:4} terminator structure causes transcription termination, while the {2:3} antiterminator structure allows transcription to procee into the structural genes of the operon. Attenuation control, which involves the formation of one of these two alternative structures, is governe by the coupling effects of the translation of the peptie coing region (#27 71), specifically the two tanem trp coons (#54 59), an the transcription of the leaer region. A brief escription of the complex mechanisms, which have been reporte in etail (Lanrick an Yanofsky, 1984; Lanrick et al., 1985; Lanrick an Yanofsky, 1987; Roesser an Yanofsky, 1988; Roesser et al., 1989; Yanofsky an Crawfor, 1987), is presente. At the onset of transcription from the trp promoter, the RNA polymerase transcribes the trp leaer region an pauses after leaer segment 2 (up to #92) is synthesize. The transcription pause has been foun to be ue to the formation of the {1:2} pause structure (Fig. 2a) (Lanrick an Yanofsky, 1984; Winkler an Yanofsky, 1981). Translation of the short leaer peptie coing region begins with the ribosome bining to the start coon. The translating ribosome approaches an isrupts the {1:2} pause structure, releasing the pause transcription complex. This ensures that the translating ribosome woul be place on the transcript close behin the transcribing polymerase (Lanrick et al., 1985; Winkler an Yanofsky, 1981). Polymerase an ribosome then move in unison over the leaer region an leaer transcript, respectively. It has been reporte that the 70S translating ribosome is estimate to mask 13 base pairs of RNA both upstream an ownstream of the coon being translate (Roesser an Yanofsky, 1988; Yager an von Hippel, 1987). Hence, in the moel we assume that the Figure 1. Alternate seconary structures of Escherichia coli trp leaer transcript. KOH ET AL.: MODEL OF Trp ATTENUATOR 503

3 Figure 3. Schematic iagram showing mechanism of trp attenuator: alternative scenarios for (a) trp excess an (b) trp limiting. Figure 2. Schematic iagram showing mechanism of trp attenuator: (a) ribosome loaing, an (b) pause isruption. {1:2} pause structure is isrupte when the ribosome starts translating the val coon (at #42), four coons before the first trp coon (Fig. 2b). The position of the two tanem trp coons at the beginning of structure {1:2} plays an important role in attenuation control. After isruption of the pause structure, two basic scenarios are possible. In the presence of sufficient available tryptophan, the translating ribosome continues uninterrupte to the stop coon where it is subsequently release from the transcript (Fig. 3a). The position of the ribosome at segment 2 interferes with the formation of the {2:3} structure. This sequence of events favors the formation of the {3:4} terminator structure an results in transcription termination of the trp mrna. Uner tryptophan starvation, the translating ribosome stalls at either of the two trp coons at segment 1, preventing the formation of the {1:2} structure. This conition facilitates the formation of the antiterminator structure {2:3}. This allows transcription to procee into the clone genes (Fig. 3b). Hence, attenuation control involves coupling of the translation an transcription processes (Roesser et al., 1989). The mathematical equations are evelope as follows. The total translating time (TL) is efine as the perio from the start of translation of the val (#42) coon (ie., the moment the {1:2} pause structure is isrupte by the moving ribosome) to the time when the ribosome is release from the stop (#71) coon. This perio comprises the average translation times from val to gly (#42 to #53), two trp coons an from arg to stop (#60 to #71) coons, an the ribosome release time, t r. Hence, TL = 4 + Trp Stalling Time TST + 4 A TL A TL + RB release time t r (1) where A TL is the average rate of translation in coons/s. The trp stalling time (TST), efine as the time it takes to translate the two tanem trp coons, may be erive from the mechanism of translation an amino-acryl trna synthetase as outline below. The general rate propagation equation for translation of amino acis 1 to n is erive in the Appenix to be t RB mrna trna 1 n n = n k I RB mrna trna n k i=1 P1 trna i i k Pi (2) trna i When n, the last coon to be translate is trp, Equation (2) becomes t RB mrna trna 1 n n = k I RB mrna trna n k P1 trna n 1 k i i Pi i=1 trna trna Trp Trp (3) i trna Trp Assuming that only tryptophan is limiting, that is, all other amino acis are available in excess, then translation of the 504 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 58, NO. 5, JUNE 5, 1998

4 trp leaer peptie is limite by charge trna Trp Trp at the two trp coons. By collecting constant terms together as A TL, an assuming constant intracellular volume, Equation (3) as applie to translation of trp coons only, can be simplifie to: Cn t trna Trp Trp = A TL trna Trp where Cn is the number of trp coons being translate. Hence, the total trp stalling time at two tanem trp coons is TST = 2 trna Trp (5) A TL trna Trp Trp The relationship of trna Trp/ trna Trp Trp an tryptophan concentration can be erive from the mechanism of tryptophanyl trna synthetase (TrpRS). A simplifie two-step mechanism of tryptophanyl trna synthetase (TrpRS) in charging trna trp is as follows (Hershey, 1987): K m1 A TrpRS + T B TrpRS-T + trna Trp K m2 T + trna Trp Trp K m TrpRS-T (4) trna Trp Trp + TrpRS trna Trp Trp The equilibrium relationship can be written as: K m1 = T TrpRS TrpRS T K m2 = TrpRS T trnatrp (7) trna Trp Trp TrpRS Assuming constant intracellular volume, we combine Equations (6) an (7) to yiel (6) trna Trp Trp trna Trp = T (8) K m where K m K m1 K m2 Values of K m1 an K m2 have been reporte to be 20 M an 1, respectively (Hershey, 1987). From a material balance of tryptophan, the total trp concentration can be expresse as T t = T + TrpRS T + trna Trp Trp + 2 PCN (9) The term 2 [PCN] arises from the Trp molecules involve in inuction. The equation oes not account for Trp molecules which are complexe with aporepressor that are not yet boun with DNA, as the amount in this transient state is consiere insignificant. Assuming constant cell volume, [PCN] is equivalent to approximately M per plasmi. Further, because there are typically about 800 molecules of aminoacryltrna synthetase per cell (Hershey, 1987; Neihart et al., 1977), [TrpRS] is approximately 1.6 M. Substituting Equations (6) an (8) into (9), rearranging, an noting that [trna Trp ]/20 << 1, we obtain the following expression for [T]: T = T PCN (10) 1.08 Substituting Equations (8) an (10) into Equation (5), we have TST = 2 K m 1.08 (11) A TL T PCN Therefore, the total time taken for translation, TL, erive by accounting for: (a) the average translation rate, A TL ; (b) trp stalling time at either of the two trp coons, which is assume to epen on an equilibrium process between available tryptophan an charge trna Trp ; an (c) average ribosome release time at the stop coon (#69 71), t r, is TL = 4 2 K m 1.08 A TL A TL T PCN t A r (12) TL Transcription of mrna, which ha pause at the {1:2} structure (#92), resumes when the translating ribosome isrupts this pause structure. The position of the leaer transcript (#TC) with respect to translation is obtaine as #TC 92 + B TC TL (13) where B TC is the average transcription rate of trp mrna. We have efine the repression coefficient uner attenuator control, R A, as the probability of forming {3:4} terminator structure. Because {2:3} an {3:4} structures are mutually exclusive, R A can be written as R A P{3:4} 1 P{2:3} (14) where P{3:4} an P{2:3} are the probabilities of forming {3:4} terminator an {2:3} antiterminator structures, respectively. A simulation of all the possible positions of the leaer transcript, #TC in Equation (13), etermines the relative probabilities of {2:3} or {3:4} formation, which are mutually exclusive. The average transcription (B TC ) an translation (A TL ) rates for E. coli at 37 C are 50 nucleoties/s an 17 coons/ s, respectively (Gausing, 1972; Kassavetis an Chamberlin, 1981). The average ribosome release time (t r ) at the UGA coon in the translational reaing frame of the prfb gene has been estimate to be 0.6 secons (Curran an Yarus, 1988). These values use for the moel simulation are summarize in Table I. It is known that the {3:4} termination structure followe by the series of seven uracil nucleoties causes transcription termination of the trp mrna (Lanick an Yanofsky, 1987; Yanofsky an Crawfor, 1987). Hence, we assume that once transcription has passe the seven uracil nucleoties (#141) without the formation of {3:4} terminator structure, KOH ET AL.: MODEL OF Trp ATTENUATOR 505

5 Table I. Values of A TL,B TC,K m an t r use in our moel. Values Use transcription termination woul not be possible. Attenuation repression, R A, woul then be at its minimum (given an arbitrary value of 0). SIMULATION RESULTS References A TL 17 coons/s Kassavetis an Chamberlin (1981); Roesser et al. (1989) B TC 51 nucleoties/s Kassavetis an Chamberlin (1981); Roesser et al. (1989) K m 20 M Hershey (1987) t r 0.6 s (average value) Curran an Yarus (1988); Roesser et al. (1989) Figure 4, generate from Equations (11) an (12) for PCN of 10, shows the position of the mrna being transcribe when translation of the peptie coing region is at (a) secon trp coon, an (b) stop coon before ribosome is release. Points (i) an (ii) on the graph inicate the position of the ribosome at the time nucleotie #141 is being transcribe. To the left of point (i) in Figure 4, R A woul be minimum, because ribosome is bining on segment 1 which prevents structure {1:2} formation. This results in formation of antiterminator {2:3}. Hence, P{2:3} is maximum an R A is minimum (given an arbitrary value of 0). Similarly, to the right of point (ii) in Figure 4, R A woul be maximum, because ribosome bins segment 2 which prevents structure {2:3} formation. This results in terminator {3:4} formation. Hence, P{2:3} is minimum resulting in maximum R A (given an arbitrary value of 1). For tryptophan levels between those represente by points (i) an (ii), both {2:3} an {3:4} structures compete for formation, an we have assume that the probabilities woul then epen on the relative stability of each structure corresponing to their Gibbs free energy (Roesser an Yanofsky, 1988; Roesser et al., 1989). Because the Gibbs free energy for both structure are approximately equal (Oxener et al., 1979; Zuker an Stieger, 1981), a linear relationship of R A is assume between the two extreme points as shown in Figure 4. To stuy the effects of the level of tryptophan an plasmi copy number (PCN) on attenuator mechanism, simulation was carrie out for E. coli with PCN of 10 an 100. Results of the attenuator repression coefficients (R A ) calculate from the mathematical moel are shown in Figure 5. The attenuator mechanism appears to be on/off control over a narrow range of tryptophan concentration for both low an high copy number plasmis. This shows that attenuator is not eactivate until very low tryptophan concentration an that the rate of erepression is extremely sensitive to tryptophan concentration at low levels. In aition, increasing the PCN from 10 to 100 has no significant effect on the regulating range of tryptophan. The repressor repression coefficient calculate from our previous moel (Koh an Yap, 1993) is also plotte for comparison. As shown in Figure 5, the regulating range of tryptophan for the trp repressor mechanism is much wier. This suggests that the response to changes in tryptophan levels are miler. For high PCN, such as R R (100), effective repression was not achieve because of limiting aporepressor levels (Koh an Yap, 1993). DISCUSSION From our moeling, it appears that the tryptophan requirement for attenuation action is very low compare with the repressor mechanism. The total tryptophan level regulate by attenuator falls within a narrow range of 1 to 5 M, as compare with 1 to 100 M for repressor mechanism. This shows that attenuation by transcription termination is not Figure 4. Position of mrna being transcribe (#TC) when translation of the peptie coing region is at secon trp coon (a), an at stop coon (b); an repression coefficient (c) as preicte by our moel. Generate for PCN of 10. X-axis represents total tryptophan, [T t ]. Figure 5. Repressor (R R ) an Attenuator (R A ) repression coefficients calculate from our moels for PCN of 10 (---) an 100 ( ). Repression coefficients 0 an 1 are arbitrary values representing minimum an maximum repression respectively. 506 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 58, NO. 5, JUNE 5, 1998

6 relaxe until tryptophan starvation is severe. In contrast, repressor action regulate transcription initiation over the range from excess to moerate tryptophan levels. These finings are consistent with observations reporte in literature. One reason suggeste by Yanofsky et al. (1984) is that trna Trp charging i not become growth-limiting until the intracellular tryptophan concentration was so low that it was inaequate to activate the trp aporepressor. This suggests that repressor an attenuator come into play inepenently in regulating trp operon transcription. The ifferent requirements of tryptophan in controling repression an attenuation can be explaine by the low concentration of aporepressor an high level of trna Trp present in E. coli. From their mechanisms, both the repressor an attenuator require only two tryptophan molecules per active site for repression. However, the tryptophan level require to effectively repress repressor mechanism is relatively high. This is because of the low aporepressor concentration (30 copy/cell) present in the cell. Hence, from equilibrium analysis (K I [ApoR-T][T]/[TrpR] 30 M), a low aporepressor level will result in a high tryptophan concentration to generate sufficient trp repressor, [TrpR], for effective repression. For the attenuator, because of the relative abunance of trna Trp (about 6000 copy/cell) an a reasonable equilibrium constant (K m 20 M), the requirements of tryptophan to form charge trna Trp are lower. Hence, a significantly smaller amount of tryptophan is neee to activate the attenuator mechanism. The overall repression coefficient for the combine action of trp repressor an attenuator, R OV, can be written as R OV (repressor an attenuator) 1 (1 R R )(1 R A ) (15) R OV, calculate by Equation (15), are shown in Figure 6 (PCN 10) an Figure 7 (PCN 100) by assuming the minimum an maximum R A of 0.05 an 0.85, respectively. The last value correspons to basal level expression of about 15% as reporte in literature (Roesser et al., 1989). For both Figure 7. Plot of R R,R A an R OV for PCN of 10, assuming minimum an maximum R A of 0.05 an 0.85, respectively. cases of high an low PCN, simulation results show that the attenuator mechanism starts to eactivate only when the repressor is about 40% represse, an becomes significantly eactivate when the repressor is about 20% represse. In conclusion, Figure 8 compares the repressor with attenuator mechanisms (R OV ) an repressor mechanism without attenuator (R R ) for plasmi copy number of 10 an 100. The small ifference between R OV (10) an R OV (100) compare with R R (10) an R R (100) implie that unlike the repressor mechanism, the attenuator mechanism is not significantly affecte by changes in the plasmi copy number. The operating range of tryptophan remains the same from 1 to 5 m. Control of clone gene expression appeare to be onoff over this narrow range for the attenuator mechanism. The simulation results also showe that presence of attenuator ownstream of the repressor significantly reuce the expression of clone genes. This is evience by reports that removal of the attenuator improve the expresse effi- Figure 6. Plot of R R,R A an R OV for PCN of 10, assuming minimum an maximum R A of 0.05 an 0.85, respectively. Figure 8. Plot of R R an R OV for PCN of 10 (---) an 100 ( ), assuming minimum an maximum R A of 0.05 an 0.85, respectively. KOH ET AL.: MODEL OF Trp ATTENUATOR 507

7 ciency of the plasmi (Seow et al., 1989; Tacon et al., 1983). NOMENCLATURE A TL average rate of translation (coons/s) B TC average rate of transcription (nucleoties/s) K m1,k m2 equilibrium constants as efine by Equations (6) an (7) mrna messenger RNA PCN plasmi copy number R A attenuator repression coefficient as efine by Equation (12) R R repressor repression coefficient as efine in (Koh an Yap, 1993) R OV overall repression coefficient as efine by Equation (13) RB translating ribosome TST total trp stalling time at both trp coons (s) TL total translation time (s) t r ribosome release time (s) trna i uncharge amino aci i transfer RNA trna i i charge amino aci i transfer RNA TrpRS tryptophanyl trna synthetase #TC position of leaer transcript wrt to translation P{2:3} probability of forming {2:3} antiterminator structure P{3:4} probability of forming {3:4} terminator structure [ApoR] total aporepressor concentration [T] free tryptophan concentration [T t ] total tryptophan concentration APPENDIX The erivation of translation rate equations from mechanism of translation: 1. Initiation: RB an charge trna bin to mrna in two elementary steps. a b K 1 RB + mrna RB mrna RB mrna + trna i k 2 i i RB mrna trna i We propose the hypothesis that step (a) is significantly faster than step (b), on the grouns that charge species are not involve in the reaction. This allows us to apply the steay-state assumption, giving (RB-mRNA) K 1 (RB)(mRNA) The rate of reaction (b) is written as RB mrna trna i i = k t 2 RB mrna trna i i RB mrna trna i i = k t 1 RB mrna trna i i (A1) where k I K 1 k 2 ( (moles 2 -s) 1 ) 2. Propagation: Aition of more amino aci(s) to mrna: (a) aing charge TRNA i RB mrna trna i i + trna j k 3j j RB mrna trna i i trna j (b) releasing uncharge trna i RB mrna trna i k 4j i j trna j trna i j j + trna i RB mrna By assuming steay state an equating rate of formation (2a) to rate of epletion (2b), we can erive: t RB mrna trna i j j = k 1 k pj RB mrna (trna i i) (trna i trna i j (A2) where k pj = k 3j (imensionless) k 4j (c) on further propagation with another charge trna k RB mrna trna i j i + trna k k 3k k i j mrna trna j k trna k By similar erivations, we have: t RB mrna trna i j k k = RB k I k pj k pk RB mrna (trna i (trna i j ) (trna i ) (trna j ) (trna k k) (A3) By extening the expression for amino acis 1 to n, t RB mrna trna 1 n n = References n k I RB mrna trna n k i=1 p1 i ) trna i i k pi (A4) trna i Bertran, K., Yanofsky, C Regulation of transcription termination in the leaer region of the tryptophan operon of E. coli involves tryptophan or its metabolic prouct. J. Mol. Biol. 103: Curran, J. F., Yarus, M Use of trna suppressors to probe regulation of E. coli release factor 2. J. Mol. Biol. 203: Elsenberg, S. P., Soll, L., Yarus, M Role of trna Trp an leaer RNA seconary structure in attenuation of the trp operon, p In: D. Soll, P. Schimmel, J. Abelson (e.), Transfer RNA: Biological aspects. Col Spring Harbor Laboratory, Col Spring Harbor, NY. Gausing, K Efficiency of protein an mrna synthesis in bacteriophage T4-infecte cells of E. coli. J. Mol. Biol. 71: Hershey, J. W. B In: F. C. Neihart, (e.), Escherichia coli an Salmonella typhimurium: Cellular an molecular biology, Vol. 1, pp American Society for Microbiology, Washington, DC. Kassavetis, G. A., Chamberlin, M. J Pausing an termination of transcription within the early region of bacteriophage T7. J. Biol. Chem. 256: BIOTECHNOLOGY AND BIOENGINEERING, VOL. 58, NO. 5, JUNE 5, 1998

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