THE JOURNAL. OF BIOLOGICAL CHEMWI’RY Vol. 254, No. 23, Issue of December 10, pp. 11927-11937, 1979 Printed in CI. S. A.

A Kinetic Model of Protein Synthesis APPLICATION TO HEMOGLOBIN SYNTHESIS AND TRANSLATIONAL CONTROL*

(Received for publication, October 2, 1978, and in revised form, August 6, 1979)

John E. Bergmann+ and Harvey F. Lodish

From the Department of Biology, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

We present a kinetic model of protein synthesis which encompasses initiation, elongation, and termi- nation parameters. We have investigated the depend- ence of the total rate of protein synthesis and the size of the translating polysomes on each of these parame- ters and in particular on the level of active 40 S ribo- somes and initiation factors. This model qualitatively fits experimental data for the ratio of (Y- to P-globin synthesis in reticulocytes, both under normal condi- tions and in the presence of inhibitors of chain initia- tion. This model has also been used to examine the effect that limiting amounts of certain tRNAs might have on the total rate of protein synthesis. In addition, the role of initiation factor discrimination and mRNA length are examined with respect to the differential translation of mRNAs.

Most messenger RNA in eukaryotic cells is long lived, with lifetimes from several days to as little as an hour (1, 2). Even those mRNAs with the shortest lifetimes, on the order of an hour, would give rise to over 100 polypeptide products each, if translated with the same efficiency as an average cellular mRNA. Thus, there has been considerable interest in mech- anisms whereby developing cells and cells responding to sud- den environmental changes can alter the relative efficiency with which different mRNAs are translated.

Examples of this type of control are found in rabbit reticu- locytes, where the rate of synthesis of (Y- and P-globin is differentially affected by starvation for iron (3) and in Dicty- ostelium discoideum, where the translation of several mRNAs has been preferentially inhibited in early development (4, 5).

Four basic mechanisms of translational co’ntrol have been proposed:

1. Cytoplasmic mRNA may be masked and thus segregated into a totally active portion and a totally inactive portion. Such masking could be either due to noncovalent interactions of the mRNA with proteins, or small RNAs, or both, or to covalent modifications of the mRNA.

2. In a given cell, there may be different pathways for the initiation of protein synthesis, and thus there may be initiation factors with different mRNA specificities that are responsible for the initiation of protein synthesis on different classes of mRNA.

3. There is only one pathway for the initiation of protein synthesis in a given cell, but differences in the affinity of

* This work was supported by Grants AI08814 and AM15322 from the National Institutes of Health. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “aduertisement” in accord- ance with 18 USC. Section 1734 solely to indicate this fact.

$ Present address, Department of Biology, University of California, San Diego, La Jolla, Calif. 92093.

different mRNAs for the 40 S subunits, or initiation factors, or both, may lead to changes in the relative efficiencies of these mRNAs when the activity or concentration of these components is altered.

4. Changes in the level of one or a few isoaccepting species of tRNA may differentially alter the time it takes ribosomes to translate different mRNAs and consequently change their translational efficiency.

Such possibilities are difficult to assess without a quantita- tive framework. Although no theoretical argument can predict whether the first two mechanisms occur in nature, one should be able to calculate to what extent the last two mechanisms can vary the relative quantity of different products and hence evaluate whether these latter mechanisms are sufficient to account for experimental observations.

A number of other kinetic models of protein synthesis have been elaborated. MacDonald and Gibbs (6) and Hiernaux (7) developed a model similar to the one we use here, but one which contains an additional ad hoc assumption concerning ribosome distribution along the mRNA. They did not use this model to investigate possible mechanisms of translational control. Lodish (8) further simplified their model and showed that steric hindrance between translating ribosomes could lead to changes in the relative translational efficiencies of different mRNAs such as (Y- and P-globin mRNA in response to changes in the overall efficiency of the translational appa- ratus. Unfortunately, it was not clear how much the simpli- fying assumptions had affected the accuracy of the model’s quantitative predictions. Gordon (9) and later Vassart et al. (10) used computer simulation to model the translation proc- ess. However, these workers did not systematically investigate the dependence of translation rate on each of the rate con- stants over a physiologically meaningful range. In this paper, we show how the polysome size and the rate of production of completed polypeptides is affected by the initiation, elonga- tion, and termination rate constants, and in particular by ribosome and initiation factor limitation. We then demon- strate how these results are influenced by local reductions in the elongation rate as might be caused by tRNA limitation or mRNA secondary structure. In addition, we show that the relationship between rate of synthesis and the initiation, elon- gation, and termination rate constants is unaffected by mRNA length.

MODEL AND METHODS OF SOLUTION

The translation process may be conceptually divided into three phases: initiation, elongation, and termination. We modeled each of these independently. During initiation, there now appear to be at least three mRNA binding events: 1) The binding of one or more initiation factors to the mRNA, 2) the binding of the 40 S ribosomal subunit to the mRNA.factor complex, and 3) the joining of the 60 S ribosomal subunit to the 40 S.mRNA complex (11-14). Although artificial RNAs may be synthesized which will bind 40 S subunits, but fail to bind the 60 S subunit in vitro (15), naturally occurring mRNA

11927

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11928 A Kinetic Model of Protein Synthesis

complexes seem to bind the large ribosome subunits rapidly (16). For example, when the kinetics of ribosome binding are followed in vitro using labeled vesicular stomatitis virus or reo virus mRNAs few, if any, 40 S. mRNA intermediates can be detected so long as 60 S subunits are present in the reactions (17-19).

Thus, the binding of 60 S subunits does not appear to be rate- limiting. An appropriate simplification would be that the formation of 80 S initiation complexes immediately follows the formation of 40 S mRNA complexes. However, should the rate of 60 S subunit binding limit the initiation rate in some system, a theoretical treatment such as that used below for cases of initiation factor limitation would be applicable. Thus, the formation of 80 S complexes can be approxi- mated by the rate of joining of an mRNA.factor complex with activated 40 S ribosomal subunits. For an mRNA entering the trans- lation cycle for the first time, this rate can be algebraically expressed as follows:

Q = K,mR+ (1)

where Q is the rate of formation per mRNA of an 80 S initiation complex, K, is a proportionality constant that may depend on the mRNA, R$ is the concentration of activated 40 S ribosomal subunits, and m is the fraction of mRNAs in mRNA factor complexes (see end of this section).

It is known that once such an mRNA has bound a ribosome, it may not bind another ribosome until the first ribosome has moved sufficiently down the mRNA that it does not block the initiation region. This phenomenon has been used to measure experimentally the rate of binding of ribosomes to mRNAs in vitro (17-19). In describing initiation on actively translating mRNAs, we must there- fore take into account the proportion (PI) of such mRNAs on which there is not steric hindrance to initiation at any given time. Our equation now becomes:

Q = KlrnPIR$ (2)

This proportion of available mRNAs (P,) depends not only on the average time between initiation events, but also on the time it takes a ribosome to leave the initiation region.

After formation of the 80 S initiation complex, a ribosome is ready to begin elongating the polypeptide chain. In order to discuss the elongation rate along an mRNA, it is necessary to refer to the position of a ribosome on that mRNA. We will refer to a ribosome residing at position i when it contains a nascent polypeptide chain i amino acids long. The local elongation rate at position i along a group of identical mRNAs would then refer to the rate of movement of ribosomes from position i - 1 to position i, or equivalently to the rate of formation of nascent chains i amino acids in length.

By analogy with Equation 2, this rate (Q<) may be expressed as follows:

Qt = K,.X I-1. P, (3)

where K, is the elongation rate constant at position i along the mRNA, X,-1 is the fraction of mRNAs with ribosomes at position i - 1, and P, is the fraction of those mRNAs with a ribosome at position i - 1 on which the progress of that ribosome is not impeded by other ribosomes further along the mRNA.

Several factors may affect K,. For example, the availability of a specific isoaccepting tRNA or its synthetase, the affinity of EF-1 for this aminoacylated tRNA, the affinity of the ribosome for the EF-1 aminoacyl-tRNA. GTP complex, and the local secondary structure of the mRNA may all affect this rate constant. Again, we do not try to introduce a rate constant for each possible variable or determine how the local elongation rate would depend on changes in, say, the availability of charged tRNA. We simply assign one elongation rate constant (K,) to each position along the mRNA. This constant is, of course, a function of all of these parameters.

As we discuss later, the determination of P, is complicated by the fact that ribosomes may not share the same space. For instance, the fraction of mRNAs with ribosomes at position i - 1 (i.e. X,-t) and those with ribosomes at position i (X,) are, in the steady state, both non-zero. However, there can be no mRNAs with ribosomes at position i - 1 that simultaneously have ribosomes at position i. The ribosomes are too big and may not be crowded that closely together.

The terminal event in protein synthesis is the release of the completed chain from the ribosome and the release of the ribosome from the mRNA. This occurs when a ribosome reaches one of the three termination codons, UAA, UAG, or UGA, and is mediated by GTP and a soluble release factor, R (20). Again, the rate should be

proportional to the fraction of polysomes containing completed, but as yet unreleased polypeptide chains. Since this last reaction is a dissociation reaction, steric hindrance by other ribosomes probably plays no part. Thus:

Qt = Kt-5 (4)

where Q, is the termination rate, K, is the termination rate constant, and X, is the fraction of polysomes with completed, yet unreleased, chains. Data from prokaryotes indicates that the efficiency with which suppressor tRNAs compete with termination factors depends on the position of the termination codon along a mRNA (20). Such data may implicate neighboring codons, local mRNA secondary struc- ture, or conformation of the nascent chain as modifiers of the rate constant of the termination reaction.

Since the lifetimes of eukaryotic mRNA is on the order of hours, and the time it takes a ribosome to bind and translate an entire mRNA is only a few minutes, most protein synthesis will occur under steady state conditions. Consequently, we wished to find a solution to our equations under such steady state conditions. This means that a single rate constant, Q, suffices for the initiation rate, for all of the elongation rates, and for the termination rate:

Q = KlmPIR$ = K,P,X,-, = K,X, for i greater than 1 (5)

The problem, then, is to solve this system of equations for Q as a function of the independent variables K,, R$, m, K,, and K,. In order to do this, the conditional probabilities (P,) that describe the possi- bility of steric hindrance must also be solved as a function of our independent variables.

The simplest way to model steric hindrance of ribosomes is to assume that it is an all-or-nothing phenomenon. That is, if two neighboring ribosomes are not touching, we assume they do not interact at all. However, if two ribosomes are just touching, we assumed that the ribosome with the shorter nascent chain would be totally prevented from advancing. In contrast, the ribosome with the longer nascent chain would be totally unimpeded in its progress. Since both electron microscopic measurements and mRNA protection stud- ies indicated that mammalian ribosomes cover approximately 12 codons, we chose this as the distance between two “touching” ribo- somes. One consequence of such an assumption is that ribosomes that have nascent chains within 12 codons of completion will not have any chance of finding another ribosome impeding their progress (i.e. P, = 1, for all i greater than t - 12, where t represents the number of codons in the mRNA)

The choice of 12 codons as the region of the mRNA covered by a ribosome is not crucial to the findings discussed in this paper. The choice of 11 or 13 codons would leave our findings essentially unaf- fected. However, large deviations (1 or 24 codons) in our choice would qualitatively affect the relationships between the various kinetic rate constants and the calculated parameters. Such a large error in the estimated size of a ribosome would cause our model to make grossly incorrect predictions of the average polysome size.

Numerical Analysis of Our Model

The model described above is similar to models proposed by others (6-10). We developed two approaches for numerical analysis of it, one based on the work of MacDonald and Gibbs (6) and a computer simulation quite similar to that described by Vassart et al. (10). Although the former approach was able to find solutions more rapidly than the latter approach, there were values of the rate constants for which this approach was unable to find any steady state solutions. This was probably due to instabilities inherent in the analytic for- mulation of the model as proposed by MacDonald and Gibbs (7). We therefore relied on computer simulation.

The computer was programmed to carry out a “simulated transla- tion” with 100 mRNAs. Since the computer could “memorize” the positions of all of the ribosomes that were actively translating an mRNA, there was no need to calculate the values of the X, or the P,. The computer would simply test whether a ribosome of known position could move during a given short time interval. In such a short time interval, reactions are probabilistic events. If the probabil- ity of a reaction is high, the average rate over many such time intervals is proportionately high.

In principle, this second method of simulation is totally flexible. Any rules for ribosome-ribosome interaction can be utilized; any experimentally measurable parameter may be monitored in the sim- ulation; and both transient and steady state situations may be fol- lowed.

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A Kinetic Model of Protein Synthesis 11929

We chose our simulated time interval such that the probability of an unobstructed ribosome adding one amino acid to its nascent chain was 0.1. Since ribosomes in our rabbit reticulocyte lysates are able to polymerize about 100 amino acids/min onto a growing polypeptide,’ this time interval would correspond to about one-thousandth of a minute. In order to simulate translation during such an interval, we programmed the computer to examine the binding region of one of the mRNAs. If the first 12 codons were unoccupied, the computer was to place a ribosome at position 1 of that mRNA with a probability that was proportional to the rate constant for initiation. To do this, the computer would generate a random number between 0 and 999. This number was then compared to the rate constant for initiation. If the random number was less than the rate constant for initiation, a ribosome would be placed at position 1 of this mRNA. Otherwise, this position would remain unoccupied. Regardless of the outcome of this event, the computer would locate the next ribosome along the mRNA, test whether there was space available for the ribosome to advance, and if space were available and if a newly generated random number was less than the elongation rate constant for that position, the ribosome would be advanced by one. The computer would continue down this hypothetical mRNA locating ribosomes and occasionally moving them according to this protocol. If a ribosome were located at the terminal position, the computer would test whether its random number was less than the termination rate constant and if so, remove the ribosome from the terminal position. Having thus dealt with all of the ribosomes on the first mRNA, the computer would follow the same protocol with every successive mRNA until all 100 had been examined. This completed the simulation of one-thousandth of a minute, and the computer would begin again with the first mRNA. The computer would record the number of termination events, ribo- somes per mRNA, and mRNAs with 0, 1, 2, 3, . . . ribosomes during every simulated time interval.

It was necessary to insure that we had continued the simulation long enough to reach a steady state condition and that we averaged enough data to acquire statistically significant values. Accordingly, we simulated the translation of our 100 mRNAs over several thousand cycles. The data from consecutive groups of 1,000 cycles were inde- pendently averaged. Since we started with naked mRNAs, the average number of completed chains and the average size of the polysomes increased over the first few groups of 1,000 cycles. This transient condition usually lasted for less than 3,000 cycles. In order to insure that the transients were not included in our sampling of data, we allowed the computer to simulate 6,000 cycles before we began to gather data on the polysome size and the frequency of chain comple- tion. To get statistically significant data, the 4,000 subsequent cycles were averaged. This would be equivalent to data collected for the last 4 min of a lo-min translation experiment.

In simulating translation on the larger mRNA similar considera- tions forced us to disregard the first 50,009 cycles and average the data over the subsequent 50,000 cycles.

The computer instructions written in Fortran IV were run on a Digital PDP-11/50 computer. Should new experimental studies sug- gest new variables, our programs are available upon request.

In modeling the possible effects of alterations in the level of mRNA binding : litiation factors, a more analytical approach was taken. We began by assuming that the limiting factor (f) must bind to the mRNA prior to the 40 S initiation complex. Analogous equations would follow if the event were subsequent to binding of the 40 S initiation complex, but prior to elongation events. If the concentration of the free factor is f , and it is in equilibrium with an mRNA.factor complex, we have:

Case 1

[Ml + If1 - [Mfl (6)

mRNA + factor o mRNA. factor complex

[Mf] + [R$] ++ [80 S initiation complex] (7)

mRNA. factor complex + 40 S complex ++ 80 S initiation complex

Alternatively, this binding reaction may be far from equilibrium. If the subsequent reaction is much faster than the binding of this factor, the relevant equations are:

’ B. F. Roberts and J. E. Bergmann, unpublished observation.

Case 2

[Ml + [fl- [Mfl (8) Message + factor -+ mRNA. factor complex

[Mf] + [KS] ++ [80 S initiation complex] (9)

mRNA factor complex + 40 S complex ++ 80 S initiation complex

The effective fraction of messages available for initiation to be used in Equations 1 and 2 is:

[Mfl m=[Ml

For the equilibrium condition (Case 1) we have the well known expression:

[Mfl Keq = [W[f 1

From this equation one may easily derive the fraction of total mRNA that is bound:

[Mfl LSf 1 Fraction = m = ([Ml + [Mf]) = (Ke,[f] + 1)

(10)

In the case where the mRNA and factor are far from equilibrium (Case 2), the fraction of mRNA that is bound is:

Fraction = m = 1 - exp(-K[f](t)) (11)

where t is time. If the subsequent reaction requires an average time 7 the average fraction of bound mRNA would be:

Fraction = m = 1 - exp{-K[ f](T)] (12)

RESULTS

Our model can be used to calculate the steady state rate of protein synthesis, the ribosome distribution along an mRNA, and the average polysome size as a function of a particular set of rate constants K,, m, R$, K, (for 1 < i < t), and Kt. It is easiest to illustrate our findings by modeling a greatly simpli- fied translation process. Some of the complexities, including local variations in the elongation rate, will be introduced later.

Physiologically Relevant Values for our Independent Pa- rameters-we begin by modeling the translation of cr-globin mRNA as it occurs in rabbit reticulocyte lysates at 37°C. We then illustrate the dependence of translation rate and poly- some size on each of the parameters by varying one parameter at a time about its physiological value.

In reticulocyte lysates at 37°C the rate of globin polymeri- zation is roughly 100 amino acids/min.’ This rate appears to be relatively uniform along the mRNA (21,22) although there are some regions along the mRNA where this rate is appar- ently reduced (23). Thus, we will assume at first that all of the rate constants, K,, are identical. The rate of termination (Kt) has not been determined at 37”C, but at 25°C it is one-tenth of the rate of elongation (24). I f we assume that the termina- tion rate is also one-tenth of the elongation rate at 37°C we arrive at an estimate for that rate of 10 chains/min at 37°C (24). Finally, when naked radioactive vesicular stomatitis virus (VS virus) and reo virus mRNAs are added to the reticulocyte lysate system, the measured time constant for binding has been in the range of 15 s to 1 min (17-19). Thus, K,mR+ is probably in the range of one through ten initiations per min (see Equation 1). Accordingly, we may assume that the follow- ing values of the rate constants fall within the physiological range: (a) 1 < K,mR+ < 10 initiations/min; (b) K, = 100 amino acids/min; (c) KI = 10 chains/min.

As mentioned previously, the region of an mRNA covered by a ribosome is assumed to be 12 codons or 36 nucleotides

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A Kinetic Model of Protein Synthesis

and the length of the coding region modeled here is 141 codons (except where otherwise stated).

The Rate of Protein Synthesis and the Average Polysome Size as a Function of the Initiation Rate Constant-We first examined the dependence of the rate of protein synthesis (Q) on the initiation rate constant (KlmR-&) for physiological values of the elongation and termination rates (Kc = 100, K, = 10). The results of our calculations are plotted in Fig. 1A (curve labeled “Kc = 100”). The dependence of Q on the initiation rate was subsequently determined for other values of the assumed single elongation rate constant K, while the termination rate was held at 10 chains/min (Fig. 1). Thus, in Fig. 1 A, the top curve (K, = 400/min) represents the situation in which elongation is 4 times the normal rate. The next curve (Kl = lOO/min) represents a near normal rate of elongation, and the lower curves represent situations of reduced elonga- tion rate as might occur in cells treated with low doses of cyclohexamide or other elongation inhibitors (Ki = 50 or K, = 20).

All of the curves show saturation behavior. Incrementally increasing the initiation rate constants results in ever smaller

Ki=20 Ki=20 ,+4-o-o-o~-p-- ,+4-o-o-o~-p--

----_ ----_ Simpler mode Simpler mode

I I I I I

K,= 100

i I I I I

2 4 6 6 IO

K,mR*

FIG. 1. The rate of protein synthesis per message and poly- some size as a function of the initiation rate constant. A, the termination rate constant used for both sets of calculations was 10 chains/min. The elongation rate constant in each curve is uniform along the entire mRNA. In the top curve, the elongation constant (K,) is 400 amino acids/min and in the other curves it is successively 100, 50, and 20 amino acids/min as marked. The dashed line repre- sents data calculated using the simple model (Ref. 7). In that model the elongation rate was everywhere equal (here we used 20 amino acids/min), the termination rate was infinitely fast, and the distribu- tion of ribosomes was assumed to be uniform along the mRNA. B, the average number of ribosomes per mRNA and the average ribo- some spacing along the mRNA was calculated assuming the elonga- tion rate constant was uniformly 100 amino acids/min, and the termination rate constant was 10 chains/min.

gains in the steady state rate of protein synthesis. Fig. 1A also shows that, for two mRNAs of different binding affinity, say, 3 and 5/min (K,mR$ = 3 or KlmR-$ = 5), reducing the elongation rate constant from 100 to 20 amino acids/min makes the elongation rate-limiting and tends to equalize their productivity. For K,mR$ = 5, reduction of K, from 100 to 20 reduces Q from 3.1 to 1.0 chains completed per mRNA per min, a 3-fold reduction. For KlmR $ = 3, the same decrease in Ki reduces Q from 2.2 to 0.97 chains/mRNA/min, a P-fold reduction. The two mRNAs now are translated at essentially equal efficiency. This phenomenon is intuitive and has already been used as a method of quantitating mRNA (17). However, such a 5-fold reduction in the elongation rate would fail to quantitate messages accurately with initiation rate constants of less than two per min.

In contrast to the predictions of the model presented by Lodish (7), the rate of protein synthesis is never inhibited by increasing the initiation rate. The dashed line in Fig. 1 shows that for low values of the elongation rate constant and high initiation rates the previous model predicts a decreasing rate of protein synthesis. However, it is also important to note that for higher values of the elongation rate or lower values of the initiation rate there is complete agreement between the rate of protein synthesis predicted by the earlier model and that presented here.

Fig. 1B shows the relationship between the initiation rate constant and the average polysome size (and average ribosome separation) for physiological values of the elongation and termination rate constants. Such a graph is very useful if one wishes to determine the relationship between the initiation and elongation rate constants from a polysome distribution in an experimental system. It is important to note that the polysome size is a function only of the ratios of the assumed rate constants. Lowering all of the constants (K,, K,, Kt) 2- fold, for instance, would reduce 2-fold the rate of protein synthesis, but leave the polysome distribution unchanged.

Interaction between Ribosomes-At high rates of chain initiation, relative to elongation, mRNAs become saturated with ribosomes. If both the elongation and termination rates were infinitely fast, the rate of protein synthesis would equal the initiation rate constant (the top curve in Fig. 2C). In contrast, when the elongation rate is in the physiological range (Ki = 100) and the termination rate is very rapid (Kt = 999) the same saturation behavior as seen in Fig. 1A is evident (compare closed and open circles in Fig. 2C). Does this satu- ration result from a slower overall rate of ribosome move- ment? In order to understand the mechanism behind this saturation, we analyzed the average time it would take each active ribosome to complete one polypeptide chain as a func- tion of the initiation rate constant. The two curves in Fig. 2B represent the dependence of the transit time on the initiation rate constant (K,mR$) for K! = 999 (closed circles) and Kt = 10 (open circles). The results indicate that the time it took a ribosome to traverse the entire mRNA did not significantly change as the mRNA became saturated with ribosomes (Fig. 2B). For instance, when the initiation rate constant increases 5-fold from 1 to 5 (from KlmR$ = 1 to K,rnR$ = 5; K, = 10) the rate of protein synthesis (Q) increases only 3-fold from 0.9 (90% of KlmR$) to 3.1 (only 60% of K,mR$). In contrast, the time it takes a ribosome to traverse the mRNA and release the completed polypeptide increases by only 7%, upon chang- ing the initiation rate (from 1.53 to 1.64 min). When the termination rate is very fast (KI = 999), the transit time is increased by only 3% (from 1.41 to 1.45 min). Evidently, steric hindrance of ribosomes, at the level of elongation, does not occur to a significant extent. Rather, as the initiation rate constant increases, the fraction of mRNAs whose initiation

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A Kinetic Model of Protein Synthesis 11931

I00 r l \p 075

1

\ l \.

ci 1. \* 0.50 A* l* nan .*- ” .” l K,=lO

I I

B 0

20 t / oKf’l0

.A”

P

/̂O /

.o-o /” . -.,.-•Kf=99

I Ltr=*-•

-.-a-.- .c I I

K,mR*

FIG. 2. Interaction between ribosomes. The elongation rate constant used in these calculations was 100 amino acids/min at all positions along the mRNA. Panel C shows the rate of protein syn- thesis as a function of the initiation rate constant K,mR*. The open circles represent data calculated for a termination constant of 10 chains/min. The closed circles represent data calculated for a ter- mination constant of 999 chains/min. The solid line labeled “no interference” shows the rate of protein synthesis that would result if ribosomes did not interfere with each other (i.e. if they were infinitely small or if more than one could be in one place at the same time). Panel B shows the time required for a ribosome to bind to an mRNA, to traverse the entire coding region of that mRNA, and to be released as a function of the initiation rate constant KlmR*. It was calculated by dividing the average number of ribosomes per mRNA by the number of chains completed per mRNA per min. Again the closed circles represent a fast termination rate (999 chains/min) and the open circles represent the slower rate measured in vitro (IO chains/ min). The scatter is due to averaging a finite number of stochastic events. Panel A shows the probability (PI) that the initiation region is not blocked by a translating ribosome. It was calculated by dividing the number of completed chains per mRNA per min (which equals the number of initiated chains per mRNA per min) by the initiation rate constant KlmR$. A termination rate constant of 10 chains/min was used in the calculation.

region is available for ribosome binding (PI) drops precipi- tously (Fig. 2A). Thus, under physiological conditions, steric hindrance of ribosomes is most evident in the initiation region of an mRNA.

Rate of Chain Completion versus the Termination Rate Constant-Although termination rate constants of 10 or 999 result in similar rates of initiation and thus protein synthesis (Fig. 2C), the lower termination rate constant markedly in- creases the transit time at high initiation rates (Fig. 2B). As will be shown below, this greater transit time is the result of ribosomes queuing up behind the ribosome at the terminal codon that is waiting to be released. So long as this queue does not reach back to the initiation region, the rate of protein synthesis remains unaffected.

Fig. 3B illustrates that the predicted rate of protein synthe-

\ 8 P

I I

E ‘=

B 3- K,mR*= 4 s 0-O 0

K,mR*=l 0

I I 5 10

KT

FIG. 3. Rate of protein synthesis versus the termination rate constant. In these calculations the elongation rate constant was everywhere equal to 100 amino acids/min. Panel B shows the rate of protein synthesis uersus the termination rate constant K, for two different values of the initiation rate constant K,mR$ (KlmR$ = 4 and KlmR* = 1). Panel A shows the average number of ribosomes per mRNA as a function of K, for these two values of the initiation rate constant &mR$. Squares represent a rate constant of one initiation per min, and circles represent four initiations per min.

sis is relatively independent of the rate constant for termina- tion (Kt) so long as & remains greater than the overall rate constant for initiation KlmR$ For the initiation rate constant equal to one initiation per min and the elongation rate con- stant equal to 100 amino acids/min (K,mR$ = 1, K, = loo), the calculated rate of protein synthesis was 0.89 chains/ mRNA/min when K, was set equal to 10. The rate was still 0.86 chains/min when K, was 1. This agreement falls within the statistical scatter for these values. In contrast, for K, = 0.75, the termination rate-limited protein synthesis and the calculated rate of protein synthesis dropped to 0.73 chains/ mRNA/min. Since KtXt equals the rate of chain termination (Equation 4), we conclude that as long as K! is greater than K,mR+, reducing Kt increases the probability of the terminal position being occupied in such a manner that the product K& remains unchanged. However, when Kt is smaller than the initiation rate, ribosomes with comp1et.e but unreleased chains begin blocking ribosomes 12 codons from the termi- nation codon. For smaller values of K,, these blocked ribo- somes will remain at position t - 12 long enough to block other ribosomes at position t - 24, etc. Fig. 3A shows that for termination rates less than twice the initiation rate, the av- erage polysome size is noticeably affected.

Agreement with Experimental Data-The best experimen- tal system for testing the predictions of such a model is the translation system from rabbit reticulocytes (25). The major endogenous products of this system are (Y- and P-globin poly- peptide, which constitute greater than 90% of the total prod- uct. Interestingly, the /3-globin mRNA appears to have a greater affinity for ribosomes than does the a-globin mRNA. Treatments that limit the initiation rate increase the relative translation of ,L?-globin, and treatments that slow the elonga-

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11932 A Kinetic Model of Protein Synthesis

6

1 n B

f

% maximal synthesis FIG. 4. Comparison of theoretical calculations with experi-

mental data on the ratio of a//3 globin synthesis in the presence of inhibitors. The data come from experiments reported by Lodish (7) using initiation inhibitors. To calculate the curves we chose values for the rate constants as described under “Results.” The values of K,, m, K,, and K, were all held constant; only R.+ was changed. For various values of R# the rates of (Y- and P-globin synthesis were tabulated and the ratio of these rates were calculated. We also tabulated the sum of these rates. We next normalized both the ratio of rates and sum of rates for all values of R$ to the values realized for R$ = 1. The values of K,,m and Klom are, respectively, 3.7 and 6.9 (Curue I), 3.1 and 4.9 (&rue 2).

tion rate favor the translation of a-globin. We wished to compare the predictions of our model for the translation of (Y- and P-globin with these experimental data. We first chose values of our translation parameters that are applicable to globin synthesis in reticulocytes under standard conditions. We then calculated how the relative rates of (Y- and P-globin synthesis would vary, if the rate of initiation were slowed.

As mentioned earlier, the best available values for the elongation and termination rate constants at 37°C are lOO/ min and lO/min, respectively. The most straightforward method of determining the initiation rate constants for (Y- and P-globin is from their polysome size using Fig. 1B. A number of groups have sized the polysomes synthesizing (Y- and p- globin (24-28). Although P-globin mRNA was consistently found associated with more ribosomes than a-globin mRNA, the precise values measured for their average polysome sizes differed from group to group. Predictions of changes in the relative iate of a- and P-globin polypeptide synthesis are rather strongly affected by the assumed values of the initiation rate constants under normal conditions. Accordingly, we de- cided to illustrate our prediction starting with two extreme sets of assumptions. We used the data of Boyer (27) and assumed that under normal conditions a-globin is synthesized on polysomes with an average of 4 ribosomes (KlmR$ = 3.7) and that P-polysomes have an average of 6.5 ribosomes (KlmR$ = 6.9). Our alternate assumption was from the data of Lodish (24)) that (Y- and /3-polysomes contained an average of 3.5 (K,mR$ = 3.1) and 5 (KlmR$ = 4.9), respectively (see Fig. 1B).

Using these values for K,,m and Klgm we used our model to predict the relative rates of (Y- and ,&globin synthesis as R$ was reduced from one to zero. As can be seen from Fig. 4, the different measurements of relative polysome size have led to rather different curves, both of which are in qualitative agree- ment with the experimental data.

Unfortunately, data relating the relative rates c~- and p- globin synthesis in the presence of elongation inhibitors ex- hibited so much scatter that it was pointless to make such a quantitative comparison (26).

To summarize, although theory and experiment are in qual- itative agreement, the experimental data are not yet precise enough to demonstrate whether the sole competition between (Y- and P-globin mRNAs is for active 40 S initiation complexes

or whether there is in addition a competition for initiation factors such as eIF-4B (see below).

As mentioned above, we have assumed that each ribosome covers 12 codons. Since the assumed size of a ribosome affects the predicted polysome size for any given choice of the rate constants, we also calculated the average number of ribosomes translating (Y- and ,&globin mRNA for reduced values of the overall elongation rate constant (KJ. When Ki is reduced 5- fold to 20 amino acids/min, the predicted rate of total protein synthesis falls 2.5-fold. The predicted polysome sizes are 7.8 for a-globin (assuming K,rnR* = 3.1) and 8.7 for P-globin (assuming K,mR$ = 4.9). Lodish (26) measured the (Y- and ,&globin polysome distribution in reticulocyte lysates in the presence of elongation inhibitors. He found that when elon- gation was slowed, both (Y- and /?-globin were made on poly- somes with a model size of 6 to 7 ribosomes. This small discrepancy between our calculations and the experimental data indicates either that ribosomes actually cover a larger region of the mRNA then we assumed or that the initiation rate constant as well as the elongation rate constant was below normal in the cited experiments.

Effect of Messenger Length-As we have discussed how each of the translation rate constants affects the overall rate of protein synthesis when relatively short mRNAs such as globin mRNA are being translated, it was important to ascer- tain whether the same relationships would exist when longer mRNAs were being translated. Accordingly, we simulated translation on an mRNA approximately 6 times as large as globin using values of KI, Ki, and Kt that would in turn limit translation for each parameter. The results are summarized in Table I. For mRNAs of 141 or 837 codons, the number of completed chains synthesized per min and the ribosome den- sity are nearly independent of mRNA length. After succeeding in overcoming the steric hindrance of other ribosomes and initiating polypeptide synthesis, the translating ribosome will find little interference in progressing down the mRNA unless termination is severely limited.

Selective Reduction in the Elongation Rate Constant at Certain Positions-Cell types differ in their levels of the different isoaccepting species of tRNA. Likewise, different mRNAs differ in their requirements for these tRNAs. It has therefore been suggested that translational control could be exerted at the level of either tRNA availability or at the level of tRNA synthetase activity. We therefore wished to examine what effect local reductions in the elongation rate constant along the mRNA might produce. Smith (29) showed that in rabbit reticulocytes the quantity of most tRNA species that

TABLE I

Effect of mRNA length on parameters ofprotein synthesis Average Average

polysome ribosome Rate of chain

size separation completion

K]rnR$ = 1 K,=lOO K, = 10

KlmR$ = 5 K,=lOO K, = 3

KlmR$ = 5 K, = 20 K, = 10

KlmR$ = 5 K,=lOO K, = 10

837 codons

141 codons

837 codons

141 codons

837 codons

141 codons

837 codons

141 codons

7.67 109 0.091

1.38 102 0.090

66.7 12.5 2.21

10.5 13.5 2.17

52.5 15.9 1.02

8.75 16.1 1.04

27.1 30.9 3.11

5.11 27.6 3.10

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-I

FIG. 5. The effect of a local reduction in the elongation rate. In these calculations K, was set equal to 100 amino acids/min for all positions but one. At that position K, was either set equal to 6 (open and closed circles) or 16 (triangles) amino acids/min. K, was set equal to 10 chains/min, and KlmR$ was set equal to either five initiations per min (closed circles and triangles) or 10 initiations/min (open circles). In panel B we have plotted the rate of protein synthesis as a per cent of control (K, = 100 for all positions) uersu.s the position along the mRNA of the elongation rate reduction. In Panel A, we have plotted the average number of ribosomes per mRNA as a per cent of the average number in the control situation (K, = 100 for all positions).

could transfer a given amino acid to a growing chain is roughly proportional to the number of times that amino acid occurs in the sequences of a- and /3-globin. In contrast, the leucyl- tRNAs are present in only about one-sixth of the expected concentration. We thus modeled the translation of a-globin with the same parameters previously established except that the elongation rate constants were reduced 6-fold at the 17 positions at which leucine occurs in the sequence of a-globin. To our surprise, the predicted rate of protein synthesis was reduced by only lo%, from 2.19 to 1.97 completed chains/ mRNA/min. Interestingly, when the elongation rate was re- duced at all of the same leucine positions except for the one at position 3, less than a 1% inhibition resulted.

We then decided to examine the effect on the overall rate of translation of a reduction in elongation at only a single point along the mRNA as a function of the position of that reduction. For these studies we modeled mRNAs with initia- tion rate constants of 5 and 10 initiations/min (K,mR$ = 5, KlmR+ = 10).

Fig. 5 summarizes the effect a 5- or 16-fold reduction in one of the K, would have on overall translation and polysome size as a function of the position of the block along the mRNA. For slowed elongation in any one of the positions 1 to 12, the extent of inhibition on the overall translation rate is greatest, approximately 11% for the 5-fold reduction and 33% for the 15-fold reduction. The mechanism of inhibition seems to be the blocking of the initiation site since the average polysome size is reduced (Panel A). This equivalent inhibition for slowed

elongation at any of positions 1 through 12 would thus be explained, since a ribosome stuck at any of these positions blocks the initiation site equivalently. Likewise positions 13 to 24 are equivalent. However, in this case, the initiation block is less severe. As discussed previously, reduction in the rate constant for termination can cause a queue of ribosomes to form on the mRNA without significantly hampering the rate of initiation or protein synthesis. Similarly, for reductions in the elongation rate constant further toward the 3’-end of the mRNA, the inhibition of protein synthesis is less pronounced and the average number of ribosomes is increased.

Lowering elongation 5-fold at positions 1, 2, and 3 simulta- neously is equivalent to reducing it 15-fold at position 1 (data not shown). This is about 3 times the inhibition produced by limiting elongation 5-fold at position 1. Thus, there is additiv- ity in the effects of these elongation blocks.

The Role of Factors with Different Affinities for Different Messages-In our discussion of the translation of a- and p- globin mRNA, we modeled a block in initiation as a reduction in the concentration of active 40 S ribosomal subunits (RS). Here we would like to examine some possible effects of altering the level of one of the mRNA binding initiation factors. Golini et al. (11) have found evidence that eIF-M3 (now called eIF- 4B) is required in different amounts for translation of enceph- alomyocarditis virus (EMC) and globin mRNAs.

Also, Kabat and Chappell have shown that ,8-globin mRNA has a 50-fold higher affinity for eIF-4B and a-globin mRNA (12). Although modulation of the concentration or activity of free eIF-4B has not yet been shown to occur in uiuo, it is certainly a possibility. These studies have demonstrated that the differences in the affinity of eIF-4B for different mRNAs could be used by the cell as a mechanism for differential control of protein synthesis. We need two alternate models to calculate quantitatively how the rate of protein synthesis should depend on factor concentration (see “Model and Meth- ods of Solution”). We assumed that the factor. mRNA-binding reaction was either in equilibrium or far from it.

The fraction of mRNA bound in either situation is displayed in Fig. 6 (the circles in Panels B and D). As can be seen, similar results are obtained whether the mRNA and factor are nearly in equilibrium or far from it. Intermediate situations might be expected to show similar behavior. As previously indicated, the rate of protein synthesis is not strictly propor- tional to the initiation rate constant K,mR*. For large values of K,R$, the rate of protein synthesis would rise and saturate rapidly as the concentration of factor increases. For small values of KIR$ the rate of protein synthesis should be nearly proportional to m. The squares and triangles in Fig. 6, B and D indicate how the rate of protein synthesis would be affected by changes in the concentration of free factor ( f) for mRNAs such as a- and P-globin (K, R $ = 3 and K, R $ = 5). The values of K, R $ for a- and P-globin do not differ greatly, but one can still see the effect mentioned. Panels A and C show how the ratio of translation rate of two a-like mRNAs (KIR$ = 3) or two P-like mRNAs (K, R f= 5) would vary with factor concen- tration if their affinity for the limiting factor differed 50-fold (12). The major conclusion from this graph is that changing the concentration off affects differently the amount of protein made by the two mRNAs, a reduction in f inhibits preferen- tially the translation of the mRNA with the lower constant for binding to the factor, an increase in f will favor that poorer mRNA (Fig. 6).

An interesting situation arises in Case 2 if the subsequent reaction were to speed up. This increased rate would be reflected in a reduced time constant (7). In Case 2 the fraction of mRNA which is associated with factor is related to the product of factor concentration and 7. Thus, a decrease in T

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11934 A Kinetic Model of Protein Synthesis

1 2 3 4 5 1 2 3 4 5

Factor Concentration

FIG. 6. Effect of changes in factor concentration on trans- lation. D, the fraction of mRNA associated with our hypothetical factor (m) was calculated using the formula:

Ke,[fl) m = 1 + &<,[fl

(see text) and was plotted as a function of factor concentration [f] assuming K, = 1 (open circles) or K,, = 0.02 (closed circles). Using the value for m previously calculated, the rate of protein synthesis was then calculated using approach 1, and this rate was divided by the maximal rate (i.e. the rate for m = 1). This normalized rate was plotted as a function of [f ] assuming the following parameters: KIR+ = 3, K, = 100, Kt = 10, Km = 1 (open triangle), K1R-j = 3, K, = 100, K( = 10, Kw = 0.02 (closed triangles), &R+ = 5, K, = 100, K, = 10, K, = 1 (open squares), and KIR$ = 5, K, = 100, K, = 10, K,, = 0.02 (closed squares). C, the relative fraction of mRNA bound (ml/m2)

would have a similar effect as a decrease in the factor concen- tration ( f).

Finally, it should be mentioned that we know of no reason why mRNAs with a high affinity for 40 S initiation complexes must necessarily have a high affinity for such an initiation factor. It is, therefore, conceivable that limiting different components of a translation reaction will alternatively favor one mRNA or another.

DISCUSSION

It is important to emphasize that we did not attempt to model the dependence of the overall translation parameters on any specific reaction (such as tRNA concentration); not enough is known about this myriad of reactions and their relative rates. Rather, we grouped these reactions into initia- tion, elongation, and termination steps. As each of these steps was assigned a rate constant, we were able to predict the dependence of the rate of protein synthesis and the average polysome size on the overall rate of each of these steps.

We feel that the most important outcome of this study is the demonstration of the pivotal role of initiation in the control of protein synthesis. To summarize:

was calculated for the two mRNAs in D. This ratio was plotted as a function of [f ] (open circles). The relative translational efficiencies of these two mRNAs was calculated and plotted as a function of [f 1. The assumed values of the rate constants were: K, = 100, K, = 10, K,R$ = 3 (open triangzes), and K, = 100, K, = 10, K,R# = 5 (open squares). B, the fraction of mRNA associated with our hypothetical factor (m) was calculated using the formula m = 1 - exp(-K[f]T) (see text) and was then plotted as a function of factor concentration [f] assuming K, = 0.8 (open circles) or K, = 0.016 (closed circles). Using this value for m, the rate of protein synthesis was then calcu- lated and this rate was divided by the maximal rate (i.e. the rate for m = 1). The normalized rate was plotted as a function of [f 1. The same relationship between symbols and assumed rate constants was used as in D. A, the values of the relative fraction of mRNA bound and the relative translational efficiency were calculated and plotted as in C except that the values of m for the two mRNAs were taken from B rather than D.

1. For small, physiological values of the initiation rate constant, initiation is the rate-limiting step in translation. The overall rate of protein synthesis is roughly proportional to the initiation rate constant. As the initiation rate constant is increased, the ribosomes interfere with each other to a greater and greater extent, and the overall rate of protein synthesis increases proportionally less.

2. As long as the termination rate is not limiting, this interference occurs primarily within the ribosome binding region. Under physiological conditions, ribosomes bind so rapidly to the mRNA that, at any given time, the ribosome binding region is blocked on a significant percentage of the mRNAs. Increasing the rate constant for elongation reduces the amount of time ribosomes spend in the ribosome binding region and thus increases the rate of protein synthesis. Thus the elongation rate constant becomes a limiting factor in the initiation process.

3. When the initiation rate is so fast that elongation be- comes limiting, the high density of ribosomes on the mRNA does not cause a reduction in the actual transit time.

4. When decreasing termination rates are studied, the ri- bosomes are seen to form a queue behind those caught at the

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terminal codon. As the termination rate is decreased, this queuing is at first seen only as an increase in the transit time for a translating ribosome. If ribosomes are not limited, the rate of chain completion per mRNA is unaffected. Further reduction in the termination rate causes the queue to extend all the way to the initiation region; when this occurs, initiation is interfered with and the rate of polypeptide synthesis is reduced.

5. Local reductions in the elongation rate near the 3’-end of the coding region mimic the effect of a reduction in the termination rate. The average polysome size increases and the rate of protein synthesis is reduced only slightly. I f the same local reduction in the elongation rate constant occurs nearer the 5’-end of the coding region, the average polysome size is reduced and protein synthesis is more significantly inhibited. The greatest inhibition of protein synthesis results from a reduction in the elongation rate within the ribosome binding region. However, even if the elongation rate constant were reduced 16-fold at a codon within the 36 nucleotide ribosome binding region, the rate of protein synthesis would be reduced by only 33%.

6. Since the major interaction between ribosomes occurs in the ribosome binding region, the relationships described above are equally true for mRNAs significantly longer than globin. For a given set of initiation, elongation, and termination rate constants, the same number of polypeptide chains will be completed per min on each longer mRNA, and the average separation between translating ribosomes will be the same on both mRNAs. This, of course, means that the longer mRNA will be found on proportionately larger polysomes, and that a proportionately large quantity of amino acids will be incor- porated into the larger polypeptide product.

7. Limiting a factor required for binding of the 40 S initia- tion complex to an mRNA has a similar effect to limiting the concentration of active 40 S initiation complexes. In addition, since different mRNAs require different quantities of such factors, variations in the level of such a factor could differen- tially affect the fraction of different mRNAs that are able to bind to the 40 S initiation complex, and initiate protein synthesis.

These findings were derived without regard to the limited resources of the cell. In particular, we assumed that the availability of ribosomes is unlimited. Most cells have very few spare ribosomes. Were a general reduction in the rate of termination to occur, ribosomes would begin to queue up. However, long before this queue reached back to the initiation region, the pool of free ribosomal subunits available for initi- ation would be exhausted. The overall initiation rate constant would be reduced and messages with a higher affinity for 40 S initiation complexes would gain a translational advantage. Thus, a general reduction in the termination rate constant would paradoxically mimic a reduction in the level of 40 S initiation complexes, except that the cellular polysome would not run off.

In the introduction, we outlined four possible mechanisms of translational control. We stated that a model such as ours could be used to estimate the extent to which two of these mechanisms would be able to effect such control. To what extent can changes in the level of the different components universally required for the initiation of protein synthesis differentially affect the rate of translation of different mRNAs?

As outlined under “Model and Methods of Solution,” there are two types of mRNA recognition reaction that occur during initiation. One reaction involves the interaction (perhaps bind- ing) of initiation factors with the mRNA. The other reaction involves the binding of ribosomes to the mRNA. As the

forward rate of either of these reaction increases, the rate of protein synthesis increases. However, as this occurs, other reactions limit the rate of translation to a greater and greater extent. Consequently, the rate of translation of messages with a high affinity for one of these initiation components will respond less to changes in the concentration of that compo- nent than messages with a low affinity for the component (Figs. 1 and 6). Using the results in this paper, one can evaluate the extent to which the average rates of ribosome binding and ribosome movement limit the rate of protein synthesis in any cell or cell-free translation system from which one can isolate intact polysomes.

As one example, the average polysome during exponential growth in both HeLa cells and Dictyostelium discoideum contains approximately 10 ribosomes and the average trans- lation product is from 300 to 500 amino acids long (4, 31).’ Using the data of Fig. lB, we calculate that the average spacing between ribosomes is between 30 and 50 codons. This would correspond to an initiation rate of roughly three chains/ min for a typical cellular mRNA if the elongation rate were 100 amino acids/min (Fig. 1B).

The fraction (PI) of an average mRNA molecule that is not blocked to initiation by translating ribosomes is about 0.75. For a “poorer” mRNA with a lower rate constant for chain initiation, K1, the value of P, would be higher. Consequently, as R$ is reduced from its physiological value, translation of the poorer mRNA would be reduced proportionally more than would that of the average cellular mRNA. For a typical cellular mRNA, the reduction in R $ would be partly compen- sated by an increase in PI. An analysis similar to that of Fig. 4 shows that the maximum change in the relative reduction in translation of such a “poor” mRNA is the reciprocal of the starting value of PI, or a factor of 1.3 in this case. Likewise, an increase in the elongation rate of all mRNAs in the cell would also reduce the relative translation of a poorer initiating mRNA, but, again, the maximum shift could be, in this case, no more than 30%.

What if RI+ were to increase? Translation of the poor messenger would be enhanced preferentially. In this situation one cannot put an absolute limit on the increase in the fraction of total protein synthesis programmed by these mRNAs. However, we do know that the relative increase in the pro- ductivity of the poorer mRNAs will be less than the increase in RI+. In addition, increasing R* can never make the poorer mRNAs more efficient than the average mRNA.

In contrast, an “efficient” mRNA with a high value of K1 would already be saturated with ribosomes under standard conditions. The efficiency of such messages would thus not change significantly with an increase in R$. The bulk of cellular mRNA would be translated about 2% times more efficiently. Thus the fractional contribution of the most effi- cient mRNAs to the total translational production would decrease, but by no more than 2.5-fold. I f R$ were to decrease, translation of these efficient mRNAs would be inhibited less than the overall rate of protein synthesis. Again, the relative rates of synthesis cannot change more than the change in R+.

To summarize two situations, we can put an absolute limit on the change in the relative rates of translation of such exceptional mRNAs. If R$ increases, the translation of effi- cient messages will not be stimulated coordinately. The rela- tive decrease in translational efficiency will be less than 2.5- fold. I f R+ decreases, the translation of less efficient mRNAs will be preferentially inhibited. However, the decrease in their relative rates of translation will be less than 30%. As long as one can estimate the average number of ribosomes translating

’ J. E. Bergmann, unpublished observations.

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the polypeptides of interest, one can use the results presented here to estimate the changes in relative rates of translation of the mRNAs that would follow a change in either R$ or the elongation rate constant.

As indicated in Fig. 6, changes in the concentration of an initiation factor can also lead to a shift in the relative efficiency of different mRNAs. The work of Kabat and Chappell (12) and of Golini et al. (11) indicates that initiation factors which are probably required for the translation of all mRNAs can exhibit very different affinities for different mRNAs. For instance, in a reconstituted cell-free system with excess globin mRNA, translation of ,&mRNA was about 50-fold more effi- cient than was a-mRNA. Addition of eIF-4B equalized trans- lation of the two mRNAs (12). This implies that under these reaction conditions eIF-4B has a 50-fold greater affinity for ,&mRNA than for a-mRNA (12). However, in intact reticu- locytes and in crude reticulocyte lysates, the relative transla- tion efficiency of a- and /?-globin mRNA differs only LCfold. If the 50-fold difference in affinity of eIF-4B for the two mRNAs also occurs in these systems, then the present model predicts that in reticulocytes this factor must be present in vast excess for the translation of P-globin mRNA. Should the concentration of eIF-4B be reduced, the translation of a-globin mRNA would decline long before the translation of P-globin mRNA would be affected. It should be possible to reduce the rate of translation of a-globin mRNA to only about 10% of the rate of ,&globin mRNA translation without significantly re- ducing the total level of fi-globin production (Fig. 6) or the average size of the polysomes synthesizing ,8-globin. Under such conditions, the total rate of protein synthesis would only be inhibited by 50%. Should the activity of eIF-4B be reduced sufficiently, the ratio of a- to ,&globin synthesis could be reduced 50-fold. Thus, there is a far greater potential for selective reduction of the translational efficiency of “poor” mRNAs by reducing the concentration of initiation factors required for ribosome binding to mRNA than by reducing the concentration of activated ribosomal subunits.

Before concluding, we wish to mention three aspects of translation that we did not attempt to incorporate in our model.

First, although the rate constants for initiation, elongation, and termination are in principal independent, they are inter- related by auxiliary control mechanisms in some cells. For instance, in Ehrlich ascites tumor cells, starvation for either leucine, tryptophan, or valine primarily inhibits initiation (32). These cells must have evolved some mechanism for sensing amino acid starvation and blocking initiation in re- sponse. Even in the absence of specific feedback mechanisms, large increases in the amount of total mRNA to be translated without concomitant increases in the capacity of the transla- tion system may lead to “competition” among these mRNAs for the limited translational resources (11, 12). In the formu- lation of our model, this would be equivalent to a reduction in the concentration of free initiation factor, ribosomal subunit (R$), or one of the rate constants k, K,, or K,, or a combi- nation of these effects. The resultant shift in translational efficiencies would depend on which “constants” had been most affected. Using our model, we were able to gauge the dependence of the overall rate of protein synthesis on each of these rates. However, such manipulation of individual rate constants may be very rare in nature.

Second, in modeling initiation, we assumed that the rate- limiting step is the binding of the 40 S subunit to the mRNA and that this reaction is blocked by a translating ribosome situated on any of the fist 12 codons. However, the equations apply to any class of reactions which limit the rate of this binding by modifying the 40 S subunit prior to binding (re-

cycling reactions of initiation factors that bind 40 S subunits) or to structural transitions of the mRNA over the entire ribosome binding region which are prerequisite to the binding of the 40 S subunit. Our equations would be incorrect, how- ever, if the rate-limiting step in ribosome binding were actually mediated by events that could occur before the previously bound ribosome vacated the ribosome binding region, for example, if the rate of binding of a small initiation factor to the mRNA limited the rate of ribosome binding. If this were the case, these rate-limiting events might occur before the entire ribosome binding region were vacated by the previous ribosome, and immediately after that ribosome left the ribo- some binding region, the next ribosome would bind. This binding mechanism would exhibit greatly reduced ribosome- ribosome interference in the binding region. In contrast to the results presented in this paper, such a model would predict little or no detectable shift in the ratio of a//3 globin synthesis upon addition of initiation inhibitors.” It is therefore inap- plicable to at least the globin translation system of rabbit reticulocytes (Fig. 4).

Third, from phage systems such as Qp, f2, r17, and ms2, it is known that ribosomes can have a profound effect on mRNA secondary structure, even exposing previously masked initia- tion sites (25). It is therefore not hard to imagine that ribo- somes might interact in more complex ways than are modeled here. For instance, Von Heijne et al. (32) suggested that ribosomes may be slowed by hairpin loops in the mRNA and that one ribosome situated on one side of such a loop might thus help a neighboring ribosome through this region by holding the loop open. By analogy with the case of point variations in the elongation rate, such a hairpin loop at the 3’- end of a messenger may cause a 33% increase in the transit time without seriously affecting the rate of production of completed polypeptide chains (Fig. 5). In contrast, a similar hairpin loop at the 5’-end of the mRNA would have a huge effect on the availability of the initiation site and thus on the overall rate of protein synthesis.

In this study, we focused our attention on the rate of synthesis per mRNA of completed polypeptide chains. This is the important parameter to follow when examining possible mechanisms whereby the relative production rate of different polypeptides might be controlled translationally. We have not followed such parameters as the actual elongation rate with as much care. Although the rate of movement of ribosomes along an mRNA is not central to the question of translation control, it is of importance to the cell from the point of view of efficiency. For example, should the termination factor or some tRNAs become limiting, the ratio of different poly- peptide products might be seriously affected, but the number of ribosomes required to support the normal level of poly- peptide synthesis would be significantly increased. It would require far less energy for the cell to synthesize a few more tRNAs or termination factors than it would to synthesize all of these extra ribosomes. From this point of view, the in uiuo packing density of reticulocyte ribosomes on HeLa cell or D. discoideum mRNAs represents a good balance between the imposed initiation and elongation rate constants.

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J E Bergmann and H F Lodishtranslational control.

A kinetic model of protein synthesis. Application to hemoglobin synthesis and

1979, 254:11927-11937.J. Biol. Chem. 

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