Genome-Scale Analysis of Translation Elongation with a Ribosome Flow Model
[['Gene translation is a complex process through which an mRNA sequence is decoded by the ribosome to produce a specific protein .', 'The elongation step of this process is an iterative procedure in which each codon in the mRNA sequence is recognized by a specific tRNA , which adds one additional amino-acid to the growing peptide [1] .', 'As gene translation is a central process in all living organisms , its understanding has ramifications to human health [2] , [3] , [4] , biotechnology [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] and evolution [4] , [7] , [11] , [13] .', 'In recent years there has been a sharp growth in the number of new technologies for measuring different features related to the process of gene translation [5] , [6] , [10] , [14] , [15] , [16] , [17] , [18] , [19] .', 'However , this process is still enigmatic , with contradicting conclusions in different studies .', 'In particular , the identity of the essential parameters that determine translation rates is still under debate [6] , [20] , [21] .', 'Recent studies have suggested that the order of codons along the mRNA ( and not only the composition of codons ) plays an important role in determining translation efficiency [7] , [20] , [22] , [23] .', 'Starting with the seminal work of MacDonald et al . [24] , [25] and the work of Heinrich et al . [24] , [25] theoretical models for the movement of ribosomes ( and other biological ‘machines’ ) have been presented [26] , [27] , [28] .', "Despite being relatively realistic these models haven't been used for the analysis of large scale genomic data .", 'The models that have been used for this purpose , while making promising and worthy first strides , have not attempted to capture the nature of the translation elongation process on all its various physical aspects [6] , [13] , [26] , [27] , [28] , [29] , [30] .', 'The most widely used predictors of translation efficiency are the codon adaptation index ( CAI ) [28] and the tRNA adaptation index ( tAI ) [27] .', 'As we describe later , the tAI is the mean adaptation of a gene ( i . e . , of its codons ) to the tRNA pool of the organism .', 'The CAI is similar to the tAI albeit in this predictor the weight of each codon is computed based on its frequency in a set of highly expressed genes .', 'Based on measures such as the tAI , it is possible to estimate the translation rate of single codons .', 'Thus , it possible to study ( local ) translation rate profiles along genes [7] , [31] .', 'As we depict later , in this study we take into account some additional physical aspects of translation elongation .', 'The aim of the present research is twofold: First , we address the need for a simple , physically plausible computational model that is solely based on the coding sequence ( i . e . a vector of codons in each gene ) .', 'In addition we further require that the model will allow for a computationally efficient analysis of the translation process on a genome-wide scale and across many species .', 'Focusing on the coding sequence , we by no means wish to imply that it is only factor taking place in the determination of translation rates .', 'Nevertheless , since it has been widely recognized as a prime factor in the translation elongation process , we will herby study it in isolation .', 'To this end , we introduce a new approach for modeling translation elongation .', 'Our model is aimed at capturing the effect of codon order on translation rates , the stochastic nature of the translation process and the interactions between ribosomes .', 'We demonstrate that our approach gives more accurate predictions of translation rates , protein abundance and ribosome densities in endogenous and heterologous genes in comparison to contemporary approaches .', 'Second , using our model , we address the need for a better understanding of the translation process .', 'Our analysis unravels several central and yet uncharacterized aspects of this process .'], ['Our model is based on the Totally Asymmetric Exclusion Process ( TASEP , see , for example [24] , [25] , and subsequent studies [32] .', 'In the TASEP , initiation time as well as the time a ribosome spends translating each codon is exponentially distributed ( mean translation times are of course is codon dependent ) .', 'In addition , ribosomes span over several codons and if two ribosomes are adjacent , the trailing one is delayed until the ribosome in front of it has proceeded onwards ( Figure 1A , Methods , see also Text S1 ) .', 'Despite its rather simple description , the mathematical tractability of the model described above is poor and full , large scale , simulations of it are relatively slow .', 'In order to allow for analytical treatment and in order to reduce simulation times , we introduced two simplifications .', 'First , instead of describing the dynamics at the level of a single mRNA molecule we describe the dynamics after it was averaged over many identical mRNA molecules ( Methods ) .', 'Second , we limit ourselves to a spatial resolution that is of the size of a single ribosome .', 'These simplifications will be further explained and justified later .', 'The simplified model , entitled Ribosome Flow Model ( RFM ) , is illustrated in Figure 1 B–C .', 'mRNA molecules are coarse-grained into sites of codons; ( in Figure 1B C\u200a=\u200a3 ) ; in practice , as we discuss with more details latter , we use C\u200a=\u200a25 ( unless otherwise mentioned ) , a value that is close to various geometrical properties of the ribosome such as its footprint on the mRNA sequence and the length of its exit channel [7] , [14] , [22] , [33] , [34] , [35] .', 'As we report later , the choice C\u200a=\u200a25 is not arbitrary and was made since it gives the best predictions of protein abundance levels .', 'Ribosomes arrive at the first site with initiation rate but are only able to bind if this site is not occupied by another ribosome .', 'The initiation rate is a function of physical features such as the number of available free ribosomes [7] , [36] , [37] , the folding energy of the 5′UTRs [6] , [20] , the folding energy at the beginning of the coding sequence [6] , [20] , [38] , [39] and the base pairing potential between the 5′UTR and the ribosomal rRNA [40] .', 'As some of these features and their combined effect are unknown and out of the scope of this paper , we assume a global initiation rate or infer the initiation rate from the coding sequences ( as we show in the section ‘Optimality of the translation machinery’ ) .', 'We do so for the sake of simplicity and in order to avoid over-fitting of data .', 'A ribosome that occupies the site moves , with rate , to the consecutive site provided the latter is not occupied by another ribosome .', 'Transition rates are determined by the codon composition of each site and the tRNA pool of the organism .', 'Briefly , taking into account the affinity between tRNA species and codons , the translation rate of a codon is proportional to the abundance of the tRNA species that recognize it ( Figure 1 , see more details in the Methods section ) .', 'Denoting the probability that the site is occupied at time by , it follows that the rate of ribosome flow into/out of the system is given by: and respectively .', 'The rate of ribosome ‘flow’ from site to site is given by: ( see the Methods section ) .', 'As we discuss in details ( see the Methods section and Figure 1D ) , the RFM and the full TASEP model , give similar predictions , yet the RFM runs markedly faster .', 'In this paper we focus on the steady state solution of the equations presented in Figure 1C and specifically in the rate of protein production at steady state .', 'Steady state is a widely used assumption in cases like these ( see , for example , [7] , [32] , [33] ) and is hence a good starting point for a large scale study as the one conducted here .', 'In addition , a pioneering analysis that took into account mRNA degradation and was not based on the steady state assumption , was unable to improve the predictive power of the model with respect to existing data ( Methods ) .', 'We note however , that this line of investigation is far from being exhausted and that it should be revisited once degradation rates of mRNA molecules and proteins become available ( this data is currently lacking for the vast majority of genomes and heterologous genes ) .', 'We denote the steady state site occupation probabilities by and the steady state ribosome flow through the system by .', 'The latter denotes the number of ribosomes passing through a given site per unit time and we note that this rate is nothing but the steady state rate of protein production .', 'One advantage of the RFM is its amenability to both analytical and numerical analysis .', 'In particular one can study ribosome density profiles and protein production rates from the equilibrium dynamics of the translation process .', 'The Methods section describes how to solve the model analytically under steady state conditions; in this section we discuss some of the basic properties of the solution .'], ['We described a novel analysis of large scale genomic data by a predictor/model that is based on the physical and dynamical nature of gene translation .', 'Given the copy numbers of the tRNA genes in the host genome , our model , the RFM , is based only on codon-bias; It can hence be applied when only the coding sequence of a gene is available and without additional data or information .', 'Despite its relative simplicity , we show that our model predicts features such as protein abundance in endogenous and heterologous genes better than alternative ( ‘non-physical’ ) approaches .', 'We demonstrate that the gap between the performance of the RFM and alternative predictors is especially large in the case of heterologous genes; thus , it should be very helpful in the common challenge of predicting the protein abundance of potential heterologous proteins before expressing them in the desired host ( see , for example , [5] , [6] , [7] , [21] , [53] , [54] , [55] , [56] ) .', 'In addition , we have demonstrated that our approach can be used for accurately inferring various variables that cannot be inferred by the common predictors used nowadays .', 'From a Systems Biology point of view , by using our model we were able to demonstrate the global optimality of the process of gene translation [6] , [7] , [20] .', 'We discovered that increasing the number of available ribosomes ( or the initiation rate , ) increases the genomic translation rate and the mean ribosomal density only up to a certain point .', 'After this point , the system is ‘saturated’: adding more ribosomes/increasing the initiation rate does not result in an increase of these two variables .', 'Quite strikingly , in all the organisms we have analyzed , the global initiation rate is optimized to the pre-saturation point .', 'The fact that similar results were not observed in artificial genes supports the conclusion that this feature is under selection .', 'Optimality of the translation machinery is perhaps not so surprising .', 'Protein production is a central and complex process in the cell .', 'For example , at any given time point there are around 60 , 000 mRNA molecules in S . cerevisiae [36] that are translated by 187 , 000 ( ±56 , 000 ) ribosomes [37] .', 'The process of gene translation consumes a very large amount of energy and thus the problem of fine tuning the number of ribosomes and the translation rate should have a significant influence on the fitness of the organisms [6] , [7] , [20] .', 'Specifically , increasing the translation rate of highly expressed genes ( the ‘supply’ ) while decreasing the number of working ribosomes/ribosomal density ( the ‘cost’ ) should improve the fitness of an organism .', 'It was already suggested that there is selection for improving translation efficiency of highly expressed genes relatively to lowly expressed genes ( see , for example , [6] , [20] ) .', 'By using our model , we can actually estimate the translation cost of highly and lowly expressed genes as the ratio between the translation rate and the average number of ribosomes working on the transcript .', 'The number of proteins produced per unit time , per ribosome , for highly expressed genes ( top 20% ) is 0 . 000162/0 . 42\u200a=\u200a0 . 000386 ( in arbitrary units ) .', 'This number is 10% higher than that of the lowly expressed genes ( lower 20%; 0 . 000125/0 . 36\u200a=\u200a0 . 000347 ) .', 'Again , this result demonstrates ‘optimality’: as highly expressed genes produce more mRNA molecules , decreasing the cost of translation should result in a much larger effect on the fitness of the organism .', 'Finally , the goal of this study was to model the process of translation elongation , emphasizing the effect of codon order .', 'In the future , in order to decrease the gap between the predictions of our models and measurements of protein abundance , we intend to develop a more comprehensive model of this process .', 'While promising strides in this direction were already made [57] , [58] , may features of the translation process are yet to be accounted for .', 'Unfortunately , large-scale biological measurements of translation rates , initiation rates , tRNA levels , mRNA/protein degradation rates and many other quantities that are related to the process of gene translation are currently unavailable .', 'Large scale measurements that are available ( e . g . protein abundance ) are related to the modeled process ( Methods ) , but are indirect .', 'This fact hinders the implementation and validation ( as opposed to formulation ) of more sophisticated models .', 'In addition , it is important to note that the ability to predict measurements of protein abundance may also be hindered due to bias and noise in the current pool of existing data ( see , for example , [17] , [59] ) .', 'As new data accumulates , the implementation of more comprehensive models will become possible and our understanding of the translation process will deepen further .'], ['In the TASEP an mRNA transcript with codons is modeled as a chain of sites , each of which is labeled by the index , where .', 'The first and last codons , , , are associated with the start and stop codons , respectively .', 'At any time , t , attached to the mRNA are M ( t ) ribosomes .', 'Being a large complex of molecules , each ribosome will cover codons .', 'A codon may be covered by no more than a single ribosome .', 'To locate a ribosome , we arbitrarily assume that the codon being translated is the one in the ‘middle’ of the ribosome .', 'For example , if the first , ( l+1 ) /2 codons are not covered , a ribosome can bind to the first codon on the mRNA strand , and then it is said to be “on codon ” .', 'A complete specification of the configuration of the mRNA strand is given by the codon occupation numbers: if codon is being translated and otherwise .', 'Note that when the ( l−1 ) /2 codons before and after codon are covered by the ribosome that is on site .', 'Since these codons are not the ones being translated , the codon occupations numbers for them are equal to zero .', 'We will now specify the dynamics of the TASEP model .', 'A free ribosome will attach to codon with rate , provided that the first codons on the mRNA are empty .', 'An attached ribosome located at codon will move to the next codon with rate , provided codon is not covered by another ribosome .', 'In case ( ribosome is bulging out of the mRNA strand ) an attached ribosome will move to the next codon with rate .', 'In order to simulate this dynamics , we assume that the time between initiation attempts is distributed exponentially with rate .', 'Similarly the time between jump attempts from site to site is assumed to be exponentially distributed with rate ( The exponential distribution is of course , an approximation as the process of translating a single codon involves more than one step [1] ) .', 'Note that in the case of the jump attempt is in fact a termination step .', 'We define an “event” as an initiation , jump attempt , or termination step .', 'From our definition it follows that the time between events is exponentially distributed ( minimum of exponentially distributed random variables ) with rate .', 'Note that a jump attempt from codon can only be made if there is a ribosome translating this codon and hence the rate depends on the set of site occupation numbers .', 'The probability that a specific event was an initiation attempt is given by: .', 'Similarly , the probability that a specific event was a jump attempt ( or termination event ) from site to site is given by .', 'At each step of the simulation , we determine the nature of the event and the time passed till its occurrence by these rules .', 'The set of site occupation numbers are then updated accordingly and the simulation proceeds to the next event .', 'For example if an initiation attempt was made , we check if the first codons on the mRNA are not covered .', 'If so , we set , otherwise the attempt fails and remains as is .', 'If a jump attempt from codon to codon was made , we check if site is not covered .', 'If so , we set and , otherwise the attempt fails and remain as is .', 'Starting with an empty mRNA strand we simulate the system for 250 , 000 steps ( events ) .', 'The system is then simulated for an additional 1 , 000 , 000 steps where we keep track of the total number of terminations and the total time that have passed from the point this phase have started .', 'The steady state rate of protein production was determined by dividing the number of termination events by the total time that has passed .', 'The number of steps in the first and second stages was determined after observing that increasing the number of steps fourfold had a negligible effect on the predicted protein production rate .', 'The TASEP model mentioned above is a generalization ( elongated particles and site dependent rates ) of the simple TASEP model ( see , for example , [60] ) .', 'In the case of the ribosome flow model , we make two approximations .', 'The first is coarse graining ( dividing into chunks/sites ) , this approximation is quite common and was applied to various physical and biophysical problems .', 'The second approximation is nothing but the mean field approximation .', 'This means that in order to write the master equation for our model ( Figure 1C ) we have implicitly neglected the fact that there could be correlations between sites .', 'We hence write approximate equations for the average ( over many identical mRNA systems ) occupation probabilities .', 'Doing so , we assume that the probability that site i is occupied/empty and that site i+1 is occupied/empty is well approximated by the probability that site i is occupied/empty times the probability that site i+1 is occupied/empty .', 'Although in general this is not always true , this approximation is also common in the TASEP literature .', 'Within the framework of the RFM , abortions were modeled by adding an abortion probability to the model .', 'The abortion probability determines the percent of ribosome-ribosome collisions that will result in abortion , i . e . , in premature detachment of the ribosome from the mRNA strand .', 'Mathematically , abortion adds the following term to the model: where is the abortion probability .', 'For every this term is added to the i-th and ( i+1 ) -th rows of equation ( 1 ) .', 'This modification of the RFM corresponds to mutual abortion , i . e . for a situation where after an abortive collision both ribosomes will stop processing the mRNA transcript .', 'Scanning different values for , we discovered that maximal correlations were obtain in the case of , i . e . in the limit were abortions due to ribosome-ribosome collisions are negligible .', 'In order to examine the steady state assumption ( within the limitations of existing data ) , we analyzed the RFM model without it .', 'Analysis was performed on the S . cerevisiae data where we simulated the model only for a time period proportional to the half life of the corresponding transcript [61] .', 'In this case , steady state was not achieved and the translation rate was taken as the mean translation rate over the elapsing time period .', 'This modification however , was unable to improve the predictive power of the model and in effect resulted in an opposite outcome .', 'Zhang model [33] similar to the TASEP model with the only change that the codon translation times are deterministic .', 'Here we would like to discuss the relation between translation rates and protein concentration/abundance .', 'In what follows we will provide justification for the intuitive expectation that protein abundance should stand in high positive correlation with translation rates .', 'Generally speaking , protein abundance levels are determined by a balance between protein production and degradation rates .', 'Fixing the degradation rate , protein abundance levels will rise when the production rate is increased .', 'Fixing the production rate , protein abundance levels will decrease when the degradation rate is increased .', 'This said , one must also bear in mind that protein degradation rates are unavailable in most of the analyzed cases .', 'And so , any current real data analysis is forced to average out the effect of protein degradation and focus on the contribution of the production rate to the determination of protein abundance levels .', 'Let denote the concentration of protein and let us assume that this protein is translated from a certain mRNA transcript whose copy numbers are denoted by .', 'In general , the dynamics of this process may be described by the following differential equation: .', 'Here and are the translation rate per mRNA molecule and the degradation rate of protein correspondingly .', 'One possible choice for is: where is constant .', 'Although this is a common first order approximation we will not base our conclusions on this particular choice and would only require that is a monotonically increasing function of the concentration .', 'In general , the function depends on the protein , i . e . it can be different from protein to protein .', 'Here however , we will replace the protein specific function with a genomic average degradation function which will be assumed monotonically increasing .', 'Note that by definition , this function does not depend on the index .', 'The steady state solution of the above differential equation ( with replaced by ) is: where is the steady state concentration of the protein .', 'From the monotonicity of it follows that is a monotonically increasing function of .', '.', 'This fact provides justification for the use of as a predictor for , i . e . one expects and to be positively correlated .', 'Indeed , we have shown that this predictor performs very well , see Text S2 .', 'We will now show that itself can also be used as a predictor for , the advantage of this predictor is that it is solely based on the coding sequence and no additional information is required for its computation .', 'The set of mRNA copy numbers may generally depend on the set of translation rates , for example via the concentration of proteins that are involved in mRNA transcription and regulation .', 'Fortunately , it is known that in endogenous genes translation rates are positively correlated with mRNA levels .', 'Highly expressed genes are under selection to have higher mRNA levels , higher translation rate and higher protein abundance ( note that this is not a causal relation; see , for example , [6] ) .', 'Since mRNA levels are positively correlated with translation rates , higher values of do indeed imply higher values of and vice versa .', 'Since in hetrogenouse gene expression mRNA copy numbers are usually independent of the mRNA variant of the protein , a similar trend is observed in this case as well .', 'In building a predictor which is solely based on coding sequences , these empirical observation provide justification for using as a predictor for .', 'Indeed , as we have demonstrated throughout the paper , this predictor out performs other commonly used predictors .', 'Our measure was based on the tAI [27]; as describe below , we adjusted it to our model: Let ni be the number of tRNA isoacceptors recognizing codon i .', 'Let tCGNij be the copy number of the jth tRNA that recognizes the ith codon , and let Sij be the selective constraint on the efficiency of the codon-anticodon coupling .', 'We define the absolute adaptiveness , Wi , for each codon i as:The Sij-values can be organized in a vector ( S-vector ) as described in [27]; each component in this vector is related to one wobble nucleoside-nucleoside paring: I∶U , G∶U , G∶C , I∶C , U∶A , I∶A , etc .', 'Sensitivity analysis of the tAI of codons to Sij -values in S . cerevisiae showed that one codon ( CGA ) is extremely sensitive to these s-values .', 'Increasing/decreasing the s-values by +−0 . 5 resulted in a change of up to one order of magnitude ( usually much less ) in all other codons .', 'In the case of CGA , the change was up to 4000 times higher .', 'The tAI of this codon is relatively low and the model is sensitive to this value .', 'Thus , we replaced the Wi of this codon by mean tAI of this codons over all possible changes ( +−0 . 5 ) of Sij -values .', 'From Wi we obtain pi , which is the probability that a tRNA will be coupled to the codonThe expected time on codon is .', 'The expected time on a site is the sum of times of all the codons in the site .', 'The bottleneck was defined as the slowest window in a gene .', 'The time of a window in the sum of times corresponding to its codons; the size of a window is 15 codons ( the results were robust to small changes in the size of the window ) .', 'Figure S17 depicts the running time of our model as a function of λ and site .', 'As can be seen , when the site size is larger than 10 codons , for all λ the typical running time for a gene is less than 0 . 1 second .', 'Measurements of ribosome densities in S . cerevisiae at a resolution of single nucleotides were downloaded from [14] .', 'For comparison to the predictions of various models the profiles were aligned to the beginning of the coding sequences ( similarly to the way it was done in [7] , [20] ) .', 'We computed and plotted the mean densities in sites of size 15 codons for each of the profiles ( measured and predicted ) .', 'To estimate the dependence of the translation rate of genes ( at their ‘working point’ ) on codon order , DTCO , we performed the following steps: We call this quantity DTCO and we use it as a measure for the dependence of the translation rate on codon order .', "To estimate the dependence of protein abundance on the codon order , DPCO , we performed the following steps: To compute the ‘working point's of genes in a certain organism we first found the where the correlation between the mean predicted translation rate and protein abundance [16] , [17] , [62] is maximal . We computed the ratio ( in percentages ) between the mean genomic translation rate at this point and the mean maximal translation rate ( for very large ) ; let Q% denote this value . ( this value was 93% , 95% , and 99% in S . cerevisiae , S . pombe , and E . coli respectively ) The ‘working point’ of a gene in a certain organism is the where the translation rate of the gene is Q% of its maximal translation rate .", 'For each gene we computed the mean ratio between the synthetic version of the gene and its native version over 41 values of ( between 0 . 0002 and 0 . 0094 ) .', 'The empirical p-value for the Spearman correlation is the probability that a random permutation of the two vectors will give higher correlation .', 'It was computed by performing 100 such permutation and computing the Spearman correlation of each of them .', 'The Wilcoxon rank test that we used is a paired non-parametric test where we compared ( 1 ) the vector of distances between the predictions of our model and the real data ( a distance for each point ) ; ( 2 ) the vector of distances between the predictions of tAI and the real data; ( 3 ) the vector of distances between the predictions of Zhang model and the real data .', 'We compared ( 1 ) to ( 2 ) and ( 1 ) to ( 3 ) and checked the following statistical question: “is there improvement ( in terms of the distance between predicted and real data points ) when a more sophisticated model ( RFM ) is used instead of a less sophisticated one ( e . g . the tAI ) .', 'Jackknifing ( see , e . g . , [65] ) was performed as described below .', 'Repeat 100 times: Report the number of cases ( 0–100 ) that we get C\u200a=\u200a25 .', 'The result confidence level was 100 demonstrating a very high confidence .']]
['Introduction', 'Results', 'Discussion', 'Methods']
['We describe the first large scale analysis of gene translation that is based on a model that takes into account the physical and dynamical nature of this process .', 'The Ribosomal Flow Model ( RFM ) predicts fundamental features of the translation process , including translation rates , protein abundance levels , ribosomal densities and the relation between all these variables , better than alternative ( ‘non-physical’ ) approaches .', "In addition , we show that the RFM can be used for accurate inference of various other quantities including genes' initiation rates and translation costs .", 'These quantities could not be inferred by previous predictors .', 'We find that increasing the number of available ribosomes ( or equivalently the initiation rate ) increases the genomic translation rate and the mean ribosome density only up to a certain point , beyond which both saturate .', 'Strikingly , assuming that the translation system is tuned to work at the pre-saturation point maximizes the predictive power of the model with respect to experimental data .', 'This result suggests that in all organisms that were analyzed ( from bacteria to Human ) , the global initiation rate is optimized to attain the pre-saturation point .', 'The fact that similar results were not observed for heterologous genes indicates that this feature is under selection .', "Remarkably , the gap between the performance of the RFM and alternative predictors is strikingly large in the case of heterologous genes , testifying to the model's promising biotechnological value in predicting the abundance of heterologous proteins before expressing them in the desired host ."]
['Gene translation is a central process in all living organisms .', 'However , this process is still enigmatic , and contradicting conclusions regarding the essential parameters that determine translation rates appear in different studies .', 'We introduce a new approach for modeling the process of translation elongation .', 'Taking into account the stochastic nature of the translation process and the excluded volume interactions between ribosomes , our model is aimed at capturing the effect of codon order and composition on translation rates .', 'We demonstrate that in comparison to commonly used approaches , our approach gives more accurate predictions of translation rates , protein abundance levels and ribosome densities across many species .', 'Using our model , we address the need for a better understanding of the inner workings of the translation process .', 'To this end , we analyze large scale genomic measurements made in several organisms .', 'Our analysis unravels several central and previously uncharacterized aspects of the translation process .', 'For example , we show that in all organisms that were analyzed ( from bacteria to Human ) , ribosome allocation is optimized to give maximal translation rate in minimal cost .', 'In addition , we provide the first direct estimate for the effect of codon order on protein abundance , showing that in E . coli and S . cerevisiae it can solely account for more than 20% of the variation in this quantity .']
['biotechnology', 'systems biology', 'computerized simulations', 'biochemistry', 'computer science', 'computer modeling', 'protein abundance', 'genetics', 'molecular genetics', 'biology', 'computational biology', 'proteomics', 'biophysics', 'genetics and genomics']