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Oleg and , −8 −10 −10 b eateto hmsr,Rc nvriy oso,T 77005; TX Houston, University, Rice Chemistry, of Department 1073/pnas.1614838114/-/DCSupplemental. at online information supporting contains article This 2 Submission. 1 Direct PNAS a is article This interest. of conflict no paper. declare the authors wrote The O.A.I. and A.B.K., K.B., and research; formed ftentok(,1,1) ti o la o uhdistributed such how clear not is step It each 15). for 14, substrates (4, wrong network 19). and the (18, right of steps the have assume of systems for biological types or rates that few different 26) show a data 25, only experimental contrast, (22, of In constants selection rate substrate lack- of of is on disparity focus stages tuned mainly is still initial proofreading accuracy the of and models current speed Several between ing. balance the how up 24). (21, speeds the step of binding step selectivity tRNA–ribosome hydrolysis possible initial maximal GTP prevents the but fast that synthesis in a protein example, suggested For process, authors (18). selection regime The with tRNA this comes accuracy. use speed may in in systems gain loss biological large small new a relatively regime, a cat- this the a demonstrated In modifying by (18). study model rate recent KPR alytic the A in (9, regime 23). slowest occur speed–accuracy (15, the must is reactions fast process polymerization reasonably the biological vanish- contrast, when at In i.e., achieved 21). rate, is catalytic error studies low possible These ingly minimum 22). the (21, that specificity indicate of description Michaelis– the (MM) on based Menten mainly The is (20). trade-off process this the on of understanding compromise, is, speed a and reaction be accuracy the between could trade-off, there of or Hence, time increase. completion to The expected (9). thus, progress- state without product configuration to initial ing its by to accuracy system the the enhances resetting Proofreading rapidly. sufficiently also mecha- regulatory present. driven widely chemically are such concept nisms that the show broaden and results KPR (18) These of growth (19). microtubule chemotaxis as bacterial such or phenomena other and reading uhrcnrbtos ...adOAI eindrsac;KB,ABK,adOAI per- O.A.I. and A.B.K., K.B., research; designed O.A.I. and A.B.K. contributions: Author owo orsodnemyb drse.Eal oy@ieeuo [email protected]. or [email protected] Email: addressed. be may correspondence whom work. To this to equally contributed A.B.K. and O.A.I. eacmlse oqikywt iia errors. minimal can with processes quickly biological so a accomplished complex in provide be how enhanced findings of be resulting picture can The microscopic accuracy regimes. and parameter speed certain both that further study indicates theoretical with established Our accuracy constraints. than we energetic rather additional translation, speed maximize protein processes systems these and fundamental that replication the analyzing DNA always By of processes down. biological the them in that slows accuracy believed the widely is of It enhancement mechanism proofreading. error-correcting kinetic an as to known This attributed molecules. is similar between characteristic discriminating level in remarkable a accuracy showing of in unique are processes Biological Significance ept h ubro tde,acerqatttv itr of picture quantitative clear a studies, of number the Despite but accurately just not information genetic process must Cells a,c,1,2 PNAS | a 6 2017 16, May | o.114 vol. www.pnas.org/lookup/suppl/doi:10. | o 20 no. | 5183–5188

CHEMISTRY BIOPHYSICS AND COMPUTATIONAL BIOLOGY discrimination of the reaction rates affects the trade-off. More- nate substrate over other near/noncognate substrates. During replication, over, proofreading steps come with an extra energy cost to gain dNTP molecules complementary to the DNA template are chosen. Similarly, higher accuracy (11), but the role of this cost in the trade-off is during protein synthesis, aminoacyl(aa)-tRNAs are picked by ribosome based not apparent. Therefore, to understand the fundamental mech- on the complementarity of their anticodon to the mRNA codon. Wrong sub- anisms of proofreading in real biological systems, one needs to strates that bind initially can be removed by error-correction proofreading mechanisms. Kinetic experiments coupled with modeling revealed a lot of answer the following questions: (i) How does the system set its mechanistic details about both of the processes (3, 14, 15, 24). The schemes priorities when choosing between accuracy and speed, two seem- depicted in Fig. 1 represent the key steps to understand the KPR in these ingly opposite objectives? (ii) Can speed and accuracy change in networks. the same direction; in other words, can perturbations of a kinetic The schemes in Fig. 1 A and C are for DNA replication (3, 14). E denotes parameter from its naturally selected value improve both speed the T7 DNAP enzyme in complex with a DNA primer template. The R and and accuracy? (iii) How does the extra energy expenditure due W substrates are correct and incorrect base-paired dNTP molecules, respec- to KPR affect the speed–accuracy optimization? tively. Step 1 generates enzyme–DNA complexes ER(or EW) with the primer elongated by one nucleotide. Addition of another correct nucleotide to ER Here we focus on the role of reaction kinetics in governing ∗ ∗ the speed–accuracy trade-off. To this end, we develop a general- (EW) gives rise to PR (PW). ER and EW complexes denote the primer shifted to the exonuclease site (Exo) from the polymerase site (Pol) of DNAP. This ized framework to study one-loop KPR networks, assuming dis- commences proofreading in step 2. Excision of the nucleotide in step 3 resets tinct rate constants for every step of the right (R) and wrong (W) the system to its initial state. pathways. Based on this approach, we model the overall selection The schemes in Fig. 1 B and D show the aa-tRNA selection process by of the correct substrate over the incorrect one as a first-passage ribosome during translation (29). Here, E denotes the E. coli ribosome with problem, to obtain a full dynamic description of the process (27, mRNA. Cognate (near-cognate) aa-tRNAs in ternary complex with elonga- 28). This general framework is applied to two important exam- tion factor Tu (EFTu) and GTP bind with ribosome in step 1 to form ER (EW). ples, namely, DNA replication by T7 DNA polymerase (DNAP) GTP hydrolysis in step 2 results in the complex ER∗ (EW∗). The latter can take (3, 14) and protein synthesis by Escherichia coli ribosome (22, one of two routes. It can progress to the product PR (P W) with the elonga- 29) (Fig. 1 A and B)). Starting from the experimentally measured tion of the peptide chain by one amino acid. Alternatively, it can dissociate in the proofreading step (step 3), rejecting the aa-tRNA. rate constants for each system, we vary their values to analyze the In both schemes, we take the rate constants of the W cycle to be related resulting changes in speed and accuracy and to assess the trade- to those of the R cycle through k±i, W = f±ik±i, R, i = 1, 2, 3 and similarly, for off. The role played by the extra energy consumption or cost of the catalytic step, kp, W = fpkp, R. The set of rate constants k1, R/W , k−3, R/W proofreading (11) is also investigated. By comparing the behavior are effectively first order containing the substrate concentrations. The fac- of the two systems, we search for general properties of biological tors fi provide the energetic discrimination between the R and W path- error correction. ways. Completion of one cycle (returning to the starting state E) effectively amounts to hydrolysis of one dNTP molecule for DNA replication and one Methods GTP molecule for aa-tRNA selection. The chemical potential difference, ∆µ Proofreading Networks of Replication and Translation. DNA replication as (in units of kBT) is equal for both the cycles (19). well as protein synthesis use nucleotide complementarity to select the cog- 3 3  Y ki, R   Y ki, W  ∆µ = ln = ln . [1] k k i=1 −i, R i=1 −i, W This leads to the condition AB: Polymerase Pol T Y fi : DNA = 1. [2] T f−i T T M i=1, 2, 3 , : dNTP Exo M M , : dNMP 1 T + T D Accuracy and Speed from First-Passage Description. We determine the Pol Pol 3 2 D error and speed of the substrate selection kinetics from the first-passage probability density (27, 28). With this method, we can analyze an arbitrary 1 M : Ribosome catalytic reaction scheme and focus on the transitions starting from the ini- Exo Exo : mRNA : codon tial state E that lead to the final state PR. The description allows us to get M Pol :tRNA analytical expression for both speed and accuracy for an arbitrary set of 2 3 , : amino acids kinetic parameters. Therefore, we allow different rates for the R and W substrates for each step of the network as experimentally observed. Further- T : EFTu.GTP ExoM more, we do not assume any step to be completely irreversible. Otherwise, D : EFTu.GDP the chemical potential difference over the cycle would diverge (Eq. 1). This 1 1 k difference is linked to the hydrolysis of some energy-rich molecules supply- P P k1,W 1,R CDW R EW E ER ing large but finite free energy. k k k −1,W k−1,R p,W p,R Let us denote FR,E(t) as the probability density to reach state PR at time t 1 1 2 k k k k 2 k k −2,W −3,W −3,R −2,R 1,W 1,R k 3 k for the first time before reaching state PW if the system is in state E at time E 2,W k k 2,R EW ER 3,W 3,R t = 0. The corresponding probability density FW,E(t) is specified in the same k −1,W k−1,R EW**ER manner. The evolution equations of ( ) are known as the backward 2 k k k k 2 FR/W,E t −2,W −3,W 3 −3,R −2,R k k k p,W k p,R master equation (27, 30). It is more convenient to solve them in Laplace 2,W k k 2,R 3,W 3,R space (Supporting Information). We define the error, η as the ratio of the EW **ER P P W R probabilities to reach the end states PR/W [also called the splitting proba- bility (27)] given by Fig. 1. Schematic representation of proofreading networks for (A) DNA ∞ ΠW Z replication by T7 DNAP enzyme and (B) aminoacyl(aa)-tRNA selection by η = ; Π = F (t)dt. [3] Π R/W R/W,E E. coli ribosome during translation. Corresponding chemical networks are R 0 shown for (C) replication and (D) translation. Reaction steps comprising It is important to note that this definition is equivalent to the traditional the cycles are labeled 1 to 3. Rate constants of each step are denoted one (9, 21) defined as the ratio of the wrong product formation rate to the by k±i, R/W, i = 1, 2, 3; subscript indicates right (R) or wrong (W) path- right one (see Supporting Information). ways. The rate constants of the steps leading to product (end) states are The speed of a reaction is naturally quantified by the net rate of the labeled as kp, R/W. The translation network in D is related to the replica- product formation. As with any chemical reaction rate, it can be defined tion network in C by the following transformation of rate constant indices: as the inverse of the mean first-passage time (MFPT), i.e., the mean time ±1 ←→∓3, ±2 ←→∓2. The steps involved in each case are, of course, dif- it takes to cross the energy barrier that separates reactants and products ferent. For details, see Methods. for the first time. For example, a well-known application of this approach

5184 | www.pnas.org/cgi/doi/10.1073/pnas.1614838114 Banerjee et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 aejee al. et Banerjee at Thus, accuracy. and speed pathway both R compromising the thereby affect adversely more, cycles futile proof- These correct unnecessary cycles. of rate, reading lots sliding undergo Pol–Exo must the incorporation than substrate smaller path- polymerization sufficiently the W When is to and rates. rate smaller R due much the has arises latter between rates the rates ways; polymerization these low of magnitudes for different trade-off of of lack slope positive the with branch This slope direction. the negative same of with the values in branch lower change this For call branch. trade-off We the error. corresponding minimum value the the than to greater becomes constant rate tion 2C (higher Fig. speed from indicates lower curve (lower this to accuracy of sponds higher slope i.e., Negative 2C. trade-off, Fig. speed–accuracy in shown is curve of range in The increase MFPT, with monotonously the increases in hand, speed inter- shown other the some as the case at On the error 2A. indeed Fig. minimum is a This rate. has polymerization system mediate the words, other In pattern limits variation these error of the ratios understand suitable to give we Here, Information). porting n Eq. and S1) (Table values parameter Here, for one general the from limit follow the expressions in Explicit obtained bounds lower k are them of constant, rate merization in rate sliding error, exonucleolytic The higher ( the path and W path the R polymerization the faster our the in in to rates due enzyme justified the is from We approach DNA (23). This the al. model. of et dissociation Wong consider of not data experimental do the in on listed based are are They 1A) the (Fig. of parameters network model involves reaction The corresponding that (23). DNAP mechanism of proofreading site exonuclease the the incorporated by T7 Wrongly removed (14). by is strand dNTP template Replication a DNA over primer in DNA Accuracy over DNAP. Speed of Importance case two both. the for for conclusions similar mechanisms reach KPR we studies, and dif- in parameters despite trade-off in Notably, speed–accuracy region. ferences parameter the kinetic relevant study underlying biologically can the of we terms and in important parameters, These characterized fundamentally KPR translation. best and are arbitrary two processes replication an study DNA to to processes: applied biologically chosen be we’ve can scheme, formalism our Although Results by simply it denote the In each probability reach corresponding the to of MFPT moment the first of (27). the density expression by the given case, is of our state presence product In the (21). neglecting pathway literature to in contrast W the in speed the incor- toward together the the them of speed consider of measure the to prevalent presence important that the the is note it by We Thus, affected substrate. (31). be rect nevertheless MFPT can the product the of for correct inverse expression the traditional the as in rate results kinetics MM single-molecule for 1,R η ∞ → –τ Results h 7DA nyectlzsteplmrzto fa of polymerization the catalyzes enzyme DNAP T7 The K uv sdntda h o-rd-f rnh Intuitively, branch. non-trade-off the as denoted is curve M (η η ,R and aisaogtrelmt safnto ftepoly- the of function a as limits three among varies , H al S1 Table (k = htteei rd-f nywe h polymeriza- the when only trade-off a is there that τ ,ada nemdaecs with case intermediate an and ), η η M losassvrlodr fmgiue The magnitude. of orders several spans also L efcson focus we Discussion, τ −2,R . = τ R/W f ). −1 f 2 = + , Π k k 1,R R/W 1 3,R η η M H = ( Z /k 0 = τ ∞ 2,R n ievra ti evident is It versa. vice and ) k F t p f f p 2 ,R rmteexperimental the From ). /,E R/W, τ k R ) eexpect we 5, −1,R stemaueo pe and speed of measure the as 2)wt fixed with (23) τ (t k erae,adhence and decreases, , k )dt 3,R 1,R K . M k ro n MFPT and error , ,R 1,R . k k . 1,R 1,R η k M η −1,R → al S1. Table Fg 2B). (Fig. (see η < f η 1 corre- ) , 0 f L p (η (η η , Sup- All . η M [5] L –τ [4] H ). ), . h soitdetaeeg ot(1;ti a etittesystem the restrict may this (11); cost energy increase extra product can associated the to rate the proofreading resets progressing in without pathway speedup Therefore, condition proofreading formation. starting trade-off the the the that to to note system left We route? moving sys- that by the speeds the as of similar long gain branch at can as system errors important the However, lower more accurate. be reasonably remains to tem appears speed fore, in alteration minimum slight the with greatly from change direction either the in of moves branch non-trade-off the on positioned otemnmmMP.Tesedacrc rd-f appears in trade-off speed–accuracy The after MFPT. minimum the to In error minimum. responding (local) this to mum close system’s finite pretty the at lies particular, maximum system local actual a the and square) low large very at the fashion asymptotic an in k approached is value error The tolera- a also is there of course, level of by upper Thus, ble MFPT accuracy. the more the lower up of further giving slope can the system down The moving is process. accuracy the of in amount selected lost Significant by is speed. drop constant high-enough achieve rate would to polymerization speed the system’s Thus, the ∼3,500-fold. error, minimum this achieve error minimum the particular, is In triangle). (red point error mum the of branch accuracy. and speed for both allowing in regime improvement suboptimal is there rates, polymerization low in minimum local a edn eeae yvarying by generated reading 2. Fig. inse.( tri- step. (red in tion error minimum minimum the the to from corresponding away far MFPT, of is Variation that (B) angle). system actual the of (Eq. tion limits constant predicted rate the polymerization by bounded the of function a as 2,R CD AB fl oe hnta fteata ytm oee,to However, system. actual the of that than lower ∼150-fold h o–x ldn sa motn tpi ro correction. error in step important an is sliding Pol–Exo The h culsse gencrl)i iutdo h trade-off the on situated is circle) (green system actual The η τ τ 10 10 10 10 MFPT, (s) 10 Error,10 10 k ncnrs,tegoa iiu fMP sotie in obtained is MFPT of minimum global the contrast, In . η 1 10 adas eoetelclmxmm.Tu h ytmis system the Thus maximum). local the before also (and -3 3 6 9 -9 -6 -3 2,R k τ –τ 2,R -10 h hnei error, in change The (A) DNAP. T7 for trade-off Speed–accuracy Polymerization wti esta .1) nteohrhn,tecor- the hand, other the On 0.01%). than less a (within η → h minimum The 2D. Fig. in plotted is step this for curve The D) Polymerization rateconstant,k rse h au orsodn otelclminimum local the to corresponding value the crosses .0 1000 1 0.001 L 0 ii.TeMP lohsalclmnmm(yel- minimum local a has also MFPT The limit. η η Error, –τ –τ η 10 τ –τ η η tle a wyfo h mini- the from away far lies It 2C. Fig. in curve ylo qae erteata au gendot). (green value actual the near square) (yellow -8 uv.Te,wa sterao o o taking not for reason the is what Then, curve. . uv o h o–x ldn tpivle nproof- in involved step sliding Pol–Exo the for curve is PNAS η fl ihrta htcorresponding that than higher ∼1.6-fold η k 1,R τ M τ η | k with , au sams dnia otemini- the to identical almost is value 2, 10 H a 6 2017 16, May R 0 -6 η keeping (C . η k .Tegencrl niae h posi- the indicates circle green The 5). –τ 1, The ) R 0.015

h e ragegvsthe gives triangle red The . τ MFPT,0.01 (s) 10 10 uv.Hwvr htmeans that However, curve. MFPT, τ (s) -3 3 10 1 f τ 2 η -2 xd(eio lt.Teeis There plot). (semilog fixed –τ 10 until | -10 Pol-Exo sliding o.114 vol. uv o h polymeriza- the for curve k 1, 1,R η k R η τ ( 2,R 110 Error, stolw There- low. too is = –τ =k on,errcan error point, 10 k Interestingly, . | p, -8 uv.A one As curve. k R o 20 no. p,R .Teerris error The ). 2,R η (s 2 10 -1 τ | ) -6 value 0 5185 10 η 4 ,

CHEMISTRY BIOPHYSICS AND COMPUTATIONAL BIOLOGY to go to the more advantageous regime that has greater KPR rate A 10 B and so, somewhat larger cost. We will further elaborate on this Proofreading 0.1 point in our next case study. (s)

tRNA Selection by E. coli Ribosome Is Optimized for Speed τ Rather than Accuracy with a Cost Constraint. During transla- 1 0.05

tion, the ribosome decodes the mRNA sequences by select- Cost, C ing aa-tRNAs in ternary complex with EFTu and GTP (4, 15). Noncognate aa-tRNAs are removed by proofreading dissocia- MFPT, k 0 tion of the complex from the ribosome A site after GTP hydrol- 3,R 0.1 ysis (24, 29). The model parameters of the network (Fig. 1B) 10-5 10-4 10-3 10-2 0 0.001 0.01 0.1 1 k -1 for WT E. coli ribosome are listed in Table S2. They are based Error, η 3,R (s ) on the experimental data of Zaher and Green (29). We chose −3 −1 Fig. 4. (A) An η–τ diagram for the proofreading step. The actual system k−2,R = k−3,R = 10 s to ensure that both step 2 and step 3 are nearly irreversible (29). There remains one free parameter (green dot, WT) has a τ value similar to the local minimum in τ (yellow f f 2 f = 1 square). The dashed line shows the range up to which the system can lower −2 (as −3 gets fixed from Eq. ). We assumed −2 , but our the error with no loss in speed. (B) The proofreading cost, C, as a function main conclusions are independent of this choice (Fig. S1). of k3, R. Its value at the local minimum in τ (yellow square) is approximately We show the η–τ curves for GTP hydrolysis and ternary com- threefold higher than that of the actual system (green dot). plex binding steps in Fig. 3 A and B, respectively, for three vari- eties of E. coli ribosome. One is the WT, and the other two are mutants. One mutant, rpsL141, is hyperaccurate (HYP), and the that speed is indeed more important. The robustness of this other mutant, rpsD12, is more error-prone (ERR) than WT (29). result is also tested successfully against fluctuations of the rate Variation of the hydrolysis rate constant, k2,R (keeping f2 fixed) constants (Fig. S3). Interestingly, the WT ribosome is faster and, results in quite large changes in error and MFPT. The trends are hence, better optimized for speed than both the mutants. It is similar for all three systems (see Tables S3 and S4 for parameter important to note that the more accurate mutant HYP was not sets of mutants). As for the polymerization steps in DNA repli- chosen by the natural selection. This point further emphasizes cation, error varies among three bounds for the GTP hydrolysis the importance of speed over accuracy in translation. step. They are obtained from the general expression of η (see The change in the ternary complex binding rate constant, k1,R Supporting Information) for low, intermediate, and high values of (with f1 fixed) also affects both the error and the MFPT signifi- k2,R, cantly, but on a smaller scale than hydrolysis (Fig. 3B). There is always a trade-off between speed and accuracy, unlike the cases f−3 f1f2 f1 η = α , η = α , η = α , [6] studied so far. The minimum in error is obtained in the k1,R → 0 L f M f f H f 3 −1 3 3 limit, whereas the maximum speed is achieved for very large k1,R.

where α = kp,W /k3,R. For the parameter set of the system (Table With increase in k1,R, τ falls several orders in magnitude. Inter- τ S2, f−2 = 1), one gets η M < ηL, ηH. Thus, the error vs. hydrolysis estingly, all of the systems have values almost identical to their rate curve passes through a minimum. Interestingly, there is also respective saturation limits. To attain that state, they sacrifice an a minimum in τ as shown in Fig. 3A. The two minima are at dif- order of magnitude in terms of accuracy. Therefore, regarding ferent k2,R values, however. The speed–accuracy trade-off occurs speed–accuracy trade-off, the system is inclined to be faster with between the minimum η (red triangle, WT) and the minimum τ higher but tolerable error. (yellow square, WT) points. As is evident from Fig. 3A, all of Next, we explore the effects of variation of the proofread- the systems are positioned close to the minimum τ and far away ing step rate constant, k3,R (keeping f3 fixed) on system per- from minimum η. For example, the WT ribosome would become formance. The resulting η–τ diagram is plotted in Fig. 4A for ∼500-fold slower to achieve the minimum error, although the the WT ribosome. The global minimum of τ is obtained in the latter is ∼50-fold lower than the actual value. Hence, speed is k3,R → 0 limit, whereas the minimum of η lies in the large k3,R preferred to accuracy. We tested the generality of this claim limit. There is a local minimum (yellow square) of τ at some against multiple parameter variations (Fig. S2), and it appears intermediate k3,R along with a local maximum. Mutant ribo- somes have similar trends (not shown in the figure). The nature of the η–τ curve is qualitatively similar to that obtained for the proofreading Pol–Exo sliding step in DNA replication (Fig. 2D)

ABGTP hydrolysis 103 Ternary-complex binding with two speed–accuracy trade-off branches. The actual system 0 104 0 (green circle) is located on the non-trade-off branch that links k k 2,R WT 1,R the two trade-off branches of the η–τ curve. It has an MFPT HYP 2 (s) 10 (s)

ERR τ close to (∼1.1-fold higher than) the (local) minimum τ value. τ 102 However, the minimum τ point also has an approximately five- 10 fold lower η. More important is the fact that the system can attain much lower errors with similar, even slightly higher, speeds if it MFPT, MFPT, 1 1 moves left up to a certain level (the dashed line in Fig. 4A). What prevents the system from gaining in both speed and accuracy? 10-6 10-4 10-2 10-5 10-4 10-3 10-2 10-1 Because correction by proofreading resets the system without Error, η Error, η a product formation, it has a cost associated with futile cycles where the correct substrate was inserted and then removed. The Fig. 3. Speed–accuracy trade-off in aa-tRNA selection by three varieties of cost of proofreading, C , is defined as the ratio of the resetting E. coli ribosome. One is the wild-type (WT). The other two are hyperaccu- flux to the product formation flux including both R and W path- rate (HYP) and more error-prone (ERR) mutants. (A) η–τ curves for the GTP hydrolysis step. The actual system (green circle, WT) is situated close to the ways (11) (see Supporting Information); this gives a measure of minimum τ (yellow square) and far away from minimum η (red triangle); the amount of extra energy-rich molecules consumed due to the this is also true for the mutants. (B) Speed–accuracy trade-off for the ternary presence of the proofreading step. Specifically, the cost C can complex binding step. The minimum error is achieved in the k1, R → 0 limit. quantify the moles of dNTP (or GTP) used for proofreading per MFPTs for all of the systems are close to saturation. mole of product (11). This quantity can be easily computed from

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ERR) over speed of of varieties in detail in explained speed as maximum fronts, Information. the Pareto Supporting of using also curves analysis are accuracy advanced vs. conclusions more a Our by mechanisms optimization. supported molecular speed–accuracy the and the transitions of various dis- of the roles clarifies branches tinct non-trade-off error–time and the trade-off of into partitioning variation curves The range with parameters. improve certain kinetic can a certain speed over and of accuracy only both present and rates, are of and that, trade-offs reveals hydrolysis steps, study like these Our the for steps, straightforward. lower as other the not of are and proofreading, role speed the the the Indeed, higher 21). 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Fig. in curve .coli E. oeua ilg fteGene the of Biology Molecular seta elBiology Cell Essential iooefrhrcnrsteimportance the confirms further ribosome k 3,R GradSi e ok,4hEd. 4th York), New Sci, (Garland erlclmnmmo the of minimum local near W ejmn e York). New Benjamin, (WA τ point loakolde upr rmWlhFudto rn -59adfrom and C-1559 Grant CHE-1360979. Foundation Grant Welch NSF from A.B.K. support PHY-1427654. acknowledges Grant (NSF) also Foundation Science National Physics logical ACKNOWLEDGMENTS. proof- systems. of biological mechanisms in processes fundamental reading the will elucidate predic- testing to such our believe help test We further to organisms. important and be systems other will in It tions ways. var- distinct adjusting in by rates achieved ious is ultimate speed the and how accuracy of between picture balance quantitative coherent a optimize presents (see thus better accuracy to not cost. and discrimination energy that speed arguments and distribute our speed systems to improving support biological additional make), (correcting R gives not observation cycles the did This futile for it avoids rate errors ribosome catalytic the result, the a a than for rate As slower catalytic substrate. much the and than the be substrate faster for may much allows W be it this to (34), Although rate minimization chain. error proofreading and are of polypeptide R terms step the in the in catalytic suboptimal of acid the incorporation amino (34). of the error W rates minimizing between the of different ribosome, view significantly of for here point example, note the For to from optimal interesting not is steps discriminatory is It act of distribution correction speed. observed error the experimentally of that tailor cost the to and to constraints error precedence as of give levels to Tolerable no appear accuracy latter. almost systems of maximization biological with have the speed, sufficiently between to and reduced Therefore, selected is speed. error in be loss the to that seem rates proof- steps hand, such other error-correction the On binding, or accuracy. to of substrate reading chosen cost like be the at to steps speed seem enhance catalysis the and these of intermediates), optimize (of Rates hydrolysis important to quantities. two strategies vital in similar two trade-off reveal accuracy–speed the networks the that biological on so in results fine-tuned improvement Our the is with rate compared Hence, insignificant KPR accuracy. minimum. is the global speed in the studies, loss minimum, to case local magnitude the both sys- to in for value the similar MFPT. MFPT of is the and both of which error proximity for the the feature is reduce does interesting tems also further cost most to the would extra the systems Furthermore, This of mutation the proofreading. accuracy such allow of and not step that costs speed proofreading show energetic both increase the we in increase up However, an enzymes. speeds to slightly lead implies possi- would that that selected branch Biologically, maximum mutation non-trade-off curves. the is the that error–time to cases on respective close reside their the systems is of actual both system The the con- in one. of rate ble step speed A proofreading that step. gen- such the proofreading a the of be for stant from diagrams to apparent trade-off becomes appears this the correction; there error of networks, mechanism eral translation and cation mutant. elongation ERR chain the peptide for of smaller speed be the can also not but that accuracy indicate pre- results the ascribed Our only was faster. (33). mutant proteins be less-active ERR to should for sumably growth ribosome and hindered (ERR) the error erroneous Hence, between more compromise the ever-present speed, the prevail- on indicates the to notion already according ing However, ribosomes 32). mutant (21, opti- optimization and of an that comparison such WT that implies with note mutant. choice rates We (HYP) natural critical. growth accurate is the speed more as of the latter mization to the leads of this Rejection error; lower a .Kne A eee 20)DArpiainfidelity. replication DNA (2000) K Bebenek TA, Kunkel 3. ept ifrn cee n aaee auso h repli- the of values parameter and schemes different Despite 497–529. hswr sspotdb etrfrTertclBio- Theoretical for Center by supported is work This PNAS | a 6 2017 16, May .Orstudy Our Information). Supporting | o.114 vol. nuRvBiochem Rev Annu | o 20 no. .coli E. | 5187 69:

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