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Determining selection free energetics from nucleotide pre-insertion to insertion in viral T7 RNA polymerase transcription fidelity control

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An elongation cycle of a transcribing RNA poly-merase (RNAP) usually consists of multiple kinet-ics steps, so there exist multiple kinetic checkpoints where non-cognate nucleotides can be selected against. We conducted comprehensive free energy
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  Nucleic Acids Research, 2019  1 doi: 10.1093/nar/gkz213 Determining selection free energetics from nucleotidepre-insertion to insertion in viral T7 RNA polymerasetranscription fidelity control Chunhong Long 1 , Chao E 1 , Lin-Tai Da  2 and Jin Yu  1,* 1 Beijing Computational Science Research Center, Beijing 100193, China and  2 Shanghai Center for SystemsBiomedicine, Shanghai JiaoTong University, Shanghai 200240, China Received November 20, 2018; Revised March 10, 2019; Editorial Decision March 15, 2019; Accepted March 18, 2019 ABSTRACTAn elongation cycle of a transcribing RNA poly-merase (RNAP) usually consists of multiple kinet-ics steps, so there exist multiple kinetic check-points where non-cognate nucleotides can be se-lected against. We conducted comprehensive freeenergy calculations on various nucleotide insertionsfor viral T7 RNAP employing all-atom molecular dy-namics simulations. By comparing insertion free en-ergy profiles between the non-cognate nucleotidespecies (rGTP and dATP) and a cognate one (rATP),we obtained selection free energetics from the nu-cleotide pre-insertion to the insertion checkpoints,andfurtherinferredtheselectionenergetics downtothe catalytic stage. We find that the insertion of basemismatch rGTP proceeds mainly through an  off-path  along which both pre-insertion screening and inser-tion inhibition play significant roles. In comparison,the selection against dATP is found to go throughan off-path  pre-insertionscreeningalongwithan on- path  insertioninhibition.Interestingly,wenoticethattwo magnesium ions switch roles of leave and stayduring the dATP  on-path   insertion. Finally, we inferthatsubstantialselectionenergeticisstillrequiredtocatalytically inhibit the mismatched rGTP to achieveanelongationerrorrate ∼ 10 − 4 orlower;whilenocat-alytic selection seems to be further needed againstdATP to obtain an error rate ∼ 10 − 2 .INTRODUCTION Transcription is the 󿬁rst step of gene expression in living or-ganisms. It is directed by RNA polymerases (RNAPs) thattranscribe genetic information from DNA to RNA, basedon the Watson–Crick (WC) base pairing between the syn-thesizing RNA and the template DNA strand. The 󿬁delityof transcription is highly crucial for maintaining normalgene expression, protein function, and cellular regulation.The transcription 󿬁delity is controlled by nucleotide selec-tions upon binding and incorporation along with proof-reading during the RNAP transcription elongation (1–8). Without an RNAP, the template-based polymerization re-action proceeds extremely slowly and the error rate canhardly drop below ∼ 10 − 2 , due to comparatively small freeenergy differences between cognate and non-cognate nu-cleotide additions (e.g. around 2–3 k B T). The accelera-tion of polymerization along with nucleotide selection andproofreading conductedvia an RNAP can quench the tran-scription error rate down to  ∼ 10 − 4  –10 − 7 (9). In bacterio-phageT7RNAPtranscription,thebasemismatcherrorratecan be achieved at  ∼ 10 − 4 or lower (10,11), without detec- tion of the proofreading mechanism. Hence, the nucleotideselection in T7 RNAP plays a primary role in the viral tran-scription 󿬁delity control, and it is of high interest to revealhow the nucleotide selection proceeds in structural and en-ergetic detail.The single-subunit T7 RNAP adopts a hand-like struc-turethatappearscommonforviralRNAPsandalargeclassof DNA polymerases (DNAPs) (12–16) (see Figure 1A). In these polymerases, the 󿬁ngers subdomain of the hand-likestructure opens and closes throughout each nucleotide ad-dition cycle (NAC) to allow insertion of an incoming nucle-oside triphosphate (NTP), from an initial binding or pre-insertion site to the active site of RNAP. Presumably, anopen structure of the single-subunit polymerase convertsinto a closed form upon a cognate NTP insertion, likely viaacombinedconformationalselectionandinduced-󿬁tmech-anism of the nucleotide binding and insertion, e.g., as beingsuggested by studies of eukaryotic DNAP    (17). In com-parison, non-cognate NTP binding or insertion may leadto an open or half-open intermediate state, as shown forDNAP I (18,19). The nucleotide selection can happen at multiple check-points upon the nucleotide binding or insertion, prior to orduring catalytic reaction (6). The experimental character- ization on the stepwise selectivity of the RNAP had beenconducted, e.g. for T7DNAP and a bacterial RNAP (2,16). * To whom correspondence should be addressed. Tel: +86 10 56981807; Fax: +86 10 56981700; Email: jinyu@csrc.ac.cn C  The Author(s) 2019. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http: // creativecommons.org / licenses / by / 4.0 / ), whichpermits unrestricted reuse, distribution, and reproduction in any medium, provided the srcinal work is properly cited. D ownl   o a d  e d f  r  omh  t   t   p s :  /   /   a c  a d  emi   c . o u p. c  om /  n ar  /   a d v  an c  e- ar  t  i   c l   e- a b  s  t  r  a c  t   /   d  oi   /  1  0 .1  0  9  3  /  n ar  /   gk z 2 1  3  /   5 4 2  0  5  3 1  b  y T h  e C h i  n e s  Uni  v  er  s i   t   y  of  H on gK  on g , j  i  n y  u @ c  s r  c . a c . c n on2  8 M ar  c h 2  0 1  9   2  Nucleic Acids Research, 2019 Figure 1.  The structural and kinetic illustrations of the T7 RNAP elongation cycle. ( A ) Crystal structures of the T7 RNAP elongation complexes. In theleft panel, the RNAP subdomains are colored red for the ‘palm’, green for the ‘thumb’, dark blue for the ‘󿬁ngers’ of the hand-like structure, and magentafor the N-terminal. The DNA template strand and RNA are shown in cyan and blue, respectively. The sequence regions of the respective subdomains arealso given. In the right panel, an alignment between the pre-insertion structure (PDB 1S0V, non-transparent) (20) and the substrate insertion structure (PDB 1S76, transparent) (32) of T7 RNAP is provided, in a zoom-in view around the active site. An illustration of the O-helix rotation angle is provided, with the O-helix open in the pre-insertion state, and closed in the insertion state. ( B ) A kinetic scheme of the NAC of T7 RNAP. The NTP insertion processfrom the initial pre-insertion state (III) to the 󿬁nal substrate insertion state (IV) is our focus in this work. In T7 RNAP, a pre-insertion complex had been obtainedwith a ‘semi-open’ conformation of the 󿬁ngers subdomain(20). Since the WC base pairing was not observed in thecrystal structure of the pre-insertion complex, it was notclear whether the nucleotide selection started from the ini-tial binding or not. Nevertheless, our previous study in-dicated that the WC base pairing between the incomingNTP and the template transition nucleotide TN(i) (dTTPhere) was able to form in an equilibrated solution struc-ture from molecular dynamics (MD) simulation (21). No- tably, a critical residue Tyr639 at the C-terminal end of anO-helix on the 󿬁ngers subdomain interacted closely withthe non-cognate nucleotide at pre-insertion. The close as-sociation with Tyr639 seemed to drag the non-cognate nu-cleotide to an ‘ off-path ’ pre-insertion con󿬁guration (22), inwhich the nucleotide could dissociate easily. Besides, thetemplate TN(i) deviated signi󿬁cantly away from the non-cognate NTP in the ‘ off-path ’ con󿬁guration, while in a con-structed ‘ on-path ’ pre-insertion con󿬁guration, TN(i) asso-ciated closely with the incoming NTP even if the WC basepairing was lack of  (22). Thus, it seemed that essential nucleotide selection in T7 RNAP started early at the nu-cleotide pre-insertion stage, e.g., coordinated by this highlyconserved ‘gating’ residue Tyr639 (23,24). On the other hand, biochemical and kinetic studies havedemonstrated that a slow step follows the initial NTP bind-ing to allow for the nucleotide insertion (25). We have also shown generically that the slow or rate-limiting step canplay a signi󿬁cant role in the 󿬁delity control of the template-based polymerization (26). It is highly likely that the non-proofreading T7 RNAP relies on the slow nucleotide in-sertion to conduct substantial nucleotide selection, or tran-scription 󿬁delity control. Hence, it is desirable to charac-terize the stepwise nucleotide selection in a structure-basedandquantitativemanner,particularlytotheslownucleotideinsertion step, using free energy and related measures.In current work, we employed intensive all-atom MDsimulations above microseconds in aggregation to inves-tigate the complete structural dynamics and free energet-ics of the nucleotide insertion, from a comparatively open-form pre-insertion structure, to a closed-form substrate orinsertion structure of T7 RNAP that is ready for cataly-sis (see Figure 1B), for both the cognate and non-cognatenucleotides. By constructing the potential of mean forces(PMFs) using the umbrella sampling methodology (27–30), we not only provided free energy pro󿬁les for various nu-cleotides during the insertion process, but also derived cor-respondingly the nucleotide selection energetics from thepre-insertion to the insertion checkpoints (6). The PMFs were constructed along the collective coordinates of an es-sential set of atoms, which were regarded highly relevantto the nucleotide insertion. The essential set encompassedthe majority of atoms involved in the open-to-close con-formational transition of the RNAP 󿬁ngers subdomain,the insertion NTP  per se , and the corresponding templatenucleotide. The collective coordinate was de󿬁ned accord-ing to the difference between the root-mean-square devi-ations ( rmsds ) of a current structure from the respectivepre-insertion and insertion reference structures. The non-cognate nucleotides included a mismatched ribo-nucleotide(rNTP) and a deoxy-ribonucleotide (dNTP). Following theprevious clues (22), both an  on-path  and an  off-path  inser-tion processes of the non-cognate nucleotides were probedforthefreeenergycalculations.Finally,wewereabletoinferthe selection free energetics down to the catalytic stage by󿬁tting with experimentally measured error rates via a chem-ical master equation (CME) approach onto the T7 RNAPelongation kinetics (26,31). This way, we completely char- acterized the 󿬁delity control in this prototypical viral tran-scription system, with both classical structural dynamicsand free energetic details.Below, we present how we performed the free energy cal-culations using all-atom MD simulations: Mainly, we con-structed individual PMFs for the cognate and non-cognatenucleotide insertion processes by performing the umbrellasampling simulations. Consequently, we obtained the ac-tivation free energies or barriers for those individual nu-cleotideinsertions,alongwithrepresentativeconformationson the insertion paths. In particular, in order to align theseindividual PMFs together and determine the selection free D ownl   o a d  e d f  r  omh  t   t   p s :  /   /   a c  a d  emi   c . o u p. c  om /  n ar  /   a d v  an c  e- ar  t  i   c l   e- a b  s  t  r  a c  t   /   d  oi   /  1  0 .1  0  9  3  /  n ar  /   gk z 2 1  3  /   5 4 2  0  5  3 1  b  y T h  e C h i  n e s  Uni  v  er  s i   t   y  of  H on gK  on g , j  i  n y  u @ c  s r  c . a c . c n on2  8 M ar  c h 2  0 1  9   Nucleic Acids Research, 2019  3 energetics arising between the non-cognate and cognate nu-cleotides, we also calculated the relative binding free ener-gies between them at the nucleotide pre-insertion, by per-forming alchemical MD simulations. In the end, we wereable to demonstrate how nucleotide selection free energet-ics distributed from the pre-insertion to the insertion stage,by additionally incorporating previous knowledge on nu-cleotide dissociation at pre-insertion. Furthermore, we alsoaddress how we inferred the selection energetics for the cat-alytic stage in the elongation kinetic framework by numeri-cally 󿬁tting the calculated elongation error rates with exper-imentally measured values. MATERIALS AND METHODS Below we 󿬁rst show how we obtained initial and 󿬁nal struc-tures for both the  on-path  and  off-path  nucleotide insertionsimulations, along with general MD simulation setup. ThenweillustratetheumbrellasamplingmethodtoconstructthePMFs for individual nucleotide insertion processes. In oursimulation system, the template DNA transition nucleotide(TN) at site  i   is a dTTP, so the cognate ribo-nucleotide isan rATP; a mismatched ribo-nucleotide rGTP and a deoxy-ribonucleotide dATP have been used as the non-cognatespecies in this study. Followed by that, we show how to de-termine the relative free energetics between the cognate andnon-cognate nucleotides, by conducting alchemical simula-tions and obtaining the relative binding free energies be-tween the rGTP / dATP  on-path  pre-insertion con󿬁gurationand that of the cognate rATP. In the end, based on the nu-cleotide selection free energetics derived from the MD sim-ulation results, we show how we calculated the elongationerror rates according to the CME approach, and inferredthe selection free energetics during catalysis. Theinitialand󿬁nalstructuresoftheinsertionalongwithMDsetup The high-resolution structures of the T7 RNAP elonga-tion complexes (protein, nucleic acids, or NAs, along withthe NTP substrate) were captured by crystallization stud-ies in two conformational states key to this study, the pre-insertion and the insertion complexes (with PDB codes1S0V and 1S76, respectively) (20,32), as the initial and 󿬁nal referencestructuresofthenucleotideinsertion,respectively.The missing residues were added based on the correspond-ing parts from other elongation complex structures in thepost-translocation and product states (PDB:1MSW,1S77)(32,33). We also modi󿬁ed the srcinal DNA / RNA se-quences in the insertion state structure (1S76) to be consis-tent with that in the pre-insertion structure (1S0V).Firstly, the initial pre-insertion structures of the cognateand non-cognate complexes, for both the  on-path  and  off- path  con󿬁gurations were constructed (see SupplementaryFigure S1A). The cognate rATP pre-insertion structure wasobtained after an equilibrium MD simulation of 100 ns,starting from the crystal structure of the pre-insertion com-plex(PDB:1S0V)(20).Thecrystalwaterswithin10 ˚AoftherATP molecule were retained. After the 100-ns equilibriumsimulation of the rATP pre-insertion complex,  ∼ 20 win-dowsof100-nsalchemicalsimulationseachwereconductedto transform rATP gradually into rGTP and dATP, respec-tively, so that the dATP and rGTP  on-path  initial struc-tures were obtained in the last window, along with the rela-tive binding free energies between the  on-path  dATP / rGTPand rATP at pre-insertion (addressed later), as conductedin our previous alchemical simulation study (22). In com-parison,toobtainthe off-path initialstructures,thecognaterATP in the pre-insertion crystal complex was directly con-verted into the non-cognate rGTP and dATP, respectively;after energy minimization, 100-ns equilibrium simulationswereconductedfortherespectivenon-cognatepre-insertioncomplexes to obtain the  off-path  initial structures, as con-ducted in another of our previous simulation studies (21).Then for the 󿬁nal substrate insertion structures, the cog-nate rATP structure was obtained from the equilibratedcomplex of the crystal structure (PDB: 1S76) (32); the non-cognate rGTP and dATP substrate structures were con-structed by directly converting rATP into rGTP and dATP,respectively, based on the insertion crystal structure, andwere then subjected to MD equilibration (see Supplemen-tary Figure S1B).All MD simulations were performed using GROMACS-5.1.2 package (34,35) and the Amber99sb force 󿬁eld with ParmBsc0 nucleic acid parameters was used (36–39). The rATP / rGTP / dATP parameters were obtained from Carl-son  et al.  (40). For the equilibrium MD simulation, theRNAPcomplexwassolvatedwithexplicitTIP3Pwater(41)in a cubic box with a size of   ∼ 120 ˚A, and the minimumdistance from the protein to the wall was set to 13 ˚A. Alarger simulation box (up to ∼ 165 ˚A) with expanded num-ber of water molecules was tested, with no further energeticchanges of protein-DNA interactions within the RNAPpre-insertion complex found, and no further essential con-formation changes such as the O-helix rotational motionseither. To neutralize the system and make the salt concen-tration 0.1 M with counter ions, 176 Na + ions and 142 Cl − ions were added. Two magnesium ions were kept as thatfrom respective crystal structures of the pre-insertion andinsertioncomplexes(20,32).Thefullsimulationsystemcon- tained  ∼ 156 000 atoms, with  ∼ 140 000 atoms for the wa-ter molecules. For all simulations, the cut-off of van derWaals (vdW) and the short-range electrostatic interactionswere set to 9 and 10 ˚A, respectively. Particle-mesh-Ewald(PME) method (42,43) was used to evaluate the long-range electrostatic interactions. All MD simulations were run at1 bar and 310 K using the Parrinello − Rahman Barostat(44,45) and the velocity rescaling thermostat (46), respec- tively. Before each of the equilibrium NPT simulation, weminimized the initial structure for 50 000 steps with thesteepest-descent algorithm followed by 100-ps NVT MDsimulation. The time step was 2 fs and the neighbor list wasupdated every 5 steps. Umbrella sampling simulations In order to obtain the free energy pro󿬁les or PMFs betweenthe pre-insertion and the insertion states of T7 RNAP, forboth the cognate and non-cognate substrate species, welaunched reaction paths along the changes of the  rmsd   of an essential set of atoms (see  δ rmsd   and the atom selectionaddressed later). The choice of this reaction coordinate is D ownl   o a d  e d f  r  omh  t   t   p s :  /   /   a c  a d  emi   c . o u p. c  om /  n ar  /   a d v  an c  e- ar  t  i   c l   e- a b  s  t  r  a c  t   /   d  oi   /  1  0 .1  0  9  3  /  n ar  /   gk z 2 1  3  /   5 4 2  0  5  3 1  b  y T h  e C h i  n e s  Uni  v  er  s i   t   y  of  H on gK  on g , j  i  n y  u @ c  s r  c . a c . c n on2  8 M ar  c h 2  0 1  9   4  Nucleic Acids Research, 2019 due to such  δ rmsd   being highly collective and relevant tothe substantial conformational changes involved in the nu-cleotide insertion. To avoid too large deviations from thetwo-end structures at the pre-insertion and insertion states,both forward (pre-insertion to insertion) and backward (in-sertion to pre-insertion) paths were launched, and the 󿬁rsthalf of these two paths were merged into one insertion path.Subsequently, we generated a series of con󿬁gurations alongthe insertion paths for the cognate rATP and non-cognaterGTP / dATP( on-path and off-path );theneachofthesecon-󿬁gurations was subjected to the umbrella sampling simula-tion with force constraints (47). Finally, the PMFs alongthe  δ rmsd   reaction coordinate were obtained by using aweightedhistogramanalysismethod(WHAM)(28,30).The technical details are provided below. Launch the initial nucleotide insertion pathway along the re-actioncoordinate.  Basedonthemodeledpre-insertionandinsertion structures, we obtained the initial forward andbackward insertion paths by using a modi󿬁ed version of the Climber algorithm (48). In the respective paths, the in- sertion and the pre-insertion structures were set as the 󿬁-nal reference structures. We selected C   atoms of 󿬁ve he-lices in the 󿬁ngers subdomain (residue 627–639, 568–589,612–624, 642–660 and 669–687) and heavy atoms of sub-strate rATP / rGTP / dATP and template TN( i  ) as the mor-phed regions. These regions undergo substantial conforma-tional changes as observed from the crystal structures (seeSupplementary Figure S2A). We excluded the 󿬂exible loopregions on the 󿬁ngers subdomain that may involve irrele-vant motions. Indeed, we chose the above morphed regionto serve as a minimum set to be essential for the nucleotideinsertion. Inclusion of a larger set of atoms, e.g. from theDNA or RNA strand, the 󿬁nal morphed structures actu-ally demonstrated larger deviations from the insertion tar-get (see Supplementary Figure S2B and C), likely due to ex-tra 󿬂uctuations brought about by the DNA / RNA strand.IntheClimbersimulation,externalforceswerethenappliedto the atoms in the morphed region, whereas the remain-der of the system responded to the structural changes in themorphed region; the target number of morphing cycles wasset to 700, and each morphing cycle consisted of 100 itera-tions of morphing, with 10 steps of conjugate gradient en-ergy minimization for each 10 iterations; the minimum dis-tance (or the  rmsd  ) to the target structure was set to 0.4 ˚Aand was reached after 400 morphing cycles.In launching the reaction paths for the subsequent um-brella sampling simulations, we used  δ rmsd   as the reactioncoordinate, which is de󿬁ned as  δ rmsd   = rmsd  ( X  ,  X  init ) − rmsd  ( X  ,  X   final  ),where X  representsacollectivecoordinateof our selected structural regions (speci󿬁ed above or seeSupplementary Figure S2A);  X  init  and  X   󿬁nal   refer to corre-sponding coordinates of the reference structures near theequilibrium initial pre-insertion and 󿬁nal insertion com-plexes, respectively; and  rmsd   is measured between the twoset of coordinates denoted inside the parenthesis.  δ rmsd  has been successfully used as an order parameter or re-action coordinate to characterize the transition pathwaybetween a pair of structures in biomolecular simulations(49,50). Along the  δ rmsd   reaction coordinate here, the in-terval distance between two neighboring windows was setto 0.1 ˚A, so that 27 windows were obtained for the cog-nate rATP (or non-cognate rGTP / dATP  on-path ) insertionas  δ rmsd   ranges from –1.3 to 1.3 ˚A, and 45 or 53 windowswereobtainedforthenon-cognaterGTP / dATP off-path in-sertion as  δ rmsd   spans from –2.2 to 2.2 ˚A or –2.6 to 2.6˚A. The choice of the number of windows ensured suf󿬁cientoverlaps between neighboring simulation windows that isrequired for the construction of the PMF (see below). Conducting the umbrella sampling simulations.  The um-brella sampling simulations were performed by usingPLUMED (51) to add force constraints on the collective δ rmsd   coordinate, with each window simulated for ∼ 40 ns.The same MD setup was used as speci󿬁ed above.The 27 structures (45 or 53 structures for the non-cognate  off-path ) along the reaction path were subjectedto the umbrella sampling simulations with the forces ap-plied to the selected structure regions according to  F   = k  ( δ rmsd  − δ rmsd  0), where  δ rmsd  0 was the speci󿬁ed valuefor the simulation window, around which  δ rmsd   was re-strained, and  k   adopted a value at 210 000 kJ / (mol · nm 2 )forregularwindows(or10timeslargerforwindowsnearthefreeenergybarrier,or10timessmallerforwindowsnearthefree energy minima). Constructing the PMFs and error analyses.  The PMFs orthefreeenergypro󿬁lesalongthe δ rmsd   reactioncoordinatewere obtained by using the WHAM (28,30) on a series of  40-ns trajectories from the umbrella simulation windows,while the 󿬁rst 10-ns pre-equilibration data were not used.The WHAM was used to transform the biased sampling re-sults to the unbiased sampling ones. Basically, one calcu-lates the unbiased probabilities from the biased samplingsby using the equation below P i   ( δ rmsd  ) ∝ e − 12  k  ( δ rmsd  − δ rmsd  0)2 k B T  P  i   ( δ rmsd  ) (1)where  P i  ( δ rmsd  ) and  P  i   ( δ rmsd  ) are the unbiased and bi-ased probabilities, respectively.  12 k  ( δ rmsd  − δ rmsd  0) 2 is theharmonic restraint potential. Note that the full probabilitydistribution  P ( δ rmsd  ) is not simply the addition of the in-dividual probability distributions obtained from each win-dow, but a linear combination of them. Lastly, accordingto  G  ( δ rmsd  ) =− k  B  TlnP ( δ rmsd  ), the free energy pro󿬁le  G  along the coordinate  δ rmsd   or the PMF was obtained.During the construction of PMF by using WHAM, weperformed bootstrapping in order to estimate errors (52). The WHAM computes the PMF based on all the  δ rmsd  i  (t)obtained from the simulation windows ( i   =  1, 2,...,  n ).In order to get the bootstrapped trajectories  δ rmsd  b , i  ( t ),one re-samples the  δ rmsd  i   in each window. Each boot-strapped trajectory  δ rmsd  b , i  ( t ) produces a new histogram h b , i  ( δ rmsd  ). Then, via the WHAM procedure, one com-putes a bootstrapped PMF  G  b ( δ rmsd  ) based on the newset of   n  histograms  h b , i  . The whole process is repeated  N  times ( N   =  200 used), generating  N   bootstrapped PMFs G  b ,  j  ( δ rmsd  )(  j  = 1,2,..., N  ).TheuncertaintyofthePMFisthen estimated by the standard deviation calculated by the D ownl   o a d  e d f  r  omh  t   t   p s :  /   /   a c  a d  emi   c . o u p. c  om /  n ar  /   a d v  an c  e- ar  t  i   c l   e- a b  s  t  r  a c  t   /   d  oi   /  1  0 .1  0  9  3  /  n ar  /   gk z 2 1  3  /   5 4 2  0  5  3 1  b  y T h  e C h i  n e s  Uni  v  er  s i   t   y  of  H on gK  on g , j  i  n y  u @ c  s r  c . a c . c n on2  8 M ar  c h 2  0 1  9   Nucleic Acids Research, 2019  5 N   bootstrapped PMFs (52). σ  PMF  ( δ rmsd  ) =  ( N  − 1) − 1  N  j  = 1  G  b ,  j   ( δ rmsd  ) − G  b ( δ rmsd  )   2  12  (2) Evaluating the relative binding free energies between the  on- path  non-cognate and cognate NTPs at pre-insertion Though we obtained the  on-path  and  off-path  PMFs for thenon-cognate rGTP / dATP insertion individually, how thesePMFs deviated from that of the cognate rATP at the be-ginning of the insertion process needed to be determined.Accordingly, we calculated the relative binding free energiesbetween the  on-path  non-cognate substrate species and thecognateoneatthepre-insertionsite,byusingthealchemicalmethod illustrated below. The relative binding free energy via a thermodynamic cycle. For the substrates or ligands rGTP / dATP (non-cognate or nc ) and rATP (cognate or  c ) at the pre-insertion site, therelative binding free energies between them can be obtainedvia a thermodynamic cycle as  G  b  ≡  G  bnc −  G  bc =  G   proa  −  G  sol a  (3)where   G  bnc and   G  bc are the binding free energies of thenon-cognate and cognate nucleotides at the pre-insertionsite, respectively;   G   proa  and   G  sol a  are the free energiesevaluated by transforming the cognate rATP alchemicallyinto the non-cognate rGTP / dATP in the protein complexand in the free solution, respectively (22). Then the free energy perturbation (FEP) method (53) was used to cal- culate the alchemical energy. In order to accurately evalu-ate the free energy change, the bidirectional sampling us-ing the Bennett acceptance ratio (BAR) method (54) wasimplemented in the GROMACS package (34,35,55), with both forward and backward alchemical transformationsperformed in the simulation (56). The implementation of the alchemical simulations.  In thealchemical simulation, three dummy atoms were addedto rATP in order to convert rATP (rGTP / dATP) torGTP / dATP (rATP) in the forward (backward) direction.For the forward simulation, the transformation of the cog-nate into the non-cognate nucleotide was controlled via aparameter    from 0 to 1, with an increment of 0.05, and itwas  vice versa  for the backward path (22). During the simulation, the vdW and electrostatic interac-tion were simultaneously changed. The LINCS algorithmwas used to constrain all the chemical bonds (57). In the free-solution simulation, NTP was solvated in a cubic boxwith ∼ 4000 TIP3P water molecules, the minimum distancefrom NTP to the wall was set to 10 ˚A. Ten Na + ions andeight Cl − ions were added to keep the ionic concentrationat 0.1 M and neutralize the system. The simulations withthe protein complex were the same as speci󿬁ed above. Ineach direction, 21 windows of 100-ns simulation each werecarried out in the protein complex and in the free solution,respectively (22). Deriving the elongation error rate from the stepwise selectionenergetics Here, we use a 󿬁ve-state kinetic scheme including the pre-translocation state (I), post-translocation state (II), pre-insertionstate(III),substrateinsertionstate(IV),andprod-uct state (V) to describe an RNAP elongation or NAC cycle(see Figure 1B and the linear scheme with rates denoted be-low). Importantly, the RNAP can differentiate the cognateand non-cognate NTP species upon the nucleotide bind-ing as well as during the insertion and catalysis processes(6,25,26). I Translocationk I +  k II − NTPbinding II k II +  k III − Insertion III k III +  k IV − IV Catalysisk IV +  k V − V PPireleasek V +  k I − I  (4)Correspondingly,therearefourkineticcheckpointsuponthe NTP binding (pre-insertion) and incorporation steps,as described in one our previous modeling work (6). The󿬁rst selection checkpoint ( III  →  II  ) rejects non-cognateNTP immediately upon the NTP binding or pre-insertion,with a selection strength  η − III   ≡  k  ncIII  − k  cIII  − = e  − b  / k  B  T  , where  − b  is de󿬁ned as the selection free energy at the pre-insertion state, or the difference between the dissociationfree energy barriers of the cognate (  E  cd  ) and the non-cognate (  E  ncd   ) NTP (  − b  ≡  E  cd   −  E  ncd   ). The next se-lection checkpoint ( III   →  IV  ) inhibits the non-cognatenucleotides from inserting into the active site, with a se-lection strength  η + III   ≡  k  cIII  + k  ncIII  + = e  + in / k  B  T  , where   + in  is de-󿬁ned as the insertion selection free energy, or the dif-ference between the insertion free energy barriers of thenon-cognate and the cognate NTP (  + in  ≡  E  ncin  −  E  cin ).The third selection checkpoint (IV →  III) destabilizesthe non-cognate nucleotides after being inserted at thesubstrate state  IV   ( η − IV   ≡  k  ncIV  − k  cIV  − = e  − in / k  B  T  ), where   − in  isthe difference between the free energy barriers to re-verse the insertion process of the cognate and the non-cognate nucleotides (  − in  ≡  E  cre v −  E  ncre v ). The last se-lection checkpoint (IV  →  V) inhibits the catalytic re-action of the non-cognate nucleotides comparing to thecognate one ( η + IV   ≡  k  cIV  + k  ncIV  + = e  + c  / k  B  T  ), where   + c  is the cat-alytic selection free energy or the free energy barrier dif-ference between the non-cognate and cognate nucleotidespecies during the catalysis (  + c  ≡  E  nccat −  E  ccat ). In gen-eral, every checkpoint can play some role during thenucleotide selection (  >  0), while an important check-point may contribute signi󿬁cantly (   0). Correspond-ingly, the populations and probability 󿬂uxes of the non-cognate and cognate species can be treated separately,with the respective 󿬂uxes or elongation rates as, e.g.  J  nc = P ncV   k  V  + − ErrP I  k  I  −  and  J  c =  P cV  k  V  + − (1 − Err ) P I  k  I  − ,where ( P I  ,  P II  ,  P cIII  ,  P ncIII  ,  P cIV  ,  P ncIV  ,  P cV  ,  P ncV   ) is the vectorfor the state population distributions, and  Err  denotes theelongation error rate. The error rate is de󿬁ned as the ra-tio between the non-cognate and total elongation rates or󿬂uxes as  Err  ≡  J  nc / J  , with  J   =  J  c +  J  nc being the to-tal 󿬂ux or elongation rate at the steady-state condition.More calculation details can be found in references (6,26). The mainly elongation kinetic parameters of T7 RNAP D ownl   o a d  e d f  r  omh  t   t   p s :  /   /   a c  a d  emi   c . o u p. c  om /  n ar  /   a d v  an c  e- ar  t  i   c l   e- a b  s  t  r  a c  t   /   d  oi   /  1  0 .1  0  9  3  /  n ar  /   gk z 2 1  3  /   5 4 2  0  5  3 1  b  y T h  e C h i  n e s  Uni  v  er  s i   t   y  of  H on gK  on g , j  i  n y  u @ c  s r  c . a c . c n on2  8 M ar  c h 2  0 1  9 
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