Allosteric networks in thrombin distinguishprocoagulant vs. anticoagulant activitiesPaul M. Gaspera, Brian Fuglestada, Elizabeth A. Komivesa, Phineus R. L. Markwicka,b,c,1,and J. Andrew McCammona,b,d,1

Departments of aChemistry and Biochemistry and dPharmacology, bHoward Hughes Medical Institute, and cSan Diego Supercomputer Center, University ofCalifornia at San Diego, La Jolla, CA 92093

This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2011.

Contributed by J. Andrew McCammon, October 29, 2012 (sent for review September 24, 2012)

The serine protease α-thrombin is a dual-action protein that medi-ates the blood-clotting cascade. Thrombin alone is a procoagulant,cleaving fibrinogen to make the fibrin clot, but the thrombin–thrombomodulin (TM) complex initiates the anticoagulant path-way by cleaving protein C. A TM fragment consisting of only thefifth and sixth EGF-like domains (TM56) is sufficient to bind throm-bin, but the presence of the fourth EGF-like domain (TM456) iscritical to induce the anticoagulant activity of thrombin. Crystal-lography of the thrombin–TM456 complex revealed no significantstructural changes in thrombin, suggesting that TM4 may onlyprovide a scaffold for optimal alignment of protein C for its cleav-age by thrombin. However, a variety of experimental data havesuggested that the presence of TM4 may affect the dynamic prop-erties of the active site loops. In the present work, we have usedboth conventional and accelerated molecular dynamics simulationto study the structural dynamic properties of thrombin, thrombin:TM56, and thrombin:TM456 across a broad range of time scales.Two distinct yet interrelated allosteric pathways are identifiedthat mediate both the pro- and anticoagulant activities of throm-bin. One allosteric pathway, which is present in both thrombin:TM56 and thrombin:TM456, directly links the TM5 domain to thethrombin active site. The other allosteric pathway, which is onlypresent on slow time scales in the presence of the TM4 domain,involves an extended network of correlated motions linking theTM4 and TM5 domains and the active site loops of thrombin.

allostery | thrombosis

Thrombin is a dual-action serine protease that plays a pivotalrole in the blood-clotting cascade. The specific functional

activity of thrombin is mediated by its interaction with the co-factor thrombomodulin (TM). In the absence of TM, thrombinacts as a procoagulant, cleaving fibrinogen to fibrin. However,when in complex with TM, thrombin acts as an anticoagulant bycleaving, and thereby activating, protein C (1, 2). TM contains sixEGF-like domains; the fifth domain interacts directly withthrombin at the fibrinogen binding site, anion binding exosite 1(ABE1). It has been shown that a TM fragment consisting ofonly the fifth and sixth EGF-like domains (TM56) is sufficient tobind thrombin and inhibit fibrinogen cleavage, but the additionalpresence of the fourth EGF-like domain of TM (TM456) is criticalto induce the anticoagulant activity of thrombin (3, 4). TM456binding to thrombin significantly increases the association rate,ka, of a variety of active site-directed inhibitors of thrombin (5–8),and the ka for protein C binding is 1,000-fold higher for thethrombin–TM456 complex compared with thrombin alone (9).The mechanism by which TM456 enhances protein C cleavage

is not yet fully understood and is particularly intriguing becauseABE1 is distal to the active site and the essential TM4 domainmakes no direct contact with thrombin whatsoever (10) (Fig. 1).The simplest explanation for the dramatically increased associ-ation rates is that TM456 alters the structure of thrombin, mostnotably the conformation of the loops that surround the active

site, a process generally referred to as structural or enthalpicallostery (11). However, a comparative analysis of theX-ray crystalstructures of thrombin [Protein Data Bank (PDB) ID code 1PPB](12) and thrombin:TM456 (PDB ID code 1DX5) (10) revealed nosignificant structural differences in the thrombin active site loops.It should be noted that in these X-ray crystal structures, the activesite is occupied by an inhibitor, potentially stabilizing the loops in aclosed conformation.To date, the most robust argument for the role of TM4 in the

activation of protein C comes from a recent molecular modelingstudy (10), which suggests that TM4 forms an extended bindingsurface for protein C, providing optimal alignment for insertioninto the active site and subsequent cleavage. Critical electrostaticinteractions between protein C and residues in TM4, includingGlu382 in the β4-β5 loop, Asp398, and Glu357 as well as hydro-phobic interactions with the aromatic residues Tyr358 and Phe376,were identified. The importance of these residues for the acti-vation of protein C has been empirically validated by alanine-scanning mutagenesis and H/D exchange experiments (13, 14).However, the proposed “docking and optimal alignment” mech-anism may be insufficient to explain the 1,000-fold increase inobserved association rates, particularly for smaller substrates andother inhibitors, which may enter the active site of thrombinwithout directly interacting with the TM4 domain.Several studies, including fluorescence (15), hydrogen/deuterium

(H/D) exchange (16), and isothermal titration calorimetry (17),have identified changes in the thrombin active site region thatoccur on binding to different constructs of TM in the absence ofprotein C. These studies suggest that the presence of TM4 mayaffect the dynamic properties of both the active site and the loopssurrounding it, a process referred to as entropic allostery (18–20).A very recent NMR/molecular dynamics simulation study onthrombin bound to the inhibitor D-Phe-Pro-Arg-chlorormethylketone (PPACK) identified significant dynamic motions in theactive site loops across time scales ranging from picoseconds totens of microseconds even with inhibitor bound (21).In the present work, we use both conventional molecular dy-

namics (CMD) simulation and an enhanced conformational spacesampling algorithm, accelerated molecular dynamics (AMD) (22),to study the conformational behavior and potential allostericpathways in thrombin, thrombin:TM56, and thrombin:TM456.AMD is an extended, biased potential molecular dynamics ap-proach that allows for the efficient study of biomolecular systems

Author contributions: P.M.G., P.R.L.M., and J.A.M. designed research; P.M.G. and P.R.L.M.performed research; P.M.G., B.F., E.A.K., and P.R.L.M. analyzed data; and P.M.G., E.A.K.,and P.R.L.M. wrote the paper.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.1Towhom correspondence may be addressed. E-mail: pmarkwick@ucsd.edu or jmccammon@ucsd.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1218414109/-/DCSupplemental.

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up to time scales several orders of magnitude greater thanthose accessible using CMD while maintaining a fully atomisticrepresentation of the system. AMD has already been used withgreat success to study the dynamics and conformational behaviorof a variety of biomolecular systems, including polypeptides andboth natively unstructured and folded proteins (23). Communitynetwork models (24) have been used to identify potential allo-steric pathways. This information is supplemented by both ageneralized correlated motion analysis (25) and the calculationof backbone amino-nitrogen–amino-proton, NHN order param-eters to compare the dynamic behavior of thrombin in the threedifferent systems across a variety of time scales.

ResultsWe initially performed a set of six independent 20-ns CMD sim-ulations for each of the three systems: thrombin, thrombin:TM56,

and thrombin:TM456. For all three systems, a rather large con-formational transition in the active site loops was observed duringthe equilibration procedure. Central to this conformationalrelaxation was a reorientation of both the extended 148CTγ-loop (residues 178–192) and the 220CT loop (residues 265–274),forming a more “open” active site pocket. Notably, the extended148CT γ-loop moves closer to the ABE1 70CT loop (residues 93–109) (residue numbering details are provided in SI Text). Thisobservation confirms the hypothesis that the presence of the in-hibitor in the available X-ray crystal structures, which was re-moved before performing the CMD simulations, promotes aclosed loop conformation. After this initial structural relaxation,the conformational dynamics of each of the three systems rapidlystabilized and the backbone rmsd to the average structure for thethrombin molecule was found to be 1.4 Å, 1.2 Å, and 1.2 Å forthrombin, thrombin:TM56, and thrombin:TM456, respectively.The molecular ensembles generated from the CMD simulations

were subjected to a community network analysis, which identifiescommunities (clusters of highly connected residues) based onresidue-by-residue correlation and proximity (22). A measure of“betweenness” of the intercommunity edges (Methods) affords theidentification and characterization of potential allosteric path-ways. Community network analysis results for thrombin, thrombin:TM56, and thrombin:TM456 are shown in Fig. 2.Several interesting and highly reproducible communities of

residues were observed in the analyses in the majority of theCMD trajectories. In all cases, TM4, TM5, and TM6 are each re-presented by a single community. By contrast, the thrombin mol-ecule in all systems consists of multiple interconnected communities

Fig. 1. Structure of thrombin:TM456. (A) Structure of thrombin lookingdirectly into the active site. Important regions are highlighted by spheres:90CT loop (red), 148CT (γ) loop (cyan), 170CT loop (green), 186CT loop (purple),220CT loop (blue), and 60CT insertion (yellow). The ABE1 binding site com-prises the 30CT loop (orange) and the 70CT loop (magenta). Chymotrypsinand sequential residue numbering for these regions is provided in SI Text. (B)Domain architecture of thrombin:TM456. Thrombin is depicted as a ribbon[light chain (coral) and heavy chain (gray)], and TM is depicted as a surface[TM4 (violet), TM5 (tan), and TM6 (blue)].

Fig. 2. Community analysis results (Left) and corresponding structurescolored by community (Right) for thrombin (A), thrombin:TM56 (B), andthrombin:TM456 (C). The communities are represented by circles, and theedge width is proportional to the cumulative betweenness of intercom-munity edges, which is a measure of the strength of the potential allostericinteraction between communities.

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divided between, most notably, the TM binding site (ABE1) andthe proteolytic active site, including the catalytic triad (H57CT,D102CT, and S195CT), the 60CT insertion, and the active siteloops [90CT, 148CT (γ), 170CT, 186CT, and 220CT]. However, thenumber of thrombin communities differs from one system to thenext. On average, isolated thrombin ostensibly comprised eightdistinct large communities, whereas the thrombin molecule inthrombin:TM56 and thrombin:TM456 comprised only five to sixlarge communities, on average. Similarly, the metric of cumulativebetweenness of intercommunity edges, which is a direct measureof the strength of the potential allosteric interaction betweencommunities, is greater in the two thrombin–TM complexescompared with thrombin alone. In the thrombin:TM56 system, astrong allosteric pathway is consistently observed linking the TM5,ABE1, and active site communities. The TM4 domain, whichforms a strong allosteric connection to TM5, acts to enhance thestrength of this allosteric pathway further. A second and very im-portant difference between the community networks for thrombin:TM56 and thrombin:TM456 is the presence of a strong commu-nication between TM5 and the 148CT γ-loop of thrombin, which isonly observed in the thrombin:TM456 construct.The fast time-scale dynamics of thrombin in the isolated throm-

bin, thrombin:TM56, and thrombin:TM456 systems were analyzedby calculating backbone NHN order parameters, which provide aquantitative measure of the extent of (internal) reorientationdynamics of the N-H bond vector per residue (Fig. 3A). Similarto the recent NMR/molecular dynamics simulation study onthrombin:PPACK, a strongly heterogeneous distribution of fasttime-scale motions was observed in all three systems (21). In theisolated thrombin system, order parameters in the 30CT loop(residues 53–61), which forms part of ABE1, and in the 60CTinsertion (residues 83–91) were as low as 0.66 and 0.64, respec-tively. By contrast, in both the thrombin–TM complexes, theseorder parameters were substantially higher, with the lowest valuebeing 0.76. Reduced fast time-scale dynamics (and hence higherorder parameters) in the 30CT loop are readily explained becausethis region makes direct contact with the TM5 domain. However,the same cannot be said for the 60CT insertion. Significantly, thecommunity network analysis models for both thrombin:TM56and thrombin:TM456 (Fig. 2) identified a strong allosteric path-way connecting TM5 to the active site of thrombin via the 60CTinsertion. Higher order parameters in these same loops were alsoobserved experimentally (21). The dynamic communication ob-served between the active site, the 30CT loop, and the 60CT in-sertion is a prime example of entropic allostery. No othersignificant differences in the fast time-scale NHN order param-eters for the three systems were observed. Calculated backbonerms atomic fluctuations also revealed no other significant dif-ferences, and the average structures of thrombin for the threesystems were remarkably similar (backbone rmsd < 0.5 Å).To access microsecond-millisecond time-scale motions more

typical of allosteric regulation, a series of AMD simulations wasperformed at two acceleration levels: a moderate accelerationlevel (level 1), which samples configurational dynamics up totime scales of several hundred nanoseconds, and an aggressiveacceleration level (level 2), probing dynamics up to several tensof microseconds (details are provided in SI Text). After freeenergy weighting of the AMD trajectories, a representative en-semble of structures was obtained. Whereas no substantial do-main reorientation was observed for the TM EGF domains in theCMD, the AMD trajectories showed some domain reorientation,although with limited extent of motion. From the free energy-weighted trajectories, averaged thrombin NHN order parameterswere calculated (Fig. 3A). In contrast to the fast time-scale dy-namics, marked differences in the order parameters were ob-served for the three systems, particularly at the most aggressiveacceleration level (Fig. 3B). Both TM-bound systems exhibitconsiderably less dynamics in the 30CT loop (residues 53–61) and

the 60CT insertion (residues 83–91), consistent with what wasobserved for the fast time-scale order parameters. However, onslow time scales, thrombin:TM456 exhibits remarkably more re-orientation dynamics in the active site loop regions: the 90CTloop (residues 122–132), the 148CT loop (residues 184–192), the170CT loop (residues 213–221), the 186CT loop (residues 228–234), and the 220CT loop (residues 265–274). By contrast, thrombin:TM56 shows either no more or, in some regions, even less slowtime-scale dynamics compared with the isolated thrombin system.A residue-by-residue cross-correlation analysis (25) (Methods)

applied to the free energy-weighted molecular ensembles obtainedat the most aggressive acceleration level also revealed strikingdifferences between the three systems (Fig. 4). In all three systems,we observed cross-correlated motion between the 30CT loop andthe 60CT insertion, and the strength of this cross-correlation wasmarkedly enhanced in the thrombin:TM456 system. Addition-ally, the thrombin:TM456 system exhibited a complex pattern ofstrongly correlated motions across the active site loops (Fig. 5)directly coinciding with the observation of enhanced slow time-scale dynamics in the level 2 AMD trajectories of the thrombin–TM456 complex (Fig. 3B). In contrast, correlations between thecorresponding regions in both the thrombin:TM56 and the iso-lated thrombin systems were very weak or absent.To confirm that the pattern of strongly correlated motions

observed in the thrombin–TM456 complex was due to TM4, we

Fig. 3. (A) Thrombin residue NHN order parameters for isolated thrombin(Top), thrombin:TM56 (Middle), and thrombin:TM456 (Bottom) systems. Theblack line depicts fast time-scale order parameters obtained from a series of20-ns CMD simulations. The red line depicts order parameters obtainedfrom a set of free energy-weighted AMD trajectories at acceleration level 2,probing dynamics on time scales up to several tens of microseconds. Orderparameters for acceleration level 1 were intermediate and are not shown inthe figure for clarity. (B) Slow time-scale (level 2 acceleration) differentialNHN backbone order parameters for thrombin [TM56 (black) and thrombin:TM456 (red)] compared with the isolated thrombin system. Positive valuesindicate an increase in the amount of reorientation dynamics relative to theisolated thrombin system, and negative values indicate fewer dynamics.

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extended our analysis to include the TM domains. To circumventcomplications from the reorientation dynamics of the TM domains,multiple cross-correlation analyses were performed after super-posing the molecular ensemble on different regions of the sys-tem, and the complete cross-correlated dynamics map (Fig. 6)was then reconstructed. The results clearly show that the com-plex network of correlated motions observed in thrombin:TM456propagates from the TM4 domain through the TM5 domain andinto the thrombin molecule (Fig. 6). Global reorientation dy-namics of TM4 contribute significantly to the entire network ofcorrelated motion by inducing global reorientation dynamics ofTM5, and hence the specific orientation and interactions of TM5with thrombin. Additionally, interdomain, residue-by-residue cor-relations are observed between regions of TM4 (residues 359–369)and TM5 (residues 404–414). Both global domain correlations andspecific residue correlations in TM extend into ABE1 of thrombin,

including the 30CT loop (residues 53–61), the 60CT insert (residues83–91), and the 70CT loop (residues 93–109). TM5 residues(404–414) are strongly correlated because they lie in close prox-imity to the 30CT loop. In addition, Asp416 and Asp417 from TM5make a significant contact with Thr105/Arg106 in thrombin.All these TM residues were identified previously as critical byalanine scanning mutagenesis (13). The network of correlatedmotion continues from ABE1 into the thrombin active siteloops and remains especially strong in the 148CT loop (residues180–190) and includes the 90CT loop (residues 122–132) andthe 170CT loop (residues 210–220).

DiscussionThe work presented in this paper provides unique and detailedinsight into the functional dynamics of the thrombin:TM system,which not only rationalizes the available experimental data butexplicitly identifies and defines the important role played by theTM4 domain in the activation of protein C. The results show twodistinct but interrelated allosteric pathways that mediate theanticoagulant activity of the thrombin–TM complexes. One path-way connects the TM5 domain with ABE1, the 60CT insertion, andthe active site. This allosteric network, which exists in both thethrombin:TM56 and thrombin:TM456 systems, was previouslyidentified using H/D exchange (16). Community network modelsfurther indicate that TM4 strengthens this allosteric pathway(Fig. 2), leading to a significant enhancement in the cross-cor-related motion between the 30CT loop and the 60CT insertion inthe thrombin:TM456 system compared with the isolated thrombinand thrombin:TM56 systems (Fig. 4). Indeed, binding of TM56 to

Fig. 4. Normalized comparative analysis of observed thrombin cross-cor-related motions in isolated thrombin (A) and thrombin:TM56 (Upper) andthrombin:TM456 (Lower) (B) obtained from representative free energy-weighted (level 2) AMD molecular ensembles. Blue boxes have been insertedto highlight the most significant cross-correlated motions common to allthree systems. In the case of thrombin:TM456, significant cross-correlatedmotions are observed between the active site loops (black boxes), which areeither absent or very weak in the case of thrombin and thrombin:TM56(green boxes shown for comparative purposes). Correlated motions extendinto the light chain. The functional consequences of this phenomenon arenot clear but are in agreement with mutagenesis experiments indicating apotential allosteric role for the light chain (37).

Fig. 5. Slow time-scale cross-correlated molecular motions for thrombin inthe thrombin:TM456 system projected onto a random snapshot taken fromthe thrombin:TM456 level 2 AMD trajectory. For reasons of clarity, the TMdomains are not shown. The catalytic triad [residues His79(57CT), Asp135(102CT), and Ser241(195CT)] are shown in yellow. The active site loops thatexhibit enhanced slow time-scale dynamics and strongly interconnectedcorrelated motions (compare with Fig. 4B) are shown using a “ball-and-stick”representation: blue, extended 90CT loop (residues 125–140); red, extended148CT loop (residues 175–192); green, 220CT loop (residues 263–274); andorange, residues 103–110, which form part of the 70CT loop. Regions in andneighboring ABE1, the 30CT loop (residues 53–61, tan) and 60CT insertion(residues 83–91, black), respectively, shown in cartoon format, are more rigidthan in the isolated thrombin system but also show extensive correlatedmotions on both fast and slow time scales.

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thrombin stabilizes some thrombin active site loops on slow timescales, as shown by the backbone NHN order parameters calcu-lated from AMD simulations (Fig. 3B).The addition of the fourth EGF-like domain (TM456) activates

slow time-scale dynamics in the active site loops of thrombin viaanother allosteric pathway. Global reorientation and intradomainconfigurational dynamics of TM4 are strongly coupled to both theglobal and intradomain dynamics of TM5. The importance ofseveral of the most highly cross-correlated TM residues in theseregions was previously characterized in an NMR study, whichfound that backbone dynamics of Tyr358 and Gln359 are cor-related with anticoagulant activity and that backbone dynamicsof Tyr413 and Ile414 are inversely correlated with thrombinbinding (24). This tight coupling between TM4 and TM5 waspreviously shown experimentally to depend on M388 in theTM4-TM5 linker (25, 26). The specific orientation and inter-actions of TM5 induced via coupling to TM4 mediate specificinteractions with ABE1. The dynamics of ABE1 are, in turn,highly correlated with the dynamics of the thrombin active siteloops only in the TM4-containing construct. Through this com-plex pattern of extended correlated motions, slow time-scale con-figurational dynamics of TM4 are directly linked to the thrombinactive site, providing evidence for entropic allostery between TM4and thrombin (Figs. 5 and 6). The community network analysisalso reveals that when TM456 is bound, the information transferbetween the loop regions of thrombin is significantly enhanced,resulting in the observation of fewer yet larger communities andincreased potential for communication between communities.This enhanced communication is particularly strong for the pathconnecting the active site loops to TM4 via ABE1 and TM5 and,interestingly, includes a direct allosteric interaction between the148CT loop and TM5. The highly correlated motions between theactive site loops on slower time scales observed in thrombin:TM456 overlap directly with the different communities identifiedin the community network model. In particular, the 90CT loopcoalesces with the active site into a single community consistentwith H/D exchange experiments that identified subtle changes inthe 90CT loop only in the presence of TM456 (15). Our obser-vation of different slow time-scale dynamic behavior of the activesite loops of thrombin in thrombin:TM456 vs. thrombin:TM56

provides a mechanism for these heretofore inexplicable experi-mental results.The slow conformational loop dynamics, mainly of the active

site loops of thrombin, which only occur in thrombin:TM456,probably facilitate the association of small substrates and inhib-itors (that may enter the active site without interacting directlywith TM4), thereby increasing the association rate by severalorders of magnitude. For the specific case of the significantlyenhanced ka of protein C, two complementary mechanisms exist.First, following the work of Fuentes-Prior et al. (10), the pres-ence of TM4 forms an extended binding surface for protein C,providing optimal alignment for insertion into the active site andsubsequent cleavage. This docking and optimal alignment mech-anism probably works together with the allosteric mechanismidentified in this study, in which the altered dynamics of theactive site loops caused by TM binding increase the protein C ka.The binding of protein C to TM4 may also affect dynamics withinTM4 to enhance the allosteric network and further promoteprotein C cleavage.

MethodsCMD and Computational Details. Atomic coordinates for thrombin wereobtained from the Protein Data Bank (PDB) 1.9-Å X-ray crystal structure (PDBID code 1PPB) (12), and the initial coordinates for thrombin:TM56 and throm-bin:TM456 were taken from the 2.3-Å X-ray crystal structure (PDB ID code1DX5; chains A, M, and I) (10). The active site inhibitor was removed from allstructures. For thrombin:TM56 and thrombin:TM456, residues Arg456 andHis475, which had been mutated to facilitate crystallization, were restoredto WT. Each system was placed at the center of a periodically repeating box,and the simulation cell size was defined such that the distance between theedge of the simulation box and the surface of the solute was at least 12 Å.All simulations were performed in explicit solvent, and an appropriatenumber of Cl− or Na+ counter ions were introduced to obtain cell neutrality.A set of six standard CMD simulations was performed for each system. Foreach of these simulations, a different random seed generator for the Max-wellian distribution of atomic velocities was used, and after standard energyminimization and equilibration procedures, a 20-ns production run CMDsimulation was performed under periodic boundary conditions with a timestep of 2 fs. Bonds involving protons were constrained using the SHAKEalgorithm. Electrostatic interactions were treated using the particle meshEwald method (26) with a direct space sum limit of 10 Å. The ff99SB forcefield (27) was used for the solute residues, and the TIP3P water force field(28) was used for the solvent molecules. These initial six 20-ns CMD simu-lations acted as a control set and were used as the starting point for theAMD simulations. These simulations also provided the average (unbiased) di-hedral angle energy, <V0(dih)>, and total energy, <V0(tot)>, values used todefine the acceleration parameters in the AMD simulations described below.

AMD. The details of the AMD protocol have been discussed previously (22, 23),and only a brief summary is provided here. In AMD, a reference or “boostenergy,” Eb, is defined, which lies above theminimum of the potential energysurface (PES). At each step in the simulation, if the instantaneous potentialenergy, V(r), lies below the boost energy, a continuous nonnegative bias po-tential,ΔV(r), is added to the actual potential. If the potential energy is greaterthan the boost energy, it remains unaltered. The application of the bias po-tential results in a raising and flattening of the PES, decreasing the magnitudeof the energy barriers and thereby accelerating the exchange between low-energy conformational states, although still maintaining the essential detailsof the potential energy landscape. Explicitly, themodified potential,Vp (r), onwhich the system evolves during an AMD simulation is given by (22):

VpðrÞ = VðrÞ ; VðrÞ≥ Eb

VpðrÞ = VðrÞ+ΔVðrÞ ; VðrÞ< Eb

and ΔV(r) is defined as:

ΔVðrÞ = ðEb −VðrÞÞ2Eb −VðrÞ+ α

The extent of acceleration is determined by the choice of the boost energy,Eb, and the acceleration parameter, α. Conformational space sampling can

Fig. 6. Extended cross-correlated dynamic map for thrombin:TM456obtained from a representative free energy-weighted (level 2) AMD trajec-tory. The TM domains are defined as TM4 (residues 345–389), TM5 (residues390–426), and TM6 (residues 427–462). Magenta boxes are drawn to high-light the most significant correlations between TM domains and TM domainswith thrombin. Significant correlations within thrombin are indicated byblack boxes as in Fig. 4.

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be enhanced by either increasing the boost energy or decreasing α. In thepresent work, we have implemented a “dual boost” AMD approach (29), inwhich two acceleration potentials are applied simultaneously to the system:The first acceleration potential is applied to the torsional terms only, and asecond, weaker acceleration is applied across the entire potential. For eachof the three systems, thrombin, thrombin:TM56, and thrombin:TM456 dual-boost AMD simulations were performed at two (torsional) accelerationlevels. For the most aggressive AMD simulations (level 2), the specific ac-celeration parameters were defined as Eb(dih) − <V0(dih)> = [4 kcal/mol *No. residues], and the acceleration parameter, α(dih), was set to one-fifth ofthis value. The specific choice of these AMD parameters was based on therecent NMR/AMD study of thrombin:PPACK (details are provided in SI Text)(21). For the second, moderate AMD simulations (level 1), the α(dih) pa-rameter was kept the same and Eb(dih) − <V0(dih)> was reduced to [2 kcal/mol * No. residues]. In all AMD simulations, the total background accelera-tion parameters were fixed at Eb(tot) − <V0(tot)> = α(tot) = [0.16 kcal/mol *No. atoms in simulations cell]. For each of the three systems, six AMD sim-ulations were performed at both acceleration levels for 10,000,000 steps (theequivalent of 20-ns standard molecular dynamics). The physical conditionsand computational parameters used in the AMD simulations were identicalto those defined above for the CMD simulations, and all molecular dynamicssimulations were performed using an in-house modified version of theAMBER10 simulations suite (30). For each AMD trajectory, a corrected canonicalensemble was obtained by performing a Boltzmann free energy reweight-ing protocol using the bias potential block averaging method to removestatistical noise errors (details are provided in SI Text). In this way, six rep-resentative free energy-weighted molecular ensembles were generated atboth acceleration levels, along with the six unbiased 20-ns CMD simulationsfor all three systems.

Trajectory Analysis. Allosteric networks were characterized using a commu-nity network analysis approach previously applied to investigate allostery intRNA–protein complexes and other protein systems (24, 31, 32). This ap-proach constructs a dynamic contact map consisting of a network graph inwhich each residue is treated as a “node” connected by edges to other nodeswhen two residues are deemed to be “in contact.” The dynamic contact mapis subsequently decomposed into communities (i.e., clusters of residues) ofhighly intraconnected but loosely interconnected nodes using the Girvan–Newman algorithm (33). Central to this method is calculation of edge be-tweenness, the number of shortest paths that cross an edge. The edge

betweenness is calculated for all edges, and the edge with the greatestbetweenness is removed. This process is repeated, and a modularity score istracked to identify the division that results in the optimal communitystructure. Network graph calculations were performed using the pythonmodule NetworkX (33).

Residue-by-residue cross-correlations were calculated using the general-ized cross-correlation approach applied to all backbone Cα atomic coor-dinates based on the mutual information method developed by Lange andGrubmüller (25) using the g_correlation module in GROMACS 3.3.3 (34).

The internal dynamics were monitored by calculating backbone NHN orderparameters (S2) from the different CMD and AMD simulations, which pro-vide a quantitative measure of the extent of reorientational motion of thegiven bond vector (35). In all cases, molecular ensembles generated from thestandard CMD simulations and the free energy-weighted AMD trajectorieswere superposed onto the heavy backbone atoms of all residues for the ap-propriate average structure. Order parameters were calculated as follows (36):

S2 =12

"3X3i =1

X3j=1

Æμiμjæ2 − 1

#;

where μi are the Cartesian coordinates of the normalized internuclear vectorof interest. The resulting order parameters were then averaged over allmolecular dynamics/AMD trajectories.

Supplementary Information. Chymotrypsin and corresponding sequentialresidue numbering for thrombin is provided in SI Text. A detailed account ofthe AMD protocol, including the specific choice of acceleration levels and amore comprehensive description of the community network analysis, isprovided in SI Text.

ACKNOWLEDGMENTS. P.M.G. was supported by a Cell and MolecularGenetics (CMG) training grant (National Institutes of Health Grant T32GM007240), and this work was also supported by a grant from the Center forTheoretical Biophysics (National Science Foundation Grant PHY-0822283).B.F. and E.A.K. received support from National Institutes of Health GrantHL070999. Additional support was provided by the National Institutes ofHealth, National Science Foundation, Center for Theoretical Biological Physics(CTBP), Howard Hughes Medical Institute, National Biomedical ComputationResource (NBCR), and San Diego Supercomputer Center.

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