Probing Translocation in Mutants of the Anthrax Channel: Atomically

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Probing Translocation in Mutants of the Anthrax Channel: Atomically Detailed Simulations with Milestoning Piao Ma, Alfredo E. Cardenas, Mangesh Ishwar Chaudhari, Ron Elber, and Susan B. Rempe J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b08304 • Publication Date (Web): 19 Oct 2018 Downloaded from http://pubs.acs.org on October 26, 2018

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The Journal of Physical Chemistry

Probing Translocation in Mutants of the Anthrax Channel: Atomically Detailed Simulations with Milestoning Piao Ma†, Alfredo E. Cardenas‡, Mangesh I. Chaudhario, Ron Elber†,‡,*, and Susan B. Rempeo †Department of Chemistry, University of Texas at Aust.in, Austin, TX, 78712 ‡Institute

for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, 78712

oBiological

and Engineering Sciences, Sandia National Laboratories, Albuquerque, NM 87185

*Correspondence: [email protected] Abstract Anthrax toxin consists of a cation channel and two protein factors. Translocation of the anthrax protein factors from endosomal to the cytosolic compartment is a complex process that utilizes the cation channel. An atomically detailed understanding of the function of the anthrax translocation machinery is incomplete. We report atomically detailed simulations of the lethal factor and channel mutants. Kinetic and thermodynamic properties of early events in the translocation process are computed within the Milestoning theory and algorithm. Several mutants of the channel illustrate that long-range electrostatic interactions provide the dominant driving force for translocation. No external energy input is required because the lower pH in the endosome relative to the cytosol drives the initial translocation process forward. Channel mutants with variable sizes cause smaller effects on translocation events relative to charge manipulations. Comparison with available experimental data is provided.

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1. Introduction The transport of molecules across biological membranes is frequently assisted by the presence of channels and pumps.1-5 Pumps require an input of biological energy (such as an ATP molecule) while channels do not. Instead, channels may exploit solution conditions, such as concentration gradients, to translocate desired molecules across the cellular membrane barrier in a specific direction. An intriguing set of channels are bacterial transporters that translocate toxin proteins from the endosome of mammalian cells to the cytosol.6,7 The translocation exploits the pH difference between the endosome (low pH) and the cytosol (higher pH)8 to drive the toxin through the membrane barrier. The toxins of anthrax, diphtheria, botulinum and tetanus9 use similar mechanisms. The concrete example that we focus on in the present study is the anthrax channel and a toxin protein (lethal factor – LF) that anthrax transports to the cytosol.10 The active channel that transports the lethal factor also forms in planar lipid bilayers without the addition of other proteins.11 Given a phospholipid membrane and low pH at the entrance site makes the anthrax machinery complete, and translocation does not require assistance from cellular components. The anthrax system consists of three major parts: (i) a protective antigen (PA) that forms a cation channel after being processed, (ii) the LF, which is a zinc dependent protease that cleaves mitogen-activated protein kinase kinases (MAPKK), and (iii) the edema factor (EF), which is a calmodulin-dependent adenylate cyclase.10 The PA binds first to receptors on the cell surface, and is cleaved by a furin-related protease to obtain the protein PA63. PA63 forms a prepore complex from seven or eight identical monomers - (PA63)7-8 - that binds LF and EF. We study the complex with seven monomers. The complex is endocytosed to an acidic cellular compartment, the endosome. In the endosome, the complex undergoes a conformational change to a ring-shaped homo-heptamer that acts as a protein channel for LF. The lower pH is necessary for formation of the protein transporter in the endosome, as well as to unfold LF and allow protein ratcheting through the formed channel.12


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Fig.1 Model of the anthrax channel constructed in reference 13 and used in this work. The model is based on the crystal structure of lethal factor14 (reactant in red, product in yellow ribbons) and a cryo-EM structure of the channel15 (light blue). The  clamp and two other mutation sites are shown in space-filling models. See text for more details.

The structure of the anthrax channel was determined by cryo-electron microscopy (cryo-EM)15 (Fig. 1). The structure consists of a cap that includes the binding sites of the toxin proteins, LF or EF, and a stem composed of a beta sheet barrel that forms a “hole” through the membrane of an outer diameter of about 40 Å and inner diameter of 25-30 Å. The length of the cap and the stem are around 75 Å and 100 Å, significantly longer than a typical width of a cellular membrane (about 40 Å).16 The channel is too narrow to allow transport of stable protein secondary structural elements, such as helices, through the channel. Therefore, the transported proteins must unfold prior to translocation.17 Examining the structure of the channel more closely, we note that it is narrower near the boundary of the cap and the stem, a domain that is called the  clamp. The clamp consists of a ring of seven hydrophobic residues (phenylalanine F427), each from a different monomer. The clamp reduces the free volume accessible to the LF chain, and creates a checkpoint for proton transport. The coordinates of LF bound to the channel cap were determined by X-ray crystallography.14 An unstructured component of the LF protein is the N terminal segment (LFN), with a sequence AGGHGDVGMHVKEKEKNKDENKRKDEERNK. The sequence includes 17 charged residues out of a total of 30 (not including the histidine residues and the charge of the N-terminus). The N terminus is believed to enter the channel first,18 Therefore, the hydrophobic clamp also creates a significant dielectric barrier for displacement of the charged groups of LFN.


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The overall delivery of LF toxin from the endosome to the cytosol can be divided into two major steps: (i) pore formation and (ii) translocation. Experiments were conducted to differentiate between factors that influence these steps. The unique features of the channel  clamp motivated a considerable body of experimental research.19-21 In particular, F427 of the clamp was mutated to several residues. The function of the mutants, especially their ability to assemble into a channel and capacity for translocation, were examined in vivo. The effects of variable pH and electric field gradients were also studied in lipid bilayers. Most experiments focus on the translocation of LFB (LF binding domain). Lysine (K), aspartic acid (D), or alanine (A) at position 427 inhibited the pH-induced pore formation step, whereas tryptophan (W), or histidine (H) had virtually no effect on this step, as shown in Table 1.21 F427 side chains are close to one another, and it was suggested by experiments that hydrophobic and or stacking interactions between aromatic (Trp, Tyr and His) or aliphatic side chains (Leu), or hydrogen bonds could foster prepore-to-pore conformation transition and stabilize the channel, whereas electrostatic repulsions (Asp, Lys, Arg) between side chains inhibit the conversion. 20,21

In this study, we investigated computationally the translocation step of LF delivery through several of the channel mutants that were examined experimentally.21 In Table 1, we list the experimental results for the wild type (WT) and selected mutants. Table 1: Ability to form a channel and to translocate LF by wild type (WT) and mutants of PA in vivo, as reported in.21 PA Pore Formation Translocation (reported as cytotoxicity) WT(F) ++++ + F427A ++ F427W ++++ + F427H ++++ F427D + F427K Pore formation is ranked according to activity, ++++ 75-100% of the wild type, ++, 30-50% of the wild type, + 5-30% of the wild type. Cytotoxicity is either toxic (+) or non-toxic (-). Additional information was provided in reference 8, in which the translocation of LF by different channel mutants was examined for effects from various pH and electric field gradients ( pH and  ) in planar lipid bilayers. Both fields have significant effects on translocation and we discuss some pertinent observations for the mutants mentioned above. The half lifetimes t1/2 of the complete LFB translocation through the channel was measured for different mutants.8 LFB translocation is the fastest through the wild type channel with or without pH gradient. The mutant F427D is the worst transporter and barely active (Table 2 of reference 8). This channel mutant shows marginal permeability with a t1/2 that is


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about one hundred times longer than that of the wild type. The lysine mutation is inactive. These observations are consistent with experimental findings that leading positively charged residues of LFN interact with the mutated residues and alter translocation.22 The alanine mutant, according to Table 2 of reference 8, translocates LFN ten times slower than the native channel, but only a factor of 2-3 times slower than the tryptophan mutant. Hence, even though the alanine channel is less stable than the tryptophan channel, the translocation rates differ by a small factor. The F427A mutant is not influenced significantly by pH gradient since the  clamp that forms an efficient barrier for proton permeation is less effective after the mutation. The smaller alanine residue reduces the barrier. The F427W channel translocation rate benefits significantly from the presence of a pH gradient (by a factor of 11), while F427A enhances translocation with pH gradient by only a factor of 3. For comparison, the rate enhancement of the native channel by pH gradient is a factor of 17. Recently we investigated the initial events of LF translocation through the wild type channel.13 We examined the translocation of LFN into the channel and past the  clamp using molecular dynamics simulations and the Milestoning theory.23 We illustrated a profound impact of the protonation state of the permeating LFN on the free energy landscape and on the mean first passage time (MFPT) of the translocation process. Others used umbrella sampling to compute free energy profiles for translocation through the anthrax channel.24 We showed that maximum protonation states of the different residues of LFN were consistent with experimental observables and with the attractive model of the channel as a ratchet.12 Here, we expand our earlier investigation and examine the effect of the mutations listed in Table 1 and several other residues motivated by our early simulations. Prior works proposed that the pH gradient helps the anthrax channel act as a non-equilibrium ratchet.12 For an effective ratchet, we expect an energy landscape that strongly motivates the system to go forward, instead of backward. The emerging landscape makes the approach to equilibrium, which requires reversibility of reactions, unlikely. Hence the LF translocation is strongly biased toward the cytosol and the probability of returning to the endosome is negligible. We recently computed the free energy profile and the kinetics along the anthrax channel and showed that the channel does behave like a ratchet for high protonation state.13 The existence of ample experimental measurements of structure14-16 and function10 makes the anthrax PA channel a good candidate for theoretical studies of the mutants. The present investigation provides atomically detailed pictures and mechanisms of the transport, illustrates that the process is driven by electrostatic interactions, and shows that translocation can be manipulated by steric and charge


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variations that affect stability and/or permeability of the channel. Remarkably, the early step of the process, translocation of LFN only, correlates well with a wide range of observations for the complete translocation process of the toxin transport. Complete toxin transport includes LF unfolding, complete passage to the cytosol, and LF refolding. 2. Methods 2.1 System Preparation The atomic model of the protective antigen pore (PA channel) is based on the cryoEM structure15 (PDB: 3J9C). We modeled the unstructured 28 N-terminal residues of LF based on the crystal structure14 (PDB: 1JKY) using Modeller 9.17.25 The LF and the channel were docked to match the experimental structure of LF binding to the PA channel (PDB: 3KWV).26 We solvated the protein in a cylinder of explicit aqueous solution of 100 mM NaCl and TIP3P water molecules. A half-harmonic potential with a force constant of 10 kcal/mol Å2 was applied at the boundary and restrained the solution in the cylinder. The radius of the cylinder is 85 Å and its height is 310 Å. The total number of atoms is about 680,000. 2.2 Atomically Detailed Simulations of the Channel Mutants and Milestoning23,27 The parallel version of the NAMD program28 and CHARMM 36 force field29 were used in the simulations. The -clamp is flexible and free to move, and we observed significant movements of the side chains of -clamp residues. The fluctuations are influenced by the -clamp mutations and the location of the permeating LFN. For the reactant position of LFN, we computed fluctuations of the -clamp residues to be 0.97 Å and 0.95 Å for the wild type and F427W channels, respectively. At the product position of LFN (the permeating peptide passing the -clamp), we have 1.10 Å for the wild type and 0.75 Å for F427W. Hence, the tryptophan residue restricts somewhat the thermal motions at this important position. The translocation of the N-terminal segment of LF is modeled with milestones along a one-dimensional reaction coordinate. The coordinate is the distance along the channel axis between the N-terminus of LF and the center of mass of the  -clamp. An initial structure at each milestone is generated by steering the N-terminus of LF along the channel. This procedure was used and described in our previous simulations of the wild type (WT) channel.13 We modeled the mutants of F427 of the anthrax channel using VMD.30 The modeling was carried out at each milestone along the reaction coordinate. We generated seven mutants: F427A, F427W, F427H, F427K, F427D, G474V and E465K. We further considered two states of the histidine mutant F427H: (1) protonated F427HP, and (2) not protonated F427H. The structures obtained from each of the mutations were minimized for 1000 conjugate gradient steps. Sampling configurations conditioned to be at the milestones were conducted as follows: The N


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terminus was restrained to the milestone by a harmonic potential with a force constant of 500 kcal/mol Å2. A sampling trajectory of 2.5 ns was conducted with the restraint. The first 500 ps were considered equilibration and omitted. We saved configurations every 10 ps during the remaining 2 ns of the trajectory. Thus, the sample at each milestone consists of 200 structures. The next step is to run short trajectories until they hit for the first time another adjacent milestone. The trajectory data were analyzed to get the free energy, MFPT (mean first passage time) and reverse MFPT of the early translocation process with the Milestoning theory.23,31 The calculations of the mutants follows the algorithms presented in the previous paper, in which the WT was simulated.13 The initial conditions at each milestone  are characterized by the distribution in the milestone q  x  where x is the position in milestone  . Once the initial conditions are prepared, we launch trajectories starting from the initial configurations until the trajectories hit for the first time another milestone  . The statistics of hits determine the transition probabilities from milestone  to  or





the kernel, K x , x . Let n be the number of trajectories initiated at milestone

 . Let n be the number of trajectories initiated at milestone  and are terminated at milestone  . We estimate the transition probability between the two milestones as K  n n . We also determine the milestone average lifetime, t . Let t l be the length of a trajectory l that was initiated at milestone  until it L

terminated at any other milestone. The average lifetime is given by t   t l , l1

where L is the total number of trajectories that we initiated at milestone  . With K and t in hand, we are ready to use the Milestoning theory.31 The basic Milestoning equation is for the stationary flux, which in a vector matrix form we write as q s t  q s t K , and solve numerically for the stationary flux. The free energy at



the milestone is given by F  kT log qs, t



and is computed with reflecting

boundary condition at the product state. The mean first passage time (MFPT) is    qs, t qs, f where qs, f is the flux at the product milestone, which is set in the 

MFPT calculation to be absorbing. 2.3 Mutants For each mutant, we consider three protonation conditions representing, low intermediate and high values of pH: (i) H, E, D, K and R all protonated; (ii) H, K, and R protonated, but D and E not; (iii) K and R protonated. In (i) – (iii), we approximate the protonation state as fixed. Only the results of (i) are reported in the main text. The results for (ii) and (iii) are in the Supplementary Information. The high


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protonation state (low pH) was found in our earlier study of the wild type to match the experimental behavior better than other protonation states.13 2.4 Modeling a constant pH and a variable protonation state of F427H For each configuration at the milestones, we compute the pKa of the histidine F427H of the anthrax channel at pH=5 using the program PROPKA3,32 which is implemented in PDB2PQR.33 The pKa values are estimated for the 200 sampled structures, and are shown in Fig. 2 (left panel). Based on the pKa, we estimated the protonation probability as P  exp  pKa-pH   exp  pKa-pH   1 , the average protonation probability for H427 as a function of the reaction coordinate is shown in Fig. 2 (right panel). This estimate makes it possible to model a variable protonation state. The trajectories between milestones have a fixed protonation state. However, the protonation state is allowed to change at the milestone and is sampled from the above distribution. We modified the transition matrix and the lifetime to include different protonation probabilities at each milestone  - p . 𝐾𝛼𝛽 = 𝑝𝛼𝐾F427HP + (1 ― 𝑝𝛼)𝐾F427H 𝛼𝛽 𝛼𝛽 F427H ( ) 𝑡𝛼 = 𝑝𝛼𝑡F427HP + 1 ― 𝑝 𝑡 𝛼 𝛼 𝛼 2.5 The Electric Fields of Channel Mutants The wild type PA channel was solvated in a 212*155*156.8 Å3 box of aqueous solution of 100 mM NaCl. The system was minimized for 1000 steps. Next, the protein was constrained and a 100 ps simulation conducted to relax the water distribution around the protein. A constant pressure simulation (NPT) at 1 atmosphere was then conducted for 500 ps to determine an equilibrated volume. The final structure of the NPT simulation was used to model the seven  -clamp (F427) mutants. A trajectory of 6 ns was run for the WT and for each of the mutants of the PA channel. The first 500 ps was considered an equilibration and ignored. Structures of the remaining 5.5 ns trajectory were saved each 25 ps and used to calculate the electric field of the channel with the particle meshed Ewald (PME) algorithm.34,35 The reported electric field is an average over the ensemble of configurations. 2.6 Statistical Analysis Statistical errors in trajectory sampling and their effect on the free energy and the MFPT were discussed in Ref. 13. We follow the same protocol in the present study. In brief, the elements of the transition matrix, K , are assumed to be sampled from the  distribution

 

P K 

  n 

  

 n  n  n



n 1

K

1 K 

n n 1




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The Milestones average life times, t , are sampled from a normal distribution with a 2  2 1 1 1   2 mean t   t l , and a variance    tl   L  tl   . L l L  L  1 l  l 

We consider a total of 1,000 samples of transition matrices and lifetime vectors: K and t . For each of the samples we compute the free energy and the MFPT. The resulting distributions of the free energy and the MFPT determine the error bars. 3. Results 3.1 Protonation state of F427H We consider first the mutation of the phenylalanine at position 427 to histidine. This mutation is particularly intriguing because the overall size of histidine and its aromatic character are similar to phenylalanine. In contrast to phenylalanine, histidine can be protonated at moderate pH conditions. Changes in the charge value at the  clamp can have a profound effect on translocation rate. The flips in protonation states of the histidine residue require modeling to understand better the behavior of this mutant. Sophisticated algorithms to model variable protonation states in equilibrium are available.36-38 However, the complexity of the system at hand and the desire to investigate non-equilibrium kinetics motivated us to look for a simple modeling approach for varying protonation state. We use the empirical program PROPKA3 to predict the pKa of the  -clamp histidine for individual structures.32,33 All the sampled structures of the Milestoning simulations along the translocation coordinate (see Methods) were input to the program and results were averaged for each of the reaction coordinate values. The endosomal pH was set to ~ 5, which allows us to calculate the probability that the H427 is protonated.

Fig. 2. Predicted pKa and protonation probability for the mutated histidine residue H427 as a function of the reaction coordinate. The pH is set to 5.


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As the N terminus of LF, which is positively charged, approaches closer to the  clamp coordinates (~0 along the reaction coordinate in Fig. 2), the pKa decreases and the histidine is less likely to be protonated. Hence, the presence of a permeating N terminal inside the channel alters the protonation state of channel residues. The mutant F427H is likely to be unprotonated when the LFN is near the  clamp. According to experiment (Table 1), the channel assembles, but does not transport the toxin protein. Our discussion so far explains how the channel can become stable in the presence of LFN. In the next section, we explain why the channel does not conduct. 3.2 General consideration for the translocation of LFN through the  clamp The calculations in this section were conducted using the theory and algorithm of Milestoning.23,31 Milestoning provides the free energy profile and the rate of the process. More precisely, the Milestoning algorithm makes it possible to compute all the moments of the first passage time, in addition to the free energy, in the space of coarse variables.31 Typically, only the first moment of the first passage time distribution, the mean first passage time (MFPT), can be computed or measured experimentally. A similar technology was used in our earlier investigation of anthrax.13 See Methods and Supplementary Information for details. The N terminus of the anthrax lethal factor (LFN) contains 30 residues, of which 28 are not detected by X-ray crystallography.14 The sequence AGGHGDVGMHVKEKEKNKDENKRKDEERNK contains eighteen charged elements, eight negatively and nine positively charged amino acids under neutral pH conditions and the N terminal. We do not include histidines as charged residues. As a consequence, the N terminus is expected to be well solvated in water and believed to be unstructured. Despite the lack of a well-defined conformation, LFN is critical for the translocation process. A lethal factor with its N-terminal segment removed does not translocate through the channel even though binding of LF to the mouth of the channel is unaffected.11 Evidence is available that the translocation of LFN initiates the translocation process.18 Our calculations focus on this initial step. In our earlier study,13 we considered limiting protonation conditions: (i) H, E, D , K and R all protonated, (ii) H, K, and R protonated, but D and E not, (iii) K and R protonated. In (i) – (iii), we used the approximation of a fixed protonation state. The results showed a profound effect of protonation state on translocation, with the high protonation state (model (i)) acting like a ratchet.12 Here, we performed a similar set of studies for all the mutants listed in Table 1 and two additional mutants G474V and E465K (Fig. 1). We also explored a kinetic model in which the channel  -clamp histidine (F427H) protonation state changed according to the environmental pH of 5. The mutants G474V and E465K contain mutations in two non-  -clamp positions in the channel that were suggested by an


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analysis of the Milestoning calculations. We counted the number of close encounters (collisions) between the channel residues and the LFN and determined that G474V and E465K have the largest number of collisions of non-  -clamp residues with LFN.13 We mutated the glycine to a bulkier residue and switched the negative charge of glutamic acid at 465 to a positively charged lysine to assess whether these sites have a significant effect on translocation. Those mutations were not studied experimentally. The results are, therefore, predictions that we hope will be tested in a wet laboratory. For clarity, we discuss in the main text only the investigations of the fully protonated LFN (model (i)). The results for alternative protonation models (models (ii)-(iii)) are described in the Supplementary Material (Figs. S1 to S8). 3.3 LFN translocation through mutants of the  clamp that are charged In Fig. 3, we show the free energy along the reaction coordinate for the translocation of LFN starting from the channel mouth (near the  clamp) and passing the  clamp. The reaction coordinate is the position of the backbone nitrogen of the first residue of LFN along the channel axis. The coordinate is zero at the  clamp. The initial and final states of the calculation are illustrated in Fig. 1.

Fig. 3. The free energy profile computed for the translocation of the N terminal of the lethal factor through the anthrax channel (see Fig. 1 for the positions of the reactant and product). The reaction coordinate is the position of the N-terminal residue along the channel axis. The  clamp is near zero. See text for more details.


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The WT profile is replotted using the same data reported in reference 13. The other two free energy curves on Fig. 3 are for the two charged  clamp mutants, F427D and F427K. As the anthrax channel is cation selective, changing the hydrophobic residue of phenylalanine to a negatively charged aspartic acid enhances translocation of the positively charged LFN. Experimentally, however, F427D functions only marginally, an observation that was attributed to the reduced stability of the channel complex.21 If assembly of F427D could be stabilized, then we predict a highly efficient translocation of LFN through the  clamp. Calculations of the free energy profile were conducted under the condition that the channel is stable, in contrast to experimental results, and hence the disagreement in the comparison. The lysine mutation is not only unstable, but it also repels other positive charges. The double disruption of the channel function (poor channel construction and poor support for translocation) makes F427K a failed transporter, as observed experimentally. Fig. 2 of reference 21 shows that the K mutant does not function as a channel, while D shows weak permeability. Qualitatively, Fig. 3 agrees that F427D is a better channel than F427K. Fig. 4 examines the mean first passage time (MFPT) along the reaction coordinate of the same channels as in Fig. 3. The MFPTs forward and backward are shown in the left and right panels, respectively. For an efficient transporter, the forward MFPT should be much shorter than the MFPT backward, thus committing the system to going forward. Such a setup can be achieved by having a deep free energy minimum at the product side without a significant barrier along the pathway. Or that setup can be achieved by a kinetic design for a non-equilibrium system as a ratchet 12 that permits only forward reaction.

Fig. 4 The forward (left panel) and backward (right panel) mean first passage times (MFPTs) of the translocation of LFN mutants through the anthrax channel as a function of the reaction coordinate. The MFPT is in picoseconds and shown using a logarithmic scale. The reaction coordinate is the position of the N terminus along the channel axis. The zero is the approximate position of the  clamp.

In Fig. 4, we show the translocation times as a function of channel depths for three channels: WT, F427D and F427K. The time scale forward is exceptionally short for the native and the aspartic acid mutant, as we expect from the free energy profiles. The backward times suggest that the wild type and the aspartic acid mutant lock the


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LFN past the  clamp, as the time backward is exceptionally slow. The lysine mutant experiences a large barrier going forward with a time scale of milliseconds. Going backward is extremely fast for F427K and is in the nanosecond time scale. 3.4 LFN translocation through uncharged mutants of the  clamp Fig. 5 examines LFN translocation for two hydrophobic mutations at the ends of the size scale: alanine and tryptophan. Experiments report that the F427W mutant forms pores as stable as the native channel.21 Here, we examine the translocation under the assumption that a channel is formed.

Fig. 5 The free energy profile for the translocation of LFN through the anthrax channel for the wild type (WT) and for two hydrophobic mutants at the  clamp: alanine and tryptophan. See text for more details.

The free energy profiles for LFN translocation are strikingly similar for F427W and F427A mutants and are significantly different from the native. This observation agrees with Table 2 of reference 8. The profile for the native protein decreases mildly as a function of the reaction coordinate and then drops sharply into a significant minimum of -8 kcal/mol past the  clamp. In contrast, the free energy landscape for F427A and F427W are mostly flat and show only modest and gradual decline to about -4 kcal/mol. Both mutations perturb translocation, but using different mechanisms. F427W makes the  clamp narrower and creates a steric barrier at this critical position. Such a barrier is expected to reduce the translocation


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rate (Fig. 6 left panel). F427A poses a smaller steric barrier, but its smaller size suggests poor locking of the LFN past the  clamp. In Fig. 6, we plot the forward and backward MFPTs of the two mutants and the wild type channels. The time courses illustrate the significance of the  clamp as a critical bottleneck, in accord with recent experiments.39 The bottleneck can be effective in both forward and backward reactions. For translocation efficiency, the permeating chain is not only motivated to go forward, but is also blocked from going backward. The latter profile is at least as important as the former. For example, we observe that the backward rate of the wild type is significantly slower near the  clamp. Another example concerns the alanine mutant, for which the backward reaction is not slowed down even while the forward rate is similar to the wild type, making that channel a significantly less effective transporter.

Fig. 6 The forward (left panel) and backward (right panel) MFPT for the translocation of LFN past the  clamp mutants F427A and F427W. Note the significant rise in the forward translocation time for the tryptophan mutant, reflecting a significant barrier at the clamp position.

The free energy profiles of both mutants are combinations of the forward and the backward rates and are similar (Fig. 5). However, the tryptophan mutant is slower to cross the barrier forward compared with the alanine mutant. The lack of significant barrier for LFN forward translocation or retreat in the alanine mutant supports the “flickering” model proposed earlier.20 The LFN passes easily the  clamp in F427A, similar to the native protein. But the WT locks the LFN chain after passing the ring of phenylalanine residues. This locking is reflected in significant slowing of the MFPT backward (Fig. 6 right panel). Faster backward reaction is observed for the alanine mutant, which is not committed to go forward and diffuses backward easily. Interestingly, the backward reaction is also faster for the tryptophan mutant compared with WT, which explains why F427W is not a better translocator in our simulations than the alanine variant. F427W is slower at the beginning of the reverse reaction, but as the reaction progresses backward, the overall MFPT becomes comparable to the mutant F427A and significantly faster than the


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backward reaction of the wild type. Experimentally, the tryptophan mutant is a somewhat better translocation machine than the alanine mutant, which we attribute to stability considerations, and retention of pH gradient because the alanine  clamp is more open than the wild type and cannot block proton permeation efficiently. Indeed, experiments also suggest that F427A is a less stable channel than F427W which, of course, affects translocation. In the present study, however, we do not consider channel stability. 3.5 LFN translocation through a histidine mutant of the  clamp with variable protonation In Fig. 7, we show the translocation free energy profile for F427H (dark blue) and F427HP (red, HP is a protonated histidine). The positively charged histidine shows markedly different behavior from the unprotonated channel, with a significant barrier at the  clamp. This barrier is consistent with the experimental finding that the F427H mutant does not translocate LF.21 We also show a free energy profile with an alternative protonation state for H427 (light blue).

Fig. 7 The translocation free energy of LFN through the channel with a histidine substitution. We show the free energy profile for a neutral histidine F427H (dark blue) and the protonated histidine F427HP (red). Also shown is the free energy for a model histidine that switches between protonation states according to an independent estimate of its pKa (Fig. 2). Since the histidine is predicted to be protonated most of the time, the curve for the switching histidine is close to that of the protonated histidine. See Methods and text for more details.


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Using Milestoning theory and pKa calculations (Fig. 2), we model the equilibrium protonation of histidine 427 (see Method). The simplifying assumption we use is that the protonation state changes much more rapidly than motion along the reaction coordinate. Hence, the protonation state is assumed be in a local equilibrium determined by the value of the pKa as the LFN chain progresses along the reaction coordinate. Since the channel is designed to transport positively charged ions, and the LFN is positively charged overall, the addition of electrostatic repulsion (protonated histidine) at the critical barrier of the  clamp significantly diminishes the translocation. 3.6 LFN translocation through the wild type channel and its  -clamp mutants is guided and enforced by the electric field The observation of significant slowdown of the lethal factor translocation by an addition of positive charges to the channel illustrates a general design principle of the anthrax channel. The primary drive for translocation is of electrostatic support for the transport of positively charged species. We expect that mutations anywhere along the channel, not necessarily in the  clamp, that modify the electric field felt by the permeant protein will have a significant effect on translocation. Considerable support for this picture is already available in the mutants F427K and F427HP that block translocation. Experimentally, the mutant F427D shows marginal permeability due to the enhancement of the channel’s ability to pull inside a positive charge, even though the structure of the channel complex is defective. In Fig. 8, we compare the electric fields computed for the wild type and the mutant F427D. The more significant reach of the negative electric potential explains the predicted rapid translocation of LFN and the profound effect this mutation has on the forward and the reverse rates (Fig. 4). Of course, this prediction is conditional on a stable pore formation while experimental evidence suggests that the channel is only marginally stable.21 A second stabilizing mutation (beside F427D) or a mixture of monomers (e.g., a mix of F427W and F427D mutants) may produce a more stable pore and much faster translocation rate than the native channel.

Fig. 8 The electrostatic field computed using an average over configurations from 6 ns molecular dynamics trajectories of the WT (right) and of the F427D mutant (left). Red color denotes negative electric potential (attractive to cations). The channel mouth is on the left


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of each panel at the endosome. Note the more significant reach of the negative electric potential toward the channel mouth in F427D. The electrostatic fields for other mutants of the channel are shown in Supplemental Information (Fig. S9).

In contrast to the strong effect of electrostatic fields, we have seen a more limited influence of spatial constraints, channel narrowing, and enhanced packing on translocation. The two uncharged mutants, F427W and F427A, do not show significantly different translocation in our calculations. 3.7 The effect of non  -clamp mutants on translocation To further explore the effects of volume and charge on translocation, we consider two new mutants: G474V and E465K. Both mutants are non  -clamp (see Fig. 1 for location). The first mutation replaces a small residue (glycine) by a bulkier one (valine). The second mutation converts the negative charge of glutamic acid (E) to the positive charge of a lysine (K). The selection of these sites was done according to a collision count conducted in reference 13. In Fig. 9, we show the forward and backward MFPT for those mutants. For comparison we also show, on the same scale, the time courses for the wild type.

Fig. 9 The forward (left panel) and backward (right panel) MFPTs as a function of the reaction coordinate for the mutants G474V (red) and E564K (green). Also shown is the wild type protein (black). See text for more details.

The left panel of Fig. 9 illustrates that the forward reaction is affected more significantly by changes in charge than by steric effects. On one hand, changing glycine to valine hardly slowed down the mean first passage time along the reaction coordinate. On the other hand, modifying the typically negatively charged residue of glutamic acid to a positively charged lysine slowed down the forward translocation by 1-2 orders of magnitude. Interestingly, the backward reaction shows an unexpected behavior. The backtracking of the LFN is the fastest for G474V, with E465K a close second. The WT is the slowest to backtrack. While it is not surprising that the presence of lysine delayed forward movement of positive charges of the LFN and sped up backward motion of LFN, it is less clear why a bulkier residue


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(valine versus glycine) would make the backward translocation faster by more than one order of magnitude. Overall, the WT channel is the most efficient transporter. It is the channel variant that supports fastest forward translocation and slowest backward translocation. 4. Discussion In the present study, we used atomically detailed simulations with advanced sampling techniques to investigate the initial translocation of the anthrax lethal factor. We studied the translocation of the unstructured N terminal segment of the lethal factor until it passes the  clamp. We compared features of the early translocation events with global measures of LF translocation and toxicity in several mutants. These global measures are available experimentally, and provide ample data for comparisons and further study. Since many of the experiments study the entire translocation process of LFB and the simulation addresses only the early events, we are able to partition the effects of different steps of the toxin delivery. However, quantitative comparison of experiments to theory is difficult to make since the two methods do not probe the same observables. The first observation, for which the theory is consistent with experiment and is supported by the study of mutants, is the profound effect of electric field manipulations on translocation. The anthrax toxin exploits the pH difference between the endosomal and cytosolic compartments, and the placements of its own charges to drive forward several critical elements of the translocation process. The experiments discussed in reference 21 illustrate two critical steps of translocation: pore formation and protein translocation. Pore formation is mainly driven by the low pH in the endosome while the translocation step is influenced by the pH gradient. We also anticipate that unfolding of the LF protein in preparation for translocation through the narrow channel is also assisted by the low solution pH in the endosomal compartment. We studied only one step of the transport process, the translocation of the unstructured N terminal segment of the LF protein. Once the channel is formed with the LF and EF proteins bound to it, the translocation of the N terminal is the initiation step for the transport of the lethal factor to the cytosol. In reference 13, we showed that this single step is affected profoundly by the lower pH in the endosomal compartment. At the limit of maximum protonation, the free energy profile and the MFPT for LFN translocation suggest that the system operates like a ratchet. In other words, the system supports barrier-less forward motion of LFN, but presents a high barrier for backward displacements. Forward-translocation-only is a nonequilibrium process since detailed balance is broken by the removal of reversed translocation of LFN.


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The new data presented in this article illustrates that manipulating the channel charges by point mutations affects the translocation of LFN. For example, the mutation E465K replaces a negative charge in the channel by a positive one. As a result, this variant slows down the forward rate by repelling the incoming positively charged LFN and speeds up the backward translocation. The mutants F427D and F427K show a similar effect with respect to the sign of the charge, both experimentally and computationally (Fig. 4 and reference 21), although other factors also play a role in global translocation. It is not surprising that the lysine mutant that carries another positive charge does not support translocation. Computationally, however, the aspartic acid mutant is predicted to be a good transporter, as is also illustrated in the induced electric field in Fig. 8. Experimentally, however, F427D does not translocate the LF protein.21 We hypothesize that the channel is distorted as a result of the last mutations. The calculations are conducted under the constraint that the structural deviations of the channel mutants from the WT are small. Experimentally, mutating the  -clamp phenylalanine residue to a charged residue significantly decreases the pore stability and its ability to form. The lysine mutant perturbs translocation at two levels, channel formation and free energy profile for transport. The combination of two factors makes the lysine mutant non-toxic. D427 is also less stable than the wild type due to the insertion of a charge in the hydrophobic ring at the  clamp, which increases the electrostatic repulsion. However, since the negatively charged residues are well placed to support LFN translocation, that channel variant retains marginal capacity for translocation according to experiment.7 It is also possible that the aspartic acid at the 427 position is protonated with finite probability.21 The simulations were conducted while forcing the channel to remain stable and, therefore, probe only the translocation pathways. Under these conditions, the computations found F427D to be a good transporter. Experimentally21, however, F427D transports ions but not the whole LF protein. It is possible that a perturbation to the channel prevents the translocation of the whole protein but impact less the early events of the process. A second observation concerns a mutant with an unexpected behavior: F427H, which can be protonated or not. Experimentally, it was shown that the histidine mutant is able to form a channel.21 This observation suggests that the histidine is uncharged since its size and physical properties are similar to phenylalanine. Surprisingly, however, the cytotoxicity of the F427H mutant was low. According to our pKa calculations, the tendency of F427H to acquire a proton is a function of the translocation depths of LFN (Fig. 2). The following dynamic picture is therefore proposed. The presence of LFN partially induces change of protonation state of the F427H to an uncharged state. But the histidine remains positively charged most of the time, and rejects the LFN chain. The transient characteristic of the charge, however, allows some uncharged histidine that supports channel integration and translocation of positive ions like potassium and rubidium.21


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Finally, we comment on size effects, which are found to be significantly smaller than the manipulation of electrostatic fields. Size affects mostly the backward translocation rates, while electrostatic adjustments operate in both directions and tend to alter translocation more strongly. For example, changing F427 to alanine speeds the backward translocation of LFN, creating a flickering state in which LFN is not locked in. That observation is in accord with experiment.20 The tryptophan mutation alters both forward and backward translocation, which makes the transport slower than the wild type. Nevertheless, the simulations suggest that the combined effect of tryptophan substitution on the effective free energy profile is comparable to the alanine mutant. Experiments indicate that the tryptophan mutant is the better transporter.21 This observation can be explained by a reduced channel stability of the F427A mutant or a weaker retention of the pH gradient across the channel. 5. Conclusions In the present investigation, we combined molecular dynamics simulations, steered molecular dynamics, and the method of Milestoning to shed light on early events during the translocation of the lethal factor of anthrax through the anthrax channel. By examining the free energy profile and the mean first passage time, we illustrated that the electric field is the prime driving force of the translocation. The electric field can be adjusted by varying the pH and the protonation state of channel and permeating residues, or by site directed mutagenesis of the channel amino acids. We explored essentially all possibilities in the present manuscript, and showed that the translocation is consistent with the electric field as a prime driver and with available experimental data, with the single exception of F427D. In future studies, it will be of interest to examine channel assembly, by the impact on stability of point mutations that were examined experimentally and can be probed computationally by free energy simulations and thermodynamic cycles.40 6. Supporting Information The free energy and MFPTs results of LFN translocation under alternative protonation models (models (ii)-(iii)) (Fig. S1 to S8). The electrostatic fields for mutants of the channel (F427W, F427A, F427H, F427HP, F427K, E465K, and G474V) (Fig. S9)

7. ACKNOWLEDGMENTS This work was supported by an NIH grant GM59796, a Welch grant F1896, and by the Defense Threat Reduction Agency-Joint Science and Technology Office for Chemical and Biological Defense (IAA no. DTRTA10027IA-3167). Sandia National Laboratories (SNL) is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA- 0003525. The work was performed,


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in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. DOE’s Office of Science by Los Alamos National Laboratory (contract no. DE- AC52-06NA25396) and SNL. The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government. AUTHOR CONTRIBUTIONS RE is the corresponding author. He supervised the work and wrote the paper. All authors conceived the project, discussed the results, and edited the paper. PM and AES conducted the simulations, and PM performed the numerical analysis. DECLARATION OF INTERESTS The authors declare no competing interest.


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8. References (1) Hille, B.; Ion channels of excitable membranes; Sinauer Associates: Sunderland, 2001. (2) Roux, B.; Ion conduction and selectivity in K+ channels. Ann. Rev. Biophys. Biomol. Struct. 2005, 34, 153-171. (3) Varma, S.; Rogers, D. M.; Pratt, L. R.; Rempe, S. B. Perspectives on: Ion selectivity design principles for K+ selectivity in membrane transport. J. Gen. Physiol. 2011, 137, 479-488. (4) Nestorovich, E. M.; Bezrukov, S. M. Obstructing toxin pathways by targeted pore blockage. Chem. Rev. 2012, 112, 6388-6430. (5) Vermaas, J. V., Rempe, S. B., & Tajkhorshid, E. Electrostatic lock in the transport cycle of the multidrug resistance transporter EmrE. Proc. Natl. Acad. Sci. U.S.A. 2018, 115, E7502-E7511. (6) Zhao, J. M.; London, E. Similarity of the conformation of diphtheriatoxin at high-temperature to that in the membrane-penetrating low-pH state. Proc. Natl. Acad. Sci. U. S. A. 1986, 83, 2002-2006. (7) Alouf, J.; Ladant, D.; Popoff, M. The comprehensive sourcebook of bacterial protein toxins; Elsevier, 2015. (8) Krantz, B. A.; Finkelstein, A.; Collier, R. J. Protein translocation through the anthrax toxin transmembrane pore is driven by a proton gradient. J. Mol. Biol. 2006, 355, 968-979. (9) Hoch, D. H.; Romeromira, M.; Ehrlich, B. E.; Finkelstein, A.; Dasgupta, B. R.; Simpson, L. L. Channels formed by botulinum, tetanus, and diphtheria toxins in planar lipid bilayers - relevance to translocation of proteins across membranes. Proc. Natl. Acad. Sci. U.S.A. 1985, 82, 1692-1696. (10) Young, J. A. T.; Collier, R. J. Anthrax toxin: Receptor binding, internalization, pore formation, and translocation. Ann. Rev. Biochem., 2007, 76, 243-265. (11) Zhang, S.; Udho, E.; Wu, Z. Y.; Collier, R. J.; Finkelstein, A. Protein translocation through anthrax toxin channels formed in planar lipid bilayers. Biophys. J. 2004, 87, 3842-3849. (12) Feld, G. K.; Brown, M. J.; Krantz, B. A. Ratcheting up protein translocation with anthrax toxin. Protein Sci. 2012, 21, 606-624. (13) Ma, P.; Carednas, A. E.; Chaughari, M. L.; Elber, R.; Rempe, S. B. The impact of protonation on early translocation of anthrax lethal factor: Kinetics from molecular dynamics simulations and milestoning theory. J. Am. Chem. Soc. 2017, 139, 14837-14840. (14) Pannifer, A. D.; Wong, T. Y.; Schwarzenbacher, R.; Renatus, M.; Petosa, C.; Bienkowska, J.; Lacy, D. B.; Collier, R. J.; Park, S.; Leppla, S. H.; et al. Crystal structure of the anthrax lethal factor. Nature 2001, 414, 229-233. (15) Jiang, J. S.; Pentelute, B. L.; Collier, R. J.; Zhou, Z. H. Atomic structure of anthrax protective antigen pore elucidates toxin translocation. Nature 2015, 521, 545-U323.


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(16) Nguyen, T. L. Three-dimensional model of the pore form of anthrax protective antigen. Structure and biological implications. J. of Biomol. Struct. Dyn. 2004, 22, 253-265. (17) Basilio, D.; Jennings-Antipov, L. D.; Jakes, K. S.; Finkelstein, A. Trapping a translocating protein within the anthrax toxin channel: implications for the secondary structure of permeating proteins. J. Gen. Physiol. 2011, 137, 343-356. (18) Zhang, S.; Finkelstein, A.; Collier, R. J. Evidence that translocation of anthrax toxin's lethal factor is initiated by entry of its N terminus into the protective antigen channel. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 16756-16761. (19) Sellman, B. R.; Nassi, S.; Collier, R. J. Point mutations in anthrax protective antigen that block translocation. J. Biol. Chem. 2001, 276, 8371-8376. (20) Krantz, B. A.; Melnyk, R. A.; Zhang, S.; Juris, S. J.; Lacy, D. B.; Wu, Z. Y.; Finkelstein, A.; Collier, R. J. A phenylalanine clamp catalyzes protein translocation through the anthrax toxin pore. Science 2005, 309, 777-781. (21) Sun, J.; Lang, A. E.; Aktories, K.; Collier, R. J. Phenylalanine-427 of anthrax protective antigen functions in both pore formation and protein translocation. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 4346-4351. (22) Blanke, S. R., J. C. Milne, E. L. Benson and R. J. Collier (1996). Fused polycationic peptide mediates delivery of diphtheria toxin A chain to the cytosol in the presence of anthrax protective antigen. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 8437-8442. (23) Elber, R. A new paradigm for atomically detailed simulations of kinetics in biophysical systems. Q. Rev. Biophys. 2017, 50, e8. (24) Baker, C. A.; Schudel, B.; Chaudhari, M. I.; Wu, K.; Dunford, D.; Singh, A. K.; Rempe, S. B.; Hatch, A. V. Nanoporous hydrogels for the observation of anthrax exotoxin translocation dynamics. ACS Appl. Mater. Interfaces 2018, 10, 1334213349. (25) Fiser, A.; Sali, A. MODELLER: Generation and refinement of homologybased protein structure models. In Methods in Enzymology, Carter, C. W., Sweet, R. M., eds., Academic Press, San Diego, 2003, 374, 461-491. (26) Feld, G. K.; Thoren, K. L.; Kintzer, A. F.; Sterling, H. J.; Tang, II; Greenberg, S. G.; Williams, E. R.; Krantz, B. A. Structural basis for the unfolding of anthrax lethal factor by protective antigen oligomers. Nat. Struct. Mol. Biol. 2010, 17, 1383-U245. (27) Faradjian, A. K.; Elber, R. Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 2004, 120, 10880-10889. (28) Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale, L.; Schulten, K. Scalable molecular dynamics with NAMD. J. Comput. Chem. 2005, 26, 1781-1802. (29) Best, R. B.; Zhu, X.; Shim, J.; Lopes, P. E. M.; Mittal, J.; Feig, M.; MacKerell, A. D. Optimization of the additive CHARMM all-Atom protein force field targeting improved sampling of the backbone phi, psi and side-chain chi(1) and chi(2) dihedral angles. J. Chem. Theory Comput. 2012, 8, 3257-3273. (30) Humphrey, W., A. Dalke and K. Schulten. VMD: Visual molecular dynamics. J. of Mol. Graphics & Modell. 1996, 14, 33-38.


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(31) Bello-Rivas, J. M.; Elber, R. Exact milestoning. J. Chem. Phys. 2015, 142. (32) Olsson, M. H. M.; Sondergaard, C. R.; Rostkowski, M.; Jensen, J. H. PROPKA3: Consistent treatment of internal and surface residues in empirical pK(a) predictions. J. Chem. Theory Comput. 2011, 7, 525-537. (33) Dolinsky, T. J.; Nielsen, J. E.; McCammon, J. A.; Baker, N. A. PDB2PQR: an automated pipeline for the setup of Poisson-Boltzmann electrostatics calculations. Nucleic Acids Res. 2004, 32, W665-W667. (34) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A smooth particle mesh Ewald method. J. Chem. Phys. 1995, 103, 8577-8593. (35) Aksimentiev, A.; Schulten, K. Imaging alpha-hemolysin with molecular dynamics: Ionic conductance, osmotic permeability, and the electrostatic potential map. Biophys. J. 2005, 88, 3745-3761. (36) Chen, Y. J.; Roux, B. Constant-pH hybrid nonequilibrium molecular dynamics monte carlo simulation method. J. Chem. Theory Comput. 2015, 11, 39193931. (37) Panahi, A.; Brooks, C. L. Membrane environment modulates the pK(a) values of transmembrane helices. J. Phys. Chem. B 2015, 119, 4601-4607. (38) Chen, W.; Huang, Y. D.; Shen, J. N. Conformational activation of a transmembrane proton channel from constant pH molecular dynamics. J. Phys. Chem. Lett. 2016, 7, 3961-3966. (39) Ghosal, K.; Colby, J. M.; Das, D.; Joy, S. T.; Arora, P. S.; Krantz, B. A. Dynamic phenylalanine clamp interactions define single-channel polypeptide translocation through the anthrax toxin protective antigen channel. J. Mol. Biol. 2017, 429, 900-910. (40) Lybrand, T. P.; McCammon, J. A.; Wipff, G. Theoretical calculation of relative binding-affinity in host guest systems. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 833-835.


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Probing Translocation in Mutants of the Anthrax Channel: Atomically

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