1.1. Voronoi diagram construction.

Representation and processing of Voronoi diagram of balls of equal radii, i.e., ordinary Voronoi diagram of points, is more effective than working with Voronoi diagram of balls with variable radii, i.e., weighted Voronoi diagram, and algorithms for its construction are also better studied [45], [46]. MOLE 1.2 and CAVER 2.0 constructs ordinary Voronoi diagram without considering the differences in radii of individual atoms, i.e., they represent the structure by a set of balls of equal radii, where each ball represents one atom. This can result in the error in the pathway radius estimation as large as r₁−r₂, where r₁ is the radius of the largest atom in the system and r₂ radius of the smallest one. To take differences in atom radii into account and still have molecule represented by balls of equal radii, CAVER 3.0 approximates all atoms in the input structure which are larger than the smallest atom in the structure by a user-specified number of balls with the van der Waals (VDW) radius equal to the VDW radius of the smallest atom, analogously to the solution used in MolAxis 1.4 [39]. By this way, the input structure is represented by a set of balls of equal radii. The representation determines a surface which is never above the VDW surface of the input structure and therefore the pathway radius may be overestimated up to a certain limit, but not underestimated. The upper limits of the overestimation are provided in the output data. If more than four ball centers are co-spherical, more than four Voronoi edges may join in a Voronoi vertex [45]. Handling such degenerate cases complicates design of the algorithm and makes the data structures less efficient. To avoid this, the coordinates of the center of each ball are changed by a pseudorandom value lower than 0.001 Å. In the following text, the resulting set of balls will be referred to as a representation of input structure (RIS). Furthermore, the distance between a point and a ball will always denote the distance of the point and the closest point on the surface of the ball. Finally, Delaunay triangulation [47] of the RIS centers is used to construct the vertices and edges of the Voronoi diagram [45].

1.2. Cost function.

The axes of the pathways are identified as simple paths in a graph composed of Voronoi vertices and edges, i.e., the axis of a pathway is a sequence of Voronoi edges, where each of the two consecutive edges share a vertex. The pathway is then composed of balls with center on the pathway axis and a maximum radius at which the ball does not collide with the RIS. We define the cost of a path so as to reflect the probability that the pathway is actually used as a route for transportation of the substances. In the simplified case of a path of length L and constant radius r, the cost of the path iswhere n is a non-negative real number. Therefore, if two paths have equal radii, the shorter has a lower cost. If they have the same length, then the wider has a lower cost, unless n is zero. The parameter n controls the balance between width and length and can be set to a real number from 0 to 100. If set to 0, only the length of the path is taken into account. On the other hand, if n is a high number, a path that is only slightly narrower than the widest path will have a higher cost unless it is many times longer. The default is set to an established value of n = 2 to give priority to wide paths with a reasonable length [37], [39]. The cost of a path with continuously changing width can be expressed as

The function r(l) defines the radius of the largest ball which does not collide with the RIS and is centered at the point on the pathway axis in the distance l from the starting vertex measured along the path. The user-defined threshold value r_max is used for r(l), if the actual radius of the ball is larger than r_max. The minimum value 0.1 Å is used for r(l) if the actual radius of the ball is smaller than 0.1 Å. The value L is the total path length. The cost of the pathway is computed by summing the costs of individual edges forming the pathway axis. The cost of each edge is integrated numerically using trapezoidal rule with a uniform grid. The minimum number of trapezoids is 8 and minimum grid distance 0.1 Å. Prior to the search for the lowest cost paths, all edges which cannot be traversed by a probe of radius of the user-specified value r_B are removed. Because of the approximated VDW molecular surface, some edges appear to be wider than they are in reality. Consequently, some edges are not removed from the Voronoi diagram even though their real width is slightly narrower than r_B. This can happen only if the real edge width is similar to r_B, and may lead to false positive results, i.e., identification of pathways which are in some pathway segment narrower than r_B (Text S1).

Cost of each pathway is transformed into a new measure of pathway importance called throughput. A throughput of a pathway is computed as e^−cost, where e is Euler's number. Throughput values ranges from 0 to 1—the higher the value, the greater the importance of the pathway. The pathway A has a greater throughput than B if and only if A has a lower cost than B.

1.3. Pathway identification.

The starting point for the calculation of the pathways is initially placed into the center of gravity of the user-specified residues, atoms or a point defined by x, y and z coordinates. Each of these entities contributes by the same weight. The starting Voronoi vertex is then identified in the vicinity of the initial starting point by the following starting point optimization procedure. The closest Voronoi vertex within the distance d_max from the initial starting point, which is at least r_min far from the RIS, is used as a starting point for the calculation of pathways. If no such vertex can be found, then the vertex with maximum distance to RIS is selected from all vertices located within the d_max distance from the initial starting point. In the case that no vertex exists within the d_max distance, the whole procedure is repeated with the value of 3 Å instead of the user-provided d_max value. If still no vertex is found, the Voronoi vertex closest to the initial starting point is used as the starting Voronoi vertex.

A proper setting of r_min and d_max parameters enables to find an optimal starting point even in cases where the user-specified position of the starting point is too close to RIS, outside (but still close to) the target cavity, or intersects with RIS, thus minimizing the effects of the user-selected starting point location on the calculation results. On the other hand, if a completely wrong initial starting point is selected, the starting point optimization procedure does not help and consequently no or irrelevant pathways are found. It is also important to note that the position of the starting point directly influences overall length of identified pathways and hence also their costs and throughputs. The starting point used for analysis of pathways in a particular macromolecule should be therefore always reported together with the output data to allow reproduction of the calculations.

Pathways are identified as the paths in a graph composed of Voronoi vertices and Voronoi edges. First, two groups of vertices are identified: bulk solvent vertices and surface vertices. A vertex is called a bulk solvent vertex if it can be accessed from the structure exterior by a shell probe with a radius r_S (e.g. r_S = 3 Å). Then, a ball called a bulk solvent ball is placed into each bulk solvent vertex. The radius of each bulk solvent ball is the largest possible, but satisfying the condition that the ball does not intersect RIS. Next, surface vertices are found by a search in the neighborhood of each bulk solvent ball. Starting in a bulk solvent ball of a center A and radius r, a vertex is called a surface vertex if it can be accessed by a probe of the radius r_B traveling from A through Voronoi edges so that the probe never intersects RIS and always lies inside a ball of the center A and the radius r+d_s, where d_s is by default set to the value of 4 Å. This way, a set of surface vertices and a set of bulk solvent vertices are defined. Furthermore, a surface boundary vertex is defined as a surface vertex connected by an edge to a vertex that does not belong to surface vertices. Similarly, a bulk solvent boundary vertex is a bulk solvent vertex connected by an edge to a vertex that does not belong to bulk solvent vertices.

The pathway search itself consists of two steps. In the first step, the lowest cost path to every surface boundary vertex is found by Dijkstra's algorithm [48]. In the second step, each path is prolonged by finding a single lowest cost path continuation to a bulk solvent boundary vertex. Then, points are placed on each pathway axis in regular intervals and a ball is placed into each point. The radius of the ball is the maximum possible, but such that the ball does not collide with RIS. Finally, balls from the end of the path are removed one by one until the ball with the radius smaller or equal to r_S is reached.

1.4. Removal of redundant pathways.

Several pathways with nearly identical axes may be identified within one snapshot. To remove such redundant pathways, the following iterative procedure is employed. The lowest cost pathway P is selected and all pathways within a user specified distance from P are discarded. The procedure is repeated with the next remaining lowest cost pathway, until all pathways are either selected or discarded.

2.1. Calculation of pathway distances.

Previously, we proposed a method for estimation of a distance (i.e. dissimilarity) of two pathways, which evaluated the distance between each ball from the first pathway and its respective closest ball from the second pathway [49]. To accelerate the computation of all pairwise pathway similarities, we have now designed a more efficient algorithm. The basic idea is to represent each pathway by a sequence of N points and then compute only distances between pairs of points with the corresponding order, thus performing only N distance computations for each pair of pathways. First, a point S is constructed as the center of gravity of the starting Voronoi vertices from all snapshots. Then, a set of points P is constructed iteratively by processing the pathways ordered by their cost in ascending order. For the pathway being processed, an extreme point X is identified as the pathway axis point of the greatest distance from S. The distance |SX| will be called a straight length of a pathway. Then, the point Y from P is identified such that the angle XSY is minimal. If P is still empty or the angle size is greater than the user specified value, the extreme point X is added to P and its weight is set to one. Otherwise, X is discarded and the point Y is moved along the SY half-line so that its new distance to S is |SX|+w_Y·|SY|, where w_Y is the weight of the point Y. The weight of the point Y is then increased by one. In the end, each point in the set P captures averaged straight lengths of pathways whose end points are close to each other.

Next, all the pathways are processed once more. First, a set of points Q is identified within P such that for the extreme point X of the actually processed pathway and any point Y from Q, the size of the angle XSY is not greater than a parameter called smoothness. Then, the distance d_end is computed asThus an average of straight lengths of the pathways in the vicinity of the actually processed pathway was estimated.

Next, the geometry of each pathway axis is converted into N points by the following procedure. For each pathway, the distance d_end is divided into a sequence of N+2 intervals I_start, I₁, I₂, …, I_N and I_end. The size of the intervals I_start and I_end is z_start and z_end, where values z_end and z_start may be specified by the user and the intervals themselves determine the pathway beginning and end sections that are not used for the evaluation of pathway similarities. For each i from 1 to N, the center of gravity G_i of all points whose distance from S falls within the interval I_i is computed. Thus, each pathway is characterized by a sequence of points G₁, G₂, _…, G_N. The distance of two pathways A and B is defined aswhere |G_AiG_Bi| denotes the Euclidean distance of two corresponding points from pathways A and B and w is a linear function w(x) = ax+b. The coefficients a and b are derived from the user defined weighting parameter q so that the ratio between the weights of the end point w(1) and starting point w(0) equals q and w(0.5) equals 1. The weighting of the point distances allows the user to emphasize either the importance of the pathway end section by setting q>1, or of the pathway beginning section by setting q<1. In practice, the weighting is performed by identification of such points K_i lying on the halfline SG_i thatand then the distance of the pathways A and B is calculated as

Pathway distances are calculated on the fly during the above described algorithm for the removal of redundant pathways, as well as for all pairs of non-redundant pathways identified throughout the MD simulation, which is used to establish the correspondence between pathways in different snapshots. The matrix of pairwise distances of all non-redundant pathways is stored on the hard disk for further processing. The presented algorithm for the calculation of pathway distances has several advantageous properties: (i) the algorithm is fast and scalable as only a small and adjustable number of distances need be evaluated for each pair of pathways; (ii) each pathway is characterized by the same number (3N) of coordinates, which allows fast clustering of pathways; and (iii) pairwise distances of pathways can be calculated using only selected pathway sections and/or the importance of the pathway beginning or end sections can be emphasized according to the needs of individual users.

2.2. Clustering of pathways.

The clustering of pathways is based on the pre-calculated distance matrix. Average-link hierarchical clustering [50] is used to construct a tree hierarchy of pathway axes based on their pairwise distances. The size of the clusters may be then optimized rapidly by cutting the tree at a varying level of detail. This accurate clustering becomes demanding with respect to computer time and disk capacity for datasets containing more than 50,000 pathways. Therefore, a fast approximate algorithm based on supervised machine learning was also implemented, enabling the classification of even larger datasets with hundreds of thousands of pathways. In the first step, a set of pathways of manageable size is randomly sampled from the pathway dataset and clustered using the average-link hierarchical clustering. Each pathway is then assigned to one of the N+1 classes. N classes correspond to the N clusters with highest priority and the last class contains pathways belonging to all remaining clusters. This dataset is then used for training a k-nearest neighbor classifier as implemented in the program Weka 3.6 [51]. Finally, the classifier is used to assign each of the remaining pathways from the original dataset either to one of the N clusters or to the last class containing pathways from clusters with lower priorities.

Identification of pathways in static crystal structures.

CAVER 3.0 was tested on a variety of biomolecular structures (Protocol S1), which had previously been used for the validation of MOLE 1.2 [37] and MolAxis 1.4 [40]. Comparison of the results obtained by CAVER 3.0, MOLE 1.2 and MolAxis 1.4 with the identical set of protein structures is shown in Supporting Table S1. The pathways identified by CAVER 3.0 are generally shorter than the pathways identified by MOLE 1.2 and MolAxis 1.4 due to the more accurate definition of protein surface at which the pathways end. MOLE 1.2 tends to identify narrower pathways than the two other tools. The differences in the pathways identified by MOLE- are caused by the construction of the Voronoi diagrams without considering the variability in atom radii. MOLE 1.2 also employs a distinct search strategy—CAVER 3.0 and MolAxis 1.4 search for all pathways simultaneously, while MOLE 1.2 performs a consecutive search and penalizes repeated searches of the same parts of the Voronoi diagram.

Identification of pathways in molecular dynamics trajectories.

CAVER 3.0 and MOLE 1.2 were used for the analysis of 1,000 snapshots from a 10 ns MD simulation of haloalkane dehalogenase DhaA using various settings of clustering parameters (Protocol S2 and S3). MolAxis 1.4 does not employ an algorithm for pathway clustering and therefore is not suitable for automatic analysis of tunnels in MD simulations. The average-link algorithm implemented in CAVER 3.0 provided robust results with better separated clusters than the clustering algorithm implemented in MOLE 1.2 (Figure S1). Another advantage of the hierarchical algorithm implemented in CAVER 3.0 is the possibility to modify the results from clustering by adjusting the threshold value without a need to repeat the clustering procedure. This significantly speeds-up the search for the optimal clustering parameters. CAVER 3.0 additionally provides other options to control the clustering results—based on the user-defined parameters, the pairwise distance of the pathways may be calculated using only selected pathway sections, with constant weights along the entire pathway length or with a higher weight on either the beginning or end sections of the pathway. Settings that provided comparable clusters for the p1 tunnel (previously also named the upper or main tunnel [36]) were selected and the time evolution of the p1 tunnel calculated by both tools was compared (Figure S1C and S1F). This comparison revealed that the average bottleneck radius of the p1 tunnel calculated by CAVER 3.0 (1.4 Å, mean error<0.04 Å) differs from that calculated by MOLE 1.2 (1.1 Å; Figure 1A). This discrepancy is due to the calculation error of MOLE 1.2 (Figure 1B), which is proportional to the difference between the radii of individual atoms making up the pathway and considerably varies in individual snapshots. For example, in a sample snapshot, MOLE 1.2 identified a p1 tunnel with a bottleneck radius of 0.5 Å, while the bottleneck calculated by CAVER 3.0 was 1.2 Å with the maximum approximation error of 0.04 Å (Figure 1C).

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Figure 1. Comparison of the p1 tunnel of DhaA calculated by CAVER 3.0 and MOLE 1.2.

(A) Time evolution of the bottleneck radius calculated by CAVER 3.0 (blue) and MOLE 1.2 (red). Only a part of the 10 ns MD simulation is shown for clarity. The sample snapshot (black arrows) was taken at 0.81 ns. (B) Geometry of the p1 tunnel in the sample snapshot calculated by CAVER 3.0 (blue) and MOLE 1.2 (red). Hydrogen atom of the bottleneck residue Ala145 (white ball) is shown together with the sulfur atom of the bottleneck residue Cys176 (yellow ball) and with sphere representation of the tunnels. The underestimation of the bottleneck radius by MOLE 1.2 is visible as an empty space between the tunnel and the hydrogen atom of Ala145. (C) Profile of the p1 tunnel in the sample snapshot calculated by CAVER 3.0 (blue) and MOLE 1.2 (red). The dashed line indicates the profile representing the maximum possible difference between the CAVER-calculated (solid line) and the correct profile of the p1 tunnel.

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Description of model system.

Haloalkane dehalogenase DhaA isolated from various strains of Rhodococcus spp. [55]–[58] catalyzes hydrolytic cleavage of the carbon-halogen bond in a variety of halogenated compounds. The active site of DhaA is buried inside the protein core and is connected with the outside solvent by access tunnels [59]. The access tunnels of DhaA were studied in detail using classical and random acceleration molecular dynamics (RAMD) simulations [15], [60]. This study suggested five pathways for the release of products and/or the exchange of water solvent, named p1, p2a, p2b, p2c and p3 [15]. Key residues of the access tunnels identified by RAMD were randomized by directed evolution, resulting in 25 unique mutants with higher activities towards toxic recalcitrant compound 1,2,3-trichloropropane, with the best mutant showing 32-fold improvement over the wild type enzyme [28]. The wealth of available knowledge on access tunnels of DhaA makes this enzyme a good model system to validate the ability of CAVER 3.0 to identify and characterize tunnels in trajectories from MD simulations.

Identification of tunnels.

CAVER 3.0 was used for the analysis of 10,000 snapshots from a 10 ns classical MD simulation of DhaA in explicit water solvent (Protocol S2 and S3). In each snapshot, all possible pathways with the bottleneck radius equal or larger than 0.9 Å were identified, leading to a set of nearly 30,000 pathways. The pathways were clustered by the average-link algorithm based on the pairwise distances of the pathways. All five previously described DhaA tunnels [15] were identified among the top four ranked pathway clusters (Figure 2, Table S2). The p2a and p2b tunnels possess a common opening and thus were initially identified as a single pathway (p2ab). Therefore, the clustering threshold was decreased in order to evaluate the relative importance of the p2a and p2b tunnels to each other (Figure 2). We note that the localization of the p2a and p2b tunnels differs slightly from the study of Klvana et al. [15], where these tunnels were observed to run roughly parallel to each other. In our analysis, we found out that these tunnels may cross each other and consequently four different pathways may in theory be identified by geometrical analysis. The lower clustering threshold also led to the splitting of the p1 tunnel into three branches—the dominant p1a tunnel, corresponding to the p1 tunnel observed in previous analyses [15] and the less frequent and narrower p1a′ and p1b tunnels (Figure 2, Table 1).

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Figure 2. Comparison of the DhaA tunnels identified by CAVER 3.0 with the previously proposed pathways.

(A) The top ranked collective pathways identified throughout the molecular dynamics simulation of DhaA by CAVER 3.0 are all depicted in one frame as pathway centerlines. The p2a and p2b tunnels were initially identified as one collective pathway—p2ab—using the clustering threshold of 4.3. Decreasing the clustering threshold to 3.5 led to the separation of the p2a and p2b tunnels as well as the splitting of the p1 collective pathway into three clusters—p1a, p1a′ and p1b. A random subsample of identified tunnels is shown for clarity. (B) Representative DhaA pathways (surface representation) for the release of products and/or exchange of water solvent as identified previously by RAMD and classical MD simulations [15].

https://doi.org/10.1371/journal.pcbi.1002708.g002

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Table 1. Characteristics of the top ranked tunnels of DhaA identified by CAVER 3.0 in molecular dynamics trajectory using the probe radius of 0.9 Å and the clustering threshold of 3.5.

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We found a good agreement between the results of CAVER 3.0 and the previous MD and RAMD study of DhaA product release pathways [15] (Text S2): (i) all five previously proposed DhaA pathways were reliably identified by CAVER 3.0, with estimated relative importance p1≫p2b≫p2a>p2c∼p3; (ii) the p1 tunnel was found to be the dominant transport pathway—it was the most frequently identified collective pathway, had by far the highest maximum and mean radii of bottlenecks and was frequently open for water molecules (Table 1, Figure 3); (iii) based on all studied characteristics, the p2b and p2a tunnels were found to be the second and the third most important, respectively; (iv) the p2c and p3 pathways were only rarely identified, however, compared to other possible tunnels ranked at lower places, the p2c and p3 pathways were still significantly more frequent and showed a considerable widening of the bottlenecks in some snapshots (up to 1.2 Å, Table S2).

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Figure 3. Time evolution of the bottleneck radii of DhaA tunnels identified by CAVER 3.0.

The color map ranges from very narrow (green) to wide (red) bottlenecks. White color indicates that no pathway with bottleneck radius ≥0.9 Å was identified for the given pathway cluster in the given snapshot.

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It is important to note that RAMD and other methods specialized in the simulation of ligand migration through protein structure provide information specific to a particular ligand [31]. The specificity of obtained results represents an advantage in many instances, but it may become a drawback if the user aims for a general overview of the possible transport pathways in the studied protein. In contrast, CAVER 3.0 facilitates the analysis of pathways in classical MD simulations and thus provides a general picture of the variability of potential transport pathways.

Analysis of tunnel dynamics.

The capability of CAVER 3.0 to analyze dynamical systems is essential for the identification of biochemically relevant tunnels. All previously known DhaA tunnels were reliably identified by the analysis of the 10 ns MD simulation snapshots, while only two of them—p1 and p2ab—were found in the crystal structures of DhaA (PDB-IDs 1CQW, 1BN7 and 1BN6) under the same calculation settings (Protocol S4). By decreasing the probe radius from 0.9 Å to 0.8 Å, more than ten potential tunnels were identified in each crystal structure, including the p1 variants (p1a, p1a′ and p1b), p2ab and p3 tunnels (Table S3). The p2c tunnel was not observed. While the p1 tunnel was clearly wider and had higher throughput than all other tunnels in all three crystal structures, the remaining tunnels (with the exception of p2a and p2b in the structure PDB-ID 1BN6) had very similar characteristics to one another (Table S3), demonstrating that it is difficult to identify the biochemically relevant tunnels by analyzing the static crystal structures only. Such analysis may easily overlook relevant tunnels that are temporarily closed, and/or identify tunnels whose relevancy is disputable. In contrast, tunnel characteristics obtained from the analysis of MD simulation, such as the frequency of tunnel identification, the frequency of tunnel opening or the bottleneck radius fluctuation, may be used as indicators of the tunnel's functional relevancy (Table S2). This can be demonstrated on the exemplary analysis of the time evolution of the p1 tunnel bottleneck. In all three available crystal structures of DhaA with added hydrogen atoms, the value of the bottleneck radius 1.2 Å (PDB-IDs 1BN6, 1BN7) and 1.3 Å (PDB-ID 1CQW) indicates that the p1 tunnel may not be relevant, considering the usual probe radius of 1.4 Å. In the MD simulation, however, the p1 tunnel was open in a large number of snapshots (bottleneck radius wider than 1.4 Å), suggesting the importance of the tunnel for enzyme function (Figure 3 and Figure 4). The maximum radius of the p1 tunnel bottleneck in the MD simulation was 2.3 Å (Figure 4 and Table S4).

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Figure 4. Time evolution of the DhaA p1 tunnel.

(A) Evolution of the p1 tunnel bottleneck radius over time. The dotted orange lines indicate bottleneck radii of the p1 tunnel in DhaA crystal structures with added hydrogen atoms: PDB-IDs 1BN6 and 1BN7 (bottleneck radius 1.2 Å) and 1CQW (1.3 Å). The four green circles indicate bottleneck radii of the p1 tunnel from the 2.76 ns (bottleneck radius 1.4 Å), 5.85 ns (2.3 Å), 7.57 ns (0.9 Å) and the 7.72 ns (0.9 Å) snapshots from the molecular dynamics simulation of DhaA. (B) The p1 tunnel identified in DhaA crystal structures with added hydrogen atoms (PDB-IDs 1CQW, 1BN6, 1BN7). (C) The p1 tunnel identified in the 2.76 ns, 5.85 ns, 7.57 ns and 7.72 ns snapshots of the MD trajectory of DhaA.

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Analysis of bottleneck dynamics.

The residues forming the tunnel bottleneck represent promising hotspots for the modification of tunnel properties, since their substitutions have potentially the most pronounced impact on the tunnel geometry. Similarly to other tunnel characteristics, the analysis of the bottlenecks is more informative when the dynamics of the protein is considered. The list of the bottleneck residues obtained by the analysis of the MD trajectory using CAVER 3.0 suggested the existence of two distinct bottlenecks along the DhaA p1 tunnel, while only one of them can be identified in the crystal structures (Table S4). The analysis of the bottlenecks in the MD trajectory also revealed the structural details of the tunnel gating.

The most frequent bottleneck in the DhaA p1 tunnel is formed mainly by Phe149 (71% of p1 tunnels), Cys176 (59%), Ala172 (50%) and Ala145 (38%) residues, mostly in combinations Ala145-Phe149-Cys176 and Phe149-Ala172-Cys176 (26% and 24% of all p1 pathways, respectively). Comparison of structures with an open and closed p1 tunnels suggested that the gating in this bottleneck is mediated by the movement of the N-terminal part of the cap domain (Glu139-Phe149) carrying the bottleneck residues Ala145 and Phe149, movement of the C-terminal part of the α5-helix with the bottleneck residue Cys176, and by the conformational change of the bottleneck residues Phe149 and Cys176 (Figure 5A). The proposed structural basis of gating in the bottleneck is in agreement with the results from RAMD analysis [15].

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Figure 5. Bottleneck dynamics and structural basis of gating in the p1 tunnel of DhaA.

(A) The bottleneck 1 represents the most frequent bottleneck of the p1 tunnel and is mostly formed by Ala145, Phe149, Ala172 and Cys176. Comparison of snapshots with an open (red) and closed (blue) p1 tunnels suggested that the gating is mediated by: (i) movement of the N-terminal part of the cap domain carrying Ala145 and Phe149; (ii) movement of the α5-helix with Cys176 and Ala172; and (iii) conformational change of the bottleneck residues Phe149 and Cys176. The bottleneck radius in the selected snapshots with an open and closed tunnel was 2.3 Å and 0.9 Å, respectively. (B) The bottleneck 2 of the p1 tunnel is mostly formed by Thr148, Ala172 and Lys175. Comparison of snapshots with an open (red) and closed (green) p1 tunnel suggested that gating is mediated by: (i) movement of the N-terminal part of the cap domain carrying Thr148; (ii) movement of the α5-helix carrying Ala172; and (iii) the conformational change of the bottleneck residues Thr148 and Lys175. The bottleneck radius in the selected snapshot with an open and closed tunnel was 2.3 Å and 0.9 Å, respectively.

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The second bottleneck is positioned at the tunnel entrance from the bulk solvent and is formed predominantly by Lys175 (26% of all p1 pathways), Thr148 (23%) and Ala172 (50%; also included in the first bottleneck), most often in the combination Thr148-Ala172-Lys175 (16% of all p1 pathways). The gating in the second bottleneck seems to be mediated mainly by the conformational change of Lys175 (Figure 5B). This residue has previously been observed to participate in the chloride ion release during MD simulations [15]. The gating is also facilitated by the movement of the N-terminal part of the cap domain (Glu139-Phe149) with the bottleneck residue Thr148, by the conformational change of Thr148 and by the movement of the α5-helix with the bottleneck residue Ala172. Unlike the first bottleneck, the second one cannot be observed in the crystal structures, and can only be identified by the analysis of MD trajectories.

The importance of the bottleneck residues identified by CAVER 3.0 for the catalytic properties of DhaA had already been demonstrated experimentally (Table S5, Table 2). Two independent directed evolution experiments provided DhaA variants C176Y+Y273F and C176F+G3D with 3.5-times [61] and 4-times [62] higher activity towards the important environmental pollutant 1,2,3-trichloropropane (TCP). Both these variants carried mutation in the position Cys176, which forms the bottleneck of the p1 tunnel. In another study [28], the DhaA variant C176Y+Y273F was used as a template for focused directed evolution, subjecting Ile135 (bottleneck of p2a, p2c and p3 tunnels), Val245 (bottleneck of p2b and p1b tunnels) and Leu246 (bottleneck of p2a and p2b tunnels) to simultaneous saturation mutagenesis. The best variant I135F+C176Y+V245F+L246I+Y273F showed 32-times higher activity towards TCP than the wild type enzyme, which is due to decreased accessibility of buried active site for water molecules [28]. A focused directed evolution of the DhaA variant H272F was conducted to improve the binding of a fluorescent probe into the enzyme active site [63]. The best variant K175M+C176G+Y273L, with four orders of magnitude improved binding rate, carried two substitutions in the p1 tunnel bottlenecks (K175M and C176G) and one in the active site cavity (Y273L). Altogether, these four examples demonstrate that analysis of access tunnels using CAVER 3.0 can be useful for the selection of suitable hot-spots for engineering of enzyme catalytic properties. The study of dynamical systems enables the identification of all important bottlenecks and provides invaluable information about their relative relevance.

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Table 2. DhaA variants with modified catalytic properties, carrying substitutions in the bottleneck residues (in bold) identified by CAVER 3.0.

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