Identification of Protein Cryptic Sites via Conformational Dynamics Capturing and Water-Based Pocket Characterization in Molecular Dynamics Simulations

Abstract

Employing molecular dynamics (MD) simulation to study the formation of novel protein cryptic sites has attracted increasing interest in the field of drug discovery. One specific challenge in this area is finding a viable method to accurately identify and characterize cryptic site transitions from MD simulation results while minimizing the need for extensive human input. Since the formation of cryptic sites often involves significant conformational changes in the protein structure, a method capable of capturing and describing these dynamic pocket transitions with precision is essential. In this paper, we present a new procedure, Conformational Dynamics Capturing and Water-Based Characterization (CDC-WBC). This procedure dynamically identifies the cryptic site region by tracking protein conformational changes observed during molecular dynamics (MD) simulations. The procedure also incorporates water density information to enhance the characterization of cryptic sites across frames. We evaluate the CDC-WBC procedure by applying it to characterize the opening process of the two well-studied cryptic sites in TEM1 β-lactamase. The results demonstrate that the CDC-WBC method accurately captures the open-closed transitions of the two cryptic sites. For comparison, three commonly used protein cavity detection methods in cryptic sites studies, POVME2, Epock, and MDpocket, are applied to identify the ‘CBT’ cryptic site in TEM1 β-lactamase. The results show that the CDC-WBC method outperforms these methods in characterizing the transitions of the ‘CBT’ cryptic site. Additionally, using a benchmark set of 84 protein systems (93 cryptic pockets) from the CryptoSite dataset, CDC-WBC consistently shows better performance in distinguishing between the open and closed states of cryptic sites, further highlighting its capability for precise characterization of dynamic cryptic site transitions. The detailed implementation of the CDC-WBC procedure and demo data sets are uploaded to GitHub: https://github.com/TianmingQu/CDC-WBC.git

I. Introduction

A cryptic site is a type of ligand binding site that is usually invisible in experimentally solved unbound protein structures but can become detectable upon proper ligand binding [1]. In the past decades, cryptic sites have attracted increasing attention since the discovery of a new druggable cryptic site allows a protein to broaden its potential as a drug target. In addition, cryptic sites are expected to have a high binding specificity since their formation is usually coupled with unique conformational changes of a protein system [2]. Although the concept of cryptic sites was introduced long ago, identifying them has remained a challenging task. In early times, most cryptic sites were discovered serendipitously by experiments. For instance, the well-studied cryptic site in TEM1 β-lactamase was captured in a high-throughput ligand screening experiment [3]. However, as has been widely acknowledged, identifying cryptic sites through experimental methods is an infeasible task, primarily for the following two reasons: 1) Ligands that preferentially bind to a cryptic site are rare and unique; 2) Conformations of an open cryptic site are lowly populated and thus are hard to capture with experimental methods.

Consequently, over the last decade, MD simulations have been extensively applied in cryptic site sampling studies [4]. This popularity stems from the fact that MD simulation results contain complete information on all atoms within the target system, enabling direct visualization of protein conformational transitions. Overall, two major questions arise when sampling and identifying cryptic sites: 1) How can we predictively sample a novel cryptic site? 2) How can we accurately identify the sampled cryptic site from MD simulation? As for the first question, cryptic sites are challenging to access using conventional MD simulation techniques, since proteins tend to fluctuate aimlessly in their functional environment, and active conformational transitions responsible for cryptic site formation are typically rare events occurring over long timescales. As a result, in most cryptic site prediction studies, enhanced sampling methods that can accelerate protein structural transitions are employed [5-10]. As for the second question, a detailed analysis must be performed once the open conformation of the cryptic site has been sampled. In this paper, we will focus on solving the second question by developing a new computational procedure for cryptic site identification and characterization. As we will demonstrate later in the paper, our method surpasses three widely used—POVME2, Epock, and MDpocket—in its ability to identify and characterize cryptic sites sampled from MD trajectories.

Among various protein cavity identification methods, Pocket Volume Measure (POVME, POVME2) [11, 12], MDpocket [13, 14], and Epock [15] are widely used in cryptic site studies [16-23]. It is worth noting that all these three methods can analyze MD simulation trajectories. The application of POVME2 and Epock is straightforward. In terms of pocket identification, both methods rely on defining geometric regions, such as spheres or rectangular prisms, to filter a grid-based voxel map for identifying protein cavities. Specifically, user-defined spheres or prisms outline the regions of interest and exclusion, with grid points within the defined inclusion regions considered part of the identified pocket. The defined geometric region is then used to filter grids in all frames of MD trajectories. In the MDpocket method, pocket detection relies on Fpocket [24], which divides the protein-occupied space using Voronoi vertices centered on each heavy atom. Alpha spheres are then centered at the intersections shared by four neighboring Voronoi cells, representing the inscribed spheres of the tetrahedra formed by these atoms. If the centers of two alpha spheres are within a specified cutoff distance, they form clusters that define potential binding pockets. To detect pockets from the MD trajectory, a hybrid grid-based and alpha-sphere-based approach is also employed. Initially, MDpocket creates a grid map to cover the entire protein region in the first frame. Then the Fpocket method is applied on each snapshot to identify alpha spheres within the protein. The alpha spheres are subsequently assigned to the closest grid point. As a result, by the end of the analysis, the cavity grids accumulate contributions from multiple alpha spheres originating from different snapshots. Notably, in MDpocket analysis, the pocket detection process would identify all the protein surface cavities, so the pocket of interest needs to be painstakingly selected.

However, although widely applied, the aforementioned methods remain suboptimal for cryptic site identification studies. The key limitation of POVME2 and Epock is that their pocket identification process is not well-suited to capturing the dynamic, multi-level conformational changes often associated with cryptic sites. Ideally, to describe the opening of a cryptic site, the pocket region should be dynamically redefined for each frame of an MD trajectory. However, in POVME2 and Epock, the inclusion spheres or prisms are only defined once for the entire trajectory, preventing adaptation to the structural changes occurring during cryptic site formation. Although MDpocket applies Fpocket to each frame of the trajectory, defining suitable alpha-sphere parameters for cryptic site characterization remains challenging. This underscores a second drawback of these methods—the reliance on extensive human input. For instance, defining inclusion and exclusion regions in POVME2 and Epock, as well as adjusting alpha-sphere parameters in MDpocket, often requires manual intervention, even though default parameters are provided. This manual intervention not only increases the complexity of the process but also introduces variability, as different parameter choices may lead to inconsistent pocket characterization results.

To address the aforementioned concerns, we present a new procedure, named ‘Conformational Dynamics Capturing and Water-Based Characterization (CDC-WBC)’, specifically designed to identify and characterize cryptic sites from MD simulation trajectories. The CDC-WBC procedure dynamically identifies the cryptic site region in each MD trajectory frame by tracking protein conformational changes. In addition, CDC-WBC characterizes the identified cryptic site region by incorporating water density information derived from MD simulation trajectories. Although water-based analyses have been used before in protein-ligand studies—most notably in Schrödinger’s WaterMap program [24-28]—those tools operate on one or a few static pocket definitions and are seldom used for pocket opening characterizations. Specifically, WaterMap excels at ranking waters already present in a known cavity, distinguishing long-residence, energetically favorable molecules from those that are easily displaced, but it offers no information about when or where a cavity first emerges during the large-scale motions that create cryptic sites. CDC-WBC fills this gap by coupling an adaptive pocket boundary with a time-resolved water-density metric, enabling automatic detection and quantitative tracking of cryptic-site opening and closing events throughout an MD trajectory. The general workflow of CDC-WBC for each MD trajectory frame involves the following steps: 1) Generate a grid box based on the dimensions of the water box in MD simulation. 2) Calculate the water density value for each grid. 3) Generate a set of cryptic site residues and save their heavy atom coordinates. 4) Define a best-fit sphere using the heavy atom coordinates of the cryptic site residues. 5) Discard all grid points that lie outside this sphere or within the van der Waals radius of protein heavy atoms. 6) Discard grid points that fall outside the convex-hull region of the entire protein heavy atoms. 7) Further refine the cavity grids by discarding those with a density value lower than 0.01 water/ų. 8) Reweight the remaining grids based on their density values and calculate the final reweighted volume.

To evaluate the CDC-WBC procedure, we applied TEM1 β-lactamase as a template system in this study. We first sampled the two well-studied cryptic sites within this protein using an enhanced sampling MD simulation technique. We then used the CDC-WBC procedure to identify the opening process of these two cryptic sites. Our results show that the water density maps from our new method provide a straightforward visualization of the pocket formation process. Moreover, the open-closed transitions of the two cryptic sites are accurately captured. For comparison, we applied three well-known methods introduced above—POVME2, Epock, and MDpocket—to identify the CBT cryptic site, which is the first cryptic site experimentally verified in TEM1 β-lactamase. The results indicate that these methods are less effective in distinguishing the dynamic transitions of the CBT site. Finally, to further demonstrate our procedure’s advantages, we utilized 84 proteins (93 cryptic sites) from the CryptoSite dataset [30] and performed 10-ns short MD simulations on the holo and apo states of these proteins. It is worth mentioning that these short MD simulations were not enhanced sampling simulations but rather restrained, regular MD simulations, aiming to assess whether the CDC-WBC procedure can better distinguish between holo and apo cryptic sites. We also compared the results with those obtained from POVME2, Epock, and MDpocket. The findings reveal that our new procedure outperforms all three methods.

2. Theoretical Method and Computational Details

2.1. Simulation Setup

2.1.1. Enhanced Sampling of TEM1 β-lactamase

The enhanced sampling MD simulation presented in this study is conducted with an M182T mutant of TEM1 β-lactamase (PDB ID: 1JWP). Initially, the protein is placed in a cubic water box measuring 88 Å on each side, containing 21634 TIP3P water molecules. All crystallographic water molecules are removed from the initial structure. The system is neutralized by adding potassium and chloride ions at a concentration of 0.15 M. The simulation is performed in an NPT ensemble and employs the orthogonal space tempering method implemented in a modified version of the CHARMM program developed by the Yang group [31-33]. The CHARMM36* force field is used for the protein and ions, and the TIP3P model is applied to the water molecules. Periodic boundary conditions and long-range electrostatic interactions are handled using the Particle Mesh Ewald (PME) algorithm. The Nosé-Hoover thermostat is used to maintain a constant temperature of 300 K, and a Langevin piston is applied to maintain a constant pressure of 1.0 atm. All bonds involving hydrogen atoms are constrained using the SHAKE algorithm. The backbone RMSD of the simulated protein is selected as the order parameter for the enhanced sampling technique. To capture the system’s evolution, coordinates are saved every 4 ps and the OST recursion frequency is updated at each step.

2.1.2. Constrained Regular MD Simulation of Protein Systems Selected from CryptoSite Database

To further demonstrate the effectiveness of the CDC-WBC procedure, we select 84 protein systems (93 cryptic sites) from the CryptoSite training set [30], each available in both apo and holo forms. For these simulations, we perform regular 10-ns MD runs of each protein form, saving coordinates every 4 ps. To accelerate the process, all simulations are run on GPUs. The regular MD setups are prepared using CHARMM-GUI, employing the CHARMM36* force field and the TIP3P water model. All ligands in the holo forms are removed to run pure protein MD simulations. To maintain the holo and apo forms during the 10 ns simulations, an RMSD restraint is applied to each simulation, restricting RMSD changes to within 0–1 Å.

2.2. The Conformational Dynamics Capturing and Water-Based Characterization (CDC-WBC) Method Workflow

2.2.1. Calculate Water Density Fluctuation from MD Simulation

The general workflow of CDC-WBC can be illustrated in Fig. 1. The first step in the application of CDC-WBC is to calculate water density maps from the MD simulation trajectory. Following the procedure developed by Willard and Chandler [34], the instantaneous water density map of each MD trajectory frame can be calculated with a spatial coarse-graining approach using the following equation [35]:

$$\rho (\mathit{r},t)={\sum }_i{(2\pi {\xi }^2)}^{-\frac{3}{2}}exp\left[-\frac{{(\mathit{r}-{\mathit{r}}_i(t))}^2}{2{\xi }^2}\right]$$ (1)

where ${\mathbf{r}}_{\mathbf{i}}(\mathbf{t})$ is the position of the $\mathrm{i}\text{-th}$ particle at time $\mathrm{t}$, and $\xi$ represents the coarse-graining length, set to the TIP3P water oxygen Lennard-Jones (LJ) parameter of 1.7682 Å. With the $\xi$ defined, the interfaces are considered to be the collection of points with a field value of $\mathrm{c}$,

$$\rho (\mathit{s},t)=c.$$ (2)

Fig. 1. Workflow of the CDC-WBC Method:

The procedure begins with an MD simulation trajectory. Using this trajectory, the CDC-WBC method first calculates water density maps for each frame via a grid-based approach. Simultaneously, it identifies cryptic site residues (CSRs) by analyzing the dynamic fluctuations of protein residues. Subsequently, the CDC-WBC method retains only the “raw cryptic site grids” located within the best-fit sphere region. These raw pocket grids are then refined through the three steps described in Section 2.2.3. Finally, the volume of the cryptic site is determined using the refined grids.

In practical applications, to implement Equation (1), a grid box with evenly spaced voxels is first constructed for each MD simulation frame. The dimensions of this grid box match those of the water box used in the MD sampling process. Then, the instantaneous water density at each grid voxel is calculated by summing the coarse-grained contributions from all water molecules. To simplify the calculation, the water molecules are represented by their corresponding oxygen atoms. It is important to note that, before CDC-WBC analysis, the MD simulation trajectory must be RMS-aligned to a reference structure. This step is necessary to remove the effects of global rotations and translations of the solute. Moreover, the calculation is performed on GPUs to accelerate the density calculation process.

2.2.2. Identify Target Cryptic Site Fluctuation and Shape Transformation Region

In the cryptic site identification step, the CDC-WBC analysis workflow begins by defining the cryptic site transition region. To achieve this, a set of ‘cryptic site residues (CSRs)’ needs to be defined first. As discussed above, cryptic site formation usually involves large-scale conformational changes in protein systems. Therefore, our procedure intends to capture these dynamic transitions by tracking the dynamic fluctuations of the CSRs. Notably, in the CDC-WBC method, for well-studied cryptic sites, CSRs can be defined as the residues that directly interact with the cryptic site binder. Otherwise, the embedded algorithm for identifying CSRs can be used. In CDC-WBC, an ‘RMSF+GMM’ algorithm is applied. To be more specific, the CDC-WBC procedure first calculates the protein RMSF values from the MD trajectory. Furthermore, the residues with an RMSF higher than a cutoff value (default as 25% of the maximum RMSF value) are selected and their average coordinates are calculated throughout the MD trajectory. Finally, the Gaussian Mixture Model (GMM) algorithm from the Python scikit-learn package is used to cluster the protein residues based on the average coordinates of their heavy atoms, and CSRs are then selected from the clustering results. It is important to note that because the algorithm relies on the RMSF of the protein system, it may be less effective for cryptic sites formed through small-scale local conformational changes, such as the flipping of a few residues. With the identified CSRs, a ‘best-fit sphere’ is then defined for cryptic site identification. The calculation of the best-fit sphere and radius is rather straightforward. The first step is to calculate the geometric center of all the CSRs’ heavy atoms. Then, we apply a least-squares optimization algorithm to determine the sphere that best fits the CSR region.

2.2.3. Cryptic Site Volume Calculation

After completing the first two steps, the CDC-WBC procedure temporarily retains only those grids located within the best-fit sphere region as raw grids. Afterward, three refinement steps are applied: 1) Discard grid voxels within the van der Waals radius of any protein heavy atoms; 2) Discard grid voxels that lie outside the protein’s convex region; 3) Discard grid voxels with a water density lower than 0.01 molecules/ų, as these areas are rarely visited by water molecules. After these three refinement steps, the remaining grids are saved as the final refined grids (in PDB format). Finally, the cryptic site volume from each frame is calculated using a density-weighted scheme. To better incorporate water density information from the refined grids, we define the following Gaussian-based reweighting function for each grid voxel:

$${\mathit{W}}_{\mathit{i}}=0.5\times e^{-\frac{{({\mathit{density}}_{\mathit{i}}-mea{n}_{density})}^2}{2\times (st{d}_{density})}}+0.5$$ (3)

Here, ${\mathbf{W}}_{\mathbf{i}}$ represents the weighted density vector for the grid voxels in the $\mathrm{i}\text{-th}$ frame, and ${\mathbf{density}}_{\mathbf{i}}$ represents the density vector of the refined grids of the ith frame. The purpose of this weighting function is to relatively reduce the influence of low-density regions (~0.01 molecules/ų) and bulk-density regions (~0.033 molecules/ų) within the cryptic pocket. This approach ensures that regions indicative of transient cryptic sites are emphasized, while still acknowledging that both lower and higher-density areas are important for overall pocket characterization.

3. Results and Discussion

3.1. The Molecular Dynamics Simulation of TEM1 β-lactamase Successfully Sampled the Two Well-Studied Cryptic Sites

To demonstrate the effectiveness of CDC-WBC, we select TEM1 β-lactamase (Fig. 2) as our representative system. TEM1 β-lactamase is a bacterial enzyme that contributes to antibiotic resistance by catalyzing the hydrolytic cleavage of the β-lactam ring, a characteristic structural feature of these antibiotics [37, 38]. Among various protein systems with experimentally identified cryptic sites, TEM1 β-lactamase is the most extensively studied through molecular dynamics (MD) sampling methods. Located at the opposite face of the central β-sheet from the active site, the first cryptic site in this enzyme forms through an outward separation of two packing helices: helices 11 and 12, with a backbone movement of approximately 3 Å from the apo conformation (Fig 2). Upon helix unpacking, nonpolar residues at the interface of the two helices, together with some nearby charged residues, form a sizable pocket that can be occupied by two CBT ligands. For clarity, we refer to this first cryptic site as the “CBT” site throughout the following discussion. Notably, the unpacking motion of these helices is intimately coupled with a conformational change in the active site, particularly the displacement of the catalytic residue R244, which may explain the observed inhibitory effect associated with ligand binding at the CBT site [3]. In addition to this well-characterized CBT site, Bowman et al. identified a second cryptic site formed by microsecond-to-millisecond-scale transitions near the active site, specifically involving the "omega-loop" opening [36]. We refer to this second cryptic site as the “omega-loop” cryptic site in the sections that follow.

Fig. 2. Illustration of cryptic site formation in TEM1 β-lactamase:

From the apo (PDB: 1JWP, shown in gold) to the holo (PDB: 1PZO, shown in cyan) structure, the cryptic site emerges as helices 11 and 12 expand, resulting in an approximately 3 Å shift in the protein’s backbone.

During the 250-ns enhanced sampling simulations, the regions of helices 11 and 12 as well as the omega-loop region of TEM1 β-lactamase undergo significant conformational changes (Fig. 3A-C), with global RMSD fluctuations reaching up to approximately 3 Å (Fig. 3D). To further investigate the dynamic motions of these key secondary structures, we analyze the time-dependent RMSD fluctuations for helices 11 and 12 (Fig. 3E) and the distance between two residues—Asn175 on the omega loop and Arg65 on the underlying loop (Fig. 3F). As illustrated in Fig. 3E, Helix-11 experiences relatively larger RMSD fluctuations, reaching up to approximately 3 Å. In contrast, Helix-12 exhibits more modest RMSD fluctuations, peaking at approximately 2.0 Å. This aligns with the fact that the major conformational change associated with cryptic site opening occurs in Helix-11. For the omega-loop, we use the distance between the Cα atoms of Asn175 and Arg65 to monitor its opening transitions: the omega loop first moves downward during the initial 100 ns, and then moves upward, indicating the opening of the ‘omega-loop’ cryptic site. To further characterize the opening transitions of the two cryptic sites, we apply the CDC-WBC procedure in the following section to identify and analyze their formation process.

Fig. 3. Enhanced sampling MD simulation results of TEM1 β-lactamase.

A. The initial MD simulation structure, where both cryptic sites remain in a closed conformation. B. The open conformation of the omega-loop site, led by the outward fluctuation of the omega-loop. C. The open conformation of the CBT site, led by the unpacking of Helix 11 and Helix 12. D. RMSD vs. time plot of the 250-ns TEM1 β-lactamase simulation; it shows an RMSD change of up to 3 Å. E. Time-resolved RMSD plot for Helices 11 and 12 over 250-ns. A larger fluctuation for Helix 11 (up to 3 Å) is observed compared to Helix 12 (up to 2.0 Å). The two opening events for the CBT site are marked in the plot. F. Distance–time plot between residues Asn175 and Arg65 used to monitor the opening of the omega loop. It shows a three-stage fluctuation: initially decreasing from 10 to 6 Å, then sharply increasing to 14 Å, and finally decreasing to 5 Å. The opening and closing events for the omega-loop site are marked in the plot.

3.2. Detection of Cryptic Sites Opening in TEM1 β-lactamase Using Water Density Maps

Following the CDC-WBC procedure, we first calculate water density maps from the MD simulation trajectory of TEM1 β-lactamase. More specifically, we build a grid box with dimensions of 88 Å × 88 Å × 88 Å, matching the dimensions of the water box in the simulation system. The grid spacing is set to 2 Å. Next, for all trajectory frames, the instantaneous density within each grid voxel is calculated using the Gaussian convolution equation (Eq. 1). As a result, a water density map is generated for each MD trajectory frame, and the grid density data are then saved separately as density files. It is worth noting that the saved density files can be loaded into computational tools such as VMD, ChimeraX, and PyMOL, providing a straightforward means of visualizing the density distribution around the protein system.

From the calculated water density maps, we observe that fluctuations in water density around TEM1 β-lactamase successfully capture the openings of both cryptic sites. To visualize this process more clearly, Figure 4 shows 2D water density maps at three distinct time points (0 ns, 163 ns, and 250 ns), sliced along the Z-axis at Y = 22 Å and Y = 29 Å, respectively (the X-, Y-, and Z-axes correspond to the three spatial dimensions of the simulation box). For clarification, the water density ranges from 0 (no water) to 0.034 molecules/ų (bulk water density), corresponding to a color change from blue to red. At the beginning of the simulation, neither cryptic site is open, and CDC-WBC detects no obvious cavities in the corresponding regions (0 ns, Fig. 4A and 4C, sliced at Y = 22 Å and 29 Å). As the simulation progresses, at 163 ns (Fig. 4D, sliced at Y = 29 Å), the open state of the ‘omega-loop’ site is captured. As the simulation continues, at 250 ns (Fig. 4B, sliced at Y = 22 Å), another obvious cavity is captured, corresponding to the opening of the ‘CBT’ cryptic site. Clearly, by tracking water density fluctuations around the protein, our procedure can easily detect cryptic site openings as water flows into the newly formed cavity. More importantly, these results demonstrate that water density information can be effectively utilized to characterize cryptic sites. This is because during the opening of a cryptic site, water density within the site’s region undergoes dynamic changes. Having successfully recognized the two cryptic sites and calculated their water density maps, the next step in the CDC-WBC procedure is to adaptively track the opening process of these sites by identifying the cryptic site region in each MD trajectory frame.

Fig. 4. 2D water density maps derived from the MD trajectory of TEM1 β-lactamase.

The two cryptic site regions are indicated by dashed circles. A. Water density map calculated at 0 ns, which is sliced along the Y-axis at Y = 22 Å. At this point, no cavity is detected. B. Water density map calculated at 250 ns, which is sliced along the Y-axis at Y = 22 Å. Compared to 0 ns, the CDC-WBC method successfully detects the opening of the CBT cryptic site. C. Water density map calculated at 0 ns, which is sliced along the Y-axis at Y = 29 Å. Similar to the CBT site, no cavity is detected in the omega-loop region at 0 ns. D. Water density map calculated at 163 ns, which is sliced along the Y-axis at Y = 29 Å. The opening of the omega-loop cryptic site is detected. The X-, Y-, and Z-axes correspond to the three spatial dimensions of the simulation box.

3.3. Identification of Cryptic Site Residues (CSR) and Best-Fit Sphere from TEM1 β-lactamase

Following the successful detection of both the ‘CBT’ and ‘Omega-loop’ cryptic sites, the next step in the CDC-WBC procedure is to identify the cryptic site residues (CSRs) for further analysis. As previously discussed, an effective cryptic site identification method should adaptively monitor the transition of the cryptic site region throughout its opening process. To achieve this, the CDC-WBC method first applies the ‘RMSF+GMM’ procedure to determine a set of CSRs. Subsequently, a best-fit sphere is dynamically defined for each MD simulation frame, based on the positions of the CSR heavy atoms, as described in Section 2.2.2. Specifically, the RMSF values from the TEM1 β-lactamase trajectory are calculated first and we note that certain residues around the cryptic sites exhibit significant RMSF fluctuations (Fig. 5A). Then the residues with an RMSF larger than the cutoff value (0.98Å in the present CBT cryptic site study) are selected, and their average coordinates are calculated. Finally, to identify the CSRs, the Gaussian Mixture Model (GMM) from the Python scikit-learn package is applied to cluster the residues based on their averaged coordinates. As depicted in Fig. 5B-C, based on our observations from the TEM1 β-lactamase trajectory, we select three clusters that best describe the two cryptic pocket regions as CSR residues. Specifically, helices 11 and 12 are colored as green spheres, while the omega loop and part of the beta-sheet domain are colored blue and pink, respectively. With the CSRs identified, the CDC-WBC procedure then uses a least-squares optimization algorithm to define a best-fit sphere for each MD trajectory frame, based on the Cartesian coordinates of the CSR heavy atoms (Fig. 6A-C).

Fig. 5. Determination of Cryptic Site Residues (CSRs) in TEM1 β-lactamase using CDC-WBC.

A. RMSF values for all residues in TEM1 β-lactamase, which are calculated from the simulation trajectory. B–C. GMM clustering of high-fluctuation residues. The green, pink, and light blue clusters are selected as CSRs in TEM1 β-lactamase.

Fig. 6. Definition of the ‘best-fit sphere’ from CSR positions.

A. Best-fit spheres for the CBT site (blue) and the omega-loop site (green) in the initial TEM1 β-lactamase structure in which the omega-loop site is slightly open and the CBT site is closed. B. Best-fit sphere for the fully open omega-loop site. C. Best-fit sphere for the fully open CBT site.

3.4. The CDC-WBC Procedure Accurately Characterizes the Open-Close Transitions of TEM1 β-lactamase Cryptic Sites along the MD Trajectory

Following the definition of the best-fit spheres for each frame (Fig. 7A), the CDC-WBC procedure can then characterize the dynamic transitions of the cryptic sites of interest along the MD trajectory. As the initial step, all grid voxels falling outside the best-fit sphere region are discarded, and the remaining grids are saved as 'raw grids' (Fig. 7B). Next, to ensure that the grids accurately represent the cryptic site, the raw grids are refined through the following three steps: 1) Filter out grid voxels outside the convex-hull region defined by all protein heavy atoms; 2) Discard grid voxels within the van der Waals radius of any protein heavy atom; 3) Discard grid voxels with a water density lower than 0.01 water/ų. These three steps remove invalid grid voxels, resulting in refined pocket grids (Fig. 7C) that better describe the cryptic site region. The cryptic site volume fluctuations for each frame in the TEM1 β-lactamase trajectory are then calculated using these refined pocket grids. To better incorporate water information into the cryptic site identification process, we employ a reweighting procedure for the volume calculation step (in addition to the water density-based filtering), as described in detail in Section 2.2.3. The results show that the CDC-WBC procedure captures all the key transition events for the two cryptic sites (Fig. 7D). In detail, for the omega-loop site, an initial rapid opening transition is observed around 75 ns, whereas the CBT site shows only a slight opening event during the same period. At approximately 120 ns, the omega-loop site begins a significant opening transition and reaches its peak volume at about 150 ns. Following this, the omega-loop site completes its closing transition by around 175 ns, while the CBT site begins to open. The CBT site reaches its first maximum opening at around 190 ns, followed by a closing event. Finally, at around 225 ns, the CBT cryptic site opens again and reaches its maximum at 250 ns. To clarify the correlation between cryptic sites’ volume and local motions, Fig. 7F re-plots the data from Fig. 3E-F, coloring each time point by the weighted pocket volume. Large-volume frames (light yellow to red) cluster where helix 11 and helix 12 reach their highest RMSDs, confirming that their concerted motion accompanies opening of the CBT pocket. Likewise, large volumes for the Ω-loop site coincide with an increased 65–175 Cα distance, consistent with the loop flipping outward. It is important to note that all these transitions align closely with the MD simulation observations, strongly validating the CDC-WBC method’s ability to accurately identify and characterize key conformational transitions during the cryptic site opening and closing processes.

Fig. 7. Identification and characterization of two well-studied cryptic sites in TEM1 β-lactamase.

A. Best-fit spheres of the two cryptic sites, which are defined using CSRs. B. Initial identification of raw pocket grids throughout the MD trajectory. C. Cryptic site grids refined through three steps as described in the Methods section. D. Volume fluctuations of the two cryptic sites over the MD simulation trajectory. E. Visualization of the shape of the cryptic sites in TEM1 β-lactamase, saved as PDB files and viewable using VMD, PyMOL, or ChimeraX. F. RMSD changes of Helices 11 and 12, and distance changes between residues 65 and 175, colored by weighted pocket volume. This panel reproduces the data from Figs. 3E-F, with each time point shaded from deep blue (smallest pocket volume) to deep red (largest pocket volume).

3.5. Comparative Evaluation of the CDC-WBC Procedure and Three Protein Pocket Identification Methods

3.5.1. Comparative Analysis on Identifying the ‘CBT’ Cryptic Site Among CDC-WBC and POVME2, Epock and MDpocket

To demonstrate the effectiveness of our CDC-WBC procedure, we conduct a comparative study against three widely used protein cavity detection methods: POVME2, Epock, and MDpocket. As mentioned above, all three methods have been widely applied in cryptic site characterization studies. Since the primary goal of the CDC-WBC procedure is to identify cryptic site formation from MD trajectories, we also apply all three methods to characterize the opening process of the ‘CBT’ cryptic site in the 250-ns TEM1 β-lactamase trajectory. For parameter selection, the inclusion sphere for POVME2 is generated using its built-in ‘Pocket Identification’ algorithm (Fig. 8A). Following the instructions on the POVME2 website, we manually choose the sphere obtained from the algorithm that best encloses the CBT site; its center coordinates and radius are (4.03, 4.10, −12.87 Å; 13.77 Å). All other POVME2 parameters are left at their default values. Epock, a derivative of POVME2 that lacks its own pocket identification algorithm, is run with exactly the same inclusion sphere; its precision parameter was set to 0, and a 2-Å grid was used, with all remaining settings kept at the defaults. MDpocket requires two steps for trajectory-volume analysis. In the first step, the program scans the entire protein surface with the supplied extractIso.py script (isovalue = 0.2) to enumerate potential pockets. In the second step, the user selects the desired pocket—in this case, the CBT site shown in Fig. 8B. During this step, the alpha spheres are reassigned adaptively as the cryptic pocket opens and closes. The full set of configuration files used for POVME2, Epock, and MDpocket has been deposited alongside the CDC-WBC code in our public GitHub repository.

Fig. 8. Pocket region definition for POVME2, Epock, and MDpocket applications.

A. The cyan sphere represents the inclusion sphere defined using POVME2’s Pocket Identification algorithm. B. The blue surface represents the pocket region selected from the first MDpocket run, which is then used in the second run for volume characterization.

To evaluate how effectively our CDC-WBC method and the other three methods identify different open states of the ‘CBT’ cryptic site, we define the following procedure. We first divide the computed volumes from each method into 5-ns segments along the MD trajectory, and for each segment we calculate its mean and standard deviation. Next, we define an 'Identification Effectiveness' metric to evaluate the ‘separation’ of two adjacent segments’ volume distributions:

$$IdentificationEffectiveness=\frac{\mid \overline{X_{ı}}-\overline{X_j}\mid }{\frac{({\sigma }_i+{\sigma }_j)}{2}}$$ (4)

Here, ${\overline{X}}_{ı}$ and ${\overline{X}}_j$ are the means of two segments, and ${\sigma }_i$ and ${\sigma }_j$ are their corresponding standard deviations. If this value is less than 1 for two adjacent segments, they are considered to overlap significantly and are merged into a single state.

From the analysis results of the four methods (Fig. 9), the CDC-WBC procedure provides the most detailed characterization of the CBT cryptic site transitions (Fig. 9A). It not only captures major open-close events, such as the pocket opening at ~175 ns and ~250 ns and the closing event at ~210 ns, but also identifies 12 distinct substates throughout the trajectory using the 'Identification Effectiveness' metric. This indicates its superior ability to detect both global transitions and subtle conformational changes. In contrast, the MDpocket (Fig. 9B) method successfully captures key cryptic site transitions, including the initial opening at ~175 ns, closing at ~225 ns, and reopening at ~250 ns. However, it identifies only 6 distinct states, demonstrating a reduced ability to resolve substates compared to CDC-WBC. Similarly, POVME2 (Fig. 9C) captures major opening events at ~175 ns and ~250 ns, reflecting its capability to detect cryptic site transitions. However, it separates only 7 states and provides less distinct differentiation between substates, making it less effective than the CDC-WBC procedure. Lastly, the Epock method (Fig. 9D), derived from POVME2, is the least effective in characterizing cryptic site opening transitions. It identifies only 6 states and detects a single prominent opening event at ~200 ns, with volume fluctuations showing limited agreement with MD simulation results. In terms of run-time, the three CPU-only methods are faster—Epock finishes in a few seconds, POVME2 in roughly 5-6 min, and MDpocket in about 20 min—whereas CDC-WBC needs ~30 min on a single NVIDIA 3070 Ti GPU because of its water-density calculation step. Even so, the CDC-WBC volume trace aligns most closely with the actual opening and closing events observed in the trajectory, providing the highest temporal resolution among the four approaches.

Fig. 9. Comparative analysis of CDC-WBC among three widely used cavity detection methods (POVME2, Epock, and MDpocket).

A. CDC-WBC captures a volume fluctuation ranging from ~200 ų to ~2500 ų, identifying pocket opening events at ~60 ns, ~175 ns, and ~250 ns, and a closing event at ~225 ns. B. POVME2 identifies a volume fluctuation from ~750 ų to ~2250 ų, detecting cryptic site openings at ~175 ns and ~250 ns. C. Epock is unable to capture detailed transitions of the CBT cryptic site, identifying only one prominent opening event. D. MDpocket successfully tracks open-close transitions, showing fluctuations between ~0 ų and ~1000 ų.

3.5.2. Benchmarking CDC-WBC for Cryptic Site Identification: Comparative Study Among POVME2, Epock, and MDpocket on 93 Cryptic Sites from the CryptoSite Dataset

To further validate the efficiency of the CDC-WBC procedure in cryptic site identification, we conduct a benchmark analysis on 84 proteins with 93 cryptic sites from the CryptoSite dataset (Support Information). For each of these systems, a 10-ns regular MD simulation is performed on both the apo and holo structures. Notably, to ensure that the protein structure remains in its apo or holo form during the short simulation, a backbone RMSD restraint is applied in the simulation setup (Section 2.1.2). With the short MD trajectories, CDC-WBC, POVME2, Epock, and MDpocket are applied to identify cryptic sites in apo and holo protein structures. Since protein fluctuations are restrained, the cryptic site residues (CSRs) are defined following the procedure in the CryptoSite paper. Specifically, CSRs are the residues having at least one atom within 5 Å of any ligand atom in the holo structure. The best-fit spheres are then calculated based on these cryptic site residues. For the POVME2 and the Epock methods, initially, we attempt to use POVME2's pocket identification algorithm to define the cryptic site region in the 84 protein systems. However, the algorithm is not able to identify cryptic site regions for multiple protein systems. Consequently, the best-fit sphere from the CDC-WBC procedure is used as an inclusion sphere in POVME2 and Epock. Additionally, as demonstrated in the previous comparative study, dynamically defining the cryptic site region for each frame in MD simulations is crucial for precise characterization. Subsequently, in this benchmark analysis, we assign a specific inclusion sphere for each frame when applying POVME2 and Epock. The other parameters are set the same as in the ‘CBT’ cryptic site study. For MDpocket, we generated the frequency grid with extractIso.py (isovalue = 0.2); a lower threshold of 0.01 was needed only for the deeply buried pockets in 1FXX, 2GPO, 3CFN, and 1RYO. The resulting grids were then trimmed to the single pocket that matches the cryptic-site definition in the original CryptoSite paper [30].

To evaluate the effectiveness of different methods in identifying cryptic sites, we utilize the ‘Identification Effectiveness’ metric again to quantify the separation of volume distributions between the holo and apo forms for each method. In simple terms, the method with better identification capability should result in a more distinct separation (a larger ‘Identification Effectiveness’ value) of the volume distributions. For comparison purposes, in each benchmark system, we calculate the difference in ‘Identification Effectiveness’ between the CDC-WBC procedure and each of the other three methods. A resulting value greater than −1 is classified as positive, indicating that the CDC-WBC procedure performs competitively with or better than the other three methods. We then calculate the percentage of such instances, referred to as the ‘positive rate’. As shown in Fig. 10, the CDC-WBC procedure achieves a positive rate of 81.52% against MDpocket, 82.61% against POVME2, and 75% against Epock, indicating that the CDC-WBC procedure often outperforms these methods in cryptic site identification. Even for the negative comparison results, the maximum effective difference is −5, which still indicates a comparable performance in these cases.

Fig. 10. Comparison of Cryptic Site Identification Effectiveness for CDC-WBC vs. MDpocket (A), POVME2 (B), and Epock (C) across 84 benchmark protein systems (93 cryptic sites).

The CDC-WBC procedure consistently demonstrates higher effectiveness for most cryptic sites. Even in negative comparisons, the maximum effectiveness difference is only −5 across the three methods, indicating a generally comparable performance in these cases.

3.6. Conclusions

Identifying a novel cryptic site accurately and precisely from MD sampling results has long been a major challenge in related studies. To the best of our knowledge, the major tools currently used in cryptic site studies are not specifically designed for cryptic site identification, but rather for investigating general protein cavities. As a result, since the formation of a cryptic site usually involves large conformational changes in the protein structure, methods intended for general cavity detection may be unsuitable for cryptic sites.

In the present study, we show that a new procedure, Conformational Dynamics Capturing and Water-Based Characterization (CDC-WBC), can accurately and precisely identify two well-studied cryptic sites from the MD simulation trajectory of TEM1 β-lactamase. The calculated volume fluctuations capture both essential and minor transition events observed in the enhanced sampling MD simulation results. The effectiveness of the CDC-WBC procedure relies on dynamically defining and refining the cryptic site region. Using the RMSF and GMM procedures, the CDC-WBC approach defines a best-fit sphere for cryptic site identification in each MD trajectory frame. Together with the best-fit spheres, the convex hull of the protein’s heavy atoms dynamically filters out grids that fall outside the cryptic site region. Then, by discarding grids that are too close to protein heavy atoms or have a water density value lower than a predefined cutoff, the CDC-WBC procedure further refines the target region for each frame. Finally, the cryptic site volume for each frame is calculated using a water-density-based weighting function. This weighting function reduces the emphasis on low-density and bulk-density regions, thereby highlighting areas that may indicate cryptic site formation.

To demonstrate the effectiveness of our CDC-WBC procedure, we conduct two comparative studies against three methods widely used in cryptic site studies: POVME2, Epock, and MDpocket. We first apply them to identify and characterize the ‘CBT’ cryptic site sampled from TEM1 β-lactamase. From the analysis, CDC-WBC shows better performance than the other methods. The calculated volume fluctuation aligns well with the dynamic transitions of the CBT cryptic site observed from the MD trajectory. The results prove that in order to accurately demonstrate the transition details of cryptic site formation, it is essential to adaptively identify and refine the cryptic site region. To further demonstrate CDC-WBC’s effectiveness, we carry out a benchmark study on 84 protein systems with 93 known cryptic sites. In this process, the ‘Identification Effectiveness’ metric is used to quantify the results for comparison. From the benchmark results, the CDC-WBC procedure shows overall better results than the other three methods. Even for the negative comparison results, a comparable performance is still observed.

In conclusion, CDC-WBC is a protein cavity characterization algorithm specifically designed for cryptic sites. By leveraging the protein conformational changes during cryptic site formation and water density information, CDC-WBC achieves accurate and precise identification and characterization of cryptic sites sampled from MD simulation. Moreover, this is, to our knowledge, the first method to integrate water density information into the cryptic site characterization process. Our results demonstrate that compared to existing methods, CDC-WBC is more suitable for cryptic site studies.

Supplementary Material

Benchmarking CryptoSite Protein PDBs and Per-Pair Identification Effectiveness for All 93 Apo-Holo Systems (DOCX)