Dynamic Connection between Enzymatic Catalysis and Collective Protein Motions

Magnesium induced structural reorganization in the active site of adenylate kinase

Phosphoryl transfer is a fundamental reaction in cellular signaling and metabolism that requires Mg2+ as an essential cofactor. While the primary function of Mg2+ is electrostatic activation of substrates, such as ATP, the full spectrum of catalytic mechanisms exerted by Mg2+ is not known. In this study, we integrate structural biology methods, molecular dynamic (MD) simulations, phylogeny, and enzymology assays to provide molecular insights into Mg2+-dependent structural reorganization in the active site of the metabolic enzyme adenylate kinase. Our results demonstrate that Mg2+ induces a conformational rearrangement of the substrates (ATP and ADP), resulting in a 30° adjustment of the angle essential for reversible phosphoryl transfer, thereby optimizing it for catalysis. MD simulations revealed transitions between conformational substates that link the fluctuation of the angle to large-scale enzyme dynamics. The findings contribute detailed insight into Mg2+ activation of enzymes and may be relevant for reversible and irreversible phosphoryl transfer reactions.

A comparative study of two α-L-rhamnosidases with high sequence identity

The GH78 α-L-rhamnosidase from Aspergillus tubingensis (AT-Rha) was proved to be a new clade of Aspergillus α-L-rhamnosidases in the previous study. A putative α-L-rhamnosidase from A. kawachii IFO 4308 (AK-Rha) has 92 % identity in amino acid sequence with AT-Rha. In this study, AK-Rha was expressed in P. pastoris and characterized. Similar to AT-rRha, the recombinant AK-Rha (AK-rRha) showed a narrow substrate specificity to naringin. Interestingly, the enzyme activity of AK-rRha was 0.816 U/mg toward naringin, significantly lower than 125.142 U/mg of AT-rRha. Their large differences in catalytic efficiency was mainly due to their differences in kcat values between AK-rRha (0.67 s-1) and AT-rRha (4.89 × 104 s-1). The molecular dynamics simulation exhibited that the overall conformation of AK-Rha was rigid and that of AT-Rha was flexible; the Loop Y-L located above the catalytic domain formed different steric hindrances to naringin, and interacted with the flavonoid matrices at different strengths. The polar solvation energy analysis implied that the glycosidic bond was more easily hydrolysed in AT-Rha. The comparative study verified that the main feature of AK-Rha and AT-Rha represented Aspergillus α-L-rhamnosidase was the narrow substrate specificity toward naringin, and provided an insight of the relationships between their catalytic abilities and structures.

Substrate Turnover Dynamics Guide Ketol-Acid Reductoisomerase Redesign for Increased Specific Activity

The task of adapting enzymes for specific applications is often hampered by our incomplete ability to tune and tailor catalytic functions, particularly when seeking increased activity. Here, we develop and demonstrate a rational approach to address this challenge, applied to ketol-acid reductoisomerase (KARI), which has uses in industrial-scale isobutanol production. While traditional structure-based computational enzyme redesign strategies typically focus on the enzyme-bound ground state (GS) and transition state (TS), we postulated that additionally treating the underlying dynamics of complete turnover events that connect and pass through both states could further elucidate the structural properties affecting catalysis and help identify mutations that lead to increased catalytic activity. To examine the dynamics of substrate conversion with atomistic detail, we adapted and applied computational methods based on path sampling techniques to gather thousands of QM/MM simulations of attempted substrate turnover events by KARI: both productive (reactive) and unproductive (nonreactive) attempts. From these data, machine learning models were constructed and used to identify specific conformational features (interatomic distances, angles, and torsions) associated with successful, productive catalysis. Multistate protein redesign techniques were then used to select mutations that stabilized reactive-like structures over nonreactive-like ones while also meeting additional criteria consistent with enhanced specific activity. This procedure resulted in eight high-confidence enzyme mutants with a significant improvement in calculated specific activity relative to wild type (WT), with the fastest variant's increase in calculated k cat being (2 ± 1) × 104-fold. Collectively, these results suggest that introducing mutations designed to increase the population of reaction-promoting conformations of the enzyme-substrate complex before it reaches the barrier can provide an effective approach to engineering improved enzyme catalysts.

Biocatalytic approach for the synthesis of chiral alcohols for the development of pharmaceutical intermediates and other industrial applications: A review

Biocatalysis has emerged as a strong tool for the synthesis of active pharmaceutical ingredients (APIs). In the early twentieth century, whole cell biocatalysis was used to develop the first industrial biocatalytic processes, and the precise work of enzymes was unknown. Biocatalysis has evolved over the years into an essential tool for modern, cost-effective, and sustainable pharmaceutical manufacturing. Meanwhile, advances in directed evolution enable the rapid production of process-stable enzymes with broad substrate scope and high selectivity. Large-scale synthetic pathways incorporating biocatalytic critical steps towards >130 APIs of authorized pharmaceuticals and drug prospects are compared in terms of steps, reaction conditions, and scale with the corresponding chemical procedures. This review is designed on the functional group developed during the reaction forming alcohol functional groups. Some important biocatalyst sources, techniques, and challenges are described. A few APIs and their utilization in pharmaceutical drugs are explained here in this review. Biocatalysis has provided shorter, more efficient, and more sustainable alternative pathways toward existing small molecule APIs. Furthermore, non-pharmaceutical applications of biocatalysts are also mentioned and discussed. Finally, this review includes the future outlook and challenges of biocatalysis. In conclusion, Further research and development of promising enzymes are required before they can be used in industry.

Protecting Lyophilized Escherichia coli Adenylate Kinase

Drying protein-based drugs, usually via lyophilization, can facilitate storage at ambient temperature and improve accessibility but many proteins cannot withstand drying and must be formulated with protective additives called excipients. However, mechanisms of protection are poorly understood, precluding rational formulation design. To better understand dry proteins and their protection, we examine Escherichia coli adenylate kinase (AdK) lyophilized alone and with the additives trehalose, maltose, bovine serum albumin, cytosolic abundant heat soluble protein D, histidine, and arginine. We apply liquid-observed vapor exchange NMR to interrogate the residue-level structure in the presence and absence of additives. We pair these observations with differential scanning calorimetry data of lyophilized samples and AdK activity assays with and without heating. We show that the amino acids do not preserve the native structure as well as sugars or proteins and that after heating the most stable additives protect activity best.

Kinetic View of Enzyme Catalysis from Enhanced Sampling QM/MM Simulations

The rate constants of enzyme-catalyzed reactions (kcat) are often approximated from the barrier height of the reactive step. We introduce an enhanced sampling QM/MM approach that directly calculates the kinetics of enzymatic reactions, without introducing the transition-state theory assumptions, and takes into account the dynamical equilibrium between the reactive and non-reactive conformations of the enzyme/substrate complex. Our computed kcat values are in order-of-magnitude agreement with the experimental data for two representative enzymatic reactions.

Substrate Conformational Switch Enables the Stereoselective Dimerization in P450 NascB: Insights from Molecular Dynamics Simulations and Quantum Mechanical/Molecular Mechanical Calculations

P450 NascB catalyzes the coupling of cyclo-(l-tryptophan-l-proline) (1) to generate (-)-naseseazine C (2) through intramolecular C-N bond formation and intermolecular C-C coupling. A thorough understanding of its catalytic mechanism is crucial for the engineering or design of P450-catalyzed C-N dimerization reactions. By employing MD simulations, QM/MM calculations, and enhanced sampling, we assessed various mechanisms from recent works. Our study demonstrates that the most favorable pathway entails the transfer of a hydrogen atom from N7-H to Cpd I. Subsequently, there is a conformational change in the substrate radical, shifting it from the Re-face to the Si-face of N7 in Substrate 1. The Si-face conformation of Substrate 1 is stabilized by the protein environment and the π-π stacking interaction between the indole ring and heme porphyrin. The subsequent intermolecular C3-C6' bond formation between Substrate 1 radical and Substrate 2 occurs via a radical attack mechanism. The conformational switch of the Substrate 1 radical not only lowers the barrier of the intermolecular C3-C6' bond formation but also yields the correct stereoselectivity observed in experiments. In addition, we evaluated the reactivity of the ferric-superoxide species, showing it is not reactive enough to initiate the hydrogen atom abstraction from the indole NH group of the substrate. Our simulation provides a comprehensive mechanistic insight into how the P450 enzyme precisely controls both the intramolecular C-N cyclization and intermolecular C-C coupling. The current findings align with the available experimental data, emphasizing the pivotal role of substrate dynamics in governing P450 catalysis.

Allosteric activation unveils protein-mass modulation of ATP phosphoribosyltransferase product release

Heavy-isotope substitution into enzymes slows down bond vibrations and may alter transition-state barrier crossing probability if this is coupled to fast protein motions. ATP phosphoribosyltransferase from Acinetobacter baumannii is a multi-protein complex where the regulatory protein HisZ allosterically enhances catalysis by the catalytic protein HisGS. This is accompanied by a shift in rate-limiting step from chemistry to product release. Here we report that isotope-labelling of HisGS has no effect on the nonactivated reaction, which involves negative activation heat capacity, while HisZ-activated HisGS catalytic rate decreases in a strictly mass-dependent fashion across five different HisGS masses, at low temperatures. Surprisingly, the effect is not linked to the chemical step, but to fast motions governing product release in the activated enzyme. Disruption of a specific enzyme-product interaction abolishes the isotope effects. Results highlight how altered protein mass perturbs allosterically modulated thermal motions relevant to the catalytic cycle beyond the chemical step.

Identification of the Thermal Activation Network in Human 15-Lipoxygenase-2: Divergence from Plant Orthologs and Its Relationship to Hydrogen Tunneling Activation Barriers

The oxidation of polyunsaturated fatty acids by lipoxygenases (LOXs) is initiated by a C-H cleavage step in which the hydrogen atom is transferred quantum mechanically (i.e., via tunneling). In these reactions, protein thermal motions facilitate the conversion of ground-state enzyme-substrate complexes to tunneling-ready configurations and are thus important for transferring energy from the solvent to the active site for the activation of catalysis. In this report, we employed temperature-dependent hydrogen-deuterium exchange mass spectrometry (TDHDX-MS) to identify catalytically linked, thermally activated peptides in a representative animal LOX, human epithelial 15-LOX-2. TDHDX-MS of wild-type 15-LOX-2 was compared to two active site mutations that retain structural stability but have increased activation energies (Ea) of catalysis. The Ea value of one variant, V427L, is implicated to arise from suboptimal substrate positioning by increased active-site side chain rotamer dynamics, as determined by X-ray crystallography and ensemble refinement. The resolved thermal network from the comparative Eas of TDHDX-MS between wild-type and V426A is localized along the front face of the 15-LOX-2 catalytic domain. The network contains a clustering of isoleucine, leucine, and valine side chains within the helical peptides. This thermal network of 15-LOX-2 is different in location, area, and backbone structure compared to a model plant lipoxygenase from soybean that exhibits a low Ea value of catalysis compared to the human ortholog. The presented data provide insights into the divergence of thermally activated protein motions in plant and animal LOXs and their relationships to the enthalpic barriers for facilitating hydrogen tunneling.

Perspectives on Computational Enzyme Modeling: From Mechanisms to Design and Drug Development

Understanding enzyme mechanisms is essential for unraveling the complex molecular machinery of life. In this review, we survey the field of computational enzymology, highlighting key principles governing enzyme mechanisms and discussing ongoing challenges and promising advances. Over the years, computer simulations have become indispensable in the study of enzyme mechanisms, with the integration of experimental and computational exploration now established as a holistic approach to gain deep insights into enzymatic catalysis. Numerous studies have demonstrated the power of computer simulations in characterizing reaction pathways, transition states, substrate selectivity, product distribution, and dynamic conformational changes for various enzymes. Nevertheless, significant challenges remain in investigating the mechanisms of complex multistep reactions, large-scale conformational changes, and allosteric regulation. Beyond mechanistic studies, computational enzyme modeling has emerged as an essential tool for computer-aided enzyme design and the rational discovery of covalent drugs for targeted therapies. Overall, enzyme design/engineering and covalent drug development can greatly benefit from our understanding of the detailed mechanisms of enzymes, such as protein dynamics, entropy contributions, and allostery, as revealed by computational studies. Such a convergence of different research approaches is expected to continue, creating synergies in enzyme research. This review, by outlining the ever-expanding field of enzyme research, aims to provide guidance for future research directions and facilitate new developments in this important and evolving field.

Elucidating Dynamics of Adenylate Kinase from Enzyme Opening to Ligand Release

This study explores ligand-driven conformational changes in adenylate kinase (AK), which is known for its open-to-close conformational transitions upon ligand binding and release. By utilizing string free energy simulations, we determine the free energy profiles for both enzyme opening and ligand release and compare them with profiles from the apoenzyme. Results reveal a three-step ligand release process, which initiates with the opening of the adenosine triphosphate-binding subdomain (ATP lid), followed by ligand release and concomitant opening of the adenosine monophosphate-binding subdomain (AMP lid). The ligands then transition to nonspecific positions before complete dissociation. In these processes, the first step is energetically driven by ATP lid opening, whereas the second step is driven by ATP release. In contrast, the AMP lid opening and its ligand release make minor contributions to the total free energy for enzyme opening. Regarding the ligand binding mechanism, our results suggest that AMP lid closure occurs via an induced-fit mechanism triggered by AMP binding, whereas ATP lid closure follows conformational selection. This difference in the closure mechanisms provides an explanation with implications for the debate on ligand-driven conformational changes of AK. Additionally, we determine an X-ray structure of an AK variant that exhibits significant rearrangements in the stacking of catalytic arginines, explaining its reduced catalytic activity. In the context of apoenzyme opening, the sequence of events is different. Here, the AMP lid opens first while the ATP lid remains closed, and the free energy associated with ATP lid opening varies with orientation, aligning with the reported AK opening and closing rate heterogeneity. Finally, this study, in conjunction with our previous research, provides a comprehensive view of the intricate interplay between various structural elements, ligands, and catalytic residues that collectively contribute to the robust catalytic power of the enzyme.

1H, 13C, 15N backbone resonance assignment of Escherichia coli adenylate kinase

Adenylate kinase reversibly catalyzes the conversion of ATP plus AMP to two ADPs. This essential catalyst is present in every cell, and the Escherichia coli protein is often employed as a model enzyme. Our aim is to use the E. coli enzyme to understand dry protein structure and protection. Here, we report the expression, purification, steady-state assay, NMR conditions and 1H, 13C, 15N backbone resonance NMR assignments of its C77S variant. These data will also help others utilize this prototypical enzyme.

Insights into Enzymatic Catalysis from Binding and Hydrolysis of Diadenosine Tetraphosphate by E. coli Adenylate Kinase

Adenylate kinases play a crucial role in cellular energy homeostasis through the interconversion of ATP, AMP, and ADP in all living organisms. Here, we explore how adenylate kinase (AdK) from Escherichia coli interacts with diadenosine tetraphosphate (AP4A), a putative alarmone associated with transcriptional regulation, stress, and DNA damage response. From a combination of EPR and NMR spectroscopy together with X-ray crystallography, we found that AdK interacts with AP4A with two distinct modes that occur on disparate time scales. First, AdK dynamically interconverts between open and closed states with equal weights in the presence of AP4A. On a much slower time scale, AdK hydrolyses AP4A, and we suggest that the dynamically accessed substrate-bound open AdK conformation enables this hydrolytic activity. The partitioning of the enzyme into open and closed states is discussed in relation to a recently proposed linkage between active site dynamics and collective conformational dynamics.

Mechanistic Basis for a Connection between the Catalytic Step and Slow Opening Dynamics of Adenylate Kinase

Escherichia coli adenylate kinase (AdK) is a small, monomeric enzyme that synchronizes the catalytic step with the enzyme's conformational dynamics to optimize a phosphoryl transfer reaction and the subsequent release of the product. Guided by experimental measurements of low catalytic activity in seven single-point mutation AdK variants (K13Q, R36A, R88A, R123A, R156K, R167A, and D158A), we utilized classical mechanical simulations to probe mutant dynamics linked to product release, and quantum mechanical and molecular mechanical calculations to compute a free energy barrier for the catalytic event. The goal was to establish a mechanistic connection between the two activities. Our calculations of the free energy barriers in AdK variants were in line with those from experiments, and conformational dynamics consistently demonstrated an enhanced tendency toward enzyme opening. This indicates that the catalytic residues in the wild-type AdK serve a dual role in this enzyme's function─one to lower the energy barrier for the phosphoryl transfer reaction and another to delay enzyme opening, maintaining it in a catalytically active, closed conformation for long enough to enable the subsequent chemical step. Our study also discovers that while each catalytic residue individually contributes to facilitating the catalysis, R36, R123, R156, R167, and D158 are organized in a tightly coordinated interaction network and collectively modulate AdK's conformational transitions. Unlike the existing notion of product release being rate-limiting, our results suggest a mechanistic interconnection between the chemical step and the enzyme's conformational dynamics acting as the bottleneck of the catalytic process. Our results also suggest that the enzyme's active site has evolved to optimize the chemical reaction step while slowing down the overall opening dynamics of the enzyme.

Connecting Conformational Motions to Rapid Dynamics in Human Purine Nucleoside Phosphorylase

The influence of protein motions on enzyme catalysis remains a topic of active discussion. Protein motions occur across a variety of time scales, from vibrational fluctuations in femtoseconds, to collective motions in milliseconds. There have been numerous studies that show conformational motions may assist in catalysis, protein folding, and substrate specificity. It is also known through transition path sampling studies that rapid promoting vibrations contribute to enzyme catalysis. Human purine nucleoside phosphorylase (PNP) is one enzyme that contains both an important conformational motion and a rapid promoting vibration. The slower motion in this enzyme is associated with a loop motion, that when open allows substrate entry and product release but closes over the active site during catalysis. We examine the differences between an unconstrained PNP structure and a PNP structure with constraints on the loop motion. To investigate possible coupling between the slow and fast protein dynamics, we employed transition path sampling, reaction coordinate identification, electric field calculations, and free energy calculations reported here.

Accelerated Enveloping Distribution Sampling (AEDS) Allows for Efficient Sampling of Orthogonal Degrees of Freedom

One of the most challenging aspects in the molecular simulation of proteins is the study of slowly relaxing processes, such as loop rearrangements or ligands that adopt different conformations in the binding site. State-of-the-art methods used to calculate binding free energies rely on performing several short simulations (lambda steps), in which the ligand is slowly transformed into the endstates of interest. This makes capturing the slowly relaxing processes even more difficult, as they would need to be observed in all of the lambda steps. One attractive alternative is the use of a reference state capable of sampling all of the endstates of interest in a single simulation. However, the energy barriers between the states can be too high to overcome, thus hindering the sampling of all of the relevant conformations. Accelerated enveloping distribution sampling (AEDS) is a recently developed reference state technique that circumvents the high-energy-barrier challenge by adding a boosting potential that flattens the energy landscape without distorting the energy minima. In the present work, we apply AEDS to the well-studied benchmark system T4 lysozyme L99A. The T4 lysozyme L99A mutant contains a hydrophobic pocket in which there is a valine (valine 111), whose conformation influences the binding efficiencies of the different ligands. Incorrectly sampling the dihedral angle can lead to errors in predicted binding free energies of up to 16 kJ mol^-1. This protein constitutes an ideal scenario to showcase the advantages and challenges when using AEDS in the presence of slow relaxing processes. We show that AEDS is able to successfully sample the relevant degrees of freedom, providing accurate binding free energies, without the need of previous information of the system in the form of collective variables. Additionally, we showcase the capabilities of AEDS to efficiently screen a set of ligands. These results represent a promising first step toward the development of free-energy methods that can respond to more intricate molecular events.

Protein dynamics: The future is bright and complicated!

Biological life depends on motion, and this manifests itself in proteins that display motion over a formidable range of time scales spanning from femtoseconds vibrations of atoms at enzymatic transition states, all the way to slow domain motions occurring on micro to milliseconds. An outstanding challenge in contemporary biophysics and structural biology is a quantitative understanding of the linkages among protein structure, dynamics, and function. These linkages are becoming increasingly explorable due to conceptual and methodological advances. In this Perspective article, we will point toward future directions of the field of protein dynamics with an emphasis on enzymes. Research questions in the field are becoming increasingly complex such as the mechanistic understanding of high-order interaction networks in allosteric signal propagation through a protein matrix, or the connection between local and collective motions. In analogy to the solution to the "protein folding problem," we argue that the way forward to understanding these and other important questions lies in the successful integration of experiment and computation, while utilizing the present rapid expansion of sequence and structure space. Looking forward, the future is bright, and we are in a period where we are on the doorstep to, at least in part, comprehend the importance of dynamics for biological function.

Insights into the evolution of enzymatic specificity and catalysis: From Asgard archaea to human adenylate kinases

Enzymatic catalysis is critically dependent on selectivity, active site architecture, and dynamics. To contribute insights into the interplay of these properties, we established an approach with NMR, crystallography, and MD simulations focused on the ubiquitous phosphotransferase adenylate kinase (AK) isolated from Odinarchaeota (OdinAK). Odinarchaeota belongs to the Asgard archaeal phylum that is believed to be the closest known ancestor to eukaryotes. We show that OdinAK is a hyperthermophilic trimer that, contrary to other AK family members, can use all NTPs for its phosphorylation reaction. Crystallographic structures of OdinAK-NTP complexes revealed a universal NTP-binding motif, while ¹⁹F NMR experiments uncovered a conserved and rate-limiting dynamic signature. As a consequence of trimerization, the active site of OdinAK was found to be lacking a critical catalytic residue and is therefore considered to be "atypical." On the basis of discovered relationships with human monomeric homologs, our findings are discussed in terms of evolution of enzymatic substrate specificity and cold adaptation.

Role of Repeated Conformational Transitions in Substrate Binding of Adenylate Kinase

The catalytic cycle of the enzyme adenylate kinase involves large conformational motions between open and closed states. A previous single-molecule experiment showed that substrate binding tends to accelerate both the opening and the closing rates and that a single turnover event often involves multiple rounds of conformational switching. In this work, we showed that the repeated conformational transitions of adenylate kinase are essential for the relaxation of incorrectly bound substrates into the catalytically competent conformation by combining all-atom and coarse-grained molecular simulations. In addition, free energy calculations based on all-atom and coarse-grained models demonstrated that the enzyme with incorrectly bound substrates has much a lower free energy barrier for domain opening compared to that with the correct substrate conformation, which may explain the the acceleration of the domain opening rate by substrate binding. The results of this work provide mechanistic understanding to previous experimental observations and shed light onto the interplay between conformational dynamics and enzyme catalysis.

Correlating the Local and Global Dynamics of an Enzyme in the Crowded Milieu

Enzymes are dynamic biological macromolecules, with their catalytic function(s) being largely influenced by the changes in local fluctuations of amino acid side chains as well as global structural modulations that the enzyme undergoes. Such local and global motions can be highly affected inside the crowded physiological interior of the cell. Here, we have addressed the role of dynamic structural flexibility in affecting the activation energy barrier of a flexible multidomain enzyme adenylate kinase (AK3L1, UniProtKB: Q9UIJ7). Activation energy profiles of both local (at three different sites along the polypeptide backbone) and global dynamics of the enzyme have been monitored using solvation studies on the subnanosecond time scale and tryptophan quenching studies over the temperature range of 278-323 K, respectively, under crowded conditions (Ficoll 70, Dextran 40, Dextran 70, and PEG 8). This study not only provides the site-specific mapping of dynamics but reveals that the activation energies associated with these local motions undergo a significant decrease in the presence of macromolecular crowders, providing new insights into how crowding affects internal protein dynamics. The crowded scenario also aids in enhancing the coupling between the local and global motions of the enzyme. Moreover, select portions/regions of the enzyme when taken together can well mirror the overall dynamics of the biomolecule, showing possible energy hotspots along the polypeptide backbone.

Response of Terahertz Protein Vibrations to Ligand Binding: Calmodulin-Peptide Complexes as a Case Study

Terahertz vibrations are sensitive reporters of the structure and interactions of proteins. Ligand binding alters the nature and distribution of these collective vibrations. The ligand-induced changes in the terahertz protein vibrations contribute to the binding entropy and to the overall thermodynamic stability of the resultant protein-ligand complexes. Here, we have examined the response of the low-frequency (below 6 terahertz) collective vibrations of the calcium-loaded calmodulin (CaM) to binding to five different ligands, both in the presence and absence of water, using normal-mode analysis and molecular dynamics simulations. A comparison of the vibrational spectra of hydrated and dry systems reveals that protein-solvent interactions stiffen the terahertz protein vibrations and that these solvent-coupled collective vibrations contribute significantly to the hydration-sensitive variation in the vibrational entropy of CaM. In the absence of water, the low-frequency vibrations of CaM are stiffened by ligand binding. On the contrary, the number and the cumulative vibrational entropy of low-frequency vibrational modes (ω < 200 cm^-1) of the hydrated CaM are increased noticeably after binding to the peptides, indicating binding-induced softening of collective vibrations of the protein. Although the calculated and experimental binding affinities of the chosen complexes correlated reasonably well, no systematic correlation was observed between the protein vibrational entropy and the binding affinity. The results underscored the importance of the interplay of protein-ligand and solvent interactions in modulating the low-frequency vibrations of proteins.