Folding Free Energy Changes Research Articles

Thermodynamic Details of Pinholin S2168 Activation Revealed Using Alchemical Free Energy Simulations.

Pinholin S2168 is a viral integral membrane protein whose function is to form nanoscopic "pinholes" in bacterial cell membranes to induce cell lysis as part of the viral replication cycle. Pinholin can transition from an inactive to an active conformation by exposing a transmembrane domain (TMD1) to the extracellular fluid. Upon activation, several copies of the protein assemble via interactions among a second transmembrane domain (TMD2) to form a single pore, thus hastening cell lysis and viral escape. The following experiments provide conformational descriptors of pinholin in active and inactive states and elucidate the molecular driving forces that control pinholin activity. In the present study, molecular dynamics (MD) simulations have been used to refine experimentally derived conformational descriptors into an atomistically detailed model of irsS2168, an antiholin mutant. To provide additional details about the thermodynamics of pinholin activation and to overcome large intrinsic kinetic barriers to activation, alchemical free energy simulations have been conducted. Alchemical mutations reveal the change in folding free energy upon mutation. The results suggest that alchemical mutations are an effective tool to rationalize experimental observations and predict the effects of site mutations on conformational states for proteins integrated into lipid bilayers. S16F, A17Q, A17Q+G21Q, and A17Q+G21Q+G14Q mutants reveal how changes in hydrophilicity and disruption of the glycine zipper motif influence pinholin's thermodynamic equilibrium, favoring the active conformation. These findings align with experimental observations from DEER spectroscopy, demonstrating that mutations increasing the hydrophilicity of TMD1 promote activation by making TMD1 more likely to exit the membrane and enter the extracellular fluid.

Application of an alchemical free energy method for the prediction of thermostable DuraPETase variants

Non-equilibrium (NEQ) alchemical free energy calculations are an emerging tool for accurately predicting changes in protein folding free energy resulting from amino acid mutations. In this study, this method in combination with the Rosetta ddg monomer tool was applied to predict more thermostable variants of the polyethylene terephthalate (PET) degrading enzyme DuraPETase. The Rosetta ddg monomer tool efficiently enriched promising mutations prior to more accurate prediction by NEQ alchemical free energy calculations. The relative change in folding free energy of 96 single amino acid mutations was calculated by NEQ alchemical free energy calculation. Experimental validation of ten of the highest scoring variants identified two mutations (DuraPETaseS61M and DuraPETaseS223Y) that increased the melting temperature (Tm) of the enzyme by up to 1 °C. The calculated relative change in folding free energy showed an excellent correlation with experimentally determined Tm resulting in a Pearson’s correlation coefficient of r = − 0.84. Limitations in the prediction of strongly stabilizing mutations were, however, encountered and are discussed. Despite these challenges, this study demonstrates the practical applicability of NEQ alchemical free energy calculations in prospective enzyme engineering projects.Key points• Rosetta ddg monomer enriches stabilizing mutations in a library of DuraPETase variants• NEQ free energy calculations accurately predict changes in Tmof DuraPETase• The DuraPETase variants S223Y, S42M, and S61M have increased TmGraphical

Most Monogenic Disorders Are Caused by Mutations Altering Protein Folding Free Energy.

Revealing the molecular effect that pathogenic missense mutations have on the corresponding protein is crucial for developing therapeutic solutions. This is especially important for monogenic diseases since, for most of them, there is no treatment available, while typically, the treatment should be provided in the early development stages. This requires fast targeted drug development at a low cost. Here, we report an updated database of monogenic disorders (MOGEDO), which includes 768 proteins and the corresponding 2559 pathogenic and 1763 benign mutations, along with the functional classification of the corresponding proteins. Using the database and various computational tools that predict folding free energy change (ΔΔG), we demonstrate that, on average, 70% of pathogenic cases result in decreased protein stability. Such a large fraction indicates that one should aim at in silico screening for small molecules stabilizing the structure of the mutant protein. We emphasize that knowledge of ΔΔG is essential because one wants to develop stabilizers that compensate for ΔΔG, but do not make protein over-stable, since over-stable protein may be dysfunctional. We demonstrate that, by using ΔΔG and predicted solvent exposure of the mutation site, one can develop a predictive method that distinguishes pathogenic from benign mutations with a success rate even better than some of the leading pathogenicity predictors. Furthermore, hydrophobic-hydrophobic mutations have stronger correlations between folding free energy change and pathogenicity compared with others. Also, mutations involving Cys, Gly, Arg, Trp, and Tyr amino acids being replaced by any other amino acid are more likely to be pathogenic. To facilitate further detection of pathogenic mutations, the wild type of amino acids in the 768 proteins mentioned above was mutated to other 19 residues (14,847,817 mutations), the ΔΔG was calculated with SAAFEC-SEQ, and 5,506,051 mutations were predicted to be pathogenic.

Improving the thermostability of Pseudoalteromonas Porphyrae κ-carrageenase by rational design and MD simulation

The industrial applications of the κ-carrageenases have been restricted by their poor thermostability. In this study, based on the folding free energy change (ΔΔG) and the flexibility analysis using molecular dynamics (MD) simulation for the alkaline κ-carrageenase KCgCD from Pseudoalteromonas porphyrae (WT), the mutant S190R was identified with improved thermostability. After incubation at 50 °C for 30 min, the residual activity of S190R was 63.7%, 25.7% higher than that of WT. The Tm values determined by differential scanning calorimetry were 66.2 °C and 64.4 °C for S190R and WT, respectively. The optimal temperature of S190R was 10 °C higher than that of WT. The κ-carrageenan hydrolysates produced by S190R showed higher xanthine oxidase inhibitory activity compared with the untreated κ-carrageenan. MD simulation analysis of S190R showed that the residues (V186–M194 and P196–G197) in F5 and the key residue R150 in F3 displayed the decreased flexibility, and residues of T169–N173 near the catalytic center displayed the increased flexibility. These changed flexibilities might be the reasons for the improved thermostability of mutant S190R. This study provides a useful rational design strategy of combination of ΔΔG calculation and MD simulation to improve the κ-carrageenase’s thermostability for its better industrial applications.

Estimating RNA Secondary Structure Folding Free Energy Changes with efn2.

A number of analyses require estimates of the folding free energy changes of specific RNA secondary structures. These predictions are often based on a set of nearest neighbor parameters that models the folding stability of a RNA secondary structure as the sum of folding stabilities of the structural elements that comprise the secondary structure. In the software suite RNAstructure, the free energy change calculation is implemented in the program efn2. The efn2 program estimates the folding free energy change and the experimental uncertainty in the folding free energy change. It can be run through the graphical user interface for RNAstructure, from the command line, or a web server. This chapter provides detailed protocols for using efn2.

Comparing Supervised Learning and Rigorous Approach for Predicting Protein Stability upon Point Mutations in Difficult Targets.

Accurate prediction of protein stability upon a point mutation has important applications in drug discovery and personalized medicine. It remains a challenging issue in computational biology. Existing computational prediction methods, which range from mechanistic to supervised learning approaches, have experienced limited progress over the last few decades. This stagnation is largely due to their heavy reliance on both the quantity and quality of the training data. This is evident in recent state-of-the-art methods that continue to yield substantial errors on two challenging blind test sets: frataxin and p53, with average root-mean-square errors exceeding 3 and 1.5 kcal/mol, respectively, which is still above the theoretical 1 kcal/mol prediction barrier. Rigorous approaches, on the other hand, offer greater potential for accuracy without relying on training data but are computationally demanding and require both wild-type and mutant structure information. Although they showed high accuracy for conserving mutations, their performance is still limited for charge-changing mutation cases. This might be due to the lack of an available mutant structure, often represented by a simplified capped peptide. The recent advances in protein structure prediction methods now make it possible to obtain structures comparable to experimental ones, including complete mutant structure information. In this work, we compare the performance of supervised learning-based methods and rigorous approaches for predicting protein stability on point mutations in difficult targets: frataxin and p53. The rigorous alchemical method significantly surpasses state-of-the-art techniques in terms of both the root-mean-squared error and Pearson correlation coefficient in these two challenging blind test sets. Additionally, we propose an improved alchemical method that employs the pmx double-system/single-box approach to accurately predict the folding free energy change upon both conserving and charge-changing mutations. The enhanced protocol can accurately predict both types of mutations, thereby outperforming existing state-of-the-art methods in overall performance.

Exploring the adaptability of the secondary structure of mRNA to temperature in intertidal snails based on SHAPE experiment.

RNA-based thermal regulation mechanism is an important strategy for organisms to cope with temperature changes. Inhabiting on intertidal rocky shore, a key interface of the ocean, atmosphere and terrestrial environments, intertidal species have developed variable thermal adaptation mechanisms, however, adaptions at the RNA level remain largely uninvestigated. For investigating the relationship between mRNA structural stability and species distribution, in the present study, the secondary structures of cytosolic malate dehydrogenase (cMDH) mRNAs of Echinolittorina malaccana, E. radiata and Littorina brevicula were determined using the selective 2'-hydroxyl acylation analyzed by primer extension (SHAPE), and the change in folding free energy of formation (ΔGfold) were calculated. The results showed that ΔGfold increased as the temperature increased. The difference in ΔGfold (ΔΔGfold) between two specific temperatures (0° to 25°C, 0° to 37°C, and 0° to 25°C) among the three species were different, and the ΔΔGfold value of E. malaccana was significantly lower than those of E. radiata and L. brevicula. The number of stems of cMDH mRNA of the snails decreased with temperature increased, and the breakpoint temperature of E. malaccana was the highest among them. The number of loops was also reduced with temperature increased, while the length of the loop structure increased accordingly. Consequently, these structural changes can potentially affect the translational efficiency of mRNA. These results implied that there were interspecific differences in the thermal stability of RNA secondary structures in intertidal snails, and these differences may be related to their distribution.

Predicting the Effect of Single Mutations on Protein Stability and Binding with Respect to Types of Mutations.

The development of methods and algorithms to predict the effect of mutations on protein stability, protein-protein interaction, and protein-DNA/RNA binding is necessitated by the needs of protein engineering and for understanding the molecular mechanism of disease-causing variants. The vast majority of the leading methods require a database of experimentally measured folding and binding free energy changes for training. These databases are collections of experimental data taken from scientific investigations typically aimed at probing the role of particular residues on the above-mentioned thermodynamic characteristics, i.e., the mutations are not introduced at random and do not necessarily represent mutations originating from single nucleotide variants (SNV). Thus, the reported performance of the leading algorithms assessed on these databases or other limited cases may not be applicable for predicting the effect of SNVs seen in the human population. Indeed, we demonstrate that the SNVs and non-SNVs are not equally presented in the corresponding databases, and the distribution of the free energy changes is not the same. It is shown that the Pearson correlation coefficients (PCCs) of folding and binding free energy changes obtained in cases involving SNVs are smaller than for non-SNVs, indicating that caution should be used in applying them to reveal the effect of human SNVs. Furthermore, it is demonstrated that some methods are sensitive to the chemical nature of the mutations, resulting in PCCs that differ by a factor of four across chemically different mutations. All methods are found to underestimate the energy changes by roughly a factor of 2.

Clustered tree regression to learn protein energy change with mutated amino acid.

Accurate and effective prediction of mutation-induced protein energy change remains a great challenge and of great interest in computational biology. However, high resource consumption and insufficient structural information of proteins severely limit the experimental techniques and structure-based prediction methods. Here, we design a structure-independent protocol to accurately and effectively predict the mutation-induced protein folding free energy change with only sequence, physicochemical and evolutionary features. The proposed clustered tree regression protocol is capable of effectively exploiting the inherent data patterns by integrating unsupervised feature clustering by K-means and supervised tree regression using XGBoost, and thus enabling fast and accurate protein predictions with different mutations, with an average Pearson correlation coefficient of 0.83 and an average root-mean-square error of 0.94kcal/mol. The proposed sequence-based method not only eliminates the dependence on protein structures, but also has potential applications in protein predictions with rare structural information.

Protein engineering for feedback resistance in 3-deoxy-D-arabino-heptulosonate 7-phosphate synthase

The shikimate pathway delivers aromatic amino acids (AAAs) in prokaryotes, fungi, and plants and is highly utilized in the industrial synthesis of bioactive compounds. Carbon flow into this pathway is controlled by the initial enzyme 3-deoxy-D-arabino-heptulosonate 7-phosphate synthase (DAHPS). AAAs produced further downstream, phenylalanine (Phe), tyrosine (Tyr), and tryptophan (Trp), regulate DAHPS by feedback inhibition. Corynebacterium glutamicum, the industrial workhorse for amino acid production, has two isoenzymes of DAHPS, AroF (Tyr sensitive) and AroG (Phe and Tyr sensitive). Here, we introduce feedback resistance against Tyr in the class I DAHPS AroF (AroFcg). We pursued a consensus approach by drawing on structural modeling, sequence and structural comparisons, knowledge of feedback-resistant variants in E. coli homologs, and computed folding free energy changes. Two types of variants were predicted: Those where substitutions putatively either destabilize the inhibitor binding site or directly interfere with inhibitor binding. The recombinant variants were purified and assessed in enzyme activity assays in the presence or absence of Tyr. Of eight AroFcg variants, two yielded > 80% (E154N) and > 50% (P155L) residual activity at 5 mM Tyr and showed > 50% specific activity of the wt AroFcg in the absence of Tyr. Evaluation of two and four further variants at positions 154 and 155 yielded E154S, completely resistant to 5 mM Tyr, and P155I, which behaves similarly to P155L. Hence, feedback-resistant variants were found that are unlikely to evolve by point mutations from the parental gene and, thus, would be missed by classical strain engineering.Key points• We introduce feedback resistance against Tyr in the class I DAHPS AroF• Variants at position 154 (155) yield > 80% (> 50%) residual activity at 5 mM Tyr• The variants found are unlikely to evolve by point mutations from the parental gene

Best templates outperform homology models in predicting the impact of mutations on protein stability.

Prediction of protein stability change upon mutation (ΔΔG) is crucial for facilitating protein engineering and understanding of protein folding principles. Robust prediction of protein folding free energy change requires the knowledge of protein three-dimensional (3D) structure. In case, protein 3D structure is not available, one can predict the structure from protein sequence; however, the perspectives of ΔΔG predictions for predicted protein structures are unknown. The accuracy of using 3D structures of the best templates for the ΔΔG prediction is also unclear. To investigate these questions, we used a representative set of seven diverse and accurate publicly available tools (FoldX, Eris, Rosetta, DDGun, ACDC-NN, ThermoNet and DynaMut) for stability change prediction combined with AlphaFold or I-Tasser for protein 3D structure prediction. We found that best templates perform consistently better than (or similar to) homology models for all ΔΔG predictors. Our findings imply using the best template structure for the prediction of protein stability change upon mutation if the protein 3D structure is not available. The data are available at https://github.com/ivankovlab/template-vs-model. Supplementary data are available at Bioinformatics online.

A Test and Refinement of Folding Free Energy Nearest Neighbor Parameters for RNA Including N6-Methyladenosine

RNA folding free energy change parameters are widely used to predict RNA secondary structure and to design RNA sequences. These parameters include terms for the folding free energies of helices and loops. Although the full set of parameters has only been traditionally available for the four common bases and backbone, it is well known that covalent modifications of nucleotides are widespread in natural RNAs. Covalent modifications are also widely used in engineered sequences. We recently derived a full set of nearest neighbor terms for RNA that includes N6-methyladenosine (m6A). In this work, we test the model using 98 optical melting experiments, matching duplexes with or without N6-methylation of A. Most experiments place RRACH, the consensus site of N6-methylation, in a variety of contexts, including helices, bulge loops, internal loops, dangling ends, and terminal mismatches. For matched sets of experiments that include either A or m6A in the same context, we find that the parameters for m6A are as accurate as those for A. Across all experiments, the root mean squared deviation between estimated and experimental free energy changes is 0.67 kcal/mol. We used the new experimental data to refine the set of nearest neighbor parameter terms for m6A. These parameters enable prediction of RNA secondary structures including m6A, which can be used to model how N6-methylation of A affects RNA structure.

Effects of macromolecular crowding on folding of small globular proteins

The effects of inert spherical crowders on the melting temperature and the folding stability of small globular proteins are investigated by using molecular dynamics simulations with a Gō-like model for the proteins. The energy parameter in the Gō-like model is obtained individually for each protein by matching the model’s melting temperature to the experimental meltingtemperature in the absence of crowders. It is shown that both the melting temperature and the folding stability of protein increase in the presence of the crowders. Specifically, as the crowders’ volume fraction φc increases from 0 to 0.4 the melting temperature increases by more than 20 Kelvins, whereas the folding stability is enhanced by up to ∼3.6 kcal/mol depending on the protein and the temperature. At room temperature (300 K), the stability enhancement is 1.2–1.4 kcal/mol, which is close to prior experimental data. It is also shown that the dependence of the folding free energy change on φc can be fitted well to the scaled particle theory by assuming a linear dependence of the effective size of the unfolded state on φc .

Significantly Improving the Thermostability and Catalytic Efficiency of Streptomyces mobaraenesis Transglutaminase through Combined Rational Design.

Streptomyces mobaraenesis transglutaminase has been widely used in food processing. We here significantly improved the catalytic properties of S2P-S23V-Y24N-S199A-K294L (TGm1), a highly stabilized variant of the transglutaminase. First, a virtual proline scan was performed based on folding free energy changes to obtain TGm1 variants with enhanced thermostability. Second, the residues within 15 Å of Cys64 in the enzyme-substrate complex of TGm1 were subjected to virtual saturation mutagenesis to generate the variants with reduced binding free energy and increased activity. After combining the favorable mutations, we obtained the variant FRAPD-TGm1-E28T-A265P-A287P (FRAPD-TGm2), exhibiting 66.9 min of half-life at 60 °C (t1/2(60 °C)), 67.8 °C of melting temperature (Tm), and 71.8 U/mg of specific activity, which are 2-fold, 2.6 °C, and 43.8% higher than those of FRAPD-TGm1, respectively. At last, to increase the surface negative net charge of FRAPD-TGm2, we introduced the mutations N96E-S144E-N163D-R183E-R208E-K325E, yielding FRAPD-TGm3. The latter's t1/2(60 °C), Tm, and specific activity were 122.9 min, 68.6 °C, and 83.7 U/mg, which are 83.8%, 0.8 °C, and 16.6% higher than the former, respectively. FRAPD-TGm3 is thus a robust candidate for transglutaminase application.

Identification of Hotspot Residues in Binding of SARS-CoV-2 Spike and Human ACE2 Proteins

Coronaviruses are a large family of viruses that can cause respiratory infections with varying severity from common cold to severe diseases such as novel coronavirus disease (COVID-19). COVID-19 has been declared as a global pandemic by the World Health Organization on March 11, 2020 and with the development of vaccines it slowed down as of this date. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) uses its spike glycoprotein (Sgp) to bind human angiotensin-converting enzyme 2 (hACE2) receptor, and mediates membrane fusion and virus entry. The recognition of Sgp to human ACE2 and its high affinity for it has been of great importance since this provides the first step in viral entry to human cells. Therefore, it is crucial to identify key residues (hotspots) in this process. In this study, computational alanine scanning has been performed for Sgp and hACE2. The residues identified with significance in binding and other residues in close proximity were studied further through molecular mechanics-based protein binding free energy change prediction methods. Moreover, the interfacial residues in both proteins were investigated for their cooperative binding. Additionally, folding free energy changes upon mutation to Ala were calculated to assess their effect on stability of Sgp and hACE2. Our results taken together with findings from previous studies revealed the residues that are most significant and are relatively significant in binding of Sgp to human ACE2 protein.

Surface salt bridges contribute to the extreme thermal stability of an FN3-like domain from a thermophilic bacterium.

This study uses differential scanning calorimetry, X-ray crystallography, and molecular dynamics simulations to investigate the structural basis for the high thermal stability (melting temperature 97.5°C) of a FN3-like protein domain from thermophilic bacteria Thermoanaerobacter tengcongensis (FN3tt). FN3tt adopts a typical FN3 fold with a three-stranded beta sheet packing against a four-stranded beta sheet. We identified three solvent exposed arginine residues (R23, R25, and R72), which stabilize the protein through salt bridge interactions with glutamic acid residues on adjacent strands. Alanine mutation of the three arginine residues reduced melting temperature by up to 22°C. Crystal structures of the wild type (WT) and a thermally destabilized (∆Tm -19.7°C) triple mutant (R23L/R25T/R72I) were found to be nearly identical, suggesting that the destabilization is due to interactions of the arginine residues. Molecular dynamics simulations showed that the salt bridge interactions in the WT were stable and provided a dynamical explanation for the cooperativity observed between R23 and R25 based on calorimetry measurements. In addition, folding free energy changes computed using free energy perturbation molecular dynamics simulations showed high correlation with melting temperature changes. This work is another example of surface salt bridges contributing to the enhanced thermal stability of thermophilic proteins. The molecular dynamics simulation methods employed in this study may be broadly useful for in silico surface charge engineering of proteins.

Large-scale in silico mutagenesis experiments reveal optimization of genetic code and codon usage for protein mutational robustness

BackgroundHow, and the extent to which, evolution acts on DNA and protein sequences to ensure mutational robustness and evolvability is a long-standing open question in the field of molecular evolution. We addressed this issue through the first structurome-scale computational investigation, in which we estimated the change in folding free energy upon all possible single-site mutations introduced in more than 20,000 protein structures, as well as through available experimental stability and fitness data.ResultsAt the amino acid level, we found the protein surface to be more robust against random mutations than the core, this difference being stronger for small proteins. The destabilizing and neutral mutations are more numerous in the core and on the surface, respectively, whereas the stabilizing mutations are about 4% in both regions. At the genetic code level, we observed smallest destabilization for mutations that are due to substitutions of base III in the codon, followed by base I, bases I+III, base II, and other multiple base substitutions. This ranking highly anticorrelates with the codon-anticodon mispairing frequency in the translation process. This suggests that the standard genetic code is optimized to limit the impact of random mutations, but even more so to limit translation errors. At the codon level, both the codon usage and the usage bias appear to optimize mutational robustness and translation accuracy, especially for surface residues.ConclusionOur results highlight the non-universality of mutational robustness and its multiscale dependence on protein features, the structure of the genetic code, and the codon usage. Our analyses and approach are strongly supported by available experimental mutagenesis data.

Estimating uncertainty in predicted folding free energy changes of RNA secondary structures.

Nearest neighbor parameters for estimating the folding stability of RNA are commonly used in secondary structure prediction, for generating folding ensembles of structures, and for analyzing RNA function. Previously, we demonstrated that we could quantify the uncertainties in each nearest neighbor parameter by perturbing the underlying optical melting data within experimental error and rederiving the parameters, which accounts for the substantial correlations that exist between the parameters. In this contribution, we describe a method to estimate uncertainty in the estimated folding stabilities of RNA structures, accounting for correlations in the nearest neighbor parameters. This method is incorporated in the RNA structure software package.

Additive Effects of Macromolecular Crowding and Confinement on Protein Stability

Folding of protein in vivo typically occurs in a solution highly crowded by macromolecules and in a confined space. It has been found that the effects of macromolecular crowding and confinement are similar in terms of the enhancement of protein stability. However, these effects are often considered separately in theoretical and simulation studies. In this study, by using coarse-grained models and Langevin dynamics, we show that the two effects are additive to each other when they are both present. Both crowding and confinement give rise to the folding temperature and the folding stability of protein. It is shown that the folding free energy change due to crowding in the confined condition can be fitted to Minton scaled particle theory by assuming a linear dependence of the effective radius of the protein unfolded state on the volume fraction of crowders.

Chemical Denaturation and Protein Precipitation Approach for Discovery and Quantitation of Protein–Drug Interactions

Described here is a mass spectrometry-based proteomics approach for the large-scale analysis of protein-drug interactions. The approach involves the evaluation of ligand-induced protein folding free energy changes (ΔΔ Gf) using chemical denaturation and protein precipitation (CPP) to identify the protein targets of drugs and to quantify protein-drug binding affinities. This is accomplished in a chemical denaturant-induced unfolding experiment where the folded and unfolded protein fractions in each denaturant containing buffer are quantified by the amount of soluble or precipitated protein (respectively) that forms upon abrupt dilution of the chemical denaturant and subsequent centrifugation of the sample. In the proof-of-principle studies performed here, the CPP technique was able to identify the well-known protein targets of cyclosporin A and geldanamycin in a yeast. The technique was also used to identify protein targets of sinefungin, a broad-based methyltransferase inhibitor, in a human MCF-7 cell lysate. The CPP technique also yielded dissociation constant ( Kd) measurements for these well-studied drugs that were in general agreement with previously reported Kd or IC50 values. In comparison to a similar energetics-based technique, termed stability of proteins from rates of oxidation (SPROX), the CPP technique yielded significantly better (∼50% higher) proteomic coverage and a largely reduced false discovery rate.