Towards the understanding of molecular motors and its relationship with local unfolding.

Molecular motors are machines essential for life since they convert chemical energy into mechanical work. However, the precise mechanism by which nucleotide binding, catalysis, or release of products is coupled to the work performed by the molecular motor is still not entirely clear. This is due, in part, to a lack of understanding of the role of force in the mechanical-structural processes involved in enzyme catalysis. From a mechanical perspective, one promising hypothesis is the Haldane-Pauling hypothesis which considers the idea that part of the enzymatic catalysis is strain-induced. It suggests that enzymes cannot be efficient catalysts if they are fully complementary to the substrates. Instead, they must exert strain on the substrate upon binding, using enzyme-substrate energy interaction (binding energy) to accelerate the reaction rate. A novel idea suggests that during catalysis, significant strain energy is built up, which is then released by a local unfolding/refolding event known as 'cracking'. Recent evidence has also shown that in catalytic reactions involving conformational changes, part of the heat released results in a center-of-mass acceleration of the enzyme, raising the possibility that the heat released by the reaction itself could affect the enzyme's integrity. Thus, it has been suggested that this released heat could promote or be linked to the cracking seen in proteins such as adenylate kinase (AK). We propose that the energy released as a consequence of ligand binding/catalysis is associated with the local unfolding/refolding events (cracking), and that this energy is capable of driving the mechanical work.

Probing the energy barriers and stages of membrane protein unfolding using solid-state NMR spectroscopy.

Understanding how the amino acid sequence dictates protein structure and defines its stability is a fundamental problem in molecular biology. It is especially challenging for membrane proteins that reside in the complex environment of a lipid bilayer. Here, we obtain an atomic-level picture of the thermally induced unfolding of a membrane-embedded α-helical protein, human aquaporin 1, using solid-state nuclear magnetic resonance spectroscopy. Our data reveal the hierarchical two-step pathway that begins with unfolding of a structured extracellular loop and proceeds to an intermediate state with a native-like helical packing. In the second step, the transmembrane domain unravels as a single unit, resulting in a heterogeneous misfolded state with high helical content but with nonnative helical packing. Our results show the importance of loops for the kinetic stabilization of the whole membrane protein structure and support the three-stage membrane protein folding model.

Molecular dynamics simulations suggest the potential toxicity of fluorinated graphene to HP35 protein via unfolding the α-helix structure.

Fluorinated graphene, a two-dimensional nanomaterial composed of three atomic layers, a central carbon layer sandwiched between two layers of fluorine atoms, has attracted considerable attention across various fields, particularly for its potential use in biomedical applications. Nonetheless, scant effort has been devoted to assessing the potential toxicological implications of this nanomaterial. In this study, we scrutinize the potential impact of fluorinated graphene on a protein model, HP35 by utilizing extensive molecular dynamics (MD) simulation methods. Our MD results elucidate that upon adsorption to the nanomaterial, HP35 undergoes a denaturation process initiated by the unraveling of the second helix of the protein and the loss of the proteins hydrophobic core. In detail, substantial alterations in various structural features of HP35 ensue, including alterations in hydrogen bonding, Q value, and RMSD. Subsequent analyses underscore that hydrophobic and van der Waals interactions (predominant), alongside electrostatic energy (subordinate), exert influence over the adsorption of HP35 on the fluorinated graphene surface. Mechanistic scrutiny attests that the unrestrained lateral mobility of HP35 on the fluorinated graphene nanomaterial primarily causes the exposure of HP35's hydrophobic core, resulting in the eventual structural denaturation of HP35. A trend in the features of 2D nanostructures is proposed that may facilitate the denaturation process. Our findings not only substantiate the potential toxicity of fluorinated graphene but also unveil the underlying molecular mechanism, which thereby holds significance for the prospective utilization of such nanomaterials in the field of biomedicine.

Ligand-dependent folding and unfolding dynamics and free energy landscapes of acylphosphatase.

Acylphosphatase (AcP) is an enzyme which catalyses the hydrolysis of acylphosphate. The binding with the phosphate ion (Pi) assumes significance in preserving both the stability and enzymatic activity of AcP. While previous studies using single molecule force spectroscopy explored the mechanical properties of AcP, the influence of Pi on its folding and unfolding dynamic behaviors remains unexplored. In this work, using stable magnetic tweezers, we measured and compared the force-dependent folding and unfolding rates of AcP in the Tris buffer and phosphate buffer within a force range from 2 pN to 40 pN. We found that Pi exerts no discernible effect on the folding dynamics but consistently decreases the force-dependent unfolding rate of AcP by a constant ratio across the entire force spectrum. The free energy landscapes of AcP in the absence and presence of Pi are constructed. Our results reveal that Pi selectively binds to the native state of AcP, stabilizing it and suggesting the general properties of specific ligand-receptor interactions.

The effect of chrysin binding on the conformational dynamics and unfolding pathway of human serum albumin.

Studies on the interactions between ligands and proteins provide insights into how a possible medication alters the structures and activities of the target or carrier proteins. The natural flavonoid aglycone Chrysin (CHR) has demonstrated anti-inflammatory, antioxidant, antiapoptotic, neuroprotective, and antineoplastic effects, both in vitro and in vivo. In this work, we investigated the impact of CHR binding on the as-yet-unexplored conformation, dynamics, and unfolding mechanism of human serum albumin (HSA). We determined CHR binding to HSA domain-II with the association constant (Ka) of 2.70 ± 0.21 × 105 M-1. The urea-induced sequential unfolding mechanism of HSA was used to elucidate the debatable binding location of CHR. CHR binding induced both secondary and tertiary structural alterations in the protein as studied by far-UV circular dichroism and intrinsic fluorescence spectroscopy. Red edge excitation shift (REES) indicated a decrease in conformational dynamics of the protein on the complex formation. This suggested an ordered compact and spatial arrangement of the CHR-boundmolecule. The binding of CHR was found to significantly modulate the urea-induced unfolding pathway of HSA. Urea-induced unfolding pathway of HSA became a two-state process (N-U) from a three-state process (N-I-U). The interaction of CHR is found to increase the thermal stability of the protein by ∼4 °C. This study focuses on the fundamental sciences and demonstrates how prospective medication compounds can alter the dynamics and stability of protein structure.

Collision induced unfolding and molecular dynamics simulations of norovirus capsid dimers reveal strain-specific stability profiles.

Collision induced unfolding (CIU) is a method used with ion mobility mass spectrometry to examine protein structures and their stability. Such experiments yield information about higher order protein structures, yet are unable to provide details about the underlying processes. That information can however be provided using molecular dynamics simulations. Here, we investigate the gas-phase unfolding of norovirus capsid dimers from the Norwalk and Kawasaki strains by employing molecular dynamics simulations over a range of temperatures, representing different levels of activation, together with CIU experiments. The dimers have highly similar structures, but their CIU reveals different stability that can be explained by the different dynamics that arises in response to the activation seen in the simulations, including a part of the sequence with previously observed strain-specific dynamics in solution. Our findings show how similar protein variants can be examined using mass spectrometric techniques in conjunction with atomistic molecular dynamics simulations to reveal differences in stability as well as differences in how and where unfolding takes place upon activation.

Time-Resolved Ultraviolet Photodissociation Mass Spectrometry Probes the Mutation-Induced Alterations in Protein Stability and Unfolding Dynamics.

How mutations impact protein stability and structure dynamics is crucial for understanding the pathological process and rational drug design. Herein, we establish a time-resolved native mass spectrometry (TR-nMS) platform via a rapid-mixing capillary apparatus for monitoring the acid-initiated protein unfolding process. The molecular details in protein structure unfolding are further profiled by a 193 nm ultraviolet photodissociation (UVPD) analysis of the structure-informative photofragments. Compared with the wild-type dihydrofolate reductase (WT-DHFR), the M42T/H114R mutant (MT-DHFR) exhibits a significant stability decrease in TR-nMS characterization. UVPD comparisons of the unfolding intermediates and original DHFR forms indicate the special stabilization effect of cofactor NADPH on DHFR structure, and the M42T/H114R mutations lead to a significant decrease in NADPH-DHFR interactions, thus promoting the structure unfolding. Our study paves the way for probing the mutation-induced subtle changes in the stability and structure dynamics of drug targets.

Study of Monoclonal Antibody Aggregation at the Air-Liquid Interface under Flow by ATR-FTIR Spectroscopic Imaging.

Throughout bioprocessing, transportation, and storage, therapeutic monoclonal antibodies (mAbs) experience stress conditions that may cause protein unfolding and/or chemical modifications. Such structural changes may lead to the formation of aggregates, which reduce mAb potency and may cause harmful immunogenic responses in patients. Therefore, aggregates need to be detected and removed or ideally prevented from forming. Air-liquid interfaces, which arise during various stages of bioprocessing, are one of the stress factors causing mAb aggregation. In this study, the behavior of an immunoglobulin G (IgG) at the air-liquid interface was investigated under flow using macro attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopic imaging. This chemically specific imaging technique allows observation of adsorption of IgG to the air-liquid interface and detection of associated secondary structural changes. Chemical images revealed that IgG rapidly accumulated around an injected air bubble under flow at 45 °C; however, no such increase was observed at 25 °C. Analysis of the second derivative spectra of IgG at the air-liquid interface revealed changes in the protein secondary structure associated with increased intermolecular ß-sheet content, indicative of aggregated IgG. The addition of 0.01% w/v polysorbate 80 (PS80) reduced the amount of IgG at the air-liquid interface in a static setup at 30 °C; however, this protective effect was lost at 45 °C. These results suggest that the presence of air-liquid interfaces under flow may be detrimental to mAb stability at elevated temperatures and demonstrate the power of ATR-FTIR spectroscopic imaging for studying the structural integrity of mAbs under bioprocessing conditions.

α-catenin middle- and actin-binding domain unfolding mutants differentially impact epithelial strength and sheet migration.

α-catenin (α-cat) displays force-dependent unfolding and binding to actin filaments through direct and indirect means, but features of adherens junction structure and function most vulnerable to loss of these allosteric mechanisms have not been directly compared. By reconstituting an α-cat F-actin-binding domain unfolding mutant known to exhibit enhanced binding to actin (α-cat-H0-FABD+) into α-cat knockout Madin Darby Canine Kidney (MDCK) cells, we show that partial loss of the α-cat catch bond mechanism (via an altered H0 α-helix) leads to stronger epithelial sheet integrity with greater colocalization between the α-cat-H0-FABD+ mutant and actin. α-cat-H0-FABD+ -expressing cells are less efficient at closing scratch-wounds, suggesting reduced capacity for more dynamic cell-cell coordination. Evidence that α-cat-H0-FABD+ is equally accessible to the conformationally sensitive α18 antibody epitope as WT α-cat and shows similar vinculin recruitment suggests this mutant engages lower tension cortical actin networks, as its M-domain is not persistently open. Conversely, α-cat-M-domain salt-bridge mutants with persistent recruitment of vinculin and phosphorylated myosin light chain show only intermediate monolayer adhesive strengths, but display less directionally coordinated and thereby slower migration speeds during wound-repair. These data show α-cat M- and FABD-unfolding mutants differentially impact cell-cell cohesion and migration properties, and suggest signals favoring α-cat-cortical actin interaction without persistent M-domain opening may improve epithelial monolayer strength through enhanced coupling to lower tension actin networks.

Collision-Induced Unfolding Reveals Disease-Associated Stability Shifts in Mitochondrial Transfer Ribonucleic Acids.

Ribonucleic acids (RNAs) remain challenging targets for structural biology, creating barriers to understanding their vast functions in cellular biology and fully realizing their applications in biotechnology. The inherent dynamism of RNAs creates numerous obstacles in capturing their biologically relevant higher-order structures (HOSs), and as a result, many RNA functions remain unknown. In this study, we describe the development of native ion mobility-mass spectrometry and collision-induced unfolding (CIU) for the structural characterization of a variety of RNAs. We evaluate the ability of these techniques to preserve native structural features in the gas phase across a wide range of functional RNAs. Finally, we apply these tools to study the elusive mitochondrial encephalopathy, lactic acidosis, and stroke-like episodes-associated A3243G mutation. Our data demonstrate that our experimentally determined conditions preserve some solution-state memory of RNAs via the correlated complexity of CIU fingerprints and RNA HOS, the observation of predicted stability shifts in the control RNA samples, and the retention of predicted magnesium binding events in gas-phase RNA ions. Significant differences in collision cross section and stability are observed as a function of the A3243G mutation across a subset of the mitochondrial tRNA maturation pathway. We conclude by discussing the potential application of CIU for the development of RNA-based biotherapeutics and, more broadly, transcriptomic characterization.

The Role of Force Fields and Water Models in Protein Folding and Unfolding Dynamics.

Protein folding is a fascinating, not fully understood phenomenon in biology. Molecular dynamics (MD) simulations are an invaluable tool to study conformational changes in atomistic detail, including folding and unfolding processes of proteins. However, the accuracy of the conformational ensembles derived from MD simulations inevitably relies on the quality of the underlying force field in combination with the respective water model. Here, we investigate protein folding, unfolding, and misfolding of fast-folding proteins by examining different force fields with their recommended water models, i.e., ff14SB with the TIP3P model and ff19SB with the OPC model. To this end, we generated long conventional MD simulations highlighting the perks and pitfalls of these setups. Using Markov state models, we defined kinetically independent conformational substates and emphasized their distinct characteristics, as well as their corresponding state probabilities. Surprisingly, we found substantial differences in thermodynamics and kinetics of protein folding, depending on the combination of the protein force field and water model, originating primarily from the different water models. These results emphasize the importance of carefully choosing the force field and the respective water model as they determine the accuracy of the observed dynamics of folding events. Thus, the findings support the hypothesis that the water model is at least equally important as the force field and hence needs to be considered in future studies investigating protein dynamics and folding in all areas of biophysics.

Plasma-Droplet Fusion-Mass Spectrometry Reveals Sub-Millisecond Protein Unfolding Dynamics Induced by Reactive Oxygen Species.

Investigating the connection between reactive oxygen species (ROS) and oxidative protein unfolding is critical to reveal the mechanisms underlying disease involving elevated ROS and protein misfolding. This could inform the development of therapeutics targeting cells based on their redox status. In this study, we developed a plasma-droplet fusion-mass spectrometry platform to rapidly assess protein resilience to ROS. This home-built system fuses ROS generated from the microplasma source with protein microdroplets from a tunable nanospray source. At the droplet-plasma intersection, ROS interact with proteins before entering the mass spectrometer for mass identification and structural characterization. Benefiting from the small-sized microdroplet with adjustable traveling velocity, the platform enables the first sub-millisecond kinetic study of ROS-induced protein unfolding, with a rate constant of approximately 1.81 ms-1. Capturing ROS-induced protein unfolding intermediates and the resultant ligand release dynamics can be extended to many more protein systems. We foresee broad applications for establishing previously undetected protein unfolding events when biologically impactful ROS are enriched in time and space with functional proteins and complexes.

Lithium Chloride Effects Field-Induced Protein Unfolding and the Transport Energetics Inside a Nanopipette.

The tapered geometry of nanopipettes offers a unique perspective on protein transport through nanopores since both a gradual and fast confinement are possible depending on the translocation direction. The protein capture rate, unfolding, speed of translocation, and clogging probability are studied by toggling the LiCl concentration between 2 and 4 M. Interestingly, the proteins in this study could be transported with or against electrophoresis and offer vastly different attributes of sensing. Herein, a ruleset for studying proteins is developed that prevents irreversible pore clogging and yields upward of >100,000 events/nanopore. The extended duration of experiments further revealed that the capture rate takes ∼2 h to reach a steady state, emphasizing the importance of reaching equilibrated transport for studying the energetics and kinetics of protein transport (i.e., diffusion vs barrier-limited). Even in the equilibrated transport state, improper lowpass filtering was shown to distort the classification of diffusion-limited vs barrier-limited transport. Finally, electric-field-induced protein unfolding was found to be most prominent in electroosmotic-dominant transport, whereas electrophoretic-dominant events show no evidence of unfolding. Thus, our findings showcase the optimal conditions for protein translocations and the impact on studying protein unfolding, transporting energetics, and acquiring high bandwidth data.

Biophysical and in-silico studies on the structure-function relationship of Brugia malayi protein disulfide isomerase.

Human Lymphatic filariasis is caused by parasitic nematodes Wuchereria bancrofti, Brugia malayi, and Brugia timori. Protein disulfide isomerase (PDI), a redox-active enzyme, helps to form and isomerize the disulfide bonds, thereby acting as a chaperone. Such activity is essential for activating many essential enzymes and functional proteins. Brugia malayi protein disulfide isomerase (BmPDI) is crucial for parasite survival and an important drug target. Here, we used a combination of spectroscopic and computational analysis to study the structural and functional changes in the BmPDI during unfolding. Tryptophan fluorescence data revealed two well-separated transitions during the unfolding process, suggesting that the unfolding of the BmPDI is non-cooperative. The binding of the fluorescence probe 8-anilino-1-naphthalene sulfonic acid dye (ANS) validated the results obtained by the pH unfolding. The dynamics of molecular simulation performed at different pH conditions revealed the structural basis of BmPDI unfolding. Detailed analysis suggested that under different pH, both the global structure and the conformational dynamics of the active site residues were differentially altered. Our multiparametric study reveals the differential dynamics and collective motions of BmPDI unfolding, providing insights into its structure-function relationship.Communicated by Ramaswamy H. Sarma.

Collision-Induced Unfolding, Tandem MS, Bottom-up Proteomics, and Interactomics for Identification of Protein Complexes in Native Surface Mass Spectrometry.

Endogenously occurring salts and nonvolatile matrix components in untreated biological surfaces can suppress protein ionization and promote adduct formation, challenging protein identification. Characterization of labile proteins within biological specimens is particularly demanding because additional purification or sample treatment steps can be time-intensive and can disrupt noncovalent interactions. It is demonstrated that the combined use of collision-induced unfolding, tandem mass spectrometry, and bottom-up proteomics improves protein characterization in native surface mass spectrometry (NSMS). This multiprong analysis is achieved by acquiring NSMS, MS/MS, ion mobility (IM), and bottom-up proteomics data from a single surface extracted sample. The validity of this multiprong approach was confirmed by the successful characterization of nine surface-deposited proteins, with molecular weights ranging from 8 to 147 kDa, in two separate mixtures. Bottom-up proteomics provided a list of proteins to match against observed proteins in NSMS and their detected subunits in tandem MS. The method was applied to characterize endogenous proteins from untreated chicken liver samples. The subcapsular liver sampling for NSMS analysis allowed for the detection of endogenous proteins with molecular weights of up to ∼220 kDa. Moreover, using IM-MS, collision cross sections and collision-induced unfolding pathways of enzymatic proteins and protein complexes of up to 145 kDa were obtained.

Unfolding of protein using MoS2/SnS2heterostructure for nanopore-based sequencing.

Protein sequencing is crucial for understanding the complex mechanisms driving biological functions. However, proteins are usually folded in their native state and the mechanism of fast protein conformation transitions still remains unclear, which make protein sequencing challenging. Molecular dynamics simulations with accurate force field are now able to observe the entire folding/unfolding process, providing valuable insights into protein folding mechanisms. Given that proteins can be unfolded, nanopore technology shows great potential for protein sequencing. In this study, we proposed to use MoS2/SnS2heterostructures to firstly unfold proteins and then detect them by a nanopore in the heterostructural membrane. All-atom molecular dynamics simulations performed in this work provided rich atomic-level information for a comprehensive understanding of protein unfolding process and mechanism on the MoS2/SnS2heterostructure, it was found that the strong binding of protein to SnS2nanostripe and hydrogen bond breaking were the main reasons for unfolding the protein on the heterostructure. After the protein was fully unfolded, it was restrained on the nanostripe because of the affinity of protein to the SnS2nanostripe. Thus by integrating the proposed unfolding technique with nanopore technology, detection of linear unfolded peptide was realized in this work, allowing for the identification of protein components, which is essential for sequencing proteins in the near future.

Appearance of de Gennes length in force-induced transitions.

Using Langevin dynamic simulations, a simple coarse-grained model of a DNA protein construct is used to study the DNA rupture and the protein unfolding. We identify three distinct states: (i) zipped DNA and collapsed protein, (ii) unzipped DNA and stretched protein, and (iii) unzipped DNA and collapsed protein. Here, we find a phase diagram that shows these states depending on the size of the DNA handle and the protein. For a less stable protein, unfolding is solely governed by the size of the linker DNA, whereas if the protein's stability increases, complete unfolding becomes impossible because the rupture force for DNA has reached a saturation regime influenced by the de Gennes length. We show that unfolding occurs via a few intermediate states by monitoring the force-extension curve of the entire protein. We extend our study to a heterogeneous protein system, where similar intermediate states in two systems can lead to different protein unfolding paths.

Development of an Automated, High-Throughput Methodology for Native Mass Spectrometry and Collision-Induced Unfolding.

Native ion mobility mass spectrometry (nIM-MS) has emerged as a useful technology for the rapid evaluation of biomolecular structures. When combined with collisional activation in a collision-induced unfolding (CIU) experiment, nIM-MS experimentation can be leveraged to gain greater insight into biomolecular conformation and stability. However, nIM-MS and CIU remain throughput limited due to nonautomated sample preparation and introduction. Here, we explore the use of a RapidFire robotic sample handling system to develop an automated, high-throughput methodology for nMS and CIU. We describe native RapidFire-MS (nRapidFire-MS) capable of performing online desalting and sample introduction in as little as 10 s per sample. When combined with CIU, our nRapidFire-MS approach can be used to collect CIU fingerprints in 30 s following desalting by using size exclusion chromatography cartridges. When compared to nMS and CIU data collected using standard approaches, ion signals recorded by nRapidFire-MS exhibit identical ion collision cross sections, indicating that the same conformational populations are tracked by the two approaches. Our data further suggest that nRapidFire-MS can be extended to study a variety of biomolecular classes, including proteins and protein complexes ranging from 5 to 300 kDa and oligonucleotides. Furthermore, nRapidFire-MS data acquired for biotherapeutics suggest that nRapidFire-MS has the potential to enable high-throughput nMS analyses of biopharmaceutical samples. We conclude by discussing the potential of nRapidFire-MS for enabling the development of future CIU assays capable of catalyzing breakthroughs in protein engineering, inhibitor discovery, and formulation development for biotherapeutics.

Single-molecule analysis of osmolyte-mediated nanomechanical unfolding behavior of a protein domain.

The small organic molecules, known as osmolytes being ubiquitously present in different cell types, affect protein folding, stability and aggregation. However, it is unknown how the osmolytes affect the nanomechanical unfolding behavior of protein domain. Here, we show the osmolyte-dependent mechanical unfolding properties of protein titin immunoglobulin-27 (I27) domain using an atomic force microscopy (AFM)-based single-molecule force spectroscopy. We found that amines and methylamines improved the mechanical stability of I27 domain, whereas polyols had no effect. Interestingly, glycine betaine (GB) or trimethylamine-N-oxide (TMAO) increased the average unfolding force of the protein domain. The kinetic parameters analyzed at single-molecule level reveal that stabilizing effect of osmolytes is due to a decrease in the unfolding rate constant of I27, which was confirmed by molecular dynamics simulations. Our study reveals different effects that diverse osmolytes have on the mechanical properties of the protein, and suggests the potential use of osmolytes in modulating the mechanical stability of proteins required for various nano-biotechnological applications.

Enhanced Stability Differentiation of Therapeutic Polyclonal Antibodies with All Ion Unfolding-Ion Mobility-Mass Spectrometry.

Compared with monoclonal antibodies, polyclonal antibodies (pAbs) have rather significant characteristics, including lower cost, shorter production cycle, and higher affinity. Therefore, to facilitate their applications in clinic, it is equally critical to comprehensively characterize the conformational stabilities of pAb at the molecular weight-resolved scale, which is technically challenging due to the lack of an effective analytical tool capable of simultaneously providing both stability and molecular weight information within an acceptable error range. Ion mobility-mass spectrometry (IM-MS) has grown as an alternative to rapidly assess protein conformational stability with accurate molecular weight information maintained, especially when equipped with a collision-induced unfolding (CIU) regime. Dynamic and transient conformational intermediates can be captured with the CIU-IM-MS technique, adding to traditional static structural measurements with collisional cross section. Most CIU-IM-MS-centered protocols are focusing on the application to isolated, targeted protein ions, namely, analyzing one single charge state at one time, limiting its analytical throughput and speed. In this study, we employed an enhanced unfolding regime, all ion unfolding (AIU), capable of the simultaneous operation of numerous ions at a time during stepped unfolding processes to analyze pAb. Results show that AIU can quantitatively characterize the subtle differences in conformational stability among four structurally similar pAbs with improved resolving capability by around a 2-4-fold increment in both stability and structure differentiating parameters. Besides, AIU also benefits from considerably saved time cost and improved spectrum quality with an elevated signal-to-noise ratio.