Photoinduced hole hopping through tryptophans in proteins.

Hole hopping through tryptophan/tyrosine chains enables rapid unidirectional charge transport over long distances. We have elucidated structural and dynamical factors controlling hopping speed and efficiency in two modified azurin constructs that include a rhenium(I) sensitizer, Re(His)(CO)3(dmp)+, and one or two tryptophans (W1, W2). Experimental kinetics investigations showed that the two closely spaced (3 to 4 Å) intervening tryptophans dramatically accelerated long-range electron transfer (ET) from CuI to the photoexcited sensitizer. In our theoretical work, we found that time-dependent density-functional theory (TDDFT) quantum mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) trajectories of low-lying triplet excited states of ReI(His)(CO)3(dmp)+-W1(-W2) exhibited crossings between sensitizer-localized (*Re) and charge-separated [ReI(His)(CO)3(dmp•-)/(W1•+ or W2•+)] (CS1 or CS2) states. Our analysis revealed that the distances, angles, and mutual orientations of ET-active cofactors fluctuate in a relatively narrow range in which the cofactors are strongly coupled, enabling adiabatic ET. Water-dominated electrostatic field fluctuations bring *Re and CS1 states to a crossing where *Re(CO)3(dmp)+←W1 ET occurs, and CS1 becomes the lowest triplet state. ET is promoted by solvation dynamics around *Re(CO)3(dmp)+(W1); and CS1 is stabilized by Re(dmp•-)/W1•+ electron/hole interaction and enhanced W1•+ solvation. The second hop, W1•+←W2, is facilitated by water fluctuations near the W1/W2 unit, taking place when the electrostatic potential at W2 drops well below that at W1•+ Insufficient solvation and reorganization around W2 make W1•+←W2 ET endergonic, shifting the equilibrium toward W1•+ and decreasing the charge-separation yield. We suggest that multiscale TDDFT/MM/MD is a suitable technique to model the simultaneous evolution of photogenerated excited-state manifolds.

Anion-cation contrast of small molecule solvation in salt solutions.

The contributions from anions and cations from salt are inseparable in their perturbation of molecular systems by experimental and computational methods, rendering it difficult to dissect the effects exerted by the anions and cations individually. Here we investigate the solvation of a small molecule, caffeine, and its perturbation by monovalent salts from various parts of the Hofmeister series. Using molecular dynamics and the energy-representation theory of solvation, we estimate the solvation free energy of caffeine and decompose it into the contributions from anions, cations, and water. We also decompose the contributions arising from the solute-solvent and solute-ions interactions and that from excluded volume, enabling us to pin-point the mechanism of salt. Anions and cations revealed high contrast in their perturbation of caffeine solvation, with the cations salting-in caffeine via binding to the polar ketone groups, while the anions were found to be salting-out via perturbations of water. In agreement with previous findings, the perturbation by salt is mostly anion dependent, with the magnitude of the excluded-volume effect found to be the governing mechanism. The free-energy decomposition as conducted in the present work can be useful to understand ion-specific effects and the associated Hofmeister series.

Nonadiabatic excited-state dynamics of ReCl(CO)3(bpy) in two different solvents.

We present a study of excited-states relaxation of the complex ReCl(CO)3(bpy) (bpy = 2,2-bipyridine) using a nonadiabatic TD-DFT dynamics on spin-mixed potential energy surfaces in explicit acetonitrile (ACN) and dimethylsulfoxide (DMSO) solutions up to 800 fs. ReCl(CO)3(bpy) belongs to a group of important photosensitizers which show ultrafast biexponential subpicosecond fluorescence decay kinetics. The choice of solvents was motivated by the different excited-state relaxation dynamics observed in subpicosecond time-resolved IR (TRIR) experiments. Simulations of intersystem crossing (ISC) showed the development of spin-mixed states in both solvents. Transformation of time-dependent populations of spin-mixed states enabled to monitor the temporal evolution of individual singlet and triplet states, fitting of bi-exponential decay kinetics, and simulating the time-resolved fluorescence spectra that show only minor differences between the two solvents. Analysis of structural relaxation and solvent reorganization employing time-resolved proximal distribution functions pointed to the factors influencing the fluorescence decay time constants. Nonadiabatic dynamics simulations of time-evolution of electronic, molecular, and solvent structures emerge as a powerful technique to interpret time-resolved spectroscopic data and ultrafast photochemical reactivity.

The development of a fully integrated 3D printed electrochemical platform and its application to investigate the chemical reaction between carbon dioxide and hydrazine.

The combination of computer assisted design and 3D printing has recently enabled fast and inexpensive manufacture of customized 'reactionware' for broad range of electrochemical applications. In this work bi-material fused deposition modeling 3D printing is utilized to construct an integrated platform based on a polyamide electrochemical cell and electrodes manufactured from a polylactic acid-carbon nanotube conductive composite. The cell contains separated compartments for the reference and counter electrode and enables reactants to be introduced and inspected under oxygen-free conditions. The developed platform was employed in a study investigating the electrochemical oxidation of aqueous hydrazine coupled to its bulk reaction with carbon dioxide. The analysis of cyclic voltammograms obtained in reaction mixtures with systematically varied composition confirmed that the reaction between hydrazine and carbon dioxide follows 1/1 stoichiometry and the corresponding equilibrium constant amounts to (2.8 ± 0.6) × 103. Experimental characteristics were verified by results of numerical simulations based on the finite-element-method.

Self-association of a highly charged arginine-rich cell-penetrating peptide.

Small-angle X-ray scattering (SAXS) measurements reveal a striking difference in intermolecular interactions between two short highly charged peptides-deca-arginine (R10) and deca-lysine (K10). Comparison of SAXS curves at high and low salt concentration shows that R10 self-associates, while interactions between K10 chains are purely repulsive. The self-association of R10 is stronger at lower ionic strengths, indicating that the attraction between R10 molecules has an important electrostatic component. SAXS data are complemented by NMR measurements and potentials of mean force between the peptides, calculated by means of umbrella-sampling molecular dynamics (MD) simulations. All-atom MD simulations elucidate the origin of the R10-R10 attraction by providing structural information on the dimeric state. The last two C-terminal residues of R10 constitute an adhesive patch formed by stacking of the side chains of two arginine residues and by salt bridges formed between the like-charge ion pair and the C-terminal carboxyl groups. A statistical analysis of the Protein Data Bank reveals that this mode of interaction is a common feature in proteins.

Arginine "Magic": Guanidinium Like-Charge Ion Pairing from Aqueous Salts to Cell Penetrating Peptides.

It is a textbook knowledge that charges of the same polarity repel each other. For two monovalent ions in the gas phase at a close contact this repulsive interaction amounts to hundreds of kilojoules per mole. In aqueous solutions, however, this Coulomb repulsion is strongly attenuated by a factor equal to the dielectric constant of the medium. The residual repulsion, which now amounts only to units of kilojoules per mole, may be in principle offset by attractive interactions. Probably the smallest cationic pair, where a combination of dispersion and cavitation forces overwhelms the Coulomb repulsion, consists of two guanidinium ions in water. Indeed, by a combination of molecular dynamics with electronic structure calculations and electrophoretic, as well as spectroscopic, experiments, we have demonstrated that aqueous guanidinium cations form (weakly) thermodynamically stable like-charge ion pairs. The importance of pairing of guanidinium cations in aqueous solutions goes beyond a mere physical curiosity, since it has significant biochemical implications. Guanidinium chloride is known to be an efficient and flexible protein denaturant. This is due to the ability of the orientationally amphiphilic guanidinium cations to disrupt various secondary structural motifs of proteins by pairing promiscuously with both hydrophobic and hydrophilic groups, including guanidinium-containing side chains of arginines. The fact that the cationic guanidinium moiety forms the dominant part of the arginine side chain implies that the like-charge ion pairing may also play a role for interactions between peptides and proteins. Indeed, arginine-arginine pairing has been frequently found in structural protein databases. In particular, when strengthened by a presence of negatively charged glutamate, aspartate, or C-terminal carboxylic groups, this binding motif helps to stabilize peptide or protein dimers and is also found in or near active sites of several enzymes. The like-charge pairing of the guanidinium side-chain groups may also hold the key to the understanding of the arginine "magic", that is, the extraordinary ability of arginine-rich polypeptides to passively penetrate across cellular membranes. Unlike polylysines, which are also highly cationic but lack the ease in crossing membranes, polyarginines do not exhibit mutual repulsion. Instead, they accumulate at the membrane, weaken it, and might eventually cross in a concerted, "train-like" manner. This behavior of arginine-rich cell penetrating peptides can be exploited when devising smart strategies how to deliver in a targeted way molecular cargos into the cell.

Tuning the collapse transition of weakly charged polymers by ion-specific screening and adsorption.

The experimentally observed swelling and collapse response of weakly charged polymers to the addition of specific salts displays quite convoluted behavior that is not easy to categorize. Here we use a minimalistic implicit-solvent/explicit-salt simulation model with a focus on ion-specific interactions between ions and a single weakly charged polyelectrolyte to qualitatively explain the observed effects. In particular, we demonstrate ion-specific screening and bridging effects cause collapse at low salt concentrations whereas the same strong ion-specific direct interactions drive re-entrant swelling at high concentrations. Consistently with experiments, a distinct salt concentration at which the salting-out power of anions inverts from the reverse to direct Hofmeister series is observed. At this so called isospheric point, the ion-specific effects vanish. Furthermore, with additional simplifying assumptions, an ion-specific mean-field model is developed for the collapse transition which quantitatively agrees with the simulations. Our work demonstrates the sensitivity of the structural behavior of charged polymers to the addition of specific salt beyond simple screening and shall be useful for further guidance of experiments.

Guanidinium can both Cause and Prevent the Hydrophobic Collapse of Biomacromolecules.

A combination of Fourier transform infrared and phase transition measurements as well as molecular computer simulations, and thermodynamic modeling were performed to probe the mechanisms by which guanidinium (Gnd+) salts influence the stability of the collapsed versus uncollapsed state of an elastin-like polypeptide (ELP), an uncharged thermoresponsive polymer. We found that the cation's action was highly dependent upon the counteranion with which it was paired. Specifically, Gnd+ was depleted from the ELP/water interface and was found to stabilize the collapsed state of the macromolecule when paired with well-hydrated anions such as SO42-. Stabilization in this case occurred via an excluded volume (or depletion) effect, whereby SO42- was strongly partitioned away from the ELP/water interface. Intriguingly, at low salt concentrations, Gnd+ was also found to stabilize the collapsed state of the ELP when paired with SCN-, which is a strong binder for the ELP. In this case, the anion and cation were both found to be enriched in the collapsed state of the polymer. The collapsed state was favored because the Gnd+ cross-linked the polymer chains together. Moreover, the anion helped partition Gnd+ to the polymer surface. At higher salt concentrations (>1.5 M), GndSCN switched to stabilizing the uncollapsed state because a sufficient amount of Gnd+ and SCN- partitioned to the polymer surface to prevent cross-linking from occurring. Finally, in a third case, it was found that salts which interacted in an intermediate fashion with the polymer (e.g., GndCl) favored the uncollapsed conformation at all salt concentrations. These results provide a detailed, molecular-level, mechanistic picture of how Gnd+ influences the stability of polypeptides in three distinct physical regimes by varying the anion. It also helps explain the circumstances under which guanidinium salts can act as powerful and versatile protein denaturants.

Charged patchy particle models in explicit salt: Ion distributions, electrostatic potentials, and effective interactions.

We introduce a set of charged patchy particle models (CPPMs) in order to systematically study the influence of electrostatic charge patchiness and multipolarity on macromolecular interactions by means of implicit-solvent, explicit-ion Langevin dynamics simulations employing the Gromacs software. We consider well-defined zero-, one-, and two-patched spherical globules each of the same net charge and (nanometer) size which are composed of discrete atoms. The studied mono- and multipole moments of the CPPMs are comparable to those of globular proteins with similar size. We first characterize ion distributions and electrostatic potentials around a single CPPM. Although angle-resolved radial distribution functions reveal the expected local accumulation and depletion of counter- and co-ions around the patches, respectively, the orientation-averaged electrostatic potential shows only a small variation among the various CPPMs due to space charge cancellations. Furthermore, we study the orientation-averaged potential of mean force (PMF), the number of accumulated ions on the patches, as well as the CPPM orientations along the center-to-center distance of a pair of CPPMs. We compare the PMFs to the classical Derjaguin-Verwey-Landau-Overbeek theory and previously introduced orientation-averaged Debye-Hückel pair potentials including dipolar interactions. Our simulations confirm the adequacy of the theories in their respective regimes of validity, while low salt concentrations and large multipolar interactions remain a challenge for tractable theoretical descriptions.

Tuning the critical solution temperature of polymers by copolymerization.

We study statistical copolymerization effects on the upper critical solution temperature (CST) of generic homopolymers by means of coarse-grained Langevin dynamics computer simulations and mean-field theory. Our systematic investigation reveals that the CST can change monotonically or non-monotonically with copolymerization, as observed in experimental studies, depending on the degree of non-additivity of the monomer (A-B) cross-interactions. The simulation findings are confirmed and qualitatively explained by a combination of a two-component Flory-de Gennes model for polymer collapse and a simple thermodynamic expansion approach. Our findings provide some rationale behind the effects of copolymerization and may be helpful for tuning CST behavior of polymers in soft material design.

Like-charged protein-polyelectrolyte complexation driven by charge patches.

We study the pair complexation of a single, highly charged polyelectrolyte (PE) chain (of 25 or 50 monomers) with like-charged patchy protein models (CPPMs) by means of implicit-solvent, explicit-salt Langevin dynamics computer simulations. Our previously introduced set of CPPMs embraces well-defined zero-, one-, and two-patched spherical globules each of the same net charge and (nanometer) size with mono- and multipole moments comparable to those of globular proteins with similar size. We observe large binding affinities between the CPPM and the like-charged PE in the tens of the thermal energy, kBT, that are favored by decreasing salt concentration and increasing charge of the patch(es). Our systematic analysis shows a clear correlation between the distance-resolved potentials of mean force, the number of ions released from the PE, and CPPM orientation effects. In particular, we find a novel two-site binding behavior for PEs in the case of two-patched CPPMs, where intermediate metastable complex structures are formed. In order to describe the salt-dependence of the binding affinity for mainly dipolar (one-patched) CPPMs, we introduce a combined counterion-release/Debye-Hückel model that quantitatively captures the essential physics of electrostatic complexation in our systems.

Electrophoretic mobilities of neutral analytes and electroosmotic flow markers in aqueous solutions of Hofmeister salts.

Small neutral organic compounds have traditionally the role of EOF markers in electrophoresis, as they are expected to have zero electrophoretic mobility in external electric fields. The BGE contains, however, ions that have unequal affinities to the neutral molecules, which in turn results in their mobilization. In this study we focused on two EOF markers-thiourea and DMSO, as well as on N-methyl acetamide (NMA) as a model of the peptide bond. By means of CE and all atom molecular dynamics simulations we explored mobilization of these neutral compounds in large set of Hofmeister salts. Employing a statistical mechanics approach, we were able to reproduce by simulations the experimental electrophoretic mobility coefficients. We also established the role of the chemical composition of marker and the BGE on the measured electrophoretic mobility coefficient. For NMA, we interpreted the results in terms of the relative affinities of cations versus anions to the peptide bond.

Tryptophan to Tryptophan Hole Hopping in an Azurin Construct.

Electron transfer (ET) between neutral and cationic tryptophan residues in the azurin construct [ReI(H126)(CO)3(dmp)](W124)(W122)CuI (dmp = 4,7-Me2-1,10-phenanthroline) was investigated by Born-Oppenheimer quantum-mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) simulations. We focused on W124•+ ← W122 ET, which is the middle step of the photochemical hole-hopping process *ReII(CO)3(dmp•-) ← W124 ← W122 ← CuI, where sequential hopping amounts to nearly 10,000-fold acceleration over single-step tunneling (ACS Cent. Sci. 2019, 5, 192-200). In accordance with experiments, UKS-DFT QM/MM/MD simulations identified forward and reverse steps of W124•+ ↔ W122 ET equilibrium, as well as back ET ReI(CO)3(dmp•-) → W124•+ that restores *ReII(CO)3(dmp•-). Strong electronic coupling between the two indoles (≥40 meV in the crossing region) makes the productive W124•+ ← W122 ET adiabatic. Energies of the two redox states are driven to degeneracy by fluctuations of the electrostatic potential at the two indoles, mainly caused by water solvation, with contributions from the protein dynamics in the W122 vicinity. ET probability depends on the orientation of Re(CO)3(dmp) relative to W124 and its rotation diminishes the hopping yield. Comparison with hole hopping in natural systems reveals structural and dynamics factors that are important for designing efficient hole-hopping processes.

Unveiling the Borohydride Ion through Force-Field Development.

The borohydride ion, BH4-, is an essential reducing agent in many technological processes, yet its full understanding has been elusive, because of at least two significant challenges. One challenge arises from its marginal stability in aqueous solutions outside of basic pH conditions, which considerably limits the experimental thermodynamic data. The other challenge comes from its unique and atypical hydration shell, stemming from the negative excess charge on its hydrogen atoms, which complicates the accurate modeling in classical atomistic simulations. In this study, we combine experimental and computer simulation techniques to devise a classical force field for NaBH4 and deepen our understanding of its characteristics. We report the first measurement of the ion's activity coefficient and extrapolate it to neutral pH conditions. Given the difficulties in directly measuring its solvation free energies, owing to its instability, we resort to quantum chemistry calculations. This combined strategy allows us to derive a set of nonpolarizable force-field parameters for the borohydride ion for classical molecular dynamics simulations. The derived force field simultaneously captures the solvation free energy, the hydration structure, as well as the activity coefficient of NaBH4 salt across a broad concentration range. The obtained insights into the hydration shell of the BH4- ion are crucial for accurately modeling and understanding its interactions with other molecules, ions, materials, and interfaces.

Effective Inclusion of Electronic Polarization Improves the Description of Electrostatic Interactions: The prosECCo75 Biomolecular Force Field.

prosECCo75 is an optimized force field effectively incorporating electronic polarization via charge scaling. It aims to enhance the accuracy of nominally nonpolarizable molecular dynamics simulations for interactions in biologically relevant systems involving water, ions, proteins, lipids, and saccharides. Recognizing the inherent limitations of nonpolarizable force fields in precisely modeling electrostatic interactions essential for various biological processes, we mitigate these shortcomings by accounting for electronic polarizability in a physically rigorous mean-field way that does not add to computational costs. With this scaling of (both integer and partial) charges within the CHARMM36 framework, prosECCo75 addresses overbinding artifacts. This improves agreement with experimental ion binding data across a broad spectrum of systems─lipid membranes, proteins (including peptides and amino acids), and saccharides─without compromising their biomolecular structures. prosECCo75 thus emerges as a computationally efficient tool providing enhanced accuracy and broader applicability in simulating the complex interplay of interactions between ions and biomolecules, pivotal for improving our understanding of many biological processes.

Salt Effects on Caffeine across Concentration Regimes.

Salts affect the solvation thermodynamics of molecules of all sizes; the Hofmeister series is a prime example in which different ions lead to salting-in or salting-out of aqueous proteins. Early work of Tanford led to the discovery that the solvation of molecular surface motifs is proportional to the solvent accessible surface area (SASA), and later studies have shown that the proportionality constant varies with the salt concentration and type. Using multiscale computer simulations combined with vapor-pressure osmometry on caffeine-salt solutions, we reveal that this SASA description captures a rich set of molecular driving forces in tertiary solutions at changing solute and osmolyte concentrations. Central to the theoretical work is a new potential energy function that depends on the instantaneous surface area, salt type, and concentration. Used in, e.g., Monte Carlo simulations, this allows for a highly efficient exploration of many-body interactions and the resulting thermodynamics at elevated solute and salt concentrations.

Herbal concoction Unveiled: A computational analysis of phytochemicals' pharmacokinetic and toxicological profiles using novel approach methodologies (NAMs).

Herbal medications have an extensive history of use in treating various diseases, attributed to their perceived efficacy and safety. Traditional medicine practitioners and contemporary healthcare providers have shown particular interest in herbal syrups, especially for respiratory illnesses associated with the SARS-CoV-2 virus. However, the current understanding of the pharmacokinetic and toxicological properties of phytochemicals in these herbal mixtures is limited. This study presents a comprehensive computational analysis utilizing novel approach methodologies (NAMs) to investigate the pharmacokinetic and toxicological profiles of phytochemicals in herbal syrup, leveraging in-silico techniques and prediction tools such as PubChem, SwissADME, and Molsoft's database. Although molecular dynamics, docking, and broader system-wide analyses were not considered, future studies hold potential for further investigation in these areas. By combining drug-likeness with molecular simulation, researchers identify diverse phytochemicals suitable for complex medication development examining their pharmacokinetic-toxicological profiles in phytopharmaceutical syrup. The study focuses on herbal solutions for respiratory infections, with the goal of adding to the pool of all-natural treatments for such ailments. This research has the potential to revolutionize environmental and alternative medicine by leveraging in-silico models and innovative analytical techniques to identify novel phytochemicals with enhanced therapeutic benefits and explore network-based and systems biology approaches for a deeper understanding of their interactions with biological systems. Overall, our study offers valuable insights into the computational analysis of the pharmacokinetic and toxicological profiles of herbal concoction. This paves the way for advancements in environmental and alternative medicine. However, we acknowledge the need for future studies to address the aforementioned topics that were not adequately covered in this research.

Coronavirus-mimicking nanoparticles (CorNPs) in artificial saliva droplets and nanoaerosols: Influence of shape and environmental factors on particokinetics/particle aerodynamics.

Severe acute respiratory syndrome coronavirus 2, abbreviated as SARS-CoV-2, has been associated with the transmission of infectious COVID-19 disease through breathing and speech droplets emitted by infected carriers including asymptomatic cases. As part of SARS-CoV-2 global pandemic preparedness, we studied the transmission of aerosolized air mimicking the infected person releasing speech aerosol with droplets containing CorNPs using a vibrating mesh nebulizer as human patient simulator. Generally speech produces nanoaerosols with droplets of <5 µm in diameter that can travel distances longer than 1 m after release. It is assumed that speech aerosol droplets are a main element of the current Corona virus pandemic, unlike droplets larger than 5 m, which settle down within a 1 m radius. There are no systemic studies, which take into account speech-generated aerosol/droplet experimental validation and their aerodynamics/particle kinetics analysis. In this study, we cover these topics and explore role of residual water in aerosol droplet stability by exploring drying dynamics. Furthermore, a candle experiment was designed to determine whether air pollution might influence respiratory virus like nanoparticle transmission and air stability.

Molecular mechanisms of ion-specific effects on proteins.

The specific binding sites of Hofmeister ions with an uncharged 600-residue elastin-like polypeptide, (VPGVG)(120), were elucidated using a combination of NMR and thermodynamic measurements along with molecular dynamics simulations. It was found that the large soft anions such as SCN(-) and I(-) interact with the polypeptide backbone via a hybrid binding site that consists of the amide nitrogen and the adjacent α-carbon. The hydrocarbon groups at these sites bear a slight positive charge, which enhances anion binding without disrupting specific hydrogen bonds to water molecules. The hydrophobic side chains do not contribute significantly to anion binding or the corresponding salting-in behavior of the biopolymer. Cl(-) binds far more weakly to the amide nitrogen/α-carbon binding site, while SO(4)(2-) is repelled from both the backbone and hydrophobic side chains of the polypeptide. The Na(+) counterions are also repelled from the polypeptide. The identification of these molecular-level binding sites provides new insights into the mechanism of peptide-anion interactions.

Counterion condensation in short cationic peptides: limiting mobilities beyond the Onsager-Fuoss theory.

We investigated the effect of the background electrolyte (BGE) anions on the electrophoretic mobilities of the cationic amino acids arginine and lysine and the polycationic peptides tetraarginine, tetralysine, nonaarginine, and nonalysine. BGEs composed of sodium chloride, sodium propane-1,3-disulfonate, and sodium sulfate were used. For the amino acids, determination of the limiting mobility by extrapolation, using the Onsager-Fuoss (OF) theory expression, yielded consistent estimates. For the peptides, however, the estimates of the limiting mobilities were found to spuriously depend on the BGE salt. This paradox was resolved using molecular modeling. Simulations, on all-atom as well as coarse-grained levels, show that significant counterion condensation, an effect not accounted for in OF theory, occurs for the tetra- and nonapeptides, even for low BGE concentrations. Including this effect in the quantitative estimation of the BGE effect on mobility removed the discrepancy between the estimated limiting mobilities in different salts. The counterion condensation was found to be mainly due to electrostatic interactions, with specific ion effects playing a secondary role. Therefore, the conclusions are likely to be generalizable to other analytes with a similar density of charged groups and OF theory is expected to fail in a predictable way for such analytes.