Representability and Dynamical Consistency in Coarse-Grained Models.

We address the challenge of representativity and dynamical consistency when unbonded fine-grained particles are collected together into coarse-grained particles. We implement a hybrid procedure for identifying and tracking the underlying fine-grained particles─e.g., atoms or molecules─by exchanging them between the coarse-grained particles periodically at a characteristic time. The exchange involves a back-mapping of the coarse-grained particles into fine-grained particles and a subsequent reassignment to coarse-grained particles conserving total mass and momentum. We find that an appropriate choice of the characteristic exchange time can lead to the correct effective diffusion rate of the fine-grained particles when simulated in hybrid coarse-grained dynamics. In the compressed (supercritical) fluid regime, without the exchange term, fine-grained particles remain associated with a given coarse-grained particle, leading to substantially lower diffusion rates than seen in all-atom molecular dynamics of the fine-grained particles. Thus, this work confirms the need for addressing the representativity of fine-grained particles within coarse-grained particles and offers a simple exchange mechanism so as to retain dynamical consistency between the fine- and coarse-grained scales.

6aH-Benzo[α]fluorene: NMR evidence of the unexpected product of the reaction of butyryl chloride with 1,2-diphenylacetylene.

The reaction of butyryl chloride with ethynylbenzene in the presence of AlCl3 afforded a mixture of the Z/E-isomers of 1-chloro-2-phenylhex-1-en-3-one. 1,2-Diphenylethyne under these conditions gave a novel polycarbocycle core, 6aH-benzo[a]fluorene. The chemical structure of 11-chloro-5,6-diphenyl-6a-propyl-6aH-benzo[a]fluorene was established by means of IE-MS, 1 H, 13 C NMR, COSY, HSQC, HMBC, and 2D INADEQUATE technique.

Reading Targeted DNA Damage in the Active Demethylation Pathway: Role of Accessory Domains of Eukaryotic AP Endonucleases and Thymine-DNA Glycosylases.

Base excision DNA repair (BER) is an important process used by all living organisms to remove nonbulky lesions from DNA. BER is usually initiated by DNA glycosylases that excise a damaged base leaving an apurinic/apyrimidinic (AP) site, and an AP endonuclease then cuts DNA at the AP site, and the repair is completed by correct nucleotide insertion, end processing, and nick ligation. It has emerged recently that the BER machinery, in addition to genome protection, is crucial for active epigenetic demethylation in the vertebrates. This pathway is initiated by TET dioxygenases that oxidize the regulatory 5-methylcytosine, and the oxidation products are treated as substrates for BER. T:G mismatch-specific thymine-DNA glycosylase (TDG) and AP endonuclease 1 (APE1) catalyze the first two steps in BER-dependent active demethylation. In addition to the well-structured catalytic domains, these enzymes possess long tails that are structurally uncharacterized but involved in multiple interactions and regulatory functions. In this review, we describe the known roles of the tails in TDG and APE1, discuss the importance of order and disorder in their structure, and consider the evolutionary aspects of these accessory protein regions. We also propose that the tails may be important for the enzymes' oligomerization on DNA, an aspect of their function that only recently gained attention.

Mechanism of stimulation of DNA binding of the transcription factors by human apurinic/apyrimidinic endonuclease 1, APE1.

Aerobic respiration generates reactive oxygen species (ROS), which can damage nucleic acids, proteins and lipids. A number of transcription factors (TFs) contain redox-sensitive cysteine residues at their DNA-binding sites, hence ROS-induced thiol oxidation strongly inhibits their recognition of the cognate DNA sequences. Major human apurinic/apyrimidinic (AP) endonuclease 1 (APE1/APEX1/HAP-1), referred also as a redox factor 1 (Ref-1), stimulates the DNA binding activities of the oxidized TFs such as AP-1 and NF-κB. Also, APE1 participates in the base excision repair (BER) and nucleotide incision repair (NIR) pathways to remove oxidative DNA base damage. At present, the molecular mechanism underlying the TF-stimulating/redox function of APE1 and its biological role remains disputed. Here, we provide evidence that, instead of direct cysteine reduction in TFs by APE1, APE1-catalyzed NIR and TF-stimulating activities may be based on transient cooperative binding of APE1 to DNA and induction of conformational changes in the helix. The structure of DNA duplex strongly influences NIR and TF-stimulating activities. Homologous plant AP endonucleases lacking conserved cysteine residues stimulate DNA binding of the p50 subunit of NF-κB. APE1 acts synergistically with low-molecular-weight reducing agents on TFs. Finally, APE1 stimulates DNA binding of the redox-insensitive p50-C62S mutant protein. Electron microscopy imaging of APE1 complexes with DNA revealed preferential polymerization of APE1 on the gapped and intrinsically curved DNA duplexes. Molecular modeling offers a structural explanation how full-length APE1 can oligomerize on DNA. In conclusion, we propose that DNA-directed APE1 oligomerization can be regarded as a substitute for diffusion of APE1 along the DNA contour to probe for anisotropic flexibility. APE1 oligomers exacerbate pre-existing distortions in DNA and enable both NIR activity and DNA binding by TFs regardless of their oxidation state.

Residue coevolution reveals functionally important intramolecular interactions in formamidopyrimidine-DNA glycosylase.

In protein evolution, functionally important intramolecular interactions, such as polar bridges or hydrophobic interfaces, tend to be conserved. We have analyzed coevolution of physicochemical properties in pairs of amino acid residues in the formamidopyrimidine-DNA glycosylase (Fpg) protein family, identified three conserved polar bridges (Arg54-Glu131, Gln234-Arg244, and Tyr170-Ser208 in the E. coli protein) located in known functional regions of the protein, and analyzed their roles by site-directed mutagenesis. The structure and molecular dynamic modeling showed that the coevolving pairs do not form isolated bridges but rather participate in tight local clusters of hydrogen bonds. The Arg54-Glu131 bridge, connecting the N- and C-terminal domains, was important for DNA binding, as its abolishment or even ion pair reversal inactivated Fpg and greatly decreased the enzyme's affinity for DNA. Mutations of the Gln234-Arg244 bridge, located at the base of the single Fpg ß-hairpin zinc finger, did not affect the activity but sharply decreased the melting temperature of the protein, with the bridge reversal partially restoring the thermal stability. Finally, Tyr170 mutation to Phe decreased Fpg binding but did not fully inactivate the protein, whereas Ser208 replacement with Ala had no effect; molecular dynamics showed that in both wild-type and S208 A Fpg, Tyr170 quickly re-orients to form an alternative set of hydrogen bonds. Thus, the coevolution analysis approach, combined with biochemical and computational studies, provides a powerful tool for understanding intramolecular interactions important for the function of DNA repair enzymes.

Structural basis for the recognition and processing of DNA containing bulky lesions by the mammalian nucleotide excision repair system.

Mammalian nucleotide excision repair (NER) eliminates the broadest diversity of bulky lesions from DNA with wide specificity. However, the double incision efficiency for structurally different adducts can vary over several orders of magnitude. Therefore, great attention is drawn to the question of the relationship among structural properties of bulky DNA lesions and the rate of damage elimination. This paper studies the properties of several structurally diverse synthetic (model) DNAs containing bulky modifications. Model DNAs have been designed using modified nucleosides (exo-N-{2-N-[N-(4-azido-2,5-difluoro-3-chloropyridin-6-yl)-3-aminopropionyl]aminoethyl}-2'-deoxycytidine (Fap-dC) and 5-{1-[6-(5[6]-fluoresceinylcarbomoyl)hexanoyl]-3-aminoallyl}-2'-deoxyuridine (Flu-dU)) and the nonnucleosidic reagent N-[6-(9-antracenylcarbomoyl)hexanoyl]-3-amino-1,2-propandiol (nAnt). The impact of these lesions on spatial organization and stability of the model DNA was evaluated. Their affinity for the damage sensor XPC was also studied. It was expected, that the values of melting temperature decrease, bending angles and KD values clearly define the row of model DNA substrate properties such as Flu-dU-DNA>>nAnt≈Fap-dC-DNA. Unexpectedly the experimentally estimated levels of the substrate properties were actually in the row: nAnt-DNA>>Flu-dU-DNA>>Fap-dC-DNA. Molecular dynamics simulations have revealed structural and energetic bases for the discrepancies observed. DNA destabilization patterns plotted explain these results on a structural basis in terms of differences in dynamic perturbations of stacking interactions.

Molecular dynamics simulation of the opposite-base preference and interactions in the active site of formamidopyrimidine-DNA glycosylase.

BACKGROUND: Formamidopyrimidine-DNA glycosylase (Fpg) removes abundant pre-mutagenic 8-oxoguanine (oxoG) bases from DNA through nucleophilic attack of its N-terminal proline at C1' of the damaged nucleotide. Since oxoG efficiently pairs with both C and A, Fpg must excise oxoG from pairs with C but not with A, otherwise a mutation occurs. The crystal structures of several Fpg-DNA complexes have been solved, yet no structure with A opposite the lesion is available. RESULTS: Here we use molecular dynamic simulation to model interactions in the pre-catalytic complex of Lactococcus lactis Fpg with DNA containing oxoG opposite C or A, the latter in either syn or anti conformation. The catalytic dyad, Pro1-Glu2, was modeled in all four possible protonation states. Only one transition was observed in the experimental reaction rate pH dependence plots, and Glu2 kept the same set of interactions regardless of its protonation state, suggesting that it does not limit the reaction rate. The adenine base opposite oxoG was highly distorting for the adjacent nucleotides: in the more stable syn models it formed non-canonical bonds with out-of-register nucleotides in both the damaged and the complementary strand, whereas in the anti models the adenine either formed non-canonical bonds or was expelled into the major groove. The side chains of Arg109 and Phe111 that Fpg inserts into DNA to maintain its kinked conformation tended to withdraw from their positions if A was opposite to the lesion. The region showing the largest differences in the dynamics between oxoG:C and oxoG:A substrates was unexpectedly remote from the active site, located near the linker joining the two domains of Fpg. This region was also highly conserved among 124 analyzed Fpg sequences. Three sites trapping water molecules through multiple bonds were identified on the protein-DNA interface, apparently helping to maintain enzyme-induced DNA distortion and participating in oxoG recognition. CONCLUSION: Overall, the discrimination against A opposite to the lesion seems to be due to incorrect DNA distortion around the lesion-containing base pair and, possibly, to gross movement of protein domains connected by the linker.

8-Oxoguanine Affects DNA Backbone Conformation in the EcoRI Recognition Site and Inhibits Its Cleavage by the Enzyme.

8-oxoguanine is one of the most abundant and impactful oxidative DNA lesions. However, the reasons underlying its effects, especially those not directly explained by the altered base pairing ability, are poorly understood. We report the effect of the lesion on the action of EcoRI, a widely used restriction endonuclease. Introduction of 8-oxoguanine inside, or adjacent to, the GAATTC recognition site embedded within the Drew-Dickerson dodecamer sequence notably reduced the EcoRI activity. Solution NMR revealed that 8-oxoguanine in the DNA duplex causes substantial alterations in the sugar-phosphate backbone conformation, inducing a BI→BII transition. Moreover, molecular dynamics of the complex suggested that 8-oxoguanine, although does not disrupt the sequence-specific contacts formed by the enzyme with DNA, shifts the distribution of BI/BII backbone conformers. Based on our data, we propose that the disruption of enzymatic cleavage can be linked with the altered backbone conformation and dynamics in the free oxidized DNA substrate and, possibly, at the protein-DNA interface.

Nonequilibrium structure in sequential assembly.

The assembly of monomeric constituents into molecular superstructures through sequential-arrival processes has been simulated and theoretically characterized. When the energetic interactions allow for complete overlap of the particles, the model is equivalent to that of the sequential absorption of soft particles on a surface. In the present work, we consider more general cases by including arbitrary aggregating geometries and varying prescriptions of the connectivity network. The resulting theory accounts for the evolution and final-state configurations through a system of equations governing structural generation. We find that particle geometries differ significantly from those in equilibrium. In particular, variations of structural rigidity and morphology tune particle energetics and result in significant variation in the nonequilibrium distributions of the assembly in comparison to the corresponding equilibrium case.

Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties.

The dynamical properties of a system of soft rods governed by stochastic hard collisions (SHCs) have been determined over a varying range of softness using molecular dynamics simulations in one dimension and analytic theory. The SHC model allows for interpenetration of the system's constituent particles in the simulations, generating overlapping clustering behavior analogous to the spatial structures observed in systems governed by deterministic bounded potentials. Through variation of an assigned softness parameter δ, the limiting ranges of intermolecular softness are bridged, connecting the limiting ensemble behavior from hard to ideal (completely soft). Various dynamical and structural observables are measured from simulation and compared to developed theoretical values. The spatial properties are found to be well predicted by theories developed for the deterministic penetrable-sphere model with a transformation from energetic to probabilistic arguments. While the overlapping spatial structures are complex, the dynamical properties can be adequately approximated through a theory built on impulsive interactions with Enskog corrections. Our theory suggests that as the softness of interaction is varied toward the ideal limit, correlated collision processes are less important to the energy transfer mechanism, and Markovian processes dominate the evolution of the configuration space ensemble. For interaction softness close to hard limit, collision processes are highly correlated and overlapping spatial configurations give rise to entanglement of single-particle trajectories.

Effective surface coverage of coarse-grained soft matter.

The surface coverage of coarse-grained macromolecules bound to a solid substrate is not simply proportional to the two-dimensional number density because macromolecules can overlap. As a function of the overlap probability δ, we have developed analytical formulas and computational models capable of characterizing this nonlinear relationship. For simplicity, we ignore site-site interactions that would be induced by length-scale mismatches between binding sites and the radius of gyration of the incident coarse-grained macromolecular species. The interactions between macromolecules are modeled with a finite bounded potential that allows multiple macromolecules to occupy the same binding site. The softness of the bounded potential is thereby reduced to the single parameter δ. Through variation of this parameter, completely hard (δ = 0) and completely soft (δ = 1) behavior can be bridged. For soft macromolecular interactions (δ > 0), multiple occupancy reduces the fraction of sites ϕ occupied on the substrate. We derive the exact transition probability between sequential configurations and use this probability to predict ϕ and the distribution of occupied sites. Due to the complexity of the exact ϕ expressions and their analytical intractability at the thermodynamic limit, we apply a simplified mean-field (MF) expression for ϕ. The MF model is found to be in excellent agreement with the exact result. Both the exact and MF models are applied to an example dynamical system with multibody interactions governed by a stochastic bounded potential. Both models show agreement with results measured from simulation.

Structure of a tractable stochastic mimic of soft particles.

The structure and assembly of soft particles is difficult to characterize because their interpenetrability allows them to be packed at ever higher density albeit with an increasing penalty in energy and/or pressure. Alternatively, the use of impenetrable particles (such as hard spheres) as a reference model for soft particles can fail because the packing densities are limited by the impossibility of complete space filling. We recently introduced the stochastic penetration algorithm (SPA) so as to allow for the computationally efficient integration of hard sphere models while including overlaps seen in soft interactions [Craven et al., J. Chem. Phys., 2013, 138, 244901]. Moving beyond the initial one-dimensional case studied earlier, we now consider the spatial properties of systems of stochastically penetrable spheres in dimensions d≤ 3 through the use of molecular dynamics simulations and analytic methods. The stochastic potential allows spheres to either interpenetrate with a probability δ or collide elastically otherwise. For δ > 0 the particles interpenetrate (overlap), reducing the effective volume occupied by the particles in the system. We find that the occupied volume can be accurately predicted using analytic expressions derived from mean field arguments for the particle overlap probabilities with the exception of an observed clustering regime. This anomalous clustering behavior occurs at high densities and small δ. We find that this regime is coincident with that observed in deterministic penetrable models. The behavior of the stochastic penetrable particles also indicates that soft particles would be characterizable through a single reduced parameter that captures their overlap probability.

Temperature-driven irreversible generalized Langevin equation can capture the nonequilibrium dynamics of two dissipated coupled oscillators.

Kawai and Komatsuzaki [J. Chem. Phys. 134, 114523 (2011)] recently derived the nonequilibrium generalized Langevin equation (GLE) for a nonstationary system using the projection operator technique. In the limit when the environment is slowly changing (that is, a quasi-equilibrium bath), it should reduce to the irreversible GLE approach (iGLE) [J. Chem. Phys. 111, 7701 (1999)]. Kawai and Komatsuzaki, however, found that the driven harmonic oscillator, an example of a nonequilibrium system does not obey the iGLE presumably because it did not quite satisfy the limiting conditions of the latter. Notwithstanding the lack of a massive quasi-equilibrium bath (one of the conditions under which the iGLE had been derived earlier), we found that the temperature-driven iGLE (T-iGLE) [J. Chem. Phys. 126, 244506 (2007)] can reproduce the nonequilibrium dynamics of a driven dissipated pair of harmonic oscillators. It requires a choice of the function representing the coupling between the oscillator coordinate and the bath and shows that the T-iGLE representation is consistent with the projection operator formalism if only dominant bath modes are taken into account. Moreover, we also show that the more readily applicable phenomenological iGLE model is recoverable from the Kawai and Komatsuzaki model beyond the adiabatic limit used in the original T-iGLE theory.

DNA damage processing by human 8-oxoguanine-DNA glycosylase mutants with the occluded active site.

8-Oxoguanine-DNA glycosylase (OGG1) removes premutagenic lesion 8-oxoguanine (8-oxo-G) from DNA and then nicks the nascent abasic (apurinic/apyrimidinic) site by ß-elimination. Although the structure of OGG1 bound to damaged DNA is known, the dynamic aspects of 8-oxo-G recognition are not well understood. To comprehend the mechanisms of substrate recognition and processing, we have constructed OGG1 mutants with the active site occluded by replacement of Cys-253, which forms a wall of the base-binding pocket, with bulky leucine or isoleucine. The conformational dynamics of OGG1 mutants were characterized by single-turnover kinetics and stopped-flow kinetics with fluorescent detection. Additionally, the conformational mobility of wild type and the mutant OGG1 substrate complex was assessed using molecular dynamics simulations. Although pocket occlusion distorted the active site and greatly decreased the catalytic activity of OGG1, it did not fully prevent processing of 8-oxo-G and apurinic/apyrimidinic sites. Both mutants were notably stimulated in the presence of free 8-bromoguanine, indicating that this base can bind to the distorted OGG1 and facilitate ß-elimination. The results agree with the concept of enzyme plasticity, suggesting that the active site of OGG1 is flexible enough to compensate partially for distortions caused by mutation.

Stochastic dynamics of penetrable rods in one dimension: occupied volume and spatial order.

The occupied volume of a penetrable hard rod (HR) system in one dimension is probed through the use of molecular dynamics simulations. In these dynamical simulations, collisions between penetrable rods are governed by a stochastic penetration algorithm (SPA), which allows for rods to either interpenetrate with a probability δ, or collide elastically otherwise. The limiting values of this parameter, δ = 0 and δ = 1, correspond to the HR and the ideal limits, respectively. At intermediate values, 0 < δ < 1, mixing of mutually exclusive and independent events is observed, making prediction of the occupied volume nontrivial. At high hard core volume fractions φ0, the occupied volume expression derived by Rikvold and Stell [J. Chem. Phys. 82, 1014 (1985)] for permeable systems does not accurately predict the occupied volume measured from the SPA simulations. Multi-body effects contribute significantly to the pair correlation function g2(r) and the simplification by Rikvold and Stell that g2(r) = δ in the penetrative region is observed to be inaccurate for the SPA model. We find that an integral over the penetrative region of g2(r) is the principal quantity that describes the particle overlap ratios corresponding to the observed penetration probabilities. Analytic formulas are developed to predict the occupied volume of mixed systems and agreement is observed between these theoretical predictions and the results measured from simulation.

MDTRA: a molecular dynamics trajectory analyzer with a graphical user interface.

Most of existing software for analysis of molecular dynamics (MD) simulation results is based on command-line, script-guided processes that require the researchers to have an idea about programming language constructions used, often applied to the one and only product. Here, we describe an open-source cross-platform program, MD Trajectory Reader and Analyzer (MDTRA), that performs a large number of MD analysis tasks assisted with a graphical user interface. The program has been developed to facilitate the process of search and visualization of results. MDTRA can handle trajectories as sets of protein data bank files and presents tools and guidelines to convert some other trajectory formats into such sets. The parameters analyzed by MDTRA include interatomic distances, angles, dihedral angles, angles between planes, one-dimensional and two-dimensional root-mean-square deviation, solvent-accessible area, and so on. As an example of using the program, we describe the application of MDTRA to analyze the MD of formamidopyrimidine-DNA glycosylase, a DNA repair enzyme from Escherichia coli.

Excited-state proton transfer in N-methyl-6-hydroxyquinolinium salts: solvent and temperature effects.

The excited-state proton transfer (ESPT) reaction of the "super"photoacid N-methyl-6-hydroxyquinolinium (MHQ) was studied using both fluorescence upconversion and time-correlated single photon counting (TCSPC) techniques. The ultrafast ESPT kinetics were investigated in various alcohols and water and determined to be solvent-controlled. The ESPT temperature dependence of MHQ was also studied in various alcohols and compared to that observed for another "super"photoacid, 5,8-dicyano-2-naphthol (DCN2). A full set of kinetic and thermodynamic parameters describing the ESPT was obtained. The protolytic photodissociation rate constant for MHQ was higher than that for DCN2, while the ESPT activation energies of MHQ were smaller. These findings are attributed to the approximately 3 orders of magnitude differences in excited-state acidities of MHQ and DCN2.

Diffusional effects on the reversible excited-state proton transfer. From experiments to Brownian dynamics simulations.

We have studied an excited state proton transfer (ESPT) from the cationic "super" photoacid N-methyl 6-hydroxyquinolinium perfluorobutane sulfonate to non-aqueous solvents using picosecond and nanosecond time-resolved fluorescence spectroscopy. Upon the photoinduced adiabatic deprotonation from the hydroxyl moiety, a quinolinium zwitterion with a highly anisotropic charge distribution is formed. Due to the complexity of the resultant photodissociated system, the typical description of the reversible ESPT within the framework of the Spherically Symmetric Diffusion Problem (SSDP) is not possible. Additional complications are caused by the presence of a counteranion particle which affects the proton mobility. To better understand the ESPT process, we have performed extensive Brownian dynamics (BD) simulations of this three-body system as a tool to reveal the nature of the nonstationary interaction potentials and to elucidate the role of a counterion in the diffusion and reactive properties of the proton. Moreover, our results demonstrated that the anisotropy of the potential force can be taken into account after adapting this force for use in the SSDP. The results of both BD simulations and SSDP calculation with the adapted force field were used to fit the experimental kinetics of this three-body problem adequately.

Nonequilibrium heat flows through a nanorod sliding across a surface.

The temperature-ramped irreversible Langevin equation [A. V. Popov and R. Hernandez, J. Chem. Phys. 134, 244506 (2007)] has been seen to describe the nonequilibrium atomic oscillations of a nanorod dragged across a surface. The nanorod and surface consist of hydroxylated α-Al(2)O(3) layers as was studied earlier by Hase and co-workers [J. Chem. Phys. 122, 094713 (2005)]. The present approach corresponds to the reduced Frenkel-Kontorova-Tomlinson model in which only one element of the vibrational chain representing a surface layer is considered explicitly. The key new concept centers on a separation of the environment into two effective reduced-dimensional baths: an equilibrium bath arising from the thermostated vibrations of the crystal lattice and a nonequilibrium bath arising from driven oscillations at the contact between the nanorod and the surface. The temperature of the latter is defined by the mean energy of a representative atomic oscillator for a given layer. The temporal temperature fluctuations and the dependence of the static part of the temperature on the sliding velocity are close to those found in the MD simulations of Hase and co-workers.

Diffusion in a nonequilibrium binary mixture of hard spheres swelling at different rates.

The nonequilibrium dynamics of a probe in a driven binary mixture of effective hard-sphere particles has been measured computationally in molecular dynamics simulations so as to obtain a better understanding of the energy and spatial correlations that persist through the coupling between the binary components. The driving of the particles is manifested through a change of the effective volume (or equivalently, diameter of the hard spheres) and each component is assumed to have a different time-dependent profile. Such a driving is possible in a suspension of one-component colloidal mesogens, for example, in which the particle volume has been seen to change with pH or temperature changes in the solution. It can also be realized by growing nanoparticles during a nucleation process. The full particle dynamics has been projected onto Langevin-type models of the probe motion by representing the environment using two different reservoirs and distinct bath-probe coupling coefficients with different nonstationary properties. The bath particles corresponding to each reservoir swell with time at various rates, nonsynchronously changing their volume fractions. Under the assumption of a weak bath-bath interactions, the coupling coefficients between the probe and two baths are expressed via those in the case of a simple-consisting of one bath-environment. The general form of the resulting irreversible Langevin equation is in agreement with the MD simulations of a hard sphere probe particle diffusing in the nonstationary binary mixture.