A multiscale modelling framework that employs molecular dynamics and hydrodynamics principles has been developed to describe the dynamics of hybrid particles. Based on the principle of least action, the equations of motion for hybrid particles were derived and verified by using the Gauss principle of least constraints testifying to their accuracy and applicability under various system constraints. The proposed scheme has been implemented in a popular open-source molecular dynamics code GROMACS. The simulation for liquid argon under equilibrium conditions in the hydrodynamic limit (s = 1) has demonstrated that the standard deviation of the density exhibits a remarkable agreement with predictions from a pure hydrodynamics model, validating the robustness of the proposed framework.

Chemistry experiments involving biological aspects are in high demand. This laboratory exercise blends biochemistry and physical chemistry, illustrates key concepts of the virus capsid surface, and is designed for a chemistry laboratory course for students majoring in biology in college. The experimental part provides a mastery of spectrophotometric and potentiometric methods as well as numerical and graphical analysis of the data obtained. The experimental determination of pKa for neutral red, NR, and p-nitrophenol, NP, attracted to the surface of the MS2 bacteriophage results in an estimation of its local surface potential, Psi. A distinctive feature of this lab is the twofold result: the positive Psi value in the NP localization patch and the negative Psi value in the NR localization patch. Discussions with students are focused on considering the surface (i) as an unstructured continuum that is characterized by physical quantities such as electrophoretic mobility and zeta potential and (ii) as a discontinuum containing certain charged groups that form discrete patches diverse in charge density and in the sign of the charges. The full-atom model of the MS2 capsid recently presented in the scientific literature provides reasonable confirmation of the experimental results obtained.

Non-small-cell lung cancer (NSCLC) is the primary form of lung cancer globally and remains a leading cause of mortality. Anaplastic lymphoma kinase (ALK) mutations, such as I1171N + L1198H, have been discovered to confer resistance to current ALK inhibitors, reducing their therapeutic effectiveness. Addressing drug resistance necessitates exploring selective inhibitors for innovative therapeutic approaches. In this study, a structure-based pharmacophore model, using ALK-approved inhibitors, was developed to screen an In-house database for potential mutant ALK inhibitors. Compounds with requisite pharmacophoric features were evaluated for binding potential against the I1171N + L1198H ALK mutant phenotype. Selected hits underwent assessment for chemical reactivity, and dynamics stability. The study identified five chemical scaffolds (NS1-5) with favorable binding modes and pharmacokinetic properties. The conformational ensembles featured the average RMSD values, ranging from 0.4 to 0.6 nm. RMSF analysis revealed consistent side chain fluctuations with reduced flexibility, while Rog analysis indicated convergence of most complexes. NS1 and NS5, in particular emerged as promising candidates, exhibiting remarkable performance than others, with binding free energies of -210.12 +- 9.94 and -163.68 +- 11.14 kcal/mol, respectively. These findings thus suggest further exploration and optimisation of NS1 and NS5 for mutant ALK inhibitors for the treatment of NSCLC.

This study investigates the adsorption properties and electronic characteristics of pristine and alkali metal (Li, Na, K)-decorated BC3 monolayers for the detection of toxic warfare agents, crucial for environmental protection and human health. Physisorption is observed for H2CO, COCl2, and CSCl2 on the BC3 monolayer, with adsorption energies of -8.06, -8.63, and -9.56 kcal/mol, respectively. Alkali metal decoration induces chemisorption, significantly enhancing adsorption energies (e.g., H2CO on KBC3 with -20.85 kcal/mol). LiBC3 and KBC3 exhibit high sensitivity to CSCl2 and COCl2, respectively, with short recovery times (4.59 and 2.72 sec). The reduced work function (phi) (4.34) of CSCl2@LiBC3 compared to pristine BC3 (4.98) confirms the heightened sensitivity of LiBC3 to CSCl2. Therefore, Li and K-decorated BC3 monolayers emerge as promising candidates for CSCl2 and COCl2 sensors, offering strong adsorption, high sensitivity, and rapid recovery times.

We present radioprotective, antiglycating, and photoprotective properties of a water-soluble C60 fullerene derivative with l-arginine (C60-Arg) and composite films based on collagen containing C60-Arg. The synthesis of these materials is described. The identification of the synthesised materials was carried out using modern physicochemical methods of analysis. The physicochemical properties of aqueous solutions of C60-Arg, such as, particle size distribution, zeta potentials, distribution coefficient in the octan-1-ol-water system were measured. The computer simulation of the process of C60-Arg association in aqueous and isotonic solutions was carried out using Molecular Dynamics. Composite films based on collagen containing C60-Arg demonstrate significant improvement in mechanical properties, cell adhesion, and cell proliferation when the nano-modifier is added. This shows high potential for the use of the C60-Arg adduct in biomedicine.

Cyclin-dependent kinase 2 (CDK2) regulates cell cycle checkpoints in the synthesis and mitosis phases and plays a pivotal role in cancerous cell proliferation. The activation of CDK2, influenced by various protein signaling pathways, initiates the phosphorylation process. Due to its crucial role in carcinogenesis, CDK2 is a druggable hotspot target to suppress cancer cell proliferation. In this context, several studies have identified spirooxindoles as an effective class of CDK2 inhibitors. In the present study, three spirooxindoles (SOI1, SOI2, and SOI3) were studied to understand their inhibitory mechanism against CDK2 through a structure-based approach. Molecular docking and molecular dynamics (MD) simulations were performed to explore their interactions with CDK2 at the molecular level. The calculated binding free energy for the spirooxindole-based CDK2 inhibitors aligned well with experimental results regarding CDK2 inhibition. Energy decomposition (ED) analysis identified key binding residues, including I10, G11, T14, R36, F82, K89, L134, P155, T158, Y159, and T160, in the CDK2 active site and T-loop phosphorylation. Molecular mechanics (MM) energy was identified as the primary contributor to stabilizing inhibitor binding in the CDK2 protein structure. Furthermore, the analysis of binding affinity revealed that the inhibitor SOI1 binds more strongly to CDK2 compared to the other inhibitors under investigation. It demonstrated a robust interaction with the crucial residue T160 in the T-loop phosphorylation site, responsible for kinase activation. These insights into the inhibitory mechanism are anticipated to contribute to the development of potential CDK2 inhibitors using the spirooxindole scaffold.

Despite the waning threat of the COVID-19 pandemic, its detrimental impact on global health persists. Regardless of natural immunity or immunity obtained through vaccination, emerging variants of the virus continue to undergo mutations and propagate globally. The persistent mutations in SARS-CoV-2, along with the subsequent formation of recombinant sub-variants has become a challenge for researchers and health professionals, raising concerns about the efficacy of current vaccines. Gaining a better understanding of the biochemical interactions between the Spike Protein (RBD) of SARS-CoV-2 variants and the human ACE2 receptor can prove to be beneficial in designing and developing antiviral therapeutics that are equally effective against all strains and emerging variants. Our objective in this study was to investigate the interfacial binding pattern of the SARS-CoV-2 RBD-ACE2 complex of the Wild Type (WT), Omicron, and the Omicron recombinant sub-variant XBB.1.16. We aimed to examine the atomic level factors and observe how mutations influence the interaction between the virus and its host using Molecular Dynamics simulation, MM/GBSA energy calculations, and Principal Component Analysis. Our findings reveal a higher degree of structural deviation and flexibility in XBB.1.16 compared to WT and Omicron. PCA indicated a wider cluster and significant flexibility in the movements of XBB.1.16 which can also be observed in free energy landscapes, while the normal mode analysis revealed converging motions within the RBD-ACE2 complexes which can facilitate the interaction between them. The calculated binding free energies show the least binding affinity in the case of XBB.1.16, suggesting the possibility of greater binding affinity. These observed deviations in XBB.1.16 when compared to its parent lineage Omicron, and WT can be attributed to the mutations specific to it. Collectively, these results enhance our understanding of the impact of mutations on the interaction between this strain and the host, taking us one step closer to designing effective antiviral therapeutics against the continually mutating strains.

We review all aspects of the synthesis, properties, and applications of endometallofullerenes (EMF) over the last 20 years. EMF represent a new class of nanosized objects with specific physicochemical properties defined by the encapsulation of individual atoms and small molecules with significant potential of practical applications in biology and medicine. One such application is an EMF based anticancer drug capable of activating antitumour immune response, inhibition of the tumour development, and inhibition of angiogenesis and metastasis. Another, separate application direction is the use of EMF as contrast agents.

Surface electrostatic potential Ψis a key characteristic of colloid particles. Since the surface of the particles adsorbs various compounds and facilitates chemical reactions between them, Ψlargely affects the properties of adsorbed reactants and governs the flow of chemical reactions occurring between them. One of the most popular methods for estimating Ψin hydrophilic colloids, such as micellar surfactant solutions and related systems, is the application of molecular probes, predominantly acid-base indicator dyes. The Ψvalue is calculated from the difference of the probe's indices of the apparent acidity constant between the examined colloid solution and, usually, some other colloid solution with noncharged particles. Here, we show how to implement this method in silico using alchemical free energy calculations within the framework of molecular dynamics simulations. The proposed implementation is tested on surfactant micelles and is shown to predict experimental Ψvalues with quantitative accuracy depending on the kind of surfactant. The sources of errors in the method are discussed, and recommendations for its application are given.

Exploiting acid-base indicators as molecular probes is one of the most popular methods for determining the surface electrostatic potential Ψin hydrophilic colloids like micellar surfactant solutions and related systems. Specifically, the indicator's apparent acidity constant index is measured in the colloid solution of interest and, as a rule, in a nonionic surfactant solution; the difference between the two is proportional to Ψ. Despite the widespread use of this approach, a major problem remains unresolved, namely, the dissimilarity of Ψvalues obtained with different indicators for the same system. The common point of view recognizes the effect of several factors (the choice of the nonionic surfactant, the probe's localization, and the degree of hydration of micellar pseudophase) but does not allow to quantitatively assess their impact and decide which indicator reports the most correct Ψvalue. Here, based on the ability to predict the reported Ψvalues in silico, we examined the role of these factors using molecular dynamics simulations for five probes and two surfactants. The probe's hydration in the Stern layer was found responsible for approximately half of the dissimilarity range. The probe's localization is found important but hard to quantify because of the irregular structure of the Stern layer. The most accurate indicators among the examined set were identified. Supplementing experiments on measuring Ψwith molecular dynamics simulation is proposed as a way of improving the efficacy of the indicator method: the simulations can guide the choice of the most suitable probe and nonionic surfactant for the given nanoparticles.

The `nut-and-bolt' mechanism of a bacteriophage-bacteria flagellum translocation motion is modelled by numerically integrating the 3D Stokes equations using a Finite-Element Method (FEM). Following the works by Katsamba and Lauga (Phys Rev Fluids 4(1): 013101, 2019), two mechanical models of the flagellum-phage complex are considered. In the first model, the phage fiber wraps around the smooth flagellum surface separated by some distance. In the second model, the phage fiber is partly immersed in the flagellum volume via a helical groove imprinted in the flagellum and replicating the fiber shape. In both cases, the results of the Stokes solution for the translocation speed are compared with the Resistive Force Theory (RFT) solutions (obtained in Katsamba and Lauga Phys Rev Fluids 4(1): 013101, 2019) and the asymptotic theory in a limiting case. The previous RFT solutions of the same mechanical models of the flagellum-phage complex showed opposite trends for how the phage translocation speed depends on the phage tail length. The current work uses complete hydrodynamics solutions, which are free from the RFT assumptions to understand the divergence of the two mechanical models of the same biological system. A parametric investigation is performed by changing pertinent geometrical parameters of the flagellum-phage complex and computing the resulting phage translocation speed. The FEM solutions are compared with the RFT results using insights provided from the velocity field visualisation in the fluid domain.

We report the synthesis of covalent conjugates of nanodiamonds with doxorubicin and a cytostatic drug from the class of 1,3,5-triazines. The obtained conjugates were identified using a number of physicochemical methods (IR-spectroscopy, NMR-spectroscopy, XRD, XPS, TEM). As a result of our study, it was found that ND-СONH-Dox and ND-COO-Diox showed good hemocompatibility, since they did not affect plasma coagulation hemostasis, platelet functional activity, and erythrocyte membrane. The ND-COO-Diox conjugates are also capable of binding to human serum albumin due to the presence of ND in their composition. In the study of the cytotoxic properties of ND-СONH-Dox and ND-COO-Diox in the T98G glioblastoma cell line, indicating that ND-СONH-Dox and ND-COO-Diox demonstrate greater cytotoxicity at lower concentrations of Dox and Diox in the composition of the conjugates compared to individual drugs; the cytotoxic effect of ND-COO-Diox was statistically significantly higher than that of ND-СONH-Dox at all concentrations studied. Greater cytotoxicity at lower concentrations of Dox and Diox in the composition of conjugates compared to individual cytostatics makes it promising to further study the specific antitumor activity and acute toxicity of these conjugates in models of glioblastoma in vivo. Our results demonstrated that ND-СONH-Dox and ND-COO-Diox enter HeLa cells predominantly via a nonspecific actin-dependent mechanism, while for ND-СONH-Dox a clathrin-dependent endocytosis pathway. All data obtained provide that the synthesized nanomaterials show a potential application as the agents for intertumoral administration.

With the goal to understand virus stability in aqueous solutions, the colloidal nanostructure and properties of a model virus, the MS2 bacteriophage, has been investigated by studying the effect of adding electrolytes and various colloidal surfactants to its water solution at physiological conditions. The charge of the virus particles influences their colloidal properties. It was found that the dzeta-potential value is reduced from -35 mV to -10 mV in 0.01M CaCl2 and 0.1M NaCl solutions as well as at higher electrolytes concentrations, while the size of the MS2 aggregates were about 600 - 900 nm with individual particles of size around 30 nm also recorded. The 2 : 1 electrolyte causes destabilisation of MS2 bacteriophage particles in aqueous solution at lower concentration. The addition of cationic, anionic, and non-ionic colloidal surfactants below and above critical micelle concentration to MS2 bacteriophage suspension caused destabilisation of MS2 particles. We also investigated the capsid's surface of another virus, PCV2, using dynamic light scattering and laser Doppler electrophoresis. The hydrodynamic diameter and the dzeta-potential of PCV2 empty capsid were found to be equal to 22 +- 1 nm and -41 +- 4 mV (using Ohshima approximations). The electrostatic potential of the surface was measured using acid-base probes and found to be equal to -91 +- 3 and +14 +- 2 mV for positively and negatively charged probes respectively, which indicate the `mosaic' way of the charge distribution on the surface, similar to MS2's surface studied previously. Our data provides new information about the virus surface, the complex process of virus aggregation-disaggregation and virus capsid disassembly.

For the first time, a complete all-atom molecular dynamics (MD) model of a virus, bacteriophage MS2, in its entirety, including a protein outer shell, native genomic RNA with necessary divalent ions, and surrounding explicit aqueous solution with ions at physiological concentration, was built. The model is based on an experimentally measured cryo-EM structure, which was substantially augmented by reconstructing missing or low-resolution parts of the measured density (where the atomistic structure cannot be fit unambiguously). The model was tested by a quarter of a microsecond MD run, and various biophysical characteristics are obtained and analyzed. The developed methodology of building the model can be used for reconstructing other large biomolecular structures when experimental data are fragmented and/or of varying resolution, while the model itself can be used for studying the biology of MS2, including the dynamics of its interaction with the host bacteria.

A new hybrid multiscaling model has been developed on the basis of the modified control volume function. Following the two-phase analogy of the same substance, the continuum and particle representations are coupled together in the framework of the mass and momentum conservation laws. The new functional form of the control volume function is elaborated by using the continuum discretization principle based on the Delaunay triangulation. The derived mass and momentum equations possess the invariant form for both micro-scale particle and large-scale continuum representations.

Graphene based nanomaterials (GBN) have been recently applied in a broad range of science and technology fields such as nanobiomedicine, electronics, energy storage and power generation exploiting their unique electronic structure, physical properties, and opportunities for modifying their surface using covalent and non-covalent interactions. In the present review we systematised the origins of GBN functionalisation using organic and inorganic molecules, polymers, biomolecules, and anticancer drugs. We show that varying the procedure of GBN functionalisation allows to obtain nanomaterials with desired properties that can be applied to the development of materials with enhanced physicochemical properties, nanoplatforms for drug delivery, nanobiosensors for detection of various biomolecules, as well as nanomaterials for bioimaging and diagnostics. The review can be useful for experts in the fields of material science and nanobiomedicine.

We present a comprehensive study of a water-soluble substance from the class of triazine derivatives alkylating agents. The performed physicochemical investigations of this cytostatic drug's aqueous solutions include the measurements of density, viscosity, speed of sound, refraction index, stability, solubility, distribution between water and octan-1-ol, as well as electronic structure calculations and molecular dynamics modelling. Biologically, the substance was investigated for its cytotoxicity as well as in vitro (on Capan-2 and SK-MEL-1 cell lines) and in vivo (transplantable Ehrlich ascites carcinoma model) therapeutic activity.

MS2 bacteriophage is often used as a model for evaluating pathogenic viruses' behavior in aqueous solution. However, the questions of the virus surface's hydrophilic/hydrophobic balance, the charge distribution, and the binding mechanism are open. Using the dynamic light scattering method and laser Doppler electrophoresis, the hydrodynamic diameter and the ζ-potential of the virus particles were measured at their concentration of 5 ·10¹¹ particles per mL and ionic strength 0.03 M. The values were found to be 30 nm and -29 or -34 mV (by Smoluchowski or Ohshima approximations), respectively. The MS2 bacteriophage surface was also investigated using a series of acid-base indicator dyes of various charge type, size, and structure. Their spectral and acid-base properties (pKa) are very sensitive to the microenvironment in aqueous solution, including containing nanoparticles. The electrostatic potential of the surface Ψ was estimated using the common formula: Ψ= 59 (pKai - pKa) in mV at 25 C. The Ψ values were -50 and +10 mV, respectively, which indicate the “mosaic” way of the charge distribution on the surface. These data are in good agreement with the obtained ζ-potential values and provide even more information about the virus surface. It was found that the surface of the MS2 virus is hydrophilic in solution in contrast to the commonly accepted hypothesis of the hydrophobicity of virus particles. No hydrophobic interactions between various molecular probes and the capsid were observed.

It is very difficult to reconstruct computationally a large biomolecular complex in its biological entirety from experimental data. The resulting atomistic model should not contain gaps structurally and it should yield stable dynamics. We, for the first time, reconstruct from the published incomplete cryo-EM density a complete MS2 virus at atomistic resolution, that is, the capsid with the genome, and validate the result by all-atom molecular dynamics with explicit water. The available experimental data includes a high resolution protein capsid and an inhomogeneously resolved genome map. For the genomic RNA, apart from 16 hairpins with atomistic resolution, the strands near the capsid's inner surface were resolved up to the nucleic backbone level, and the innermost density was completely unresolved. As a result, only 242 nucleotides (out of 3569) were positioned, while only a fragmented backbone was outlined for the rest of the genome, making a detailed model reconstruction necessary. For model reconstruction, in addition to the available atomistic structure information, we extensively used the predicted secondary structure of the genome (base pairing). The technique was based on semi-automatic building of relatively large strands of RNA with subsequent manual positioning over the traced backbone. The entire virus structure (capsid + genome) was validated by a molecular dynamics run in physiological solution with ions at standard conditions confirming the stability of the model.

Light fullerenes, C60 and C70, have significant potential in biomedical applications due to their ability to absorb reactive oxygen species, inhibit the development of tumors, inactivate viruses and bacteria, and as the basis for developing systems for targeted drug delivery. However, the hydrophobicity of individual fullerenes complicates their practical use; therefore, creating water-soluble derivatives of fullerenes is increasingly important. Currently, the most studied soluble adducts of fullerenes are polyhydroxy fullerenes or fullerenols. Unfortunately, investigations of fullerenol biocompatibility are fragmental. They often lack reproducibility both in the synthesis of the compounds and their biological action. We here investigate the biocompatibility of a well-defined fullerenol C60(OH)24 obtained using methods that minimize the content of impurities and quantitatively characterize the product's composition. We carry out comprehensive biochemical and biophysical investigations of C60(OH)24 that include photodynamic properties, cyto- and genotoxicity, hemocompatibility (spontaneous and photo-induced hemolysis, platelet aggregation), and the thermodynamic characteristics of C60(OH)24 binding to human serum albumin and DNA. The performed studies show good biocompatibility of fullerenol C60(OH)24, which makes it a promising object for potential use in biomedicine.

We present a new modification of graphene oxide with very high content (85 wt %) of oxygen-containing functional groups (hydroxy, epoxy, lactol, carboxyl, and carbonyl groups) that forms stable aqueous dispersion in up to 9 gL-1 concentration solutions. A novel faster method of the synthesis is described that produces up to 1 kg of the material and allows controlling the particle size in solution. The synthesized compound was characterized by various physicochemical methods and molecular dynamics modeling, revealing a unique structure in the form of a multilayered wafer of several sheets thick, where each sheet is highly corrugated. The ragged structure of the sheets forms pockets with hindered mobility of water that leads to the possibility of trapping guest molecules.

Dissociation of a ligand isoniazid from a protein catalase was investigated using all-atom molecular dynamics (MD) simulations. Random acceleration MD (τ-RAMD) was used, in which a random artificial force applied to the ligand facilitates its dissociation. We have suggested a novel approach to extrapolate such obtained dissociation times to the zero-force limit assuming never before attempted universal exponential dependence of the bond strength on the applied force, allowing direct comparison with experimentally measured values. We have found that our calculated dissociation time was equal to 36.1 s with statistically significant values distributed in the interval of 0.2-72.0 s, which quantitatively matches the experimental value of 50 +- 8 s despite the extrapolation over 9 orders of magnitude in time.

Spatiotemporal regulation of viral capsid assembly ensures selection of the viral genome for encapsidation. The porcine circovirus 2 is the smallest autonomously replicating pathogenic virus, and thus serves as a model system to study the minimal genetic and biochemical information needed to generate a pathogenic virus. Despite its simplicity, it remains described how PCV2 capsid assembly is regulated to occur within the nucleus of the infected cell. We report that pure PCV2 capsid proteins, in the absence of nucleic acids, require acidic conditions to assemble into empty capsids in vitro. By employing Constant pH Molecular Dynamics simulation with Replica Exchange in pH dimension, for 10 us of total simulation, we unveil the atomistic mechanism of pH-dependency for capsid assembly. The results show that the appropriate protonation configuration for a cluster of acidic amino acids, located on the surface of the capsid protein and near subunit-subunit interface, is necessary to properly position the GH-loop for driving capsid assembly. The GH-loop defines a major subunit-subunit interface. We demonstrate that assembly is prohibited at neutral pH because deprotonation of these amino acids results in their electrostatic repulsion, shifting the GH-loop to a position incompetent with capsid assembly. We propose that encapsulation of nucleic acid overcomes this repulsive force to properly position the GH-loop. To the best of our knowledge, our findings provide the first atomic resolution mechanism responsible for regulating capsid assembly. The findings are useful for development of therapeutics that inhibit PCV2 self-assembly.

Supramolecular chemistry offers an exciting opportunity to assemble materials with molecular precision. However, there remains an unmet need to turn molecular self-assembly into functional materials and devices. Harnessing the inherent properties of both disordered proteins and graphene oxide (GO), we report a disordered protein-GO co-assembling system that through a diffusion-reaction process and disorder-to-order transitions generates hierarchically organized materials that exhibit high stability and access to non-equilibrium on demand. We use experimental approaches and molecular dynamics simulations to describe the underlying molecular mechanism of formation and establish key rules for its design and regulation. Through rapid prototyping techniques, we demonstrate the system's capacity to be controlled with spatio-temporal precision into well-defined capillary-like fluidic microstructures with a high level of biocompatibility and, importantly, the capacity to withstand flow. Our study presents an innovative approach to transform rational supramolecular design into functional engineering with potential widespread use in microfluidic systems and organ-on-a-chip platforms.

Novel monomethine cyanine dyes Cl-YO, F-YO, Cl-YO-Et, Cl-YO-Bu, and YO-Pent were evaluated as agents to detect and characterise a small virus, the MS2 bacteriophage, using the dye and virus intrinsic fluorescence, kinetic and thermal properties, chemical denaturation, and molecular docking and quantum chemistry modelling. The examined compounds demonstrated enhanced fluorescence responses and high affinities ( 1 μM-1) for the intact bacteriophage at physiological ionic strength. The linear Scatchard plots revealed the existence of one binding mode for most dyes. Strong evidence that the cyanines bind to the bacteriophage external surface were obtained, although the possibility of the dye penetration through the virus shell and subsequent complexation with the viral RNA was also tested. The main arguments in favour of the former were that i) the fluorescence of the MS2-bound fluorophores decreased under the influence of protein denaturants, urea and guanidine hydrochloride; ii) the fluorescence responses of the dyes to MS2 and bovine serum albumin were similar; and (iii) one order of magnitude higher sensitivity of the dyes to the yeast RNA was found. Simple docking studies suggested that one cyanine molecule is trapped in a cleft formed by three proteins composing the virus shell. Significant role of electrostatic forces in the stabilisation of the dye-MS2 complexes at low ionic strength (10 mM) was demonstrated, while the influence of steric, hydrophobic, and van-der-Waals interactions was expected to increase at physiological ionic strength. The spectral properties of the novel cyanine dyes compared to other fluorophores demonstrated higher sensitivity of the cyanines to MS2, rendering them promising agents for the investigation of the changes in the virus structure under the influence of heat (Cl-YO-Et, Cl-YO-Bu), denaturants (Cl-YO, F-YO), and ionic strength (all the compounds).

Abstract Tumor Necrosis Factor-alpha (TNF-α), a multifunctional cytokine responsible for providing resistance against infections, inflammation, and cancers. TNF-α has emerged as a promising drug target against several autoimmune and inflammatory disorders. Several synthetic antibodies (Infliximab, Etanercept, and Adalimumab) are available, but their potential to cause severe side effects has prompted them to develop alternative small molecules-based therapies for inhibition of TNF-α. In the present study, combined in silico approaches based on pharmacophore modeling, virtual screening, molecular docking, and molecular dynamics studies were employed to understand significant direct interactions between TNF-α protein and small molecule inhibitors. Initially, four different small molecule libraries (17.5 million molecules) were virtually screened against the selected pharmacophore model. The identified hits were further subjected to molecular docking studies. The three potent lead compounds (ZINC05848961, ZINC09402309, ZINC04502991) were further subjected to 100 ns molecular dynamic studies to examine their stability. Our docking and molecular dynamic analysis revealed that the selected lead compounds target the TNF receptor (TNFR) and efficiently block the production of TNF. Moreover, in silico ADMET (Absorption, Distribution, Metabolism, Excretion and Toxicity) analysis revealed that all the predicted compounds have good pharmacokinetic properties with high gastrointestinal absorption and a decent bioavailability score. Furthermore, toxicity profiles further evidenced that these compounds have no risk of being mutagenic, tumorigenic, reproductive and irritant except ZINC11915498. In conclusion, the present study could serve as the starting point to develop new therapeutic regimens to treat various TNF- related diseases. Communicated by Ramaswamy H. Sarma

We investigate the temperature effect on the size and stability of two major blood plasma proteins, human serum albumin and fibrinogen in aqueous NaCl solution. Dynamic Light Scattering measurements were carried out in the physiological temperature range up to 45C. The analysis of the results provided the temperature dependences of the macromolecular hydrodynamic radius and the ζ-potential. For albumin the hydrodynamic radius remained unchanged, while the ζ-potential increased sharply at approximately 40C. For fibrinogen the radius increased significantly above 45C and the ζ-potential increased similar to albumin at slightly below 40C. The dynamics of albumin macromolecule was simulated using classical Molecular Dynamics, which showed no change in the gyration radius, root mean square deviation, and the composition of disulfide and salt bridges, but substantial change in the secondary structure of the protein. We conclude that these changes in the structure and dynamics of the proteins are correlated with the qualitative change of water dynamics at 42C in the hydration shell of the proteins.

We report on combined experimental and theoretical investigations of the water/micelle interface of cationic, anionic, zwitterionic, and non-ionic surfactants using a new hydrophobic acid-base indicator 2,6-dinitro-4-n-dodecylphenol. The indices of the so-called apparent ionization constant, pKaapp, of the indicator fixed in the micellar pseudophase are determined by the spectrophotometric method. The data allows estimating the Stern layer's electrostatic potential of the ionic micelles Psi. Molecular Dynamics modeling was used to locate the dye molecule and, in particular, its ionizing group OH->O- within the micelles of the studied surfactants. The comparison of the Psi values estimated using 2,6-dinitro-4-n-dodecylphenol with both our computer simulation and literature experimental results reveals obstacles in monitoring electrical interfacial potentials. In particular, the Psi values of the surfactant micelles with alkylammonium groups determined via 2,6-dinitro-4-n-dodecylphenol are overestimated. The reason is specific interactions of the indicator anion with the surfactant head groups. For anionic surfactants, however, this indicator is quite suitable, which is confirmed by the location of HA and A- equilibrium forms in the pseudophase.

Molecular Dynamics simulation results of modelling an entire capsid of the PCV2 virus in explicit water are presented. Particular attention has been given to the distribution of ions inside the capsid. Because the internal surface of the capsid is positively charged, the correct distribution of chloride ions is important. It is demonstrated that this distribution is ultimately connected to the stability of the capsid.

The all-atom model of an MS2 bacteriophage particle without its genome (the capsid) was built using high resolution cryo-EM measurements for initial conformation. The structural characteristics of the capsid and the dynamics of the surrounding solution were examined using Molecular Dynamics simulation. The model demonstrates the overall preservation of the cryo-EM structure of the capsid at physiological conditions (room temperature and ions composition). The formation of a dense anion layer near the inner surface and a diffuse cation layer near the outer surface of the capsid was detected. The flow of water molecules and ions across the capsid through its pores were quantified, which was considerable for water and substantial for ions.

We present the results of Molecular Dynamics simulations of a viral capsid with the aim to analyse ion distribution on the capsid's surface that defines its stability. Two systems were modelled, a stable capsid with neutralising number of ions and an unstable capsid with low number of ions. For the ion distribution analysis the capsid's structure was identical and fixed in both simulations. It was then released for the stability analysis. The ion distribution demonstrated two types of the local regions on the inner surface of the capsid's wall: highly occupied with chloride ions in both systems despite a largely uniform electrostatic potential everywhere on the surface, and the regions that lose acid. The latter regions are located close to the cracks that are formed when the capsid is destabilised and thus could initiate the collapse of the capsid.

Classical molecular dynamics modeling of whole viruses or their capsids in explicit water is discussed, and known examples from the literature are analyzed. Only works on all-atom modeling in explicit water are included. Physical chemistry of the whole system is the focus, which includes the structure and dynamics of the biomolecules as well as water and ion behavior in and around the virus particle. It was demonstrated that in most investigations molecular phenomena that currently can not be studied experimentally are successfully reproduced and explained by the simulations. These include, for example, transport and distribution of ions inside viruses that ultimately connected to their stability, the hydrodynamic pressure in the capsid related to viruses' elastic properties, the role of metal ions in virus swelling, and others. Current and future tendencies in the development of all-atom virus simulations are outlined.

Water is essential for protein three-dimensional structure, conformational dynamics, and activity. Human serum albumin (HSA) is one of major blood plasma proteins, and its functioning is fundamentally determined by the dynamics of surrounding water. The goal of this study is to link the conformational dynamics of albumin to the thermal motions in water taking place in the physiological temperature range. We report the results of photon correlation spectroscopy and molecular dynamics simulations of {HSA} in aqueous solution. The experimental data processing produced the temperature dependence of the {HSA} hydrodynamic radius and its zeta potential. Molecular dynamics reproduced the results of experiments and revealed changes in the secondary structure caused by the destruction of hydrogen bonds in the macromolecule's globule.

Present experimental methods do not have sufficient resolution to investigate all processes in virus particles at atomistic details. We report the results of molecular dynamics simulations and analyze the connection between the number of ions inside an empty capsid of PCV2 virus and its stability. We compare the crystallographic structures of the capsids with unresolved N-termini and without them in realistic conditions (room temperature and aqueous solution) and show that the structure is preserved. We find that the chloride ions play a key role in the stability of the capsid. A low number of chloride ions results in loss of the native icosahedral symmetry, while an optimal number of chloride ions create a neutralizing layer next to the positively charged inner surface of the capsid. Understanding the dependence of the capsid stability on the distribution of the ions will help clarify the details of the viral life cycle that is ultimately connected to the role of packaged viral genome inside the capsid.

The 3-dimentional (3-D) elasticity dynamic theory is applied to investigate the mechanical properties of virus capsid. The idealized model of virus is based on the 3-D mathematical physics boundary problem formulated in spherical coordinate system for the steady-state oscillation process. The virus is modeled as the hollow elastic sphere, which is situated and fullfilled with two different acoustic mediums. The stated boundary value problem is solved with the help of the integral transformation method and method of the discontinuous solutions. As a result, the exact solution of the problem is derived. The numerical calculations of the virus elastic characteristics are conducted.

The virus capsid PCV2 is investigated by the construction of the idealized virus model. It is described by the 3-D dynamical elasticity problem formulated in the spherical coordinate system for the steady-state oscillation process. The virus is modeled as the hollow elastic sphere, which is surrounded and fulfilled with the two different acoustic mediums. The integral Fourier and Legendre transformations were applied to the stated initial-boundary value problem. With the help of the discontinuous solutions method the expressions for the displacements and acoustic potentials were derived in the exact form depending on the unknown jumps of the displacements and stresses. The conditions at the virus surfaces allowed to express the displacement and stress jumps via jumps of the acoustic potentials, which were obtained after solving of the two linear equations system. As a result, the exact solution of the problem is derived. The numerical calculations of the virus elastic characteristics are conducted. This problem is the first step in the virus simulation with the help of the elasticity equations. It was established that more complicated statement of the problem in the frame of the anisotropic elastic problem should be used for the more adequate virus modeling.

Abstract Simulations of complete virus capsid at atomistic details have been performed using standard molecular dynamics as well as original hybrid molecular dynamics/hydrodynamics methodologies. The results show that the capsid is stable in water solution at room temperature and ions composition similar to physiological conditions. Detailed analysis of the flow of water molecules and ions through the capsid's wall is performed. It demonstrates that ions do not cross the capsid shell, while water exhibits substantial flows in both directions. This behaviour can be classified as a semipermeable membrane and may play a role in mechanical properties of the virus particle.

Elastic properties of virus shells (capsids) are important as they protect the virus genome and play important role in virus internalization (the process of virus entering the cell). These properties can also be measured experimentally by direct deformation of the capsid with a microscope's tip. A 3D mathematical model of a virus under an external non-stationary load is proposed in this paper. The apparatus of the boundary value problems of mathematical physics was used during modeling. The stated initial boundary value problem of elasticity was solved with the help of the integral transformation method and the method of discontinuous solutions. As a result, the analytical solution of the problem was obtained in Laplace transformation domain. The numerical calculations of the virus elastic characteristics were illustrated for the case of a steady-state oscillation.

A hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework based on the analogy with two-phase hydrodynamics has been extended to dynamically tracking the feature of interest at all-atom resolution. In the model, the hydrodynamics description is used as an effective boundary condition to close the molecular dynamics solution without resorting to standard periodic boundary conditions. The approach is implemented in a popular Molecular Dynamics package {GROMACS} and results for two biomolecular systems are reported. A small peptide dialanine and a complete capsid of a virus porcine circovirus 2 in water are considered and shown to reproduce the structural and dynamic properties compared to those obtained in theory, purely atomistic simulations, and experiment.

A new 3D implementation of a hybrid model based on the analogy with two-phase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the Landau-Lifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single "zoom-in" user-defined function s that has the meaning of a partial concentration in the two-phase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported.

Open Peer Review on `Molecular Dynamics Simulations of the Temperature Induced Unfolding of Crambin Follow the Arrhenius Equation'

Two-dimensional `Mercedes Benz' (MB) or BN2D water model (Naim, 1971) is implemented in Molecular Dynamics. It is known that the MB model can capture abnormal properties of real water (high heat capacity, minima of pressure and isothermal compressibility, negative thermal expansion coefficient) (Silverstein et al., 1998). In this work formulas for calculating the thermodynamic, structural and dynamic properties in microcanonical (NVE) and isothermal-isobaric (NPT) ensembles for the model from Molecular Dynamics simulation are derived and verified against known Monte Carlo results. The convergence of the thermodynamic properties and the system's numerical stability are investigated. The results qualitatively reproduce the peculiarities of real water making the model a visually convenient tool that also requires less computational resources, thus allowing simulations of large (hydrodynamic scale) molecular systems. We provide the open source code written in C/C++ for the BN2D water model implementation using Molecular Dynamics.

A multiscale Molecular Dynamics/Hydrodynamics implementation of the 2D Mercedes Benz (MB or BN2D) [1] water model is developed and investigated. The concept and the governing equations of multiscale coupling together with the results of the two-way coupling implementation are reported. The sensitivity of the multiscale model for obtaining macroscopic and microscopic parameters of the system, such as macroscopic density and velocity fluctuations, radial distribution and velocity autocorrelation functions of MB particles, is evaluated. Critical issues for extending the current model to large systems are discussed.

Introducation to a Theme Issue `Multi-scale systems in fluids and soft matter: approaches, numerics and applications' of Phil. Trans. R. Soc. A.

Fluctuations of liquids at the scales where the hydrodynamic and atomistic descriptions overlap are considered. Importance of these fluctuations for atomistic motions is discussed and examples of their accurate modelling with a multi-space-time-scale Fluctuating Hydrodynamics scheme are provided. For resolving microscopic details of liquid systems, including bimolecular solutions, together with macroscopic fluctuations in space-time, a novel hybrid atomistic/ Fluctuating Hydrodynamics approach is introduced. For smooth transition between the atomistic and continuum representations, an analogy with two-phase hydrodynamics is used that leads to a strict preservation of macroscopic mass and momentum conservation laws. Examples of numerical implementation of the new hybrid approach for the multiscale simulation of liquid argon in equilibrium conditions are provided.

A novel framework for modelling biomolecular systems at multiple scales in space and time simultaneously is described. The atomistic molecular dynamics representation is smoothly connected with statistical continuum hydrodynamics description. The system behaves correctly at the limits of pure molecular dynamics (hydrodynamics) and at the intermediate regimes when the atoms move partly as atomistic particles, and at the same time follow the hydrodynamic flows. The corresponding contributions are controlled by a parameter, which is defined as an arbitrary function of space and time, thus, allowing an effective separation of the atomistic `core' and continuum `environment'. To fill the scale gap between the atomistic and the continuum representations our special purpose computer for molecular dynamics, MDGRAPE-4, as well as GPU-based computing were used for developing the framework. These hardware developments also include interactive molecular dynamics simulations that allow to intervene the modelling through force-feedback devices.

A time dependent electromagnetic pulse generated by a current running laterally to the direction of the pulse propagation is considered in paraxial approximation. It is shown that the pulse envelope moves in the time-spatial coordinates on the surface of a parabolic cylinder for the Airy pulse and a hyperbolic cylinder for the Gaussian. These pulses propagate in time with deceleration along the dominant propagation direction and drift uniformly in the lateral direction. The Airy pulse stops at infinity while the asymptotic velocity of the Gaussian is nonzero.

Transitions between metastable conformations of a dipeptide are investigated using classical molecular dynamics simulation with explicit water molecules. The distribution of the surrounding water at different moments before the transitions and the dynamical correlations of water with the peptide's configurational motions indicate that the water molecules represent an integral part of the molecular system during the conformational changes, in contrast with the metastable periods when water and peptide dynamics are essentially decoupled.

Protein functional motions are ultimately connected to water dynamics. The goal of this study is to link the conformational dynamics of albumin to a dynamic transition taking place at  42C in water. We report the results of dynamic light scattering measurements of albumin aqueous solution in the temperature interval 20-65C. The processing of the experimental data produced the temperature dependence of the macromolecular hydrodynamic radius. We demonstrate that the growth of the macromolecular size in this temperature range can be divided into two stages that are connected to the dynamical properties of water.

A version of the thermodynamic perturbation theory based on scaling transformation of the partition function has been applied to the statistical foundation of the equation of state in the high pressure region. Two modifications of the equations of state have been obtained on the basis of the free energy functional perturbation series. The comparative analysis of the experimental PVT-data on the isothermal compression for supercritical fluids of inert gases has been carried out.

We derive the equation of state for supercritical fluids in the framework of the Sutherland and Katz potential models using the free energy perturbation expansion. The derived equation of state quantitatively agrees with experimental data on isothermal compression of water in the high pressure region. It establishes an explicit relationship between the thermodynamic experimental data and the parameters of the molecular potential. This can be used in calibration protocols for simulation forcefields for the high pressure regions.

A hidden Markov state model has been applied to classical molecular dynamics simulated small peptide in explicit water. The methodology allows increasing the time resolution of the model and describe the dynamics with the precision of 0.3ps (comparing to 6ps for the standard methodology). It also permits the investigation of the mechanisms of transitions between the conformational states of the peptide. The detailed description of one of such transitions for the studied molecule is presented.

The process of binding of small ligands to dihydrofolate reductase protein has been investigated using all-atom molecular dynamics simulations. The existence of a mechanism that facilitates the search of the binding site by the ligand is demonstrated. The mechanism consists of ligand diffusing on the protein's surface. It has been discussed in the literature before, but has not been explicitly confirmed for realistic molecular systems. The strength of this nonspecific binding is roughly estimated and found to be essential for the binding kinetics.

We suggest a new method for the analysis of experimental time series that can distinguish high dimensional dynamics from stochastic motion. It is based on the idea of statistical complexity, i.e. the Shannon entropy of the so-called e-machine (a Markov-type model of the observed time series). This approach has been recently demonstrated to be efficient for making a distinction between a molecular trajectory in water and noise. In this paper we analyse the difference between chaos and noise using the Chirikov-Taylor Standard map as an example in order to elucidate the basic mechanism that makes the value of complexity in deterministic systems high. In particular, we show that the value of statistical complexity is high for the case of chaos, and attains zero value for the case of stochastic noise. We further study the Markov property of the data generated by the Standard map to clarify the role of long time memory in differentiating the cases of deterministic systems and stochastic motion.

To help understand how sugar interactions with proteins stabilise biomolecular structures, we compare the three main hypotheses for the phenomenon with the results of long molecular dynamics simulations on lysozyme in aqueous trehalose solution (0.75 M). We show that the water replacement and water entrapment hypotheses need not be mutually exclusive, because the trehalose molecules assemble in distinctive clusters on the surface of the protein. The flexibility of the protein backbone is reduced under the sugar patches supporting earlier findings that link reduced flexibility of the protein with its higher stability. The results explain the apparent contradiction between different experimental and theoretical results for trehalose effects on proteins.

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare theorem.

A trajectory of liquid water simulated using classical molecular dynamics has been analysed in the framework of symbolic dynamics. The behaviour of symbolic subsequences (words) of nine symbols long has been studied at a very long time of 1us. Contrary to naive expectations, the molecular trajectory behaves very differently compared to both a random signal and a random surrogate with spectral properties identical to the molecular trajectory. The molecular system characteristics resemble those of a chaotic map, the Standard map. We conclude that the most probable reason for deviations from randomness in the molecular system is its deterministic dynamics, in particular, the stickiness of periodic islands in the bulk of chaotic motion.

The question of significant deviations of protein folding times simulated using molecular dynamics from experimental values is investigated. It is shown that, in the framework of Markov State Model describing the conformational dynamics of peptides and proteins, the folding time is very sensitive to the simulation model parameters, such as forcefield and temperature. Using two peptides as examples we show that the deviations in the folding times can reach an order of magnitude for modest variations of the molecular model. We, therefore, conclude that the folding rate values obtained in molecular dynamics simulations have to be treated with care.

A novel statistical analysis of Molecular Dynamics generated trajectories is applied to various bulk liquids and a peptide in water. The analysis provides unique information on the full dimensional trajectory. In particular, it demonstrates that the phase space exploration is a very slow process that has the time scale of hundreds of nanoseconds even in bulk water and argon. Most importantly, the areas of the phase space visited at these times are different, in contrast to the commonly assumed uniform random search process. For a 21-residue peptide in explicit water it has been found that the peptide exhibits nanoseconds long periods that significantly differ in the rates of the phase space exploration. During these periods the rates remain the same but different from other periods and from the phase space covering rate in water.

Conformational transitions in proteins define their biological activity and can be investigated in detail using Markov State Model. The fundamental assumption on the transitions between the states, their Markov property, is critical in this framework. We test this assumption by analysing the transitions obtained directly from the dynamics of an MD simulated peptide VPAL (Valine - Proline - Alanine - Leucine) and states defined phenomenologically using clustering in dihedral space. We find that the transitions are Markovian at the time scale of  50ps and longer. However, at the time scale of 30-40ps the dynamics looses its Markov property. Our methodology reveals the mechanism that leads to non-Markov behaviour. It also provides a way of regrouping the conformations into new states that now posses the required Markov property of their dynamics.

A framework that connects Computational Mechanics and molecular dynamics has been developed and described. As the key part of the framework the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore it is shown that causal states, the constituent parts of the main construct of Computational Mechanics, e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that these areas of the phase space can be divided into two classes according to their Poincare return times. The first class is characterised by predominantly short time returns, typical to quasi-periodic trajectories of the dynamical system. This class includes a limited number of areas that are robust with respect to different total length of the molecular trajectory. The second class has a chaotic behaviour of the return times distributed exponentially in accordance with the Poincare theorem. In contrast to the first class, the number of such areas grows logarithmically with the length of the trajectory. We put forward and numerically illustrate a hypothesis that explains this behaviour by the presence of temporal non-stationarity in molecular trajectory.

A recently developed spectral method for identifying metastable states in Markov chains is used to analyse the conformational dynamics of a four residue peptide Valine-Proline-Alanine-Leucine. We compare our results to empirically defined conformational states and show that the found metastable states correctly reproduce the conformational dynamics of the system.

A 21-residue peptide in explicit water has been simulated using classical molecular dynamics. The system's trajectory has been analysed with a novel approach that quantifies the process of how atom's environment trajectories are explored. The approach is based on the measure of Statistical Complexity that extracts complete dynamical information from the signal. The introduced characteristic quantifies the system's dynamics at the nanoseconds time scale. It has been found that the peptide exhibits nanoseconds long periods that significantly differ in the rates of the exploration of the dynamically allowed configurations of the environment. During these periods the rates remain the same but different from other periods and from the rate for water. Periods of dynamical frustration are detected when only limited routes in the space of possible trajectories of the surrounding atoms are realised.

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Elementary conformational changes of the backbone of a 21-residue peptide A5(A3RA)3A are studied using molecular dynamics simulations in explicit water. The processes of the conformational transitions and the regimes of stationary fluctuations between them are investigated using minimal perturbations of the system. The perturbations consist of a few degrees rotation of the velocity of one of the systems' atoms and keep the system on the same energy surface. It is found that (i) the system dynamics is insignificantly changed by the perturbations in the regimes between the transitions; (ii) it is very sensitive to the perturbations just before the transitions that prevents the peptide from making the transitions; and (iii) the perturbation of any atom of the system, including distant water molecules is equally effective in preventing the transition. The latter implies strongly collective dynamics of the peptide and water during the transitions.

It is shown that regimes with dynamical chaos are inherent not only to nonlinear system but they can be generated by initially linear systems and the requirements for chaotic dynamics and characteristics need further elaboration. Three simplest physical models are considered as examples. In the first, dynamic chaos in the interaction of three linear oscillators is investigated. Analogous process is shown in the second model of electromagnetic wave scattering in a double periodical inhomogeneous medium occupying half-space. The third model is a linear parametric problem for the electromagnetic field in homogeneous dielectric medium which permittivity is modulated in time.

The dynamics of peptides and proteins generated by classical MD is described using a Markov model. The model is built by clustering the trajectory into conformational states and estimating transition probabilities between the states. Assuming that it is possible to influence the dynamics of the system by varying simulation parameters, we show how to use the Markov model to determine the parameter values that preserve the folded state of the protein and at the same time reduce the folding time in the simulation. We investigate this by applying the method to two systems. The first system is an imaginary peptide described by given transition probabilities with a total folding time of 1us. We find that only small changes in the transition probabilities are needed to accelerate (or decelerate) the folding. This implies that folding times for slowly folding peptides and proteins calculated using MD cannot be meaningfully compared to experimental results. The second system is a four residue peptide VPAL (Valine - Proline - Alanine - Leucine) in water. We control the dynamics of the transitions by varying the temperature and the atom masses. The simulation results show that it is possible to find the combinations of parameter values that accelerate the dynamics and at the same time preserve the native state of the peptide. A method for accelerating larger systems without performing simulations for the whole folding process is outlined.

We investigate the sensitivity of a Markov model with states and transition probabilities obtained from clustering a molecular dynamics trajectory. We have examined a 500ns molecular dynamics trajectory of the peptide valine-proline-alanine-leucine in explicit water. The sensitivity is quantified by varying the boundaries of the clusters and investigating the resulting variation in transition probabilities and the average transition time between states. In this way, we represent the effect of clustering using different clustering algorithms. It is found that in terms of the investigated quantities, the peptide dynamics described by the Markov model is sensitive to the clustering; in particular, the average transition times are found to vary up to 46%. Moreover, inclusion of nonphysical sparsely populated clusters can lead to serious errors of up to 814%. In the investigation, the time step used in the transition matrix is determined by the minimum time scale on which the system behaves approximately Markovian. This time step is found to be about 100ps. It is concluded that the description of peptide dynamics with transition matrices should be performed with care, and that using standard clustering algorithms to obtain states and transition probabilities may not always produce reliable results.

Statistical complexity, a measure introduced in computational mechanics has been applied to MD simulated liquid water and other molecular systems. It has been found that statistical complexity does not converge in these systems but grows logarithmically without a limit. The coefficient of the growth has been introduced as a new molecular parameter which is invariant for a given liquid system. Using this new parameter extremely long time correlations in the system undetectable by traditional methods are elucidated. The existence of hundreds of picosecond and even nanosecond long correlations in bulk water has been demonstrated.

Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the short-time correlations corresponding to the velocity autocorrelation decay times (<0.1ps), remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longer-time correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced.

Pseudoscalar measures of electronic chirality for molecular systems are derived using the spectral moment theory applied to the frequency-dependent rotational susceptibility. In this scheme a one-electron chirality operator k naturally emerges as a quantum counterpart of the triple scalar product, involving velocity, acceleration and second acceleration. Averaging k over an electronic state vector gives rise to an additive chirality invariant (k-index), considered as a quantitative measure of chirality. A simple computational technique for quick calculation of the k-index is developed and various structural classes (cyclic hydrocarbons, cage-shaped systems, etc.) are studied. Reasonable behaviour of the chirality index is demonstrated. The chirality changes during the beta-turn formation in Leu-Enkephalin is presented as a useful example of the chirality analysis for conformational transitions.

Assuming that the dynamics of peptides and proteins can be described by Markov transitions between different configurational states, we present a method which can calculate the mean first passage time (MFPT) between sets of initial and final states. The method is described in detail and differences between this and a method commonly employed [1] are explained. It is shown that the proposed method is (i) more general in allowing sets of final states, (ii) significantly faster, (iii) more accurate since it does not involve the calculation of infinite summations. Particular attention is given to the biologically important case of multiple final states.

Leu-Enkephalin in explicit water is simulated using classical molecular dynamics. A beta-turn transition is investigated by calculating the topological complexity (in the ?computational mechanics? framework [J. P. Crutchfield and K. Young, Phys. Rev. Lett., 63, 105 (1989)]) of the dynamics of both the peptide and the neighbouring water molecules. The complexity of the atomic trajectories of the (relatively short) simulations used in this study reflect the degree of phase space mixing in the system. It is demonstrated that the dynamic complexity of the hydrogen atoms of the peptide and almost all of the hydrogens of the neighbouring waters exhibit a minimum precisely at the moment of the beta-turn transition. This indicates the appearance of simplified periodic patterns in the atomic motion, which could correspond to high-dimensional tori in the phase space. It is hypothesized that this behaviour is the manifestation of the effect described in the approach to molecular transitions by Komatsuzaki and Berry [T. Komatsuzaki and R.S. Berry, Adv. Chem. Phys., 123, 79 (2002)], where a ?quasi-regular? dynamics at the transition is suggested. Therefore, for the first time, the less chaotic character of the folding transition in a realistic molecular system is demonstrated.

ters in Cardiology challenge presents the clinically important problem of developing and testing fully automated methods for measurement of the QT interval with clinically acceptable accuracy. For this purpose a fully automated method was developed using time-frequency methods of continuous (CWT) and fast wavelet transforms (FWT). It consists of QRS detection and P, T wave boundaries identification which is implemented using consecutive ECG data filtering with CWT and FWT transforms. The frequency of the CWT transform can be adjusted for more precise identification of the T wave boundaries for an individual patient. A representative beat with a T wave is selected from an automatically annotated signal if it is not annotated as ectopic, noise or artefact. The final score is the highest one in division three and second place in division two.

Using an exactly solvable model a process of modulation of an electromagnetic field in a time-varying medium is investigated. A correlation between the Hurst's index of a transformed electromagnetic signal and its complexity is considered for the first time.

Novel molecular complexity measures are designed based on the quantum molecular kinematics previously suggested in [A.V.Luzanov, E.N.Babich, J. Mol. Stucture (Theochem), 333, 279 (1995)]. The Hamiltonian matrix constructed in a quasi-topological approximation describes the temporal evolution of the modelled electronic system and determines the time derivatives for the dynamic quantities. This allows to define the average kinematic characteristics closely related to the curvatures of the electron paths. A special attention has been given to the computational scheme for this chirality measure. The calculations on realistic molecular systems demonstrate reasonable behaviour of the proposed molecular complexity indices.

All-atom molecular dynamics simulations for a single molecule of Leu-Enkephalin in aqueous solution have been used to study the role of the water network during the formation of beta-turns. We give a detailed account of the intramolecular hydrogen bonding, the water-peptide hydrogen bonding, and the orientation and residence times of water molecules focusing on the short critical periods of transition to the stable beta-turns. These studies suggest that, when intramolecular hydrogen bonding between the first and fourth residue of the beta-turn is not present, the disruption of the water network and the establishment of water bridges constitute decisive factors in the formation and stability of the beta-turn. Finally, we provide possible explanations and mechanisms for the formations of different kinds of beta-turns.

Isotropic scattering Raman spectra of liquid acetonitrile (AN) solutions of LiBF4 and NaI at various temperatures and concentrations have been investigated. For the first time imaginary as well as real parts of the solvent vibrational correlation functions have been extracted from the spectra. Such imaginary parts are currently an important component of modern theories of vibrational relaxation in liquids. This investigation thus provides the first experimental data on imaginary parts of a correlation function in {AN} solutions. Using the fitting algorithm we recently developed, statistically confident models for the Raman spectra were deduced. The parameters of the band shapes, with an additional correction, of the nu(2) {AN} vibration (CN stretching), together with their confidence intervals are also reported for the first time. It is shown that three distinct species, with lifetimes greater than 10e-13 s, of the {AN} molecules can be detected in solutions containing Li+ and Na+. These species are attributed to {AN} molecules directly solvating cations; the single oriented and polarised molecules interleaving the cation and anion of a Solvent Shared Ion Pair (SShIP); and molecules solvating anions. These last are considered to be equivalent to the next layer of solvent molecules, because the {CN} end of the molecule is distant from the anion and thus less affected by the ionic charge compared with the anion situation. Calculations showed that at the concentrations employed, 1 and 0.3 M, there were essentially no other solvent molecules remaining that could be considered as bulk solvent. Calculations also showed that the internuclear distance in these solutions supported the proposal that the ionic entity dominating in solution was the SShIP, and other evidence was adduced that confirmed the absence of Contact Ion Pairs at these concentrations. The parameters of the shape of the vibrational correlation functions of all three species are reported. The parameters of intramolecular anharmonic coupling between the potential surfaces in {AN} and the dynamics of the intermolecular environment fluctuations and intermolecular energy transfer are presented. These results will assist investigations made at higher and lower concentrations, when additional species and interactions with {AN} molecules will be present.

The simulated classical dynamics of a small molecule exhibiting self-organizing behavior via a fast transition between two states is analyzed by calculation of the statistical complexity of the system. It is shown that the complexity of molecular descriptors such as atom coordinates and dihedral angles have different values before and after the transition. This provides a new tool to identify metastable states during molecular self-organization. The highly concerted collective motion of the molecule is revealed. Low-dimensional subspaces dynamics is found sensitive to the processes in the whole, high-dimensional phase space of the system.

A possibility of a strong change of an electromagnetic signal by a short sequence of time cycles of pulses that modulate the medium parameters is shown. The backward wave is demonstrated to be an inevitable result of the medium time change. Dependence of the relation between backward and forward waves on the parameters of the medium modulation is investigated. The finite statistical complexity of the electromagnetic signal transformed by a finite sequence of modulating cycles is calculated. Increase of the complexity with the number of cycles is shown.

Methods for the calculation of complexity have been investigated as a possible alternative for the analysis of the dynamics of molecular systems. "Computational mechanics" is the approach chosen to describe emergent behavior in molecular systems that evolve in time. A novel algorithm has been developed for symbolization of a continuous physical trajectory of a dynamic system. A method for calculating statistical complexity has been implemented and tested on representative systems. It is shown that the computational mechanics approach is suitable for analyzing the dynamic complexity of molecular systems and offers new insight into the process.

The computational mechanics approach has been applied to the orientational behavior of water molecules in a molecular dynamics simulated water-Na+ system. The distinctively different statistical complexity of water molecules in the bulk and in the first solvation shell of the ion is demonstrated. It is shown that the molecules undergo more complex orientational motion when surrounded by other water molecules compared to those constrained by the electric field of the ion. However the spatial coordinates of the oxygen atom shows the opposite complexity behavior in that complexity is higher for the solvation shell molecules. New information about the dynamics of water molecules in the solvation shell is provided that is additional to that given by traditional methods of analysis.

The development of a sophisticated model is presented for fitting the experimental Raman spectra of liquid acetonitrile. A new approach for extracting all possible band shape details of highly overlapping spectral bands is derived and implemented. A unique, statistically justified resolution is obtained of the [small nu] vibrational band into its components at 25, 50 and 75[degree]C. The parameters of both the real and imaginary parts of the vibrational correlation functions are reported for the first time together with their confidence intervals. The quantitative characteristics obtained of the nu mode dynamics can be considered as experimental data and used for testing theoretical models of vibrational relaxation.

A novel implementation of the de Broglie-Bohm mechanics is presented. The method employs the use of n-dimensional Delaunay tesselation for the purpose of computing the quantum potential term and is fully generalizable for the multidimensional case. We simulate the scattering of a Gaussian wavepacket from an Eckart barrier in two- and three-dimensions and compare our results against the dynamics obtained using a numerically exact propagation scheme.

The problem of the uniqueness of parameters obtained during fitting of experimental spectra containing closely overlapping bands has been evaluated, since conventional methods of fitting do not produce reliable results. It is here shown that, despite the difficulties inherent in both the formal mathematical problem and its numerical solutions, typical and representative spectra can be resolved unambiguously within a reasonably chosen theoretical model. Reliable values of the parameters of the model, including parameters of band shape, can also be obtained. A random search method of global minimisation of a function with a significant number of arguments is derived. A program and algorithm to implement this method for spectra decomposition have been developed. The program allows the microdynamics of liquids to be obtained directly upon performing numerical Fourier transformations on a model (theoretical) time correlation function together with using model spectra obtained thereby in each fitting step. A model spectrum for any desired accuracy and frequency range can hence be generated without the unavoidable errors inherent in conventional methods. The apparatus function of the spectrophotometer is also now readily incorporated. Using the algorithm, the parameters of the microdynamics of acetonitrile molecules are obtainable for the first time upon decomposition of its nu Raman vibration, and a value of 0.069 was obtained for the dimensionless modulation speed in liquid acetonitrile. This method has also enabled for the first time the detection of molecules in the second solvation shell around Li in acetonitrile, from within its Raman spectrum.

Исследованы люминесценция и структура тонких пленок (10 нм) фуллерита С60, полученных осаждением в вакууме на скол монокристалла NaCl. По данным электронно-оптических исследований, пленки С60 были сплошными, достаточно однородными, имели ГЦК-решетку, ориентированную таким образом, что плоскость (111) была параллельна плоскости (001) монокристалла NaCl. Проведены измерения спектров фотолюминесценции пленок фуллерита С60, на NaCl и в свободном состоянии при температуре 5К. Экспериментальные спектры с плохо выраженной структурой разделены на составляющие полосы гауссовой формы. Отмечено влияние подложки и длины волны возбуждения на спектры люминесценции. Обсуждаются механизмы формирования спектров люминесценции.

The method for handling a transient electromagnetic problem with arbitrary time dependence of a medium parameter is proposed. The method is based on the evolutionary approach, which reduces the problem to a Volterra integral equation. A parameter's arbitrary time variation is approximated by a stepped function. The problem is exactly solved at each step by virtue of the same resolvent. Various parameter time dependences are considered. ?© 1997 John Wiley & Sons, Inc.

The region of the 2(a1) (CN) and 4(a1) (CC) stretching vibrations of isotropic and anisotropic Raman spectra of acetonitrile and 1 M NaI, NaBPh4 , and Bu4NI solutions in acetonitrile at ca. 22°C were stud- ied. The spectra were decomposed into components assuming that the lineshape of a separate band is described by integrated convolution of the Lorentzian and Gaussian functions. The spectra of Na+-containing solutions were found to exhibit a new band in the region of the 2 and 4 vibrations, which corresponds to the solvent molecules incorporated in the first solvation shell of Na+. Vibrational and rotational relaxation times of aceto- nitrile molecules were calculated by the suggested method. Molecular relaxation was found to slow down on going from the neat solvent to electrolyte solutions and, in the latter, with an increase in the electrostatic influ- ence of ions. Autocorrelation functions of the corresponding relaxation processes in neat acetonitrile and, espe- cially, in electrolyte solutions considerably deviate from a pure exponential form.

IR spectra of (BuNI)-hexan-1-ol solutions at 25, 55, 85, 115 and 145 [degree]C in the OH stretching region have been investigated. The OH stretching spectra and the H NMR chemical shifts of the hexanol OH-group were obtained from BuNI-hexanol-CCl solutions in the alcohol concentration range 3 [times] 10-7.8 mol dm . The relationship between absorbance and wavenumber is represented as the product of a Lorentzian and a Gaussian curve. Using this dependence deconvolution of the OH-band was carried out by the Simplex method. From these data, it was established that BuNI is a structure-breaker at moderate temperatures and/or low concentrations of CCl. At higher temperatures or in very dilute solutions of BuNI-hexanol in CCl, BuNI is observed to be a structure-maker.

На основе выбранной модели равновесии, уравнения концентрационной зависимости молярной электрической проводимости из кондуктометричесних данных рассчитаны предельные молярные электрические проводимости и константы ассоциации 1-1-электролитов в 1-пропаноле в интервале 200-368 К. Обнаружены минимумы на политермах констант ассоциации.