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The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. D. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale invariance of the system, which is associated with discrete and equidistant timescales on a logarithmic scale. Examples include such diverse fields as financial crashes, random diffusion, and quantum topological materials. Recent time-resolved experiments and molecular dynamics simulations suggest that discrete scale invariance may also apply to hierarchical dynamics in proteins, where several fast local conformational changes are a prerequisite for a slow global transition to occur. Employing entropy-based timescale analysis and Markov state modeling to a simple one-dimensional hierarchical model and biomolecular simulation data, it is found that hierarchical systems quite generally give rise to logarithmically spaced discrete timescales. By introducing a one-dimensional reaction coordinate that collectively accounts for the hierarchically coupled degrees of freedom, the free energy landscape exhibits a characteristic staircase shape with two metastable end states, which causes the log-periodic time evolution of the system. The period of the log-oscillations reflects the effective roughness of the energy landscape and can, in simple cases, be interpreted in terms of the barriers of the staircase landscape. [ABSTRACT FROM AUTHOR]

Recent time-resolved experiments and accompanying molecular dynamics simulations allow us to monitor the flow of vibrational energy in biomolecules. As a simple means to describe these experimental and simulated data, Buchenberg et al. [J. Phys. Chem. Lett. 7, 25 (2016)] suggested a master equation model that accounts for the energy transport from an initially excited residue to some target residue. The transfer rates of the model were obtained from two scaling rules, which account for the energy transport through the backbone and via tertiary contacts, respectively, and were parameterized using simulation data of a small α-helical protein at low temperatures. To extend the applicability of the model to general proteins at room temperature, here a new parameterization is presented, which is based on extensive nonequilibrium molecular dynamics simulations of a number of model systems. With typical transfer times of 0.5–1 ps between adjacent residues, backbone transport represents the fastest channel of energy flow. It is well described by a diffusive-type scaling rule, which requires only an overall backbone diffusion coefficient and interatom distances as input. Contact transport, e.g., via hydrogen bonds, is considerably slower (6–30 ps) at room temperature. A new scaling rule depending on the inverse square contact distance is suggested, which is shown to successfully describe the energy transport in the allosteric protein PDZ3. Since both scaling rules require only the structure of the considered system, the model provides a simple and general means to predict energy transport in proteins. To identify the pathways of energy transport, Monte Carlo Markov chain simulations are performed, which highlight the competition between backbone and contact transport channels. [ABSTRACT FROM AUTHOR]

Conventional drug delivery systems suffer from poor absorption and poor bioavailability at the target site due to either very weak or very strong adsorption of drug on the carrier. Porous 2D nanostructures can offer better drug delivery system provided the system chosen has suitable cavity with heteroatoms for reasonable interaction with drug molecules. C2N is a surface of choice in this regard; therefore, potential of C2N surface as drug delivery system for nitrosourea and fluorouracil (drugs) is explored here. Both nitrosourea and fluorouracil interacted with the electron rich central cavity of C2N. Different structural and electronic parameters show that both drugs have good adsorption on C2N surface and thus can be carried to the target easily. Values of interaction and basis set superposition error (BSSE) corrected energies are slightly higher for nitrosourea@C2N as compared to fluorouracil@C2N. While all other properties such as non-covalent interaction (NCI), symmetry-adapted perturbation theory (SAPT0), quantum theory of atoms in molecules (QTAIM), natural bond orbital (NBO), electron density difference (EDD) and frontier molecular orbital (FMO) analyses illustrate that C2N is better carrier for nitrosourea than fluorouracil. The off-loading of drug is explored through molecular dynamics simulations which reveal that slightly elevated temperature can cause off-loading of the drug at the target cancer cell, which usually have temperature higher than the normal cells. MD simulations reveal that atomic interactions between the drugs and C2N are destabilized at higher temperatures. Comparison of the loading and off-loading mechanism with other surfaces reported in the literature reveal that C2N is a better carrier for these drugs. [ABSTRACT FROM AUTHOR]