Green’s functions in quantum transition state theory

Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space

Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.

Anomalous diffusion probes microstructure dynamics of entangled F-actin networks

We study the thermal motion of colloidal tracer particles in entangled actin filament (F-actin) networks, where the particle radius is comparable to the mesh size of the F-actin network. In this regime, the ensemble-averaged mean-squared displacement of the particles is proportional to tau(gamma), where 0<gamma<1 from 0.1<tau<100 s and depends only on the ratio of the probe radius to mesh size. By directly imaging hundreds of particles over 20 min, we determine this anomalous subdiffusion is due to the dynamics of infrequent and large jumps particles make between distinct pores in the network.

Conformational dynamics of protein side chains and enzyme-substrate interaction

The electric interaction of charged and polar protein side chains with dipole moments of the bonds of substrate molecules bound in enzyme active sites is considered. The conformational motion of the side chains leads to the fact that the electric interaction, besides a constant (electrostatic) part, contains a fluctuating one, which is a random force (noise) exerted on the substrate molecule. On the time scale of enzyme turnovers this noise can be considered as the white one with good approximation. The noise is external, and the explicit expression for its intensity has been obtained. The possible functional role of the noise as an activating factor in enzyme catalysis is discussed.