The computational cost of describing a general quantum system fully coupled by anharmonic interactions scales exponentially with the system size. Thus, an efficient basis representation of wave functions is essential, and when it comes to the large-amplitude motion of high-dimensional systems, the dynamic bases of Gaussian functions are often employed. The time dependence of such bases is determined from the variational principle or from classical dynamics; the former is challenging in implementation due to singular matrices, while the latter may not cover the configuration space relevant to quantum dynamics. Here we describe a method using Quantum Trajectory-guided Adaptable Gaussian (QTAG) bases “tuned”including the basis position, phase, and widthto the wave function evolution, thanks to the continuity of the probability density in the course of the quantum trajectory dynamics. Thus, an efficient basis in configuration space is generated, bypassing the variational equations on the parameters of the Gaussians. We also propose a time propagator with basis transformation by projections which lends efficiency and stability to the QTAG dynamics, as demonstrated on standard tests and the ammonia inversion model.

An efficient basis representation of time-dependent wavefunctions is essential for theoretical studies of high-dimensional molecular systems exhibiting large-amplitude motion. For fully coupled anharmonic systems, the complexity of a general wavefunction scales exponentially with the system size; therefore, for practical reasons, it is desirable to adapt the basis to the time-dependent wavefunction at hand. Often times on this quest for a minimal basis representation, time-dependent Gaussians are employed, in part because of their localization in both configuration and momentum spaces and also because of their direct connection to classical and semiclassical dynamics, guiding the evolution of the basis function parameters. In this work, the quantum-trajectory guided adaptable Gaussian (QTAG) bases method [J. Chem. Theory Comput.2020161834] is generalized to include correlated, i.e., non-factorizable, basis functions, and the performance of the QTAG dynamics is assessed on benchmark system/bath tunneling models of up to 20 dimensions. For the popular choice of initial conditions describing tunneling between the reactant/product wells, the minimal “semiclassical” description of the bath modes using essentially a single multidimensional basis function combined with the multi-Gaussian representation of the tunneling mode is shown to capture the dominant features of dynamics in a highly efficient manner.

The effect of proteolytic enzymes including Cathepsin K, a cysteine cathepsin, in onset and progression of cancers in human has been research intensive. Cathepsin K involves in many aspects and stages of cancers including apoptosis, cell proliferation, cancer immunology, inflammatory cell recruitment to tumors and aiding in the process of mobilization of normal healthy cells from their tissue compartments assisting in metastasis and angiogenesis. The objective of this review is to collect together and summarize and analyze the biochemical and physiological pathways of how cathepsin K is involved in onset and progression of cancers with more emphasis on breast and prostate cancers and cathepsin K regulated mechanisms underlying metastasis of such cancers to bones. Information for the review was gathered through published literature from global databases such as Google Scholar, PUBMED and NCBI on different studies on physiological interactions between enzymatic activity of cathepsin K with cancers and metastasis to bones. Analysis of published studies reveal that immunohistochemical studies of breast cancer cells indicate that they overexpress cathepsin K resulting in induction of aberrant mechanisms of cell signaling in breast cancers, creating a higher tendency for their metastasis to bones. Immunohistochemical, immunoprecipitation and fluorgenic assays of several studies done on the association of the same enzymatic activity on prostate cancers shows elevated levels of cathepsin K. Lesions derived from prostate cancer cell masses were observed to undergo increased bone formation and resorption levels. Such resorption levels cause secretion of biological factors promoting tumor expansion. In addition, studies indicate that Cathepsin K was observed to be a key component promoting higher bone resorption levels in patients suffering from cancer. Authors suggest that, to completely understand the association of cathepsin K on cancerous cells and their mechanism in metastasis, distributary patterns of cathepsin K in healthy human tissues needs to be extensively studied initially. It is also suggested that metastasis of breast and prostate cancers to bone could be terminated and overcome by successful production of efficient and precise inhibitory therapeutics targeting the enzymatic activity of Cathepsin K with minimum unintended adverse health effects.