Computing generalized Langevin equations and generalized Fokker–Planck equations

The Mori–Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker–Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori–Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.     

Anomalous nanoparticle surface diffusion in LCTEM is revealed by deep learning-assisted analysis

The motion of nanoparticles near surfaces is of fundamental importance in physics, biology, and chemistry. Liquid cell transmission electron microscopy (LCTEM) is a promising technique for studying motion of nanoparticles with high spatial resolution. Yet, the lack of understanding of how the electron beam of the microscope affects the particle motion has held back advancement in using LCTEM for in situ single nanoparticle and macromolecule tracking at interfaces. Here, we experimentally studied the motion of a model system of gold nanoparticles dispersed in water and moving adjacent to the silicon nitride membrane of a commercial LC in a broad range of electron beam dose rates. We find that the nanoparticles exhibit anomalous diffusive behavior modulated by the electron beam dose rate. We characterized the anomalous diffusion of nanoparticles in LCTEM using a convolutional deep neural-network model and canonical statistical tests. The results demonstrate that the nanoparticle motion is governed by fractional Brownian motion at low dose rates, resembling diffusion in a viscoelastic medium, and continuous-time random walk at high dose rates, resembling diffusion on an energy landscape with pinning sites. Both behaviors can be explained by the presence of silanol molecular species on the surface of the silicon nitride membrane and the ionic species in solution formed by radiolysis of water in presence of the electron beam.

Understanding the motion of nanoparticles in boundary layers is of fundamental importance in scientific fields such as biophysics and colloidal self-assembly, and of practical importance in technological applications such as drug delivery and additive manufacturing. The physics behind the motion of nanoparticles is particularly challenging to understand due to the multitude of effects including particle–-particle interactions, particle–surface interactions, and changes in the rheological properties in boundary layers close to a liquid–solid interface.The common technique to study the motion of particles has been optical microscopy, which has limitations in terms of spatial resolution. The advent of in situ liquid cell transmission electron microscopy (LCTEM) has now made it possible to visualize the motion of nanoparticles near a surface with an unprecedented spatial resolution at the nanometer length scale (1–3). However, the electron beam of a transmission electron microscope (TEM), which is the key acquisition tool to enable nanoscale visualization, can significantly influence both interactions and dynamics of nanoparticles (4–6). Previous literature has reported that the motion of nanoparticles near the surface of an LC and in the presence of the electron beam is subdiffusive (i.e., non-Brownian, or “anomalous”) (7–16). Such subdiffusive motion suggests that the nanoparticle motion is significantly influenced by interactions with the nearby substrate or interface, but what precisely is the nature of these interactions and the forces that create them? Are they stable or fluctuating? Do they arise because of the electron beam or are they native to the system? How do the changes in rheology within a few nanometers of the interface figure into the picture? The nature of the observed anomalies are still very much under debate as the new technique of LCTEM continues to be developed (7–12, 14–16).Two canonical processes that describe anomalous motion are continuous-time random walk (CTRW) and fractional Brownian motion (FBM) (17–20). In the context of particle diffusion, each of these types of subdiffusive motions implies a distinct physical picture of the environment. CTRW indicates a random energy landscape of potential wells, where the time a particle spends in any well diverges when averaged over all well depths. FBM, on the other hand, indicates a viscoelastic environment such as those found in crowded fluids (21–24). The goal of this work is to identify the type of anomalous motion of nanoparticles near the surface in LCTEM, elucidate the nanoscopic physical features in the system that give rise to this motion, and understand how the electron beam can influence them.A key challenge in studying the motion of nanoparticles under the effect of the electron beam is that one needs to resort to a limited number of short trajectories from a single in situ LCTEM experiment. This is because achieving high spatial resolution requires a relatively small field of view, which limits the number of nanoparticles accessible (experiments are done in dilute solutions to avoid interactions between nanoparticles). Moreover, state-of-the-art cameras on TEMs are limited by lower bounds on time resolution (hundreds of frames per second) and upper bounds on measurement time (minutes-long trajectories) (25). This limitation creates a challenge for canonical methods used to characterize diffusive particle dynamics such as the mean-squared displacement (MSD) analysis. These methods often rely on features of the trajectory that converge upon averaging over very long single-particle trajectories (for systems obeying ergodicity) or hundreds of medium-length trajectories collected under the same experimental conditions (20, 26, 27). Here, we show that physics-informed artificial intelligence can be used as a complementary tool for LCTEM to extract hidden features that exist in short trajectories of single nanoparticles in LCTEM in order to elucidate the type of anomalous diffusion.In this study, we collected a large dataset from a model system of gold nanoparticles dispersed in water and diffusing near a silicon nitride (SiN_x) membrane of a commercial LC irradiated by a broad range of electron beam dose rates. Inspired by the recent advances in using machine-learning tools to study the diffusion of single microparticles in biological media (26–29), we developed a convolutional deep neural-network model, dubbed MotionNet (MoNet), which solves an inverse problem of determining the underlying diffusion mechanism behind the anomalous motion of nanoparticles in LCTEM. The architecture of the neural network employed in MoNet is designed based on classical tests in statistics (30) and is trained on thousands of simulated short trajectories from three classes of diffusion, i.e., Brownian, FBM, and CTRW. Guided by MoNet, our analysis reveals that at low dose rates the anomalous diffusive motion of nanoparticles in LCTEM is governed by viscoelasticity-dominated FBM, while at high dose rates the motion is governed by a pinning-site-mediated CTRW process (24). The prediction results were benchmarked against the statistical p-variation test (30) to confirm the behavior in low and high dose-rate limits.The dose-rate-dependent transition can be explained by the existence of silanol molecular groups on the surface of the SiN_x membrane, which act as pinning sites and exhibit a broad distribution of restoring forces (15, 31). At low dose rates, the binding strength of these pinning sites is high compared to the thermal energy and their effective restoring force acts similar to the effect of a viscoelastic environment. This results in nanoparticle motion confined to the local vicinity of a pinning site. Upon increasing the dose rate and thus passivating the charges on the pinning sites, the binding strength decreases, making nanoparticles more mobile, which allows them to diffuse over the SiN_x membrane only making intermittent stops on randomly distributed pinning sites. This understanding provides us with important insight into the mechanism of nanoparticle motion near a substrate in LCTEM and opens up the path to use in situ LCTEM as a technique for studying motions of nanoparticles in complex systems at the nanoscale. Furthermore, we show that neural networks can extract features to classify the underlying diffusive behavior of the system and determine the extent of anomaly, particularly when canonical statistical methods require extreme amounts of data and may not be able to classify the behavior of the system due to experimental limitations.     

Sources and patterns of pain in lumbar disc disease; revisiting Francis Murphey’s theory

Object  

Francis Murphey’s theory was analyzed to determine whether or not his opinion is evidence-based medicine and whether or not it can be applied clinically.     

Inherited arrhythmic disorders: long QT and Brugada syndromes

Inherited arrhythmic disorders comprise a group of syndromes with unique genetic abnormalities and presentations but with very similar clinical outcomes and complications, the most terrifying of which are life-threatening arrhythmias and sudden cardiac death. Advances in molecular biology have enabled us to define and pinpoint many such disorders, which were previously labeled as idiopathic, to specific genes on various chromosomes. The current trend in the management of these potentially deadly disorders is to use pharmacotherapy (antiarrhythmic agents) and defibrillators for the prevention of sudden death; however, targeted therapy at a molecular level appears to be the path of the future. Herein, we review long QT and Brugada syndromes and focus on the genetics, pathophysiology, and clinical manifestations of these inherited arrhythmogenic disorders that affect patients with structurally normal hearts.     

Functionality of the 5'- and intergenic IRES elements of cricket paralysis virus in a range of insect cell lines,and its relationship with viral activities

Cricket paralysis virus (Dicistroviridae: Cripavirus) (CrPV) naturally has a wide range of insect hosts which is reflected in its ability to infect several cultured insect cell lines. The expression of viral gene products is controlled by two kinds of internal ribosome entry site (IRES) elements, 5' and intergenic (IG). Using seven cultured cell lines we tested the functionality of both IRES elements by transfection with bi-cistronic RNA constructs. In six of the seven cell lines, expression initiated from both IRES's was significantly higher than that from a control construct and in five of these six lines the expression from the 5'-IRES was higher than that from the IG-IRES. Permissiveness of each of the cell lines for replication of CrPV was tested by infection with purified virions and transfection with viral RNA. Only three of the cell lines were fully permissive for CrPV replication and no correlation between permissiveness and IRES activity was apparent. These results suggest that while IRES function is required for permissiveness, additional cellular and/or viral factors, involved in processing of viral products, packaging of viral particles and interacting with the cap-dependent translation machinery of host cells, are necessary for CrPV to be able to replicate in any given cell.