The singularly perturbed Hodgkin-Huxley equations as a tool for the analysis of repetitive nerve activity

A qualitative analysis of the Hodgkin-Huxley model (Hodgkin and Huxley 1952), which closely mimics the ionic processes at a real nerve membrane, is performed by means of a singular perturbation theory. This was achieved by introducing a perturbation parameter that, if decreased, speeds up the fast variables of the Hodgkin-Huxley equations (membrane potential and sodium activation), whereas it does not affect the slow variables (sodium inactivation and potassium activation). In the most extreme case, if the perturbation parameter is set to zero, the original four-dimensional system degenerates to a system with only two differential equations. This degenerate system is easier to analyze and much more intuitive than the original Hodgkin-Huxley equations. It shows, like the original model, an infinite train of action potentials if stimulated by an input current in a suitable range. Additionally, explanations for the increased sensitivity to depolarizing current steps that precedes an action potential can be found by analysis of the degenerate system. Using the theory of Mishchenko and Rozov (1980) it is shown that the degenerate system does not only represent a simplification of the original Hodgkin-Huxley equations but also gives a valid approximation of the original model at least for stimulating currents that are constant within a suitable range.     

BetaDock: Shape-Priority Docking Method Based on Beta-Complex

Abstract

This paper presents an approach and a software, BetaDock, to the docking problem by putting the priority on shape complementarity between a receptor and a ligand. The approach is based on the theory of the β-complex. Given the Voronoi diagram of the receptor whose topology is stored in the quasi-triangulation, the β-complex corresponding to water molecule is computed. Then, the boundary of the β-complex defines the β-shape which has the complete proximity information among all atoms on the receptor boundary. From the β-shape, we first compute pockets where the ligand may bind. Then, we quickly place the ligand within each pocket by solving the singular value decomposition problem and the assignment problem. Using the conformations of the ligands within the pockets as the initial solutions, we run the genetic algorithm to find the optimal solution for the docking problem. The performance of the proposed algorithm was verified through a benchmark test and showed that BetaDock is superior to a popular docking software AutoDock 4.     

Heuristics for the Hodgkin–Huxley system

Hodgkin and Huxley (HH) discovered that voltages control ionic currents in nerve membranes. This led them to describe electrical activity in a neuronal membrane patch in terms of an electronic circuit whose characteristics were determined using empirical data. Due to the complexity of this model, a variety of heuristics, including relaxation oscillator circuits and integrate-and-fire models, have been used to investigate activity in neurons, and these simpler models have been successful in suggesting experiments and explaining observations. Connections between most of the simpler models had not been made clear until recently. Shown here are connections between these heuristics and the full HH model. In particular, we study a new model (Type III circuit): It includes the van der Pol-based models; it can be approximated by a simple integrate-and-fire model; and it creates voltages and currents that correspond, respectively, to the h and V components of the HH system.     

Reliability of ultrasound speckle tracking with singular value decomposition for quantifying displacement in the carpal tunnel

Inhibited movement patterns of carpal tunnel structures have been found in carpal tunnel syndrome (CTS) patients. Motion analysis on ultrasound images allows us to non-invasively study the (relative) movement of carpal tunnel structures and recently a speckle tracking method using singular value decomposition (SVD) has been proposed to optimize this tracking. This study aims to assess the reliability of longitudinal speckle tracking with SVD in both healthy volunteers and patients with CTS.Images from sixteen healthy volunteers and twenty-two CTS patients were used. Ultrasound clips of the third superficial flexor tendon and surrounding subsynovial connective tissue (SSCT) were acquired during finger flexion-extension. A custom made tracking algorithm was used for the analysis. Intra-class correlation coefficients (ICCs) were calculated using a single measure, two-way random model with absolute agreement and Bland-Altman plots were added for graphical representation.ICC values varied between 0.73 and 0.95 in the control group and 0.66–0.98 in the CTS patients, with the majority of the results classified as good to excellent. Tendon tracking showed higher reliability values compared to the SSCT, but values between the control and CTS groups were comparable.Speckle tracking with SVD can reliably be used to analyze longitudinal movement of anatomical structures with different sizes and compositions within the context of the carpal tunnel in both a healthy as well as a pathological state. Based on these results, this technique also holds relevant potential for areas where ultrasound based dynamic imaging requires quantification of motion.     

Cranial integration in Homo: singular warps analysis of the midsagittal plane in ontogeny and evolution

This study addresses some enduring issues of ontogenetic and evolutionary integration in the form of the hominid cranium. Our sample consists of 38 crania: 20 modern adult Homo sapiens, 14 sub-adult H. sapiens, and four archaic Homo. All specimens were CT-scanned except for two infant H. sapiens, who were imaged by MR instead. For each specimen 84 landmarks and semi-landmarks were located on the midsagittal plane and converted to Procrustes shape coordinates. Integration was quantified by the method of singular warps, a new geometric-statistical approach to visualizing correlations among regions. The two classic patterns of integration, evolutionary and ontogenetic, were jointly explored by comparing analyses of overlapping subsamples that span ranges of different hypothetical factors. Evolutionary integration is expressed in the subsample of 24 adult Homo, and ontogenetic integration in the subsample of 34 H. sapiens. In this data set, vault, cranial base, and face show striking and localized patterns of covariation over ontogeny, similar but not identical to the patterns seen over evolution. The principal differences between ontogeny and phylogeny pertain to the cranial base. There is also a component of cranial length to height ratio not reducible to either process. Our methodology allows a separation of these independent processes (and their impact on cranial shape) that conventional methods have not found.     

非线性种群反应扩散系统奇摄动ROBIN问题

研究了一类具有非线性种群反应扩散系统奇摄动Robin初始边值问题.在适当的条件下,利用微分不等式理论,讨论了问题解的存在性和渐近性态.     

Meta-analysis for surrogacy: accelerated failure time models and semicompeting risks modeling

There has been great recent interest in the medical and statistical literature in the assessment and validation of surrogate endpoints as proxies for clinical endpoints in medical studies. More recently, authors have focused on using metaanalytical methods for quantification of surrogacy. In this article, we extend existing procedures for analysis based on the accelerated failure time model to this setting. An advantage of this approach relative to proportional hazards model is that it allows for analysis in the semicompeting risks setting, where we model the region where the surrogate endpoint occurs before the true endpoint. Several estimation methods and attendant inferential procedures are presented. In addition, between- and within-trial methods for evaluating surrogacy are developed; a novel principal components procedure is developed for quantifying trial-level surrogacy. The methods are illustrated by application to data from several studies in colorectal cancer.     

Optimal fed-batch operation of recombinant cells subject to plasmid instability and death

Optimal feed rate strategy is studied for fed-batch culture of recombinant cells with plasmid instability and with different death rates for the plasmid-free cells (PFC) and plasmid-bearing cells (PBC). Most of the fed-batch fermentation is known to have first-order singularity and therefore a single singular arc. However, this study shows that a singular arc with second-order singularity and therefore two distinct singular arcs are possible for a recombinant cell process if PFC and PBC are subjected to death, and their specific growth rates are proportional to each other. Two types of singular arcs are elucidated and analyzed. The optimal policies over the singular arcs are theoretically explored as these findings reveal qualitative information on the singular arc, which is critically important in providing the optimal initial conditions in numerical computation of optimal feed rate profile.