Mean-square stability of a stochastic model for bacteriophage infection with time delays

We consider the stability properties of the positive equilibrium of a stochastic model for bacteriophage infection with discrete time delay. Conditions for mean-square stability of the trivial solution of the linearized system around the equilibrium are given by the construction of suitable Lyapunov functionals. The numerical simulations of the strong solutions of the arising stochastic delay differential system suggest that, even for the original non-linear model, the longer the incubation time the more the phage and bacteria populations can coexist on a stable equilibrium in a noisy environment for very long time.     

Modeling and numerical simulation of biotin carboxylase kinetics: implications for half-sites reactivity

Biotin carboxylase catalyzes the ATP-dependent carboxylation of biotin and is one component of the multienzyme complex acetyl-CoA carboxylase that catalyzes the first committed step in fatty acid synthesis in all organisms. In Escherichia coli, biotin carboxylase exists as a homodimer where each subunit contains a complete active site. In a previous study (Janiyani, K., Bordelon, T., Waldrop, G.L., Cronan Jr., J.E., 2001. J. Biol. Chem. 276, 29864-29870), hybrid dimers were constructed where one subunit was wild-type and the other contained an active site mutation that reduced activity at least 100-fold. The activity of the hybrid dimers was only slightly greater than the activity of the mutant homodimers and far less than the expected 50% activity for completely independent active sites. Thus, there is communication between the two subunits of biotin carboxylase. The dominant negative effect of the mutations on the wild-type active site was interpreted as alternating catalytic cycles of the active sites in the homodimer. In order to test the hypothesis of oscillating catalytic cycles, mathematical modeling and numerical simulations of the kinetics of wild-type, hybrid dimers, and mutant homodimers of biotin carboxylase were performed. Numerical simulations of biotin carboxylase kinetics were the most similar to the experimental data when an oscillating active site model was used. In contrast, alternative models where the active sites were independent did not agree with the experimental data. Thus, the numerical simulations of the proposed kinetic model support the hypothesis that the two active sites of biotin carboxylase alternate their catalytic cycles.     

山罗花和天柱山罗花四个居群的数值分析

对山罗花和天柱山罗花的4个居群的15项形态特征进行了数值分析。结果表明:形态性状在4个居群间均存在一定程度的变异,居群间变异系数的平均值从小到大排列为:天柱山居群(天柱山罗花)、天柱山居群(山罗花)、黄山居群(山罗花)、鹞落坪居群(山罗花);天柱山罗花与山罗花种间的形态差异已达到极显著水平,山罗花的3个居群间部分性状也具有极显著的形态差异;以形态特征为基础的Q-聚类分析可以把天柱山罗花和山罗花聚为两类,但山罗花(天柱山居群)和其他2个居群在较远处聚在一起,R-聚类分析发现了强正相关关系、弱正相关关系、弱负相关关系的性状。     

Detailed identification of desert-originated bacteria carried by Asian dust storms to Japan

Several halotolerant bacteria were isolated from dust allowed to settle passively on saline medium in Higashi-Hiroshima, Japan during Asia dust events in 2005–2006. The primary identification, based on the sequence similarity of the 16S rRNA gene, revealed that these isolates were strains of Bacillus subtilis, B. licheniformis, Staphylococcus epidermidis, Gracillibacillus sp., and Halomonas venusta. A parallel investigation carried out on desert sand collected directly from sand dunes in Dunhuang, Gobi Desert, China resulted in the revivification of seven bacterial strains that were highly identical to the B. subtilis and B. licheniformis strains obtained in Higashi-Hiroshima (99.7 and 100% of 16S rDNA sequence similarity, respectively). A subsequent genetic analysis on the group of B. licheniformis isolates based on the universally house-keeping genes, gyrB and parE, revealed high sequence similarities in both genes among the strains of both locations (99.0–99.4%), which clustered them in a monophyletic line. Phenotype characterized by numerical taxonomy for 150 physiological tests confirmed the close relatedness between strains (similarity coefficient S _SM = 96.0%). The remarkable agreement between phenotype and genotype of the bacterial isolates allows us to conclude that there may have been an aerosolized dispersion of a Gobi Desert B. licheniformis by dust storms to Japan. This study provides evidence of microbial transport by yellow dust events in North-East Asia.     

Hydrodynamic characteristics of a fringing coral reef on the east coast of Ishigaki Island,southwest Japan

To investigate the characteristics of currents on a fringing coral reef, a field survey was conducted, mostly under weak wind conditions in summer, on the east coast of Ishigaki Island, southwest Japan, which is encompassed by well-developed fringing reefs. For the same study period, numerical simulations of the current were also performed using a shallow water turbulent flow model with high accuracy reef bathymetry data, which were estimated from high-resolution imagery obtained from satellite remote sensing. The numerical simulation results showed good agreement with the observed data and revealed that the currents have an appreciable magnitude of tide-averaged velocities, even during neap tides, which are governed mostly by wave set-up effects. The results also indicated that temporal variations in velocity and water surface elevation during a tide cycle in the reef exhibit highly asymmetrical patterns; in spring tides especially, the velocities around channels indicate rapid transitions over a short period from peak ebb flow to peak flood flow. The simulations also indicated that a big channel penetrating deeply into the reef attracts the tide-averaged mean flow, even from distant areas of the reef.     

Optimal deep brain stimulation of the subthalamic nucleus—a computational study

Deep brain stimulation (DBS) of the subthalamic nucleus, typically with periodic, high frequency pulse trains, has proven to be an effective treatment for the motor symptoms of Parkinson’s disease (PD). Here, we use a biophysically-based model of spiking cells in the basal ganglia (Terman et al., Journal of Neuroscience, 22, 2963–2976, 2002; Rubin and Terman, Journal of Computational Neuroscience, 16, 211–235, 2004) to provide computational evidence that alternative temporal patterns of DBS inputs might be equally effective as the standard high-frequency waveforms, but require lower amplitudes. Within this model, DBS performance is assessed in two ways. First, we determine the extent to which DBS causes Gpi (globus pallidus pars interna) synaptic outputs, which are burstlike and synchronized in the unstimulated Parkinsonian state, to cease their pathological modulation of simulated thalamocortical cells. Second, we evaluate how DBS affects the GPi cells’ auto- and cross-correlograms. In both cases, a nonlinear closed-loop learning algorithm identifies effective DBS inputs that are optimized to have minimal strength. The network dynamics that result differ from the regular, entrained firing which some previous studies have associated with conventional high-frequency DBS. This type of optimized solution is also found with heterogeneity in both the intrinsic network dynamics and the strength of DBS inputs received at various cells. Such alternative DBS inputs could potentially be identified, guided by the model-free learning algorithm, in experimental or eventual clinical settings. Action Editor: Steven J. Schiff Xiao-Jiang Feng and Eric Shea-Brown contributed equally to this work.     

Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks

We discuss numerical methods for simulating large-scale, integrate-and-fire (I&F) neuronal networks. Important elements in our numerical methods are (i) a neurophysiologically inspired integrating factor which casts the solution as a numerically tractable integral equation, and allows us to obtain stable and accurate individual neuronal trajectories (i.e., voltage and conductance time-courses) even when the I&F neuronal equations are stiff, such as in strongly fluctuating, high-conductance states; (ii) an iterated process of spike-spike corrections within groups of strongly coupled neurons to account for spike-spike interactions within a single large numerical time-step; and (iii) a clustering procedure of firing events in the network to take advantage of localized architectures, such as spatial scales of strong local interactions, which are often present in large-scale computational models—for example, those of the primary visual cortex. (We note that the spike-spike corrections in our methods are more involved than the correction of single neuron spike-time via a polynomial interpolation as in the modified Runge-Kutta methods commonly used in simulations of I&F neuronal networks.) Our methods can evolve networks with relatively strong local interactions in an asymptotically optimal way such that each neuron fires approximately once in operations, where N is the number of neurons in the system. We note that quantifications used in computational modeling are often statistical, since measurements in a real experiment to characterize physiological systems are typically statistical, such as firing rate, interspike interval distributions, and spike-triggered voltage distributions. We emphasize that it takes much less computational effort to resolve statistical properties of certain I&F neuronal networks than to fully resolve trajectories of each and every neuron within the system. For networks operating in realistic dynamical regimes, such as strongly fluctuating, high-conductance states, our methods are designed to achieve statistical accuracy when very large time-steps are used. Moreover, our methods can also achieve trajectory-wise accuracy when small time-steps are used. Action Editor: Nicolas Brunel     

Simulation study on water quality based on sediment release flume experiment in Lake Taihu, China

Sediments have a significant influence on the overlying water, and nutrient release from sediments is an important source for lake eutrophication, particularly in shallow lakes. Sediment resuspension is primarily driven by wind-induced currents. In this research, the correlation between release rate of suspended sediment and flow velocity was studied, and an experiment on hydrodynamic forces was conducted in a rectangle flume using water and sediments collected from three sites in Lake Taihu, a eutrophic lake in China. It was shown that the starting velocities of sediment in Lake Taihu at three different incipient standards gained from the experiment were 15, 30, and 40 cm s⁻¹ and the release rate of suspended sediment could reach up to 643.4, 5377.1, and 13980.5 g m⁻² d⁻¹, respectively. Based on the experiment, a water quantity and quality numerical model of wind-induced current with sediment pollution for Lake Taihu was developed. The model was calibrated and validated by applying it to the study of the water quality of Lake Taihu. The calculated values were generally in good agreement with field observations, which indicated that the developed model could represent the dynamics of sediment resuspension to a certain extent. This study provides a new approach and a practical tool for planning and management policy and operations to protect the water quality and ecosystems of shallow lakes.     

Anthropometry and numerical taxonomy in clinical genetics: An example of applied biological anthropology

Biological anthropologists can contribute a unique perspective as well as technical expertise to the diagnosis and classification of genetic disorders. Anthropometry has been used with increasing frequency to characterize syndromes and to establish ranges of variation within syndromes. The specific anthropometric-radiologic technique of metacarpophalangeal pattern profile analysis has proven useful in discriminating individuals with the Prader-Labhart-Willi (PLW) syndrome from unaffected persons. Analysis of these data also indicate a negative correlation between age and Z-score transformations of individual hand bone lengths. These findings sound a cautionary note to clinical investigators who would use the Z-score transformation to standardize for age and sex. Problems encountered in the classification of genetic syndromes afford many parallels with those faced by anthropologists in the classification of living and fossil populations. The reliance on “key” traits and the necessity of focusing on pedigree analysis results in a deemphasis of the total range of variation and typological thinking. Application of numerical taxonomic techniques to the classification of the heterogeneous connective tissue disease osteogenesis imperfecta (OI) illustrates the heuristic value of this technique and points out the need to consider phenotypic overlap when defining typologies. Clinical genetics affords just one example of an area in medicine where the unique training and generalist perspective of the biological anthropologist is in demand. The decline in the availability of positions in the traditional academic habitat for biological anthropologists makes it imperative that graduate students be aware of alternatives and that they obtain training in the practical skills which such alternatives will demand.     

Internodal sodium channels ensure active processes under myelin manifesting in depolarizing afterpotentials

The current opinion about processes in myelinated axon is that action potential saltatorially propagates between nodes of Ranvier and passively charges internodal axolemma thus causing depolarizing afterpotentials (DAP). Demyelination blocks the conduction that gives additional argument in favor of hypothesis that internode is not able to be activated by the existing internodal sodium channels. The results of our modeling study shows that, when periaxonal space is sufficiently narrow, saltatorial action potential is able to activate internodes. Low density of internodal sodium channels is sufficient to generate active internodal waves that slowly propagate from nodes towards corresponding midinternodes where they collide. The periaxonal width that stops internodal wave propagation (about 400 nm) is significantly larger than the highest value of the physiological range for this parameter (30 nm). Internodal activation is directly manifested as transmembrane internodal potential or as a full-sized action potential in periaxonal space where it can hardly be detected, and only as a small deflection in intracellular space. However, changes in the periaxonal potential cause transmyelin currents that lead to significant DAP. The shape and amplitude of DAP depends on myelin parameters and densities of internodal channels. Several technical parameters affect the results of calculations. Internodal spatial segmentation has to be sufficiently fine (at most 20 microm) for the model to be able to simulate internodal activation. We employ 338 internodal segments as compared with up to 21 used in previous models. Ionic accumulation together with related diffusive and electrical processes alter the calculated DAP amplitude. Inclusion of these processes in calculations demands such increase in the total number of segments that the numerical methods used up to now become unapplicable. To overcome the problem, an iterative implicit approach is proposed. It reduces a matrix of general type in multi-cable models to tridiagonal one and accelerates calculations considerably.