Antibacterial and biofilm removal activity of a podoviridae Staphylococcus aureus bacteriophage SAP-2 and a derived recombinant cell-wall-degrading enzyme

Antibacterial and biofilm removal activity of a new podoviridae Staphylococcus aureus bacteriophage (SAP-2), which belongs to the φ29-like phage genus of the Podoviridae family, and a cell-wall-degrading enzyme (SAL-2), which is derived from bacteriophage SAP-2, have been characterized. The cell-wall-degrading enzyme SAL-2 was expressed in Escherichia coli in a soluble form using a low-temperature culture. The cell-wall-degrading enzyme SAL-2 had specific lytic activity against S. aureus, including methicillin-resistant strains, and showed a minimum inhibitory concentration of about 1 μg/ml. In addition, this enzyme showed a broader spectrum of activity within the Staphylococcus genus compared with bacteriophage SAP-2 in its ability to remove the S. aureus biofilms. Thus, the cell-wall-degrading enzyme SAL-2 can be used to prevent and treat biofilm-associated S. aureus infections either on its own or in combination with other cell-wall-degrading enzymes with anti-S. aureus activity.     

Boundary Layer Flow Past a Stretching Surface in a Porous Medium Saturated by a Nanofluid: Brinkman-Forchheimer Model

In this study, the steady forced convection flow and heat transfer due to an impermeable stretching surface in a porous medium saturated with a nanofluid are investigated numerically. The Brinkman-Forchheimer model is used for the momentum equations (porous medium), whereas, Bongiorno’s model is used for the nanofluid. Uniform temperature and nanofluid volume fraction are assumed at the surface. The boundary layer equations are transformed to ordinary differential equations in terms of the governing parameters including Prandtl and Lewis numbers, viscosity ratio, porous medium, Brownian motion and thermophoresis parameters. Numerical results for the velocity, temperature and concentration profiles, as well as for the reduced Nusselt and Sherwood numbers are obtained and presented graphically.     

On the spread of SARS-CoV-2 under quarantine: A study based on probabilistic cellular automaton

Currently, SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) is a major worldwide public-health problem. Here, its propagation is modeled by using a probabilistic cellular automaton (PCA). In this model, sick individuals can either remain asymptomatic during the infection or become symptomatic. In order to derive an analytical expression for the basic reproduction number $R_0,$ a mean-field approximation written in terms of ordinary differential equations (ODE) is proposed and analyzed. By considering time-constant and time-varying parameters in both approaches (PCA and ODE), numerical simulations are performed in order to evaluate the impact of distinct quarantine regimes on the SARS-CoV-2 pandemic.     

落叶松人工林树干形状模型和可变参数

对以往树木干形的一系列可变参数削度方程进行比较,根据模型拟合统计量(残差平方和及相关指数),选出其中对落叶松干形拟合效果较好(残差平方和较小、相关指数较高)的模型,并根据模型中可变参数的意义提出了5种描述干形的指数.结果表明:Lee等提出的削度方程的拟合效果较好,可以用来描述落叶松人工林的树干形状;5种描述干形的指数分别为根部梢头削度率、影响点、圆柱体和抛物线体范围值、最小可变参数、最小可变参数所在的相对高度,这些指数可以作为比较干形的方法和工具.较大密度(870株.hm-2)和较小密度林分(275株.hm-2)的林木干形质量都较差,只有适中密度林分(487株.hm-2)的落叶松干形质量较好.     

Homochiral Growth Through Enantiomeric Cross-Inhibition

The stability and conservation properties of a recently proposed polymerization model are studied. The achiral (racemic) solution is linearly unstable once the relevant control parameter (here the fidelity of the catalyst) exceeds a critical value. The growth rate is calculated for different fidelity parameters and cross-inhibition rates. A chirality parameter is defined and shown to be conserved by the nonlinear terms of the model. Finally, a truncated version of the model is used to derive a set of two ordinary differential equations and it is argued that these equations are more realistic than those used in earlier models of that form.     

An ESR study of the effect of an electrostatic field on binding of divalent cations to the surface of serum low-density lipoproteins

The ESR technique has been used to study binding of Mn(II) ions to low-density lipoprotein (LDL) in solutions of various electrolyte ionic strengths. A model of the binding has been proposed which describes all the observations in electrolytes of ten different concentrations in terms of two types of binding sites and two corresponding sets of intrinsic binding parameters (n1 = 8, Kd1 = 1.31 X 10(-3) mol X l-1 and n2 = 170, Kd2 = 5.71 X 10(-2) mol X l-1). These parameters, together with the values of the potential (phi 0) responsible for binding of the ions to specific charged sites on the surface, reproduce the observed binding curves well in all the systems studied. The phi 0 values are obtained as an appropriate solution of the Poisson-Boltzmann equation.     

Quasi-periodic behaviour in a model for the lithium-induced,electrical oscillations of frog skin

The fact that oscillations can be induced in studies of the maintenance of the electrical potential of frog skin by addition of lithium allowed evaluation of several parameters fundamental to the functioning of the system in vivo (e.g. relative volumes of internal compartments, characteristic times of ionic exchanges between compartments). A realistic model was thus proposed under the form of a set of ordinary differential equations. In the past, numerical simulations using such a model reproduced the periodic experimental oscillations and was able to provide an explanation for the global synchronised oscillations of the whole skin. In that paper, new numerical simulations reproduce the non-periodic oscillations which were observed two decades ago, but not reproduced by the model. Moreover, the dynamical process under which all the local oscillators are synchronised is explained in terms of a tangent bifurcation.     

The energy flux theory 35 years later: formulations and applications

Several models have been proposed for the energetic behavior of the photosynthetic apparatus and a variety of experimental techniques are nowadays available to determine parameters that can quantify this behavior. The Energy Flux Theory (EFT) developed by Strasser 35 years ago provides a straightforward way to formulate any possible energetic communication between any complex arrangement of interconnected pigment systems and any energy transduction by these systems. We here revisit the EFT, starting from the basic general definitions and equations and presenting applications in formulating the energy distribution in photosystem (PS) II units with variable connectivity, as originally derived, where certain simplifications were adopted. We then proceed to the derivation of equations for a PSII model of higher complexity, which corresponds, from the formalistic point of view, to the later formulated and now broadly accepted exciton–radical-pair model. We also compare the formulations derived with the EFT with those obtained, by different approaches, in the classic papers on energetic connectivity. Moreover, we apply the EFT for the evaluation of the excitation energy distribution between PSII and PSI and the distinction between state transitions and PSII to PSI excitation energy migration. Our analysis demonstrates that the EFT is a powerful approach for the formulation of any possible model, at any complexity level, even of models that may be proposed in the future, with the advantage that any possible energetic communication or energy transduction can be easily formulated mathematically by trivial algebraic equations. Moreover, the biophysical parameters introduced by the EFT and applicable for any possible model can be linked with obtainable experimental signals, provided that the theoretical resolution of the model does not go beyond the experimental resolution.     

Personality development in psychotherapy: a synergetic model of state-trait dynamics

Theoretical models of psychotherapy not only try to predict outcome but also intend to explain patterns of change. Studies showed that psychotherapeutic change processes are characterized by nonlinearity, complexity, and discontinuous transitions. By this, theoretical models of psychotherapy should be able to reproduce these dynamic features. Using time series derived from daily measures through internet-based real-time monitoring as empirical reference, we earlier presented a model of psychotherapy which includes five state variables and four trait variables. In mathematical terms, the traits modulate the shape of the functions which define the nonlinear interactions between the variables (states) of the model. The functions are integrated into five coupled nonlinear difference equations. In the present paper, we model how traits (dispositions or competencies of a person) can continuously be altered by new experiences and states (cognition, emotion, behavior). Adding equations that link states to traits, this model not only describes how therapeutic interventions modulate short-term change and fluctuations of psychological states, but also how these can influence traits. Speaking in terms of Synergetics (theory of self-organization in complex systems), the states correspond to the order parameters and the traits to the control parameters of the system. In terms of psychology, trait dynamics is driven by the states—i.e., by the concrete experiences of a client—and creates a process of personality development at a slower time scale than that of the state dynamics (separation of time scales between control and order parameter dynamics).     

Modelling and simulation of vertebrate retina

In the present work we investigate the neuronal activities in a vertebrate retina by modelling and simulations using the results of (Oguztöreli, 1979). The basic retinal network considered here consists of interconnected five neurons: a receptor cell (rod or cone), a horizontal cell, a bipolar cell, an amacrine cell, and a retinal ganglion cell. The mathematical model for the basic network is a system of nonlinear ordinary integral differential difference equations. A number of simulations describing the dynamics of the neural activities in the basic network under different conditions are presented, actual and steady-state solutions are discussed. An algorithm is proposed for the determination of the system parameters experimentally.This work was supported by the Natural Sciences and Engineering Research Council Canada under Grant NSERCA-4345 through the University of Alberta     

基于分布式水文模型的水源涵养不同功能评估方法——以渭河涵养区为例

为了实现水源涵养量计算和不同功能的综合评估,基于分布式水文模型(WEP-L)提出了一种新方法,即利用WEP-L模型计算次降水过程中降水量和地表产流、冠层截留量的差值作为水源涵养量,并分别评估削洪(地表径流量)、补枯(地下径流量)、维持植被生态系统用水(植被蒸腾量)等不同水源涵养功能的评估方法。为了验证该方法的合理性,以渭河流域咸阳站以上区域为例,对比了该方法和InVEST模型方法的计算结果,由于两种方法在评估内容和使用模型上都存在差异,为了保证计算结果的可比性,先对比了基于相同评价内容的WEP-L模型法I和InVEST模型方法,再对比了基于不同评价内容的WEP-L模型法I和WEP-L模型法II,结论如下:基于相同评价内容的WEP模型法I和InVEST模型法计算结果数值接近,研究区2000-2018年水源涵养量年均值分别为12.43 mm(5.76亿m³)和12.08 mm(5.6亿m³),两种方法所得结果空间分布特征相似,稍有差异之处与InVEST模型的参数没有经过本地化处理有关;基于不同评价内容的WEP-L模型法Ⅰ和WEP-L模型法II计算结果数值相差较大,研究区2000-2018年水源涵养量均值分别为12.43 mm和432.57 mm,空间分布特征上有差异的地方分布于研究区的北部、东部及东北部,主要与两种方法评价时是否考虑蒸散发有关。WEP-L模型法II评估结果中削洪、补枯、维持植被生态系统用水等功能多年变化趋势分别为:2006-2010年期间增加、2012年以后下降以及增加。2012年后补枯功能和维持植被生态系统用水功能之间可能存在权衡关系。通过不同方法计算结果差异原因分析,证明了基于WEP-L模型的不同涵养功能评估方法的合理性,其结果也可为渭河涵养区水资源和生态保护策略的制定提供更多依据。     

Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system

HIV dynamics studies have significantly contributed to the understanding of HIV infection and antiviral treatment strategies. But most studies are limited to short-term viral dynamics due to the difficulty of establishing a relationship of antiviral response with multiple treatment factors such as drug exposure and drug susceptibility during long-term treatment. In this article, a mechanism-based dynamic model is proposed for characterizing long-term viral dynamics with antiretroviral therapy, described by a set of nonlinear differential equations without closed-form solutions. In this model we directly incorporate drug concentration, adherence, and drug susceptibility into a function of treatment efficacy, defined as an inhibition rate of virus replication. We investigate a Bayesian approach under the framework of hierarchical Bayesian (mixed-effects) models for estimating unknown dynamic parameters. In particular, interest focuses on estimating individual dynamic parameters. The proposed methods not only help to alleviate the difficulty in parameter identifiability, but also flexibly deal with sparse and unbalanced longitudinal data from individual subjects. For illustration purposes, we present one simulation example to implement the proposed approach and apply the methodology to a data set from an AIDS clinical trial. The basic concept of the longitudinal HIV dynamic systems and the proposed methodologies are generally applicable to any other biomedical dynamic systems.     

Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species

We consider a system of delay differential equations modeling the predator-prey ecoepidemic dynamics with a transmissible disease in the predator population. The time lag in the delay terms represents the predator gestation period. We analyze essential mathematical features of the proposed model such as local and global stability and in addition study the bifurcations arising in some selected situations. Threshold values for a few parameters determining the feasibility and stability conditions of some equilibria are discovered and similarly a threshold is identified for the disease to die out. The parameter thresholds under which the system admits a Hopf bifurcation are investigated both in the presence of zero and non-zero time lag. Numerical simulations support our theoretical analysis.     

Bactria and Lytic Phage Coexistence in a Chemostat with Periodic Nutrient Supply

The dynamics of bacteria and bacteriophage coexistence was examined in a chemostat in which the externally driven supply of nutrient for bacteria, and washout rate oscillates periodically. The proposed mathematical model for three interacting variables, bacteria, phage, and nutrient, consists of 3 differential equations with time delay, due to the phage latent period of lysing. The study was carried out in an interval of physical parameters where an equivalent model with constant supply of nutrient and washout rate is mathematically unstable, running in limit cycle regimes, with known self-frequencies. It addresses mainly the asymptotically persistent dynamics of the system. Bifurcation maps in terms of two externally controlled parameters, the amplitude and frequency of the controlled nutrient supply were constructed for various latent lysis periods, in order to determine the frequency entrainment, i.e., the resulting main operating frequency of the system, relative to the known external and self-frequencies. Also presented are bifurcation maps for the rich variety of dynamical types observed in the study. Bifurcation diagrams in terms of the lysing time delay were also included for completion. A new type of entrainment, combining in a simple way the external and self-periods (reciprocal frequencies), is shown to exist for a range of parameters.     

Some Formal Approaches to the Analysis of Kinetic Data in Terms of Linear Compartmental Systems

A formal approach to the routine analysis of kinetic data in terms of linear compartmental systems is presented. The methods of analysis are general in that they include much of the theory in common use, such as direct solution of differential equations, integral equations, transfer functions, fitting of data to sums of exponentials, matrix solutions, etc. The key to the formalism presented lies in the fact that a basic operational unit—called “compartment”—has been defined, in terms of which physical and mathematical models as well as input and output functions can be expressed. Additional features for calculating linear combinations of functions and for setting linear dependence relations between parameters add to the versatility of this method. The actual computations for the values of model parameters to yield a least squares fit of the data are performed on a digital computer. A general computer program was developed that permits the routine fitting of data and the evolution of models.     

Development of a variational scheme for model inversion of multi-area model of brain. Part II: VBEM method

In Part I and Part II of these two companion papers (henceforth called Part I and Part II), we develop and evaluate a variational Bayesian expectation maximization (VBEM) method for model inversion of our multi-area extended neural mass model (MEN). In this paper, we develop the VBEM method to estimate posterior distributions of parameters of MEN. We choose suitable prior distributions for the model parameters in order to use properties of a conjugate-exponential model in implementing VBEM. Consequently, VBEM leads to analytically tractable forms. The proposed VBEM algorithm starts with initialization and consists of repeated iterations of a variational Bayesian expectation step (VB E-step) and a variational Bayesian maximization step (VB M-step). Posterior distributions of the model parameters are updated in the VB M-step. Distribution of the hidden state is updated in the VB E-step. We develop a variational extended Kalman smoother (VEKS) to infer the distribution of the hidden state in the VB E-step and derive the forward and backward passes of VEKS, analogous to the Kalman smoother. In Part I, we evaluate and validate the VBEM method using simulation studies.     

A new method of identifying a systems based on the minimal quadratic discrepancy criterion for biophysics problems

A wide range of biophysical systems are described by nonlinear dynamic models mathematically presented as a set of ordinary differential equations in the Cauchy explicit form: [formula: see text] Fij(X1(t),..,XN(t),t), (i = 1,...,N, j = 1,...,M), where Fij (X1(t), ..., XN(t), t) is a set of basis functions satisfying the Lipschitz condition. We investigate the problem of evaluation of model constants aij (the system identification) using experimental data about the time dependence of the dynamic parameters of the system Xi(t). A new method of system identification for the class of similar nonlinear dynamic models is proposed. It is shown that the problem of identifying an initial nonlinear model can be reduced to the solution of a system of linear equations for the matrix of the dynamic model constants [aj]i. It is proposed to determine the set of dynamic model constants aij using the criterion of minimal quadratic discrepancy for the time dependence of the set of dynamic parameters Xi(t). An important special case of the nonlinear model, the quadratic model, is considered. Test problems of identification using this method are presented for two nonlinear systems: the Van der Pol type multiparametric nonlinear oscillator and the strange attractor of Ressler, a widely known example of dynamic systems showing the stochastic behavior.     

The possible role of intracellular Ca2+-stores in the rhythm-inotropic relationship of frog heart muscle (a simulation study)

The hypothesis that intracellular calcium stores play an essential role in determining force-frequency relationships of frog myocardium was tested quantitatively. A simplified mathematical model of excitation-contraction coupling in frog heart muscle was developed and its behaviour under various patterns of stimulation was analysed by means of computer simulation. The model represents a system of ordinary differential equations for individual fluxes within the cell Ca2+-recirculation system and includes a one-compartmental intracellular pool as opposed to the two-compartmental structure of the mammalian sarcoplasmic reticulum (Kaufmann et al. 1974). The behaviour of the model is consistent with available experimental data concerning the basic rhythm-inotropic characteristics of amphibian myocardium and offers some evidence in favour of the basic concept. Within the framework of the proposed model the staircase phenomena in amphibia were accounted for and the impact of different intracellular Ca-movements on the resulting contractile response and rhythm-inotropic phenomena was elucidated.