Optimization of Culture Conditions for Fermentation of Soymilk Using Lactobacillus casei by Response Surface Methodology

Soymilk was fermented with Lactobacillus casei, and statistical experimental design was used to investigate factors affecting viable cells of L. casei, including temperature, glucose, niacin, riboflavin, pyridoxine, folic acid and pantothenic acid. Initial screening by Plackett-Burman design revealed that among these factors, temperature, glucose and niacin have significant effects on the growth of L. casei. Further optimization with Box-Behnken design and response surface analysis showed that a second-order polynomial model fits the experimental data appropriately. The optimum conditions for temperature, glucose and niacin were found to be 15.77 °C, 5.23 and 0.63 g/L, respectively. The concentration of viable L. casei cells under these conditions was 8.23 log₁₀ (CFU/mL). The perfect agreement between the observed values and the values predicted by the equation confirms the statistical significance of the model and the model’s adequate precision in predicting optimum conditions.     

β Cells Operate Collectively to Help Maintain Glucose Homeostasis

Residing in the islets of Langerhans in the pancreas, β cells contribute to glucose homeostasis by managing the body’s insulin supply. Although it has been acknowledged that healthy β cells engage in heavy cell-to-cell communication to perform their homeostatic function, the exact role and effects of such communication remain partly understood. We offer a novel, to our knowledge, perspective on the subject in the form of 1) a dynamical network model that faithfully mimics fast calcium oscillations in response to above-threshold glucose stimulation and 2) empirical data analysis that reveals a qualitative shift in the cross-correlation structure of measured signals below and above the threshold glucose concentration. Combined together, these results point to a glucose-induced transition in β-cell activity thanks to increasing coordination through gap-junctional signaling and paracrine interactions. Our data and the model further suggest how the conservation of entire cell-cell conductance, observed in coupled but not uncoupled β cells, emerges as a collective phenomenon. An overall implication is that improving the ability to monitor β-cell signaling should offer means to better understand the pathogenesis of diabetes mellitus.     

An exact solution for the modified nonlinear Schrödinger’s equation for Davydov solitons in α-helix proteins

The solitons in α-helix proteins that are governed by the nonlinear Schrödinger’s equation is investigated in presence of perturbation terms in this paper. The integration of this perturbed nonlinear Schrödinger’s equation is carried out. The solitary wave ansatz is used to carry out the integration and the parameter domain is identified.     

Homogenization of Heterogeneously Coupled Bistable ODE's—Applied to Excitation Waves in Pancreatic Islets of Langerhans

We consider a lattice of coupled identical differential equations. The coupling is between nearest neighbors and of resistance type, but the strength of coupling varies from site to site. Such a lattice can, for example, model an islet of Langerhans, where the sites in the lattice model individual but identical -cells, and the coupling between cells is made of gap junctions.By using a homogenization technique we approximate the coupled discrete equations by a PDE, basically a nonlinear heat equation (a Fisher equation). For appropriate parameters this equation is known to have wave-solutions. Of importance is the fact, that the resulting diffusion coefficient does not only depend on the average of the coupling, but also on the variance of the strength. This means that the heterogeneity of the coupling strength influences the wave velocity—the greater the variance, the slower is the wave. This result is illustrated by simulations, both of a simple prototype equation, and for a full model of coupled beta-cells in both one and two dimensions, and implies that the natural heterogeneity in the islets of Langerhans should be taken into account.     

Wave speed in excitable random networks with spatially constrained connections

Very fast oscillations (VFO) in neocortex are widely observed before epileptic seizures, and there is growing evidence that they are caused by networks of pyramidal neurons connected by gap junctions between their axons. We are motivated by the spatio-temporal waves of activity recorded using electrocorticography (ECoG), and study the speed of activity propagation through a network of neurons axonally coupled by gap junctions. We simulate wave propagation by excitable cellular automata (CA) on random (Erdös-Rényi) networks of special type, with spatially constrained connections. From the cellular automaton model, we derive a mean field theory to predict wave propagation. The governing equation resolved by the Fisher-Kolmogorov PDE fails to describe wave speed. A new (hyperbolic) PDE is suggested, which provides adequate wave speed that saturates with network degree , in agreement with intuitive expectations and CA simulations. We further show that the maximum length of connection is a much better predictor of the wave speed than the mean length. When tested in networks with various degree distributions, wave speeds are found to strongly depend on the ratio of network moments rather than on mean degree , which is explained by general network theory. The wave speeds are strikingly similar in a diverse set of networks, including regular, Poisson, exponential and power law distributions, supporting our theory for various network topologies. Our results suggest practical predictions for networks of electrically coupled neurons, and our mean field method can be readily applied for a wide class of similar problems, such as spread of epidemics through spatial networks.     

A model of the complex response of Staphylococcus aureus to methicillin

It is widely accepted that β-lactam antimicrobials cause cell death through a mechanism that interferes with cell wall synthesis. Later studies have also revealed that β-lactams modify the autolysis function (the natural process of self-exfoliation of the cell wall) of cells. The dynamic equilibrium between growth and autolysis is perturbed by the presence of the antimicrobial. Studies with Staphylococcus aureus to determine the minimum inhibitory concentration (MIC) have revealed complex responses to methicillin exposure. The organism exhibits four qualitatively different responses: homogeneous sensitivity, homogeneous resistance, heterogeneous resistance and the so-called ‘Eagle-effect’. A mathematical model is presented that links antimicrobial action on the molecular level with the overall response of the cell population to antimicrobial exposure. The cell population is modeled as a probability density function F(x,t) that depends on cell wall thickness x and time t. The function F(x,t) is the solution to a Fokker-Planck equation. The fixed point solutions are perturbed by the antimicrobial load and the advection of F(x,t) depends on the rates of cell wall synthesis, autolysis and the antimicrobial concentration. Solutions of the Fokker-Planck model are presented for all four qualitative responses of S. aureus to methicillin exposure.     

Travelling Waves of Attached and Detached Cells in a Wound-Healing Cell Migration Assay

During a wound-healing cell migration assay experiment, cells are observed to detach and undergo mitosis before reattaching as a pair of cells on the substrate. During experiments with mice 3T3 fibroblasts, cell detachment can be confined to the wavefront region or it can occur over the whole wave profile. A multi-species continuum approach to modelling a wound-healing assay is taken to account for this phenomenon. The first cell population is composed of attached motile cells, while the second population is composed of detached immotile cells undergoing mitosis and returning to the migrating population after successful division. The first model describes cell division occurring only in the wavefront region, while a second model describes cell division over the whole of the scrape wound. The first model reverts to the Fisher equation when the reattachment rate relative to the detachment rate is large, while the second case does not revert to the Fisher equation in any limit. The models yield travelling wave solutions. The minimum wave speed is slower than the minimum Fisher wave speed and its dependence on the cell detachment and reattachment rate parameters is analysed. Approximate travelling wave profiles of the two cell populations are determined asymptotically under certain parameter regimes.     

Investigation of growth and metabolism of Saccharomyces cerevisiae (baker's yeast) using microcalorimetry and bioluminometry

The heat evolution of aerated and non-aerated batch cultures of Saccharomyces cerevisiae (baker's yeast) in complex glucose medium was investigated by flow microcalorimetry. The course of heat output, substrate consumption and intracellular ATP concentration were extensively studied during the occurrence of an unexpected late peak. The results showed that the acetate could not be responsible for the occurrence of the late peak after the cessation of the growth. Enzyme induction and storage carbohydrate mobilization could be associated with this phenomenon. Linear relationships existed between initial glucose concentration, biomass concentration and total heat output and also between the log of viable cell numbers and the log of integrated heat output. A logistic equation was derived that fit the heat output curves. A model is proposed for predicting the biomass concentration from the power-time curves during the anaerobic growth of S. cerevisiae.     

Calcium oscillations in a triplet of pancreatic acinar cells

We use a mathematical model of calcium dynamics in pancreatic acinar cells to investigate calcium oscillations in a ring of three coupled cells. A connected group of cells is modeled in two different ways: 1), as coupled point oscillators, each oscillator being described by a spatially homogeneous model; and 2), as spatially distributed cells coupled along their common boundaries by gap-junctional diffusion of inositol trisphosphate and/or calcium. We show that, although the point-oscillator model gives a reasonably accurate general picture, the behavior of the spatially distributed cells cannot always be predicted from the simpler analysis; spatially distributed diffusion and cell geometry both play important roles in determining behavior. In particular, oscillations in which two cells are in synchrony, with the third phase-locked but not synchronous, appears to be more dominant in the spatially distributed model than in the point-oscillator model. In both types of model, intercellular coupling leads to a variety of synchronous, phase-locked, or asynchronous behaviors. For some parameter values there are multiple, simultaneous stable types of oscillation. We predict 1), that intercellular calcium diffusion is necessary and sufficient to coordinate the responses in neighboring cells; 2), that the function of intercellular inositol trisphosphate diffusion is to smooth out any concentration differences between the cells, thus making it easier for the diffusion of calcium to synchronize the oscillations; 3), that groups of coupled cells will tend to respond in a clumped manner, with groups of synchronized cells, rather than with regular phase-locked periodic intercellular waves; and 4), that enzyme secretion is maximized by the presence of a pacemaker cell in each cluster which drives the other cells at a frequency greater than their intrinsic frequency.     

A model for glucose-induced wave propagation in pancreatic islets of Langerhans

A reaction-diffusion type model is constructed, describing the spatio-temporal dynamics of the basic intracellular variables assumed to be involved in the initiation of the insulin secretion process by beta -cells in the pancreatic islets of Langerhans. The model includes equations for the electric membrane potential of the cells, with respective kinetics for ionic currents, for concentrations of both free and stored intracellular calcium, and for the intra- and extracellular concentrations of glucose. An empirical expression connecting the equation for the intracellular glucose concentration to the electrical equation is introduced. The model reproduces the events observed in experiments in vitro upon external glucose application to the islets of Langerhans, such as usual bursting oscillations of the membrane potential and corresponding oscillations of the intracellular calcium concentration. It also allows simulation of electric wave propagation through the islet, initiated by the spatial gradient of glucose concentration within the islet. The gradient emerges due to glucose diffusing into the islets from the external medium, being high at the edges. The latter results show that glucose diffusion presents a means for wave initiation in the islets, which supports our previous assumption (Aslanidi et al., 2001).     

An Efficient Wavelet-Based Approximation Method to Gene Propagation Model Arising in Population Biology

In this paper, we have applied an efficient wavelet-based approximation method for solving the Fisher’s type and the fractional Fisher’s type equations arising in biological sciences. To the best of our knowledge, until now there is no rigorous wavelet solution has been addressed for the Fisher’s and fractional Fisher’s equations. The highest derivative in the differential equation is expanded into Legendre series; this approximation is integrated while the boundary conditions are applied using integration constants. With the help of Legendre wavelets operational matrices, the Fisher’s equation and the fractional Fisher’s equation are converted into a system of algebraic equations. Block-pulse functions are used to investigate the Legendre wavelets coefficient vectors of nonlinear terms. The convergence of the proposed methods is proved. Finally, we have given some numerical examples to demonstrate the validity and applicability of the method.     

Propagation of fast and slow intercellular Ca(2+) waves in primary cultured arterial smooth muscle cells

Smooth muscle contraction is regulated by changes in cytosolic Ca²⁺ concentration ([Ca²⁺]_i). In response to stimulation, Ca²⁺ increase in a single cell can propagate to neighbouring cells through gap junctions, as intercellular Ca²⁺ waves. To investigate the mechanisms underlying Ca²⁺ wave propagation between smooth muscle cells, we used primary cultured rat mesenteric smooth muscle cells (pSMCs). Cells were aligned with the microcontact printing technique and a single pSMC was locally stimulated by mechanical stimulation or by microejection of KCl. Mechanical stimulation evoked two distinct Ca²⁺ waves: (1) a fast wave (2 mm/s) that propagated to all neighbouring cells, and (2) a slow wave (20 μm/s) that was spatially limited in propagation. KCl induced only fast Ca²⁺ waves of the same velocity as the mechanically induced fast waves. Inhibition of gap junctions, voltage-operated calcium channels, inositol 1,4,5-trisphosphate (IP₃) and ryanodine receptors, shows that the fast wave was due to gap junction mediated membrane depolarization and subsequent Ca²⁺ influx through voltage-operated Ca²⁺ channels, whereas, the slow wave was due to Ca²⁺ release primarily through IP₃ receptors. Altogether, these results indicate that temporally and spatially distinct mechanisms allow intercellular communication between SMCs. In intact arteries this may allow fine tuning of vessel tone.     

Longitudinal displacements of base pairs in DNA and effects on the dynamics of nonlinear excitations

A model of the DNA is proposed and studied analytically and numerically. The model is an extension of a well known model and describes the double helix as two chains of pendula (each pendulum representing a base). Each base (or pendulum) can rotate and translate along the helix axis. In the continuum limit the system is described by the perturbed Sine–Gordon equation describing the twist of the bases and by a nonlinear partial differential equation (PDE) describing the longitudinal displacements of the bases. This coupled system of PDEs was studied analytically using different approaches and the corresponding results were tested through numerical simulations. It was found that if the coupling parameters satisfy a well defined relationship, then there exist bounded travelling wave solutions.     

Fire-diffuse-fire calcium waves in confined intracellular spaces

The propagation of fire-diffuse-fire Ca²⁺ waves through a three-dimensional rectangular domain is considered. The domain is infinite in extent in the direction of propagation but with lateral barriers to diffusion which contain Ca²⁺ pumps. The Ca²⁺ concentration profile due to the firing of a release site (spark) is derived analytically based on the Green’s function for the diffusion equation on the domain. The existence, stability and speed of these waves is shown to be critically dependent on the dimensions of the domain and the Ca²⁺ pump rate. It is shown that the smaller the dimensions of the region, the lower the Ca²⁺ release flux required for wave propagation, and the higher the wave speed. Also it is shown that the region may support multiple Ca²⁺ wavefronts of varying wave speed. This model is relevant to subsarcolemmal waves in atrial myocytes (Kockskämper et al., 2001, Biophys. J. 81, 2590–2605), and the results may be of importance in understanding the roles of the endoplasmic/sarcoplasmic reticulum, surface membranes and Ca²⁺ pumps in the intracellular Ca²⁺ dynamics of cells.     

Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms

We study kinetic models for chemotaxis, incorporating the ability of cells to assess temporal changes of the chemoattractant concentration as well as its spatial variations. For prescribed smooth chemoattractant density, the macroscopic limit is carried out rigorously. It leads to a drift equation with a chemotactic sensitivity depending on the time derivative of the chemoattractant density. As an application it is shown by numerical experiments that the new model can resolve the chemotactic wave paradox. For this purpose, the macroscopic equation is coupled to a simple activation-inhibition model for the chemoattractant which produces the chemoattractant waves typical for the slime mold Dictyostelium discoideum.     

Beneficial effects of intercellular interactions between pancreatic islet cells in blood glucose regulation

Glucose homeostasis is controlled by the islets of Langerhans which are equipped with α-cells increasing the blood glucose level, β-cells decreasing it, and δ-cells the precise role of which still needs identifying. Although intercellular communications between these endocrine cells have recently been observed, their roles in glucose homeostasis have not been clearly understood. In this study, we construct a mathematical model for an islet consisting of two-state α-, β-, and δ-cells, and analyze effects of known chemical interactions between them with emphasis on the combined effects of those interactions. In particular, such features as paracrine signals of neighboring cells and cell-to-cell variations in response to external glucose concentrations as well as glucose dynamics, depending on insulin and glucagon hormone, are considered explicitly. Our model predicts three possible benefits of the cell-to-cell interactions: First, the asymmetric interaction between α- and β-cells contributes to the dynamic stability while the perturbed glucose level recovers to the normal level. Second, the inhibitory interactions of δ-cells for glucagon and insulin secretion prevent the wasteful co-secretion of them at the normal glucose level. Finally, the glucose dose-responses of insulin secretion is modified to become more pronounced at high glucose levels due to the inhibition by δ-cells. It is thus concluded that the intercellular communications in islets of Langerhans should contribute to the effective control of glucose homeostasis.     

Invasions Slow Down or Collapse in the Presence of Reactive Boundaries

Motivated by the propagation of thin bacterial films around planar obstacles, this paper considers the dynamics of travelling wave solutions to the Fisher–KPP equation \(u_t = u(1-u) + u_{xx} + u_{yy}\) in a planar strip \(-\infty< x < \infty \), \(0 \le y \le L\). We examine the propagation of fronts in the presence of a mixed boundary condition (also referred to as a ‘partially absorbing’ or ‘reactive’ boundary) \(u_y = \alpha u\), with \(\alpha >0\), at \(y=0\). The presence of boundary conditions of this kind leads to the development of front solutions that propagate in x but contain transverse structure in y. Motivated by the observation that the speed of propagation in the Fisher–KPP equation is determined (for exponentially decaying initial conditions) by the behaviour at the leading edge, we analyse the linearised Fisher–KPP equation in order to estimate the speed of the stable travelling front, a function of the width L and the imposed boundary conditions. For wide strips the speed estimate based on the linearised equation agrees well with the results of numerical simulations. For narrow channels numerical simulations indicate that the stable front propagates more slowly, and for sufficiently small L or sufficiently large \(\alpha \) the front speed falls to zero and the front collapses. The reason for the collapse is the non-existence, far behind the front, of a stable positive equilibrium solution u(x, y). While existence of these equilibrium states can be demonstrated via phase plane arguments, the investigation of stability is similar to calculations of critical patch sizes carried out in similar ecological models.     

Excitation wave propagation as a possible mechanism for signal transmission in pancreatic islets of Langerhans

In response to glucose application, beta-cells forming pancreatic islets of Langerhans start bursting oscillations of the membrane potential and intracellular calcium concentration, inducing insulin secretion by the cells. Until recently, it has been assumed that the bursting activity of beta-cells in a single islet of Langerhans is synchronized across the whole islet due to coupling between the cells. However, time delays of several seconds in the activity of distant cells are usually observed in the islets of Langerhans, indicating that electrical/calcium wave propagation through the islets can occur. This work presents both experimental and theoretical evidence for wave propagation in the islets of Langerhans. Experiments with Fura-2 fluorescence monitoring of spatiotemporal calcium dynamics in the islets have clearly shown such wave propagation. Furthermore, numerical simulations of the model describing a cluster of electrically coupled beta-cells have supported our view that the experimentally observed calcium waves are due to electric pulses propagating through the cluster. This point of view is also supported by independent experimental results. Based on the model equations, an approximate analytical expression for the wave velocity is introduced, indicating which parameters can alter the velocity. We point to the possible role of the observed waves as signals controlling the insulin secretion inside the islets of Langerhans, in particular, in the regions that cannot be reached by any external stimuli such as high glucose concentration outside the islets.     

Intracellular Glucose Concentration in Derepressed Yeast Cells Consuming Glucose Is High Enough To Reduce the Glucose Transport Rate by 50%

In Saccharomyces cerevisiae cells exhibiting high-affinity glucose transport, the glucose consumption rate at extracellular concentrations above 10 mM was only half of the zero trans-influx rate. To determine if this regulation of glucose transport might be a consequence of intracellular free glucose we developed a new method to measure intracellular glucose concentrations in cells metabolizing glucose, which compares glucose stereoisomers to correct for adhering glucose. The intracellular glucose concentration was 1.5 mM, much higher than in most earlier reports. We show that for the simplest model of a glucose carrier, this concentration is sufficient to reduce the glucose influx by 50%. We conclude that intracellular glucose is the most likely candidate for the observed regulation of glucose import and hence glycolysis. We discuss the possibility that intracellular glucose functions as a primary signal molecule in these cells.     

山西崦山自然保护区侧柏群落优势种群种间关系分析

在样方调查的基础上,采用方差比率法、Fisher精确检验、Jaccard指数和Spearman秩相关系数研究了山西阳城崦山自然保护区侧柏群落优势种群的种间关系。结果表明：（1）群落优势种总体呈正关联,但关联性较弱,种的分布具有相对独立性。（2）Fisher精确检验与Jaccard指数结合使用可以取得较好的研究结果。（3）Jaccard指数结果表明在乔、灌、草各层中占据明显优势地位的种群其种间联结程度较大。（4）根据研究结果把侧柏群落的优势种群划分为3个生态种组：白皮松生态种组、侧柏生态种组和白莲蒿生态种组。