Generation of zonal flows and large-scale magnetic fields by drift-Alfvén turbulence

The possibility of generating zonal perturbations by drift-Alfvén turbulence in a plasma with a finite pressure (1>β>m_e/m_i) is investigated. A set of coupled equations is derived that includes the equation for the spectral function of the turbulence and the averaged equations for zonal perturbations. It is shown that, in particular cases, the equation for the spectral function possesses action invariants; i.e., it takes the form of a conservation law for some quantities that are proportional to the spectral function of turbulence. Two types of instability of the zonal perturbations are revealed. The first type of instability generates only a zonal flow. Two regimes of this instability—resonant and hydrodynamic regimes—are examined, and the corresponding instability growth rates are determined. The second type of instability takes place when the resonant interaction of drift-Alfvén waves with electrons is taken into account. Because of this instability, the generation of a zonal magnetic field is inevitably accompanied by the generation of a zonal flow. It is found that the growth rate of the second type of instability is slower than that of the first type.     

Stochastic Gompertz model of tumour cell growth

In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker--Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves. Within this framework the action of therapy is also examined by simply incorporating a therapy term into the deterministic cell growth term.     

Multistability and dynamic transitions of intracellular Min protein patterns

Cells owe their internal organization to self‐organized protein patterns, which originate and adapt to growth and external stimuli via a process that is as complex as it is little understood. Here, we study the emergence, stability, and state transitions of multistable Min protein oscillation patterns in live Escherichia coli bacteria during growth up to defined large dimensions. De novo formation of patterns from homogenous starting conditions is observed and studied both experimentally and in simulations. A new theoretical approach is developed for probing pattern stability under perturbations. Quantitative experiments and simulations show that, once established, Min oscillations tolerate a large degree of intracellular heterogeneity, allowing distinctly different patterns to persist in different cells with the same geometry. Min patterns maintain their axes for hours in experiments, despite imperfections, expansion, and changes in cell shape during continuous cell growth. Transitions between multistable Min patterns are found to be rare events induced by strong intracellular perturbations. The instances of multistability studied here are the combined outcome of boundary growth and strongly nonlinear kinetics, which are characteristic of the reaction–diffusion patterns that pervade biology at many scales.     

The plant cytoskeleton takes center stage in abiotic stress responses and resilience

Stress resilience behaviours in plants are defensive mechanisms that develop under adverse environmental conditions to promote growth, development and yield. Over the past decades, improving stress resilience, especially in crop species, has been a focus of intense research for global food security and economic growth. Plants have evolved specific mechanisms to sense external stress and transmit information to the cell interior and generate appropriate responses. Plant cytoskeleton, comprising microtubules and actin filaments, takes a center stage in stress-induced signalling pathways, either as a direct target or as a signal transducer. In the past few years, it has become apparent that the function of the plant cytoskeleton and other associated proteins are not merely limited to elementary processes of cell growth and proliferation, but they also function in stress response and resilience. This review summarizes recent advances in the role of plant cytoskeleton and associated proteins in abiotic stress management. We provide a thorough overview of the mechanisms that plant cells employ to withstand different abiotic stimuli such as hypersalinity, dehydration, high temperature and cold, among others. We also discuss the crucial role of the plant cytoskeleton in organellar positioning under the influence of high light intensity.     

Cell division in Escherichia coli after changes in the velocity of DNA replication

A method of computer analysis was developed to evaluate the kinetic changes in the rate of cell division in non-synchronous cultures of E. coli resulting from changes in the velocity or initiation of chromosome replication. This method takes into account that the cell division pathway in E. coli includes a reaction of indeterminate length described by a probability function that applies to the cell population. The analysis yields a hypothetical cell number kinetics as it would be observed if the stochastic element in the division pathway were absent. Since this derived cell number curve responds to experimentally induced perturbations of replication at defined times whereas the actual cell number curve reflects these perturbations only in a blurred fashion, replication and division events can be precisely correlated with this method. The method was applied to the evaluation of thymine starvation experiments with two Thy- derivatives of E. coli B/r; one of the strains has a mutationally altered (60% increased) cell mass at initiation of chromosome replication. In both strains, the stochastic phase of the cell cycle had the same half-life value of 10 min and began 18 min after each termination of replication. This suggests that the time of cell division is linked to replication, not to cell mass or length. This interpretation is supported by results of experiments in which the rate of cell growth was altered at the time of thymine starvation.     

Asymptotic behaviour of solutions to abstract logistic equations

We analyze the asymptotic behaviour of solutions of the abstract differential equation u'(t)=Au(t)-F(u(t))u(t)+f. Our results are applicable to models of structured population dynamics in which the state space consists of population densities with respect to the structure variables. In the equation the linear term A corresponds to internal processes independent of crowding, the nonlinear logistic term F corresponds to the influence of crowding, and the source term f corresponds to external effects. We analyze three separate cases and show that for each case the solutions stabilize in a way governed by the linear term. We illustrate the results with examples of models of structured population dynamics -- a model for the proliferation of cell lines with telomere shortening, a model of proliferating and quiescent cell populations, and a model for the growth of tumour cord cell populations.     

Inorganic Carbon Limitation and Chemical Composition of Two Freshwater Green Microalgae

Two freshwater chlorophytes, Chlorella vulgaris and Scenedesmus obliquus, were grown in inorganic carbon-limited continuous cultures in which HCO₃⁻ was the sole source of inorganic carbon. The response of the steady-state growth rate to the external total inorganic carbon concentration was reasonably well described by the Monod equation; however, the response to the internal nutrient concentration was only moderately well represented by the Droop equation when the internal carbon concentration was defined on a cellular basis. The Droop equation was totally inapplicable when total biomass (dry weight) was used to define internal carbon because the ratio of carbon to dry weight did not vary over the entire growth rate spectrum. In batch cultures, maximum growth rates were achieved at the CO₂ levels present in atmospheric air and at HCO₃⁻ concentrations of 3 mM. No growth was observed at 100% CO₂. Both nitrogen uptake and chlorophyll synthesis were tightly coupled to carbon assimilation, as indicated by the constant C/N and C/chlorophyll ratios found at all growth rates. The main influence of inorganic carbon limitation appears to be not on the chemical structure of the biomass, but rather on cell size; higher steady-state growth rates lead to bigger cells.     

Effect of temperature on plant elongation and cell wall extensibility

Lockhart equation was derived for explaining plant cell expansion where both cell wall extension and water uptake must occur concomitantly. Its fundamental contribution was to express turgor pressure explicitly in terms of osmosis and wall mechanics. Here we present a new equation in which pressure is determined by temperature. It also accounts for the role of osmosis and consequently the role of water uptake in growing cell. By adopting literature data, we also attempt to report theoretically the close relation between plant elongation and cell wall extensibility. This is accomplished by the modified equation of growth solved for various temperatures in case of two different species. The results enable to interpret empirical data in terms of our model and fully confirm its applicability to the investigation of the problem of plant cell extensibility in function of environmental temperature. Moreover, by separating elastic effects from growth process we specified the characteristic temperature common for both processes which corresponds to the resonance energy of biochemical reactions as well as to the rapid softening of the elastic modes toward the high temperature end where we encountered viscoelastic and/or plastic behavior as dominating. By introducing analytical formulae connected with growth and elastic properties of the cell wall, we conclude with the statement how these both processes contribute quantitatively to the resonance-like shape of the elongation curve. In addition, the tension versus temperature "phase diagram" for a living plant cell is presented.     

The notion of the internal and external limitations of monotonic growth functions. A reformulation of the logistic equation

The boundary value (plateau) of non-periodic growth functions constitutes one of the parameters of various usual models such as the logistic equation. Its double interpretation involves either a limit of an internal or endogenous nature or an external environment-dependent limit. Using the autocatalytic model of structured cell populations (Buis, model II, 2003), a reformulation of the logistic equation is put forward and illustrated in the case of three cell classes (juvenile, mature, senescing). The agonistic component corresponds exactly to the only active fraction of the population (non-senescing mature cells), whereas the antagonistic component is interpreted in terms of an external limit (available substrate or source). The occurrence and properties of an external limit are investigated using the same autocatalytic model with two major modifications: the absence of competition (non-limiting source) and the occurrence of a maximum number of mitoses per cell filiation (Lück and Lück, 1978). The analysis, which is carried out according to the principle of deterministic cell automata (L-systems), shows the flexibility of the model, which exhibits a diversity of kinetic properties: shifts from the sigmoidal form, number and position of growth rate extremums, number of phases of the temporal structure. These characteristics correspond to the diversity of the experimental growth curves where the singularities of the growth rate gradient are often not accounted for satisfactorily by the usual global models.     

Mathematical model for contact inhibited cell division

We present a mathematical model for cell growth, which takes into account cell-cell interactions and leads to non-exponential inhibited growth of number of cells. The resulting difference equation is solved and extended to a differential equation which turns out to be of a non-linear diffusion type.     

Feedback Mechanism for Microtubule Length Regulation by Stathmin Gradients

We formulate and analyze a theoretical model for the regulation of microtubule (MT) polymerization dynamics by the signaling proteins Rac1 and stathmin. In cells, the MT growth rate is inhibited by cytosolic stathmin, which, in turn, is inactivated by Rac1. Growing MTs activate Rac1 at the cell edge, which closes a positive feedback loop. We investigate both tubulin sequestering and catastrophe promotion as mechanisms for MT growth inhibition by stathmin. For a homogeneous stathmin concentration in the absence of Rac1, we find a switchlike regulation of the MT mean length by stathmin. For constitutively active Rac1 at the cell edge, stathmin is deactivated locally, which establishes a spatial gradient of active stathmin. In this gradient, we find a stationary bimodal MT-length distribution for both mechanisms of MT growth inhibition by stathmin. One subpopulation of the bimodal length distribution can be identified with fast-growing and long pioneering MTs in the region near the cell edge, which have been observed experimentally. The feedback loop is closed through Rac1 activation by MTs. For tubulin sequestering by stathmin, this establishes a bistable switch with two stable states: one stable state corresponds to upregulated MT mean length and bimodal MT length distributions, i.e., pioneering MTs; the other stable state corresponds to an interrupted feedback with short MTs. Stochastic effects as well as external perturbations can trigger switching events. For catastrophe-promoting stathmin, we do not find bistability.     

Cell kinetic response of an experimental tumour to irradiation. Use of the stathmokinetic method

The cell kinetic perturbations following irradiation (20 Gy) were studied by combining the metaphase arrest method using vincristine with histological indices of cell death. The metaphase arrest method yielded remarkably constant values of rate of entry into mitosis (rM) of around 24 new cells/1,000 cells/hour during a 7 day period in which there was no tumour growth. The time course of cell death as indicated by changes in the pyknotic index during this period may reflect the processes of reoxygenation and repopulation known to influence the results of fractionated radiotherapy.     

Temperature effects on steady-state growth,phosphorus uptake,and the chemical composition of a marine phytoplankter

The marine chrysophyteMonochrysis lutheri was grown in phosphorus-limited continuous cultures at temperatures of 15°, 18.8° and 23°C. The effect of temperature on the maximum growth rate was well-defined by the Arrhenius equation, but the Q₁₀ for this alga (1.7) was somewhat lower than has been determined previously for many other phytoplankton species (2.0–2.2). The minimum phosphorus cell quota was relatively unaffected by temperature at 18.8°C and 23°C, but doubled in magnitude at 15°C. As a result, the internal nutrient equation of Droop described the relationship between specific growth rate and phosphorus cell quota well at 18.8° and 23°C, but was less successful at 15°C. The major limitation in using the Droop equation is that the ratio between the minimum and maximum cell quotas must be known, thus necessitating the need to establish the true maximum growth rate by the cell washout technique. In addition, the phosphorus uptake rate on a cell basis at a given steady state growth rate (=specific uptake rate) increased dramatically at 15°C, whereas the turnover rate of total available phosphorus was unaffected by temperature. Both the nitrogen and carbon cell quotas were relatively unaffected by growth rate at a given temperature, but the average values increased slightly with decreasing temperature. The overall conclusion is that phytoplankton growth and limiting-nutrient uptake rates are only synchronous at or near the optimum temperature. Because these types of responses are species specific, much additional data on temperature effects will be required before the importance of including such effects in phytoplankton-nutrient models can be determined.     

Nuclear deformations,from signaling to perturbation and damage

During cell growth and motility in crowded tissues or interstitial spaces, cells must integrate multiple physical and biochemical environmental inputs. After a number of recent studies, the view of the nucleus as a passive object that cells have to drag along has become obsolete, placing the nucleus as a central player in sensing some of these inputs. In the present review, we will focus on changes in nuclear shape caused by external and internal forces. Depending on their magnitude, nuclear deformations can generate signaling events that modulate cell behavior and fate, or be a source of perturbations or even damage, having detrimental effects on cellular functions. On very large deformations, nuclear envelope rupture events become frequent, leading to uncontrolled nucleocytoplasmic mixing and DNA damage. We will also discuss the consequences of repeated compromised nuclear integrity, which can trigger DNA surveillance mechanisms, with critical consequences to cell fate and tissue homeostasis.     

Characterization of a whole‐cell catalyst co‐expressing glycerol dehydrogenase and glucose dehydrogenase and its application in the synthesis of L‐glyceraldehyde

A whole‐cell catalyst using Escherichia coli BL21(DE3) as a host, co‐expressing glycerol dehydrogenase (GlyDH) from Gluconobacter oxydans and glucose dehydrogenase (GDH) from Bacillus subtilis for cofactor regeneration, has been successfully constructed and used for the reduction of aliphatic aldehydes, such as hexanal or glyceraldehyde to the corresponding alcohols. This catalyst was characterized in terms of growth conditions, temperature and pH dependency, and regarding the influence of external cofactor and permeabilization. In the case of external cofactor addition we found a 4.6‐fold increase in reaction rate caused by the addition of 1 mM NADP⁺. Due to the fact that pH and temperature are also factors which may affect the reaction rate, their effect on the whole‐cell catalyst was studied as well. Comparative studies between the whole‐cell catalyst and the cell‐free system were investigated. Furthermore, the successful application of the whole‐cell catalyst in repetitive batch conversions could be demonstrated in the present study. Since the GlyDH was recently characterized and successfully applied in the kinetic resolution of racemic glyceraldehyde, we were now able to transfer and establish the process to a whole‐cell system, which facilitated the access to L ‐glyceraldehyde in high enantioselectivity at 54% conversion. All in all, the whole‐cell catalyst shows several advantages over the cell‐free system like a higher thermal, a similar operational stability and the ability to recycle the catalyst without any loss‐of‐activity. The results obtained making the described whole‐cell catalyst an improved catalyst for a more efficient production of enantiopure L ‐glyceraldehyde. Biotechnol. Bioeng. 2010;106: 541–552. © 2010 Wiley Periodicals, Inc.     

Prediction of predator–prey populations modelled by perturbed ODEs

In this paper we explore a stochastic model in continuous time for predator-prey interactions, which accounts for the periodical behaviour observed in many animal populations. More precisely, we consider a solution to the classical Lotka-Volterra system of equations, but we view the actual population sizes as random perturbations of the solutions to this ODE system. Namely, we assume that the perturbations follow correlated Ornstein-Uhlenbeck processes; this approach generalizes the one of Froda and Colavita [Aust N Z J Stat 2:235-254, 2005] who considered only i.i.d. errors. This type of perturbed deterministic model allows to perform parameter estimation and to predict population sizes at future times. On the other hand, the present model refines the previous one since it takes into account the variability due to external factors and the time dependence in the random component. Moreover, this more flexible model improves the predictions of population sizes at future times. In order to illustrate this last point, we analyse two data sets.     

Denitrification and a numerical modelling approach for shallow waters

A numerical model (`DiffDeni') has been developed to describe the disappearance of nitrate from the water column of 10–200 cm deep waters. The disappearance is caused by bacterial denitrification in the sediments. The model employs the molecular diffusion constant, an acceleration factor describing eddy diffusion, and three bacterial growth constants, viz. the inoculum size, the maximum growth rate and the half saturation constant for the hyperbolic process. The values of these system-constants were varied over a wide range. The curves obtained were compared with the curves for well-defined situations, viz. in which diffusion takes place without any or with a complete, immediate reaction. These cases have analytical solutions, and were simulated closely by the model `DiffDeni', though this model is based on different assumptions. It is shown that, when the bacterial growth rate is above a critical value, a negative exponential curve describes the nitrate disappearance well. On the other hand, a more complicated negative exponential equation can be used to describe the first phase of this denitrification in which bacterial activity is low and nitrate behaves as a conservative compound. The change-over period from phase 1 (no reaction) to phase 2 (complete, immediate reaction) which may vary between <1 and 50 days cannot be described analytically (mathematically correctly). The influence of temperature on denitrification is assessed and it is shown that both bacterial activity and diffusion may influence the denitrification rate.     

Analytical solution for a hybrid Logistic-Monod cell growth model in batch and continuous stirred tank reactor culture

Monod and Logistic growth models have been widely used as basic equations to describe cell growth in bioprocess engineering. In the case of the Monod equation, the specific growth rate is governed by a limiting nutrient, with the mathematical form similar to the Michaelis–Menten equation. In the case of the Logistic equation, the specific growth rate is determined by the carrying capacity of the system, which could be growth-inhibiting factors (i.e., toxic chemical accumulation) other than the nutrient level. Both equations have been found valuable to guide us build unstructured kinetic models to analyze the fermentation process and understand cell physiology. In this work, we present a hybrid Logistic-Monod growth model, which accounts for multiple growth-dependent factors including both the limiting nutrient and the carrying capacity of the system. Coupled with substrate consumption and yield coefficient, we present the analytical solutions for this hybrid Logistic-Monod model in both batch and continuous stirred tank reactor (CSTR) culture. Under high biomass yield (Y_x/s) conditions, the analytical solution for this hybrid model is approaching to the Logistic equation; under low biomass yield condition, the analytical solution for this hybrid model converges to the Monod equation. This hybrid Logistic-Monod equation represents the cell growth transition from substrate-limiting condition to growth-inhibiting condition, which could be adopted to accurately describe the multi-phases of cell growth and may facilitate kinetic model construction, bioprocess optimization, and scale-up in industrial biotechnology.     

Motor control and learning in altered dynamic environments

Dynamic perturbations of reaching movements are an important technique for studying motor learning and adaptation. Adaptation to non-contacting, velocity-dependent inertial Coriolis forces generated by arm movements during passive body rotation is very rapid, and when complete the Coriolis forces are no longer sensed. Adaptation to velocity-dependent forces delivered by a robotic manipulandum takes longer and the perturbations continue to be perceived even when adaptation is complete. These differences reflect adaptive self-calibration of motor control versus learning the behavior of an external object or 'tool'. Velocity-dependent inertial Coriolis forces also arise in everyday behavior during voluntary turn and reach movements but because of anticipatory feedforward motor compensations do not affect movement accuracy despite being larger than the velocity-dependent forces typically used in experimental studies. Progress has been made in understanding: the common features that determine adaptive responses to velocity-dependent perturbations of jaw and limb movements; the transfer of adaptation to mechanical perturbations across different contact sites on a limb; and the parcellation and separate representation of the static and dynamic components of multiforce perturbations.     

温度对谷胱甘肽分批发酵的影响及动力学模型

研究了24～32℃范围内产朊假丝酵母生产谷胱甘肽的分批发酵过程,发现较高温度对细胞生长有促进作用,而较低温度则更有利于谷胱甘肽产量的提高。应用改进的Logistic和LuedekingPiret方程分别对细胞生长动力学和谷胱甘肽合成动力学进行了模拟,得到不同温度下各种动力学参数。在此基础上,进一步研究了温度同细胞生长动力学参数之间的内在联系,得到谷胱甘肽分批发酵过程中细胞浓度的变化同温度以及底物浓度之间的一般关系式：dX-dt＝［0.0224(T+1.7)］2X(1-X/X_max)1+S｛8.26×10.6×exp［-31477/R/(T+273)］｝。验证实验结果表明,该模型具有很好的适用性。