Prediction of limit cycles in mathematical models of biological oscillations

Three conjectures are given which predict the existence of unique stable limit cycle oscillations in a class of piecewise linear (PL) differential equations. The equations are appropriate to model biological or other complex systems in which there are switchlike interactions between the elements of the network. Methods are presented which can be used to develop mathematical models which are conjectured to display stable limit cycle oscillations, from qualitative experimental information about relative phases of activity in the dynamical systems. Several illustrative numerical examples are given, and one experimental example from neurobiology is discussed. Presented at the Society for Mathematical Biology Meeting, University of Pennsylvania, Philadelphia, August 19–21, 1976.     

Looking deeply into the nature of biological control

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Unstable steady state operations of substrate inhibited cultures by dissolved oxygen control

Microorganism kinetic growth characterized by substrate inhibition was investigated by means of a continuous stirred tank reactor equipped with a feedback controller of the medium feeding flow rate. The aerobic growth of Pseudomonas sp. OX1 with phenol as carbon/energy source was adopted as a case study to test a new control strategy using dissolved oxygen concentration as a state variable. The controller was successful in steadily operating bioconversion under intrinsically unstable conditions. A simple model of the controlled system was proposed to set the feedback controller.The specific growth rate of Pseudomonas sp. OX1 was successfully described by means of the Haldane model. The regression of the experimental data yielded μ_M = 0.26 h⁻¹, K_Ph = 5 × 10⁻³ g/L and K_I = 0.2 g/L. The biomass-to-substrate fractional yield as a function of the specific growth rate did not change moving from substrate-inhibited to substrate-deficient state. The data was modelled according to the Pirt model: m = 1.7 × 10⁻² g/(g h), . The specific growth rates calculated for batch and continuous growth were compared.     

Comparing functional responses in predator-infected eco-epidemics models

The current paper deals with the mathematical models of predator–prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator–prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results.     

A mathematical modelling framework for elucidating the role of feedback control in translation termination

Translation is the final stage of gene expression where messenger RNA is used as a template for protein polymerization from appropriate amino acids. Release of the completed protein requires a release factor protein acting at the termination/stop codon to liberate it. In this paper we focus on a complex feedback control mechanism involved in the translation and synthesis of release factor proteins, which has been observed in different systems. These release factor proteins are involved in the termination stage of their own translation. Further, mutations in the release factor gene can result in a premature stop codon. In this case translation can result either in early termination and the production of a truncated protein or readthrough of the premature stop codon and production of the complete release factor protein. Thus during translation of the release factor mRNA containing a premature stop codon, the full length protein negatively regulates its production by its action on a premature stop codon, while positively regulating its production by its action on the regular stop codon. This paper develops a mathematical modelling framework to investigate this complex feedback control system involved in translation. A series of models is established to carefully investigate the role of individual mechanisms and how they work together. The steady state and dynamic behaviour of the resulting models are examined both analytically and numerically.     

两种群均具有常收获率或常投放率的Lotka-Volterra系统可以存在三个极限环

证明了两种群均具有常收获率或常投放率的Lotka-Volterra系统可以存在三个极限环。     

Mechanisms underlying gamma ('40 Hz') network oscillations in the hippocampus--a mini-review

Gamma-frequency oscillations (approximately 30-100 Hz) in cortical network activity have been proposed to provide a temporal structure for various forms of cognitive processing. This review provides an update on recent experiments addressing the mechanisms underlying gamma-frequency network oscillations in the rodent hippocampus. Particular emphasis is placed on the correlation between in vivo observations and in vitro models.     

新一代生物防治及其在天敌瓢虫中的研究进展

生物防治是一种利用自然天敌控制有害生物的手段.当前生物防治的发展面临着使用成本高和效果不稳定的两大难题.这要求我们更精准地选育和释放天敌.随着测序技术的进步,学界提出了新一代生物防治(Next Generation Biological Control),旨在利用遗传学和基因组学来认识天敌昆虫种下水平的多样性和变异规律...     

Global land-use change and the importance of zoophytophagous bugs in biological control: Coppicing willows as a timely example

Perennial plants, such as willows, miscanthus, and hybrid poplars, are promising bioenergy crops while lowering atmospheric CO₂. Increases in the acreage of perennial bioenergy crops will pose new challenges and opportunities for biological control. In this review, we suggest that zoophytophagous bugs could be expected to become increasingly important in biological control of arthropod pests in perennial bioenergy crops. The main reasons are: (1) perennial bioenergy crops provide suitable habitats for arboreal natural enemies like zoophytophagous bugs; (2) zoophytophagous bugs often increase in response to low disturbance frequencies; and (3) plant-feeding by zoophytophagous bugs will not likely affect plant biomass production in perennial crops. We review aspects of the biology of zoophytophagous bugs expected to be important in biological control of pests in perennial systems. We also present a predator–prey model investigating how alternative harvest methods affect biological control of herbivorous pests by zoophytophagous bugs in willow biomass plantations. Although there is good evidence that zoophytophagous bugs can provide pest control, more research is needed about factors affecting the dispersal and population dynamics of zoophytophagous bugs in agricultural landscapes.     

生防细菌产生的拮抗物质及其在生物防治中的作用

利用生防细菌防治植物病害是生物防治的一个主要内容．生防细菌防治植物病害发生发展的一个重要机制是产生拮抗物质．生防细菌的拮抗物质种类多,作用范围广谱．同一种拮抗物质可以由多种细菌菌株产生,而同一细菌也可以产生多种不同结构的拮抗物质．运用现代分子生物学技术和先进的分析测试手段可以加快对产生拮抗物质生防细菌的研究,了解生防细菌在寄主植物根围和叶围的定植效果。明确拮抗物质在生物防治中的作用．拮抗物质的产生除与细菌基因型有关外,一些外在的生物和非生物因素如病原菌存在与否、温度、pH和C、N营养等也影响拮抗物质产生．文中论述了生防细菌应用中存在的问题。指出混合菌剂的研制对防止病原菌抗性产生具有重要作用,应是今后生防菌剂研制中的重点．     

Role of mermithid nematodes in biological control of mosquitoes

Mermithid nematodes have been reported from at least 63 species of mosquitoes from all over the world, but until recently they have received little attention. Such nematodes are prime candidates as biological control agents because they have adapted to the life cycle of the host; are host specific; produce high levels of parasitism; kill the hosts; are easily handled; have a high reproductive potential; are free swimming and can be disseminated easily in the infective stage; and can be used in an inundative or inoculative manner to control mosquitoes. Nevertheless, with the exception of one mermithid species, little is known about factors that influence parasitism in mosquitoes. Also, only one species of mermithid has been successfully mass cultured to date. The exception is the mermithid Reesimermis nielseni. With this mermithid, high levels of parasitism can be obtained in natural populations of mosquitoes at reasonable dosages; preparasitic nematodes can be applied easily by using many of the standard techniques used to apply insecticides; and R. nielseni can establish itself in many of the sites in which it is released. The same potentials exist for mermithids of other aquatic insects.     

Concentration oscillations in three-component reaction systems

Based on the sufficient conditions for the existence of oscillation modes in the mathematical models of biological systems, simple three-component schemes of chemical reactions with oscillatory behavior including only mono- and bimolecular steps are suggested.     

Screening Trichoderma species for biological control activity against Phytophthora ramorum in soil

Despite efforts of eradication and sanitation, Phytophthora ramorum persists in the United States and abroad. Fungicides have limited effectiveness, but there are concerns that they may only inhibit pathogen growth and hasten resistance development after repeated fungicide applications. Biological control is an active control measure that can work continuously as long as the agent is alive and active. The goal of this study was to examine whether Trichoderma spp. have the potential as a biological control agent against P. ramorum. Sixteen Trichoderma spp. isolates were screened for mycoparasitism of P. ramorum in a dual culture assay. The different Trichoderma spp. isolates demonstrated variable mycoparasitic activities with some isolates showing no activity while others completely eliminated the pathogen after 4 weeks. Seven isolates of T. asperellum were consistent among replicated trials in eliminating recovery of P. ramorum from the exposed agar plugs and preventing leaf disk necrosis. Further testing of six T. asperellum isolates against two different P. ramorum isolates (A1 and A2 mating types) resulted in the same high level of mycoparasitic activity. Soil assays involving P. ramorum-infested potting mix and selected Trichoderma spp. isolates demonstrated that two isolates (04-22 and 02-64) were consistent among the repetitions to eliminate P. ramorum propagules to non-detectable levels. Based on these results, specific T. asperellum isolates have the potential to remediate P. ramorum-infested soil and have the potential to be developed into a commercially-viable product.     

Estimating economic benefits of biological control of Ambrosia artemisiifolia by Ophraella communa in southeastern France

The North American common ragweed, Ambrosia artemisiifolia, which produces highly allergenic pollen, is invasive in different parts of the world, including Europe. In 2013, common ragweed in northern Italy was found attacked by another accidentally introduced species, the North American leaf beetle Ophraella communa, which is used for biological control of common ragweed in China. Since the establishment of O. communa, ragweed pollen concentrations in northern Italy have significantly dropped. Here we set out to estimate the potential economic benefits of establishment of O. communa in the Rhône-Alpes region in south-eastern France, where detailed data on the economic impact of common ragweed are available. Extrapolating from the change in airborne ragweed pollen concentrations in the Milan area, we estimated that establishment of O. communa in the Rhône-Alpes region will reduce the number of days with ragweed pollen concentrations at which sensitive people express symptoms by 50% and the medical costs due to common ragweed by 5.2–6.8 M € annually. Our findings suggest that investments of public funds are justified to conduct a complete assessment of the potential risks and benefits associated with the accidental establishment of O. communa in Europe.     

Controllability of non-linear biochemical systems

Mathematical methods of biochemical pathway analysis are rapidly maturing to a point where it is possible to provide objective rationale for the natural design of metabolic systems and where it is becoming feasible to manipulate these systems based on model predictions, for instance, with the goal of optimizing the yield of a desired microbial product. So far, theory-based metabolic optimization techniques have mostly been applied to steady-state conditions or the minimization of transition time, using either linear stoichiometric models or fully kinetic models within biochemical systems theory (BST). This article addresses the related problem of controllability, where the task is to steer a non-linear biochemical system, within a given time period, from an initial state to some target state, which may or may not be a steady state. For this purpose, BST models in S-system form are transformed into affine non-linear control systems, which are subjected to an exact feedback linearization that permits controllability through independent variables. The method is exemplified with a small glycolytic-glycogenolytic pathway that had been analyzed previously by several other authors in different contexts.     

Application of Bacillus subtilis in the biological control of the phytopathogenic fungus Sporisorium reilianum

Sporisorium reilianum is the causal agent of head smut in corn, a worldwide disease that causes significant economic losses in the principal areas where maize is cultivated. To attack this problem, resistant commercial hybrids and synthetic fungicide seed treatment have been used, but with low effectiveness. In this study, a native strain of Bacillus subtilis isolated from the soil of corn crops in Mixquiahuala, Hidalgo, in central Mexico, was applied as a seed treatment in the field to test for the biological control of head smut. It significantly decreased the Smut Incidence Percentage (SIP) while increasing maize productivity. This work represents the first report in which B. subtilis has been used to control S. reilianum in the field.     

Environmental safety of biological control: Policy and practice in New Zealand

Introduction of biological control agents into New Zealand is regulated under the Hazardous Substances and New Organisms Act 1996 (HSNO). The legislation is strongly focused on the health and safety of people and the environment. HSNO is implemented by the Environmental Risk Management Authority, a quasi-judicial body of 6–8 people appointed by the Minister for the Environment. The process by which biological control applications are received and processed is described. Two case studies of weed biological control agents which have been through the HSNO process, and the scientific issues that arose in considering the environmental safety of these agents are discussed. The case studies presented are the applications to release the gall fly Procecidochares alani (Diptera: Tephritidae) to control mist flower Ageratina riparia, and three biological control agents, Macrolabis pilosellae (Diptera: Cecidomyiidae), Cheilosia urbana, and Cheilosia psilophthalma (Diptera: Syrphidae) for biological control of hawkweeds (Hieracium spp.). Both applications were approved for agent release into the environment.