Error catastrophe in and the evolution of the protein synthesizing machinery

The theory of the propagation of errors in the system of enzymes translating genetic information proposed earlier is developed further. It is shown that if initially for some of these enzymes the normal molecules are more than, for some less than, and for some equal to the erroneous ones, the evolution of the system can lead to many asymptotic conditions including error catastrophe and complete recovery from errors.     

Error propagation in E. coli protein synthesis

A new approach to the error catastrophe theory, proposed by Leslie Orgel, is presented here. Our model is a development of previous models, but differs in several respects: the overall activity is assumed to be dependent on the error level, the effect of errors in the translating system, giving rise to additional errors in the succeeding generation of products, is explicitly included as a special term in our model, and scavenging enzymes are assumed to break down and eliminate products with a loose structure. Their efficiency is dependent on the error level. The model also takes into account the dilution of incorrect ribosomes and enzymes, and is described by a time-dependence in terms of ribosome/enzyme generations. The model and the contribution to the time development are discussed in the light of experiments on E. coli treated with streptomycin.     

Catastrophe Theory Enables Moves to be Detected Towards and Away from Self-Organization: The Example of Epileptic Seizure Onset

Macroscopic systems with many interacting subunits, when driven far from equilibrium, exhibit self-organization, for example when a pathological rhythm appears suddenly in an epileptic patient. Sudden changes occurring while conditions vary smoothly have, in cases of interest, underlying mathematics that are the subject of Thom’s catastrophe theory. The assumption made herein that the system’s state variables, akin to order parameters, reduce in practice to only one single real variable, ensures that the system derives from a potential function, and warrants recourse to the catastrophe theory. The order parameter is, furthermore, interpreted as a measure of the electropathophysiological activity in the brain, increasing monotonously with the degree of neuronal synchronism. With two neuronal influences, excitatory and inhibitory, as control parameters, the catastrophe is the archetypal cusp. Implementation of catastrophe theory leads to equations showing that fluctuations in a system’s dynamics may be utilised for signalling steps precursory to oncoming catastrophes. Pre-seizure dynamics in epileptic patients exhibit steps towards and away from catastrophe; the steps away are interpreted in terms of homeostatic feedback, consequent on changing patterns of neuronal activity. A number of characteristics of epileptic seizures of differing types merely follow from the geometry of the cusp equilibrium surface. In particular, types of seizures are distinguished by their angle of final approach to onset in parameter space. The measurable parameters by which approach to catastrophe is characterized, may be of use in investigations of the organism’s plasticity in epileptic patients, and in tests of therapeutic means for preventing seizures. There is no need to resort to a model, in the usual sense of the word, and therefore no differential equation needs to be set up.     

害虫种群动态模型的燕尾突变分析

在农田生态系统中,以作物状况、气象因素及天敌分别为3种控制变量,以害虫种群数量动态为状态变量,建立了燕尾突变模型,并用燕尾突变模型的性质分析害虫种群数量动态中产生的突变现象.具体对燕尾突变的分歧点集所分各个控制区域的系统势函数形式和平衡点情况进行了分析,说明了害虫种群数量发生突变的条件和机理,为实际应用提供理论依据.同时利用燕尾突变的性质直观描述了害虫种群数量变化中的突跳和滞后等现象.     

Biological power laws and Darwin's principle

Assuming that the repertoire of responses by living systems to perturbation gives a measure of their Darwinian fitness in a rapidly fluctuating environment, those that fulfill allometries (power laws) are described by means of catastrophes, whose variables and parameters are smooth functions of biological attributes. Using empirical allometries from a given system as input, a method is proposed to construct its associated catastrophe, allowing specific predictions on its susceptibility to perturbation and related properties, based on general results from catastrophe theory. The method is discussed within the macroecological context, and an example is provided by applying it to ecological systems that satisfy the self-thinning rule.     

Topological Approach of Jungian Psychology

In this work, we compare two global approaches which are usually considered as completely unconnected one with the other. The former is Thom’s topology and the latter is Jung’s psychology. More precisely, it seemed to us interesting to adapt some morphologies of Thom’s catastrophe theory to some Jung’s notions. Thus, we showed that the swallowtail, which is one of these morphologies, was able to describe geometrically the structural organisation of the psyche according to Jung, with its collective unconscious, personal unconscious and conscious. Moreover, we have correlated this morphology with Jung’s evolutive processes like individualisation and individuation. These comparisons incited us to think that some morphologies of Thom’s catastrophe theory are the geometrical dealing of Jung’s archetypes.     

基于椭圆脐点突变模型的大熊猫生存状态研究

得益于有力的保护,大熊猫受威胁等级由"濒危"降为"易危"。根据全国大熊猫调查数据,近年来,大熊猫野生种群与栖息地面积总体上均处于持续增加态势;同时,大熊猫栖息地破碎化与局域种群隔离也呈加剧的趋势。两相对比,形成悖论现象,难以正确认知当前大熊猫的生存状态。大熊猫作为高度特化的K对策大型动物,其生存高度依赖于栖息地生态系统,极易受栖息地丧失与破碎化的影响。对大熊猫生存状态的研究,不应局限于栖息地或种群等单项指标的变化,而应基于系统科学的整体视角。结合全国第三、四次大熊猫调查数据,对大熊猫野生种群数量与栖息地及潜在栖息地的面积进行复相关分析,发现大熊猫野生种群数量与栖息地、潜在栖息地的面积之间存在着高度显著正相关,表明三者之间存在着稳定而密切的耦合关系,进而建立了大熊猫种群与栖息地、潜在栖息地之间的耦合函数。突变理论作为一种成熟的系统科学理论,提供了较完备的数学方法,利用系统中少量的关键指标便可实现对系统行为的刻画。基于突变理论,以大熊猫分布区生态系统为研究对象,选取了大熊猫种群数量、栖息地与潜在栖息地的面积为系统关键指标,利用种群与栖息地、潜在栖息地之间的耦合函数,构建了"大熊猫—栖息地"系统椭圆脐点突变模型,对生态系统的稳定性进行研究。发现虽然野生种群数量、栖息地与潜在栖息地的面积均持续增长,但严峻的局域种群生存危机与栖息地的高度破碎化,从总体上削弱了系统的稳定性,大熊猫分布区生态系统的稳定性处于持续下降态势,且濒临系统临界状态,生态系统具有较大的退化压力,大熊猫的生存危机依然严峻。     

A Catastrophe Model for the Switch from Vegetative to Reproductive Growth in the Shoot Apex

A mathematical model is constructed to describe the morphopneticswitch that occurs when a vegetative plant apex becomes reproductive.The cusp equation from catastrophe theory is modified, and isused to relate primordial size at initiation to apex size. Theresulting equation may be viewed as an equation of state definingthe allowed organizational modes of the shoot apex. The modelsimulates the growth of the apex from the vetative stage toearly reproductive growth, and makes reasonable predictionsabout apex size and growth rate, primordial sizes, and the lengthsof the plastochron. flowering, mathematical model, catastrophe theory, shoot apex     

Polarons and conformons

Orgel's “error catastrophe” theory of cellular senescence may be adapted as a theory of oncogenesis which is capable of explaining tumour progression as well as tumour induction. The theory gives rise to a number of predictions and suggestions for experiment.     

The parameter-free track structure model of Scholz and Kraft for heavy-ion cross sections

The "parameter-free", "local effects" theory of Scholz and Kraft is an extension to mammalian cells of the theory of RBE for dry enzymes and viruses of Butts and Katz. Its claim for parameter freedom has been challenged elsewhere. Here we examine its conceptual base and find errors in its use of the physical concept of cross section and its neglect of the radiobiological relationship between target size and radiosensitivity in evaluating the radiation damage to "point targets".     

高粱蚜灰色灾变长期预测模型

本文应用灰色系统灾变预测理论建立了吕梁地区高粱蚜发生量预测模型．     

Dynamics of a bistable system: The click mechanism in dipteran flight

Summary A mathematical model based upon catastrophe theory is derived to describe the kinematics of the wing beat in Dipteran flight. The parameters of the model correspond to anatomical and physiological characteristics of the insect.Order of authors decided by coin flip.     

An approach to the nonlinear dynamics of Russian wheat aphid population growth with the cusp catastrophe model

Many insect field populations, especially aphids, often exhibit irregular and even catastrophic fluctuations. The objective of the present study is to explore whether or not the population intrinsic rates of growth ( r _m) obtained under laboratory conditions can shed some light on the irregular changes of insect field populations. We propose to use the catastrophe theory, one of the earliest nonlinear dynamics theories, to answer the question. To collect the necessary data, we conducted a laboratory experiment to investigate population growth of the Russian wheat aphid (RWA), Diuraphis noxia (Mordvilko), in growth chambers. The experiment was designed as the factorial combinations of five temperatures and five host plant-growth stages (25 treatments in total): 1800 newly born RWA nymphs arranged in the 25 treatments (each treatment with 72 repetitions) were observed for their development, reproduction and survival through their entire lifetimes. After obtaining the population intrinsic rates of growth ( r _m) from the experimental data under various environmental conditions, we built a cusp catastrophe model for RWA population growth by utilizing r _m as the system state variable, and temperature and host plant-growth stage as control variables. The cusp catastrophe model suggests that RWA population growth is intrinsically catastrophic , and dramatic jumps from one state to another might occur even if the temperature and plant-growth stage change smoothly . Other basic behaviors of the cusp catastrophe model, such as catastrophic jumps , hystersis and divergence , are also expected in RWA populations. These results suggest that the answer to the previously proposed question should be "yes".     

A criticism of catastrophe modelling of the differentiative process in amphibian development

A criticism of Zeeman's (1975) general theory of developmental organization, with special reference to amphibian embryogenesis, and based on a mathematical theorem using catastrophe theory to model the process of differentiation, leads to the conclusion that the model itself is not a rigorous scientific theory. Catastrophe theory in itself offers no new insight, merely a modelling of concepts of continuous organization, of process. These concepts are of considerable interest, but the claim that the theorem proves the necessity for primary waves in development is spurious.     

Perspectives and mechanisms for targeting mitotic catastrophe in cancer treatment

Mitotic catastrophe is distinct from other cell death modes due to unique nuclear alterations characterized as multi and/or micronucleation. Mitotic catastrophe is a common and virtually unavoidable consequence during cancer therapy. However, a comprehensive understanding of mitotic catastrophe remains lacking. Herein, we summarize the anticancer drugs that induce mitotic catastrophe, including microtubule-targeting agents, spindle assembly checkpoint kinase inhibitors, DNA damage agents and DNA damage response inhibitors. Based on the relationships between mitotic catastrophe and other cell death modes, we thoroughly evaluated the roles played by mitotic catastrophe in cancer treatment as well as its advantages and disadvantages. Some strategies for overcoming its shortcomings while fully utilizing its advantages are summarized and proposed in this review. We also review how mitotic catastrophe regulates cancer immunotherapy. These summarized findings suggest that the induction of mitotic catastrophe can serve as a promising new therapeutic approach for overcoming apoptosis resistance and strengthening cancer immunotherapy.     

Bifurcation from a limit cycle in a two predator-one prey ecosystem modeled on a chemostat

Pattern formation in a unicomponent reaction-diffusion system with trigger type dynamics and combined boundary conditions is considered. The boundary permeabilities and reservoir concentrations as well as the dimension of the system are the control parameters. The whole assemblage of steady states, their bifurcations and changes under the variation of these parameters is described. Among all steady distributions possible for given values of the parameters, only the simplest ones prove to be asymptotically stable. The relation to catastrophe theory is discussed.     

Depolymerizing kinesins Kip3 and MCAK shape cellular microtubule architecture by differential control of catastrophe

Microtubules are dynamic filaments whose ends alternate between periods of slow growth and rapid shortening as they explore intracellular space and move organelles. A key question is how regulatory proteins modulate catastrophe, the conversion from growth to shortening. To study this process, we reconstituted microtubule dynamics in the absence and presence of the kinesin-8 Kip3 and the kinesin-13 MCAK. Surprisingly, we found that, even in the absence of the kinesins, the microtubule catastrophe frequency depends on the age of the microtubule, indicating that catastrophe is a multistep process. Kip3 slowed microtubule growth in a length-dependent manner and increased the rate of aging. In contrast, MCAK eliminated the aging process. Thus, both kinesins are catastrophe factors; Kip3 mediates fine control of microtubule length by narrowing the distribution of maximum lengths prior to catastrophe, whereas MCAK promotes rapid restructuring of the microtubule cytoskeleton by making catastrophe a first-order random process.